LMFDB - Embedded newform 37.7.g.a.8.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,7,Mod(8,37)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("37.8");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	37.g (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.51200109393$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			8.13
Character	$\chi$	$=$	37.8
Dual form			37.7.g.a.14.13

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.90851 + 1.58318i) q^{2} +(1.50469 + 0.868733i) q^{3} +(-23.0216 - 13.2915i) q^{4} +(-121.426 + 32.5360i) q^{5} +(7.51511 + 7.51511i) q^{6} +(268.634 - 465.288i) q^{7} +(-391.802 - 391.802i) q^{8} +(-362.991 - 628.718i) q^{9} +O(q^{10})$	\(q+(5.90851 + 1.58318i) q^{2} +(1.50469 + 0.868733i) q^{3} +(-23.0216 - 13.2915i) q^{4} +(-121.426 + 32.5360i) q^{5} +(7.51511 + 7.51511i) q^{6} +(268.634 - 465.288i) q^{7} +(-391.802 - 391.802i) q^{8} +(-362.991 - 628.718i) q^{9} -768.957 q^{10} +739.901i q^{11} +(-23.0936 - 39.9993i) q^{12} +(-600.629 + 160.938i) q^{13} +(2323.86 - 2323.86i) q^{14} +(-210.974 - 56.5302i) q^{15} +(-844.012 - 1461.87i) q^{16} +(751.624 - 2805.10i) q^{17} +(-1149.36 - 4289.47i) q^{18} +(-6966.72 + 1866.73i) q^{19} +(3227.88 + 864.907i) q^{20} +(808.423 - 466.743i) q^{21} +(-1171.40 + 4371.71i) q^{22} +(3015.61 + 3015.61i) q^{23} +(-249.169 - 929.911i) q^{24} +(154.028 - 88.9282i) q^{25} -3803.62 q^{26} -2527.98i q^{27} +(-12368.8 + 7141.13i) q^{28} +(24620.3 - 24620.3i) q^{29} +(-1157.04 - 668.018i) q^{30} +(-5750.85 + 5750.85i) q^{31} +(6505.75 + 24279.8i) q^{32} +(-642.776 + 1113.32i) q^{33} +(8881.96 - 15384.0i) q^{34} +(-17480.6 + 65238.4i) q^{35} +19298.8i q^{36} +(50112.1 + 7382.98i) q^{37} -44118.3 q^{38} +(-1043.57 - 279.625i) q^{39} +(60322.5 + 34827.2i) q^{40} +(33656.9 + 19431.8i) q^{41} +(5515.51 - 1477.88i) q^{42} +(-55747.7 - 55747.7i) q^{43} +(9834.42 - 17033.7i) q^{44} +(64532.5 + 64532.5i) q^{45} +(13043.5 + 22592.0i) q^{46} -37354.5 q^{47} -2932.88i q^{48} +(-85504.2 - 148098. i) q^{49} +(1050.87 - 281.579i) q^{50} +(3567.85 - 3567.85i) q^{51} +(15966.6 + 4278.23i) q^{52} +(2196.30 + 3804.10i) q^{53} +(4002.25 - 14936.6i) q^{54} +(-24073.4 - 89843.2i) q^{55} +(-287552. + 77049.3i) q^{56} +(-12104.4 - 3243.37i) q^{57} +(184448. - 106491. i) q^{58} +(73978.1 - 276090. i) q^{59} +(4105.58 + 4105.58i) q^{60} +(-99454.7 - 371170. i) q^{61} +(-43083.5 + 24874.3i) q^{62} -390047. q^{63} +261791. i q^{64} +(67695.7 - 39084.1i) q^{65} +(-5560.44 + 5560.44i) q^{66} +(234492. + 135384. i) q^{67} +(-54587.7 + 54587.7i) q^{68} +(1917.80 + 7157.32i) q^{69} +(-206568. + 357786. i) q^{70} +(329160. - 570121. i) q^{71} +(-104112. + 388553. i) q^{72} -351403. i q^{73} +(284399. + 122959. i) q^{74} +309.019 q^{75} +(185197. + 49623.3i) q^{76} +(344267. + 198763. i) q^{77} +(-5723.26 - 3304.33i) q^{78} +(-172281. + 46162.6i) q^{79} +(150048. + 150048. i) q^{80} +(-262424. + 454532. i) q^{81} +(168098. + 168098. i) q^{82} +(495218. + 857743. i) q^{83} -24814.9 q^{84} +365067. i q^{85} +(-241127. - 417644. i) q^{86} +(58434.5 - 15657.5i) q^{87} +(289894. - 289894. i) q^{88} +(-813069. - 217861. i) q^{89} +(279124. + 483457. i) q^{90} +(-86467.0 + 322699. i) q^{91} +(-29342.1 - 109506. i) q^{92} +(-13649.2 + 3657.29i) q^{93} +(-220709. - 59138.8i) q^{94} +(785204. - 453338. i) q^{95} +(-11303.5 + 42185.3i) q^{96} +(-947626. - 947626. i) q^{97} +(-270737. - 1.01040e6i) q^{98} +(465189. - 268577. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9}+O(q^{10}) $ 72 * q - 2 * q^2 - 6 * q^3 + 264 * q^4 + 52 * q^5 - 132 * q^6 - 2 * q^7 - 1968 * q^8 + 8094 * q^9	\( 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9} + 1864 q^{10} + 1178 q^{12} + 2898 q^{13} + 10168 q^{14} + 1418 q^{15} + 23668 q^{16} - 16734 q^{17} + 30222 q^{18} - 20756 q^{19} + 27910 q^{20} - 22326 q^{21} + 40188 q^{22} + 23388 q^{23} + 51426 q^{24} - 54060 q^{25} + 31064 q^{26} - 84486 q^{28} - 101426 q^{29} - 280062 q^{30} - 112740 q^{31} + 66416 q^{32} + 27376 q^{33} + 45094 q^{34} + 152710 q^{35} - 23168 q^{37} - 67600 q^{38} + 386674 q^{39} - 473862 q^{40} - 566622 q^{41} - 569640 q^{42} - 33332 q^{43} + 667736 q^{44} + 399362 q^{45} + 303310 q^{46} + 352424 q^{47} - 402226 q^{49} - 190836 q^{50} - 525822 q^{51} - 290936 q^{52} + 365094 q^{53} + 1191884 q^{54} - 343392 q^{55} + 2217442 q^{56} + 73378 q^{57} - 581028 q^{58} - 576604 q^{59} + 2105904 q^{60} - 213462 q^{61} - 423156 q^{62} - 1483688 q^{63} + 2273880 q^{65} - 846680 q^{66} + 1591698 q^{67} - 3165948 q^{68} + 2464258 q^{69} + 2158358 q^{70} - 1388114 q^{71} + 1672988 q^{72} - 3228324 q^{74} + 1857268 q^{75} - 3488628 q^{76} + 846288 q^{77} - 6537300 q^{78} - 781076 q^{79} - 3635536 q^{80} - 2236868 q^{81} + 3720360 q^{82} - 944002 q^{83} + 6632744 q^{84} - 1174862 q^{86} - 1073982 q^{87} - 427452 q^{88} + 3381078 q^{89} + 412204 q^{90} - 2879114 q^{91} + 696698 q^{92} - 543710 q^{93} - 3545780 q^{94} - 268230 q^{95} - 9026178 q^{96} - 1842138 q^{97} - 7266130 q^{98} + 8295480 q^{99}+O(q^{100}) \) 72 * q - 2 * q^2 - 6 * q^3 + 264 * q^4 + 52 * q^5 - 132 * q^6 - 2 * q^7 - 1968 * q^8 + 8094 * q^9 + 1864 * q^10 + 1178 * q^12 + 2898 * q^13 + 10168 * q^14 + 1418 * q^15 + 23668 * q^16 - 16734 * q^17 + 30222 * q^18 - 20756 * q^19 + 27910 * q^20 - 22326 * q^21 + 40188 * q^22 + 23388 * q^23 + 51426 * q^24 - 54060 * q^25 + 31064 * q^26 - 84486 * q^28 - 101426 * q^29 - 280062 * q^30 - 112740 * q^31 + 66416 * q^32 + 27376 * q^33 + 45094 * q^34 + 152710 * q^35 - 23168 * q^37 - 67600 * q^38 + 386674 * q^39 - 473862 * q^40 - 566622 * q^41 - 569640 * q^42 - 33332 * q^43 + 667736 * q^44 + 399362 * q^45 + 303310 * q^46 + 352424 * q^47 - 402226 * q^49 - 190836 * q^50 - 525822 * q^51 - 290936 * q^52 + 365094 * q^53 + 1191884 * q^54 - 343392 * q^55 + 2217442 * q^56 + 73378 * q^57 - 581028 * q^58 - 576604 * q^59 + 2105904 * q^60 - 213462 * q^61 - 423156 * q^62 - 1483688 * q^63 + 2273880 * q^65 - 846680 * q^66 + 1591698 * q^67 - 3165948 * q^68 + 2464258 * q^69 + 2158358 * q^70 - 1388114 * q^71 + 1672988 * q^72 - 3228324 * q^74 + 1857268 * q^75 - 3488628 * q^76 + 846288 * q^77 - 6537300 * q^78 - 781076 * q^79 - 3635536 * q^80 - 2236868 * q^81 + 3720360 * q^82 - 944002 * q^83 + 6632744 * q^84 - 1174862 * q^86 - 1073982 * q^87 - 427452 * q^88 + 3381078 * q^89 + 412204 * q^90 - 2879114 * q^91 + 696698 * q^92 - 543710 * q^93 - 3545780 * q^94 - 268230 * q^95 - 9026178 * q^96 - 1842138 * q^97 - 7266130 * q^98 + 8295480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	5.90851	+	1.58318i	0.738563	+	0.197897i	0.608440	−	0.793600i	$-0.291796\pi$
$2$	5.90851	+	1.58318i	0.738563	+	0.197897i	0.130124	+	0.991498i	$0.458462\pi$
$3$	1.50469	+	0.868733i	0.0557293	+	0.0321753i	0.527606	−	0.849489i	$-0.323090\pi$
$3$	1.50469	+	0.868733i	0.0557293	+	0.0321753i	−0.471876	+	0.881665i	$0.656423\pi$
$4$	−23.0216	−	13.2915i	−0.359713	−	0.207680i
$5$	−121.426	+	32.5360i	−0.971408	+	0.260288i	−0.709422	−	0.704784i	$-0.751044\pi$
$5$	−121.426	+	32.5360i	−0.971408	+	0.260288i	−0.261986	+	0.965072i	$0.584377\pi$
$6$	7.51511	+	7.51511i	0.0347922	+	0.0347922i
$7$	268.634	−	465.288i	0.783190	−	1.35653i	−0.146884	−	0.989154i	$-0.546924\pi$
$7$	268.634	−	465.288i	0.783190	−	1.35653i	0.930074	−	0.367372i	$-0.119742\pi$
$8$	−391.802	−	391.802i	−0.765237	−	0.765237i
$9$	−362.991	−	628.718i	−0.497929	−	0.862439i
$10$	−768.957			−0.768957
$11$			739.901i			0.555898i	0.960596	+	0.277949i	$0.0896547\pi$
$11$			739.901i			0.555898i	−0.960596	+	0.277949i	$0.910345\pi$
$12$	−23.0936	−	39.9993i	−0.0133644	−	0.0231477i
$13$	−600.629	+	160.938i	−0.273386	+	0.0732536i	−0.392907	−	0.919578i	$-0.628531\pi$
$13$	−600.629	+	160.938i	−0.273386	+	0.0732536i	0.119521	+	0.992832i	$0.461864\pi$
$14$	2323.86	−	2323.86i	0.846889	−	0.846889i
$15$	−210.974	−	56.5302i	−0.0625107	−	0.0167497i
$16$	−844.012	−	1461.87i	−0.206058	−	0.356902i
$17$	751.624	−	2805.10i	0.152987	−	0.570955i	−0.846283	−	0.532734i	$-0.821164\pi$
$17$	751.624	−	2805.10i	0.152987	−	0.570955i	0.999269	−	0.0382202i	$-0.0121688\pi$
$18$	−1149.36	−	4289.47i	−0.197078	−	0.735505i
$19$	−6966.72	+	1866.73i	−1.01570	+	0.272157i	−0.728011	−	0.685565i	$-0.759555\pi$
$19$	−6966.72	+	1866.73i	−1.01570	+	0.272157i	−0.287693	+	0.957723i	$0.592888\pi$
$20$	3227.88	+	864.907i	0.403484	+	0.108113i
$21$	808.423	−	466.743i	0.0872932	−	0.0503988i
$22$	−1171.40	+	4371.71i	−0.110011	+	0.410566i
$23$	3015.61	+	3015.61i	0.247851	+	0.247851i	0.820088	−	0.572237i	$-0.193924\pi$
$23$	3015.61	+	3015.61i	0.247851	+	0.247851i	−0.572237	+	0.820088i	$0.693924\pi$
$24$	−249.169	−	929.911i	−0.0180244	−	0.0672679i
$25$	154.028	−	88.9282i	0.00985780	−	0.00569140i
$26$	−3803.62			−0.216410
$27$		−	2527.98i		−	0.128435i
$28$	−12368.8	+	7141.13i	−0.563447	+	0.325306i
$29$	24620.3	−	24620.3i	1.00949	−	1.00949i	0.00953060	−	0.999955i	$-0.496966\pi$
$29$	24620.3	−	24620.3i	1.00949	−	1.00949i	0.999955	−	0.00953060i	$-0.00303373\pi$
$30$	−1157.04	−	668.018i	−0.0428534	−	0.0247414i
$31$	−5750.85	+	5750.85i	−0.193040	+	0.193040i	−0.797008	−	0.603968i	$-0.793585\pi$
$31$	−5750.85	+	5750.85i	−0.193040	+	0.193040i	0.603968	+	0.797008i	$0.293585\pi$
$32$	6505.75	+	24279.8i	0.198540	+	0.740961i
$33$	−642.776	+	1113.32i	−0.0178862	+	0.0309798i
$34$	8881.96	−	15384.0i	0.225981	−	0.391411i
$35$	−17480.6	+	65238.4i	−0.407710	+	1.52159i
$36$			19298.8i			0.413641i
$37$	50112.1	+	7382.98i	0.989321	+	0.145756i
$37$	50112.1	+	7382.98i	0.989321	+	0.145756i
$38$	−44118.3			−0.804021
$39$	−1043.57	−	279.625i	−0.0175926	−	0.00471391i
$40$	60322.5	+	34827.2i	0.942539	+	0.544175i
$41$	33656.9	+	19431.8i	0.488340	+	0.281943i	0.723885	−	0.689920i	$-0.242354\pi$
$41$	33656.9	+	19431.8i	0.488340	+	0.281943i	−0.235546	+	0.971863i	$0.575688\pi$
$42$	5515.51	−	1477.88i	0.0744454	−	0.0199476i
$43$	−55747.7	−	55747.7i	−0.701167	−	0.701167i	0.263494	−	0.964661i	$-0.415125\pi$
$43$	−55747.7	−	55747.7i	−0.701167	−	0.701167i	−0.964661	+	0.263494i	$0.915125\pi$
$44$	9834.42	−	17033.7i	0.115449	−	0.199964i
$45$	64532.5	+	64532.5i	0.708175	+	0.708175i
$46$	13043.5	+	22592.0i	0.134005	+	0.232103i
$47$	−37354.5			−0.359790			−0.179895	−	0.983686i	$-0.557576\pi$
$47$	−37354.5			−0.359790			−0.179895	+	0.983686i	$0.557576\pi$
$48$		−	2932.88i		−	0.0265199i
$49$	−85504.2	−	148098.i	−0.726774	−	1.25881i
$50$	1050.87	−	281.579i	0.00840692	−	0.00225263i
$51$	3567.85	−	3567.85i	0.0268965	−	0.0268965i
$52$	15966.6	+	4278.23i	0.113554	+	0.0304266i
$53$	2196.30	+	3804.10i	0.0147525	+	0.0255520i	0.873307	−	0.487170i	$-0.161971\pi$
$53$	2196.30	+	3804.10i	0.0147525	+	0.0255520i	−0.858555	+	0.512722i	$0.828637\pi$
$54$	4002.25	−	14936.6i	0.0254169	−	0.0948572i
$55$	−24073.4	−	89843.2i	−0.144694	−	0.540004i
$56$	−287552.	+	77049.3i	−1.63739	+	0.438737i
$57$	−12104.4	−	3243.37i	−0.0653612	−	0.0175135i
$58$	184448.	−	106491.i	0.945343	−	0.545794i
$59$	73978.1	−	276090.i	0.360203	−	1.34430i	−0.513606	−	0.858026i	$-0.671691\pi$
$59$	73978.1	−	276090.i	0.360203	−	1.34430i	0.873809	−	0.486270i	$-0.161643\pi$
$60$	4105.58	+	4105.58i	0.0190073	+	0.0190073i
$61$	−99454.7	−	371170.i	−0.438163	−	1.63525i	−0.733381	−	0.679817i	$-0.762059\pi$
$61$	−99454.7	−	371170.i	−0.438163	−	1.63525i	0.295218	−	0.955430i	$-0.404608\pi$
$62$	−43083.5	+	24874.3i	−0.180774	+	0.104370i
$63$	−390047.			−1.55989
$64$			261791.i			0.998652i
$65$	67695.7	−	39084.1i	0.246502	−	0.142318i
$66$	−5560.44	+	5560.44i	−0.0193409	+	0.0193409i
$67$	234492.	+	135384.i	0.779656	+	0.450135i	0.836308	−	0.548259i	$-0.184709\pi$
$67$	234492.	+	135384.i	0.779656	+	0.450135i	−0.0566523	+	0.998394i	$0.518043\pi$
$68$	−54587.7	+	54587.7i	−0.173607	+	0.173607i
$69$	1917.80	+	7157.32i	0.00583788	+	0.0217873i
$70$	−206568.	+	357786.i	−0.602239	+	1.04311i
$71$	329160.	−	570121.i	0.919669	−	1.59291i	0.119752	−	0.992804i	$-0.461790\pi$
$71$	329160.	−	570121.i	0.919669	−	1.59291i	0.799917	−	0.600110i	$-0.204877\pi$
$72$	−104112.	+	388553.i	−0.278936	+	1.04100i
$73$		−	351403.i		−	0.903309i	−0.892193	−	0.451655i	$-0.850834\pi$
$73$		−	351403.i		−	0.903309i	0.892193	−	0.451655i	$-0.149166\pi$
$74$	284399.	+	122959.i	0.701831	+	0.303434i
$75$	309.019			0.000732491
$76$	185197.	+	49623.3i	0.421884	+	0.113043i
$77$	344267.	+	198763.i	0.754090	+	0.435374i
$78$	−5723.26	−	3304.33i	−0.0120604	−	0.00696305i
$79$	−172281.	+	46162.6i	−0.349427	+	0.0936287i	−0.429264	−	0.903179i	$-0.641227\pi$
$79$	−172281.	+	46162.6i	−0.349427	+	0.0936287i	0.0798365	+	0.996808i	$0.474560\pi$
$80$	150048.	+	150048.i	0.293063	+	0.293063i
$81$	−262424.	+	454532.i	−0.493797	+	0.855282i
$82$	168098.	+	168098.i	0.304874	+	0.304874i
$83$	495218.	+	857743.i	0.866089	+	1.50011i	0.865962	+	0.500110i	$0.166707\pi$
$83$	495218.	+	857743.i	0.866089	+	1.50011i	0.000126846		1.00000i	$0.499960\pi$
$84$	−24814.9			−0.0418673
$85$			365067.i			0.594450i
$86$	−241127.	−	417644.i	−0.379097	−	0.656616i
$87$	58434.5	−	15657.5i	0.0887384	−	0.0237774i
$88$	289894.	−	289894.i	0.425394	−	0.425394i
$89$	−813069.	−	217861.i	−1.15334	−	0.309037i	−0.369038	−	0.929414i	$-0.620313\pi$
$89$	−813069.	−	217861.i	−1.15334	−	0.309037i	−0.784303	+	0.620378i	$0.786979\pi$
$90$	279124.	+	483457.i	0.382886	+	0.663178i
$91$	−86467.0	+	322699.i	−0.114743	+	0.428227i
$92$	−29342.1	−	109506.i	−0.0376815	−	0.140629i
$93$	−13649.2	+	3657.29i	−0.0169691	+	0.00454685i
$94$	−220709.	−	59138.8i	−0.265728	−	0.0712015i
$95$	785204.	−	453338.i	0.915824	−	0.528751i
$96$	−11303.5	+	42185.3i	−0.0127762	+	0.0476813i
$97$	−947626.	−	947626.i	−1.03830	−	1.03830i	−0.999237	−	0.0390608i	$-0.987563\pi$
$97$	−947626.	−	947626.i	−1.03830	−	1.03830i	−0.0390608	−	0.999237i	$-0.512437\pi$
$98$	−270737.	−	1.01040e6i	−0.287654	−	1.07354i
$99$	465189.	−	268577.i	0.479429	−	0.276798i
$100$	−4727.97			−0.00472797
$101$			883856.i			0.857862i	0.903337	+	0.428931i	$0.141110\pi$
$101$			883856.i			0.857862i	−0.903337	+	0.428931i	$0.858890\pi$
$102$	26729.2	−	15432.1i	0.0251875	−	0.0145420i
$103$	−314134.	+	314134.i	−0.287477	+	0.287477i	−0.836082	−	0.548605i	$-0.815159\pi$
$103$	−314134.	+	314134.i	−0.287477	+	0.287477i	0.548605	+	0.836082i	$0.315159\pi$
$104$	298383.	+	172272.i	0.265262	+	0.153149i
$105$	−82977.6	+	82977.6i	−0.0716791	+	0.0716791i
$106$	6954.28	+	25953.7i	0.00583895	+	0.0217912i
$107$	614318.	−	1.06403e6i	0.501466	−	0.868565i	−0.498532	−	0.866871i	$-0.666128\pi$
$107$	614318.	−	1.06403e6i	0.501466	−	0.868565i	0.999999	−	0.00169379i	$-0.000539150\pi$
$108$	−33600.8	+	58198.2i	−0.0266734	+	0.0461996i
$109$	−406385.	+	1.51665e6i	−0.313804	+	1.17113i	0.611295	+	0.791403i	$0.290649\pi$
$109$	−406385.	+	1.51665e6i	−0.313804	+	1.17113i	−0.925098	+	0.379728i	$0.876018\pi$
$110$		−	568952.i		−	0.427462i
$111$	68989.3	+	54643.1i	0.0504444	+	0.0399546i
$112$	−906922.			−0.645529
$113$	−92544.9	−	24797.3i	−0.0641383	−	0.0171858i	0.226607	−	0.973986i	$-0.427237\pi$
$113$	−92544.9	−	24797.3i	−0.0641383	−	0.0171858i	−0.290745	+	0.956800i	$0.593903\pi$
$114$	−66384.3	−	38327.0i	−0.0448075	−	0.0258696i
$115$	−464289.	−	268057.i	−0.305278	−	0.176252i
$116$	−894042.	+	239558.i	−0.572775	+	0.153475i
$117$	319207.	+	319207.i	0.199304	+	0.199304i
$118$	874201.	−	1.51416e6i	0.532066	−	0.921565i
$119$	−1.10327e6	−	1.10327e6i	−0.654697	−	0.654697i
$120$	60511.2	+	104808.i	0.0350180	+	0.0606530i
$121$	1.22411e6			0.690977
$122$		−	2.35052e6i		−	1.29445i
$123$	33762.1	+	58477.7i	0.0181432	+	0.0314250i
$124$	208831.	−	55956.2i	0.109529	−	0.0293483i
$125$	1.37310e6	−	1.37310e6i	0.703025	−	0.703025i
$126$	−2.30459e6	−	617514.i	−1.15208	−	0.308699i
$127$	1.04925e6	+	1.81735e6i	0.512231	+	0.887210i	0.999899	+	0.0141813i	$0.00451419\pi$
$127$	1.04925e6	+	1.81735e6i	0.512231	+	0.887210i	−0.487668	+	0.873029i	$0.662152\pi$
$128$	1906.43	−	7114.91i	0.000909058	−	0.00339265i
$129$	−35453.1	−	132313.i	−0.0165153	−	0.0616358i
$130$	461858.	−	123754.i	0.210222	−	0.0563288i
$131$	−354484.	−	94983.7i	−0.157682	−	0.0422508i	0.179114	−	0.983828i	$-0.442677\pi$
$131$	−354484.	−	94983.7i	−0.157682	−	0.0422508i	−0.336797	+	0.941577i	$0.609343\pi$
$132$	29595.5	−	17087.0i	0.0128678	−	0.00742922i
$133$	−1.00293e6	+	3.74300e6i	−0.426302	+	1.59098i
$134$	1.17116e6	+	1.17116e6i	0.486745	+	0.486745i
$135$	82250.4	+	306963.i	0.0334300	+	0.124763i
$136$	−1.39353e6	+	804555.i	−0.553987	+	0.319845i
$137$	499301.			0.194178			0.0970892	−	0.995276i	$-0.469047\pi$
$137$	499301.			0.194178			0.0970892	+	0.995276i	$0.469047\pi$
$138$			45325.3i			0.0172466i
$139$	−1.75343e6	+	1.01234e6i	−0.652895	+	0.376949i	−0.789564	−	0.613668i	$-0.789694\pi$
$139$	−1.75343e6	+	1.01234e6i	−0.652895	+	0.376949i	0.136669	+	0.990617i	$0.456360\pi$
$140$	1.26955e6	−	1.26955e6i	0.462664	−	0.462664i
$141$	−56206.9	−	32451.1i	−0.0200508	−	0.0115763i
$142$	2.84745e6	−	2.84745e6i	0.994468	−	0.994468i
$143$	−119078.	−	444406.i	−0.0407215	−	0.151975i
$144$	−612737.	+	1.06129e6i	−0.205204	+	0.355424i
$145$	−2.18850e6	+	3.79059e6i	−0.717865	+	1.24338i
$146$	556334.	−	2.07627e6i	0.178763	−	0.667151i
$147$		−	297122.i		−	0.0935367i
$148$	−1.05553e6	−	836035.i	−0.325601	−	0.257893i
$149$	2.96479e6			0.896263			0.448132	−	0.893968i	$-0.352090\pi$
$149$	2.96479e6			0.896263			0.448132	+	0.893968i	$0.352090\pi$
$150$	1825.84	+	489.233i	0.000540991	+	0.000144958i
$151$	−4.54053e6	−	2.62148e6i	−1.31879	−	0.761404i	−0.335257	−	0.942127i	$-0.608823\pi$
$151$	−4.54053e6	−	2.62148e6i	−1.31879	−	0.761404i	−0.983534	+	0.180723i	$0.942156\pi$
$152$	3.46096e6	+	1.99818e6i	0.985520	+	0.568990i
$153$	−2.03645e6	+	545665.i	−0.568590	+	0.152353i
$154$	1.71943e6	+	1.71943e6i	0.470784	+	0.470784i
$155$	511193.	−	885412.i	0.137274	−	0.237766i
$156$	20308.1	+	20308.1i	0.00534928	+	0.00534928i
$157$	1.92087e6	+	3.32704e6i	0.496362	+	0.859724i	0.999991	−	0.00419554i	$-0.00133549\pi$
$157$	1.92087e6	+	3.32704e6i	0.496362	+	0.859724i	−0.503629	+	0.863920i	$0.668002\pi$
$158$	−1.09101e6			−0.276603
$159$			7632.00i			0.00189866i
$160$	−1.57993e6	−	2.73653e6i	−0.385726	−	0.668097i
$161$	2.21322e6	−	593031.i	0.530332	−	0.142102i
$162$	−2.27014e6	+	2.27014e6i	−0.533959	+	0.533959i
$163$	3.72571e6	+	998300.i	0.860292	+	0.230515i	0.661885	−	0.749605i	$-0.269757\pi$
$163$	3.72571e6	+	998300.i	0.860292	+	0.230515i	0.198407	+	0.980120i	$0.436423\pi$
$164$	−516557.	−	894703.i	−0.117108	−	0.202837i
$165$	41826.7	−	156100.i	0.00931112	−	0.0347496i
$166$	1.56804e6	+	5.85200e6i	0.342794	+	1.27932i
$167$	4.36548e6	−	1.16973e6i	0.937308	−	0.251151i	0.242340	−	0.970191i	$-0.422085\pi$
$167$	4.36548e6	−	1.16973e6i	0.937308	−	0.251151i	0.694968	+	0.719041i	$0.255419\pi$
$168$	−499612.	−	133871.i	−0.105367	−	0.0282330i
$169$	−3.84528e6	+	2.22008e6i	−0.796652	+	0.459947i
$170$	−577966.	+	2.15700e6i	−0.117640	+	0.439039i
$171$	3.70250e6	+	3.70250e6i	0.740468	+	0.740468i
$172$	542429.	+	2.02437e6i	0.106600	+	0.397837i
$173$	−3.85254e6	+	2.22426e6i	−0.744061	+	0.429584i	−0.823544	−	0.567252i	$-0.808006\pi$
$173$	−3.85254e6	+	2.22426e6i	−0.744061	+	0.429584i	0.0794827	+	0.996836i	$0.474673\pi$
$174$	370049.			0.0702444
$175$		−	95556.6i		−	0.0178298i
$176$	1.08164e6	−	624485.i	0.198401	−	0.114547i
$177$	351163.	−	351163.i	0.0633270	−	0.0633270i
$178$	−4.45911e6	−	2.57447e6i	−0.790658	−	0.456486i
$179$	5.16562e6	−	5.16562e6i	0.900665	−	0.900665i	−0.0948290	−	0.995494i	$-0.530230\pi$
$179$	5.16562e6	−	5.16562e6i	0.900665	−	0.900665i	0.995494	+	0.0948290i	$0.0302304\pi$
$180$	−627906.	−	2.34338e6i	−0.107666	−	0.401814i
$181$	3.99118e6	−	6.91293e6i	0.673079	−	1.16581i	−0.303948	−	0.952689i	$-0.598305\pi$
$181$	3.99118e6	−	6.91293e6i	0.673079	−	1.16581i	0.977026	−	0.213118i	$-0.0683619\pi$
$182$	−1.02178e6	+	1.76978e6i	−0.169490	+	0.293565i
$183$	172799.	−	644896.i	0.0281961	−	0.105229i
$184$		−	2.36304e6i		−	0.379330i
$185$	−6.32512e6	+	733959.i	−0.998972	+	0.115920i
$186$	−86436.5			−0.0134325
$187$	2.07550e6	+	556127.i	0.317393	+	0.0850451i
$188$	859960.	+	496498.i	0.129421	+	0.0747212i
$189$	−1.17624e6	−	679102.i	−0.174225	−	0.100589i
$190$	5.35710e6	−	1.43543e6i	0.781033	−	0.209277i
$191$	−5.91678e6	−	5.91678e6i	−0.849152	−	0.849152i	0.140875	−	0.990027i	$-0.455008\pi$
$191$	−5.91678e6	−	5.91678e6i	−0.849152	−	0.849152i	−0.990027	+	0.140875i	$0.955008\pi$
$192$	−227426.	+	393914.i	−0.0321319	+	0.0556541i
$193$	−6.44336e6	−	6.44336e6i	−0.896273	−	0.896273i	0.0988315	−	0.995104i	$-0.468490\pi$
$193$	−6.44336e6	−	6.44336e6i	−0.896273	−	0.896273i	−0.995104	+	0.0988315i	$0.968490\pi$
$194$	−4.09879e6	−	7.09932e6i	−0.561372	−	0.972325i
$195$	135815.			0.0183165
$196$			4.54593e6i			0.603747i
$197$	371933.	+	644206.i	0.0486481	+	0.0842609i	0.889324	−	0.457278i	$-0.151175\pi$
$197$	371933.	+	644206.i	0.0486481	+	0.0842609i	−0.840676	+	0.541538i	$0.817842\pi$
$198$	3.17378e6	−	850411.i	0.408866	−	0.109555i
$199$	−8.04375e6	+	8.04375e6i	−1.02070	+	1.02070i	−0.0209215	+	0.999781i	$0.506660\pi$
$199$	−8.04375e6	+	8.04375e6i	−1.02070	+	1.02070i	−0.999781	+	0.0209215i	$0.993340\pi$
$200$	−95190.6	−	25506.3i	−0.0118988	−	0.00318828i
$201$	235225.	+	407422.i	0.0289664	+	0.0501714i
$202$	−1.39930e6	+	5.22227e6i	−0.169769	+	0.633585i
$203$	−4.84169e6	−	1.80694e7i	−0.578773	−	2.16001i
$204$	−129560.	+	34715.4i	−0.0152609	+	0.00408914i
$205$	−4.71905e6	−	1.26447e6i	−0.547763	−	0.146773i
$206$	−2.35339e6	+	1.35873e6i	−0.269211	+	0.155429i
$207$	801330.	−	2.99061e6i	0.0903443	−	0.337169i
$208$	742209.	+	742209.i	0.0824776	+	0.0824776i
$209$	−1.38119e6	−	5.15468e6i	−0.151292	−	0.564628i
$210$	−621642.	+	358905.i	−0.0671247	+	0.0387545i
$211$	9.63685e6			1.02586			0.512930	−	0.858431i	$-0.328560\pi$
$211$	9.63685e6			1.02586			0.512930	+	0.858431i	$0.328560\pi$
$212$		−	116769.i		−	0.0122552i
$213$	990567.	−	571904.i	0.102505	−	0.0591813i
$214$	5.31425e6	−	5.31425e6i	0.542251	−	0.542251i
$215$	8.58302e6	+	4.95541e6i	0.863624	+	0.498614i
$216$	−990467.	+	990467.i	−0.0982831	+	0.0982831i
$217$	1.13093e6	+	4.22068e6i	0.110676	+	0.413050i
$218$	−4.80225e6	+	8.31775e6i	−0.463528	+	0.802854i
$219$	305275.	−	528752.i	0.0290643	−	0.0503408i
$220$	−639945.	+	2.38831e6i	−0.0601000	+	0.224296i
$221$			1.80579e6i			0.167298i
$222$	321114.	+	432082.i	0.0293495	+	0.0394918i
$223$	1.49704e6			0.134995			0.0674975	−	0.997719i	$-0.478499\pi$
$223$	1.49704e6			0.134995			0.0674975	+	0.997719i	$0.478499\pi$
$224$	1.30448e7	+	3.49534e6i	1.16063	+	0.310989i
$225$	−111822.	−	64560.2i	−0.00981698	−	0.00566783i
$226$	−507544.	−	293030.i	−0.0439692	−	0.0253856i
$227$	8.81826e6	−	2.36285e6i	0.753885	−	0.202003i	0.138645	−	0.990342i	$-0.455725\pi$
$227$	8.81826e6	−	2.36285e6i	0.753885	−	0.202003i	0.615241	+	0.788339i	$0.289059\pi$
$228$	235554.	+	235554.i	0.0198741	+	0.0198741i
$229$	−7.89711e6	+	1.36782e7i	−0.657600	+	1.13900i	0.323635	+	0.946182i	$0.395095\pi$
$229$	−7.89711e6	+	1.36782e7i	−0.657600	+	1.13900i	−0.981235	+	0.192814i	$0.938238\pi$
$230$	−2.31887e6	−	2.31887e6i	−0.190587	−	0.190587i
$231$	345344.	+	598153.i	0.0280166	+	0.0485262i
$232$	−1.92926e7			−1.54499
$233$			1.21008e7i			0.956638i	0.878186	+	0.478319i	$0.158754\pi$
$233$			1.21008e7i			0.956638i	−0.878186	+	0.478319i	$0.841246\pi$
$234$	1.38068e6	+	2.39140e6i	0.107757	+	0.186640i
$235$	4.53580e6	−	1.21536e6i	0.349503	−	0.0936489i
$236$	−5.37276e6	+	5.37276e6i	−0.408753	+	0.408753i
$237$	−299333.	−	80206.0i	−0.0224859	−	0.00602507i
$238$	−4.77200e6	−	8.26534e6i	−0.353972	−	0.613098i
$239$	1.11257e6	−	4.15217e6i	0.0814956	−	0.304146i	−0.913132	−	0.407664i	$-0.866343\pi$
$239$	1.11257e6	−	4.15217e6i	0.0814956	−	0.304146i	0.994628	+	0.103518i	$0.0330101\pi$
$240$	95424.3	+	356128.i	0.00690280	+	0.0257616i
$241$	1.63427e7	−	4.37901e6i	1.16754	−	0.312842i	0.377568	−	0.925982i	$-0.376760\pi$
$241$	1.63427e7	−	4.37901e6i	1.16754	−	0.312842i	0.789974	+	0.613140i	$0.210094\pi$
$242$	7.23265e6	+	1.93798e6i	0.510330	+	0.136743i
$243$	−2.38573e6	+	1.37740e6i	−0.166266	+	0.0959935i
$244$	−2.64381e6	+	9.86684e6i	−0.181996	+	0.679217i
$245$	1.52009e7	+	1.52009e7i	1.03365	+	1.03365i
$246$	106903.	+	398967.i	0.00718099	+	0.0267998i
$247$	3.88399e6	−	2.24242e6i	0.257743	−	0.148808i
$248$	4.50638e6			0.295442
$249$			1.72085e6i			0.111467i
$250$	1.02868e7	−	5.93909e6i	0.658356	−	0.380102i
$251$	−3.68143e6	+	3.68143e6i	−0.232807	+	0.232807i	−0.813863	−	0.581056i	$-0.802640\pi$
$251$	−3.68143e6	+	3.68143e6i	−0.232807	+	0.232807i	0.581056	+	0.813863i	$0.302640\pi$
$252$	8.97951e6	+	5.18432e6i	0.561114	+	0.323959i
$253$	−2.23125e6	+	2.23125e6i	−0.137780	+	0.137780i
$254$	3.32229e6	+	1.23989e7i	0.202738	+	0.756630i
$255$	−317146.	+	549313.i	−0.0191266	+	0.0331283i
$256$	8.39983e6	−	1.45489e7i	0.500669	−	0.867184i
$257$	−8.45615e6	+	3.15588e7i	−0.498165	+	1.85918i	0.0133615	+	0.999911i	$0.495747\pi$
$257$	−8.45615e6	+	3.15588e7i	−0.498165	+	1.85918i	−0.511527	+	0.859267i	$0.670920\pi$
$258$		−	837900.i		−	0.0487903i
$259$	1.68970e7	−	2.13332e7i	0.972548	−	1.22788i
$260$	−2.07795e6			−0.118227
$261$	−2.44162e7	−	6.54230e6i	−1.37327	−	0.367967i
$262$	−1.94410e6	−	1.12242e6i	−0.108097	−	0.0624099i
$263$	−2.37682e7	−	1.37226e7i	−1.30656	−	0.754341i	−0.325037	−	0.945701i	$-0.605377\pi$
$263$	−2.37682e7	−	1.37226e7i	−1.30656	−	0.754341i	−0.981520	+	0.191360i	$0.938710\pi$
$264$	688042.	−	184360.i	0.0373941	−	0.0100197i
$265$	−390458.	−	390458.i	−0.0209815	−	0.0209815i
$266$	−1.18517e7	+	2.05277e7i	−0.629702	+	1.09068i
$267$	−1.03415e6	−	1.03415e6i	−0.0543315	−	0.0543315i
$268$	−3.59892e6	−	6.23351e6i	−0.186968	−	0.323838i
$269$	−2.05582e6			−0.105616			−0.0528078	−	0.998605i	$-0.516817\pi$
$269$	−2.05582e6			−0.105616			−0.0528078	+	0.998605i	$0.516817\pi$
$270$			1.94391e6i			0.0987608i
$271$	−1.11017e7	−	1.92286e7i	−0.557802	−	0.966142i	−0.997680	−	0.0680840i	$-0.978311\pi$
$271$	−1.11017e7	−	1.92286e7i	−0.557802	−	0.966142i	0.439877	−	0.898058i	$-0.355022\pi$
$272$	−4.73507e6	+	1.26876e6i	−0.235299	+	0.0630482i
$273$	−410446.	+	410446.i	−0.0201729	+	0.0201729i
$274$	2.95013e6	+	790484.i	0.143413	+	0.0384274i
$275$	65798.0	+	113965.i	0.00316384	+	0.00547993i
$276$	50981.0	−	190264.i	0.00242483	−	0.00904958i
$277$	−8.61130e6	−	3.21378e7i	−0.405163	−	1.51209i	−0.803756	−	0.594959i	$-0.797168\pi$
$277$	−8.61130e6	−	3.21378e7i	−0.405163	−	1.51209i	0.398593	−	0.917128i	$-0.369499\pi$
$278$	−1.19629e7	+	3.20544e6i	−0.556802	+	0.149195i
$279$	5.70316e6	+	1.52816e6i	0.262605	+	0.0703648i
$280$	3.24094e7	−	1.87116e7i	1.47638	−	0.852386i
$281$	7.31580e6	−	2.73029e7i	0.329718	−	1.23053i	−0.579765	−	0.814784i	$-0.696856\pi$
$281$	7.31580e6	−	2.73029e7i	0.329718	−	1.23053i	0.909483	−	0.415741i	$-0.136478\pi$
$282$	−280723.	−	280723.i	−0.0125179	−	0.0125179i
$283$	−6.96355e6	−	2.59883e7i	−0.307236	−	1.14662i	−0.931004	−	0.365010i	$-0.881066\pi$
$283$	−6.96355e6	−	2.59883e7i	−0.307236	−	1.14662i	0.623768	−	0.781610i	$-0.285601\pi$
$284$	−1.51556e7	+	8.75008e6i	−0.661634	+	0.381994i
$285$	1.57532e6			0.0680509
$286$		−	2.81430e6i		−	0.120302i
$287$	1.80828e7	−	1.04401e7i	0.764926	−	0.441630i
$288$	1.29036e7	−	1.29036e7i	0.540175	−	0.540175i
$289$	1.36001e7	+	7.85202e6i	0.563441	+	0.325303i
$290$	−1.89320e7	+	1.89320e7i	−0.776250	+	0.776250i
$291$	−602650.	−	2.24912e6i	−0.0244560	−	0.0912711i
$292$	−4.67068e6	+	8.08986e6i	−0.187600	+	0.324932i
$293$	−1.26930e7	+	2.19849e7i	−0.504615	+	0.874019i	0.495371	+	0.868682i	$0.335032\pi$
$293$	−1.26930e7	+	2.19849e7i	−0.504615	+	0.874019i	−0.999986	+	0.00533700i	$0.998301\pi$
$294$	470397.	−	1.75554e6i	0.0185107	−	0.0690828i
$295$			3.59315e7i			1.39962i
$296$	−1.67413e7	−	2.25266e7i	−0.645527	−	0.868603i
$297$	1.87046e6			0.0713967
$298$	1.75175e7	+	4.69380e6i	0.661947	+	0.177368i
$299$	−2.29659e6	−	1.32594e6i	−0.0859151	−	0.0496031i
$300$	−7114.13	−	4107.34i	−0.000263486	−	0.000152124i
$301$	−4.09145e7	+	1.09630e7i	−1.50030	+	0.402004i
$302$	−2.26775e7	−	2.26775e7i	−0.823331	−	0.823331i
$303$	−767835.	+	1.32993e6i	−0.0276020	+	0.0478080i
$304$	8.60890e6	+	8.60890e6i	0.306427	+	0.306427i
$305$	2.41528e7	+	4.18338e7i	0.851270	+	1.47444i
$306$	−1.28963e7			−0.450090
$307$		−	5.40409e7i		−	1.86770i	−0.357661	−	0.933852i	$-0.616426\pi$
$307$		−	5.40409e7i		−	1.86770i	0.357661	−	0.933852i	$-0.383574\pi$
$308$	−5.28372e6	−	9.15168e6i	−0.180837	−	0.313219i
$309$	−745573.	+	199776.i	−0.0252706	+	0.00677123i
$310$	4.42215e6	−	4.42215e6i	0.148439	−	0.148439i
$311$	1.12782e7	+	3.02197e6i	0.374936	+	0.100464i	0.441366	−	0.897327i	$-0.354494\pi$
$311$	1.12782e7	+	3.02197e6i	0.374936	+	0.100464i	−0.0664297	+	0.997791i	$0.521161\pi$
$312$	299316.	+	518431.i	0.00985522	+	0.0170697i
$313$	−2.59830e6	+	9.69700e6i	−0.0847339	+	0.316231i	−0.995264	−	0.0972124i	$-0.969007\pi$
$313$	−2.59830e6	+	9.69700e6i	−0.0847339	+	0.316231i	0.910530	+	0.413443i	$0.135674\pi$
$314$	6.08216e6	+	2.26989e7i	0.196458	+	0.733190i
$315$	4.73618e7	−	1.26906e7i	1.51529	−	0.406022i
$316$	4.57976e6	+	1.22714e6i	0.145138	+	0.0388897i
$317$	−3.02171e6	+	1.74458e6i	−0.0948582	+	0.0547664i	−0.546679	−	0.837342i	$-0.684108\pi$
$317$	−3.02171e6	+	1.74458e6i	−0.0948582	+	0.0547664i	0.451821	+	0.892109i	$0.350775\pi$
$318$	−12082.8	+	45093.7i	−0.000375740	+	0.00140228i
$319$	1.82166e7	+	1.82166e7i	0.561171	+	0.561171i
$320$	−8.51762e6	−	3.17882e7i	−0.259937	−	0.970098i
$321$	1.84872e6	−	1.06736e6i	0.0558927	−	0.0322697i
$322$	1.40157e7			0.419805
$323$			2.09454e7i			0.621558i
$324$	1.20829e7	−	6.97604e6i	0.355250	−	0.205104i
$325$	−78201.8	+	78201.8i	−0.00227807	+	0.00227807i
$326$	2.04329e7	+	1.17969e7i	0.589762	+	0.340499i
$327$	−1.92905e6	+	1.92905e6i	−0.0551695	+	0.0551695i
$328$	−5.57340e6	−	2.08002e7i	−0.157942	−	0.589449i
$329$	−1.00347e7	+	1.73806e7i	−0.281784	+	0.488064i
$330$	494267.	−	856096.i	0.0137537	−	0.0238221i
$331$	−1.48022e7	+	5.52426e7i	−0.408171	+	1.52332i	0.389959	+	0.920832i	$0.372489\pi$
$331$	−1.48022e7	+	5.52426e7i	−0.408171	+	1.52332i	−0.798131	+	0.602484i	$0.794178\pi$
$332$		−	2.63289e7i		−	0.719478i
$333$	−1.35484e7	−	3.41863e7i	−0.366906	−	0.925805i
$334$	2.76453e7			0.741963
$335$	−3.28782e7	−	8.80969e6i	−0.874529	−	0.234329i
$336$	−1.36464e6	−	787873.i	−0.0359749	−	0.0207701i
$337$	−4.19693e6	−	2.42310e6i	−0.109658	−	0.0633113i	0.444168	−	0.895944i	$-0.353499\pi$
$337$	−4.19693e6	−	2.42310e6i	−0.109658	−	0.0633113i	−0.553826	+	0.832632i	$0.686833\pi$
$338$	−2.62347e7	+	7.02956e6i	−0.679400	+	0.182045i
$339$	−117709.	−	117709.i	−0.00302142	−	0.00302142i
$340$	4.85230e6	−	8.40443e6i	0.123456	−	0.213831i
$341$	−4.25505e6	−	4.25505e6i	−0.107310	−	0.107310i
$342$	1.60145e7	+	2.77380e7i	0.400346	+	0.693420i
$343$	−2.86684e7			−0.710429
$344$			4.36841e7i			1.07312i
$345$	−465741.	−	806687.i	−0.0113419	−	0.0196448i
$346$	−2.62842e7	+	7.04282e6i	−0.634550	+	0.170027i
$347$	1.20953e7	−	1.20953e7i	0.289486	−	0.289486i	−0.547391	−	0.836877i	$-0.684379\pi$
$347$	1.20953e7	−	1.20953e7i	0.289486	−	0.289486i	0.836877	+	0.547391i	$0.184379\pi$
$348$	−1.55337e6	−	416224.i	−0.0368584	−	0.00987618i
$349$	3.29371e7	+	5.70488e7i	0.774836	+	1.34205i	0.934887	+	0.354946i	$0.115501\pi$
$349$	3.29371e7	+	5.70488e7i	0.774836	+	1.34205i	−0.160051	+	0.987109i	$0.551166\pi$
$350$	151283.	−	564597.i	0.00352847	−	0.0131684i
$351$	406849.	+	1.51838e6i	0.00940831	+	0.0351123i
$352$	−1.79646e7	+	4.81361e6i	−0.411899	+	0.110368i
$353$	−3.84240e7	−	1.02957e7i	−0.873531	−	0.234062i	−0.205917	−	0.978569i	$-0.566018\pi$
$353$	−3.84240e7	−	1.02957e7i	−0.873531	−	0.234062i	−0.667614	+	0.744508i	$0.732684\pi$
$354$	2.63080e6	−	1.51889e6i	0.0593033	−	0.0342387i
$355$	−2.14191e7	+	7.99371e7i	−0.478758	+	1.78675i
$356$	1.58225e7	+	1.58225e7i	0.350691	+	0.350691i
$357$	−701631.	−	2.61852e6i	−0.0154207	−	0.0575508i
$358$	3.86992e7	−	2.23430e7i	0.843437	−	0.486959i
$359$	7.36595e7			1.59201			0.796005	−	0.605290i	$-0.206943\pi$
$359$	7.36595e7			1.59201			0.796005	+	0.605290i	$0.206943\pi$
$360$		−	5.05678e7i		−	1.08384i
$361$	4.30754e6	−	2.48696e6i	0.0915604	−	0.0528624i
$362$	3.45264e7	−	3.45264e7i	0.727822	−	0.727822i
$363$	1.84190e6	+	1.06342e6i	0.0385076	+	0.0222324i
$364$	6.27978e6	−	6.27978e6i	0.130209	−	0.130209i
$365$	1.14332e7	+	4.26694e7i	0.235121	+	0.877482i
$366$	2.04197e6	−	3.53680e6i	0.0416492	−	0.0721385i
$367$	1.31660e7	−	2.28042e7i	0.266352	−	0.461336i	−0.701565	−	0.712606i	$-0.747515\pi$
$367$	1.31660e7	−	2.28042e7i	0.266352	−	0.461336i	0.967917	+	0.251270i	$0.0808482\pi$
$368$	1.86322e6	−	6.95364e6i	0.0373870	−	0.139530i
$369$		−	2.82142e7i		−	0.561551i
$370$	−3.85340e7	−	5.67719e6i	−0.760745	−	0.112080i
$371$	2.36001e6			0.0462159
$372$	362838.	+	97222.0i	0.00704828	+	0.00188858i
$373$	−2.63041e7	−	1.51867e7i	−0.506870	−	0.292642i	0.224676	−	0.974434i	$-0.427868\pi$
$373$	−2.63041e7	−	1.51867e7i	−0.506870	−	0.292642i	−0.731546	+	0.681792i	$0.761201\pi$
$374$	1.13826e7	+	6.57177e6i	0.217584	+	0.125622i
$375$	3.25894e6	−	873230.i	0.0617991	−	0.0165590i
$376$	1.46355e7	+	1.46355e7i	0.275325	+	0.275325i
$377$	−1.08253e7	+	1.87500e7i	−0.202031	+	0.349928i
$378$	−5.87468e6	−	5.87468e6i	−0.108770	−	0.108770i
$379$	1.46876e6	+	2.54397e6i	0.0269795	+	0.0467299i	0.879200	−	0.476453i	$-0.158078\pi$
$379$	1.46876e6	+	2.54397e6i	0.0269795	+	0.0467299i	−0.852220	+	0.523183i	$0.824744\pi$
$380$	−2.41022e7			−0.439245
$381$			3.64606e6i			0.0659248i
$382$	−2.55920e7	−	4.43267e7i	−0.459108	−	0.795198i
$383$	1.44740e6	−	387828.i	0.0257627	−	0.00690309i	−0.245915	−	0.969291i	$-0.579088\pi$
$383$	1.44740e6	−	387828.i	0.0257627	−	0.00690309i	0.271677	+	0.962388i	$0.412422\pi$
$384$	9049.55	−	9049.55i	0.000159821	−	0.000159821i
$385$	−4.82699e7	−	1.29339e7i	−0.845852	−	0.226645i
$386$	−2.78696e7	−	4.82716e7i	−0.484584	−	0.839324i
$387$	−1.48137e7	+	5.52855e7i	−0.255582	+	0.953846i
$388$	9.22048e6	+	3.44113e7i	0.157855	+	0.589123i
$389$	9.60677e7	−	2.57413e7i	1.63203	−	0.437301i	0.677527	−	0.735498i	$-0.263052\pi$
$389$	9.60677e7	−	2.57413e7i	1.63203	−	0.437301i	0.954504	+	0.298197i	$0.0963852\pi$
$390$	802463.	+	215019.i	0.0135279	+	0.00362479i
$391$	1.07257e7	−	6.19248e6i	0.179430	−	0.103594i
$392$	−2.45242e7	+	9.15256e7i	−0.407133	+	1.51944i
$393$	−450873.	−	450873.i	−0.00742809	−	0.00742809i
$394$	1.17767e6	+	4.39513e6i	0.0192547	+	0.0718594i
$395$	1.94175e7	−	1.12107e7i	0.315066	−	0.181903i
$396$	−1.42792e7			−0.229942
$397$			6.66799e7i			1.06567i	0.846219	+	0.532835i	$0.178874\pi$
$397$			6.66799e7i			1.06567i	−0.846219	+	0.532835i	$0.821126\pi$
$398$	−6.02612e7	+	3.47918e7i	−0.955848	+	0.551859i
$399$	−4.76077e6	+	4.76077e6i	−0.0749477	+	0.0749477i
$400$	−260003.	−	150113.i	−0.00406255	−	0.00234551i
$401$	5.86113e7	−	5.86113e7i	0.908967	−	0.908967i	−0.0872223	−	0.996189i	$-0.527799\pi$
$401$	5.86113e7	−	5.86113e7i	0.908967	−	0.908967i	0.996189	+	0.0872223i	$0.0277991\pi$
$402$	744807.	+	2.77966e6i	0.0114648	+	0.0427871i
$403$	2.52860e6	−	4.37966e6i	0.0386335	−	0.0669152i
$404$	1.17478e7	−	2.03478e7i	0.178161	−	0.308584i
$405$	1.70764e7	−	6.37302e7i	0.257059	−	0.959357i
$406$		−	1.14429e8i		−	1.70984i
$407$	−5.46267e6	+	3.70779e7i	−0.0810256	+	0.549962i
$408$	−2.79577e6			−0.0411644
$409$	7.74658e7	+	2.07569e7i	1.13224	+	0.303384i	0.775829	−	0.630944i	$-0.217332\pi$
$409$	7.74658e7	+	2.07569e7i	1.13224	+	0.303384i	0.356415	+	0.934328i	$0.383999\pi$
$410$	−2.58807e7	−	1.49422e7i	−0.375512	−	0.216802i
$411$	751294.	+	433760.i	0.0108214	+	0.00624775i
$412$	1.14072e7	−	3.05655e6i	0.163113	−	0.0437059i
$413$	−1.08588e8	−	1.08588e8i	−1.54146	−	1.54146i
$414$	9.46933e6	−	1.64014e7i	0.133450	−	0.231142i
$415$	−8.80399e7	−	8.80399e7i	−1.23179	−	1.23179i
$416$	−7.81509e6	−	1.35361e7i	−0.108556	−	0.188025i
$417$	−3.51782e6			−0.0485138
$418$		−	3.26431e7i		−	0.446954i
$419$	3.69680e6	+	6.40304e6i	0.0502555	+	0.0870450i	0.890059	−	0.455846i	$-0.150663\pi$
$419$	3.69680e6	+	6.40304e6i	0.0502555	+	0.0870450i	−0.839803	+	0.542891i	$0.817330\pi$
$420$	3.01318e6	−	807378.i	0.0406703	−	0.0108976i
$421$	−2.67567e7	+	2.67567e7i	−0.358580	+	0.358580i	−0.863289	−	0.504709i	$-0.831600\pi$
$421$	−2.67567e7	+	2.67567e7i	−0.358580	+	0.358580i	0.504709	+	0.863289i	$0.331600\pi$
$422$	5.69394e7	+	1.52569e7i	0.757662	+	0.203015i
$423$	1.35593e7	+	2.34854e7i	0.179150	+	0.310297i
$424$	629940.	−	2.35097e6i	0.00826422	−	0.0308425i
$425$	−133681.	−	498905.i	−0.00174142	−	0.00649907i
$426$	6.75820e6	−	1.81085e6i	0.0874183	−	0.0234237i
$427$	−1.99418e8	−	5.34339e7i	−2.56142	−	0.686330i
$428$	−2.82852e7	+	1.63305e7i	−0.360768	+	0.208289i
$429$	206894.	−	772141.i	0.00262046	−	0.00977968i
$430$	4.28675e7	+	4.28675e7i	0.539167	+	0.539167i
$431$	−2.46270e7	−	9.19092e7i	−0.307595	−	1.14796i	−0.930688	−	0.365814i	$-0.880791\pi$
$431$	−2.46270e7	−	9.19092e7i	−0.307595	−	1.14796i	0.623093	−	0.782148i	$-0.285876\pi$
$432$	−3.69558e6	+	2.13365e6i	−0.0458386	+	0.0264649i
$433$	7.85311e7			0.967338			0.483669	−	0.875251i	$-0.339304\pi$
$433$	7.85311e7			0.967338			0.483669	+	0.875251i	$0.339304\pi$
$434$			2.67284e7i			0.326966i
$435$	−6.58603e6	+	3.80245e6i	−0.0800122	+	0.0461951i
$436$	2.95142e7	−	2.95142e7i	0.356100	−	0.356100i
$437$	−2.66382e7	−	1.53796e7i	−0.319198	−	0.184289i
$438$	2.64083e6	−	2.64083e6i	0.0314281	−	0.0314281i
$439$	3.11281e7	+	1.16172e8i	0.367924	+	1.37311i	0.863413	+	0.504498i	$0.168322\pi$
$439$	3.11281e7	+	1.16172e8i	0.367924	+	1.37311i	−0.495489	+	0.868614i	$0.665011\pi$
$440$	−2.57687e7	+	4.46327e7i	−0.302506	+	0.523956i
$441$	−6.20745e7	+	1.07516e8i	−0.723764	+	1.25360i
$442$	−2.85889e6	+	1.06695e7i	−0.0331078	+	0.123560i
$443$		−	8.98549e7i		−	1.03355i	−0.856122	−	0.516774i	$-0.827133\pi$
$443$		−	8.98549e7i		−	1.03355i	0.856122	−	0.516774i	$-0.172867\pi$
$444$	−861954.	−	2.17495e6i	−0.00984771	−	0.0248485i
$445$	1.05816e8			1.20080
$446$	8.84525e6	+	2.37008e6i	0.0997024	+	0.0267152i
$447$	4.46110e6	+	2.57562e6i	0.0499481	+	0.0288376i
$448$	1.21808e8	+	7.03259e7i	1.35470	+	0.782134i
$449$	5.81104e7	−	1.55706e7i	0.641970	−	0.172015i	0.0768746	−	0.997041i	$-0.475506\pi$
$449$	5.81104e7	−	1.55706e7i	0.641970	−	0.172015i	0.565096	+	0.825025i	$0.308839\pi$
$450$	−558488.	−	558488.i	−0.00612881	−	0.00612881i
$451$	−1.43776e7	+	2.49027e7i	−0.156732	+	0.271467i
$452$	1.80094e6	+	1.80094e6i	0.0195022	+	0.0195022i
$453$	−4.55473e6	−	7.88902e6i	−0.0489968	−	0.0848650i
$454$	5.58436e7			0.596768
$455$		−	4.19973e7i		−	0.445849i
$456$	3.47178e6	+	6.01330e6i	0.0366149	+	0.0634188i
$457$	−8.14915e7	+	2.18356e7i	−0.853814	+	0.228779i	−0.659076	−	0.752076i	$-0.729052\pi$
$457$	−8.14915e7	+	2.18356e7i	−0.853814	+	0.228779i	−0.194738	+	0.980855i	$0.562386\pi$
$458$	−6.83152e7	+	6.83152e7i	−0.711084	+	0.711084i
$459$	−7.09124e6	−	1.90009e6i	−0.0733304	−	0.0196488i
$460$	7.12579e6	+	1.23422e7i	0.0732082	+	0.126800i
$461$	−1.41583e7	+	5.28395e7i	−0.144514	+	0.539332i	0.855263	+	0.518194i	$0.173396\pi$
$461$	−1.41583e7	+	5.28395e7i	−0.144514	+	0.539332i	−0.999777	+	0.0211379i	$0.993271\pi$
$462$	1.09348e6	+	4.08093e6i	0.0110888	+	0.0413841i
$463$	6.74955e7	−	1.80854e7i	0.680036	−	0.182215i	0.0977646	−	0.995210i	$-0.468831\pi$
$463$	6.74955e7	−	1.80854e7i	0.680036	−	0.182215i	0.582271	+	0.812994i	$0.302164\pi$
$464$	−5.67716e7	−	1.52119e7i	−0.568299	−	0.152275i
$465$	1.53837e6	−	888180.i	0.0153004	−	0.00883369i
$466$	−1.91578e7	+	7.14979e7i	−0.189316	+	0.706538i
$467$	6.30977e7	+	6.30977e7i	0.619531	+	0.619531i	0.945411	−	0.325880i	$-0.105661\pi$
$467$	6.30977e7	+	6.30977e7i	0.619531	+	0.619531i	−0.325880	+	0.945411i	$0.605661\pi$
$468$	−3.10591e6	−	1.15914e7i	−0.0303006	−	0.113084i
$469$	1.25985e8	−	7.27375e7i	1.22124	−	0.705082i
$470$	2.87240e7			0.276663
$471$			6.67489e6i			0.0638824i
$472$	−1.37157e8	+	7.91878e7i	−1.30435	+	0.753065i
$473$	4.12477e7	−	4.12477e7i	0.389778	−	0.389778i
$474$	−1.64163e6	−	947796.i	−0.0154149	−	0.00889979i
$475$	−907066.	+	907066.i	−0.00846365	+	0.00846365i
$476$	1.07349e7	+	4.00631e7i	0.0995352	+	0.371470i
$477$	1.59447e6	−	2.76171e6i	0.0146914	−	0.0254462i
$478$	1.31473e7	−	2.27717e7i	0.120379	−	0.208503i
$479$	−1.70823e7	+	6.37521e7i	−0.155432	+	0.580080i	0.843636	+	0.536915i	$0.180411\pi$
$479$	−1.70823e7	+	6.37521e7i	−0.155432	+	0.580080i	−0.999068	+	0.0431644i	$0.986256\pi$
$480$		−	5.49017e6i		−	0.0496434i
$481$	−3.12870e7	+	3.63050e6i	−0.281144	+	0.0326236i
$482$	1.03494e8			0.924215
$483$	3.84540e6	+	1.03037e6i	0.0341272	+	0.00914435i
$484$	−2.81809e7	−	1.62703e7i	−0.248553	−	0.143502i
$485$	1.45898e8	+	8.42345e7i	1.27887	+	0.738354i
$486$	−1.62768e7	+	4.36135e6i	−0.141795	+	0.0379938i
$487$	8.68844e6	+	8.68844e6i	0.0752237	+	0.0752237i	0.743718	−	0.668494i	$-0.233061\pi$
$487$	8.68844e6	+	8.68844e6i	0.0752237	+	0.0752237i	−0.668494	+	0.743718i	$0.733061\pi$
$488$	−1.06458e8	+	1.84392e8i	−0.916053	+	1.58665i
$489$	4.73878e6	+	4.73878e6i	0.0405266	+	0.0405266i
$490$	6.57490e7	+	1.13881e8i	0.558858	+	0.967970i
$491$	1.65095e8			1.39472			0.697362	−	0.716719i	$-0.254357\pi$
$491$	1.65095e8			1.39472			0.697362	+	0.716719i	$0.254357\pi$
$492$		−	1.79500e6i		−	0.0150720i
$493$	−5.05573e7	−	8.75677e7i	−0.421932	−	0.730808i
$494$	2.64987e7	−	7.10031e6i	0.219808	−	0.0588974i
$495$	−4.77476e7	+	4.77476e7i	−0.393673	+	0.393673i
$496$	1.32608e7	+	3.55321e6i	0.108674	+	0.0291190i
$497$	−1.76847e8	−	3.06308e8i	−1.44055	−	2.49511i
$498$	−2.72442e6	+	1.01677e7i	−0.0220590	+	0.0823252i
$499$	2.01149e7	+	7.50700e7i	0.161889	+	0.604178i	0.998417	+	0.0562531i	$0.0179154\pi$
$499$	2.01149e7	+	7.50700e7i	0.161889	+	0.604178i	−0.836528	+	0.547925i	$0.815418\pi$
$500$	−4.98615e7	+	1.33603e7i	−0.398892	+	0.106883i
$501$	7.58487e6	+	2.03236e6i	0.0603163	+	0.0161617i
$502$	−2.75802e7	+	1.59234e7i	−0.218015	+	0.125871i
$503$	3.96549e7	−	1.47994e8i	0.311597	−	1.16289i	−0.615520	−	0.788121i	$-0.711054\pi$
$503$	3.96549e7	−	1.47994e8i	0.311597	−	1.16289i	0.927116	−	0.374773i	$-0.122279\pi$
$504$	1.52821e8	+	1.52821e8i	1.19369	+	1.19369i
$505$	−2.87571e7	−	1.07323e8i	−0.223291	−	0.833334i
$506$	−1.67158e7	+	9.65089e6i	−0.129026	+	0.0744931i
$507$	−7.71462e6			−0.0591957
$508$		−	5.57843e7i		−	0.425521i
$509$	4.54635e6	−	2.62484e6i	0.0344754	−	0.0199044i	−0.482663	−	0.875806i	$-0.660330\pi$
$509$	4.54635e6	−	2.62484e6i	0.0344754	−	0.0199044i	0.517139	+	0.855902i	$0.326997\pi$
$510$	−2.74352e6	+	2.74352e6i	−0.0206822	+	0.0206822i
$511$	−1.63504e8	−	9.43988e7i	−1.22536	−	0.707463i
$512$	7.23307e7	−	7.23307e7i	0.538906	−	0.538906i
$513$	4.71905e6	+	1.76117e7i	0.0349544	+	0.130452i
$514$	−9.99265e7	+	1.73078e8i	−0.735853	+	1.27454i
$515$	2.79234e7	−	4.83647e7i	0.204431	−	0.354084i
$516$	−942453.	+	3.51728e6i	−0.00685979	+	0.0256011i
$517$		−	2.76386e7i		−	0.200007i
$518$	1.33611e8	−	9.92965e7i	0.961284	−	0.714405i
$519$	−7.72917e6			−0.0552880
$520$	−4.18365e7	−	1.12101e7i	−0.297540	−	0.0797256i
$521$	1.12947e8	+	6.52101e7i	0.798661	+	0.461107i	0.843003	−	0.537909i	$-0.180786\pi$
$521$	1.12947e8	+	6.52101e7i	0.798661	+	0.461107i	−0.0443418	+	0.999016i	$0.514119\pi$
$522$	−1.33906e8	−	7.73105e7i	−0.941429	−	0.543534i
$523$	−1.46505e8	+	3.92558e7i	−1.02411	+	0.274409i	−0.731514	−	0.681827i	$-0.761186\pi$
$523$	−1.46505e8	+	3.92558e7i	−1.02411	+	0.274409i	−0.292596	+	0.956236i	$0.594519\pi$
$524$	6.89832e6	+	6.89832e6i	0.0479457	+	0.0479457i
$525$	83013.2	−	143783.i	0.000573680	−	0.000993642i
$526$	−1.18709e8	−	1.18709e8i	−0.815693	−	0.815693i
$527$	1.18092e7	+	2.04542e7i	0.0806844	+	0.139749i
$528$	2.17004e6			0.0147423
$529$		−	1.29848e8i		−	0.877139i
$530$	−1.68886e6	−	2.92519e6i	−0.0113440	−	0.0196484i
$531$	−2.00436e8	+	5.37067e7i	−1.33873	+	0.358711i
$532$	7.28393e7	−	7.28393e7i	0.483761	−	0.483761i
$533$	−2.33426e7	−	6.25463e6i	−0.154159	−	0.0413067i
$534$	−4.47306e6	−	7.74756e6i	−0.0293752	−	0.0508793i
$535$	−3.99749e7	+	1.49188e8i	−0.261051	+	0.974256i
$536$	−3.88306e7	−	1.44918e8i	−0.252162	−	0.941082i
$537$	1.22602e7	−	3.28511e6i	0.0791725	−	0.0212142i
$538$	−1.21468e7	−	3.25473e6i	−0.0780038	−	0.0209010i
$539$	1.09578e8	−	6.32646e7i	0.699770	−	0.404012i
$540$	2.18647e6	−	8.16001e6i	0.0138855	−	0.0518214i
$541$	−5.67971e7	−	5.67971e7i	−0.358702	−	0.358702i	0.504632	−	0.863334i	$-0.331628\pi$
$541$	−5.67971e7	−	5.67971e7i	−0.358702	−	0.358702i	−0.863334	+	0.504632i	$0.831628\pi$
$542$	−3.51519e7	−	1.31189e8i	−0.220775	−	0.823945i
$543$	1.20110e7	−	6.93455e6i	0.0750204	−	0.0433130i
$544$	7.29971e7			0.453429
$545$		−	1.97383e8i		−	1.21932i
$546$	−3.07493e6	+	1.77531e6i	−0.0188911	+	0.0109068i
$547$	1.61984e8	−	1.61984e8i	0.989713	−	0.989713i	−0.0102345	−	0.999948i	$-0.503258\pi$
$547$	1.61984e8	−	1.61984e8i	0.989713	−	0.989713i	0.999948	+	0.0102345i	$0.00325780\pi$
$548$	−1.14947e7	−	6.63648e6i	−0.0698485	−	0.0403270i
$549$	−1.97260e8	+	1.97260e8i	−1.19213	+	1.19213i
$550$	208340.	+	777536.i	0.00125223	+	0.00467340i
$551$	−1.25563e8	+	2.17482e8i	−0.750600	+	1.30008i
$552$	2.05285e6	−	3.55564e6i	0.0122051	−	0.0211398i
$553$	−2.48017e7	+	9.25613e7i	−0.146658	+	0.547336i
$554$		−	2.03520e8i		−	1.19695i
$555$	−1.01550e7	−	4.39046e6i	−0.0594017	−	0.0256821i
$556$	5.38223e7			0.313140
$557$	−9.87113e7	−	2.64496e7i	−0.571217	−	0.153057i	−0.0383624	−	0.999264i	$-0.512214\pi$
$557$	−9.87113e7	−	2.64496e7i	−0.571217	−	0.153057i	−0.532855	+	0.846207i	$0.678881\pi$
$558$	3.12778e7	+	1.80583e7i	0.180026	+	0.103938i
$559$	4.24556e7	+	2.45118e7i	0.243052	+	0.140326i
$560$	1.10124e8	−	2.95076e7i	0.627072	−	0.168023i
$561$	2.63985e6	+	2.63985e6i	0.0149517	+	0.0149517i
$562$	8.64509e7	−	1.49737e8i	0.487036	−	0.843570i
$563$	6.68184e7	+	6.68184e7i	0.374430	+	0.374430i	0.869088	−	0.494658i	$-0.164707\pi$
$563$	6.68184e7	+	6.68184e7i	0.374430	+	0.374430i	−0.494658	+	0.869088i	$0.664707\pi$
$564$	862649.	+	1.49415e6i	0.00480836	+	0.00832832i
$565$	1.20442e7			0.0667777
$566$		−	1.64577e8i		−	0.907652i
$567$	1.40992e8	+	2.44206e8i	0.773474	+	1.33970i
$568$	−3.52340e8	+	9.44091e7i	−1.92272	+	0.515192i
$569$	−6.52720e7	+	6.52720e7i	−0.354315	+	0.354315i	−0.861712	−	0.507397i	$-0.830608\pi$
$569$	−6.52720e7	+	6.52720e7i	−0.354315	+	0.354315i	0.507397	+	0.861712i	$0.330608\pi$
$570$	9.30779e6	+	2.49401e6i	0.0502599	+	0.0134671i
$571$	5.06128e7	+	8.76640e7i	0.271864	+	0.470883i	0.969339	−	0.245726i	$-0.0790264\pi$
$571$	5.06128e7	+	8.76640e7i	0.271864	+	0.470883i	−0.697475	+	0.716609i	$0.745693\pi$
$572$	−3.16547e6	+	1.18137e7i	−0.0169141	+	0.0631244i
$573$	−3.76282e6	−	1.40430e7i	−0.0200009	−	0.0746444i
$574$	1.23371e8	−	3.30571e7i	0.652344	−	0.174795i
$575$	732661.	+	196316.i	0.00385389	+	0.00103265i
$576$	1.64593e8	−	9.50275e7i	0.861277	−	0.497258i
$577$	−4.10726e7	+	1.53285e8i	−0.213809	+	0.797945i	0.772774	+	0.634681i	$0.218869\pi$
$577$	−4.10726e7	+	1.53285e8i	−0.213809	+	0.797945i	−0.986583	+	0.163263i	$0.947798\pi$
$578$	6.79251e7	+	6.79251e7i	0.351760	+	0.351760i
$579$	−4.09770e6	−	1.52928e7i	−0.0211108	−	0.0787865i
$580$	1.00766e8	−	5.81771e7i	0.516450	−	0.298173i
$581$	5.32130e8			2.71325
$582$		−	1.42430e7i		−	0.0722493i
$583$	−2.81466e6	+	1.62504e6i	−0.0142043	+	0.00820086i
$584$	−1.37680e8	+	1.37680e8i	−0.691246	+	0.691246i
$585$	−4.91458e7	−	2.83743e7i	−0.245482	−	0.141729i
$586$	−1.09802e8	+	1.09802e8i	−0.545656	+	0.545656i
$587$	3.51541e7	+	1.31197e8i	0.173805	+	0.648648i	0.996752	+	0.0805307i	$0.0256615\pi$
$587$	3.51541e7	+	1.31197e8i	0.173805	+	0.648648i	−0.822947	+	0.568118i	$0.807672\pi$
$588$	−3.94920e6	+	6.84022e6i	−0.0194257	+	0.0336464i
$589$	2.93293e7	−	5.07998e7i	0.143534	−	0.248608i
$590$	−5.68860e7	+	2.12301e8i	−0.276980	+	1.03371i
$591$			1.29244e6i			0.00626107i
$592$	−3.15022e7	−	7.94887e7i	−0.151836	−	0.383125i
$593$	−1.56677e8			−0.751349			−0.375675	−	0.926752i	$-0.622589\pi$
$593$	−1.56677e8			−0.751349			−0.375675	+	0.926752i	$0.622589\pi$
$594$	1.10516e7	+	2.96127e6i	0.0527310	+	0.0141292i
$595$	1.69861e8	+	9.80695e7i	0.806387	+	0.465568i
$596$	−6.82543e7	−	3.94067e7i	−0.322397	−	0.186136i
$597$	−1.90912e7	+	5.11548e6i	−0.0897244	+	0.0240416i
$598$	−1.14702e7	−	1.14702e7i	−0.0536374	−	0.0536374i
$599$	−1.71018e8	+	2.96211e8i	−0.795721	+	1.37823i	0.126659	+	0.991946i	$0.459574\pi$
$599$	−1.71018e8	+	2.96211e8i	−0.795721	+	1.37823i	−0.922380	+	0.386283i	$0.873759\pi$
$600$	−121074.	−	121074.i	−0.000560529	−	0.000560529i
$601$	1.11559e8	+	1.93226e8i	0.513904	+	0.890108i	0.999870	+	0.0161299i	$0.00513454\pi$
$601$	1.11559e8	+	1.93226e8i	0.513904	+	0.890108i	−0.485966	+	0.873978i	$0.661532\pi$
$602$	−2.59100e8			−1.18762
$603$		−	1.96572e8i		−	0.896541i
$604$	6.96869e7	+	1.20701e8i	0.316257	+	0.547774i
$605$	−1.48638e8	+	3.98276e7i	−0.671220	+	0.179853i
$606$	−6.64228e6	+	6.64228e6i	−0.0298469	+	0.0298469i
$607$	−8.78711e7	−	2.35450e7i	−0.392898	−	0.105277i	0.0569607	−	0.998376i	$-0.481859\pi$
$607$	−8.78711e7	−	2.35450e7i	−0.392898	−	0.105277i	−0.449859	+	0.893100i	$0.648526\pi$
$608$	−9.06474e7	−	1.57006e8i	−0.403315	−	0.698563i
$609$	8.41227e6	−	3.13950e7i	0.0372444	−	0.138998i
$610$	7.64764e7	+	2.85414e8i	0.336928	+	1.25743i
$611$	2.24362e7	−	6.01175e6i	0.0983615	−	0.0263559i
$612$	5.41351e7	+	1.45055e7i	0.236170	+	0.0632816i
$613$	3.57897e8	−	2.06632e8i	1.55373	−	0.897048i	0.555900	−	0.831249i	$-0.312374\pi$
$613$	3.57897e8	−	2.06632e8i	1.55373	−	0.897048i	0.997833	−	0.0657988i	$-0.0209595\pi$
$614$	8.55565e7	−	3.19301e8i	0.369614	−	1.37942i
$615$	−6.00223e6	−	6.00223e6i	−0.0258040	−	0.0258040i
$616$	−5.70088e7	−	2.12760e8i	−0.243893	−	0.910223i
$617$	3.71207e8	−	2.14317e8i	1.58038	−	0.912432i	0.585575	−	0.810618i	$-0.300869\pi$
$617$	3.71207e8	−	2.14317e8i	1.58038	−	0.912432i	0.994803	−	0.101814i	$-0.0324647\pi$
$618$	−4.72151e6			−0.0200039
$619$		−	8.06404e7i		−	0.340002i	−0.985444	−	0.170001i	$-0.945623\pi$
$619$		−	8.06404e7i		−	0.340002i	0.985444	−	0.170001i	$-0.0543770\pi$
$620$	−2.35370e7	+	1.35891e7i	−0.0987587	+	0.0570184i
$621$	7.62340e6	−	7.62340e6i	0.0318327	−	0.0318327i
$622$	6.18528e7	+	3.57107e7i	0.257033	+	0.148398i
$623$	−3.19787e8	+	3.19787e8i	−1.32250	+	1.32250i
$624$	472013.	+	1.76158e6i	0.00194267	+	0.00725016i
$625$	−1.23444e8	+	2.13811e8i	−0.505627	+	0.875771i
$626$	−3.07042e7	+	5.31812e7i	−0.125163	+	0.216788i
$627$	2.39977e6	−	8.95608e6i	0.00973572	−	0.0363342i
$628$		−	1.02125e8i		−	0.412339i
$629$	5.83754e7	−	1.35020e8i	0.234573	−	0.542558i
$630$	2.99929e8			1.19949
$631$	−2.82570e7	−	7.57143e6i	−0.112470	−	0.0301363i	0.202145	−	0.979356i	$-0.435209\pi$
$631$	−2.82570e7	−	7.57143e6i	−0.112470	−	0.0301363i	−0.314615	+	0.949219i	$0.601875\pi$
$632$	8.55866e7	+	4.94135e7i	0.339043	+	0.195746i
$633$	1.45005e7	+	8.37185e6i	0.0571704	+	0.0330073i
$634$	−2.06158e7	+	5.52398e6i	−0.0808969	+	0.0216763i
$635$	−1.86535e8	−	1.86535e8i	−0.728515	−	0.728515i
$636$	101441.	−	175701.i	0.000394314	−	0.000682972i
$637$	7.51909e7	+	7.51909e7i	0.290902	+	0.290902i
$638$	7.87928e7	+	1.36473e8i	0.303406	+	0.525515i
$639$	−4.77928e8			−1.83172
$640$			925962.i			0.00353226i
$641$	−1.25811e7	−	2.17911e7i	−0.0477689	−	0.0827382i	0.841152	−	0.540798i	$-0.181878\pi$
$641$	−1.25811e7	−	2.17911e7i	−0.0477689	−	0.0827382i	−0.888921	+	0.458060i	$0.848544\pi$
$642$	1.26130e7	−	3.37963e6i	0.0476664	−	0.0127722i
$643$	−1.48417e8	+	1.48417e8i	−0.558277	+	0.558277i	−0.928817	−	0.370540i	$-0.879173\pi$
$643$	−1.48417e8	+	1.48417e8i	−0.558277	+	0.558277i	0.370540	+	0.928817i	$0.379173\pi$
$644$	−5.88343e7	−	1.57646e7i	−0.220279	−	0.0590235i
$645$	8.60986e6	+	1.49127e7i	0.0320861	+	0.0555748i
$646$	−3.31604e7	+	1.23756e8i	−0.123005	+	0.459060i
$647$	9.59068e7	+	3.57929e8i	0.354109	+	1.32155i	0.881602	+	0.471993i	$0.156465\pi$
$647$	9.59068e7	+	3.57929e8i	0.354109	+	1.32155i	−0.527494	+	0.849559i	$0.676868\pi$
$648$	2.80904e8	−	7.52681e7i	1.03237	−	0.276621i
$649$	2.04279e8	+	5.47365e7i	0.747292	+	0.200236i
$650$	−585864.	+	338249.i	−0.00213332	+	0.00123167i
$651$	−1.96495e6	+	7.33328e6i	−0.00712210	+	0.0265800i
$652$	−7.25028e7	−	7.25028e7i	−0.261585	−	0.261585i
$653$	8.24565e7	+	3.07732e8i	0.296132	+	1.10518i	0.940314	+	0.340308i	$0.110531\pi$
$653$	8.24565e7	+	3.07732e8i	0.296132	+	1.10518i	−0.644182	+	0.764872i	$0.722802\pi$
$654$	−1.44518e7	+	8.34376e6i	−0.0516641	+	0.0298283i
$655$	4.61340e7			0.164171
$656$		−	6.56027e7i		−	0.232386i
$657$	−2.20933e8	+	1.27556e8i	−0.779049	+	0.449784i
$658$	−8.68066e7	+	8.68066e7i	−0.304702	+	0.304702i
$659$	7.25237e6	+	4.18716e6i	0.0253410	+	0.0146306i	0.512617	−	0.858617i	$-0.328676\pi$
$659$	7.25237e6	+	4.18716e6i	0.0253410	+	0.0146306i	−0.487276	+	0.873248i	$0.662009\pi$
$660$	−3.03772e6	+	3.03772e6i	−0.0105661	+	0.0105661i
$661$	−2.53362e7	−	9.45558e7i	−0.0877276	−	0.327404i	0.908089	−	0.418777i	$-0.137541\pi$
$661$	−2.53362e7	−	9.45558e7i	−0.0877276	−	0.327404i	−0.995817	+	0.0913731i	$0.970874\pi$
$662$	−1.74918e8	+	3.02967e8i	−0.602921	+	1.04429i
$663$	−1.56875e6	+	2.71715e6i	−0.00538286	+	0.00932339i
$664$	1.42038e8	−	5.30092e8i	0.485177	−	1.81070i
$665$		−	4.87129e8i		−	1.65645i
$666$	−2.59277e7	−	2.23440e8i	−0.0877690	−	0.756376i
$667$	1.48491e8			0.500405
$668$	−1.16048e8	−	3.10949e7i	−0.389321	−	0.104318i
$669$	2.25258e6	+	1.30053e6i	0.00752317	+	0.00434351i
$670$	−1.80314e8	−	1.04104e8i	−0.599522	−	0.346134i
$671$	2.74629e8	−	7.35866e7i	0.909031	−	0.243574i
$672$	1.65918e7	+	1.65918e7i	0.0546747	+	0.0546747i
$673$	1.55577e8	−	2.69467e8i	0.510388	−	0.884017i	−0.489540	−	0.871981i	$-0.662835\pi$
$673$	1.55577e8	−	2.69467e8i	0.510388	−	0.884017i	0.999928	−	0.0120364i	$-0.00383140\pi$
$674$	−2.09614e7	−	2.09614e7i	−0.0684605	−	0.0684605i
$675$	−224809.	−	389380.i	−0.000730974	−	0.00126608i
$676$	1.18033e8			0.382088
$677$			1.39402e8i			0.449266i	0.974443	+	0.224633i	$0.0721183\pi$
$677$			1.39402e8i			0.449266i	−0.974443	+	0.224633i	$0.927882\pi$
$678$	−509131.	−	881840.i	−0.00163358	−	0.00282944i
$679$	−6.95484e8	+	1.86354e8i	−2.22166	+	0.595292i
$680$	1.43034e8	−	1.43034e8i	0.454896	−	0.454896i
$681$	1.53214e7	+	4.10537e6i	0.0485130	+	0.0129990i
$682$	−1.84045e7	−	3.18775e7i	−0.0580191	−	0.100492i
$683$	1.01262e8	−	3.77915e8i	0.317823	−	1.18613i	−0.603510	−	0.797355i	$-0.706232\pi$
$683$	1.01262e8	−	3.77915e8i	0.317823	−	1.18613i	0.921333	−	0.388775i	$-0.127102\pi$
$684$	−3.60256e7	−	1.34449e8i	−0.112575	−	0.420137i
$685$	−6.06281e7	+	1.62453e7i	−0.188626	+	0.0505423i
$686$	−1.69387e8	−	4.53872e7i	−0.524697	−	0.140592i
$687$	−2.37654e7	+	1.37210e7i	−0.0732951	+	0.0423170i
$688$	−3.44442e7	+	1.28548e8i	−0.105767	+	0.394729i
$689$	−1.93139e6	−	1.93139e6i	−0.00590489	−	0.00590489i
$690$	−1.47470e6	−	5.50367e6i	−0.00448908	−	0.0167535i
$691$	1.14238e8	−	6.59555e7i	0.346240	−	0.199902i	−0.316788	−	0.948496i	$-0.602604\pi$
$691$	1.14238e8	−	6.59555e7i	0.346240	−	0.199902i	0.663028	+	0.748594i	$0.269271\pi$
$692$	1.18256e8			0.356865
$693$		−	2.88596e8i		−	0.867143i
$694$	9.06140e7	−	5.23160e7i	0.271092	−	0.156515i
$695$	1.79974e8	−	1.79974e8i	0.536112	−	0.536112i
$696$	−2.90293e7	−	1.67601e7i	−0.0861013	−	0.0497106i
$697$	7.98055e7	−	7.98055e7i	0.235686	−	0.235686i
$698$	1.04291e8	+	3.89219e8i	0.306676	+	1.14453i
$699$	−1.05124e7	+	1.82080e7i	−0.0307801	+	0.0533127i
$700$	−1.27009e6	+	2.19987e6i	−0.00370290	+	0.00641361i
$701$	−1.90727e7	+	7.11803e7i	−0.0553679	+	0.206636i	−0.988068	−	0.154016i	$-0.950779\pi$
$701$	−1.90727e7	+	7.11803e7i	−0.0553679	+	0.206636i	0.932700	+	0.360652i	$0.117446\pi$
$702$			9.61547e6i			0.0277945i
$703$	−3.62898e8	+	4.21103e7i	−1.04453	+	0.121206i
$704$	−1.93699e8			−0.555149
$705$	7.88080e6	+	2.11165e6i	0.0224907	+	0.00602637i
$706$	−2.10728e8	−	1.21664e8i	−0.598838	−	0.345739i
$707$	4.11248e8	+	2.37434e8i	1.16371	+	0.671869i
$708$	−1.27518e7	+	3.41684e6i	−0.0359313	+	0.00962776i
$709$	−2.48578e8	−	2.48578e8i	−0.697466	−	0.697466i	0.266397	−	0.963863i	$-0.414167\pi$
$709$	−2.48578e8	−	2.48578e8i	−0.697466	−	0.697466i	−0.963863	+	0.266397i	$0.914167\pi$
$710$	−2.53110e8	+	4.38399e8i	−0.707186	+	1.22488i
$711$	9.15597e7	+	9.15597e7i	0.254739	+	0.254739i
$712$	2.33203e8	+	4.03920e8i	0.646093	+	1.11907i
$713$	−3.46846e7			−0.0956903
$714$		−	1.65824e7i		−	0.0455567i
$715$	2.89184e7	+	5.00881e7i	0.0791144	+	0.137030i
$716$	−1.87580e8	+	5.02619e7i	−0.511031	+	0.136930i
$717$	5.28121e6	−	5.28121e6i	0.0143277	−	0.0143277i
$718$	4.35218e8	+	1.16616e8i	1.17580	+	0.315055i
$719$	−2.32017e8	−	4.01864e8i	−0.624212	−	1.08117i	−0.988693	−	0.149956i	$-0.952087\pi$
$719$	−2.32017e8	−	4.01864e8i	−0.624212	−	1.08117i	0.364481	−	0.931211i	$-0.381247\pi$
$720$	3.98720e7	−	1.48804e8i	0.106824	−	0.398674i
$721$	6.17757e7	+	2.30550e8i	0.164821	+	0.615119i
$722$	2.93885e7	−	7.87461e6i	0.0780845	−	0.0209227i
$723$	2.83949e7	+	7.60839e6i	0.0751321	+	0.0201316i
$724$	−1.83767e8	+	1.06098e8i	−0.484230	+	0.279570i
$725$	1.60278e6	−	5.98166e6i	0.00420591	−	0.0156967i
$726$	9.19931e6	+	9.19931e6i	0.0240406	+	0.0240406i
$727$	−1.60746e8	−	5.99913e8i	−0.418348	−	1.56129i	−0.778034	−	0.628222i	$-0.783783\pi$
$727$	−1.60746e8	−	5.99913e8i	−0.418348	−	1.56129i	0.359687	−	0.933073i	$-0.382884\pi$
$728$	1.60312e8	−	9.25561e7i	0.415501	−	0.239889i
$729$	3.77828e8			0.975240
$730$			2.70213e8i			0.694606i
$731$	−1.98279e8	+	1.14477e8i	−0.507604	+	0.293065i
$732$	−1.25498e7	+	1.25498e7i	−0.0319965	+	0.0319965i
$733$	−2.50599e8	−	1.44684e8i	−0.636309	−	0.367373i	0.146882	−	0.989154i	$-0.453076\pi$
$733$	−2.50599e8	−	1.44684e8i	−0.636309	−	0.367373i	−0.783191	+	0.621781i	$0.786409\pi$
$734$	1.13895e8	−	1.13895e8i	0.288015	−	0.288015i
$735$	9.66714e6	+	3.60783e7i	0.0243465	+	0.0908623i
$736$	−5.35996e7	+	9.28372e7i	−0.134440	+	0.232857i
$737$	−1.00171e8	+	1.73501e8i	−0.250229	+	0.433410i
$738$	4.46682e7	−	1.66704e8i	0.111130	−	0.414741i
$739$		−	4.27124e8i		−	1.05833i	−0.848519	−	0.529164i	$-0.822506\pi$
$739$		−	4.27124e8i		−	1.05833i	0.848519	−	0.529164i	$-0.177494\pi$
$740$	1.55370e8	+	6.71736e7i	0.383417	+	0.165769i
$741$	7.79226e6			0.0191518
$742$	1.39441e7	+	3.73632e6i	0.0341334	+	0.00914601i
$743$	7.18707e7	+	4.14946e7i	0.175221	+	0.101164i	0.585045	−	0.811001i	$-0.301077\pi$
$743$	7.18707e7	+	4.14946e7i	0.175221	+	0.101164i	−0.409825	+	0.912164i	$0.634410\pi$
$744$	6.78071e6	+	3.91484e6i	0.0164648	+	0.00950595i
$745$	−3.60003e8	+	9.64625e7i	−0.870637	+	0.233287i
$746$	−1.31375e8	−	1.31375e8i	−0.316443	−	0.316443i
$747$	3.59519e8	−	6.22706e8i	0.862502	−	1.49390i
$748$	−4.03895e7	−	4.03895e7i	−0.0965080	−	0.0965080i
$749$	−3.30054e8	−	5.71669e8i	−0.785487	−	1.36050i
$750$	2.06379e7			0.0489196
$751$			4.68687e7i			0.110653i	0.998468	+	0.0553264i	$0.0176199\pi$
$751$			4.68687e7i			0.110653i	−0.998468	+	0.0553264i	$0.982380\pi$
$752$	3.15276e7	+	5.46074e7i	0.0741374	+	0.128410i
$753$	−8.73760e6	+	2.34123e6i	−0.0204648	+	0.00548353i
$754$	−9.36463e7	+	9.36463e7i	−0.218462	+	0.218462i
$755$	6.36631e8	+	1.70585e8i	1.47927	+	0.396369i
$756$	1.80526e7	+	3.12681e7i	0.0417806	+	0.0723662i
$757$	−1.47802e8	+	5.51605e8i	−0.340716	+	1.27157i	0.556821	+	0.830632i	$0.312021\pi$
$757$	−1.47802e8	+	5.51605e8i	−0.340716	+	1.27157i	−0.897538	+	0.440938i	$0.854646\pi$
$758$	4.65063e6	+	1.73564e7i	0.0106784	+	0.0398521i
$759$	−5.29570e6	+	1.41898e6i	−0.0121115	+	0.00324527i
$760$	−4.85263e8	−	1.30026e8i	−1.10544	−	0.296202i
$761$	−3.24310e8	+	1.87240e8i	−0.735879	+	0.424860i	−0.820569	−	0.571547i	$-0.806343\pi$
$761$	−3.24310e8	+	1.87240e8i	−0.735879	+	0.424860i	0.0846902	+	0.996407i	$0.473010\pi$
$762$	−5.77237e6	+	2.15428e7i	−0.0130463	+	0.0486896i
$763$	5.96510e8	+	5.96510e8i	1.34290	+	1.34290i
$764$	5.75708e7	+	2.14857e8i	0.129099	+	0.481803i
$765$	2.29524e8	−	1.32516e8i	0.512677	−	0.295994i
$766$	9.16595e6			0.0203935
$767$			1.77734e8i			0.393898i
$768$	2.52783e7	−	1.45944e7i	0.0558038	−	0.0322183i
$769$	1.57209e8	−	1.57209e8i	0.345698	−	0.345698i	−0.512806	−	0.858504i	$-0.671394\pi$
$769$	1.57209e8	−	1.57209e8i	0.345698	−	0.345698i	0.858504	+	0.512806i	$0.171394\pi$
$770$	−2.64726e8	−	1.52840e8i	−0.579863	−	0.334784i
$771$	−4.01401e7	+	4.01401e7i	−0.0875820	+	0.0875820i
$772$	6.26944e7	+	2.33979e8i	0.136263	+	0.508539i
$773$	−1.60342e8	+	2.77721e8i	−0.347144	+	0.601271i	−0.985741	−	0.168271i	$-0.946182\pi$
$773$	−1.60342e8	+	2.77721e8i	−0.347144	+	0.601271i	0.638597	+	0.769541i	$0.279515\pi$
$774$	−1.75054e8	+	3.03202e8i	−0.377527	+	0.653896i
$775$	−374380.	+	1.39720e6i	−0.000804280	+	0.00300161i
$776$			7.42563e8i			1.58909i
$777$	4.39577e7	−	1.74209e7i	0.0937069	−	0.0371370i
$778$	6.08370e8			1.29190
$779$	−2.70752e8	−	7.25477e7i	−0.572742	−	0.153466i
$780$	−3.12668e6	−	1.80519e6i	−0.00658869	−	0.00380398i
$781$	4.21833e8	+	2.43546e8i	0.885498	+	0.511243i
$782$	7.31766e7	−	1.96076e7i	0.153021	−	0.0410020i
$783$	−6.22397e7	−	6.22397e7i	−0.129653	−	0.129653i
$784$	−1.44333e8	+	2.49992e8i	−0.299515	+	0.518774i
$785$	−3.41492e8	−	3.41492e8i	−0.705946	−	0.705946i
$786$	−1.95018e6	−	3.37780e6i	−0.00401611	−	0.00695611i
$787$	9.71467e8			1.99298			0.996492	−	0.0836826i	$-0.0266682\pi$
$787$	9.71467e8			1.99298			0.996492	+	0.0836826i	$0.0266682\pi$
$788$		−	1.97742e7i		−	0.0404130i
$789$	−2.38425e7	−	4.12964e7i	−0.0485423	−	0.0840777i
$790$	1.32477e8	−	3.54970e7i	0.268694	−	0.0719964i
$791$	−3.63986e7	+	3.63986e7i	−0.0735454	+	0.0735454i
$792$	−2.87491e8	−	7.70329e7i	−0.578693	−	0.155060i
$793$	1.19471e8	+	2.06930e8i	0.239575	+	0.414957i
$794$	−1.05566e8	+	3.93978e8i	−0.210894	+	0.787066i
$795$	−248315.	−	926723.i	−0.000494198	−	0.00184437i
$796$	2.92094e8	−	7.82663e7i	0.579140	−	0.155180i
$797$	−7.83868e8	−	2.10037e8i	−1.54835	−	0.414878i	−0.619395	−	0.785080i	$-0.712622\pi$
$797$	−7.83868e8	−	2.10037e8i	−1.54835	−	0.414878i	−0.928951	+	0.370201i	$0.879289\pi$
$798$	−3.56662e7	+	2.05919e7i	−0.0701856	+	0.0405217i
$799$	−2.80765e7	+	1.04783e8i	−0.0550431	+	0.205424i
$800$	3.16123e6	+	3.16123e6i	0.00617427	+	0.00617427i
$801$	1.58163e8	+	5.90273e8i	0.307757	+	1.14856i
$802$	4.39097e8	−	2.53513e8i	0.851212	−	0.491447i
$803$	2.60003e8			0.502148
$804$		−	1.25060e7i		−	0.0240630i
$805$	−2.49448e8	+	1.44019e8i	−0.478181	+	0.276078i
$806$	2.18740e7	−	2.18740e7i	0.0417757	−	0.0417757i
$807$	−3.09337e6	−	1.78596e6i	−0.00588588	−	0.00339821i
$808$	3.46296e8	−	3.46296e8i	0.656468	−	0.656468i
$809$	1.34761e8	+	5.02935e8i	0.254518	+	0.949874i	0.968358	+	0.249565i	$0.0802878\pi$
$809$	1.34761e8	+	5.02935e8i	0.254518	+	0.949874i	−0.713840	+	0.700309i	$0.753046\pi$
$810$	2.01793e8	−	3.49515e8i	0.379709	−	0.657674i
$811$	4.69299e8	−	8.12849e8i	0.879806	−	1.52387i	0.0282525	−	0.999601i	$-0.491006\pi$
$811$	4.69299e8	−	8.12849e8i	0.879806	−	1.52387i	0.851553	−	0.524268i	$-0.175661\pi$
$812$	−1.28707e8	+	4.80341e8i	−0.240400	+	0.897183i
$813$		−	3.85775e7i		−	0.0717898i
$814$	−9.09773e7	+	2.10427e8i	−0.168679	+	0.390147i
$815$	−4.84878e8			−0.895694
$816$	−8.22703e6	−	2.20443e6i	−0.0151416	−	0.00405719i
$817$	4.92444e8	+	2.84313e8i	0.903006	+	0.521351i
$818$	4.24845e8	+	2.45285e8i	0.776195	+	0.448136i
$819$	2.34274e8	−	6.27734e7i	0.426453	−	0.114268i
$820$	9.18335e7	+	9.18335e7i	0.166556	+	0.166556i
$821$	−2.27135e8	+	3.93410e8i	−0.410445	+	0.710911i	−0.994938	−	0.100487i	$-0.967960\pi$
$821$	−2.27135e8	+	3.93410e8i	−0.410445	+	0.710911i	0.584494	+	0.811398i	$0.301293\pi$
$822$	3.75231e6	+	3.75231e6i	0.00675589	+	0.00675589i
$823$	−1.53706e8	−	2.66226e8i	−0.275734	−	0.477586i	0.694586	−	0.719410i	$-0.255588\pi$
$823$	−1.53706e8	−	2.66226e8i	−0.275734	−	0.477586i	−0.970320	+	0.241824i	$0.922254\pi$
$824$	2.46156e8			0.439977
$825$			228644.i			0.000407190i
$826$	−4.69681e8	−	8.13511e8i	−0.833417	−	1.44352i
$827$	5.87783e8	−	1.57496e8i	1.03920	−	0.278454i	0.301420	−	0.953491i	$-0.402539\pi$
$827$	5.87783e8	−	1.57496e8i	1.03920	−	0.278454i	0.737783	+	0.675038i	$0.235873\pi$
$828$	−5.81977e7	+	5.81977e7i	−0.102521	+	0.102521i
$829$	−8.32583e8	−	2.23090e8i	−1.46138	−	0.391576i	−0.561416	−	0.827534i	$-0.689743\pi$
$829$	−8.32583e8	−	2.23090e8i	−1.46138	−	0.391576i	−0.899967	+	0.435957i	$0.856410\pi$
$830$	−3.80801e8	−	6.59567e8i	−0.665985	−	1.15352i
$831$	1.49618e7	−	5.58384e7i	0.0260725	−	0.0973037i
$832$	−4.21321e7	−	1.57239e8i	−0.0731548	−	0.273018i
$833$	−4.79696e8	+	1.28534e8i	−0.829910	+	0.222374i
$834$	−2.07851e7	−	5.56934e6i	−0.0358305	−	0.00960076i
$835$	−4.92024e8	+	2.84070e8i	−0.845136	+	0.487940i
$836$	−3.67163e7	+	1.37027e8i	−0.0628406	+	0.234524i
$837$	1.45380e7	+	1.45380e7i	0.0247930	+	0.0247930i
$838$	1.17054e7	+	4.36851e7i	0.0198909	+	0.0742337i
$839$	−2.67652e8	+	1.54529e8i	−0.453194	+	0.261652i	−0.709178	−	0.705029i	$-0.750934\pi$
$839$	−2.67652e8	+	1.54529e8i	−0.453194	+	0.261652i	0.255984	+	0.966681i	$0.417600\pi$
$840$	6.50215e7			0.109703
$841$		−	6.17498e8i		−	1.03812i
$842$	−2.00453e8	+	1.15731e8i	−0.335796	+	0.193872i
$843$	3.47270e7	−	3.47270e7i	0.0579675	−	0.0579675i
$844$	−2.21856e8	−	1.28089e8i	−0.369015	−	0.213051i
$845$	3.94685e8	−	3.94685e8i	0.654155	−	0.654155i
$846$	4.29337e7	+	1.60231e8i	0.0709066	+	0.264627i
$847$	3.28837e8	−	5.69563e8i	0.541166	−	0.937328i
$848$	3.70741e6	−	6.42142e6i	0.00607971	−	0.0105304i
$849$	1.20989e7	−	4.51539e7i	0.0197708	−	0.0737857i
$850$		−	3.15942e6i		−	0.00514459i
$851$	1.28854e8	+	1.73383e8i	0.209079	+	0.281330i
$852$	−3.04059e7			−0.0491631
$853$	1.94307e8	+	5.20644e7i	0.313070	+	0.0838869i	0.411933	−	0.911214i	$-0.364854\pi$
$853$	1.94307e8	+	5.20644e7i	0.313070	+	0.0838869i	−0.0988628	+	0.995101i	$0.531520\pi$
$854$	−1.09367e9	−	6.31429e8i	−1.75595	−	1.01380i
$855$	−5.70044e8	−	3.29115e8i	−0.912031	−	0.526562i
$856$	−6.57579e8	+	1.76198e8i	−1.04840	+	0.280918i
$857$	1.90655e7	+	1.90655e7i	0.0302905	+	0.0302905i	0.722090	−	0.691799i	$-0.243182\pi$
$857$	1.90655e7	+	1.90655e7i	0.0302905	+	0.0302905i	−0.691799	+	0.722090i	$0.743182\pi$
$858$	2.44487e6	−	4.23465e6i	0.00387075	−	0.00670433i
$859$	−3.31292e8	−	3.31292e8i	−0.522674	−	0.522674i	0.395704	−	0.918378i	$-0.370501\pi$
$859$	−3.31292e8	−	3.31292e8i	−0.522674	−	0.522674i	−0.918378	+	0.395704i	$0.870501\pi$
$860$	−1.31730e8	−	2.28163e8i	−0.207104	−	0.358715i
$861$	3.62786e7			0.0568384
$862$		−	5.82035e8i		−	0.908715i
$863$	4.23073e8	+	7.32784e8i	0.658238	+	1.14010i	0.981072	+	0.193646i	$0.0620312\pi$
$863$	4.23073e8	+	7.32784e8i	0.658238	+	1.14010i	−0.322834	+	0.946456i	$0.604635\pi$
$864$	6.13789e7	−	1.64464e7i	0.0951651	−	0.0254994i
$865$	3.95430e8	−	3.95430e8i	0.610971	−	0.610971i
$866$	4.64002e8	+	1.24329e8i	0.714440	+	0.191434i
$867$	1.36426e7	+	2.36297e7i	0.0209334	+	0.0362578i
$868$	3.00635e7	−	1.12199e8i	0.0459706	−	0.171565i
$869$	−3.41557e7	−	1.27471e8i	−0.0520480	−	0.194246i
$870$	−4.49336e7	+	1.20399e7i	−0.0682360	+	0.0182838i
$871$	−1.62631e8	−	4.35768e7i	−0.246121	−	0.0659479i
$872$	7.53447e8	−	4.35003e8i	1.13633	−	0.656059i
$873$	−2.51810e8	+	9.39769e8i	−0.378470	+	1.41247i
$874$	−1.33043e8	−	1.33043e8i	−0.199278	−	0.199278i
$875$	−2.70025e8	−	1.00775e9i	−0.403069	−	1.50427i
$876$	−1.40559e7	+	8.11516e6i	−0.0209096	+	0.0120721i
$877$	−9.93519e8			−1.47291			−0.736457	−	0.676485i	$-0.763503\pi$
$877$	−9.93519e8			−1.47291			−0.736457	+	0.676485i	$0.763503\pi$
$878$			7.35682e8i			1.08694i
$879$	−3.81979e7	+	2.20536e7i	−0.0562436	+	0.0324723i
$880$	−1.11021e8	+	1.11021e8i	−0.162913	+	0.162913i
$881$	7.42236e8	+	4.28530e8i	1.08546	+	0.626691i	0.932364	−	0.361520i	$-0.117742\pi$
$881$	7.42236e8	+	4.28530e8i	1.08546	+	0.626691i	0.153097	+	0.988211i	$0.451075\pi$
$882$	−5.36985e8	+	5.36985e8i	−0.782630	+	0.782630i
$883$	−2.67109e8	−	9.96866e8i	−0.387978	−	1.44795i	−0.833419	−	0.552642i	$-0.813620\pi$
$883$	−2.67109e8	−	9.96866e8i	−0.387978	−	1.44795i	0.445441	−	0.895311i	$-0.353047\pi$
$884$	2.40017e7	−	4.15722e7i	0.0347445	−	0.0601792i
$885$	−3.12149e7	+	5.40657e7i	−0.0450331	+	0.0779996i
$886$	1.42257e8	−	5.30909e8i	0.204537	−	0.763341i
$887$		−	8.50667e8i		−	1.21896i	−0.792802	−	0.609479i	$-0.791379\pi$
$887$		−	8.50667e8i		−	1.21896i	0.792802	−	0.609479i	$-0.208621\pi$
$888$	−5.62085e6	−	4.84394e7i	−0.00802718	−	0.0691766i
$889$	1.12745e9			1.60470
$890$	6.25215e8	+	1.67526e8i	0.886869	+	0.237636i
$891$	−3.36308e8	−	1.94168e8i	−0.475450	−	0.274501i
$892$	−3.44642e7	−	1.98979e7i	−0.0485594	−	0.0280358i
$893$	2.60238e8	−	6.97305e7i	0.365440	−	0.0979194i
$894$	2.22808e7	+	2.22808e7i	0.0311830	+	0.0311830i
$895$	−4.59172e8	+	7.95308e8i	−0.640480	+	1.10934i
$896$	−2.79835e6	−	2.79835e6i	−0.00389025	−	0.00389025i
$897$	−2.30377e6	−	3.99025e6i	−0.00319199	−	0.00552869i
$898$	3.67997e8			0.508177
$899$			2.83176e8i			0.389741i
$900$	1.71621e6	+	2.97256e6i	0.00235419	+	0.00407759i
$901$	1.23217e7	−	3.30159e6i	0.0168460	−	0.00451386i
$902$	−1.24376e8	+	1.24376e8i	−0.169479	+	0.169479i
$903$	−7.10875e7	−	1.90478e7i	−0.0965451	−	0.0258692i
$904$	2.65436e7	+	4.59749e7i	0.0359298	+	0.0622322i
$905$	−2.59714e8	+	9.69267e8i	−0.350389	+	1.30767i
$906$	−1.44219e7	−	5.38233e7i	−0.0193927	−	0.0723745i
$907$	2.25572e8	−	6.04418e7i	0.302317	−	0.0810057i	−0.104472	−	0.994528i	$-0.533315\pi$
$907$	2.25572e8	−	6.04418e7i	0.302317	−	0.0810057i	0.406789	+	0.913522i	$0.366648\pi$
$908$	−2.34416e8	−	6.28117e7i	−0.313134	−	0.0839041i
$909$	5.55696e8	−	3.20831e8i	0.739854	−	0.427155i
$910$	6.64894e7	−	2.48142e8i	0.0882324	−	0.329288i
$911$	9.78693e7	+	9.78693e7i	0.129447	+	0.129447i	0.768862	−	0.639415i	$-0.220823\pi$
$911$	9.78693e7	+	9.78693e7i	0.129447	+	0.129447i	−0.639415	+	0.768862i	$0.720823\pi$
$912$	5.47489e6	+	2.04326e7i	0.00721757	+	0.0269363i
$913$	−6.34645e8	+	3.66412e8i	−0.833909	+	0.481457i
$914$	−5.16063e8			−0.675871
$915$			8.39293e7i			0.109560i
$916$	3.63608e8	−	2.09929e8i	0.473094	−	0.273141i
$917$	−1.39421e8	+	1.39421e8i	−0.180810	+	0.180810i
$918$	−3.88905e7	−	2.24534e7i	−0.0502707	−	0.0290238i
$919$	−2.45339e8	+	2.45339e8i	−0.316097	+	0.316097i	−0.847266	−	0.531169i	$-0.821753\pi$
$919$	−2.45339e8	+	2.45339e8i	−0.316097	+	0.316097i	0.531169	+	0.847266i	$0.321753\pi$
$920$	7.68838e7	+	2.86934e8i	0.0987351	+	0.368484i
$921$	4.69472e7	−	8.13149e7i	0.0600939	−	0.104086i
$922$	−1.67309e8	+	2.89788e8i	−0.213465	+	0.369732i
$923$	−1.05949e8	+	3.95406e8i	−0.134738	+	0.502850i
$924$		−	1.83606e7i		−	0.0232740i
$925$	8.37522e6	−	3.31919e6i	0.0105821	−	0.00419379i
$926$	4.27430e8			0.538310
$927$	3.11530e8	+	8.34741e7i	0.391075	+	0.104788i
$928$	7.57950e8	+	4.37603e8i	0.948412	+	0.547566i
$929$	−4.23465e8	−	2.44488e8i	−0.528166	−	0.304937i	0.212103	−	0.977247i	$-0.431969\pi$
$929$	−4.23465e8	−	2.44488e8i	−0.528166	−	0.304937i	−0.740269	+	0.672311i	$0.765302\pi$
$930$	1.04956e7	−	2.81230e6i	0.0130485	−	0.00349633i
$931$	8.72142e8	+	8.72142e8i	1.08078	+	1.08078i
$932$	1.60839e8	−	2.78581e8i	0.198675	−	0.344115i
$933$	1.43449e7	+	1.43449e7i	0.0176625	+	0.0176625i
$934$	2.72918e8	+	4.72708e8i	0.334959	+	0.580166i
$935$	−2.70113e8			−0.330454
$936$		−	2.50132e8i		−	0.305029i
$937$	−6.98403e8	−	1.20967e9i	−0.848960	−	1.47044i	−0.882138	−	0.470992i	$-0.843896\pi$
$937$	−6.98403e8	−	1.20967e9i	−0.848960	−	1.47044i	0.0331780	−	0.999449i	$-0.489437\pi$
$938$	8.59540e8	−	2.30313e8i	1.04150	−	0.279068i
$939$	−1.23338e7	+	1.23338e7i	−0.0148970	+	0.0148970i
$940$	−1.20576e8	−	3.23081e7i	−0.145170	−	0.0388981i
$941$	4.39025e8	+	7.60414e8i	0.526891	+	0.912602i	0.999509	+	0.0313342i	$0.00997563\pi$
$941$	4.39025e8	+	7.60414e8i	0.526891	+	0.912602i	−0.472618	+	0.881267i	$0.656691\pi$
$942$	−1.05676e7	+	3.94386e7i	−0.0126422	+	0.0471812i
$943$	4.28972e7	+	1.60095e8i	0.0511557	+	0.190916i
$944$	−4.66047e8	+	1.24877e8i	−0.554005	+	0.148445i
$945$	1.64921e8	+	4.41905e7i	0.195426	+	0.0523641i
$946$	3.09015e8	−	1.78410e8i	0.365011	−	0.210739i
$947$	−7.75776e7	+	2.89524e8i	−0.0913454	+	0.340906i	−0.996440	−	0.0843045i	$-0.973133\pi$
$947$	−7.75776e7	+	2.89524e8i	−0.0913454	+	0.340906i	0.905095	+	0.425210i	$0.139800\pi$
$948$	5.82507e6	+	5.82507e6i	0.00683716	+	0.00683716i
$949$	5.65541e7	+	2.11063e8i	0.0661706	+	0.246952i
$950$	−6.79545e6	+	3.92336e6i	−0.00792588	+	0.00457601i
$951$	−6.06231e6			−0.00704850
$952$			8.64524e8i			1.00200i
$953$	8.05101e8	−	4.64825e8i	0.930190	−	0.537045i	0.0433182	−	0.999061i	$-0.486207\pi$
$953$	8.05101e8	−	4.64825e8i	0.930190	−	0.537045i	0.886872	+	0.462016i	$0.152874\pi$
$954$	1.37932e7	−	1.37932e7i	0.0158862	−	0.0158862i
$955$	9.10959e8	+	5.25943e8i	1.04590	+	0.603849i
$956$	−8.08020e7	+	8.08020e7i	−0.0924801	+	0.0924801i
$957$	1.15850e7	+	4.32357e7i	0.0132178	+	0.0493295i
$958$	−2.01862e8	+	3.49635e8i	−0.229593	+	0.397666i
$959$	1.34129e8	−	2.32319e8i	0.152079	−	0.263408i
$960$	1.47991e7	−	5.52309e7i	0.0167271	−	0.0624264i
$961$			8.21359e8i			0.925471i
$962$	−1.90607e8	−	2.80820e7i	−0.214099	−	0.0315430i
$963$	−8.91966e8			−0.998779
$964$	−4.34439e8	−	1.16408e8i	−0.484951	−	0.129942i
$965$	9.92032e8	+	5.72750e8i	1.10394	+	0.637357i
$966$	2.10893e7	+	1.21759e7i	0.0233954	+	0.0135074i
$967$	−7.05909e8	+	1.89148e8i	−0.780673	+	0.209181i	−0.627082	−	0.778954i	$-0.715751\pi$
$967$	−7.05909e8	+	1.89148e8i	−0.780673	+	0.209181i	−0.153592	+	0.988134i	$0.549084\pi$
$968$	−4.79607e8	−	4.79607e8i	−0.528761	−	0.528761i
$969$	−1.81960e7	+	3.15164e7i	−0.0199988	+	0.0346390i
$970$	7.28683e8	+	7.28683e8i	0.798406	+	0.798406i
$971$	4.58592e7	+	7.94305e7i	0.0500921	+	0.0867620i	0.889984	−	0.455991i	$-0.150715\pi$
$971$	4.58592e7	+	7.94305e7i	0.0500921	+	0.0867620i	−0.839892	+	0.542753i	$0.817382\pi$
$972$	7.32312e7			0.0797439
$973$			1.08780e9i			1.18089i
$974$	3.75803e7	+	6.50911e7i	0.0406709	+	0.0704441i
$975$	−185606.	+	49733.0i	−0.000200253	+	5.36576e-5i
$976$	−4.58662e8	+	4.58662e8i	−0.493336	+	0.493336i
$977$	−1.50163e9	−	4.02362e8i	−1.61020	−	0.431452i	−0.662099	−	0.749416i	$-0.730334\pi$
$977$	−1.50163e9	−	4.02362e8i	−1.61020	−	0.431452i	−0.948103	+	0.317964i	$0.897001\pi$
$978$	2.04968e7	+	3.55014e7i	0.0219113	+	0.0379515i
$979$	1.61196e8	−	6.01591e8i	0.171793	−	0.641140i
$980$	−1.47906e8	−	5.51994e8i	−0.157148	−	0.586484i
$981$	1.10106e9	−	2.95028e8i	1.16628	−	0.312504i
$982$	9.75463e8	+	2.61374e8i	1.03009	+	0.276012i
$983$	−5.74271e7	+	3.31556e7i	−0.0604584	+	0.0349057i	−0.529925	−	0.848045i	$-0.677780\pi$
$983$	−5.74271e7	+	3.31556e7i	−0.0604584	+	0.0349057i	0.469466	+	0.882950i	$0.344446\pi$
$984$	9.68360e6	−	3.61397e7i	0.0101637	−	0.0379314i
$985$	−6.61222e7	−	6.61222e7i	−0.0691892	−	0.0691892i
$986$	−1.60082e8	−	5.97436e8i	−0.166999	−	0.623248i
$987$	−3.01982e7	+	1.74349e7i	−0.0314072	+	0.0181330i
$988$	−1.19221e8			−0.123618
$989$		−	3.36226e8i		−	0.347570i
$990$	−3.57710e8	+	2.06524e8i	−0.368660	+	0.212846i
$991$	2.07625e7	−	2.07625e7i	0.0213334	−	0.0213334i	−0.696360	−	0.717693i	$-0.745198\pi$
$991$	2.07625e7	−	2.07625e7i	0.0213334	−	0.0213334i	0.717693	+	0.696360i	$0.245198\pi$
$992$	−1.77043e8	−	1.02216e8i	−0.181361	−	0.104709i
$993$	−7.02638e7	+	7.02638e7i	−0.0717603	+	0.0717603i
$994$	−5.59962e8	−	2.08981e9i	−0.570163	−	2.12788i
$995$	7.15009e8	−	1.23843e9i	0.725842	−	1.25719i
$996$	2.28728e7	−	3.96168e7i	0.0231494	−	0.0400960i
$997$	−2.80583e8	+	1.04715e9i	−0.283124	+	1.05663i	0.667076	+	0.744990i	$0.267546\pi$
$997$	−2.80583e8	+	1.04715e9i	−0.283124	+	1.05663i	−0.950200	+	0.311642i	$0.899121\pi$
$998$			4.75397e8i			0.478261i
$999$	1.86640e7	−	1.26682e8i	0.0187202	−	0.127063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.7.g.a.8.13	✓	72
37.14	odd	12	inner	37.7.g.a.14.13	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.7.g.a.8.13	✓	72	1.1	even	1	trivial
37.7.g.a.14.13	yes	72	37.14	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	37.g (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(5.90851 + 1.58318i) q^{2} +(1.50469 + 0.868733i) q^{3} +(-23.0216 - 13.2915i) q^{4} +(-121.426 + 32.5360i) q^{5} +(7.51511 + 7.51511i) q^{6} +(268.634 - 465.288i) q^{7} +(-391.802 - 391.802i) q^{8} +(-362.991 - 628.718i) q^{9} +O(q^{10})\)	\(q+(5.90851 + 1.58318i) q^{2} +(1.50469 + 0.868733i) q^{3} +(-23.0216 - 13.2915i) q^{4} +(-121.426 + 32.5360i) q^{5} +(7.51511 + 7.51511i) q^{6} +(268.634 - 465.288i) q^{7} +(-391.802 - 391.802i) q^{8} +(-362.991 - 628.718i) q^{9} -768.957 q^{10} +739.901i q^{11} +(-23.0936 - 39.9993i) q^{12} +(-600.629 + 160.938i) q^{13} +(2323.86 - 2323.86i) q^{14} +(-210.974 - 56.5302i) q^{15} +(-844.012 - 1461.87i) q^{16} +(751.624 - 2805.10i) q^{17} +(-1149.36 - 4289.47i) q^{18} +(-6966.72 + 1866.73i) q^{19} +(3227.88 + 864.907i) q^{20} +(808.423 - 466.743i) q^{21} +(-1171.40 + 4371.71i) q^{22} +(3015.61 + 3015.61i) q^{23} +(-249.169 - 929.911i) q^{24} +(154.028 - 88.9282i) q^{25} -3803.62 q^{26} -2527.98i q^{27} +(-12368.8 + 7141.13i) q^{28} +(24620.3 - 24620.3i) q^{29} +(-1157.04 - 668.018i) q^{30} +(-5750.85 + 5750.85i) q^{31} +(6505.75 + 24279.8i) q^{32} +(-642.776 + 1113.32i) q^{33} +(8881.96 - 15384.0i) q^{34} +(-17480.6 + 65238.4i) q^{35} +19298.8i q^{36} +(50112.1 + 7382.98i) q^{37} -44118.3 q^{38} +(-1043.57 - 279.625i) q^{39} +(60322.5 + 34827.2i) q^{40} +(33656.9 + 19431.8i) q^{41} +(5515.51 - 1477.88i) q^{42} +(-55747.7 - 55747.7i) q^{43} +(9834.42 - 17033.7i) q^{44} +(64532.5 + 64532.5i) q^{45} +(13043.5 + 22592.0i) q^{46} -37354.5 q^{47} -2932.88i q^{48} +(-85504.2 - 148098. i) q^{49} +(1050.87 - 281.579i) q^{50} +(3567.85 - 3567.85i) q^{51} +(15966.6 + 4278.23i) q^{52} +(2196.30 + 3804.10i) q^{53} +(4002.25 - 14936.6i) q^{54} +(-24073.4 - 89843.2i) q^{55} +(-287552. + 77049.3i) q^{56} +(-12104.4 - 3243.37i) q^{57} +(184448. - 106491. i) q^{58} +(73978.1 - 276090. i) q^{59} +(4105.58 + 4105.58i) q^{60} +(-99454.7 - 371170. i) q^{61} +(-43083.5 + 24874.3i) q^{62} -390047. q^{63} +261791. i q^{64} +(67695.7 - 39084.1i) q^{65} +(-5560.44 + 5560.44i) q^{66} +(234492. + 135384. i) q^{67} +(-54587.7 + 54587.7i) q^{68} +(1917.80 + 7157.32i) q^{69} +(-206568. + 357786. i) q^{70} +(329160. - 570121. i) q^{71} +(-104112. + 388553. i) q^{72} -351403. i q^{73} +(284399. + 122959. i) q^{74} +309.019 q^{75} +(185197. + 49623.3i) q^{76} +(344267. + 198763. i) q^{77} +(-5723.26 - 3304.33i) q^{78} +(-172281. + 46162.6i) q^{79} +(150048. + 150048. i) q^{80} +(-262424. + 454532. i) q^{81} +(168098. + 168098. i) q^{82} +(495218. + 857743. i) q^{83} -24814.9 q^{84} +365067. i q^{85} +(-241127. - 417644. i) q^{86} +(58434.5 - 15657.5i) q^{87} +(289894. - 289894. i) q^{88} +(-813069. - 217861. i) q^{89} +(279124. + 483457. i) q^{90} +(-86467.0 + 322699. i) q^{91} +(-29342.1 - 109506. i) q^{92} +(-13649.2 + 3657.29i) q^{93} +(-220709. - 59138.8i) q^{94} +(785204. - 453338. i) q^{95} +(-11303.5 + 42185.3i) q^{96} +(-947626. - 947626. i) q^{97} +(-270737. - 1.01040e6i) q^{98} +(465189. - 268577. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9}+O(q^{10}) \) 72 * q - 2 * q^2 - 6 * q^3 + 264 * q^4 + 52 * q^5 - 132 * q^6 - 2 * q^7 - 1968 * q^8 + 8094 * q^9	\( 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9} + 1864 q^{10} + 1178 q^{12} + 2898 q^{13} + 10168 q^{14} + 1418 q^{15} + 23668 q^{16} - 16734 q^{17} + 30222 q^{18} - 20756 q^{19} + 27910 q^{20} - 22326 q^{21} + 40188 q^{22} + 23388 q^{23} + 51426 q^{24} - 54060 q^{25} + 31064 q^{26} - 84486 q^{28} - 101426 q^{29} - 280062 q^{30} - 112740 q^{31} + 66416 q^{32} + 27376 q^{33} + 45094 q^{34} + 152710 q^{35} - 23168 q^{37} - 67600 q^{38} + 386674 q^{39} - 473862 q^{40} - 566622 q^{41} - 569640 q^{42} - 33332 q^{43} + 667736 q^{44} + 399362 q^{45} + 303310 q^{46} + 352424 q^{47} - 402226 q^{49} - 190836 q^{50} - 525822 q^{51} - 290936 q^{52} + 365094 q^{53} + 1191884 q^{54} - 343392 q^{55} + 2217442 q^{56} + 73378 q^{57} - 581028 q^{58} - 576604 q^{59} + 2105904 q^{60} - 213462 q^{61} - 423156 q^{62} - 1483688 q^{63} + 2273880 q^{65} - 846680 q^{66} + 1591698 q^{67} - 3165948 q^{68} + 2464258 q^{69} + 2158358 q^{70} - 1388114 q^{71} + 1672988 q^{72} - 3228324 q^{74} + 1857268 q^{75} - 3488628 q^{76} + 846288 q^{77} - 6537300 q^{78} - 781076 q^{79} - 3635536 q^{80} - 2236868 q^{81} + 3720360 q^{82} - 944002 q^{83} + 6632744 q^{84} - 1174862 q^{86} - 1073982 q^{87} - 427452 q^{88} + 3381078 q^{89} + 412204 q^{90} - 2879114 q^{91} + 696698 q^{92} - 543710 q^{93} - 3545780 q^{94} - 268230 q^{95} - 9026178 q^{96} - 1842138 q^{97} - 7266130 q^{98} + 8295480 q^{99}+O(q^{100}) \) 72 * q - 2 * q^2 - 6 * q^3 + 264 * q^4 + 52 * q^5 - 132 * q^6 - 2 * q^7 - 1968 * q^8 + 8094 * q^9 + 1864 * q^10 + 1178 * q^12 + 2898 * q^13 + 10168 * q^14 + 1418 * q^15 + 23668 * q^16 - 16734 * q^17 + 30222 * q^18 - 20756 * q^19 + 27910 * q^20 - 22326 * q^21 + 40188 * q^22 + 23388 * q^23 + 51426 * q^24 - 54060 * q^25 + 31064 * q^26 - 84486 * q^28 - 101426 * q^29 - 280062 * q^30 - 112740 * q^31 + 66416 * q^32 + 27376 * q^33 + 45094 * q^34 + 152710 * q^35 - 23168 * q^37 - 67600 * q^38 + 386674 * q^39 - 473862 * q^40 - 566622 * q^41 - 569640 * q^42 - 33332 * q^43 + 667736 * q^44 + 399362 * q^45 + 303310 * q^46 + 352424 * q^47 - 402226 * q^49 - 190836 * q^50 - 525822 * q^51 - 290936 * q^52 + 365094 * q^53 + 1191884 * q^54 - 343392 * q^55 + 2217442 * q^56 + 73378 * q^57 - 581028 * q^58 - 576604 * q^59 + 2105904 * q^60 - 213462 * q^61 - 423156 * q^62 - 1483688 * q^63 + 2273880 * q^65 - 846680 * q^66 + 1591698 * q^67 - 3165948 * q^68 + 2464258 * q^69 + 2158358 * q^70 - 1388114 * q^71 + 1672988 * q^72 - 3228324 * q^74 + 1857268 * q^75 - 3488628 * q^76 + 846288 * q^77 - 6537300 * q^78 - 781076 * q^79 - 3635536 * q^80 - 2236868 * q^81 + 3720360 * q^82 - 944002 * q^83 + 6632744 * q^84 - 1174862 * q^86 - 1073982 * q^87 - 427452 * q^88 + 3381078 * q^89 + 412204 * q^90 - 2879114 * q^91 + 696698 * q^92 - 543710 * q^93 - 3545780 * q^94 - 268230 * q^95 - 9026178 * q^96 - 1842138 * q^97 - 7266130 * q^98 + 8295480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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