LMFDB - Embedded newform 37.7.g.a.8.18

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			8.18
Character	$\chi$	$=$	37.8
Dual form			37.7.g.a.14.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(14.9428 + 4.00391i) q^{2} +(13.6514 + 7.88162i) q^{3} +(151.830 + 87.6593i) q^{4} +(-121.406 + 32.5306i) q^{5} +(172.432 + 172.432i) q^{6} +(6.42619 - 11.1305i) q^{7} +(1217.70 + 1217.70i) q^{8} +(-240.260 - 416.143i) q^{9} +O(q^{10})$	\(q+(14.9428 + 4.00391i) q^{2} +(13.6514 + 7.88162i) q^{3} +(151.830 + 87.6593i) q^{4} +(-121.406 + 32.5306i) q^{5} +(172.432 + 172.432i) q^{6} +(6.42619 - 11.1305i) q^{7} +(1217.70 + 1217.70i) q^{8} +(-240.260 - 416.143i) q^{9} -1944.40 q^{10} -1118.24i q^{11} +(1381.79 + 2393.34i) q^{12} +(1767.99 - 473.732i) q^{13} +(140.591 - 140.591i) q^{14} +(-1913.75 - 512.788i) q^{15} +(7710.12 + 13354.3i) q^{16} +(1327.16 - 4953.03i) q^{17} +(-1923.96 - 7180.32i) q^{18} +(-6406.28 + 1716.56i) q^{19} +(-21284.7 - 5703.23i) q^{20} +(175.452 - 101.298i) q^{21} +(4477.35 - 16709.7i) q^{22} +(8860.03 + 8860.03i) q^{23} +(7025.83 + 26220.8i) q^{24} +(149.531 - 86.3315i) q^{25} +28315.6 q^{26} -19066.0i q^{27} +(1951.38 - 1126.63i) q^{28} +(-32020.6 + 32020.6i) q^{29} +(-26543.7 - 15325.0i) q^{30} +(32262.3 - 32262.3i) q^{31} +(33215.8 + 123963. i) q^{32} +(8813.57 - 15265.6i) q^{33} +(39663.0 - 68698.3i) q^{34} +(-418.096 + 1560.36i) q^{35} -84244.2i q^{36} +(-49855.5 - 8952.79i) q^{37} -102601. q^{38} +(27869.3 + 7467.56i) q^{39} +(-187449. - 108224. i) q^{40} +(-10215.9 - 5898.18i) q^{41} +(3027.34 - 811.173i) q^{42} +(-77884.0 - 77884.0i) q^{43} +(98024.5 - 169783. i) q^{44} +(42706.4 + 42706.4i) q^{45} +(96918.9 + 167868. i) q^{46} -60434.9 q^{47} +243073. i q^{48} +(58741.9 + 101744. i) q^{49} +(2580.07 - 691.327i) q^{50} +(57155.5 - 57155.5i) q^{51} +(309962. + 83054.1i) q^{52} +(59574.4 + 103186. i) q^{53} +(76338.4 - 284899. i) q^{54} +(36377.2 + 135762. i) q^{55} +(21378.8 - 5728.43i) q^{56} +(-100984. - 27058.5i) q^{57} +(-606685. + 350270. i) q^{58} +(-12907.4 + 48171.0i) q^{59} +(-245615. - 245615. i) q^{60} +(10295.8 + 38424.4i) q^{61} +(611264. - 352913. i) q^{62} -6175.83 q^{63} +998455. i q^{64} +(-199234. + 115028. i) q^{65} +(192821. - 192821. i) q^{66} +(471232. + 272066. i) q^{67} +(635683. - 635683. i) q^{68} +(51120.1 + 190783. i) q^{69} +(-12495.1 + 21642.1i) q^{70} +(-306789. + 531375. i) q^{71} +(214173. - 799304. i) q^{72} +250701. i q^{73} +(-709135. - 333397. i) q^{74} +2721.73 q^{75} +(-1.12314e6 - 300945. i) q^{76} +(-12446.6 - 7186.05i) q^{77} +(386546. + 223172. i) q^{78} +(364263. - 97603.9i) q^{79} +(-1.37048e6 - 1.37048e6i) q^{80} +(-24879.0 + 43091.7i) q^{81} +(-129039. - 129039. i) q^{82} +(-210396. - 364417. i) q^{83} +35518.7 q^{84} +644501. i q^{85} +(-851965. - 1.47565e6i) q^{86} +(-689499. + 184751. i) q^{87} +(1.36169e6 - 1.36169e6i) q^{88} +(585981. + 157013. i) q^{89} +(467161. + 809146. i) q^{90} +(6088.59 - 22722.9i) q^{91} +(568557. + 2.12189e6i) q^{92} +(694703. - 186145. i) q^{93} +(-903066. - 241976. i) q^{94} +(721921. - 416801. i) q^{95} +(-523589. + 1.95406e6i) q^{96} +(-796994. - 796994. i) q^{97} +(470395. + 1.75554e6i) q^{98} +(-465349. + 268669. 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 $

$2$	14.9428	+	4.00391i	1.86785	+	0.500489i	0.999993	+	0.00367499i	$0.00116979\pi$
$2$	14.9428	+	4.00391i	1.86785	+	0.500489i	0.867857	+	0.496814i	$0.165497\pi$
$3$	13.6514	+	7.88162i	0.505606	+	0.291912i	0.731026	−	0.682350i	$-0.239042\pi$
$3$	13.6514	+	7.88162i	0.505606	+	0.291912i	−0.225420	+	0.974262i	$0.572375\pi$
$4$	151.830	+	87.6593i	2.37235	+	1.36968i
$5$	−121.406	+	32.5306i	−0.971248	+	0.260245i	−0.709355	−	0.704852i	$-0.751014\pi$
$5$	−121.406	+	32.5306i	−0.971248	+	0.260245i	−0.261893	+	0.965097i	$0.584347\pi$
$6$	172.432	+	172.432i	0.798298	+	0.798298i
$7$	6.42619	−	11.1305i	0.0187352	−	0.0324504i	−0.856506	−	0.516137i	$-0.827369\pi$
$7$	6.42619	−	11.1305i	0.0187352	−	0.0324504i	0.875241	+	0.483687i	$0.160703\pi$
$8$	1217.70	+	1217.70i	2.37833	+	2.37833i
$9$	−240.260	−	416.143i	−0.329575	−	0.570841i
$10$	−1944.40			−1.94440
$11$		−	1118.24i		−	0.840153i	−0.907489	−	0.420077i	$-0.862003\pi$
$11$		−	1118.24i		−	0.840153i	0.907489	−	0.420077i	$-0.137997\pi$
$12$	1381.79	+	2393.34i	0.799650	+	1.38503i
$13$	1767.99	−	473.732i	0.804731	−	0.215627i	0.167071	−	0.985945i	$-0.446569\pi$
$13$	1767.99	−	473.732i	0.804731	−	0.215627i	0.637660	+	0.770318i	$0.279903\pi$
$14$	140.591	−	140.591i	0.0512357	−	0.0512357i
$15$	−1913.75	−	512.788i	−0.567038	−	0.151937i
$16$	7710.12	+	13354.3i	1.88235	+	3.26033i
$17$	1327.16	−	4953.03i	0.270132	−	1.00815i	−0.688901	−	0.724855i	$-0.741907\pi$
$17$	1327.16	−	4953.03i	0.270132	−	1.00815i	0.959034	−	0.283293i	$-0.0914268\pi$
$18$	−1923.96	−	7180.32i	−0.329897	−	1.23119i
$19$	−6406.28	+	1716.56i	−0.933997	+	0.250264i	−0.693558	−	0.720401i	$-0.743958\pi$
$19$	−6406.28	+	1716.56i	−0.933997	+	0.250264i	−0.240439	+	0.970664i	$0.577291\pi$
$20$	−21284.7	−	5703.23i	−2.66059	−	0.712904i
$21$	175.452	−	101.298i	0.0189453	−	0.0109381i
$22$	4477.35	−	16709.7i	0.420487	−	1.56928i
$23$	8860.03	+	8860.03i	0.728201	+	0.728201i	0.970261	−	0.242060i	$-0.0778231\pi$
$23$	8860.03	+	8860.03i	0.728201	+	0.728201i	−0.242060	+	0.970261i	$0.577823\pi$
$24$	7025.83	+	26220.8i	0.508235	+	1.89676i
$25$	149.531	−	86.3315i	0.00956995	−	0.00552522i
$26$	28315.6			1.61104
$27$		−	19066.0i		−	0.968651i
$28$	1951.38	−	1126.63i	0.0888931	−	0.0513225i
$29$	−32020.6	+	32020.6i	−1.31291	+	1.31291i	−0.393651	+	0.919260i	$0.628788\pi$
$29$	−32020.6	+	32020.6i	−1.31291	+	1.31291i	−0.919260	+	0.393651i	$0.871212\pi$
$30$	−26543.7	−	15325.0i	−0.983098	−	0.567592i
$31$	32262.3	−	32262.3i	1.08295	−	1.08295i	0.0867204	−	0.996233i	$-0.472361\pi$
$31$	32262.3	−	32262.3i	1.08295	−	1.08295i	0.996233	−	0.0867204i	$-0.0276387\pi$
$32$	33215.8	+	123963.i	1.01367	+	3.78305i
$33$	8813.57	−	15265.6i	0.245251	−	0.424787i
$34$	39663.0	−	68698.3i	1.00913	−	1.74787i
$35$	−418.096	+	1560.36i	−0.00975151	+	0.0363931i
$36$		−	84244.2i		−	1.80564i
$37$	−49855.5	−	8952.79i	−0.984256	−	0.176747i
$37$	−49855.5	−	8952.79i	−0.984256	−	0.176747i
$38$	−102601.			−1.86982
$39$	27869.3	+	7467.56i	0.469821	+	0.125888i
$40$	−187449.	−	108224.i	−2.92889	−	1.69100i
$41$	−10215.9	−	5898.18i	−0.148227	−	0.0855788i	0.424052	−	0.905638i	$-0.360607\pi$
$41$	−10215.9	−	5898.18i	−0.148227	−	0.0855788i	−0.572279	+	0.820059i	$0.693941\pi$
$42$	3027.34	−	811.173i	0.0408614	−	0.0109488i
$43$	−77884.0	−	77884.0i	−0.979587	−	0.979587i	0.0202091	−	0.999796i	$-0.493567\pi$
$43$	−77884.0	−	77884.0i	−0.979587	−	0.979587i	−0.999796	+	0.0202091i	$0.993567\pi$
$44$	98024.5	−	169783.i	1.15074	−	1.99314i
$45$	42706.4	+	42706.4i	0.468658	+	0.468658i
$46$	96918.9	+	167868.i	0.995714	+	1.72463i
$47$	−60434.9			−0.582095			−0.291048	−	0.956709i	$-0.594004\pi$
$47$	−60434.9			−0.582095			−0.291048	+	0.956709i	$0.594004\pi$
$48$			243073.i			2.19792i
$49$	58741.9	+	101744.i	0.499298	+	0.864809i
$50$	2580.07	−	691.327i	0.0206406	−	0.00553062i
$51$	57155.5	−	57155.5i	0.430871	−	0.430871i
$52$	309962.	+	83054.1i	2.20444	+	0.590679i
$53$	59574.4	+	103186.i	0.400159	+	0.693095i	0.993745	−	0.111675i	$-0.0356217\pi$
$53$	59574.4	+	103186.i	0.400159	+	0.693095i	−0.593586	+	0.804771i	$0.702288\pi$
$54$	76338.4	−	284899.i	0.484799	−	1.80930i
$55$	36377.2	+	135762.i	0.218646	+	0.815997i
$56$	21378.8	−	5728.43i	0.121736	−	0.0326191i
$57$	−100984.	−	27058.5i	−0.545289	−	0.146110i
$58$	−606685.	+	350270.i	−3.10942	+	1.79522i
$59$	−12907.4	+	48171.0i	−0.0628467	+	0.234547i	−0.990204	−	0.139631i	$-0.955408\pi$
$59$	−12907.4	+	48171.0i	−0.0628467	+	0.234547i	0.927357	+	0.374178i	$0.122075\pi$
$60$	−245615.	−	245615.i	−1.13711	−	1.13711i
$61$	10295.8	+	38424.4i	0.0453597	+	0.169285i	0.984890	−	0.173181i	$-0.0554046\pi$
$61$	10295.8	+	38424.4i	0.0453597	+	0.169285i	−0.939530	+	0.342466i	$0.888738\pi$
$62$	611264.	−	352913.i	2.56480	−	1.48079i
$63$	−6175.83			−0.0246987
$64$			998455.i			3.80880i
$65$	−199234.	+	115028.i	−0.725477	+	0.418855i
$66$	192821.	−	192821.i	0.670693	−	0.670693i
$67$	471232.	+	272066.i	1.56679	+	0.904586i	0.996540	+	0.0831138i	$0.0264865\pi$
$67$	471232.	+	272066.i	1.56679	+	0.904586i	0.570249	+	0.821472i	$0.306847\pi$
$68$	635683.	−	635683.i	2.02169	−	2.02169i
$69$	51120.1	+	190783.i	0.155612	+	0.580754i
$70$	−12495.1	+	21642.1i	−0.0364287	+	0.0630964i
$71$	−306789.	+	531375.i	−0.857166	+	1.48466i	0.0174544	+	0.999848i	$0.494444\pi$
$71$	−306789.	+	531375.i	−0.857166	+	1.48466i	−0.874621	+	0.484808i	$0.838890\pi$
$72$	214173.	−	799304.i	0.573808	−	2.14148i
$73$			250701.i			0.644446i	0.946664	+	0.322223i	$0.104430\pi$
$73$			250701.i			0.644446i	−0.946664	+	0.322223i	$0.895570\pi$
$74$	−709135.	−	333397.i	−1.74998	−	0.822747i
$75$	2721.73			0.00645150
$76$	−1.12314e6	−	300945.i	−2.55855	−	0.685561i
$77$	−12446.6	−	7186.05i	−0.0272633	−	0.0157405i
$78$	386546.	+	223172.i	0.814549	+	0.470280i
$79$	364263.	−	97603.9i	0.738811	−	0.197964i	0.130262	−	0.991480i	$-0.458418\pi$
$79$	364263.	−	97603.9i	0.738811	−	0.197964i	0.608550	+	0.793516i	$0.291752\pi$
$80$	−1.37048e6	−	1.37048e6i	−2.67672	−	2.67672i
$81$	−24879.0	+	43091.7i	−0.0468143	+	0.0810847i
$82$	−129039.	−	129039.i	−0.234034	−	0.234034i
$83$	−210396.	−	364417.i	−0.367963	−	0.637330i	0.621284	−	0.783585i	$-0.286611\pi$
$83$	−210396.	−	364417.i	−0.367963	−	0.637330i	−0.989247	+	0.146255i	$0.953278\pi$
$84$	35518.7			0.0599265
$85$			644501.i			1.04946i
$86$	−851965.	−	1.47565e6i	−1.33945	−	2.31999i
$87$	−689499.	+	184751.i	−1.04707	+	0.280562i
$88$	1.36169e6	−	1.36169e6i	1.99816	−	1.99816i
$89$	585981.	+	157013.i	0.831215	+	0.222723i	0.649244	−	0.760580i	$-0.275085\pi$
$89$	585981.	+	157013.i	0.831215	+	0.222723i	0.181971	+	0.983304i	$0.441752\pi$
$90$	467161.	+	809146.i	0.640824	+	1.10994i
$91$	6088.59	−	22722.9i	0.00807965	−	0.0301536i
$92$	568557.	+	2.12189e6i	0.730148	+	2.72495i
$93$	694703.	−	186145.i	0.863675	−	0.231421i
$94$	−903066.	−	241976.i	−1.08727	−	0.291332i
$95$	721921.	−	416801.i	0.842013	−	0.486136i
$96$	−523589.	+	1.95406e6i	−0.591802	+	2.20864i
$97$	−796994.	−	796994.i	−0.873252	−	0.873252i	0.119573	−	0.992825i	$-0.461847\pi$
$97$	−796994.	−	796994.i	−0.873252	−	0.873252i	−0.992825	+	0.119573i	$0.961847\pi$
$98$	470395.	+	1.75554e6i	0.499786	+	1.86523i
$99$	−465349.	+	268669.i	−0.479594	+	0.276893i
$100$	30271.0			0.0302710
$101$		−	862862.i		−	0.837485i	−0.908105	−	0.418742i	$-0.862471\pi$
$101$		−	862862.i		−	0.837485i	0.908105	−	0.418742i	$-0.137529\pi$
$102$	1.08291e6	−	625217.i	1.02045	−	0.589156i
$103$	93651.2	−	93651.2i	0.0857042	−	0.0857042i	−0.662955	−	0.748659i	$-0.730698\pi$
$103$	93651.2	−	93651.2i	0.0857042	−	0.0857042i	0.748659	+	0.662955i	$0.230698\pi$
$104$	2.72976e6	+	1.57602e6i	2.42674	+	1.40108i
$105$	−18005.7	+	18005.7i	−0.0155540	+	0.0155540i
$106$	477062.	+	1.78042e6i	0.400550	+	1.49487i
$107$	137122.	−	237503.i	0.111933	−	0.193873i	−0.804617	−	0.593794i	$-0.797629\pi$
$107$	137122.	−	237503.i	0.111933	−	0.193873i	0.916549	+	0.399921i	$0.130963\pi$
$108$	1.67131e6	−	2.89479e6i	1.32674	−	2.29798i
$109$	191320.	−	714015.i	0.147734	−	0.551351i	−0.851884	−	0.523730i	$-0.824540\pi$
$109$	191320.	−	714015.i	0.147734	−	0.551351i	0.999618	−	0.0276210i	$-0.00879316\pi$
$110$			2.17431e6i			1.63359i
$111$	−610034.	−	515160.i	−0.446051	−	0.376681i
$112$	198187.			0.141065
$113$	408489.	+	109454.i	0.283103	+	0.0758573i	0.397577	−	0.917569i	$-0.369851\pi$
$113$	408489.	+	109454.i	0.283103	+	0.0758573i	−0.114473	+	0.993426i	$0.536518\pi$
$114$	−1.40064e6	−	808660.i	−0.945393	−	0.545823i
$115$	−1.36388e6	−	787438.i	−0.896775	−	0.517753i
$116$	−7.66860e6	+	2.05480e6i	−4.91295	+	1.31642i
$117$	−621919.	−	621919.i	−0.388308	−	0.388308i
$118$	−385745.	+	668130.i	−0.234776	+	0.406645i
$119$	−46601.1	−	46601.1i	−0.0276538	−	0.0276538i
$120$	−1.70596e6	−	2.95480e6i	−0.987244	−	1.70996i
$121$	521092.			0.294143
$122$			615391.i			0.338900i
$123$	−92974.4	−	161036.i	−0.0499629	−	0.0865383i
$124$	7.72648e6	−	2.07030e6i	4.05244	−	1.08585i
$125$	1.37333e6	−	1.37333e6i	0.703146	−	0.703146i
$126$	−92284.2	−	24727.5i	−0.0461334	−	0.0123614i
$127$	−421089.	−	729348.i	−0.205571	−	0.356060i	0.744743	−	0.667351i	$-0.232572\pi$
$127$	−421089.	−	729348.i	−0.205571	−	0.356060i	−0.950315	+	0.311291i	$0.899239\pi$
$128$	−1.87191e6	+	6.98607e6i	−0.892597	+	3.33122i
$129$	−449371.	−	1.67708e6i	−0.209332	−	0.781238i
$130$	−3.43768e6	+	921123.i	−1.56472	+	0.419264i
$131$	−3.38918e6	−	908129.i	−1.50758	−	0.403955i	−0.591951	−	0.805974i	$-0.701642\pi$
$131$	−3.38918e6	−	908129.i	−1.50758	−	0.403955i	−0.915632	+	0.402019i	$0.868309\pi$
$132$	2.67634e6	−	1.54518e6i	1.16364	−	0.671828i
$133$	−22061.9	+	82336.0i	−0.00937750	+	0.0349973i
$134$	5.95220e6	+	5.95220e6i	2.47379	+	2.47379i
$135$	620228.	+	2.31472e6i	0.252087	+	0.940800i
$136$	7.64741e6	−	4.41523e6i	3.04017	−	1.75524i
$137$	−121154.			−0.0471167			−0.0235584	−	0.999722i	$-0.507500\pi$
$137$	−121154.			−0.0471167			−0.0235584	+	0.999722i	$0.507500\pi$
$138$			3.05551e6i			1.16264i
$139$	1.32241e6	−	763492.i	0.492403	−	0.284289i	−0.233168	−	0.972436i	$-0.574909\pi$
$139$	1.32241e6	−	763492.i	0.492403	−	0.284289i	0.725571	+	0.688148i	$0.241576\pi$
$140$	−200259.	+	200259.i	−0.0729808	+	0.0729808i
$141$	−825018.	−	476325.i	−0.294311	−	0.169920i
$142$	−6.71187e6	+	6.71187e6i	−2.34411	+	2.34411i
$143$	−529748.	−	1.97705e6i	−0.181160	−	0.676097i
$144$	3.70487e6	−	6.41702e6i	1.24075	−	2.14905i
$145$	2.84584e6	−	4.92914e6i	0.933484	−	1.61684i
$146$	−1.00378e6	+	3.74617e6i	−0.322538	+	1.20373i
$147$			1.85193e6i			0.583004i
$148$	−6.78479e6	−	5.72961e6i	−2.09291	−	1.76742i
$149$	2.00102e6			0.604913			0.302457	−	0.953163i	$-0.402193\pi$
$149$	2.00102e6			0.604913			0.302457	+	0.953163i	$0.402193\pi$
$150$	40670.2	+	10897.6i	0.0120504	+	0.00322891i
$151$	4.59723e6	+	2.65421e6i	1.33526	+	0.770913i	0.986100	−	0.166151i	$-0.0531338\pi$
$151$	4.59723e6	+	2.65421e6i	1.33526	+	0.770913i	0.349159	+	0.937063i	$0.386467\pi$
$152$	−9.89121e6	−	5.71069e6i	−2.81656	−	1.62614i
$153$	−2.38003e6	+	637728.i	−0.664521	+	0.178058i
$154$	−157215.	−	157215.i	−0.0430458	−	0.0430458i
$155$	−2.86732e6	+	4.96634e6i	−0.769983	+	1.33365i
$156$	3.57681e6	+	3.57681e6i	0.942153	+	0.942153i
$157$	482325.	+	835411.i	0.124635	+	0.215875i	0.921590	−	0.388164i	$-0.126891\pi$
$157$	482325.	+	835411.i	0.124635	+	0.215875i	−0.796955	+	0.604039i	$0.793557\pi$
$158$	5.83390e6			1.47907
$159$			1.87817e6i			0.467244i
$160$	−8.06520e6	−	1.39693e7i	−1.96904	−	3.41048i
$161$	155553.	−	41680.2i	0.0372734	−	0.00998739i
$162$	−544298.	+	544298.i	−0.128024	+	0.128024i
$163$	3.76272e6	+	1.00822e6i	0.868839	+	0.232805i	0.665586	−	0.746321i	$-0.268182\pi$
$163$	3.76272e6	+	1.00822e6i	0.868839	+	0.232805i	0.203253	+	0.979126i	$0.434849\pi$
$164$	−1.03406e6	−	1.79105e6i	−0.234431	−	0.406046i
$165$	−573422.	+	2.14004e6i	−0.127651	+	0.476398i
$166$	−1.68482e6	−	6.28782e6i	−0.368323	−	1.37460i
$167$	2.24531e6	−	601628.i	0.482088	−	0.129175i	−0.00958670	−	0.999954i	$-0.503052\pi$
$167$	2.24531e6	−	601628.i	0.482088	−	0.129175i	0.491675	+	0.870779i	$0.336385\pi$
$168$	336999.	+	90298.7i	0.0710724	+	0.0190438i
$169$	−1.27876e6	+	738293.i	−0.264929	+	0.152957i
$170$	−2.58053e6	+	9.63065e6i	−0.525244	+	1.96024i
$171$	2.25351e6	+	2.25351e6i	0.450683	+	0.450683i
$172$	−4.99790e6	−	1.86524e7i	−0.982205	−	3.66564i
$173$	−3.21442e6	+	1.85585e6i	−0.620818	+	0.358430i	−0.777188	−	0.629269i	$-0.783354\pi$
$173$	−3.21442e6	+	1.85585e6i	−0.620818	+	0.358430i	0.156369	+	0.987699i	$0.450021\pi$
$174$	−1.10428e7			−2.09619
$175$		−	2219.13i		−	0.000414065i
$176$	1.49334e7	−	8.62179e6i	2.73918	−	1.58146i
$177$	−555869.	+	555869.i	−0.100243	+	0.100243i
$178$	8.12753e6	+	4.69243e6i	1.44112	+	0.832028i
$179$	−3.90062e6	+	3.90062e6i	−0.680102	+	0.680102i	−0.960023	−	0.279921i	$-0.909692\pi$
$179$	−3.90062e6	+	3.90062e6i	−0.680102	+	0.680102i	0.279921	+	0.960023i	$0.409692\pi$
$180$	2.74052e6	+	1.02277e7i	0.469910	+	1.75373i
$181$	4.29631e6	−	7.44143e6i	0.724536	−	1.25493i	−0.234629	−	0.972085i	$-0.575387\pi$
$181$	4.29631e6	−	7.44143e6i	0.724536	−	1.25493i	0.959165	−	0.282848i	$-0.0912793\pi$
$182$	181961.	−	315166.i	0.0301831	−	0.0522787i
$183$	−162295.	+	605693.i	−0.0264820	+	0.0988323i
$184$			2.15778e7i			3.46380i
$185$	6.34400e6	−	534910.i	1.00195	−	0.0844823i
$186$	1.11261e7			1.72904
$187$	−5.53870e6	−	1.48409e6i	−0.846999	−	0.226953i
$188$	−9.17585e6	−	5.29768e6i	−1.38093	−	0.797282i
$189$	−212213.	−	122521.i	−0.0314331	−	0.0181479i
$190$	1.24564e7	−	3.33767e6i	1.81606	−	0.486612i
$191$	−1.25678e6	−	1.25678e6i	−0.180367	−	0.180367i	0.611149	−	0.791516i	$-0.290708\pi$
$191$	−1.25678e6	−	1.25678e6i	−0.180367	−	0.180367i	−0.791516	+	0.611149i	$0.790708\pi$
$192$	−7.86944e6	+	1.36303e7i	−1.11183	+	1.92575i
$193$	−2.61503e6	−	2.61503e6i	−0.363752	−	0.363752i	0.501440	−	0.865192i	$-0.332804\pi$
$193$	−2.61503e6	−	2.61503e6i	−0.363752	−	0.363752i	−0.865192	+	0.501440i	$0.832804\pi$
$194$	−8.71823e6	−	1.51004e7i	−1.19405	−	2.06816i
$195$	−3.62643e6			−0.489074
$196$			2.05971e7i			2.73551i
$197$	−3.85922e6	−	6.68436e6i	−0.504778	−	0.874301i	−0.999985	−	0.00552584i	$-0.998241\pi$
$197$	−3.85922e6	−	6.68436e6i	−0.504778	−	0.874301i	0.495207	−	0.868775i	$-0.335092\pi$
$198$	−8.02935e6	+	2.15146e6i	−1.03439	+	0.277164i
$199$	−4.77351e6	+	4.77351e6i	−0.605730	+	0.605730i	−0.941827	−	0.336098i	$-0.890893\pi$
$199$	−4.77351e6	+	4.77351e6i	−0.605730	+	0.605730i	0.336098	+	0.941827i	$0.390893\pi$
$200$	287210.	+	76957.6i	0.0359012	+	0.00961970i
$201$	4.28864e6	+	7.42814e6i	0.528119	+	0.914728i
$202$	3.45482e6	−	1.28936e7i	0.419152	−	1.56430i
$203$	150634.	+	562175.i	0.0180068	+	0.0672022i
$204$	1.36881e7	−	3.66773e6i	1.61233	−	0.432023i
$205$	1.43215e6	+	383743.i	0.166237	+	0.0445429i
$206$	1.77438e6	−	1.02444e6i	0.202977	−	0.117189i
$207$	1.55832e6	−	5.81575e6i	0.175690	−	0.655684i
$208$	1.99578e7	+	1.99578e7i	2.21780	+	2.21780i
$209$	1.91953e6	+	7.16379e6i	0.210260	+	0.784700i
$210$	−341149.	+	196963.i	−0.0368372	+	0.0212680i
$211$	−847004.			−0.0901650			−0.0450825	−	0.998983i	$-0.514355\pi$
$211$	−847004.			−0.0901650			−0.0450825	+	0.998983i	$0.514355\pi$
$212$			2.08890e7i			2.19235i
$213$	−8.37618e6	+	4.83599e6i	−0.866777	+	0.500434i
$214$	2.99993e6	−	2.99993e6i	0.306105	−	0.306105i
$215$	1.19892e7	+	6.92197e6i	1.20635	+	0.696489i
$216$	2.32167e7	−	2.32167e7i	2.30377	−	2.30377i
$217$	−151771.	−	566418.i	−0.0148529	−	0.0554316i
$218$	5.71771e6	−	9.90336e6i	0.551890	−	0.955901i
$219$	−1.97593e6	+	3.42240e6i	−0.188121	+	0.325836i
$220$	−6.37760e6	+	2.38015e7i	−0.598948	+	2.23531i
$221$		−	9.38565e6i		−	0.869536i
$222$	−7.05296e6	−	1.01405e7i	−0.644633	−	0.926827i
$223$	7.51851e6			0.677980			0.338990	−	0.940790i	$-0.389915\pi$
$223$	7.51851e6			0.677980			0.338990	+	0.940790i	$0.389915\pi$
$224$	1.59322e6	+	426902.i	0.141753	+	0.0379826i
$225$	−71852.5	−	41484.0i	−0.00630803	−	0.00364195i
$226$	5.66573e6	+	3.27111e6i	0.490829	+	0.283380i
$227$	−2.00839e7	+	5.38147e6i	−1.71700	+	0.460070i	−0.977124	−	0.212670i	$-0.931784\pi$
$227$	−2.00839e7	+	5.38147e6i	−1.71700	+	0.460070i	−0.739879	+	0.672740i	$0.765117\pi$
$228$	−1.29605e7	−	1.29605e7i	−1.09349	−	1.09349i
$229$	1.14703e7	−	1.98671e7i	0.955141	−	1.65435i	0.221096	−	0.975252i	$-0.429037\pi$
$229$	1.14703e7	−	1.98671e7i	0.955141	−	1.65435i	0.734045	−	0.679101i	$-0.237630\pi$
$230$	−1.72274e7	−	1.72274e7i	−1.41591	−	1.41591i
$231$	−113275.	−	196199.i	−0.00918966	−	0.0159170i
$232$	−7.79831e7			−6.24506
$233$		−	5.15374e6i		−	0.407431i	−0.979030	−	0.203716i	$-0.934698\pi$
$233$		−	5.15374e6i		−	0.407431i	0.979030	−	0.203716i	$-0.0653018\pi$
$234$	−6.80310e6	−	1.17833e7i	−0.530957	−	0.919644i
$235$	7.33716e6	−	1.96599e6i	0.565359	−	0.151487i
$236$	−6.18237e6	+	6.18237e6i	−0.470348	+	0.470348i
$237$	5.74196e6	+	1.53855e6i	0.431336	+	0.115576i
$238$	−509764.	−	882937.i	−0.0378127	−	0.0654936i
$239$	711528.	−	2.65546e6i	0.0521192	−	0.194512i	−0.934958	−	0.354760i	$-0.884563\pi$
$239$	711528.	−	2.65546e6i	0.0521192	−	0.194512i	0.987077	+	0.160248i	$0.0512294\pi$
$240$	−7.90732e6	−	2.95105e7i	−0.571999	−	2.13473i
$241$	1.01817e7	−	2.72817e6i	0.727390	−	0.194904i	0.123923	−	0.992292i	$-0.460452\pi$
$241$	1.01817e7	−	2.72817e6i	0.727390	−	0.194904i	0.603467	+	0.797388i	$0.293786\pi$
$242$	7.78657e6	+	2.08640e6i	0.549414	+	0.147215i
$243$	−1.27162e7	+	7.34172e6i	−0.886216	+	0.511657i
$244$	−1.80504e6	+	6.73651e6i	−0.124256	+	0.463730i
$245$	−1.04414e7	−	1.04414e7i	−0.710005	−	0.710005i
$246$	−744522.	−	2.77860e6i	−0.0500118	−	0.186647i
$247$	−1.05131e7	+	6.06973e6i	−0.697652	+	0.402790i
$248$	7.85717e7			5.15123
$249$		−	6.63305e6i		−	0.429651i
$250$	2.60201e7	−	1.50227e7i	1.66529	−	0.961455i
$251$	−1.24824e7	+	1.24824e7i	−0.789361	+	0.789361i	−0.981389	−	0.192028i	$-0.938493\pi$
$251$	−1.24824e7	+	1.24824e7i	−0.789361	+	0.789361i	0.192028	+	0.981389i	$0.438493\pi$
$252$	−937678.	−	541369.i	−0.0585939	−	0.0338292i
$253$	9.90767e6	−	9.90767e6i	0.611801	−	0.611801i
$254$	−3.37201e6	−	1.25845e7i	−0.205772	−	0.767953i
$255$	−5.07971e6	+	8.79832e6i	−0.306351	+	0.530615i
$256$	−2.39927e7	+	4.15565e7i	−1.43007	+	2.47696i
$257$	−4.24288e6	+	1.58346e7i	−0.249955	+	0.932844i	0.720873	+	0.693067i	$0.243741\pi$
$257$	−4.24288e6	+	1.58346e7i	−0.249955	+	0.932844i	−0.970828	+	0.239777i	$0.922926\pi$
$258$		−	2.68594e7i		−	1.56400i
$259$	−420030.	+	497384.i	−0.0241758	+	0.0286281i
$260$	−4.03331e7			−2.29478
$261$	2.10184e7	+	5.63187e6i	1.18217	+	0.316760i
$262$	−4.70078e7	−	2.71400e7i	−2.61376	−	1.50906i
$263$	3.44960e6	+	1.99163e6i	0.189628	+	0.109482i	0.591808	−	0.806079i	$-0.298414\pi$
$263$	3.44960e6	+	1.99163e6i	0.189628	+	0.109482i	−0.402181	+	0.915560i	$0.631748\pi$
$264$	2.93212e7	−	7.85660e6i	1.59357	−	0.426995i
$265$	−1.05894e7	−	1.05894e7i	−0.569028	−	0.569028i
$266$	−659332.	+	1.14200e6i	−0.0350315	+	0.0606764i
$267$	6.76192e6	+	6.76192e6i	0.355252	+	0.355252i
$268$	4.76982e7	+	8.26158e7i	2.47798	+	4.29199i
$269$	1.73072e7			0.889140			0.444570	−	0.895744i	$-0.353356\pi$
$269$	1.73072e7			0.889140			0.444570	+	0.895744i	$0.353356\pi$
$270$			3.70718e7i			1.88344i
$271$	8.33054e6	+	1.44289e7i	0.418567	+	0.724979i	0.995796	−	0.0916032i	$-0.0291991\pi$
$271$	8.33054e6	+	1.44289e7i	0.418567	+	0.724979i	−0.577228	+	0.816583i	$0.695866\pi$
$272$	7.63769e7	−	2.04651e7i	3.79538	−	1.01697i
$273$	262211.	−	262211.i	0.0128873	−	0.0128873i
$274$	−1.81038e6	−	485089.i	−0.0880070	−	0.0235814i
$275$	−96539.7	−	167212.i	−0.00464203	−	0.00804023i
$276$	−8.96231e6	+	3.34478e7i	−0.426278	+	1.59089i
$277$	−4.35146e6	−	1.62399e7i	−0.204737	−	0.764088i	−0.989530	−	0.144330i	$-0.953897\pi$
$277$	−4.35146e6	−	1.62399e7i	−0.204737	−	0.764088i	0.784793	−	0.619758i	$-0.212769\pi$
$278$	2.28174e7	−	6.11391e6i	1.06202	−	0.284567i
$279$	−2.11770e7	−	5.67437e6i	−0.975108	−	0.261279i
$280$	−2.40917e6	+	1.39093e6i	−0.109747	+	0.0633625i
$281$	−4.69504e6	+	1.75221e7i	−0.211602	+	0.789710i	0.775733	+	0.631061i	$0.217380\pi$
$281$	−4.69504e6	+	1.75221e7i	−0.211602	+	0.789710i	−0.987335	+	0.158649i	$0.949286\pi$
$282$	−1.04209e7	−	1.04209e7i	−0.464685	−	0.464685i
$283$	4.61597e6	+	1.72270e7i	0.203659	+	0.760066i	0.989854	+	0.142088i	$0.0453815\pi$
$283$	4.61597e6	+	1.72270e7i	0.203659	+	0.760066i	−0.786195	+	0.617979i	$0.787952\pi$
$284$	−9.31599e7	+	5.37859e7i	−4.06700	+	2.34808i
$285$	1.31403e7			0.567636
$286$		−	3.16637e7i		−	1.35352i
$287$	−131299.	+	75805.6i	−0.00555413	+	0.00320668i
$288$	4.36059e7	−	4.36059e7i	1.82544	−	1.82544i
$289$	−1.86741e6	−	1.07815e6i	−0.0773655	−	0.0446670i
$290$	6.22607e7	−	6.22607e7i	2.55282	−	2.55282i
$291$	−4.59845e6	−	1.71617e7i	−0.186609	−	0.696434i
$292$	−2.19762e7	+	3.80640e7i	−0.882683	+	1.52885i
$293$	−1.89155e7	+	3.27626e7i	−0.751994	+	1.30249i	0.194861	+	0.980831i	$0.437575\pi$
$293$	−1.89155e7	+	3.27626e7i	−0.751994	+	1.30249i	−0.946855	+	0.321661i	$0.895759\pi$
$294$	−7.41495e6	+	2.76730e7i	−0.291787	+	1.08896i
$295$		−	6.26814e6i		−	0.244159i
$296$	−4.98074e7	−	7.16110e7i	−1.92052	−	2.76124i
$297$	−2.13204e7			−0.813815
$298$	2.99009e7	+	8.01191e6i	1.12989	+	0.302752i
$299$	1.98617e7	+	1.14672e7i	0.743026	+	0.428986i
$300$	413241.	+	238585.i	0.0153052	+	0.00883648i
$301$	−1.36738e6	+	366389.i	−0.0501408	+	0.0134352i
$302$	5.80683e7	+	5.80683e7i	2.10823	+	2.10823i
$303$	6.80075e6	−	1.17792e7i	0.244472	−	0.423437i
$304$	−7.23167e7	−	7.23167e7i	−2.57405	−	2.57405i
$305$	−2.49994e6	−	4.33002e6i	−0.0881110	−	0.152613i
$306$	−3.81178e7			−1.33034
$307$		−	8.44716e6i		−	0.291942i	−0.989289	−	0.145971i	$-0.953369\pi$
$307$		−	8.44716e6i		−	0.291942i	0.989289	−	0.145971i	$-0.0466305\pi$
$308$	−1.25985e6	−	2.18212e6i	−0.0431187	−	0.0746838i
$309$	2.01659e6	−	540344.i	0.0683506	−	0.0183145i
$310$	−6.27306e7	+	6.27306e7i	−2.10569	+	2.10569i
$311$	−2.69126e7	−	7.21120e6i	−0.894693	−	0.239732i	−0.217957	−	0.975958i	$-0.569939\pi$
$311$	−2.69126e7	−	7.21120e6i	−0.894693	−	0.239732i	−0.676736	+	0.736226i	$0.736606\pi$
$312$	2.48433e7	+	4.30298e7i	0.817984	+	1.41679i
$313$	1.39364e7	−	5.20114e7i	0.454483	−	1.69615i	−0.235120	−	0.971966i	$-0.575548\pi$
$313$	1.39364e7	−	5.20114e7i	0.454483	−	1.69615i	0.689603	−	0.724188i	$-0.257785\pi$
$314$	3.86237e6	+	1.44146e7i	0.124757	+	0.465600i
$315$	749783.	−	200904.i	0.0239885	−	0.00642771i
$316$	6.38621e7	+	1.71118e7i	2.02387	+	0.542293i
$317$	3.59016e7	−	2.07278e7i	1.12703	−	0.650692i	0.183845	−	0.982955i	$-0.441145\pi$
$317$	3.59016e7	−	2.07278e7i	1.12703	−	0.650692i	0.943187	+	0.332263i	$0.107812\pi$
$318$	−7.52003e6	+	2.80652e7i	−0.233851	+	0.872742i
$319$	3.58068e7	+	3.58068e7i	1.10305	+	1.10305i
$320$	−3.24804e7	−	1.21218e8i	−0.991222	−	3.69929i
$321$	3.74381e6	−	2.16149e6i	0.113188	−	0.0653489i
$322$	2.49128e6			0.0746198
$323$			3.40087e7i			1.00921i
$324$	−7.55479e6	+	4.36176e6i	−0.222120	+	0.128241i
$325$	223471.	−	223471.i	0.00650985	−	0.00650985i
$326$	5.21888e7	+	3.01312e7i	1.50634	+	0.869689i
$327$	8.23937e6	−	8.23937e6i	0.235641	−	0.235641i
$328$	−5.25775e6	−	1.96222e7i	−0.148997	−	0.556066i
$329$	−388366.	+	672669.i	−0.0109057	+	0.0188892i
$330$	−1.71371e7	+	2.96823e7i	−0.476864	+	0.825953i
$331$	−3.63543e6	+	1.35676e7i	−0.100247	+	0.374127i	−0.997763	−	0.0668555i	$-0.978703\pi$
$331$	−3.63543e6	+	1.35676e7i	−0.100247	+	0.374127i	0.897516	+	0.440983i	$0.145370\pi$
$332$		−	7.37728e7i		−	2.01596i
$333$	8.25266e6	+	2.28980e7i	0.223492	+	0.620105i
$334$	3.59600e7			0.965119
$335$	−6.60609e7	−	1.77010e7i	−1.75715	−	0.470828i
$336$	2.70552e6	+	1.56203e6i	0.0713235	+	0.0411786i
$337$	8.97713e6	+	5.18295e6i	0.234557	+	0.135421i	0.612672	−	0.790337i	$-0.290095\pi$
$337$	8.97713e6	+	5.18295e6i	0.234557	+	0.135421i	−0.378116	+	0.925758i	$0.623428\pi$
$338$	−2.20643e7	+	5.91212e6i	−0.571401	+	0.153106i
$339$	4.71376e6	+	4.71376e6i	0.120995	+	0.120995i
$340$	−5.64965e7	+	9.78549e7i	−1.43742	+	2.48969i
$341$	−3.60771e7	−	3.60771e7i	−0.909847	−	0.909847i
$342$	2.46509e7	+	4.26966e7i	0.616246	+	1.06737i
$343$	3.02202e6			0.0748884
$344$		−	1.89679e8i		−	4.65955i
$345$	−1.24126e7	−	2.14992e7i	−0.302277	−	0.523559i
$346$	−5.54631e7	+	1.48613e7i	−1.33899	+	0.358780i
$347$	3.92079e6	−	3.92079e6i	0.0938395	−	0.0938395i	−0.658629	−	0.752468i	$-0.728863\pi$
$347$	3.92079e6	−	3.92079e6i	0.0938395	−	0.0938395i	0.752468	+	0.658629i	$0.228863\pi$
$348$	−1.20882e8	−	3.23902e7i	−2.86830	−	0.768558i
$349$	4.06669e7	+	7.04371e7i	0.956675	+	1.65701i	0.730487	+	0.682926i	$0.239293\pi$
$349$	4.06669e7	+	7.04371e7i	0.956675	+	1.65701i	0.226188	+	0.974084i	$0.427374\pi$
$350$	8885.20	−	33160.0i	0.000207235	−	0.000773411i
$351$	−9.03216e6	−	3.37085e7i	−0.208867	−	0.779503i
$352$	1.38621e8	−	3.71434e7i	3.17835	−	0.851635i
$353$	4.78402e7	+	1.28188e7i	1.08760	+	0.291422i	0.757706	−	0.652596i	$-0.226320\pi$
$353$	4.78402e7	+	1.28188e7i	1.08760	+	0.291422i	0.329894	+	0.944018i	$0.392987\pi$
$354$	−1.05319e7	+	6.08059e6i	−0.237409	+	0.137068i
$355$	1.99601e7	−	7.44921e7i	0.446147	−	1.66504i
$356$	7.52061e7	+	7.52061e7i	1.66687	+	1.66687i
$357$	−268876.	−	1.00346e6i	−0.00590946	−	0.0220544i
$358$	−7.39039e7	+	4.26684e7i	−1.61071	+	0.929945i
$359$	−4.16877e7			−0.901000			−0.450500	−	0.892777i	$-0.648754\pi$
$359$	−4.16877e7			−0.901000			−0.450500	+	0.892777i	$0.648754\pi$
$360$			1.04007e8i			2.22924i
$361$	−2.64903e6	+	1.52942e6i	−0.0563073	+	0.0325090i
$362$	9.39938e7	−	9.39938e7i	1.98141	−	1.98141i
$363$	7.11361e6	+	4.10705e6i	0.148720	+	0.0858637i
$364$	2.91631e6	−	2.91631e6i	0.0604685	−	0.0604685i
$365$	−8.15545e6	−	3.04366e7i	−0.167714	−	0.625917i
$366$	−4.85028e6	+	8.40093e6i	−0.0989290	+	0.171350i
$367$	1.56092e7	−	2.70359e7i	0.315778	−	0.546943i	−0.663825	−	0.747888i	$-0.731068\pi$
$367$	1.56092e7	−	2.70359e7i	0.315778	−	0.546943i	0.979603	+	0.200945i	$0.0644012\pi$
$368$	−5.00077e7	+	1.86631e8i	−1.00345	+	3.74491i
$369$			5.66839e6i			0.112819i
$370$	9.69389e7	+	1.74078e7i	1.91378	+	0.343667i
$371$	1.53135e6			0.0299883
$372$	1.21794e8	+	3.26347e7i	2.36591	+	0.633944i
$373$	−4.70514e7	−	2.71652e7i	−0.906664	−	0.523463i	−0.0273076	−	0.999627i	$-0.508693\pi$
$373$	−4.70514e7	−	2.71652e7i	−0.906664	−	0.523463i	−0.879356	+	0.476164i	$0.842027\pi$
$374$	−7.68215e7	−	4.43529e7i	−1.46848	−	0.847827i
$375$	2.95719e7	−	7.92378e6i	0.560772	−	0.150258i
$376$	−7.35917e7	−	7.35917e7i	−1.38441	−	1.38441i
$377$	−4.14430e7	+	7.17814e7i	−0.773441	+	1.33964i
$378$	−2.68050e6	−	2.68050e6i	−0.0496295	−	0.0496295i
$379$	−3.74222e7	−	6.48172e7i	−0.687403	−	1.19062i	−0.972675	−	0.232171i	$-0.925417\pi$
$379$	−3.74222e7	−	6.48172e7i	−0.687403	−	1.19062i	0.285272	−	0.958447i	$-0.407916\pi$
$380$	1.46146e8			2.66340
$381$		−	1.32755e7i		−	0.240035i
$382$	−1.37477e7	−	2.38118e7i	−0.246627	−	0.427171i
$383$	8.34871e6	−	2.23703e6i	0.148601	−	0.0398176i	−0.183752	−	0.982973i	$-0.558824\pi$
$383$	8.34871e6	−	2.23703e6i	0.148601	−	0.0398176i	0.332353	+	0.943155i	$0.392158\pi$
$384$	−8.06157e7	+	8.06157e7i	−1.42372	+	1.42372i
$385$	1.74486e6	+	467533.i	0.0305758	+	0.00819276i
$386$	−2.86056e7	−	4.95463e7i	−0.497380	−	0.861488i
$387$	−1.36984e7	+	5.11233e7i	−0.236341	+	0.882035i
$388$	−5.11440e7	−	1.90872e8i	−0.875587	−	3.26773i
$389$	3.00037e7	−	8.03947e6i	0.509713	−	0.136577i	0.00520905	−	0.999986i	$-0.498342\pi$
$389$	3.00037e7	−	8.03947e6i	0.509713	−	0.136577i	0.504504	+	0.863409i	$0.331675\pi$
$390$	−5.41890e7	−	1.45199e7i	−0.913518	−	0.244776i
$391$	5.56427e7	−	3.21253e7i	0.930846	−	0.537424i
$392$	−5.23637e7	+	1.95424e8i	−0.869305	+	3.24429i
$393$	−3.91094e7	−	3.91094e7i	−0.644323	−	0.644323i
$394$	−3.09039e7	−	1.15335e8i	−0.505272	−	1.88570i
$395$	−4.10486e7	+	2.36994e7i	−0.666050	+	0.384544i
$396$	−9.42055e7			−1.51702
$397$		−	8.59253e7i		−	1.37325i	−0.727012	−	0.686625i	$-0.759092\pi$
$397$		−	8.59253e7i		−	1.37325i	0.727012	−	0.686625i	$-0.240908\pi$
$398$	−9.04424e7	+	5.22169e7i	−1.43457	+	0.828251i
$399$	−950115.	+	950115.i	−0.0149575	+	0.0149575i
$400$	2.30580e6	+	1.33125e6i	0.0360281	+	0.0208008i
$401$	−3.30965e7	+	3.30965e7i	−0.513274	+	0.513274i	−0.915528	−	0.402254i	$-0.868227\pi$
$401$	−3.30965e7	+	3.30965e7i	−0.513274	+	0.513274i	0.402254	+	0.915528i	$0.368227\pi$
$402$	3.43427e7	+	1.28169e8i	0.528635	+	1.97289i
$403$	4.17558e7	−	7.23231e7i	0.637972	−	1.10500i
$404$	7.56379e7	−	1.31009e8i	1.14708	−	1.98681i
$405$	1.61866e6	−	6.04093e6i	0.0243664	−	0.0909366i
$406$			9.00360e6i			0.134536i
$407$	−1.00114e7	+	5.57506e7i	−0.148495	+	0.826926i
$408$	1.39197e8			2.04950
$409$	1.02878e7	+	2.75660e6i	0.150366	+	0.0402906i	0.333217	−	0.942850i	$-0.391866\pi$
$409$	1.02878e7	+	2.75660e6i	0.150366	+	0.0402906i	−0.182851	+	0.983141i	$0.558532\pi$
$410$	1.98638e7	+	1.14684e7i	0.288212	+	0.166399i
$411$	−1.65391e6	−	954887.i	−0.0238225	−	0.0137539i
$412$	2.24285e7	−	6.00970e6i	0.320707	−	0.0859333i
$413$	453222.	+	453222.i	0.00643369	+	0.00643369i
$414$	4.65715e7	−	8.06642e7i	0.656325	−	1.13679i
$415$	3.73981e7	+	3.73981e7i	0.523245	+	0.523245i
$416$	1.17451e8	+	2.03431e8i	1.63146	+	2.82577i
$417$	2.40702e7			0.331949
$418$			1.14733e8i			1.57094i
$419$	−9.50491e6	−	1.64630e7i	−0.129213	−	0.223803i	0.794159	−	0.607710i	$-0.207912\pi$
$419$	−9.50491e6	−	1.64630e7i	−0.129213	−	0.223803i	−0.923372	+	0.383907i	$0.874578\pi$
$420$	−4.31218e6	+	1.15545e6i	−0.0582035	+	0.0155956i
$421$	−7.53497e7	+	7.53497e7i	−1.00980	+	1.00980i	−0.00984756	+	0.999952i	$0.503135\pi$
$421$	−7.53497e7	+	7.53497e7i	−1.00980	+	1.00980i	−0.999952	+	0.00984756i	$0.996865\pi$
$422$	−1.26566e7	−	3.39133e6i	−0.168415	−	0.0451266i
$423$	1.45201e7	+	2.51495e7i	0.191844	+	0.332284i
$424$	−5.31058e7	+	1.98194e8i	−0.696698	+	2.60011i
$425$	−229152.	−	855205.i	−0.00298508	−	0.0111405i
$426$	−1.44527e8	+	3.87258e7i	−1.86947	+	0.500923i
$427$	493844.	+	132325.i	0.00634317	+	0.00169965i
$428$	4.16386e7	−	2.40401e7i	0.531087	−	0.306623i
$429$	8.35055e6	−	3.11647e7i	0.105765	−	0.394721i
$430$	1.51437e8	+	1.51437e8i	1.90470	+	1.90470i
$431$	−405867.	−	1.51472e6i	−0.00506935	−	0.0189191i	0.963345	−	0.268266i	$-0.0864507\pi$
$431$	−405867.	−	1.51472e6i	−0.00506935	−	0.0189191i	−0.968414	+	0.249347i	$0.919784\pi$
$432$	2.54613e8	−	1.47001e8i	3.15812	−	1.82334i
$433$	1.02843e8			1.26681			0.633407	−	0.773819i	$-0.281656\pi$
$433$	1.02843e8			1.26681			0.633407	+	0.773819i	$0.281656\pi$
$434$		−	9.07155e6i		−	0.110972i
$435$	7.76993e7	−	4.48597e7i	0.943950	−	0.544990i
$436$	9.16383e7	−	9.16383e7i	1.10565	−	1.10565i
$437$	−7.19686e7	−	4.15511e7i	−0.862380	−	0.497895i
$438$	−4.32289e7	+	4.32289e7i	−0.514460	+	0.514460i
$439$	2.37377e7	+	8.85904e7i	0.280573	+	1.04711i	0.952014	+	0.306054i	$0.0990089\pi$
$439$	2.37377e7	+	8.85904e7i	0.280573	+	1.04711i	−0.671441	+	0.741058i	$0.734324\pi$
$440$	−1.21021e8	+	2.09614e8i	−1.42070	+	2.46072i
$441$	2.82267e7	−	4.88900e7i	0.329112	−	0.570039i
$442$	3.75793e7	−	1.40248e8i	0.435193	−	1.62416i
$443$			9.40160e7i			1.08141i	0.841212	+	0.540705i	$0.181842\pi$
$443$			9.40160e7i			1.08141i	−0.841212	+	0.540705i	$0.818158\pi$
$444$	−4.74631e7	−	1.31692e8i	−0.542259	−	1.50456i
$445$	−7.62494e7			−0.865279
$446$	1.12348e8	+	3.01034e7i	1.26637	+	0.339322i
$447$	2.73167e7	+	1.57713e7i	0.305848	+	0.176581i
$448$	1.11133e7	+	6.41626e6i	0.123597	+	0.0713588i
$449$	−4.21477e7	+	1.12934e7i	−0.465623	+	0.124763i	−0.484001	−	0.875068i	$-0.660817\pi$
$449$	−4.21477e7	+	1.12934e7i	−0.465623	+	0.124763i	0.0183771	+	0.999831i	$0.494150\pi$
$450$	−907579.	−	907579.i	−0.00995971	−	0.00995971i
$451$	−6.59560e6	+	1.14239e7i	−0.0718993	+	0.124533i
$452$	5.24264e7	+	5.24264e7i	0.567720	+	0.567720i
$453$	4.18390e7	+	7.24673e7i	0.450077	+	0.779556i
$454$	−3.21657e8			−3.43736
$455$			2.95676e6i			0.0313894i
$456$	−9.00190e7	−	1.55917e8i	−0.949379	−	1.64437i
$457$	3.58911e7	−	9.61699e6i	0.376043	−	0.100761i	−0.0658467	−	0.997830i	$-0.520975\pi$
$457$	3.58911e7	−	9.61699e6i	0.376043	−	0.100761i	0.441890	+	0.897069i	$0.354308\pi$
$458$	2.50944e8	−	2.50944e8i	2.61205	−	2.61205i
$459$	−9.44343e7	−	2.53036e7i	−0.976544	−	0.261664i
$460$	−1.38053e8	−	2.39114e8i	−1.41831	−	2.45658i
$461$	−827366.	+	3.08777e6i	−0.00844490	+	0.0315168i	−0.970020	−	0.243026i	$-0.921860\pi$
$461$	−827366.	+	3.08777e6i	−0.00844490	+	0.0315168i	0.961575	+	0.274543i	$0.0885266\pi$
$462$	−907089.	−	3.38530e6i	−0.00919865	−	0.0343298i
$463$	2.57202e6	−	689170.i	0.0259138	−	0.00694358i	−0.245839	−	0.969311i	$-0.579063\pi$
$463$	2.57202e6	−	689170.i	0.0259138	−	0.00694358i	0.271753	+	0.962367i	$0.412397\pi$
$464$	−6.74496e8	−	1.80731e8i	−6.75189	−	1.80916i
$465$	−7.82857e7	+	4.51982e7i	−0.778616	+	0.449534i
$466$	2.06351e7	−	7.70113e7i	0.203915	−	0.761021i
$467$	−6.65088e6	−	6.65088e6i	−0.0653023	−	0.0653023i	0.673701	−	0.739004i	$-0.264703\pi$
$467$	−6.65088e6	−	6.65088e6i	−0.0653023	−	0.0653023i	−0.739004	+	0.673701i	$0.764703\pi$
$468$	−3.99092e7	−	1.48943e8i	−0.389346	−	1.45306i
$469$	6.05645e6	−	3.49669e6i	0.0587083	−	0.0338953i
$470$	1.17509e8			1.13182
$471$			1.52060e7i			0.145530i
$472$	−7.43753e7	+	4.29406e7i	−0.707299	+	0.408359i
$473$	−8.70933e7	+	8.70933e7i	−0.823003	+	0.823003i
$474$	7.96408e7	+	4.59806e7i	0.747826	+	0.431757i
$475$	−809742.	+	809742.i	−0.00755555	+	0.00755555i
$476$	−2.99044e6	−	1.11605e7i	−0.0277277	−	0.103481i
$477$	2.86267e7	−	4.95829e7i	0.263765	−	0.456854i
$478$	2.12644e7	−	3.68311e7i	0.194702	−	0.337234i
$479$	−1.13233e7	+	4.22591e7i	−0.103031	+	0.384516i	−0.998114	−	0.0613827i	$-0.980449\pi$
$479$	−1.13233e7	+	4.22591e7i	−0.103031	+	0.384516i	0.895084	+	0.445898i	$0.147116\pi$
$480$		−	2.54267e8i		−	2.29915i
$481$	−9.23855e7	+	7.78971e6i	−0.830173	+	0.0699981i
$482$	1.63066e8			1.45620
$483$	2.45201e6	+	657015.i	0.0217611	+	0.00583087i
$484$	7.91175e7	+	4.56785e7i	0.697809	+	0.402880i
$485$	1.22687e8	+	7.08331e7i	1.07540	+	0.620885i
$486$	−2.19412e8	+	5.87912e7i	−1.91140	+	0.512157i
$487$	−3.44542e7	−	3.44542e7i	−0.298301	−	0.298301i	0.542047	−	0.840348i	$-0.317649\pi$
$487$	−3.44542e7	−	3.44542e7i	−0.298301	−	0.298301i	−0.840348	+	0.542047i	$0.817649\pi$
$488$	−3.42523e7	+	5.93267e7i	−0.294734	+	0.510494i
$489$	4.34199e7	+	4.34199e7i	0.371332	+	0.371332i
$490$	−1.14218e8	−	1.97831e8i	−0.970833	−	1.68153i
$491$	−1.62459e7			−0.137246			−0.0686228	−	0.997643i	$-0.521860\pi$
$491$	−1.62459e7			−0.137246			−0.0686228	+	0.997643i	$0.521860\pi$
$492$		−	3.26003e7i		−	0.273732i
$493$	1.16103e8	+	2.01095e8i	0.968949	+	1.67827i
$494$	−1.81398e8	+	4.86053e7i	−1.50470	+	0.403184i
$495$	4.77562e7	−	4.77562e7i	0.393744	−	0.393744i
$496$	6.79586e8	+	1.82095e8i	5.56929	+	1.49229i
$497$	3.94297e6	+	6.82943e6i	0.0321184	+	0.0556308i
$498$	2.65582e7	−	9.91164e7i	0.215035	−	0.802523i
$499$	5.43766e7	+	2.02936e8i	0.437634	+	1.63327i	0.734684	+	0.678409i	$0.237330\pi$
$499$	5.43766e7	+	2.02936e8i	0.437634	+	1.63327i	−0.297050	+	0.954862i	$0.596003\pi$
$500$	3.28899e8	−	8.81282e7i	2.63119	−	0.705026i
$501$	3.53933e7	+	9.48361e6i	0.281454	+	0.0754155i
$502$	−2.36500e8	+	1.36543e8i	−1.86947	+	1.07934i
$503$	−1.16188e7	+	4.33618e7i	−0.0912969	+	0.340725i	−0.996432	−	0.0843993i	$-0.973103\pi$
$503$	−1.16188e7	+	4.33618e7i	−0.0912969	+	0.340725i	0.905135	+	0.425124i	$0.139770\pi$
$504$	−7.52032e6	−	7.52032e6i	−0.0587415	−	0.0587415i
$505$	2.80694e7	+	1.04757e8i	0.217951	+	0.813406i
$506$	1.87718e8	−	1.08379e8i	1.44895	−	0.836553i
$507$	−2.32758e7			−0.178600
$508$		−	1.47650e8i		−	1.12627i
$509$	1.61669e8	−	9.33398e7i	1.22595	−	0.707805i	0.259773	−	0.965670i	$-0.416352\pi$
$509$	1.61669e8	−	9.33398e7i	1.22595	−	0.707805i	0.966181	+	0.257865i	$0.0830190\pi$
$510$	−1.11133e8	+	1.11133e8i	−0.837784	+	0.837784i
$511$	2.79042e6	+	1.61105e6i	0.0209125	+	0.0120739i
$512$	−1.97600e8	+	1.97600e8i	−1.47224	+	1.47224i
$513$	3.27278e7	+	1.22142e8i	0.242418	+	0.904717i
$514$	−1.26801e8	+	2.19626e8i	−0.933756	+	1.61731i
$515$	−8.32329e6	+	1.44164e7i	−0.0609359	+	0.105544i
$516$	7.87831e7	−	2.94023e8i	0.573435	−	2.14009i
$517$			6.75809e7i			0.489049i
$518$	−8.26790e6	+	5.75055e6i	−0.0594848	+	0.0413733i
$519$	−5.85083e7			−0.418519
$520$	−3.82678e8	−	1.02538e8i	−2.72159	−	0.729249i
$521$	−5.79866e7	−	3.34786e7i	−0.410029	−	0.236730i	0.280773	−	0.959774i	$-0.409409\pi$
$521$	−5.79866e7	−	3.34786e7i	−0.410029	−	0.236730i	−0.690802	+	0.723044i	$0.742742\pi$
$522$	2.91524e8	+	1.68312e8i	2.04957	+	1.18332i
$523$	−8.43685e7	+	2.26065e7i	−0.589760	+	0.158026i	−0.541344	−	0.840801i	$-0.682084\pi$
$523$	−8.43685e7	+	2.26065e7i	−0.589760	+	0.158026i	−0.0484165	+	0.998827i	$0.515417\pi$
$524$	−4.34975e8	−	4.34975e8i	−3.02322	−	3.02322i
$525$	17490.3	−	30294.2i	0.000120870	−	0.000209354i
$526$	4.35724e7	+	4.35724e7i	0.299402	+	0.299402i
$527$	−1.16979e8	−	2.02613e8i	−0.799236	−	1.38432i
$528$	2.71815e8			1.84659
$529$			8.96425e6i			0.0605546i
$530$	−1.15836e8	−	2.00634e8i	−0.778067	−	1.34765i
$531$	2.31472e7	−	6.20226e6i	0.154602	−	0.0414254i
$532$	−1.05672e7	+	1.05672e7i	−0.0701817	+	0.0701817i
$533$	−2.08559e7	−	5.58832e6i	−0.137736	−	0.0369062i
$534$	7.39679e7	+	1.28116e8i	0.485758	+	0.841357i
$535$	−8.92135e6	+	3.32949e7i	−0.0582598	+	0.217429i
$536$	2.42525e8	+	9.05116e8i	1.57493	+	5.87773i
$537$	−8.39919e7	+	2.25056e7i	−0.542394	+	0.145334i
$538$	2.58618e8	+	6.92966e7i	1.66078	+	0.445005i
$539$	1.13775e8	−	6.56878e7i	0.726572	−	0.419487i
$540$	−1.08738e8	+	4.05814e8i	−0.690555	+	2.57719i
$541$	−1.98204e8	−	1.98204e8i	−1.25176	−	1.25176i	−0.954930	−	0.296831i	$-0.904070\pi$
$541$	−1.98204e8	−	1.98204e8i	−1.25176	−	1.25176i	−0.296831	−	0.954930i	$-0.595930\pi$
$542$	6.67095e7	+	2.48963e8i	0.418976	+	1.56364i
$543$	1.17301e8	−	6.77238e7i	0.732660	−	0.423001i
$544$	6.58076e8			4.08770
$545$			9.29095e7i			0.573945i
$546$	4.96803e6	−	2.86830e6i	0.0305216	−	0.0176216i
$547$	1.46076e8	−	1.46076e8i	0.892515	−	0.892515i	−0.102244	−	0.994759i	$-0.532602\pi$
$547$	1.46076e8	−	1.46076e8i	0.892515	−	0.892515i	0.994759	+	0.102244i	$0.0326023\pi$
$548$	−1.83948e7	−	1.06203e7i	−0.111777	−	0.0645347i
$549$	1.35164e7	−	1.35164e7i	0.0816851	−	0.0816851i
$550$	−773073.	−	2.88515e6i	−0.00464657	−	0.0173412i
$551$	1.50168e8	−	2.60098e8i	0.897681	−	1.55483i
$552$	−1.70068e8	+	2.94566e8i	−1.01112	+	1.75132i
$553$	1.25444e6	−	4.68164e6i	0.00741780	−	0.0276836i
$554$		−	2.60092e8i		−	1.52967i
$555$	9.08202e7	+	4.26987e7i	0.531256	+	0.249768i
$556$	2.67709e8			1.55754
$557$	−2.22239e8	−	5.95487e7i	−1.28604	−	0.344593i	−0.449885	−	0.893087i	$-0.648535\pi$
$557$	−2.22239e8	−	5.95487e7i	−1.28604	−	0.344593i	−0.836155	+	0.548493i	$0.815202\pi$
$558$	−2.93725e8	−	1.69582e8i	−1.69059	−	0.976061i
$559$	−1.74595e8	−	1.00802e8i	−0.999529	−	0.577078i
$560$	−2.40611e7	+	6.44714e6i	−0.137009	+	0.0367116i
$561$	−6.39137e7	−	6.39137e7i	−0.361998	−	0.361998i
$562$	−1.40314e8	+	2.43031e8i	−0.790482	+	1.36916i
$563$	−3.94515e7	−	3.94515e7i	−0.221074	−	0.221074i	0.587876	−	0.808951i	$-0.299964\pi$
$563$	−3.94515e7	−	3.94515e7i	−0.221074	−	0.221074i	−0.808951	+	0.587876i	$0.799964\pi$
$564$	−8.35086e7	−	1.44641e8i	−0.465472	−	0.806222i
$565$	−5.31537e7			−0.294705
$566$			2.75902e8i			1.52162i
$567$	319755.	+	553831.i	0.00175415	+	0.00303828i
$568$	−1.02063e9	+	2.73478e8i	−5.56961	+	1.49237i
$569$	1.46396e8	−	1.46396e8i	0.794680	−	0.794680i	−0.187571	−	0.982251i	$-0.560062\pi$
$569$	1.46396e8	−	1.46396e8i	0.794680	−	0.794680i	0.982251	+	0.187571i	$0.0600615\pi$
$570$	1.96352e8	+	5.26125e7i	1.06026	+	0.284095i
$571$	−2.08743e7	−	3.61553e7i	−0.112125	−	0.194207i	0.804502	−	0.593950i	$-0.202432\pi$
$571$	−2.08743e7	−	3.61553e7i	−0.112125	−	0.194207i	−0.916627	+	0.399744i	$0.869099\pi$
$572$	9.28748e7	−	3.46613e8i	0.496260	−	1.85207i
$573$	−7.25128e6	−	2.70621e7i	−0.0385435	−	0.143846i
$574$	−2.26550e6	+	607038.i	−0.0119792	+	0.00320982i
$575$	2.08974e6	+	559945.i	0.0109923	+	0.00294538i
$576$	4.15500e8	−	2.39889e8i	2.17422	−	1.25529i
$577$	−6.64774e6	+	2.48097e7i	−0.0346056	+	0.129150i	−0.981068	−	0.193665i	$-0.937963\pi$
$577$	−6.64774e6	+	2.48097e7i	−0.0346056	+	0.129150i	0.946462	+	0.322815i	$0.104629\pi$
$578$	−2.35876e7	−	2.35876e7i	−0.122152	−	0.122152i
$579$	−1.50881e7	−	5.63095e7i	−0.0777317	−	0.290099i
$580$	8.64171e8	−	4.98929e8i	4.42910	−	2.55714i
$581$	−5.40818e6			−0.0275755
$582$		−	2.74855e8i		−	1.39423i
$583$	1.15387e8	−	6.66187e7i	0.582306	−	0.336195i
$584$	−3.05279e8	+	3.05279e8i	−1.53270	+	1.53270i
$585$	9.57361e7	+	5.52733e7i	0.478198	+	0.276088i
$586$	−4.13829e8	+	4.13829e8i	−2.05650	+	2.05650i
$587$	2.70919e7	+	1.01108e8i	0.133944	+	0.499887i	1.00000		6.04049e-5i	$-1.92275e-5\pi$
$587$	2.70919e7	+	1.01108e8i	0.133944	+	0.499887i	−0.866056	+	0.499948i	$0.833353\pi$
$588$	−1.62339e8	+	2.81179e8i	−0.798527	+	1.38309i
$589$	−1.51301e8	+	2.62061e8i	−0.740451	+	1.28250i
$590$	2.50971e7	−	9.36635e7i	0.122199	−	0.456052i
$591$		−	1.21667e8i		−	0.589403i
$592$	−2.64834e8	−	7.34814e8i	−1.27646	−	3.54170i
$593$	8.51252e7			0.408220			0.204110	−	0.978948i	$-0.434570\pi$
$593$	8.51252e7			0.408220			0.204110	+	0.978948i	$0.434570\pi$
$594$	−3.18586e8	−	8.53650e7i	−1.52008	−	0.407306i
$595$	7.17361e6	+	4.14169e6i	0.0340555	+	0.0196619i
$596$	3.03816e8	+	1.75408e8i	1.43507	+	0.828536i
$597$	−1.02788e8	+	2.75419e7i	−0.483080	+	0.129441i
$598$	2.50877e8	+	2.50877e8i	1.17316	+	1.17316i
$599$	1.32191e8	−	2.28962e8i	0.615066	−	1.06533i	−0.375307	−	0.926901i	$-0.622463\pi$
$599$	1.32191e8	−	2.28962e8i	0.615066	−	1.06533i	0.990373	−	0.138425i	$-0.0442040\pi$
$600$	3.31426e6	+	3.31426e6i	0.0153438	+	0.0153438i
$601$	−1.76477e8	−	3.05666e8i	−0.812950	−	1.40807i	−0.910791	−	0.412868i	$-0.864527\pi$
$601$	−1.76477e8	−	3.05666e8i	−0.812950	−	1.40807i	0.0978410	−	0.995202i	$-0.468806\pi$
$602$	−2.18995e7			−0.100380
$603$		−	2.61466e8i		−	1.19252i
$604$	4.65333e8	+	8.05981e8i	2.11180	+	3.65775i
$605$	−6.32637e7	+	1.69514e7i	−0.285685	+	0.0765492i
$606$	1.48785e8	−	1.48785e8i	0.668562	−	0.668562i
$607$	6.46192e7	+	1.73147e7i	0.288932	+	0.0774190i	0.400374	−	0.916352i	$-0.368880\pi$
$607$	6.46192e7	+	1.73147e7i	0.288932	+	0.0774190i	−0.111442	+	0.993771i	$0.535547\pi$
$608$	−4.25580e8	−	7.37126e8i	−1.89352	−	3.27968i
$609$	−2.37449e6	+	8.86170e6i	−0.0105128	+	0.0392342i
$610$	−2.00191e7	−	7.47122e7i	−0.0881971	−	0.329156i
$611$	−1.06848e8	+	2.86300e7i	−0.468430	+	0.125515i
$612$	−4.17264e8	−	1.11806e8i	−1.82036	−	0.487763i
$613$	−2.54856e8	+	1.47141e8i	−1.10640	+	0.638782i	−0.937895	−	0.346918i	$-0.887228\pi$
$613$	−2.54856e8	+	1.47141e8i	−1.10640	+	0.638782i	−0.168508	+	0.985700i	$0.553895\pi$
$614$	3.38217e7	−	1.26224e8i	0.146114	−	0.545303i
$615$	1.65263e7	+	1.65263e7i	0.0710476	+	0.0710476i
$616$	−6.40579e6	−	2.39067e7i	−0.0274050	−	0.102277i
$617$	7.08314e7	−	4.08945e7i	0.301558	−	0.174104i	−0.341585	−	0.939851i	$-0.610964\pi$
$617$	7.08314e7	−	4.08945e7i	0.301558	−	0.174104i	0.643142	+	0.765747i	$0.277630\pi$
$618$	3.22970e7			0.136835
$619$		−	1.35237e8i		−	0.570195i	−0.958499	−	0.285097i	$-0.907974\pi$
$619$		−	1.35237e8i		−	0.570195i	0.958499	−	0.285097i	$-0.0920259\pi$
$620$	−8.70693e8	+	5.02695e8i	−3.65334	+	2.10926i
$621$	1.68925e8	−	1.68925e8i	0.705373	−	0.705373i
$622$	−3.73276e8	−	2.15511e8i	−1.55117	−	0.895568i
$623$	5.51326e6	−	5.51326e6i	0.0228005	−	0.0228005i
$624$	1.15151e8	+	4.29751e8i	0.473932	+	1.76874i
$625$	−1.23404e8	+	2.13743e8i	−0.505464	+	0.875490i
$626$	4.16498e8	−	7.21396e8i	1.69781	−	2.94070i
$627$	−3.02580e7	+	1.12925e8i	−0.122755	+	0.458127i
$628$			1.69121e8i			0.682840i
$629$	−1.10510e8	+	2.35054e8i	−0.444067	+	0.944531i
$630$	1.20083e7			0.0480240
$631$	3.20990e7	+	8.60091e6i	0.127763	+	0.0342339i	0.322134	−	0.946694i	$-0.395600\pi$
$631$	3.20990e7	+	8.60091e6i	0.127763	+	0.0342339i	−0.194371	+	0.980928i	$0.562267\pi$
$632$	5.62416e8	+	3.24711e8i	2.22796	+	1.28631i
$633$	−1.15628e7	−	6.67576e6i	−0.0455880	−	0.0263202i
$634$	6.19463e8	−	1.65985e8i	2.43079	−	0.651329i
$635$	7.48489e7	+	7.48489e7i	0.292324	+	0.292324i
$636$	−1.64639e8	+	2.85164e8i	−0.639974	+	1.10847i
$637$	1.52055e8	+	1.52055e8i	0.588277	+	0.588277i
$638$	3.91687e8	+	6.78422e8i	1.50826	+	2.61239i
$639$	2.94837e8			1.13000
$640$		−	9.09046e8i		−	3.46773i
$641$	−3.27324e7	−	5.66942e7i	−0.124281	−	0.215260i	0.797171	−	0.603754i	$-0.206329\pi$
$641$	−3.27324e7	−	5.66942e7i	−0.124281	−	0.215260i	−0.921452	+	0.388493i	$0.872996\pi$
$642$	6.45974e7	−	1.73088e7i	0.244124	−	0.0654128i
$643$	6.31841e7	−	6.31841e7i	0.237670	−	0.237670i	−0.578214	−	0.815885i	$-0.696250\pi$
$643$	6.31841e7	−	6.31841e7i	0.237670	−	0.237670i	0.815885	+	0.578214i	$0.196250\pi$
$644$	2.72713e7	+	7.30731e6i	0.102105	+	0.0273590i
$645$	1.09113e8	+	1.88989e8i	0.406627	+	0.704298i
$646$	−1.36168e8	+	5.08185e8i	−0.505099	+	1.88506i
$647$	−6.84173e7	−	2.55337e8i	−0.252611	−	0.942759i	−0.969404	−	0.245472i	$-0.921057\pi$
$647$	−6.84173e7	−	2.55337e8i	−0.252611	−	0.942759i	0.716792	−	0.697287i	$-0.245610\pi$
$648$	−8.27682e7	+	2.21777e7i	−0.304185	+	0.0815062i
$649$	5.38670e7	+	1.44336e7i	0.197055	+	0.0528008i
$650$	4.23404e6	−	2.44452e6i	0.0154175	−	0.00890132i
$651$	2.39241e6	−	8.92858e6i	0.00867145	−	0.0323623i
$652$	4.82916e8	+	4.82916e8i	1.74232	+	1.74232i
$653$	2.72858e7	+	1.01832e8i	0.0979933	+	0.365716i	0.997456	−	0.0712810i	$-0.0227087\pi$
$653$	2.72858e7	+	1.01832e8i	0.0979933	+	0.365716i	−0.899463	+	0.436997i	$0.856042\pi$
$654$	1.56109e8	−	9.01296e7i	0.558078	−	0.322206i
$655$	4.41009e8			1.56936
$656$		−	1.81903e8i		−	0.644358i
$657$	1.04327e8	−	6.02334e7i	0.367876	−	0.212393i
$658$	−8.49658e6	+	8.49658e6i	−0.0298240	+	0.0298240i
$659$	−3.17612e8	−	1.83374e8i	−1.10979	−	0.640738i	−0.171016	−	0.985268i	$-0.554705\pi$
$659$	−3.17612e8	−	1.83374e8i	−1.10979	−	0.640738i	−0.938775	+	0.344530i	$0.888038\pi$
$660$	−2.74658e8	+	2.74658e8i	−0.955344	+	0.955344i
$661$	−1.29181e8	−	4.82110e8i	−0.447295	−	1.66933i	−0.709805	−	0.704399i	$-0.751217\pi$
$661$	−1.29181e8	−	4.82110e8i	−0.447295	−	1.66933i	0.262509	−	0.964929i	$-0.415450\pi$
$662$	−1.08647e8	+	1.88182e8i	−0.374493	+	0.648641i
$663$	7.39741e7	−	1.28127e8i	0.253828	−	0.439642i
$664$	1.87551e8	−	6.99952e8i	0.640643	−	2.39091i
$665$		−	1.07138e7i		−	0.0364315i
$666$	3.16362e7	+	3.75203e8i	0.107093	+	1.27012i
$667$	−5.67407e8			−1.91213
$668$	3.93644e8	+	1.05477e8i	1.32061	+	0.353856i
$669$	1.02638e8	+	5.92580e7i	0.342791	+	0.197910i
$670$	−9.16262e8	−	5.29004e8i	−3.04646	−	1.75887i
$671$	4.29678e7	−	1.15132e7i	0.142225	−	0.0381091i
$672$	1.83850e7	+	1.83850e7i	0.0605836	+	0.0605836i
$673$	−2.18716e7	+	3.78828e7i	−0.0717523	+	0.124279i	−0.899669	−	0.436572i	$-0.856192\pi$
$673$	−2.18716e7	+	3.78828e7i	−0.0717523	+	0.124279i	0.827917	+	0.560851i	$0.189526\pi$
$674$	1.13391e8	+	1.13391e8i	0.370340	+	0.370340i
$675$	−1.64599e6	−	2.85094e6i	−0.00535201	−	0.00926995i
$676$	−2.58873e8			−0.838005
$677$			3.85648e8i			1.24287i	0.783466	+	0.621434i	$0.213450\pi$
$677$			3.85648e8i			1.24287i	−0.783466	+	0.621434i	$0.786550\pi$
$678$	5.15633e7	+	8.93102e7i	0.165444	+	0.286558i
$679$	−1.39926e7	+	3.74930e6i	−0.0446980	+	0.0119768i
$680$	−7.84811e8	+	7.84811e8i	−2.49596	+	2.49596i
$681$	−3.16588e8	−	8.48294e7i	−1.00243	−	0.268599i
$682$	−3.94643e8	−	6.83542e8i	−1.24409	−	2.15483i
$683$	−9.60736e7	+	3.58551e8i	−0.301538	+	1.12535i	0.634347	+	0.773048i	$0.281269\pi$
$683$	−9.60736e7	+	3.58551e8i	−0.301538	+	1.12535i	−0.935885	+	0.352306i	$0.885398\pi$
$684$	1.44610e8	+	5.39692e8i	0.451887	+	1.68647i
$685$	1.47088e7	−	3.94121e6i	0.0457620	−	0.0122619i
$686$	4.51574e7	+	1.20999e7i	0.139880	+	0.0374808i
$687$	3.13170e8	−	1.80809e8i	0.965850	−	0.557634i
$688$	4.39593e8	−	1.64058e9i	1.34985	−	5.03771i
$689$	1.54210e8	+	1.54210e8i	0.471470	+	0.471470i
$690$	−9.93977e7	−	3.70957e8i	−0.302572	−	1.12922i
$691$	−3.56356e8	+	2.05742e8i	−1.08006	+	0.623576i	−0.930914	−	0.365239i	$-0.880987\pi$
$691$	−3.56356e8	+	2.05742e8i	−1.08006	+	0.623576i	−0.149151	+	0.988814i	$0.547654\pi$
$692$	−6.50729e8			−1.96373
$693$			6.90608e6i			0.0207507i
$694$	7.42861e7	−	4.28891e7i	0.222244	−	0.128312i
$695$	−1.35711e8	+	1.35711e8i	−0.404261	+	0.404261i
$696$	−1.06458e9	−	6.14633e8i	−3.15754	−	1.82301i
$697$	−4.27721e7	+	4.27721e7i	−0.126317	+	0.126317i
$698$	3.25653e8	+	1.21535e9i	0.957611	+	3.57385i
$699$	4.06198e7	−	7.03556e7i	0.118934	−	0.206000i
$700$	194527.	−	336931.i	0.000567135	−	0.000982307i
$701$	−9.61937e7	+	3.59000e8i	−0.279250	+	1.04217i	0.673690	+	0.739014i	$0.264708\pi$
$701$	−9.61937e7	+	3.59000e8i	−0.279250	+	1.04217i	−0.952940	+	0.303160i	$0.901958\pi$
$702$		−	5.39863e8i		−	1.56053i
$703$	3.34757e8	−	2.82258e7i	0.963526	−	0.0812421i
$704$	1.11652e9			3.19998
$705$	1.15657e8	+	3.09903e7i	0.330070	+	0.0884420i
$706$	6.63542e8	+	3.83096e8i	1.88562	+	1.08866i
$707$	−9.60407e6	−	5.54491e6i	−0.0271767	−	0.0156905i
$708$	−1.33125e8	+	3.56707e7i	−0.375111	+	0.100511i
$709$	4.93137e7	+	4.93137e7i	0.138366	+	0.138366i	0.772897	−	0.634531i	$-0.218807\pi$
$709$	4.93137e7	+	4.93137e7i	0.138366	+	0.138366i	−0.634531	+	0.772897i	$0.718807\pi$
$710$	5.96520e8	−	1.03320e9i	1.66667	−	2.88676i
$711$	−1.28135e8	−	1.28135e8i	−0.356500	−	0.356500i
$712$	5.22355e8	+	9.04746e8i	1.44719	+	2.50661i
$713$	5.71689e8			1.57722
$714$		−	1.60711e7i		−	0.0441519i
$715$	1.28629e8	+	2.22792e8i	0.351902	+	0.609512i
$716$	−9.34158e8	+	2.50307e8i	−2.54496	+	0.681920i
$717$	3.06426e7	−	3.06426e7i	0.0831321	−	0.0831321i
$718$	−6.22931e8	−	1.66914e8i	−1.68293	−	0.450940i
$719$	−5.42375e7	−	9.39421e7i	−0.145919	−	0.252740i	0.783796	−	0.621018i	$-0.213281\pi$
$719$	−5.42375e7	−	9.39421e7i	−0.145919	−	0.252740i	−0.929716	+	0.368278i	$0.879947\pi$
$720$	−2.41044e8	+	8.99587e8i	−0.645800	+	2.41016i
$721$	−440563.	−	1.64420e6i	−0.00117545	−	0.00438682i
$722$	−4.57075e7	+	1.22473e7i	−0.121444	+	0.0325408i
$723$	1.60496e8	+	4.30047e7i	0.424667	+	0.113789i
$724$	1.30462e9	−	7.53223e8i	3.43771	−	1.98476i
$725$	−2.02367e6	+	7.55244e6i	−0.00531038	+	0.0198186i
$726$	8.98530e7	+	8.98530e7i	0.234813	+	0.234813i
$727$	6.85367e7	+	2.55782e8i	0.178369	+	0.665683i	0.995953	+	0.0898735i	$0.0286463\pi$
$727$	6.85367e7	+	2.55782e8i	0.178369	+	0.665683i	−0.817584	+	0.575809i	$0.804687\pi$
$728$	3.50838e7	−	2.02557e7i	0.0909312	−	0.0524992i
$729$	−1.95185e8			−0.503806
$730$		−	4.87461e8i		−	1.25306i
$731$	−4.89126e8	+	2.82397e8i	−1.25219	+	0.722950i
$732$	−7.77359e7	+	7.77359e7i	−0.198193	+	0.198193i
$733$	2.88951e8	+	1.66826e8i	0.733690	+	0.423596i	0.819771	−	0.572692i	$-0.194101\pi$
$733$	2.88951e8	+	1.66826e8i	0.733690	+	0.423596i	−0.0860805	+	0.996288i	$0.527434\pi$
$734$	3.41494e8	−	3.41494e8i	0.863565	−	0.863565i
$735$	−6.02443e7	−	2.24835e8i	−0.151724	−	0.566241i
$736$	−8.04024e8	+	1.39261e9i	−2.01667	+	3.49298i
$737$	3.04236e8	−	5.26952e8i	0.759991	−	1.31634i
$738$	−2.26957e7	+	8.47016e7i	−0.0564644	+	0.210728i
$739$			3.97630e8i			0.985249i	0.870242	+	0.492624i	$0.163962\pi$
$739$			3.97630e8i			0.985249i	−0.870242	+	0.492624i	$0.836038\pi$
$740$	1.01010e9	+	4.74895e8i	2.49270	+	1.17193i
$741$	−1.91357e8			−0.470316
$742$	2.28826e7	+	6.13137e6i	0.0560136	+	0.0150088i
$743$	5.90135e8	+	3.40715e8i	1.43875	+	0.830662i	0.997763	−	0.0668519i	$-0.0212955\pi$
$743$	5.90135e8	+	3.40715e8i	1.43875	+	0.830662i	0.440986	+	0.897514i	$0.354629\pi$
$744$	1.07261e9	+	6.19272e8i	2.60449	+	1.50370i
$745$	−2.42936e8	+	6.50945e7i	−0.587521	+	0.157426i
$746$	−5.94313e8	−	5.94313e8i	−1.43153	−	1.43153i
$747$	−1.01100e8	+	1.75110e8i	−0.242543	+	0.420096i
$748$	−7.10848e8	−	7.10848e8i	−1.69853	−	1.69853i
$749$	−1.76235e6	−	3.05247e6i	−0.00419417	−	0.00726451i
$750$	4.73614e8			1.12264
$751$			3.60352e7i			0.0850761i	0.999095	+	0.0425380i	$0.0135444\pi$
$751$			3.60352e7i			0.0850761i	−0.999095	+	0.0425380i	$0.986456\pi$
$752$	−4.65960e8	−	8.07066e8i	−1.09571	−	1.89782i
$753$	−2.68783e8	+	7.20201e7i	−0.629529	+	0.168682i
$754$	−9.06681e8	+	9.06681e8i	−2.11515	+	2.11515i
$755$	−6.44475e8	−	1.72687e8i	−1.49749	−	0.401253i
$756$	−2.14803e7	−	3.72050e7i	−0.0497136	−	0.0861064i
$757$	8.89284e7	−	3.31885e8i	0.205000	−	0.765069i	−0.784450	−	0.620192i	$-0.787055\pi$
$757$	8.89284e7	−	3.31885e8i	0.205000	−	0.765069i	0.989450	−	0.144877i	$-0.0462786\pi$
$758$	−2.99670e8	−	1.11839e9i	−0.688076	−	2.56793i
$759$	2.13342e8	−	5.71647e7i	0.487922	−	0.130738i
$760$	1.38662e9	+	3.71545e8i	3.15877	+	0.846390i
$761$	−7.18230e8	+	4.14670e8i	−1.62971	+	0.940912i	−0.645527	+	0.763737i	$0.723362\pi$
$761$	−7.18230e8	+	4.14670e8i	−1.62971	+	0.940912i	−0.984180	+	0.177174i	$0.943304\pi$
$762$	5.31538e7	−	1.98373e8i	0.120135	−	0.448349i
$763$	−6.71788e6	−	6.71788e6i	−0.0151237	−	0.0151237i
$764$	−8.06487e7	−	3.00985e8i	−0.180849	−	0.674939i
$765$	2.68205e8	−	1.54848e8i	0.599076	−	0.345877i
$766$	1.33710e8			0.297493
$767$			9.12807e7i			0.202299i
$768$	−6.55066e8	+	3.78202e8i	−1.44611	+	0.834912i
$769$	4.89568e8	−	4.89568e8i	1.07655	−	1.07655i	0.0797323	−	0.996816i	$-0.474593\pi$
$769$	4.89568e8	−	4.89568e8i	1.07655	−	1.07655i	0.996816	−	0.0797323i	$-0.0254065\pi$
$770$	2.42011e7	+	1.39725e7i	0.0530106	+	0.0306057i
$771$	−1.82724e8	+	1.82724e8i	−0.398687	+	0.398687i
$772$	−1.67809e8	−	6.26274e8i	−0.364724	−	1.36117i
$773$	−7.54927e6	+	1.30757e7i	−0.0163443	+	0.0283092i	−0.874082	−	0.485779i	$-0.838536\pi$
$773$	−7.54927e6	+	1.30757e7i	−0.0163443	+	0.0283092i	0.857738	+	0.514088i	$0.171869\pi$
$774$	−4.09386e8	+	7.09078e8i	−0.882898	+	1.52922i
$775$	2.03894e6	−	7.60944e6i	0.00438026	−	0.0163474i
$776$		−	1.94100e9i		−	4.15376i
$777$	−9.65417e6	+	3.47945e6i	−0.0205803	+	0.00741734i
$778$	4.80529e8			1.02042
$779$	7.55708e7	+	2.02491e7i	0.159861	+	0.0428345i
$780$	−5.50602e8	−	3.17890e8i	−1.16026	−	0.669874i
$781$	5.94206e8	+	3.43065e8i	1.24734	+	0.720151i
$782$	9.60084e8	−	2.57254e8i	2.00766	−	0.537950i
$783$	6.10503e8	+	6.10503e8i	1.27175	+	1.27175i
$784$	−9.05814e8	+	1.56892e9i	−1.87971	+	3.25575i
$785$	−8.57336e7	−	8.57336e7i	−0.177232	−	0.177232i
$786$	−4.27814e8	−	7.40995e8i	−0.881023	−	1.52598i
$787$	−4.71271e8			−0.966822			−0.483411	−	0.875394i	$-0.660602\pi$
$787$	−4.71271e8			−0.966822			−0.483411	+	0.875394i	$0.660602\pi$
$788$		−	1.35318e9i		−	2.76553i
$789$	3.13945e7	+	5.43769e7i	0.0639180	+	0.110709i
$790$	−7.08271e8	+	1.89781e8i	−1.43654	+	0.384920i
$791$	3.84331e6	−	3.84331e6i	0.00776561	−	0.00776561i
$792$	−8.93816e8	−	2.39497e8i	−1.79917	−	0.482087i
$793$	3.64057e7	+	6.30566e7i	0.0730046	+	0.126448i
$794$	3.44037e8	−	1.28396e9i	0.687296	−	2.56502i
$795$	−6.10981e7	−	2.28021e8i	−0.121598	−	0.453810i
$796$	−1.14321e9	+	3.06321e8i	−2.26666	+	0.607349i
$797$	−6.74529e8	−	1.80740e8i	−1.33237	−	0.357008i	−0.478774	−	0.877938i	$-0.658919\pi$
$797$	−6.74529e8	−	1.80740e8i	−1.33237	−	0.357008i	−0.853599	+	0.520930i	$0.825585\pi$
$798$	−1.80016e7	+	1.03932e7i	−0.0354243	+	0.0204522i
$799$	−8.02068e7	+	2.99336e8i	−0.157243	+	0.586838i
$800$	1.56687e7	+	1.56687e7i	0.0306029	+	0.0306029i
$801$	−7.54480e7	−	2.81576e8i	−0.146808	−	0.547895i
$802$	−6.27070e8	+	3.62039e8i	−1.21561	+	0.701831i
$803$	2.80344e8			0.541434
$804$			1.50376e9i			2.89341i
$805$	−1.75291e7	+	1.01205e7i	−0.0336026	+	0.0194005i
$806$	9.13524e8	−	9.13524e8i	1.74468	−	1.74468i
$807$	2.36267e8	+	1.36409e8i	0.449555	+	0.259551i
$808$	1.05071e9	−	1.05071e9i	1.99181	−	1.99181i
$809$	−1.76602e8	−	6.59087e8i	−0.333541	−	1.24479i	−0.905442	−	0.424470i	$-0.860460\pi$
$809$	−1.76602e8	−	6.59087e8i	−0.333541	−	1.24479i	0.571900	−	0.820323i	$-0.306206\pi$
$810$	4.83747e7	−	8.37874e7i	0.0910255	−	0.157661i
$811$	−1.67049e8	+	2.89337e8i	−0.313170	+	0.542427i	−0.979047	−	0.203635i	$-0.934724\pi$
$811$	−1.67049e8	+	2.89337e8i	−0.313170	+	0.542427i	0.665877	+	0.746062i	$0.268058\pi$
$812$	−2.64090e7	+	9.85598e7i	−0.0493269	+	0.184091i
$813$			2.62632e8i			0.488739i
$814$	−3.72819e8	+	7.92986e8i	−0.691234	+	1.47025i
$815$	−4.89615e8			−0.904444
$816$	1.20395e9	+	3.22597e8i	2.21583	+	0.593731i
$817$	6.32639e8	+	3.65255e8i	1.16009	+	0.669776i
$818$	1.42691e8	+	8.23826e7i	0.260697	+	0.150513i
$819$	−1.09188e7	+	2.92569e6i	−0.0198758	+	0.00532570i
$820$	1.83805e8	+	1.83805e8i	0.333362	+	0.333362i
$821$	4.06298e8	−	7.03728e8i	0.734201	−	1.27167i	−0.220873	−	0.975303i	$-0.570890\pi$
$821$	4.06298e8	−	7.03728e8i	0.734201	−	1.27167i	0.955073	−	0.296370i	$-0.0957762\pi$
$822$	−2.08908e7	−	2.08908e7i	−0.0376132	−	0.0376132i
$823$	−2.42939e8	−	4.20783e8i	−0.435811	−	0.754847i	0.561551	−	0.827442i	$-0.310205\pi$
$823$	−2.42939e8	−	4.20783e8i	−0.435811	−	0.754847i	−0.997361	+	0.0725959i	$0.976872\pi$
$824$	2.28079e8			0.407665
$825$		−	3.04356e6i		−	0.00542025i
$826$	4.95774e6	+	8.58706e6i	0.00879718	+	0.0152372i
$827$	−1.57862e8	+	4.22990e7i	−0.279101	+	0.0747849i	−0.395654	−	0.918400i	$-0.629482\pi$
$827$	−1.57862e8	+	4.22990e7i	−0.279101	+	0.0747849i	0.116553	+	0.993184i	$0.462815\pi$
$828$	7.46406e8	−	7.46406e8i	1.31487	−	1.31487i
$829$	−1.88387e8	−	5.04780e7i	−0.330664	−	0.0886010i	0.0896677	−	0.995972i	$-0.471419\pi$
$829$	−1.88387e8	−	5.04780e7i	−0.330664	−	0.0886010i	−0.420331	+	0.907371i	$0.638086\pi$
$830$	4.09094e8	+	7.08571e8i	0.715465	+	1.23922i
$831$	6.85931e7	−	2.55993e8i	0.119530	−	0.446093i
$832$	4.73000e8	+	1.76526e9i	0.821280	+	3.06506i
$833$	5.81901e8	−	1.55920e8i	1.00673	−	0.269753i
$834$	3.59676e8	+	9.63750e7i	0.620031	+	0.166137i
$835$	−2.53022e8	+	1.46083e8i	−0.434610	+	0.250922i
$836$	−3.36530e8	+	1.25595e9i	−0.575976	+	2.14957i
$837$	−6.15111e8	−	6.15111e8i	−1.04900	−	1.04900i
$838$	−7.61136e7	−	2.84060e8i	−0.129339	−	0.482701i
$839$	1.53268e7	−	8.84895e6i	0.0259517	−	0.0149832i	−0.486968	−	0.873420i	$-0.661897\pi$
$839$	1.53268e7	−	8.84895e6i	0.0259517	−	0.0149832i	0.512920	+	0.858437i	$0.328564\pi$
$840$	−4.38512e7			−0.0739850
$841$		−	1.45581e9i		−	2.44747i
$842$	−1.42763e9	+	8.24242e8i	−2.39155	+	1.38076i
$843$	−2.02196e8	+	2.02196e8i	−0.337513	+	0.337513i
$844$	−1.28601e8	−	7.42478e7i	−0.213903	−	0.123497i
$845$	1.31232e8	−	1.31232e8i	0.217505	−	0.217505i
$846$	1.16274e8	+	4.33942e8i	0.192032	+	0.716672i
$847$	3.34863e6	−	5.80000e6i	0.00551083	−	0.00954504i
$848$	−9.18652e8	+	1.59115e9i	−1.50648	+	2.60930i
$849$	−7.27627e7	+	2.71554e8i	−0.118901	+	0.443745i
$850$		−	1.36967e7i		−	0.0223027i
$851$	−3.62399e8	−	5.21043e8i	−0.588029	−	0.845444i
$852$	−1.69568e9			−2.74173
$853$	−1.04397e9	−	2.79731e8i	−1.68206	−	0.450706i	−0.713736	−	0.700415i	$-0.752998\pi$
$853$	−1.04397e9	−	2.79731e8i	−1.68206	−	0.450706i	−0.968321	+	0.249709i	$0.919665\pi$
$854$	6.84960e6	+	3.95462e6i	0.0109974	+	0.00634938i
$855$	−3.46898e8	−	2.00281e8i	−0.555013	−	0.320437i
$856$	4.56182e8	−	1.22234e8i	0.727305	−	0.194881i
$857$	4.23159e8	+	4.23159e8i	0.672297	+	0.672297i	0.958245	−	0.285948i	$-0.0923084\pi$
$857$	4.23159e8	+	4.23159e8i	0.672297	+	0.672297i	−0.285948	+	0.958245i	$0.592308\pi$
$858$	2.49561e8	−	4.32253e8i	0.395107	−	0.684346i
$859$	−6.65535e8	−	6.65535e8i	−1.05000	−	1.05000i	−0.998682	−	0.0513228i	$-0.983656\pi$
$859$	−6.65535e8	−	6.65535e8i	−1.05000	−	1.05000i	−0.0513228	−	0.998682i	$-0.516344\pi$
$860$	1.21355e9	+	2.10193e9i	1.90793	+	3.30463i
$861$	−2.38988e6			−0.00374427
$862$		−	2.42592e7i		−	0.0378751i
$863$	5.18580e8	+	8.98206e8i	0.806832	+	1.39747i	0.915047	+	0.403347i	$0.132153\pi$
$863$	5.18580e8	+	8.98206e8i	0.806832	+	1.39747i	−0.108215	+	0.994128i	$0.534514\pi$
$864$	2.36348e9	−	6.33291e8i	3.66446	−	0.981889i
$865$	3.29878e8	−	3.29878e8i	0.509689	−	0.509689i
$866$	1.53677e9	+	4.11776e8i	2.36622	+	0.634026i
$867$	−1.69952e7	−	2.94365e7i	−0.0260776	−	0.0451678i
$868$	2.66083e7	−	9.93036e7i	0.0406872	−	0.151847i
$869$	−1.09145e8	−	4.07335e8i	−0.166320	−	0.620715i
$870$	1.34066e9	−	3.59228e8i	2.03592	−	0.545523i
$871$	9.62022e8	+	2.57773e8i	1.45590	+	0.390106i
$872$	1.10243e9	−	6.36488e8i	1.66265	−	0.959932i
$873$	−1.40177e8	+	5.23149e8i	−0.210686	+	0.786290i
$874$	−9.09046e8	−	9.09046e8i	−1.36161	−	1.36161i
$875$	−6.46056e6	−	2.41111e7i	−0.00964375	−	0.0359910i
$876$	−6.00011e8	+	3.46417e8i	−0.892580	+	0.515331i
$877$	9.79454e8			1.45206			0.726031	−	0.687661i	$-0.241363\pi$
$877$	9.79454e8			1.45206			0.726031	+	0.687661i	$0.241363\pi$
$878$			1.41883e9i			2.09627i
$879$	−5.16444e8	+	2.98169e8i	−0.760426	+	0.439032i
$880$	−1.53253e9	+	1.53253e9i	−2.24885	+	2.24885i
$881$	4.29905e7	+	2.48206e7i	0.0628702	+	0.0362981i	0.531106	−	0.847306i	$-0.321777\pi$
$881$	4.29905e7	+	2.48206e7i	0.0628702	+	0.0362981i	−0.468235	+	0.883604i	$0.655110\pi$
$882$	6.17537e8	−	6.17537e8i	0.900031	−	0.900031i
$883$	3.29644e8	+	1.23025e9i	0.478809	+	1.78694i	0.606451	+	0.795121i	$0.292593\pi$
$883$	3.29644e8	+	1.23025e9i	0.478809	+	1.78694i	−0.127642	+	0.991820i	$0.540741\pi$
$884$	8.22739e8	−	1.42503e9i	1.19098	−	2.06284i
$885$	4.94031e7	−	8.55686e7i	0.0712729	−	0.123448i
$886$	−3.76432e8	+	1.40486e9i	−0.541234	+	2.01991i
$887$		−	1.17086e9i		−	1.67778i	−0.544303	−	0.838888i	$-0.683206\pi$
$887$		−	1.17086e9i		−	1.67778i	0.544303	−	0.838888i	$-0.316794\pi$
$888$	−1.15528e8	−	1.37015e9i	−0.164986	−	1.95672i
$889$	−1.08240e7			−0.0154057
$890$	−1.13938e9	−	3.05296e8i	−1.61621	−	0.433063i
$891$	4.81871e7	+	2.78208e7i	0.0681236	+	0.0393312i
$892$	1.14154e9	+	6.59067e8i	1.60841	+	0.928614i
$893$	3.87163e8	−	1.03740e8i	0.543675	−	0.145677i
$894$	3.45041e8	+	3.45041e8i	0.482901	+	0.482901i
$895$	3.46669e8	−	6.00448e8i	0.483555	−	0.837541i
$896$	6.57291e7	+	6.57291e7i	0.0913763	+	0.0913763i
$897$	1.80760e8	+	3.13086e8i	0.250452	+	0.433796i
$898$	−6.75023e8			−0.932158
$899$			2.06611e9i			2.84364i
$900$	−7.27293e6	−	1.25971e7i	−0.00997658	−	0.0172799i
$901$	5.90148e8	−	1.58130e8i	0.806838	−	0.216192i
$902$	−1.44297e8	+	1.44297e8i	−0.196625	+	0.196625i
$903$	−2.15544e7	−	5.77548e6i	−0.0292734	−	0.00784377i
$904$	3.64135e8	+	6.30701e8i	0.492899	+	0.853726i
$905$	−2.79524e8	+	1.04320e9i	−0.377114	+	1.40741i
$906$	3.35039e8	+	1.25038e9i	0.450517	+	1.68135i
$907$	−3.50139e8	+	9.38194e7i	−0.469265	+	0.125739i	−0.485700	−	0.874126i	$-0.661435\pi$
$907$	−3.50139e8	+	9.38194e7i	−0.469265	+	0.125739i	0.0164345	+	0.999865i	$0.494768\pi$
$908$	−3.52109e9	−	9.43472e8i	−4.70348	−	1.26029i
$909$	−3.59074e8	+	2.07311e8i	−0.478070	+	0.276014i
$910$	−1.18386e7	+	4.41823e7i	−0.0157100	+	0.0586306i
$911$	8.07141e7	+	8.07141e7i	0.106756	+	0.106756i	0.758467	−	0.651711i	$-0.225948\pi$
$911$	8.07141e7	+	8.07141e7i	0.106756	+	0.106756i	−0.651711	+	0.758467i	$0.725948\pi$
$912$	−4.17249e8	−	1.55719e9i	−0.550061	−	2.05285i
$913$	−4.07507e8	+	2.35274e8i	−0.535455	+	0.309145i
$914$	5.74819e8			0.752822
$915$		−	7.88143e7i		−	0.102883i
$916$	3.48307e9	−	2.01095e9i	4.53186	−	2.61647i
$917$	−3.18874e7	+	3.18874e7i	−0.0413534	+	0.0413534i
$918$	−1.30980e9	−	7.56213e8i	−1.69308	−	0.977499i
$919$	4.25264e7	−	4.25264e7i	0.0547914	−	0.0547914i	−0.679180	−	0.733972i	$-0.737665\pi$
$919$	4.25264e7	−	4.25264e7i	0.0547914	−	0.0547914i	0.733972	+	0.679180i	$0.237665\pi$
$920$	−7.01938e8	−	2.61967e9i	−0.901437	−	3.36421i
$921$	6.65773e7	−	1.15315e8i	0.0852212	−	0.147607i
$922$	−2.47263e7	+	4.28272e7i	−0.0315476	+	0.0546421i
$923$	−2.90672e8	+	1.08480e9i	−0.369656	+	1.37958i
$924$		−	3.97186e7i		−	0.0503475i
$925$	−8.22783e6	+	2.96539e6i	−0.0103959	+	0.00374676i
$926$	4.11925e7			0.0518783
$927$	−6.14730e7	−	1.64716e7i	−0.0771694	−	0.0206775i
$928$	−5.03296e9	−	2.90578e9i	−6.29767	−	3.63596i
$929$	−7.20775e8	−	4.16140e8i	−0.898985	−	0.519029i	−0.0221145	−	0.999755i	$-0.507040\pi$
$929$	−7.20775e8	−	4.16140e8i	−0.898985	−	0.519029i	−0.876871	+	0.480726i	$0.840373\pi$
$930$	−1.35078e9	+	3.61940e8i	−1.67933	+	0.449974i
$931$	−5.50967e8	−	5.50967e8i	−0.682773	−	0.682773i
$932$	4.51773e8	−	7.82494e8i	0.558049	−	0.966570i
$933$	−3.10557e8	−	3.10557e8i	−0.382382	−	0.382382i
$934$	−7.27532e7	−	1.26012e8i	−0.0892918	−	0.154658i
$935$	7.20709e8			0.881709
$936$		−	1.51462e9i		−	1.84704i
$937$	1.71034e8	+	2.96240e8i	0.207905	+	0.360101i	0.951054	−	0.309024i	$-0.100002\pi$
$937$	1.71034e8	+	2.96240e8i	0.207905	+	0.360101i	−0.743150	+	0.669125i	$0.766669\pi$
$938$	1.04501e8	−	2.80009e7i	0.126623	−	0.0339284i
$939$	6.00185e8	−	6.00185e8i	0.724917	−	0.724917i
$940$	1.28634e9	+	3.44674e8i	1.54872	+	0.414978i
$941$	2.41682e8	+	4.18605e8i	0.290051	+	0.502383i	0.973822	−	0.227314i	$-0.0729943\pi$
$941$	2.41682e8	+	4.18605e8i	0.290051	+	0.502383i	−0.683770	+	0.729697i	$0.739661\pi$
$942$	−6.08835e7	+	2.27220e8i	−0.0728361	+	0.271828i
$943$	−3.82555e7	−	1.42772e8i	−0.0456204	−	0.170258i
$944$	−7.42809e8	+	1.99035e8i	−0.883001	+	0.236599i
$945$	2.97497e7	+	7.97140e6i	0.0352522	+	0.00944581i
$946$	−1.65013e9	+	9.52704e8i	−1.94915	+	1.12534i
$947$	−9.21592e7	+	3.43943e8i	−0.108515	+	0.404982i	−0.998720	−	0.0505769i	$-0.983894\pi$
$947$	−9.21592e7	+	3.43943e8i	−0.108515	+	0.404982i	0.890205	+	0.455559i	$0.150561\pi$
$948$	7.36936e8	+	7.36936e8i	0.864977	+	0.864977i
$949$	1.18765e8	+	4.43237e8i	0.138960	+	0.518606i
$950$	−1.53420e7	+	8.85768e6i	−0.0178941	+	0.0103312i
$951$	6.53475e8			0.759779
$952$		−	1.13492e8i		−	0.131539i
$953$	9.32245e8	−	5.38232e8i	1.07709	−	0.621857i	0.146979	−	0.989140i	$-0.453045\pi$
$953$	9.32245e8	−	5.38232e8i	1.07709	−	0.621857i	0.930109	+	0.367282i	$0.119712\pi$
$954$	6.26289e8	−	6.26289e8i	0.721323	−	0.721323i
$955$	1.93464e8	+	1.11696e8i	0.222121	+	0.128242i
$956$	3.40807e8	−	3.40807e8i	0.390063	−	0.390063i
$957$	2.06596e8	+	7.71028e8i	0.235715	+	0.879699i
$958$	−3.38404e8	+	5.86132e8i	−0.384892	+	0.666652i
$959$	−778556.	+	1.34850e6i	−0.000882743	+	0.00152896i
$960$	5.11996e8	−	1.91079e9i	0.578699	−	2.15973i
$961$		−	1.19420e9i		−	1.34557i
$962$	−1.41169e9	−	2.53503e8i	−1.58567	−	0.284746i
$963$	−1.31780e8			−0.147561
$964$	1.78503e9	+	4.78299e8i	1.99258	+	0.533910i
$965$	4.02549e8	+	2.32412e8i	0.447958	+	0.258629i
$966$	3.40093e7	+	1.96353e7i	0.0377282	+	0.0217824i
$967$	−5.82519e8	+	1.56085e8i	−0.644215	+	0.172617i	−0.566112	−	0.824328i	$-0.691553\pi$
$967$	−5.82519e8	+	1.56085e8i	−0.644215	+	0.172617i	−0.0781030	+	0.996945i	$0.524886\pi$
$968$	6.34535e8	+	6.34535e8i	0.699567	+	0.699567i
$969$	−2.68043e8	+	4.64265e8i	−0.294601	+	0.510263i
$970$	1.54967e9	+	1.54967e9i	1.69795	+	1.69795i
$971$	−3.31494e8	−	5.74165e8i	−0.362092	−	0.627161i	0.626213	−	0.779652i	$-0.284604\pi$
$971$	−3.31494e8	−	5.74165e8i	−0.362092	−	0.627161i	−0.988305	+	0.152491i	$0.951271\pi$
$972$	−2.57428e9			−2.80322
$973$		−	1.96254e7i		−	0.0213049i
$974$	−3.76890e8	−	6.52793e8i	−0.407886	−	0.706478i
$975$	4.81200e6	−	1.28937e6i	0.00519172	−	0.00139112i
$976$	−4.33750e8	+	4.33750e8i	−0.466541	+	0.466541i
$977$	−5.03586e8	−	1.34936e8i	−0.539995	−	0.144691i	−0.0214954	−	0.999769i	$-0.506843\pi$
$977$	−5.03586e8	−	1.34936e8i	−0.539995	−	0.144691i	−0.518500	+	0.855078i	$0.673509\pi$
$978$	4.74965e8	+	8.22664e8i	0.507745	+	0.879440i
$979$	1.75579e8	−	6.55270e8i	0.187122	−	0.698348i
$980$	−6.70037e8	−	2.50061e9i	−0.711903	−	2.65686i
$981$	−3.43099e8	+	9.19330e7i	−0.363423	+	0.0973788i
$982$	−2.42759e8	−	6.50470e7i	−0.256354	−	0.0686899i
$983$	−5.09787e8	+	2.94326e8i	−0.536696	+	0.309861i	−0.743739	−	0.668471i	$-0.766949\pi$
$983$	−5.09787e8	+	2.94326e8i	−0.536696	+	0.309861i	0.207043	+	0.978332i	$0.433616\pi$
$984$	8.28792e7	−	3.09310e8i	0.0869882	−	0.324644i
$985$	6.85978e8	+	6.85978e8i	0.717797	+	0.717797i
$986$	9.29728e8	+	3.46979e9i	0.969897	+	3.61970i
$987$	−1.06034e7	+	6.12190e6i	−0.0110280	+	0.00636700i
$988$	−2.12827e9			−2.20677
$989$		−	1.38011e9i		−	1.42667i
$990$	9.04823e8	−	5.22400e8i	0.932520	−	0.538391i
$991$	4.36011e8	−	4.36011e8i	0.447998	−	0.447998i	−0.446690	−	0.894689i	$-0.647397\pi$
$991$	4.36011e8	−	4.36011e8i	0.447998	−	0.447998i	0.894689	+	0.446690i	$0.147397\pi$
$992$	5.07095e9	+	2.92771e9i	5.19462	+	2.99912i
$993$	−1.56563e8	+	1.56563e8i	−0.159898	+	0.159898i
$994$	3.15746e7	+	1.17838e8i	0.0321498	+	0.119985i
$995$	4.24248e8	−	7.34818e8i	0.430675	−	0.745952i
$996$	5.81449e8	−	1.00710e9i	0.588483	−	1.01928i
$997$	−5.04112e7	+	1.88137e8i	−0.0508676	+	0.189840i	−0.986684	−	0.162646i	$-0.947997\pi$
$997$	−5.04112e7	+	1.88137e8i	−0.0508676	+	0.189840i	0.935817	+	0.352487i	$0.114664\pi$
$998$			3.25016e9i			3.26974i
$999$	−1.70693e8	+	9.50543e8i	−0.171207	+	0.953401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.7.g.a.8.18	✓	72
37.14	odd	12	inner	37.7.g.a.14.18	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.7.g.a.8.18	✓	72	1.1	even	1	trivial
37.7.g.a.14.18	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)

\(f(q)\)	\(=\)	\(q+(14.9428 + 4.00391i) q^{2} +(13.6514 + 7.88162i) q^{3} +(151.830 + 87.6593i) q^{4} +(-121.406 + 32.5306i) q^{5} +(172.432 + 172.432i) q^{6} +(6.42619 - 11.1305i) q^{7} +(1217.70 + 1217.70i) q^{8} +(-240.260 - 416.143i) q^{9} +O(q^{10})\)	\(q+(14.9428 + 4.00391i) q^{2} +(13.6514 + 7.88162i) q^{3} +(151.830 + 87.6593i) q^{4} +(-121.406 + 32.5306i) q^{5} +(172.432 + 172.432i) q^{6} +(6.42619 - 11.1305i) q^{7} +(1217.70 + 1217.70i) q^{8} +(-240.260 - 416.143i) q^{9} -1944.40 q^{10} -1118.24i q^{11} +(1381.79 + 2393.34i) q^{12} +(1767.99 - 473.732i) q^{13} +(140.591 - 140.591i) q^{14} +(-1913.75 - 512.788i) q^{15} +(7710.12 + 13354.3i) q^{16} +(1327.16 - 4953.03i) q^{17} +(-1923.96 - 7180.32i) q^{18} +(-6406.28 + 1716.56i) q^{19} +(-21284.7 - 5703.23i) q^{20} +(175.452 - 101.298i) q^{21} +(4477.35 - 16709.7i) q^{22} +(8860.03 + 8860.03i) q^{23} +(7025.83 + 26220.8i) q^{24} +(149.531 - 86.3315i) q^{25} +28315.6 q^{26} -19066.0i q^{27} +(1951.38 - 1126.63i) q^{28} +(-32020.6 + 32020.6i) q^{29} +(-26543.7 - 15325.0i) q^{30} +(32262.3 - 32262.3i) q^{31} +(33215.8 + 123963. i) q^{32} +(8813.57 - 15265.6i) q^{33} +(39663.0 - 68698.3i) q^{34} +(-418.096 + 1560.36i) q^{35} -84244.2i q^{36} +(-49855.5 - 8952.79i) q^{37} -102601. q^{38} +(27869.3 + 7467.56i) q^{39} +(-187449. - 108224. i) q^{40} +(-10215.9 - 5898.18i) q^{41} +(3027.34 - 811.173i) q^{42} +(-77884.0 - 77884.0i) q^{43} +(98024.5 - 169783. i) q^{44} +(42706.4 + 42706.4i) q^{45} +(96918.9 + 167868. i) q^{46} -60434.9 q^{47} +243073. i q^{48} +(58741.9 + 101744. i) q^{49} +(2580.07 - 691.327i) q^{50} +(57155.5 - 57155.5i) q^{51} +(309962. + 83054.1i) q^{52} +(59574.4 + 103186. i) q^{53} +(76338.4 - 284899. i) q^{54} +(36377.2 + 135762. i) q^{55} +(21378.8 - 5728.43i) q^{56} +(-100984. - 27058.5i) q^{57} +(-606685. + 350270. i) q^{58} +(-12907.4 + 48171.0i) q^{59} +(-245615. - 245615. i) q^{60} +(10295.8 + 38424.4i) q^{61} +(611264. - 352913. i) q^{62} -6175.83 q^{63} +998455. i q^{64} +(-199234. + 115028. i) q^{65} +(192821. - 192821. i) q^{66} +(471232. + 272066. i) q^{67} +(635683. - 635683. i) q^{68} +(51120.1 + 190783. i) q^{69} +(-12495.1 + 21642.1i) q^{70} +(-306789. + 531375. i) q^{71} +(214173. - 799304. i) q^{72} +250701. i q^{73} +(-709135. - 333397. i) q^{74} +2721.73 q^{75} +(-1.12314e6 - 300945. i) q^{76} +(-12446.6 - 7186.05i) q^{77} +(386546. + 223172. i) q^{78} +(364263. - 97603.9i) q^{79} +(-1.37048e6 - 1.37048e6i) q^{80} +(-24879.0 + 43091.7i) q^{81} +(-129039. - 129039. i) q^{82} +(-210396. - 364417. i) q^{83} +35518.7 q^{84} +644501. i q^{85} +(-851965. - 1.47565e6i) q^{86} +(-689499. + 184751. i) q^{87} +(1.36169e6 - 1.36169e6i) q^{88} +(585981. + 157013. i) q^{89} +(467161. + 809146. i) q^{90} +(6088.59 - 22722.9i) q^{91} +(568557. + 2.12189e6i) q^{92} +(694703. - 186145. i) q^{93} +(-903066. - 241976. i) q^{94} +(721921. - 416801. i) q^{95} +(-523589. + 1.95406e6i) q^{96} +(-796994. - 796994. i) q^{97} +(470395. + 1.75554e6i) q^{98} +(-465349. + 268669. 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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