LMFDB - Embedded newform 37.7.g.a.8.3

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			8.3
Character	$\chi$	$=$	37.8
Dual form			37.7.g.a.14.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.0056 - 3.48484i) q^{2} +(38.1387 + 22.0194i) q^{3} +(101.576 + 58.6446i) q^{4} +(226.086 - 60.5794i) q^{5} +(-419.282 - 419.282i) q^{6} +(-208.015 + 360.292i) q^{7} +(-507.354 - 507.354i) q^{8} +(605.206 + 1048.25i) q^{9} +O(q^{10})$	\(q+(-13.0056 - 3.48484i) q^{2} +(38.1387 + 22.0194i) q^{3} +(101.576 + 58.6446i) q^{4} +(226.086 - 60.5794i) q^{5} +(-419.282 - 419.282i) q^{6} +(-208.015 + 360.292i) q^{7} +(-507.354 - 507.354i) q^{8} +(605.206 + 1048.25i) q^{9} -3151.48 q^{10} -1444.80i q^{11} +(2582.64 + 4473.26i) q^{12} +(1258.38 - 337.181i) q^{13} +(3960.91 - 3960.91i) q^{14} +(9956.53 + 2667.84i) q^{15} +(1077.13 + 1865.65i) q^{16} +(-1597.88 + 5963.38i) q^{17} +(-4218.09 - 15742.1i) q^{18} +(-2736.80 + 733.324i) q^{19} +(26517.4 + 7105.32i) q^{20} +(-15866.8 + 9160.71i) q^{21} +(-5034.87 + 18790.4i) q^{22} +(5825.09 + 5825.09i) q^{23} +(-8178.19 - 30521.4i) q^{24} +(33913.2 - 19579.8i) q^{25} -17540.9 q^{26} +21200.8i q^{27} +(-42258.4 + 24397.9i) q^{28} +(7186.86 - 7186.86i) q^{29} +(-120193. - 69393.7i) q^{30} +(-3077.28 + 3077.28i) q^{31} +(4377.83 + 16338.3i) q^{32} +(31813.5 - 55102.6i) q^{33} +(41562.8 - 71988.9i) q^{34} +(-25202.8 + 94058.3i) q^{35} +141968. i q^{36} +(-36106.3 - 35525.5i) q^{37} +38149.2 q^{38} +(55417.3 + 14849.0i) q^{39} +(-145441. - 83970.2i) q^{40} +(-14827.9 - 8560.89i) q^{41} +(238281. - 63847.1i) q^{42} +(25165.9 + 25165.9i) q^{43} +(84729.5 - 146756. i) q^{44} +(200331. + 200331. i) q^{45} +(-55459.2 - 96058.2i) q^{46} -26720.7 q^{47} +94871.1i q^{48} +(-27715.8 - 48005.1i) q^{49} +(-509293. + 136465. i) q^{50} +(-192251. + 192251. i) q^{51} +(147594. + 39547.7i) q^{52} +(79918.0 + 138422. i) q^{53} +(73881.3 - 275729. i) q^{54} +(-87524.9 - 326647. i) q^{55} +(288333. - 77258.5i) q^{56} +(-120525. - 32294.7i) q^{57} +(-118514. + 68424.3i) q^{58} +(50234.5 - 187478. i) q^{59} +(854885. + 854885. i) q^{60} +(-36420.5 - 135923. i) q^{61} +(50745.7 - 29298.0i) q^{62} -503567. q^{63} -365618. i q^{64} +(264074. - 152463. i) q^{65} +(-605777. + 605777. i) q^{66} +(-250559. - 144660. i) q^{67} +(-512026. + 512026. i) q^{68} +(93896.4 + 350426. i) q^{69} +(655555. - 1.13545e6i) q^{70} +(-199803. + 346070. i) q^{71} +(224779. - 838887. i) q^{72} -162427. i q^{73} +(345784. + 587854. i) q^{74} +1.72454e6 q^{75} +(-320998. - 86011.1i) q^{76} +(520548. + 300539. i) q^{77} +(-668988. - 386240. i) q^{78} +(-249660. + 66896.2i) q^{79} +(356544. + 356544. i) q^{80} +(-25633.3 + 44398.3i) q^{81} +(163012. + 163012. i) q^{82} +(-502952. - 871138. i) q^{83} -2.14891e6 q^{84} +1.44503e6i q^{85} +(-239598. - 414995. i) q^{86} +(432348. - 115847. i) q^{87} +(-733023. + 733023. i) q^{88} +(94523.3 + 25327.4i) q^{89} +(-1.90730e6 - 3.30354e6i) q^{90} +(-140277. + 523521. i) q^{91} +(250076. + 933297. i) q^{92} +(-185123. + 49603.7i) q^{93} +(347518. + 93117.2i) q^{94} +(-574327. + 331588. i) q^{95} +(-192794. + 719518. i) q^{96} +(-1.08320e6 - 1.08320e6i) q^{97} +(193170. + 720919. i) q^{98} +(1.51450e6 - 874399. 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 $

$2$	−13.0056	−	3.48484i	−1.62570	−	0.435604i	−0.673030	−	0.739616i	$-0.735007\pi$
$2$	−13.0056	−	3.48484i	−1.62570	−	0.435604i	−0.952668	+	0.304011i	$0.901674\pi$
$3$	38.1387	+	22.0194i	1.41254	+	0.815533i	0.995628	−	0.0934122i	$-0.0297774\pi$
$3$	38.1387	+	22.0194i	1.41254	+	0.815533i	0.416916	+	0.908945i	$0.363111\pi$
$4$	101.576	+	58.6446i	1.58712	+	0.916323i
$5$	226.086	−	60.5794i	1.80868	−	0.484636i	0.813406	−	0.581696i	$-0.197611\pi$
$5$	226.086	−	60.5794i	1.80868	−	0.484636i	0.995278	+	0.0970605i	$0.0309440\pi$
$6$	−419.282	−	419.282i	−1.94112	−	1.94112i
$7$	−208.015	+	360.292i	−0.606457	+	1.05041i	0.385362	+	0.922765i	$0.374076\pi$
$7$	−208.015	+	360.292i	−0.606457	+	1.05041i	−0.991819	+	0.127649i	$0.959257\pi$
$8$	−507.354	−	507.354i	−0.990926	−	0.990926i
$9$	605.206	+	1048.25i	0.830187	+	1.43793i
$10$	−3151.48			−3.15148
$11$		−	1444.80i		−	1.08550i	−0.839896	−	0.542748i	$-0.817384\pi$
$11$		−	1444.80i		−	1.08550i	0.839896	−	0.542748i	$-0.182616\pi$
$12$	2582.64	+	4473.26i	1.49458	+	2.58869i
$13$	1258.38	−	337.181i	0.572770	−	0.153473i	0.0392034	−	0.999231i	$-0.487518\pi$
$13$	1258.38	−	337.181i	0.572770	−	0.153473i	0.533567	+	0.845758i	$0.320851\pi$
$14$	3960.91	−	3960.91i	1.44348	−	1.44348i
$15$	9956.53	+	2667.84i	2.95008	+	0.790472i
$16$	1077.13	+	1865.65i	0.262972	+	0.455480i
$17$	−1597.88	+	5963.38i	−0.325236	+	1.21380i	0.588839	+	0.808250i	$0.299585\pi$
$17$	−1597.88	+	5963.38i	−0.325236	+	1.21380i	−0.914075	+	0.405546i	$0.867081\pi$
$18$	−4218.09	−	15742.1i	−0.723266	−	2.69927i
$19$	−2736.80	+	733.324i	−0.399009	+	0.106914i	−0.452743	−	0.891641i	$-0.649554\pi$
$19$	−2736.80	+	733.324i	−0.399009	+	0.106914i	0.0537338	+	0.998555i	$0.482888\pi$
$20$	26517.4	+	7105.32i	3.31468	+	0.888165i
$21$	−15866.8	+	9160.71i	−1.71329	+	0.989171i
$22$	−5034.87	+	18790.4i	−0.472847	+	1.76469i
$23$	5825.09	+	5825.09i	0.478762	+	0.478762i	0.904735	−	0.425974i	$-0.140068\pi$
$23$	5825.09	+	5825.09i	0.478762	+	0.478762i	−0.425974	+	0.904735i	$0.640068\pi$
$24$	−8178.19	−	30521.4i	−0.591594	−	2.20786i
$25$	33913.2	−	19579.8i	2.17044	−	1.25311i
$26$	−17540.9			−0.998005
$27$			21200.8i			1.07711i
$28$	−42258.4	+	24397.9i	−1.92504	+	1.11142i
$29$	7186.86	−	7186.86i	0.294676	−	0.294676i	−0.544248	−	0.838924i	$-0.683185\pi$
$29$	7186.86	−	7186.86i	0.294676	−	0.294676i	0.838924	+	0.544248i	$0.183185\pi$
$30$	−120193.	−	69393.7i	−4.45161	−	2.57014i
$31$	−3077.28	+	3077.28i	−0.103296	+	0.103296i	−0.756866	−	0.653570i	$-0.773270\pi$
$31$	−3077.28	+	3077.28i	−0.103296	+	0.103296i	0.653570	+	0.756866i	$0.273270\pi$
$32$	4377.83	+	16338.3i	0.133601	+	0.498605i
$33$	31813.5	−	55102.6i	0.885258	−	1.53331i
$34$	41562.8	−	71988.9i	1.05747	−	1.83159i
$35$	−25202.8	+	94058.3i	−0.587821	+	2.19378i
$36$			141968.i			3.04288i
$37$	−36106.3	−	35525.5i	−0.712817	−	0.701350i
$37$	−36106.3	−	35525.5i	−0.712817	−	0.701350i
$38$	38149.2			0.695240
$39$	55417.3	+	14849.0i	0.934225	+	0.250325i
$40$	−145441.	−	83970.2i	−2.27251	−	1.31203i
$41$	−14827.9	−	8560.89i	−0.215143	−	0.124213i	0.388556	−	0.921425i	$-0.372974\pi$
$41$	−14827.9	−	8560.89i	−0.215143	−	0.124213i	−0.603699	+	0.797212i	$0.706307\pi$
$42$	238281.	−	63847.1i	3.21619	−	0.861774i
$43$	25165.9	+	25165.9i	0.316524	+	0.316524i	0.847430	−	0.530907i	$-0.178149\pi$
$43$	25165.9	+	25165.9i	0.316524	+	0.316524i	−0.530907	+	0.847430i	$0.678149\pi$
$44$	84729.5	−	146756.i	0.994665	−	1.72281i
$45$	200331.	+	200331.i	2.19842	+	2.19842i
$46$	−55459.2	−	96058.2i	−0.569771	−	0.986872i
$47$	−26720.7			−0.257368			−0.128684	−	0.991686i	$-0.541075\pi$
$47$	−26720.7			−0.257368			−0.128684	+	0.991686i	$0.541075\pi$
$48$			94871.1i			0.857848i
$49$	−27715.8	−	48005.1i	−0.235580	−	0.408037i
$50$	−509293.	+	136465.i	−4.07434	+	1.09172i
$51$	−192251.	+	192251.i	−1.44930	+	1.44930i
$52$	147594.	+	39547.7i	1.04968	+	0.281262i
$53$	79918.0	+	138422.i	0.536806	+	0.929775i	0.999074	+	0.0430345i	$0.0137025\pi$
$53$	79918.0	+	138422.i	0.536806	+	0.929775i	−0.462268	+	0.886740i	$0.652964\pi$
$54$	73881.3	−	275729.i	0.469195	−	1.75106i
$55$	−87524.9	−	326647.i	−0.526070	−	1.96332i
$56$	288333.	−	77258.5i	1.64184	−	0.439929i
$57$	−120525.	−	32294.7i	−0.650810	−	0.174384i
$58$	−118514.	+	68424.3i	−0.607417	+	0.350693i
$59$	50234.5	−	187478.i	0.244594	−	0.912838i	−0.728993	−	0.684521i	$-0.760011\pi$
$59$	50234.5	−	187478.i	0.244594	−	0.912838i	0.973587	−	0.228316i	$-0.0733220\pi$
$60$	854885.	+	854885.i	3.95780	+	3.95780i
$61$	−36420.5	−	135923.i	−0.160456	−	0.598830i	−0.998576	−	0.0533442i	$-0.983012\pi$
$61$	−36420.5	−	135923.i	−0.160456	−	0.598830i	0.838120	−	0.545486i	$-0.183655\pi$
$62$	50745.7	−	29298.0i	0.212924	−	0.122932i
$63$	−503567.			−2.01389
$64$		−	365618.i		−	1.39472i
$65$	264074.	−	152463.i	0.961582	−	0.555170i
$66$	−605777.	+	605777.i	−2.10708	+	2.10708i
$67$	−250559.	−	144660.i	−0.833077	−	0.480977i	0.0218280	−	0.999762i	$-0.493051\pi$
$67$	−250559.	−	144660.i	−0.833077	−	0.480977i	−0.854905	+	0.518785i	$0.826385\pi$
$68$	−512026.	+	512026.i	−1.62842	+	1.62842i
$69$	93896.4	+	350426.i	0.285826	+	1.06672i
$70$	655555.	−	1.13545e6i	1.91124	−	3.31036i
$71$	−199803.	+	346070.i	−0.558249	+	0.966916i	0.439394	+	0.898295i	$0.355193\pi$
$71$	−199803.	+	346070.i	−0.558249	+	0.966916i	−0.997643	+	0.0686212i	$0.978140\pi$
$72$	224779.	−	838887.i	0.602224	−	2.24753i
$73$		−	162427.i		−	0.417533i	−0.977966	−	0.208766i	$-0.933055\pi$
$73$		−	162427.i		−	0.417533i	0.977966	−	0.208766i	$-0.0669448\pi$
$74$	345784.	+	587854.i	0.853315	+	1.45069i
$75$	1.72454e6			4.08780
$76$	−320998.	−	86011.1i	−0.731242	−	0.195936i
$77$	520548.	+	300539.i	1.14022	+	0.658307i
$78$	−668988.	−	386240.i	−1.40973	−	0.813905i
$79$	−249660.	+	66896.2i	−0.506369	+	0.135681i	−0.502954	−	0.864313i	$-0.667754\pi$
$79$	−249660.	+	66896.2i	−0.506369	+	0.135681i	−0.00341493	+	0.999994i	$0.501087\pi$
$80$	356544.	+	356544.i	0.696375	+	0.696375i
$81$	−25633.3	+	44398.3i	−0.0482337	+	0.0835432i
$82$	163012.	+	163012.i	0.295650	+	0.295650i
$83$	−502952.	−	871138.i	−0.879614	−	1.52354i	−0.851766	−	0.523923i	$-0.824468\pi$
$83$	−502952.	−	871138.i	−0.879614	−	1.52354i	−0.0278480	−	0.999612i	$-0.508865\pi$
$84$	−2.14891e6			−3.62560
$85$			1.44503e6i			2.35300i
$86$	−239598.	−	414995.i	−0.376693	−	0.652451i
$87$	432348.	−	115847.i	0.656562	−	0.175925i
$88$	−733023.	+	733023.i	−1.07565	+	1.07565i
$89$	94523.3	+	25327.4i	0.134081	+	0.0359270i	0.325236	−	0.945633i	$-0.394556\pi$
$89$	94523.3	+	25327.4i	0.134081	+	0.0359270i	−0.191154	+	0.981560i	$0.561223\pi$
$90$	−1.90730e6	−	3.30354e6i	−2.61632	−	4.53160i
$91$	−140277.	+	523521.i	−0.186150	+	0.694721i
$92$	250076.	+	933297.i	0.321151	+	1.19855i
$93$	−185123.	+	49603.7i	−0.230151	+	0.0616687i
$94$	347518.	+	93117.2i	0.418402	+	0.112111i
$95$	−574327.	+	331588.i	−0.669867	+	0.386748i
$96$	−192794.	+	719518.i	−0.217911	+	0.813257i
$97$	−1.08320e6	−	1.08320e6i	−1.18685	−	1.18685i	−0.977934	−	0.208912i	$-0.933008\pi$
$97$	−1.08320e6	−	1.08320e6i	−1.18685	−	1.18685i	−0.208912	−	0.977934i	$-0.566992\pi$
$98$	193170.	+	720919.i	0.205239	+	0.765964i
$99$	1.51450e6	−	874399.i	1.56086	−	0.901165i
$100$	4.59300e6			4.59300
$101$		−	1.60116e6i		−	1.55407i	−0.629456	−	0.777036i	$-0.716722\pi$
$101$		−	1.60116e6i		−	1.55407i	0.629456	−	0.777036i	$-0.283278\pi$
$102$	3.17030e6	−	1.83037e6i	2.98745	−	1.72480i
$103$	−513500.	+	513500.i	−0.469925	+	0.469925i	−0.901890	−	0.431965i	$-0.857820\pi$
$103$	−513500.	+	513500.i	−0.469925	+	0.469925i	0.431965	+	0.901890i	$0.357820\pi$
$104$	−809512.	−	467372.i	−0.719653	−	0.415492i
$105$	−3.03231e6	+	3.03231e6i	−2.61942	+	2.61942i
$106$	−557002.	−	2.07876e6i	−0.467670	−	1.74537i
$107$	−8777.99	+	15203.9i	−0.00716546	+	0.0124109i	−0.869586	−	0.493782i	$-0.835614\pi$
$107$	−8777.99	+	15203.9i	−0.00716546	+	0.0124109i	0.862420	+	0.506193i	$0.168948\pi$
$108$	−1.24331e6	+	2.15348e6i	−0.986983	+	1.70950i
$109$	−56666.9	+	211484.i	−0.0437573	+	0.163304i	−0.984347	−	0.176240i	$-0.943606\pi$
$109$	−56666.9	+	211484.i	−0.0437573	+	0.163304i	0.940590	+	0.339545i	$0.110273\pi$
$110$			4.55325e6i			3.42092i
$111$	−594799.	−	2.14993e6i	−0.434912	−	1.57201i
$112$	−896237.			−0.637924
$113$	2.21842e6	+	594425.i	1.53748	+	0.411966i	0.925450	−	0.378870i	$-0.123687\pi$
$113$	2.21842e6	+	594425.i	1.53748	+	0.411966i	0.612028	+	0.790836i	$0.290354\pi$
$114$	1.45496e6	+	840023.i	0.982058	+	0.566991i
$115$	1.66985e6	+	964088.i	1.09795	+	0.633904i
$116$	1.15148e6	−	308538.i	0.737705	−	0.197667i
$117$	1.11503e6	+	1.11503e6i	0.696189	+	0.696189i
$118$	−1.30666e6	+	2.26320e6i	−0.795272	+	1.37745i
$119$	−1.81618e6	−	1.81618e6i	−1.07775	−	1.07775i
$120$	−3.69794e6	−	6.40503e6i	−2.14001	−	3.70661i
$121$	−315873.			−0.178302
$122$			1.89468e6i			1.04341i
$123$	−377011.	−	653002.i	−0.202600	−	0.350913i
$124$	−493043.	+	132110.i	−0.258595	+	0.0692902i
$125$	3.89511e6	−	3.89511e6i	1.99430	−	1.99430i
$126$	6.54919e6	+	1.75485e6i	3.27398	+	0.877260i
$127$	−597385.	−	1.03470e6i	−0.291637	−	0.505131i	0.682560	−	0.730830i	$-0.260867\pi$
$127$	−597385.	−	1.03470e6i	−0.291637	−	0.505131i	−0.974197	+	0.225699i	$0.927533\pi$
$128$	−993937.	+	3.70942e6i	−0.473946	+	1.76879i
$129$	405656.	+	1.51393e6i	0.188968	+	0.705239i
$130$	−3.96575e6	+	1.06262e6i	−1.80508	+	0.483669i
$131$	−1.16681e6	−	312645.i	−0.519021	−	0.139071i	−0.0102075	−	0.999948i	$-0.503249\pi$
$131$	−1.16681e6	−	312645.i	−0.519021	−	0.139071i	−0.508814	+	0.860877i	$0.669916\pi$
$132$	6.46295e6	−	3.73138e6i	2.81002	−	1.62236i
$133$	305084.	−	1.13859e6i	0.129678	−	0.483964i
$134$	2.75455e6	+	2.75455e6i	1.14482	+	1.14482i
$135$	1.28433e6	+	4.79320e6i	0.522007	+	1.94816i
$136$	3.83624e6	−	2.21485e6i	1.52507	−	0.880498i
$137$	2.18207e6			0.848609			0.424304	−	0.905520i	$-0.360519\pi$
$137$	2.18207e6			0.848609			0.424304	+	0.905520i	$0.360519\pi$
$138$		−	4.88471e6i		−	1.85867i
$139$	−3.85612e6	+	2.22633e6i	−1.43584	+	0.828983i	−0.997557	−	0.0698534i	$-0.977747\pi$
$139$	−3.85612e6	+	2.22633e6i	−1.43584	+	0.828983i	−0.438284	+	0.898837i	$0.644414\pi$
$140$	−8.07600e6	+	8.07600e6i	−2.94315	+	2.94315i
$141$	−1.01909e6	−	588373.i	−0.363543	−	0.209892i
$142$	3.80456e6	−	3.80456e6i	1.32874	−	1.32874i
$143$	−487157.	−	1.81810e6i	−0.166595	−	0.621740i
$144$	−1.30377e6	+	2.25820e6i	−0.436631	+	0.756268i
$145$	1.18947e6	−	2.06022e6i	0.390166	−	0.675788i
$146$	−566032.	+	2.11246e6i	−0.181879	+	0.678782i
$147$		−	2.44113e6i		−	0.768493i
$148$	−1.58414e6	−	5.72596e6i	−0.488662	−	1.76629i
$149$	−2.05076e6			−0.619950			−0.309975	−	0.950745i	$-0.600321\pi$
$149$	−2.05076e6			−0.619950			−0.309975	+	0.950745i	$0.600321\pi$
$150$	−2.24286e7	−	6.00973e6i	−6.64552	−	1.78066i
$151$	132502.	+	76499.8i	0.0384849	+	0.0222193i	0.519119	−	0.854702i	$-0.326260\pi$
$151$	132502.	+	76499.8i	0.0384849	+	0.0222193i	−0.480634	+	0.876921i	$0.659593\pi$
$152$	1.76058e6	+	1.01647e6i	0.501332	+	0.289444i
$153$	−7.21815e6	+	1.93410e6i	−2.01536	+	0.540013i
$154$	−5.72271e6	−	5.72271e6i	−1.56689	−	1.56689i
$155$	−509309.	+	882150.i	−0.136769	+	0.236890i
$156$	4.75823e6	+	4.75823e6i	1.25335	+	1.25335i
$157$	−2.17644e6	−	3.76971e6i	−0.562404	−	0.974112i	−0.997286	−	0.0736243i	$-0.976543\pi$
$157$	−2.17644e6	−	3.76971e6i	−0.562404	−	0.974112i	0.434883	−	0.900487i	$-0.356790\pi$
$158$	3.48009e6			0.882307
$159$			7.03898e6i			1.75113i
$160$	1.97953e6	+	3.42864e6i	0.483283	+	0.837071i
$161$	−3.31044e6	+	887030.i	−0.793246	+	0.212550i
$162$	488097.	−	488097.i	0.114805	−	0.114805i
$163$	7.69877e6	+	2.06288e6i	1.77770	+	0.476333i	0.990161	−	0.139931i	$-0.0446880\pi$
$163$	7.69877e6	+	2.06288e6i	1.77770	+	0.476333i	0.787539	+	0.616264i	$0.211355\pi$
$164$	−1.00410e6	−	1.73915e6i	−0.227639	−	0.394282i
$165$	3.85449e6	−	1.43851e7i	0.858055	−	3.20230i
$166$	3.50541e6	+	1.30824e7i	0.766327	+	2.85997i
$167$	2.81245e6	−	753594.i	0.603859	−	0.161804i	0.0560796	−	0.998426i	$-0.482140\pi$
$167$	2.81245e6	−	753594.i	0.603859	−	0.161804i	0.547779	+	0.836623i	$0.315473\pi$
$168$	1.26978e7	+	3.40237e6i	2.67794	+	0.717552i
$169$	−2.71032e6	+	1.56480e6i	−0.561514	+	0.324190i
$170$	5.03570e6	−	1.87935e7i	1.02498	−	3.82526i
$171$	−2.42504e6	−	2.42504e6i	−0.484987	−	0.484987i
$172$	1.08039e6	+	4.03208e6i	0.212322	+	0.792398i
$173$	2.54689e6	−	1.47045e6i	0.491895	−	0.283996i	−0.233465	−	0.972365i	$-0.575007\pi$
$173$	2.54689e6	−	1.47045e6i	0.491895	−	0.283996i	0.725360	+	0.688369i	$0.241673\pi$
$174$	−6.02665e6			−1.14400
$175$			1.62915e7i			3.03982i
$176$	2.69548e6	−	1.55624e6i	0.494422	−	0.285455i
$177$	6.04402e6	−	6.04402e6i	1.08995	−	1.08995i
$178$	−1.14107e6	−	658796.i	−0.202326	−	0.116813i
$179$	−7.40126e6	+	7.40126e6i	−1.29047	+	1.29047i	−0.355968	+	0.934498i	$0.615849\pi$
$179$	−7.40126e6	+	7.40126e6i	−1.29047	+	1.29047i	−0.934498	+	0.355968i	$0.884151\pi$
$180$	8.60037e6	+	3.20970e7i	1.47469	+	5.50360i
$181$	3.06671e6	−	5.31170e6i	0.517174	−	0.895772i	−0.482627	−	0.875826i	$-0.660317\pi$
$181$	3.06671e6	−	5.31170e6i	0.517174	−	0.895772i	0.999801	−	0.0199460i	$-0.00634943\pi$
$182$	3.64877e6	−	6.31986e6i	0.605247	−	1.04832i
$183$	1.60391e6	−	5.98588e6i	0.261714	−	0.976730i
$184$		−	5.91077e6i		−	0.948834i
$185$	−1.03152e7	−	5.84449e6i	−1.62916	−	0.923064i
$186$	2.58050e6			0.401019
$187$	8.61587e6	+	2.30861e6i	1.31757	+	0.353042i
$188$	−2.71417e6	−	1.56703e6i	−0.408473	−	0.235832i
$189$	−7.63848e6	−	4.41008e6i	−1.13141	−	0.653222i
$190$	8.62499e6	−	2.31106e6i	1.25747	−	0.336938i
$191$	−3.61015e6	−	3.61015e6i	−0.518114	−	0.518114i	0.398886	−	0.917000i	$-0.369397\pi$
$191$	−3.61015e6	−	3.61015e6i	−0.518114	−	0.518114i	−0.917000	+	0.398886i	$0.869397\pi$
$192$	8.05068e6	−	1.39442e7i	1.13744	−	1.97010i
$193$	705661.	+	705661.i	0.0981576	+	0.0981576i	0.754480	−	0.656323i	$-0.227889\pi$
$193$	705661.	+	705661.i	0.0981576	+	0.0981576i	−0.656323	+	0.754480i	$0.727889\pi$
$194$	1.03129e7	+	1.78625e7i	1.41246	+	2.44645i
$195$	1.34286e7			1.81104
$196$		−	6.50152e6i		−	0.863469i
$197$	−635315.	−	1.10040e6i	−0.0830980	−	0.143930i	0.821481	−	0.570236i	$-0.193148\pi$
$197$	−635315.	−	1.10040e6i	−0.0830980	−	0.143930i	−0.904579	+	0.426306i	$0.859815\pi$
$198$	−2.27441e7	+	6.09428e6i	−2.93004	+	0.785103i
$199$	−4.34985e6	+	4.34985e6i	−0.551969	+	0.551969i	−0.927009	−	0.375040i	$-0.877629\pi$
$199$	−4.34985e6	+	4.34985e6i	−0.551969	+	0.551969i	0.375040	+	0.927009i	$0.377629\pi$
$200$	−2.71399e7	−	7.27210e6i	−3.39248	−	0.909013i
$201$	−6.37065e6	−	1.10343e7i	−0.784505	−	1.35880i
$202$	−5.57978e6	+	2.08240e7i	−0.676960	+	2.52645i
$203$	1.09440e6	+	4.08434e6i	0.130824	+	0.488241i
$204$	−3.08025e7	+	8.25351e6i	−3.62824	+	0.972183i
$205$	−3.87099e6	−	1.03723e6i	−0.449325	−	0.120396i
$206$	8.46783e6	−	4.88890e6i	0.968658	−	0.559255i
$207$	−2.58076e6	+	9.63152e6i	−0.290962	+	1.08589i
$208$	1.98450e6	+	1.98450e6i	0.220526	+	0.220526i
$209$	1.05950e6	+	3.95412e6i	0.116055	+	0.433123i
$210$	5.00040e7	−	2.88698e7i	5.39942	−	3.11736i
$211$	−4.11555e6			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$211$	−4.11555e6			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$212$			1.87471e7i			1.96755i
$213$	−1.52405e7	+	8.79910e6i	−1.57710	+	0.910541i
$214$	167146.	−	167146.i	0.0170551	−	0.0170551i
$215$	7.21417e6	+	4.16510e6i	0.725890	+	0.419093i
$216$	1.07563e7	−	1.07563e7i	1.06734	−	1.06734i
$217$	−468601.	−	1.74884e6i	−0.0458589	−	0.171148i
$218$	1.47397e6	−	2.55300e6i	0.142272	−	0.246423i
$219$	3.57655e6	−	6.19476e6i	0.340511	−	0.589783i
$220$	1.02657e7	−	3.83122e7i	0.964100	−	3.59807i
$221$			8.04295e6i			0.745141i
$222$	243548.	+	3.00339e7i	0.0222600	+	2.74507i
$223$	−1.52620e7			−1.37625			−0.688125	−	0.725592i	$-0.741566\pi$
$223$	−1.52620e7			−1.37625			−0.688125	+	0.725592i	$0.741566\pi$
$224$	−6.79720e6	−	1.82131e6i	−0.604765	−	0.162046i
$225$	4.10489e7	+	2.36996e7i	3.60375	+	2.08062i
$226$	−2.67804e7	−	1.54617e7i	−2.32002	−	1.33946i
$227$	1.69734e7	−	4.54800e6i	1.45108	−	0.388815i	0.554679	−	0.832064i	$-0.312841\pi$
$227$	1.69734e7	−	4.54800e6i	1.45108	−	0.388815i	0.896398	+	0.443249i	$0.146174\pi$
$228$	−1.03485e7	−	1.03485e7i	−0.873120	−	0.873120i
$229$	9.31022e6	−	1.61258e7i	0.775271	−	1.34281i	−0.159371	−	0.987219i	$-0.550947\pi$
$229$	9.31022e6	−	1.61258e7i	0.775271	−	1.34281i	0.934642	−	0.355590i	$-0.115720\pi$
$230$	−1.83577e7	−	1.83577e7i	−1.50881	−	1.50881i
$231$	1.32354e7	+	2.29243e7i	1.07374	+	1.85977i
$232$	−7.29257e6			−0.584005
$233$			1.21822e7i			0.963069i	0.876427	+	0.481534i	$0.159920\pi$
$233$			1.21822e7i			0.963069i	−0.876427	+	0.481534i	$0.840080\pi$
$234$	−1.06159e7	−	1.83872e7i	−0.828531	−	1.43506i
$235$	−6.04116e6	+	1.61873e6i	−0.465497	+	0.124730i
$236$	1.60972e7	−	1.60972e7i	1.22465	−	1.22465i
$237$	−1.09947e7	−	2.94602e6i	−0.825922	−	0.221305i
$238$	1.72914e7	+	2.99495e7i	1.28262	+	2.22156i
$239$	−1.08727e6	+	4.05776e6i	−0.0796425	+	0.297230i	−0.994246	−	0.107122i	$-0.965836\pi$
$239$	−1.08727e6	+	4.05776e6i	−0.0796425	+	0.297230i	0.914603	+	0.404352i	$0.132503\pi$
$240$	5.74724e6	+	2.14490e7i	0.415744	+	1.55158i
$241$	−1.34169e6	+	359504.i	−0.0958518	+	0.0256834i	−0.306426	−	0.951894i	$-0.599133\pi$
$241$	−1.34169e6	+	359504.i	−0.0958518	+	0.0256834i	0.210574	+	0.977578i	$0.432467\pi$
$242$	4.10811e6	+	1.10077e6i	0.289865	+	0.0776691i
$243$	1.14295e7	−	6.59883e6i	0.796543	−	0.459884i
$244$	4.27173e6	−	1.59423e7i	0.294059	−	1.09744i
$245$	−9.17425e6	−	9.17425e6i	−0.623839	−	0.623839i
$246$	2.62764e6	+	9.80650e6i	0.176507	+	0.658732i
$247$	−3.19666e6	+	1.84559e6i	−0.212132	+	0.122474i
$248$	3.12254e6			0.204717
$249$		−	4.42987e7i		−	2.86941i
$250$	−6.42321e7	+	3.70844e7i	−4.11085	+	2.37340i
$251$	−8.89485e6	+	8.89485e6i	−0.562493	+	0.562493i	−0.930015	−	0.367522i	$-0.880206\pi$
$251$	−8.89485e6	+	8.89485e6i	−0.562493	+	0.562493i	0.367522	+	0.930015i	$0.380206\pi$
$252$	−5.11501e7	−	2.95315e7i	−3.19628	−	1.84537i
$253$	8.41607e6	−	8.41607e6i	0.519694	−	0.519694i
$254$	4.16358e6	+	1.55387e7i	0.254077	+	0.948229i
$255$	−3.18187e7	+	5.51117e7i	−1.91894	+	3.32371i
$256$	1.41537e7	−	2.45149e7i	0.843626	−	1.46120i
$257$	2.28938e6	−	8.54408e6i	0.134871	−	0.503345i	−0.865127	−	0.501552i	$-0.832763\pi$
$257$	2.28938e6	−	8.54408e6i	0.134871	−	0.503345i	0.999998	−	0.00179311i	$-0.000570764\pi$
$258$		−	2.11032e7i		−	1.22882i
$259$	2.03102e7	−	5.61901e6i	1.16900	−	0.323415i
$260$	3.57647e7			2.03486
$261$	1.18832e7	+	3.18408e6i	0.668359	+	0.179086i
$262$	1.40855e7	+	8.13226e6i	0.783192	+	0.452176i
$263$	1.84324e7	+	1.06419e7i	1.01324	+	0.584996i	0.912139	−	0.409880i	$-0.134429\pi$
$263$	1.84324e7	+	1.06419e7i	1.01324	+	0.584996i	0.101103	+	0.994876i	$0.467763\pi$
$264$	−4.40972e7	+	1.18158e7i	−2.39662	+	0.642173i
$265$	2.64538e7	+	2.64538e7i	1.42151	+	1.42151i
$266$	−7.93560e6	+	1.37449e7i	−0.421633	+	0.730290i
$267$	3.04730e6	+	3.04730e6i	0.160096	+	0.160096i
$268$	−1.69671e7	−	2.93879e7i	−0.881461	−	1.52673i
$269$	3.27831e7			1.68420			0.842098	−	0.539324i	$-0.181320\pi$
$269$	3.27831e7			1.68420			0.842098	+	0.539324i	$0.181320\pi$
$270$		−	6.68140e7i		−	3.39450i
$271$	−2.22158e6	−	3.84789e6i	−0.111623	−	0.193337i	0.804802	−	0.593544i	$-0.202272\pi$
$271$	−2.22158e6	−	3.84789e6i	−0.111623	−	0.193337i	−0.916425	+	0.400207i	$0.868938\pi$
$272$	−1.28467e7	+	3.44226e6i	−0.638388	+	0.171056i
$273$	−1.68776e7	+	1.68776e7i	−0.829512	+	0.829512i
$274$	−2.83791e7	−	7.60416e6i	−1.37958	−	0.369658i
$275$	−2.82888e7	−	4.89976e7i	−1.36024	−	2.35601i
$276$	−1.10130e7	+	4.11012e7i	−0.523818	+	1.95491i
$277$	1.49205e6	+	5.56842e6i	0.0702013	+	0.261995i	0.992102	−	0.125430i	$-0.0400312\pi$
$277$	1.49205e6	+	5.56842e6i	0.0702013	+	0.261995i	−0.921901	+	0.387425i	$0.873364\pi$
$278$	5.79095e7	−	1.55168e7i	2.69535	−	0.722218i
$279$	−5.08815e6	−	1.36337e6i	−0.234286	−	0.0627769i
$280$	6.05076e7	−	3.49341e7i	2.75636	−	1.59138i
$281$	−9.97337e6	+	3.72211e7i	−0.449493	+	1.67753i	0.254300	+	0.967125i	$0.418155\pi$
$281$	−9.97337e6	+	3.72211e7i	−0.449493	+	1.67753i	−0.703793	+	0.710405i	$0.748512\pi$
$282$	1.12035e7	+	1.12035e7i	0.499582	+	0.499582i
$283$	6.65614e6	+	2.48411e7i	0.293673	+	1.09600i	0.942266	+	0.334866i	$0.108691\pi$
$283$	6.65614e6	+	2.48411e7i	0.293673	+	1.09600i	−0.648593	+	0.761135i	$0.724642\pi$
$284$	−4.05903e7	+	2.34348e7i	−1.77201	+	1.02307i
$285$	−2.92055e7			−1.26162
$286$			2.53431e7i			1.08333i
$287$	6.16884e6	−	3.56158e6i	0.260950	−	0.150660i
$288$	−1.44771e7	+	1.44771e7i	−0.606043	+	0.606043i
$289$	−1.21049e7	−	6.98879e6i	−0.501498	−	0.289540i
$290$	−2.26493e7	+	2.26493e7i	−0.928668	+	0.928668i
$291$	−1.74605e7	−	6.51634e7i	−0.708561	−	2.64439i
$292$	9.52549e6	−	1.64986e7i	0.382595	−	0.662673i
$293$	4.06563e6	−	7.04188e6i	0.161631	−	0.279953i	−0.773823	−	0.633402i	$-0.781658\pi$
$293$	4.06563e6	−	7.04188e6i	0.161631	−	0.279953i	0.935454	+	0.353449i	$0.114991\pi$
$294$	−8.50695e6	+	3.17484e7i	−0.334759	+	1.24934i
$295$		−	4.54292e7i		−	1.76957i
$296$	294707.	+	3.63427e7i	0.0113636	+	1.40133i
$297$	3.06308e7			1.16920
$298$	2.66714e7	+	7.14657e6i	1.00785	+	0.270053i
$299$	9.29426e6	+	5.36605e6i	0.347697	+	0.200743i
$300$	1.75171e8	+	1.01135e8i	6.48781	+	3.74574i
$301$	−1.43019e7	+	3.83219e6i	−0.524439	+	0.140523i
$302$	−1.45667e6	−	1.45667e6i	−0.0528860	−	0.0528860i
$303$	3.52566e7	−	6.10662e7i	1.26740	−	2.19519i
$304$	−4.31602e6	−	4.31602e6i	−0.153625	−	0.153625i
$305$	−1.64683e7	−	2.85239e7i	−0.580428	−	1.00533i
$306$	1.00616e8			3.51159
$307$		−	7.07512e6i		−	0.244522i	−0.992498	−	0.122261i	$-0.960985\pi$
$307$		−	7.07512e6i		−	0.244522i	0.992498	−	0.122261i	$-0.0390145\pi$
$308$	3.52500e7	+	6.10547e7i	1.20644	+	2.08962i
$309$	−3.08912e7	+	8.27726e6i	−1.04703	+	0.280551i
$310$	9.69801e6	−	9.69801e6i	0.325535	−	0.325535i
$311$	−3.06437e6	−	821096.i	−0.101873	−	0.0272969i	0.207522	−	0.978230i	$-0.433460\pi$
$311$	−3.06437e6	−	821096.i	−0.101873	−	0.0272969i	−0.309396	+	0.950933i	$0.600127\pi$
$312$	−2.05825e7	−	3.56499e7i	−0.677695	−	1.17380i
$313$	−1.43450e7	+	5.35363e7i	−0.467808	+	1.74588i	0.179600	+	0.983740i	$0.442520\pi$
$313$	−1.43450e7	+	5.35363e7i	−0.467808	+	1.74588i	−0.647408	+	0.762144i	$0.724147\pi$
$314$	1.51691e7	+	5.66118e7i	0.489971	+	1.82860i
$315$	−1.13849e8	+	3.05058e7i	−3.64249	+	0.976003i
$316$	−2.92824e7	−	7.84620e6i	−0.927996	−	0.248656i
$317$	−7.78779e6	+	4.49628e6i	−0.244476	+	0.141148i	−0.617232	−	0.786781i	$-0.711746\pi$
$317$	−7.78779e6	+	4.49628e6i	−0.244476	+	0.141148i	0.372756	+	0.927929i	$0.378413\pi$
$318$	2.45297e7	−	9.15461e7i	0.762800	−	2.84681i
$319$	−1.03835e7	−	1.03835e7i	−0.319870	−	0.319870i
$320$	−2.21489e7	−	8.26609e7i	−0.675931	−	2.52261i
$321$	−669562.	+	386572.i	−0.0202430	+	0.0116873i
$322$	4.61453e7			1.38217
$323$		−	1.74924e7i		−	0.519088i
$324$	−5.20744e6	+	3.00652e6i	−0.153105	+	0.0883952i
$325$	3.60736e7	−	3.60736e7i	1.05085	−	1.05085i
$326$	−9.29382e7	−	5.36579e7i	−2.68251	−	1.54875i
$327$	−6.81795e6	+	6.81795e6i	−0.194989	+	0.194989i
$328$	3.17959e6	+	1.18664e7i	0.0901052	+	0.336277i
$329$	5.55830e6	−	9.62726e6i	0.156083	−	0.270343i
$330$	−1.00260e8	+	1.73655e8i	−2.78988	+	4.83221i
$331$	−8.34044e6	+	3.11269e7i	−0.229988	+	0.858326i	0.750357	+	0.661033i	$0.229882\pi$
$331$	−8.34044e6	+	3.11269e7i	−0.229988	+	0.858326i	−0.980345	+	0.197293i	$0.936785\pi$
$332$		−	1.17982e8i		−	3.22404i
$333$	1.53877e7	−	5.93486e7i	0.416717	−	1.60723i
$334$	−3.92037e7			−1.05217
$335$	−6.54112e7	−	1.75269e7i	−1.73987	−	0.466197i
$336$	−3.41813e7	−	1.97346e7i	−0.901096	−	0.520248i
$337$	−2.35347e7	−	1.35878e7i	−0.614921	−	0.355025i	0.159968	−	0.987122i	$-0.448861\pi$
$337$	−2.35347e7	−	1.35878e7i	−0.614921	−	0.355025i	−0.774889	+	0.632097i	$0.782194\pi$
$338$	4.07024e7	−	1.09062e7i	1.05407	−	0.282437i
$339$	7.15189e7	+	7.15189e7i	1.83578	+	1.83578i
$340$	−8.47435e7	+	1.46780e8i	−2.15610	+	3.73448i
$341$	4.44605e6	+	4.44605e6i	0.112127	+	0.112127i
$342$	2.30882e7	+	3.99899e7i	0.577180	+	0.999704i
$343$	−2.58843e7			−0.641437
$344$		−	2.55360e7i		−	0.627303i
$345$	4.24573e7	+	7.35381e7i	1.03394	+	1.79083i
$346$	−3.82481e7	+	1.02485e7i	−0.923383	+	0.247420i
$347$	2.39650e7	−	2.39650e7i	0.573575	−	0.573575i	−0.359551	−	0.933125i	$-0.617070\pi$
$347$	2.39650e7	−	2.39650e7i	0.573575	−	0.573575i	0.933125	+	0.359551i	$0.117070\pi$
$348$	5.07098e7	+	1.35876e7i	1.20324	+	0.322408i
$349$	−2.11171e7	−	3.65759e7i	−0.496773	−	0.860436i	0.503220	−	0.864158i	$-0.332149\pi$
$349$	−2.11171e7	−	3.65759e7i	−0.496773	−	0.860436i	−0.999993	+	0.00372207i	$0.998815\pi$
$350$	5.67733e7	−	2.11881e8i	1.32416	−	4.94183i
$351$	7.14851e6	+	2.66786e7i	0.165308	+	0.616938i
$352$	2.36055e7	−	6.32507e6i	0.541233	−	0.145023i
$353$	−7.64581e6	−	2.04869e6i	−0.173820	−	0.0465749i	0.170859	−	0.985295i	$-0.445346\pi$
$353$	−7.64581e6	−	2.04869e6i	−0.173820	−	0.0465749i	−0.344679	+	0.938721i	$0.612012\pi$
$354$	−9.96684e7	+	5.75436e7i	−2.24671	+	1.29714i
$355$	−2.42080e7	+	9.03454e7i	−0.541095	+	2.01939i
$356$	8.11593e6	+	8.11593e6i	0.179882	+	0.179882i
$357$	−2.92755e7	−	1.09258e8i	−0.643427	−	2.40130i
$358$	1.22050e8	−	7.04655e7i	2.66004	−	1.53578i
$359$	7.30080e7			1.57793			0.788964	−	0.614439i	$-0.210618\pi$
$359$	7.30080e7			1.57793			0.788964	+	0.614439i	$0.210618\pi$
$360$		−	2.03277e8i		−	4.35693i
$361$	−3.37906e7	+	1.95090e7i	−0.718248	+	0.414681i
$362$	−5.83947e7	+	5.83947e7i	−1.23097	+	1.23097i
$363$	−1.20470e7	−	6.95532e6i	−0.251859	−	0.145411i
$364$	−4.49505e7	+	4.49505e7i	−0.932030	+	0.932030i
$365$	−9.83975e6	−	3.67225e7i	−0.202351	−	0.755185i
$366$	−4.17196e7	+	7.22605e7i	−0.850936	+	1.47386i
$367$	−6.99901e6	+	1.21226e7i	−0.141592	+	0.245244i	−0.928096	−	0.372340i	$-0.878555\pi$
$367$	−6.99901e6	+	1.21226e7i	−0.141592	+	0.245244i	0.786504	+	0.617585i	$0.211889\pi$
$368$	−4.59317e6	+	1.71420e7i	−0.0921657	+	0.343967i
$369$		−	2.07244e7i		−	0.412480i
$370$	1.13789e8	+	1.11958e8i	2.24643	+	2.21029i
$371$	−6.64965e7			−1.30220
$372$	−2.17130e7	−	5.81798e6i	−0.421785	−	0.113017i
$373$	−3.53099e7	−	2.03862e7i	−0.680409	−	0.392834i	0.119600	−	0.992822i	$-0.461839\pi$
$373$	−3.53099e7	−	2.03862e7i	−0.680409	−	0.392834i	−0.800009	+	0.599988i	$0.795172\pi$
$374$	−1.04009e8	−	6.00498e7i	−1.98819	−	1.14788i
$375$	2.34323e8	−	6.27865e7i	4.44345	−	1.19062i
$376$	1.35569e7	+	1.35569e7i	0.255032	+	0.255032i
$377$	6.62050e6	−	1.14670e7i	0.123557	−	0.214007i
$378$	8.39745e7	+	8.39745e7i	1.55479	+	1.55479i
$379$	3.16628e7	+	5.48416e7i	0.581610	+	1.00738i	0.995289	+	0.0969552i	$0.0309104\pi$
$379$	3.16628e7	+	5.48416e7i	0.581610	+	1.00738i	−0.413679	+	0.910423i	$0.635756\pi$
$380$	−7.77835e7			−1.41754
$381$		−	5.26162e7i		−	0.951359i
$382$	3.43713e7	+	5.95329e7i	0.616604	+	1.06799i
$383$	2.36575e7	−	6.33901e6i	0.421088	−	0.112830i	−0.0420518	−	0.999115i	$-0.513389\pi$
$383$	2.36575e7	−	6.33901e6i	0.421088	−	0.112830i	0.463140	+	0.886285i	$0.346723\pi$
$384$	−1.19587e8	+	1.19587e8i	−2.11198	+	2.11198i
$385$	1.35895e8	+	3.64129e7i	2.38134	+	0.638078i
$386$	−6.71842e6	−	1.16366e7i	−0.116817	−	0.202333i
$387$	−1.11495e7	+	4.16106e7i	−0.192364	+	0.717911i
$388$	−4.65028e7	−	1.73551e8i	−0.796131	−	2.97120i
$389$	3.22206e7	−	8.63348e6i	0.547374	−	0.146669i	0.0254748	−	0.999675i	$-0.491890\pi$
$389$	3.22206e7	−	8.63348e6i	0.547374	−	0.146669i	0.521900	+	0.853007i	$0.325224\pi$
$390$	−1.74647e8	−	4.67965e7i	−2.94420	−	0.788895i
$391$	−4.40451e7	+	2.54294e7i	−0.736829	+	0.425409i
$392$	−1.02939e7	+	3.84173e7i	−0.170892	+	0.637776i
$393$	−3.76163e7	−	3.76163e7i	−0.619723	−	0.619723i
$394$	4.42794e6	+	1.65253e7i	0.0723957	+	0.270185i
$395$	−5.23920e7	+	3.02485e7i	−0.850107	+	0.490809i
$396$	2.05115e8			3.30303
$397$			1.08324e8i			1.73123i	0.500713	+	0.865613i	$0.333071\pi$
$397$			1.08324e8i			1.73123i	−0.500713	+	0.865613i	$0.666929\pi$
$398$	7.17308e7	−	4.14138e7i	1.13778	−	0.656895i
$399$	3.67066e7	−	3.67066e7i	0.577863	−	0.577863i
$400$	7.30579e7	+	4.21800e7i	1.14153	+	0.659063i
$401$	−1.74043e7	+	1.74043e7i	−0.269912	+	0.269912i	−0.829065	−	0.559153i	$-0.811127\pi$
$401$	−1.74043e7	+	1.74043e7i	−0.269912	+	0.269912i	0.559153	+	0.829065i	$0.311127\pi$
$402$	4.44014e7	+	1.65708e8i	0.683468	+	2.55074i
$403$	−2.83478e6	+	4.90998e6i	−0.0433116	+	0.0750179i
$404$	9.38995e7	−	1.62639e8i	1.42403	−	2.46649i
$405$	−3.10571e6	+	1.15907e7i	−0.0467515	+	0.174479i
$406$		−	5.69331e7i		−	0.850720i
$407$	−5.13270e7	+	5.21663e7i	−0.761312	+	0.773761i
$408$	1.95079e8			2.87230
$409$	9.01946e7	+	2.41676e7i	1.31829	+	0.353234i	0.848336	−	0.529458i	$-0.177605\pi$
$409$	9.01946e7	+	2.41676e7i	1.31829	+	0.353234i	0.469952	+	0.882692i	$0.344271\pi$
$410$	4.67299e7	+	2.69795e7i	0.678021	+	0.391456i
$411$	8.32214e7	+	4.80479e7i	1.19870	+	0.692068i
$412$	−8.22730e7	+	2.20450e7i	−1.17643	+	0.315223i
$413$	5.70972e7	+	5.70972e7i	0.810522	+	0.810522i
$414$	6.71285e7	−	1.16270e8i	0.946033	−	1.63858i
$415$	−1.66483e8	−	1.66483e8i	−2.32930	−	2.32930i
$416$	1.10179e7	+	1.90836e7i	0.153045	+	0.265082i
$417$	−1.96090e8			−2.70425
$418$		−	5.51178e7i		−	0.754681i
$419$	−1.01454e7	−	1.75724e7i	−0.137921	−	0.238885i	0.788789	−	0.614664i	$-0.210709\pi$
$419$	−1.01454e7	−	1.75724e7i	−0.137921	−	0.238885i	−0.926709	+	0.375779i	$0.877375\pi$
$420$	−4.85837e8	+	1.30180e8i	−6.55756	+	1.75709i
$421$	6.16408e7	−	6.16408e7i	0.826080	−	0.826080i	−0.160892	−	0.986972i	$-0.551437\pi$
$421$	6.16408e7	−	6.16408e7i	0.826080	−	0.826080i	0.986972	+	0.160892i	$0.0514371\pi$
$422$	5.35252e7	+	1.43420e7i	0.712231	+	0.190842i
$423$	−1.61715e7	−	2.80099e7i	−0.213663	−	0.370076i
$424$	2.96823e7	−	1.10776e8i	0.389403	−	1.45327i
$425$	6.25724e7	+	2.33523e8i	0.815110	+	3.04203i
$426$	2.28875e8	−	6.13268e7i	2.96053	−	0.793271i
$427$	5.65480e7	+	1.51520e7i	0.726329	+	0.194619i
$428$	−1.78326e6	+	1.02956e6i	−0.0227448	+	0.0131317i
$429$	2.14538e7	−	8.00667e7i	0.271727	−	1.01410i
$430$	−7.93098e7	−	7.93098e7i	−0.997520	−	0.997520i
$431$	5.72430e6	+	2.13634e7i	0.0714974	+	0.266832i	0.992416	−	0.122922i	$-0.0392266\pi$
$431$	5.72430e6	+	2.13634e7i	0.0714974	+	0.266832i	−0.920919	+	0.389754i	$0.872560\pi$
$432$	−3.95532e7	+	2.28361e7i	−0.490604	+	0.283250i
$433$	−1.16649e8			−1.43688			−0.718438	−	0.695591i	$-0.755142\pi$
$433$	−1.16649e8			−1.43688			−0.718438	+	0.695591i	$0.755142\pi$
$434$			2.43777e7i			0.298211i
$435$	9.07297e7	−	5.23828e7i	1.10225	−	0.636386i
$436$	−1.81584e7	+	1.81584e7i	−0.219087	+	0.219087i
$437$	−2.02138e7	−	1.16704e7i	−0.242217	−	0.139844i
$438$	−6.81028e7	+	6.81028e7i	−0.810481	+	0.810481i
$439$	1.99481e7	+	7.44474e7i	0.235781	+	0.879946i	0.977795	+	0.209562i	$0.0672039\pi$
$439$	1.99481e7	+	7.44474e7i	0.235781	+	0.879946i	−0.742014	+	0.670384i	$0.766129\pi$
$440$	−1.21320e8	+	2.10132e8i	−1.42421	+	2.46680i
$441$	3.35475e7	−	5.81060e7i	0.391151	−	0.677493i
$442$	2.80284e7	−	1.04603e8i	0.324587	−	1.21137i
$443$			8.82167e7i			1.01470i	0.861739	+	0.507352i	$0.169376\pi$
$443$			8.82167e7i			1.01470i	−0.861739	+	0.507352i	$0.830624\pi$
$444$	6.56651e7	−	2.53262e8i	0.750214	−	2.89349i
$445$	2.29047e7			0.259923
$446$	1.98492e8	+	5.31856e7i	2.23737	+	0.599501i
$447$	−7.82134e7	−	4.51565e7i	−0.875707	−	0.505590i
$448$	1.31729e8	+	7.60539e7i	1.46503	+	0.845838i
$449$	−1.06025e8	+	2.84092e7i	−1.17130	+	0.313848i	−0.791469	−	0.611209i	$-0.790684\pi$
$449$	−1.06025e8	+	2.84092e7i	−1.17130	+	0.313848i	−0.379828	+	0.925057i	$0.624017\pi$
$450$	−4.51276e8	−	4.51276e8i	−4.95227	−	4.95227i
$451$	−1.23687e7	+	2.14233e7i	−0.134833	+	0.233537i
$452$	1.90478e8	+	1.90478e8i	2.06266	+	2.06266i
$453$	3.36896e6	+	5.83520e6i	0.0362411	+	0.0627714i
$454$	−2.36598e8			−2.52838
$455$			1.26859e8i			1.34675i
$456$	4.47642e7	+	7.75339e7i	0.472103	+	0.817706i
$457$	1.76111e8	−	4.71887e7i	1.84517	−	0.494413i	0.845930	−	0.533294i	$-0.179046\pi$
$457$	1.76111e8	−	4.71887e7i	1.84517	−	0.494413i	0.999244	+	0.0388808i	$0.0123793\pi$
$458$	−1.77281e8	+	1.77281e8i	−1.84529	+	1.84529i
$459$	−1.26429e8	−	3.38764e7i	−1.30740	−	0.350316i
$460$	1.13077e8	+	1.95856e8i	1.16172	+	2.01216i
$461$	2.61940e6	−	9.77573e6i	0.0267362	−	0.0997807i	−0.951268	−	0.308364i	$-0.900219\pi$
$461$	2.61940e6	−	9.77573e6i	0.0267362	−	0.0997807i	0.978005	+	0.208583i	$0.0668852\pi$
$462$	−9.22461e7	−	3.44267e8i	−0.935453	−	3.49116i
$463$	9.39773e6	−	2.51811e6i	0.0946847	−	0.0253707i	−0.211166	−	0.977450i	$-0.567726\pi$
$463$	9.39773e6	−	2.51811e6i	0.0946847	−	0.0253707i	0.305850	+	0.952080i	$0.401059\pi$
$464$	2.11494e7	+	5.66695e6i	0.211711	+	0.0567278i
$465$	−3.88488e7	+	2.24294e7i	−0.386383	+	0.223079i
$466$	4.24529e7	−	1.58436e8i	0.419517	−	1.56566i
$467$	1.06436e8	+	1.06436e8i	1.04506	+	1.04506i	0.998936	+	0.0461191i	$0.0146854\pi$
$467$	1.06436e8	+	1.06436e8i	1.04506	+	1.04506i	0.0461191	+	0.998936i	$0.485315\pi$
$468$	4.78690e7	+	1.78650e8i	0.467000	+	1.74287i
$469$	1.04240e8	−	6.01829e7i	1.01045	−	0.583384i
$470$	8.42099e7			0.811091
$471$		−	1.91696e8i		−	1.83463i
$472$	−1.20604e8	+	6.96309e7i	−1.14693	+	0.662180i
$473$	3.63595e7	−	3.63595e7i	0.343585	−	0.343585i
$474$	1.32726e8	+	7.66295e7i	1.24630	+	0.719550i
$475$	−7.84554e7	+	7.84554e7i	−0.732052	+	0.732052i
$476$	−7.79700e7	−	2.90988e8i	−0.722947	−	2.69808i
$477$	−9.67338e7	+	1.67548e8i	−0.891298	+	1.54377i
$478$	2.82812e7	−	4.89845e7i	0.258949	−	0.448513i
$479$	5.03263e7	−	1.87820e8i	0.457919	−	1.70898i	−0.221443	−	0.975173i	$-0.571077\pi$
$479$	5.03263e7	−	1.87820e8i	0.457919	−	1.70898i	0.679362	−	0.733803i	$-0.262257\pi$
$480$			1.74352e8i			1.57653i
$481$	−5.74138e7	−	3.25300e7i	−0.515919	−	0.292314i
$482$	1.87022e7			0.167014
$483$	−1.45788e8	−	3.90637e7i	−1.29384	−	0.346682i
$484$	−3.20849e7	−	1.85243e7i	−0.282986	−	0.163382i
$485$	−3.10516e8	−	1.79277e8i	−2.72182	−	1.57144i
$486$	−1.71643e8	+	4.59917e7i	−1.49527	+	0.400655i
$487$	−7.96324e7	−	7.96324e7i	−0.689451	−	0.689451i	0.272660	−	0.962110i	$-0.412097\pi$
$487$	−7.96324e7	−	7.96324e7i	−0.689451	−	0.689451i	−0.962110	+	0.272660i	$0.912097\pi$
$488$	−5.04830e7	+	8.74391e7i	−0.434396	+	0.752396i
$489$	2.48198e8	+	2.48198e8i	2.12261	+	2.12261i
$490$	8.73458e7	+	1.51287e8i	0.742427	+	1.28592i
$491$	1.65417e8			1.39745			0.698725	−	0.715391i	$-0.253751\pi$
$491$	1.65417e8			1.39745			0.698725	+	0.715391i	$0.253751\pi$
$492$		−	8.84387e7i		−	0.742587i
$493$	3.13742e7	+	5.43418e7i	0.261838	+	0.453517i
$494$	4.80061e7	−	1.28632e7i	0.398213	−	0.106701i
$495$	2.89437e8	−	2.89437e8i	2.38637	−	2.38637i
$496$	−9.05577e6	−	2.42649e6i	−0.0742130	−	0.0198853i
$497$	−8.31241e7	−	1.43975e8i	−0.677108	−	1.17279i
$498$	−1.54374e8	+	5.76131e8i	−1.24993	+	4.66480i
$499$	1.37986e7	+	5.14969e7i	0.111053	+	0.414457i	0.998961	−	0.0455639i	$-0.0145085\pi$
$499$	1.37986e7	+	5.14969e7i	0.111053	+	0.414457i	−0.887908	+	0.460021i	$0.847842\pi$
$500$	6.24076e8	−	1.67221e8i	4.99261	−	1.33776i
$501$	1.23857e8	+	3.31873e7i	0.984934	+	0.263912i
$502$	1.46680e8	−	8.46856e7i	1.15947	−	0.669420i
$503$	−2.90942e7	+	1.08581e8i	−0.228614	+	0.853199i	0.752310	+	0.658809i	$0.228939\pi$
$503$	−2.90942e7	+	1.08581e8i	−0.228614	+	0.853199i	−0.980924	+	0.194390i	$0.937727\pi$
$504$	2.55487e8	+	2.55487e8i	1.99562	+	1.99562i
$505$	−9.69975e7	−	3.62000e8i	−0.753158	−	2.81083i
$506$	−1.38784e8	+	8.01272e7i	−1.07125	+	0.618484i
$507$	−1.37824e8			−1.05755
$508$		−	1.40134e8i		−	1.06894i
$509$	−1.87003e8	+	1.07966e8i	−1.41806	+	0.818718i	−0.996129	−	0.0879087i	$-0.971982\pi$
$509$	−1.87003e8	+	1.07966e8i	−1.41806	+	0.818718i	−0.421933	+	0.906627i	$0.638648\pi$
$510$	6.05877e8	−	6.05877e8i	4.56745	−	4.56745i
$511$	5.85213e7	+	3.37873e7i	0.438582	+	0.253215i
$512$	−9.57163e7	+	9.57163e7i	−0.713142	+	0.713142i
$513$	−1.55471e7	−	5.80224e7i	−0.115159	−	0.429778i
$514$	−5.95494e7	+	1.03143e8i	−0.438519	+	0.759537i
$515$	−8.49874e7	+	1.47202e8i	−0.622204	+	1.07769i
$516$	−4.75791e7	+	1.77568e8i	−0.346312	+	1.29245i
$517$			3.86059e7i			0.279372i
$518$	−2.83727e8	+	2.30077e6i	−2.04132	+	0.0165533i
$519$	1.29514e8			0.926431
$520$	−2.11332e8	−	5.66263e7i	−1.50299	−	0.402724i
$521$	1.50457e8	+	8.68666e7i	1.06390	+	0.614242i	0.926508	−	0.376275i	$-0.122795\pi$
$521$	1.50457e8	+	8.68666e7i	1.06390	+	0.614242i	0.137390	+	0.990517i	$0.456129\pi$
$522$	−1.43451e8	−	8.28217e7i	−1.00854	−	0.582281i
$523$	−4.26940e7	+	1.14398e7i	−0.298443	+	0.0799676i	−0.404934	−	0.914346i	$-0.632705\pi$
$523$	−4.26940e7	+	1.14398e7i	−0.298443	+	0.0799676i	0.106490	+	0.994314i	$0.466039\pi$
$524$	−1.00184e8	−	1.00184e8i	−0.696314	−	0.696314i
$525$	−3.58729e8	+	6.21338e8i	−2.47907	+	4.29388i
$526$	−2.02638e8	−	2.02638e8i	−1.39240	−	1.39240i
$527$	−1.34339e7	−	2.32682e7i	−0.0917845	−	0.158975i
$528$	1.37069e8			0.931191
$529$		−	8.01725e7i		−	0.541575i
$530$	−2.51860e8	−	4.36235e8i	−1.69173	−	2.93017i
$531$	2.26925e8	−	6.08045e7i	1.51565	−	0.406118i
$532$	9.77614e7	−	9.77614e7i	0.649280	−	0.649280i
$533$	−2.15456e7	−	5.77314e6i	−0.142291	−	0.0381268i
$534$	−2.90126e7	−	5.02513e7i	−0.190530	−	0.330007i
$535$	−1.06353e6	+	3.96915e6i	−0.00694527	+	0.0259201i
$536$	5.37281e7	+	2.00516e8i	0.348905	+	1.30213i
$537$	−4.45245e8	+	1.19303e8i	−2.87526	+	0.770423i
$538$	−4.26363e8	−	1.14244e8i	−2.73799	−	0.733643i
$539$	−6.93575e7	+	4.00436e7i	−0.442922	+	0.255721i
$540$	−1.50639e8	+	5.62191e8i	−0.956654	+	3.57028i
$541$	7.37227e7	+	7.37227e7i	0.465596	+	0.465596i	0.900484	−	0.434888i	$-0.143212\pi$
$541$	7.37227e7	+	7.37227e7i	0.465596	+	0.465596i	−0.434888	+	0.900484i	$0.643212\pi$
$542$	1.54837e7	+	5.77859e7i	0.0972470	+	0.362931i
$543$	2.33921e8	−	1.35054e8i	1.46106	−	0.843545i
$544$	−1.04427e8			−0.648656
$545$			5.12463e7i			0.316572i
$546$	2.78319e8	−	1.60687e8i	1.70988	−	0.987197i
$547$	3.33150e6	−	3.33150e6i	0.0203553	−	0.0203553i	−0.696856	−	0.717211i	$-0.745418\pi$
$547$	3.33150e6	−	3.33150e6i	0.0203553	−	0.0203553i	0.717211	+	0.696856i	$0.245418\pi$
$548$	2.21645e8	+	1.27967e8i	1.34684	+	0.777599i
$549$	1.20439e8	−	1.20439e8i	0.727864	−	0.727864i
$550$	1.97163e8	+	7.35824e8i	1.18505	+	4.42268i
$551$	−1.43987e7	+	2.49393e7i	−0.0860735	+	0.149084i
$552$	1.30151e8	−	2.25429e8i	0.773805	−	1.34027i
$553$	2.78308e7	−	1.03866e8i	0.164570	−	0.614182i
$554$		−	7.76202e7i		−	0.456505i
$555$	−2.64717e8	−	4.50036e8i	−1.54847	−	2.63250i
$556$	−5.22250e8			−3.03846
$557$	3.01267e8	+	8.07243e7i	1.74336	+	0.467131i	0.983188	−	0.182594i	$-0.0584495\pi$
$557$	3.01267e8	+	8.07243e7i	1.74336	+	0.467131i	0.760169	+	0.649725i	$0.225116\pi$
$558$	6.14232e7	+	3.54627e7i	0.353533	+	0.204112i
$559$	4.01535e7	+	2.31827e7i	0.229873	+	0.132717i
$560$	−2.02626e8	+	5.42936e7i	−1.15380	+	0.309161i
$561$	2.77764e8	+	2.77764e8i	1.57321	+	1.57321i
$562$	2.59419e8	−	4.49327e8i	1.46148	−	2.53136i
$563$	−6.94782e7	−	6.94782e7i	−0.389335	−	0.389335i	0.485115	−	0.874450i	$-0.338778\pi$
$563$	−6.94782e7	−	6.94782e7i	−0.389335	−	0.389335i	−0.874450	+	0.485115i	$0.838778\pi$
$564$	−6.90099e7	−	1.19529e8i	−0.384657	−	0.666246i
$565$	5.37563e8			2.98047
$566$		−	3.46268e8i		−	1.90969i
$567$	−1.06642e7	−	1.84710e7i	−0.0585033	−	0.101331i
$568$	2.76951e8	−	7.42088e7i	1.51133	−	0.404958i
$569$	−1.23178e8	+	1.23178e8i	−0.668648	+	0.668648i	−0.957403	−	0.288755i	$-0.906759\pi$
$569$	−1.23178e8	+	1.23178e8i	−0.668648	+	0.668648i	0.288755	+	0.957403i	$0.406759\pi$
$570$	3.79834e8	+	1.01776e8i	2.05102	+	0.549568i
$571$	9.41299e7	+	1.63038e8i	0.505614	+	0.875749i	0.999979	+	0.00649484i	$0.00206739\pi$
$571$	9.41299e7	+	1.63038e8i	0.505614	+	0.875749i	−0.494365	+	0.869255i	$0.664599\pi$
$572$	5.71383e7	−	2.13243e8i	0.305309	−	1.13943i
$573$	−5.81931e7	−	2.17180e8i	−0.309320	−	1.15440i
$574$	−9.26409e7	+	2.48231e7i	−0.489855	+	0.131256i
$575$	3.11601e8	+	8.34933e7i	1.63906	+	0.439186i
$576$	3.83258e8	−	2.21274e8i	2.00551	−	1.15788i
$577$	−6.93697e7	+	2.58891e8i	−0.361112	+	1.34769i	0.511503	+	0.859282i	$0.329089\pi$
$577$	−6.93697e7	+	2.58891e8i	−0.361112	+	1.34769i	−0.872615	+	0.488408i	$0.837578\pi$
$578$	1.33077e8	+	1.33077e8i	0.689160	+	0.689160i
$579$	1.13748e7	+	4.24512e7i	0.0586012	+	0.218703i
$580$	2.41642e8	−	1.39512e8i	1.23848	−	0.715036i
$581$	4.18485e8			2.13379
$582$			9.08335e8i			4.60762i
$583$	1.99992e8	−	1.15465e8i	1.00927	−	0.582701i
$584$	−8.24081e7	+	8.24081e7i	−0.413744	+	0.413744i
$585$	3.19639e8	+	1.84544e8i	1.59659	+	0.921789i
$586$	−7.74157e7	+	7.74157e7i	−0.384712	+	0.384712i
$587$	2.21523e7	+	8.26733e7i	0.109523	+	0.408744i	0.998819	−	0.0485876i	$-0.0154720\pi$
$587$	2.21523e7	+	8.26733e7i	0.109523	+	0.408744i	−0.889296	+	0.457331i	$0.848805\pi$
$588$	1.43159e8	−	2.47960e8i	0.704187	−	1.21969i
$589$	6.16527e6	−	1.06786e7i	0.0301722	−	0.0522597i
$590$	−1.58313e8	+	5.90833e8i	−0.770834	+	2.87679i
$591$		−	5.59570e7i		−	0.271077i
$592$	2.73867e7	−	1.05627e8i	0.132000	−	0.509109i
$593$	−1.96820e8			−0.943854			−0.471927	−	0.881638i	$-0.656441\pi$
$593$	−1.96820e8			−0.943854			−0.471927	+	0.881638i	$0.656441\pi$
$594$	−3.98372e8	−	1.06743e8i	−1.90077	−	0.509310i
$595$	−5.20634e8	−	3.00588e8i	−2.47162	−	1.42699i
$596$	−2.08307e8	−	1.20266e8i	−0.983934	−	0.568074i
$597$	−2.61678e8	+	7.01165e7i	−1.22983	+	0.329532i
$598$	−1.02178e8	−	1.02178e8i	−0.477806	−	0.477806i
$599$	−1.63340e8	+	2.82913e8i	−0.759996	+	1.31635i	0.182855	+	0.983140i	$0.441466\pi$
$599$	−1.63340e8	+	2.82913e8i	−0.759996	+	1.31635i	−0.942852	+	0.333213i	$0.891867\pi$
$600$	−8.74951e8	−	8.74951e8i	−4.05070	−	4.05070i
$601$	−1.25755e8	−	2.17815e8i	−0.579300	−	1.00338i	−0.995560	−	0.0941309i	$-0.969993\pi$
$601$	−1.25755e8	−	2.17815e8i	−0.579300	−	1.00338i	0.416260	−	0.909246i	$-0.363341\pi$
$602$	1.99359e8			0.913792
$603$		−	3.50197e8i		−	1.59720i
$604$	8.97261e6	+	1.55410e7i	0.0407200	+	0.0705291i
$605$	−7.14143e7	+	1.91354e7i	−0.322492	+	0.0864115i
$606$	−6.71338e8	+	6.71338e8i	−3.01664	+	3.01664i
$607$	−2.35777e8	−	6.31763e7i	−1.05423	−	0.282480i	−0.310232	−	0.950661i	$-0.600407\pi$
$607$	−2.35777e8	−	6.31763e7i	−1.05423	−	0.282480i	−0.743999	+	0.668180i	$0.767073\pi$
$608$	−2.39625e7	−	4.15043e7i	−0.106616	−	0.184664i
$609$	−4.81959e7	+	1.79869e8i	−0.213382	+	0.796353i
$610$	1.14778e8	+	4.28359e8i	0.505674	+	1.88720i
$611$	−3.36247e7	+	9.00971e6i	−0.147413	+	0.0394991i
$612$	−8.46612e8	−	2.26849e8i	−3.69343	−	0.989652i
$613$	−9.72722e7	+	5.61601e7i	−0.422287	+	0.243807i	−0.696055	−	0.717988i	$-0.745063\pi$
$613$	−9.72722e7	+	5.61601e7i	−0.422287	+	0.243807i	0.273769	+	0.961796i	$0.411730\pi$
$614$	−2.46556e7	+	9.20160e7i	−0.106515	+	0.397519i
$615$	−1.24795e8	−	1.24795e8i	−0.536504	−	0.536504i
$616$	−1.11623e8	−	4.16582e8i	−0.477541	−	1.78221i
$617$	−2.20956e8	+	1.27569e8i	−0.940699	+	0.543113i	−0.890179	−	0.455610i	$-0.849421\pi$
$617$	−2.20956e8	+	1.27569e8i	−0.940699	+	0.543113i	−0.0505198	+	0.998723i	$0.516088\pi$
$618$	4.30602e8			1.82436
$619$		−	3.02047e8i		−	1.27351i	−0.771066	−	0.636756i	$-0.780276\pi$
$619$		−	3.02047e8i		−	1.27351i	0.771066	−	0.636756i	$-0.219724\pi$
$620$	−1.03467e8	+	5.97365e7i	−0.434136	+	0.250648i
$621$	−1.23497e8	+	1.23497e8i	−0.515680	+	0.515680i
$622$	3.69926e7	+	2.13577e7i	0.153725	+	0.0887529i
$623$	−2.87875e7	+	2.87875e7i	−0.119053	+	0.119053i
$624$	3.19887e7	+	1.19384e8i	0.131657	+	0.491350i
$625$	3.38731e8	−	5.86700e8i	1.38744	−	2.40312i
$626$	3.73130e8	−	6.46281e8i	1.52103	−	2.63450i
$627$	−4.66592e7	+	1.74135e8i	−0.189293	+	0.706452i
$628$		−	5.10547e8i		−	2.06137i
$629$	2.69546e8	−	1.58550e8i	1.08313	−	0.637111i
$630$	1.58698e9			6.34674
$631$	−3.74701e7	−	1.00401e7i	−0.149141	−	0.0399622i	0.183476	−	0.983024i	$-0.441265\pi$
$631$	−3.74701e7	−	1.00401e7i	−0.149141	−	0.0399622i	−0.332617	+	0.943062i	$0.607932\pi$
$632$	1.60606e8	+	9.27259e7i	0.636225	+	0.367324i
$633$	−1.56962e8	−	9.06219e7i	−0.618846	−	0.357291i
$634$	1.16954e8	−	3.13376e7i	0.458929	−	0.122970i
$635$	−1.97742e8	−	1.97742e8i	−0.772284	−	0.772284i
$636$	−4.12799e8	+	7.14988e8i	−1.60460	+	2.77925i
$637$	−5.10632e7	−	5.10632e7i	−0.197556	−	0.197556i
$638$	9.88592e7	+	1.71229e8i	0.380675	+	0.659349i
$639$	−4.83689e8			−1.85380
$640$			8.98859e8i			3.42888i
$641$	−1.11418e8	−	1.92982e8i	−0.423041	−	0.732729i	0.573194	−	0.819420i	$-0.305704\pi$
$641$	−1.11418e8	−	1.92982e8i	−0.423041	−	0.732729i	−0.996235	+	0.0866909i	$0.972371\pi$
$642$	1.00552e7	−	2.69428e6i	0.0380001	−	0.0101821i
$643$	5.29955e7	−	5.29955e7i	0.199345	−	0.199345i	−0.600374	−	0.799719i	$-0.704982\pi$
$643$	5.29955e7	−	5.29955e7i	0.199345	−	0.199345i	0.799719	+	0.600374i	$0.204982\pi$
$644$	−3.88279e8	−	1.04039e8i	−1.45374	−	0.389528i
$645$	1.83426e8	+	3.17703e8i	0.683568	+	1.18397i
$646$	−6.09580e7	+	2.27498e8i	−0.226117	+	0.843880i
$647$	−5.92181e7	−	2.21005e8i	−0.218646	−	0.815999i	−0.984851	−	0.173402i	$-0.944524\pi$
$647$	−5.92181e7	−	2.21005e8i	−0.218646	−	0.815999i	0.766205	−	0.642596i	$-0.222143\pi$
$648$	3.55308e7	−	9.52045e6i	0.130581	−	0.0349891i
$649$	−2.70867e8	−	7.25786e7i	−0.990882	−	0.265506i
$650$	−5.94869e8	+	3.43448e8i	−2.16611	+	1.25061i
$651$	2.06366e7	−	7.70168e7i	0.0747989	−	0.279153i
$652$	6.61030e8	+	6.61030e8i	2.38494	+	2.38494i
$653$	5.88826e7	+	2.19753e8i	0.211469	+	0.789215i	0.987380	+	0.158371i	$0.0506243\pi$
$653$	5.88826e7	+	2.19753e8i	0.211469	+	0.789215i	−0.775910	+	0.630843i	$0.782709\pi$
$654$	1.12431e8	−	6.49119e7i	0.401931	−	0.232055i
$655$	−2.82738e8			−1.00615
$656$		−	3.68848e7i		−	0.130658i
$657$	1.70264e8	−	9.83020e7i	0.600381	−	0.346630i
$658$	−1.05838e8	+	1.05838e8i	−0.371506	+	0.371506i
$659$	−5.70227e7	−	3.29221e7i	−0.199247	−	0.115035i	0.397057	−	0.917794i	$-0.370031\pi$
$659$	−5.70227e7	−	3.29221e7i	−0.199247	−	0.115035i	−0.596304	+	0.802759i	$0.703365\pi$
$660$	1.23513e9	−	1.23513e9i	4.29618	−	4.29618i
$661$	−9.71076e7	−	3.62410e8i	−0.336240	−	1.25486i	−0.902519	−	0.430650i	$-0.858284\pi$
$661$	−9.71076e7	−	3.62410e8i	−0.336240	−	1.25486i	0.566279	−	0.824213i	$-0.308382\pi$
$662$	2.16945e8	−	3.75759e8i	0.747782	−	1.29520i
$663$	−1.77101e8	+	3.06748e8i	−0.607687	+	1.05254i
$664$	−1.86801e8	+	6.97150e8i	−0.638079	+	2.38134i
$665$		−	2.75901e8i		−	0.938184i
$666$	−4.06946e8	+	7.18240e8i	−1.37757	+	2.43135i
$667$	8.37283e7			0.282160
$668$	3.29870e8	+	8.83885e7i	1.10666	+	0.296528i
$669$	−5.82074e8	−	3.36060e8i	−1.94401	−	1.12238i
$670$	7.89632e8	+	4.55894e8i	2.62543	+	1.51579i
$671$	−1.96381e8	+	5.26201e7i	−0.650027	+	0.174174i
$672$	−2.19132e8	−	2.19132e8i	−0.722103	−	0.722103i
$673$	−7.92639e7	+	1.37289e8i	−0.260034	+	0.450392i	−0.966251	−	0.257603i	$-0.917067\pi$
$673$	−7.92639e7	+	1.37289e8i	−0.260034	+	0.450392i	0.706217	+	0.707996i	$0.250401\pi$
$674$	2.58732e8	+	2.58732e8i	0.845025	+	0.845025i
$675$	4.15107e8	+	7.18987e8i	1.34974	+	2.33781i
$676$	−3.67070e8			−1.18825
$677$			2.02833e8i			0.653691i	0.945078	+	0.326846i	$0.105986\pi$
$677$			2.02833e8i			0.653691i	−0.945078	+	0.326846i	$0.894014\pi$
$678$	−6.80913e8	−	1.17938e9i	−2.18475	−	3.78411i
$679$	6.15592e8	−	1.64947e8i	1.96645	−	0.526909i
$680$	7.33144e8	−	7.33144e8i	2.33164	−	2.33164i
$681$	7.47486e8	+	2.00288e8i	2.36680	+	0.634183i
$682$	−4.23297e7	−	7.33172e7i	−0.133442	−	0.231128i
$683$	1.14805e7	−	4.28456e7i	0.0360327	−	0.134476i	−0.945566	−	0.325429i	$-0.894491\pi$
$683$	1.14805e7	−	4.28456e7i	0.0360327	−	0.134476i	0.981599	+	0.190953i	$0.0611579\pi$
$684$	−1.04109e8	−	3.88540e8i	−0.325327	−	1.21414i
$685$	4.93335e8	−	1.32189e8i	1.53487	−	0.411266i
$686$	3.36641e8	+	9.02026e7i	1.04278	+	0.279413i
$687$	7.10159e8	−	4.10011e8i	2.19021	−	1.26452i
$688$	−1.98437e7	+	7.40575e7i	−0.0609335	+	0.227407i
$689$	1.47240e8	+	1.47240e8i	0.450162	+	0.450162i
$690$	−2.95913e8	−	1.10436e9i	−0.900776	−	3.36174i
$691$	1.40200e8	−	8.09447e7i	0.424928	−	0.245332i	−0.272256	−	0.962225i	$-0.587770\pi$
$691$	1.40200e8	−	8.09447e7i	0.424928	−	0.245332i	0.697183	+	0.716893i	$0.254436\pi$
$692$	3.44936e8			1.04093
$693$			7.27552e8i			2.18607i
$694$	−3.95194e8	+	2.28165e8i	−1.18231	+	0.682607i
$695$	−7.36944e8	+	7.36944e8i	−2.19523	+	2.19523i
$696$	−2.78129e8	−	1.60578e8i	−0.824933	−	0.476275i
$697$	7.47451e7	−	7.47451e7i	0.220742	−	0.220742i
$698$	1.47179e8	+	5.49281e8i	0.432793	+	1.61521i
$699$	−2.68244e8	+	4.64612e8i	−0.785414	+	1.36038i
$700$	−9.55411e8	+	1.65482e9i	−2.78545	+	4.82455i
$701$	6.90203e7	−	2.57587e8i	0.200365	−	0.747774i	−0.790447	−	0.612530i	$-0.790152\pi$
$701$	6.90203e7	−	2.57587e8i	0.200365	−	0.747774i	0.990812	−	0.135243i	$-0.0431816\pi$
$702$		−	3.71882e8i		−	1.07496i
$703$	1.24868e8	+	7.07486e7i	0.359405	+	0.203635i
$704$	−5.28243e8			−1.51396
$705$	−2.66045e8	−	7.12867e7i	−0.759256	−	0.203442i
$706$	9.22989e7	+	5.32888e7i	0.262290	+	0.151433i
$707$	5.76886e8	+	3.33065e8i	1.63242	+	0.942477i
$708$	9.68374e8	−	2.59475e8i	2.72862	−	0.731132i
$709$	2.20276e8	+	2.20276e8i	0.618057	+	0.618057i	0.945033	−	0.326976i	$-0.106029\pi$
$709$	2.20276e8	+	2.20276e8i	0.618057	+	0.618057i	−0.326976	+	0.945033i	$0.606029\pi$
$710$	6.29678e8	−	1.09063e9i	1.75931	−	3.04722i
$711$	−2.21219e8	−	2.21219e8i	−0.615481	−	0.615481i
$712$	−3.51068e7	−	6.08067e7i	−0.0972638	−	0.168466i
$713$	−3.58509e7			−0.0989081
$714$			1.52298e9i			4.18408i
$715$	−2.20278e8	−	3.81534e8i	−0.602634	−	1.04379i
$716$	−1.18583e9	+	3.17742e8i	−3.23060	+	0.865638i
$717$	−1.30816e8	+	1.30816e8i	−0.354899	+	0.354899i
$718$	−9.49512e8	−	2.54421e8i	−2.56524	−	0.687353i
$719$	−2.50163e8	−	4.33296e8i	−0.673034	−	1.16573i	−0.977039	−	0.213059i	$-0.931657\pi$
$719$	−2.50163e8	−	4.33296e8i	−0.673034	−	1.16573i	0.304005	−	0.952670i	$-0.401676\pi$
$720$	−1.57964e8	+	5.89529e8i	−0.423214	+	1.57946i
$721$	−7.81944e7	−	2.91825e8i	−0.208627	−	0.778605i
$722$	5.07452e8	−	1.35971e8i	1.34829	−	0.361273i
$723$	−5.90863e7	−	1.58321e7i	−0.156341	−	0.0418913i
$724$	6.23005e8	−	3.59692e8i	1.64163	−	0.947797i
$725$	1.03012e8	−	3.84447e8i	0.270318	−	1.00884i
$726$	1.32440e8	+	1.32440e8i	0.346106	+	0.346106i
$727$	−4.95981e7	−	1.85103e8i	−0.129081	−	0.481737i	0.870871	−	0.491511i	$-0.163555\pi$
$727$	−4.95981e7	−	1.85103e8i	−0.129081	−	0.481737i	−0.999952	+	0.00977458i	$0.996889\pi$
$728$	3.36781e8	−	1.94441e8i	0.872877	−	0.503956i
$729$	6.18582e8			1.59667
$730$			5.11887e8i			1.31585i
$731$	−1.90286e8	+	1.09861e8i	−0.487140	+	0.281251i
$732$	5.13958e8	−	5.13958e8i	1.31037	−	1.31037i
$733$	−1.12615e8	−	6.50185e7i	−0.285947	−	0.165091i	0.350166	−	0.936688i	$-0.386125\pi$
$733$	−1.12615e8	−	6.50185e7i	−0.285947	−	0.165091i	−0.636113	+	0.771596i	$0.719459\pi$
$734$	1.33272e8	−	1.33272e8i	0.337015	−	0.337015i
$735$	−1.47883e8	−	5.51905e8i	−0.372439	−	1.38996i
$736$	−6.96707e7	+	1.20673e8i	−0.174750	+	0.302676i
$737$	−2.09004e8	+	3.62006e8i	−0.522099	+	0.904302i
$738$	−7.22212e7	+	2.69533e8i	−0.179678	+	0.670569i
$739$			4.18466e8i			1.03688i	0.855115	+	0.518438i	$0.173486\pi$
$739$			4.18466e8i			1.03688i	−0.855115	+	0.518438i	$0.826514\pi$
$740$	−7.05027e8	−	1.19859e9i	−1.73985	−	2.95785i
$741$	−1.62555e8			−0.399528
$742$	8.64826e8	+	2.31729e8i	2.11698	+	0.567243i
$743$	1.36793e8	+	7.89776e7i	0.333502	+	0.192547i	0.657395	−	0.753546i	$-0.271658\pi$
$743$	1.36793e8	+	7.89776e7i	0.333502	+	0.192547i	−0.323893	+	0.946094i	$0.604992\pi$
$744$	1.19090e8	+	6.87565e7i	0.289172	+	0.166953i
$745$	−4.63648e8	+	1.24234e8i	−1.12129	+	0.300450i
$746$	3.88183e8	+	3.88183e8i	0.935019	+	0.935019i
$747$	6.08779e8	−	1.05444e9i	1.46049	−	2.52964i
$748$	7.39773e8	+	7.39773e8i	1.76764	+	1.76764i
$749$	−3.65190e6	−	6.32528e6i	−0.00869108	−	0.0150534i
$750$	−3.26630e9			−7.74235
$751$			9.37899e7i			0.221430i	0.993852	+	0.110715i	$0.0353141\pi$
$751$			9.37899e7i			0.221430i	−0.993852	+	0.110715i	$0.964686\pi$
$752$	−2.87817e7	−	4.98514e7i	−0.0676804	−	0.117226i
$753$	−5.35097e8	+	1.43379e8i	−1.25328	+	0.335815i
$754$	−1.26064e8	+	1.26064e8i	−0.294089	+	0.294089i
$755$	3.45910e7	+	9.26863e6i	0.0803753	+	0.0215365i
$756$	−5.17255e8	−	8.95912e8i	−1.19713	−	2.07348i
$757$	−4.70579e7	+	1.75623e8i	−0.108479	+	0.404849i	−0.998717	−	0.0506476i	$-0.983871\pi$
$757$	−4.70579e7	+	1.75623e8i	−0.108479	+	0.404849i	0.890238	+	0.455496i	$0.150538\pi$
$758$	−2.20679e8	−	8.23587e8i	−0.506704	−	1.89104i
$759$	5.06294e8	−	1.35661e8i	1.15792	−	0.310263i
$760$	4.59620e8	+	1.23155e8i	1.04703	+	0.280550i
$761$	8.74322e7	−	5.04790e7i	0.198389	−	0.114540i	−0.397515	−	0.917596i	$-0.630127\pi$
$761$	8.74322e7	−	5.04790e7i	0.198389	−	0.114540i	0.595904	+	0.803056i	$0.296794\pi$
$762$	−1.83359e8	+	6.84304e8i	−0.414416	+	1.54662i
$763$	−6.44084e7	−	6.44084e7i	−0.145000	−	0.145000i
$764$	−1.54987e8	−	5.78419e8i	−0.347548	−	1.29707i
$765$	−1.51475e9	+	8.74543e8i	−3.38343	+	1.95343i
$766$	−3.29770e8			−0.733711
$767$		−	2.52855e8i		−	0.560385i
$768$	1.07961e9	−	6.23311e8i	2.38332	−	1.37601i
$769$	3.11366e8	−	3.11366e8i	0.684688	−	0.684688i	−0.276365	−	0.961053i	$-0.589130\pi$
$769$	3.11366e8	−	3.11366e8i	0.684688	−	0.684688i	0.961053	+	0.276365i	$0.0891298\pi$
$770$	−1.64050e9	−	9.47143e8i	−3.59339	−	2.07464i
$771$	2.75449e8	−	2.75449e8i	0.601006	−	0.601006i
$772$	3.02946e7	+	1.13061e8i	0.0658436	+	0.245732i
$773$	−5.45991e7	+	9.45685e7i	−0.118208	+	0.204742i	−0.919058	−	0.394123i	$-0.871048\pi$
$773$	−5.45991e7	+	9.45685e7i	−0.118208	+	0.204742i	0.800850	+	0.598866i	$0.204382\pi$
$774$	2.90012e8	−	5.02316e8i	0.625451	−	1.08331i
$775$	−4.41079e7	+	1.64613e8i	−0.0947570	+	0.353638i
$776$			1.09913e9i			2.35215i
$777$	8.98331e8	+	2.32916e8i	1.91502	+	0.496520i
$778$	−4.49134e8			−0.953755
$779$	4.68590e7	+	1.25558e7i	0.0991243	+	0.0265603i
$780$	1.36402e9	+	7.87516e8i	2.87433	+	1.65949i
$781$	5.00000e8	+	2.88675e8i	1.04958	+	0.605977i
$782$	6.61449e8	−	1.77235e8i	1.38317	−	0.370620i
$783$	1.52367e8	+	1.52367e8i	0.317400	+	0.317400i
$784$	5.97070e7	−	1.03416e8i	0.123902	−	0.214604i
$785$	−7.20429e8	−	7.20429e8i	−1.48930	−	1.48930i
$786$	3.58135e8	+	6.20308e8i	0.737529	+	1.27744i
$787$	5.58739e8			1.14626			0.573132	−	0.819463i	$-0.305728\pi$
$787$	5.58739e8			1.14626			0.573132	+	0.819463i	$0.305728\pi$
$788$		−	1.49031e8i		−	0.304578i
$789$	4.68657e8	+	8.11738e8i	0.954167	+	1.65267i
$790$	7.86799e8	−	2.10822e8i	1.59582	−	0.427597i
$791$	−6.75631e8	+	6.75631e8i	−1.36515	+	1.36515i
$792$	−1.21202e9	−	3.24760e8i	−2.43969	−	0.653712i
$793$	−9.16612e7	−	1.58762e8i	−0.183809	−	0.318366i
$794$	3.77492e8	−	1.40882e9i	0.754130	−	2.81445i
$795$	4.26418e8	+	1.59141e9i	0.848660	+	3.16724i
$796$	−6.96933e8	+	1.86743e8i	−1.38182	+	0.370258i
$797$	−1.18310e8	−	3.17010e7i	−0.233693	−	0.0626179i	0.140072	−	0.990141i	$-0.455267\pi$
$797$	−1.18310e8	−	3.17010e7i	−0.233693	−	0.0626179i	−0.373765	+	0.927523i	$0.621933\pi$
$798$	−6.05307e8	+	3.49474e8i	−1.19115	+	0.687712i
$799$	4.26966e7	−	1.59346e8i	0.0837052	−	0.312392i
$800$	4.68366e8	+	4.68366e8i	0.914777	+	0.914777i
$801$	3.06567e7	+	1.14412e8i	0.0596523	+	0.222625i
$802$	2.87003e8	−	1.65701e8i	0.556370	−	0.321221i
$803$	−2.34674e8			−0.453230
$804$		−	1.49442e9i		−	2.87544i
$805$	−6.94707e8	+	4.01089e8i	−1.33172	+	0.768871i
$806$	5.39784e7	−	5.39784e7i	0.103090	−	0.103090i
$807$	1.25030e9	+	7.21863e8i	2.37900	+	1.37352i
$808$	−8.12356e8	+	8.12356e8i	−1.53997	+	1.53997i
$809$	−2.28776e8	−	8.53802e8i	−0.432080	−	1.61254i	−0.747959	−	0.663745i	$-0.768966\pi$
$809$	−2.28776e8	−	8.53802e8i	−0.432080	−	1.61254i	0.315879	−	0.948800i	$-0.397701\pi$
$810$	8.07831e7	−	1.39920e8i	0.152008	−	0.263285i
$811$	−3.56771e8	+	6.17945e8i	−0.668847	+	1.15848i	0.309380	+	0.950939i	$0.399879\pi$
$811$	−3.56771e8	+	6.17945e8i	−0.668847	+	1.15848i	−0.978227	+	0.207538i	$0.933455\pi$
$812$	−1.28361e8	+	4.79050e8i	−0.239754	+	0.894772i
$813$		−	1.95671e8i		−	0.364129i
$814$	8.49329e8	−	4.99587e8i	1.57472	−	0.926270i
$815$	1.86555e9			3.44615
$816$	−5.65753e8	−	1.51593e8i	−1.04125	−	0.279003i
$817$	−8.73287e7	−	5.04193e7i	−0.160137	−	0.0924550i
$818$	−1.08881e9	−	6.28626e8i	−1.98927	−	1.14850i
$819$	−6.33677e8	+	1.69793e8i	−1.15350	+	0.309078i
$820$	−3.32370e8	−	3.32370e8i	−0.602809	−	0.602809i
$821$	4.63667e7	−	8.03094e7i	0.0837869	−	0.145123i	−0.821087	−	0.570803i	$-0.806632\pi$
$821$	4.63667e7	−	8.03094e7i	0.0837869	−	0.145123i	0.904874	+	0.425680i	$0.139965\pi$
$822$	−9.14904e8	−	9.14904e8i	−1.64725	−	1.64725i
$823$	−2.58024e8	−	4.46910e8i	−0.462871	−	0.801716i	0.536231	−	0.844071i	$-0.319847\pi$
$823$	−2.58024e8	−	4.46910e8i	−0.462871	−	0.801716i	−0.999103	+	0.0423546i	$0.986514\pi$
$824$	5.21052e8			0.931322
$825$		−	2.49161e9i		−	4.43729i
$826$	−5.43608e8	−	9.41557e8i	−0.964597	−	1.67073i
$827$	2.90034e8	−	7.77144e7i	0.512782	−	0.137400i	0.00685614	−	0.999976i	$-0.497818\pi$
$827$	2.90034e8	−	7.77144e7i	0.512782	−	0.137400i	0.505926	+	0.862577i	$0.331151\pi$
$828$	−8.26979e8	+	8.26979e8i	−1.45681	+	1.45681i
$829$	3.43092e8	+	9.19311e7i	0.602208	+	0.161361i	0.547027	−	0.837115i	$-0.315760\pi$
$829$	3.43092e8	+	9.19311e7i	0.602208	+	0.161361i	0.0551814	+	0.998476i	$0.482426\pi$
$830$	1.58504e9	+	2.74538e9i	2.77209	+	4.80140i
$831$	−6.57082e7	+	2.45226e8i	−0.114503	+	0.427331i
$832$	−1.23279e8	−	4.60085e8i	−0.214052	−	0.798854i
$833$	3.30559e8	−	8.85731e7i	0.571892	−	0.153238i
$834$	2.55026e9	+	6.83341e8i	4.39630	+	1.17798i
$835$	5.90202e8	−	3.40753e8i	1.01377	−	0.585303i
$836$	−1.24268e8	+	4.63776e8i	−0.212687	+	0.793760i
$837$	−6.52409e7	−	6.52409e7i	−0.111261	−	0.111261i
$838$	7.07104e7	+	2.63895e8i	0.120158	+	0.448434i
$839$	−2.36388e8	+	1.36479e8i	−0.400258	+	0.231089i	−0.686595	−	0.727040i	$-0.740896\pi$
$839$	−2.36388e8	+	1.36479e8i	−0.400258	+	0.231089i	0.286337	+	0.958129i	$0.407562\pi$
$840$	3.07691e9			5.19130
$841$			4.91521e8i			0.826332i
$842$	−1.01648e9	+	5.86867e8i	−1.70280	+	0.983112i
$843$	−1.19996e9	+	1.19996e9i	−2.00301	+	2.00301i
$844$	−4.18039e8	−	2.41355e8i	−0.695328	−	0.401448i
$845$	−5.17969e8	+	5.17969e8i	−0.858487	+	0.858487i
$846$	1.12710e8	+	4.20640e8i	0.186145	+	0.694704i
$847$	6.57062e7	−	1.13806e8i	0.108132	−	0.187291i
$848$	−1.72165e8	+	2.98198e8i	−0.282329	+	0.489009i
$849$	−2.93128e8	+	1.09397e9i	−0.478999	+	1.78765i
$850$		−	3.25516e9i		−	5.30049i
$851$	−3.38362e6	−	4.17262e8i	−0.00549026	−	0.677049i
$852$	−2.06408e9			−3.33740
$853$	−7.78785e6	−	2.08675e6i	−0.0125479	−	0.00336219i	0.252540	−	0.967587i	$-0.418734\pi$
$853$	−7.78785e6	−	2.08675e6i	−0.0125479	−	0.00336219i	−0.265088	+	0.964224i	$0.585401\pi$
$854$	−6.82637e8	−	3.94121e8i	−1.09601	−	0.632784i
$855$	−6.95173e8	−	4.01358e8i	−1.11223	−	0.642146i
$856$	1.21673e7	−	3.26022e6i	0.0193987	−	0.00519788i
$857$	1.99154e8	+	1.99154e8i	0.316407	+	0.316407i	0.847385	−	0.530978i	$-0.178175\pi$
$857$	1.99154e8	+	1.99154e8i	0.316407	+	0.316407i	−0.530978	+	0.847385i	$0.678175\pi$
$858$	−5.58038e8	+	9.66551e8i	−0.883491	+	1.53025i
$859$	5.88116e8	+	5.88116e8i	0.927863	+	0.927863i	0.997568	−	0.0697051i	$-0.0222058\pi$
$859$	5.88116e8	+	5.88116e8i	0.927863	+	0.927863i	−0.0697051	+	0.997568i	$0.522206\pi$
$860$	4.88522e8	+	8.46145e8i	0.768049	+	1.33030i
$861$	3.13695e8			0.491472
$862$		−	2.97791e8i		−	0.464933i
$863$	−4.58661e8	−	7.94423e8i	−0.713607	−	1.23600i	−0.963494	−	0.267729i	$-0.913727\pi$
$863$	−4.58661e8	−	7.94423e8i	−0.713607	−	1.23600i	0.249887	−	0.968275i	$-0.419606\pi$
$864$	−3.46385e8	+	9.28135e7i	−0.537053	+	0.143903i
$865$	4.86737e8	−	4.86737e8i	0.752049	−	0.752049i
$866$	1.51709e9	+	4.06504e8i	2.33593	+	0.625909i
$867$	−3.07778e8	−	5.33087e8i	−0.472259	−	0.817976i
$868$	5.49618e7	−	2.05120e8i	0.0840431	−	0.313653i
$869$	9.66513e7	+	3.60707e8i	0.147282	+	0.549662i
$870$	−1.36254e9	+	3.65091e8i	−2.06914	+	0.554426i
$871$	−3.64074e8	−	9.75533e7i	−0.550979	−	0.147634i
$872$	1.36047e8	−	7.85470e7i	0.205183	−	0.118462i
$873$	4.79904e8	−	1.79103e9i	0.721293	−	2.69190i
$874$	2.22223e8	+	2.22223e8i	0.332854	+	0.332854i
$875$	5.93138e8	+	2.21362e9i	0.885383	+	3.30430i
$876$	7.26579e8	−	4.19491e8i	1.08086	−	0.624037i
$877$	−6.58079e8			−0.975616			−0.487808	−	0.872951i	$-0.662203\pi$
$877$	−6.58079e8			−0.975616			−0.487808	+	0.872951i	$0.662203\pi$
$878$		−	1.03775e9i		−	1.53323i
$879$	3.10116e8	−	1.79045e8i	0.456622	−	0.263631i
$880$	5.15133e8	−	5.15133e8i	0.755912	−	0.755912i
$881$	4.29310e8	+	2.47862e8i	0.627832	+	0.362479i	0.779912	−	0.625889i	$-0.215264\pi$
$881$	4.29310e8	+	2.47862e8i	0.627832	+	0.362479i	−0.152080	+	0.988368i	$0.548597\pi$
$882$	−6.38794e8	+	6.38794e8i	−0.931012	+	0.931012i
$883$	2.67731e8	+	9.99187e8i	0.388882	+	1.45133i	0.831956	+	0.554841i	$0.187221\pi$
$883$	2.67731e8	+	9.99187e8i	0.388882	+	1.45133i	−0.443075	+	0.896485i	$0.646112\pi$
$884$	−4.71676e8	+	8.16967e8i	−0.682790	+	1.18263i
$885$	1.00032e9	−	1.73261e9i	1.44315	−	2.49960i
$886$	3.07421e8	−	1.14731e9i	0.442010	−	1.64960i
$887$		−	4.31829e8i		−	0.618787i	−0.950934	−	0.309394i	$-0.899874\pi$
$887$		−	4.31829e8i		−	0.618787i	0.950934	−	0.309394i	$-0.100126\pi$
$888$	−7.89004e8	+	1.39255e9i	−1.12678	+	1.98871i
$889$	4.97060e8			0.707462
$890$	−2.97889e8	−	7.98190e7i	−0.422556	−	0.113223i
$891$	6.41464e7	+	3.70349e7i	0.0906858	+	0.0523575i
$892$	−1.55025e9	−	8.95036e8i	−2.18427	−	1.26109i
$893$	7.31293e7	−	1.95949e7i	0.102692	−	0.0275163i
$894$	8.59848e8	+	8.59848e8i	1.20340	+	1.20340i
$895$	−1.22495e9	+	2.12168e9i	−1.70864	+	2.95945i
$896$	−1.12972e9	−	1.12972e9i	−1.57053	−	1.57053i
$897$	2.36314e8	+	4.09308e8i	0.327425	+	0.567117i
$898$	1.47791e9			2.04089
$899$			4.42320e7i			0.0608777i
$900$	2.77971e9	+	4.81460e9i	3.81305	+	6.60439i
$901$	−9.53163e8	+	2.55399e8i	−1.30315	+	0.349177i
$902$	2.35519e8	−	2.35519e8i	0.320927	−	0.320927i
$903$	−6.29839e8	−	1.68765e8i	−0.855394	−	0.229202i
$904$	−8.23942e8	−	1.42711e9i	−1.11530	−	1.93175i
$905$	3.71559e8	−	1.38668e9i	0.501282	−	1.87081i
$906$	−2.34805e7	−	8.76305e7i	−0.0315735	−	0.117834i
$907$	−3.34463e8	+	8.96192e7i	−0.448256	+	0.120110i	−0.475883	−	0.879508i	$-0.657872\pi$
$907$	−3.34463e8	+	8.96192e7i	−0.448256	+	0.120110i	0.0276270	+	0.999618i	$0.491205\pi$
$908$	1.99079e9	+	5.33432e8i	2.65931	+	0.712560i
$909$	1.67841e9	−	9.69033e8i	2.23464	−	1.29017i
$910$	4.42081e8	−	1.64987e9i	0.586648	−	2.18940i
$911$	−9.58352e8	−	9.58352e8i	−1.26756	−	1.26756i	−0.947343	−	0.320222i	$-0.896243\pi$
$911$	−9.58352e8	−	9.58352e8i	−1.26756	−	1.26756i	−0.320222	−	0.947343i	$-0.603757\pi$
$912$	−6.95713e7	−	2.59644e8i	−0.0917161	−	0.342289i
$913$	−1.25862e9	+	7.26662e8i	−1.65379	+	0.954817i
$914$	−2.45487e9			−3.21506
$915$		−	1.45049e9i		−	1.89343i
$916$	1.89138e9	−	1.09199e9i	2.46089	−	1.42080i
$917$	3.55357e8	−	3.55357e8i	0.460847	−	0.460847i
$918$	1.52622e9	+	8.81165e8i	1.97283	+	1.13901i
$919$	7.28523e8	−	7.28523e8i	0.938635	−	0.938635i	−0.0595880	−	0.998223i	$-0.518979\pi$
$919$	7.28523e8	−	7.28523e8i	0.938635	−	0.938635i	0.998223	+	0.0595880i	$0.0189787\pi$
$920$	−3.58071e8	−	1.33634e9i	−0.459839	−	1.71614i
$921$	1.55790e8	−	2.69836e8i	0.199416	−	0.345399i
$922$	−6.81337e7	+	1.18011e8i	−0.0869298	+	0.150567i
$923$	−1.34740e8	+	5.02856e8i	−0.171353	+	0.639497i
$924$			3.10473e9i			3.93557i
$925$	−1.92006e9	−	4.97827e8i	−2.42600	−	0.629004i
$926$	−1.30998e8			−0.164980
$927$	−8.49048e8	−	2.27502e8i	−1.06584	−	0.285592i
$928$	1.48884e8	+	8.59581e7i	0.186296	+	0.107558i
$929$	−8.41212e8	−	4.85674e8i	−1.04920	−	0.605756i	−0.126775	−	0.991932i	$-0.540463\pi$
$929$	−8.41212e8	−	4.85674e8i	−1.04920	−	0.605756i	−0.922425	+	0.386176i	$0.873796\pi$
$930$	5.83414e8	−	1.56325e8i	0.725317	−	0.194348i
$931$	1.11056e8	+	1.11056e8i	0.137623	+	0.137623i
$932$	−7.14420e8	+	1.23741e9i	−0.882482	+	1.52850i
$933$	−9.87911e7	−	9.87911e7i	−0.121639	−	0.121639i
$934$	−1.01335e9	−	1.75518e9i	−1.24371	−	2.15417i
$935$	2.08778e9			2.55417
$936$		−	1.13143e9i		−	1.37974i
$937$	4.16673e8	+	7.21699e8i	0.506497	+	0.877278i	0.999972	+	0.00751818i	$0.00239313\pi$
$937$	4.16673e8	+	7.21699e8i	0.506497	+	0.877278i	−0.493475	+	0.869760i	$0.664274\pi$
$938$	−1.56543e9	+	4.19455e8i	−1.89681	+	0.508249i
$939$	−1.72594e9	+	1.72594e9i	−2.08462	+	2.08462i
$940$	−7.08564e8	−	1.89859e8i	−0.853091	−	0.228585i
$941$	5.74982e8	+	9.95898e8i	0.690057	+	1.19521i	0.971819	+	0.235730i	$0.0757480\pi$
$941$	5.74982e8	+	9.95898e8i	0.690057	+	1.19521i	−0.281761	+	0.959485i	$0.590919\pi$
$942$	−6.68028e8	+	2.49311e9i	−0.799175	+	2.98256i
$943$	−3.65059e7	−	1.36242e8i	−0.0435339	−	0.162471i
$944$	4.03876e8	−	1.08218e8i	0.480101	−	0.128643i
$945$	−1.99411e9	−	5.34321e8i	−2.36295	−	0.633150i
$946$	−5.99584e8	+	3.46170e8i	−0.708233	+	0.408899i
$947$	−1.14734e7	+	4.28195e7i	−0.0135096	+	0.0504187i	−0.972352	−	0.233522i	$-0.924975\pi$
$947$	−1.14734e7	+	4.28195e7i	−0.0135096	+	0.0504187i	0.958842	+	0.283940i	$0.0916417\pi$
$948$	−9.44025e8	−	9.44025e8i	−1.10805	−	1.10805i
$949$	−5.47674e7	−	2.04395e8i	−0.0640801	−	0.239150i
$950$	1.29376e9	−	7.46954e8i	1.50898	−	0.871210i
$951$	−3.96021e8			−0.460444
$952$			1.84289e9i			2.13594i
$953$	1.27221e9	−	7.34513e8i	1.46988	−	0.848635i	0.470450	−	0.882427i	$-0.344092\pi$
$953$	1.27221e9	−	7.34513e8i	1.46988	−	0.848635i	0.999429	+	0.0337916i	$0.0107582\pi$
$954$	1.84196e9	−	1.84196e9i	2.12146	−	2.12146i
$955$	−1.03490e9	−	5.97502e8i	−1.18820	−	0.686008i
$956$	−3.48406e8	+	3.48406e8i	−0.398760	+	0.398760i
$957$	−1.67376e8	−	6.24654e8i	−0.190966	−	0.712695i
$958$	−1.30905e9	+	2.26733e9i	−1.48888	+	2.57881i
$959$	−4.53903e8	+	7.86184e8i	−0.514645	+	0.891391i
$960$	9.75411e8	−	3.64028e9i	1.10249	−	4.11454i
$961$			8.68564e8i			0.978660i
$962$	6.33339e8	+	6.23150e8i	0.711395	+	0.699950i
$963$	−2.12500e7			−0.0237947
$964$	−1.57366e8	−	4.21660e7i	−0.175662	−	0.0470686i
$965$	2.02288e8	+	1.16791e8i	0.225107	+	0.129965i
$966$	1.75992e9	+	1.01609e9i	1.95237	+	1.12720i
$967$	1.20061e9	−	3.21703e8i	1.32777	−	0.355776i	0.475889	−	0.879506i	$-0.342127\pi$
$967$	1.20061e9	−	3.21703e8i	1.32777	−	0.355776i	0.851884	+	0.523730i	$0.175460\pi$
$968$	1.60259e8	+	1.60259e8i	0.176684	+	0.176684i
$969$	3.85171e8	−	6.67136e8i	0.423333	−	0.733235i
$970$	3.41370e9	+	3.41370e9i	3.74033	+	3.74033i
$971$	−1.78796e8	−	3.09684e8i	−0.195299	−	0.338268i	0.751699	−	0.659506i	$-0.229235\pi$
$971$	−1.78796e8	−	3.09684e8i	−0.195299	−	0.338268i	−0.946999	+	0.321238i	$0.895901\pi$
$972$	1.54795e9			1.68561
$973$		−	1.85244e9i		−	2.01097i
$974$	7.58160e8	+	1.31317e9i	0.820511	+	1.42117i
$975$	2.17012e9	−	5.81481e8i	2.34137	−	0.627367i
$976$	2.14355e8	−	2.14355e8i	0.230560	−	0.230560i
$977$	2.20054e8	+	5.89632e7i	0.235964	+	0.0632263i	0.374863	−	0.927080i	$-0.377690\pi$
$977$	2.20054e8	+	5.89632e7i	0.235964	+	0.0632263i	−0.138899	+	0.990307i	$0.544356\pi$
$978$	−2.36303e9	−	4.09288e9i	−2.52611	−	4.37535i
$979$	3.65930e7	−	1.36567e8i	0.0389987	−	0.145545i
$980$	−3.93859e8	−	1.46990e9i	−0.418468	−	1.56174i
$981$	−2.55983e8	+	6.85904e7i	−0.271146	+	0.0726534i
$982$	−2.15135e9	−	5.76452e8i	−2.27183	−	0.608735i
$983$	1.01111e8	−	5.83762e7i	0.106448	−	0.0614576i	−0.445831	−	0.895117i	$-0.647092\pi$
$983$	1.01111e8	−	5.83762e7i	0.106448	−	0.0614576i	0.552279	+	0.833660i	$0.313758\pi$
$984$	−1.40025e8	+	5.22581e8i	−0.146967	+	0.548490i
$985$	−2.10297e8	−	2.10297e8i	−0.220052	−	0.220052i
$986$	−2.18668e8	−	8.16081e8i	−0.228116	−	0.851339i
$987$	4.23972e8	−	2.44781e8i	0.440947	−	0.254581i
$988$	−4.32937e8			−0.448904
$989$			2.93187e8i			0.303079i
$990$	−4.77294e9	+	2.75566e9i	−4.91904	+	2.84001i
$991$	−1.51629e8	+	1.51629e8i	−0.155798	+	0.155798i	−0.780702	−	0.624904i	$-0.785138\pi$
$991$	−1.51629e8	+	1.51629e8i	−0.155798	+	0.155798i	0.624904	+	0.780702i	$0.285138\pi$
$992$	−6.37493e7	−	3.68057e7i	−0.0653041	−	0.0377034i
$993$	−1.00349e9	+	1.00349e9i	−1.02486	+	1.02486i
$994$	5.79348e8	+	2.16216e9i	0.589903	+	2.20155i
$995$	−7.19926e8	+	1.24695e9i	−0.730834	+	1.26584i
$996$	2.59788e9	−	4.49967e9i	2.62931	−	4.55410i
$997$	1.60429e8	−	5.98729e8i	0.161881	−	0.604150i	−0.836536	−	0.547912i	$-0.815423\pi$
$997$	1.60429e8	−	5.98729e8i	0.161881	−	0.604150i	0.998417	−	0.0562379i	$-0.0179105\pi$
$998$		−	7.17833e8i		−	0.722158i
$999$	7.53169e8	−	7.65484e8i	0.755433	−	0.767785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.7.g.a.8.3	✓	72
37.14	odd	12	inner	37.7.g.a.14.3	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.7.g.a.8.3	✓	72	1.1	even	1	trivial
37.7.g.a.14.3	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)

\(f(q)\)	\(=\)	\(q+(-13.0056 - 3.48484i) q^{2} +(38.1387 + 22.0194i) q^{3} +(101.576 + 58.6446i) q^{4} +(226.086 - 60.5794i) q^{5} +(-419.282 - 419.282i) q^{6} +(-208.015 + 360.292i) q^{7} +(-507.354 - 507.354i) q^{8} +(605.206 + 1048.25i) q^{9} +O(q^{10})\)	\(q+(-13.0056 - 3.48484i) q^{2} +(38.1387 + 22.0194i) q^{3} +(101.576 + 58.6446i) q^{4} +(226.086 - 60.5794i) q^{5} +(-419.282 - 419.282i) q^{6} +(-208.015 + 360.292i) q^{7} +(-507.354 - 507.354i) q^{8} +(605.206 + 1048.25i) q^{9} -3151.48 q^{10} -1444.80i q^{11} +(2582.64 + 4473.26i) q^{12} +(1258.38 - 337.181i) q^{13} +(3960.91 - 3960.91i) q^{14} +(9956.53 + 2667.84i) q^{15} +(1077.13 + 1865.65i) q^{16} +(-1597.88 + 5963.38i) q^{17} +(-4218.09 - 15742.1i) q^{18} +(-2736.80 + 733.324i) q^{19} +(26517.4 + 7105.32i) q^{20} +(-15866.8 + 9160.71i) q^{21} +(-5034.87 + 18790.4i) q^{22} +(5825.09 + 5825.09i) q^{23} +(-8178.19 - 30521.4i) q^{24} +(33913.2 - 19579.8i) q^{25} -17540.9 q^{26} +21200.8i q^{27} +(-42258.4 + 24397.9i) q^{28} +(7186.86 - 7186.86i) q^{29} +(-120193. - 69393.7i) q^{30} +(-3077.28 + 3077.28i) q^{31} +(4377.83 + 16338.3i) q^{32} +(31813.5 - 55102.6i) q^{33} +(41562.8 - 71988.9i) q^{34} +(-25202.8 + 94058.3i) q^{35} +141968. i q^{36} +(-36106.3 - 35525.5i) q^{37} +38149.2 q^{38} +(55417.3 + 14849.0i) q^{39} +(-145441. - 83970.2i) q^{40} +(-14827.9 - 8560.89i) q^{41} +(238281. - 63847.1i) q^{42} +(25165.9 + 25165.9i) q^{43} +(84729.5 - 146756. i) q^{44} +(200331. + 200331. i) q^{45} +(-55459.2 - 96058.2i) q^{46} -26720.7 q^{47} +94871.1i q^{48} +(-27715.8 - 48005.1i) q^{49} +(-509293. + 136465. i) q^{50} +(-192251. + 192251. i) q^{51} +(147594. + 39547.7i) q^{52} +(79918.0 + 138422. i) q^{53} +(73881.3 - 275729. i) q^{54} +(-87524.9 - 326647. i) q^{55} +(288333. - 77258.5i) q^{56} +(-120525. - 32294.7i) q^{57} +(-118514. + 68424.3i) q^{58} +(50234.5 - 187478. i) q^{59} +(854885. + 854885. i) q^{60} +(-36420.5 - 135923. i) q^{61} +(50745.7 - 29298.0i) q^{62} -503567. q^{63} -365618. i q^{64} +(264074. - 152463. i) q^{65} +(-605777. + 605777. i) q^{66} +(-250559. - 144660. i) q^{67} +(-512026. + 512026. i) q^{68} +(93896.4 + 350426. i) q^{69} +(655555. - 1.13545e6i) q^{70} +(-199803. + 346070. i) q^{71} +(224779. - 838887. i) q^{72} -162427. i q^{73} +(345784. + 587854. i) q^{74} +1.72454e6 q^{75} +(-320998. - 86011.1i) q^{76} +(520548. + 300539. i) q^{77} +(-668988. - 386240. i) q^{78} +(-249660. + 66896.2i) q^{79} +(356544. + 356544. i) q^{80} +(-25633.3 + 44398.3i) q^{81} +(163012. + 163012. i) q^{82} +(-502952. - 871138. i) q^{83} -2.14891e6 q^{84} +1.44503e6i q^{85} +(-239598. - 414995. i) q^{86} +(432348. - 115847. i) q^{87} +(-733023. + 733023. i) q^{88} +(94523.3 + 25327.4i) q^{89} +(-1.90730e6 - 3.30354e6i) q^{90} +(-140277. + 523521. i) q^{91} +(250076. + 933297. i) q^{92} +(-185123. + 49603.7i) q^{93} +(347518. + 93117.2i) q^{94} +(-574327. + 331588. i) q^{95} +(-192794. + 719518. i) q^{96} +(-1.08320e6 - 1.08320e6i) q^{97} +(193170. + 720919. i) q^{98} +(1.51450e6 - 874399. 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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