LMFDB - Embedded newform 416.2.bd.a.83.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(83,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("416.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bd (of order $8$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			83.10
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24384 + 0.672951i) q^{2} +(1.34047 + 0.555241i) q^{3} +(1.09427 - 1.67409i) q^{4} +(1.54705 - 3.73491i) q^{5} +(-2.04098 + 0.211441i) q^{6} -0.167444i q^{7} +(-0.234521 + 2.81869i) q^{8} +(-0.632754 - 0.632754i) q^{9} +O(q^{10})$	\(q+(-1.24384 + 0.672951i) q^{2} +(1.34047 + 0.555241i) q^{3} +(1.09427 - 1.67409i) q^{4} +(1.54705 - 3.73491i) q^{5} +(-2.04098 + 0.211441i) q^{6} -0.167444i q^{7} +(-0.234521 + 2.81869i) q^{8} +(-0.632754 - 0.632754i) q^{9} +(0.589131 + 5.68672i) q^{10} +(0.115501 + 0.0478422i) q^{11} +(2.39636 - 1.63648i) q^{12} +(0.804107 - 3.51474i) q^{13} +(0.112681 + 0.208273i) q^{14} +(4.14755 - 4.14755i) q^{15} +(-1.60513 - 3.66382i) q^{16} -4.75422 q^{17} +(1.21286 + 0.361232i) q^{18} +(1.08803 + 2.62674i) q^{19} +(-4.55967 - 6.67692i) q^{20} +(0.0929715 - 0.224453i) q^{21} +(-0.175861 + 0.0182187i) q^{22} +(-0.822050 - 0.822050i) q^{23} +(-1.87942 + 3.64815i) q^{24} +(-8.02068 - 8.02068i) q^{25} +(1.36507 + 4.91290i) q^{26} +(-2.16258 - 5.22093i) q^{27} +(-0.280315 - 0.183229i) q^{28} +(-0.362881 + 0.876073i) q^{29} +(-2.36779 + 7.94999i) q^{30} +(1.60097 + 1.60097i) q^{31} +(4.46210 + 3.47702i) q^{32} +(0.128262 + 0.128262i) q^{33} +(5.91349 - 3.19936i) q^{34} +(-0.625388 - 0.259044i) q^{35} +(-1.75169 + 0.366879i) q^{36} +(9.94226 + 4.11822i) q^{37} +(-3.12101 - 2.53505i) q^{38} +(3.02941 - 4.26493i) q^{39} +(10.1647 + 5.23657i) q^{40} +1.57976 q^{41} +(0.0354044 + 0.341749i) q^{42} +(2.99613 + 7.23329i) q^{43} +(0.206482 - 0.141007i) q^{44} +(-3.34218 + 1.38438i) q^{45} +(1.57570 + 0.469298i) q^{46} +(5.14120 + 5.14120i) q^{47} +(-0.117333 - 5.80247i) q^{48} +6.97196 q^{49} +(15.3740 + 4.57891i) q^{50} +(-6.37289 - 2.63974i) q^{51} +(-5.00407 - 5.19223i) q^{52} +(0.952080 + 2.29853i) q^{53} +(6.20333 + 5.03868i) q^{54} +(0.357373 - 0.357373i) q^{55} +(0.471971 + 0.0392691i) q^{56} +4.12519i q^{57} +(-0.138188 - 1.33390i) q^{58} +(4.80965 - 11.6115i) q^{59} +(-2.40481 - 11.4819i) q^{60} +(-1.39878 + 3.37697i) q^{61} +(-3.06872 - 0.913973i) q^{62} +(-0.105951 + 0.105951i) q^{63} +(-7.89000 - 1.32208i) q^{64} +(-11.8833 - 8.44076i) q^{65} +(-0.245852 - 0.0732233i) q^{66} +(5.27576 - 2.18529i) q^{67} +(-5.20242 + 7.95898i) q^{68} +(-0.645497 - 1.55837i) q^{69} +(0.952206 - 0.0986463i) q^{70} -12.4430 q^{71} +(1.93193 - 1.63514i) q^{72} +8.93301i q^{73} +(-15.1379 + 1.56825i) q^{74} +(-6.29807 - 15.2049i) q^{75} +(5.58800 + 1.05291i) q^{76} +(0.00801088 - 0.0193400i) q^{77} +(-0.898007 + 7.34354i) q^{78} +14.3833 q^{79} +(-16.1673 + 0.326920i) q^{80} -5.51470i q^{81} +(-1.96497 + 1.06310i) q^{82} +(4.24121 + 10.2392i) q^{83} +(-0.274018 - 0.401255i) q^{84} +(-7.35503 + 17.7566i) q^{85} +(-8.59435 - 6.98080i) q^{86} +(-0.972863 + 0.972863i) q^{87} +(-0.161940 + 0.314342i) q^{88} +6.33972 q^{89} +(3.22552 - 3.97107i) q^{90} +(-0.588521 - 0.134643i) q^{91} +(-2.27573 + 0.476636i) q^{92} +(1.25713 + 3.03497i) q^{93} +(-9.85461 - 2.93505i) q^{94} +11.4939 q^{95} +(4.05072 + 7.13838i) q^{96} +(-7.29863 + 7.29863i) q^{97} +(-8.67200 + 4.69179i) q^{98} +(-0.0428116 - 0.103356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.24384	+	0.672951i	−0.879527	+	0.475848i
$2$	−1.24384	+	0.672951i	−0.879527	+	0.475848i
$3$	1.34047	+	0.555241i	0.773920	+	0.320568i	0.734459	−	0.678653i	$-0.237436\pi$
$3$	1.34047	+	0.555241i	0.773920	+	0.320568i	0.0394612	+	0.999221i	$0.487436\pi$
$4$	1.09427	−	1.67409i	0.547137	−	0.837043i
$5$	1.54705	−	3.73491i	0.691863	−	1.67030i	−0.0491308	−	0.998792i	$-0.515645\pi$
$5$	1.54705	−	3.73491i	0.691863	−	1.67030i	0.740994	−	0.671512i	$-0.234355\pi$
$6$	−2.04098	+	0.211441i	−0.833226	+	0.0863202i
$7$		−	0.167444i		−	0.0632878i	−0.999499	−	0.0316439i	$-0.989926\pi$
$7$		−	0.167444i		−	0.0632878i	0.999499	−	0.0316439i	$-0.0100742\pi$
$8$	−0.234521	+	2.81869i	−0.0829157	+	0.996557i
$9$	−0.632754	−	0.632754i	−0.210918	−	0.210918i
$10$	0.589131	+	5.68672i	0.186300	+	1.79830i
$11$	0.115501	+	0.0478422i	0.0348250	+	0.0144250i	0.400028	−	0.916503i	$-0.369000\pi$
$11$	0.115501	+	0.0478422i	0.0348250	+	0.0144250i	−0.365203	+	0.930928i	$0.619000\pi$
$12$	2.39636	−	1.63648i	0.691770	−	0.472410i
$13$	0.804107	−	3.51474i	0.223019	−	0.974814i
$13$	0.804107	−	3.51474i	0.223019	−	0.974814i
$14$	0.112681	+	0.208273i	0.0301154	+	0.0556633i
$15$	4.14755	−	4.14755i	1.07089	−	1.07089i
$16$	−1.60513	−	3.66382i	−0.401283	−	0.915954i
$17$	−4.75422			−1.15307			−0.576534	−	0.817073i	$-0.695595\pi$
$17$	−4.75422			−1.15307			−0.576534	+	0.817073i	$0.695595\pi$
$18$	1.21286	+	0.361232i	0.285873	+	0.0851431i
$19$	1.08803	+	2.62674i	0.249612	+	0.602616i	0.998171	−	0.0604517i	$-0.0192541\pi$
$19$	1.08803	+	2.62674i	0.249612	+	0.602616i	−0.748559	+	0.663068i	$0.769254\pi$
$20$	−4.55967	−	6.67692i	−1.01957	−	1.49300i
$21$	0.0929715	−	0.224453i	0.0202881	−	0.0489797i
$22$	−0.175861	+	0.0182187i	−0.0374936	+	0.00388425i
$23$	−0.822050	−	0.822050i	−0.171409	−	0.171409i	0.616189	−	0.787598i	$-0.288676\pi$
$23$	−0.822050	−	0.822050i	−0.171409	−	0.171409i	−0.787598	+	0.616189i	$0.788676\pi$
$24$	−1.87942	+	3.64815i	−0.383635	+	0.744675i
$25$	−8.02068	−	8.02068i	−1.60414	−	1.60414i
$26$	1.36507	+	4.91290i	0.267712	+	0.963499i
$27$	−2.16258	−	5.22093i	−0.416188	−	1.00477i
$28$	−0.280315	−	0.183229i	−0.0529746	−	0.0346270i
$29$	−0.362881	+	0.876073i	−0.0673854	+	0.162683i	−0.953984	−	0.299856i	$-0.903061\pi$
$29$	−0.362881	+	0.876073i	−0.0673854	+	0.162683i	0.886599	+	0.462539i	$0.153061\pi$
$30$	−2.36779	+	7.94999i	−0.432297	+	1.45146i
$31$	1.60097	+	1.60097i	0.287542	+	0.287542i	0.836108	−	0.548565i	$-0.184826\pi$
$31$	1.60097	+	1.60097i	0.287542	+	0.287542i	−0.548565	+	0.836108i	$0.684826\pi$
$32$	4.46210	+	3.47702i	0.788795	+	0.614656i
$33$	0.128262	+	0.128262i	0.0223276	+	0.0223276i
$34$	5.91349	−	3.19936i	1.01415	−	0.548686i
$35$	−0.625388	−	0.259044i	−0.105710	−	0.0437864i
$36$	−1.75169	+	0.366879i	−0.291948	+	0.0611466i
$37$	9.94226	+	4.11822i	1.63450	+	0.677031i	0.995725	−	0.0923646i	$-0.0294425\pi$
$37$	9.94226	+	4.11822i	1.63450	+	0.677031i	0.638772	+	0.769396i	$0.279443\pi$
$38$	−3.12101	−	2.53505i	−0.506294	−	0.411240i
$39$	3.02941	−	4.26493i	0.485094	−	0.682936i
$40$	10.1647	+	5.23657i	1.60719	+	0.827975i
$41$	1.57976			0.246717			0.123359	−	0.992362i	$-0.460633\pi$
$41$	1.57976			0.246717			0.123359	+	0.992362i	$0.460633\pi$
$42$	0.0354044	+	0.341749i	0.00546301	+	0.0527330i
$43$	2.99613	+	7.23329i	0.456905	+	1.10307i	0.969644	+	0.244522i	$0.0786309\pi$
$43$	2.99613	+	7.23329i	0.456905	+	1.10307i	−0.512739	+	0.858545i	$0.671369\pi$
$44$	0.206482	−	0.141007i	0.0311284	−	0.0212576i
$45$	−3.34218	+	1.38438i	−0.498223	+	0.206371i
$46$	1.57570	+	0.469298i	0.232324	+	0.0691943i
$47$	5.14120	+	5.14120i	0.749921	+	0.749921i	0.974464	−	0.224543i	$-0.0720889\pi$
$47$	5.14120	+	5.14120i	0.749921	+	0.749921i	−0.224543	+	0.974464i	$0.572089\pi$
$48$	−0.117333	−	5.80247i	−0.0169355	−	0.837514i
$49$	6.97196			0.995995
$50$	15.3740	+	4.57891i	2.17421	+	0.647556i
$51$	−6.37289	−	2.63974i	−0.892383	−	0.369637i
$52$	−5.00407	−	5.19223i	−0.693940	−	0.720033i
$53$	0.952080	+	2.29853i	0.130778	+	0.315727i	0.975682	−	0.219192i	$-0.0703422\pi$
$53$	0.952080	+	2.29853i	0.130778	+	0.315727i	−0.844903	+	0.534919i	$0.820342\pi$
$54$	6.20333	+	5.03868i	0.844166	+	0.685678i
$55$	0.357373	−	0.357373i	0.0481882	−	0.0481882i
$56$	0.471971	+	0.0392691i	0.0630698	+	0.00524755i
$57$			4.12519i			0.546395i
$58$	−0.138188	−	1.33390i	−0.0181450	−	0.175149i
$59$	4.80965	−	11.6115i	0.626164	−	1.51169i	−0.218190	−	0.975906i	$-0.570015\pi$
$59$	4.80965	−	11.6115i	0.626164	−	1.51169i	0.844353	−	0.535787i	$-0.179985\pi$
$60$	−2.40481	−	11.4819i	−0.310459	−	1.48231i
$61$	−1.39878	+	3.37697i	−0.179096	+	0.432376i	−0.987777	−	0.155871i	$-0.950182\pi$
$61$	−1.39878	+	3.37697i	−0.179096	+	0.432376i	0.808681	+	0.588247i	$0.200182\pi$
$62$	−3.06872	−	0.913973i	−0.389728	−	0.116075i
$63$	−0.105951	+	0.105951i	−0.0133485	+	0.0133485i
$64$	−7.89000	−	1.32208i	−0.986250	−	0.165260i
$65$	−11.8833	−	8.44076i	−1.47394	−	1.04695i
$66$	−0.245852	−	0.0732233i	−0.0302623	−	0.00901317i
$67$	5.27576	−	2.18529i	0.644537	−	0.266976i	−0.0363783	−	0.999338i	$-0.511582\pi$
$67$	5.27576	−	2.18529i	0.644537	−	0.266976i	0.680915	+	0.732362i	$0.261582\pi$
$68$	−5.20242	+	7.95898i	−0.630886	+	0.965168i
$69$	−0.645497	−	1.55837i	−0.0777087	−	0.187606i
$70$	0.952206	−	0.0986463i	0.113810	−	0.0117905i
$71$	−12.4430			−1.47671			−0.738357	−	0.674410i	$-0.764398\pi$
$71$	−12.4430			−1.47671			−0.738357	+	0.674410i	$0.764398\pi$
$72$	1.93193	−	1.63514i	0.227680	−	0.192703i
$73$			8.93301i			1.04553i	0.852477	+	0.522765i	$0.175100\pi$
$73$			8.93301i			1.04553i	−0.852477	+	0.522765i	$0.824900\pi$
$74$	−15.1379	+	1.56825i	−1.75975	+	0.182306i
$75$	−6.29807	−	15.2049i	−0.727239	−	1.75571i
$76$	5.58800	+	1.05291i	0.640988	+	0.120777i
$77$	0.00801088	−	0.0193400i	0.000912925	−	0.00220399i
$78$	−0.898007	+	7.34354i	−0.101679	+	0.831492i
$79$	14.3833			1.61824			0.809122	−	0.587641i	$-0.199943\pi$
$79$	14.3833			1.61824			0.809122	+	0.587641i	$0.199943\pi$
$80$	−16.1673	+	0.326920i	−1.80756	+	0.0365508i
$81$		−	5.51470i		−	0.612744i
$82$	−1.96497	+	1.06310i	−0.216995	+	0.117400i
$83$	4.24121	+	10.2392i	0.465533	+	1.12390i	0.966093	+	0.258194i	$0.0831273\pi$
$83$	4.24121	+	10.2392i	0.465533	+	1.12390i	−0.500560	+	0.865702i	$0.666873\pi$
$84$	−0.274018	−	0.401255i	−0.0298978	−	0.0437806i
$85$	−7.35503	+	17.7566i	−0.797765	+	1.92597i
$86$	−8.59435	−	6.98080i	−0.926753	−	0.752759i
$87$	−0.972863	+	0.972863i	−0.104302	+	0.104302i
$88$	−0.161940	+	0.314342i	−0.0172628	+	0.0335090i
$89$	6.33972			0.672009			0.336004	−	0.941860i	$-0.390924\pi$
$89$	6.33972			0.672009			0.336004	+	0.941860i	$0.390924\pi$
$90$	3.22552	−	3.97107i	0.340000	−	0.418588i
$91$	−0.588521	−	0.134643i	−0.0616938	−	0.0141144i
$92$	−2.27573	+	0.476636i	−0.237261	+	0.0496927i
$93$	1.25713	+	3.03497i	0.130358	+	0.314712i
$94$	−9.85461	−	2.93505i	−1.01642	−	0.302727i
$95$	11.4939			1.17925
$96$	4.05072	+	7.13838i	0.413425	+	0.728558i
$97$	−7.29863	+	7.29863i	−0.741063	+	0.741063i	−0.972783	−	0.231719i	$-0.925565\pi$
$97$	−7.29863	+	7.29863i	−0.741063	+	0.741063i	0.231719	+	0.972783i	$0.425565\pi$
$98$	−8.67200	+	4.69179i	−0.876004	+	0.473943i
$99$	−0.0428116	−	0.103356i	−0.00430273	−	0.0103877i
$100$	−22.2041	+	4.65050i	−2.22041	+	0.465050i
$101$	−4.28791	−	10.3519i	−0.426663	−	1.03006i	−0.980338	−	0.197323i	$-0.936775\pi$
$101$	−4.28791	−	10.3519i	−0.426663	−	1.03006i	0.553675	−	0.832733i	$-0.313225\pi$
$102$	9.70327	−	1.00524i	0.960766	−	0.0995331i
$103$	5.94537	−	5.94537i	0.585815	−	0.585815i	−0.350680	−	0.936495i	$-0.614050\pi$
$103$	5.94537	−	5.94537i	0.585815	−	0.585815i	0.936495	+	0.350680i	$0.114050\pi$
$104$	9.71838	+	3.09081i	0.952966	+	0.303079i
$105$	−0.694481	−	0.694481i	−0.0677745	−	0.0677745i
$106$	−2.73103	−	2.21829i	−0.265261	−	0.215460i
$107$	−17.4698	+	7.23622i	−1.68887	+	0.699552i	−0.999687	−	0.0250362i	$-0.992030\pi$
$107$	−17.4698	+	7.23622i	−1.68887	+	0.699552i	−0.689182	+	0.724588i	$0.742030\pi$
$108$	−11.1067	−	2.09277i	−1.06875	−	0.201377i
$109$	−2.26257	+	0.937189i	−0.216715	+	0.0897664i	−0.488400	−	0.872620i	$-0.662419\pi$
$109$	−2.26257	+	0.937189i	−0.216715	+	0.0897664i	0.271685	+	0.962386i	$0.412419\pi$
$110$	−0.204020	+	0.685010i	−0.0194526	+	0.0653131i
$111$	11.0407	+	11.0407i	1.04794	+	1.04794i
$112$	−0.613483	+	0.268769i	−0.0579687	+	0.0253963i
$113$			0.849823i			0.0799447i	0.999201	+	0.0399723i	$0.0127270\pi$
$113$			0.849823i			0.0799447i	−0.999201	+	0.0399723i	$0.987273\pi$
$114$	−2.77605	−	5.13107i	−0.260001	−	0.480569i
$115$	−4.34204	+	1.79853i	−0.404897	+	0.167714i
$116$	1.06953	+	1.56616i	0.0993035	+	0.145414i
$117$	−2.73277	+	1.71516i	−0.252645	+	0.158567i
$118$	1.83156	+	17.6795i	0.168609	+	1.62753i
$119$			0.796064i			0.0729751i
$120$	10.7180	+	12.6633i	0.978412	+	1.15600i
$121$	−7.76712	−	7.76712i	−0.706102	−	0.706102i
$122$	−0.532670	−	5.14172i	−0.0482256	−	0.465509i
$123$	2.11762	+	0.877148i	0.190940	+	0.0790897i
$124$	4.43206	−	0.928263i	0.398010	−	0.0833605i
$125$	−23.6904	+	9.81288i	−2.11893	+	0.877691i
$126$	0.0604859	−	0.203085i	0.00538852	−	0.0180923i
$127$	14.1303			1.25387			0.626933	−	0.779073i	$-0.284310\pi$
$127$	14.1303			1.25387			0.626933	+	0.779073i	$0.284310\pi$
$128$	10.7036	−	3.66513i	0.946073	−	0.323955i
$129$			11.3596i			1.00015i
$130$	20.4611	+	2.50209i	1.79456	+	0.219448i
$131$	−16.9635	−	7.02653i	−1.48211	−	0.613911i	−0.512528	−	0.858670i	$-0.671291\pi$
$131$	−16.9635	−	7.02653i	−1.48211	−	0.613911i	−0.969584	+	0.244759i	$0.921291\pi$
$132$	0.355076	−	0.0743682i	0.0309054	−	0.00647292i
$133$	0.439831	−	0.182184i	0.0381382	−	0.0157974i
$134$	−5.09161	+	6.26849i	−0.439848	+	0.541515i
$135$	−22.8453			−1.96621
$136$	1.11496	−	13.4007i	0.0956074	−	1.14910i
$137$		−	11.5094i		−	0.983314i	−0.870789	−	0.491657i	$-0.836391\pi$
$137$		−	11.5094i		−	0.983314i	0.870789	−	0.491657i	$-0.163609\pi$
$138$	1.85160	+	1.50397i	0.157619	+	0.128027i
$139$	0.979057	−	0.405539i	0.0830425	−	0.0343973i	−0.340776	−	0.940145i	$-0.610690\pi$
$139$	0.979057	−	0.405539i	0.0830425	−	0.0343973i	0.423818	+	0.905747i	$0.360690\pi$
$140$	−1.11801	+	0.763488i	−0.0944889	+	0.0645266i
$141$	4.03702	+	9.74623i	0.339978	+	0.820780i
$142$	15.4771	−	8.37355i	1.29881	−	0.702692i
$143$	0.261029	−	0.367487i	0.0218283	−	0.0307308i
$144$	−1.30264	+	3.33395i	−0.108553	+	0.277829i
$145$	2.71066	+	2.71066i	0.225108	+	0.225108i
$146$	−6.01148	−	11.1112i	−0.497514	−	0.919572i
$147$	9.34570	+	3.87112i	0.770821	+	0.319284i
$148$	17.7738	−	12.1378i	1.46100	−	0.997717i
$149$	−1.87501	−	0.776656i	−0.153607	−	0.0636262i	0.304555	−	0.952495i	$-0.401492\pi$
$149$	−1.87501	−	0.776656i	−0.153607	−	0.0636262i	−0.458162	+	0.888869i	$0.651492\pi$
$150$	18.0659	+	14.6741i	1.47508	+	1.19814i
$151$	15.1813			1.23544			0.617718	−	0.786400i	$-0.288057\pi$
$151$	15.1813			1.23544			0.617718	+	0.786400i	$0.288057\pi$
$152$	−7.65913	+	2.45080i	−0.621238	+	0.198786i
$153$	3.00825	+	3.00825i	0.243203	+	0.243203i
$154$	0.00305061	+	0.0294468i	0.000245825	+	0.00237289i
$155$	8.45626	−	3.50270i	0.679223	−	0.281343i
$156$	−3.82486	−	9.73849i	−0.306234	−	0.779704i
$157$	−1.17723	+	2.84209i	−0.0939532	+	0.226823i	−0.963869	−	0.266378i	$-0.914173\pi$
$157$	−1.17723	+	2.84209i	−0.0939532	+	0.226823i	0.869916	+	0.493201i	$0.164173\pi$
$158$	−17.8905	+	9.67924i	−1.42329	+	0.770039i
$159$			3.60974i			0.286271i
$160$	19.8895	−	11.2864i	1.57240	−	0.892270i
$161$	−0.137647	+	0.137647i	−0.0108481	+	0.0108481i
$162$	3.71112	+	6.85940i	0.291573	+	0.538925i
$163$	4.24566	+	10.2499i	0.332546	+	0.802837i	0.998389	+	0.0567448i	$0.0180721\pi$
$163$	4.24566	+	10.2499i	0.332546	+	0.802837i	−0.665843	+	0.746092i	$0.731928\pi$
$164$	1.72869	−	2.64466i	0.134988	−	0.206513i
$165$	0.677476	−	0.280620i	0.0527415	−	0.0218462i
$166$	−12.1658	−	9.88177i	−0.944253	−	0.766974i
$167$			1.63379i			0.126426i	0.998000	+	0.0632132i	$0.0201348\pi$
$167$			1.63379i			0.126426i	−0.998000	+	0.0632132i	$0.979865\pi$
$168$	0.610860	+	0.314697i	0.0471288	+	0.0242794i
$169$	−11.7068	−	5.65246i	−0.900525	−	0.434805i
$170$	−2.80086	−	27.0359i	−0.214816	−	2.07356i
$171$	0.973625	−	2.35054i	0.0744549	−	0.179750i
$172$	15.3877	+	2.89942i	1.17330	+	0.221079i
$173$	−3.26898	+	7.89203i	−0.248536	+	0.600020i	−0.998080	−	0.0619350i	$-0.980273\pi$
$173$	−3.26898	+	7.89203i	−0.248536	+	0.600020i	0.749544	+	0.661955i	$0.230273\pi$
$174$	0.555396	−	1.86477i	0.0421044	−	0.141368i
$175$	−1.34301	+	1.34301i	−0.101522	+	0.101522i
$176$	−0.0101099	−	0.499969i	−0.000762066	−	0.0376866i
$177$	12.8944	−	12.8944i	0.969202	−	0.969202i
$178$	−7.88559	+	4.26632i	−0.591050	+	0.319774i
$179$	−2.69384	−	1.11583i	−0.201347	−	0.0834007i	0.279731	−	0.960078i	$-0.409755\pi$
$179$	−2.69384	−	1.11583i	−0.201347	−	0.0834007i	−0.481078	+	0.876678i	$0.659755\pi$
$180$	−1.33969	+	7.10999i	−0.0998548	+	0.529948i
$181$	−14.1781	+	5.87274i	−1.05385	+	0.436518i	−0.841263	−	0.540625i	$-0.818188\pi$
$181$	−14.1781	+	5.87274i	−1.05385	+	0.436518i	−0.212583	+	0.977143i	$0.568188\pi$
$182$	0.822634	−	0.228572i	0.0609777	−	0.0169429i
$183$	−3.75006	+	3.75006i	−0.277212	+	0.277212i
$184$	2.50989	−	2.12431i	0.185032	−	0.156606i
$185$	30.7624	−	30.7624i	2.26170	−	2.26170i
$186$	−3.60605	−	2.92903i	−0.264408	−	0.214767i
$187$	−0.549119	−	0.227453i	−0.0401556	−	0.0166330i
$188$	14.2327	−	2.98094i	1.03803	−	0.217407i
$189$	−0.874211	+	0.362110i	−0.0635895	+	0.0263396i
$190$	−14.2966	+	7.73484i	−1.03718	+	0.561144i
$191$			12.8849i			0.932318i	0.884701	+	0.466159i	$0.154363\pi$
$191$			12.8849i			0.932318i	−0.884701	+	0.466159i	$0.845637\pi$
$192$	−9.84223	−	6.15306i	−0.710302	−	0.444059i
$193$	−10.8423	−	10.8423i	−0.780448	−	0.780448i	0.199458	−	0.979906i	$-0.436082\pi$
$193$	−10.8423	−	10.8423i	−0.780448	−	0.780448i	−0.979906	+	0.199458i	$0.936082\pi$
$194$	4.16670	−	13.9899i	0.299152	−	1.00442i
$195$	−11.2425	−	17.9127i	−0.805092	−	1.28275i
$196$	7.62923	−	11.6717i	0.544945	−	0.833691i
$197$	−0.823725	+	1.98865i	−0.0586880	+	0.141685i	−0.950503	−	0.310714i	$-0.899432\pi$
$197$	−0.823725	+	1.98865i	−0.0586880	+	0.141685i	0.891815	+	0.452399i	$0.149432\pi$
$198$	0.122804	+	0.0997485i	0.00872734	+	0.00708882i
$199$	−3.15196	+	3.15196i	−0.223437	+	0.223437i	−0.809944	−	0.586507i	$-0.800503\pi$
$199$	−3.15196	+	3.15196i	−0.223437	+	0.223437i	0.586507	+	0.809944i	$0.300503\pi$
$200$	24.4888	−	20.7268i	1.73162	−	1.46560i
$201$	8.28536			0.584405
$202$	12.2998	+	9.99059i	0.865413	+	0.702935i
$203$	0.146693	+	0.0607622i	0.0102958	+	0.00426467i
$204$	−11.3928	+	7.78018i	−0.797658	+	0.544721i
$205$	2.44397	−	5.90027i	0.170694	−	0.412093i
$206$	−3.39414	+	11.3960i	−0.236481	+	0.794000i
$207$			1.04031i			0.0723066i
$208$	−14.1681	+	2.69553i	−0.982379	+	0.186901i
$209$			0.355446i			0.0245867i
$210$	1.33118	+	0.396471i	0.0918599	+	0.0273591i
$211$	−5.28688	+	12.7637i	−0.363964	+	0.878687i	0.630748	+	0.775987i	$0.282748\pi$
$211$	−5.28688	+	12.7637i	−0.363964	+	0.878687i	−0.994712	+	0.102699i	$0.967252\pi$
$212$	4.88977	+	0.921349i	0.335831	+	0.0632785i
$213$	−16.6795	−	6.90887i	−1.14286	−	0.473388i
$214$	16.8600	−	20.7570i	1.15253	−	1.41892i
$215$	31.6509			2.15857
$216$	15.2233	−	4.87122i	1.03582	−	0.331444i
$217$	0.268072	−	0.268072i	0.0181979	−	0.0181979i
$218$	2.18360	−	2.68831i	0.147892	−	0.182076i
$219$	−4.95997	+	11.9744i	−0.335164	+	0.809157i
$220$	−0.207210	−	0.989338i	−0.0139701	−	0.0667012i
$221$	−3.82290	+	16.7099i	−0.257156	+	1.12403i
$222$	−21.1627	−	6.30300i	−1.42035	−	0.423030i
$223$	−11.4720	−	11.4720i	−0.768222	−	0.768222i	0.209571	−	0.977793i	$-0.432793\pi$
$223$	−11.4720	−	11.4720i	−0.768222	−	0.768222i	−0.977793	+	0.209571i	$0.932793\pi$
$224$	0.582205	−	0.747150i	0.0389002	−	0.0499211i
$225$			10.1502i			0.676682i
$226$	−0.571890	−	1.05704i	−0.0380415	−	0.0703135i
$227$	13.0739	−	5.41538i	0.867744	−	0.359431i	0.0960125	−	0.995380i	$-0.469391\pi$
$227$	13.0739	−	5.41538i	0.867744	−	0.359431i	0.771731	+	0.635949i	$0.219391\pi$
$228$	6.90592	+	4.51408i	0.457356	+	0.298952i
$229$	9.83077	+	4.07204i	0.649635	+	0.269088i	0.683070	−	0.730353i	$-0.260644\pi$
$229$	9.83077	+	4.07204i	0.649635	+	0.269088i	−0.0334344	+	0.999441i	$0.510644\pi$
$230$	4.19048	−	5.15907i	0.276312	−	0.340179i
$231$	0.0214767	−	0.0214767i	0.00141306	−	0.00141306i
$232$	−2.38427	−	1.22831i	−0.156535	−	0.0806423i
$233$	7.99196	−	7.99196i	0.523571	−	0.523571i	−0.395077	−	0.918648i	$-0.629282\pi$
$233$	7.99196	−	7.99196i	0.523571	−	0.523571i	0.918648	+	0.395077i	$0.129282\pi$
$234$	2.24490	−	3.97241i	0.146754	−	0.259684i
$235$	27.1556	−	11.2482i	1.77144	−	0.733754i
$236$	−14.1756	−	20.7580i	−0.922756	−	1.35123i
$237$	19.2803	+	7.98617i	1.25239	+	0.518758i
$238$	−0.535712	−	0.990176i	−0.0347251	−	0.0641836i
$239$	−0.518131	+	0.518131i	−0.0335151	+	0.0335151i	−0.723666	−	0.690151i	$-0.757544\pi$
$239$	−0.518131	+	0.518131i	−0.0335151	+	0.0335151i	0.690151	+	0.723666i	$0.257544\pi$
$240$	−21.8532	−	8.53850i	−1.41062	−	0.551158i
$241$	−10.3809	+	10.3809i	−0.668691	+	0.668691i	−0.957413	−	0.288722i	$-0.906770\pi$
$241$	−10.3809	+	10.3809i	−0.668691	+	0.668691i	0.288722	+	0.957413i	$0.406770\pi$
$242$	14.8879	+	4.43416i	0.957034	+	0.285038i
$243$	−3.42575	+	8.27049i	−0.219762	+	0.530552i
$244$	4.12268	+	6.03701i	0.263928	+	0.386480i
$245$	10.7860	−	26.0397i	0.689092	−	1.66361i
$246$	−3.22426	+	0.334026i	−0.205571	+	0.0212967i
$247$	10.1072	−	1.71197i	0.643107	−	0.108930i
$248$	−4.88809	+	4.13717i	−0.310394	+	0.262710i
$249$			16.0802i			1.01904i
$250$	22.8635	−	28.1481i	1.44601	−	1.78024i
$251$	−26.6225	+	11.0274i	−1.68040	+	0.696044i	−0.999345	−	0.0361906i	$-0.988478\pi$
$251$	−26.6225	+	11.0274i	−1.68040	+	0.696044i	−0.681053	+	0.732234i	$0.738478\pi$
$252$	0.0614316	+	0.293309i	0.00386983	+	0.0184768i
$253$	−0.0556192	−	0.134277i	−0.00349675	−	0.00844190i
$254$	−17.5759	+	9.50903i	−1.10281	+	0.596650i
$255$	−19.7184	+	19.7184i	−1.23481	+	1.23481i
$256$	−10.8471	+	11.7618i	−0.677943	+	0.735114i
$257$			1.49040i			0.0929688i	0.998919	+	0.0464844i	$0.0148018\pi$
$257$			1.49040i			0.0929688i	−0.998919	+	0.0464844i	$0.985198\pi$
$258$	−7.64444	−	14.1295i	−0.475922	−	0.879664i
$259$	0.689570	−	1.66477i	0.0428478	−	0.103444i
$260$	−27.1341	+	10.6571i	−1.68279	+	0.660926i
$261$	0.783953	−	0.324724i	0.0485255	−	0.0200999i
$262$	25.8284	−	2.67577i	1.59569	−	0.165309i
$263$	20.6831	+	20.6831i	1.27537	+	1.27537i	0.943228	+	0.332146i	$0.107773\pi$
$263$	20.6831	+	20.6831i	1.27537	+	1.27537i	0.332146	+	0.943228i	$0.392227\pi$
$264$	−0.391611	+	0.331451i	−0.0241020	+	0.0203994i
$265$	10.0577			0.617840
$266$	−0.424479	+	0.522593i	−0.0260265	+	0.0320422i
$267$	8.49820	+	3.52007i	0.520081	+	0.215425i
$268$	2.11476	−	11.2234i	0.129179	−	0.685578i
$269$	6.23575	+	2.58293i	0.380200	+	0.157484i	0.564595	−	0.825368i	$-0.309032\pi$
$269$	6.23575	+	2.58293i	0.380200	+	0.157484i	−0.184395	+	0.982852i	$0.559032\pi$
$270$	28.4159	−	15.3738i	1.72934	−	0.935620i
$271$	−13.7184	−	13.7184i	−0.833333	−	0.833333i	0.154638	−	0.987971i	$-0.450579\pi$
$271$	−13.7184	−	13.7184i	−0.833333	−	0.833333i	−0.987971	+	0.154638i	$0.950579\pi$
$272$	7.63116	+	17.4186i	0.462707	+	1.05616i
$273$	−0.714136	−	0.507255i	−0.0432215	−	0.0307005i
$274$	7.74526	+	14.3158i	0.467908	+	0.864852i
$275$	−0.542672	−	1.31013i	−0.0327244	−	0.0790036i
$276$	−3.31519	−	0.624662i	−0.199551	−	0.0376002i
$277$	24.3471	−	10.0849i	1.46287	−	0.605942i	0.497652	−	0.867377i	$-0.334196\pi$
$277$	24.3471	−	10.0849i	1.46287	−	0.605942i	0.965221	+	0.261435i	$0.0841957\pi$
$278$	−0.944882	+	1.16328i	−0.0566702	+	0.0697690i
$279$		−	2.02604i		−	0.121296i
$280$	0.876831	−	1.70202i	0.0524007	−	0.101715i
$281$	31.9260			1.90455			0.952274	−	0.305245i	$-0.0987383\pi$
$281$	31.9260			1.90455			0.952274	+	0.305245i	$0.0987383\pi$
$282$	−11.5801	−	9.40602i	−0.689587	−	0.560121i
$283$	−16.4236	+	6.80289i	−0.976283	+	0.404390i	−0.813047	−	0.582198i	$-0.802193\pi$
$283$	−16.4236	+	6.80289i	−0.976283	+	0.404390i	−0.163235	+	0.986587i	$0.552193\pi$
$284$	−13.6161	+	20.8307i	−0.807965	+	1.23607i
$285$	15.4072	+	6.38188i	0.912645	+	0.378030i
$286$	−0.0773767	+	0.632755i	−0.00457538	+	0.0374156i
$287$		−	0.264521i		−	0.0156142i
$288$	−0.623310	−	5.02351i	−0.0367289	−	0.296013i
$289$	5.60262			0.329566
$290$	−5.19577	−	1.54748i	−0.305106	−	0.0908714i
$291$	−13.8361	+	5.73109i	−0.811085	+	0.335963i
$292$	14.9546	+	9.77516i	0.875154	+	0.572048i
$293$	−5.33878	−	2.21139i	−0.311895	−	0.129191i	0.221245	−	0.975218i	$-0.428988\pi$
$293$	−5.33878	−	2.21139i	−0.311895	−	0.129191i	−0.533140	+	0.846027i	$0.678988\pi$
$294$	−14.2296	+	1.47416i	−0.829889	+	0.0859745i
$295$	−35.9273	−	35.9273i	−2.09177	−	2.09177i
$296$	−13.9396	+	27.0583i	−0.810225	+	1.57273i
$297$		−	0.706487i		−	0.0409945i
$298$	2.85487	−	0.295758i	0.165378	−	0.0171328i
$299$	−3.55031	+	2.22828i	−0.205320	+	0.128865i
$300$	−32.3461	−	6.09478i	−1.86750	−	0.351882i
$301$	1.21117	−	0.501682i	0.0698106	−	0.0289165i
$302$	−18.8831	+	10.2163i	−1.08660	+	0.587880i
$303$		−	16.2573i		−	0.933956i
$304$	7.87747	−	8.20262i	0.451804	−	0.470453i
$305$	10.4487	+	10.4487i	0.598290	+	0.598290i
$306$	−5.76619	−	1.71737i	−0.329631	−	0.0981758i
$307$	−21.9239	+	9.08120i	−1.25127	+	0.518291i	−0.907218	−	0.420661i	$-0.861798\pi$
$307$	−21.9239	+	9.08120i	−1.25127	+	0.518291i	−0.344048	+	0.938952i	$0.611798\pi$
$308$	−0.0236107	−	0.0345741i	−0.00134535	−	0.00197004i
$309$	11.2707	−	4.66848i	0.641168	−	0.265581i
$310$	−8.16108	+	10.0474i	−0.463518	+	0.570656i
$311$	−16.0453	−	16.0453i	−0.909848	−	0.909848i	0.0864119	−	0.996259i	$-0.472460\pi$
$311$	−16.0453	−	16.0453i	−0.909848	−	0.909848i	−0.996259	+	0.0864119i	$0.972460\pi$
$312$	11.3111	+	9.53917i	0.640362	+	0.540049i
$313$	3.40491	−	3.40491i	0.192457	−	0.192457i	−0.604300	−	0.796757i	$-0.706547\pi$
$313$	3.40491	−	3.40491i	0.192457	−	0.192457i	0.796757	+	0.604300i	$0.206547\pi$
$314$	−0.448300	−	4.32732i	−0.0252990	−	0.244205i
$315$	0.231805	+	0.559628i	0.0130608	+	0.0315314i
$316$	15.7392	−	24.0788i	0.885400	−	1.35454i
$317$	10.0593	+	24.2852i	0.564984	+	1.36399i	0.905737	+	0.423840i	$0.139318\pi$
$317$	10.0593	+	24.2852i	0.564984	+	1.36399i	−0.340753	+	0.940153i	$0.610682\pi$
$318$	−2.42918	−	4.48993i	−0.136222	−	0.251783i
$319$	−0.0838266	+	0.0838266i	−0.00469339	+	0.00469339i
$320$	−17.1441	+	27.4231i	−0.958385	+	1.53300i
$321$	−27.4356			−1.53130
$322$	0.0785811	−	0.263841i	0.00437915	−	0.0147033i
$323$	−5.17275	−	12.4881i	−0.287819	−	0.694857i
$324$	−9.23208	−	6.03459i	−0.512894	−	0.335255i
$325$	−34.6401	+	21.7411i	−1.92149	+	1.20598i
$326$	−12.1786	−	9.89215i	−0.674512	−	0.547876i
$327$	−3.55328			−0.196497
$328$	−0.370487	+	4.45285i	−0.0204567	+	0.245868i
$329$	0.860862	−	0.860862i	0.0474608	−	0.0474608i
$330$	−0.653828	+	0.804955i	−0.0359921	+	0.0443113i
$331$	−5.20508	+	12.5662i	−0.286097	+	0.690700i	−0.999954	−	0.00959195i	$-0.996947\pi$
$331$	−5.20508	+	12.5662i	−0.286097	+	0.690700i	0.713857	+	0.700292i	$0.246947\pi$
$332$	21.7823	+	4.10431i	1.19546	+	0.225253i
$333$	−3.68518	−	8.89682i	−0.201947	−	0.487543i
$334$	−1.09946	−	2.03217i	−0.0601598	−	0.111196i
$335$		−	23.0853i		−	1.26128i
$336$	−0.971587	+	0.0196466i	−0.0530044	+	0.00107181i
$337$	−4.69307			−0.255648			−0.127824	−	0.991797i	$-0.540799\pi$
$337$	−4.69307			−0.255648			−0.127824	+	0.991797i	$0.540799\pi$
$338$	18.3652	−	0.847369i	0.998937	−	0.0460908i
$339$	−0.471856	+	1.13916i	−0.0256277	+	0.0618708i
$340$	21.6777	+	31.7435i	1.17564	+	1.72153i
$341$	0.108320	+	0.261508i	0.00586586	+	0.0141614i
$342$	0.370765	+	3.57889i	0.0200487	+	0.193524i
$343$		−	2.33952i		−	0.126322i
$344$	−21.0910	+	6.74879i	−1.13715	+	0.363870i
$345$	−6.81899			−0.367122
$346$	−1.24486	−	12.0163i	−0.0669240	−	0.645999i
$347$	11.0734	+	26.7334i	0.594449	+	1.43513i	0.879167	+	0.476515i	$0.158100\pi$
$347$	11.0734	+	26.7334i	0.594449	+	1.43513i	−0.284718	+	0.958611i	$0.591900\pi$
$348$	0.564079	+	2.69323i	0.0302378	+	0.144373i
$349$	13.3561	−	5.53227i	0.714934	−	0.296135i	0.00458953	−	0.999989i	$-0.498539\pi$
$349$	13.3561	−	5.53227i	0.714934	−	0.296135i	0.710345	+	0.703854i	$0.248539\pi$
$350$	0.766710	−	2.57427i	0.0409824	−	0.137601i
$351$	−20.0892	+	3.40272i	−1.07228	+	0.181624i
$352$	0.349030	+	0.615078i	0.0186034	+	0.0327837i
$353$	−15.0043	+	15.0043i	−0.798600	+	0.798600i	−0.982875	−	0.184275i	$-0.941006\pi$
$353$	−15.0043	+	15.0043i	−0.798600	+	0.798600i	0.184275	+	0.982875i	$0.441006\pi$
$354$	−7.36125	+	24.7159i	−0.391246	+	1.31363i
$355$	−19.2500	+	46.4736i	−1.02168	+	2.46656i
$356$	6.93738	−	10.6132i	0.367681	−	0.562501i
$357$	−0.442007	+	1.06710i	−0.0233935	+	0.0564769i
$358$	4.10160	−	0.424916i	0.216776	−	0.0224575i
$359$			6.78539i			0.358119i	0.983838	+	0.179060i	$0.0573055\pi$
$359$			6.78539i			0.358119i	−0.983838	+	0.179060i	$0.942694\pi$
$360$	−3.11832	−	9.74524i	−0.164350	−	0.513619i
$361$	7.71907	−	7.71907i	0.406267	−	0.406267i
$362$	13.6832	−	16.8459i	0.719171	−	0.885400i
$363$	−6.09897	−	14.7242i	−0.320113	−	0.772821i
$364$	−0.869407	+	0.837900i	−0.0455693	+	0.0439179i
$365$	33.3640	+	13.8198i	1.74635	+	0.723363i
$366$	2.14086	−	7.18808i	0.111905	−	0.375727i
$367$	7.20556			0.376127			0.188064	−	0.982157i	$-0.439779\pi$
$367$	7.20556			0.376127			0.188064	+	0.982157i	$0.439779\pi$
$368$	−1.69234	+	4.33134i	−0.0882193	+	0.225787i
$369$	−0.999600	−	0.999600i	−0.0520371	−	0.0520371i
$370$	−17.5619	+	58.9651i	−0.912999	+	3.06545i
$371$	0.384874	−	0.159420i	0.0199816	−	0.00827667i
$372$	6.45644	+	1.21655i	0.334751	+	0.0630751i
$373$	−12.2576	−	29.5926i	−0.634677	−	1.53225i	−0.833681	−	0.552246i	$-0.813771\pi$
$373$	−12.2576	−	29.5926i	−0.634677	−	1.53225i	0.199004	−	0.979999i	$-0.436229\pi$
$374$	0.836081	−	0.0866160i	0.0432327	−	0.00447880i
$375$	−37.2048			−1.92125
$376$	−15.6972	+	13.2857i	−0.809519	+	0.685159i
$377$	2.78738	+	1.97989i	0.143557	+	0.101970i
$378$	0.843696	−	1.03871i	0.0433950	−	0.0534254i
$379$	−13.1898	−	5.46338i	−0.677513	−	0.280635i	0.0172737	−	0.999851i	$-0.494501\pi$
$379$	−13.1898	−	5.46338i	−0.677513	−	0.280635i	−0.694787	+	0.719216i	$0.744501\pi$
$380$	12.5775	−	19.2418i	0.645210	−	0.987083i
$381$	18.9413	+	7.84574i	0.970392	+	0.401950i
$382$	−8.67090	−	16.0267i	−0.443642	−	0.819999i
$383$	−2.96879	−	2.96879i	−0.151698	−	0.151698i	0.627178	−	0.778876i	$-0.284210\pi$
$383$	−2.96879	−	2.96879i	−0.151698	−	0.151698i	−0.778876	+	0.627178i	$0.784210\pi$
$384$	16.3829	+	1.03008i	0.836035	+	0.0525659i
$385$	−0.0598399	−	0.0598399i	−0.00304972	−	0.00304972i
$386$	20.7825	+	6.18976i	1.05780	+	0.315050i
$387$	2.68108	−	6.47270i	0.136287	−	0.329026i
$388$	4.23184	+	20.2052i	0.214839	+	1.02576i
$389$	−14.2653	−	34.4396i	−0.723281	−	1.74616i	−0.663781	−	0.747927i	$-0.731049\pi$
$389$	−14.2653	−	34.4396i	−0.723281	−	1.74616i	−0.0595006	−	0.998228i	$-0.518951\pi$
$390$	26.0382	+	14.7148i	1.31850	+	0.745114i
$391$	3.90821	+	3.90821i	0.197647	+	0.197647i
$392$	−1.63507	+	19.6518i	−0.0825836	+	0.992565i
$393$	−18.8377	−	18.8377i	−0.950236	−	0.950236i
$394$	−0.313682	−	3.02789i	−0.0158031	−	0.152543i
$395$	22.2517	−	53.7203i	1.11960	−	2.70296i
$396$	−0.219875	−	0.0414297i	−0.0110491	−	0.00208192i
$397$	−0.839703	−	2.02722i	−0.0421435	−	0.101743i	0.901406	−	0.432975i	$-0.142536\pi$
$397$	−0.839703	−	2.02722i	−0.0421435	−	0.101743i	−0.943550	+	0.331231i	$0.892536\pi$
$398$	1.79942	−	6.04165i	0.0901966	−	0.302840i
$399$	0.690737			0.0345801
$400$	−16.5120	+	42.2606i	−0.825602	+	2.11303i
$401$	1.35223	−	1.35223i	0.0675272	−	0.0675272i	−0.672537	−	0.740064i	$-0.734795\pi$
$401$	1.35223	−	1.35223i	0.0675272	−	0.0675272i	0.740064	+	0.672537i	$0.234795\pi$
$402$	−10.3057	+	5.57565i	−0.514000	+	0.278088i
$403$	6.91434	−	4.33964i	0.344428	−	0.216173i
$404$	−22.0222	−	4.14951i	−1.09564	−	0.206446i
$405$	−20.5969	−	8.53153i	−1.02347	−	0.423935i
$406$	−0.223352	+	0.0231388i	−0.0110848	+	0.00114836i
$407$	0.951320	+	0.951320i	0.0471552	+	0.0471552i
$408$	8.93517	−	17.3441i	0.442357	−	0.858661i
$409$		−	23.2371i		−	1.14900i	−0.818504	−	0.574501i	$-0.805196\pi$
$409$		−	23.2371i		−	1.14900i	0.818504	−	0.574501i	$-0.194804\pi$
$410$	0.930686	+	8.98367i	0.0459633	+	0.443672i
$411$	6.39049	−	15.4280i	0.315219	−	0.761007i
$412$	−3.44721	−	16.4589i	−0.169832	−	0.810874i
$413$	−1.94428	−	0.805346i	−0.0956717	−	0.0396285i
$414$	−0.700078	−	1.29398i	−0.0344070	−	0.0635956i
$415$	44.8038			2.19933
$416$	15.8088	−	12.8872i	0.775092	−	0.631848i
$417$	1.53757			0.0752950
$418$	−0.239198	−	0.442118i	−0.0116996	−	0.0216247i
$419$	5.64401	+	2.33783i	0.275728	+	0.114210i	0.516263	−	0.856430i	$-0.327323\pi$
$419$	5.64401	+	2.33783i	0.275728	+	0.114210i	−0.240535	+	0.970641i	$0.577323\pi$
$420$	−1.92257	+	0.402670i	−0.0938120	+	0.0196483i
$421$	6.61577	−	15.9719i	0.322433	−	0.778422i	−0.676679	−	0.736279i	$-0.736581\pi$
$421$	6.61577	−	15.9719i	0.322433	−	0.778422i	0.999112	−	0.0421436i	$-0.0134187\pi$
$422$	−2.01329	−	19.4338i	−0.0980055	−	0.946021i
$423$		−	6.50623i		−	0.316344i
$424$	−6.70211	+	2.14456i	−0.325483	+	0.104149i
$425$	38.1321	+	38.1321i	1.84968	+	1.84968i
$426$	25.3959	−	2.63096i	1.23044	−	0.127470i
$427$	0.565452	+	0.234218i	0.0273641	+	0.0113346i
$428$	−7.00265	+	37.1644i	−0.338486	+	1.79641i
$429$	0.553945	−	0.347672i	0.0267447	−	0.0167858i
$430$	−39.3686	+	21.2995i	−1.89852	+	1.02715i
$431$	−4.74711	+	4.74711i	−0.228660	+	0.228660i	−0.812133	−	0.583472i	$-0.801694\pi$
$431$	−4.74711	+	4.74711i	−0.228660	+	0.228660i	0.583472	+	0.812133i	$0.301694\pi$
$432$	−15.6573	+	16.3036i	−0.753312	+	0.784406i
$433$	−35.3538			−1.69899			−0.849497	−	0.527593i	$-0.823094\pi$
$433$	−35.3538			−1.69899			−0.849497	+	0.527593i	$0.823094\pi$
$434$	−0.153039	+	0.513838i	−0.00734611	+	0.0246650i
$435$	2.12849	+	5.13863i	0.102053	+	0.246378i
$436$	−0.906938	+	4.81329i	−0.0434345	+	0.230515i
$437$	1.26490	−	3.05373i	0.0605082	−	0.146080i
$438$	−1.88880	−	18.2321i	−0.0902504	−	0.871163i
$439$	−21.1592	−	21.1592i	−1.00988	−	1.00988i	−0.999951	−	0.00992460i	$-0.996841\pi$
$439$	−21.1592	−	21.1592i	−1.00988	−	1.00988i	−0.00992460	−	0.999951i	$-0.503159\pi$
$440$	0.923512	+	1.09114i	0.0440267	+	0.0520178i
$441$	−4.41154	−	4.41154i	−0.210073	−	0.210073i
$442$	−6.48984	−	23.3570i	−0.308690	−	1.11098i
$443$	7.27080	+	17.5533i	0.345446	+	0.833980i	0.997146	+	0.0755033i	$0.0240563\pi$
$443$	7.27080	+	17.5533i	0.345446	+	0.833980i	−0.651700	+	0.758477i	$0.725944\pi$
$444$	30.5646	−	6.40155i	1.45053	−	0.303804i
$445$	9.80788	−	23.6783i	0.464938	−	1.12246i
$446$	21.9894	+	6.54923i	1.04123	+	0.310115i
$447$	−2.08217	−	2.08217i	−0.0984832	−	0.0984832i
$448$	−0.221374	+	1.32113i	−0.0104590	+	0.0624176i
$449$	−10.5786	−	10.5786i	−0.499236	−	0.499236i	0.411964	−	0.911200i	$-0.364843\pi$
$449$	−10.5786	−	10.5786i	−0.499236	−	0.499236i	−0.911200	+	0.411964i	$0.864843\pi$
$450$	−6.83061	−	12.6253i	−0.321998	−	0.595160i
$451$	0.182465	+	0.0755793i	0.00859192	+	0.00355889i
$452$	1.42268	+	0.929939i	0.0669171	+	0.0437406i
$453$	20.3501	+	8.42927i	0.956129	+	0.396042i
$454$	−12.6175	+	15.5339i	−0.592169	+	0.729044i
$455$	−1.41335	+	1.98978i	−0.0662590	+	0.0932822i
$456$	−11.6276	−	0.967443i	−0.544513	−	0.0453047i
$457$	−8.47358			−0.396377			−0.198189	−	0.980164i	$-0.563506\pi$
$457$	−8.47358			−0.396377			−0.198189	+	0.980164i	$0.563506\pi$
$458$	−14.9682	+	1.55067i	−0.699417	+	0.0724579i
$459$	10.2814	+	24.8214i	0.479894	+	1.15857i
$460$	−1.74048	+	9.23704i	−0.0811502	+	0.430679i
$461$	19.6702	−	8.14766i	0.916132	−	0.379474i	0.125731	−	0.992064i	$-0.459872\pi$
$461$	19.6702	−	8.14766i	0.916132	−	0.379474i	0.790401	+	0.612590i	$0.209872\pi$
$462$	−0.0122608	+	0.0411663i	−0.000570423	+	0.00191523i
$463$	18.4109	+	18.4109i	0.855627	+	0.855627i	0.990819	−	0.135193i	$-0.0431653\pi$
$463$	18.4109	+	18.4109i	0.855627	+	0.855627i	−0.135193	+	0.990819i	$0.543165\pi$
$464$	3.79224	−	0.0766835i	0.176050	−	0.00355994i
$465$	13.2802			0.615854
$466$	−4.56251	+	15.3189i	−0.211354	+	0.709635i
$467$	33.8363	+	14.0155i	1.56576	+	0.648559i	0.986078	−	0.166285i	$-0.0531772\pi$
$467$	33.8363	+	14.0155i	1.56576	+	0.648559i	0.579681	+	0.814844i	$0.303177\pi$
$468$	−0.119061	+	6.45175i	−0.00550359	+	0.298232i
$469$	−0.365913	−	0.883393i	−0.0168963	−	0.0407913i
$470$	−26.2078	+	32.2654i	−1.20887	+	1.48829i
$471$	−3.15608	+	3.15608i	−0.145425	+	0.145425i
$472$	31.6013	+	16.2801i	1.45457	+	0.749351i
$473$			0.978796i			0.0450051i
$474$	−29.3559	+	3.04120i	−1.34836	+	0.139687i
$475$	12.3415	−	29.7950i	0.566267	−	1.36709i
$476$	1.33268	+	0.871112i	0.0610833	+	0.0399273i
$477$	0.851968	−	2.05683i	0.0390089	−	0.0941759i
$478$	0.295795	−	0.993149i	0.0135293	−	0.0454256i
$479$	−8.74720	+	8.74720i	−0.399670	+	0.399670i	−0.878117	−	0.478447i	$-0.841200\pi$
$479$	−8.74720	+	8.74720i	−0.399670	+	0.399670i	0.478447	+	0.878117i	$0.341200\pi$
$480$	32.9279	−	4.08565i	1.50295	−	0.186484i
$481$	22.4691	−	31.6330i	1.02450	−	1.44234i
$482$	5.92631	−	19.8980i	0.269936	−	0.906327i
$483$	−0.260939	+	0.108084i	−0.0118731	+	0.00491801i
$484$	−21.5022	+	4.50348i	−0.977372	+	0.204704i
$485$	15.9684	+	38.5511i	0.725087	+	1.75052i
$486$	−1.30456	−	12.5925i	−0.0591759	−	0.571209i
$487$	25.0041			1.13304			0.566522	−	0.824047i	$-0.308289\pi$
$487$	25.0041			1.13304			0.566522	+	0.824047i	$0.308289\pi$
$488$	−9.19057	−	4.73471i	−0.416037	−	0.214330i
$489$			16.0971i			0.727936i
$490$	4.10740	+	39.6476i	0.185553	+	1.79110i
$491$	−8.43661	−	20.3678i	−0.380739	−	0.919184i	−0.991823	−	0.127619i	$-0.959266\pi$
$491$	−8.43661	−	20.3678i	−0.380739	−	0.919184i	0.611085	−	0.791565i	$-0.290734\pi$
$492$	3.78568	−	2.58524i	0.170672	−	0.116552i
$493$	1.72522	−	4.16505i	0.0776999	−	0.187584i
$494$	−11.4197	+	8.93108i	−0.513796	+	0.401828i
$495$	−0.452259			−0.0203275
$496$	3.29588	−	8.43542i	0.147990	−	0.378761i
$497$			2.08351i			0.0934580i
$498$	−10.8212	−	20.0012i	−0.484909	−	0.896274i
$499$	3.20391	+	7.73492i	0.143427	+	0.346263i	0.979226	−	0.202773i	$-0.0649952\pi$
$499$	3.20391	+	7.73492i	0.143427	+	0.346263i	−0.835799	+	0.549035i	$0.814995\pi$
$500$	−9.49614	+	50.3978i	−0.424680	+	2.25386i
$501$	−0.907147	+	2.19005i	−0.0405283	+	0.0978440i
$502$	25.6932	−	31.6320i	1.14674	−	1.41180i
$503$	4.00991	−	4.00991i	0.178793	−	0.178793i	−0.612036	−	0.790830i	$-0.709649\pi$
$503$	4.00991	−	4.00991i	0.178793	−	0.178793i	0.790830	+	0.612036i	$0.209649\pi$
$504$	−0.273794	−	0.323489i	−0.0121958	−	0.0144094i
$505$	−45.2972			−2.01570
$506$	0.159543	+	0.129590i	0.00709255	+	0.00576096i
$507$	−12.5542	−	14.0771i	−0.557550	−	0.625184i
$508$	15.4625	−	23.6554i	0.686035	−	1.04954i
$509$	−10.1900	−	24.6008i	−0.451664	−	1.09041i	−0.971689	−	0.236262i	$-0.924078\pi$
$509$	−10.1900	−	24.6008i	−0.451664	−	1.09041i	0.520026	−	0.854151i	$-0.325922\pi$
$510$	11.2570	−	37.7960i	0.498468	−	1.67364i
$511$	1.49578			0.0661693
$512$	5.57691	−	21.9294i	0.246467	−	0.969151i
$513$	11.3611	−	11.3611i	0.501604	−	0.501604i
$514$	−1.00297	−	1.85382i	−0.0442391	−	0.0817686i
$515$	−13.0077	−	31.4033i	−0.573186	−	1.38379i
$516$	19.0169	+	12.4305i	0.837173	+	0.547221i
$517$	0.347849	+	0.839782i	0.0152984	+	0.0369336i
$518$	0.262594	+	2.53475i	0.0115377	+	0.111371i
$519$	−8.76395	+	8.76395i	−0.384695	+	0.384695i
$520$	26.5787	−	31.5157i	1.16556	−	1.38205i
$521$	23.9151	+	23.9151i	1.04774	+	1.04774i	0.998802	+	0.0489379i	$0.0155836\pi$
$521$	23.9151	+	23.9151i	1.04774	+	1.04774i	0.0489379	+	0.998802i	$0.484416\pi$
$522$	−0.756588	+	0.931467i	−0.0331150	+	0.0407692i
$523$	−15.2407	+	6.31292i	−0.666431	+	0.276045i	−0.690142	−	0.723674i	$-0.742452\pi$
$523$	−15.2407	+	6.31292i	−0.666431	+	0.276045i	0.0237112	+	0.999719i	$0.492452\pi$
$524$	−30.3258	+	20.7095i	−1.32479	+	0.904699i
$525$	−2.54596	+	1.05457i	−0.111115	+	0.0460253i
$526$	−39.6451	−	11.8077i	−1.72861	−	0.514841i
$527$	−7.61136	−	7.61136i	−0.331556	−	0.331556i
$528$	0.264051	−	0.675807i	0.0114913	−	0.0294107i
$529$		−	21.6485i		−	0.941238i
$530$	−12.5102	+	6.76835i	−0.543408	+	0.293998i
$531$	−10.3906	+	4.30391i	−0.450912	+	0.186774i
$532$	0.176304	−	0.935675i	0.00764373	−	0.0405667i
$533$	1.27030	−	5.55245i	0.0550227	−	0.240503i
$534$	−12.9392	+	1.34047i	−0.559935	+	0.0580080i
$535$			76.4430i			3.30492i
$536$	4.92238	+	15.3832i	0.212614	+	0.664454i
$537$	−2.99146	−	2.99146i	−0.129091	−	0.129091i
$538$	−9.49446	+	0.983603i	−0.409335	+	0.0424061i
$539$	0.805271	+	0.333554i	0.0346855	+	0.0143672i
$540$	−24.9990	+	38.2451i	−1.07579	+	1.64581i
$541$	−15.3040	+	6.33914i	−0.657972	+	0.272541i	−0.686585	−	0.727050i	$-0.740891\pi$
$541$	−15.3040	+	6.33914i	−0.657972	+	0.272541i	0.0286128	+	0.999591i	$0.490891\pi$
$542$	26.2953	+	7.83167i	1.12948	+	0.336399i
$543$	−22.2660			−0.955527
$544$	−21.2138	−	16.5305i	−0.909534	−	0.708741i
$545$			9.90040i			0.424087i
$546$	1.22963	+	0.150366i	0.0526232	+	0.00643506i
$547$	14.7496	+	6.10949i	0.630648	+	0.261223i	0.675028	−	0.737792i	$-0.264131\pi$
$547$	14.7496	+	6.10949i	0.630648	+	0.261223i	−0.0443805	+	0.999015i	$0.514131\pi$
$548$	−19.2677	−	12.5944i	−0.823077	−	0.538007i
$549$	3.02187	−	1.25170i	0.128970	−	0.0534213i
$550$	1.55665	+	1.26440i	0.0663757	+	0.0539140i
$551$	−2.69605			−0.114855
$552$	4.54394	−	1.45399i	0.193403	−	0.0618857i
$553$		−	2.40839i		−	0.102415i
$554$	−23.4972	+	28.9284i	−0.998300	+	1.22905i
$555$	58.3166	−	24.1555i	2.47540	−	1.02534i
$556$	0.392449	−	2.08280i	0.0166435	−	0.0883302i
$557$	−14.5724	−	35.1809i	−0.617453	−	1.49066i	−0.854651	−	0.519202i	$-0.826229\pi$
$557$	−14.5724	−	35.1809i	−0.617453	−	1.49066i	0.237198	−	0.971461i	$-0.423771\pi$
$558$	1.36342	+	2.52006i	0.0577184	+	0.106683i
$559$	27.8324	−	4.71427i	1.17718	−	0.199392i
$560$	0.0547408	+	2.70711i	0.00231322	+	0.114396i
$561$	−0.609787	−	0.609787i	−0.0257452	−	0.0257452i
$562$	−39.7109	+	21.4847i	−1.67510	+	0.906276i
$563$	−19.8298	−	8.21375i	−0.835725	−	0.346168i	−0.0765582	−	0.997065i	$-0.524393\pi$
$563$	−19.8298	−	8.21375i	−0.835725	−	0.346168i	−0.759166	+	0.650897i	$0.774393\pi$
$564$	20.7336	+	3.90671i	0.873043	+	0.164502i
$565$	3.17402	+	1.31472i	0.133532	+	0.0553107i
$566$	15.8503	−	19.5140i	0.666239	−	0.820234i
$567$	−0.923401			−0.0387792
$568$	2.91815	−	35.0730i	0.122443	−	1.47163i
$569$	19.2787	+	19.2787i	0.808204	+	0.808204i	0.984362	−	0.176158i	$-0.0563669\pi$
$569$	19.2787	+	19.2787i	0.808204	+	0.808204i	−0.176158	+	0.984362i	$0.556367\pi$
$570$	−23.4588	+	2.43028i	−0.982582	+	0.101793i
$571$	−9.20125	+	3.81128i	−0.385060	+	0.159497i	−0.566812	−	0.823847i	$-0.691823\pi$
$571$	−9.20125	+	3.81128i	−0.385060	+	0.159497i	0.181752	+	0.983344i	$0.441823\pi$
$572$	−0.329569	−	0.839116i	−0.0137800	−	0.0350852i
$573$	−7.15422	+	17.2718i	−0.298872	+	0.721540i
$574$	0.178010	+	0.329022i	0.00742998	+	0.0137331i
$575$			13.1868i			0.549928i
$576$	4.15587	+	5.82898i	0.173161	+	0.242874i
$577$	−13.8986	+	13.8986i	−0.578607	+	0.578607i	−0.934519	−	0.355912i	$-0.884170\pi$
$577$	−13.8986	+	13.8986i	−0.578607	+	0.578607i	0.355912	+	0.934519i	$0.384170\pi$
$578$	−6.96876	+	3.77029i	−0.289862	+	0.156823i
$579$	−8.51372	−	20.5539i	−0.353818	−	0.854192i
$580$	7.50409	−	1.57168i	0.311590	−	0.0652604i
$581$	1.71449	−	0.710163i	0.0711288	−	0.0294625i
$582$	13.3531	−	16.4396i	0.553505	−	0.681442i
$583$			0.311033i			0.0128817i
$584$	−25.1794	−	2.09498i	−1.04193	−	0.0866909i
$585$	2.17826	+	12.8601i	0.0900598	+	0.531700i
$586$	8.12874	−	0.842118i	0.335795	−	0.0347876i
$587$	−5.99353	+	14.4697i	−0.247379	+	0.597226i	−0.997980	−	0.0635297i	$-0.979764\pi$
$587$	−5.99353	+	14.4697i	−0.247379	+	0.597226i	0.750601	+	0.660756i	$0.229764\pi$
$588$	16.7073	−	11.4095i	0.688999	−	0.470518i
$589$	−2.46343	+	5.94724i	−0.101504	+	0.245052i
$590$	68.8651	+	20.5105i	2.83513	+	0.844403i
$591$	−2.20836	+	2.20836i	−0.0908396	+	0.0908396i
$592$	−0.870255	−	43.0369i	−0.0357673	−	1.76881i
$593$	33.8721	−	33.8721i	1.39096	−	1.39096i	0.567783	−	0.823178i	$-0.307801\pi$
$593$	33.8721	−	33.8721i	1.39096	−	1.39096i	0.823178	−	0.567783i	$-0.192199\pi$
$594$	0.475431	+	0.878756i	0.0195072	+	0.0360558i
$595$	2.97323	+	1.23155i	0.121891	+	0.0504887i
$596$	−3.35197	+	2.28906i	−0.137302	+	0.0937637i
$597$	−5.97520	+	2.47501i	−0.244549	+	0.101295i
$598$	2.91649	−	5.16080i	0.119264	−	0.211041i
$599$	24.6953	−	24.6953i	1.00902	−	1.00902i	0.00906172	−	0.999959i	$-0.497116\pi$
$599$	24.6953	−	24.6953i	1.00902	−	1.00902i	0.999959	−	0.00906172i	$-0.00288448\pi$
$600$	44.3349	−	14.1864i	1.80996	−	0.579159i
$601$	−20.4462	+	20.4462i	−0.834017	+	0.834017i	−0.988064	−	0.154047i	$-0.950769\pi$
$601$	−20.4462	+	20.4462i	−0.834017	+	0.834017i	0.154047	+	0.988064i	$0.450769\pi$
$602$	−1.16889	+	1.43907i	−0.0476405	+	0.0586521i
$603$	−4.72101	−	1.95551i	−0.192254	−	0.0796344i
$604$	16.6125	−	25.4148i	0.675952	−	1.03411i
$605$	−41.0257	+	16.9934i	−1.66793	+	0.690880i
$606$	10.9404	+	20.2214i	0.444422	+	0.821440i
$607$		−	27.1619i		−	1.10247i	−0.834351	−	0.551234i	$-0.814157\pi$
$607$		−	27.1619i		−	1.10247i	0.834351	−	0.551234i	$-0.185843\pi$
$608$	−4.27834	+	15.5039i	−0.173509	+	0.628766i
$609$	0.162900	+	0.162900i	0.00660103	+	0.00660103i
$610$	−20.0279	−	5.96503i	−0.810908	−	0.241517i
$611$	22.2041	−	13.9359i	0.898281	−	0.563787i
$612$	8.32792	−	1.74423i	0.336636	−	0.0705061i
$613$	8.81016	−	21.2696i	0.355839	−	0.859071i	−0.640037	−	0.768344i	$-0.721081\pi$
$613$	8.81016	−	21.2696i	0.355839	−	0.859071i	0.995876	−	0.0907270i	$-0.0289191\pi$
$614$	21.1587	−	26.0493i	0.853894	−	1.05126i
$615$	6.55214	−	6.55214i	0.264208	−	0.264208i
$616$	0.0526346	+	0.0271158i	0.00212071	+	0.00109253i
$617$	−21.2107			−0.853909			−0.426954	−	0.904273i	$-0.640414\pi$
$617$	−21.2107			−0.853909			−0.426954	+	0.904273i	$0.640414\pi$
$618$	−10.8773	+	13.3915i	−0.437549	+	0.538684i
$619$	34.0488	+	14.1035i	1.36854	+	0.566866i	0.941391	−	0.337317i	$-0.109519\pi$
$619$	34.0488	+	14.1035i	1.36854	+	0.566866i	0.427145	+	0.904183i	$0.359519\pi$
$620$	3.38964	−	17.9894i	0.136131	−	0.722472i
$621$	−2.51411	+	6.06961i	−0.100888	+	0.243565i
$622$	30.7556	+	9.16009i	1.23319	+	0.367286i
$623$		−	1.06155i		−	0.0425299i
$624$	−20.4885	−	4.25342i	−0.820198	−	0.170273i
$625$			46.9479i			1.87791i
$626$	−1.94382	+	6.52650i	−0.0776907	+	0.260851i
$627$	−0.197358	+	0.476465i	−0.00788173	+	0.0190282i
$628$	3.46969	+	5.08080i	0.138456	+	0.202746i
$629$	−47.2677	−	19.5789i	−1.88469	−	0.780663i
$630$	−0.664931	−	0.540093i	−0.0264915	−	0.0215178i
$631$	−17.1976			−0.684626			−0.342313	−	0.939586i	$-0.611210\pi$
$631$	−17.1976			−0.684626			−0.342313	+	0.939586i	$0.611210\pi$
$632$	−3.37318	+	40.5419i	−0.134178	+	1.61267i
$633$	−14.1738	+	14.1738i	−0.563358	+	0.563358i
$634$	−28.8549	−	23.4375i	−1.14597	−	0.930822i
$635$	21.8604	−	52.7756i	0.867503	−	2.09434i
$636$	6.04301	+	3.95004i	0.239621	+	0.156629i
$637$	5.60621	−	24.5046i	0.222126	−	0.970910i
$638$	0.0478556	−	0.160678i	0.00189462	−	0.00636131i
$639$	7.87337	+	7.87337i	0.311466	+	0.311466i
$640$	2.87008	−	45.6471i	0.113450	−	1.80436i
$641$			30.1213i			1.18972i	0.803830	+	0.594859i	$0.202792\pi$
$641$			30.1213i			1.18972i	−0.803830	+	0.594859i	$0.797208\pi$
$642$	34.1254	−	18.4628i	1.34682	−	0.728669i
$643$	28.2104	−	11.6851i	1.11251	−	0.460817i	0.250709	−	0.968062i	$-0.419336\pi$
$643$	28.2104	−	11.6851i	1.11251	−	0.460817i	0.861802	+	0.507245i	$0.169336\pi$
$644$	0.0798097	+	0.381057i	0.00314494	+	0.0150157i
$645$	42.4270	+	17.5739i	1.67056	+	0.691970i
$646$	14.8380	+	12.0522i	0.583792	+	0.474188i
$647$	−13.9589	+	13.9589i	−0.548781	+	0.548781i	−0.926088	−	0.377307i	$-0.876850\pi$
$647$	−13.9589	+	13.9589i	−0.548781	+	0.548781i	0.377307	+	0.926088i	$0.376850\pi$
$648$	15.5442	+	1.29331i	0.610634	+	0.0508061i
$649$	1.11104	−	1.11104i	0.0436123	−	0.0436123i
$650$	28.4560	−	50.3536i	1.11614	−	1.97503i
$651$	0.508187	−	0.210498i	0.0199174	−	0.00825006i
$652$	21.8052	+	4.10862i	0.853957	+	0.160906i
$653$	−3.10496	−	1.28612i	−0.121507	−	0.0503297i	0.321102	−	0.947045i	$-0.395947\pi$
$653$	−3.10496	−	1.28612i	−0.121507	−	0.0503297i	−0.442608	+	0.896715i	$0.645947\pi$
$654$	4.41971	−	2.39118i	0.172824	−	0.0935026i
$655$	−52.4870	+	52.4870i	−2.05084	+	2.05084i
$656$	−2.53573	−	5.78795i	−0.0990035	−	0.225982i
$657$	5.65240	−	5.65240i	0.220521	−	0.220521i
$658$	−0.491456	+	1.65009i	−0.0191589	+	0.0643273i
$659$	−8.54734	+	20.6351i	−0.332957	+	0.803830i	0.665398	+	0.746489i	$0.268262\pi$
$659$	−8.54734	+	20.6351i	−0.332957	+	0.803830i	−0.998355	+	0.0573404i	$0.981738\pi$
$660$	0.271562	−	1.44123i	0.0105705	−	0.0560998i
$661$	−1.83372	+	4.42699i	−0.0713234	+	0.172190i	−0.955521	−	0.294923i	$-0.904706\pi$
$661$	−1.83372	+	4.42699i	−0.0713234	+	0.172190i	0.884198	+	0.467113i	$0.154706\pi$
$662$	−1.98214	−	19.1331i	−0.0770381	−	0.743628i
$663$	−14.4025	+	20.2764i	−0.559346	+	0.787471i
$664$	−29.8557	+	9.55333i	−1.15863	+	0.370741i
$665$		−	1.92458i		−	0.0746321i
$666$	10.5709	+	8.58627i	0.409614	+	0.332711i
$667$	1.01848	−	0.421869i	0.0394358	−	0.0163348i
$668$	2.73511	+	1.78781i	0.105824	+	0.0691725i
$669$	−9.00815	−	21.7476i	−0.348275	−	0.840811i
$670$	15.5353	+	28.7144i	0.600180	+	1.10933i
$671$	−0.323123	+	0.323123i	−0.0124740	+	0.0124740i
$672$	1.19528	−	0.678268i	0.0461088	−	0.0261647i
$673$			13.4817i			0.519680i	0.965652	+	0.259840i	$0.0836699\pi$
$673$			13.4817i			0.519680i	−0.965652	+	0.259840i	$0.916330\pi$
$674$	5.83743	−	3.15821i	0.224849	−	0.121650i
$675$	−24.5300	+	59.2207i	−0.944161	+	2.27941i
$676$	−22.2732	+	13.4129i	−0.856660	+	0.515881i
$677$	−3.00640	+	1.24529i	−0.115545	+	0.0478605i	−0.439707	−	0.898141i	$-0.644918\pi$
$677$	−3.00640	+	1.24529i	−0.115545	+	0.0478605i	0.324162	+	0.946002i	$0.394918\pi$
$678$	−0.179687	−	1.73447i	−0.00690084	−	0.0666120i
$679$	1.22211	+	1.22211i	0.0469002	+	0.0469002i
$680$	−48.3254	−	24.8958i	−1.85320	−	0.954711i
$681$	20.5320			0.786787
$682$	−0.310715	−	0.252380i	−0.0118979	−	0.00966412i
$683$	−41.3661	−	17.1344i	−1.58283	−	0.655629i	−0.593970	−	0.804487i	$-0.702440\pi$
$683$	−41.3661	−	17.1344i	−1.58283	−	0.655629i	−0.988859	+	0.148858i	$0.952440\pi$
$684$	−2.86959	−	4.20206i	−0.109722	−	0.160670i
$685$	−42.9866	−	17.8056i	−1.64243	−	0.680318i
$686$	1.57438	+	2.90998i	0.0601101	+	0.111104i
$687$	10.9169	+	10.9169i	0.416505	+	0.416505i
$688$	21.6923	−	22.5876i	0.827010	−	0.861146i
$689$	8.84430	−	1.49806i	0.336941	−	0.0570714i
$690$	8.48173	−	4.58885i	0.322894	−	0.174694i
$691$	0.000934320		0.00225565i	3.55432e−5		8.58089e-5i	0.923897	−	0.382641i	$-0.124985\pi$
$691$	0.000934320		0.00225565i	3.55432e−5		8.58089e-5i	−0.923862	+	0.382726i	$0.874985\pi$
$692$	9.63477	+	14.1086i	0.366259	+	0.536328i
$693$	−0.0173064	+	0.00716853i	−0.000657414	+	0.000272310i
$694$	−31.7638	−	25.8003i	−1.20574	−	0.979365i
$695$		−	4.28408i		−	0.162504i
$696$	−2.51404	−	2.97035i	−0.0952944	−	0.112591i
$697$	−7.51053			−0.284482
$698$	−12.8899	+	15.8692i	−0.487889	+	0.600659i
$699$	15.1504	−	6.27552i	0.573042	−	0.237362i
$700$	0.778697	+	3.71794i	0.0294320	+	0.140525i
$701$	11.2131	+	4.64462i	0.423513	+	0.175425i	0.584252	−	0.811572i	$-0.301388\pi$
$701$	11.2131	+	4.64462i	0.423513	+	0.175425i	−0.160739	+	0.986997i	$0.551388\pi$
$702$	22.6978	−	17.7515i	0.856674	−	0.669986i
$703$			30.5965i			1.15397i
$704$	−0.848055	−	0.530178i	−0.0319623	−	0.0199818i
$705$	42.6468			1.60617
$706$	8.56579	−	28.7602i	0.322378	−	1.08240i
$707$	−1.73337	+	0.717984i	−0.0651899	+	0.0270026i
$708$	−7.47635	−	35.6963i	−0.280978	−	1.34155i
$709$	−30.7731	−	12.7466i	−1.15571	−	0.478709i	−0.279263	−	0.960215i	$-0.590090\pi$
$709$	−30.7731	−	12.7466i	−1.15571	−	0.478709i	−0.876443	+	0.481505i	$0.840090\pi$
$710$	−7.33057	−	70.7600i	−0.275111	−	2.65558i
$711$	−9.10106	−	9.10106i	−0.341317	−	0.341317i
$712$	−1.48680	+	17.8697i	−0.0557201	+	0.669695i
$713$		−	2.63215i		−	0.0985748i
$714$	−0.168320	−	1.62475i	−0.00629923	−	0.0608048i
$715$	−0.968709	−	1.54344i	−0.0362276	−	0.0577214i
$716$	−4.81579	+	3.28871i	−0.179974	+	0.122905i
$717$	−0.982227	+	0.406852i	−0.0366819	+	0.0151942i
$718$	−4.56624	−	8.43994i	−0.170411	−	0.314976i
$719$		−	39.5495i		−	1.47495i	−0.675376	−	0.737474i	$-0.736018\pi$
$719$		−	39.5495i		−	1.47495i	0.675376	−	0.737474i	$-0.263982\pi$
$720$	10.4368	+	10.0230i	0.388955	+	0.373537i
$721$	−0.995515	−	0.995515i	−0.0370749	−	0.0370749i
$722$	−4.40672	+	14.7958i	−0.164001	+	0.550644i
$723$	−19.6791	+	8.15136i	−0.731874	+	0.303152i
$724$	−5.68318	+	30.1617i	−0.211214	+	1.12095i
$725$	9.93726	−	4.11615i	0.369061	−	0.152870i
$726$	17.4948	+	14.2102i	0.649294	+	0.527392i
$727$	−2.37508	−	2.37508i	−0.0880869	−	0.0880869i	0.661690	−	0.749777i	$-0.269839\pi$
$727$	−2.37508	−	2.37508i	−0.0880869	−	0.0880869i	−0.749777	+	0.661690i	$0.769839\pi$
$728$	0.517536	−	1.62728i	0.0191812	−	0.0603111i
$729$	−20.8827	+	20.8827i	−0.773432	+	0.773432i
$730$	−50.7996	+	5.26272i	−1.88018	+	0.194782i
$731$	−14.2442	−	34.3887i	−0.526843	−	1.27191i
$732$	2.17434	+	10.3815i	0.0803657	+	0.383712i
$733$	5.27301	+	12.7302i	0.194763	+	0.470200i	0.990848	−	0.134986i	$-0.0430989\pi$
$733$	5.27301	+	12.7302i	0.194763	+	0.470200i	−0.796084	+	0.605186i	$0.793099\pi$
$734$	−8.96256	+	4.84899i	−0.330814	+	0.178979i
$735$	28.9166	−	28.9166i	1.06660	−	1.06660i
$736$	−0.809781	−	6.52635i	−0.0298489	−	0.240565i
$737$	0.713907			0.0262971
$738$	1.91602	+	0.570660i	0.0705298	+	0.0210063i
$739$	14.5255	+	35.0677i	0.534329	+	1.28998i	0.928631	+	0.371004i	$0.120986\pi$
$739$	14.5255	+	35.0677i	0.534329	+	1.28998i	−0.394302	+	0.918981i	$0.629014\pi$
$740$	−17.8365	−	85.1614i	−0.655681	−	3.13059i
$741$	14.4990	+	3.31710i	0.532633	+	0.121857i
$742$	−0.371439	+	0.457294i	−0.0136360	+	0.0167878i
$743$	11.2363			0.412219			0.206109	−	0.978529i	$-0.433920\pi$
$743$	11.2363			0.412219			0.206109	+	0.978529i	$0.433920\pi$
$744$	−8.84946	+	2.83168i	−0.324437	+	0.103814i
$745$	−5.80149	+	5.80149i	−0.212550	+	0.212550i
$746$	35.1609	+	28.5596i	1.28733	+	1.04564i
$747$	3.79524	−	9.16252i	0.138861	−	0.335239i
$748$	−0.981662	+	0.670378i	−0.0358931	+	0.0245114i
$749$	1.21166	+	2.92521i	0.0442731	+	0.106885i
$750$	46.2768	−	25.0370i	1.68979	−	0.914222i
$751$			3.24205i			0.118304i	0.998249	+	0.0591520i	$0.0188396\pi$
$751$			3.24205i			0.118304i	−0.998249	+	0.0591520i	$0.981160\pi$
$752$	10.5841	−	27.0887i	0.385962	−	0.987824i
$753$	−41.8095			−1.52362
$754$	−4.79942	−	0.586899i	−0.174784	−	0.0213736i
$755$	23.4863	−	56.7008i	0.854752	−	2.06355i
$756$	−0.350422	+	1.85975i	−0.0127447	+	0.0676386i
$757$	9.49906	+	22.9328i	0.345249	+	0.833505i	0.997167	+	0.0752157i	$0.0239645\pi$
$757$	9.49906	+	22.9328i	0.345249	+	0.833505i	−0.651918	+	0.758289i	$0.726035\pi$
$758$	20.0826	−	2.08050i	0.729431	−	0.0755673i
$759$		−	0.210876i		−	0.00765431i
$760$	−2.69556	+	32.3977i	−0.0977783	+	1.17519i
$761$	6.33846			0.229769			0.114884	−	0.993379i	$-0.463350\pi$
$761$	6.33846			0.229769			0.114884	+	0.993379i	$0.463350\pi$
$762$	−28.8397	+	2.98773i	−1.04475	+	0.108234i
$763$	0.156926	+	0.378854i	0.00568111	+	0.0137154i
$764$	21.5704	+	14.0996i	0.780391	+	0.510105i
$765$	15.8895	−	6.58164i	0.574485	−	0.237960i
$766$	5.69054	+	1.69484i	0.205608	+	0.0612372i
$767$	−36.9441	−	26.2416i	−1.33397	−	0.947530i
$768$	−21.0708	+	9.74362i	−0.760329	+	0.351593i
$769$	5.25446	−

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24384 + 0.672951i) q^{2} +(1.34047 + 0.555241i) q^{3} +(1.09427 - 1.67409i) q^{4} +(1.54705 - 3.73491i) q^{5} +(-2.04098 + 0.211441i) q^{6} -0.167444i q^{7} +(-0.234521 + 2.81869i) q^{8} +(-0.632754 - 0.632754i) q^{9} +O(q^{10})\)	\(q+(-1.24384 + 0.672951i) q^{2} +(1.34047 + 0.555241i) q^{3} +(1.09427 - 1.67409i) q^{4} +(1.54705 - 3.73491i) q^{5} +(-2.04098 + 0.211441i) q^{6} -0.167444i q^{7} +(-0.234521 + 2.81869i) q^{8} +(-0.632754 - 0.632754i) q^{9} +(0.589131 + 5.68672i) q^{10} +(0.115501 + 0.0478422i) q^{11} +(2.39636 - 1.63648i) q^{12} +(0.804107 - 3.51474i) q^{13} +(0.112681 + 0.208273i) q^{14} +(4.14755 - 4.14755i) q^{15} +(-1.60513 - 3.66382i) q^{16} -4.75422 q^{17} +(1.21286 + 0.361232i) q^{18} +(1.08803 + 2.62674i) q^{19} +(-4.55967 - 6.67692i) q^{20} +(0.0929715 - 0.224453i) q^{21} +(-0.175861 + 0.0182187i) q^{22} +(-0.822050 - 0.822050i) q^{23} +(-1.87942 + 3.64815i) q^{24} +(-8.02068 - 8.02068i) q^{25} +(1.36507 + 4.91290i) q^{26} +(-2.16258 - 5.22093i) q^{27} +(-0.280315 - 0.183229i) q^{28} +(-0.362881 + 0.876073i) q^{29} +(-2.36779 + 7.94999i) q^{30} +(1.60097 + 1.60097i) q^{31} +(4.46210 + 3.47702i) q^{32} +(0.128262 + 0.128262i) q^{33} +(5.91349 - 3.19936i) q^{34} +(-0.625388 - 0.259044i) q^{35} +(-1.75169 + 0.366879i) q^{36} +(9.94226 + 4.11822i) q^{37} +(-3.12101 - 2.53505i) q^{38} +(3.02941 - 4.26493i) q^{39} +(10.1647 + 5.23657i) q^{40} +1.57976 q^{41} +(0.0354044 + 0.341749i) q^{42} +(2.99613 + 7.23329i) q^{43} +(0.206482 - 0.141007i) q^{44} +(-3.34218 + 1.38438i) q^{45} +(1.57570 + 0.469298i) q^{46} +(5.14120 + 5.14120i) q^{47} +(-0.117333 - 5.80247i) q^{48} +6.97196 q^{49} +(15.3740 + 4.57891i) q^{50} +(-6.37289 - 2.63974i) q^{51} +(-5.00407 - 5.19223i) q^{52} +(0.952080 + 2.29853i) q^{53} +(6.20333 + 5.03868i) q^{54} +(0.357373 - 0.357373i) q^{55} +(0.471971 + 0.0392691i) q^{56} +4.12519i q^{57} +(-0.138188 - 1.33390i) q^{58} +(4.80965 - 11.6115i) q^{59} +(-2.40481 - 11.4819i) q^{60} +(-1.39878 + 3.37697i) q^{61} +(-3.06872 - 0.913973i) q^{62} +(-0.105951 + 0.105951i) q^{63} +(-7.89000 - 1.32208i) q^{64} +(-11.8833 - 8.44076i) q^{65} +(-0.245852 - 0.0732233i) q^{66} +(5.27576 - 2.18529i) q^{67} +(-5.20242 + 7.95898i) q^{68} +(-0.645497 - 1.55837i) q^{69} +(0.952206 - 0.0986463i) q^{70} -12.4430 q^{71} +(1.93193 - 1.63514i) q^{72} +8.93301i q^{73} +(-15.1379 + 1.56825i) q^{74} +(-6.29807 - 15.2049i) q^{75} +(5.58800 + 1.05291i) q^{76} +(0.00801088 - 0.0193400i) q^{77} +(-0.898007 + 7.34354i) q^{78} +14.3833 q^{79} +(-16.1673 + 0.326920i) q^{80} -5.51470i q^{81} +(-1.96497 + 1.06310i) q^{82} +(4.24121 + 10.2392i) q^{83} +(-0.274018 - 0.401255i) q^{84} +(-7.35503 + 17.7566i) q^{85} +(-8.59435 - 6.98080i) q^{86} +(-0.972863 + 0.972863i) q^{87} +(-0.161940 + 0.314342i) q^{88} +6.33972 q^{89} +(3.22552 - 3.97107i) q^{90} +(-0.588521 - 0.134643i) q^{91} +(-2.27573 + 0.476636i) q^{92} +(1.25713 + 3.03497i) q^{93} +(-9.85461 - 2.93505i) q^{94} +11.4939 q^{95} +(4.05072 + 7.13838i) q^{96} +(-7.29863 + 7.29863i) q^{97} +(-8.67200 + 4.69179i) q^{98} +(-0.0428116 - 0.103356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more