LMFDB - Embedded newform 680.2.bw.a.43.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [680,2,Mod(43,680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(680, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 4, 6, 1]))

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

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

chi := DirichletCharacter("680.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.bw (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:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$104$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			43.17
Character	$\chi$	$=$	680.43
Dual form			680.2.bw.a.427.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21233 - 0.728189i) q^{2} +(-0.0135844 - 0.0327956i) q^{3} +(0.939481 + 1.76561i) q^{4} +(0.252941 - 2.22172i) q^{5} +(-0.00741267 + 0.0496510i) q^{6} +(2.00134 - 4.83165i) q^{7} +(0.146738 - 2.82462i) q^{8} +(2.12043 - 2.12043i) q^{9} +O(q^{10})$	\(q+(-1.21233 - 0.728189i) q^{2} +(-0.0135844 - 0.0327956i) q^{3} +(0.939481 + 1.76561i) q^{4} +(0.252941 - 2.22172i) q^{5} +(-0.00741267 + 0.0496510i) q^{6} +(2.00134 - 4.83165i) q^{7} +(0.146738 - 2.82462i) q^{8} +(2.12043 - 2.12043i) q^{9} +(-1.92448 + 2.50926i) q^{10} +(-3.58180 + 1.48363i) q^{11} +(0.0451419 - 0.0547955i) q^{12} +(-3.78984 - 3.78984i) q^{13} +(-5.94463 + 4.40020i) q^{14} +(-0.0762985 + 0.0218853i) q^{15} +(-2.23475 + 3.31751i) q^{16} +(3.70777 + 1.80346i) q^{17} +(-4.11473 + 1.02658i) q^{18} +(2.63383 + 2.63383i) q^{19} +(4.16032 - 1.64066i) q^{20} -0.185644 q^{21} +(5.42267 + 0.809580i) q^{22} +(-1.31860 + 3.18338i) q^{23} +(-0.0946283 + 0.0335583i) q^{24} +(-4.87204 - 1.12393i) q^{25} +(1.83481 + 7.35425i) q^{26} +(-0.196732 - 0.0814891i) q^{27} +(10.4110 - 1.00567i) q^{28} +(-1.42107 + 3.43077i) q^{29} +(0.108435 + 0.0290276i) q^{30} +(0.729663 - 1.76156i) q^{31} +(5.12503 - 2.39459i) q^{32} +(0.0973129 + 0.0973129i) q^{33} +(-3.18177 - 4.88634i) q^{34} +(-10.2283 - 5.66852i) q^{35} +(5.73595 + 1.75175i) q^{36} +(-0.575535 - 1.38946i) q^{37} +(-1.27514 - 5.11099i) q^{38} +(-0.0728074 + 0.175773i) q^{39} +(-6.23838 - 1.04047i) q^{40} +(-0.414729 - 1.00125i) q^{41} +(0.225061 + 0.135184i) q^{42} +5.12864i q^{43} +(-5.98454 - 4.93021i) q^{44} +(-4.17465 - 5.24734i) q^{45} +(3.91668 - 2.89912i) q^{46} +(0.519612 - 0.519612i) q^{47} +(0.139157 + 0.0282237i) q^{48} +(-14.3898 - 14.3898i) q^{49} +(5.08808 + 4.91034i) q^{50} +(0.00877787 - 0.146097i) q^{51} +(3.13090 - 10.2519i) q^{52} +3.61147i q^{53} +(0.179164 + 0.242050i) q^{54} +(2.39022 + 8.33300i) q^{55} +(-13.3539 - 6.36200i) q^{56} +(0.0505990 - 0.122157i) q^{57} +(4.22105 - 3.12441i) q^{58} +(0.780898 - 0.780898i) q^{59} +(-0.110322 - 0.114153i) q^{60} +(7.86852 - 3.25925i) q^{61} +(-2.16734 + 1.60426i) q^{62} +(-6.00148 - 14.4889i) q^{63} +(-7.95694 - 0.828960i) q^{64} +(-9.37856 + 7.46134i) q^{65} +(-0.0471130 - 0.188837i) q^{66} +(5.89290 - 5.89290i) q^{67} +(0.299168 + 8.24078i) q^{68} +0.122313 q^{69} +(8.27234 + 14.3203i) q^{70} +(-5.69563 + 13.7505i) q^{71} +(-5.67825 - 6.30055i) q^{72} +(9.04705 - 3.74741i) q^{73} +(-0.314056 + 2.10359i) q^{74} +(0.0293238 + 0.175049i) q^{75} +(-2.17588 + 7.12474i) q^{76} +20.2752i q^{77} +(0.216262 - 0.160077i) q^{78} +(-2.69275 + 1.11537i) q^{79} +(6.80531 + 5.80412i) q^{80} -8.98866i q^{81} +(-0.226308 + 1.51584i) q^{82} -1.01502 q^{83} +(-0.174409 - 0.327774i) q^{84} +(4.94462 - 7.78143i) q^{85} +(3.73462 - 6.21760i) q^{86} +0.131818 q^{87} +(3.66510 + 10.3349i) q^{88} +13.0061 q^{89} +(1.23999 + 9.40143i) q^{90} +(-25.8959 + 10.7264i) q^{91} +(-6.85941 + 0.662594i) q^{92} -0.0676834 q^{93} +(-1.00832 + 0.251565i) q^{94} +(6.51782 - 5.18541i) q^{95} +(-0.148152 - 0.135549i) q^{96} +(-4.21813 - 10.1835i) q^{97} +(6.96664 + 27.9236i) q^{98} +(-4.44902 + 10.7409i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 8 q^{3}+O(q^{10}) $ 416 * q - 8 * q^3	$ 416 q - 8 q^{3} - 12 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{14} - 16 q^{16} - 8 q^{18} - 32 q^{19} + 12 q^{20} + 4 q^{22} + 24 q^{24} - 16 q^{25} + 8 q^{26} + 16 q^{27} - 20 q^{28} - 16 q^{30} - 16 q^{33} - 16 q^{35} - 72 q^{36} + 16 q^{38} - 24 q^{40} - 16 q^{41} - 24 q^{42} + 32 q^{46} - 100 q^{48} - 48 q^{50} - 16 q^{51} + 24 q^{52} + 16 q^{54} - 8 q^{56} - 32 q^{57} - 72 q^{58} - 40 q^{60} + 48 q^{62} + 48 q^{64} - 8 q^{65} - 8 q^{66} - 16 q^{67} - 116 q^{68} + 80 q^{70} + 24 q^{72} + 32 q^{73} - 16 q^{74} + 16 q^{75} - 40 q^{76} - 76 q^{78} + 16 q^{80} - 36 q^{82} - 16 q^{83} - 48 q^{86} + 72 q^{88} + 56 q^{90} - 16 q^{91} - 104 q^{92} - 24 q^{94} - 8 q^{96} - 40 q^{98}+O(q^{100}) $ 416 * q - 8 * q^3 - 12 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^14 - 16 * q^16 - 8 * q^18 - 32 * q^19 + 12 * q^20 + 4 * q^22 + 24 * q^24 - 16 * q^25 + 8 * q^26 + 16 * q^27 - 20 * q^28 - 16 * q^30 - 16 * q^33 - 16 * q^35 - 72 * q^36 + 16 * q^38 - 24 * q^40 - 16 * q^41 - 24 * q^42 + 32 * q^46 - 100 * q^48 - 48 * q^50 - 16 * q^51 + 24 * q^52 + 16 * q^54 - 8 * q^56 - 32 * q^57 - 72 * q^58 - 40 * q^60 + 48 * q^62 + 48 * q^64 - 8 * q^65 - 8 * q^66 - 16 * q^67 - 116 * q^68 + 80 * q^70 + 24 * q^72 + 32 * q^73 - 16 * q^74 + 16 * q^75 - 40 * q^76 - 76 * q^78 + 16 * q^80 - 36 * q^82 - 16 * q^83 - 48 * q^86 + 72 * q^88 + 56 * q^90 - 16 * q^91 - 104 * q^92 - 24 * q^94 - 8 * q^96 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$-1$

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 $

$2$	−1.21233	−	0.728189i	−0.857246	−	0.514908i
$2$	−1.21233	−	0.728189i	−0.857246	−	0.514908i
$3$	−0.0135844	−	0.0327956i	−0.00784294	−	0.0189345i	0.919910	−	0.392131i	$-0.128262\pi$
$3$	−0.0135844	−	0.0327956i	−0.00784294	−	0.0189345i	−0.927752	+	0.373196i	$0.878262\pi$
$4$	0.939481	+	1.76561i	0.469740	+	0.882805i
$5$	0.252941	−	2.22172i	0.113119	−	0.993581i
$5$	0.252941	−	2.22172i	0.113119	−	0.993581i
$6$	−0.00741267	+	0.0496510i	−0.00302621	+	0.0202699i
$7$	2.00134	−	4.83165i	0.756434	−	1.82619i	0.237472	−	0.971394i	$-0.423681\pi$
$7$	2.00134	−	4.83165i	0.756434	−	1.82619i	0.518961	−	0.854798i	$-0.326319\pi$
$8$	0.146738	−	2.82462i	0.0518799	−	0.998653i
$9$	2.12043	−	2.12043i	0.706810	−	0.706810i
$10$	−1.92448	+	2.50926i	−0.608573	+	0.793498i
$11$	−3.58180	+	1.48363i	−1.07995	+	0.447331i	−0.850492	−	0.525987i	$-0.823696\pi$
$11$	−3.58180	+	1.48363i	−1.07995	+	0.447331i	−0.229460	+	0.973318i	$0.573696\pi$
$12$	0.0451419	−	0.0547955i	0.0130313	−	0.0158181i
$13$	−3.78984	−	3.78984i	−1.05111	−	1.05111i	−0.998621	−	0.0524914i	$-0.983284\pi$
$13$	−3.78984	−	3.78984i	−1.05111	−	1.05111i	−0.0524914	−	0.998621i	$-0.516716\pi$
$14$	−5.94463	+	4.40020i	−1.58877	+	1.17600i
$15$	−0.0762985	+	0.0218853i	−0.0197002	+	0.00565075i
$16$	−2.23475	+	3.31751i	−0.558688	+	0.829378i
$17$	3.70777	+	1.80346i	0.899265	+	0.437404i
$17$	3.70777	+	1.80346i	0.899265	+	0.437404i
$18$	−4.11473	+	1.02658i	−0.969851	+	0.241968i
$19$	2.63383	+	2.63383i	0.604241	+	0.604241i	0.941435	−	0.337194i	$-0.109478\pi$
$19$	2.63383	+	2.63383i	0.604241	+	0.604241i	−0.337194	+	0.941435i	$0.609478\pi$
$20$	4.16032	−	1.64066i	0.930275	−	0.366864i
$21$	−0.185644			−0.0405108
$22$	5.42267	+	0.809580i	1.15612	+	0.172603i
$23$	−1.31860	+	3.18338i	−0.274947	+	0.663782i	−0.999681	−	0.0252473i	$-0.991963\pi$
$23$	−1.31860	+	3.18338i	−0.274947	+	0.663782i	0.724734	+	0.689029i	$0.241963\pi$
$24$	−0.0946283	+	0.0335583i	−0.0193159	+	0.00685006i
$25$	−4.87204	−	1.12393i	−0.974408	−	0.224786i
$26$	1.83481	+	7.35425i	0.359836	+	1.44229i
$27$	−0.196732	−	0.0814891i	−0.0378611	−	0.0156826i
$28$	10.4110	−	1.00567i	1.96750	−	0.190053i
$29$	−1.42107	+	3.43077i	−0.263886	+	0.637078i	−0.999172	−	0.0406793i	$-0.987048\pi$
$29$	−1.42107	+	3.43077i	−0.263886	+	0.637078i	0.735286	+	0.677757i	$0.237048\pi$
$30$	0.108435	+	0.0290276i	0.0197975	+	0.00529970i
$31$	0.729663	−	1.76156i	0.131051	−	0.316386i	−0.844710	−	0.535225i	$-0.820227\pi$
$31$	0.729663	−	1.76156i	0.131051	−	0.316386i	0.975761	+	0.218839i	$0.0702269\pi$
$32$	5.12503	−	2.39459i	0.905986	−	0.423308i
$33$	0.0973129	+	0.0973129i	0.0169400	+	0.0169400i
$34$	−3.18177	−	4.88634i	−0.545669	−	0.838001i
$35$	−10.2283	−	5.66852i	−1.72890	−	0.958155i
$36$	5.73595	+	1.75175i	0.955992	+	0.291958i
$37$	−0.575535	−	1.38946i	−0.0946173	−	0.228426i	0.869484	−	0.493961i	$-0.164452\pi$
$37$	−0.575535	−	1.38946i	−0.0946173	−	0.228426i	−0.964101	+	0.265535i	$0.914452\pi$
$38$	−1.27514	−	5.11099i	−0.206855	−	0.829112i
$39$	−0.0728074	+	0.175773i	−0.0116585	+	0.0281462i
$40$	−6.23838	−	1.04047i	−0.986375	−	0.164513i
$41$	−0.414729	−	1.00125i	−0.0647698	−	0.156368i	0.888180	−	0.459495i	$-0.151970\pi$
$41$	−0.414729	−	1.00125i	−0.0647698	−	0.156368i	−0.952950	+	0.303127i	$0.901970\pi$
$42$	0.225061	+	0.135184i	0.0347277	+	0.0208593i
$43$			5.12864i			0.782110i	0.920367	+	0.391055i	$0.127890\pi$
$43$			5.12864i			0.782110i	−0.920367	+	0.391055i	$0.872110\pi$
$44$	−5.98454	−	4.93021i	−0.902203	−	0.743257i
$45$	−4.17465	−	5.24734i	−0.622320	−	0.782227i
$46$	3.91668	−	2.89912i	0.577484	−	0.427451i
$47$	0.519612	−	0.519612i	0.0757932	−	0.0757932i	−0.668194	−	0.743987i	$-0.732932\pi$
$47$	0.519612	−	0.519612i	0.0757932	−	0.0757932i	0.743987	+	0.668194i	$0.232932\pi$
$48$	0.139157	+	0.0282237i	0.0200856	+	0.00407373i
$49$	−14.3898	−	14.3898i	−2.05568	−	2.05568i
$50$	5.08808	+	4.91034i	0.719564	+	0.694427i
$51$	0.00877787	−	0.146097i	0.00122915	−	0.0204577i
$52$	3.13090	−	10.2519i	0.434177	−	1.42168i
$53$			3.61147i			0.496074i	0.968751	+	0.248037i	$0.0797854\pi$
$53$			3.61147i			0.496074i	−0.968751	+	0.248037i	$0.920215\pi$
$54$	0.179164	+	0.242050i	0.0243812	+	0.0329388i
$55$	2.39022	+	8.33300i	0.322297	+	1.12362i
$56$	−13.3539	−	6.36200i	−1.78449	−	0.850157i
$57$	0.0505990	−	0.122157i	0.00670200	−	0.0161801i
$58$	4.22105	−	3.12441i	0.554251	−	0.410255i
$59$	0.780898	−	0.780898i	0.101664	−	0.101664i	−0.654445	−	0.756109i	$-0.727098\pi$
$59$	0.780898	−	0.780898i	0.101664	−	0.101664i	0.756109	+	0.654445i	$0.227098\pi$
$60$	−0.110322	−	0.114153i	−0.0142425	−	0.0147370i
$61$	7.86852	−	3.25925i	1.00746	−	0.417304i	0.182933	−	0.983125i	$-0.441441\pi$
$61$	7.86852	−	3.25925i	1.00746	−	0.417304i	0.824528	+	0.565822i	$0.191441\pi$
$62$	−2.16734	+	1.60426i	−0.275253	+	0.203741i
$63$	−6.00148	−	14.4889i	−0.756116	−	1.82543i
$64$	−7.95694	−	0.828960i	−0.994617	−	0.103620i
$65$	−9.37856	+	7.46134i	−1.16327	+	0.925466i
$66$	−0.0471130	−	0.188837i	−0.00579921	−	0.0232443i
$67$	5.89290	−	5.89290i	0.719933	−	0.719933i	−0.248658	−	0.968591i	$-0.579990\pi$
$67$	5.89290	−	5.89290i	0.719933	−	0.719933i	0.968591	+	0.248658i	$0.0799896\pi$
$68$	0.299168	+	8.24078i	0.0362794	+	0.999342i
$69$	0.122313			0.0147248
$70$	8.27234	+	14.3203i	0.988734	+	1.71160i
$71$	−5.69563	+	13.7505i	−0.675946	+	1.63188i	0.0953814	+	0.995441i	$0.469593\pi$
$71$	−5.69563	+	13.7505i	−0.675946	+	1.63188i	−0.771328	+	0.636438i	$0.780407\pi$
$72$	−5.67825	−	6.30055i	−0.669189	−	0.742527i
$73$	9.04705	−	3.74741i	1.05888	−	0.438601i	0.215824	−	0.976432i	$-0.430756\pi$
$73$	9.04705	−	3.74741i	1.05888	−	0.438601i	0.843053	+	0.537831i	$0.180756\pi$
$74$	−0.314056	+	2.10359i	−0.0365082	+	0.244537i
$75$	0.0293238	+	0.175049i	0.00338602	+	0.0202129i
$76$	−2.17588	+	7.12474i	−0.249590	+	0.817264i
$77$			20.2752i			2.31058i
$78$	0.216262	−	0.160077i	0.0244869	−	0.0181251i
$79$	−2.69275	+	1.11537i	−0.302958	+	0.125489i	−0.528984	−	0.848632i	$-0.677427\pi$
$79$	−2.69275	+	1.11537i	−0.302958	+	0.125489i	0.226025	+	0.974121i	$0.427427\pi$
$80$	6.80531	+	5.80412i	0.760856	+	0.648920i
$81$		−	8.98866i		−	0.998740i
$82$	−0.226308	+	1.51584i	−0.0249915	+	0.167396i
$83$	−1.01502			−0.111413			−0.0557063	−	0.998447i	$-0.517741\pi$
$83$	−1.01502			−0.111413			−0.0557063	+	0.998447i	$0.517741\pi$
$84$	−0.174409	−	0.327774i	−0.0190295	−	0.0357631i
$85$	4.94462	−	7.78143i	0.536320	−	0.844015i
$86$	3.73462	−	6.21760i	0.402715	−	0.670461i
$87$	0.131818			0.0141324
$88$	3.66510	+	10.3349i	0.390701	+	1.10171i
$89$	13.0061			1.37864			0.689321	−	0.724456i	$-0.257909\pi$
$89$	13.0061			1.37864			0.689321	+	0.724456i	$0.257909\pi$
$90$	1.23999	+	9.40143i	0.130706	+	0.990997i
$91$	−25.8959	+	10.7264i	−2.71463	+	1.12444i
$92$	−6.85941	+	0.662594i	−0.715143	+	0.0690802i
$93$	−0.0676834			−0.00701845
$94$	−1.00832	+	0.251565i	−0.104000	+	0.0259469i
$95$	6.51782	−	5.18541i	0.668714	−	0.532012i
$96$	−0.148152	−	0.135549i	−0.0151207	−	0.0138344i
$97$	−4.21813	−	10.1835i	−0.428287	−	1.03398i	−0.979831	−	0.199830i	$-0.935961\pi$
$97$	−4.21813	−	10.1835i	−0.428287	−	1.03398i	0.551544	−	0.834146i	$-0.314039\pi$
$98$	6.96664	+	27.9236i	0.703737	+	2.82071i
$99$	−4.44902	+	10.7409i	−0.447143	+	1.07950i
$100$	−2.59277	−	9.65803i	−0.259277	−	0.965803i
$101$		−	14.3933i		−	1.43218i	−0.698007	−	0.716091i	$-0.745929\pi$
$101$		−	14.3933i		−	1.43218i	0.698007	−	0.716091i	$-0.254071\pi$
$102$	−0.117028	+	0.170726i	−0.0115875	+	0.0169044i
$103$	5.94890	−	5.94890i	0.586162	−	0.586162i	−0.350428	−	0.936590i	$-0.613964\pi$
$103$	5.94890	−	5.94890i	0.586162	−	0.586162i	0.936590	+	0.350428i	$0.113964\pi$
$104$	−11.2610	+	10.1487i	−1.10423	+	0.995166i
$105$	−0.0469570	+	0.412447i	−0.00458253	+	0.0402507i
$106$	2.62983	−	4.37829i	0.255432	−	0.425257i
$107$	0.852394	+	2.05786i	0.0824040	+	0.198941i	0.959711	−	0.280988i	$-0.0906623\pi$
$107$	0.852394	+	2.05786i	0.0824040	+	0.198941i	−0.877307	+	0.479929i	$0.840662\pi$
$108$	−0.0409481	−	0.423910i	−0.00394023	−	0.0407907i
$109$	−5.24541	−	12.6635i	−0.502419	−	1.21295i	−0.948162	−	0.317787i	$-0.897060\pi$
$109$	−5.24541	−	12.6635i	−0.502419	−	1.21295i	0.445743	−	0.895161i	$-0.352940\pi$
$110$	3.17028	−	11.8429i	0.302274	−	1.12917i
$111$	−0.0377500	+	0.0377500i	−0.00358307	+	0.00358307i
$112$	11.5566	+	17.4370i	1.09199	+	1.64764i
$113$	−9.55454	−	3.95762i	−0.898815	−	0.372302i	−0.115051	−	0.993360i	$-0.536703\pi$
$113$	−9.55454	−	3.95762i	−0.898815	−	0.372302i	−0.783765	+	0.621058i	$0.786703\pi$
$114$	−0.150296	+	0.111248i	−0.0140765	+	0.0104194i
$115$	6.73905	+	3.73477i	0.628419	+	0.348269i
$116$	−7.39246	+	0.714085i	−0.686373	+	0.0663011i
$117$	−16.0722			−1.48587
$118$	−1.51535	+	0.378063i	−0.139499	+	0.0348036i
$119$	16.1342	−	14.3053i	1.47902	−	1.31136i
$120$	0.0506216	+	0.218726i	0.00462110	+	0.0199668i
$121$	2.84993	−	2.84993i	0.259085	−	0.259085i
$122$	−11.9126	−	1.77849i	−1.07851	−	0.161017i
$123$	−0.0272026	+	0.0272026i	−0.00245277	+	0.00245277i
$124$	3.79573	−	0.366654i	0.340867	−	0.0329265i
$125$	−3.72939	+	10.5400i	−0.333567	+	0.942727i
$126$	−3.27486	+	21.9355i	−0.291748	+	1.95417i
$127$			4.40218i			0.390630i	0.980741	+	0.195315i	$0.0625730\pi$
$127$			4.40218i			0.390630i	−0.980741	+	0.195315i	$0.937427\pi$
$128$	9.04278	+	6.79913i	0.799276	+	0.600964i
$129$	0.168197	−	0.0696694i	0.0148089	−	0.00613405i
$130$	16.8032	−	2.21623i	1.47373	−	0.194376i
$131$	−5.56650	+	13.4387i	−0.486347	+	1.17415i	0.470198	+	0.882561i	$0.344183\pi$
$131$	−5.56650	+	13.4387i	−0.486347	+	1.17415i	−0.956545	+	0.291585i	$0.905817\pi$
$132$	−0.0803930	+	0.263240i	−0.00699731	+	0.0229121i
$133$	17.9969	−	7.45456i	1.56053	−	0.646392i
$134$	−11.4353	+	2.85299i	−0.987858	+	0.246460i
$135$	−0.230807	+	0.416471i	−0.0198647	+	0.0358441i
$136$	5.63816	−	10.2084i	0.483468	−	0.875362i
$137$	9.54788	−	9.54788i	0.815731	−	0.815731i	−0.169755	−	0.985486i	$-0.554298\pi$
$137$	9.54788	−	9.54788i	0.815731	−	0.815731i	0.985486	+	0.169755i	$0.0542978\pi$
$138$	−0.148284	−	0.0890672i	−0.0126228	−	0.00758191i
$139$	3.09083	−	7.46193i	0.262161	−	0.632912i	−0.736911	−	0.675990i	$-0.763716\pi$
$139$	3.09083	−	7.46193i	0.262161	−	0.632912i	0.999072	+	0.0430775i	$0.0137163\pi$
$140$	0.399072	−	23.3847i	0.0337278	−	1.97637i
$141$	−0.0240996	−	0.00998237i	−0.00202955	−	0.000840667i
$142$	16.9179	−	12.5226i	1.41972	−	1.05087i
$143$	19.1972	+	7.95172i	1.60535	+	0.664956i
$144$	2.29592	+	11.7732i	0.191326	+	0.981099i
$145$	7.26274	+	4.02500i	0.603138	+	0.334258i
$146$	−13.6968	−	2.04487i	−1.13356	−	0.169235i
$147$	−0.276445	+	0.667396i	−0.0228008	+	0.0550459i
$148$	1.91255	−	2.32154i	0.157210	−	0.190830i
$149$		−	10.2517i		−	0.839851i	−0.907559	−	0.419925i	$-0.862056\pi$
$149$		−	10.2517i		−	0.839851i	0.907559	−	0.419925i	$-0.137944\pi$
$150$	0.0919190	−	0.233570i	0.00750515	−	0.0190709i
$151$	17.1167	+	17.1167i	1.39294	+	1.39294i	0.818663	+	0.574274i	$0.194716\pi$
$151$	17.1167	+	17.1167i	1.39294	+	1.39294i	0.574274	+	0.818663i	$0.305284\pi$
$152$	7.82604	−	7.05307i	0.634776	−	0.572080i
$153$	11.6862	−	4.03794i	0.944771	−	0.326448i
$154$	14.7642	−	24.5802i	1.18973	−	1.98073i
$155$	−3.72913	−	2.06667i	−0.299531	−	0.165999i
$156$	−0.378747	+	0.0365856i	−0.0303240	+	0.00292919i
$157$	−0.0419974	+	0.0419974i	−0.00335176	+	0.00335176i	−0.708781	−	0.705429i	$-0.750754\pi$
$157$	−0.0419974	+	0.0419974i	−0.00335176	+	0.00335176i	0.705429	+	0.708781i	$0.250754\pi$
$158$	4.07670	+	0.608633i	0.324325	+	0.0484202i
$159$	0.118440	−	0.0490596i	0.00939293	−	0.00389068i
$160$	−4.02377	−	11.9921i	−0.318107	−	0.948055i
$161$	12.7420	+	12.7420i	1.00421	+	1.00421i
$162$	−6.54545	+	10.8972i	−0.514259	+	0.856166i
$163$	5.37295	−	12.9715i	0.420842	−	1.01600i	−0.561257	−	0.827641i	$-0.689682\pi$
$163$	5.37295	−	12.9715i	0.420842	−	1.01600i	0.982100	−	0.188362i	$-0.0603177\pi$
$164$	1.37818	−	1.67290i	0.107618	−	0.130632i
$165$	0.240816	−	0.191587i	0.0187475	−	0.0149150i
$166$	1.23053	+	0.739124i	0.0955080	+	0.0573672i
$167$	−1.86963	−	4.51368i	−0.144676	−	0.349279i	0.834885	−	0.550424i	$-0.185534\pi$
$167$	−1.86963	−	4.51368i	−0.144676	−	0.349279i	−0.979562	+	0.201145i	$0.935534\pi$
$168$	−0.0272411	+	0.524372i	−0.00210169	+	0.0404562i
$169$			15.7258i			1.20968i
$170$	−11.6609	+	5.83303i	−0.894348	+	0.447373i
$171$	11.1697			0.854167
$172$	−9.05518	+	4.81826i	−0.690451	+	0.367389i
$173$	−11.4445	+	4.74045i	−0.870106	+	0.360410i	−0.772652	−	0.634830i	$-0.781070\pi$
$173$	−11.4445	+	4.74045i	−0.870106	+	0.360410i	−0.0974547	+	0.995240i	$0.531070\pi$
$174$	−0.159807	−	0.0959887i	−0.0121150	−	0.00727689i
$175$	−15.1810	+	21.2906i	−1.14758	+	1.60942i
$176$	3.08247	−	15.1982i	0.232350	−	1.14561i
$177$	−0.0362180	−	0.0150020i	−0.00272231	−	0.00112762i
$178$	−15.7676	−	9.47088i	−1.18183	−	0.709873i
$179$	6.29582	−	6.29582i	0.470572	−	0.470572i	−0.431528	−	0.902100i	$-0.642025\pi$
$179$	6.29582	−	6.29582i	0.470572	−	0.470572i	0.902100	+	0.431528i	$0.142025\pi$
$180$	5.34274	−	12.3006i	0.398225	−	0.916830i
$181$	7.76237	+	18.7400i	0.576972	+	1.39293i	0.895517	+	0.445027i	$0.146806\pi$
$181$	7.76237	+	18.7400i	0.576972	+	1.39293i	−0.318545	+	0.947908i	$0.603194\pi$
$182$	39.2053	+	5.85316i	2.90609	+	0.433865i
$183$	−0.213778	−	0.213778i	−0.0158029	−	0.0158029i
$184$	8.79836	+	4.19167i	0.648623	+	0.309014i
$185$	−3.23257	+	0.927222i	−0.237663	+	0.0681707i
$186$	0.0820546	+	0.0492863i	0.00601653	+	0.00361385i
$187$	−15.9561	−	0.958682i	−1.16683	−	0.0701057i
$188$	1.40560	+	0.429266i	0.102514	+	0.0313075i
$189$	−0.787454	+	0.787454i	−0.0572788	+	0.0572788i
$190$	−11.6777	+	1.54022i	−0.847189	+	0.111739i
$191$	13.1658			0.952647			0.476323	−	0.879270i	$-0.341969\pi$
$191$	13.1658			0.952647			0.476323	+	0.879270i	$0.341969\pi$
$192$	0.0809038	+	0.272213i	0.00583873	+	0.0196453i
$193$	10.7089	+	4.43576i	0.770842	+	0.319293i	0.733213	−	0.679999i	$-0.238020\pi$
$193$	10.7089	+	4.43576i	0.770842	+	0.319293i	0.0376285	+	0.999292i	$0.488020\pi$
$194$	−2.30173	+	15.4173i	−0.165255	+	1.10690i
$195$	0.372101	+	0.206218i	0.0266467	+	0.0147675i
$196$	11.8878	−	38.9256i	0.849128	−	2.78040i
$197$	−2.35271	+	5.67996i	−0.167624	+	0.404680i	−0.985262	−	0.171053i	$-0.945283\pi$
$197$	−2.35271	+	5.67996i	−0.167624	+	0.404680i	0.817638	+	0.575733i	$0.195283\pi$
$198$	13.2151	−	9.78174i	0.939153	−	0.695158i
$199$	−5.62116	+	13.5707i	−0.398473	+	0.962000i	0.589555	+	0.807728i	$0.299303\pi$
$199$	−5.62116	+	13.5707i	−0.398473	+	0.962000i	−0.988028	+	0.154272i	$0.950697\pi$
$200$	−3.88958	+	13.5967i	−0.275035	+	0.961434i
$201$	−0.273313	−	0.113210i	−0.0192780	−	0.00798520i
$202$	−10.4810	+	17.4494i	−0.737441	+	1.22773i
$203$	13.7322	+	13.7322i	0.963814	+	0.963814i
$204$	0.266197	−	0.121757i	0.0186375	−	0.00852471i
$205$	−2.32938	+	0.668154i	−0.162691	+	0.0466659i
$206$	−11.5439	+	2.88009i	−0.804304	+	0.200666i
$207$	3.95414	+	9.54614i	0.274832	+	0.663503i
$208$	21.0422	−	4.10349i	1.45901	−	0.284526i
$209$	−13.3414	−	5.52621i	−0.922847	−	0.382256i
$210$	0.357267	−	0.465828i	0.0246538	−	0.0321452i
$211$	6.15039	+	14.8484i	0.423410	+	1.02220i	0.981334	+	0.192311i	$0.0615981\pi$
$211$	6.15039	+	14.8484i	0.423410	+	1.02220i	−0.557924	+	0.829892i	$0.688402\pi$
$212$	−6.37645	+	3.39291i	−0.437936	+	0.233026i
$213$	0.528326			0.0362003
$214$	0.465131	−	3.11551i	0.0317957	−	0.212972i
$215$	11.3944	+	1.29725i	0.777090	+	0.0884714i
$216$	−0.259044	+	0.543736i	−0.0176257	+	0.0369965i
$217$	−7.05095	−	7.05095i	−0.478650	−	0.478650i
$218$	−2.86230	+	19.1720i	−0.193859	+	1.29849i
$219$	−0.245797	−	0.245797i	−0.0166094	−	0.0166094i
$220$	−12.4673	+	12.0489i	−0.840543	+	0.812335i
$221$	−7.21701	−	20.8867i	−0.485469	−	1.40499i
$222$	0.0732545	−	0.0182763i	0.00491652	−	0.00122662i
$223$		−	13.0756i		−	0.875608i	−0.899070	−	0.437804i	$-0.855756\pi$
$223$		−	13.0756i		−	0.875608i	0.899070	−	0.437804i	$-0.144244\pi$
$224$	−1.31293	−	29.5547i	−0.0877237	−	1.97471i
$225$	−12.7140	+	7.94761i	−0.847602	+	0.529841i
$226$	8.70134	+	11.7554i	0.578805	+	0.781961i
$227$	−3.03485	+	7.32678i	−0.201430	+	0.486295i	−0.992025	−	0.126045i	$-0.959772\pi$
$227$	−3.03485	+	7.32678i	−0.201430	+	0.486295i	0.790594	+	0.612340i	$0.209772\pi$
$228$	0.263218	−	0.0254259i	0.0174320	−	0.00168387i
$229$	−9.79726	−	9.79726i	−0.647421	−	0.647421i	0.304948	−	0.952369i	$-0.401361\pi$
$229$	−9.79726	−	9.79726i	−0.647421	−	0.647421i	−0.952369	+	0.304948i	$0.901361\pi$
$230$	−5.45032	−	9.43507i	−0.359384	−	0.622130i
$231$	0.664938	−	0.275426i	0.0437497	−	0.0181217i
$232$	9.48208	+	4.51741i	0.622529	+	0.296582i
$233$	17.5019	−	7.24951i	1.14659	−	0.474931i	0.273198	−	0.961958i	$-0.411918\pi$
$233$	17.5019	−	7.24951i	1.14659	−	0.474931i	0.873387	+	0.487026i	$0.161918\pi$
$234$	19.4848	+	11.7036i	1.27376	+	0.765088i
$235$	−1.02300	−	1.28586i	−0.0667331	−	0.0838803i
$236$	2.11240	+	0.645122i	0.137506	+	0.0419939i
$237$	0.0731587	+	0.0731587i	0.00475217	+	0.00475217i
$238$	−29.9769	+	5.59399i	−1.94311	+	0.362604i
$239$	−2.74482			−0.177548			−0.0887739	−	0.996052i	$-0.528295\pi$
$239$	−2.74482			−0.177548			−0.0887739	+	0.996052i	$0.528295\pi$
$240$	0.0979036	−	0.302029i	0.00631965	−	0.0194959i
$241$	−16.5587	−	6.85884i	−1.06664	−	0.441817i	−0.220836	−	0.975311i	$-0.570879\pi$
$241$	−16.5587	−	6.85884i	−1.06664	−	0.441817i	−0.845804	+	0.533494i	$0.820879\pi$
$242$	−5.53034	+	1.37976i	−0.355504	+	0.0886945i
$243$	−0.884985	+	0.366573i	−0.0567718	+	0.0235156i
$244$	13.1469	+	10.8307i	0.841643	+	0.693366i
$245$	−35.6097	+	28.3302i	−2.27502	+	1.80995i
$246$	0.0527871	−	0.0131698i	0.00336558	−	0.000839678i
$247$		−	19.9636i		−	1.27025i
$248$	−4.86867	−	2.31951i	−0.309161	−	0.147289i
$249$	0.0137884	+	0.0332881i	0.000873802	+	0.00210955i
$250$	12.1964	−	10.0622i	0.771366	−	0.636392i
$251$		−	17.9374i		−	1.13220i	−0.824337	−	0.566100i	$-0.808452\pi$
$251$		−	17.9374i		−	1.13220i	0.824337	−	0.566100i	$-0.191548\pi$
$252$	19.9434	−	24.2083i	1.25632	−	1.52498i
$253$		−	13.3585i		−	0.839845i
$254$	3.20562	−	5.33689i	0.201139	−	0.334866i
$255$	−0.322366	−	0.0564560i	−0.0201874	−	0.00353541i
$256$	−6.01177	−	14.8276i	−0.375736	−	0.926727i
$257$		−	6.20655i		−	0.387154i	−0.981085	−	0.193577i	$-0.937991\pi$
$257$		−	6.20655i		−	0.387154i	0.981085	−	0.193577i	$-0.0620090\pi$
$258$	−0.254642	−	0.0380169i	−0.0158533	−	0.00236683i
$259$	−7.86524			−0.488722
$260$	−21.9848	−	9.54908i	−1.36344	−	0.592209i
$261$	4.26142	+	10.2880i	0.263775	+	0.636810i
$262$	16.5344	−	12.2387i	1.02150	−	0.756108i
$263$	−27.0986			−1.67097			−0.835486	−	0.549512i	$-0.814814\pi$
$263$	−27.0986			−1.67097			−0.835486	+	0.549512i	$0.814814\pi$
$264$	0.289151	−	0.260592i	0.0177960	−	0.0160383i
$265$	8.02366	+	0.913490i	0.492890	+	0.0561153i
$266$	−27.2465	−	4.06777i	−1.67059	−	0.249411i
$267$	−0.176679	−	0.426542i	−0.0108126	−	0.0261039i
$268$	15.9408	+	4.86830i	0.973742	+	0.297379i
$269$	18.7038	+	7.74736i	1.14039	+	0.472365i	0.871300	−	0.490751i	$-0.163277\pi$
$269$	18.7038	+	7.74736i	1.14039	+	0.472365i	0.269089	+	0.963115i	$0.413277\pi$
$270$	0.583084	−	0.336828i	0.0354854	−	0.0204987i
$271$			0.635539i			0.0386063i	0.999814	+	0.0193031i	$0.00614476\pi$
$271$			0.635539i			0.0386063i	−0.999814	+	0.0193031i	$0.993855\pi$
$272$	−14.2689	+	8.27027i	−0.865182	+	0.501459i
$273$	0.703560	+	0.703560i	0.0425814	+	0.0425814i
$274$	−18.5278	+	4.62251i	−1.11931	+	0.279256i
$275$	19.1181	−	3.20262i	1.15287	−	0.193125i
$276$	0.114911	+	0.215958i	0.00691683	+	0.0129991i
$277$	9.96895	−	4.12927i	0.598976	−	0.248104i	−0.0625309	−	0.998043i	$-0.519917\pi$
$277$	9.96895	−	4.12927i	0.598976	−	0.248104i	0.661507	+	0.749939i	$0.269917\pi$
$278$	−9.18080	+	6.79560i	−0.550628	+	0.407573i
$279$	−2.18807	−	5.28246i	−0.130996	−	0.316253i
$280$	−17.5123	+	28.0593i	−1.04656	+	1.67687i
$281$	16.0075	+	16.0075i	0.954930	+	0.954930i	0.999027	−	0.0440975i	$-0.0140412\pi$
$281$	16.0075	+	16.0075i	0.954930	+	0.954930i	−0.0440975	+	0.999027i	$0.514041\pi$
$282$	0.0219475	+	0.0296510i	0.00130696	+	0.00176569i
$283$	11.9723	+	4.95909i	0.711680	+	0.294787i	0.708999	−	0.705209i	$-0.249147\pi$
$283$	11.9723	+	4.95909i	0.711680	+	0.294787i	0.00268022	+	0.999996i	$0.499147\pi$
$284$	−29.6289	+	2.86204i	−1.75815	+	0.169831i
$285$	−0.258599	−	0.143315i	−0.0153181	−	0.00848925i
$286$	−17.4829	−	23.6193i	−1.03379	−	1.39664i
$287$	−5.66768			−0.334553
$288$	5.78970	−	15.9448i	0.341161	−	0.939558i
$289$	10.4951	+	13.3736i	0.617356	+	0.786684i
$290$	−5.87387	−	10.1683i	−0.344926	−	0.597102i
$291$	−0.276672	+	0.276672i	−0.0162188	+	0.0162188i
$292$	15.1160	+	12.4529i	0.884596	+	0.728753i
$293$	6.63836	+	6.63836i	0.387817	+	0.387817i	0.873908	−	0.486091i	$-0.161578\pi$
$293$	6.63836	+	6.63836i	0.387817	+	0.387817i	−0.486091	+	0.873908i	$0.661578\pi$
$294$	0.821132	−	0.607799i	0.0478894	−	0.0354476i
$295$	−1.53741	−	1.93246i	−0.0895116	−	0.112512i
$296$	−4.00916	+	1.42178i	−0.233028	+	0.0826392i
$297$	0.825554			0.0479035
$298$	−7.46517	+	12.4284i	−0.432445	+	0.719958i
$299$	17.0618	−	7.06723i	0.986710	−	0.408709i
$300$	−0.281519	+	0.216230i	−0.0162535	+	0.0124840i
$301$	24.7798	+	10.2641i	1.42828	+	0.591615i
$302$	−8.28687	−	33.2153i	−0.476856	−	1.91132i
$303$	−0.472035	+	0.195523i	−0.0271177	+	0.0112325i
$304$	−14.6237	+	2.85180i	−0.838727	+	0.163562i
$305$	−5.25085	−	18.3060i	−0.300663	−	1.04820i
$306$	−17.1079	−	3.61443i	−0.977991	−	0.206623i
$307$	−4.28651	+	4.28651i	−0.244644	+	0.244644i	−0.818768	−	0.574124i	$-0.805343\pi$
$307$	−4.28651	+	4.28651i	−0.244644	+	0.244644i	0.574124	+	0.818768i	$0.305343\pi$
$308$	−35.7981	+	19.0482i	−2.03979	+	1.08537i
$309$	−0.275910	−	0.114285i	−0.0156959	−	0.00650147i
$310$	3.01600	+	5.22100i	0.171297	+	0.296533i
$311$	−9.49060	−	3.93114i	−0.538163	−	0.222914i	0.0970114	−	0.995283i	$-0.469072\pi$
$311$	−9.49060	−	3.93114i	−0.538163	−	0.222914i	−0.635174	+	0.772369i	$0.719072\pi$
$312$	0.485807	+	0.231446i	0.0275034	+	0.0131030i
$313$	−5.73853	+	13.8540i	−0.324361	+	0.783077i	0.674630	+	0.738156i	$0.264303\pi$
$313$	−5.73853	+	13.8540i	−0.324361	+	0.783077i	−0.998991	+	0.0449203i	$0.985697\pi$
$314$	0.0814967	−	0.0203326i	0.00459913	−	0.00114743i
$315$	−33.7082	+	9.66876i	−1.89924	+	0.544773i
$316$	−4.49910	−	3.70647i	−0.253094	−	0.208505i
$317$	−22.3713	−	9.26650i	−1.25650	−	0.520459i	−0.347665	−	0.937619i	$-0.613025\pi$
$317$	−22.3713	−	9.26650i	−1.25650	−	0.520459i	−0.908833	+	0.417160i	$0.863025\pi$
$318$	−0.179313	−	0.0267706i	−0.0100554	−	0.00150122i
$319$		−	14.3967i		−	0.806058i
$320$	−3.85435	+	17.4684i	−0.215465	+	0.976512i
$321$	0.0559095	−	0.0559095i	0.00312056	−	0.00312056i
$322$	−6.16892	−	24.7262i	−0.343780	−	1.37793i
$323$	5.01561	+	14.5156i	0.279076	+	0.807671i
$324$	15.8705	−	8.44467i	0.881692	−	0.469149i
$325$	14.2048	+	22.7238i	0.787938	+	1.26049i
$326$	−15.9595	+	11.8131i	−0.883913	+	0.654269i
$327$	−0.344053	+	0.344053i	−0.0190262	+	0.0190262i
$328$	−2.88899	+	1.02453i	−0.159518	+	0.0565703i
$329$	−1.47067	−	3.55050i	−0.0810804	−	0.195745i
$330$	−0.431460	+	0.0569069i	−0.0237511	+	0.00313262i
$331$	13.4516	+	13.4516i	0.739365	+	0.739365i	0.972455	−	0.233090i	$-0.0748837\pi$
$331$	13.4516	+	13.4516i	0.739365	+	0.739365i	−0.233090	+	0.972455i	$0.574884\pi$
$332$	−0.953589	−	1.79212i	−0.0523350	−	0.0983555i
$333$	−4.16664	−	1.72588i	−0.228331	−	0.0945776i
$334$	−1.02021	+	6.83350i	−0.0558234	+	0.373913i
$335$	−11.6018	−	14.5829i	−0.633874	−	0.796750i
$336$	0.414867	−	0.615875i	0.0226329	−	0.0335987i
$337$	−6.12728	+	2.53800i	−0.333774	+	0.138254i	−0.543275	−	0.839555i	$-0.682816\pi$
$337$	−6.12728	+	2.53800i	−0.333774	+	0.138254i	0.209501	+	0.977808i	$0.432816\pi$
$338$	11.4514	−	19.0648i	0.622872	−	1.03699i
$339$			0.367108i			0.0199386i
$340$	18.3843	+	1.41977i	0.997031	+	0.0769978i
$341$			7.39210i			0.400305i
$342$	−13.5413	−	8.13365i	−0.732231	−	0.439817i
$343$	−64.5034	+	26.7182i	−3.48286	+	1.44265i
$344$	14.4865	+	0.752569i	0.781057	+	0.0405758i
$345$	0.0309381	−	0.271745i	0.00166565	−	0.0146303i
$346$	17.3264	+	2.58675i	0.931473	+	0.139065i
$347$	−26.4182	−	10.9428i	−1.41820	−	0.587438i	−0.463794	−	0.885943i	$-0.653512\pi$
$347$	−26.4182	−	10.9428i	−1.41820	−	0.587438i	−0.954408	+	0.298505i	$0.903512\pi$
$348$	0.123841	+	0.232740i	0.00663857	+	0.0124762i
$349$	11.3173	+	11.3173i	0.605801	+	0.605801i	0.941846	−	0.336045i	$-0.109089\pi$
$349$	11.3173	+	11.3173i	0.605801	+	0.605801i	−0.336045	+	0.941846i	$0.609089\pi$
$350$	33.9080	−	14.7566i	1.81246	−	0.788774i
$351$	0.436753	+	1.05441i	0.0233121	+	0.0562805i
$352$	−14.8041	+	16.1806i	−0.789062	+	0.862428i
$353$	3.74286	−	3.74286i	0.199213	−	0.199213i	−0.600450	−	0.799662i	$-0.705012\pi$
$353$	3.74286	−	3.74286i	0.199213	−	0.199213i	0.799662	+	0.600450i	$0.205012\pi$
$354$	0.0329839	+	0.0445609i	0.00175307	+	0.00236839i
$355$	29.1089	+	16.1321i	1.54494	+	0.856204i
$356$	12.2190	+	22.9636i	0.647603	+	1.21707i
$357$	−0.688323	−	0.334801i	−0.0364299	−	0.0177196i
$358$	−12.2172	+	3.04805i	−0.645697	+	0.161095i
$359$	−10.8900	+	10.8900i	−0.574751	+	0.574751i	−0.933452	−	0.358701i	$-0.883220\pi$
$359$	−10.8900	+	10.8900i	−0.574751	+	0.574751i	0.358701	+	0.933452i	$0.383220\pi$
$360$	−15.4343	+	11.0218i	−0.813459	+	0.580900i
$361$		−	5.12591i		−	0.269785i
$362$	4.23574	−	28.3715i	0.222625	−	1.49117i
$363$	−0.132180	−	0.0547506i	−0.00693763	−	0.00287366i
$364$	−43.2674	−	35.6448i	−2.26783	−	1.86830i
$365$	−6.03731	−	21.0478i	−0.316007	−	1.10169i
$366$	0.103498	+	0.414840i	0.00540994	+	0.0216840i
$367$	8.57708	−	20.7069i	0.447720	−	1.08089i	−0.525454	−	0.850822i	$-0.676105\pi$
$367$	8.57708	−	20.7069i	0.447720	−	1.08089i	0.973174	−	0.230070i	$-0.0738954\pi$
$368$	−7.61417	−	11.4885i	−0.396916	−	0.598882i
$369$	−3.00247	−	1.24367i	−0.156303	−	0.0647426i
$370$	4.59413	+	1.22983i	0.238837	+	0.0639356i
$371$	17.4494	+	7.22776i	0.905926	+	0.375247i
$372$	−0.0635873	−	0.119502i	−0.00329685	−	0.00619592i
$373$	11.4203	−	11.4203i	0.591319	−	0.591319i	−0.346669	−	0.937988i	$-0.612687\pi$
$373$	11.4203	−	11.4203i	0.591319	−	0.591319i	0.937988	+	0.346669i	$0.112687\pi$
$374$	18.6460	+	12.7813i	0.964160	+	0.660906i
$375$	0.396327	−	0.0208719i	0.0204662	−	0.00107782i
$376$	−1.39146	−	1.54395i	−0.0717590	−	0.0796233i
$377$	18.3877	−	7.61643i	0.947015	−	0.392266i
$378$	1.52807	−	0.381237i	0.0785954	−	0.0196087i
$379$	−14.5914	−	6.04396i	−0.749510	−	0.310457i	−0.0249686	−	0.999688i	$-0.507949\pi$
$379$	−14.5914	−	6.04396i	−0.749510	−	0.310457i	−0.724542	+	0.689231i	$0.757949\pi$
$380$	15.2788	+	6.63633i	0.783785	+	0.340436i
$381$	0.144372	−	0.0598009i	0.00739641	−	0.00306369i
$382$	−15.9613	−	9.58722i	−0.816652	−	0.490525i
$383$	6.72506			0.343635			0.171817	−	0.985129i	$-0.445036\pi$
$383$	6.72506			0.343635			0.171817	+	0.985129i	$0.445036\pi$
$384$	0.100141	−	0.388925i	0.00511029	−	0.0198473i
$385$	45.0458	+	5.12844i	2.29575	+	0.261370i
$386$	−9.75260	−	13.1757i	−0.496394	−	0.670625i
$387$	10.8749	+	10.8749i	0.552803	+	0.552803i
$388$	14.0172	−	17.0148i	0.711615	−	0.863794i
$389$	−5.32951	+	5.32951i	−0.270217	+	0.270217i	−0.829187	−	0.558971i	$-0.811196\pi$
$389$	−5.32951	+	5.32951i	−0.270217	+	0.270217i	0.558971	+	0.829187i	$0.311196\pi$
$390$	−0.300943	−	0.520963i	−0.0152388	−	0.0263800i
$391$	−10.6302	+	9.42520i	−0.537591	+	0.476653i
$392$	−42.7571	+	38.5340i	−2.15956	+	1.94626i
$393$	0.516348			0.0260463
$394$	6.98835	−	5.17275i	0.352068	−	0.260599i
$395$	1.79694	+	6.26465i	0.0904137	+	0.315209i
$396$	−23.1439	+	2.23562i	−1.16303	+	0.112344i
$397$	0.985424	+	0.408176i	0.0494570	+	0.0204858i	0.407275	−	0.913306i	$-0.366479\pi$
$397$	0.985424	+	0.408176i	0.0494570	+	0.0204858i	−0.357818	+	0.933791i	$0.616479\pi$
$398$	16.6967	−	12.3589i	0.836931	−	0.619493i
$399$	−0.488953	−	0.488953i	−0.0244783	−	0.0244783i
$400$	14.6164	−	13.6514i	0.730822	−	0.682568i
$401$	−5.38206	−	12.9934i	−0.268767	−	0.648862i	0.730658	−	0.682743i	$-0.239213\pi$
$401$	−5.38206	−	12.9934i	−0.268767	−	0.648862i	−0.999426	+	0.0338813i	$0.989213\pi$
$402$	0.248907	+	0.336271i	0.0124143	+	0.0167717i
$403$	−9.44134	+	3.91073i	−0.470307	+	0.194807i
$404$	25.4129	−	13.5222i	1.26434	−	0.672754i
$405$	−19.9702	−	2.27360i	−0.992330	−	0.112976i
$406$	−6.64831	−	26.6476i	−0.329950	−	1.32250i
$407$	4.12290	+	4.12290i	0.204364	+	0.204364i
$408$	−0.411381	−	0.0462322i	−0.0203664	−	0.00228883i
$409$			20.9865i			1.03772i	0.854860	+	0.518858i	$0.173643\pi$
$409$			20.9865i			1.03772i	−0.854860	+	0.518858i	$0.826357\pi$
$410$	3.31052	+	0.886210i	0.163495	+	0.0437668i
$411$	−0.442830	−	0.183426i	−0.0218432	−	0.00904776i
$412$	16.0923	+	4.91455i	0.792811	+	0.242123i
$413$	−2.21019	−	5.33587i	−0.108756	−	0.262561i
$414$	2.15768	−	14.4524i	0.106044	−	0.710298i
$415$	−0.256740	+	2.25508i	−0.0126029	+	0.110697i
$416$	−28.4982	−	10.3479i	−1.39724	−	0.507349i
$417$	−0.286705			−0.0140400
$418$	12.1501	+	16.4147i	0.594280	+	0.802868i
$419$	−7.05984	−	17.0440i	−0.344896	−	0.832652i	−0.997206	−	0.0747001i	$-0.976200\pi$
$419$	−7.05984	−	17.0440i	−0.344896	−	0.832652i	0.652310	−	0.757952i	$-0.273800\pi$
$420$	−0.772336	+	0.304579i	−0.0376861	+	0.0148619i
$421$	21.0532			1.02607			0.513035	−	0.858368i	$-0.328521\pi$
$421$	21.0532			1.02607			0.513035	+	0.858368i	$0.328521\pi$
$422$	3.35612	−	22.4797i	0.163373	−	1.09430i
$423$		−	2.20360i		−	0.107143i
$424$	10.2010	+	0.529941i	0.495406	+	0.0257362i
$425$	−16.0374	−	12.9538i	−0.777930	−	0.628351i
$426$	−0.640504	−	0.384721i	−0.0310325	−	0.0186398i
$427$		−	44.5408i		−	2.15548i
$428$	−2.83257	+	3.43831i	−0.136917	+	0.166197i
$429$		−	0.737601i		−	0.0356117i
$430$	−12.8691	−	9.86996i	−0.620603	−	0.475972i
$431$	−10.4544	−	25.2391i	−0.503570	−	1.21573i	−0.947527	−	0.319677i	$-0.896426\pi$
$431$	−10.4544	−	25.2391i	−0.503570	−	1.21573i	0.443957	−	0.896048i	$-0.353574\pi$
$432$	0.709989	−	0.470553i	0.0341593	−	0.0226395i
$433$			10.3594i			0.497843i	0.968524	+	0.248921i	$0.0800760\pi$
$433$			10.3594i			0.497843i	−0.968524	+	0.248921i	$0.919924\pi$
$434$	3.41364	+	13.6825i	0.163860	+	0.656781i
$435$	0.0333423	−	0.292863i	0.00159864	−	0.0140417i
$436$	17.4309	−	21.1585i	0.834789	−	1.01331i
$437$	−11.8575	+	4.91152i	−0.567219	+	0.234950i
$438$	0.119000	+	0.476973i	0.00568604	+	0.0227907i
$439$	16.5053	+	6.83673i	0.787756	+	0.326299i	0.740041	−	0.672562i	$-0.234806\pi$
$439$	16.5053	+	6.83673i	0.787756	+	0.326299i	0.0477150	+	0.998861i	$0.484806\pi$
$440$	23.8883	−	5.52868i	1.13883	−	0.263569i
$441$	−61.0249			−2.90595
$442$	−6.46006	+	30.5769i	−0.307274	+	1.45439i
$443$	−12.3296	−	12.3296i	−0.585796	−	0.585796i	0.350694	−	0.936490i	$-0.385946\pi$
$443$	−12.3296	−	12.3296i	−0.585796	−	0.585796i	−0.936490	+	0.350694i	$0.885946\pi$
$444$	−0.102117	−	0.0311863i	−0.00484627	−	0.00148004i
$445$	3.28977	−	28.8958i	0.155950	−	1.36979i
$446$	−9.52152	+	15.8519i	−0.450857	+	0.750611i
$447$	−0.336210	+	0.139263i	−0.0159022	+	0.00658690i
$448$	−19.9297	+	36.7861i	−0.941592	+	1.73798i
$449$	9.69145	−	4.01433i	0.457368	−	0.189448i	−0.142091	−	0.989854i	$-0.545383\pi$
$449$	9.69145	−	4.01433i	0.457368	−	0.189448i	0.599459	+	0.800406i	$0.295383\pi$
$450$	21.2009	−	0.376895i	0.999422	−	0.0177670i
$451$	2.97095	+	2.97095i	0.139897	+	0.139897i
$452$	−1.98870	−	20.5877i	−0.0935404	−	0.968363i
$453$	0.328832	−	0.793872i	0.0154499	−	0.0372993i
$454$	9.01451	−	6.67251i	0.423072	−	0.313157i
$455$	17.2810	+	60.2466i	0.810144	+	2.82440i
$456$	−0.337621	−	0.160848i	−0.0158106	−	0.00753239i
$457$			22.4971i			1.05237i	0.850371	+	0.526184i	$0.176378\pi$
$457$			22.4971i			1.05237i	−0.850371	+	0.526184i	$0.823622\pi$
$458$	4.74324	+	19.0118i	0.221637	+	0.888361i
$459$	−0.582474	−	0.656941i	−0.0271876	−	0.0306634i
$460$	−0.262933	+	15.4073i	−0.0122593	+	0.718367i
$461$	23.8882	+	23.8882i	1.11259	+	1.11259i	0.992800	+	0.119787i	$0.0382211\pi$
$461$	23.8882	+	23.8882i	1.11259	+	1.11259i	0.119787	+	0.992800i	$0.461779\pi$
$462$	−1.00669	−	0.150293i	−0.0468352	−	0.00699228i
$463$	−14.5492	−	14.5492i	−0.676157	−	0.676157i	0.282971	−	0.959128i	$-0.408680\pi$
$463$	−14.5492	−	14.5492i	−0.676157	−	0.676157i	−0.959128	+	0.282971i	$0.908680\pi$
$464$	−8.20587	−	12.3813i	−0.380948	−	0.574789i
$465$	−0.0171199	+	0.150373i	−0.000793918	+	0.00697340i
$466$	−26.4970	−	3.95588i	−1.22745	−	0.183253i
$467$	26.8827			1.24398			0.621992	−	0.783024i	$-0.286324\pi$
$467$	26.8827			1.24398			0.621992	+	0.783024i	$0.286324\pi$
$468$	−15.0995	−	28.3772i	−0.697975	−	1.31174i
$469$	−16.6788	−	40.2661i	−0.770154	−	1.85932i
$470$	0.303860	+	2.30382i	0.0140160	+	0.106267i
$471$	0.00194784		0.000806821i	8.97516e−5		3.71763e-5i
$472$	−2.09115	−	2.32033i	−0.0962531	−	0.106802i
$473$	−7.60900	−	18.3697i	−0.349862	−	0.844642i
$474$	−0.0354190	−	0.141966i	−0.00162685	−	0.00652070i
$475$	−9.87188	−	15.7923i	−0.452953	−	0.724602i
$476$	40.4153	+	15.0471i	1.85243	+	0.689682i
$477$	7.65787	+	7.65787i	0.350630	+	0.350630i
$478$	3.32763	+	1.99875i	0.152202	+	0.0914207i
$479$	26.2147	+	10.8585i	1.19778	+	0.496138i	0.890282	−	0.455410i	$-0.150507\pi$
$479$	26.2147	+	10.8585i	1.19778	+	0.496138i	0.307501	+	0.951548i	$0.400507\pi$
$480$	−0.338626	+	0.294866i	−0.0154561	+	0.0134587i
$481$	−3.08466	+	7.44703i	−0.140648	+	0.339556i
$482$	15.0801	+	20.3730i	0.686878	+	0.927967i
$483$	0.244790	−	0.590975i	0.0111383	−	0.0268903i
$484$	7.70932	+	2.35441i	0.350424	+	0.107019i
$485$	−23.6917	+	6.79567i	−1.07579	+	0.308576i
$486$	1.33983	+	0.200030i	0.0607758	+	0.00907354i
$487$	8.57770	+	3.55300i	0.388693	+	0.161002i	0.568467	−	0.822706i	$-0.307537\pi$
$487$	8.57770	+	3.55300i	0.388693	+	0.161002i	−0.179774	+	0.983708i	$0.557537\pi$
$488$	−8.05151	−	22.7038i	−0.364475	−	1.02775i
$489$	−0.498395			−0.0225382
$490$	63.8004	−	8.41488i	2.88221	−	0.380145i
$491$	23.0290	−	23.0290i	1.03929	−	1.03929i	0.0400892	−	0.999196i	$-0.487236\pi$
$491$	23.0290	−	23.0290i	1.03929	−	1.03929i	0.999196	−	0.0400892i	$-0.0127642\pi$
$492$	−0.0735854	−	0.0224728i	−0.00331749	−	0.00101315i
$493$	−11.4563	+	10.1576i	−0.515964	+	0.457477i
$494$	−14.5373	+	24.2024i	−0.654062	+	1.08892i
$495$	22.7378	+	12.6013i	1.02199	+	0.566384i
$496$	4.21339	+	6.35732i	0.189187	+	0.285452i
$497$	55.0385	+	55.0385i	2.46882	+	2.46882i
$498$	0.00752398	−	0.0503966i	0.000337158	−	0.00225833i
$499$	−3.75111	−	9.05598i	−0.167923	−	0.405401i	0.817408	−	0.576060i	$-0.195410\pi$
$499$	−3.75111	−	9.05598i	−0.167923	−	0.405401i	−0.985330	+	0.170659i	$0.945410\pi$
$500$	−22.1132	+	3.31749i	−0.988933	+	0.148363i
$501$	−0.122631	+	0.122631i	−0.00547875	+	0.00547875i
$502$	−13.0618	+	21.7460i	−0.582978	+	0.970574i
$503$	5.40706	+	2.23968i	0.241089	+	0.0998624i	0.499957	−	0.866050i	$-0.333349\pi$
$503$	5.40706	+	2.23968i	0.241089	+	0.0998624i	−0.258867	+	0.965913i	$0.583349\pi$
$504$	−41.8062	+	14.8258i	−1.86219	+	0.660395i
$505$	−31.9777	−	3.64065i	−1.42299	−	0.162007i
$506$	−9.72755	+	16.1949i	−0.432442	+	0.719953i
$507$	0.515736	−	0.213625i	0.0229047	−	0.00948742i
$508$	−7.77253	+	4.13577i	−0.344850	+	0.183495i
$509$	16.3006			0.722510			0.361255	−	0.932467i	$-0.382348\pi$
$509$	16.3006			0.722510			0.361255	+	0.932467i	$0.382348\pi$
$510$	0.349703	+	0.303187i	0.0154851	+	0.0134253i
$511$		−	51.2120i		−	2.26549i
$512$	−3.50908	+	22.3537i	−0.155081	+	0.987902i
$513$	−0.303530	−	0.732787i	−0.0134012	−	0.0323533i
$514$	−4.51955	+	7.52438i	−0.199349	+	0.331886i
$515$	−11.7120	−	14.7215i	−0.516094	−	0.648706i
$516$	0.281027	+	0.231517i	0.0123715	+	0.0101920i
$517$	−1.09023	+	2.63205i	−0.0479484	+	0.115758i
$518$	9.53526	+	5.72739i	0.418955	+	0.251647i
$519$	0.310932	+	0.310932i	0.0136484	+	0.0136484i
$520$	19.6992	+	27.5857i	0.863869	+	1.20971i
$521$	−1.82662	+	0.756612i	−0.0800258	+	0.0331478i	−0.422337	−	0.906439i	$-0.638790\pi$
$521$	−1.82662	+	0.756612i	−0.0800258	+	0.0331478i	0.342311	+	0.939587i	$0.388790\pi$
$522$	2.32536	−	15.5755i	0.101778	−	0.681723i
$523$	−13.6333	+	13.6333i	−0.596144	+	0.596144i	−0.939284	−	0.343140i	$-0.888510\pi$
$523$	−13.6333	+	13.6333i	−0.596144	+	0.596144i	0.343140	+	0.939284i	$0.388510\pi$
$524$	−28.9571	+	2.79715i	−1.26500	+	0.122194i
$525$	0.904464	+	0.208650i	0.0394740	+	0.00910623i
$526$	32.8524	+	19.7329i	1.43243	+	0.860396i
$527$	5.88233	−	5.21554i	0.256238	−	0.227192i
$528$	−0.540307	+	0.105367i	−0.0235138	+	0.00458549i
$529$	7.86823	+	7.86823i	0.342097	+	0.342097i
$530$	−9.06212	−	6.95020i	−0.393633	−	0.301897i
$531$		−	3.31168i		−	0.143715i
$532$	30.0696	+	24.7721i	1.30368	+	1.07401i
$533$	−2.22280	+	5.36632i	−0.0962802	+	0.232441i
$534$	−0.0964097	+	0.645765i	−0.00417205	+	0.0279450i
$535$	4.78759	−	1.37326i	0.206985	−	0.0593711i
$536$	−15.7805	−	17.5099i	−0.681613	−	0.756313i
$537$	−0.292000	−	0.120950i	−0.0126007	−	0.00521939i
$538$	−17.0336	−	23.0122i	−0.734370	−	0.992128i
$539$	72.8902	+	30.1921i	3.13960	+	1.30047i
$540$	−0.952164	−	0.0162492i	−0.0409746	−	0.000699254i
$541$	2.62610	−	6.33997i	0.112905	−	0.272576i	−0.857319	−	0.514785i	$-0.827872\pi$
$541$	2.62610	−	6.33997i	0.112905	−	0.272576i	0.970224	+	0.242208i	$0.0778718\pi$
$542$	0.462793	−	0.770482i	0.0198787	−	0.0330950i
$543$	0.509143	−	0.509143i	0.0218494	−	0.0218494i
$544$	23.3210	+	0.364205i	0.999878	+	0.0156152i
$545$	−29.4616	+	8.45068i	−1.26200	+	0.361987i
$546$	−0.340621	−	1.36527i	−0.0145772	−	0.0584282i
$547$	−19.8449	+	8.22001i	−0.848505	+	0.351462i	−0.764201	−	0.644978i	$-0.776867\pi$
$547$	−19.8449	+	8.22001i	−0.848505	+	0.351462i	−0.0843035	+	0.996440i	$0.526867\pi$
$548$	25.8279	+	7.88778i	1.10331	+	0.336949i
$549$	9.77363	−	23.5956i	0.417129	−	1.00704i
$550$	−25.5096	−	10.0390i	−1.08773	−	0.428064i
$551$	−12.7789	+	5.29320i	−0.544400	+	0.225498i
$552$	0.0179481	−	0.345488i	0.000763920	−	0.0147050i
$553$			15.2427i			0.648184i
$554$	−15.0925	−	2.25324i	−0.641220	−	0.0957312i
$555$	0.0743212	+	0.0934183i	0.00315476	+	0.00396539i
$556$	16.0786	−	1.55314i	0.681886	−	0.0658677i
$557$	0.937247	−	0.937247i	0.0397124	−	0.0397124i	−0.686972	−	0.726684i	$-0.741060\pi$
$557$	0.937247	−	0.937247i	0.0397124	−	0.0397124i	0.726684	+	0.686972i	$0.241060\pi$
$558$	−1.19398	+	7.99741i	−0.0505450	+	0.338557i
$559$	19.4367	−	19.4367i	0.822086	−	0.822086i
$560$	41.6632	−	21.2649i	1.76059	−	0.898605i
$561$	0.185313	+	0.536313i	0.00782394	+	0.0226432i
$562$	−7.74988	−	31.0629i	−0.326909	−	1.31031i
$563$	11.7967			0.497172			0.248586	−	0.968610i	$-0.420034\pi$
$563$	11.7967			0.497172			0.248586	+	0.968610i	$0.420034\pi$
$564$	−0.00501612	−	0.0519287i	−0.000211217	−	0.00218659i
$565$	−11.2094	+	20.2264i	−0.471585	+	0.850932i
$566$	−10.9032	−	14.7302i	−0.458296	−	0.619154i
$567$	−43.4301	−	17.9893i	−1.82389	−	0.755481i
$568$	38.0040	+	18.1057i	1.59461	+	0.759698i
$569$	−1.96457	+	1.96457i	−0.0823591	+	0.0823591i	−0.747086	−	0.664727i	$-0.768548\pi$
$569$	−1.96457	+	1.96457i	−0.0823591	+	0.0823591i	0.664727	+	0.747086i	$0.268548\pi$
$570$	0.209146	+	0.362054i	0.00876018	+	0.0151648i
$571$	−4.06255	−	9.80786i	−0.170012	−	0.410446i	0.815792	−	0.578346i	$-0.196302\pi$
$571$	−4.06255	−	9.80786i	−0.170012	−	0.410446i	−0.985804	+	0.167900i	$0.946302\pi$
$572$	3.99572	+	41.3652i	0.167070	+	1.72956i
$573$	−0.178850	−	0.431781i	−0.00747155	−	0.0180379i
$574$	6.87109	+	4.12714i	0.286794	+	0.172264i
$575$	10.0022	−	14.0276i	0.417119	−	0.584990i
$576$	−18.6299	+	15.1144i	−0.776245	+	0.629765i
$577$	−23.6219	+	23.6219i	−0.983392	+	0.983392i	−0.999864	−	0.0164720i	$-0.994757\pi$
$577$	−23.6219	+	23.6219i	−0.983392	+	0.983392i	0.0164720	+	0.999864i	$0.494757\pi$
$578$	−2.98493	−	23.8556i	−0.124157	−	0.992263i
$579$		−	0.411461i		−	0.0170997i
$580$	−0.283366	+	16.6046i	−0.0117661	+	0.689467i
$581$	−2.03139	+	4.90421i	−0.0842762	+	0.203461i
$582$	0.536888	−	0.133948i	0.0222547	−	0.00555232i
$583$	−5.35808	−	12.9356i	−0.221909	−	0.535736i
$584$	−9.25745	−	26.1043i	−0.383076	−	1.08021i
$585$	−4.06532	+	35.7078i	−0.168080	+	1.47634i
$586$	−3.21389	−	12.8818i	−0.132765	−	0.532144i
$587$	13.4282			0.554240			0.277120	−	0.960835i	$-0.410620\pi$
$587$	13.4282			0.554240			0.277120	+	0.960835i	$0.410620\pi$
$588$	−1.43808	+	0.138913i	−0.0593052	+	0.00572867i
$589$	6.56145	−	2.71784i	0.270360	−	0.111987i
$590$	0.456656	+	3.46230i	0.0188002	+	0.142541i
$591$	0.218238			0.00897710
$592$	5.89574	+	1.19576i	0.242313	+	0.0491456i
$593$	−7.75557			−0.318483			−0.159242	−	0.987240i	$-0.550905\pi$
$593$	−7.75557			−0.318483			−0.159242	+	0.987240i	$0.550905\pi$
$594$	−1.00084	−	0.601159i	−0.0410651	−	0.0246659i
$595$	−27.7013	−	39.4640i	−1.13564	−	1.61786i
$596$	18.1005	−	9.63126i	0.741424	−	0.394512i
$597$	0.521418			0.0213402
$598$	−25.8308	−	3.85642i	−1.05630	−	0.157701i
$599$			11.7777i			0.481224i	0.970621	+	0.240612i	$0.0773481\pi$
$599$			11.7777i			0.481224i	−0.970621	+	0.240612i	$0.922652\pi$
$600$	0.498750	−	0.0571420i	0.0203614	−	0.00233281i
$601$	−34.4961	+	14.2888i	−1.40713	+	0.582850i	−0.951591	−	0.307368i	$-0.900552\pi$
$601$	−34.4961	+	14.2888i	−1.40713	+	0.582850i	−0.455535	+	0.890218i	$0.650552\pi$
$602$	−22.5670	−	30.4879i	−0.919763	−	1.24259i
$603$		−	24.9910i		−	1.01771i
$604$	−14.1406	+	46.3022i	−0.575373	+	1.88401i
$605$	−5.61087	−	7.05260i	−0.228114	−	0.286729i
$606$	0.714640	+	0.106692i	0.0290302	+	0.00433408i
$607$	6.12678	−	2.53779i	0.248678	−	0.103006i	−0.254863	−	0.966977i	$-0.582030\pi$
$607$	6.12678	−	2.53779i	0.248678	−	0.103006i	0.503541	+	0.863971i	$0.332030\pi$
$608$	19.8054	+	7.19150i	0.803214	+	0.291654i
$609$	0.263813	−	0.636900i	0.0106902	−	0.0258085i
$610$	−6.96449	+	26.0165i	−0.281984	+	1.05338i
$611$	−3.93849			−0.159334
$612$	18.1084	+	16.8396i	0.731987	+	0.680702i
$613$	29.1967	−	29.1967i	1.17924	−	1.17924i	0.199306	−	0.979937i	$-0.436131\pi$
$613$	29.1967	−	29.1967i	1.17924	−	1.17924i	0.979937	−	0.199306i	$-0.0638687\pi$
$614$	8.31805	−	2.07527i	0.335689	−	0.0837510i
$615$	0.0535557	+	0.0673171i	0.00215958	+	0.00271449i
$616$	57.2698	+	2.97515i	2.30746	+	0.119872i
$617$	−5.25700	−	12.6915i	−0.211639	−	0.510942i	0.782036	−	0.623233i	$-0.214181\pi$
$617$	−5.25700	−	12.6915i	−0.211639	−	0.510942i	−0.993675	+	0.112291i	$0.964181\pi$
$618$	0.251272	+	0.339466i	0.0101076	+	0.0136553i
$619$	13.9224	−	5.76687i	0.559590	−	0.231790i	−0.0849170	−	0.996388i	$-0.527063\pi$
$619$	13.9224	−	5.76687i	0.559590	−	0.231790i	0.644507	+	0.764598i	$0.277063\pi$
$620$	0.145497	−	8.52578i	0.00584330	−	0.342404i
$621$	0.518822	−	0.518822i	0.0208196	−	0.0208196i
$622$	8.64312	+	11.6768i	0.346557	+	0.468196i
$623$	26.0295	−	62.8408i	1.04285	−	2.51766i
$624$	−0.420421	−	0.634348i	−0.0168303	−	0.0253942i
$625$	22.4736	+	10.9516i	0.898943	+	0.438066i
$626$	17.0453	−	12.6169i	0.681269	−	0.504273i
$627$			0.512611i			0.0204717i
$628$	−0.113607	−	0.0346953i	−0.00453340	−	0.00138449i
$629$	0.371896	−	6.18976i	0.0148284	−	0.246802i
$630$	47.9060	+	12.8242i	1.90862	+	0.510929i
$631$	26.2239	+	26.2239i	1.04396	+	1.04396i	0.998988	+	0.0449669i	$0.0143182\pi$
$631$	26.2239	+	26.2239i	1.04396	+	1.04396i	0.0449669	+	0.998988i	$0.485682\pi$
$632$	2.75538	+	7.76966i	0.109603	+	0.309061i
$633$	0.403411	−	0.403411i	0.0160342	−	0.0160342i
$634$	20.3736	+	27.5246i	0.809140	+	1.09314i
$635$	9.78040	+	1.11349i	0.388123	+	0.0441877i
$636$	0.197892	+	0.163029i	0.00784694	+	0.00646451i
$637$			109.070i			4.32150i
$638$	−10.4835	+	17.4535i	−0.415045	+	0.690989i
$639$	17.0797	+	41.2340i	0.675662	+	1.63119i
$640$	17.3930	−	18.3707i	0.687519	−	0.726166i
$641$	−4.18843	+	10.1118i	−0.165433	+	0.399390i	−0.984756	−	0.173942i	$-0.944350\pi$
$641$	−4.18843	+	10.1118i	−0.165433	+	0.399390i	0.819323	+	0.573332i	$0.194350\pi$
$642$	−0.108493	+	0.0270680i	−0.00428189	+	0.00106829i
$643$	−18.7882	−	45.3588i	−0.740936	−	1.78878i	−0.602033	−	0.798471i	$-0.705643\pi$
$643$	−18.7882	−	45.3588i	−0.740936	−	1.78878i	−0.138902	−	0.990306i	$-0.544357\pi$
$644$	−10.5266	+	34.4684i	−0.414805	+	1.35824i
$645$	−0.112242	−	0.391308i	−0.00441951	−	0.0154077i
$646$	4.48955	−	21.2500i	0.176639	−	0.836070i
$647$	−4.24686	−	4.24686i	−0.166961	−	0.166961i	0.618681	−	0.785642i	$-0.287667\pi$
$647$	−4.24686	−	4.24686i	−0.166961	−	0.166961i	−0.785642	+	0.618681i	$0.787667\pi$
$648$	−25.3895	−	1.31898i	−0.997395	−	0.0518145i
$649$	−1.63846	+	3.95558i	−0.0643150	+	0.155270i
$650$	−0.673624	−	37.8924i	−0.0264217	−	1.48626i
$651$	−0.135457	+	0.327023i	−0.00530899	+	0.0128170i
$652$	27.9503	−	2.69990i	1.09462	−	0.105736i
$653$	−6.04118	−	2.50234i	−0.236410	−	0.0979241i	0.261333	−	0.965249i	$-0.415838\pi$
$653$	−6.04118	−	2.50234i	−0.236410	−	0.0979241i	−0.497743	+	0.867324i	$0.665838\pi$
$654$	0.667640	−	0.166569i	0.0261068	−	0.00651338i
$655$	28.4490	+	15.7664i	1.11159	+	0.616044i
$656$	4.24846	+	0.861665i	0.165874	+	0.0336424i
$657$	11.2375	−	27.1297i	0.438417	−	1.05843i
$658$	−0.802507	+	5.37530i	−0.0312850	+	0.209551i
$659$	−41.3713			−1.61160			−0.805798	−	0.592190i	$-0.798263\pi$
$659$	−41.3713			−1.61160			−0.805798	+	0.592190i	$0.798263\pi$
$660$	0.564510	+	0.245195i	0.0219735	+	0.00954419i
$661$	−2.07225	−	2.07225i	−0.0806012	−	0.0806012i	0.665657	−	0.746258i	$-0.268151\pi$
$661$	−2.07225	−	2.07225i	−0.0806012	−	0.0806012i	−0.746258	+	0.665657i	$0.768151\pi$
$662$	−6.51243	−	26.1030i	−0.253113	−	1.01452i
$663$	−0.586952	+	0.520419i	−0.0227953	+	0.0202114i
$664$	−0.148942	+	2.86704i	−0.00578007	+	0.111263i
$665$	−12.0098	−	41.8696i	−0.465718	−	1.62363i
$666$	3.79457	+	5.12644i	0.147037	+	0.198645i
$667$	−9.04763	−	9.04763i	−0.350326	−	0.350326i
$668$	6.21291	−	7.54154i	0.240385	−	0.291791i
$669$	−0.428822	+	0.177624i	−0.0165792	+	0.00686734i
$670$	3.44607	+	26.1276i	0.133133	+	1.00940i
$671$	−23.3479	+	23.3479i	−0.901336	+	0.901336i
$672$	−0.951429	+	0.444541i	−0.0367022	+	0.0171485i
$673$	2.91543	−	7.03847i	0.112382	−	0.271313i	−0.857675	−	0.514192i	$-0.828092\pi$
$673$	2.91543	−	7.03847i	0.112382	−	0.271313i	0.970057	+	0.242879i	$0.0780918\pi$
$674$	9.27642	+	1.38493i	0.357314	+	0.0533454i
$675$	0.866899	+	0.618131i	0.0333670	+	0.0237919i
$676$	−27.7656	+	14.7741i	−1.06791	+	0.568234i
$677$	−4.35675	−	10.5181i	−0.167443	−	0.404244i	0.817777	−	0.575535i	$-0.195206\pi$
$677$	−4.35675	−	10.5181i	−0.167443	−	0.404244i	−0.985220	+	0.171291i	$0.945206\pi$
$678$	0.267324	−	0.445056i	0.0102665	−	0.0170923i
$679$	−57.6449			−2.21221
$680$	−21.2540	−	15.1085i	−0.815054	−	0.579385i
$681$	0.281512			0.0107876
$682$	5.38285	−	8.96165i	0.206120	−	0.343159i
$683$	15.2828	+	36.8960i	0.584781	+	1.41179i	0.888435	+	0.459003i	$0.151793\pi$
$683$	15.2828	+	36.8960i	0.584781	+	1.41179i	−0.303654	+	0.952782i	$0.598207\pi$
$684$	10.4937	+	19.7213i	0.401237	+	0.754063i
$685$	−18.7976	−	23.6277i	−0.718220	−	0.902770i
$686$	97.6552	+	14.5795i	3.72849	+	0.556647i
$687$	−0.188217	+	0.454396i	−0.00718093	+	0.0173363i
$688$	−17.0143	−	11.4612i	−0.648665	−	0.436956i
$689$	13.6869	−	13.6869i	0.521429	−	0.521429i
$690$	−0.235389	+	0.306916i	−0.00896111	+	0.0116841i
$691$	34.5643	−	14.3170i	1.31489	−	0.544645i	0.388581	−	0.921414i	$-0.372965\pi$
$691$	34.5643	−	14.3170i	1.31489	−	0.544645i	0.926307	+	0.376770i	$0.122965\pi$
$692$	−19.1216	−	15.7529i	−0.726896	−	0.598835i
$693$	42.9922	+	42.9922i	1.63314	+	1.63314i
$694$	24.0591	+	32.5037i	0.913271	+	1.23382i
$695$	−15.7965	−	8.75438i	−0.599195	−	0.332073i
$696$	0.0193428	−	0.372337i	0.000733188	−	0.0141134i
$697$	0.267987	−	4.46033i	0.0101507	−	0.168947i
$698$	−5.47915	−	21.9614i	−0.207389	−	0.831252i
$699$	−0.475504	−	0.475504i	−0.0179852	−	0.0179852i
$700$	−51.8532	−	6.80159i	−1.95987	−	0.257076i
$701$	50.4617			1.90591			0.952956	−	0.303109i	$-0.0980247\pi$
$701$	50.4617			1.90591			0.952956	+	0.303109i	$0.0980247\pi$
$702$	0.238325	−	1.59634i	0.00899502	−	0.0602498i
$703$	2.14375	−	5.17547i	0.0808530	−	0.195196i
$704$	29.7300	−	8.83597i	1.12049	−	0.333018i
$705$	−0.0282738	+	0.0510175i	−0.00106485	+	0.00192143i
$706$	−7.26309	+	1.81207i	−0.273350	+	0.0681980i
$707$	−69.5432	−	28.8057i	−2.61544	−	1.08335i
$708$	−0.00753847	−	0.0780410i	−0.000283313	−	0.00293296i
$709$	−12.3012	+	29.6977i	−0.461980	+	1.11532i	0.505603	+	0.862766i	$0.331270\pi$
$709$	−12.3012	+	29.6977i	−0.461980	+	1.11532i	−0.967583	+	0.252553i	$0.918730\pi$
$710$	−23.5424	−	40.7543i	−0.883529	−	1.52948i
$711$	−3.34472	+	8.07486i	−0.125437	+	0.302831i
$712$	1.90849	−	36.7372i	0.0715237	−	1.37678i
$713$	4.64559	+	4.64559i	0.173979	+	0.173979i
$714$	0.590675	+	0.907118i	0.0221055	+	0.0339481i
$715$	22.5222	−	40.6393i	0.842283	−	1.51982i
$716$	17.0308	+	5.20116i	0.636469	+	0.194376i
$717$	0.0372867	+	0.0900181i	0.00139250	+	0.00336179i
$718$	21.1322	−	5.27227i	0.788647	−	0.196759i
$719$	1.17672	−	2.84086i	0.0438843	−	0.105946i	−0.900417	−	0.435027i	$-0.856739\pi$
$719$	1.17672	−	2.84086i	0.0438843	−	0.105946i	0.944302	+	0.329081i	$0.106739\pi$
$720$	26.7374	−	2.12295i	0.996444	−	0.0791176i
$721$	−16.8373	−	40.6487i	−0.627052	−	1.51384i
$722$	−3.73263	+	6.21429i	−0.138914	+	0.231272i
$723$			0.636226i			0.0236615i
$724$	−25.7949	+	31.3112i	−0.958662	+	1.16367i
$725$	10.7795	−	15.1177i	0.400339	−	0.561456i
$726$	0.120376	+	0.162628i	0.00446759	+	0.00603567i
$727$	25.3538	−	25.3538i	0.940319	−	0.940319i	−0.0579975	−	0.998317i	$-0.518472\pi$
$727$	25.3538	−	25.3538i	0.940319	−	0.940319i	0.998317	+	0.0579975i	$0.0184715\pi$
$728$	26.4982	+	74.7201i	0.982088	+	2.76931i
$729$	−19.0438	−	19.0438i	−0.705325	−	0.705325i
$730$	−8.00761	+	29.9132i	−0.296375	+	1.10714i
$731$	−9.24930	+	19.0158i	−0.342098	+	0.703325i
$732$	0.176608	−	0.578288i	0.00652762	−	0.0213741i
$733$			29.3446i			1.08387i	0.840421	+	0.541934i	$0.182308\pi$
$733$			29.3446i			1.08387i	−0.840421	+	0.541934i	$0.817692\pi$
$734$	−25.4768	+	18.8578i	−0.940365	+	0.696055i
$735$	1.41284	+	0.782993i	0.0521134	+	0.0288811i
$736$	0.865037	+	19.4725i	0.0318857	+	0.717764i
$737$	−12.3643	+	29.8501i	−0.455445	+	1.09954i
$738$	2.73436	+	3.69410i	0.100653	+	0.135982i
$739$	31.7089	−	31.7089i	1.16643	−	1.16643i	0.183389	−	0.983040i	$-0.441293\pi$
$739$	31.7089	−	31.7089i	1.16643	−	1.16643i	0.983040	−	0.183389i	$-0.0587069\pi$
$740$	−4.67405	−	4.83635i	−0.171821	−	0.177788i
$741$	−0.654717	+	0.271193i	−0.0240516	+	0.00996251i
$742$	−15.8912	−	21.4689i	−0.583384	−	0.788147i
$743$	11.3071	+	27.2977i	0.414817	+	1.00146i	0.983826	+	0.179125i	$0.0573267\pi$
$743$	11.3071	+	27.2977i	0.414817	+	1.00146i	−0.569010	+	0.822331i	$0.692673\pi$
$744$	−0.00993176	+	0.191180i	−0.000364116	+	0.00700899i
$745$	−22.7763	−	2.59307i	−0.834460	−	0.0950029i
$746$	−22.1612	+	5.52900i	−0.811380	+	0.202431i
$747$	−2.15227	+	2.15227i	−0.0787475	+	0.0787475i
$748$	−13.2978	−	29.0729i	−0.486216	−	1.06301i
$749$	11.6488			0.425637
$750$	−0.495677	−	0.263297i	−0.0180996	−	0.00961426i
$751$	10.8333	−	26.1540i	0.395314	−	0.954372i	−0.593448	−	0.804872i	$-0.702234\pi$
$751$	10.8333	−	26.1540i	0.395314	−	0.954372i	0.988762	−	0.149500i	$-0.0477663\pi$
$752$	0.562615	+	2.88502i	0.0205165	+	0.105206i
$753$	−0.588268	+	0.243669i	−0.0214377	+	0.00887978i
$754$	−27.8381	−	4.15610i	−1.01381	−	0.151356i
$755$	42.3580	−	33.6989i	1.54156	−	1.22643i
$756$	−2.13013	−	0.650538i	−0.0774722	−	0.0236598i
$757$		−	25.4847i		−	0.926259i	−0.886291	−	0.463129i	$-0.846726\pi$
$757$		−	25.4847i		−	0.926259i	0.886291	−	0.463129i	$-0.153274\pi$
$758$	13.2884	+	17.9526i	0.482658	+	0.652067i
$759$	−0.438101	+	0.181467i	−0.0159021	+	0.00658685i
$760$	−13.6904	−	19.1712i	−0.496603	−	0.695414i
$761$			31.1534i			1.12931i	0.825328	+	0.564654i	$0.190990\pi$
$761$			31.1534i			1.12931i	−0.825328	+	0.564654i	$0.809010\pi$
$762$	−0.218573	−	0.0326319i	−0.00791806	−	0.00118213i
$763$	−71.6837			−2.59512
$764$	12.3691	+	23.2457i	0.447497	+	0.841001i
$765$	−6.01525	−	26.9847i	−0.217482	−	0.975634i
$766$	−8.15298	−	4.89712i	−0.294579	−	0.176940i
$767$	−5.91896			−0.213721
$768$	−0.404615	+	0.398584i	−0.0146003	+	0.0143826i
$769$	−12.3580			−0.445641			−0.222820	−	0.974859i	$-0.571526\pi$
$769$	−12.3580			−0.445641			−0.222820	+	0.974859i	$0.571526\pi$
$770$	−50.8758	−	39.0192i	−1.83344	−	1.40615i
$771$	−0.203548	+	0.0843121i	−0.00733059	+	0.00303643i
$772$	2.22896	+	23.0750i	0.0802221	+	0.830488i
$773$	15.7696			0.567193			0.283596	−	0.958944i	$-0.408472\pi$
$773$	15.7696			0.567193			0.283596	+	0.958944i	$0.408472\pi$
$774$	−5.26498	−	21.1030i	−0.189246	−	0.758531i
$775$	−5.53481	+	7.76231i	−0.198816	+	0.278830i
$776$	−29.3834	+	10.4203i	−1.05480	+	0.374067i
$777$	0.106844	+	0.257945i	0.00383302	+	0.00925373i
$778$	10.3420	−	2.58022i	0.370779	−	0.0925055i
$779$	1.54478	−	3.72943i	0.0553475	−	0.133621i
$780$	−0.0145180	+	0.850722i	−0.000519829	+	0.0304607i
$781$		−	57.7015i		−	2.06472i
$782$	19.7506	−	3.68566i	0.706280	−	0.131799i
$783$	0.559141	−	0.559141i	0.0199821	−	0.0199821i
$784$	79.8957	−	15.5806i	2.85342	−	0.556452i
$785$	0.0826834	+	0.103929i	0.00295110	+	0.00370939i
$786$	−0.625983	−	0.375999i	−0.0223281	−	0.0134114i
$787$	−3.42342	−	8.26486i	−0.122032	−	0.294610i	0.851045	−	0.525093i	$-0.175970\pi$
$787$	−3.42342	−	8.26486i	−0.122032	−	0.294610i	−0.973076	+	0.230483i	$0.925970\pi$
$788$	−12.2389	+	1.18223i	−0.435993	+	0.0421154i
$789$	0.368118	+	0.888715i	0.0131053	+	0.0316391i
$790$	2.38338	−	8.90333i	0.0847967	−	0.316766i
$791$	−38.2437	+	38.2437i	−1.35979	+	1.35979i
$792$	29.6860	+	14.1429i	1.05485	+	0.502545i
$793$	−42.1725	−	17.4684i	−1.49759	−	0.620321i
$794$	−0.897428	−	1.21242i	−0.0318485	−	0.0430271i
$795$	−0.0790380	−	0.275550i	−0.00280319	−	0.00977275i
$796$	−29.2415	+	2.82462i	−1.03644	+	0.100116i
$797$	−6.71767			−0.237952			−0.118976	−	0.992897i	$-0.537961\pi$
$797$	−6.71767			−0.237952			−0.118976	+	0.992897i	$0.537961\pi$
$798$	0.236721	+	0.948822i	0.00837985	+	0.0335880i
$799$	2.86370	−	0.989500i	0.101310	−	0.0350060i
$800$	−27.6607	+	5.90639i	−0.977954	+	0.208822i
$801$	27.5785	−	27.5785i	0.974437	−	0.974437i
$802$	−2.93686	+	19.6715i	−0.103704	+	0.694624i
$803$	−26.8449	+	26.8449i	−0.947336	+	0.947336i
$804$	−0.0568877	−	0.588922i	−0.00200627	−	0.0207697i
$805$	31.5322	−	25.0862i	1.11136	−	0.884172i
$806$	14.2938	+	2.13399i	0.503476	+	0.0751667i
$807$		−	0.718644i		−	0.0252975i
$808$	−40.6554	−	2.11204i	−1.43025	−	0.0743014i
$809$	−8.57280	+	3.55097i	−0.301404	+	0.124845i	−0.528260	−	0.849083i	$-0.677155\pi$
$809$	−8.57280	+	3.55097i	−0.301404	+	0.124845i	0.226856	+	0.973928i	$0.427155\pi$
$810$	22.5549	+	17.2985i	0.792498	+	0.607806i
$811$	−19.1005	+	46.1128i	−0.670711	+	1.61924i	0.109695	+	0.993965i	$0.465013\pi$
$811$	−19.1005	+	46.1128i	−0.670711	+	1.61924i	−0.780406	+	0.625274i	$0.784987\pi$
$812$	−11.3446	+	37.1469i	−0.398117	+	1.30360i
$813$	0.0208429	−	0.00863340i	0.000730991	−	0.000302787i
$814$	−1.99606	−	8.00055i	−0.0699617	−	0.280419i
$815$	−27.4598	−	15.2182i	−0.961877	−	0.533070i
$816$	0.465063	+	0.355612i	0.0162805	+	0.0124489i
$817$	−13.5080	+	13.5080i	−0.472583	+	0.472583i
$818$	15.2822	−	25.4426i	0.534328	−	0.889578i
$819$	−32.1658	+	77.6552i	−1.12396	+	2.71349i
$820$	−3.36811	−	3.48506i	−0.117620	−	0.121704i
$821$	18.9882	+	7.86518i	0.662693	+	0.274497i	0.688571	−	0.725168i	$-0.258238\pi$
$821$	18.9882	+	7.86518i	0.662693	+	0.274497i	−0.0258780	+	0.999665i	$0.508238\pi$
$822$	0.403287	+	0.544837i	0.0140662	+	0.0190034i
$823$	6.14343	+	2.54469i	0.214147	+	0.0887024i	0.487178	−	0.873303i	$-0.338026\pi$
$823$	6.14343	+	2.54469i	0.214147	+	0.0887024i	−0.273031	+	0.962005i	$0.588026\pi$
$824$	−15.9304	−	17.6763i	−0.554963	−	0.615783i
$825$	−0.364740	−	0.583485i	−0.0126986	−	0.0203143i
$826$	−1.20605	+	8.07826i	−0.0419637	+	0.281079i
$827$	−16.5670	+	39.9962i	−0.576090	+	1.39080i	0.320207	+	0.947348i	$0.396248\pi$
$827$	−16.5670	+	39.9962i	−0.576090	+	1.39080i	−0.896296	+	0.443456i	$0.853752\pi$
$828$	−13.1399	+	15.9499i	−0.456644	+	0.554297i
$829$			29.5524i			1.02640i	0.858270	+	0.513198i	$0.171539\pi$
$829$			29.5524i			1.02640i	−0.858270	+	0.513198i	$0.828461\pi$
$830$	1.95338	−	2.54694i	0.0678027	−	0.0884056i
$831$	−0.270844	−	0.270844i	−0.00939547	−	0.00939547i
$832$	27.0139	+	33.2971i	0.936538	+	1.15437i
$833$	−27.4025	−	79.3052i	−0.949440	−	2.74776i
$834$	0.347581	+	0.208776i	0.0120357	+	0.00722931i
$835$	−10.5010	+	3.01208i	−0.363403	+	0.104237i
$836$	−2.77691	−	28.7476i	−0.0960414	−	0.994255i
$837$	−0.287096	+	0.287096i	−0.00992350	+	0.00992350i
$838$	−3.85239	+	25.8038i	−0.133078	+	0.891377i
$839$	15.3975	−	6.37787i	0.531582	−	0.220188i	−0.100714	−	0.994915i	$-0.532113\pi$
$839$	15.3975	−	6.37787i	0.531582	−	0.220188i	0.632296	+	0.774727i	$0.282113\pi$
$840$	1.15812	+	0.193157i	0.0399588	+	0.00666456i
$841$	10.7554	+	10.7554i	0.370875	+	0.370875i
$842$	−25.5234	−	15.3307i	−0.879593	−	0.528331i
$843$	0.307524	−	0.742429i	0.0105917	−	0.0255706i
$844$	−20.4382	+	24.8089i	−0.703512	+	0.853958i
$845$	34.9382	+	3.97770i	1.20191	+	0.136837i
$846$	−1.60464	+	2.67149i	−0.0551686	+	0.0918476i
$847$	−8.06620	−	19.4735i	−0.277158	−	0.669119i
$848$	−11.9811	−	8.07074i	−0.411433	−	0.277150i
$849$		−	0.460005i		−	0.0157873i
$850$	10.0098	+	27.3825i	0.343334	+	0.939213i
$851$	5.18210			0.177640
$852$	0.496352	+	0.932817i	0.0170047	+	0.0319578i
$853$	−13.1173	+	5.43335i	−0.449126	+	0.186034i	−0.595770	−	0.803155i	$-0.703153\pi$
$853$	−13.1173	+	5.43335i	−0.449126	+	0.186034i	0.146643	+	0.989189i	$0.453153\pi$
$854$	−32.4341	+	53.9980i	−1.10987	+	1.84778i
$855$	2.82528	−	24.8159i	0.0966224	−	0.848685i
$856$	5.93775	−	2.10572i	0.202948	−	0.0719720i
$857$	25.8389	+	10.7028i	0.882639	+	0.365601i	0.777520	−	0.628859i	$-0.216478\pi$
$857$	25.8389	+	10.7028i	0.882639	+	0.365601i	0.105119	+	0.994460i	$0.466478\pi$
$858$	−0.537113	+	0.894215i	−0.0183367	+	0.0305280i
$859$	−10.8606	+	10.8606i	−0.370558	+	0.370558i	−0.867680	−	0.497123i	$-0.834390\pi$
$859$	−10.8606	+	10.8606i	−0.370558	+	0.370558i	0.497123	+	0.867680i	$0.334390\pi$
$860$	8.41438	+	21.3368i	0.286928	+	0.727578i
$861$	0.0769919	+	0.185875i	0.00262388	+	0.00633460i
$862$	−5.70470	+	38.2109i	−0.194303	+	1.30147i
$863$	−5.63029	−	5.63029i	−0.191657	−	0.191657i	0.604755	−	0.796412i	$-0.293271\pi$
$863$	−5.63029	−	5.63029i	−0.191657	−	0.191657i	−0.796412	+	0.604755i	$0.793271\pi$
$864$	−1.20339	+	0.0534590i	−0.0409402	+	0.00181871i
$865$	7.63716	+	26.6254i	0.259671	+	0.905291i
$866$	7.54363	−	12.5590i	0.256343	−	0.426773i
$867$	0.296027	−	0.525864i	0.0100536	−	0.0178593i
$868$	5.82499	−	19.0735i	0.197713	−	0.647395i
$869$	7.99008	−	7.99008i	0.271045	−	0.271045i
$870$	−0.253682	+	0.330767i	−0.00860061	+	0.0112140i
$871$	−44.6663			−1.51346
$872$	−36.5394	+	12.9581i	−1.23738	+	0.438815i
$873$	−30.5376	−	12.6491i	−1.03354	−	0.428107i
$874$	17.9516	+	2.68010i	0.607223	+	0.0906556i
$875$	43.4619	+	39.1132i	1.46928	+	1.32227i
$876$	0.203060	−	0.664903i	0.00686076	−	0.0224650i
$877$	0.259983	−	0.627655i	0.00877901	−	0.0211944i	−0.919429	−	0.393255i	$-0.871349\pi$
$877$	0.259983	−	0.627655i	0.00877901	−	0.0211944i	0.928208	+	0.372061i	$0.121349\pi$
$878$	−15.0314	−	20.3074i	−0.507286	−	0.685340i
$879$	0.127531	−	0.307887i	0.00430151	−	0.0103848i
$880$	−32.9864	−	10.6926i	−1.11197	−	0.360448i
$881$	29.4959	+	12.2176i	0.993741	+	0.411621i	0.819498	−	0.573082i	$-0.194252\pi$
$881$	29.4959	+	12.2176i	0.993741	+	0.411621i	0.174243	+	0.984703i	$0.444252\pi$
$882$	73.9822	+	44.4377i	2.49111	+	1.49629i
$883$	1.43819	+	1.43819i	0.0483991	+	0.0483991i	0.730892	−	0.682493i	$-0.239104\pi$
$883$	1.43819	+	1.43819i	0.0483991	+	0.0483991i	−0.682493	+	0.730892i	$0.739104\pi$
$884$	30.0975	−	32.3651i	1.01229	−	1.08855i
$885$	−0.0424912	+	0.0766715i	−0.00142833	+	0.00257729i
$886$	5.96923	+	23.9258i	0.200540	+	0.803802i
$887$	6.19185	+	14.9485i	0.207902	+	0.501920i	0.993092	−	0.117334i	$-0.0374350\pi$
$887$	6.19185	+	14.9485i	0.207902	+	0.501920i	−0.785190	+	0.619254i	$0.787435\pi$
$888$	0.101090	+	0.112169i	0.00339236	+	0.00376414i
$889$	21.2698	+	8.81024i	0.713366	+	0.295486i
$890$	−25.0299	+	32.6356i	−0.839004	+	1.09395i
$891$	13.3358	+	32.1955i	0.446767	+	1.07859i
$892$	23.0864	−	12.2843i	0.772991	−	0.411308i
$893$	2.73714			0.0915947
$894$	0.509006	+	0.0759923i	0.0170237	+	0.00254156i
$895$	−12.3951	−	15.5800i	−0.414321	−	0.520782i
$896$	50.9486	−	30.0842i	1.70207	−	1.00504i
$897$	−0.463548	−	0.463548i	−0.0154774	−	0.0154774i
$898$	−14.6724	−	2.19052i	−0.489625	−	0.0730987i
$899$	5.00661	+	5.00661i	0.166980	+	0.166980i
$900$	−25.9770	−	14.9814i	−0.865899	−	0.499379i
$901$	−6.51315	+	13.3905i	−0.216984	+	0.446102i
$902$	−1.43835	−	5.76518i	−0.0478920	−	0.191960i
$903$		−	0.952100i		−	0.0316839i
$904$	−12.5808	+	26.4072i	−0.418431	+	0.878290i
$905$	43.5984	−	12.5057i	1.44926	−	0.415702i
$906$	−0.976742	+	0.722981i	−0.0324501	+	0.0240194i
$907$	4.18770	−	10.1100i	0.139050	−	0.335697i	−0.838979	−	0.544163i	$-0.816847\pi$
$907$	4.18770	−	10.1100i	0.139050	−	0.335697i	0.978030	+	0.208466i	$0.0668472\pi$
$908$	−15.7874	+	1.52501i	−0.523923	+	0.0506091i
$909$	−30.5199	−	30.5199i	−1.01228	−	1.01228i
$910$	22.9207	−	85.6224i	0.759814	−	2.83836i
$911$	−34.2135	+	14.1717i	−1.13354	+	0.469529i	−0.868984	−	0.494840i	$-0.835227\pi$
$911$	−34.2135	+	14.1717i	−1.13354	+	0.469529i	−0.264560	+	0.964369i	$0.585227\pi$
$912$	0.292180	+	0.440853i	0.00967506	+	0.0145981i
$913$	3.63558	−	1.50591i	0.120320	−	0.0498383i
$914$	16.3821	−	27.2738i	0.541873	−	0.902138i
$915$	−0.529027	+	0.420880i	−0.0174891	+	0.0139139i
$916$	8.09379	−	26.5025i	0.267427	−	0.875666i
$917$	53.7907	+	53.7907i	1.77633	+	1.77633i
$918$	0.227773	+	1.22058i	0.00751762	+	0.0402852i
$919$	−32.5256			−1.07292			−0.536460	−	0.843926i	$-0.680239\pi$
$919$	−32.5256			−1.07292			−0.536460	+	0.843926i	$0.680239\pi$
$920$	11.5382	−	18.4872i	0.380402	−	0.609505i
$921$	0.198808	+	0.0823491i	0.00655095	+	0.00271349i
$922$	−11.5652	−	46.3556i	−0.380881	−	1.52664i
$923$	73.6976	−	30.5265i	2.42578	−	1.00479i
$924$	1.11099	+	0.915262i	0.0365489	+	0.0301099i
$925$	1.24237	+	7.41639i	0.0408490	+	0.243849i
$926$	7.04382	+	28.2329i	0.231474	+	0.927791i
$927$		−	25.2284i		−	0.828610i
$928$	0.932260	+	20.9857i	0.0306029	+	0.688888i
$929$	17.3258	+	41.8282i	0.568441	+	1.37234i	0.902869	+	0.429916i	$0.141457\pi$
$929$	17.3258	+	41.8282i	0.568441	+	1.37234i	−0.334428	+	0.942421i	$0.608543\pi$
$930$	0.130255	−	0.169835i	0.00427124	−	0.00556912i
$931$		−	75.8002i		−	2.48425i
$932$	29.2425	+	24.0907i	0.957869	+	0.789117i
$933$			0.364652i			0.0119382i
$934$	−32.5907	−	19.5757i	−1.06640	−	0.640536i
$935$	−6.16588	+	35.2075i	−0.201646	+	1.15141i
$936$	−2.35841	+	45.3978i	−0.0770869	+	1.48387i
$937$			25.7211i			0.840273i	0.907461	+	0.420136i	$0.138018\pi$
$937$			25.7211i			0.840273i	−0.907461	+	0.420136i	$0.861982\pi$
$938$	−9.10121	+	60.9611i	−0.297165	+	1.99045i
$939$	0.532306			0.0173711
$940$	1.30924	−	3.01426i	0.0427027	−	0.0983142i
$941$	−22.6193	−	54.6079i	−0.737370	−	1.78017i	−0.616281	−	0.787526i	$-0.711361\pi$
$941$	−22.6193	−	54.6079i	−0.737370	−	1.78017i	−0.121089	−	0.992642i	$-0.538639\pi$
$942$	−0.00177390	−	0.00239653i	−5.77968e−5	−	7.80830e-5i
$943$	3.73421			0.121603
$944$	0.845525	+	4.33575i	0.0275195	+	0.141117i
$945$	1.55032	+	1.94868i	0.0504319	+	0.0633905i
$946$	−4.15205	+	27.8110i	−0.134995	+	0.904212i
$947$	1.24584	+	3.00773i	0.0404845	+	0.0977381i	0.942828	−	0.333279i	$-0.108155\pi$
$947$	1.24584	+	3.00773i	0.0404845	+	0.0977381i	−0.902344	+	0.431017i	$0.858155\pi$
$948$	−0.0604385	+	0.197901i	−0.00196295	+	0.00642752i
$949$	−48.4890	−	20.0848i	−1.57402	−	0.651980i
$950$	0.468149	+	26.3341i	0.0151888	+	0.854391i
$951$			0.859560i			0.0278731i
$952$	−38.0395	−	47.6720i	−1.23287	−	1.54506i
$953$	−9.06064	−	9.06064i	−0.293503	−	0.293503i	0.544960	−	0.838462i	$-0.316545\pi$
$953$	−9.06064	−	9.06064i	−0.293503	−	0.293503i	−0.838462	+	0.544960i	$0.816545\pi$
$954$	−3.70747	−	14.8602i	−0.120034	−	0.481118i
$955$	3.33019	−	29.2507i	0.107762	−	0.946532i
$956$	−2.57871	−	4.84628i	−0.0834014	−	0.156740i
$957$	−0.472146	+	0.195569i	−0.0152623	+	0.00632186i
$958$	−23.8738	−	32.2534i	−0.771329	−	1.04206i
$959$	−27.0235	−	65.2406i	−0.872635	−	2.10673i
$960$	0.625244	−	0.110891i	0.0201797	−	0.00357900i
$961$	19.3496	+	19.3496i	0.624181	+	0.624181i
$962$	9.16247	−	6.78203i	0.295410	−	0.218662i
$963$	6.17099	+	2.55611i	0.198857	+	0.0823694i
$964$	−3.44655	−	35.6800i	−0.111006	−	1.14917i
$965$	12.5637	−	22.6701i	0.404440	−	0.729776i
$966$	−0.727108	+	0.538203i	−0.0233943	+	0.0173164i
$967$	15.3723			0.494339			0.247169	−	0.968972i	$-0.420500\pi$
$967$	15.3723			0.494339			0.247169	+	0.968972i	$0.420500\pi$
$968$	−7.63177	−	8.46816i	−0.245294	−	0.272177i
$969$	0.407914	−	0.361675i	0.0131041	−	0.0116187i
$970$	33.6707	+	9.01348i	1.08110	+	0.289405i
$971$	−4.97061	+	4.97061i	−0.159515	+	0.159515i	−0.782352	−	0.622837i	$-0.785980\pi$
$971$	−4.97061	+	4.97061i	−0.159515	+	0.159515i	0.622837	+	0.782352i	$0.285980\pi$
$972$	−1.47865	−	1.21815i	−0.0474277	−	0.0390722i
$973$	−29.8676	−	29.8676i	−0.957512	−	0.957512i
$974$	−7.81173	−	10.5536i	−0.250304	−	0.338159i
$975$	0.552276	−	0.774541i	0.0176870	−	0.0248052i
$976$	−6.77159	+	33.3875i	−0.216753	+	1.06871i
$977$	−58.1732			−1.86112			−0.930562	−	0.366134i	$-0.880681\pi$
$977$	−58.1732			−1.86112			−0.930562	+	0.366134i	$0.880681\pi$
$978$	0.604218	+	0.362926i	0.0193208	+	0.0116051i
$979$	−46.5851	+	19.2962i	−1.48887	+	0.616709i
$980$	−83.4747	−	36.2572i	−2.66650	−	1.15819i
$981$	−37.9747	−	15.7296i	−1.21244	−	0.502208i
$982$	−44.6882	+	11.1493i	−1.42606	+	0.355787i
$983$	19.6113	−	8.12327i	0.625504	−	0.259092i	−0.0473375	−	0.998879i	$-0.515074\pi$
$983$	19.6113	−	8.12327i	0.625504	−	0.259092i	0.672841	+	0.739787i	$0.265074\pi$
$984$	0.0728452	+	0.0808286i	0.00232222	+	0.00257672i
$985$	12.0241	+	6.66376i	0.383121	+	0.212325i
$986$	21.2854	−	3.97208i	0.677866	−	0.126497i
$987$	−0.0964627	+	0.0964627i	−0.00307044	+	0.00307044i
$988$	35.2479	−	18.7554i	1.12138	−	0.596688i
$989$	−16.3264	−	6.76263i	−0.519151	−	0.215039i
$990$	−18.3896	−	31.8343i	−0.584460	−	1.01176i
$991$	14.2178	+	5.88922i	0.451645	+	0.187077i	0.596898	−	0.802317i	$-0.296400\pi$
$991$	14.2178	+	5.88922i	0.451645	+	0.187077i	−0.145253	+	0.989394i	$0.546400\pi$
$992$	−0.478678	−	10.7753i	−0.0151980	−	0.342116i
$993$	0.258421	−	0.623883i	0.00820074	−	0.0197983i
$994$	−26.6463	−	106.803i	−0.845170	−	3.38759i
$995$	28.7284	+	15.9212i	0.910750	+	0.504736i
$996$	−0.0458198	+	0.0556184i	−0.00145186	+	0.00176234i
$997$	−16.5568	−	6.85806i	−0.524360	−	0.217197i	0.104771	−	0.994496i	$-0.466589\pi$
$997$	−16.5568	−	6.85806i	−0.524360	−	0.217197i	−0.629131	+	0.777299i	$0.716589\pi$
$998$	−2.04689	+	13.7103i	−0.0647932	+	0.433993i
$999$			0.320252i			0.0101323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.bw.a.43.17	✓	416
5.2	odd	4		680.2.bz.a.587.69	yes	416
8.3	odd	2	inner	680.2.bw.a.43.88	yes	416
17.2	even	8		680.2.bz.a.563.69	yes	416
40.27	even	4		680.2.bz.a.587.70	yes	416
85.2	odd	8	inner	680.2.bw.a.427.88	yes	416
136.19	odd	8		680.2.bz.a.563.70	yes	416
680.427	even	8	inner	680.2.bw.a.427.17	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.bw.a.43.17	✓	416	1.1	even	1	trivial
680.2.bw.a.43.88	yes	416	8.3	odd	2	inner
680.2.bw.a.427.17	yes	416	680.427	even	8	inner
680.2.bw.a.427.88	yes	416	85.2	odd	8	inner
680.2.bz.a.563.69	yes	416	17.2	even	8
680.2.bz.a.563.70	yes	416	136.19	odd	8
680.2.bz.a.587.69	yes	416	5.2	odd	4
680.2.bz.a.587.70	yes	416	40.27	even	4

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.bw (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21233 - 0.728189i) q^{2} +(-0.0135844 - 0.0327956i) q^{3} +(0.939481 + 1.76561i) q^{4} +(0.252941 - 2.22172i) q^{5} +(-0.00741267 + 0.0496510i) q^{6} +(2.00134 - 4.83165i) q^{7} +(0.146738 - 2.82462i) q^{8} +(2.12043 - 2.12043i) q^{9} +O(q^{10})\)	\(q+(-1.21233 - 0.728189i) q^{2} +(-0.0135844 - 0.0327956i) q^{3} +(0.939481 + 1.76561i) q^{4} +(0.252941 - 2.22172i) q^{5} +(-0.00741267 + 0.0496510i) q^{6} +(2.00134 - 4.83165i) q^{7} +(0.146738 - 2.82462i) q^{8} +(2.12043 - 2.12043i) q^{9} +(-1.92448 + 2.50926i) q^{10} +(-3.58180 + 1.48363i) q^{11} +(0.0451419 - 0.0547955i) q^{12} +(-3.78984 - 3.78984i) q^{13} +(-5.94463 + 4.40020i) q^{14} +(-0.0762985 + 0.0218853i) q^{15} +(-2.23475 + 3.31751i) q^{16} +(3.70777 + 1.80346i) q^{17} +(-4.11473 + 1.02658i) q^{18} +(2.63383 + 2.63383i) q^{19} +(4.16032 - 1.64066i) q^{20} -0.185644 q^{21} +(5.42267 + 0.809580i) q^{22} +(-1.31860 + 3.18338i) q^{23} +(-0.0946283 + 0.0335583i) q^{24} +(-4.87204 - 1.12393i) q^{25} +(1.83481 + 7.35425i) q^{26} +(-0.196732 - 0.0814891i) q^{27} +(10.4110 - 1.00567i) q^{28} +(-1.42107 + 3.43077i) q^{29} +(0.108435 + 0.0290276i) q^{30} +(0.729663 - 1.76156i) q^{31} +(5.12503 - 2.39459i) q^{32} +(0.0973129 + 0.0973129i) q^{33} +(-3.18177 - 4.88634i) q^{34} +(-10.2283 - 5.66852i) q^{35} +(5.73595 + 1.75175i) q^{36} +(-0.575535 - 1.38946i) q^{37} +(-1.27514 - 5.11099i) q^{38} +(-0.0728074 + 0.175773i) q^{39} +(-6.23838 - 1.04047i) q^{40} +(-0.414729 - 1.00125i) q^{41} +(0.225061 + 0.135184i) q^{42} +5.12864i q^{43} +(-5.98454 - 4.93021i) q^{44} +(-4.17465 - 5.24734i) q^{45} +(3.91668 - 2.89912i) q^{46} +(0.519612 - 0.519612i) q^{47} +(0.139157 + 0.0282237i) q^{48} +(-14.3898 - 14.3898i) q^{49} +(5.08808 + 4.91034i) q^{50} +(0.00877787 - 0.146097i) q^{51} +(3.13090 - 10.2519i) q^{52} +3.61147i q^{53} +(0.179164 + 0.242050i) q^{54} +(2.39022 + 8.33300i) q^{55} +(-13.3539 - 6.36200i) q^{56} +(0.0505990 - 0.122157i) q^{57} +(4.22105 - 3.12441i) q^{58} +(0.780898 - 0.780898i) q^{59} +(-0.110322 - 0.114153i) q^{60} +(7.86852 - 3.25925i) q^{61} +(-2.16734 + 1.60426i) q^{62} +(-6.00148 - 14.4889i) q^{63} +(-7.95694 - 0.828960i) q^{64} +(-9.37856 + 7.46134i) q^{65} +(-0.0471130 - 0.188837i) q^{66} +(5.89290 - 5.89290i) q^{67} +(0.299168 + 8.24078i) q^{68} +0.122313 q^{69} +(8.27234 + 14.3203i) q^{70} +(-5.69563 + 13.7505i) q^{71} +(-5.67825 - 6.30055i) q^{72} +(9.04705 - 3.74741i) q^{73} +(-0.314056 + 2.10359i) q^{74} +(0.0293238 + 0.175049i) q^{75} +(-2.17588 + 7.12474i) q^{76} +20.2752i q^{77} +(0.216262 - 0.160077i) q^{78} +(-2.69275 + 1.11537i) q^{79} +(6.80531 + 5.80412i) q^{80} -8.98866i q^{81} +(-0.226308 + 1.51584i) q^{82} -1.01502 q^{83} +(-0.174409 - 0.327774i) q^{84} +(4.94462 - 7.78143i) q^{85} +(3.73462 - 6.21760i) q^{86} +0.131818 q^{87} +(3.66510 + 10.3349i) q^{88} +13.0061 q^{89} +(1.23999 + 9.40143i) q^{90} +(-25.8959 + 10.7264i) q^{91} +(-6.85941 + 0.662594i) q^{92} -0.0676834 q^{93} +(-1.00832 + 0.251565i) q^{94} +(6.51782 - 5.18541i) q^{95} +(-0.148152 - 0.135549i) q^{96} +(-4.21813 - 10.1835i) q^{97} +(6.96664 + 27.9236i) q^{98} +(-4.44902 + 10.7409i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 8 q^{3}+O(q^{10}) \) 416 * q - 8 * q^3	\( 416 q - 8 q^{3} - 12 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{14} - 16 q^{16} - 8 q^{18} - 32 q^{19} + 12 q^{20} + 4 q^{22} + 24 q^{24} - 16 q^{25} + 8 q^{26} + 16 q^{27} - 20 q^{28} - 16 q^{30} - 16 q^{33} - 16 q^{35} - 72 q^{36} + 16 q^{38} - 24 q^{40} - 16 q^{41} - 24 q^{42} + 32 q^{46} - 100 q^{48} - 48 q^{50} - 16 q^{51} + 24 q^{52} + 16 q^{54} - 8 q^{56} - 32 q^{57} - 72 q^{58} - 40 q^{60} + 48 q^{62} + 48 q^{64} - 8 q^{65} - 8 q^{66} - 16 q^{67} - 116 q^{68} + 80 q^{70} + 24 q^{72} + 32 q^{73} - 16 q^{74} + 16 q^{75} - 40 q^{76} - 76 q^{78} + 16 q^{80} - 36 q^{82} - 16 q^{83} - 48 q^{86} + 72 q^{88} + 56 q^{90} - 16 q^{91} - 104 q^{92} - 24 q^{94} - 8 q^{96} - 40 q^{98}+O(q^{100}) \) 416 * q - 8 * q^3 - 12 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^14 - 16 * q^16 - 8 * q^18 - 32 * q^19 + 12 * q^20 + 4 * q^22 + 24 * q^24 - 16 * q^25 + 8 * q^26 + 16 * q^27 - 20 * q^28 - 16 * q^30 - 16 * q^33 - 16 * q^35 - 72 * q^36 + 16 * q^38 - 24 * q^40 - 16 * q^41 - 24 * q^42 + 32 * q^46 - 100 * q^48 - 48 * q^50 - 16 * q^51 + 24 * q^52 + 16 * q^54 - 8 * q^56 - 32 * q^57 - 72 * q^58 - 40 * q^60 + 48 * q^62 + 48 * q^64 - 8 * q^65 - 8 * q^66 - 16 * q^67 - 116 * q^68 + 80 * q^70 + 24 * q^72 + 32 * q^73 - 16 * q^74 + 16 * q^75 - 40 * q^76 - 76 * q^78 + 16 * q^80 - 36 * q^82 - 16 * q^83 - 48 * q^86 + 72 * q^88 + 56 * q^90 - 16 * q^91 - 104 * q^92 - 24 * q^94 - 8 * q^96 - 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more