LMFDB - Embedded newform 416.2.bd.a.411.10

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			411.10
Character	$\chi$	$=$	416.411
Dual form			416.2.bd.a.83.10

$q$-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} +(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} - 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}+ \cdots - 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

Character values

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

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

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	0.0394612	−	0.999221i	$-0.487436\pi$
$3$	1.34047	−	0.555241i	0.773920	−	0.320568i	0.734459	+	0.678653i	$0.237436\pi$
$4$	1.09427	+	1.67409i	0.547137	+	0.837043i
$5$	1.54705	+	3.73491i	0.691863	+	1.67030i	0.740994	+	0.671512i	$0.234355\pi$
$5$	1.54705	+	3.73491i	0.691863	+	1.67030i	−0.0491308	+	0.998792i	$0.515645\pi$
$6$	−2.04098	−	0.211441i	−0.833226	−	0.0863202i
$7$			0.167444i			0.0632878i	0.999499	+	0.0316439i	$0.0100742\pi$
$7$			0.167444i			0.0632878i	−0.999499	+	0.0316439i	$0.989926\pi$
$8$	−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	−0.365203	−	0.930928i	$-0.619000\pi$
$11$	0.115501	−	0.0478422i	0.0348250	−	0.0144250i	0.400028	+	0.916503i	$0.369000\pi$
$12$	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	−0.748559	−	0.663068i	$-0.769254\pi$
$19$	1.08803	−	2.62674i	0.249612	−	0.602616i	0.998171	+	0.0604517i	$0.0192541\pi$
$20$	−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	−0.787598	−	0.616189i	$-0.788676\pi$
$23$	−0.822050	+	0.822050i	−0.171409	+	0.171409i	0.616189	+	0.787598i	$0.288676\pi$
$24$	−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	0.886599	−	0.462539i	$-0.153061\pi$
$29$	−0.362881	−	0.876073i	−0.0673854	−	0.162683i	−0.953984	+	0.299856i	$0.903061\pi$
$30$	−2.36779	−	7.94999i	−0.432297	−	1.45146i
$31$	1.60097	−	1.60097i	0.287542	−	0.287542i	−0.548565	−	0.836108i	$-0.684826\pi$
$31$	1.60097	−	1.60097i	0.287542	−	0.287542i	0.836108	+	0.548565i	$0.184826\pi$
$32$	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	0.638772	−	0.769396i	$-0.279443\pi$
$37$	9.94226	−	4.11822i	1.63450	−	0.677031i	0.995725	+	0.0923646i	$0.0294425\pi$
$38$	−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	−0.512739	−	0.858545i	$-0.671369\pi$
$43$	2.99613	−	7.23329i	0.456905	−	1.10307i	0.969644	−	0.244522i	$-0.0786309\pi$
$44$	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	−0.224543	−	0.974464i	$-0.572089\pi$
$47$	5.14120	−	5.14120i	0.749921	−	0.749921i	0.974464	+	0.224543i	$0.0720889\pi$
$48$	−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	−0.844903	−	0.534919i	$-0.820342\pi$
$53$	0.952080	−	2.29853i	0.130778	−	0.315727i	0.975682	+	0.219192i	$0.0703422\pi$
$54$	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	0.844353	+	0.535787i	$0.179985\pi$
$59$	4.80965	+	11.6115i	0.626164	+	1.51169i	−0.218190	+	0.975906i	$0.570015\pi$
$60$	−2.40481	+	11.4819i	−0.310459	+	1.48231i
$61$	−1.39878	−	3.37697i	−0.179096	−	0.432376i	0.808681	−	0.588247i	$-0.200182\pi$
$61$	−1.39878	−	3.37697i	−0.179096	−	0.432376i	−0.987777	+	0.155871i	$0.950182\pi$
$62$	−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	0.680915	−	0.732362i	$-0.261582\pi$
$67$	5.27576	+	2.18529i	0.644537	+	0.266976i	−0.0363783	+	0.999338i	$0.511582\pi$
$68$	−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	$-0.824900\pi$
$73$		−	8.93301i		−	1.04553i	0.852477	−	0.522765i	$-0.175100\pi$
$74$	−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	−0.500560	−	0.865702i	$-0.666873\pi$
$83$	4.24121	−	10.2392i	0.465533	−	1.12390i	0.966093	−	0.258194i	$-0.0831273\pi$
$84$	−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	0.231719	−	0.972783i	$-0.425565\pi$
$97$	−7.29863	−	7.29863i	−0.741063	−	0.741063i	−0.972783	+	0.231719i	$0.925565\pi$
$98$	−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	0.553675	+	0.832733i	$0.313225\pi$
$101$	−4.28791	+	10.3519i	−0.426663	+	1.03006i	−0.980338	+	0.197323i	$0.936775\pi$
$102$	9.70327	+	1.00524i	0.960766	+	0.0995331i
$103$	5.94537	+	5.94537i	0.585815	+	0.585815i	0.936495	−	0.350680i	$-0.114050\pi$
$103$	5.94537	+	5.94537i	0.585815	+	0.585815i	−0.350680	+	0.936495i	$0.614050\pi$
$104$	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	−0.689182	−	0.724588i	$-0.742030\pi$
$107$	−17.4698	−	7.23622i	−1.68887	−	0.699552i	−0.999687	+	0.0250362i	$0.992030\pi$
$108$	−11.1067	+	2.09277i	−1.06875	+	0.201377i
$109$	−2.26257	−	0.937189i	−0.216715	−	0.0897664i	0.271685	−	0.962386i	$-0.412419\pi$
$109$	−2.26257	−	0.937189i	−0.216715	−	0.0897664i	−0.488400	+	0.872620i	$0.662419\pi$
$110$	−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	$-0.987273\pi$
$113$		−	0.849823i		−	0.0799447i	0.999201	−	0.0399723i	$-0.0127270\pi$
$114$	−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	−0.969584	−	0.244759i	$-0.921291\pi$
$131$	−16.9635	+	7.02653i	−1.48211	+	0.613911i	−0.512528	+	0.858670i	$0.671291\pi$
$132$	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	$0.163609\pi$
$137$			11.5094i			0.983314i	−0.870789	+	0.491657i	$0.836391\pi$
$138$	1.85160	−	1.50397i	0.157619	−	0.128027i
$139$	0.979057	+	0.405539i	0.0830425	+	0.0343973i	0.423818	−	0.905747i	$-0.360690\pi$
$139$	0.979057	+	0.405539i	0.0830425	+	0.0343973i	−0.340776	+	0.940145i	$0.610690\pi$
$140$	−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	−0.458162	−	0.888869i	$-0.651492\pi$
$149$	−1.87501	+	0.776656i	−0.153607	+	0.0636262i	0.304555	+	0.952495i	$0.401492\pi$
$150$	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	0.869916	−	0.493201i	$-0.164173\pi$
$157$	−1.17723	−	2.84209i	−0.0939532	−	0.226823i	−0.963869	+	0.266378i	$0.914173\pi$
$158$	−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	−0.665843	−	0.746092i	$-0.731928\pi$
$163$	4.24566	−	10.2499i	0.332546	−	0.802837i	0.998389	−	0.0567448i	$-0.0180721\pi$
$164$	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	$-0.979865\pi$
$167$		−	1.63379i		−	0.126426i	0.998000	−	0.0632132i	$-0.0201348\pi$
$168$	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	0.749544	−	0.661955i	$-0.230273\pi$
$173$	−3.26898	−	7.89203i	−0.248536	−	0.600020i	−0.998080	+	0.0619350i	$0.980273\pi$
$174$	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	−0.481078	−	0.876678i	$-0.659755\pi$
$179$	−2.69384	+	1.11583i	−0.201347	+	0.0834007i	0.279731	+	0.960078i	$0.409755\pi$
$180$	−1.33969	−	7.10999i	−0.0998548	−	0.529948i
$181$	−14.1781	−	5.87274i	−1.05385	−	0.436518i	−0.212583	−	0.977143i	$-0.568188\pi$
$181$	−14.1781	−	5.87274i	−1.05385	−	0.436518i	−0.841263	+	0.540625i	$0.818188\pi$
$182$	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	$-0.845637\pi$
$191$		−	12.8849i		−	0.932318i	0.884701	−	0.466159i	$-0.154363\pi$
$192$	−9.84223	+	6.15306i	−0.710302	+	0.444059i
$193$	−10.8423	+	10.8423i	−0.780448	+	0.780448i	−0.979906	−	0.199458i	$-0.936082\pi$
$193$	−10.8423	+	10.8423i	−0.780448	+	0.780448i	0.199458	+	0.979906i	$0.436082\pi$
$194$	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	0.891815	−	0.452399i	$-0.149432\pi$
$197$	−0.823725	−	1.98865i	−0.0586880	−	0.141685i	−0.950503	+	0.310714i	$0.899432\pi$
$198$	0.122804	−	0.0997485i	0.00872734	−	0.00708882i
$199$	−3.15196	−	3.15196i	−0.223437	−	0.223437i	0.586507	−	0.809944i	$-0.300503\pi$
$199$	−3.15196	−	3.15196i	−0.223437	−	0.223437i	−0.809944	+	0.586507i	$0.800503\pi$
$200$	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	−0.994712	−	0.102699i	$-0.967252\pi$
$211$	−5.28688	−	12.7637i	−0.363964	−	0.878687i	0.630748	−	0.775987i	$-0.282748\pi$
$212$	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	−0.977793	−	0.209571i	$-0.932793\pi$
$223$	−11.4720	+	11.4720i	−0.768222	+	0.768222i	0.209571	+	0.977793i	$0.432793\pi$
$224$	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	0.771731	−	0.635949i	$-0.219391\pi$
$227$	13.0739	+	5.41538i	0.867744	+	0.359431i	0.0960125	+	0.995380i	$0.469391\pi$
$228$	6.90592	−	4.51408i	0.457356	−	0.298952i
$229$	9.83077	−	4.07204i	0.649635	−	0.269088i	−0.0334344	−	0.999441i	$-0.510644\pi$
$229$	9.83077	−	4.07204i	0.649635	−	0.269088i	0.683070	+	0.730353i	$0.260644\pi$
$230$	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	0.918648	−	0.395077i	$-0.129282\pi$
$233$	7.99196	+	7.99196i	0.523571	+	0.523571i	−0.395077	+	0.918648i	$0.629282\pi$
$234$	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	0.690151	−	0.723666i	$-0.257544\pi$
$239$	−0.518131	−	0.518131i	−0.0335151	−	0.0335151i	−0.723666	+	0.690151i	$0.757544\pi$
$240$	−21.8532	+	8.53850i	−1.41062	+	0.551158i
$241$	−10.3809	−	10.3809i	−0.668691	−	0.668691i	0.288722	−	0.957413i	$-0.406770\pi$
$241$	−10.3809	−	10.3809i	−0.668691	−	0.668691i	−0.957413	+	0.288722i	$0.906770\pi$
$242$	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	−0.681053	−	0.732234i	$-0.738478\pi$
$251$	−26.6225	−	11.0274i	−1.68040	−	0.696044i	−0.999345	+	0.0361906i	$0.988478\pi$
$252$	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	$-0.985198\pi$
$257$		−	1.49040i		−	0.0929688i	0.998919	−	0.0464844i	$-0.0148018\pi$
$258$	−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	0.332146	−	0.943228i	$-0.392227\pi$
$263$	20.6831	−	20.6831i	1.27537	−	1.27537i	0.943228	−	0.332146i	$-0.107773\pi$
$264$	−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	−0.184395	−	0.982852i	$-0.559032\pi$
$269$	6.23575	−	2.58293i	0.380200	−	0.157484i	0.564595	+	0.825368i	$0.309032\pi$
$270$	28.4159	+	15.3738i	1.72934	+	0.935620i
$271$	−13.7184	+	13.7184i	−0.833333	+	0.833333i	−0.987971	−	0.154638i	$-0.950579\pi$
$271$	−13.7184	+	13.7184i	−0.833333	+	0.833333i	0.154638	+	0.987971i	$0.450579\pi$
$272$	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	0.965221	−	0.261435i	$-0.0841957\pi$
$277$	24.3471	+	10.0849i	1.46287	+	0.605942i	0.497652	+	0.867377i	$0.334196\pi$
$278$	−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	−0.163235	−	0.986587i	$-0.552193\pi$
$283$	−16.4236	−	6.80289i	−0.976283	−	0.404390i	−0.813047	+	0.582198i	$0.802193\pi$
$284$	−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	−0.533140	−	0.846027i	$-0.678988\pi$
$293$	−5.33878	+	2.21139i	−0.311895	+	0.129191i	0.221245	+	0.975218i	$0.428988\pi$
$294$	−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	−0.344048	−	0.938952i	$-0.611798\pi$
$307$	−21.9239	−	9.08120i	−1.25127	−	0.518291i	−0.907218	+	0.420661i	$0.861798\pi$
$308$	−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	−0.996259	−	0.0864119i	$-0.972460\pi$
$311$	−16.0453	+	16.0453i	−0.909848	+	0.909848i	0.0864119	+	0.996259i	$0.472460\pi$
$312$	11.3111	−	9.53917i	0.640362	−	0.540049i
$313$	3.40491	+	3.40491i	0.192457	+	0.192457i	0.796757	−	0.604300i	$-0.206547\pi$
$313$	3.40491	+	3.40491i	0.192457	+	0.192457i	−0.604300	+	0.796757i	$0.706547\pi$
$314$	−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	−0.340753	−	0.940153i	$-0.610682\pi$
$317$	10.0593	−	24.2852i	0.564984	−	1.36399i	0.905737	−	0.423840i	$-0.139318\pi$
$318$	−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	0.713857	−	0.700292i	$-0.246947\pi$
$331$	−5.20508	−	12.5662i	−0.286097	−	0.690700i	−0.999954	+	0.00959195i	$0.996947\pi$
$332$	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	−0.284718	−	0.958611i	$-0.591900\pi$
$347$	11.0734	−	26.7334i	0.594449	−	1.43513i	0.879167	−	0.476515i	$-0.158100\pi$
$348$	0.564079	−	2.69323i	0.0302378	−	0.144373i
$349$	13.3561	+	5.53227i	0.714934	+	0.296135i	0.710345	−	0.703854i	$-0.248539\pi$
$349$	13.3561	+	5.53227i	0.714934	+	0.296135i	0.00458953	+	0.999989i	$0.498539\pi$
$350$	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	0.184275	−	0.982875i	$-0.441006\pi$
$353$	−15.0043	−	15.0043i	−0.798600	−	0.798600i	−0.982875	+	0.184275i	$0.941006\pi$
$354$	−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	$-0.942694\pi$
$359$		−	6.78539i		−	0.358119i	0.983838	−	0.179060i	$-0.0573055\pi$
$360$	−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	0.199004	+	0.979999i	$0.436229\pi$
$373$	−12.2576	+	29.5926i	−0.634677	+	1.53225i	−0.833681	+	0.552246i	$0.813771\pi$
$374$	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	−0.694787	−	0.719216i	$-0.744501\pi$
$379$	−13.1898	+	5.46338i	−0.677513	+	0.280635i	0.0172737	+	0.999851i	$0.494501\pi$
$380$	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	−0.778876	−	0.627178i	$-0.784210\pi$
$383$	−2.96879	+	2.96879i	−0.151698	+	0.151698i	0.627178	+	0.778876i	$0.284210\pi$
$384$	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	−0.0595006	+	0.998228i	$0.518951\pi$
$389$	−14.2653	+	34.4396i	−0.723281	+	1.74616i	−0.663781	+	0.747927i	$0.731049\pi$
$390$	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	−0.943550	−	0.331231i	$-0.892536\pi$
$397$	−0.839703	+	2.02722i	−0.0421435	+	0.101743i	0.901406	+	0.432975i	$0.142536\pi$
$398$	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	0.740064	−	0.672537i	$-0.234795\pi$
$401$	1.35223	+	1.35223i	0.0675272	+	0.0675272i	−0.672537	+	0.740064i	$0.734795\pi$
$402$	−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	$0.194804\pi$
$409$			23.2371i			1.14900i	−0.818504	+	0.574501i	$0.805196\pi$
$410$	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	−0.240535	−	0.970641i	$-0.577323\pi$
$419$	5.64401	−	2.33783i	0.275728	−	0.114210i	0.516263	+	0.856430i	$0.327323\pi$
$420$	−1.92257	−	0.402670i	−0.0938120	−	0.0196483i
$421$	6.61577	+	15.9719i	0.322433	+	0.778422i	0.999112	+	0.0421436i	$0.0134187\pi$
$421$	6.61577	+	15.9719i	0.322433	+	0.778422i	−0.676679	+	0.736279i	$0.736581\pi$
$422$	−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	0.583472	−	0.812133i	$-0.301694\pi$
$431$	−4.74711	−	4.74711i	−0.228660	−	0.228660i	−0.812133	+	0.583472i	$0.801694\pi$
$432$	−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	−0.00992460	+	0.999951i	$0.503159\pi$
$439$	−21.1592	+	21.1592i	−1.00988	+	1.00988i	−0.999951	+	0.00992460i	$0.996841\pi$
$440$	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	−0.651700	−	0.758477i	$-0.725944\pi$
$443$	7.27080	−	17.5533i	0.345446	−	0.833980i	0.997146	−	0.0755033i	$-0.0240563\pi$
$444$	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	−0.911200	−	0.411964i	$-0.864843\pi$
$449$	−10.5786	+	10.5786i	−0.499236	+	0.499236i	0.411964	+	0.911200i	$0.364843\pi$
$450$	−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	0.790401	−	0.612590i	$-0.209872\pi$
$461$	19.6702	+	8.14766i	0.916132	+	0.379474i	0.125731	+	0.992064i	$0.459872\pi$
$462$	−0.0122608	−	0.0411663i	−0.000570423	−	0.00191523i
$463$	18.4109	−	18.4109i	0.855627	−	0.855627i	−0.135193	−	0.990819i	$-0.543165\pi$
$463$	18.4109	−	18.4109i	0.855627	−	0.855627i	0.990819	+	0.135193i	$0.0431653\pi$
$464$	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	0.579681	−	0.814844i	$-0.303177\pi$
$467$	33.8363	−	14.0155i	1.56576	−	0.648559i	0.986078	+	0.166285i	$0.0531772\pi$
$468$	−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	0.478447	−	0.878117i	$-0.341200\pi$
$479$	−8.74720	−	8.74720i	−0.399670	−	0.399670i	−0.878117	+	0.478447i	$0.841200\pi$
$480$	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	0.611085	+	0.791565i	$0.290734\pi$
$491$	−8.43661	+	20.3678i	−0.380739	+	0.919184i	−0.991823	+	0.127619i	$0.959266\pi$
$492$	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	−0.835799	−	0.549035i	$-0.814995\pi$
$499$	3.20391	−	7.73492i	0.143427	−	0.346263i	0.979226	+	0.202773i	$0.0649952\pi$
$500$	−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	0.790830	−	0.612036i	$-0.209649\pi$
$503$	4.00991	+	4.00991i	0.178793	+	0.178793i	−0.612036	+	0.790830i	$0.709649\pi$
$504$	−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	0.520026	+	0.854151i	$0.325922\pi$
$509$	−10.1900	+	24.6008i	−0.451664	+	1.09041i	−0.971689	+	0.236262i	$0.924078\pi$
$510$	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	0.0489379	−	0.998802i	$-0.484416\pi$
$521$	23.9151	−	23.9151i	1.04774	−	1.04774i	0.998802	−	0.0489379i	$-0.0155836\pi$
$522$	−0.756588	−	0.931467i	−0.0331150	−	0.0407692i
$523$	−15.2407	−	6.31292i	−0.666431	−	0.276045i	0.0237112	−	0.999719i	$-0.492452\pi$
$523$	−15.2407	−	6.31292i	−0.666431	−	0.276045i	−0.690142	+	0.723674i	$0.742452\pi$
$524$	−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	0.0286128	−	0.999591i	$-0.490891\pi$
$541$	−15.3040	−	6.33914i	−0.657972	−	0.272541i	−0.686585	+	0.727050i	$0.740891\pi$
$542$	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	−0.0443805	−	0.999015i	$-0.514131\pi$
$547$	14.7496	−	6.10949i	0.630648	−	0.261223i	0.675028	+	0.737792i	$0.264131\pi$
$548$	−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	0.237198	+	0.971461i	$0.423771\pi$
$557$	−14.5724	+	35.1809i	−0.617453	+	1.49066i	−0.854651	+	0.519202i	$0.826229\pi$
$558$	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	−0.759166	−	0.650897i	$-0.774393\pi$
$563$	−19.8298	+	8.21375i	−0.835725	+	0.346168i	−0.0765582	+	0.997065i	$0.524393\pi$
$564$	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	−0.176158	−	0.984362i	$-0.556367\pi$
$569$	19.2787	−	19.2787i	0.808204	−	0.808204i	0.984362	+	0.176158i	$0.0563669\pi$
$570$	−23.4588	−	2.43028i	−0.982582	−	0.101793i
$571$	−9.20125	−	3.81128i	−0.385060	−	0.159497i	0.181752	−	0.983344i	$-0.441823\pi$
$571$	−9.20125	−	3.81128i	−0.385060	−	0.159497i	−0.566812	+	0.823847i	$0.691823\pi$
$572$	−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	0.355912	−	0.934519i	$-0.384170\pi$
$577$	−13.8986	−	13.8986i	−0.578607	−	0.578607i	−0.934519	+	0.355912i	$0.884170\pi$
$578$	−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	0.750601	−	0.660756i	$-0.229764\pi$
$587$	−5.99353	−	14.4697i	−0.247379	−	0.597226i	−0.997980	+	0.0635297i	$0.979764\pi$
$588$	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	0.823178	+	0.567783i	$0.192199\pi$
$593$	33.8721	+	33.8721i	1.39096	+	1.39096i	0.567783	+	0.823178i	$0.307801\pi$
$594$	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	0.999959	+	0.00906172i	$0.00288448\pi$
$599$	24.6953	+	24.6953i	1.00902	+	1.00902i	0.00906172	+	0.999959i	$0.497116\pi$
$600$	44.3349	+	14.1864i	1.80996	+	0.579159i
$601$	−20.4462	−	20.4462i	−0.834017	−	0.834017i	0.154047	−	0.988064i	$-0.450769\pi$
$601$	−20.4462	−	20.4462i	−0.834017	−	0.834017i	−0.988064	+	0.154047i	$0.950769\pi$
$602$	−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	$0.185843\pi$
$607$			27.1619i			1.10247i	−0.834351	+	0.551234i	$0.814157\pi$
$608$	−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	0.995876	+	0.0907270i	$0.0289191\pi$
$613$	8.81016	+	21.2696i	0.355839	+	0.859071i	−0.640037	+	0.768344i	$0.721081\pi$
$614$	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	0.427145	−	0.904183i	$-0.359519\pi$
$619$	34.0488	−	14.1035i	1.36854	−	0.566866i	0.941391	+	0.337317i	$0.109519\pi$
$620$	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	$-0.797208\pi$
$641$		−	30.1213i		−	1.18972i	0.803830	−	0.594859i	$-0.202792\pi$
$642$	34.1254	+	18.4628i	1.34682	+	0.728669i
$643$	28.2104	+	11.6851i	1.11251	+	0.460817i	0.861802	−	0.507245i	$-0.169336\pi$
$643$	28.2104	+	11.6851i	1.11251	+	0.460817i	0.250709	+	0.968062i	$0.419336\pi$
$644$	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	0.377307	−	0.926088i	$-0.376850\pi$
$647$	−13.9589	−	13.9589i	−0.548781	−	0.548781i	−0.926088	+	0.377307i	$0.876850\pi$
$648$	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	−0.442608	−	0.896715i	$-0.645947\pi$
$653$	−3.10496	+	1.28612i	−0.121507	+	0.0503297i	0.321102	+	0.947045i	$0.395947\pi$
$654$	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	−0.998355	−	0.0573404i	$-0.981738\pi$
$659$	−8.54734	−	20.6351i	−0.332957	−	0.803830i	0.665398	−	0.746489i	$-0.268262\pi$
$660$	0.271562	+	1.44123i	0.0105705	+	0.0560998i
$661$	−1.83372	−	4.42699i	−0.0713234	−	0.172190i	0.884198	−	0.467113i	$-0.154706\pi$
$661$	−1.83372	−	4.42699i	−0.0713234	−	0.172190i	−0.955521	+	0.294923i	$0.904706\pi$
$662$	−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	$-0.916330\pi$
$673$		−	13.4817i		−	0.519680i	0.965652	−	0.259840i	$-0.0836699\pi$
$674$	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	0.324162	−	0.946002i	$-0.394918\pi$
$677$	−3.00640	−	1.24529i	−0.115545	−	0.0478605i	−0.439707	+	0.898141i	$0.644918\pi$
$678$	−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	−0.988859	−	0.148858i	$-0.952440\pi$
$683$	−41.3661	+	17.1344i	−1.58283	+	0.655629i	−0.593970	+	0.804487i	$0.702440\pi$
$684$	−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	−0.923862	−	0.382726i	$-0.874985\pi$
$691$	0.000934320	−	0.00225565i	3.55432e−5	−	8.58089e-5i	0.923897	+	0.382641i	$0.124985\pi$
$692$	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	−0.160739	−	0.986997i	$-0.551388\pi$
$701$	11.2131	−	4.64462i	0.423513	−	0.175425i	0.584252	+	0.811572i	$0.301388\pi$
$702$	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	−0.876443	−	0.481505i	$-0.840090\pi$
$709$	−30.7731	+	12.7466i	−1.15571	+	0.478709i	−0.279263	+	0.960215i	$0.590090\pi$
$710$	−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	$0.263982\pi$
$719$			39.5495i			1.47495i	−0.675376	+	0.737474i	$0.736018\pi$
$720$	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	−0.749777	−	0.661690i	$-0.769839\pi$
$727$	−2.37508	+	2.37508i	−0.0880869	+	0.0880869i	0.661690	+	0.749777i	$0.269839\pi$
$728$	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	−0.796084	−	0.605186i	$-0.793099\pi$
$733$	5.27301	−	12.7302i	0.194763	−	0.470200i	0.990848	+	0.134986i	$0.0430989\pi$
$734$	−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	−0.394302	−	0.918981i	$-0.629014\pi$
$739$	14.5255	−	35.0677i	0.534329	−	1.28998i	0.928631	−	0.371004i	$-0.120986\pi$
$740$	−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	$-0.981160\pi$
$751$		−	3.24205i		−	0.118304i	0.998249	−	0.0591520i	$-0.0188396\pi$
$752$	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	−0.651918	−	0.758289i	$-0.726035\pi$
$757$	9.49906	−	22.9328i	0.345249	−	0.833505i	0.997167	−	0.0752157i	$-0.0239645\pi$
$758$	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	+	5.25446i	0.189481	+	0.189481i	0.795472	−	0.605991i	$-0.207223\pi$
$769$	5.25446	+	5.25446i	0.189481	+	0.189481i	−0.605991	+	0.795472i	$0.707223\pi$
$770$	0.114701	−	0.0341619i	0.00413352	−	0.00123111i
$771$	−0.827533	−	1.99784i	−0.0298029	−	0.0719505i
$772$	−30.0155	−	6.28654i	−1.08028	−	0.226257i
$773$	−4.27408	−	10.3185i	−0.153728	−	0.371132i	0.828188	−	0.560451i	$-0.189372\pi$
$773$	−4.27408	−	10.3185i	−0.153728	−	0.371132i	−0.981916	+	0.189319i	$0.939372\pi$
$774$	1.02098	−	9.85524i	0.0366983	−	0.354239i
$775$			25.6817i			0.922514i
$776$	−18.8609	+	22.2842i	−0.677066	+	0.799957i
$777$	1.84869	+	1.84869i	0.0663216	+	0.0663216i
$778$	40.9199	−	33.2374i	1.46705	−	1.19162i
$779$	1.71883	−	4.14963i	0.0615835	−	0.148676i
$780$	−42.2897	+	0.780416i	−1.51421	+	0.0279434i
$781$	−1.43719	+	0.595302i	−0.0514266	+	0.0213016i
$782$	−7.49121	+	2.23115i	−0.267885	+	0.0797857i
$783$	5.35867			0.191503
$784$	−11.1909	+	25.5440i	−0.399676	+	0.912285i
$785$	8.79371	−	8.79371i	0.313861	−	0.313861i
$786$	36.1079	−	10.7542i	1.28793	−	0.383590i
$787$	8.07902	+	3.34644i	0.287986	+	0.119288i	0.522000	−	0.852946i	$-0.325186\pi$
$787$	8.07902	+	3.34644i	0.287986	+	0.119288i	−0.234014	+	0.972233i	$0.575186\pi$
$788$	2.42779	−	3.55511i	0.0864864	−	0.126646i
$789$	16.2410	−	39.2091i	0.578193	−	1.39588i
$790$	8.47363	−	81.7936i	0.301478	−	2.91009i
$791$	0.142298			0.00505952
$792$	0.301369	+	0.0964333i	0.0107087	+	0.00342661i
$793$	10.7444	−	7.63181i	0.381544	−	0.271014i
$794$	2.40868	−	1.95646i	0.0854808	−	0.0694322i
$795$	13.4821	−	5.58445i	0.478159	−	0.198060i
$796$	1.82755	−	8.72576i	0.0647758	−	0.309276i
$797$	48.3650	−	20.0334i	1.71318	−	0.709621i	0.713214	−	0.700946i	$-0.247239\pi$
$797$	48.3650	−	20.0334i	1.71318	−	0.709621i	0.999962	−	0.00867511i	$-0.00276141\pi$
$798$	−0.859166	−	0.464832i	−0.0304141	−	0.0164549i
$799$	−24.4424	+	24.4424i	−0.864710	+	0.864710i
$800$	−7.90098	+	63.6771i	−0.279342	+	2.25133i
$801$	−4.01148	+	4.01148i	−0.141739	+	0.141739i
$802$	−0.771973	−	2.59194i	−0.0272593	−	0.0915247i
$803$	−0.427375	−	1.03178i	−0.0150818	−	0.0364106i
$804$	9.06645	+	13.8704i	0.319749	+	0.489172i
$805$	0.301153	−	0.727047i	0.0106142	−	0.0256250i
$806$	−5.67996	−	10.0508i	−0.200068	−	0.354025i
$807$	6.92468	−	6.92468i	0.243760	−	0.243760i
$808$	30.1845	+	9.65854i	1.06189	+	0.339786i
$809$	−22.9976	+	22.9976i	−0.808554	+	0.808554i	−0.984415	−	0.175861i	$-0.943729\pi$
$809$	−22.9976	+	22.9976i	−0.808554	+	0.808554i	0.175861	+	0.984415i	$0.443729\pi$
$810$	31.3606	+	3.24888i	1.10190	+	0.114154i
$811$	−17.7792	−	42.9227i	−0.624311	−	1.50722i	−0.846595	−	0.532238i	$-0.821351\pi$
$811$	−17.7792	−	42.9227i	−0.624311	−	1.50722i	0.222284	−	0.974982i	$-0.428649\pi$
$812$	0.262243	+	0.179086i	0.00920293	+	0.00628469i
$813$	−10.7721	+	26.0061i	−0.377793	+	0.912074i
$814$	−1.82348	+	0.543097i	−0.0639130	+	0.0190356i
$815$	44.8509			1.57106
$816$	0.557825	−	27.5862i	0.0195278	−	0.965711i
$817$	−15.7401	−	15.7401i	−0.550677	−	0.550677i
$818$	15.6375	−	28.9033i	0.546751	−	1.01058i
$819$	0.287193	−	0.457585i	0.0100353	−	0.0159893i
$820$	−7.20319	+	10.5479i	−0.251546	+	0.368350i
$821$	29.6693	−	12.2894i	1.03546	−	0.428903i	0.200782	−	0.979636i	$-0.435652\pi$
$821$	29.6693	−	12.2894i	1.03546	−	0.428903i	0.834682	+	0.550732i	$0.185652\pi$
$822$	2.43355	−	23.4904i	0.0848799	−	0.819323i
$823$	−11.8152	+	11.8152i	−0.411852	+	0.411852i	−0.882383	−	0.470531i	$-0.844062\pi$
$823$	−11.8152	+	11.8152i	−0.411852	+	0.411852i	0.470531	+	0.882383i	$0.344062\pi$
$824$	15.3638	−	18.1525i	0.535225	−	0.632371i
$825$			2.05750i			0.0716329i
$826$	2.96033	+	0.306683i	0.103003	+	0.0106709i
$827$	−11.4642	−	27.6770i	−0.398649	−	0.962424i	−0.987987	−	0.154537i	$-0.950611\pi$
$827$	−11.4642	−	27.6770i	−0.398649	−	0.962424i	0.589338	−	0.807887i	$-0.299389\pi$
$828$	1.74157	−	1.13838i	0.0605237	−	0.0395616i
$829$	43.1698	−	17.8815i	1.49935	−	0.621050i	0.526021	−	0.850472i	$-0.323683\pi$
$829$	43.1698	−	17.8815i	1.49935	−	0.621050i	0.973327	+	0.229421i	$0.0736834\pi$
$830$	−55.7287	−	30.1508i	−1.93437	−	1.04655i
$831$	38.2360			1.32639
$832$	−10.9912	−	26.6682i	−0.381051	−	0.924554i
$833$	−33.1463			−1.14845
$834$	−1.91249	−	1.03471i	−0.0662240	−	0.0358290i
$835$	6.10207	−	2.52756i	0.211171	−	0.0874698i
$836$	0.595048	−	0.388955i	0.0205802	−	0.0134523i
$837$	4.89632	+	11.8208i	0.169241	+	0.408585i
$838$	−8.59349	−	0.890265i	−0.296857	−	0.0307537i
$839$		−	24.5761i		−	0.848461i	−0.905554	−	0.424230i	$-0.860545\pi$
$839$		−	24.5761i		−	0.848461i	0.905554	−	0.424230i	$-0.139455\pi$
$840$	2.12040	+	1.79466i	0.0731606	+	0.0619215i
$841$	19.8703	−	19.8703i	0.685182	−	0.685182i
$842$	2.51934	−	24.3186i	0.0868223	−	0.838073i
$843$	42.7959	−	17.7266i	1.47397	−	0.610538i
$844$	15.5822	−	22.8176i	0.536361	−	0.785415i
$845$	−39.2225	−	34.9793i	−1.34930	−	1.20333i
$846$	4.37837	−	8.09270i	0.150532	−	0.278233i
$847$	−1.30056	−	1.30056i	−0.0446876	−	0.0446876i
$848$	6.89316	+	7.17769i	0.236712	+	0.246483i
$849$	−25.7926			−0.885200
$850$	−73.0912	+	21.7692i	−2.50701	+	0.746676i
$851$	−4.78765	+	11.5584i	−0.164119	+	0.396217i
$852$	−29.8180	−	20.3627i	−1.02155	−	0.697615i
$853$	−5.94133	−	14.3436i	−0.203427	−	0.491116i	0.788935	−	0.614477i	$-0.210633\pi$
$853$	−5.94133	−	14.3436i	−0.203427	−	0.491116i	−0.992362	+	0.123360i	$0.960633\pi$
$854$	−0.860948	−	0.0891922i	−0.0294610	−	0.00305209i
$855$	−7.27281	+	7.27281i	−0.248725	+	0.248725i
$856$	−16.2996	+	50.9389i	−0.557110	+	1.74106i
$857$	−11.7757	+	11.7757i	−0.402251	+	0.402251i	−0.879026	−	0.476774i	$-0.841806\pi$
$857$	−11.7757	+	11.7757i	−0.402251	+	0.402251i	0.476774	+	0.879026i	$0.341806\pi$
$858$	−0.455052	−	0.805226i	−0.0155352	−	0.0274900i
$859$	−7.95322	+	19.2008i	−0.271360	+	0.655122i	−0.999542	−	0.0302622i	$-0.990366\pi$
$859$	−7.95322	+	19.2008i	−0.271360	+	0.655122i	0.728182	+	0.685384i	$0.240366\pi$
$860$	34.6347	+	52.9863i	1.18103	+	1.80682i
$861$	0.146873	+	0.354582i	0.00500541	+	0.0120841i
$862$	2.71007	+	9.09922i	0.0923054	+	0.309921i
$863$	40.6507	−	40.6507i	1.38377	−	1.38377i	0.545949	−	0.837818i	$-0.316169\pi$
$863$	40.6507	−	40.6507i	1.38377	−	1.38377i	0.837818	−	0.545949i	$-0.183831\pi$
$864$	8.50364	+	30.8156i	0.289300	+	1.04837i
$865$	24.4187	−	24.4187i	0.830262	−	0.830262i
$866$	43.9744	+	23.7914i	1.49431	+	0.808464i
$867$	7.51014	−	3.11080i	0.255058	−	0.105648i
$868$	−0.155432	+	0.742120i	−0.00527570	+	0.0251892i
$869$	1.66129	−	0.688128i	0.0563553	−	0.0233431i
$870$	−6.10555	+	4.95926i	−0.206997	+	0.168135i
$871$	−3.43846	+	20.3002i	−0.116508	+	0.687845i
$872$	−2.11102	+	6.59728i	−0.0714882	+	0.223412i
$873$	9.23647			0.312607
$874$	0.481684	−	4.64956i	0.0162932	−	0.157274i
$875$	1.64311	−	3.96681i	0.0555471	−	0.134103i
$876$	14.6187	−	21.4067i	0.493919	−	0.723266i
$877$	28.1496	+	11.6600i	0.950545	+	0.393729i	0.803436	−	0.595392i	$-0.203003\pi$
$877$	28.1496	+	11.6600i	0.950545	+	0.393729i	0.147109	+	0.989120i	$0.453003\pi$
$878$	40.5578	−	12.0796i	1.36876	−	0.407665i
$879$	−5.92861	+	5.92861i	−0.199967	+	0.199967i
$880$	−1.88298	+	0.735718i	−0.0634753	+	0.0248011i
$881$	−5.99203			−0.201877			−0.100938	−	0.994893i	$-0.532184\pi$
$881$	−5.99203			−0.201877			−0.100938	+	0.994893i	$0.532184\pi$
$882$	8.45599	−	2.51849i	0.284728	−	0.0848021i
$883$	40.2702	−	16.6805i	1.35520	−	0.561342i	0.417464	−	0.908693i	$-0.362919\pi$
$883$	40.2702	−	16.6805i	1.35520	−	0.561342i	0.937735	+	0.347351i	$0.112919\pi$
$884$	23.7905	−	24.6850i	0.800160	−	0.830247i
$885$	−28.2112	+	68.1077i	−0.948308	+	2.28942i
$886$	−20.8562	+	16.9405i	−0.700678	+	0.569129i
$887$	−25.5472	−	25.5472i	−0.857791	−	0.857791i	0.133287	−	0.991078i	$-0.457447\pi$
$887$	−25.5472	−	25.5472i	−0.857791	−	0.857791i	−0.991078	+	0.133287i	$0.957447\pi$
$888$	−33.7095	−	28.5310i	−1.13122	−	0.957438i
$889$			2.36604i			0.0793543i
$890$	3.73493	−	36.0522i	0.125195	−	1.20847i
$891$	0.263836	+	0.636955i	0.00883882	+	0.0213388i
$892$	−31.7586	−	6.65163i	−1.06336	−	0.222713i
$893$	−7.91082	−	19.0984i	−0.264725	−	0.639104i
$894$	3.99108	−	1.18869i	0.133482	−	0.0397556i
$895$	−8.33503	−	8.33503i	−0.278609	−	0.278609i
$896$	−0.613702	+	1.79225i	−0.0205024	+	0.0598748i
$897$	−5.99631	−	1.01566i	−0.200211	−	0.0339119i
$898$	20.2770	−	6.03921i	0.676652	−	0.201531i
$899$	−1.98353	−	0.821603i	−0.0661543	−	0.0274020i
$900$	16.9924	−	11.1071i	0.566412	−	0.370238i
$901$	−4.52640	+	10.9277i	−0.150796	+	0.364054i
$902$	−0.277818	−	0.0287813i	−0.00925032	−	0.000958311i
$903$	1.90209			0.0632976
$904$	−2.39539	+	0.199301i	−0.0796694	+	0.00662867i
$905$		−	62.0393i		−	2.06225i
$906$	−30.9847	−	3.20994i	−1.02940	−	0.106643i
$907$	3.10397	−	7.49364i	0.103066	−	0.248822i	−0.863932	−	0.503609i	$-0.832005\pi$
$907$	3.10397	−	7.49364i	0.103066	−	0.248822i	0.966997	+	0.254787i	$0.0820052\pi$
$908$	5.24058	+	27.8127i	0.173915	+	0.922997i
$909$	−3.83703	−	9.26342i	−0.127266	−	0.307248i
$910$	0.418960	+	3.42608i	0.0138884	+	0.113573i
$911$	−52.0385			−1.72411			−0.862056	−	0.506814i	$-0.830823\pi$
$911$	−52.0385			−1.72411			−0.862056	+	0.506814i	$0.830823\pi$
$912$	15.1139	+	6.62148i	0.500472	+	0.219259i
$913$		−	1.38555i		−	0.0458549i
$914$	10.5398	+	5.70231i	0.348625	+	0.188616i
$915$	8.20461	−	19.8077i	0.271236	−	0.654822i
$916$	17.5745	+	12.0016i	0.580677	+	0.396545i
$917$	−1.17655	−	2.84044i	−0.0388530	−	0.0937996i
$918$	−29.4920	+	23.9550i	−0.973381	+	0.790633i
$919$	−6.59859	−	6.59859i	−0.217667	−	0.217667i	0.589847	−	0.807515i	$-0.299188\pi$
$919$	−6.59859	−	6.59859i	−0.217667	−	0.217667i	−0.807515	+	0.589847i	$0.799188\pi$
$920$	−4.05120	+	12.6606i	−0.133564	+	0.417409i
$921$	−34.4306			−1.13453
$922$	−18.9836	−	23.3715i	−0.625191	−	0.769698i
$923$	−10.0055	−	43.7340i	−0.329336	−	1.43952i
$924$	−0.0124525	+	0.0594552i	−0.000409656	+	0.00195593i
$925$	−46.7128	+	112.775i	−1.53591	+	3.70801i
$926$	−35.2898	+	10.5106i	−1.15970	+	0.345398i
$927$	−7.52392			−0.247118
$928$	−4.66534	−	2.64738i	−0.153147	−	0.0869044i
$929$	21.4042	+	21.4042i	0.702248	+	0.702248i	0.964893	−	0.262644i	$-0.0845946\pi$
$929$	21.4042	+	21.4042i	0.702248	+	0.702248i	−0.262644	+	0.964893i	$0.584595\pi$
$930$	−16.5184	−	8.93693i	−0.541661	−	0.293053i
$931$	7.58572	−	18.3136i	0.248612	−	0.600202i
$932$	−4.63385	+	22.1246i	−0.151787	+	0.724716i
$933$	−12.5993	+	30.4173i	−0.412481	+	0.995818i
$934$	−51.5187	−	5.33721i	−1.68574	−	0.174639i
$935$	−1.69903	−	1.69903i	−0.0555643	−	0.0555643i
$936$	−4.19362	+	8.10506i	−0.137073	+	0.264922i
$937$	−12.8168	+	12.8168i	−0.418706	+	0.418706i	−0.884758	−	0.466052i	$-0.845676\pi$
$937$	−12.8168	+	12.8168i	−0.418706	+	0.418706i	0.466052	+	0.884758i	$0.345676\pi$
$938$	1.04962	−	0.852557i	0.0342712	−	0.0278370i
$939$	6.45472	+	2.67363i	0.210642	+	0.0872507i
$940$	10.8852	+	57.7696i	0.355035	+	1.88424i
$941$	−49.8677	−	20.6559i	−1.62564	−	0.673362i	−0.630907	−	0.775859i	$-0.717317\pi$
$941$	−49.8677	−	20.6559i	−1.62564	−	0.673362i	−0.994733	+	0.102496i	$0.967317\pi$
$942$	1.80177	+	6.04955i	0.0587049	+	0.197105i
$943$	−1.29864	+	1.29864i	−0.0422896	+	0.0422896i
$944$	−50.2627	−	1.01637i	−1.63591	−	0.0330800i
$945$		−	3.82531i		−	0.124437i
$946$	−0.658682	+	1.21747i	−0.0214156	+	0.0395832i
$947$	24.4546	+	10.1294i	0.794666	+	0.329162i	0.742818	−	0.669493i	$-0.233489\pi$
$947$	24.4546	+	10.1294i	0.794666	+	0.329162i	0.0518483	+	0.998655i	$0.483489\pi$
$948$	34.4675	+	23.5379i	1.11945	+	0.764475i
$949$	31.3972	−	7.18310i	1.01920	−	0.233173i
$950$	4.69975	−	45.3655i	0.152480	−	1.47185i
$951$		−	38.1389i		−	1.23674i
$952$	−2.24386	+	0.186694i	−0.0727238	+	0.00605078i
$953$	−6.86834	+	6.86834i	−0.222487	+	0.222487i	−0.809545	−	0.587058i	$-0.800286\pi$
$953$	−6.86834	+	6.86834i	−0.222487	+	0.222487i	0.587058	+	0.809545i	$0.300286\pi$
$954$	0.324437	−	3.13170i	0.0105040	−	0.101393i
$955$	48.1240	−	19.9336i	1.55725	−	0.645036i
$956$	0.300420	−	1.43437i	0.00971627	−	0.0463910i
$957$	−0.158911	−	0.0658231i	−0.00513686	−	0.00212776i
$958$	4.99367	+	16.7666i	0.161338	+	0.541703i
$959$	−1.92718			−0.0622317
$960$	−38.2076	−	27.2408i	−1.23314	−	0.879193i
$961$			25.8738i			0.834639i
$962$	−6.66052	−	54.4670i	−0.214744	−	1.75609i
$963$	15.6328	−	6.47533i	0.503761	−	0.208665i
$964$	6.01897	−	28.7380i	0.193858	−	0.925588i
$965$	−57.2689	−	23.7215i	−1.84355	−	0.763623i
$966$	0.251831	+	0.310039i	0.00810252	+	0.00997534i
$967$	−39.4567			−1.26884			−0.634422	−	0.772987i	$-0.718762\pi$
$967$	−39.4567			−1.26884			−0.634422	+	0.772987i	$0.718762\pi$
$968$	23.7146	+	20.0715i	0.762218	+	0.645124i
$969$			19.6121i			0.630030i
$970$	−45.8051	+	37.2054i	−1.47071	+	1.19459i
$971$	−17.5788	−	7.28136i	−0.564129	−	0.233670i	0.0823474	−	0.996604i	$-0.473758\pi$
$971$	−17.5788	−	7.28136i	−0.564129	−	0.233670i	−0.646477	+	0.762934i	$0.723758\pi$
$972$	10.0968	−	14.7852i	0.323856	−	0.474235i
$973$	−0.0679049	+	0.163937i	−0.00217693	+	0.00525557i
$974$	−31.1011	−	16.8265i	−0.996542	−	0.539157i
$975$	−58.5056	−	9.90973i	−1.87368	−	0.317365i
$976$	14.6178	+	0.295589i	0.467905	+	0.00946157i
$977$	−23.0721	+	23.0721i	−0.738142	+	0.738142i	−0.972218	−	0.234076i	$-0.924793\pi$
$977$	−23.0721	+	23.0721i	−0.738142	+	0.738142i	0.234076	+	0.972218i	$0.424793\pi$
$978$	−10.8326	+	20.0222i	−0.346387	+	0.640239i
$979$	0.732246	−	0.303306i	0.0234027	−	0.00969371i
$980$	−31.7899	+	46.5512i	−1.01549	+	1.48702i
$981$	2.02466	−	0.838642i	0.0646425	−	0.0267758i
$982$	24.2003	−	19.6568i	0.772263	−	0.627274i
$983$	−18.0009			−0.574140			−0.287070	−	0.957910i	$-0.592681\pi$
$983$	−18.0009			−0.574140			−0.287070	+	0.957910i	$0.592681\pi$
$984$	−2.96903	−	5.76320i	−0.0946493	−	0.183724i
$985$	6.15308	−	6.15308i	0.196054	−	0.196054i
$986$	0.656978	−	6.34164i	0.0209225	−	0.201959i
$987$	1.63194	+	0.675973i	0.0519454	+	0.0215165i
$988$	8.19407	+	18.7937i	0.260688	+	0.597908i
$989$	3.48316	+	8.40909i	0.110758	+	0.267394i
$990$	0.562537	+	0.304348i	0.0178786	+	0.00967282i
$991$			43.1924i			1.37205i	0.727577	+	0.686026i	$0.240646\pi$
$991$			43.1924i			1.37205i	−0.727577	+	0.686026i	$0.759354\pi$
$992$	1.57707	−	12.7103i	0.0500722	−	0.403552i
$993$	−13.9545	−	13.9545i	−0.442833	−	0.442833i
$994$	−1.40210	+	2.59155i	−0.0444718	+	0.0821988i
$995$	6.89606	−	16.6486i	0.218620	−	0.527795i
$996$	26.9196	−	17.5961i	0.852981	−	0.557554i
$997$	−29.6069	−	12.2636i	−0.937660	−	0.388392i	−0.139081	−	0.990281i	$-0.544415\pi$
$997$	−29.6069	−	12.2636i	−0.937660	−	0.388392i	−0.798579	+	0.601889i	$0.794415\pi$
$998$	−9.19037	+	7.46493i	−0.290916	+	0.236298i
$999$			60.8138i			1.92406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bd.a.411.10	yes	216
13.5	odd	4		416.2.bi.a.187.19	yes	216
32.19	odd	8		416.2.bi.a.307.19	yes	216
416.83	even	8	inner	416.2.bd.a.83.10	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bd.a.83.10	✓	216	416.83	even	8	inner
416.2.bd.a.411.10	yes	216	1.1	even	1	trivial
416.2.bi.a.187.19	yes	216	13.5	odd	4
416.2.bi.a.307.19	yes	216	32.19	odd	8

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24}+ \cdots - 44 q^{99}+O(q^{100}) \) 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

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