LMFDB - Embedded newform 627.2.k.a.274.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [627,2,Mod(274,627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(627, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("627.274");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.k (of order $6$, degree $2$, 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:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			274.9
Character	$\chi$	$=$	627.274
Dual form			627.2.k.a.373.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.890907 + 1.54310i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.587432 - 1.01746i) q^{4} +(-1.80116 + 3.11970i) q^{5} +(1.54310 - 0.890907i) q^{6} +3.47801i q^{7} -1.47024 q^{8} +(0.500000 + 0.866025i) q^{9} +(-3.20933 - 5.55873i) q^{10} +(1.02623 + 3.15386i) q^{11} +1.17486i q^{12} +(3.10880 + 5.38460i) q^{13} +(-5.36690 - 3.09858i) q^{14} +(3.11970 - 1.80116i) q^{15} +(2.48471 - 4.30365i) q^{16} +(-1.87776 - 1.08412i) q^{17} -1.78181 q^{18} +(4.33293 - 0.475090i) q^{19} +4.23224 q^{20} +(1.73900 - 3.01204i) q^{21} +(-5.78099 - 1.22624i) q^{22} +(-1.66369 - 2.88160i) q^{23} +(1.27326 + 0.735119i) q^{24} +(-3.98836 - 6.90804i) q^{25} -11.0786 q^{26} -1.00000i q^{27} +(3.53874 - 2.04309i) q^{28} +(1.73736 + 3.00919i) q^{29} +6.41867i q^{30} +9.62118i q^{31} +(2.95706 + 5.12177i) q^{32} +(0.688195 - 3.24444i) q^{33} +(3.34582 - 1.93171i) q^{34} +(-10.8503 - 6.26445i) q^{35} +(0.587432 - 1.01746i) q^{36} -10.5939i q^{37} +(-3.12713 + 7.10939i) q^{38} -6.21760i q^{39} +(2.64814 - 4.58671i) q^{40} +(-1.56377 + 2.70854i) q^{41} +(3.09858 + 5.36690i) q^{42} +(-4.20613 - 2.42841i) q^{43} +(2.60610 - 2.89683i) q^{44} -3.60232 q^{45} +5.92879 q^{46} +(-3.17727 - 5.50319i) q^{47} +(-4.30365 + 2.48471i) q^{48} -5.09654 q^{49} +14.2130 q^{50} +(1.08412 + 1.87776i) q^{51} +(3.65242 - 6.32618i) q^{52} +(4.95920 - 2.86320i) q^{53} +(1.54310 + 0.890907i) q^{54} +(-11.6875 - 2.47910i) q^{55} -5.11350i q^{56} +(-3.98997 - 1.75503i) q^{57} -6.19129 q^{58} +(7.99216 + 4.61428i) q^{59} +(-3.66523 - 2.11612i) q^{60} +(0.789917 - 0.456059i) q^{61} +(-14.8464 - 8.57158i) q^{62} +(-3.01204 + 1.73900i) q^{63} -0.599010 q^{64} -22.3978 q^{65} +(4.39337 + 3.95245i) q^{66} +(-0.963041 + 0.556012i) q^{67} +2.54740i q^{68} +3.32739i q^{69} +(19.3333 - 11.1621i) q^{70} +(11.2832 + 6.51438i) q^{71} +(-0.735119 - 1.27326i) q^{72} +(5.54077 + 3.19896i) q^{73} +(16.3475 + 9.43822i) q^{74} +7.97672i q^{75} +(-3.02869 - 4.12951i) q^{76} +(-10.9692 + 3.56922i) q^{77} +(9.59436 + 5.53931i) q^{78} +(6.09548 - 10.5577i) q^{79} +(8.95073 + 15.5031i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.78636 - 4.82611i) q^{82} -3.77061i q^{83} -4.08619 q^{84} +(6.76429 - 3.90537i) q^{85} +(7.49455 - 4.32698i) q^{86} -3.47471i q^{87} +(-1.50880 - 4.63693i) q^{88} +(10.3166 - 5.95631i) q^{89} +(3.20933 - 5.55873i) q^{90} +(-18.7277 + 10.8124i) q^{91} +(-1.95462 + 3.38549i) q^{92} +(4.81059 - 8.33219i) q^{93} +11.3226 q^{94} +(-6.32217 + 14.3732i) q^{95} -5.91411i q^{96} +(-2.74700 - 1.58598i) q^{97} +(4.54054 - 7.86445i) q^{98} +(-2.21821 + 2.46567i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 40 q^{4} + 4 q^{5} + 40 q^{9} + 4 q^{11} - 24 q^{14} + 12 q^{15} - 40 q^{16} + 48 q^{20} - 24 q^{23} - 56 q^{25} + 80 q^{26} + 6 q^{33} - 48 q^{34} + 40 q^{36} + 60 q^{38} - 4 q^{42} + 14 q^{44}+ \cdots + 2 q^{99}+O(q^{100}) $ 80 * q - 40 * q^4 + 4 * q^5 + 40 * q^9 + 4 * q^11 - 24 * q^14 + 12 * q^15 - 40 * q^16 + 48 * q^20 - 24 * q^23 - 56 * q^25 + 80 * q^26 + 6 * q^33 - 48 * q^34 + 40 * q^36 + 60 * q^38 - 4 * q^42 + 14 * q^44 + 8 * q^45 - 16 * q^47 - 48 * q^48 - 80 * q^49 - 108 * q^53 - 24 * q^55 + 152 * q^58 - 48 * q^60 + 104 * q^64 - 36 * q^66 + 96 * q^67 - 60 * q^70 + 84 * q^71 - 60 * q^77 + 96 * q^78 - 32 * q^80 - 40 * q^81 - 20 * q^82 - 48 * q^86 + 72 * q^89 + 24 * q^91 - 104 * q^92 + 48 * q^93 + 36 * q^97 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.890907	+	1.54310i	−0.629967	+	1.09113i	0.357591	+	0.933878i	$0.383598\pi$
$2$	−0.890907	+	1.54310i	−0.629967	+	1.09113i	−0.987558	+	0.157256i	$0.949735\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.587432	−	1.01746i	−0.293716	−	0.508731i
$5$	−1.80116	+	3.11970i	−0.805504	+	1.39517i	0.110447	+	0.993882i	$0.464772\pi$
$5$	−1.80116	+	3.11970i	−0.805504	+	1.39517i	−0.915951	+	0.401291i	$0.868562\pi$
$6$	1.54310	−	0.890907i	0.629967	−	0.363711i
$7$			3.47801i			1.31456i	0.753645	+	0.657282i	$0.228294\pi$
$7$			3.47801i			1.31456i	−0.753645	+	0.657282i	$0.771706\pi$
$8$	−1.47024			−0.519808
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−3.20933	−	5.55873i	−1.01488	−	1.75783i
$11$	1.02623	+	3.15386i	0.309419	+	0.950926i
$11$	1.02623	+	3.15386i	0.309419	+	0.950926i
$12$			1.17486i			0.339154i
$13$	3.10880	+	5.38460i	0.862226	+	1.49342i	0.869775	+	0.493448i	$0.164264\pi$
$13$	3.10880	+	5.38460i	0.862226	+	1.49342i	−0.00754917	+	0.999972i	$0.502403\pi$
$14$	−5.36690	−	3.09858i	−1.43437	−	0.828131i
$15$	3.11970	−	1.80116i	0.805504	−	0.465058i
$16$	2.48471	−	4.30365i	0.621178	−	1.07591i
$17$	−1.87776	−	1.08412i	−0.455424	−	0.262939i	0.254694	−	0.967022i	$-0.418025\pi$
$17$	−1.87776	−	1.08412i	−0.455424	−	0.262939i	−0.710118	+	0.704083i	$0.751358\pi$
$18$	−1.78181			−0.419978
$19$	4.33293	−	0.475090i	0.994043	−	0.108993i
$19$	4.33293	−	0.475090i	0.994043	−	0.108993i
$20$	4.23224			0.946357
$21$	1.73900	−	3.01204i	0.379482	−	0.657282i
$22$	−5.78099	−	1.22624i	−1.23251	−	0.261434i
$23$	−1.66369	−	2.88160i	−0.346904	−	0.600856i	0.638793	−	0.769378i	$-0.279434\pi$
$23$	−1.66369	−	2.88160i	−0.346904	−	0.600856i	−0.985698	+	0.168522i	$0.946100\pi$
$24$	1.27326	+	0.735119i	0.259904	+	0.150056i
$25$	−3.98836	−	6.90804i	−0.797672	−	1.38161i
$26$	−11.0786			−2.17270
$27$		−	1.00000i		−	0.192450i
$28$	3.53874	−	2.04309i	0.668759	−	0.386108i
$29$	1.73736	+	3.00919i	0.322619	+	0.558792i	0.981028	−	0.193868i	$-0.0621034\pi$
$29$	1.73736	+	3.00919i	0.322619	+	0.558792i	−0.658409	+	0.752661i	$0.728770\pi$
$30$			6.41867i			1.17188i
$31$			9.62118i			1.72801i	0.503479	+	0.864007i	$0.332053\pi$
$31$			9.62118i			1.72801i	−0.503479	+	0.864007i	$0.667947\pi$
$32$	2.95706	+	5.12177i	0.522739	+	0.905410i
$33$	0.688195	−	3.24444i	0.119799	−	0.564784i
$34$	3.34582	−	1.93171i	0.573803	−	0.331286i
$35$	−10.8503	−	6.26445i	−1.83404	−	1.05889i
$36$	0.587432	−	1.01746i	0.0979054	−	0.169577i
$37$		−	10.5939i		−	1.74163i	−0.491608	−	0.870817i	$-0.663591\pi$
$37$		−	10.5939i		−	1.74163i	0.491608	−	0.870817i	$-0.336409\pi$
$38$	−3.12713	+	7.10939i	−0.507288	+	1.15330i
$39$		−	6.21760i		−	0.995613i
$40$	2.64814	−	4.58671i	0.418707	−	0.725222i
$41$	−1.56377	+	2.70854i	−0.244221	+	0.423002i	−0.961912	−	0.273359i	$-0.911865\pi$
$41$	−1.56377	+	2.70854i	−0.244221	+	0.423002i	0.717692	+	0.696361i	$0.245199\pi$
$42$	3.09858	+	5.36690i	0.478122	+	0.828131i
$43$	−4.20613	−	2.42841i	−0.641429	−	0.370329i	0.143736	−	0.989616i	$-0.454089\pi$
$43$	−4.20613	−	2.42841i	−0.641429	−	0.370329i	−0.785165	+	0.619287i	$0.787422\pi$
$44$	2.60610	−	2.89683i	0.392884	−	0.436713i
$45$	−3.60232			−0.537002
$46$	5.92879			0.874153
$47$	−3.17727	−	5.50319i	−0.463453	−	0.802723i	0.535678	−	0.844423i	$-0.320056\pi$
$47$	−3.17727	−	5.50319i	−0.463453	−	0.802723i	−0.999130	+	0.0416991i	$0.986723\pi$
$48$	−4.30365	+	2.48471i	−0.621178	+	0.358637i
$49$	−5.09654			−0.728077
$50$	14.2130			2.01003
$51$	1.08412	+	1.87776i	0.151808	+	0.262939i
$52$	3.65242	−	6.32618i	0.506499	−	0.877283i
$53$	4.95920	−	2.86320i	0.681199	−	0.393290i	−0.119108	−	0.992881i	$-0.538003\pi$
$53$	4.95920	−	2.86320i	0.681199	−	0.393290i	0.800307	+	0.599591i	$0.204670\pi$
$54$	1.54310	+	0.890907i	0.209989	+	0.121237i
$55$	−11.6875	−	2.47910i	−1.57594	−	0.334282i
$56$		−	5.11350i		−	0.683321i
$57$	−3.98997	−	1.75503i	−0.528485	−	0.232459i
$58$	−6.19129			−0.812957
$59$	7.99216	+	4.61428i	1.04049	+	0.600728i	0.919972	−	0.391983i	$-0.128211\pi$
$59$	7.99216	+	4.61428i	1.04049	+	0.600728i	0.120519	+	0.992711i	$0.461544\pi$
$60$	−3.66523	−	2.11612i	−0.473179	−	0.273190i
$61$	0.789917	−	0.456059i	0.101139	−	0.0583924i	−0.448578	−	0.893744i	$-0.648069\pi$
$61$	0.789917	−	0.456059i	0.101139	−	0.0583924i	0.549716	+	0.835352i	$0.314736\pi$
$62$	−14.8464	−	8.57158i	−1.88550	−	1.08859i
$63$	−3.01204	+	1.73900i	−0.379482	+	0.219094i
$64$	−0.599010			−0.0748762
$65$	−22.3978			−2.77810
$66$	4.39337	+	3.95245i	0.540786	+	0.486513i
$67$	−0.963041	+	0.556012i	−0.117654	+	0.0679277i	−0.557672	−	0.830061i	$-0.688305\pi$
$67$	−0.963041	+	0.556012i	−0.117654	+	0.0679277i	0.440018	+	0.897989i	$0.354972\pi$
$68$			2.54740i			0.308918i
$69$			3.32739i			0.400571i
$70$	19.3333	−	11.1621i	2.31077	−	1.33413i
$71$	11.2832	+	6.51438i	1.33907	+	0.773115i	0.986670	−	0.162734i	$-0.0520311\pi$
$71$	11.2832	+	6.51438i	1.33907	+	0.773115i	0.352404	+	0.935848i	$0.385364\pi$
$72$	−0.735119	−	1.27326i	−0.0866347	−	0.150056i
$73$	5.54077	+	3.19896i	0.648498	+	0.374410i	0.787880	−	0.615828i	$-0.211178\pi$
$73$	5.54077	+	3.19896i	0.648498	+	0.374410i	−0.139383	+	0.990239i	$0.544512\pi$
$74$	16.3475	+	9.43822i	1.90036	+	1.09717i
$75$			7.97672i			0.921072i
$76$	−3.02869	−	4.12951i	−0.347414	−	0.473687i
$77$	−10.9692	+	3.56922i	−1.25005	+	0.406750i
$78$	9.59436	+	5.53931i	1.08635	+	0.627203i
$79$	6.09548	−	10.5577i	0.685795	−	1.18783i	−0.287391	−	0.957813i	$-0.592788\pi$
$79$	6.09548	−	10.5577i	0.685795	−	1.18783i	0.973186	−	0.230019i	$-0.0738789\pi$
$80$	8.95073	+	15.5031i	1.00072	+	1.73330i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.78636	−	4.82611i	−0.307702	−	0.532955i
$83$		−	3.77061i		−	0.413878i	−0.978354	−	0.206939i	$-0.933650\pi$
$83$		−	3.77061i		−	0.413878i	0.978354	−	0.206939i	$-0.0663502\pi$
$84$	−4.08619			−0.445840
$85$	6.76429	−	3.90537i	0.733691	−	0.423596i
$86$	7.49455	−	4.32698i	0.808158	−	0.466590i
$87$		−	3.47471i		−	0.372528i
$88$	−1.50880	−	4.63693i	−0.160838	−	0.494299i
$89$	10.3166	−	5.95631i	1.09356	−	0.631368i	0.159039	−	0.987272i	$-0.449161\pi$
$89$	10.3166	−	5.95631i	1.09356	−	0.631368i	0.934522	+	0.355905i	$0.115827\pi$
$90$	3.20933	−	5.55873i	0.338294	−	0.585942i
$91$	−18.7277	+	10.8124i	−1.96319	+	1.13345i
$92$	−1.95462	+	3.38549i	−0.203783	+	0.352962i
$93$	4.81059	−	8.33219i	0.498835	−	0.864007i
$94$	11.3226			1.16784
$95$	−6.32217	+	14.3732i	−0.648641	+	1.47466i
$96$		−	5.91411i		−	0.603607i
$97$	−2.74700	−	1.58598i	−0.278916	−	0.161032i	0.354017	−	0.935239i	$-0.384816\pi$
$97$	−2.74700	−	1.58598i	−0.278916	−	0.161032i	−0.632932	+	0.774207i	$0.718149\pi$
$98$	4.54054	−	7.86445i	0.458664	−	0.794430i
$99$	−2.21821	+	2.46567i	−0.222939	+	0.247809i
$100$	−4.68578	+	8.11601i	−0.468578	+	0.811601i
$101$	6.54367	−	3.77799i	0.651120	−	0.375924i	−0.137765	−	0.990465i	$-0.543992\pi$
$101$	6.54367	−	3.77799i	0.651120	−	0.375924i	0.788885	+	0.614541i	$0.210659\pi$
$102$	−3.86342			−0.382536
$103$			9.11845i			0.898467i	0.893414	+	0.449234i	$0.148303\pi$
$103$			9.11845i			0.898467i	−0.893414	+	0.449234i	$0.851697\pi$
$104$	−4.57068	−	7.91665i	−0.448192	−	0.776291i
$105$	6.26445	+	10.8503i	0.611348	+	1.05889i
$106$			10.2034i			0.991039i
$107$	−3.72306			−0.359922			−0.179961	−	0.983674i	$-0.557597\pi$
$107$	−3.72306			−0.359922			−0.179961	+	0.983674i	$0.557597\pi$
$108$	−1.01746	+	0.587432i	−0.0979054	+	0.0565257i
$109$	4.26959	−	7.39514i	0.408952	−	0.708326i	−0.585820	−	0.810441i	$-0.699228\pi$
$109$	4.26959	−	7.39514i	0.408952	−	0.708326i	0.994773	+	0.102115i	$0.0325609\pi$
$110$	14.2380	−	15.8263i	1.35754	−	1.50898i
$111$	−5.29697	+	9.17462i	−0.502766	+	0.870817i
$112$	14.9681	+	8.64185i	1.41435	+	0.816578i
$113$			8.85290i			0.832811i	0.909179	+	0.416405i	$0.136710\pi$
$113$			8.85290i			0.832811i	−0.909179	+	0.416405i	$0.863290\pi$
$114$	6.26287	−	4.59335i	0.586572	−	0.430207i
$115$	11.9863			1.11773
$116$	2.04116	−	3.53539i	0.189517	−	0.328253i
$117$	−3.10880	+	5.38460i	−0.287409	+	0.497806i
$118$	−14.2406	+	8.22179i	−1.31095	+	0.756877i
$119$	3.77060	−	6.53086i	0.345650	−	0.598683i
$120$	−4.58671	+	2.64814i	−0.418707	+	0.241741i
$121$	−8.89372	+	6.47315i	−0.808520	+	0.588468i
$122$			1.62523i			0.147141i
$123$	2.70854	−	1.56377i	0.244221	−	0.141001i
$124$	9.78919	−	5.65179i	0.879095	−	0.507546i
$125$	10.7231			0.959103
$126$		−	6.19717i		−	0.552087i
$127$	5.03554	+	8.72181i	0.446832	+	0.773935i	0.998178	−	0.0603413i	$-0.0192189\pi$
$127$	5.03554	+	8.72181i	0.446832	+	0.773935i	−0.551346	+	0.834277i	$0.685886\pi$
$128$	−5.38045	+	9.31921i	−0.475569	+	0.823710i
$129$	2.42841	+	4.20613i	0.213810	+	0.370329i
$130$	19.9544	−	34.5620i	1.75011	−	3.03129i
$131$	2.61912	+	1.51215i	0.228834	+	0.132117i	0.610034	−	0.792375i	$-0.291156\pi$
$131$	2.61912	+	1.51215i	0.228834	+	0.132117i	−0.381200	+	0.924493i	$0.624489\pi$
$132$	−3.70536	+	1.20568i	−0.322510	+	0.104941i
$133$	1.65237	+	15.0700i	0.143278	+	1.30673i
$134$		−	1.98142i		−	0.171169i
$135$	3.11970	+	1.80116i	0.268501	+	0.155019i
$136$	2.76076	+	1.59392i	0.236733	+	0.136678i
$137$	3.97713	+	6.88859i	0.339789	+	0.588532i	0.984393	−	0.175985i	$-0.0563110\pi$
$137$	3.97713	+	6.88859i	0.339789	+	0.588532i	−0.644604	+	0.764517i	$0.722978\pi$
$138$	−5.13448	−	2.96440i	−0.437076	−	0.252346i
$139$	−14.2261	+	8.21347i	−1.20665	+	0.696657i	−0.962025	−	0.272962i	$-0.911997\pi$
$139$	−14.2261	+	8.21347i	−1.20665	+	0.696657i	−0.244621	+	0.969619i	$0.578663\pi$
$140$			14.7198i			1.24405i
$141$			6.35454i			0.535149i
$142$	−20.1046	+	11.6074i	−1.68714	+	0.974073i
$143$	−13.7920	+	15.3305i	−1.15334	+	1.28200i
$144$	4.96942			0.414119
$145$	−12.5170			−1.03948
$146$	−9.87262	+	5.69996i	−0.817064	+	0.471732i
$147$	4.41373	+	2.54827i	0.364039	+	0.210178i
$148$	−10.7789	+	6.22322i	−0.886023	+	0.511546i
$149$	2.59167	+	1.49630i	0.212318	+	0.122582i	0.602388	−	0.798203i	$-0.294216\pi$
$149$	2.59167	+	1.49630i	0.212318	+	0.122582i	−0.390070	+	0.920785i	$0.627549\pi$
$150$	−12.3088	−	7.10652i	−1.00501	−	0.580245i
$151$	−20.9149			−1.70203			−0.851017	−	0.525138i	$-0.824014\pi$
$151$	−20.9149			−1.70203			−0.851017	+	0.525138i	$0.824014\pi$
$152$	−6.37044	+	0.698496i	−0.516711	+	0.0566555i
$153$		−	2.16825i		−	0.175293i
$154$	4.26486	−	20.1063i	0.343672	−	1.62021i
$155$	−30.0152	−	17.3293i	−2.41088	−	1.39192i
$156$	−6.32618	+	3.65242i	−0.506499	+	0.292428i
$157$	9.02308	−	15.6284i	0.720120	−	1.24729i	−0.240831	−	0.970567i	$-0.577420\pi$
$157$	9.02308	−	15.6284i	0.720120	−	1.24729i	0.960951	−	0.276718i	$-0.0892468\pi$
$158$	10.8610	+	18.8118i	0.864057	+	1.49659i
$159$	−5.72639			−0.454133
$160$	−21.3045			−1.68427
$161$	10.0222	−	5.78634i	0.789863	−	0.456028i
$162$	−0.890907	−	1.54310i	−0.0699963	−	0.121237i
$163$	−11.9345			−0.934784			−0.467392	−	0.884050i	$-0.654806\pi$
$163$	−11.9345			−0.934784			−0.467392	+	0.884050i	$0.654806\pi$
$164$	3.67445			0.286926
$165$	8.88213	+	7.99072i	0.691473	+	0.622077i
$166$	5.81842	+	3.35926i	0.451597	+	0.260730i
$167$	−5.55197	−	9.61630i	−0.429625	−	0.744132i	0.567215	−	0.823570i	$-0.308021\pi$
$167$	−5.55197	−	9.61630i	−0.429625	−	0.744132i	−0.996840	+	0.0794379i	$0.974687\pi$
$168$	−2.55675	+	4.42842i	−0.197258	+	0.341660i
$169$	−12.8293	+	22.2210i	−0.986868	+	1.70931i
$170$			13.9173i			1.06741i
$171$	2.57791	+	3.51488i	0.197137	+	0.268790i
$172$			5.70611i			0.435087i
$173$	2.24966	−	3.89652i	0.171038	−	0.296247i	−0.767745	−	0.640756i	$-0.778621\pi$
$173$	2.24966	−	3.89652i	0.171038	−	0.296247i	0.938783	+	0.344509i	$0.111955\pi$
$174$	5.36182	+	3.09565i	0.406478	+	0.234680i
$175$	24.0262	−	13.8715i	1.81621	−	1.04859i
$176$	16.1230	+	3.41993i	1.21532	+	0.257787i
$177$	−4.61428	−	7.99216i	−0.346830	−	0.600728i
$178$			21.2261i			1.59096i
$179$			18.6165i			1.39146i	0.718302	+	0.695731i	$0.244920\pi$
$179$			18.6165i			1.39146i	−0.718302	+	0.695731i	$0.755080\pi$
$180$	2.11612	+	3.66523i	0.157726	+	0.273190i
$181$	8.55673	−	4.94023i	0.636017	−	0.367205i	−0.147062	−	0.989127i	$-0.546982\pi$
$181$	8.55673	−	4.94023i	0.636017	−	0.367205i	0.783079	+	0.621923i	$0.213648\pi$
$182$		−	38.5315i		−	2.85615i
$183$	−0.912118			−0.0674257
$184$	2.44603	+	4.23665i	0.180324	+	0.312330i
$185$	33.0499	+	19.0814i	2.42988	+	1.40289i
$186$	8.57158	+	14.8464i	0.628499	+	1.08859i
$187$	1.49218	−	7.03476i	0.109119	−	0.514432i
$188$	−3.73286	+	6.46551i	−0.272247	+	0.471546i
$189$	3.47801			0.252988
$190$	−16.5467	−	22.5609i	−1.20043	−	1.63674i
$191$	5.46061			0.395116			0.197558	−	0.980291i	$-0.436699\pi$
$191$	5.46061			0.395116			0.197558	+	0.980291i	$0.436699\pi$
$192$	0.518758	+	0.299505i	0.0374381	+	0.0216149i
$193$	1.96112	−	3.39677i	0.141165	−	0.244505i	−0.786771	−	0.617245i	$-0.788249\pi$
$193$	1.96112	−	3.39677i	0.141165	−	0.244505i	0.927936	+	0.372741i	$0.121582\pi$
$194$	4.89465	−	2.82592i	0.351415	−	0.202890i
$195$	19.3971	+	11.1989i	1.38905	+	0.801970i
$196$	2.99387	+	5.18554i	0.213848	+	0.370396i
$197$			9.41096i			0.670503i	0.942129	+	0.335252i	$0.108821\pi$
$197$			9.41096i			0.670503i	−0.942129	+	0.335252i	$0.891179\pi$
$198$	−1.82854	−	5.61960i	−0.129949	−	0.399368i
$199$	−7.48902	−	12.9714i	−0.530882	−	0.919515i	−0.999351	−	0.0360350i	$-0.988527\pi$
$199$	−7.48902	−	12.9714i	−0.530882	−	0.919515i	0.468468	−	0.883480i	$-0.344806\pi$
$200$	5.86384	+	10.1565i	0.414636	+	0.718171i
$201$	1.11202			0.0784361
$202$			13.4634i			0.947279i
$203$	−10.4660	+	6.04254i	−0.734568	+	0.424103i
$204$	1.27370	−	2.20611i	0.0891768	−	0.154459i
$205$	−5.63322	−	9.75702i	−0.393441	−	0.681460i
$206$	−14.0706	−	8.12369i	−0.980349	−	0.566004i
$207$	1.66369	−	2.88160i	0.115635	−	0.200285i
$208$	30.8979			2.14238
$209$	5.94493	+	13.1779i	0.411220	+	0.911536i
$210$	−22.3242			−1.54052
$211$	−2.85748	+	4.94931i	−0.196717	+	0.340724i	−0.947462	−	0.319868i	$-0.896361\pi$
$211$	−2.85748	+	4.94931i	−0.196717	+	0.340724i	0.750745	+	0.660592i	$0.229695\pi$
$212$	−5.82639	−	3.36387i	−0.400158	−	0.231031i
$213$	−6.51438	−	11.2832i	−0.446358	−	0.773115i
$214$	3.31690	−	5.74505i	0.226739	−	0.392723i
$215$	15.1518	−	8.74792i	1.03335	−	0.596603i
$216$			1.47024i			0.100037i
$217$	−33.4625			−2.27158
$218$	7.60761	+	13.1768i	0.515253	+	0.892444i
$219$	−3.19896	−	5.54077i	−0.216166	−	0.374410i
$220$	4.34323	+	13.3479i	0.292821	+	0.899916i
$221$		−	13.4813i		−	0.906851i
$222$	−9.43822	−	16.3475i	−0.633452	−	1.09717i
$223$	19.9332	+	11.5084i	1.33482	+	0.770661i	0.986035	−	0.166540i	$-0.0532593\pi$
$223$	19.9332	+	11.5084i	1.33482	+	0.770661i	0.348790	+	0.937201i	$0.386593\pi$
$224$	−17.8136	+	10.2847i	−1.19022	+	0.687173i
$225$	3.98836	−	6.90804i	0.265891	−	0.460536i
$226$	−13.6609	−	7.88711i	−0.908708	−	0.524643i
$227$	−14.2017			−0.942597			−0.471299	−	0.881974i	$-0.656215\pi$
$227$	−14.2017			−0.942597			−0.471299	+	0.881974i	$0.656215\pi$
$228$	0.558166	+	5.09061i	0.0369655	+	0.337134i
$229$	−5.97948			−0.395135			−0.197568	−	0.980289i	$-0.563304\pi$
$229$	−5.97948			−0.395135			−0.197568	+	0.980289i	$0.563304\pi$
$230$	−10.6787	+	18.4961i	−0.704133	+	1.21959i
$231$	11.2842	+	2.39355i	0.742445	+	0.157484i
$232$	−2.55433	−	4.42423i	−0.167700	−	0.290465i
$233$	1.58204	+	0.913393i	0.103643	+	0.0598384i	0.550926	−	0.834554i	$-0.314275\pi$
$233$	1.58204	+	0.913393i	0.103643	+	0.0598384i	−0.447283	+	0.894393i	$0.647608\pi$
$234$	−5.53931	−	9.59436i	−0.362116	−	0.627203i
$235$	22.8911			1.49325
$236$		−	10.8423i		−	0.705774i
$237$	−10.5577	+	6.09548i	−0.685795	+	0.395944i
$238$	6.71850	+	11.6368i	0.435496	+	0.754301i
$239$		−	9.19954i		−	0.595069i	−0.954711	−	0.297534i	$-0.903836\pi$
$239$		−	9.19954i		−	0.595069i	0.954711	−	0.297534i	$-0.0961643\pi$
$240$		−	17.9015i		−	1.15553i
$241$	1.44148	+	2.49672i	0.0928541	+	0.160828i	0.908711	−	0.417426i	$-0.137068\pi$
$241$	1.44148	+	2.49672i	0.0928541	+	0.160828i	−0.815857	+	0.578254i	$0.803734\pi$
$242$	−2.06522	−	19.4909i	−0.132757	−	1.25292i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−0.928046	−	0.535807i	−0.0594120	−	0.0343016i
$245$	9.17969	−	15.8997i	0.586469	−	1.01579i
$246$			5.57271i			0.355303i
$247$	16.0284	+	21.8541i	1.01986	+	1.39055i
$248$		−	14.1454i		−	0.898236i
$249$	−1.88531	+	3.26544i	−0.119476	+	0.206939i
$250$	−9.55329	+	16.5468i	−0.604203	+	1.04651i
$251$	−7.42400	−	12.8587i	−0.468599	−	0.811637i	0.530757	−	0.847524i	$-0.321908\pi$
$251$	−7.42400	−	12.8587i	−0.468599	−	0.811637i	−0.999356	+	0.0358870i	$0.988574\pi$
$252$	3.53874	+	2.04309i	0.222920	+	0.128703i
$253$	7.38086	−	8.20424i	0.464031	−	0.515796i
$254$	−17.9448			−1.12596
$255$	−7.81073			−0.489127
$256$	−10.1860	−	17.6426i	−0.636624	−	1.10266i
$257$	20.7826	−	11.9988i	1.29638	−	0.748467i	0.316606	−	0.948557i	$-0.397457\pi$
$257$	20.7826	−	11.9988i	1.29638	−	0.748467i	0.979778	+	0.200090i	$0.0641234\pi$
$258$	−8.65396			−0.538772
$259$	36.8458			2.28949
$260$	13.1572	+	22.7889i	0.815974	+	1.41331i
$261$	−1.73736	+	3.00919i	−0.107540	+	0.186264i
$262$	−4.66679	+	2.69438i	−0.288316	+	0.166459i
$263$	−19.4777	−	11.2454i	−1.20104	−	0.693423i	−0.240256	−	0.970710i	$-0.577231\pi$
$263$	−19.4777	−	11.2454i	−1.20104	−	0.693423i	−0.960787	+	0.277287i	$0.910565\pi$
$264$	−1.01181	+	4.77010i	−0.0622727	+	0.293579i
$265$			20.6283i			1.26719i
$266$	−24.7265	−	10.8762i	−1.51608	−	0.666862i
$267$	−11.9126			−0.729041
$268$	1.13144	+	0.653239i	0.0691138	+	0.0399029i
$269$	−14.0884	−	8.13397i	−0.858988	−	0.495937i	0.00468540	−	0.999989i	$-0.498509\pi$
$269$	−14.0884	−	8.13397i	−0.858988	−	0.495937i	−0.863673	+	0.504052i	$0.831842\pi$
$270$	−5.55873	+	3.20933i	−0.338294	+	0.195314i
$271$	20.1350	+	11.6249i	1.22311	+	0.706165i	0.965580	−	0.260105i	$-0.0837571\pi$
$271$	20.1350	+	11.6249i	1.22311	+	0.706165i	0.257533	+	0.966270i	$0.417090\pi$
$272$	−9.33138	+	5.38747i	−0.565798	+	0.326664i
$273$	21.6249			1.30880
$274$	−14.1730			−0.856223
$275$	17.6941	−	19.6680i	1.06699	−	1.18602i
$276$	3.38549	−	1.95462i	0.203783	−	0.117654i
$277$			8.52204i			0.512040i	0.966672	+	0.256020i	$0.0824113\pi$
$277$			8.52204i			0.512040i	−0.966672	+	0.256020i	$0.917589\pi$
$278$		−	29.2698i		−	1.75548i
$279$	−8.33219	+	4.81059i	−0.498835	+	0.288002i
$280$	15.9526	+	9.21024i	0.953350	+	0.550417i
$281$	−9.21028	−	15.9527i	−0.549439	−	0.951657i	−0.998313	−	0.0580616i	$-0.981508\pi$
$281$	−9.21028	−	15.9527i	−0.549439	−	0.951657i	0.448874	−	0.893595i	$-0.351825\pi$
$282$	−9.80567	−	5.66131i	−0.583919	−	0.337126i
$283$	−5.76284	−	3.32718i	−0.342565	−	0.197780i	0.318841	−	0.947808i	$-0.396707\pi$
$283$	−5.76284	−	3.32718i	−0.342565	−	0.197780i	−0.661406	+	0.750028i	$0.730040\pi$
$284$		−	15.3070i		−	0.908305i
$285$	12.6617	−	9.28644i	0.750017	−	0.550081i
$286$	−11.3692	−	34.9404i	−0.672272	−	2.06607i
$287$	−9.42031	−	5.43882i	−0.556063	−	0.321043i
$288$	−2.95706	+	5.12177i	−0.174246	+	0.301803i
$289$	−6.14935	−	10.6510i	−0.361726	−	0.626528i
$290$	11.1515	−	19.3150i	0.654840	−	1.13422i
$291$	1.58598	+	2.74700i	0.0929719	+	0.161032i
$292$		−	7.51670i		−	0.439881i
$293$	30.4775			1.78051			0.890257	−	0.455459i	$-0.150525\pi$
$293$	30.4775			1.78051			0.890257	+	0.455459i	$0.150525\pi$
$294$	−7.86445	+	4.54054i	−0.458664	+	0.264810i
$295$	−28.7903	+	16.6221i	−1.67624	+	0.967777i
$296$			15.5756i			0.905315i
$297$	3.15386	−	1.02623i	0.183006	−	0.0595476i
$298$	−4.61788	+	2.66614i	−0.267507	+	0.154445i
$299$	10.3442	−	17.9167i	0.598220	−	1.03615i
$300$	8.11601	−	4.68578i	0.468578	−	0.270534i
$301$	8.44604	−	14.6290i	0.486822	−	0.843200i
$302$	18.6333	−	32.2738i	1.07223	−	1.85715i
$303$	−7.55598			−0.434080
$304$	8.72146	−	19.8279i	0.500210	−	1.13721i
$305$			3.28574i			0.188141i
$306$	3.34582	+	1.93171i	0.191268	+	0.110429i
$307$	−7.12446	+	12.3399i	−0.406614	+	0.704276i	−0.994508	−	0.104662i	$-0.966624\pi$
$307$	−7.12446	+	12.3399i	−0.406614	+	0.704276i	0.587894	+	0.808938i	$0.299957\pi$
$308$	10.0752	+	9.06404i	0.574087	+	0.516472i
$309$	4.55922	−	7.89681i	0.259365	−	0.449234i
$310$	53.4815	−	30.8776i	3.03755	−	1.75373i
$311$	−2.52445			−0.143148			−0.0715742	−	0.997435i	$-0.522802\pi$
$311$	−2.52445			−0.143148			−0.0715742	+	0.997435i	$0.522802\pi$
$312$			9.14136i			0.517528i
$313$	14.0208	+	24.2848i	0.792504	+	1.37266i	0.924412	+	0.381395i	$0.124556\pi$
$313$	14.0208	+	24.2848i	0.792504	+	1.37266i	−0.131908	+	0.991262i	$0.542110\pi$
$314$	16.0775	+	27.8470i	0.907304	+	1.57150i
$315$		−	12.5289i		−	0.705924i
$316$	−14.3227			−0.805717
$317$	−2.00309	+	1.15649i	−0.112505	+	0.0649548i	−0.555197	−	0.831719i	$-0.687357\pi$
$317$	−2.00309	+	1.15649i	−0.112505	+	0.0649548i	0.442692	+	0.896674i	$0.354024\pi$
$318$	5.10169	−	8.83638i	0.286088	−	0.495520i
$319$	−7.70766	+	8.56749i	−0.431546	+	0.479687i
$320$	1.07891	−	1.86873i	0.0603131	−	0.104465i
$321$	3.22427	+	1.86153i	0.179961	+	0.103901i
$322$			20.6204i			1.14913i
$323$	−8.65126	−	3.80533i	−0.481369	−	0.211734i
$324$	1.17486			0.0652702
$325$	24.7980	−	42.9514i	1.37555	−	2.38252i
$326$	10.6326	−	18.4161i	0.588883	−	1.01997i
$327$	−7.39514	+	4.26959i	−0.408952	+	0.236109i
$328$	2.29912	−	3.98220i	0.126948	−	0.219880i
$329$	19.1402	−	11.0506i	1.05523	−	0.609238i
$330$	−20.2436	+	6.58700i	−1.11437	+	0.362603i
$331$		−	23.0878i		−	1.26902i	−0.772915	−	0.634510i	$-0.781202\pi$
$331$		−	23.0878i		−	1.26902i	0.772915	−	0.634510i	$-0.218798\pi$
$332$	−3.83645	+	2.21498i	−0.210553	+	0.121563i
$333$	9.17462	−	5.29697i	0.502766	−	0.290272i
$334$	19.7852			1.08260
$335$		−	4.00587i		−	0.218864i
$336$	−8.64185	−	14.9681i	−0.471451	−	0.816578i
$337$	−10.2387	+	17.7340i	−0.557740	+	0.966033i	0.439945	+	0.898025i	$0.354998\pi$
$337$	−10.2387	+	17.7340i	−0.557740	+	0.966033i	−0.997685	+	0.0680086i	$0.978335\pi$
$338$	−22.8594	−	39.5937i	−1.24339	−	2.15361i
$339$	4.42645	−	7.66684i	0.240412	−	0.416405i
$340$	−7.94713	−	4.58828i	−0.430993	−	0.248834i
$341$	−30.3439	+	9.87350i	−1.64321	+	0.534680i
$342$	−7.72048	+	0.846522i	−0.417476	+	0.0457747i
$343$			6.62025i			0.357460i
$344$	6.18402	+	3.57035i	0.333420	+	0.192500i
$345$	−10.3805	−	5.99316i	−0.558865	−	0.322661i
$346$	4.00847	+	6.94288i	0.215497	+	0.373251i
$347$	−4.34815	−	2.51040i	−0.233421	−	0.134766i	0.378728	−	0.925508i	$-0.376361\pi$
$347$	−4.34815	−	2.51040i	−0.233421	−	0.134766i	−0.612149	+	0.790742i	$0.709695\pi$
$348$	−3.53539	+	2.04116i	−0.189517	+	0.109418i
$349$			1.14280i			0.0611728i	0.999532	+	0.0305864i	$0.00973747\pi$
$349$			1.14280i			0.0611728i	−0.999532	+	0.0305864i	$0.990263\pi$
$350$			49.4331i			2.64231i
$351$	5.38460	−	3.10880i	0.287409	−	0.165935i
$352$	−13.1188	+	14.5822i	−0.699233	+	0.777236i
$353$	18.8801			1.00489			0.502443	−	0.864610i	$-0.332435\pi$
$353$	18.8801			1.00489			0.502443	+	0.864610i	$0.332435\pi$
$354$	16.4436			0.873966
$355$	−40.6458	+	23.4669i	−2.15726	+	1.24549i
$356$	−12.1206	−	6.99786i	−0.642393	−	0.370886i
$357$	−6.53086	+	3.77060i	−0.345650	+	0.199561i
$358$	−28.7271	−	16.5856i	−1.51827	−	0.876575i
$359$	−9.96261	−	5.75192i	−0.525806	−	0.303574i	0.213501	−	0.976943i	$-0.431513\pi$
$359$	−9.96261	−	5.75192i	−0.525806	−	0.303574i	−0.739307	+	0.673368i	$0.764847\pi$
$360$	5.29627			0.279138
$361$	18.5486	−	4.11706i	0.976241	−	0.216688i
$362$			17.6052i			0.925307i
$363$	10.9388	−	1.15905i	0.574136	−	0.0608345i
$364$	22.0025	+	12.7031i	1.15324	+	0.665826i
$365$	−19.9596	+	11.5237i	−1.04473	+	0.603178i
$366$	0.812613	−	1.40749i	0.0424759	−	0.0735705i
$367$	−5.00923	−	8.67624i	−0.261480	−	0.452896i	0.705156	−	0.709052i	$-0.250877\pi$
$367$	−5.00923	−	8.67624i	−0.261480	−	0.452896i	−0.966635	+	0.256157i	$0.917544\pi$
$368$	−16.5352			−0.861957
$369$	−3.12755			−0.162814
$370$	−58.8889	+	33.9995i	−3.06149	+	1.76755i
$371$	9.95822	+	17.2481i	0.517005	+	0.895479i
$372$	−11.3036			−0.586063
$373$	25.9211			1.34214			0.671071	−	0.741393i	$-0.265834\pi$
$373$	25.9211			1.34214			0.671071	+	0.741393i	$0.265834\pi$
$374$	9.52592	+	8.56989i	0.492573	+	0.443139i
$375$	−9.28647	−	5.36155i	−0.479551	−	0.276869i
$376$	4.67135	+	8.09101i	0.240906	+	0.417262i
$377$	−10.8022	+	18.7099i	−0.556341	+	0.963611i
$378$	−3.09858	+	5.36690i	−0.159374	+	0.276044i
$379$			4.96213i			0.254887i	0.991846	+	0.127444i	$0.0406772\pi$
$379$			4.96213i			0.254887i	−0.991846	+	0.127444i	$0.959323\pi$
$380$	18.3380	−	2.01069i	0.940719	−	0.103146i
$381$		−	10.0711i		−	0.515957i
$382$	−4.86490	+	8.42626i	−0.248910	+	0.431125i
$383$	−5.35007	−	3.08887i	−0.273376	−	0.157834i	0.357045	−	0.934087i	$-0.383784\pi$
$383$	−5.35007	−	3.08887i	−0.273376	−	0.157834i	−0.630421	+	0.776254i	$0.717118\pi$
$384$	9.31921	−	5.38045i	0.475569	−	0.274570i
$385$	8.62233	−	40.6493i	0.439434	−	2.07168i
$386$	3.49436	+	6.05241i	0.177858	+	0.308060i
$387$		−	4.85683i		−	0.246886i
$388$			3.72663i			0.189191i
$389$	−9.75626	−	16.8983i	−0.494662	−	0.856780i	0.505319	−	0.862933i	$-0.331375\pi$
$389$	−9.75626	−	16.8983i	−0.494662	−	0.856780i	−0.999981	+	0.00615299i	$0.998041\pi$
$390$	−34.5620	+	19.9544i	−1.75011	+	1.01043i
$391$			7.21461i			0.364859i
$392$	7.49313			0.378460
$393$	−1.51215	−	2.61912i	−0.0762780	−	0.132117i
$394$	−14.5220	−	8.38430i	−0.731609	−	0.422395i
$395$	21.9579	+	38.0322i	1.10482	+	1.91361i
$396$	3.81178	+	0.808536i	0.191549	+	0.0406304i
$397$	7.35626	−	12.7414i	0.369200	−	0.639473i	−0.620241	−	0.784412i	$-0.712965\pi$
$397$	7.35626	−	12.7414i	0.369200	−	0.639473i	0.989441	+	0.144938i	$0.0462984\pi$
$398$	26.6881			1.33775
$399$	6.10399	−	13.8772i	0.305582	−	0.694727i
$400$	−39.6397			−1.98198
$401$	−8.89409	−	5.13501i	−0.444150	−	0.256430i	0.261206	−	0.965283i	$-0.415880\pi$
$401$	−8.89409	−	5.13501i	−0.444150	−	0.256430i	−0.705356	+	0.708853i	$0.749213\pi$
$402$	−0.990710	+	1.71596i	−0.0494121	+	0.0855843i
$403$	−51.8062	+	29.9103i	−2.58065	+	1.48994i
$404$	−7.68793	−	4.43863i	−0.382489	−	0.220830i
$405$	−1.80116	−	3.11970i	−0.0895004	−	0.155019i
$406$		−	21.5334i		−	1.06868i
$407$	33.4119	−	10.8718i	1.65616	−	0.538894i
$408$	−1.59392	−	2.76076i	−0.0789109	−	0.136678i
$409$	−15.3748	−	26.6300i	−0.760235	−	1.31677i	−0.942729	−	0.333559i	$-0.891750\pi$
$409$	−15.3748	−	26.6300i	−0.760235	−	1.31677i	0.182494	−	0.983207i	$-0.441583\pi$
$410$	20.0747			0.991419
$411$		−	7.95426i		−	0.392355i
$412$	9.27768	−	5.35647i	0.457078	−	0.263894i
$413$	−16.0485	+	27.7968i	−0.789695	+	1.36779i
$414$	2.96440	+	5.13448i	0.145692	+	0.252346i
$415$	11.7632	+	6.79147i	0.577432	+	0.333380i
$416$	−18.3858	+	31.8451i	−0.901438	+	1.56134i
$417$	16.4269			0.804430
$418$	−25.6312	−	2.56671i	−1.25366	−	0.125542i
$419$	1.14876			0.0561205			0.0280602	−	0.999606i	$-0.491067\pi$
$419$	1.14876			0.0561205			0.0280602	+	0.999606i	$0.491067\pi$
$420$	7.35988	−	12.7477i	0.359125	−	0.622023i
$421$	−14.3341	−	8.27578i	−0.698600	−	0.403337i	0.108226	−	0.994126i	$-0.465483\pi$
$421$	−14.3341	−	8.27578i	−0.698600	−	0.403337i	−0.806826	+	0.590789i	$0.798816\pi$
$422$	−5.09151	−	8.81875i	−0.247851	−	0.429290i
$423$	3.17727	−	5.50319i	0.154484	−	0.267574i
$424$	−7.29121	+	4.20958i	−0.354093	+	0.204435i
$425$			17.2955i			0.838956i
$426$	23.2148			1.12476
$427$	1.58618	+	2.74734i	0.0767605	+	0.132953i
$428$	2.18705	+	3.78808i	0.105715	+	0.183104i
$429$	19.6095	−	6.38066i	0.946754	−	0.308061i
$430$			31.1744i			1.50336i
$431$	3.35418	+	5.80960i	0.161565	+	0.279839i	0.935430	−	0.353512i	$-0.115013\pi$
$431$	3.35418	+	5.80960i	0.161565	+	0.279839i	−0.773865	+	0.633350i	$0.781679\pi$
$432$	−4.30365	−	2.48471i	−0.207059	−	0.119546i
$433$	−28.0457	+	16.1922i	−1.34779	+	0.778146i	−0.987936	−	0.154863i	$-0.950506\pi$
$433$	−28.0457	+	16.1922i	−1.34779	+	0.778146i	−0.359853	+	0.933009i	$0.617173\pi$
$434$	29.8120	−	51.6359i	1.43102	−	2.47860i
$435$	10.8401	+	6.25851i	0.519741	+	0.300073i
$436$	−10.0324			−0.480463
$437$	−8.57770	−	11.6954i	−0.410327	−	0.559466i
$438$	11.3999			0.544709
$439$	−13.7278	+	23.7772i	−0.655190	+	1.13482i	0.326656	+	0.945143i	$0.394078\pi$
$439$	−13.7278	+	23.7772i	−0.655190	+	1.13482i	−0.981846	+	0.189679i	$0.939255\pi$
$440$	17.1834	+	3.64487i	0.819188	+	0.173762i
$441$	−2.54827	−	4.41373i	−0.121346	−	0.210178i
$442$	20.8030	+	12.0106i	0.989496	+	0.571286i
$443$	−4.08541	−	7.07614i	−0.194104	−	0.336198i	0.752503	−	0.658589i	$-0.228847\pi$
$443$	−4.08541	−	7.07614i	−0.194104	−	0.336198i	−0.946606	+	0.322392i	$0.895513\pi$
$444$	12.4464			0.590682
$445$			42.9131i			2.03428i
$446$	−35.5172	+	20.5059i	−1.68179	+	0.970982i
$447$	−1.49630	−	2.59167i	−0.0707728	−	0.122582i
$448$		−	2.08336i		−	0.0984296i
$449$			17.8535i			0.842559i	0.906931	+	0.421280i	$0.138419\pi$
$449$			17.8535i			0.842559i	−0.906931	+	0.421280i	$0.861581\pi$
$450$	7.10652	+	12.3088i	0.335004	+	0.580245i
$451$	−10.1471	−	2.15236i	−0.477810	−	0.101351i
$452$	9.00749	−	5.20048i	0.423677	−	0.244610i
$453$	18.1129	+	10.4575i	0.851017	+	0.491335i
$454$	12.6524	−	21.9145i	0.593805	−	1.02850i
$455$		−	77.8997i		−	3.65199i
$456$	5.86621	+	2.58031i	0.274711	+	0.120834i
$457$			18.8058i			0.879699i	0.898071	+	0.439850i	$0.144968\pi$
$457$			18.8058i			0.879699i	−0.898071	+	0.439850i	$0.855032\pi$
$458$	5.32716	−	9.22692i	0.248922	−	0.431146i
$459$	−1.08412	+	1.87776i	−0.0506026	+	0.0876463i
$460$	−7.04115	−	12.1956i	−0.328295	−	0.568624i
$461$	−16.8952	−	9.75445i	−0.786888	−	0.454310i	0.0519777	−	0.998648i	$-0.483448\pi$
$461$	−16.8952	−	9.75445i	−0.786888	−	0.454310i	−0.838866	+	0.544338i	$0.816781\pi$
$462$	−13.7466	+	15.2802i	−0.639552	+	0.710898i
$463$	−7.04370			−0.327349			−0.163674	−	0.986514i	$-0.552335\pi$
$463$	−7.04370			−0.327349			−0.163674	+	0.986514i	$0.552335\pi$
$464$	17.2673			0.801615
$465$	17.3293	+	30.0152i	0.803627	+	1.39192i
$466$	−2.81891	+	1.62750i	−0.130583	+	0.0753923i
$467$	−24.2154			−1.12056			−0.560278	−	0.828304i	$-0.689306\pi$
$467$	−24.2154			−1.12056			−0.560278	+	0.828304i	$0.689306\pi$
$468$	7.30484			0.337666
$469$	−1.93381	−	3.34946i	−0.0892952	−	0.154664i
$470$	−20.3939	+	35.3232i	−0.940698	+	1.62934i
$471$	−15.6284	+	9.02308i	−0.720120	+	0.415762i
$472$	−11.7504	−	6.78409i	−0.540856	−	0.312263i
$473$	3.34244	−	15.7577i	0.153686	−	0.724539i
$474$		−	21.7220i		−	0.997727i
$475$	−20.5632	−	28.0372i	−0.943505	−	1.28644i
$476$	−8.85988			−0.406092
$477$	4.95920	+	2.86320i	0.227066	+	0.131097i
$478$	14.1958	+	8.19594i	0.649300	+	0.374873i
$479$	9.28461	−	5.36047i	0.424225	−	0.244926i	−0.272659	−	0.962111i	$-0.587903\pi$
$479$	9.28461	−	5.36047i	0.424225	−	0.244926i	0.696883	+	0.717185i	$0.254570\pi$
$480$	18.4503	+	10.6523i	0.842136	+	0.486207i
$481$	57.0441	−	32.9345i	2.60099	−	1.50168i
$482$	−5.13691			−0.233980
$483$	−11.5727			−0.526576
$484$	11.8106	+	5.24649i	0.536848	+	0.238477i
$485$	9.89558	−	5.71321i	0.449335	−	0.259424i
$486$			1.78181i			0.0808248i
$487$		−	4.83747i		−	0.219207i	−0.993975	−	0.109603i	$-0.965042\pi$
$487$		−	4.83747i		−	0.219207i	0.993975	−	0.109603i	$-0.0349581\pi$
$488$	−1.16137	+	0.670516i	−0.0525726	+	0.0303528i
$489$	10.3356	+	5.96726i	0.467392	+	0.269849i
$490$	16.3565	+	28.3303i	0.738911	+	1.27983i
$491$	−11.9467	−	6.89742i	−0.539146	−	0.311276i	0.205587	−	0.978639i	$-0.434090\pi$
$491$	−11.9467	−	6.89742i	−0.539146	−	0.311276i	−0.744733	+	0.667363i	$0.767423\pi$
$492$	−3.18216	−	1.83722i	−0.143463	−	0.0828284i
$493$		−	7.53404i		−	0.339316i
$494$	−48.0029	+	5.26334i	−2.15975	+	0.236809i
$495$	−3.69679	−	11.3612i	−0.166159	−	0.510649i
$496$	41.4061	+	23.9059i	1.85919	+	1.07340i
$497$	−22.6571	+	39.2432i	−1.01631	+	1.76030i
$498$	−3.35926	−	5.81842i	−0.150532	−	0.260730i
$499$	−8.35510	+	14.4715i	−0.374026	+	0.647831i	−0.990181	−	0.139793i	$-0.955356\pi$
$499$	−8.35510	+	14.4715i	−0.374026	+	0.647831i	0.616155	+	0.787625i	$0.288689\pi$
$500$	−6.29909	−	10.9103i	−0.281704	−	0.487926i
$501$			11.1039i			0.496088i
$502$	26.4564			1.18081
$503$	6.02685	−	3.47961i	0.268724	−	0.155148i	−0.359584	−	0.933113i	$-0.617081\pi$
$503$	6.02685	−	3.47961i	0.268724	−	0.155148i	0.628308	+	0.777965i	$0.283748\pi$
$504$	4.42842	−	2.55675i	0.197258	−	0.113887i
$505$			27.2191i			1.21123i
$506$	6.08428	+	18.6986i	0.270479	+	0.831255i
$507$	22.2210	−	12.8293i	0.986868	−	0.569768i
$508$	5.91608	−	10.2469i	0.262483	−	0.454635i
$509$	33.0633	−	19.0891i	1.46551	−	0.846110i	0.466249	−	0.884654i	$-0.345605\pi$
$509$	33.0633	−	19.0891i	1.46551	−	0.846110i	0.999257	+	0.0385435i	$0.0122718\pi$
$510$	6.95864	−	12.0527i	0.308134	−	0.533703i
$511$	−11.1260	+	19.2708i	−0.492186	+	0.852492i
$512$	14.7772			0.653068
$513$	−0.475090	−	4.33293i	−0.0209757	−	0.191304i
$514$			42.7594i			1.88604i
$515$	−28.4468	−	16.4238i	−1.25352	−	0.723719i
$516$	2.85306	−	4.94164i	0.125599	−	0.217543i
$517$	14.0957	−	15.6682i	0.619930	−	0.689087i
$518$	−32.8262	+	56.8567i	−1.44230	+	2.49814i
$519$	−3.89652	+	2.24966i	−0.171038	+	0.0987490i
$520$	32.9301			1.44408
$521$			35.0180i			1.53417i	0.641547	+	0.767083i	$0.278293\pi$
$521$			35.0180i			1.53417i	−0.641547	+	0.767083i	$0.721707\pi$
$522$	−3.09565	−	5.36182i	−0.135493	−	0.234680i
$523$	−18.2891	−	31.6777i	−0.799727	−	1.38517i	−0.919794	−	0.392403i	$-0.871644\pi$
$523$	−18.2891	−	31.6777i	−0.799727	−	1.38517i	0.120066	−	0.992766i	$-0.461689\pi$
$524$		−	3.55315i		−	0.155220i
$525$	−27.7431			−1.21081
$526$	34.7056	−	20.0373i	1.51323	−	0.873666i
$527$	10.4306	−	18.0663i	0.454362	−	0.786979i
$528$	−12.2530	−	11.0232i	−0.533241	−	0.479725i
$529$	5.96424	−	10.3304i	0.259315	−	0.449146i
$530$	−31.8315	−	18.3779i	−1.38267	−	0.798286i
$531$			9.22856i			0.400485i
$532$	14.3625	−	10.5338i	0.622692	−	0.456698i
$533$	−19.4458			−0.842293
$534$	10.6130	−	18.3823i	0.459271	−	0.795481i
$535$	6.70583	−	11.6148i	0.289918	−	0.502153i
$536$	1.41590	−	0.817470i	0.0611576	−	0.0353093i
$537$	9.30825	−	16.1224i	0.401681	−	0.695731i
$538$	25.1030	−	14.4932i	1.08227	−	0.624847i
$539$	−5.23020	−	16.0738i	−0.225281	−	0.692347i
$540$		−	4.23224i		−	0.182127i
$541$	10.2327	−	5.90788i	0.439940	−	0.253999i	−0.263632	−	0.964623i	$-0.584921\pi$
$541$	10.2327	−	5.90788i	0.439940	−	0.253999i	0.703572	+	0.710624i	$0.251587\pi$
$542$	−35.8768	+	20.7135i	−1.54104	+	0.889721i
$543$	−9.88046			−0.424011
$544$		−	12.8233i		−	0.549793i
$545$	15.3804	+	26.6397i	0.658825	+	1.14112i
$546$	−19.2658	+	33.3693i	−0.824498	+	1.42807i
$547$	−13.1589	−	22.7918i	−0.562633	−	0.974509i	−0.997266	−	0.0739010i	$-0.976455\pi$
$547$	−13.1589	−	22.7918i	−0.562633	−	0.974509i	0.434633	−	0.900608i	$-0.356878\pi$
$548$	4.67259	−	8.09316i	0.199603	−	0.345723i
$549$	0.789917	+	0.456059i	0.0337128	+	0.0194641i
$550$	14.5858	+	44.8260i	0.621940	+	1.91139i
$551$	8.95748	+	12.2132i	0.381601	+	0.520300i
$552$		−	4.89206i		−	0.208220i
$553$	36.7197	+	21.2001i	1.56148	+	0.901522i
$554$	−13.1503	−	7.59235i	−0.558704	−	0.322568i
$555$	−19.0814	−	33.0499i	−0.809960	−	1.40289i
$556$	16.7138	+	9.64971i	0.708822	+	0.409239i
$557$	−35.3752	+	20.4239i	−1.49890	+	0.865388i	−0.999999	−	0.00127347i	$-0.999595\pi$
$557$	−35.3752	+	20.4239i	−1.49890	+	0.865388i	−0.498897	+	0.866661i	$0.666261\pi$
$558$		−	17.1432i		−	0.725728i
$559$		−	30.1978i		−	1.27723i
$560$	−53.9200	+	31.1307i	−2.27853	+	1.31551i
$561$	−4.80964	+	5.34619i	−0.203063	+	0.225716i
$562$	32.8220			1.38451
$563$	−41.1465			−1.73412			−0.867059	−	0.498206i	$-0.833992\pi$
$563$	−41.1465			−1.73412			−0.867059	+	0.498206i	$0.833992\pi$
$564$	6.46551	−	3.73286i	0.272247	−	0.157182i
$565$	−27.6184	−	15.9455i	−1.16191	−	0.670832i
$566$	10.2683	−	5.92841i	0.431609	−	0.249190i
$567$	−3.01204	−	1.73900i	−0.126494	−	0.0730313i
$568$	−16.5891	−	9.57769i	−0.696061	−	0.401871i
$569$	26.8976			1.12761			0.563804	−	0.825909i	$-0.309338\pi$
$569$	26.8976			1.12761			0.563804	+	0.825909i	$0.309338\pi$
$570$	3.04945	+	27.8117i	0.127727	+	1.16490i
$571$			30.0947i			1.25942i	0.776829	+	0.629711i	$0.216827\pi$
$571$			30.0947i			1.25942i	−0.776829	+	0.629711i	$0.783173\pi$
$572$	23.7001	+	5.02715i	0.990951	+	0.210196i
$573$	−4.72903	−	2.73031i	−0.197558	−	0.114060i
$574$	16.7853	−	9.69097i	0.700603	−	0.404493i
$575$	−13.2708	+	22.9857i	−0.553432	+	0.958572i
$576$	−0.299505	−	0.518758i	−0.0124794	−	0.0216149i
$577$	−2.56278			−0.106690			−0.0533449	−	0.998576i	$-0.516988\pi$
$577$	−2.56278			−0.106690			−0.0533449	+	0.998576i	$0.516988\pi$
$578$	21.9140			0.911502
$579$	−3.39677	+	1.96112i	−0.141165	+	0.0815016i
$580$	7.35291	+	12.7356i	0.305313	+	0.528817i
$581$	13.1142			0.544069
$582$	−5.65185			−0.234277
$583$	14.1194	+	12.7024i	0.584766	+	0.526078i
$584$	−8.14625	−	4.70324i	−0.337094	−	0.194622i
$585$	−11.1989	−	19.3971i	−0.463017	−	0.801970i
$586$	−27.1526	+	47.0297i	−1.12166	+	1.94278i
$587$	−7.09318	+	12.2858i	−0.292767	+	0.507087i	−0.974463	−	0.224548i	$-0.927909\pi$
$587$	−7.09318	+	12.2858i	−0.292767	+	0.507087i	0.681696	+	0.731636i	$0.261243\pi$
$588$		−	5.98774i		−	0.246930i
$589$	4.57092	+	41.6879i	0.188342	+	1.71772i
$590$		−	59.2351i		−	2.43867i
$591$	4.70548	−	8.15013i	0.193558	−	0.335252i
$592$	−45.5926	−	26.3229i	−1.87384	−	1.08186i
$593$	10.3533	−	5.97747i	0.425158	−	0.245465i	−0.272124	−	0.962262i	$-0.587726\pi$
$593$	10.3533	−	5.97747i	0.425158	−	0.245465i	0.697282	+	0.716797i	$0.254393\pi$
$594$	−1.22624	+	5.78099i	−0.0503131	+	0.237197i
$595$	13.5829	+	23.5263i	0.556844	+	0.964483i
$596$		−	3.51591i		−	0.144017i
$597$			14.9780i			0.613010i
$598$	18.4314	+	31.9242i	0.753717	+	1.30548i
$599$	24.9348	−	14.3961i	1.01881	−	0.588210i	0.105050	−	0.994467i	$-0.466500\pi$
$599$	24.9348	−	14.3961i	1.01881	−	0.588210i	0.913759	+	0.406257i	$0.133166\pi$
$600$		−	11.7277i		−	0.478781i
$601$	20.1965			0.823831			0.411916	−	0.911222i	$-0.364860\pi$
$601$	20.1965			0.823831			0.411916	+	0.911222i	$0.364860\pi$
$602$	15.0493	+	26.0661i	0.613363	+	1.06238i
$603$	−0.963041	−	0.556012i	−0.0392181	−	0.0226426i
$604$	12.2861	+	21.2802i	0.499915	+	0.865878i
$605$	−4.17528	−	39.4049i	−0.169749	−	1.60204i
$606$	6.73168	−	11.6596i	0.273456	−	0.473640i
$607$	16.8240			0.682865			0.341432	−	0.939906i	$-0.389088\pi$
$607$	16.8240			0.682865			0.341432	+	0.939906i	$0.389088\pi$
$608$	15.2460	+	20.7874i	0.618308	+	0.843041i
$609$	12.0851			0.489712
$610$	−5.07022	−	2.92729i	−0.205287	−	0.118523i
$611$	19.7550	−	34.2167i	0.799202	−	1.38426i
$612$	−2.20611	+	1.27370i	−0.0891768	+	0.0514863i
$613$	−7.09627	−	4.09703i	−0.286616	−	0.165478i	0.349799	−	0.936825i	$-0.386250\pi$
$613$	−7.09627	−	4.09703i	−0.286616	−	0.165478i	−0.636415	+	0.771347i	$0.719583\pi$
$614$	−12.6945	−	21.9875i	−0.512307	−	0.887341i
$615$			11.2664i			0.454306i
$616$	16.1273	−	5.24761i	0.649787	−	0.211432i
$617$	11.2834	+	19.5434i	0.454252	+	0.786787i	0.998645	−	0.0520429i	$-0.0165733\pi$
$617$	11.2834	+	19.5434i	0.454252	+	0.786787i	−0.544393	+	0.838830i	$0.683240\pi$
$618$	8.12369	+	14.0706i	0.326783	+	0.566004i
$619$	46.9994			1.88907			0.944533	−	0.328416i	$-0.106515\pi$
$619$	46.9994			1.88907			0.944533	+	0.328416i	$0.106515\pi$
$620$			40.7191i			1.63532i
$621$	−2.88160	+	1.66369i	−0.115635	+	0.0667618i
$622$	2.24905	−	3.89547i	0.0901787	−	0.156194i
$623$	20.7161	+	35.8813i	0.829973	+	1.43756i
$624$	−26.7584	−	15.4489i	−1.07119	−	0.618453i
$625$	0.627779	−	1.08734i	0.0251111	−	0.0434938i
$626$	−49.9650			−1.99700
$627$	1.44050	−	14.3849i	0.0575280	−	0.574477i
$628$	−21.2018			−0.846044
$629$	−11.4852	+	19.8929i	−0.457943	+	0.793181i
$630$	19.3333	+	11.1621i	0.770258	+	0.444708i
$631$	19.2213	+	33.2923i	0.765189	+	1.32535i	0.940147	+	0.340770i	$0.110688\pi$
$631$	19.2213	+	33.2923i	0.765189	+	1.32535i	−0.174958	+	0.984576i	$0.555979\pi$
$632$	−8.96182	+	15.5223i	−0.356482	+	0.617445i
$633$	4.94931	−	2.85748i	0.196717	−	0.113575i
$634$		−	4.12129i		−	0.163677i
$635$	−36.2793			−1.43970
$636$	3.36387	+	5.82639i	0.133386	+	0.231031i
$637$	−15.8441	−	27.4428i	−0.627767	−	1.08732i
$638$	−6.35366	−	19.5265i	−0.251544	−	0.773062i
$639$			13.0288i			0.515410i
$640$	−19.3821	−	33.5708i	−0.766145	−	1.32700i
$641$	25.8291	+	14.9124i	1.02019	+	0.589006i	0.914158	−	0.405357i	$-0.132853\pi$
$641$	25.8291	+	14.9124i	1.02019	+	0.589006i	0.106029	+	0.994363i	$0.466186\pi$
$642$	−5.74505	+	3.31690i	−0.226739	+	0.130908i
$643$	−10.2010	+	17.6687i	−0.402289	+	0.696784i	−0.994002	−	0.109364i	$-0.965118\pi$
$643$	−10.2010	+	17.6687i	−0.402289	+	0.696784i	0.591713	+	0.806149i	$0.298452\pi$
$644$	−11.7748	−	6.79817i	−0.463991	−	0.267885i
$645$	−17.4958			−0.688898
$646$	13.5795	−	9.95953i	0.534277	−	0.391852i
$647$	39.1357			1.53858			0.769291	−	0.638899i	$-0.220610\pi$
$647$	39.1357			1.53858			0.769291	+	0.638899i	$0.220610\pi$
$648$	0.735119	−	1.27326i	0.0288782	−	0.0500185i
$649$	−6.35105	+	29.9415i	−0.249300	+	1.17531i
$650$	44.1855	+	76.5315i	1.73310	+	3.00181i
$651$	28.9794	+	16.7313i	1.13579	+	0.655750i
$652$	7.01072	+	12.1429i	0.274561	+	0.475554i
$653$	3.12671			0.122358			0.0611788	−	0.998127i	$-0.480514\pi$
$653$	3.12671			0.122358			0.0611788	+	0.998127i	$0.480514\pi$
$654$		−	15.2152i		−	0.594962i
$655$	−9.43493	+	5.44726i	−0.368653	+	0.212842i
$656$	7.77105	+	13.4599i	0.303409	+	0.525519i
$657$			6.39793i			0.249607i
$658$			39.3802i			1.53520i
$659$	1.72814	+	2.99322i	0.0673186	+	0.116599i	0.897720	−	0.440566i	$-0.145222\pi$
$659$	1.72814	+	2.99322i	0.0673186	+	0.116599i	−0.830402	+	0.557165i	$0.811889\pi$
$660$	2.91261	−	13.7312i	0.113373	−	0.534488i
$661$	3.32617	−	1.92036i	0.129373	−	0.0746934i	−0.433917	−	0.900953i	$-0.642869\pi$
$661$	3.32617	−	1.92036i	0.129373	−	0.0746934i	0.563290	+	0.826259i	$0.309536\pi$
$662$	35.6267	+	20.5691i	1.38467	+	0.799440i
$663$	−6.74066	+	11.6752i	−0.261785	+	0.453426i
$664$			5.54370i			0.215137i
$665$	−49.9900	−	21.9885i	−1.93853	−	0.852679i
$666$			18.8764i			0.731447i
$667$	5.78086	−	10.0127i	0.223836	−	0.387695i
$668$	−6.52282	+	11.2979i	−0.252375	+	0.437127i
$669$	−11.5084	−	19.9332i	−0.444942	−	0.770661i
$670$	6.18144	+	3.56886i	0.238810	+	0.137877i
$671$	2.24898	+	2.02327i	0.0868210	+	0.0781076i
$672$	20.5693			0.793479
$673$	−19.5586			−0.753927			−0.376964	−	0.926228i	$-0.623032\pi$
$673$	−19.5586			−0.753927			−0.376964	+	0.926228i	$0.623032\pi$
$674$	−18.2435	−	31.5987i	−0.702715	−	1.21714i
$675$	−6.90804	+	3.98836i	−0.265891	+	0.153512i
$676$	30.1453			1.15944
$677$	42.2348			1.62322			0.811608	−	0.584203i	$-0.198593\pi$
$677$	42.2348			1.62322			0.811608	+	0.584203i	$0.198593\pi$
$678$	7.88711	+	13.6609i	0.302903	+	0.524643i
$679$	5.51605	−	9.55409i	0.211687	−	0.366652i
$680$	−9.94513	+	5.74182i	−0.381378	+	0.220189i
$681$	12.2990	+	7.10083i	0.471299	+	0.272104i
$682$	11.7978	−	55.6199i	0.451762	−	2.12980i
$683$		−	16.2903i		−	0.623330i	−0.950192	−	0.311665i	$-0.899113\pi$
$683$		−	16.2903i		−	0.623330i	0.950192	−	0.311665i	$-0.100887\pi$
$684$	2.06192	−	4.68768i	0.0788394	−	0.179238i
$685$	−28.6538			−1.09480
$686$	−10.2157	−	5.89803i	−0.390037	−	0.225188i
$687$	5.17838	+	2.98974i	0.197568	+	0.114066i
$688$	−20.9021	+	12.0678i	−0.796883	+	0.460081i
$689$	30.8343	+	17.8022i	1.17469	+	0.678210i
$690$	18.4961	−	10.6787i	0.704133	−	0.406531i
$691$	−51.1870			−1.94724			−0.973622	−	0.228166i	$-0.926727\pi$
$691$	−51.1870			−1.94724			−0.973622	+	0.228166i	$0.926727\pi$
$692$	−5.28608			−0.200947
$693$	−8.57562	−	7.71497i	−0.325761	−	0.293067i
$694$	7.74760	−	4.47308i	0.294095	−	0.169796i
$695$		−	59.1751i		−	2.24464i
$696$			5.10866i			0.193643i
$697$	5.87278	−	3.39065i	0.222448	−	0.128430i
$698$	−1.76346	−	1.01813i	−0.0667478	−	0.0385368i
$699$	−0.913393	−	1.58204i	−0.0345477	−	0.0598384i
$700$	−28.2276	−	16.2972i	−1.06690	−	0.615976i
$701$	22.0957	+	12.7570i	0.834543	+	0.481823i	0.855406	−	0.517959i	$-0.173308\pi$
$701$	22.0957	+	12.7570i	0.834543	+	0.481823i	−0.0208628	+	0.999782i	$0.506641\pi$
$702$			11.0786i			0.418135i
$703$	−5.03307	−	45.9028i	−0.189826	−	1.73126i
$704$	−0.614719	−	1.88920i	−0.0231681	−	0.0712018i
$705$	−19.8243	−	11.4456i	−0.746625	−	0.431064i
$706$	−16.8204	+	29.1338i	−0.633045	+	1.09647i
$707$	13.1399	+	22.7590i	0.494176	+	0.855938i
$708$	−5.42115	+	9.38971i	−0.203739	+	0.352887i
$709$	−5.16812	−	8.95144i	−0.194093	−	0.336178i	0.752510	−	0.658581i	$-0.228843\pi$
$709$	−5.16812	−	8.95144i	−0.194093	−	0.336178i	−0.946603	+	0.322402i	$0.895510\pi$
$710$		−	83.6273i		−	3.13848i
$711$	12.1910			0.457197
$712$	−15.1679	+	8.75720i	−0.568442	+	0.328190i
$713$	27.7244	−	16.0067i	1.03829	−	0.599456i
$714$		−	13.4370i		−	0.502867i
$715$	−22.9852	−	70.6396i	−0.859597	−	2.64177i
$716$	18.9416	−	10.9359i	0.707881	−	0.408695i
$717$	−4.59977	+	7.96703i	−0.171781	+	0.297534i
$718$	17.7515	−	10.2488i	0.662481	−	0.382484i
$719$	−2.07525	+	3.59444i	−0.0773938	+	0.134050i	−0.902125	−	0.431475i	$-0.857993\pi$
$719$	−2.07525	+	3.59444i	−0.0773938	+	0.134050i	0.824731	+	0.565525i	$0.191327\pi$
$720$	−8.95073	+	15.5031i	−0.333574	+	0.577767i
$721$	−31.7140			−1.18109
$722$	−10.1720	+	32.2902i	−0.378564	+	1.20172i
$723$		−	2.88297i		−	0.107219i
$724$	−10.0530	−	5.80410i	−0.373617	−	0.215708i
$725$	13.8584	−	24.0035i	0.514688	−	0.891466i
$726$	−7.95690	+	17.9122i	−0.295308	+	0.664784i
$727$	10.5694	−	18.3067i	0.391997	−	0.678959i	−0.600716	−	0.799463i	$-0.705118\pi$
$727$	10.5694	−	18.3067i	0.391997	−	0.678959i	0.992713	+	0.120504i	$0.0384510\pi$
$728$	27.5342	−	15.8969i	1.02048	−	0.589177i
$729$	−1.00000			−0.0370370
$730$		−	41.0662i		−	1.51993i
$731$	5.26541	+	9.11995i	0.194748	+	0.337313i
$732$	0.535807	+	0.928046i	0.0198040	+	0.0343016i
$733$		−	41.4186i		−	1.52983i	−0.644130	−	0.764916i	$-0.722780\pi$
$733$		−	41.4186i		−	1.52983i	0.644130	−	0.764916i	$-0.277220\pi$
$734$	17.8510			0.658894
$735$	−15.8997	+	9.17969i	−0.586469	+	0.338598i
$736$	9.83928	−	17.0421i	0.362681	−	0.628181i
$737$	−2.74188	−	2.46671i	−0.100999	−	0.0908623i
$738$	2.78636	−	4.82611i	0.102567	−	0.177652i
$739$	−15.2936	−	8.82978i	−0.562585	−	0.324809i	0.191597	−	0.981474i	$-0.438633\pi$
$739$	−15.2936	−	8.82978i	−0.562585	−	0.324809i	−0.754183	+	0.656665i	$0.771967\pi$
$740$		−	44.8361i		−	1.64821i
$741$	−2.95392	−	26.9404i	−0.108515	−	0.989682i
$742$	−35.4874			−1.30278
$743$	−4.45103	+	7.70941i	−0.163292	+	0.282831i	−0.936048	−	0.351874i	$-0.885545\pi$
$743$	−4.45103	+	7.70941i	−0.163292	+	0.282831i	0.772755	+	0.634704i	$0.218878\pi$
$744$	−7.07272	+	12.2503i	−0.259298	+	0.449118i
$745$	−9.33604	+	5.39017i	−0.342046	+	0.197480i
$746$	−23.0933	+	39.9987i	−0.845505	+	1.46446i
$747$	3.26544	−	1.88531i	0.119476	−	0.0689797i
$748$	−8.03415	+	2.61421i	−0.293758	+	0.0955848i
$749$		−	12.9488i		−	0.473140i
$750$	16.5468	−	9.55329i	0.604203	−	0.348837i
$751$	11.3368	−	6.54531i	0.413686	−	0.238842i	−0.278686	−	0.960382i	$-0.589899\pi$
$751$	11.3368	−	6.54531i	0.413686	−	0.238842i	0.692372	+	0.721540i	$0.256566\pi$
$752$	−31.5784			−1.15155
$753$			14.8480i			0.541091i
$754$	−19.2475	−	33.3376i	−0.700953	−	1.21409i
$755$	37.6712	−	65.2484i	1.37099	−	2.37463i
$756$	−2.04309	−	3.53874i	−0.0743066	−	0.128703i
$757$	9.54361	−	16.5300i	0.346868	−	0.600794i	−0.638823	−	0.769354i	$-0.720578\pi$
$757$	9.54361	−	16.5300i	0.346868	−	0.600794i	0.985691	+	0.168560i	$0.0539117\pi$
$758$	−7.65704	−	4.42080i	−0.278116	−	0.160571i
$759$	−10.4941	+	3.41465i	−0.380913	+	0.123944i
$760$	9.29509	−	21.1320i	0.337169	−	0.766538i
$761$			30.3068i			1.09862i	0.835618	+	0.549310i	$0.185110\pi$
$761$			30.3068i			1.09862i	−0.835618	+	0.549310i	$0.814890\pi$
$762$	15.5406	+	8.97240i	0.562978	+	0.325036i
$763$	25.7204	+	14.8497i	0.931140	+	0.537594i
$764$	−3.20774	−	5.55597i	−0.116052	−	0.201008i
$765$	6.76429	+	3.90537i	0.244564	+	0.141199i
$766$	9.53284	−	5.50379i	0.344435	−	0.198860i
$767$			57.3795i			2.07185i
$768$			20.3720i			0.735110i
$769$	−22.4028	+	12.9343i	−0.807867	+	0.466422i	−0.846214	−	0.532842i	$-0.821124\pi$
$769$	−22.4028	+	12.9343i	−0.807867	+	0.466422i	0.0383479	+	0.999264i	$0.487790\pi$
$770$	55.0441	+	49.5198i	1.98365	+	1.78457i
$771$	−23.9977			−0.864256
$772$	−4.60811			−0.165850
$773$	30.6946	−	17.7215i	1.10401	−	0.637400i	0.166738	−	0.986001i	$-0.446677\pi$
$773$	30.6946	−	17.7215i	1.10401	−	0.637400i	0.937271	+	0.348602i	$0.113343\pi$
$774$	7.49455	+	4.32698i	0.269386	+	0.155530i
$775$	66.4635	−	38.3727i	2.38744	−	1.37839i
$776$	4.03875	+	2.33177i	0.144983	+	0.0837057i
$777$	−31.9094	−	18.4229i	−1.14474	−	0.660918i
$778$	34.7677			1.24648
$779$	−5.48893	+	12.4788i	−0.196661	+	0.447101i
$780$		−	26.3144i		−	0.942206i
$781$	−8.96632	+	42.2710i	−0.320840	+	1.51258i
$782$	−11.1328	−	6.42755i	−0.398110	−	0.229849i
$783$	3.00919	−	1.73736i	0.107540	−	0.0620880i
$784$	−12.6634	+	21.9337i	−0.452265	+	0.783346i
$785$	32.5040	+	56.2986i	1.16012	+	2.00938i
$786$	5.38875			0.192210
$787$	5.27914			0.188181			0.0940905	−	0.995564i	$-0.470006\pi$
$787$	5.27914			0.188181			0.0940905	+	0.995564i	$0.470006\pi$
$788$	9.57530	−	5.52830i	0.341106	−	0.196938i
$789$	11.2454	+	19.4777i	0.400348	+	0.693423i
$790$	−78.2498			−2.78400
$791$	−30.7905			−1.09478
$792$	3.26130	−	3.62512i	0.115885	−	0.128813i
$793$	4.91139	+	2.83559i	0.174409	+	0.100695i
$794$	13.1075	+	22.7028i	0.465168	+	0.805694i
$795$	10.3142	−	17.8646i	0.365805	−	0.633594i
$796$	−8.79858	+	15.2396i	−0.311857	+	0.540153i
$797$			33.8975i			1.20071i	0.799733	+	0.600356i	$0.204975\pi$
$797$			33.8975i			1.20071i	−0.799733	+	0.600356i	$0.795025\pi$
$798$	15.9757	+	21.7823i	0.565534	+	0.771086i
$799$			13.7782i			0.487439i
$800$	23.5876	−	40.8549i	0.833948	−	1.44444i
$801$	10.3166	+	5.95631i	0.364520	+	0.210456i
$802$	15.8476	−	9.14963i	0.559599	−	0.323085i
$803$	−4.40302	+	20.7577i	−0.155379	+	0.732523i
$804$	−0.653239	−	1.13144i	−0.0230379	−	0.0399029i
$805$			41.6885i			1.46933i
$806$		−	106.589i		−	3.75445i
$807$	8.13397	+	14.0884i	0.286329	+	0.495937i
$808$	−9.62077	+	5.55455i	−0.338457	+	0.195408i
$809$		−	18.6363i		−	0.655218i	−0.944813	−	0.327609i	$-0.893757\pi$
$809$		−	18.6363i		−	0.655218i	0.944813	−	0.327609i	$-0.106243\pi$
$810$	6.41867			0.225529
$811$	−3.63263	−	6.29190i	−0.127559	−	0.220938i	0.795171	−	0.606385i	$-0.207381\pi$
$811$	−3.63263	−	6.29190i	−0.127559	−	0.220938i	−0.922730	+	0.385446i	$0.874047\pi$
$812$	12.2961	+	7.09916i	0.431509	+	0.249132i
$813$	−11.6249	−	20.1350i	−0.407704	−	0.706165i
$814$	−12.9907	+	61.2435i	−0.455323	+	2.14658i
$815$	21.4960	−	37.2322i	0.752972	−	1.30419i
$816$	10.7749			0.377199
$817$	−19.3786	−	8.52385i	−0.677971	−	0.298212i
$818$	54.7901			1.91569
$819$	−18.7277	−	10.8124i	−0.654398	−	0.377817i
$820$	−6.61827	+	11.4632i	−0.231120	+	0.400311i
$821$	−20.1307	+	11.6225i	−0.702568	+	0.405628i	−0.808303	−	0.588767i	$-0.799614\pi$
$821$	−20.1307	+	11.6225i	−0.702568	+	0.405628i	0.105735	+	0.994394i	$0.466280\pi$
$822$	12.2742	+	7.08651i	0.428111	+	0.247170i
$823$	14.6458	+	25.3673i	0.510521	+	0.884248i	0.999926	+	0.0121910i	$0.00388062\pi$
$823$	14.6458	+	25.3673i	0.510521	+	0.884248i	−0.489405	+	0.872057i	$0.662786\pi$
$824$		−	13.4063i		−	0.467030i
$825$	−25.1575	+	8.18591i	−0.875871	+	0.284997i
$826$	−28.5954	−	49.5288i	−0.994963	−	1.72333i
$827$	−15.5028	−	26.8516i	−0.539085	−	0.933722i	−0.998954	−	0.0457355i	$-0.985437\pi$
$827$	−15.5028	−	26.8516i	−0.539085	−	0.933722i	0.459869	−	0.887987i	$-0.347896\pi$
$828$	−3.90923			−0.135855
$829$		−	40.6909i		−	1.41325i	−0.707586	−	0.706627i	$-0.750216\pi$
$829$		−	40.6909i		−	1.41325i	0.707586	−	0.706627i	$-0.249784\pi$
$830$	−20.9598	+	12.1012i	−0.727526	+	0.420037i
$831$	4.26102	−	7.38030i	0.147813	−	0.256020i
$832$	−1.86220	−	3.22543i	−0.0645602	−	0.111822i
$833$	9.57007	+	5.52529i	0.331583	+	0.191440i
$834$	−14.6349	+	25.3483i	−0.506764	+	0.877742i
$835$	40.0000			1.38426
$836$	9.91580	−	13.7899i	0.342945	−	0.476933i
$837$	9.62118			0.332557
$838$	−1.02344	+	1.77264i	−0.0353540	+	0.0612350i
$839$	15.4372	+	8.91270i	0.532953	+	0.307701i	0.742218	−	0.670158i	$-0.233774\pi$
$839$	15.4372	+	8.91270i	0.532953	+	0.307701i	−0.209265	+	0.977859i	$0.567107\pi$
$840$	−9.21024	−	15.9526i	−0.317783	−	0.550417i
$841$	8.46319	−	14.6587i	0.291834	−	0.505471i
$842$	25.5407	−	14.7459i	0.880190	−	0.508178i
$843$			18.4206i			0.634438i
$844$	6.71431			0.231116
$845$	−46.2152	−	80.0471i	−1.58985	−	2.75370i
$846$	5.66131	+	9.80567i	0.194640	+	0.337126i
$847$	−22.5137	−	30.9324i	−0.773579	−	1.06285i
$848$		−	28.4569i		−	0.977213i
$849$	3.32718	+	5.76284i	0.114188	+	0.197780i
$850$	−26.6887	−	15.4087i	−0.915414	−	0.528514i
$851$	−30.5275	+	17.6251i	−1.04647	+	0.604180i
$852$	−7.65351	+	13.2563i	−0.262205	+	0.454152i
$853$	31.0229	+	17.9111i	1.06220	+	0.613263i	0.926041	−	0.377424i	$-0.123190\pi$
$853$	31.0229	+	17.9111i	1.06220	+	0.613263i	0.136162	+	0.990687i	$0.456523\pi$
$854$	−5.65255			−0.193426
$855$	−15.6086	+	1.71143i	−0.533803	+	0.0585296i
$856$	5.47379			0.187090
$857$	23.2754	−	40.3142i	0.795073	−	1.37711i	−0.127720	−	0.991810i	$-0.540766\pi$
$857$	23.2754	−	40.3142i	0.795073	−	1.37711i	0.922793	−	0.385296i	$-0.125901\pi$
$858$	−7.62425	+	35.9439i	−0.260287	+	1.22710i
$859$	12.6043	+	21.8313i	0.430053	+	0.744874i	0.996877	−	0.0789650i	$-0.0251615\pi$
$859$	12.6043	+	21.8313i	0.430053	+	0.744874i	−0.566824	+	0.823839i	$0.691828\pi$
$860$	−17.8014	−	10.2776i	−0.607021	−	0.350464i
$861$	5.43882	+	9.42031i	0.185354	+	0.321043i
$862$	−11.9530			−0.407122
$863$			17.2204i			0.586190i	0.956083	+	0.293095i	$0.0946852\pi$
$863$			17.2204i			0.586190i	−0.956083	+	0.293095i	$0.905315\pi$
$864$	5.12177	−	2.95706i	0.174246	−	0.100601i
$865$	8.10398	+	14.0365i	0.275544	+	0.477256i
$866$		−	57.7029i		−	1.96082i
$867$			12.2987i			0.417686i
$868$	19.6570	+	34.0469i	0.667201	+	1.15563i
$869$	39.5529	+	8.38976i	1.34174	+	0.284603i
$870$	−19.3150	+	11.1515i	−0.654840	+	0.378072i
$871$	−5.98780	−	3.45706i	−0.202889	−	0.117138i
$872$	−6.27731	+	10.8726i	−0.212577	+	0.368194i
$873$		−	3.17196i		−	0.107355i
$874$	25.6890	−	2.81671i	0.868945	−	0.0952766i
$875$			37.2950i			1.26080i
$876$	−3.75835	+	6.50965i	−0.126983	+	0.219941i
$877$	−4.97468	+	8.61640i	−0.167983	+	0.290955i	−0.937711	−	0.347417i	$-0.887059\pi$
$877$	−4.97468	+	8.61640i	−0.167983	+	0.290955i	0.769728	+	0.638372i	$0.220392\pi$
$878$	−24.4603	−	42.3665i	−0.825496	−	1.42980i
$879$	−26.3943	−	15.2387i	−0.890257	−	0.513990i
$880$	−39.7093	+	44.1391i	−1.33860	+	1.48793i
$881$	−43.7495			−1.47396			−0.736979	−	0.675916i	$-0.763748\pi$
$881$	−43.7495			−1.47396			−0.736979	+	0.675916i	$0.763748\pi$
$882$	9.08109			0.305776
$883$	−26.6560	−	46.1696i	−0.897047	−	1.55373i	−0.831250	−	0.555898i	$-0.812374\pi$
$883$	−26.6560	−	46.1696i	−0.897047	−	1.55373i	−0.0657967	−	0.997833i	$-0.520959\pi$
$884$	−13.7167	+	7.91936i	−0.461343	+	0.266357i
$885$	33.2442			1.11749
$886$	14.5589			0.489116
$887$	22.3944	+	38.7882i	0.751929	+	1.30238i	0.946887	+	0.321567i	$0.104210\pi$
$887$	22.3944	+	38.7882i	0.751929	+	1.30238i	−0.194958	+	0.980812i	$0.562457\pi$
$888$	7.78781	−	13.4889i	0.261342	−	0.452657i
$889$	−30.3345	+	17.5136i	−1.01739	+	0.587389i
$890$	−66.2191	−	38.2316i	−2.21967	−	1.28153i
$891$	−3.24444	−	0.688195i	−0.108693	−	0.0230554i
$892$		−	27.0417i		−	0.905423i
$893$	−16.3814	−	22.3355i	−0.548183	−	0.747428i
$894$	5.33227			0.178338
$895$	−58.0779	−	33.5313i	−1.94133	−	1.12083i
$896$	−32.4123	−	18.7133i	−1.08282	−	0.625166i
$897$	−17.9167	+	10.3442i	−0.598220	+	0.345382i
$898$	−27.5497	−	15.9058i	−0.919345	−	0.530784i
$899$	−28.9519	+	16.7154i	−0.965601	+	0.557490i
$900$	−9.37156			−0.312385
$901$	−12.4163			−0.413645
$902$	12.3615	−	13.7405i	0.411592	−	0.457508i
$903$	−14.6290	+	8.44604i	−0.486822	+	0.281067i
$904$		−	13.0159i		−	0.432902i
$905$			35.5926i			1.18314i
$906$	−32.2738	+	18.6333i	−1.07223	+	0.619049i
$907$	19.7057	+	11.3771i	0.654316	+	0.377770i	0.790108	−	0.612968i	$-0.210024\pi$
$907$	19.7057	+	11.3771i	0.654316	+	0.377770i	−0.135792	+	0.990737i	$0.543358\pi$
$908$	8.34251	+	14.4497i	0.276856	+	0.479529i
$909$	6.54367	+	3.77799i	0.217040	+	0.125308i
$910$	120.207	+	69.4014i	3.98482	+	2.30064i
$911$			13.6716i			0.452961i	0.974016	+	0.226480i	$0.0727219\pi$
$911$			13.6716i			0.452961i	−0.974016	+	0.226480i	$0.927278\pi$
$912$	−17.4669	+	12.8107i	−0.578388	+	0.424205i
$913$	11.8920	−	3.86950i	0.393568	−	0.128062i
$914$	−29.0192	−	16.7542i	−0.959870	−	0.554181i
$915$	1.64287	−	2.84554i	0.0543116	−	0.0940705i
$916$	3.51254	+	6.08390i	0.116058	+	0.201018i
$917$	−5.25928	+	9.10933i	−0.173677	+	0.300817i
$918$	−1.93171	−	3.34582i	−0.0637559	−	0.110429i
$919$			7.37744i			0.243359i	0.992569	+	0.121680i	$0.0388281\pi$
$919$			7.37744i			0.243359i	−0.992569	+	0.121680i	$0.961172\pi$
$920$	−17.6228			−0.581005
$921$	12.3399	−	7.12446i	0.406614	−	0.234759i
$922$	30.1041	−	17.3806i	0.991427	−	0.572400i
$923$			81.0076i			2.66640i
$924$	−4.19335	−	12.8873i	−0.137951	−	0.423960i
$925$	−73.1834	+	42.2524i	−2.40625	+	1.38925i
$926$	6.27529	−	10.8691i	0.206219	−	0.357181i
$927$	−7.89681	+	4.55922i	−0.259365	+	0.149745i
$928$	−10.2749	+	17.7967i	−0.337291	+	0.584205i
$929$	−1.09097	+	1.88962i	−0.0357936	+	0.0619964i	−0.883367	−	0.468681i	$-0.844729\pi$
$929$	−1.09097	+	1.88962i	−0.0357936	+	0.0619964i	0.847574	+	0.530678i	$0.178063\pi$
$930$	−61.7552			−2.02503
$931$	−22.0830	+	2.42131i	−0.723740	+	0.0793554i
$932$		−	2.14623i		−	0.0703019i
$933$	2.18624	+	1.26222i	0.0715742	+	0.0413234i
$934$	21.5737	−	37.3668i	0.705913	−	1.22268i
$935$	19.2587	+	17.3259i	0.629826	+	0.566617i
$936$	4.57068	−	7.91665i	0.149397	−	0.258764i
$937$	−7.22771	+	4.17292i	−0.236119	+	0.136323i	−0.613392	−	0.789779i	$-0.710195\pi$
$937$	−7.22771	+	4.17292i	−0.236119	+	0.136323i	0.377273	+	0.926102i	$0.376862\pi$
$938$	6.89140			0.225012
$939$		−	28.0417i		−	0.915105i
$940$	−13.4470	−	23.2908i	−0.438592	−	0.759663i
$941$	14.4273	+	24.9888i	0.470316	+	0.814611i	0.999424	−	0.0339435i	$-0.0108066\pi$
$941$	14.4273	+	24.9888i	0.470316	+	0.814611i	−0.529108	+	0.848555i	$0.677473\pi$
$942$		−	32.1549i		−	1.04766i
$943$	10.4066			0.338885
$944$	39.7164	−	22.9303i	1.29266	−	0.746318i
$945$	−6.26445	+	10.8503i	−0.203783	+	0.352962i
$946$	21.3378	+	19.1963i	0.693752	+	0.624127i
$947$	−24.6877	+	42.7604i	−0.802243	+	1.38953i	0.115894	+	0.993262i	$0.463027\pi$
$947$	−24.6877	+	42.7604i	−0.802243	+	1.38953i	−0.918137	+	0.396264i	$0.870306\pi$
$948$	12.4038	+	7.16137i	0.402858	+	0.232590i
$949$			39.7798i			1.29131i
$950$	61.5841	−	6.75247i	1.99805	−	0.219079i
$951$	2.31297			0.0750033
$952$	−5.54368	+	9.60193i	−0.179672	+	0.311200i
$953$	11.6491	−	20.1769i	0.377352	−	0.653592i	−0.613324	−	0.789831i	$-0.710168\pi$
$953$	11.6491	−	20.1769i	0.377352	−	0.653592i	0.990676	+	0.136239i	$0.0435014\pi$
$954$	−8.83638	+	5.10169i	−0.286088	+	0.165173i
$955$	−9.83544	+	17.0355i	−0.318267	+	0.551255i
$956$	−9.36018	+	5.40410i	−0.302730	+	0.174781i
$957$	10.9588	−	3.56584i	0.354247	−	0.115267i
$958$			19.1027i			0.617181i
$959$	−23.9586	+	13.8325i	−0.773662	+	0.446674i
$960$	−1.86873	+	1.07891i	−0.0603131	+	0.0348218i
$961$	−61.5671			−1.98603
$962$			117.366i			3.78404i
$963$	−1.86153	−	3.22427i	−0.0599870	−	0.103901i
$964$	1.69355	−	2.93331i	0.0545455	−	0.0944756i
$965$	7.06460	+	12.2362i	0.227418	+	0.393899i
$966$	10.3102	−	17.8578i	0.331725	−	0.574565i
$967$	0.0438491	+	0.0253163i	0.00141009	+	0.000814116i	0.500705	−	0.865618i	$-0.333074\pi$
$967$	0.0438491	+	0.0253163i	0.00141009	+	0.000814116i	−0.499295	+	0.866432i	$0.666408\pi$
$968$	13.0759	−	9.51708i	0.420275	−	0.305891i
$969$	5.58954	+	7.62114i	0.179562	+	0.244826i
$970$			20.3598i			0.653713i
$971$	24.5171	+	14.1549i	0.786790	+	0.454253i	0.838831	−	0.544392i	$-0.183239\pi$
$971$	24.5171	+	14.1549i	0.786790	+	0.454253i	−0.0520415	+	0.998645i	$0.516573\pi$
$972$	−1.01746	−	0.587432i	−0.0326351	−	0.0188419i
$973$	−28.5665	−	49.4786i	−0.915800	−	1.58621i
$974$	7.46469	+	4.30974i	0.239184	+	0.138093i
$975$	−42.9514	+	24.7980i	−1.37555	+	0.794172i
$976$		−	4.53270i		−	0.145088i
$977$		−	14.1407i		−	0.452401i	−0.974081	−	0.226201i	$-0.927370\pi$
$977$		−	14.1407i		−	0.452401i	0.974081	−	0.226201i	$-0.0726305\pi$
$978$	−18.4161	+	10.6326i	−0.588883	+	0.339992i
$979$	29.3726	+	26.4247i	0.938752	+	0.844539i
$980$	−21.5698			−0.689021
$981$	8.53917			0.272635
$982$	21.2868	−	12.2899i	0.679288	−	0.392187i
$983$	−22.4388	−	12.9550i	−0.715686	−	0.413202i	0.0974767	−	0.995238i	$-0.468923\pi$
$983$	−22.4388	−	12.9550i	−0.715686	−	0.413202i	−0.813163	+	0.582036i	$0.802256\pi$
$984$	−3.98220	+	2.29912i	−0.126948	+	0.0732933i
$985$	−29.3594	−	16.9507i	−0.935468	−	0.540093i
$986$	11.6258	+	6.71214i	0.370240	+	0.213758i
$987$	−22.1011			−0.703487
$988$	12.8202	−	29.1461i	0.407864	−	0.927261i
$989$			16.1605i			0.513876i
$990$	20.8250	+	4.41730i	0.661861	+	0.140391i
$991$	0.113215	+	0.0653646i	0.00359639	+	0.00207638i	0.501797	−	0.864985i	$-0.332672\pi$
$991$	0.113215	+	0.0653646i	0.00359639	+	0.00207638i	−0.498201	+	0.867062i	$0.666006\pi$
$992$	−49.2775	+	28.4504i	−1.56456	+	0.903300i
$993$	−11.5439	+	19.9946i	−0.366334	+	0.634510i
$994$	−40.3707	−	69.9241i	−1.28048	−	2.21786i
$995$	53.9557			1.71051
$996$	4.42996			0.140369
$997$	15.0552	−	8.69214i	0.476804	−	0.275283i	−0.242280	−	0.970206i	$-0.577895\pi$
$997$	15.0552	−	8.69214i	0.476804	−	0.275283i	0.719084	+	0.694924i	$0.244562\pi$
$998$	−14.8872	−	25.7855i	−0.471247	−	0.816224i
$999$	−10.5939			−0.335177

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.k.a.274.9	✓	80
11.10	odd	2	inner	627.2.k.a.274.32	yes	80
19.12	odd	6	inner	627.2.k.a.373.32	yes	80
209.164	even	6	inner	627.2.k.a.373.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.k.a.274.9	✓	80	1.1	even	1	trivial
627.2.k.a.274.32	yes	80	11.10	odd	2	inner
627.2.k.a.373.9	yes	80	209.164	even	6	inner
627.2.k.a.373.32	yes	80	19.12	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.890907 + 1.54310i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.587432 - 1.01746i) q^{4} +(-1.80116 + 3.11970i) q^{5} +(1.54310 - 0.890907i) q^{6} +3.47801i q^{7} -1.47024 q^{8} +(0.500000 + 0.866025i) q^{9} +(-3.20933 - 5.55873i) q^{10} +(1.02623 + 3.15386i) q^{11} +1.17486i q^{12} +(3.10880 + 5.38460i) q^{13} +(-5.36690 - 3.09858i) q^{14} +(3.11970 - 1.80116i) q^{15} +(2.48471 - 4.30365i) q^{16} +(-1.87776 - 1.08412i) q^{17} -1.78181 q^{18} +(4.33293 - 0.475090i) q^{19} +4.23224 q^{20} +(1.73900 - 3.01204i) q^{21} +(-5.78099 - 1.22624i) q^{22} +(-1.66369 - 2.88160i) q^{23} +(1.27326 + 0.735119i) q^{24} +(-3.98836 - 6.90804i) q^{25} -11.0786 q^{26} -1.00000i q^{27} +(3.53874 - 2.04309i) q^{28} +(1.73736 + 3.00919i) q^{29} +6.41867i q^{30} +9.62118i q^{31} +(2.95706 + 5.12177i) q^{32} +(0.688195 - 3.24444i) q^{33} +(3.34582 - 1.93171i) q^{34} +(-10.8503 - 6.26445i) q^{35} +(0.587432 - 1.01746i) q^{36} -10.5939i q^{37} +(-3.12713 + 7.10939i) q^{38} -6.21760i q^{39} +(2.64814 - 4.58671i) q^{40} +(-1.56377 + 2.70854i) q^{41} +(3.09858 + 5.36690i) q^{42} +(-4.20613 - 2.42841i) q^{43} +(2.60610 - 2.89683i) q^{44} -3.60232 q^{45} +5.92879 q^{46} +(-3.17727 - 5.50319i) q^{47} +(-4.30365 + 2.48471i) q^{48} -5.09654 q^{49} +14.2130 q^{50} +(1.08412 + 1.87776i) q^{51} +(3.65242 - 6.32618i) q^{52} +(4.95920 - 2.86320i) q^{53} +(1.54310 + 0.890907i) q^{54} +(-11.6875 - 2.47910i) q^{55} -5.11350i q^{56} +(-3.98997 - 1.75503i) q^{57} -6.19129 q^{58} +(7.99216 + 4.61428i) q^{59} +(-3.66523 - 2.11612i) q^{60} +(0.789917 - 0.456059i) q^{61} +(-14.8464 - 8.57158i) q^{62} +(-3.01204 + 1.73900i) q^{63} -0.599010 q^{64} -22.3978 q^{65} +(4.39337 + 3.95245i) q^{66} +(-0.963041 + 0.556012i) q^{67} +2.54740i q^{68} +3.32739i q^{69} +(19.3333 - 11.1621i) q^{70} +(11.2832 + 6.51438i) q^{71} +(-0.735119 - 1.27326i) q^{72} +(5.54077 + 3.19896i) q^{73} +(16.3475 + 9.43822i) q^{74} +7.97672i q^{75} +(-3.02869 - 4.12951i) q^{76} +(-10.9692 + 3.56922i) q^{77} +(9.59436 + 5.53931i) q^{78} +(6.09548 - 10.5577i) q^{79} +(8.95073 + 15.5031i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.78636 - 4.82611i) q^{82} -3.77061i q^{83} -4.08619 q^{84} +(6.76429 - 3.90537i) q^{85} +(7.49455 - 4.32698i) q^{86} -3.47471i q^{87} +(-1.50880 - 4.63693i) q^{88} +(10.3166 - 5.95631i) q^{89} +(3.20933 - 5.55873i) q^{90} +(-18.7277 + 10.8124i) q^{91} +(-1.95462 + 3.38549i) q^{92} +(4.81059 - 8.33219i) q^{93} +11.3226 q^{94} +(-6.32217 + 14.3732i) q^{95} -5.91411i q^{96} +(-2.74700 - 1.58598i) q^{97} +(4.54054 - 7.86445i) q^{98} +(-2.21821 + 2.46567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 40 q^{4} + 4 q^{5} + 40 q^{9} + 4 q^{11} - 24 q^{14} + 12 q^{15} - 40 q^{16} + 48 q^{20} - 24 q^{23} - 56 q^{25} + 80 q^{26} + 6 q^{33} - 48 q^{34} + 40 q^{36} + 60 q^{38} - 4 q^{42} + 14 q^{44}+ \cdots + 2 q^{99}+O(q^{100}) \) 80 * q - 40 * q^4 + 4 * q^5 + 40 * q^9 + 4 * q^11 - 24 * q^14 + 12 * q^15 - 40 * q^16 + 48 * q^20 - 24 * q^23 - 56 * q^25 + 80 * q^26 + 6 * q^33 - 48 * q^34 + 40 * q^36 + 60 * q^38 - 4 * q^42 + 14 * q^44 + 8 * q^45 - 16 * q^47 - 48 * q^48 - 80 * q^49 - 108 * q^53 - 24 * q^55 + 152 * q^58 - 48 * q^60 + 104 * q^64 - 36 * q^66 + 96 * q^67 - 60 * q^70 + 84 * q^71 - 60 * q^77 + 96 * q^78 - 32 * q^80 - 40 * q^81 - 20 * q^82 - 48 * q^86 + 72 * q^89 + 24 * q^91 - 104 * q^92 + 48 * q^93 + 36 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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