LMFDB - Embedded newform 483.2.r.a.181.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(34,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

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

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

chi := DirichletCharacter("483.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.r (of order $22$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			181.31
Character	$\chi$	$=$	483.181
Dual form			483.2.r.a.475.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.385364 + 2.68027i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(-5.11634 + 1.50229i) q^{4} +(2.40667 - 2.77745i) q^{5} +(0.762883 - 2.59814i) q^{6} +(2.27668 + 1.34785i) q^{7} +(-3.74845 - 8.20796i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.385364 + 2.68027i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(-5.11634 + 1.50229i) q^{4} +(2.40667 - 2.77745i) q^{5} +(0.762883 - 2.59814i) q^{6} +(2.27668 + 1.34785i) q^{7} +(-3.74845 - 8.20796i) q^{8} +(0.654861 + 0.755750i) q^{9} +(8.37174 + 5.38019i) q^{10} +(3.87913 + 0.557734i) q^{11} +(5.27806 + 0.758870i) q^{12} +(-3.02542 + 4.70765i) q^{13} +(-2.73525 + 6.62153i) q^{14} +(-3.34298 + 1.52669i) q^{15} +(11.5833 - 7.44414i) q^{16} +(-0.384369 - 0.112861i) q^{17} +(-1.77325 + 2.04644i) q^{18} +(3.23735 - 0.950573i) q^{19} +(-8.14080 + 17.8259i) q^{20} +(-1.51103 - 2.17182i) q^{21} +10.6120i q^{22} +(1.28775 + 4.61971i) q^{23} +9.02339i q^{24} +(-1.21057 - 8.41969i) q^{25} +(-13.7836 - 6.29477i) q^{26} +(-0.281733 - 0.959493i) q^{27} +(-13.6732 - 3.47583i) q^{28} +(3.22663 + 0.947424i) q^{29} +(-5.38019 - 8.37174i) q^{30} +(3.10291 - 1.41705i) q^{31} +(12.5980 + 14.5388i) q^{32} +(-3.29689 - 2.11878i) q^{33} +(0.154375 - 1.07370i) q^{34} +(9.22282 - 3.07953i) q^{35} +(-4.48584 - 2.88288i) q^{36} +(-0.641460 + 0.555829i) q^{37} +(3.79535 + 8.31065i) q^{38} +(4.70765 - 3.02542i) q^{39} +(-31.8185 - 9.34274i) q^{40} +(1.20372 + 1.04303i) q^{41} +(5.23876 - 4.88689i) q^{42} +(-9.48239 - 4.33046i) q^{43} +(-20.6848 + 2.97403i) q^{44} +3.67509 q^{45} +(-11.8858 + 5.23179i) q^{46} -2.93088i q^{47} +(-13.6290 + 1.95955i) q^{48} +(3.36658 + 6.13727i) q^{49} +(22.1005 - 6.48929i) q^{50} +(0.302750 + 0.262334i) q^{51} +(8.40681 - 28.6310i) q^{52} +(3.96588 + 6.17103i) q^{53} +(2.46313 - 1.12487i) q^{54} +(10.8849 - 9.43179i) q^{55} +(2.52909 - 23.7393i) q^{56} +(-3.33968 - 0.480174i) q^{57} +(-1.29592 + 9.01334i) q^{58} +(-4.63819 + 7.21717i) q^{59} +(14.8103 - 12.8332i) q^{60} +(-0.480733 - 1.05266i) q^{61} +(4.99383 + 7.77056i) q^{62} +(0.472272 + 2.60326i) q^{63} +(-16.0794 + 18.5566i) q^{64} +(5.79404 + 19.7327i) q^{65} +(4.40839 - 9.65304i) q^{66} +(4.59946 - 0.661302i) q^{67} +2.13611 q^{68} +(0.747713 - 4.73719i) q^{69} +(11.8081 + 23.5329i) q^{70} +(-0.365028 - 2.53883i) q^{71} +(3.74845 - 8.20796i) q^{72} +(-1.83920 - 6.26372i) q^{73} +(-1.73696 - 1.50509i) q^{74} +(-2.39649 + 8.16171i) q^{75} +(-15.1353 + 9.72690i) q^{76} +(8.07980 + 6.49828i) q^{77} +(9.92309 + 11.4519i) q^{78} +(3.42825 - 5.33445i) q^{79} +(7.20152 - 50.0876i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-2.33173 + 3.62825i) q^{82} +(-10.6060 - 12.2399i) q^{83} +(10.9936 + 8.84176i) q^{84} +(-1.23851 + 0.795945i) q^{85} +(7.95262 - 27.0841i) q^{86} +(-2.54147 - 2.20220i) q^{87} +(-9.96285 - 33.9304i) q^{88} +(-0.0437458 + 0.0957899i) q^{89} +(1.41625 + 9.85022i) q^{90} +(-13.2331 + 6.64000i) q^{91} +(-13.5287 - 21.7014i) q^{92} -3.41118 q^{93} +(7.85554 - 1.12946i) q^{94} +(5.15108 - 11.2793i) q^{95} +(-5.41986 - 18.4584i) q^{96} +(-10.0427 + 11.5899i) q^{97} +(-15.1522 + 11.3884i) q^{98} +(2.11878 + 3.29689i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{22}\right)$

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 $

$2$	0.385364	+	2.68027i	0.272494	+	1.89523i	0.422198	+	0.906504i	$0.361259\pi$
$2$	0.385364	+	2.68027i	0.272494	+	1.89523i	−0.149704	+	0.988731i	$0.547832\pi$
$3$	−0.909632	−	0.415415i	−0.525176	−	0.239840i
$3$	−0.909632	−	0.415415i	−0.525176	−	0.239840i
$4$	−5.11634	+	1.50229i	−2.55817	+	0.751146i
$5$	2.40667	−	2.77745i	1.07630	−	1.24211i	0.107512	−	0.994204i	$-0.465711\pi$
$5$	2.40667	−	2.77745i	1.07630	−	1.24211i	0.968784	−	0.247908i	$-0.0797431\pi$
$6$	0.762883	−	2.59814i	0.311446	−	1.06069i
$7$	2.27668	+	1.34785i	0.860506	+	0.509441i
$7$	2.27668	+	1.34785i	0.860506	+	0.509441i
$8$	−3.74845	−	8.20796i	−1.32528	−	2.90195i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	8.37174	+	5.38019i	2.64738	+	1.70137i
$11$	3.87913	+	0.557734i	1.16960	+	0.168163i	0.699621	−	0.714514i	$-0.253352\pi$
$11$	3.87913	+	0.557734i	1.16960	+	0.168163i	0.469980	+	0.882677i	$0.344261\pi$
$12$	5.27806	+	0.758870i	1.52364	+	0.219067i
$13$	−3.02542	+	4.70765i	−0.839101	+	1.30567i	0.111031	+	0.993817i	$0.464585\pi$
$13$	−3.02542	+	4.70765i	−0.839101	+	1.30567i	−0.950132	+	0.311849i	$0.899052\pi$
$14$	−2.73525	+	6.62153i	−0.731027	+	1.76968i
$15$	−3.34298	+	1.52669i	−0.863153	+	0.394189i
$16$	11.5833	−	7.44414i	2.89583	−	1.86104i
$17$	−0.384369	−	0.112861i	−0.0932231	−	0.0273728i	0.234788	−	0.972047i	$-0.424560\pi$
$17$	−0.384369	−	0.112861i	−0.0932231	−	0.0273728i	−0.328011	+	0.944674i	$0.606378\pi$
$18$	−1.77325	+	2.04644i	−0.417959	+	0.482351i
$19$	3.23735	−	0.950573i	0.742700	−	0.218076i	0.111573	−	0.993756i	$-0.464411\pi$
$19$	3.23735	−	0.950573i	0.742700	−	0.218076i	0.631127	+	0.775680i	$0.282593\pi$
$20$	−8.14080	+	17.8259i	−1.82034	+	3.98599i
$21$	−1.51103	−	2.17182i	−0.329733	−	0.473930i
$22$			10.6120i			2.26249i
$23$	1.28775	+	4.61971i	0.268515	+	0.963275i
$23$	1.28775	+	4.61971i	0.268515	+	0.963275i
$24$			9.02339i			1.84189i
$25$	−1.21057	−	8.41969i	−0.242114	−	1.68394i
$26$	−13.7836	−	6.29477i	−2.70319	−	1.23451i
$27$	−0.281733	−	0.959493i	−0.0542195	−	0.184655i
$28$	−13.6732	−	3.47583i	−2.58398	−	0.656869i
$29$	3.22663	+	0.947424i	0.599170	+	0.175932i	0.567233	−	0.823558i	$-0.308014\pi$
$29$	3.22663	+	0.947424i	0.599170	+	0.175932i	0.0319377	+	0.999490i	$0.489832\pi$
$30$	−5.38019	−	8.37174i	−0.982284	−	1.52846i
$31$	3.10291	−	1.41705i	0.557300	−	0.254510i	−0.116794	−	0.993156i	$-0.537262\pi$
$31$	3.10291	−	1.41705i	0.557300	−	0.254510i	0.674094	+	0.738646i	$0.264534\pi$
$32$	12.5980	+	14.5388i	2.22703	+	2.57012i
$33$	−3.29689	−	2.11878i	−0.573914	−	0.368832i
$34$	0.154375	−	1.07370i	0.0264751	−	0.184139i
$35$	9.22282	−	3.07953i	1.55894	−	0.520535i
$36$	−4.48584	−	2.88288i	−0.747641	−	0.480480i
$37$	−0.641460	+	0.555829i	−0.105455	+	0.0913777i	−0.705993	−	0.708219i	$-0.749499\pi$
$37$	−0.641460	+	0.555829i	−0.105455	+	0.0913777i	0.600537	+	0.799597i	$0.294953\pi$
$38$	3.79535	+	8.31065i	0.615687	+	1.34817i
$39$	4.70765	−	3.02542i	0.753827	−	0.484455i
$40$	−31.8185	−	9.34274i	−5.03094	−	1.47722i
$41$	1.20372	+	1.04303i	0.187990	+	0.162894i	0.743771	−	0.668434i	$-0.233035\pi$
$41$	1.20372	+	1.04303i	0.187990	+	0.162894i	−0.555781	+	0.831329i	$0.687581\pi$
$42$	5.23876	−	4.88689i	0.808358	−	0.754064i
$43$	−9.48239	−	4.33046i	−1.44605	−	0.660390i	−0.470952	−	0.882159i	$-0.656090\pi$
$43$	−9.48239	−	4.33046i	−1.44605	−	0.660390i	−0.975099	+	0.221769i	$0.928817\pi$
$44$	−20.6848	+	2.97403i	−3.11835	+	0.448351i
$45$	3.67509			0.547850
$46$	−11.8858	+	5.23179i	−1.75246	+	0.771386i
$47$		−	2.93088i		−	0.427513i	−0.976887	−	0.213756i	$-0.931430\pi$
$47$		−	2.93088i		−	0.427513i	0.976887	−	0.213756i	$-0.0685698\pi$
$48$	−13.6290	+	1.95955i	−1.96717	+	0.282837i
$49$	3.36658	+	6.13727i	0.480940	+	0.876753i
$50$	22.1005	−	6.48929i	3.12548	−	0.917725i
$51$	0.302750	+	0.262334i	0.0423935	+	0.0367342i
$52$	8.40681	−	28.6310i	1.16581	−	3.97040i
$53$	3.96588	+	6.17103i	0.544755	+	0.847656i	0.999067	−	0.0431870i	$-0.0137511\pi$
$53$	3.96588	+	6.17103i	0.544755	+	0.847656i	−0.454312	+	0.890843i	$0.650115\pi$
$54$	2.46313	−	1.12487i	0.335189	−	0.153076i
$55$	10.8849	−	9.43179i	1.46771	−	1.27178i
$56$	2.52909	−	23.7393i	0.337964	−	3.17230i
$57$	−3.33968	−	0.480174i	−0.442352	−	0.0636006i
$58$	−1.29592	+	9.01334i	−0.170163	+	1.18351i
$59$	−4.63819	+	7.21717i	−0.603842	+	0.939596i	0.395931	+	0.918280i	$0.370422\pi$
$59$	−4.63819	+	7.21717i	−0.603842	+	0.939596i	−0.999773	+	0.0213156i	$0.993215\pi$
$60$	14.8103	−	12.8332i	1.91200	−	1.65676i
$61$	−0.480733	−	1.05266i	−0.0615515	−	0.134779i	0.876357	−	0.481663i	$-0.159967\pi$
$61$	−0.480733	−	1.05266i	−0.0615515	−	0.134779i	−0.937908	+	0.346884i	$0.887240\pi$
$62$	4.99383	+	7.77056i	0.634217	+	0.986862i
$63$	0.472272	+	2.60326i	0.0595006	+	0.327980i
$64$	−16.0794	+	18.5566i	−2.00993	+	2.31958i
$65$	5.79404	+	19.7327i	0.718663	+	2.44754i
$66$	4.40839	−	9.65304i	0.542636	−	1.18821i
$67$	4.59946	−	0.661302i	0.561913	−	0.0807909i	0.144495	−	0.989506i	$-0.453844\pi$
$67$	4.59946	−	0.661302i	0.561913	−	0.0807909i	0.417418	+	0.908715i	$0.362935\pi$
$68$	2.13611			0.259041
$69$	0.747713	−	4.73719i	0.0900141	−	0.570290i
$70$	11.8081	+	23.5329i	1.41134	+	2.81272i
$71$	−0.365028	−	2.53883i	−0.0433209	−	0.301303i	−0.999950	−	0.00999492i	$-0.996818\pi$
$71$	−0.365028	−	2.53883i	−0.0433209	−	0.301303i	0.956629	−	0.291309i	$-0.0940906\pi$
$72$	3.74845	−	8.20796i	0.441759	−	0.967317i
$73$	−1.83920	−	6.26372i	−0.215262	−	0.733114i	−0.994345	−	0.106194i	$-0.966134\pi$
$73$	−1.83920	−	6.26372i	−0.215262	−	0.733114i	0.779084	−	0.626920i	$-0.215685\pi$
$74$	−1.73696	−	1.50509i	−0.201918	−	0.174963i
$75$	−2.39649	+	8.16171i	−0.276723	+	0.942433i
$76$	−15.1353	+	9.72690i	−1.73614	+	1.11575i
$77$	8.07980	+	6.49828i	0.920779	+	0.740548i
$78$	9.92309	+	11.4519i	1.12357	+	1.29667i
$79$	3.42825	−	5.33445i	0.385708	−	0.600173i	−0.593057	−	0.805161i	$-0.702079\pi$
$79$	3.42825	−	5.33445i	0.385708	−	0.600173i	0.978765	+	0.204988i	$0.0657154\pi$
$80$	7.20152	−	50.0876i	0.805154	−	5.59997i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−2.33173	+	3.62825i	−0.257497	+	0.400673i
$83$	−10.6060	−	12.2399i	−1.16416	−	1.34351i	−0.928350	−	0.371707i	$-0.878773\pi$
$83$	−10.6060	−	12.2399i	−1.16416	−	1.34351i	−0.235805	−	0.971800i	$-0.575773\pi$
$84$	10.9936	+	8.84176i	1.19950	+	0.964715i
$85$	−1.23851	+	0.795945i	−0.134336	+	0.0863323i
$86$	7.95262	−	27.0841i	0.857553	−	2.92056i
$87$	−2.54147	−	2.20220i	−0.272474	−	0.236100i
$88$	−9.96285	−	33.9304i	−1.06204	−	3.61699i
$89$	−0.0437458	+	0.0957899i	−0.00463704	+	0.0101537i	−0.911936	−	0.410332i	$-0.865413\pi$
$89$	−0.0437458	+	0.0957899i	−0.00463704	+	0.0101537i	0.907299	+	0.420485i	$0.138140\pi$
$90$	1.41625	+	9.85022i	0.149286	+	1.03830i
$91$	−13.2331	+	6.64000i	−1.38721	+	0.696061i
$92$	−13.5287	−	21.7014i	−1.41047	−	2.26253i
$93$	−3.41118			−0.353722
$94$	7.85554	−	1.12946i	0.810237	−	0.116494i
$95$	5.15108	−	11.2793i	0.528490	−	1.15723i
$96$	−5.41986	−	18.4584i	−0.553162	−	1.88390i
$97$	−10.0427	+	11.5899i	−1.01969	+	1.17678i	−0.0355491	+	0.999368i	$0.511318\pi$
$97$	−10.0427	+	11.5899i	−1.01969	+	1.17678i	−0.984137	+	0.177412i	$0.943227\pi$
$98$	−15.1522	+	11.3884i	−1.53060	+	1.15040i
$99$	2.11878	+	3.29689i	0.212945	+	0.331350i
$100$	18.8425	+	41.2593i	1.88425	+	4.12593i
$101$	3.01838	−	2.61544i	0.300340	−	0.260246i	−0.491633	−	0.870803i	$-0.663600\pi$
$101$	3.01838	−	2.61544i	0.300340	−	0.260246i	0.791973	+	0.610557i	$0.209054\pi$
$102$	−0.586457	+	0.912545i	−0.0580679	+	0.0903554i
$103$	2.23338	−	15.5335i	0.220061	−	1.53056i	−0.517739	−	0.855539i	$-0.673226\pi$
$103$	2.23338	−	15.5335i	0.220061	−	1.53056i	0.737800	−	0.675020i	$-0.235865\pi$
$104$	49.9808	+	7.18616i	4.90102	+	0.704661i
$105$	−9.66866	−	1.03006i	−0.943564	−	0.100524i
$106$	−15.0117	+	13.0077i	−1.45806	+	1.26342i
$107$	−5.84066	+	2.66734i	−0.564638	+	0.257861i	−0.677219	−	0.735781i	$-0.736815\pi$
$107$	−5.84066	+	2.66734i	−0.564638	+	0.257861i	0.112582	+	0.993642i	$0.464088\pi$
$108$	2.88288	+	4.48584i	0.277405	+	0.431651i
$109$	−0.0159038	+	0.0541635i	−0.00152331	+	0.00518792i	−0.960251	−	0.279138i	$-0.909951\pi$
$109$	−0.0159038	+	0.0541635i	−0.00152331	+	0.00518792i	0.958728	+	0.284325i	$0.0917696\pi$
$110$	29.4743	+	25.5397i	2.81027	+	2.43511i
$111$	0.814392	−	0.239127i	0.0772987	−	0.0226969i
$112$	36.4052	−	1.33536i	3.43996	−	0.126179i
$113$	−2.91415	+	0.418992i	−0.274140	+	0.0394154i	−0.278014	−	0.960577i	$-0.589676\pi$
$113$	−2.91415	+	0.418992i	−0.274140	+	0.0394154i	0.00387349	+	0.999992i	$0.498767\pi$
$114$		−	9.13628i		−	0.855691i
$115$	15.9302	+	7.54145i	1.48550	+	0.703244i
$116$	−17.9318			−1.66493
$117$	−5.53903	+	0.796392i	−0.512084	+	0.0736265i
$118$	−21.1313	−	9.65036i	−1.94530	−	0.888387i
$119$	−0.722966	−	0.775021i	−0.0662742	−	0.0710461i
$120$	25.0620	+	21.7163i	2.28783	+	1.98242i
$121$	4.18214	+	1.22799i	0.380195	+	0.111635i
$122$	2.63615	−	1.69415i	0.238665	−	0.153381i
$123$	−0.661654	−	1.44882i	−0.0596593	−	0.130636i
$124$	−13.7467	+	11.9116i	−1.23449	+	1.06969i
$125$	−10.8403	−	6.96662i	−0.969584	−	0.623114i
$126$	−6.79543	+	2.26902i	−0.605385	+	0.202140i
$127$	1.96927	−	13.6966i	0.174745	−	1.21538i	−0.693948	−	0.720025i	$-0.744130\pi$
$127$	1.96927	−	13.6966i	0.174745	−	1.21538i	0.868693	−	0.495351i	$-0.164961\pi$
$128$	−23.5657	−	15.1448i	−2.08293	−	1.33862i
$129$	6.82655	+	7.87826i	0.601044	+	0.693642i
$130$	−50.6561	+	23.1339i	−4.44283	+	2.02897i
$131$	6.34599	+	9.87456i	0.554452	+	0.862744i	0.999463	−	0.0327812i	$-0.0104364\pi$
$131$	6.34599	+	9.87456i	0.554452	+	0.862744i	−0.445011	+	0.895525i	$0.646800\pi$
$132$	20.0510	+	5.88751i	1.74522	+	0.512442i
$133$	8.65166	+	2.19932i	0.750194	+	0.190706i
$134$	3.54493	+	12.0729i	0.306235	+	1.04294i
$135$	−3.34298	−	1.52669i	−0.287718	−	0.131396i
$136$	0.514430	+	3.57794i	0.0441120	+	0.306806i
$137$			1.94789i			0.166420i	0.996532	+	0.0832098i	$0.0265172\pi$
$137$			1.94789i			0.166420i	−0.996532	+	0.0832098i	$0.973483\pi$
$138$	12.9851	+	0.178530i	1.10536	+	0.0151975i
$139$		−	16.7596i		−	1.42153i	−0.703429	−	0.710765i	$-0.748349\pi$
$139$		−	16.7596i		−	1.42153i	0.703429	−	0.710765i	$-0.251651\pi$
$140$	−42.5607	+	29.6113i	−3.59704	+	2.50261i
$141$	−1.21753	+	2.66602i	−0.102535	+	0.224519i
$142$	6.66407	−	1.95675i	0.559236	−	0.164207i
$143$	−14.3616	+	16.5742i	−1.20098	+	1.38600i
$144$	13.2114	+	3.87921i	1.10095	+	0.323267i
$145$	10.3969	−	6.68166i	0.863412	−	0.554881i
$146$	16.0797	−	7.34335i	1.33076	−	0.607740i
$147$	−0.512836	−	6.98119i	−0.0422980	−	0.575799i
$148$	2.44691	−	3.80747i	0.201135	−	0.312972i
$149$	−0.667883	−	0.0960271i	−0.0547151	−	0.00786685i	0.114903	−	0.993377i	$-0.463344\pi$
$149$	−0.667883	−	0.0960271i	−0.0547151	−	0.00786685i	−0.169618	+	0.985510i	$0.554253\pi$
$150$	−22.7991	−	3.27801i	−1.86154	−	0.267649i
$151$	16.5546	+	10.6390i	1.34719	+	0.865788i	0.997472	−	0.0710664i	$-0.0226402\pi$
$151$	16.5546	+	10.6390i	1.34719	+	0.865788i	0.349720	+	0.936854i	$0.386277\pi$
$152$	−19.9373	−	23.0089i	−1.61713	−	1.86627i
$153$	−0.166413	−	0.364395i	−0.0134537	−	0.0294596i
$154$	−14.3035	+	24.1602i	−1.15261	+	1.94689i
$155$	3.53190	−	12.0286i	0.283689	−	0.966157i
$156$	−19.5408	+	22.5513i	−1.56452	+	1.80555i
$157$	−18.8889	+	5.54628i	−1.50750	+	0.442641i	−0.928077	−	0.372387i	$-0.878539\pi$
$157$	−18.8889	+	5.54628i	−1.50750	+	0.442641i	−0.579420	+	0.815029i	$0.696721\pi$
$158$	15.6189	+	7.13290i	1.24257	+	0.567463i
$159$	−1.04395	−	7.26085i	−0.0827908	−	0.575823i
$160$	70.6999			5.58932
$161$	−3.29488	+	12.2533i	−0.259673	+	0.965697i
$162$	−2.70783			−0.212747
$163$	−2.51298	−	17.4782i	−0.196832	−	1.36900i	−0.813404	−	0.581699i	$-0.802388\pi$
$163$	−2.51298	−	17.4782i	−0.196832	−	1.36900i	0.616572	−	0.787299i	$-0.288521\pi$
$164$	−7.72559	−	3.52816i	−0.603268	−	0.275503i
$165$	−13.8193	+	4.05772i	−1.07583	+	0.315893i
$166$	28.7191	−	33.1436i	2.22904	−	2.57245i
$167$	2.56320	−	8.72945i	0.198346	−	0.675505i	−0.798908	−	0.601453i	$-0.794589\pi$
$167$	2.56320	−	8.72945i	0.198346	−	0.675505i	0.997254	−	0.0740522i	$-0.0235932\pi$
$168$	−12.1622	+	20.5434i	−0.938334	+	1.58496i
$169$	−7.60837	−	16.6600i	−0.585259	−	1.28154i
$170$	−2.61062	−	3.01282i	−0.200226	−	0.231073i
$171$	2.83841	+	1.82414i	0.217059	+	0.139495i
$172$	55.0207	+	7.91079i	4.19529	+	0.603192i
$173$	−9.79318	−	1.40805i	−0.744562	−	0.107052i	−0.240415	−	0.970670i	$-0.577284\pi$
$173$	−9.79318	−	1.40805i	−0.744562	−	0.107052i	−0.504146	+	0.863618i	$0.668193\pi$
$174$	4.92309	−	7.66047i	0.373218	−	0.580739i
$175$	8.59243	−	20.8006i	0.649526	−	1.57238i
$176$	49.0850	−	22.4164i	3.69992	−	1.68970i
$177$	7.21717	−	4.63819i	0.542476	−	0.348628i
$178$	−0.273601	−	0.0803364i	−0.0205072	−	0.00602146i
$179$	6.05220	−	6.98461i	0.452363	−	0.522055i	−0.483059	−	0.875588i	$-0.660474\pi$
$179$	6.05220	−	6.98461i	0.452363	−	0.522055i	0.935422	+	0.353533i	$0.115020\pi$
$180$	−18.8030	+	5.52106i	−1.40149	+	0.411515i
$181$	−2.66036	+	5.82537i	−0.197743	+	0.432997i	−0.982364	−	0.186979i	$-0.940130\pi$
$181$	−2.66036	+	5.82537i	−0.197743	+	0.432997i	0.784621	+	0.619976i	$0.212858\pi$
$182$	−22.8965	−	32.9095i	−1.69721	−	2.43942i
$183$			1.15723i			0.0855453i
$184$	33.0913	−	27.8866i	2.43952	−	2.05583i
$185$			3.11932i			0.229337i
$186$	−1.31454	−	9.14286i	−0.0963871	−	0.670387i
$187$	−1.42807	−	0.652177i	−0.104431	−	0.0476919i
$188$	4.40304	+	14.9954i	0.321124	+	1.09365i
$189$	0.651840	−	2.56420i	0.0474144	−	0.186518i
$190$	32.2165	+	9.45963i	2.33723	+	0.686274i
$191$	0.227827	+	0.354506i	0.0164850	+	0.0256511i	0.849398	−	0.527752i	$-0.176965\pi$
$191$	0.227827	+	0.354506i	0.0164850	+	0.0256511i	−0.832913	+	0.553404i	$0.813329\pi$
$192$	22.3350	−	10.2001i	1.61189	−	0.736127i
$193$	−10.9184	−	12.6005i	−0.785926	−	0.907007i	0.211596	−	0.977357i	$-0.432134\pi$
$193$	−10.9184	−	12.6005i	−0.785926	−	0.907007i	−0.997522	+	0.0703501i	$0.977588\pi$
$194$	−34.9342	−	22.4509i	−2.50813	−	1.61188i
$195$	2.92681	−	20.3564i	0.209593	−	1.45775i
$196$	−26.4445	−	26.3428i	−1.88890	−	1.88163i
$197$	−5.96093	−	3.83086i	−0.424699	−	0.272937i	0.310784	−	0.950480i	$-0.399408\pi$
$197$	−5.96093	−	3.83086i	−0.424699	−	0.272937i	−0.735483	+	0.677543i	$0.763045\pi$
$198$	−8.02003	+	6.94940i	−0.569959	+	0.493872i
$199$	−5.42227	−	11.8731i	−0.384374	−	0.841662i	−0.998618	−	0.0525463i	$-0.983266\pi$
$199$	−5.42227	−	11.8731i	−0.384374	−	0.841662i	0.614244	−	0.789116i	$-0.289461\pi$
$200$	−64.5707	+	41.4971i	−4.56584	+	2.93429i
$201$	−4.45853	−	1.30914i	−0.314480	−	0.0923397i
$202$	8.17326	+	7.08217i	0.575068	+	0.498300i
$203$	6.06903	+	6.50601i	0.425963	+	0.456633i
$204$	−1.94307	−	0.887372i	−0.136042	−	0.0621285i
$205$	5.79393	−	0.833042i	0.404666	−	0.0581822i
$206$	42.4945			2.96073
$207$	−2.64804	+	3.99848i	−0.184052	+	0.277914i
$208$			77.0518i			5.34258i
$209$	13.0883	−	1.88181i	0.905335	−	0.130167i
$210$	−0.965118	−	26.3115i	−0.0665995	−	1.81567i
$211$	−20.9127	+	6.14051i	−1.43969	+	0.422730i	−0.906117	−	0.423026i	$-0.860968\pi$
$211$	−20.9127	+	6.14051i	−1.43969	+	0.422730i	−0.533569	+	0.845757i	$0.679150\pi$
$212$	−29.5615	−	25.6151i	−2.03029	−	1.75926i
$213$	−0.722626	+	2.46104i	−0.0495135	+	0.168628i
$214$	−9.39996	−	14.6266i	−0.642568	−	0.999855i
$215$	−34.8486	+	15.9148i	−2.37666	+	1.08538i
$216$	−6.81942	+	5.90906i	−0.464003	+	0.402061i
$217$	8.97434	+	0.956090i	0.609218	+	0.0649036i
$218$	−0.151301	−	0.0217538i	−0.0102474	−	0.00147336i
$219$	−0.929054	+	6.46171i	−0.0627797	+	0.436642i
$220$	−41.5213	+	64.6084i	−2.79937	+	4.35590i
$221$	1.69419	−	1.46802i	0.113963	−	0.0987497i
$222$	0.954762	+	2.09064i	0.0640794	+	0.140314i
$223$	0.493843	+	0.768435i	0.0330702	+	0.0514582i	0.857395	−	0.514659i	$-0.172081\pi$
$223$	0.493843	+	0.768435i	0.0330702	+	0.0514582i	−0.824325	+	0.566117i	$0.808445\pi$
$224$	9.08538	+	50.0805i	0.607043	+	3.34614i
$225$	5.57042	−	6.42861i	0.371362	−	0.428574i
$226$	−2.24602	−	7.64924i	−0.149403	−	0.508820i
$227$	3.46954	−	7.59724i	0.230282	−	0.504247i	−0.758852	−	0.651263i	$-0.774240\pi$
$227$	3.46954	−	7.59724i	0.230282	−	0.504247i	0.989134	+	0.147016i	$0.0469669\pi$
$228$	17.8083	−	2.56045i	1.17938	−	0.169570i
$229$	−9.07595			−0.599756			−0.299878	−	0.953978i	$-0.596946\pi$
$229$	−9.07595			−0.599756			−0.299878	+	0.953978i	$0.596946\pi$
$230$	−14.0742	+	45.6033i	−0.928023	+	3.00700i
$231$	−4.65017	−	9.26752i	−0.305958	−	0.609758i
$232$	−4.31844	−	30.0354i	−0.283520	−	1.97192i
$233$	0.961932	−	2.10634i	0.0630183	−	0.137991i	−0.875502	−	0.483214i	$-0.839469\pi$
$233$	0.961932	−	2.10634i	0.0630183	−	0.137991i	0.938521	+	0.345223i	$0.112197\pi$
$234$	−4.26909	−	14.5392i	−0.279079	−	0.950456i
$235$	−8.14036	−	7.05366i	−0.531018	−	0.460130i
$236$	12.8883	−	43.8934i	0.838955	−	2.85722i
$237$	−5.33445	+	3.42825i	−0.346510	+	0.222688i
$238$	1.79866	−	2.23641i	0.116590	−	0.144965i
$239$	6.96588	+	8.03906i	0.450586	+	0.520003i	0.934910	−	0.354885i	$-0.115480\pi$
$239$	6.96588	+	8.03906i	0.450586	+	0.520003i	−0.484324	+	0.874888i	$0.660935\pi$
$240$	−27.3579	+	42.5697i	−1.76594	+	2.74786i
$241$	−1.18840	+	8.26548i	−0.0765513	+	0.532426i	0.915075	+	0.403284i	$0.132131\pi$
$241$	−1.18840	+	8.26548i	−0.0765513	+	0.532426i	−0.991626	+	0.129142i	$0.958778\pi$
$242$	−1.67969	+	11.6825i	−0.107974	+	0.750978i
$243$	0.540641	−	0.841254i	0.0346821	−	0.0539664i
$244$	4.04099	+	4.66355i	0.258698	+	0.298553i
$245$	25.1482	+	5.41989i	1.60666	+	0.346264i
$246$	3.62825	−	2.33173i	0.231329	−	0.148666i
$247$	−5.31939	+	18.1162i	−0.338465	+	1.15271i
$248$	−23.2622	−	20.1568i	−1.47715	−	1.27996i
$249$	4.56287	+	15.5397i	0.289160	+	0.984789i
$250$	14.4950	−	31.7395i	0.916741	−	2.00738i
$251$	−1.91957	−	13.3509i	−0.121162	−	0.842702i	−0.956243	−	0.292575i	$-0.905488\pi$
$251$	−1.91957	−	13.3509i	−0.121162	−	0.842702i	0.835080	−	0.550128i	$-0.185421\pi$
$252$	−6.32716	−	12.6097i	−0.398573	−	0.794334i
$253$	2.41879	+	18.6387i	0.152068	+	1.17180i
$254$	37.4694			2.35104
$255$	1.45724	−	0.209519i	0.0912559	−	0.0131206i
$256$	11.1105	−	24.3285i	0.694404	−	1.52053i
$257$	6.32792	+	21.5509i	0.394725	+	1.34431i	0.882077	+	0.471104i	$0.156144\pi$
$257$	6.32792	+	21.5509i	0.394725	+	1.34431i	−0.487353	+	0.873205i	$0.662037\pi$
$258$	−18.4851	+	21.3330i	−1.15083	+	1.32813i
$259$	−2.20958	+	0.400852i	−0.137297	+	0.0249077i
$260$	−59.2885	−	92.2548i	−3.67692	−	5.72140i
$261$	1.39698	+	3.05896i	0.0864708	+	0.189345i
$262$	−24.0209	+	20.8143i	−1.48402	+	1.28591i
$263$	2.49897	−	3.88847i	0.154093	−	0.239773i	−0.755621	−	0.655009i	$-0.772665\pi$
$263$	2.49897	−	3.88847i	0.154093	−	0.239773i	0.909714	+	0.415236i	$0.136301\pi$
$264$	−5.03265	+	35.0029i	−0.309738	+	2.15428i
$265$	26.6843	+	3.83662i	1.63920	+	0.235682i
$266$	−2.56073	+	24.0363i	−0.157009	+	1.47376i
$267$	0.0795851	−	0.0689609i	0.00487053	−	0.00422034i
$268$	−22.5389	+	10.2932i	−1.37678	+	0.628755i
$269$	2.90689	+	4.52321i	0.177236	+	0.275785i	0.918493	−	0.395436i	$-0.129407\pi$
$269$	2.90689	+	4.52321i	0.177236	+	0.275785i	−0.741257	+	0.671221i	$0.765770\pi$
$270$	2.80366	−	9.54840i	0.170626	−	0.581097i
$271$	−1.05836	−	0.917074i	−0.0642908	−	0.0557083i	0.622123	−	0.782920i	$-0.286270\pi$
$271$	−1.05836	−	0.917074i	−0.0642908	−	0.0557083i	−0.686413	+	0.727211i	$0.740816\pi$
$272$	−5.29242	+	1.55399i	−0.320900	+	0.0942247i
$273$	14.7956	−	0.542711i	0.895473	−	0.0328463i
$274$	−5.22087	+	0.750648i	−0.315404	+	0.0453483i
$275$		−	33.3362i		−	2.01025i
$276$	3.29108	+	25.3603i	0.198100	+	1.52651i
$277$	−4.65687			−0.279804			−0.139902	−	0.990165i	$-0.544679\pi$
$277$	−4.65687			−0.279804			−0.139902	+	0.990165i	$0.544679\pi$
$278$	44.9202	−	6.45855i	2.69413	−	0.387358i
$279$	3.10291	+	1.41705i	0.185767	+	0.0848368i
$280$	−59.8479	−	64.1571i	−3.57660	−	3.83412i
$281$	17.1824	+	14.8886i	1.02501	+	0.888179i	0.993783	−	0.111333i	$-0.0355121\pi$
$281$	17.1824	+	14.8886i	1.02501	+	0.888179i	0.0312301	+	0.999512i	$0.490058\pi$
$282$	−7.61484	−	2.23592i	−0.453457	−	0.133147i
$283$	−15.1760	+	9.75303i	−0.902120	+	0.579758i	−0.907418	−	0.420228i	$-0.861950\pi$
$283$	−15.1760	+	9.75303i	−0.902120	+	0.579758i	0.00529798	+	0.999986i	$0.498314\pi$
$284$	5.68167	+	12.4411i	0.337145	+	0.738245i
$285$	−9.37117	+	8.12017i	−0.555100	+	0.480997i
$286$	−49.9577	−	32.1058i	−2.95406	−	1.89846i
$287$	1.33464	+	3.99710i	0.0787815	+	0.235941i
$288$	−2.73780	+	19.0418i	−0.161326	+	1.12205i
$289$	−14.1663	−	9.10413i	−0.833312	−	0.535537i
$290$	21.9152	+	25.2915i	1.28690	+	1.48517i
$291$	13.9498	−	6.37068i	0.817754	−	0.373456i
$292$	18.8199	+	29.2843i	1.10135	+	1.71373i
$293$	−15.7272	−	4.61791i	−0.918791	−	0.269781i	−0.212054	−	0.977258i	$-0.568015\pi$
$293$	−15.7272	−	4.61791i	−0.918791	−	0.269781i	−0.706737	+	0.707477i	$0.749834\pi$
$294$	18.5138	−	4.06484i	1.07975	−	0.237066i
$295$	8.88270	+	30.2517i	0.517171	+	1.76132i
$296$	6.96670	+	3.18159i	0.404931	+	0.184926i
$297$	−0.557734	−	3.87913i	−0.0323630	−	0.225090i
$298$		−	1.82711i		−	0.105842i
$299$	−25.6439	−	7.91427i	−1.48303	−	0.457694i
$300$		−	45.3583i		−	2.61876i
$301$	−15.7516	−	22.6400i	−0.907906	−	1.30495i
$302$	−22.1358	+	48.4705i	−1.27377	+	2.78917i
$303$	−3.83211	+	1.12521i	−0.220149	+	0.0646416i
$304$	30.4231	−	35.1101i	1.74488	−	2.01370i
$305$	−4.08067	−	1.19819i	−0.233658	−	0.0686083i
$306$	0.912545	−	0.586457i	0.0521667	−	0.0335255i
$307$	−30.3670	+	13.8682i	−1.73314	+	0.791497i	−0.740265	+	0.672315i	$0.765300\pi$
$307$	−30.3670	+	13.8682i	−1.73314	+	0.791497i	−0.992872	+	0.119182i	$0.961973\pi$
$308$	−51.1013	−	21.1092i	−2.91177	−	1.20281i
$309$	−8.48439	+	13.2020i	−0.482660	+	0.751034i
$310$	33.6008	+	4.83107i	1.90840	+	0.274386i
$311$	−33.7614	−	4.85415i	−1.91443	−	0.275254i	−0.920990	−	0.389587i	$-0.872618\pi$
$311$	−33.7614	−	4.85415i	−1.91443	−	0.275254i	−0.993442	+	0.114333i	$0.963527\pi$
$312$	−42.4789	−	27.2995i	−2.40489	−	1.54553i
$313$	9.02703	+	10.4177i	0.510238	+	0.588846i	0.951160	−	0.308700i	$-0.0998938\pi$
$313$	9.02703	+	10.4177i	0.510238	+	0.588846i	−0.440922	+	0.897546i	$0.645348\pi$
$314$	−22.1446	−	48.4899i	−1.24969	−	2.73645i
$315$	8.36702	+	4.95348i	0.471428	+	0.279097i
$316$	−9.52615	+	32.4431i	−0.535888	+	1.82507i
$317$	4.56173	−	5.26451i	0.256212	−	0.295685i	−0.613042	−	0.790051i	$-0.710054\pi$
$317$	4.56173	−	5.26451i	0.256212	−	0.295685i	0.869254	+	0.494366i	$0.164600\pi$
$318$	19.0587	−	5.59614i	1.06876	−	0.313816i
$319$	11.9881	+	5.47478i	0.671205	+	0.306529i
$320$	12.8422	+	89.3194i	0.717900	+	4.99311i
$321$	6.42090			0.358380
$322$	−34.1119	−	4.10916i	−1.90098	−	0.228995i
$323$	−1.35162			−0.0752061
$324$	−0.758870	−	5.27806i	−0.0421595	−	0.293225i
$325$	43.2994	+	19.7742i	2.40182	+	1.09687i
$326$	45.8778	−	13.4709i	2.54094	−	0.746086i
$327$	0.0369669	−	0.0426621i	0.00204428	−	0.00235922i
$328$	4.04907	−	13.7899i	0.223573	−	0.761418i
$329$	3.95039	−	6.67269i	0.217792	−	0.367877i
$330$	−16.2012	−	35.4758i	−0.891849	−	1.95288i
$331$	1.38045	+	1.59313i	0.0758766	+	0.0875663i	0.792419	−	0.609978i	$-0.208822\pi$
$331$	1.38045	+	1.59313i	0.0758766	+	0.0875663i	−0.716542	+	0.697544i	$0.754276\pi$
$332$	72.6516	+	46.6904i	3.98728	+	2.56247i
$333$	−0.840134	−	0.120793i	−0.0460391	−	0.00661942i
$334$	24.3850	+	3.50604i	1.33429	+	0.191842i
$335$	9.23265	−	14.3663i	0.504433	−	0.784914i
$336$	−33.6700	−	13.9086i	−1.83685	−	0.758775i
$337$	16.6247	−	7.59225i	0.905605	−	0.413576i	0.0925134	−	0.995711i	$-0.470510\pi$
$337$	16.6247	−	7.59225i	0.905605	−	0.413576i	0.813092	+	0.582135i	$0.197783\pi$
$338$	41.7212	−	26.8126i	2.26934	−	1.45841i
$339$	2.82486	+	0.829454i	0.153425	+	0.0450498i
$340$	5.14091	−	5.93293i	0.278805	−	0.321758i
$341$	12.8269	−	3.76633i	0.694618	−	0.203958i
$342$	−3.79535	+	8.31065i	−0.205229	+	0.449389i
$343$	−0.607498	+	18.5103i	−0.0328018	+	0.999462i
$344$			94.0636i			5.07157i
$345$	−11.3578	−	13.4776i	−0.611482	−	0.725609i
$346$		−	26.7909i		−	1.44029i
$347$	3.77741	+	26.2725i	0.202782	+	1.41038i	0.795980	+	0.605323i	$0.206956\pi$
$347$	3.77741	+	26.2725i	0.202782	+	1.41038i	−0.593198	+	0.805057i	$0.702135\pi$
$348$	16.3114	+	7.44916i	0.874382	+	0.399317i
$349$	−9.00740	−	30.6764i	−0.482155	−	1.64207i	−0.737594	−	0.675245i	$-0.764038\pi$
$349$	−9.00740	−	30.6764i	−0.482155	−	1.64207i	0.255438	−	0.966825i	$-0.417780\pi$
$350$	59.0625	+	15.0142i	3.15702	+	0.802541i
$351$	5.36931	+	1.57657i	0.286593	+	0.0841512i
$352$	40.7603	+	63.4243i	2.17253	+	3.38052i
$353$	16.0810	−	7.34395i	0.855906	−	0.390879i	0.0613835	−	0.998114i	$-0.480449\pi$
$353$	16.0810	−	7.34395i	0.855906	−	0.390879i	0.794522	+	0.607235i	$0.207721\pi$
$354$	15.2128	+	17.5565i	0.808553	+	0.933120i
$355$	−7.92996	−	5.09628i	−0.420879	−	0.270482i
$356$	0.0799137	−	0.555812i	0.00423542	−	0.0294580i
$357$	0.335678	+	1.00532i	0.0177660	+	0.0532069i
$358$	21.0529	+	13.5299i	1.11268	+	0.715077i
$359$	−21.5038	+	18.6332i	−1.13493	+	0.983421i	−0.999972	−	0.00743050i	$-0.997635\pi$
$359$	−21.5038	+	18.6332i	−1.13493	+	0.983421i	−0.134956	+	0.990852i	$0.543089\pi$
$360$	−13.7759	−	30.1650i	−0.726053	−	1.58983i
$361$	−6.40695	+	4.11750i	−0.337208	+	0.216710i
$362$	−16.6388	−	4.88558i	−0.874514	−	0.256780i
$363$	−3.29408	−	2.85434i	−0.172895	−	0.149814i
$364$	57.7300	−	53.8525i	3.02587	−	2.82264i
$365$	−21.8235	−	9.96646i	−1.14229	−	0.521668i
$366$	−3.10170	+	0.445957i	−0.162128	+	0.0233105i
$367$	23.7968			1.24218			0.621091	−	0.783738i	$-0.286690\pi$
$367$	23.7968			1.24218			0.621091	+	0.783738i	$0.286690\pi$
$368$	49.3062	+	43.9253i	2.57026	+	2.28976i
$369$			1.59275i			0.0829155i
$370$	−8.36060	+	1.20207i	−0.434647	+	0.0624928i
$371$	0.711414	+	19.3949i	0.0369347	+	1.00693i
$372$	17.4527	−	5.12458i	0.904881	−	0.265697i
$373$	5.86810	+	5.08473i	0.303838	+	0.263278i	0.793413	−	0.608684i	$-0.208302\pi$
$373$	5.86810	+	5.08473i	0.303838	+	0.263278i	−0.489574	+	0.871962i	$0.662848\pi$
$374$	1.19768	−	4.07893i	0.0619307	−	0.210917i
$375$	6.96662	+	10.8403i	0.359755	+	0.559790i
$376$	−24.0565	+	10.9863i	−1.24062	+	0.566573i
$377$	−14.2221	+	12.3235i	−0.732473	+	0.634692i
$378$	7.12393	+	0.758955i	0.366415	+	0.0390364i
$379$	−0.662683	−	0.0952794i	−0.0340397	−	0.00489418i	0.125274	−	0.992122i	$-0.460019\pi$
$379$	−0.662683	−	0.0952794i	−0.0340397	−	0.00489418i	−0.159314	+	0.987228i	$0.550928\pi$
$380$	−9.40987	+	65.4471i	−0.482716	+	3.35736i
$381$	−7.48109	+	11.6408i	−0.383268	+	0.596376i
$382$	−0.862373	+	0.747251i	−0.0441229	+	0.0382327i
$383$	13.5941	+	29.7670i	0.694628	+	1.52102i	0.846366	+	0.532602i	$0.178786\pi$
$383$	13.5941	+	29.7670i	0.694628	+	1.52102i	−0.151738	+	0.988421i	$0.548487\pi$
$384$	15.1448	+	23.5657i	0.772853	+	1.20258i
$385$	37.4941	−	6.80200i	1.91087	−	0.346662i
$386$	29.5652	−	34.1201i	1.50483	−	1.73667i
$387$	−2.93690	−	10.0022i	−0.149291	−	0.508439i
$388$	33.9706	−	74.3852i	1.72459	−	3.77633i
$389$	−34.6162	+	4.97706i	−1.75511	+	0.252347i	−0.943388	−	0.331692i	$-0.892380\pi$
$389$	−34.6162	+	4.97706i	−1.75511	+	0.252347i	−0.811725	+	0.584039i	$0.801471\pi$
$390$	55.6885			2.81990
$391$	0.0264117	−	1.92101i	0.00133570	−	0.0971495i
$392$	37.7550	−	50.6380i	1.90692	−	2.55761i
$393$	−1.67048	−	11.6184i	−0.0842645	−	0.586073i
$394$	7.97059	−	17.4531i	0.401552	−	0.879277i
$395$	−6.56550	−	22.3600i	−0.330346	−	1.12506i
$396$	−15.7933	−	13.6850i	−0.793642	−	0.687695i
$397$	−2.44258	+	8.31865i	−0.122589	+	0.417501i	−0.997804	−	0.0662334i	$-0.978902\pi$
$397$	−2.44258	+	8.31865i	−0.122589	+	0.417501i	0.875215	+	0.483735i	$0.160720\pi$
$398$	29.7335	−	19.1086i	1.49041	−	0.957827i
$399$	−6.95620	−	5.59461i	−0.348245	−	0.280081i
$400$	−76.6998	−	88.5163i	−3.83499	−	4.42581i
$401$	4.41451	−	6.86912i	0.220450	−	0.343027i	−0.713359	−	0.700799i	$-0.752827\pi$
$401$	4.41451	−	6.86912i	0.220450	−	0.343027i	0.933809	+	0.357772i	$0.116463\pi$
$402$	1.79069	−	12.4545i	0.0893116	−	0.621176i
$403$	−2.71663	+	18.8946i	−0.135325	+	0.941207i
$404$	−11.5139	+	17.9160i	−0.572838	+	0.891353i
$405$	2.40667	+	2.77745i	0.119588	+	0.138012i
$406$	−15.0991	+	18.7738i	−0.749354	+	0.931728i
$407$	−2.79831	+	1.79837i	−0.138707	+	0.0891417i
$408$	1.01839	−	3.46831i	0.0504177	−	0.171707i
$409$	15.0040	+	13.0010i	0.741900	+	0.642860i	0.941498	−	0.337018i	$-0.109418\pi$
$409$	15.0040	+	13.0010i	0.741900	+	0.642860i	−0.199598	+	0.979878i	$0.563964\pi$
$410$	4.46555	+	15.2083i	0.220538	+	0.751082i
$411$	0.809184	−	1.77186i	0.0399141	−	0.0873997i
$412$	11.9091	+	82.8296i	0.586719	+	4.08072i
$413$	−20.2874	+	10.1796i	−0.998277	+	0.500906i
$414$	−11.7375	−	5.55659i	−0.576865	−	0.273091i
$415$	−59.5208			−2.92176
$416$	−106.558	+	15.3207i	−5.22442	+	0.751159i
$417$	−6.96219	+	15.2451i	−0.340940	+	0.746554i
$418$	10.0875	+	34.3549i	0.493396	+	1.68035i
$419$	20.1114	−	23.2098i	0.982505	−	1.13387i	−0.00848894	−	0.999964i	$-0.502702\pi$
$419$	20.1114	−	23.2098i	0.982505	−	1.13387i	0.990994	−	0.133907i	$-0.0427524\pi$
$420$	51.0155	−	9.25501i	2.48930	−	0.451598i
$421$	13.9350	+	21.6833i	0.679150	+	1.05678i	0.994184	+	0.107697i	$0.0343477\pi$
$421$	13.9350	+	21.6833i	0.679150	+	1.05678i	−0.315034	+	0.949080i	$0.602016\pi$
$422$	−24.5172	−	53.6851i	−1.19348	−	2.61335i
$423$	2.21501	−	1.91932i	0.107697	−	0.0933204i
$424$	35.7857	−	55.6836i	1.73791	−	2.70423i
$425$	−0.484949	+	3.37289i	−0.0235235	+	0.163609i
$426$	−6.87471	−	0.988434i	−0.333081	−	0.0478898i
$427$	0.324352	−	3.04453i	0.0156965	−	0.147335i
$428$	25.8756	−	22.4214i	1.25075	−	1.08378i
$429$	19.9489	−	9.11038i	0.963144	−	0.439853i
$430$	−56.0854	−	87.2706i	−2.70468	−	4.20856i
$431$	5.98127	−	20.3703i	0.288108	−	0.981204i	−0.680529	−	0.732721i	$-0.738250\pi$
$431$	5.98127	−	20.3703i	0.288108	−	0.981204i	0.968636	−	0.248483i	$-0.0799320\pi$
$432$	−10.4060	−	9.01685i	−0.500659	−	0.433823i
$433$	−13.0977	+	3.84584i	−0.629436	+	0.184819i	−0.580864	−	0.814001i	$-0.697285\pi$
$433$	−13.0977	+	3.84584i	−0.629436	+	0.184819i	−0.0485719	+	0.998820i	$0.515467\pi$
$434$	0.895812	+	24.4221i	0.0430003	+	1.17230i
$435$	−12.2330	+	1.75884i	−0.586526	+	0.0843298i
$436$		−	0.301011i		−	0.0144158i
$437$	8.56028	+	13.7315i	0.409494	+	0.656868i
$438$	−17.6771			−0.844646
$439$	0.652927	−	0.0938767i	0.0311625	−	0.00448049i	−0.126716	−	0.991939i	$-0.540444\pi$
$439$	0.652927	−	0.0938767i	0.0311625	−	0.00448049i	0.157878	+	0.987459i	$0.449535\pi$
$440$	−118.217	−	53.9879i	−5.63578	−	2.57377i
$441$	−2.43360	+	6.56335i	−0.115886	+	0.312541i
$442$	4.58756	+	3.97515i	0.218208	+	0.189078i
$443$	26.0410	+	7.64631i	1.23724	+	0.363287i	0.833979	−	0.551796i	$-0.186057\pi$
$443$	26.0410	+	7.64631i	1.23724	+	0.363287i	0.403264	+	0.915084i	$0.367876\pi$
$444$	−3.80747	+	2.44691i	−0.180694	+	0.116125i
$445$	0.160770	+	0.352036i	0.00762121	+	0.0166881i
$446$	−1.86930	+	1.61976i	−0.0885140	+	0.0766978i
$447$	0.567637	+	0.364798i	0.0268483	+	0.0172544i
$448$	−61.6194	+	20.5749i	−2.91124	+	0.972073i
$449$	4.63851	−	32.2615i	0.218905	−	1.52252i	−0.523187	−	0.852218i	$-0.675257\pi$
$449$	4.63851	−	32.2615i	0.218905	−	1.52252i	0.742092	−	0.670298i	$-0.233834\pi$
$450$	19.3770	+	12.4529i	0.913442	+	0.587034i
$451$	4.08766	+	4.71741i	0.192480	+	0.222134i
$452$	14.2803	−	6.52161i	0.671690	−	0.306751i
$453$	−10.6390	−	16.5546i	−0.499863	−	0.777802i
$454$	21.6997	+	6.37160i	1.01842	+	0.299034i
$455$	−13.4056	+	52.7346i	−0.628463	+	2.47224i
$456$	8.57738	+	29.2119i	0.401673	+	1.36797i
$457$	−13.6434	−	6.23071i	−0.638209	−	0.291460i	0.0699100	−	0.997553i	$-0.477729\pi$
$457$	−13.6434	−	6.23071i	−0.638209	−	0.291460i	−0.708119	+	0.706093i	$0.750456\pi$
$458$	−3.49755	−	24.3260i	−0.163430	−	1.13668i
$459$			0.400596i			0.0186982i
$460$	−92.8337	−	14.6528i	−4.32839	−	0.683190i
$461$		−	10.5437i		−	0.491069i	−0.969388	−	0.245535i	$-0.921037\pi$
$461$		−	10.5437i		−	0.491069i	0.969388	−	0.245535i	$-0.0789635\pi$
$462$	23.0474	−	16.0351i	1.07226	−	0.746018i
$463$	2.42996	−	5.32087i	0.112930	−	0.247282i	−0.844725	−	0.535201i	$-0.820236\pi$
$463$	2.42996	−	5.32087i	0.112930	−	0.247282i	0.957655	+	0.287919i	$0.0929633\pi$
$464$	44.4279	−	13.0452i	2.06251	−	0.605608i
$465$	−8.20958	+	9.47436i	−0.380710	+	0.439363i
$466$	6.01624	+	1.76653i	0.278697	+	0.0818328i
$467$	10.0738	−	6.47404i	0.466160	−	0.299583i	−0.286396	−	0.958111i	$-0.592457\pi$
$467$	10.0738	−	6.47404i	0.466160	−	0.299583i	0.752556	+	0.658528i	$0.228821\pi$
$468$	27.1431	−	12.3959i	1.25469	−	0.572998i
$469$	11.3628	+	4.69382i	0.524687	+	0.216740i
$470$	15.7687	−	24.5366i	0.727355	−	1.13179i
$471$	19.4859	+	2.80166i	0.897865	+	0.129094i
$472$	76.6243	+	11.0169i	3.52692	+	0.507094i
$473$	−34.3682	−	22.0871i	−1.58025	−	1.01556i
$474$	−11.2443	−	12.9766i	−0.516469	−	0.596037i
$475$	−11.9226	−	26.1068i	−0.547045	−	1.19786i
$476$	4.86325	+	2.87916i	0.222907	+	0.131966i
$477$	−2.06665	+	7.03837i	−0.0946256	+	0.322265i
$478$	−18.8624	+	21.7684i	−0.862747	+	0.995663i
$479$	−1.58948	+	0.466712i	−0.0726250	+	0.0213246i	−0.317843	−	0.948143i	$-0.602959\pi$
$479$	−1.58948	+	0.466712i	−0.0726250	+	0.0213246i	0.245218	+	0.969468i	$0.421140\pi$
$480$	−64.3109	−	29.3698i	−2.93538	−	1.34054i
$481$	−0.675957	−	4.70138i	−0.0308210	−	0.214365i
$482$	−22.6116			−1.02993
$483$	8.08734	−	9.77727i	0.367987	−	0.444881i
$484$	−23.2420			−1.05646
$485$	8.02087	+	55.7863i	0.364209	+	2.53313i
$486$	2.46313	+	1.12487i	0.111730	+	0.0510253i
$487$	33.3450	−	9.79097i	1.51101	−	0.443671i	0.581830	−	0.813310i	$-0.302337\pi$
$487$	33.3450	−	9.79097i	1.51101	−	0.443671i	0.929175	+	0.369639i	$0.120519\pi$
$488$	−6.83817	+	7.89167i	−0.309550	+	0.357239i
$489$	−4.97481	+	16.9427i	−0.224969	+	0.766173i
$490$	−4.83554	+	69.4925i	−0.218448	+	3.13935i
$491$	7.96388	+	17.4385i	0.359405	+	0.786987i	0.999820	+	0.0189579i	$0.00603486\pi$
$491$	7.96388	+	17.4385i	0.359405	+	0.786987i	−0.640416	+	0.768029i	$0.721238\pi$
$492$	5.56180	+	6.41866i	0.250745	+	0.289375i
$493$	−1.13329	−	0.728321i	−0.0510408	−	0.0328019i
$494$	−50.6061	−	7.27606i	−2.27688	−	0.327366i
$495$	14.2561	+	2.04972i	0.640766	+	0.0921282i
$496$	25.3933	−	39.5127i	1.14019	−	1.77417i
$497$	2.59091	−	6.27211i	0.116218	−	0.281343i
$498$	−39.8922	+	18.2182i	−1.78761	+	0.816375i
$499$	31.0020	−	19.9238i	1.38784	−	0.891911i	0.388279	−	0.921542i	$-0.373070\pi$
$499$	31.0020	−	19.9238i	1.38784	−	0.891911i	0.999561	+	0.0296308i	$0.00943316\pi$
$500$	65.9284	+	19.3583i	2.94841	+	0.865731i
$501$	−5.95791	+	6.87580i	−0.266180	+	0.307188i
$502$	35.0443	−	10.2899i	1.56410	−	0.459262i
$503$	−14.2236	+	31.1454i	−0.634201	+	1.38871i	0.270525	+	0.962713i	$0.412803\pi$
$503$	−14.2236	+	31.1454i	−0.634201	+	1.38871i	−0.904726	+	0.425993i	$0.859925\pi$
$504$	19.5972	−	13.6346i	0.872927	−	0.607332i
$505$		−	14.6779i		−	0.653158i
$506$	−49.0244	+	13.6657i	−2.17940	+	0.607513i
$507$			18.3151i			0.813402i
$508$	10.5008	+	73.0348i	0.465899	+	3.24040i
$509$	15.0858	+	6.88943i	0.668664	+	0.305369i	0.720670	−	0.693278i	$-0.243834\pi$
$509$	15.0858	+	6.88943i	0.668664	+	0.305369i	−0.0520060	+	0.998647i	$0.516561\pi$
$510$	1.12314	+	3.82505i	0.0497333	+	0.169376i
$511$	4.25531	−	16.7395i	0.188244	−	0.740511i
$512$	15.7327	+	4.61954i	0.695294	+	0.204157i
$513$	−1.82414	−	2.83841i	−0.0805376	−	0.125319i
$514$	−55.3237	+	25.2655i	−2.44022	+	1.11441i
$515$	−37.7684	−	43.5870i	−1.66427	−	1.92067i
$516$	−46.7624	−	30.0523i	−2.05860	−	1.32298i
$517$	1.63465	−	11.3693i	0.0718919	−	0.500019i
$518$	−1.92588	−	5.76778i	−0.0846184	−	0.253422i
$519$	8.32327	+	5.34904i	0.365351	+	0.234797i
$520$	140.247	−	121.524i	6.15022	−	5.32919i
$521$	12.1023	+	26.5003i	0.530211	+	1.16100i	0.965427	+	0.260673i	$0.0839446\pi$
$521$	12.1023	+	26.5003i	0.530211	+	1.16100i	−0.435216	+	0.900326i	$0.643328\pi$
$522$	−7.66047	+	4.92309i	−0.335290	+	0.215478i
$523$	−11.4670	−	3.36701i	−0.501416	−	0.147229i	0.0212371	−	0.999774i	$-0.493240\pi$
$523$	−11.4670	−	3.36701i	−0.501416	−	0.147229i	−0.522653	+	0.852545i	$0.675058\pi$
$524$	−47.3027	−	40.9880i	−2.06643	−	1.79057i
$525$	−16.4568	+	15.3515i	−0.718236	+	0.669995i
$526$	11.3851	+	5.19942i	0.496416	+	0.226706i
$527$	−1.35259	+	0.194474i	−0.0589199	+	0.00847140i
$528$	−53.9614			−2.34837
$529$	−19.6834	+	11.8981i	−0.855799	+	0.517308i
$530$			72.9994i			3.17089i
$531$	−8.49175	+	1.22093i	−0.368510	+	0.0529838i
$532$	−47.5688	+	1.74485i	−2.06237	+	0.0756487i
$533$	−8.55200	+	2.51109i	−0.370428	+	0.108767i
$534$	0.215503	+	0.186734i	0.00932572	+	0.00808078i
$535$	−6.64815	+	22.6415i	−0.287425	+	0.978878i
$536$	−22.6688	−	35.2733i	−0.979142	−	1.52357i
$537$	−8.40679	+	3.83925i	−0.362780	+	0.165676i
$538$	−11.0032	+	9.53432i	−0.474381	+	0.411054i
$539$	9.63644	+	25.6849i	0.415071	+	1.10633i
$540$	19.3973	+	2.78891i	0.834728	+	0.120016i
$541$	5.09365	−	35.4271i	0.218993	−	1.52313i	−0.522773	−	0.852472i	$-0.675102\pi$
$541$	5.09365	−	35.4271i	0.218993	−	1.52313i	0.741766	−	0.670659i	$-0.233989\pi$
$542$	2.05015	−	3.19009i	0.0880614	−	0.137026i
$543$	4.83990	−	4.19379i	0.207700	−	0.179973i
$544$	−3.20140	−	7.01009i	−0.137259	−	0.300555i
$545$	0.112161	+	0.174526i	0.00480444	+	0.00747586i
$546$	7.15632	+	39.4471i	0.306262	+	1.68818i
$547$	2.44073	−	2.81675i	0.104358	−	0.120436i	−0.701168	−	0.712996i	$-0.747338\pi$
$547$	2.44073	−	2.81675i	0.104358	−	0.120436i	0.805526	+	0.592561i	$0.201883\pi$
$548$	−2.92630	−	9.96607i	−0.125005	−	0.425729i
$549$	0.480733	−	1.05266i	0.0205172	−	0.0449263i
$550$	89.3500	−	12.8466i	3.80990	−	0.547780i
$551$	11.3463			0.483370
$552$	−41.6854	+	11.6199i	−1.77425	+	0.494576i
$553$	14.9951	−	7.52410i	0.637656	−	0.319957i
$554$	−1.79459	−	12.4817i	−0.0762449	−	0.530295i
$555$	1.29581	−	2.83743i	0.0550041	−	0.120442i
$556$	25.1778	+	85.7477i	1.06778	+	3.63651i
$557$	−4.22629	−	3.66210i	−0.179074	−	0.155168i	0.560712	−	0.828011i	$-0.310528\pi$
$557$	−4.22629	−	3.66210i	−0.179074	−	0.155168i	−0.739785	+	0.672843i	$0.765073\pi$
$558$	−2.60233	+	8.86272i	−0.110165	+	0.375189i
$559$	49.0745	−	31.5383i	2.07563	−	1.33393i
$560$	83.9064	−	104.327i	3.54569	−	4.40863i
$561$	1.02809	+	1.18648i	0.0434061	+	0.0500933i
$562$	−33.2839	+	51.7908i	−1.40400	+	2.18466i
$563$	2.70831	−	18.8367i	0.114142	−	0.793873i	−0.849675	−	0.527307i	$-0.823202\pi$
$563$	2.70831	−	18.8367i	0.114142	−	0.793873i	0.963817	−	0.266566i	$-0.0858892\pi$
$564$	2.22416	−	15.4693i	0.0936539	−	0.651377i
$565$	−5.84968	+	9.10228i	−0.246098	+	0.382936i
$566$	−31.9890	−	36.9173i	−1.34460	−	1.55175i
$567$	−1.65814	+	2.06169i	−0.0696353	+	0.0865829i
$568$	−19.4703	+	12.5128i	−0.816956	+	0.525026i
$569$	−8.22072	+	27.9972i	−0.344630	+	1.17370i	0.586784	+	0.809743i	$0.300394\pi$
$569$	−8.22072	+	27.9972i	−0.344630	+	1.17370i	−0.931415	+	0.363960i	$0.881425\pi$
$570$	−25.3755	−	21.9880i	−1.06286	−	0.920977i
$571$	4.14463	+	14.1153i	0.173447	+	0.590707i	0.999627	+	0.0273009i	$0.00869122\pi$
$571$	4.14463	+	14.1153i	0.173447	+	0.590707i	−0.826180	+	0.563406i	$0.809491\pi$
$572$	48.5796	−	106.374i	2.03121	−	4.44774i
$573$	−0.0599717	−	0.417113i	−0.00250535	−	0.0174251i
$574$	−10.1990	+	5.11754i	−0.425697	+	0.213602i
$575$	37.3376	−	16.4350i	1.55709	−	0.685385i
$576$	−24.5539			−1.02308
$577$	14.8524	−	2.13546i	0.618314	−	0.0889002i	0.173962	−	0.984752i	$-0.444343\pi$
$577$	14.8524	−	2.13546i	0.618314	−	0.0889002i	0.444352	+	0.895852i	$0.353434\pi$
$578$	18.9423	−	41.4779i	0.787896	−	1.72525i
$579$	4.69730	+	15.9975i	0.195213	+	0.664835i
$580$	−43.1560	+	49.8047i	−1.79196	+	2.06803i
$581$	−7.64879	−	42.1617i	−0.317325	−	1.74916i
$582$	22.4509	+	34.9342i	0.930619	+	1.44807i
$583$	11.9424	+	26.1501i	0.494602	+	1.08303i
$584$	−44.5183	+	38.5753i	−1.84218	+	1.59626i
$585$	−11.1187	+	17.3010i	−0.459701	+	0.715309i
$586$	6.31655	−	43.9326i	0.260934	−	1.81484i
$587$	12.1081	+	1.74088i	0.499754	+	0.0718538i	0.387582	−	0.921835i	$-0.373310\pi$
$587$	12.1081	+	1.74088i	0.499754	+	0.0718538i	0.112172	+	0.993689i	$0.464219\pi$
$588$	13.1116	+	34.9477i	0.540714	+	1.44122i
$589$	8.69822	−	7.53705i	0.358404	−	0.310559i
$590$	−77.6595	+	35.4659i	−3.19719	+	1.46011i
$591$	3.83086	+	5.96093i	0.157580	+	0.245200i
$592$	−3.29257	+	11.2135i	−0.135324	+	0.460870i
$593$	11.8011	+	10.2257i	0.484614	+	0.419920i	0.862597	−	0.505893i	$-0.168837\pi$
$593$	11.8011	+	10.2257i	0.484614	+	0.419920i	−0.377983	+	0.925813i	$0.623382\pi$
$594$	10.1822	−	2.98975i	0.417779	−	0.122671i
$595$	−3.89252	+	0.142779i	−0.159578	+	0.00585338i
$596$	3.56138	−	0.512048i	0.145880	−	0.0209743i
$597$			13.0527i			0.534209i
$598$	11.3301	−	71.7825i	0.463322	−	2.93540i
$599$	10.0413			0.410278			0.205139	−	0.978733i	$-0.434235\pi$
$599$	10.0413			0.410278			0.205139	+	0.978733i	$0.434235\pi$
$600$	75.9741	−	10.9234i	3.10163	−	0.445947i
$601$	24.8735	+	11.3594i	1.01461	+	0.463358i	0.852117	−	0.523351i	$-0.175318\pi$
$601$	24.8735	+	11.3594i	1.01461	+	0.463358i	0.162496	+	0.986709i	$0.448046\pi$
$602$	54.6111	−	50.9431i	2.22578	−	2.07628i
$603$	3.51178	+	3.04298i	0.143011	+	0.123920i
$604$	−100.682	−	29.5628i	−4.09668	−	1.20289i
$605$	13.4757	−	8.66031i	0.547865	−	0.352092i
$606$	−4.49262	−	9.83746i	−0.182500	−	0.399619i
$607$	−23.1772	+	20.0832i	−0.940735	+	0.815152i	−0.982934	−	0.183958i	$-0.941109\pi$
$607$	−23.1772	+	20.0832i	−0.940735	+	0.815152i	0.0421991	+	0.999109i	$0.486564\pi$
$608$	54.6043	+	35.0920i	2.21449	+	1.42317i
$609$	−2.81789	−	8.43924i	−0.114187	−	0.341975i
$610$	1.63893	−	11.3990i	0.0663584	−	0.461533i
$611$	13.7975	+	8.86714i	0.558189	+	0.358726i
$612$	1.39885	+	1.61436i	0.0565453	+	0.0652568i
$613$	11.2570	−	5.14091i	0.454667	−	0.207639i	−0.174899	−	0.984586i	$-0.555960\pi$
$613$	11.2570	−	5.14091i	0.454667	−	0.207639i	0.629566	+	0.776947i	$0.283233\pi$
$614$	−48.8727	−	76.0474i	−1.97234	−	3.06902i
$615$	−5.61640	−	1.64913i	−0.226475	−	0.0664991i
$616$	23.0509	−	90.6772i	0.928747	−	3.65349i
$617$	−4.99408	−	17.0083i	−0.201054	−	0.684728i	−0.996861	−	0.0791767i	$-0.974771\pi$
$617$	−4.99408	−	17.0083i	−0.201054	−	0.684728i	0.795806	−	0.605551i	$-0.207047\pi$
$618$	−38.6544	−	17.6529i	−1.55491	−	0.710102i
$619$	2.65247	+	18.4483i	0.106612	+	0.741500i	0.971070	+	0.238795i	$0.0767525\pi$
$619$	2.65247	+	18.4483i	0.106612	+	0.741500i	−0.864458	+	0.502704i	$0.832338\pi$
$620$			66.8481i			2.68468i
$621$	4.06977	−	2.53711i	0.163314	−	0.101811i
$622$		−	92.3601i		−	3.70330i
$623$	−0.228706	+	0.159120i	−0.00916292	+	0.00637503i
$624$	32.0085	−	70.0888i	1.28136	−	2.80580i
$625$	−4.62986	+	1.35945i	−0.185194	+	0.0543780i
$626$	−24.4436	+	28.2095i	−0.976965	+	1.12748i
$627$	−12.6872	−	3.72531i	−0.506680	−	0.148775i
$628$	88.3098	−	56.7533i	3.52394	−	2.26470i
$629$	0.309289	−	0.141247i	0.0123321	−	0.00563190i
$630$	−10.0523	+	24.3347i	−0.400493	+	0.969519i
$631$	19.9285	−	31.0094i	0.793343	−	1.23447i	−0.174933	−	0.984580i	$-0.555971\pi$
$631$	19.9285	−	31.0094i	0.793343	−	1.23447i	0.968276	−	0.249885i	$-0.0803928\pi$
$632$	−56.6356	−	8.14297i	−2.25284	−	0.323910i
$633$	21.5737	+	3.10183i	0.857477	+	0.123287i
$634$	15.8682	+	10.1979i	0.630208	+	0.405010i
$635$	−33.3022	−	38.4328i	−1.32156	−	1.52516i
$636$	16.2491	+	35.5806i	0.644320	+	1.41086i
$637$	−39.0774	−	2.71915i	−1.54830	−	0.107737i
$638$	−10.0541	+	34.2411i	−0.398045	+	1.35562i
$639$	1.67968	−	1.93845i	0.0664469	−	0.0766839i
$640$	−98.7787	+	29.0040i	−3.90457	+	1.14649i
$641$	−2.95019	−	1.34731i	−0.116525	−	0.0532154i	0.356299	−	0.934372i	$-0.384038\pi$
$641$	−2.95019	−	1.34731i	−0.116525	−	0.0532154i	−0.472825	+	0.881156i	$0.656766\pi$
$642$	2.47438	+	17.2097i	0.0976562	+	0.679214i
$643$	−22.7750			−0.898157			−0.449079	−	0.893492i	$-0.648248\pi$
$643$	−22.7750			−0.898157			−0.449079	+	0.893492i	$0.648248\pi$
$644$	−1.55035	−	67.6420i	−0.0610925	−	2.66547i
$645$	38.3107			1.50848
$646$	−0.520866	−	3.62270i	−0.0204932	−	0.142533i
$647$	36.4896	+	16.6643i	1.43456	+	0.655140i	0.972753	−	0.231843i	$-0.0744756\pi$
$647$	36.4896	+	16.6643i	1.43456	+	0.655140i	0.461802	+	0.886983i	$0.347203\pi$
$648$	8.65788	−	2.54218i	0.340113	−	0.0998663i
$649$	−22.0174	+	25.4094i	−0.864259	+	0.997408i
$650$	−36.3140	+	123.674i	−1.42435	+	4.85090i
$651$	−7.76617	−	4.59776i	−0.304380	−	0.180201i
$652$	39.1146	+	85.6491i	1.53185	+	3.35428i
$653$	8.84504	+	10.2077i	0.346133	+	0.399459i	0.901946	−	0.431848i	$-0.142138\pi$
$653$	8.84504	+	10.2077i	0.346133	+	0.399459i	−0.555813	+	0.831307i	$0.687593\pi$
$654$	0.128592	+	0.0826408i	0.00502833	+	0.00323151i
$655$	42.6988	+	6.13916i	1.66838	+	0.239877i
$656$	21.7076	+	3.12108i	0.847539	+	0.121858i
$657$	3.52939	−	5.49184i	0.137695	−	0.214257i
$658$	19.4069	+	8.01670i	0.756560	+	0.312523i
$659$	2.20463	−	1.00682i	0.0858802	−	0.0392202i	−0.372012	−	0.928228i	$-0.621332\pi$
$659$	2.20463	−	1.00682i	0.0858802	−	0.0392202i	0.457892	+	0.889008i	$0.348605\pi$
$660$	64.6084	−	41.5213i	2.51488	−	1.61621i
$661$	−12.8886	−	3.78442i	−0.501307	−	0.147197i	0.0212961	−	0.999773i	$-0.493221\pi$
$661$	−12.8886	−	3.78442i	−0.501307	−	0.147197i	−0.522603	+	0.852576i	$0.675039\pi$
$662$	−3.73803	+	4.31392i	−0.145283	+	0.167665i
$663$	−2.15092	+	0.631568i	−0.0835349	+	0.0245281i
$664$	−60.7090	+	132.934i	−2.35596	+	5.15884i
$665$	26.9302	−	18.7365i	1.04431	−	0.726570i
$666$		−	2.29833i		−	0.0890586i
$667$	−0.221716	+	16.1261i	−0.00858488	+	0.624407i
$668$			48.5135i			1.87704i
$669$	−0.129996	−	0.904143i	−0.00502594	−	0.0349562i
$670$	42.0634	+	19.2097i	1.62505	+	0.742136i
$671$	−1.27772	−	4.35152i	−0.0493258	−	0.167988i
$672$	12.5398	−	49.3290i	0.483735	−	1.90291i
$673$	−29.8480	−	8.76417i	−1.15056	−	0.337834i	−0.349800	−	0.936824i	$-0.613751\pi$
$673$	−29.8480	−	8.76417i	−1.15056	−	0.337834i	−0.800756	+	0.598990i	$0.795569\pi$
$674$	26.7558	+	41.6329i	1.03060	+	1.60364i
$675$	−7.73758	+	3.53363i	−0.297820	+	0.136010i
$676$	63.9551	+	73.8082i	2.45981	+	2.83878i
$677$	23.9260	+	15.3763i	0.919552	+	0.590960i	0.912528	−	0.409015i	$-0.134128\pi$
$677$	23.9260	+	15.3763i	0.919552	+	0.590960i	0.00702449	+	0.999975i	$0.497764\pi$
$678$	−1.13456	+	7.89102i	−0.0435724	+	0.303053i
$679$	−38.4857	+	12.8505i	−1.47695	+	0.493157i
$680$	11.1756	+	7.18212i	0.428564	+	0.275422i
$681$	−6.31202	+	5.46939i	−0.241877	+	0.209588i
$682$	15.0378	+	32.9282i	0.575827	+	1.26089i
$683$	7.18886	−	4.62000i	0.275074	−	0.176779i	−0.395829	−	0.918324i	$-0.629543\pi$
$683$	7.18886	−	4.62000i	0.275074	−	0.176779i	0.670903	+	0.741545i	$0.265906\pi$
$684$	−17.2626	−	5.06877i	−0.660054	−	0.193809i
$685$	5.41017	+	4.68794i	0.206712	+	0.179117i
$686$	−49.8466	+	5.50495i	−1.90315	+	0.210180i
$687$	8.25578	+	3.77029i	0.314978	+	0.143845i
$688$	−142.074	+	20.4272i	−5.41653	+	0.778779i
$689$	−41.0495			−1.56386
$690$	31.7466	−	35.6356i	1.20857	−	1.35663i
$691$			26.3845i			1.00371i	0.864951	+	0.501856i	$0.167349\pi$
$691$			26.3845i			1.00371i	−0.864951	+	0.501856i	$0.832651\pi$
$692$	52.2205	−	7.50818i	1.98513	−	0.285418i
$693$	0.380074	+	10.3618i	0.0144378	+	0.393611i
$694$	−68.9615	+	20.2489i	−2.61774	+	0.768639i
$695$	−46.5489	−	40.3348i	−1.76570	−	1.52999i
$696$	−8.54898	+	29.1151i	−0.324048	+	1.10361i
$697$	−0.344956	−	0.536762i	−0.0130661	−	0.0203313i
$698$	78.7498	−	35.9638i	2.98072	−	1.36125i
$699$	−1.75001	+	1.51639i	−0.0661914	+	0.0573552i
$700$	−12.7131	+	119.331i	−0.480510	+	4.51031i
$701$	−33.7695	−	4.85532i	−1.27546	−	0.183383i	−0.528889	−	0.848691i	$-0.677391\pi$
$701$	−33.7695	−	4.85532i	−1.27546	−	0.183383i	−0.746569	+	0.665308i	$0.768300\pi$
$702$	−2.15649	+	14.9987i	−0.0813916	+	0.566091i
$703$	−1.54828	+	2.40917i	−0.0583944	+	0.0908635i
$704$	−72.7238	+	63.0155i	−2.74088	+	2.37499i
$705$	4.47453	+	9.79786i	0.168521	+	0.369009i
$706$	25.8808	+	40.2713i	0.974036	+	1.51563i
$707$	10.3971	−	1.88620i	0.391024	−	0.0709379i
$708$	−29.9576	+	34.5729i	−1.12587	+	1.29933i
$709$	−5.99054	−	20.4019i	−0.224979	−	0.766209i	−0.992181	−	0.124804i	$-0.960170\pi$
$709$	−5.99054	−	20.4019i	−0.224979	−	0.766209i	0.767202	−	0.641405i	$-0.221648\pi$
$710$	10.6035	−	23.2183i	0.397941	−	0.871369i
$711$	6.27653	−	0.902429i	0.235388	−	0.0338437i
$712$	0.950219			0.0356109
$713$	10.5422	+	12.5097i	0.394807	+	0.468493i
$714$	−2.56515	+	1.28712i	−0.0959985	+	0.0481692i
$715$	11.4702	+	79.7772i	0.428962	+	2.98350i
$716$	−20.4722	+	44.8278i	−0.765081	+	1.67529i
$717$	−2.99685	−	10.2063i	−0.111919	−	0.381162i
$718$	−58.2287	−	50.4554i	−2.17307	−	1.88298i
$719$	8.61825	−	29.3511i	0.321406	−	1.09461i	−0.627386	−	0.778709i	$-0.715875\pi$
$719$	8.61825	−	29.3511i	0.321406	−	1.09461i	0.948792	−	0.315901i	$-0.102307\pi$
$720$	42.5697	−	27.3579i	1.58648	−	1.01957i
$721$	26.0215	−	32.3545i	0.969093	−	1.20495i
$722$	−13.5050	−	15.5856i	−0.502604	−	0.580036i
$723$	4.51461	−	7.02486i	0.167900	−	0.261257i
$724$	4.85988	−	33.8012i	0.180616	−	1.25621i
$725$	4.07096	−	28.3142i	0.151192	−	1.05156i
$726$	6.38097	−	9.92898i	0.236820	−	0.368499i
$727$	−2.57651	−	2.97345i	−0.0955574	−	0.110279i	0.705957	−	0.708255i	$-0.250517\pi$
$727$	−2.57651	−	2.97345i	−0.0955574	−	0.110279i	−0.801514	+	0.597976i	$0.795972\pi$
$728$	104.105	+	83.7274i	3.85837	+	3.10314i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	18.3028	−	62.3335i	0.677416	−	2.30707i
$731$	3.15600	+	2.73469i	0.116729	+	0.101146i
$732$	−1.73850	−	5.92080i	−0.0642570	−	0.218839i
$733$	−9.45077	+	20.6943i	−0.349072	+	0.764361i	0.650914	+	0.759151i	$0.274386\pi$
$733$	−9.45077	+	20.6943i	−0.349072	+	0.764361i	−0.999986	+	0.00521019i	$0.998342\pi$
$734$	9.17043	+	63.7817i	0.338487	+	2.35423i
$735$	−20.6241	−	15.3771i	−0.760732	−	0.567191i
$736$	−50.9420	+	76.9213i	−1.87775	+	2.83536i
$737$	18.2107			0.670800
$738$	−4.26901	+	0.613790i	−0.157144	+	0.0225939i
$739$	17.8161	−	39.0119i	0.655377	−	1.43508i	−0.231390	−	0.972861i	$-0.574327\pi$
$739$	17.8161	−	39.0119i	0.655377	−	1.43508i	0.886768	−	0.462215i	$-0.152945\pi$
$740$	−4.68613	−	15.9595i	−0.172265	−	0.586682i
$741$	12.3644	−	14.2693i	0.454219	−	0.524196i
$742$	−51.7094	+	9.38088i	−1.89831	+	0.344383i
$743$	3.95942	+	6.16097i	0.145257	+	0.226024i	0.906257	−	0.422728i	$-0.138927\pi$
$743$	3.95942	+	6.16097i	0.145257	+	0.226024i	−0.761000	+	0.648752i	$0.775291\pi$
$744$	12.7866	+	27.9988i	0.468780	+	1.02649i
$745$	−1.87408	+	1.62390i	−0.0686612	+	0.0594952i
$746$	−11.3671	+	17.6875i	−0.416179	+	0.647587i
$747$	2.30490	−	16.0309i	0.0843317	−	0.586540i
$748$	8.28624	+	1.19138i	0.302975	+	0.0435612i
$749$	−16.8925	−	1.79966i	−0.617239	−	0.0657582i
$750$	−26.3701	+	22.8499i	−0.962902	+	0.834359i
$751$	5.51488	−	2.51856i	0.201241	−	0.0919037i	−0.312245	−	0.950002i	$-0.601081\pi$
$751$	5.51488	−	2.51856i	0.201241	−	0.0919037i	0.513486	+	0.858098i	$0.328354\pi$
$752$	−21.8179	−	33.9493i	−0.795616	−	1.23800i
$753$	−3.80007	+	12.9418i	−0.138482	+	0.471627i
$754$	−38.5109	−	33.3699i	−1.40248	−	1.21526i
$755$	69.3906	−	20.3749i	2.52538	−	0.741519i
$756$	0.517141	+	14.0985i	0.0188082	+	0.512759i
$757$	−1.62100	+	0.233065i	−0.0589163	+	0.00847088i	−0.171710	−	0.985148i	$-0.554929\pi$
$757$	−1.62100	+	0.233065i	−0.0589163	+	0.00847088i	0.112794	+	0.993618i	$0.464020\pi$
$758$		−	1.81288i		−	0.0658469i
$759$	5.54257	−	17.9591i	0.201182	−	0.651875i
$760$	−111.889			−4.05862
$761$	29.1827	−	4.19585i	1.05787	−	0.152099i	0.408646	−	0.912693i	$-0.366001\pi$
$761$	29.1827	−	4.19585i	1.05787	−	0.152099i	0.649228	+	0.760594i	$0.275092\pi$
$762$	−34.0834	−	15.5654i	−1.23471	−	0.563873i
$763$	−0.109212	+	0.101877i	−0.00395375	+	0.00368820i
$764$	−1.69821	−	1.47151i	−0.0614391	−	0.0532373i
$765$	−1.41259	−	0.414774i	−0.0510723	−	0.0149962i
$766$	−74.5448	+	47.9070i	−2.69341	+	1.73095i
$767$	−19.9434	−	43.6700i	−0.720114	−	1.57683i
$768$	−20.2129	+	17.5146i	−0.729369	+	0.632002i
$769$	−2.75372	−	1.76971i	−0.0993017	−	0.0638173i	0.490048	−	0.871696i	$-0.336979\pi$
$769$	−2.75372	−	1.76971i	−0.0993017	−	0.0638173i	−0.589349	+	0.807878i	$0.700616\pi$
$770$	32.6800	+	97.8728i	1.17771	+	3.52709i
$771$	3.19650	−	22.2321i	0.115119	−	0.800670i
$772$	74.7921	+	48.0660i	2.69183	+	1.72993i
$773$	−24.5188	−	28.2962i	−0.881881	−	1.01775i	−0.999695	−	0.0247094i	$-0.992134\pi$
$773$	−24.5188	−	28.2962i	−0.881881	−	1.01775i	0.117814	−	0.993036i	$-0.462411\pi$
$774$	25.6767	−	11.7262i	0.922930	−	0.421488i
$775$	−15.6874	−	24.4101i	−0.563510	−	0.876838i
$776$	132.774	+	38.9861i	4.76633	+	1.39952i
$777$	2.17642	+	0.553264i	0.0780787	+	0.0198483i
$778$	−26.6797	−	90.8628i	−0.956514	−	3.25759i
$779$	4.88836	+	2.23244i	0.175144	+	0.0799854i
$780$	15.6067	+	108.547i	0.558811	+	3.88661i
$781$		−	10.0520i		−	0.359690i
$782$	5.15899	−	0.669497i	0.184485	−	0.0239412i
$783$		−	3.36285i		−	0.120178i
$784$	84.6829	+	46.0286i	3.02439	+	1.64388i
$785$	−30.0549	+	65.8110i	−1.07270	+	2.34889i
$786$	30.4968	−	8.95466i	1.08778	−	0.319402i
$787$	−9.90229	+	11.4279i	−0.352979	+	0.407359i	−0.904275	−	0.426950i	$-0.859588\pi$
$787$	−9.90229	+	11.4279i	−0.352979	+	0.407359i	0.551296	+	0.834309i	$0.314133\pi$
$788$	36.2532	+	10.6449i	1.29147	+	0.379209i
$789$	−3.88847	+	2.49897i	−0.138433	+	0.0889656i
$790$	57.4008	−	26.2141i	2.04223	−	0.932654i
$791$	−7.19934	−	2.97394i	−0.255979	−	0.105741i
$792$	19.1186	−	29.7491i	0.679349	−	1.05709i
$793$	6.40996	+	0.921613i	0.227624	+	0.0327274i
$794$	−23.2375	−	3.34105i	−0.824667	−	0.118569i
$795$	−22.6791	−	14.5750i	−0.804344	−	0.516920i
$796$	45.5790	+	52.6010i	1.61551	+	1.86439i
$797$	−6.02189	−	13.1861i	−0.213306	−	0.467076i	0.772489	−	0.635029i	$-0.219012\pi$
$797$	−6.02189	−	13.1861i	−0.213306	−	0.467076i	−0.985795	+	0.167953i	$0.946284\pi$
$798$	12.3144	−	20.8004i	0.435924	−	0.736327i
$799$	−0.330781	+	1.12654i	−0.0117022	+	0.0398541i
$800$	107.162	−	123.671i	3.78874	−	4.37244i
$801$	−0.101041	+	0.0296682i	−0.00357009	+	0.00104827i
$802$	20.1123	+	9.18496i	0.710189	+	0.324332i
$803$	−3.64098	−	25.3236i	−0.128487	−	0.893649i
$804$	24.7780			0.873854
$805$	26.1032	+	38.6410i	0.920018	+	1.36192i
$806$	−51.6895			−1.82068
$807$	−0.765191	−	5.32202i	−0.0269360	−	0.187344i
$808$	−32.7817	−	14.9709i	−1.15326	−	0.526674i
$809$	19.5633	−	5.74431i	0.687810	−	0.201959i	0.0808911	−	0.996723i	$-0.474223\pi$
$809$	19.5633	−	5.74431i	0.687810	−	0.201959i	0.606919	+	0.794764i	$0.292405\pi$
$810$	−6.51685	+	7.52085i	−0.228979	+	0.264256i
$811$	−6.23217	+	21.2248i	−0.218841	+	0.745304i	0.774750	+	0.632268i	$0.217876\pi$
$811$	−6.23217	+	21.2248i	−0.218841	+	0.745304i	−0.993591	+	0.113036i	$0.963942\pi$
$812$	−40.8251	−	24.1695i	−1.43268	−	0.848183i
$813$	0.581752	+	1.27386i	0.0204029	+	0.0446762i
$814$	−5.89847	−	6.80719i	−0.206741	−	0.238592i
$815$	−54.5927	−	35.0846i	−1.91230	−	1.22896i
$816$	5.45970	+	0.784987i	0.191128	+	0.0274800i
$817$	−34.8143	−	5.00554i	−1.21800	−	0.175122i
$818$	−29.0642	+	45.2248i	−1.01621	+	1.58125i
$819$	−13.6840	−	5.65267i	−0.478159	−	0.197520i
$820$	−28.3922	+	12.9663i	−0.991500	+	0.452803i
$821$	−23.5746	+	15.1505i	−0.822760	+	0.528756i	−0.882970	−	0.469430i	$-0.844459\pi$
$821$	−23.5746	+	15.1505i	−0.822760	+	0.528756i	0.0602096	+	0.998186i	$0.480823\pi$
$822$	5.06090	+	1.48601i	0.176519	+	0.0518307i
$823$	−32.2637	+	37.2343i	−1.12464	+	1.29791i	−0.175000	+	0.984568i	$0.555993\pi$
$823$	−32.2637	+	37.2343i	−1.12464	+	1.29791i	−0.949642	+	0.313338i	$0.898553\pi$
$824$	−135.870	+	39.8950i	−4.73325	+	1.38981i
$825$	−13.8484	+	30.3237i	−0.482138	+	1.05574i
$826$	−35.1021	−	50.4528i	−1.22136	−	1.75548i
$827$		−	52.6304i		−	1.83014i	−0.403297	−	0.915069i	$-0.632136\pi$
$827$		−	52.6304i		−	1.83014i	0.403297	−	0.915069i	$-0.367864\pi$
$828$	7.54138	−	24.4357i	0.262081	−	0.849200i
$829$		−	48.9074i		−	1.69863i	−0.527890	−	0.849313i	$-0.677017\pi$
$829$		−	48.9074i		−	1.69863i	0.527890	−	0.849313i	$-0.322983\pi$
$830$	−22.9372	−	159.532i	−0.796161	−	5.53742i
$831$	4.23604	+	1.93453i	0.146947	+	0.0671083i
$832$	−38.7111	−	131.838i	−1.34206	−	4.57065i
$833$	−0.601351	−	2.73893i	−0.0208356	−	0.0948983i
$834$	−43.5438	−	12.7856i	−1.50780	−	0.442730i
$835$	−18.0768	−	28.1281i	−0.625574	−	0.973412i
$836$	−64.1370	+	29.2904i	−2.21822	+	1.01303i
$837$	−2.23384	−	2.57799i	−0.0772130	−	0.0891085i
$838$	69.9586	+	44.9596i	2.41668	+	1.55310i
$839$	1.78572	−	12.4200i	0.0616500	−	0.428785i	−0.935499	−	0.353329i	$-0.885050\pi$
$839$	1.78572	−	12.4200i	0.0616500	−	0.428785i	0.997149	−	0.0754562i	$-0.0240413\pi$
$840$	27.7878	+	83.2211i	0.958769	+	2.87140i
$841$	−14.8828	−	9.56460i	−0.513201	−	0.329814i
$842$	−52.7469	+	45.7054i	−1.81778	+	1.57511i
$843$	−9.44467	−	20.6809i	−0.325292	−	0.712290i
$844$	97.7713	−	62.8338i	3.36543	−	2.16283i
$845$	−64.5831	−	18.9633i	−2.22173	−	0.652357i
$846$	5.99787	+	5.19718i	0.206211	+	0.178683i
$847$	7.86627	+	8.43265i	0.270288	+	0.289749i
$848$	91.8760	+	41.9584i	3.15504	+	1.44086i
$849$	17.8561	−	2.56733i	0.612821	−	0.0881104i
$850$	−9.22713			−0.316488
$851$	−3.39381	−	2.24759i	−0.116338	−	0.0770463i
$852$		−	13.6771i		−	0.468569i
$853$	7.72555	−	1.11077i	0.264518	−	0.0380319i	−0.00877983	−	0.999961i	$-0.502795\pi$
$853$	7.72555	−	1.11077i	0.264518	−	0.0380319i	0.273298	+	0.961930i	$0.411886\pi$
$854$	8.28514	−	0.303902i	0.283512	−	0.0103993i
$855$	11.8976	−	3.49344i	0.406888	−	0.119473i
$856$	43.7868	+	37.9415i	1.49660	+	1.29681i
$857$	−8.53421	+	29.0648i	−0.291523	+	0.992836i	0.675333	+	0.737513i	$0.264000\pi$
$857$	−8.53421	+	29.0648i	−0.291523	+	0.992836i	−0.966856	+	0.255323i	$0.917818\pi$
$858$	32.1058	+	49.9577i	1.09608	+	1.70553i
$859$	−30.3341	+	13.8531i	−1.03499	+	0.472663i	−0.859133	−	0.511753i	$-0.828996\pi$
$859$	−30.3341	+	13.8531i	−1.03499	+	0.472663i	−0.175855	+	0.984416i	$0.556269\pi$
$860$	154.389	−	133.778i	5.26461	−	4.56181i
$861$	0.446420	−	4.19032i	0.0152139	−	0.142806i
$862$	56.9029	+	8.18140i	1.93812	+	0.278660i
$863$	−2.22641	+	15.4850i	−0.0757879	+	0.527116i	0.916194	+	0.400735i	$0.131245\pi$
$863$	−2.22641	+	15.4850i	−0.0757879	+	0.527116i	−0.991982	+	0.126381i	$0.959664\pi$
$864$	10.4006	−	16.1837i	0.353837	−	0.550581i
$865$	−27.4797	+	23.8113i	−0.934339	+	0.809610i
$866$	−15.3553	−	33.6233i	−0.521793	−	1.14257i
$867$	9.10413	+	14.1663i	0.309193	+	0.481113i
$868$	−47.3521	+	8.59040i	−1.60723	+	0.291577i
$869$	16.2738	−	18.7810i	0.552051	−	0.637101i
$870$	−9.42830	−	32.1098i	−0.319649	−	1.08863i
$871$	−10.8021	+	23.6533i	−0.366016	+	0.801462i
$872$	0.504186	−	0.0724910i	0.0170739	−	0.00245486i
$873$	−15.3357			−0.519034
$874$	−33.5053	+	28.2355i	−1.13333	+	0.955079i
$875$	−15.2899	−	30.4719i	−0.516893	−	1.03014i
$876$	−4.95403	−	34.4560i	−0.167381	−	1.16416i
$877$	−14.3655	+	31.4561i	−0.485088	+	1.06220i	0.495944	+	0.868354i	$0.334822\pi$
$877$	−14.3655	+	31.4561i	−0.485088	+	1.06220i	−0.981033	+	0.193841i	$0.937905\pi$
$878$	0.503229	+	1.71384i	0.0169832	+	0.0578394i
$879$	12.3876	+	10.7339i	0.417823	+	0.362046i
$880$	55.8712	−	190.280i	1.88342	−	6.41433i
$881$	−45.6014	+	29.3063i	−1.53635	+	0.987353i	−0.547775	+	0.836625i	$0.684525\pi$
$881$	−45.6014	+	29.3063i	−1.53635	+	0.987353i	−0.988575	+	0.150727i	$0.951838\pi$
$882$	−18.5294	−	3.99341i	−0.623916	−	0.134465i
$883$	30.5290	+	35.2323i	1.02738	+	1.18566i	0.982422	+	0.186673i	$0.0597703\pi$
$883$	30.5290	+	35.2323i	1.02738	+	1.18566i	0.0449592	+	0.998989i	$0.485684\pi$
$884$	−6.46263	+	10.0560i	−0.217362	+	0.338221i
$885$	4.48702	−	31.2079i	0.150830	−	1.04904i
$886$	−10.4589	+	72.7433i	−0.351374	+	2.44386i
$887$	−0.264637	+	0.411784i	−0.00888566	+	0.0138263i	−0.845668	−	0.533709i	$-0.820798\pi$
$887$	−0.264637	+	0.411784i	−0.00888566	+	0.0138263i	0.836782	+	0.547536i	$0.184434\pi$
$888$	−5.01546	−	5.78814i	−0.168308	−	0.194237i
$889$	22.9444	−	28.5285i	0.769531	−	0.956816i
$890$	−0.881596	+	0.566568i	−0.0295512	+	0.0189914i
$891$	−1.10411	+	3.76027i	−0.0369892	+	0.125974i
$892$	−3.68108	−	3.18968i	−0.123252	−	0.106798i
$893$	−2.78601	−	9.48829i	−0.0932304	−	0.317513i
$894$	−0.759009	+	1.66200i	−0.0253851	+	0.0555855i
$895$	−4.83373	−	33.6193i	−0.161574	−	1.12377i
$896$	−33.2388	−	66.2430i	−1.11043	−	2.21302i
$897$	20.0388	+	17.8519i	0.669077	+	0.596059i
$898$	88.2570			2.94518
$899$	11.3545	−	1.63253i	0.378694	−	0.0544480i
$900$	−18.8425	+	41.2593i	−0.628084	+	1.37531i
$901$	−0.827892	−	2.81954i	−0.0275811	−	0.0939326i
$902$	−11.0687	+	12.7739i	−0.368547	+	0.425326i
$903$	4.92316	+	27.1375i	0.163833	+	0.903079i
$904$	14.3626	+	22.3487i	0.477694	+	0.743306i
$905$	9.77705	+	21.4088i	0.325000	+	0.711651i
$906$	40.2708	−	34.8948i	1.33791	−	1.15930i
$907$	2.40194	−	3.73749i	0.0797550	−	0.124101i	−0.799085	−	0.601219i	$-0.794682\pi$
$907$	2.40194	−	3.73749i	0.0797550	−	0.124101i	0.878839	+	0.477118i	$0.158318\pi$
$908$	−6.33808	+	44.0823i	−0.210337	+	1.46292i
$909$	3.95324	+	0.568390i	0.131121	+	0.0188523i
$910$	−146.509	−	15.6085i	−4.85672	−	0.517416i
$911$	19.6702	−	17.0443i	0.651704	−	0.564704i	−0.265012	−	0.964245i	$-0.585376\pi$
$911$	19.6702	−	17.0443i	0.651704	−	0.564704i	0.916715	+	0.399541i	$0.130830\pi$
$912$	−42.2591	+	19.2991i	−1.39934	+	0.639056i
$913$	−34.3152	−	53.3956i	−1.13567	−	1.76714i
$914$	11.4423	−	38.9689i	0.378478	−	1.28898i
$915$	3.21416	+	2.78508i	0.106257	+	0.0920720i
$916$	46.4356	−	13.6347i	1.53428	−	0.450504i
$917$	1.13837	+	31.0347i	0.0375922	+	1.02486i
$918$	−1.07370	+	0.154375i	−0.0354375	+	0.00509514i
$919$			8.79018i			0.289961i	0.989434	+	0.144981i	$0.0463120\pi$
$919$			8.79018i			0.289961i	−0.989434	+	0.144981i	$0.953688\pi$
$920$	2.18639	−	159.023i	0.0720831	−	5.24284i
$921$	33.3839			1.10004
$922$	28.2599	−	4.06316i	0.930691	−	0.133813i
$923$	13.0563	+	5.96260i	0.429752	+	0.196261i
$924$	37.7143	+	40.4298i	1.24071	+	1.33004i
$925$	5.45644	+	4.72803i	0.179407	+	0.155457i
$926$	15.1978	+	4.46247i	0.499430	+	0.146646i
$927$	13.2020	−	8.48439i	0.433609	−	0.278664i
$928$	26.8745	+	58.8470i	0.882200	+	1.93175i
$929$	−7.44731	+	6.45313i	−0.244338	+	0.211720i	−0.768417	−	0.639950i	$-0.778955\pi$
$929$	−7.44731	+	6.45313i	−0.244338	+	0.211720i	0.524079	+	0.851670i	$0.324410\pi$
$930$	−28.5575	−	18.3528i	−0.936437	−	0.601811i
$931$	16.7327	+	16.6683i	0.548393	+	0.546283i
$932$	−1.75724	+	12.2218i	−0.0575602	+	0.400340i
$933$	28.6939	+	18.4405i	0.939397	+	0.603714i
$934$	21.2342	+	24.5056i	0.694806	+	0.801849i
$935$	−5.24828	+	2.39681i	−0.171637	+	0.0783840i
$936$	27.2995	+	42.4789i	0.892313	+	1.38847i
$937$	55.5782	+	16.3192i	1.81566	+	0.533126i	0.999030	−	0.0440365i	$-0.0140218\pi$
$937$	55.5782	+	16.3192i	1.81566	+	0.533126i	0.816630	+	0.577162i	$0.195840\pi$
$938$	−8.20184	+	32.2643i	−0.267800	+	1.05347i
$939$	−3.88359	−	13.2263i	−0.126736	−	0.431623i
$940$	52.2455	+	23.8597i	1.70406	+	0.778218i
$941$	−2.55007	−	17.7361i	−0.0831298	−	0.578181i	−0.988229	−	0.152981i	$-0.951113\pi$
$941$	−2.55007	−	17.7361i	−0.0831298	−	0.578181i	0.905099	−	0.425200i	$-0.139796\pi$
$942$			53.3072i			1.73684i
$943$	−3.26840	+	6.90402i	−0.106434	+	0.224826i
$944$			118.126i			3.84468i
$945$	−5.55316	−	7.98163i	−0.180644	−	0.259642i
$946$	45.9550	−	100.627i	1.49413	−	3.27168i
$947$	36.6945	−	10.7745i	1.19241	−	0.350123i	0.375464	−	0.926837i	$-0.377483\pi$
$947$	36.6945	−	10.7745i	1.19241	−	0.350123i	0.816946	+	0.576714i	$0.195665\pi$
$948$	22.1426	−	25.5540i	0.719159	−	0.829954i
$949$	35.0517	+	10.2921i	1.13783	+	0.334096i
$950$	65.3786	−	42.0163i	2.12116	−	1.36319i
$951$	−6.33645	+	2.89376i	−0.205474	+	0.0938366i
$952$	−3.65134	+	8.83921i	−0.118341	+	0.286480i
$953$	−15.5392	+	24.1794i	−0.503363	+	0.783248i	−0.996220	−	0.0868624i	$-0.972316\pi$
$953$	−15.5392	+	24.1794i	−0.503363	+	0.783248i	0.492858	+	0.870110i	$0.335952\pi$
$954$	−19.6611	−	2.82684i	−0.636553	−	0.0915225i
$955$	1.53293	+	0.220401i	0.0496043	+	0.00713202i
$956$	−47.7168	−	30.6657i	−1.54327	−	0.991801i
$957$	−8.63046	−	9.96008i	−0.278983	−	0.321964i
$958$	−1.86344	−	4.08036i	−0.0602050	−	0.131831i
$959$	−2.62547	+	4.43474i	−0.0847809	+	0.143205i
$960$	25.4230	−	86.5826i	0.820522	−	2.79444i
$961$	−12.6806	+	14.6342i	−0.409053	+	0.472072i
$962$	12.3405	−	3.62349i	0.397873	−	0.116826i
$963$	−5.84066	−	2.66734i	−0.188213	−	0.0859538i
$964$	−6.33692	−	44.0743i	−0.204099	−	1.41954i
$965$	−61.2744			−1.97249
$966$	29.3223	+	17.9084i	0.943428	+	0.576194i
$967$	−7.49444			−0.241005			−0.120503	−	0.992713i	$-0.538451\pi$
$967$	−7.49444			−0.241005			−0.120503	+	0.992713i	$0.538451\pi$
$968$	−5.59727	−	38.9299i	−0.179903	−	1.25125i
$969$	1.22948	+	0.561483i	0.0394965	+	0.0180374i
$970$	−146.431	+	42.9961i	−4.70163	+	1.38052i
$971$	25.8473	−	29.8294i	0.829479	−	0.957270i	−0.170124	−	0.985423i	$-0.554417\pi$
$971$	25.8473	−	29.8294i	0.829479	−	0.957270i	0.999604	+	0.0281526i	$0.00896244\pi$
$972$	−1.50229	+	5.11634i	−0.0481860	+	0.164107i
$973$	22.5895	−	38.1563i	0.724185	−	1.22324i
$974$	39.0924	+	85.6003i	1.25260	+	2.74281i
$975$	−31.1720	−	35.9744i	−0.998304	−	1.15210i
$976$	−13.4046	−	8.61462i	−0.429071	−	0.275747i
$977$	0.101857	+	0.0146448i	0.00325870	+	0.000468530i	0.143944	−	0.989586i	$-0.454021\pi$
$977$	0.101857	+	0.0146448i	0.00325870	+	0.000468530i	−0.140685	+	0.990054i	$0.544931\pi$
$978$	−47.3279	−	6.80473i	−1.51338	−	0.217591i
$979$	−0.223121	+	0.347183i	−0.00713097	+	0.0110960i
$980$	−136.809	+	10.0499i	−4.37020	+	0.321034i
$981$	−0.0513488	+	0.0234502i	−0.00163944	+	0.000748708i
$982$	−43.6707	+	28.0655i	−1.39359	+	0.895605i
$983$	7.35575	+	2.15984i	0.234612	+	0.0688883i	0.396925	−	0.917851i	$-0.370077\pi$
$983$	7.35575	+	2.15984i	0.234612	+	0.0688883i	−0.162313	+	0.986739i	$0.551895\pi$
$984$	−9.41168	+	10.8617i	−0.300034	+	0.346257i
$985$	−24.9860	+	7.33655i	−0.796120	+	0.233762i
$986$	1.51536	−	3.31819i	0.0482590	−	0.105673i
$987$	−6.36534	+	4.42863i	−0.202611	+	0.140965i
$988$		−	100.680i		−	3.20305i
$989$	7.79449	−	49.3824i	0.247850	−	1.57027i
$990$			39.0001i			1.23951i
$991$	−2.15359	−	14.9785i	−0.0684109	−	0.475808i	−0.995011	−	0.0997612i	$-0.968192\pi$
$991$	−2.15359	−	14.9785i	−0.0684109	−	0.475808i	0.926600	−	0.376047i	$-0.122717\pi$
$992$	59.6927	+	27.2607i	1.89524	+	0.865529i
$993$	−0.593896	−	2.02262i	−0.0188467	−	0.0641860i
$994$	17.8094	+	4.52729i	0.564879	+	0.143597i
$995$	−46.0265	−	13.5146i	−1.45914	−	0.428442i
$996$	−46.6904	−	72.6516i	−1.47944	−	2.30205i
$997$	−44.2144	+	20.1920i	−1.40028	+	0.639488i	−0.965346	−	0.260972i	$-0.915957\pi$
$997$	−44.2144	+	20.1920i	−1.40028	+	0.639488i	−0.434938	+	0.900461i	$0.643230\pi$
$998$	65.3481	+	75.4157i	2.06856	+	2.38724i
$999$	0.714034	+	0.458882i	0.0225910	+	0.0145184i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.r.a.181.31	✓	320
7.6	odd	2	inner	483.2.r.a.181.32	yes	320
23.15	odd	22	inner	483.2.r.a.475.32	yes	320
161.153	even	22	inner	483.2.r.a.475.31	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.181.31	✓	320	1.1	even	1	trivial
483.2.r.a.181.32	yes	320	7.6	odd	2	inner
483.2.r.a.475.31	yes	320	161.153	even	22	inner
483.2.r.a.475.32	yes	320	23.15	odd	22	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.385364 + 2.68027i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(-5.11634 + 1.50229i) q^{4} +(2.40667 - 2.77745i) q^{5} +(0.762883 - 2.59814i) q^{6} +(2.27668 + 1.34785i) q^{7} +(-3.74845 - 8.20796i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.385364 + 2.68027i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(-5.11634 + 1.50229i) q^{4} +(2.40667 - 2.77745i) q^{5} +(0.762883 - 2.59814i) q^{6} +(2.27668 + 1.34785i) q^{7} +(-3.74845 - 8.20796i) q^{8} +(0.654861 + 0.755750i) q^{9} +(8.37174 + 5.38019i) q^{10} +(3.87913 + 0.557734i) q^{11} +(5.27806 + 0.758870i) q^{12} +(-3.02542 + 4.70765i) q^{13} +(-2.73525 + 6.62153i) q^{14} +(-3.34298 + 1.52669i) q^{15} +(11.5833 - 7.44414i) q^{16} +(-0.384369 - 0.112861i) q^{17} +(-1.77325 + 2.04644i) q^{18} +(3.23735 - 0.950573i) q^{19} +(-8.14080 + 17.8259i) q^{20} +(-1.51103 - 2.17182i) q^{21} +10.6120i q^{22} +(1.28775 + 4.61971i) q^{23} +9.02339i q^{24} +(-1.21057 - 8.41969i) q^{25} +(-13.7836 - 6.29477i) q^{26} +(-0.281733 - 0.959493i) q^{27} +(-13.6732 - 3.47583i) q^{28} +(3.22663 + 0.947424i) q^{29} +(-5.38019 - 8.37174i) q^{30} +(3.10291 - 1.41705i) q^{31} +(12.5980 + 14.5388i) q^{32} +(-3.29689 - 2.11878i) q^{33} +(0.154375 - 1.07370i) q^{34} +(9.22282 - 3.07953i) q^{35} +(-4.48584 - 2.88288i) q^{36} +(-0.641460 + 0.555829i) q^{37} +(3.79535 + 8.31065i) q^{38} +(4.70765 - 3.02542i) q^{39} +(-31.8185 - 9.34274i) q^{40} +(1.20372 + 1.04303i) q^{41} +(5.23876 - 4.88689i) q^{42} +(-9.48239 - 4.33046i) q^{43} +(-20.6848 + 2.97403i) q^{44} +3.67509 q^{45} +(-11.8858 + 5.23179i) q^{46} -2.93088i q^{47} +(-13.6290 + 1.95955i) q^{48} +(3.36658 + 6.13727i) q^{49} +(22.1005 - 6.48929i) q^{50} +(0.302750 + 0.262334i) q^{51} +(8.40681 - 28.6310i) q^{52} +(3.96588 + 6.17103i) q^{53} +(2.46313 - 1.12487i) q^{54} +(10.8849 - 9.43179i) q^{55} +(2.52909 - 23.7393i) q^{56} +(-3.33968 - 0.480174i) q^{57} +(-1.29592 + 9.01334i) q^{58} +(-4.63819 + 7.21717i) q^{59} +(14.8103 - 12.8332i) q^{60} +(-0.480733 - 1.05266i) q^{61} +(4.99383 + 7.77056i) q^{62} +(0.472272 + 2.60326i) q^{63} +(-16.0794 + 18.5566i) q^{64} +(5.79404 + 19.7327i) q^{65} +(4.40839 - 9.65304i) q^{66} +(4.59946 - 0.661302i) q^{67} +2.13611 q^{68} +(0.747713 - 4.73719i) q^{69} +(11.8081 + 23.5329i) q^{70} +(-0.365028 - 2.53883i) q^{71} +(3.74845 - 8.20796i) q^{72} +(-1.83920 - 6.26372i) q^{73} +(-1.73696 - 1.50509i) q^{74} +(-2.39649 + 8.16171i) q^{75} +(-15.1353 + 9.72690i) q^{76} +(8.07980 + 6.49828i) q^{77} +(9.92309 + 11.4519i) q^{78} +(3.42825 - 5.33445i) q^{79} +(7.20152 - 50.0876i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-2.33173 + 3.62825i) q^{82} +(-10.6060 - 12.2399i) q^{83} +(10.9936 + 8.84176i) q^{84} +(-1.23851 + 0.795945i) q^{85} +(7.95262 - 27.0841i) q^{86} +(-2.54147 - 2.20220i) q^{87} +(-9.96285 - 33.9304i) q^{88} +(-0.0437458 + 0.0957899i) q^{89} +(1.41625 + 9.85022i) q^{90} +(-13.2331 + 6.64000i) q^{91} +(-13.5287 - 21.7014i) q^{92} -3.41118 q^{93} +(7.85554 - 1.12946i) q^{94} +(5.15108 - 11.2793i) q^{95} +(-5.41986 - 18.4584i) q^{96} +(-10.0427 + 11.5899i) q^{97} +(-15.1522 + 11.3884i) q^{98} +(2.11878 + 3.29689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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