LMFDB - Embedded newform 105.3.k.d.62.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(62,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("105.62");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.k (of order $4$, 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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			62.4
Character	$\chi$	$=$	105.62
Dual form			105.3.k.d.83.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.28094 + 2.28094i) q^{2} +(1.07458 - 2.80094i) q^{3} -6.40541i q^{4} +(-1.80941 + 4.66112i) q^{5} +(3.93772 + 8.83986i) q^{6} +(-3.20922 - 6.22100i) q^{7} +(5.48661 + 5.48661i) q^{8} +(-6.69054 - 6.01969i) q^{9} +O(q^{10})$	\(q+(-2.28094 + 2.28094i) q^{2} +(1.07458 - 2.80094i) q^{3} -6.40541i q^{4} +(-1.80941 + 4.66112i) q^{5} +(3.93772 + 8.83986i) q^{6} +(-3.20922 - 6.22100i) q^{7} +(5.48661 + 5.48661i) q^{8} +(-6.69054 - 6.01969i) q^{9} +(-6.50460 - 14.7589i) q^{10} -11.1704i q^{11} +(-17.9412 - 6.88316i) q^{12} +(-5.82807 - 5.82807i) q^{13} +(21.5098 + 6.86971i) q^{14} +(11.1112 + 10.0768i) q^{15} +0.592330 q^{16} +(-6.84147 - 6.84147i) q^{17} +(28.9913 - 1.53016i) q^{18} +25.0261 q^{19} +(29.8564 + 11.5900i) q^{20} +(-20.8732 + 2.30385i) q^{21} +(25.4792 + 25.4792i) q^{22} +(-23.3593 - 23.3593i) q^{23} +(21.2635 - 9.47185i) q^{24} +(-18.4521 - 16.8677i) q^{25} +26.5870 q^{26} +(-24.0503 + 12.2711i) q^{27} +(-39.8481 + 20.5564i) q^{28} +10.6354 q^{29} +(-48.3286 + 2.35930i) q^{30} +26.9470i q^{31} +(-23.2975 + 23.2975i) q^{32} +(-31.2877 - 12.0036i) q^{33} +31.2100 q^{34} +(34.8036 - 3.70223i) q^{35} +(-38.5586 + 42.8557i) q^{36} +(-20.8846 - 20.8846i) q^{37} +(-57.0831 + 57.0831i) q^{38} +(-22.5868 + 10.0613i) q^{39} +(-35.5013 + 15.6462i) q^{40} -32.9644 q^{41} +(42.3558 - 52.8657i) q^{42} +(1.25060 - 1.25060i) q^{43} -71.5513 q^{44} +(40.1644 - 20.2933i) q^{45} +106.562 q^{46} +(59.1134 + 59.1134i) q^{47} +(0.636508 - 1.65908i) q^{48} +(-28.4018 + 39.9292i) q^{49} +(80.5625 - 3.61381i) q^{50} +(-26.5143 + 11.8108i) q^{51} +(-37.3312 + 37.3312i) q^{52} +(26.0484 + 26.0484i) q^{53} +(26.8677 - 82.8473i) q^{54} +(52.0668 + 20.2119i) q^{55} +(16.5245 - 51.7400i) q^{56} +(26.8926 - 70.0965i) q^{57} +(-24.2588 + 24.2588i) q^{58} -70.2066i q^{59} +(64.5461 - 71.1716i) q^{60} +14.1716i q^{61} +(-61.4646 - 61.4646i) q^{62} +(-15.9771 + 60.9404i) q^{63} -103.911i q^{64} +(37.7107 - 16.6200i) q^{65} +(98.7451 - 43.9861i) q^{66} +(-6.14458 - 6.14458i) q^{67} +(-43.8225 + 43.8225i) q^{68} +(-90.5294 + 40.3264i) q^{69} +(-70.9406 + 87.8297i) q^{70} -39.0498i q^{71} +(-3.68068 - 69.7361i) q^{72} +(51.1141 + 51.1141i) q^{73} +95.2731 q^{74} +(-67.0738 + 33.5574i) q^{75} -160.302i q^{76} +(-69.4914 + 35.8484i) q^{77} +(28.5700 - 74.4687i) q^{78} +16.8398i q^{79} +(-1.07177 + 2.76092i) q^{80} +(8.52661 + 80.5500i) q^{81} +(75.1900 - 75.1900i) q^{82} +(31.3367 - 31.3367i) q^{83} +(14.7571 + 133.702i) q^{84} +(44.2679 - 19.5099i) q^{85} +5.70508i q^{86} +(11.4286 - 29.7891i) q^{87} +(61.2879 - 61.2879i) q^{88} -70.8895i q^{89} +(-45.3249 + 137.901i) q^{90} +(-17.5529 + 54.9600i) q^{91} +(-149.626 + 149.626i) q^{92} +(75.4769 + 28.9568i) q^{93} -269.669 q^{94} +(-45.2824 + 116.650i) q^{95} +(40.2198 + 90.2902i) q^{96} +(114.216 - 114.216i) q^{97} +(-26.2933 - 155.859i) q^{98} +(-67.2426 + 74.7363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 48 q^{15} - 24 q^{16} - 92 q^{18} - 60 q^{21} + 112 q^{22} - 72 q^{25} + 88 q^{28} - 108 q^{30} + 416 q^{36} + 72 q^{37} + 300 q^{42} - 328 q^{43} + 32 q^{46} + 148 q^{51} - 748 q^{57} - 392 q^{58} + 544 q^{60} - 220 q^{63} - 648 q^{67} - 8 q^{70} - 8 q^{72} + 500 q^{78} - 948 q^{81} + 672 q^{85} + 1288 q^{88} + 808 q^{91} + 292 q^{93}+O(q^{100}) $ 32 * q - 48 * q^15 - 24 * q^16 - 92 * q^18 - 60 * q^21 + 112 * q^22 - 72 * q^25 + 88 * q^28 - 108 * q^30 + 416 * q^36 + 72 * q^37 + 300 * q^42 - 328 * q^43 + 32 * q^46 + 148 * q^51 - 748 * q^57 - 392 * q^58 + 544 * q^60 - 220 * q^63 - 648 * q^67 - 8 * q^70 - 8 * q^72 + 500 * q^78 - 948 * q^81 + 672 * q^85 + 1288 * q^88 + 808 * q^91 + 292 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.28094	+	2.28094i	−1.14047	+	1.14047i	−0.152108	+	0.988364i	$0.548606\pi$
$2$	−2.28094	+	2.28094i	−1.14047	+	1.14047i	−0.988364	+	0.152108i	$0.951394\pi$
$3$	1.07458	−	2.80094i	0.358195	−	0.933647i
$3$	1.07458	−	2.80094i	0.358195	−	0.933647i
$4$		−	6.40541i		−	1.60135i
$5$	−1.80941	+	4.66112i	−0.361882	+	0.932224i
$5$	−1.80941	+	4.66112i	−0.361882	+	0.932224i
$6$	3.93772	+	8.83986i	0.656287	+	1.47331i
$7$	−3.20922	−	6.22100i	−0.458460	−	0.888715i
$7$	−3.20922	−	6.22100i	−0.458460	−	0.888715i
$8$	5.48661	+	5.48661i	0.685827	+	0.685827i
$9$	−6.69054	−	6.01969i	−0.743393	−	0.668855i
$10$	−6.50460	−	14.7589i	−0.650460	−	1.47589i
$11$		−	11.1704i		−	1.01549i	−0.861506	−	0.507747i	$-0.830478\pi$
$11$		−	11.1704i		−	1.01549i	0.861506	−	0.507747i	$-0.169522\pi$
$12$	−17.9412	−	6.88316i	−1.49510	−	0.573596i
$13$	−5.82807	−	5.82807i	−0.448313	−	0.448313i	0.446480	−	0.894794i	$-0.352677\pi$
$13$	−5.82807	−	5.82807i	−0.448313	−	0.448313i	−0.894794	+	0.446480i	$0.852677\pi$
$14$	21.5098	+	6.86971i	1.53642	+	0.490694i
$15$	11.1112	+	10.0768i	0.740744	+	0.671787i
$16$	0.592330			0.0370206
$17$	−6.84147	−	6.84147i	−0.402440	−	0.402440i	0.476652	−	0.879092i	$-0.341850\pi$
$17$	−6.84147	−	6.84147i	−0.402440	−	0.402440i	−0.879092	+	0.476652i	$0.841850\pi$
$18$	28.9913	−	1.53016i	1.61063	−	0.0850091i
$19$	25.0261			1.31716			0.658581	−	0.752510i	$-0.271157\pi$
$19$	25.0261			1.31716			0.658581	+	0.752510i	$0.271157\pi$
$20$	29.8564	+	11.5900i	1.49282	+	0.579500i
$21$	−20.8732	+	2.30385i	−0.993964	+	0.109707i
$22$	25.4792	+	25.4792i	1.15814	+	1.15814i
$23$	−23.3593	−	23.3593i	−1.01562	−	1.01562i	−0.999876	−	0.0157445i	$-0.994988\pi$
$23$	−23.3593	−	23.3593i	−1.01562	−	1.01562i	−0.0157445	−	0.999876i	$-0.505012\pi$
$24$	21.2635	−	9.47185i	0.885980	−	0.394661i
$25$	−18.4521	−	16.8677i	−0.738083	−	0.674710i
$26$	26.5870			1.02258
$27$	−24.0503	+	12.2711i	−0.890754	+	0.454487i
$28$	−39.8481	+	20.5564i	−1.42315	+	0.734157i
$29$	10.6354			0.366738			0.183369	−	0.983044i	$-0.441300\pi$
$29$	10.6354			0.366738			0.183369	+	0.983044i	$0.441300\pi$
$30$	−48.3286	+	2.35930i	−1.61095	+	0.0786432i
$31$			26.9470i			0.869257i	0.900610	+	0.434629i	$0.143120\pi$
$31$			26.9470i			0.869257i	−0.900610	+	0.434629i	$0.856880\pi$
$32$	−23.2975	+	23.2975i	−0.728048	+	0.728048i
$33$	−31.2877	−	12.0036i	−0.948113	−	0.363745i
$34$	31.2100			0.917942
$35$	34.8036	−	3.70223i	0.994390	−	0.105778i
$36$	−38.5586	+	42.8557i	−1.07107	+	1.19044i
$37$	−20.8846	−	20.8846i	−0.564448	−	0.564448i	0.366120	−	0.930568i	$-0.380686\pi$
$37$	−20.8846	−	20.8846i	−0.564448	−	0.564448i	−0.930568	+	0.366120i	$0.880686\pi$
$38$	−57.0831	+	57.0831i	−1.50219	+	1.50219i
$39$	−22.5868	+	10.0613i	−0.579150	+	0.257983i
$40$	−35.5013	+	15.6462i	−0.887532	+	0.391156i
$41$	−32.9644			−0.804010			−0.402005	−	0.915637i	$-0.631687\pi$
$41$	−32.9644			−0.804010			−0.402005	+	0.915637i	$0.631687\pi$
$42$	42.3558	−	52.8657i	1.00847	−	1.25871i
$43$	1.25060	−	1.25060i	0.0290836	−	0.0290836i	−0.692415	−	0.721499i	$-0.743453\pi$
$43$	1.25060	−	1.25060i	0.0290836	−	0.0290836i	0.721499	+	0.692415i	$0.243453\pi$
$44$	−71.5513			−1.62617
$45$	40.1644	−	20.2933i	0.892543	−	0.450963i
$46$	106.562			2.31657
$47$	59.1134	+	59.1134i	1.25773	+	1.25773i	0.952173	+	0.305558i	$0.0988431\pi$
$47$	59.1134	+	59.1134i	1.25773	+	1.25773i	0.305558	+	0.952173i	$0.401157\pi$
$48$	0.636508	−	1.65908i	0.0132606	−	0.0345642i
$49$	−28.4018	+	39.9292i	−0.579629	+	0.814881i
$50$	80.5625	−	3.61381i	1.61125	−	0.0722761i
$51$	−26.5143	+	11.8108i	−0.519888	+	0.231585i
$52$	−37.3312	+	37.3312i	−0.717908	+	0.717908i
$53$	26.0484	+	26.0484i	0.491478	+	0.491478i	0.908772	−	0.417293i	$-0.137021\pi$
$53$	26.0484	+	26.0484i	0.491478	+	0.491478i	−0.417293	+	0.908772i	$0.637021\pi$
$54$	26.8677	−	82.8473i	0.497550	−	1.53421i
$55$	52.0668	+	20.2119i	0.946669	+	0.367489i
$56$	16.5245	−	51.7400i	0.295080	−	0.923929i
$57$	26.8926	−	70.0965i	0.471800	−	1.22976i
$58$	−24.2588	+	24.2588i	−0.418254	+	0.418254i
$59$		−	70.2066i		−	1.18994i	−0.803747	−	0.594971i	$-0.797163\pi$
$59$		−	70.2066i		−	1.18994i	0.803747	−	0.594971i	$-0.202837\pi$
$60$	64.5461	−	71.1716i	1.07577	−	1.18619i
$61$			14.1716i			0.232321i	0.993230	+	0.116161i	$0.0370587\pi$
$61$			14.1716i			0.232321i	−0.993230	+	0.116161i	$0.962941\pi$
$62$	−61.4646	−	61.4646i	−0.991364	−	0.991364i
$63$	−15.9771	+	60.9404i	−0.253605	+	0.967308i
$64$		−	103.911i		−	1.62362i
$65$	37.7107	−	16.6200i	0.580165	−	0.255692i
$66$	98.7451	−	43.9861i	1.49614	−	0.666456i
$67$	−6.14458	−	6.14458i	−0.0917101	−	0.0917101i	0.659763	−	0.751473i	$-0.270657\pi$
$67$	−6.14458	−	6.14458i	−0.0917101	−	0.0917101i	−0.751473	+	0.659763i	$0.770657\pi$
$68$	−43.8225	+	43.8225i	−0.644448	+	0.644448i
$69$	−90.5294	+	40.3264i	−1.31202	+	0.584441i
$70$	−70.9406	+	87.8297i	−1.01344	+	1.25471i
$71$		−	39.0498i		−	0.549997i	−0.961445	−	0.274999i	$-0.911323\pi$
$71$		−	39.0498i		−	0.549997i	0.961445	−	0.274999i	$-0.0886774\pi$
$72$	−3.68068	−	69.7361i	−0.0511205	−	0.968557i
$73$	51.1141	+	51.1141i	0.700193	+	0.700193i	0.964452	−	0.264259i	$-0.0851274\pi$
$73$	51.1141	+	51.1141i	0.700193	+	0.700193i	−0.264259	+	0.964452i	$0.585127\pi$
$74$	95.2731			1.28747
$75$	−67.0738	+	33.5574i	−0.894318	+	0.447432i
$76$		−	160.302i		−	2.10924i
$77$	−69.4914	+	35.8484i	−0.902485	+	0.465564i
$78$	28.5700	−	74.4687i	0.366282	−	0.954726i
$79$			16.8398i			0.213162i	0.994304	+	0.106581i	$0.0339903\pi$
$79$			16.8398i			0.213162i	−0.994304	+	0.106581i	$0.966010\pi$
$80$	−1.07177	+	2.76092i	−0.0133971	+	0.0345115i
$81$	8.52661	+	80.5500i	0.105267	+	0.994444i
$82$	75.1900	−	75.1900i	0.916951	−	0.916951i
$83$	31.3367	−	31.3367i	0.377551	−	0.377551i	−0.492667	−	0.870218i	$-0.663978\pi$
$83$	31.3367	−	31.3367i	0.377551	−	0.377551i	0.870218	+	0.492667i	$0.163978\pi$
$84$	14.7571	+	133.702i	0.175680	+	1.59169i
$85$	44.2679	−	19.5099i	0.520799	−	0.229528i
$86$			5.70508i			0.0663381i
$87$	11.4286	−	29.7891i	0.131364	−	0.342404i
$88$	61.2879	−	61.2879i	0.696453	−	0.696453i
$89$		−	70.8895i		−	0.796511i	−0.917274	−	0.398256i	$-0.869616\pi$
$89$		−	70.8895i		−	0.796511i	0.917274	−	0.398256i	$-0.130384\pi$
$90$	−45.3249	+	137.901i	−0.503610	+	1.53223i
$91$	−17.5529	+	54.9600i	−0.192889	+	0.603957i
$92$	−149.626	+	149.626i	−1.62637	+	1.62637i
$93$	75.4769	+	28.9568i	0.811579	+	0.311363i
$94$	−269.669			−2.86882
$95$	−45.2824	+	116.650i	−0.476657	+	1.22789i
$96$	40.2198	+	90.2902i	0.418957	+	0.940522i
$97$	114.216	−	114.216i	1.17748	−	1.17748i	0.197101	−	0.980383i	$-0.436847\pi$
$97$	114.216	−	114.216i	1.17748	−	1.17748i	0.980383	−	0.197101i	$-0.0631528\pi$
$98$	−26.2933	−	155.859i	−0.268299	−	1.59040i
$99$	−67.2426	+	74.7363i	−0.679218	+	0.754912i
$100$	−108.045	+	118.193i	−1.08045	+	1.18193i
$101$	54.9464			0.544024			0.272012	−	0.962294i	$-0.412311\pi$
$101$	54.9464			0.544024			0.272012	+	0.962294i	$0.412311\pi$
$102$	33.5378	−	87.4175i	0.328802	−	0.857034i
$103$	−109.306	−	109.306i	−1.06123	−	1.06123i	−0.997999	−	0.0632258i	$-0.979861\pi$
$103$	−109.306	−	109.306i	−1.06123	−	1.06123i	−0.0632258	−	0.997999i	$-0.520139\pi$
$104$		−	63.9528i		−	0.614931i
$105$	27.0297	−	101.461i	0.257426	−	0.966298i
$106$	−118.830			−1.12103
$107$	89.1318	−	89.1318i	0.833007	−	0.833007i	−0.154920	−	0.987927i	$-0.549512\pi$
$107$	89.1318	−	89.1318i	0.833007	−	0.833007i	0.987927	+	0.154920i	$0.0495120\pi$
$108$	78.6017	+	154.052i	0.727794	+	1.42641i
$109$		−	91.2226i		−	0.836904i	−0.908239	−	0.418452i	$-0.862573\pi$
$109$		−	91.2226i		−	0.836904i	0.908239	−	0.418452i	$-0.137427\pi$
$110$	−164.864	+	72.6592i	−1.49876	+	0.660538i
$111$	−80.9387	+	36.0542i	−0.729177	+	0.324813i
$112$	−1.90092	−	3.68489i	−0.0169725	−	0.0329008i
$113$	−98.3921	−	98.3921i	−0.870726	−	0.870726i	0.121825	−	0.992552i	$-0.461125\pi$
$113$	−98.3921	−	98.3921i	−0.870726	−	0.870726i	−0.992552	+	0.121825i	$0.961125\pi$
$114$	98.5457	+	221.227i	0.864436	+	1.94059i
$115$	151.147	−	66.6139i	1.31432	−	0.579251i
$116$		−	68.1242i		−	0.587277i
$117$	3.90974	+	74.0762i	0.0334166	+	0.633129i
$118$	160.137	+	160.137i	1.35710	+	1.35710i
$119$	−20.6050	+	64.5166i	−0.173152	+	0.542157i
$120$	5.67508	+	116.250i	0.0472924	+	0.968752i
$121$	−3.77875			−0.0312293
$122$	−32.3246	−	32.3246i	−0.264956	−	0.264956i
$123$	−35.4230	+	92.3314i	−0.287992	+	0.750661i
$124$	172.607			1.39199
$125$	112.010	−	55.4868i	0.896079	−	0.443894i
$126$	−102.559	−	175.445i	−0.813958	−	1.39242i
$127$	172.312	+	172.312i	1.35679	+	1.35679i	0.877843	+	0.478948i	$0.158982\pi$
$127$	172.312	+	172.312i	1.35679	+	1.35679i	0.478948	+	0.877843i	$0.341018\pi$
$128$	143.826	+	143.826i	1.12364	+	1.12364i
$129$	−2.15897	−	4.84672i	−0.0167362	−	0.0375714i
$130$	−48.1068	+	123.925i	−0.370052	+	0.953271i
$131$	−71.6542			−0.546979			−0.273489	−	0.961875i	$-0.588178\pi$
$131$	−71.6542			−0.546979			−0.273489	+	0.961875i	$0.588178\pi$
$132$	−76.8879	+	200.411i	−0.582484	+	1.51826i
$133$	−80.3142	−	155.687i	−0.603866	−	1.17058i
$134$	28.0309			0.209186
$135$	−13.6804	−	134.305i	−0.101336	−	0.994852i
$136$		−	75.0730i		−	0.552008i
$137$	57.1182	−	57.1182i	0.416921	−	0.416921i	−0.467220	−	0.884141i	$-0.654744\pi$
$137$	57.1182	−	57.1182i	0.416921	−	0.416921i	0.884141	+	0.467220i	$0.154744\pi$
$138$	114.510	−	298.475i	0.829784	−	2.16286i
$139$	−41.4536			−0.298227			−0.149113	−	0.988820i	$-0.547642\pi$
$139$	−41.4536			−0.298227			−0.149113	+	0.988820i	$0.547642\pi$
$140$	−23.7143	−	222.932i	−0.169388	−	1.59237i
$141$	229.095	−	102.051i	1.62479	−	0.723765i
$142$	89.0704	+	89.0704i	0.627256	+	0.627256i
$143$	−65.1021	+	65.1021i	−0.455260	+	0.455260i
$144$	−3.96301	−	3.56564i	−0.0275209	−	0.0247614i
$145$	−19.2438	+	49.5729i	−0.132716	+	0.341882i
$146$	−233.177			−1.59710
$147$	81.3191	+	122.459i	0.553191	+	0.833054i
$148$	−133.774	+	133.774i	−0.903880	+	0.903880i
$149$	62.9077			0.422199			0.211100	−	0.977465i	$-0.432296\pi$
$149$	62.9077			0.422199			0.211100	+	0.977465i	$0.432296\pi$
$150$	76.4492	−	229.534i	0.509661	−	1.53023i
$151$	−20.6412			−0.136697			−0.0683484	−	0.997662i	$-0.521773\pi$
$151$	−20.6412			−0.136697			−0.0683484	+	0.997662i	$0.521773\pi$
$152$	137.308	+	137.308i	0.903345	+	0.903345i
$153$	4.58958	+	86.9567i	0.0299972	+	0.568344i
$154$	76.7377	−	240.274i	0.498297	−	1.56022i
$155$	−125.603	−	48.7581i	−0.810343	−	0.314568i
$156$	64.4470	+	144.678i	0.413122	+	0.927423i
$157$	−213.253	+	213.253i	−1.35830	+	1.35830i	−0.482284	+	0.876015i	$0.660193\pi$
$157$	−213.253	+	213.253i	−1.35830	+	1.35830i	−0.876015	+	0.482284i	$0.839807\pi$
$158$	−38.4106	−	38.4106i	−0.243105	−	0.243105i
$159$	100.951	−	44.9687i	0.634912	−	0.282822i
$160$	−66.4378	−	150.747i	−0.415237	−	0.942171i
$161$	−70.3531	+	220.283i	−0.436976	+	1.36822i
$162$	−203.179	−	164.281i	−1.25419	−	1.01408i
$163$	−19.5250	+	19.5250i	−0.119785	+	0.119785i	−0.764458	−	0.644673i	$-0.776993\pi$
$163$	−19.5250	+	19.5250i	−0.119785	+	0.119785i	0.644673	+	0.764458i	$0.276993\pi$
$164$			211.151i			1.28750i
$165$	112.562	−	124.117i	0.682196	−	0.752222i
$166$			142.955i			0.861173i
$167$	151.924	+	151.924i	0.909725	+	0.909725i	0.996250	−	0.0865247i	$-0.0275761\pi$
$167$	151.924	+	151.924i	0.909725	+	0.909725i	−0.0865247	+	0.996250i	$0.527576\pi$
$168$	−127.164	−	101.883i	−0.756927	−	0.606447i
$169$		−	101.067i		−	0.598030i
$170$	−56.4717	+	145.474i	−0.332186	+	0.855728i
$171$	−167.438	−	150.649i	−0.979169	−	0.880990i
$172$	−8.01059	−	8.01059i	−0.0465732	−	0.0465732i
$173$	19.8589	−	19.8589i	0.114791	−	0.114791i	−0.647378	−	0.762169i	$-0.724134\pi$
$173$	19.8589	−	19.8589i	0.114791	−	0.114791i	0.762169	+	0.647378i	$0.224134\pi$
$174$	41.8793	+	94.0154i	0.240685	+	0.540319i
$175$	−45.7175	+	168.923i	−0.261243	+	0.965273i
$176$		−	6.61658i		−	0.0375942i
$177$	−196.645	−	75.4429i	−1.11099	−	0.426231i
$178$	161.695	+	161.695i	0.908399	+	0.908399i
$179$	−157.790			−0.881508			−0.440754	−	0.897628i	$-0.645289\pi$
$179$	−157.790			−0.881508			−0.440754	+	0.897628i	$0.645289\pi$
$180$	−129.987	−	257.270i	−0.722151	−	1.42928i
$181$			58.8019i			0.324872i	0.986719	+	0.162436i	$0.0519351\pi$
$181$			58.8019i			0.324872i	−0.986719	+	0.162436i	$0.948065\pi$
$182$	−85.3236	−	165.398i	−0.468811	−	0.908780i
$183$	39.6938	+	15.2286i	0.216906	+	0.0832162i
$184$		−	256.327i		−	1.39308i
$185$	135.134	−	59.5568i	0.730455	−	0.321928i
$186$	−238.207	+	106.110i	−1.28068	+	0.570483i
$187$	−76.4223	+	76.4223i	−0.408675	+	0.408675i
$188$	378.646	−	378.646i	2.01407	−	2.01407i
$189$	153.522	+	110.237i	0.812284	+	0.583262i
$190$	−162.784	−	369.358i	−0.856760	−	1.94399i
$191$			8.99622i			0.0471007i	0.999723	+	0.0235503i	$0.00749699\pi$
$191$			8.99622i			0.0471007i	−0.999723	+	0.0235503i	$0.992503\pi$
$192$	−291.050	−	111.662i	−1.51588	−	0.581571i
$193$	96.1055	−	96.1055i	0.497956	−	0.497956i	−0.412845	−	0.910801i	$-0.635465\pi$
$193$	96.1055	−	96.1055i	0.497956	−	0.497956i	0.910801	+	0.412845i	$0.135465\pi$
$194$			521.041i			2.68578i
$195$	−6.02827	−	123.485i	−0.0309142	−	0.633257i
$196$	255.763	+	181.925i	1.30491	+	0.928190i
$197$	113.154	−	113.154i	0.574386	−	0.574386i	−0.358965	−	0.933351i	$-0.616870\pi$
$197$	113.154	−	113.154i	0.574386	−	0.574386i	0.933351	+	0.358965i	$0.116870\pi$
$198$	−17.0926	−	323.846i	−0.0863262	−	1.63559i
$199$	−122.026			−0.613196			−0.306598	−	0.951839i	$-0.599191\pi$
$199$	−122.026			−0.613196			−0.306598	+	0.951839i	$0.599191\pi$
$200$	−8.69270	−	193.786i	−0.0434635	−	0.968931i
$201$	−23.8135	+	10.6077i	−0.118475	+	0.0527748i
$202$	−125.330	+	125.330i	−0.620444	+	0.620444i
$203$	−34.1314	−	66.1629i	−0.168135	−	0.325926i
$204$	75.6532	+	169.835i	0.370849	+	0.832525i
$205$	59.6461	−	153.651i	0.290956	−	0.749517i
$206$	498.643			2.42060
$207$	15.6705	+	296.902i	0.0757028	+	1.43431i
$208$	−3.45214	−	3.45214i	−0.0165968	−	0.0165968i
$209$		−	279.552i		−	1.33757i
$210$	169.774	+	293.081i	0.808449	+	1.39562i
$211$	−4.27938			−0.0202814			−0.0101407	−	0.999949i	$-0.503228\pi$
$211$	−4.27938			−0.0202814			−0.0101407	+	0.999949i	$0.503228\pi$
$212$	166.850	−	166.850i	0.787031	−	0.787031i
$213$	−109.376	−	41.9623i	−0.513503	−	0.197006i
$214$			406.609i			1.90004i
$215$	3.56634	+	8.09202i	0.0165876	+	0.0376373i
$216$	−199.282	−	64.6280i	−0.922602	−	0.299204i
$217$	167.637	−	86.4788i	0.772522	−	0.398520i
$218$	208.074	+	208.074i	0.954466	+	0.954466i
$219$	198.094	−	88.2411i	0.904538	−	0.402928i
$220$	129.465	−	333.509i	0.588480	−	1.51595i
$221$			79.7452i			0.360838i
$222$	102.379	−	266.854i	0.461166	−	1.20205i
$223$	34.9829	+	34.9829i	0.156874	+	0.156874i	0.781180	−	0.624306i	$-0.214618\pi$
$223$	34.9829	+	34.9829i	0.156874	+	0.156874i	−0.624306	+	0.781180i	$0.714618\pi$
$224$	219.701	+	70.1671i	0.980808	+	0.313246i
$225$	21.9158	+	223.930i	0.0974035	+	0.995245i
$226$	448.854			1.98608
$227$	−23.2602	−	23.2602i	−0.102468	−	0.102468i	0.654014	−	0.756482i	$-0.273084\pi$
$227$	−23.2602	−	23.2602i	−0.102468	−	0.102468i	−0.756482	+	0.654014i	$0.773084\pi$
$228$	−448.997	−	172.258i	−1.96929	−	0.755519i
$229$	91.1105			0.397862			0.198931	−	0.980013i	$-0.436253\pi$
$229$	91.1105			0.397862			0.198931	+	0.980013i	$0.436253\pi$
$230$	−192.815	+	496.700i	−0.838326	+	2.15957i
$231$	25.7350	+	233.163i	0.111407	+	1.00937i
$232$	58.3524	+	58.3524i	0.251519	+	0.251519i
$233$	−90.6015	−	90.6015i	−0.388847	−	0.388847i	0.485429	−	0.874276i	$-0.338664\pi$
$233$	−90.6015	−	90.6015i	−0.388847	−	0.388847i	−0.874276	+	0.485429i	$0.838664\pi$
$234$	−177.881	−	160.046i	−0.760177	−	0.683956i
$235$	−382.495	+	168.574i	−1.62764	+	0.717338i
$236$	−449.702			−1.90552
$237$	47.1673	+	18.0958i	0.199018	+	0.0763535i
$238$	−100.160	−	194.158i	−0.420840	−	0.815789i
$239$	406.988			1.70288			0.851439	−	0.524454i	$-0.175731\pi$
$239$	406.988			1.70288			0.851439	+	0.524454i	$0.175731\pi$
$240$	6.58147	+	5.96879i	0.0274228	+	0.0248700i
$241$		−	117.108i		−	0.485924i	−0.970036	−	0.242962i	$-0.921881\pi$
$241$		−	117.108i		−	0.485924i	0.970036	−	0.242962i	$-0.0781191\pi$
$242$	8.61911	−	8.61911i	0.0356161	−	0.0356161i
$243$	234.778	+	62.6752i	0.966166	+	0.257923i
$244$	90.7749			0.372028
$245$	−134.724	−	204.632i	−0.549895	−	0.835234i
$246$	−129.805	−	291.401i	−0.527662	−	1.18456i
$247$	−145.854	−	145.854i	−0.590501	−	0.590501i
$248$	−147.848	+	147.848i	−0.596160	+	0.596160i
$249$	−54.0984	−	121.446i	−0.217263	−	0.487736i
$250$	−128.926	+	382.051i	−0.515705	+	1.52820i
$251$	127.808			0.509195			0.254597	−	0.967047i	$-0.418057\pi$
$251$	127.808			0.509195			0.254597	+	0.967047i	$0.418057\pi$
$252$	390.348	+	102.340i	1.54900	+	0.406111i
$253$	−260.933	+	260.933i	−1.03136	+	1.03136i
$254$	−786.070			−3.09477
$255$	−7.07648	−	144.957i	−0.0277509	−	0.568459i
$256$	−240.473			−0.939346
$257$	−100.099	−	100.099i	−0.389491	−	0.389491i	0.485015	−	0.874506i	$-0.338814\pi$
$257$	−100.099	−	100.099i	−0.389491	−	0.389491i	−0.874506	+	0.485015i	$0.838814\pi$
$258$	15.9796	+	6.13059i	0.0619364	+	0.0237620i
$259$	−62.8998	+	196.946i	−0.242856	+	0.760410i
$260$	−106.458	−	241.553i	−0.409453	−	0.929049i
$261$	−71.1566	−	64.0218i	−0.272631	−	0.245294i
$262$	163.439	−	163.439i	0.623814	−	0.623814i
$263$	96.5525	+	96.5525i	0.367120	+	0.367120i	0.866426	−	0.499306i	$-0.166412\pi$
$263$	96.5525	+	96.5525i	0.367120	+	0.367120i	−0.499306	+	0.866426i	$0.666412\pi$
$264$	−105.805	−	237.523i	−0.400776	−	0.899708i
$265$	−168.547	+	74.2824i	−0.636025	+	0.280311i
$266$	538.306	+	171.922i	2.02371	+	0.646323i
$267$	−198.557	−	76.1767i	−0.743660	−	0.285306i
$268$	−39.3586	+	39.3586i	−0.146860	+	0.146860i
$269$			213.738i			0.794565i	0.917696	+	0.397282i	$0.130047\pi$
$269$			213.738i			0.794565i	−0.917696	+	0.397282i	$0.869953\pi$
$270$	337.546	+	275.138i	1.25017	+	1.01903i
$271$		−	525.042i		−	1.93743i	−0.248184	−	0.968713i	$-0.579834\pi$
$271$		−	525.042i		−	1.93743i	0.248184	−	0.968713i	$-0.420166\pi$
$272$	−4.05241	−	4.05241i	−0.0148986	−	0.0148986i
$273$	135.078	+	108.224i	0.494790	+	0.396424i
$274$			260.567i			0.950974i
$275$	−188.420	+	206.118i	−0.685164	+	0.749520i
$276$	258.308	+	579.879i	0.935897	+	2.10101i
$277$	−122.242	−	122.242i	−0.441307	−	0.441307i	0.451144	−	0.892451i	$-0.351016\pi$
$277$	−122.242	−	122.242i	−0.441307	−	0.441307i	−0.892451	+	0.451144i	$0.851016\pi$
$278$	94.5532	−	94.5532i	0.340120	−	0.340120i
$279$	162.213	−	180.290i	0.581407	−	0.646200i
$280$	211.267	+	170.641i	0.754525	+	0.609434i
$281$			262.680i			0.934803i	0.884045	+	0.467401i	$0.154810\pi$
$281$			262.680i			0.934803i	−0.884045	+	0.467401i	$0.845190\pi$
$282$	−289.782	+	755.326i	−1.02759	+	2.67846i
$283$	266.792	+	266.792i	0.942728	+	0.942728i	0.998446	−	0.0557189i	$-0.0177451\pi$
$283$	266.792	+	266.792i	0.942728	+	0.942728i	−0.0557189	+	0.998446i	$0.517745\pi$
$284$	−250.130			−0.880740
$285$	278.069	+	252.183i	0.975680	+	0.884852i
$286$		−	296.989i		−	1.03842i
$287$	105.790	+	205.072i	0.368607	+	0.714536i
$288$	296.117	−	15.6291i	1.02818	−	0.0542676i
$289$		−	195.389i		−	0.676085i
$290$	−69.1790	−	156.967i	−0.238548	−	0.541266i
$291$	−197.178	−	442.647i	−0.677586	−	1.52112i
$292$	327.407	−	327.407i	1.12126	−	1.12126i
$293$	−284.626	+	284.626i	−0.971421	+	0.971421i	−0.999603	−	0.0281818i	$-0.991028\pi$
$293$	−284.626	+	284.626i	−0.971421	+	0.971421i	0.0281818	+	0.999603i	$0.491028\pi$
$294$	−464.806	−	93.8378i	−1.58097	−	0.319176i
$295$	327.241	+	127.032i	1.10929	+	0.430618i
$296$		−	229.171i		−	0.774227i
$297$	137.074	+	268.653i	0.461529	+	0.904555i
$298$	−143.489	+	143.489i	−0.481507	+	0.481507i
$299$			272.279i			0.910632i
$300$	214.949	+	429.636i	0.716497	+	1.43212i
$301$	−11.7934	−	3.76652i	−0.0391807	−	0.0125134i
$302$	47.0815	−	47.0815i	0.155899	−	0.155899i
$303$	59.0445	−	153.902i	0.194867	−	0.507926i
$304$	14.8237			0.0487621
$305$	−66.0555	−	25.6422i	−0.216575	−	0.0840727i
$306$	−208.812	−	187.875i	−0.682392	−	0.613970i
$307$	−250.714	+	250.714i	−0.816657	+	0.816657i	−0.985622	−	0.168965i	$-0.945958\pi$
$307$	−250.714	+	250.714i	−0.816657	+	0.816657i	0.168965	+	0.985622i	$0.445958\pi$
$308$	229.624	+	445.121i	0.745532	+	1.44520i
$309$	−423.619	+	188.701i	−1.37093	+	0.610684i
$310$	397.708	−	175.279i	1.28293	−	0.565417i
$311$	−296.319			−0.952794			−0.476397	−	0.879230i	$-0.658057\pi$
$311$	−296.319			−0.952794			−0.476397	+	0.879230i	$0.658057\pi$
$312$	−179.128	−	68.7226i	−0.574128	−	0.220265i
$313$	−195.491	−	195.491i	−0.624573	−	0.624573i	0.322124	−	0.946697i	$-0.395603\pi$
$313$	−195.491	−	195.491i	−0.624573	−	0.624573i	−0.946697	+	0.322124i	$0.895603\pi$
$314$		−	972.836i		−	3.09820i
$315$	−255.141	−	184.737i	−0.809973	−	0.586468i
$316$	107.866			0.341348
$317$	43.8360	−	43.8360i	0.138284	−	0.138284i	−0.634576	−	0.772860i	$-0.718825\pi$
$317$	43.8360	−	43.8360i	0.138284	−	0.138284i	0.772860	+	0.634576i	$0.218825\pi$
$318$	−127.692	+	332.835i	−0.401549	+	1.04665i
$319$		−	118.802i		−	0.372420i
$320$	484.344	+	188.018i	1.51357	+	0.587557i
$321$	−153.873	−	345.432i	−0.479356	−	1.07611i
$322$	−341.982	−	662.925i	−1.06206	−	2.05877i
$323$	−171.215	−	171.215i	−0.530078	−	0.530078i
$324$	515.956	−	54.6165i	1.59246	−	0.168569i
$325$	9.23369	+	205.846i	0.0284113	+	0.633374i
$326$		−	89.0709i		−	0.273224i
$327$	−255.509	−	98.0263i	−0.781373	−	0.299775i
$328$	−180.863	−	180.863i	−0.551412	−	0.551412i
$329$	178.037	−	557.453i	0.541145	−	1.69438i
$330$	26.3544	+	539.852i	0.0798617	+	1.63591i
$331$	−452.094			−1.36584			−0.682922	−	0.730492i	$-0.739291\pi$
$331$	−452.094			−1.36584			−0.682922	+	0.730492i	$0.739291\pi$
$332$	−200.725	−	200.725i	−0.604593	−	0.604593i
$333$	14.0103	+	265.448i	0.0420731	+	0.797140i
$334$	−693.061			−2.07503
$335$	39.7587	−	17.5226i	0.118683	−	0.0523062i
$336$	−12.3638	+	1.36464i	−0.0367972	+	0.00406142i
$337$	203.621	+	203.621i	0.604218	+	0.604218i	0.941429	−	0.337211i	$-0.109484\pi$
$337$	203.621	+	203.621i	0.604218	+	0.604218i	−0.337211	+	0.941429i	$0.609484\pi$
$338$	230.529	+	230.529i	0.682037	+	0.682037i
$339$	−381.321	+	169.860i	−1.12484	+	0.501061i
$340$	−124.969	−	283.554i	−0.367556	−	0.833984i
$341$	301.010			0.882726
$342$	725.539	−	38.2940i	2.12146	−	0.111971i
$343$	339.547	+	48.5462i	0.989933	+	0.141534i
$344$	13.7231			0.0398927
$345$	−24.1617	−	494.936i	−0.0700338	−	1.43460i
$346$			90.5940i			0.261832i
$347$	358.869	−	358.869i	1.03421	−	1.03421i	0.0348116	−	0.999394i	$-0.488917\pi$
$347$	358.869	−	358.869i	1.03421	−	1.03421i	0.999394	−	0.0348116i	$-0.0110831\pi$
$348$	−190.812	−	73.2051i	−0.548310	−	0.210360i
$349$	−51.4939			−0.147547			−0.0737735	−	0.997275i	$-0.523504\pi$
$349$	−51.4939			−0.147547			−0.0737735	+	0.997275i	$0.523504\pi$
$350$	−281.025	−	489.582i	−0.802927	−	1.39881i
$351$	211.684	+	68.6501i	0.603089	+	0.195584i
$352$	260.244	+	260.244i	0.739329	+	0.739329i
$353$	−212.052	+	212.052i	−0.600714	+	0.600714i	−0.940502	−	0.339788i	$-0.889645\pi$
$353$	−212.052	+	212.052i	−0.600714	+	0.600714i	0.339788	+	0.940502i	$0.389645\pi$
$354$	620.616	−	276.454i	1.75315	−	0.780944i
$355$	182.016	+	70.6570i	0.512721	+	0.199034i
$356$	−454.077			−1.27550
$357$	158.565	+	127.042i	0.444161	+	0.355860i
$358$	359.910	−	359.910i	1.00534	−	1.00534i
$359$	194.091			0.540643			0.270321	−	0.962770i	$-0.412870\pi$
$359$	194.091			0.540643			0.270321	+	0.962770i	$0.412870\pi$
$360$	331.708	+	109.025i	0.921412	+	0.302847i
$361$	265.304			0.734915
$362$	−134.124	−	134.124i	−0.370508	−	0.370508i
$363$	−4.06058	+	10.5840i	−0.0111862	+	0.0291571i
$364$	352.042	+	112.434i	0.967148	+	0.308883i
$365$	−330.735	+	145.763i	−0.906123	+	0.399350i
$366$	−125.275	+	55.8038i	−0.342281	+	0.152469i
$367$	291.230	−	291.230i	0.793542	−	0.793542i	−0.188526	−	0.982068i	$-0.560371\pi$
$367$	291.230	−	291.230i	0.793542	−	0.793542i	0.982068	+	0.188526i	$0.0603710\pi$
$368$	−13.8364	−	13.8364i	−0.0375989	−	0.0375989i
$369$	220.550	+	198.436i	0.597696	+	0.537766i
$370$	−172.388	+	444.079i	−0.465913	+	1.20021i
$371$	78.4520	−	245.642i	0.211461	−	0.662107i
$372$	185.480	−	483.461i	0.498603	−	1.29963i
$373$	39.6194	−	39.6194i	0.106218	−	0.106218i	−0.652000	−	0.758219i	$-0.726070\pi$
$373$	39.6194	−	39.6194i	0.106218	−	0.106218i	0.758219	+	0.652000i	$0.226070\pi$
$374$		−	348.630i		−	0.932165i
$375$	−35.0511	−	373.358i	−0.0934695	−	0.995622i
$376$			648.665i			1.72517i
$377$	−61.9839	−	61.9839i	−0.164414	−	0.164414i
$378$	−601.618	+	98.7311i	−1.59158	+	0.261193i
$379$		−	391.187i		−	1.03216i	−0.856541	−	0.516078i	$-0.827391\pi$
$379$		−	391.187i		−	1.03216i	0.856541	−	0.516078i	$-0.172609\pi$
$380$	747.188	+	290.052i	1.96629	+	0.763296i
$381$	667.801	−	297.473i	1.75276	−	0.780769i
$382$	−20.5199	−	20.5199i	−0.0537170	−	0.0537170i
$383$	6.31835	−	6.31835i	0.0164970	−	0.0164970i	−0.698810	−	0.715307i	$-0.746287\pi$
$383$	6.31835	−	6.31835i	0.0164970	−	0.0164970i	0.715307	+	0.698810i	$0.246287\pi$
$384$	557.401	−	248.295i	1.45157	−	0.646602i
$385$	−41.3555	−	388.772i	−0.107417	−	1.00980i
$386$			438.422i			1.13581i
$387$	−15.8954	+	0.838958i	−0.0410733	+	0.00216785i
$388$	−731.601	−	731.601i	−1.88557	−	1.88557i
$389$	−234.607			−0.603103			−0.301551	−	0.953450i	$-0.597504\pi$
$389$	−234.607			−0.603103			−0.301551	+	0.953450i	$0.597504\pi$
$390$	295.413	+	267.912i	0.757468	+	0.686955i
$391$			319.624i			0.817452i
$392$	−374.906	+	63.2462i	−0.956392	+	0.161342i
$393$	−76.9985	+	200.699i	−0.195925	+	0.510685i
$394$			516.196i			1.31014i
$395$	−78.4923	−	30.4701i	−0.198715	−	0.0771394i
$396$	478.717	+	430.717i	1.20888	+	1.08767i
$397$	−244.142	+	244.142i	−0.614967	+	0.614967i	−0.944236	−	0.329269i	$-0.893198\pi$
$397$	−244.142	+	244.142i	−0.614967	+	0.614967i	0.329269	+	0.944236i	$0.393198\pi$
$398$	278.335	−	278.335i	0.699333	−	0.699333i
$399$	−522.375	+	57.6562i	−1.30921	+	0.144502i
$400$	−10.9297	−	9.99126i	−0.0273243	−	0.0249782i
$401$		−	255.719i		−	0.637703i	−0.947805	−	0.318851i	$-0.896703\pi$
$401$		−	255.719i		−	0.637703i	0.947805	−	0.318851i	$-0.103297\pi$
$402$	30.1215	−	78.5128i	0.0749292	−	0.195306i
$403$	157.049	−	157.049i	0.389700	−	0.389700i
$404$		−	351.955i		−	0.871175i
$405$	−390.881	−	106.004i	−0.965139	−	0.261739i
$406$	228.766	+	73.0621i	0.563462	+	0.179956i
$407$	−233.290	+	233.290i	−0.573194	+	0.573194i
$408$	−210.275	−	80.6723i	−0.515380	−	0.197726i
$409$	549.262			1.34294			0.671469	−	0.741033i	$-0.265664\pi$
$409$	549.262			1.34294			0.671469	+	0.741033i	$0.265664\pi$
$410$	214.420	+	486.519i	0.522976	+	1.18663i
$411$	−98.6064	−	221.363i	−0.239918	−	0.538596i
$412$	−700.151	+	700.151i	−1.69940	+	1.69940i
$413$	−436.756	+	225.309i	−1.05752	+	0.545541i
$414$	−712.960	−	641.473i	−1.72213	−	1.54945i
$415$	89.3634	+	202.765i	0.215333	+	0.488591i
$416$	271.559			0.652787
$417$	−44.5453	+	116.109i	−0.106823	+	0.278439i
$418$	637.643	+	637.643i	1.52546	+	1.52546i
$419$			476.333i			1.13683i	0.822741	+	0.568417i	$0.192444\pi$
$419$			476.333i			1.13683i	−0.822741	+	0.568417i	$0.807556\pi$
$420$	−649.902	−	173.136i	−1.54738	−	0.412230i
$421$	−736.969			−1.75052			−0.875261	−	0.483652i	$-0.839310\pi$
$421$	−736.969			−1.75052			−0.875261	+	0.483652i	$0.839310\pi$
$422$	9.76103	−	9.76103i	0.0231304	−	0.0231304i
$423$	−39.6560	−	751.345i	−0.0937494	−	1.77623i
$424$			285.835i			0.674138i
$425$	10.8393	+	241.640i	0.0255041	+	0.568564i
$426$	345.195	−	153.767i	0.810316	−	0.360956i
$427$	88.1615	−	45.4798i	0.206467	−	0.106510i
$428$	−570.926	−	570.926i	−1.33394	−	1.33394i
$429$	112.390	+	252.305i	0.261980	+	0.588123i
$430$	−26.5921	−	10.3228i	−0.0618420	−	0.0240066i
$431$		−	95.9393i		−	0.222597i	−0.993787	−	0.111299i	$-0.964499\pi$
$431$		−	95.9393i		−	0.222597i	0.993787	−	0.111299i	$-0.0355010\pi$
$432$	−14.2457	+	7.26856i	−0.0329762	+	0.0168254i
$433$	273.161	+	273.161i	0.630857	+	0.630857i	0.948283	−	0.317426i	$-0.102818\pi$
$433$	273.161	+	273.161i	0.630857	+	0.630857i	−0.317426	+	0.948283i	$0.602818\pi$
$434$	−185.118	+	579.625i	−0.426539	+	1.33554i
$435$	118.172	+	107.171i	0.271659	+	0.246370i
$436$	−584.318			−1.34018
$437$	−584.591	−	584.591i	−1.33774	−	1.33774i
$438$	−250.568	+	653.114i	−0.572073	+	1.49113i
$439$	396.491			0.903169			0.451585	−	0.892228i	$-0.350859\pi$
$439$	396.491			0.903169			0.451585	+	0.892228i	$0.350859\pi$
$440$	174.775	+	396.565i	0.397217	+	0.901284i
$441$	430.385	−	96.1775i	0.975929	−	0.218090i
$442$	−181.894	−	181.894i	−0.411526	−	0.411526i
$443$	214.203	+	214.203i	0.483528	+	0.483528i	0.906256	−	0.422728i	$-0.138928\pi$
$443$	214.203	+	214.203i	0.483528	+	0.483528i	−0.422728	+	0.906256i	$0.638928\pi$
$444$	230.942	+	518.446i	0.520140	+	1.16767i
$445$	330.425	+	128.268i	0.742527	+	0.288243i
$446$	−159.588			−0.357821
$447$	67.5996	−	176.201i	0.151230	−	0.394185i
$448$	−646.433	+	333.475i	−1.44293	+	0.744363i
$449$	−147.297			−0.328055			−0.164027	−	0.986456i	$-0.552449\pi$
$449$	−147.297			−0.328055			−0.164027	+	0.986456i	$0.552449\pi$
$450$	−560.761	−	460.783i	−1.24614	−	1.02396i
$451$			368.227i			0.816468i
$452$	−630.242	+	630.242i	−1.39434	+	1.39434i
$453$	−22.1807	+	57.8148i	−0.0489641	+	0.127627i
$454$	106.110			0.233723
$455$	−224.415	−	181.261i	−0.493220	−	0.398376i
$456$	532.142	−	237.043i	1.16698	−	0.519832i
$457$	18.8754	+	18.8754i	0.0413028	+	0.0413028i	0.727457	−	0.686154i	$-0.240702\pi$
$457$	18.8754	+	18.8754i	0.0413028	+	0.0413028i	−0.686154	+	0.727457i	$0.740702\pi$
$458$	−207.818	+	207.818i	−0.453751	+	0.453751i
$459$	248.492	+	80.5871i	0.541378	+	0.175571i
$460$	−426.690	−	968.158i	−0.927586	−	2.10469i
$461$	−191.433			−0.415256			−0.207628	−	0.978208i	$-0.566574\pi$
$461$	−191.433			−0.415256			−0.207628	+	0.978208i	$0.566574\pi$
$462$	−590.533	−	473.132i	−1.27821	−	1.02410i
$463$	362.672	−	362.672i	0.783309	−	0.783309i	−0.197079	−	0.980388i	$-0.563145\pi$
$463$	362.672	−	362.672i	0.783309	−	0.783309i	0.980388	+	0.197079i	$0.0631454\pi$
$464$	6.29967			0.0135769
$465$	−271.540	+	299.412i	−0.583956	+	0.643897i
$466$	413.314			0.886939
$467$	61.5519	+	61.5519i	0.131803	+	0.131803i	0.769931	−	0.638128i	$-0.220291\pi$
$467$	61.5519	+	61.5519i	0.131803	+	0.131803i	−0.638128	+	0.769931i	$0.720291\pi$
$468$	474.488	−	25.0435i	1.01386	−	0.0535118i
$469$	−18.5061	+	57.9448i	−0.0394587	+	0.123550i
$470$	487.941	−	1256.96i	1.03817	−	2.67438i
$471$	368.151	+	826.467i	0.781636	+	1.75471i
$472$	385.197	−	385.197i	0.816094	−	0.816094i
$473$	−13.9697	−	13.9697i	−0.0295343	−	0.0295343i
$474$	−148.861	+	66.3104i	−0.314053	+	0.139895i
$475$	−461.783	−	422.133i	−0.972175	−	0.888701i
$476$	413.256	+	131.984i	0.868184	+	0.277277i
$477$	−17.4744	−	331.081i	−0.0366340	−	0.694089i
$478$	−928.316	+	928.316i	−1.94208	+	1.94208i
$479$			572.620i			1.19545i	0.801702	+	0.597724i	$0.203928\pi$
$479$			572.620i			1.19545i	−0.801702	+	0.597724i	$0.796072\pi$
$480$	−493.627	+	24.0978i	−1.02839	+	0.0502038i
$481$			243.434i			0.506099i
$482$	267.116	+	267.116i	0.554183	+	0.554183i
$483$	541.400	+	433.768i	1.12091	+	0.898070i
$484$			24.2044i			0.0500092i
$485$	325.711	+	739.038i	0.671569	+	1.52379i
$486$	−678.475	+	392.558i	−1.39604	+	0.807732i
$487$	358.153	+	358.153i	0.735427	+	0.735427i	0.971689	−	0.236262i	$-0.0759224\pi$
$487$	358.153	+	358.153i	0.735427	+	0.735427i	−0.236262	+	0.971689i	$0.575922\pi$
$488$	−77.7540	+	77.7540i	−0.159332	+	0.159332i
$489$	33.7071	+	75.6696i	0.0689307	+	0.154744i
$490$	774.053	+	159.457i	1.57970	+	0.325422i
$491$			644.045i			1.31170i	0.754891	+	0.655850i	$0.227690\pi$
$491$			644.045i			1.31170i	−0.754891	+	0.655850i	$0.772310\pi$
$492$	591.421	+	226.899i	1.20207	+	0.461177i
$493$	−72.7618	−	72.7618i	−0.147590	−	0.147590i
$494$	665.369			1.34690
$495$	−226.685	−	448.654i	−0.457950	−	0.906372i
$496$			15.9615i			0.0321804i
$497$	−242.929	+	125.319i	−0.488791	+	0.252152i
$498$	400.408	+	153.617i	0.804032	+	0.308468i
$499$		−	530.323i		−	1.06277i	−0.847130	−	0.531386i	$-0.821672\pi$
$499$		−	530.323i		−	1.06277i	0.847130	−	0.531386i	$-0.178328\pi$
$500$	−355.416	−	717.470i	−0.710831	−	1.43494i
$501$	588.786	−	262.275i	1.17522	−	0.523503i
$502$	−291.523	+	291.523i	−0.580723	+	0.580723i
$503$	515.298	−	515.298i	1.02445	−	1.02445i	0.0247567	−	0.999694i	$-0.492119\pi$
$503$	515.298	−	515.298i	1.02445	−	1.02445i	0.999694	−	0.0247567i	$-0.00788111\pi$
$504$	−422.017	+	246.696i	−0.837335	+	0.489477i
$505$	−99.4205	+	256.112i	−0.196872	+	0.507152i
$506$		−	1190.35i		−	2.35247i
$507$	−283.083	−	108.605i	−0.558349	−	0.214211i
$508$	1103.73	−	1103.73i	2.17270	−	2.17270i
$509$		−	648.378i		−	1.27383i	−0.770935	−	0.636914i	$-0.780211\pi$
$509$		−	648.378i		−	1.27383i	0.770935	−	0.636914i	$-0.219789\pi$
$510$	346.780	+	314.498i	0.679960	+	0.616662i
$511$	153.945	−	482.017i	0.301261	−	0.943282i
$512$	−26.7994	+	26.7994i	−0.0523425	+	0.0523425i
$513$	−601.886	+	307.098i	−1.17327	+	0.598632i
$514$	456.642			0.888408
$515$	707.269	−	311.710i	1.37334	−	0.605262i
$516$	−31.0452	+	13.8291i	−0.0601652	+	0.0268006i
$517$	660.323	−	660.323i	1.27722	−	1.27722i
$518$	−305.752	−	592.694i	−0.590256	−	1.14420i
$519$	−34.2835	−	76.9636i	−0.0660568	−	0.148292i
$520$	298.092	+	115.717i	0.573253	+	0.222532i
$521$	−195.439			−0.375123			−0.187561	−	0.982253i	$-0.560058\pi$
$521$	−195.439			−0.375123			−0.187561	+	0.982253i	$0.560058\pi$
$522$	308.334	−	16.2739i	0.590679	−	0.0311761i
$523$	−516.575	−	516.575i	−0.987715	−	0.987715i	0.0122109	−	0.999925i	$-0.496113\pi$
$523$	−516.575	−	516.575i	−0.987715	−	0.987715i	−0.999925	+	0.0122109i	$0.996113\pi$
$524$			458.975i			0.875906i
$525$	424.016	+	309.574i	0.807649	+	0.589664i
$526$	−440.462			−0.837380
$527$	184.357	−	184.357i	0.349824	−	0.349824i
$528$	−18.5327	−	7.11008i	−0.0350997	−	0.0134661i
$529$			562.311i			1.06297i
$530$	215.011	−	553.879i	0.405682	−	1.04506i
$531$	−422.622	+	469.720i	−0.795899	+	0.884595i
$532$	−997.242	+	514.446i	−1.87451	+	0.967003i
$533$	192.119	+	192.119i	0.360448	+	0.360448i
$534$	626.653	−	279.143i	1.17351	−	0.522740i
$535$	254.178	+	576.730i	0.475099	+	1.07800i
$536$		−	67.4259i		−	0.125795i
$537$	−169.559	+	441.960i	−0.315752	+	0.823018i
$538$	−487.524	−	487.524i	−0.906179	−	0.906179i
$539$	446.026	+	317.261i	0.827507	+	0.588610i
$540$	−860.279	+	87.6283i	−1.59311	+	0.162275i
$541$	−165.071			−0.305123			−0.152561	−	0.988294i	$-0.548752\pi$
$541$	−165.071			−0.305123			−0.152561	+	0.988294i	$0.548752\pi$
$542$	1197.59	+	1197.59i	2.20958	+	2.20958i
$543$	164.701	+	63.1875i	0.303316	+	0.116367i
$544$	318.779			0.585990
$545$	425.199	+	165.059i	0.780182	+	0.302860i
$546$	−554.957	+	61.2524i	−1.01641	+	0.112184i
$547$	−259.758	−	259.758i	−0.474878	−	0.474878i	0.428611	−	0.903489i	$-0.359003\pi$
$547$	−259.758	−	259.758i	−0.474878	−	0.474878i	−0.903489	+	0.428611i	$0.859003\pi$
$548$	−365.866	−	365.866i	−0.667638	−	0.667638i
$549$	85.3086	−	94.8155i	0.155389	−	0.172706i
$550$	−40.3678	−	899.919i	−0.0733960	−	1.63622i
$551$	266.162			0.483053
$552$	−717.956	−	275.445i	−1.30064	−	0.498994i
$553$	104.760	−	54.0426i	0.189440	−	0.0977263i
$554$	557.655			1.00660
$555$	−21.6020	−	442.502i	−0.0389225	−	0.797300i
$556$			265.527i			0.477567i
$557$	−118.212	+	118.212i	−0.212230	+	0.212230i	−0.805214	−	0.592984i	$-0.797950\pi$
$557$	−118.212	+	118.212i	−0.212230	+	0.212230i	0.592984	+	0.805214i	$0.297950\pi$
$558$	41.2333	+	781.229i	0.0738947	+	1.40005i
$559$	−14.5771			−0.0260772
$560$	20.6152	−	2.19294i	0.0368129	−	0.00391597i
$561$	131.932	+	296.176i	0.235173	+	0.527944i
$562$	−599.158	−	599.158i	−1.06612	−	1.06612i
$563$	569.301	−	569.301i	1.01119	−	1.01119i	0.0112552	−	0.999937i	$-0.496417\pi$
$563$	569.301	−	569.301i	1.01119	−	1.01119i	0.999937	−	0.0112552i	$-0.00358273\pi$
$564$	−653.678	−	1467.45i	−1.15900	−	2.60186i
$565$	636.649	−	280.586i	1.12681	−	0.496612i
$566$	−1217.08			−2.15031
$567$	473.738	−	311.547i	0.835517	−	0.549465i
$568$	214.251	−	214.251i	0.377203	−	0.377203i
$569$	−602.118			−1.05820			−0.529102	−	0.848558i	$-0.677471\pi$
$569$	−602.118			−1.05820			−0.529102	+	0.848558i	$0.677471\pi$
$570$	−1209.47	+	59.0439i	−2.12189	+	0.103586i
$571$	−883.761			−1.54774			−0.773871	−	0.633343i	$-0.781682\pi$
$571$	−883.761			−1.54774			−0.773871	+	0.633343i	$0.781682\pi$
$572$	417.006	+	417.006i	0.729032	+	0.729032i
$573$	25.1979	+	9.66720i	0.0439754	+	0.0168712i
$574$	−709.058	−	226.456i	−1.23529	−	0.394523i
$575$	37.0092	+	825.045i	0.0643638	+	1.43486i
$576$	−625.515	+	695.223i	−1.08596	+	1.20698i
$577$	64.3197	−	64.3197i	0.111473	−	0.111473i	−0.649170	−	0.760643i	$-0.724884\pi$
$577$	64.3197	−	64.3197i	0.111473	−	0.111473i	0.760643	+	0.649170i	$0.224884\pi$
$578$	445.670	+	445.670i	0.771056	+	0.771056i
$579$	−165.912	−	372.459i	−0.286550	−	0.643280i
$580$	317.535	+	123.264i	0.547474	+	0.212525i
$581$	−295.513	−	94.3795i	−0.508627	−	0.162443i
$582$	1459.40	+	559.902i	2.50757	+	0.962031i
$583$	290.972	−	290.972i	0.499094	−	0.499094i
$584$			560.886i			0.960422i
$585$	−352.352	−	115.810i	−0.602311	−	0.197966i
$586$		−	1298.43i		−	2.21576i
$587$	512.337	+	512.337i	0.872806	+	0.872806i	0.992777	−	0.119971i	$-0.0382803\pi$
$587$	512.337	+	512.337i	0.872806	+	0.872806i	−0.119971	+	0.992777i	$0.538280\pi$
$588$	784.400	−	520.882i	1.33401	−	0.885855i
$589$			674.377i			1.14495i
$590$	−1036.17	+	456.666i	−1.75623	+	0.774010i
$591$	−195.344	−	438.531i	−0.330532	−	0.742016i
$592$	−12.3706	−	12.3706i	−0.0208962	−	0.0208962i
$593$	−195.165	+	195.165i	−0.329114	+	0.329114i	−0.852250	−	0.523135i	$-0.824762\pi$
$593$	−195.165	+	195.165i	−0.329114	+	0.329114i	0.523135	+	0.852250i	$0.324762\pi$
$594$	−925.441	−	300.124i	−1.55798	−	0.505260i
$595$	−263.437	−	212.779i	−0.442751	−	0.357613i
$596$		−	402.950i		−	0.676090i
$597$	−131.127	+	341.788i	−0.219644	+	0.572509i
$598$	−621.053	−	621.053i	−1.03855	−	1.03855i
$599$	−93.4354			−0.155986			−0.0779928	−	0.996954i	$-0.524851\pi$
$599$	−93.4354			−0.155986			−0.0779928	+	0.996954i	$0.524851\pi$
$600$	−552.125	−	183.892i	−0.920208	−	0.306486i
$601$			47.3325i			0.0787563i	0.999224	+	0.0393782i	$0.0125377\pi$
$601$			47.3325i			0.0787563i	−0.999224	+	0.0393782i	$0.987462\pi$
$602$	35.4913	−	18.3089i	0.0589557	−	0.0304134i
$603$	4.12207	+	78.0990i	0.00683593	+	0.129517i
$604$			132.216i			0.218900i
$605$	6.83729	−	17.6132i	0.0113013	−	0.0291127i
$606$	216.364	+	485.719i	0.357036	+	0.801516i
$607$	−782.862	+	782.862i	−1.28972	+	1.28972i	−0.354769	+	0.934954i	$0.615440\pi$
$607$	−782.862	+	782.862i	−1.28972	+	1.28972i	−0.934954	+	0.354769i	$0.884560\pi$
$608$	−583.046	+	583.046i	−0.958957	+	0.958957i
$609$	−221.995	+	24.5023i	−0.364524	+	0.0402337i
$610$	209.157	−	92.1804i	0.342881	−	0.151115i
$611$		−	689.034i		−	1.12772i
$612$	556.994	−	29.3981i	0.910120	−	0.0480362i
$613$	587.076	−	587.076i	0.957710	−	0.957710i	−0.0414311	−	0.999141i	$-0.513192\pi$
$613$	587.076	−	587.076i	0.957710	−	0.957710i	0.999141	+	0.0414311i	$0.0131917\pi$
$614$		−	1143.73i		−	1.86275i
$615$	−366.273	−	332.176i	−0.595566	−	0.540124i
$616$	−577.959	−	184.586i	−0.938245	−	0.299652i
$617$	−400.922	+	400.922i	−0.649793	+	0.649793i	−0.952943	−	0.303150i	$-0.901962\pi$
$617$	−400.922	+	400.922i	−0.649793	+	0.649793i	0.303150	+	0.952943i	$0.401962\pi$
$618$	535.833	−	1396.67i	0.867044	−	2.25998i
$619$	−382.132			−0.617338			−0.308669	−	0.951170i	$-0.599883\pi$
$619$	−382.132			−0.617338			−0.308669	+	0.951170i	$0.599883\pi$
$620$	−312.316	+	804.540i	−0.503735	+	1.29764i
$621$	848.443	+	275.154i	1.36625	+	0.443082i
$622$	675.887	−	675.887i	1.08663	−	1.08663i
$623$	−441.004	+	227.500i	−0.707872	+	0.365169i
$624$	−13.3789	+	5.95963i	−0.0214405	+	0.00955068i
$625$	55.9588	+	622.490i	0.0895341	+	0.995984i
$626$	891.810			1.42462
$627$	−783.009	−	300.402i	−1.24882	−	0.479111i
$628$	1365.97	+	1365.97i	2.17512	+	2.17512i
$629$			285.762i			0.454312i
$630$	1003.34	−	160.588i	1.59260	−	0.254901i
$631$	1097.98			1.74006			0.870031	−	0.492997i	$-0.164099\pi$
$631$	1097.98			1.74006			0.870031	+	0.492997i	$0.164099\pi$
$632$	−92.3934	+	92.3934i	−0.146192	+	0.146192i
$633$	−4.59856	+	11.9863i	−0.00726470	+	0.0189357i
$634$			199.975i			0.315418i
$635$	−1114.95	+	491.386i	−1.75583	+	0.773836i
$636$	−288.043	−	646.633i	−0.452898	−	1.01672i
$637$	398.238	−	67.1823i	0.625177	−	0.105467i
$638$	270.981	+	270.981i	0.424735	+	0.424735i
$639$	−235.068	+	261.264i	−0.367868	+	0.408864i
$640$	−930.630	+	410.150i	−1.45411	+	0.640860i
$641$			137.826i			0.215017i	0.994204	+	0.107509i	$0.0342873\pi$
$641$			137.826i			0.215017i	−0.994204	+	0.107509i	$0.965713\pi$
$642$	1138.89	+	436.936i	1.77397	+	0.680585i
$643$	340.846	+	340.846i	0.530087	+	0.530087i	0.920598	−	0.390511i	$-0.127702\pi$
$643$	340.846	+	340.846i	0.530087	+	0.530087i	−0.390511	+	0.920598i	$0.627702\pi$
$644$	1411.01	+	450.640i	2.19100	+	0.699752i
$645$	26.4976	−	1.29355i	0.0410815	−	0.00200551i
$646$	781.065			1.20908
$647$	192.497	+	192.497i	0.297523	+	0.297523i	0.840043	−	0.542520i	$-0.182530\pi$
$647$	192.497	+	192.497i	0.297523	+	0.297523i	−0.542520	+	0.840043i	$0.682530\pi$
$648$	−395.164	+	488.729i	−0.609822	+	0.754211i
$649$	−784.239			−1.20838
$650$	−490.586	−	448.463i	−0.754748	−	0.689943i
$651$	−62.0817	−	562.471i	−0.0953636	−	0.864010i
$652$	125.066	+	125.066i	0.191819	+	0.191819i
$653$	−178.554	−	178.554i	−0.273436	−	0.273436i	0.557046	−	0.830482i	$-0.311935\pi$
$653$	−178.554	−	178.554i	−0.273436	−	0.273436i	−0.830482	+	0.557046i	$0.811935\pi$
$654$	806.394	−	359.209i	1.23302	−	0.549250i
$655$	129.652	−	333.989i	0.197942	−	0.509907i
$656$	−19.5258			−0.0297649
$657$	−34.2897	−	649.672i	−0.0521913	−	0.988846i
$658$	865.427	+	1677.61i	1.31524	+	2.54956i
$659$	984.529			1.49397			0.746987	−	0.664838i	$-0.231500\pi$
$659$	984.529			1.49397			0.746987	+	0.664838i	$0.231500\pi$
$660$	−795.018	−	721.009i	−1.20457	−	1.09244i
$661$			730.936i			1.10580i	0.833247	+	0.552901i	$0.186479\pi$
$661$			730.936i			1.10580i	−0.833247	+	0.552901i	$0.813521\pi$
$662$	1031.20	−	1031.20i	1.55771	−	1.55771i
$663$	223.362	+	85.6929i	0.336895	+	0.129250i
$664$	343.865			0.517869
$665$	870.998	−	92.6523i	1.30977	−	0.139327i
$666$	−637.428	−	573.515i	−0.957099	−	0.861133i
$667$	−248.435	−	248.435i	−0.372467	−	0.372467i
$668$	973.137	−	973.137i	1.45679	−	1.45679i
$669$	135.577	−	60.3930i	0.202656	−	0.0902735i
$670$	−50.7193	+	130.655i	−0.0757004	+	0.195008i
$671$	158.303			0.235921
$672$	432.621	−	539.969i	0.643781	−	0.803525i
$673$	−770.416	+	770.416i	−1.14475	+	1.14475i	−0.157179	+	0.987570i	$0.550240\pi$
$673$	−770.416	+	770.416i	−1.14475	+	1.14475i	−0.987570	+	0.157179i	$0.949760\pi$
$674$	−928.898			−1.37819
$675$	650.765	+	179.247i	0.964097	+	0.265551i
$676$	−647.377			−0.957658
$677$	−430.936	−	430.936i	−0.636538	−	0.636538i	0.313162	−	0.949700i	$-0.398612\pi$
$677$	−430.936	−	430.936i	−0.636538	−	0.636538i	−0.949700	+	0.313162i	$0.898612\pi$
$678$	482.331	−	1257.21i	0.711403	−	1.85430i
$679$	−1077.08	−	343.994i	−1.58628	−	0.506618i
$680$	349.924	+	135.838i	0.514595	+	0.199761i
$681$	−90.1453	+	40.1553i	−0.132372	+	0.0589652i
$682$	−686.586	+	686.586i	−1.00672	+	1.00672i
$683$	−952.879	−	952.879i	−1.39514	−	1.39514i	−0.813319	−	0.581818i	$-0.802342\pi$
$683$	−952.879	−	952.879i	−1.39514	−	1.39514i	−0.581818	−	0.813319i	$-0.697658\pi$
$684$	−964.971	+	1072.51i	−1.41078	+	1.56800i
$685$	162.885	+	369.585i	0.237788	+	0.539540i
$686$	−885.219	+	663.757i	−1.29041	+	0.967576i
$687$	97.9059	−	255.195i	0.142512	−	0.371463i
$688$	0.740765	−	0.740765i	0.00107669	−	0.00107669i
$689$		−	303.623i		−	0.440673i
$690$	1184.03	+	1073.81i	1.71599	+	1.55625i
$691$		−	428.205i		−	0.619689i	−0.950787	−	0.309844i	$-0.899723\pi$
$691$		−	428.205i		−	0.619689i	0.950787	−	0.309844i	$-0.100277\pi$
$692$	−127.204	−	127.204i	−0.183821	−	0.183821i
$693$	680.731	+	178.471i	0.982296	+	0.257534i
$694$			1637.12i			2.35897i
$695$	75.0064	−	193.220i	0.107923	−	0.278014i
$696$	226.146	−	100.737i	0.324922	−	0.144737i
$697$	225.525	+	225.525i	0.323565	+	0.323565i
$698$	117.455	−	117.455i	0.168273	−	0.168273i
$699$	−351.128	+	156.410i	−0.502329	+	0.223763i
$700$	1082.02	+	292.839i	1.54574	+	0.418342i
$701$		−	1086.06i		−	1.54929i	−0.632393	−	0.774647i	$-0.717927\pi$
$701$		−	1086.06i		−	1.54929i	0.632393	−	0.774647i	$-0.282073\pi$
$702$	−639.427	+	326.253i	−0.910865	+	0.464748i
$703$	−522.659	−	522.659i	−0.743469	−	0.743469i
$704$	−1160.74			−1.64877
$705$	61.1440	+	1252.49i	0.0867290	+	1.77659i
$706$		−	967.358i		−	1.37020i
$707$	−176.335	−	341.822i	−0.249413	−	0.483482i
$708$	−483.243	+	1259.59i	−0.682547	+	1.77908i
$709$			384.594i			0.542446i	0.962516	+	0.271223i	$0.0874281\pi$
$709$			384.594i			0.542446i	−0.962516	+	0.271223i	$0.912572\pi$
$710$	−576.333	+	254.003i	−0.811736	+	0.357751i
$711$	101.370	−	112.667i	0.142574	−	0.158463i
$712$	388.943	−	388.943i	0.546269	−	0.546269i
$713$	629.462	−	629.462i	0.882836	−	0.882836i
$714$	−651.455	+	71.9031i	−0.912401	+	0.100705i
$715$	−185.653	−	421.245i	−0.259654	−	0.589154i
$716$			1010.71i			1.41161i
$717$	437.342	−	1139.95i	0.609961	−	1.58989i
$718$	−442.710	+	442.710i	−0.616588	+	0.616588i
$719$		−	160.221i		−	0.222838i	−0.993773	−	0.111419i	$-0.964460\pi$
$719$		−	160.221i		−	0.222838i	0.993773	−	0.111419i	$-0.0355396\pi$
$720$	23.7906	−	12.0203i	0.0330425	−	0.0166949i
$721$	−329.207	+	1030.78i	−0.456597	+	1.42966i
$722$	−605.144	+	605.144i	−0.838150	+	0.838150i
$723$	−328.012	−	125.842i	−0.453682	−	0.174056i
$724$	376.650			0.520235
$725$	−196.245	−	179.395i	−0.270683	−	0.247442i
$726$	−14.8797	−	33.4036i	−0.0204954	−	0.0460104i
$727$	655.048	−	655.048i	0.901029	−	0.901029i	−0.0944960	−	0.995525i	$-0.530124\pi$
$727$	655.048	−	655.048i	0.901029	−	0.901029i	0.995525	+	0.0944960i	$0.0301240\pi$
$728$	−397.851	+	205.239i	−0.546498	+	0.281921i
$729$	427.838	−	590.250i	0.586884	−	0.809671i
$730$	421.912	−	1086.86i	0.577961	−	1.48886i
$731$	−17.1118			−0.0234088
$732$	97.5452	−	254.255i	0.133258	−	0.347343i
$733$	−222.518	−	222.518i	−0.303572	−	0.303572i	0.538838	−	0.842410i	$-0.318864\pi$
$733$	−222.518	−	222.518i	−0.303572	−	0.303572i	−0.842410	+	0.538838i	$0.818864\pi$
$734$			1328.56i			1.81003i
$735$	−717.936	+	157.460i	−0.976783	+	0.214231i
$736$	1088.43			1.47884
$737$	−68.6376	+	68.6376i	−0.0931311	+	0.0931311i
$738$	−955.682	+	50.4409i	−1.29496	+	0.0683481i
$739$			343.180i			0.464385i	0.972670	+	0.232192i	$0.0745899\pi$
$739$			343.180i			0.464385i	−0.972670	+	0.232192i	$0.925410\pi$
$740$	−381.486	−	865.590i	−0.515521	−	1.16972i
$741$	−565.260	+	251.796i	−0.762834	+	0.339805i
$742$	381.351	+	739.240i	0.513950	+	0.996280i
$743$	−54.5399	−	54.5399i	−0.0734050	−	0.0734050i	0.669451	−	0.742856i	$-0.266529\pi$
$743$	−54.5399	−	54.5399i	−0.0734050	−	0.0734050i	−0.742856	+	0.669451i	$0.766529\pi$
$744$	255.238	+	572.987i	0.343062	+	0.770144i
$745$	−113.826	+	293.220i	−0.152786	+	0.393584i
$746$			180.739i			0.242278i
$747$	−398.297	+	21.0221i	−0.533196	+	0.0281421i
$748$	489.516	+	489.516i	0.654433	+	0.654433i
$749$	−840.533	−	268.446i	−1.12221	−	0.358405i
$750$	931.559	+	771.660i	1.24208	+	1.02888i
$751$	969.222			1.29057			0.645287	−	0.763940i	$-0.276738\pi$
$751$	969.222			1.29057			0.645287	+	0.763940i	$0.276738\pi$
$752$	35.0146	+	35.0146i	0.0465620	+	0.0465620i
$753$	137.340	−	357.982i	0.182391	−	0.475408i
$754$	282.764			0.375018
$755$	37.3484	−	96.2112i	0.0494681	−	0.127432i
$756$	706.111	−	983.370i	0.934009	−	1.30075i
$757$	−881.940	−	881.940i	−1.16505	−	1.16505i	−0.983356	−	0.181690i	$-0.941843\pi$
$757$	−881.940	−	881.940i	−1.16505	−	1.16505i	−0.181690	−	0.983356i	$-0.558157\pi$
$758$	892.277	+	892.277i	1.17715	+	1.17715i
$759$	450.464	+	1011.25i	0.593497	+	1.33235i
$760$	−888.458	+	391.564i	−1.16902	+	0.515216i
$761$	1174.77			1.54372			0.771859	−	0.635794i	$-0.219327\pi$
$761$	1174.77			1.54372			0.771859	+	0.635794i	$0.219327\pi$
$762$	−844.699	+	2201.74i	−1.10853	+	2.88942i
$763$	−567.496	+	292.753i	−0.743769	+	0.383687i
$764$	57.6245			0.0754248
$765$	−413.620	−	135.948i	−0.540680	−	0.177709i
$766$			28.8236i			0.0376288i
$767$	−409.169	+	409.169i	−0.533467	+	0.533467i
$768$	−258.408	+	673.550i	−0.336469	+	0.877018i
$769$	−397.325			−0.516678			−0.258339	−	0.966054i	$-0.583175\pi$
$769$	−397.325			−0.516678			−0.258339	+	0.966054i	$0.583175\pi$
$770$	981.097	+	792.438i	1.27415	+	1.02914i
$771$	−387.937	+	172.807i	−0.503161	+	0.224134i
$772$	−615.595	−	615.595i	−0.797403	−	0.797403i
$773$	−122.356	+	122.356i	−0.158287	+	0.158287i	−0.781807	−	0.623520i	$-0.785702\pi$
$773$	−122.356	+	122.356i	−0.158287	+	0.158287i	0.623520	+	0.781807i	$0.285702\pi$
$774$	34.3428	−	38.1701i	0.0443706	−	0.0493153i
$775$	454.535	−	497.228i	0.586496	−	0.641584i
$776$	1253.32			1.61510
$777$	484.043	+	387.814i	0.622965	+	0.499117i
$778$	535.125	−	535.125i	0.687822	−	0.687822i
$779$	−824.970			−1.05901
$780$	−790.973	+	38.6136i	−1.01407	+	0.0495046i
$781$	−436.203			−0.558519
$782$	−729.044	−	729.044i	−0.932281	−	0.932281i
$783$	−255.785	+	130.508i	−0.326673	+	0.166678i
$784$	−16.8232	+	23.6512i	−0.0214582	+	0.0301674i
$785$	−608.136	−	1379.86i	−0.774695	−	1.75778i
$786$	−282.155	−	633.413i	−0.358975	−	0.805869i
$787$	163.431	−	163.431i	0.207663	−	0.207663i	−0.595610	−	0.803273i	$-0.703090\pi$
$787$	163.431	−	163.431i	0.207663	−	0.207663i	0.803273	+	0.595610i	$0.203090\pi$
$788$	−724.799	−	724.799i	−0.919795	−	0.919795i
$789$	374.192	−	166.684i	0.474261	−	0.211260i
$790$	248.537	−	109.536i	0.314604	−	0.138653i
$791$	−296.336	+	927.860i	−0.374634	+	1.17302i
$792$	−778.983	+	41.1148i	−0.983565	+	0.0519126i
$793$	82.5930	−	82.5930i	0.104153	−	0.104153i
$794$		−	1113.75i		−	1.40270i
$795$	26.9431	+	551.912i	0.0338907	+	0.694229i
$796$			781.627i			0.981944i
$797$	−412.431	−	412.431i	−0.517479	−	0.517479i	0.399329	−	0.916808i	$-0.369243\pi$
$797$	−412.431	−	412.431i	−0.517479	−	0.517479i	−0.916808	+	0.399329i	$0.869243\pi$
$798$	1060.00	−	1323.02i	1.32832	−	1.65792i
$799$		−	808.845i		−	1.01232i
$800$	822.865	−	36.9114i	1.02858	−	0.0461392i
$801$	−426.733	+	474.289i	−0.532750	+	0.592121i
$802$	583.280	+	583.280i	0.727282	+	0.727282i
$803$	570.967	−	570.967i	0.711042	−	0.711042i
$804$	67.9469	+	152.535i	0.0845111	+	0.189720i
$805$	−899.469	−	726.506i	−1.11735	−	0.902492i
$806$			716.440i			0.888883i
$807$	598.667	+	229.679i	0.741843	+	0.284609i
$808$	301.470	+	301.470i	0.373106	+	0.373106i
$809$	677.677			0.837672			0.418836	−	0.908062i	$-0.362438\pi$
$809$	677.677			0.837672			0.418836	+	0.908062i	$0.362438\pi$
$810$	1133.37	−	649.789i	1.39922	−	0.802208i
$811$			680.395i			0.838958i	0.907765	+	0.419479i	$0.137787\pi$
$811$			680.395i			0.838958i	−0.907765	+	0.419479i	$0.862213\pi$
$812$	−423.801	+	218.625i	−0.521922	+	0.269243i
$813$	−1470.61	−	564.202i	−1.80887	−	0.693976i
$814$		−	1064.24i		−	1.30742i
$815$	−55.6797	−	126.337i	−0.0683186	−	0.155015i
$816$	−15.7052	+	6.99590i	−0.0192466	+	0.00857341i
$817$	31.2975	−	31.2975i	0.0383078	−	0.0383078i
$818$	−1252.84	+	1252.84i	−1.53158	+	1.53158i
$819$	448.281	−	262.049i	0.547351	−	0.319962i
$820$	−984.199	−	382.058i	−1.20024	−	0.465924i
$821$			93.5358i			0.113929i	0.998376	+	0.0569646i	$0.0181422\pi$
$821$			93.5358i			0.113929i	−0.998376	+	0.0569646i	$0.981858\pi$
$822$	729.832	+	280.001i	0.887874	+	0.340634i
$823$	−955.257	+	955.257i	−1.16070	+	1.16070i	−0.176378	+	0.984322i	$0.556438\pi$
$823$	−955.257	+	955.257i	−1.16070	+	1.16070i	−0.984322	+	0.176378i	$0.943562\pi$
$824$		−	1199.44i		−	1.45563i
$825$	374.851	+	749.244i	0.454365	+	0.908175i
$826$	482.299	−	1510.13i	0.583897	−	1.82825i
$827$	326.945	−	326.945i	0.395338	−	0.395338i	−0.481247	−	0.876585i	$-0.659816\pi$
$827$	326.945	−	326.945i	0.395338	−	0.395338i	0.876585	+	0.481247i	$0.159816\pi$
$828$	1901.78	−	100.376i	2.29683	−	0.121227i
$829$	502.107			0.605678			0.302839	−	0.953042i	$-0.402066\pi$
$829$	502.107			0.605678			0.302839	+	0.953042i	$0.402066\pi$
$830$	−666.329	−	258.663i	−0.802806	−	0.311643i
$831$	−473.752	+	211.033i	−0.570099	+	0.253951i
$832$	−605.603	+	605.603i	−0.727889	+	0.727889i
$833$	467.484	−	78.8641i	0.561206	−	0.0946748i
$834$	−163.233	−	366.443i	−0.195723	−	0.439381i
$835$	−983.029	+	433.244i	−1.17728	+	0.518855i
$836$	−1790.65			−2.14192
$837$	−330.670	−	648.084i	−0.395066	−	0.774294i
$838$	−1086.49	−	1086.49i	−1.29653	−	1.29653i
$839$		−	170.395i		−	0.203092i	−0.994831	−	0.101546i	$-0.967621\pi$
$839$		−	170.395i		−	0.203092i	0.994831	−	0.101546i	$-0.0323790\pi$
$840$	704.981	−	408.377i	0.839263	−	0.486164i
$841$	−727.888			−0.865503
$842$	1680.99	−	1680.99i	1.99642	−	1.99642i
$843$	735.750	+	282.271i	0.872776	+	0.334841i
$844$			27.4112i			0.0324777i
$845$	471.086	+	182.872i	0.557498	+	0.216416i
$846$	1804.23	+	1623.32i	2.13266	+	1.91882i
$847$	12.1268	+	23.5076i	0.0143174	+	0.0277539i
$848$	15.4292	+	15.4292i	0.0181948	+	0.0181948i
$849$	1033.96	−	460.578i	1.21785	−	0.542495i
$850$	−575.890	−	526.443i	−0.677518	−	0.619344i
$851$			975.697i			1.14653i
$852$	−268.786	+	700.600i	−0.315476	+	0.822300i
$853$	−554.247	−	554.247i	−0.649763	−	0.649763i	0.303173	−	0.952936i	$-0.401954\pi$
$853$	−554.247	−	554.247i	−0.649763	−	0.649763i	−0.952936	+	0.303173i	$0.901954\pi$
$854$	−97.3547	+	304.828i	−0.113998	+	0.356942i
$855$	1005.16	−	507.862i	1.17562	−	0.593991i
$856$	978.063			1.14260
$857$	−472.697	−	472.697i	−0.551572	−	0.551572i	0.375323	−	0.926894i	$-0.377532\pi$
$857$	−472.697	−	472.697i	−0.551572	−	0.551572i	−0.926894	+	0.375323i	$0.877532\pi$
$858$	−831.848	−	319.139i	−0.969520	−	0.371957i
$859$	218.046			0.253837			0.126919	−	0.991913i	$-0.459491\pi$
$859$	218.046			0.253837			0.126919	+	0.991913i	$0.459491\pi$
$860$	51.8327	−	22.8439i	0.0602706	−	0.0265627i
$861$	688.074	−	75.9450i	0.799157	−	0.0882055i
$862$	218.832	+	218.832i	0.253866	+	0.253866i
$863$	823.471	+	823.471i	0.954196	+	0.954196i	0.998996	−	0.0447996i	$-0.0142649\pi$
$863$	823.471	+	823.471i	0.954196	+	0.954196i	−0.0447996	+	0.998996i	$0.514265\pi$
$864$	274.426	−	846.201i	0.317623	−	0.979399i
$865$	56.6318	+	128.497i	0.0654703	+	0.148552i
$866$	−1246.13			−1.43895
$867$	−547.272	−	209.961i	−0.631225	−	0.242170i
$868$	−553.933	−	1073.79i	−0.638171	−	1.23708i
$869$	188.108			0.216465
$870$	−513.994	+	25.0921i	−0.590798	+	0.0288415i
$871$			71.6221i			0.0822297i
$872$	500.503	−	500.503i	0.573971	−	0.573971i
$873$	−1451.71	+	76.6214i	−1.66290	+	0.0877679i
$874$	2666.84			3.05130
$875$	−704.648	−	518.745i	−0.805312	−	0.592851i
$876$	−565.221	−	1268.87i	−0.645229	−	1.44849i
$877$	601.564	+	601.564i	0.685934	+	0.685934i	0.961331	−	0.275397i	$-0.0888092\pi$
$877$	601.564	+	601.564i	0.685934	+	0.685934i	−0.275397	+	0.961331i	$0.588809\pi$
$878$	−904.375	+	904.375i	−1.03004	+	1.03004i
$879$	491.367	+	1103.08i	0.559006	+	1.25492i
$880$	30.8407	+	11.9721i	0.0350462	+	0.0136047i
$881$	842.336			0.956113			0.478057	−	0.878329i	$-0.341341\pi$
$881$	842.336			0.956113			0.478057	+	0.878329i	$0.341341\pi$
$882$	−762.308	+	1201.06i	−0.864294	+	1.36174i
$883$	918.430	−	918.430i	1.04012	−	1.04012i	0.0409643	−	0.999161i	$-0.486957\pi$
$883$	918.430	−	918.430i	1.04012	−	1.04012i	0.999161	−	0.0409643i	$-0.0130430\pi$
$884$	510.801			0.577829
$885$	707.459	−	780.077i	0.799388	−	0.881443i
$886$	−977.170			−1.10290
$887$	496.805	+	496.805i	0.560095	+	0.560095i	0.929334	−	0.369239i	$-0.120382\pi$
$887$	496.805	+	496.805i	0.560095	+	0.560095i	−0.369239	+	0.929334i	$0.620382\pi$
$888$	−641.895	−	246.264i	−0.722855	−	0.277324i
$889$	518.968	−	1624.95i	0.583766	−	1.82784i
$890$	−1046.25	+	461.108i	−1.17556	+	0.518099i
$891$	899.779	−	95.2460i	1.00985	−	0.106898i
$892$	224.080	−	224.080i	0.251211	−	0.251211i
$893$	1479.38	+	1479.38i	1.65664	+	1.65664i
$894$	247.713	+	556.095i	0.277084	+	0.622030i
$895$	285.507	−	735.478i	0.319002	−	0.821763i
$896$	433.173	−	1356.31i	0.483452	−	1.51374i
$897$	762.638	+	292.587i	0.850209	+	0.326184i
$898$	335.975	−	335.975i	0.374137	−	0.374137i
$899$			286.592i			0.318790i
$900$	1434.37	−	140.380i	1.59374	−	0.155977i
$901$		−	356.418i		−	0.395581i
$902$	−839.905	−	839.905i	−0.931159	−	0.931159i
$903$	−23.2228	+	28.9852i	−0.0257174	+	0.0320988i
$904$		−	1079.68i		−	1.19434i
$905$	−274.083	−	106.397i	−0.302854	−	0.117565i
$906$	−81.2794	−	182.465i	−0.0897124	−	0.201397i
$907$	407.949	+	407.949i	0.449778	+	0.449778i	0.895281	−	0.445502i	$-0.146975\pi$
$907$	407.949	+	407.949i	0.449778	+	0.449778i	−0.445502	+	0.895281i	$0.646975\pi$
$908$	−148.991	+	148.991i	−0.164087	+	0.164087i
$909$	−367.621	−	330.761i	−0.404424	−	0.363873i
$910$	925.325	−	98.4313i	1.01684	−	0.108166i
$911$		−	763.804i		−	0.838424i	−0.907888	−	0.419212i	$-0.862306\pi$
$911$		−	763.804i		−	0.838424i	0.907888	−	0.419212i	$-0.137694\pi$
$912$	15.9293	−	41.5203i	0.0174663	−	0.0455266i
$913$	−350.045	−	350.045i	−0.383401	−	0.383401i
$914$	−86.1073			−0.0942093
$915$	−142.804	+	157.463i	−0.156070	+	0.172090i
$916$		−	583.600i		−	0.637118i
$917$	229.954	+	445.761i	0.250768	+	0.486108i
$918$	−750.612	+	382.983i	−0.817660	+	0.417192i
$919$			369.412i			0.401972i	0.979594	+	0.200986i	$0.0644145\pi$
$919$			369.412i			0.401972i	−0.979594	+	0.200986i	$0.935585\pi$
$920$	1194.77	+	463.800i	1.29866	+	0.504130i
$921$	432.821	+	971.648i	0.469947	+	1.05499i
$922$	436.648	−	436.648i	0.473587	−	0.473587i
$923$	−227.585	+	227.585i	−0.246571	+	0.246571i
$924$	1493.51	−	164.843i	1.61635	−	0.178402i
$925$	33.0884	+	737.639i	0.0357712	+	0.797448i
$926$			1654.47i			1.78668i
$927$	73.3276	+	1389.31i	0.0791021	+	1.49871i
$928$	−247.779	+	247.779i	−0.267003	+	0.267003i
$929$			443.766i			0.477682i	0.971059	+	0.238841i	$0.0767674\pi$
$929$			443.766i			0.477682i	−0.971059	+	0.238841i	$0.923233\pi$
$930$	−63.5759	−	1302.31i	−0.0683612	−	1.40033i
$931$	−710.785	+	999.270i	−0.763464	+	1.07333i
$932$	−580.340	+	580.340i	−0.622682	+	0.622682i
$933$	−318.420	+	829.972i	−0.341286	+	0.889573i
$934$	−280.793			−0.300635
$935$	−217.934	−	494.492i	−0.233085	−	0.528869i
$936$	−384.976	+	427.879i	−0.411299	+	0.457135i
$937$	−278.535	+	278.535i	−0.297263	+	0.297263i	−0.839941	−	0.542678i	$-0.817410\pi$
$937$	−278.535	+	278.535i	−0.297263	+	0.297263i	0.542678	+	0.839941i	$0.317410\pi$
$938$	−89.9573	−	174.380i	−0.0959033	−	0.185906i
$939$	−757.632	+	337.488i	−0.806849	+	0.359412i
$940$	1079.79	+	2450.04i	1.14871	+	2.60642i
$941$	−1197.75			−1.27285			−0.636423	−	0.771340i	$-0.719587\pi$
$941$	−1197.75			−1.27285			−0.636423	+	0.771340i	$0.719587\pi$
$942$	−2724.86	−	1045.39i	−2.89263	−	1.10976i
$943$	770.025	+	770.025i	0.816569	+	0.816569i
$944$		−	41.5855i		−	0.0440524i
$945$	−791.609	+	516.120i	−0.837682	+	0.546159i
$946$	63.7283			0.0673660
$947$	99.0939	−	99.0939i	0.104640	−	0.104640i	−0.652849	−	0.757488i	$-0.726426\pi$
$947$	99.0939	−	99.0939i	0.104640	−	0.104640i	0.757488	+	0.652849i	$0.226426\pi$
$948$	115.911	−	302.126i	0.122269	−	0.318698i
$949$		−	595.793i		−	0.627811i
$950$	2016.16	−	90.4393i	2.12228	−	0.0951993i
$951$	−75.6766	−	169.888i	−0.0795758	−	0.178641i
$952$	−467.030	+	240.926i	−0.490577	+	0.253074i
$953$	294.311	+	294.311i	0.308826	+	0.308826i	0.844454	−	0.535628i	$-0.179925\pi$
$953$	294.311	+	294.311i	0.308826	+	0.308826i	−0.535628	+	0.844454i	$0.679925\pi$
$954$	795.035	+	715.318i	0.833370	+	0.749809i
$955$	−41.9325	−	16.2778i	−0.0439084	−	0.0170449i
$956$		−	2606.92i		−	2.72691i
$957$	−332.758	−	127.663i	−0.347709	−	0.133399i
$958$	−1306.11	−	1306.11i	−1.36338	−	1.36338i
$959$	−538.637	−	172.028i	−0.561666	−	0.179382i
$960$	1047.10	−	1154.58i	1.09072	−	1.20268i
$961$	234.860			0.244392
$962$	−555.258	−	555.258i	−0.577192	−	0.577192i
$963$	−1132.89	+	59.7937i	−1.17641	+	0.0620911i
$964$	−750.124			−0.778137
$965$	274.065	+	621.853i	0.284005	+	0.644407i
$966$	−2224.30	+	245.503i	−2.30259	+	0.254144i
$967$	749.151	+	749.151i	0.774716	+	0.774716i	0.978927	−	0.204211i	$-0.0654627\pi$
$967$	749.151	+	749.151i	0.774716	+	0.774716i	−0.204211	+	0.978927i	$0.565463\pi$
$968$	−20.7325	−	20.7325i	−0.0214179	−	0.0214179i
$969$	−663.549	+	295.578i	−0.684777	+	0.305035i
$970$	−2428.63	−	942.775i	−2.50375	−	0.971933i
$971$	648.040			0.667394			0.333697	−	0.942680i	$-0.391704\pi$
$971$	648.040			0.667394			0.333697	+	0.942680i	$0.391704\pi$
$972$	401.460	−	1503.85i	0.413025	−	1.54717i
$973$	133.034	+	257.883i	0.136725	+	0.265039i
$974$	−1633.85			−1.67747
$975$	586.486	+	195.336i	0.601524	+	0.200345i
$976$			8.39425i			0.00860067i
$977$	−131.673	+	131.673i	−0.134773	+	0.134773i	−0.771275	−	0.636502i	$-0.780381\pi$
$977$	−131.673	+	131.673i	−0.134773	+	0.134773i	0.636502	+	0.771275i	$0.280381\pi$
$978$	−249.482	−	95.7141i	−0.255094	−	0.0978672i
$979$	−791.867			−0.808853
$980$	−1310.75	+	862.964i	−1.33750	+	0.880576i
$981$	−549.132	+	610.328i	−0.559767	+	0.622149i
$982$	−1469.03	−	1469.03i	−1.49596	−	1.49596i
$983$	903.757	−	903.757i	0.919387	−	0.919387i	−0.0775980	−	0.996985i	$-0.524725\pi$
$983$	903.757	−	903.757i	0.919387	−	0.919387i	0.996985	+	0.0775980i	$0.0247251\pi$
$984$	−700.939	+	312.234i	−0.712336	+	0.317311i
$985$	322.683	+	732.167i	0.327597	+	0.743316i
$986$	331.931			0.336644
$987$	−1370.08	−	1097.70i	−1.38812	−	1.11216i
$988$	−934.254	+	934.254i	−0.945601	+	0.945601i
$989$	−58.4260			−0.0590759
$990$	1540.41	+	506.299i	1.55597	+	0.511413i
$991$	−628.425			−0.634132			−0.317066	−	0.948403i	$-0.602698\pi$
$991$	−628.425			−0.634132			−0.317066	+	0.948403i	$0.602698\pi$
$992$	−627.798	−	627.798i	−0.632861	−	0.632861i
$993$	−485.813	+	1266.29i	−0.489238	+	1.27522i
$994$	268.261	−	839.954i	0.269880	−	0.845024i
$995$	220.795	−	568.778i	0.221904	−	0.571636i
$996$	−777.914	+	346.523i	−0.781038	+	0.347914i
$997$	−207.877	+	207.877i	−0.208503	+	0.208503i	−0.803631	−	0.595128i	$-0.797101\pi$
$997$	−207.877	+	207.877i	−0.208503	+	0.208503i	0.595128	+	0.803631i	$0.297101\pi$
$998$	1209.64	+	1209.64i	1.21206	+	1.21206i
$999$	758.558	+	246.004i	0.759318	+	0.246250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.k.d.62.4	yes	32
3.2	odd	2	inner	105.3.k.d.62.13	yes	32
5.3	odd	4	inner	105.3.k.d.83.14	yes	32
7.6	odd	2	inner	105.3.k.d.62.3	✓	32
15.8	even	4	inner	105.3.k.d.83.3	yes	32
21.20	even	2	inner	105.3.k.d.62.14	yes	32
35.13	even	4	inner	105.3.k.d.83.13	yes	32
105.83	odd	4	inner	105.3.k.d.83.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.k.d.62.3	✓	32	7.6	odd	2	inner
105.3.k.d.62.4	yes	32	1.1	even	1	trivial
105.3.k.d.62.13	yes	32	3.2	odd	2	inner
105.3.k.d.62.14	yes	32	21.20	even	2	inner
105.3.k.d.83.3	yes	32	15.8	even	4	inner
105.3.k.d.83.4	yes	32	105.83	odd	4	inner
105.3.k.d.83.13	yes	32	35.13	even	4	inner
105.3.k.d.83.14	yes	32	5.3	odd	4	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.28094 + 2.28094i) q^{2} +(1.07458 - 2.80094i) q^{3} -6.40541i q^{4} +(-1.80941 + 4.66112i) q^{5} +(3.93772 + 8.83986i) q^{6} +(-3.20922 - 6.22100i) q^{7} +(5.48661 + 5.48661i) q^{8} +(-6.69054 - 6.01969i) q^{9} +O(q^{10})\)	\(q+(-2.28094 + 2.28094i) q^{2} +(1.07458 - 2.80094i) q^{3} -6.40541i q^{4} +(-1.80941 + 4.66112i) q^{5} +(3.93772 + 8.83986i) q^{6} +(-3.20922 - 6.22100i) q^{7} +(5.48661 + 5.48661i) q^{8} +(-6.69054 - 6.01969i) q^{9} +(-6.50460 - 14.7589i) q^{10} -11.1704i q^{11} +(-17.9412 - 6.88316i) q^{12} +(-5.82807 - 5.82807i) q^{13} +(21.5098 + 6.86971i) q^{14} +(11.1112 + 10.0768i) q^{15} +0.592330 q^{16} +(-6.84147 - 6.84147i) q^{17} +(28.9913 - 1.53016i) q^{18} +25.0261 q^{19} +(29.8564 + 11.5900i) q^{20} +(-20.8732 + 2.30385i) q^{21} +(25.4792 + 25.4792i) q^{22} +(-23.3593 - 23.3593i) q^{23} +(21.2635 - 9.47185i) q^{24} +(-18.4521 - 16.8677i) q^{25} +26.5870 q^{26} +(-24.0503 + 12.2711i) q^{27} +(-39.8481 + 20.5564i) q^{28} +10.6354 q^{29} +(-48.3286 + 2.35930i) q^{30} +26.9470i q^{31} +(-23.2975 + 23.2975i) q^{32} +(-31.2877 - 12.0036i) q^{33} +31.2100 q^{34} +(34.8036 - 3.70223i) q^{35} +(-38.5586 + 42.8557i) q^{36} +(-20.8846 - 20.8846i) q^{37} +(-57.0831 + 57.0831i) q^{38} +(-22.5868 + 10.0613i) q^{39} +(-35.5013 + 15.6462i) q^{40} -32.9644 q^{41} +(42.3558 - 52.8657i) q^{42} +(1.25060 - 1.25060i) q^{43} -71.5513 q^{44} +(40.1644 - 20.2933i) q^{45} +106.562 q^{46} +(59.1134 + 59.1134i) q^{47} +(0.636508 - 1.65908i) q^{48} +(-28.4018 + 39.9292i) q^{49} +(80.5625 - 3.61381i) q^{50} +(-26.5143 + 11.8108i) q^{51} +(-37.3312 + 37.3312i) q^{52} +(26.0484 + 26.0484i) q^{53} +(26.8677 - 82.8473i) q^{54} +(52.0668 + 20.2119i) q^{55} +(16.5245 - 51.7400i) q^{56} +(26.8926 - 70.0965i) q^{57} +(-24.2588 + 24.2588i) q^{58} -70.2066i q^{59} +(64.5461 - 71.1716i) q^{60} +14.1716i q^{61} +(-61.4646 - 61.4646i) q^{62} +(-15.9771 + 60.9404i) q^{63} -103.911i q^{64} +(37.7107 - 16.6200i) q^{65} +(98.7451 - 43.9861i) q^{66} +(-6.14458 - 6.14458i) q^{67} +(-43.8225 + 43.8225i) q^{68} +(-90.5294 + 40.3264i) q^{69} +(-70.9406 + 87.8297i) q^{70} -39.0498i q^{71} +(-3.68068 - 69.7361i) q^{72} +(51.1141 + 51.1141i) q^{73} +95.2731 q^{74} +(-67.0738 + 33.5574i) q^{75} -160.302i q^{76} +(-69.4914 + 35.8484i) q^{77} +(28.5700 - 74.4687i) q^{78} +16.8398i q^{79} +(-1.07177 + 2.76092i) q^{80} +(8.52661 + 80.5500i) q^{81} +(75.1900 - 75.1900i) q^{82} +(31.3367 - 31.3367i) q^{83} +(14.7571 + 133.702i) q^{84} +(44.2679 - 19.5099i) q^{85} +5.70508i q^{86} +(11.4286 - 29.7891i) q^{87} +(61.2879 - 61.2879i) q^{88} -70.8895i q^{89} +(-45.3249 + 137.901i) q^{90} +(-17.5529 + 54.9600i) q^{91} +(-149.626 + 149.626i) q^{92} +(75.4769 + 28.9568i) q^{93} -269.669 q^{94} +(-45.2824 + 116.650i) q^{95} +(40.2198 + 90.2902i) q^{96} +(114.216 - 114.216i) q^{97} +(-26.2933 - 155.859i) q^{98} +(-67.2426 + 74.7363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 48 q^{15} - 24 q^{16} - 92 q^{18} - 60 q^{21} + 112 q^{22} - 72 q^{25} + 88 q^{28} - 108 q^{30} + 416 q^{36} + 72 q^{37} + 300 q^{42} - 328 q^{43} + 32 q^{46} + 148 q^{51} - 748 q^{57} - 392 q^{58} + 544 q^{60} - 220 q^{63} - 648 q^{67} - 8 q^{70} - 8 q^{72} + 500 q^{78} - 948 q^{81} + 672 q^{85} + 1288 q^{88} + 808 q^{91} + 292 q^{93}+O(q^{100}) \) 32 * q - 48 * q^15 - 24 * q^16 - 92 * q^18 - 60 * q^21 + 112 * q^22 - 72 * q^25 + 88 * q^28 - 108 * q^30 + 416 * q^36 + 72 * q^37 + 300 * q^42 - 328 * q^43 + 32 * q^46 + 148 * q^51 - 748 * q^57 - 392 * q^58 + 544 * q^60 - 220 * q^63 - 648 * q^67 - 8 * q^70 - 8 * q^72 + 500 * q^78 - 948 * q^81 + 672 * q^85 + 1288 * q^88 + 808 * q^91 + 292 * q^93

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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