LMFDB - Embedded newform 105.3.k.d.62.13

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			62.13
Character	$\chi$	$=$	105.62
Dual form			105.3.k.d.83.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.28094 - 2.28094i) q^{2} +(-2.80094 + 1.07458i) q^{3} -6.40541i q^{4} +(1.80941 - 4.66112i) q^{5} +(-3.93772 + 8.83986i) q^{6} +(-3.20922 - 6.22100i) q^{7} +(-5.48661 - 5.48661i) q^{8} +(6.69054 - 6.01969i) q^{9} +O(q^{10})$	\(q+(2.28094 - 2.28094i) q^{2} +(-2.80094 + 1.07458i) 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} +(6.88316 + 17.9412i) q^{12} +(-5.82807 - 5.82807i) q^{13} +(-21.5098 - 6.86971i) q^{14} +(-0.0592799 + 14.9999i) q^{15} +0.592330 q^{16} +(6.84147 + 6.84147i) q^{17} +(1.53016 - 28.9913i) q^{18} +25.0261 q^{19} +(-29.8564 - 11.5900i) q^{20} +(15.6738 + 13.9761i) 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} +(-12.2711 + 24.0503i) q^{27} +(-39.8481 + 20.5564i) q^{28} -10.6354 q^{29} +(34.0787 + 34.3491i) q^{30} +26.9470i q^{31} +(23.2975 - 23.2975i) q^{32} +(-12.0036 - 31.2877i) 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} +(67.6298 - 3.87246i) q^{42} +(1.25060 - 1.25060i) q^{43} +71.5513 q^{44} +(-15.9526 - 42.0775i) q^{45} +106.562 q^{46} +(-59.1134 - 59.1134i) q^{47} +(-1.65908 + 0.636508i) 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} +(-70.0965 + 26.8926i) q^{57} +(-24.2588 + 24.2588i) q^{58} +70.2066i q^{59} +(96.0805 + 0.379712i) q^{60} +14.1716i q^{61} +(61.4646 + 61.4646i) q^{62} +(-58.9200 - 22.3033i) 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} +(-69.7361 - 3.68068i) q^{72} +(51.1141 + 51.1141i) q^{73} -95.2731 q^{74} +(69.8090 + 27.4172i) q^{75} -160.302i q^{76} +(69.4914 - 35.8484i) q^{77} +(74.4687 - 28.5700i) 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} +(89.5226 - 100.397i) q^{84} +(44.2679 - 19.5099i) q^{85} -5.70508i q^{86} +(29.7891 - 11.4286i) q^{87} +(61.2879 - 61.2879i) q^{88} +70.8895i q^{89} +(-132.363 - 59.5894i) q^{90} +(-17.5529 + 54.9600i) q^{91} +(149.626 - 149.626i) q^{92} +(-28.9568 - 75.4769i) 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	$-0.451394\pi$
$2$	2.28094	−	2.28094i	1.14047	−	1.14047i	0.988364	−	0.152108i	$-0.0486063\pi$
$3$	−2.80094	+	1.07458i	−0.933647	+	0.358195i
$3$	−2.80094	+	1.07458i	−0.933647	+	0.358195i
$4$		−	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	$0.169522\pi$
$11$			11.1704i			1.01549i	−0.861506	+	0.507747i	$0.830478\pi$
$12$	6.88316	+	17.9412i	0.573596	+	1.49510i
$13$	−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
$15$	−0.0592799	+	14.9999i	−0.00395199	+	0.999992i
$16$	0.592330			0.0370206
$17$	6.84147	+	6.84147i	0.402440	+	0.402440i	0.879092	−	0.476652i	$-0.158150\pi$
$17$	6.84147	+	6.84147i	0.402440	+	0.402440i	−0.476652	+	0.879092i	$0.658150\pi$
$18$	1.53016	−	28.9913i	0.0850091	−	1.61063i
$19$	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
$21$	15.6738	+	13.9761i	0.746373	+	0.665528i
$22$	25.4792	+	25.4792i	1.15814	+	1.15814i
$23$	23.3593	+	23.3593i	1.01562	+	1.01562i	0.999876	+	0.0157445i	$0.00501183\pi$
$23$	23.3593	+	23.3593i	1.01562	+	1.01562i	0.0157445	+	0.999876i	$0.494988\pi$
$24$	21.2635	+	9.47185i	0.885980	+	0.394661i
$25$	−18.4521	−	16.8677i	−0.738083	−	0.674710i
$26$	−26.5870			−1.02258
$27$	−12.2711	+	24.0503i	−0.454487	+	0.890754i
$28$	−39.8481	+	20.5564i	−1.42315	+	0.734157i
$29$	−10.6354			−0.366738			−0.183369	−	0.983044i	$-0.558700\pi$
$29$	−10.6354			−0.366738			−0.183369	+	0.983044i	$0.558700\pi$
$30$	34.0787	+	34.3491i	1.13596	+	1.14497i
$31$			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
$33$	−12.0036	−	31.2877i	−0.363745	−	0.948113i
$34$	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	$-0.368313\pi$
$41$	32.9644			0.804010			0.402005	+	0.915637i	$0.368313\pi$
$42$	67.6298	−	3.87246i	1.61023	−	0.0922014i
$43$	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
$45$	−15.9526	−	42.0775i	−0.354502	−	0.935055i
$46$	106.562			2.31657
$47$	−59.1134	−	59.1134i	−1.25773	−	1.25773i	−0.952173	−	0.305558i	$-0.901157\pi$
$47$	−59.1134	−	59.1134i	−1.25773	−	1.25773i	−0.305558	−	0.952173i	$-0.598843\pi$
$48$	−1.65908	+	0.636508i	−0.0345642	+	0.0132606i
$49$	−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	0.417293	−	0.908772i	$-0.362979\pi$
$53$	−26.0484	−	26.0484i	−0.491478	−	0.491478i	−0.908772	+	0.417293i	$0.862979\pi$
$54$	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
$57$	−70.0965	+	26.8926i	−1.22976	+	0.471800i
$58$	−24.2588	+	24.2588i	−0.418254	+	0.418254i
$59$			70.2066i			1.18994i	0.803747	+	0.594971i	$0.202837\pi$
$59$			70.2066i			1.18994i	−0.803747	+	0.594971i	$0.797163\pi$
$60$	96.0805	+	0.379712i	1.60134	+	0.00632854i
$61$			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
$63$	−58.9200	−	22.3033i	−0.935237	−	0.354021i
$64$		−	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	$0.0886774\pi$
$71$			39.0498i			0.549997i	−0.961445	+	0.274999i	$0.911323\pi$
$72$	−69.7361	−	3.68068i	−0.968557	−	0.0511205i
$73$	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
$75$	69.8090	+	27.4172i	0.930787	+	0.365563i
$76$		−	160.302i		−	2.10924i
$77$	69.4914	−	35.8484i	0.902485	−	0.465564i
$78$	74.4687	−	28.5700i	0.954726	−	0.366282i
$79$			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	−0.870218	−	0.492667i	$-0.836022\pi$
$83$	−31.3367	+	31.3367i	−0.377551	+	0.377551i	0.492667	+	0.870218i	$0.336022\pi$
$84$	89.5226	−	100.397i	1.06575	−	1.19521i
$85$	44.2679	−	19.5099i	0.520799	−	0.229528i
$86$		−	5.70508i		−	0.0663381i
$87$	29.7891	−	11.4286i	0.342404	−	0.131364i
$88$	61.2879	−	61.2879i	0.696453	−	0.696453i
$89$			70.8895i			0.796511i	0.917274	+	0.398256i	$0.130384\pi$
$89$			70.8895i			0.796511i	−0.917274	+	0.398256i	$0.869616\pi$
$90$	−132.363	−	59.5894i	−1.47070	−	0.662105i
$91$	−17.5529	+	54.9600i	−0.192889	+	0.603957i
$92$	149.626	−	149.626i	1.62637	−	1.62637i
$93$	−28.9568	−	75.4769i	−0.311363	−	0.811579i
$94$	−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	$-0.587689\pi$
$101$	−54.9464			−0.544024			−0.272012	+	0.962294i	$0.587689\pi$
$102$	−87.4175	+	33.5378i	−0.857034	+	0.328802i
$103$	−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
$105$	93.5046	−	47.7692i	0.890520	−	0.454944i
$106$	−118.830			−1.12103
$107$	−89.1318	+	89.1318i	−0.833007	+	0.833007i	−0.987927	−	0.154920i	$-0.950488\pi$
$107$	−89.1318	+	89.1318i	−0.833007	+	0.833007i	0.154920	+	0.987927i	$0.450488\pi$
$108$	154.052	+	78.6017i	1.42641	+	0.727794i
$109$		−	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	0.992552	−	0.121825i	$-0.0388747\pi$
$113$	98.3921	+	98.3921i	0.870726	+	0.870726i	−0.121825	+	0.992552i	$0.538875\pi$
$114$	−98.5457	+	221.227i	−0.864436	+	1.94059i
$115$	151.147	−	66.6139i	1.31432	−	0.579251i
$116$			68.1242i			0.587277i
$117$	−74.0762	−	3.90974i	−0.633129	−	0.0334166i
$118$	160.137	+	160.137i	1.35710	+	1.35710i
$119$	20.6050	−	64.5166i	0.173152	−	0.542157i
$120$	82.6238	−	81.9733i	0.688532	−	0.683111i
$121$	−3.77875			−0.0312293
$122$	32.3246	+	32.3246i	0.264956	+	0.264956i
$123$	−92.3314	+	35.4230i	−0.750661	+	0.287992i
$124$	172.607			1.39199
$125$	−112.010	+	55.4868i	−0.896079	+	0.443894i
$126$	−185.266	+	83.5204i	−1.47036	+	0.662861i
$127$	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	$-0.411822\pi$
$131$	71.6542			0.546979			0.273489	+	0.961875i	$0.411822\pi$
$132$	−200.411	+	76.8879i	−1.51826	+	0.582484i
$133$	−80.3142	−	155.687i	−0.603866	−	1.17058i
$134$	−28.0309			−0.209186
$135$	89.8981	+	100.714i	0.665912	+	0.746031i
$136$		−	75.0730i		−	0.552008i
$137$	−57.1182	+	57.1182i	−0.416921	+	0.416921i	−0.884141	−	0.467220i	$-0.845256\pi$
$137$	−57.1182	+	57.1182i	−0.416921	+	0.416921i	0.467220	+	0.884141i	$0.345256\pi$
$138$	−298.475	+	114.510i	−2.16286	+	0.829784i
$139$	−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
$147$	36.6445	−	142.359i	0.249282	−	0.968431i
$148$	−133.774	+	133.774i	−0.903880	+	0.903880i
$149$	−62.9077			−0.422199			−0.211100	−	0.977465i	$-0.567704\pi$
$149$	−62.9077			−0.422199			−0.211100	+	0.977465i	$0.567704\pi$
$150$	221.768	−	96.6933i	1.47845	−	0.644622i
$151$	−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
$153$	86.9567	+	4.58958i	0.568344	+	0.0299972i
$154$	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
$162$	−164.281	−	203.179i	−1.01408	−	1.25419i
$163$	−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
$165$	−167.555	−	0.662183i	−1.01549	−	0.00401323i
$166$			142.955i			0.861173i
$167$	−151.924	−	151.924i	−0.909725	−	0.909725i	0.0865247	−	0.996250i	$-0.472424\pi$
$167$	−151.924	−	151.924i	−0.909725	−	0.909725i	−0.996250	+	0.0865247i	$0.972424\pi$
$168$	−9.31486	−	162.678i	−0.0554456	−	0.968320i
$169$		−	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	−0.762169	−	0.647378i	$-0.775866\pi$
$173$	−19.8589	+	19.8589i	−0.114791	+	0.114791i	0.647378	+	0.762169i	$0.275866\pi$
$174$	41.8793	−	94.0154i	0.240685	−	0.540319i
$175$	−45.7175	+	168.923i	−0.261243	+	0.965273i
$176$			6.61658i			0.0375942i
$177$	−75.4429	−	196.645i	−0.426231	−	1.11099i
$178$	161.695	+	161.695i	0.908399	+	0.908399i
$179$	157.790			0.881508			0.440754	−	0.897628i	$-0.354711\pi$
$179$	157.790			0.881508			0.440754	+	0.897628i	$0.354711\pi$
$180$	−269.524	+	102.183i	−1.49735	+	0.567683i
$181$			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
$183$	−15.2286	−	39.6938i	−0.0832162	−	0.216906i
$184$		−	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
$189$	188.998	−	0.844085i	0.999990	−	0.00446606i
$190$	−162.784	−	369.358i	−0.856760	−	1.94399i
$191$		−	8.99622i		−	0.0471007i	−0.999723	−	0.0235503i	$-0.992503\pi$
$191$		−	8.99622i		−	0.0471007i	0.999723	−	0.0235503i	$-0.00749699\pi$
$192$	111.662	+	291.050i	0.581571	+	1.51588i
$193$	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
$195$	87.7659	−	87.0749i	0.450082	−	0.446538i
$196$	255.763	+	181.925i	1.30491	+	0.928190i
$197$	−113.154	+	113.154i	−0.574386	+	0.574386i	−0.933351	−	0.358965i	$-0.883130\pi$
$197$	−113.154	+	113.154i	−0.574386	+	0.574386i	0.358965	+	0.933351i	$0.383130\pi$
$198$	323.846	+	17.0926i	1.63559	+	0.0863262i
$199$	−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
$207$	296.902	+	15.6705i	1.43431	+	0.0757028i
$208$	−3.45214	−	3.45214i	−0.0165968	−	0.0165968i
$209$			279.552i			1.33757i
$210$	104.320	−	322.238i	0.496762	−	1.53446i
$211$	−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
$213$	−41.9623	−	109.376i	−0.197006	−	0.513503i
$214$			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
$222$	266.854	−	102.379i	1.20205	−	0.461166i
$223$	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
$225$	−224.993	−	1.77838i	−0.999969	−	0.00790392i
$226$	448.854			1.98608
$227$	23.2602	+	23.2602i	0.102468	+	0.102468i	0.756482	−	0.654014i	$-0.226916\pi$
$227$	23.2602	+	23.2602i	0.102468	+	0.102468i	−0.654014	+	0.756482i	$0.726916\pi$
$228$	172.258	+	448.997i	0.755519	+	1.96929i
$229$	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
$231$	−156.119	+	175.084i	−0.675840	+	0.757938i
$232$	58.3524	+	58.3524i	0.251519	+	0.251519i
$233$	90.6015	+	90.6015i	0.388847	+	0.388847i	0.874276	−	0.485429i	$-0.161336\pi$
$233$	90.6015	+	90.6015i	0.388847	+	0.388847i	−0.485429	+	0.874276i	$0.661336\pi$
$234$	−177.881	+	160.046i	−0.760177	+	0.683956i
$235$	−382.495	+	168.574i	−1.62764	+	0.717338i
$236$	449.702			1.90552
$237$	−18.0958	−	47.1673i	−0.0763535	−	0.199018i
$238$	−100.160	−	194.158i	−0.420840	−	0.815789i
$239$	−406.988			−1.70288			−0.851439	−	0.524454i	$-0.824269\pi$
$239$	−406.988			−1.70288			−0.851439	+	0.524454i	$0.824269\pi$
$240$	−0.0351132	+	8.88488i	−0.000146305	+	0.0370203i
$241$		−	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
$243$	62.6752	+	234.778i	0.257923	+	0.966166i
$244$	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	$-0.581943\pi$
$251$	−127.808			−0.509195			−0.254597	+	0.967047i	$0.581943\pi$
$252$	−142.862	+	377.407i	−0.566913	+	1.49765i
$253$	−260.933	+	260.933i	−1.03136	+	1.03136i
$254$	786.070			3.09477
$255$	−103.027	+	102.216i	−0.404027	+	0.400846i
$256$	−240.473			−0.939346
$257$	100.099	+	100.099i	0.389491	+	0.389491i	0.874506	−	0.485015i	$-0.161186\pi$
$257$	100.099	+	100.099i	0.389491	+	0.389491i	−0.485015	+	0.874506i	$0.661186\pi$
$258$	6.13059	+	15.9796i	0.0237620	+	0.0619364i
$259$	−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	0.499306	−	0.866426i	$-0.333588\pi$
$263$	−96.5525	−	96.5525i	−0.367120	−	0.367120i	−0.866426	+	0.499306i	$0.833588\pi$
$264$	−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
$267$	−76.1767	−	198.557i	−0.285306	−	0.743660i
$268$	−39.3586	+	39.3586i	−0.146860	+	0.146860i
$269$		−	213.738i		−	0.794565i	−0.917696	−	0.397282i	$-0.869953\pi$
$269$		−	213.738i		−	0.794565i	0.917696	−	0.397282i	$-0.130047\pi$
$270$	434.776	+	24.6709i	1.61028	+	0.0913736i
$271$		−	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
$273$	−9.89457	−	172.802i	−0.0362439	−	0.632974i
$274$			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	$-0.845190\pi$
$281$		−	262.680i		−	0.934803i	0.884045	−	0.467401i	$-0.154810\pi$
$282$	755.326	−	289.782i	2.67846	−	1.02759i
$283$	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
$285$	−1.48354	+	375.388i	−0.00520541	+	1.31715i
$286$		−	296.989i		−	1.03842i
$287$	−105.790	−	205.072i	−0.368607	−	0.714536i
$288$	15.6291	−	296.117i	0.0542676	−	1.02818i
$289$		−	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	−0.0281818	−	0.999603i	$-0.508972\pi$
$293$	284.626	−	284.626i	0.971421	−	0.971421i	0.999603	+	0.0281818i	$0.00897172\pi$
$294$	−241.130	−	408.298i	−0.820169	−	1.38877i
$295$	327.241	+	127.032i	1.10929	+	0.430618i
$296$			229.171i			0.774227i
$297$	−268.653	−	137.074i	−0.904555	−	0.461529i
$298$	−143.489	+	143.489i	−0.481507	+	0.481507i
$299$		−	272.279i		−	0.910632i
$300$	175.619	−	447.156i	0.585395	−	1.49052i
$301$	−11.7934	−	3.76652i	−0.0391807	−	0.0125134i
$302$	−47.0815	+	47.0815i	−0.155899	+	0.155899i
$303$	153.902	−	59.0445i	0.507926	−	0.194867i
$304$	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	$-0.341943\pi$
$311$	296.319			0.952794			0.476397	+	0.879230i	$0.341943\pi$
$312$	−68.7226	−	179.128i	−0.220265	−	0.574128i
$313$	−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
$315$	−210.569	+	234.277i	−0.668472	+	0.743737i
$316$	107.866			0.341348
$317$	−43.8360	+	43.8360i	−0.138284	+	0.138284i	−0.772860	−	0.634576i	$-0.781175\pi$
$317$	−43.8360	+	43.8360i	−0.138284	+	0.138284i	0.634576	+	0.772860i	$0.281175\pi$
$318$	332.835	−	127.692i	1.04665	−	0.401549i
$319$		−	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
$327$	98.0263	+	255.509i	0.299775	+	0.781373i
$328$	−180.863	−	180.863i	−0.551412	−	0.551412i
$329$	−178.037	+	557.453i	−0.541145	+	1.69438i
$330$	−383.695	+	380.674i	−1.16271	+	1.15356i
$331$	−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
$333$	−265.448	−	14.0103i	−0.797140	−	0.0420731i
$334$	−693.061			−2.07503
$335$	−39.7587	+	17.5226i	−0.118683	+	0.0523062i
$336$	9.28408	+	8.27845i	0.0276312	+	0.0246383i
$337$	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
$342$	38.2940	−	725.539i	0.111971	−	2.12146i
$343$	339.547	+	48.5462i	0.989933	+	0.141534i
$344$	−13.7231			−0.0398927
$345$	−351.771	+	349.002i	−1.01963	+	1.01160i
$346$			90.5940i			0.261832i
$347$	−358.869	+	358.869i	−1.03421	+	1.03421i	−0.0348116	+	0.999394i	$0.511083\pi$
$347$	−358.869	+	358.869i	−1.03421	+	1.03421i	−0.999394	+	0.0348116i	$0.988917\pi$
$348$	−73.2051	−	190.812i	−0.210360	−	0.548310i
$349$	−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	−0.339788	−	0.940502i	$-0.610355\pi$
$353$	212.052	−	212.052i	0.600714	−	0.600714i	0.940502	+	0.339788i	$0.110355\pi$
$354$	−620.616	−	276.454i	−1.75315	−	0.780944i
$355$	182.016	+	70.6570i	0.512721	+	0.199034i
$356$	454.077			1.27550
$357$	11.6151	+	202.849i	0.0325352	+	0.568205i
$358$	359.910	−	359.910i	1.00534	−	1.00534i
$359$	−194.091			−0.540643			−0.270321	−	0.962770i	$-0.587130\pi$
$359$	−194.091			−0.540643			−0.270321	+	0.962770i	$0.587130\pi$
$360$	−143.337	+	318.389i	−0.398159	+	0.884413i
$361$	265.304			0.734915
$362$	134.124	+	134.124i	0.370508	+	0.370508i
$363$	10.5840	−	4.06058i	0.0291571	−	0.0111862i
$364$	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
$372$	−483.461	+	185.480i	−1.29963	+	0.498603i
$373$	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
$375$	254.108	−	275.779i	0.677621	−	0.735411i
$376$			648.665i			1.72517i
$377$	61.9839	+	61.9839i	0.164414	+	0.164414i
$378$	429.169	−	433.019i	1.13537	−	1.14555i
$379$		−	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	−0.715307	−	0.698810i	$-0.753713\pi$
$383$	−6.31835	+	6.31835i	−0.0164970	+	0.0164970i	0.698810	+	0.715307i	$0.253713\pi$
$384$	557.401	+	248.295i	1.45157	+	0.646602i
$385$	−41.3555	−	388.772i	−0.107417	−	1.00980i
$386$		−	438.422i		−	1.13581i
$387$	0.838958	−	15.8954i	0.00216785	−	0.0410733i
$388$	−731.601	−	731.601i	−1.88557	−	1.88557i
$389$	234.607			0.603103			0.301551	−	0.953450i	$-0.402496\pi$
$389$	234.607			0.603103			0.301551	+	0.953450i	$0.402496\pi$
$390$	1.57608	−	398.802i	0.00404122	−	1.02257i
$391$			319.624i			0.817452i
$392$	374.906	−	63.2462i	0.956392	−	0.161342i
$393$	−200.699	+	76.9985i	−0.510685	+	0.195925i
$394$			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
$399$	392.254	+	349.767i	0.983094	+	0.876608i
$400$	−10.9297	−	9.99126i	−0.0273243	−	0.0249782i
$401$			255.719i			0.637703i	0.947805	+	0.318851i	$0.103297\pi$
$401$			255.719i			0.637703i	−0.947805	+	0.318851i	$0.896703\pi$
$402$	78.5128	−	30.1215i	0.195306	−	0.0749292i
$403$	157.049	−	157.049i	0.389700	−	0.389700i
$404$			351.955i			0.871175i
$405$	−360.025	−	185.491i	−0.888951	−	0.458003i
$406$	228.766	+	73.0621i	0.563462	+	0.179956i
$407$	233.290	−	233.290i	0.573194	−	0.573194i
$408$	80.6723	+	210.275i	0.197726	+	0.515380i
$409$	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
$417$	116.109	−	44.5453i	0.278439	−	0.106823i
$418$	637.643	+	637.643i	1.52546	+	1.52546i
$419$		−	476.333i		−	1.13683i	−0.822741	−	0.568417i	$-0.807556\pi$
$419$		−	476.333i		−	1.13683i	0.822741	−	0.568417i	$-0.192444\pi$
$420$	−305.981	−	598.936i	−0.728527	−	1.42604i
$421$	−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
$423$	−751.345	−	39.6560i	−1.77623	−	0.0937494i
$424$			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	$0.0355010\pi$
$431$			95.9393i			0.222597i	−0.993787	+	0.111299i	$0.964499\pi$
$432$	−7.26856	+	14.2457i	−0.0168254	+	0.0329762i
$433$	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
$435$	0.630465	−	159.530i	0.00144935	−	0.366735i
$436$	−584.318			−1.34018
$437$	584.591	+	584.591i	1.33774	+	1.33774i
$438$	−653.114	+	250.568i	−1.49113	+	0.572073i
$439$	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
$441$	50.3379	+	438.118i	0.114145	+	0.993464i
$442$	−181.894	−	181.894i	−0.411526	−	0.411526i
$443$	−214.203	−	214.203i	−0.483528	−	0.483528i	0.422728	−	0.906256i	$-0.361072\pi$
$443$	−214.203	−	214.203i	−0.483528	−	0.483528i	−0.906256	+	0.422728i	$0.861072\pi$
$444$	230.942	−	518.446i	0.520140	−	1.16767i
$445$	330.425	+	128.268i	0.742527	+	0.288243i
$446$	159.588			0.357821
$447$	176.201	−	67.5996i	0.394185	−	0.151230i
$448$	−646.433	+	333.475i	−1.44293	+	0.744363i
$449$	147.297			0.328055			0.164027	−	0.986456i	$-0.447551\pi$
$449$	147.297			0.328055			0.164027	+	0.986456i	$0.447551\pi$
$450$	−517.253	+	509.140i	−1.14945	+	1.13142i
$451$			368.227i			0.816468i
$452$	630.242	−	630.242i	1.39434	−	1.39434i
$453$	57.8148	−	22.1807i	0.127627	−	0.0489641i
$454$	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	$-0.433426\pi$
$461$	191.433			0.415256			0.207628	+	0.978208i	$0.433426\pi$
$462$	43.2571	+	755.455i	0.0936300	+	1.63518i
$463$	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
$465$	−404.201	−	1.59741i	−0.869251	−	0.00343530i
$466$	413.314			0.886939
$467$	−61.5519	−	61.5519i	−0.131803	−	0.131803i	0.638128	−	0.769931i	$-0.279709\pi$
$467$	−61.5519	−	61.5519i	−0.131803	−	0.131803i	−0.769931	+	0.638128i	$0.779709\pi$
$468$	−25.0435	+	474.488i	−0.0535118	+	1.01386i
$469$	−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
$477$	−331.081	−	17.4744i	−0.694089	−	0.0366340i
$478$	−928.316	+	928.316i	−1.94208	+	1.94208i
$479$		−	572.620i		−	1.19545i	−0.801702	−	0.597724i	$-0.796072\pi$
$479$		−	572.620i		−	1.19545i	0.801702	−	0.597724i	$-0.203928\pi$
$480$	348.079	+	350.841i	0.725165	+	0.730919i
$481$			243.434i			0.506099i
$482$	−267.116	−	267.116i	−0.554183	−	0.554183i
$483$	39.6580	+	692.601i	0.0821078	+	1.43396i
$484$			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	$-0.772310\pi$
$491$		−	644.045i		−	1.31170i	0.754891	−	0.655850i	$-0.227690\pi$
$492$	226.899	+	591.421i	0.461177	+	1.20207i
$493$	−72.7618	−	72.7618i	−0.147590	−	0.147590i
$494$	−665.369			−1.34690
$495$	470.024	−	178.198i	0.949544	−	0.359995i
$496$			15.9615i			0.0321804i
$497$	242.929	−	125.319i	0.488791	−	0.252152i
$498$	−153.617	−	400.408i	−0.308468	−	0.804032i
$499$		−	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	$0.507881\pi$
$503$	−515.298	+	515.298i	−1.02445	+	1.02445i	−0.999694	+	0.0247567i	$0.992119\pi$
$504$	200.901	+	445.641i	0.398614	+	0.884208i
$505$	−99.4205	+	256.112i	−0.196872	+	0.507152i
$506$			1190.35i			2.35247i
$507$	108.605	+	283.083i	0.214211	+	0.558349i
$508$	1103.73	−	1103.73i	2.17270	−	2.17270i
$509$			648.378i			1.27383i	0.770935	+	0.636914i	$0.219789\pi$
$509$			648.378i			1.27383i	−0.770935	+	0.636914i	$0.780211\pi$
$510$	−1.85013	+	468.147i	−0.00362770	+	0.917935i
$511$	153.945	−	482.017i	0.301261	−	0.943282i
$512$	26.7994	−	26.7994i	0.0523425	−	0.0523425i
$513$	−307.098	+	601.886i	−0.598632	+	1.17327i
$514$	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	$-0.439942\pi$
$521$	195.439			0.375123			0.187561	+	0.982253i	$0.439942\pi$
$522$	−16.2739	+	308.334i	−0.0311761	+	0.590679i
$523$	−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
$525$	−53.4699	−	522.270i	−0.101847	−	0.994800i
$526$	−440.462			−0.837380
$527$	−184.357	+	184.357i	−0.349824	+	0.349824i
$528$	−7.11008	−	18.5327i	−0.0134661	−	0.0350997i
$529$			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
$537$	−441.960	+	169.559i	−0.823018	+	0.315752i
$538$	−487.524	−	487.524i	−0.906179	−	0.906179i
$539$	−446.026	−	317.261i	−0.827507	−	0.588610i
$540$	645.116	−	575.834i	1.19466	−	1.06636i
$541$	−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
$543$	−63.1875	−	164.701i	−0.116367	−	0.303316i
$544$	318.779			0.585990
$545$	−425.199	−	165.059i	−0.780182	−	0.302860i
$546$	−416.720	−	371.583i	−0.763224	−	0.680554i
$547$	−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
$552$	275.445	+	717.956i	0.498994	+	1.30064i
$553$	104.760	−	54.0426i	0.189440	−	0.0977263i
$554$	−557.655			−1.00660
$555$	314.504	−	312.028i	0.566674	−	0.562213i
$556$			265.527i			0.477567i
$557$	118.212	−	118.212i	0.212230	−	0.212230i	−0.592984	−	0.805214i	$-0.702050\pi$
$557$	118.212	−	118.212i	0.212230	−	0.212230i	0.805214	+	0.592984i	$0.202050\pi$
$558$	781.229	+	41.2333i	1.40005	+	0.0738947i
$559$	−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	$0.503583\pi$
$563$	−569.301	+	569.301i	−1.01119	+	1.01119i	−0.999937	+	0.0112552i	$0.996417\pi$
$564$	653.678	−	1467.45i	1.15900	−	2.60186i
$565$	636.649	−	280.586i	1.12681	−	0.496612i
$566$	1217.08			2.15031
$567$	−528.465	+	205.459i	−0.932038	+	0.362361i
$568$	214.251	−	214.251i	0.377203	−	0.377203i
$569$	602.118			1.05820			0.529102	−	0.848558i	$-0.322529\pi$
$569$	602.118			1.05820			0.529102	+	0.848558i	$0.322529\pi$
$570$	852.855	+	859.623i	1.49624	+	1.50811i
$571$	−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
$573$	9.66720	+	25.1979i	0.0168712	+	0.0439754i
$574$	−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
$582$	559.902	+	1459.40i	0.962031	+	2.50757i
$583$	290.972	−	290.972i	0.499094	−	0.499094i
$584$		−	560.886i		−	0.960422i
$585$	−152.258	+	338.204i	−0.260270	+	0.578126i
$586$		−	1298.43i		−	2.21576i
$587$	−512.337	−	512.337i	−0.872806	−	0.872806i	0.119971	−	0.992777i	$-0.461720\pi$
$587$	−512.337	−	512.337i	−0.872806	−	0.872806i	−0.992777	+	0.119971i	$0.961720\pi$
$588$	−911.870	−	234.723i	−1.55080	−	0.399189i
$589$			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	−0.523135	−	0.852250i	$-0.675238\pi$
$593$	195.165	−	195.165i	0.329114	−	0.329114i	0.852250	+	0.523135i	$0.175238\pi$
$594$	−925.441	+	300.124i	−1.55798	+	0.505260i
$595$	−263.437	−	212.779i	−0.442751	−	0.357613i
$596$			402.950i			0.676090i
$597$	341.788	−	131.127i	0.572509	−	0.219644i
$598$	−621.053	−	621.053i	−1.03855	−	1.03855i
$599$	93.4354			0.155986			0.0779928	−	0.996954i	$-0.475149\pi$
$599$	93.4354			0.155986			0.0779928	+	0.996954i	$0.475149\pi$
$600$	−232.587	−	533.443i	−0.387646	−	0.889071i
$601$			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
$603$	−78.0990	−	4.12207i	−0.129517	−	0.00683593i
$604$			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
$609$	−166.697	−	148.641i	−0.273723	−	0.244074i
$610$	209.157	−	92.1804i	0.342881	−	0.151115i
$611$			689.034i			1.12772i
$612$	29.3981	−	556.994i	0.0480362	−	0.910120i
$613$	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
$615$	−1.95413	+	494.462i	−0.00317744	+	0.804004i
$616$	−577.959	−	184.586i	−0.938245	−	0.299652i
$617$	400.922	−	400.922i	0.649793	−	0.649793i	−0.303150	−	0.952943i	$-0.598038\pi$
$617$	400.922	−	400.922i	0.649793	−	0.649793i	0.952943	+	0.303150i	$0.0980383\pi$
$618$	1396.67	−	535.833i	2.25998	−	0.867044i
$619$	−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
$627$	−300.402	−	783.009i	−0.479111	−	1.24882i
$628$	1365.97	+	1365.97i	2.17512	+	2.17512i
$629$		−	285.762i		−	0.454312i
$630$	54.0773	+	1014.67i	0.0858370	+	1.61059i
$631$	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
$633$	11.9863	−	4.59856i	0.0189357	−	0.00726470i
$634$			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	$-0.965713\pi$
$641$		−	137.826i		−	0.215017i	0.994204	−	0.107509i	$-0.0342873\pi$
$642$	−436.936	−	1138.89i	−0.680585	−	1.77397i
$643$	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
$645$	18.6847	+	18.8329i	0.0289685	+	0.0291983i
$646$	781.065			1.20908
$647$	−192.497	−	192.497i	−0.297523	−	0.297523i	0.542520	−	0.840043i	$-0.317470\pi$
$647$	−192.497	−	192.497i	−0.297523	−	0.297523i	−0.840043	+	0.542520i	$0.817470\pi$
$648$	−488.729	+	395.164i	−0.754211	+	0.609822i
$649$	−784.239			−1.20838
$650$	490.586	+	448.463i	0.754748	+	0.689943i
$651$	−376.613	+	422.362i	−0.578515	+	0.648790i
$652$	125.066	+	125.066i	0.191819	+	0.191819i
$653$	178.554	+	178.554i	0.273436	+	0.273436i	0.830482	−	0.557046i	$-0.188065\pi$
$653$	178.554	+	178.554i	0.273436	+	0.273436i	−0.557046	+	0.830482i	$0.688065\pi$
$654$	806.394	+	359.209i	1.23302	+	0.549250i
$655$	129.652	−	333.989i	0.197942	−	0.509907i
$656$	19.5258			0.0297649
$657$	649.672	+	34.2897i	0.988846	+	0.0521913i
$658$	865.427	+	1677.61i	1.31524	+	2.54956i
$659$	−984.529			−1.49397			−0.746987	−	0.664838i	$-0.768500\pi$
$659$	−984.529			−1.49397			−0.746987	+	0.664838i	$0.768500\pi$
$660$	−4.24155	+	1073.26i	−0.00642660	+	1.62615i
$661$			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
$663$	85.6929	+	223.362i	0.129250	+	0.336895i
$664$	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
$672$	690.770	−	39.5532i	1.02793	−	0.0588590i
$673$	−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
$675$	632.103	−	236.793i	0.936449	−	0.350804i
$676$	−647.377			−0.957658
$677$	430.936	+	430.936i	0.636538	+	0.636538i	0.949700	−	0.313162i	$-0.101388\pi$
$677$	430.936	+	430.936i	0.636538	+	0.636538i	−0.313162	+	0.949700i	$0.601388\pi$
$678$	−1257.21	+	482.331i	−1.85430	+	0.711403i
$679$	−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	$0.197658\pi$
$683$	952.879	+	952.879i	1.39514	+	1.39514i	0.581818	+	0.813319i	$0.302342\pi$
$684$	−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
$687$	−255.195	+	97.9059i	−0.371463	+	0.142512i
$688$	0.740765	−	0.740765i	0.00107669	−	0.00107669i
$689$			303.623i			0.440673i
$690$	−6.31701	+	1598.42i	−0.00915508	+	2.31656i
$691$		−	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
$693$	249.138	−	658.162i	0.359507	−	0.949728i
$694$			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	$0.282073\pi$
$701$			1086.06i			1.54929i	−0.632393	+	0.774647i	$0.717927\pi$
$702$	326.253	−	639.427i	0.464748	−	0.910865i
$703$	−522.659	−	522.659i	−0.743469	−	0.743469i
$704$	1160.74			1.64877
$705$	890.198	−	883.190i	1.26269	−	1.25275i
$706$		−	967.358i		−	1.37020i
$707$	176.335	+	341.822i	0.249413	+	0.483482i
$708$	−1259.59	+	483.243i	−1.77908	+	0.682547i
$709$			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
$714$	489.181	+	436.194i	0.685127	+	0.610916i
$715$	−185.653	−	421.245i	−0.259654	−	0.589154i
$716$		−	1010.71i		−	1.41161i
$717$	1139.95	−	437.342i	1.58989	−	0.609961i
$718$	−442.710	+	442.710i	−0.616588	+	0.616588i
$719$			160.221i			0.222838i	0.993773	+	0.111419i	$0.0355396\pi$
$719$			160.221i			0.222838i	−0.993773	+	0.111419i	$0.964460\pi$
$720$	−9.44920	−	24.9237i	−0.0131239	−	0.0346163i
$721$	−329.207	+	1030.78i	−0.456597	+	1.42966i
$722$	605.144	−	605.144i	0.838150	−	0.838150i
$723$	125.842	+	328.012i	0.174056	+	0.453682i
$724$	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
$732$	−254.255	+	97.5452i	−0.347343	+	0.133258i
$733$	−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
$735$	−597.249	−	428.391i	−0.812584	−	0.582844i
$736$	1088.43			1.47884
$737$	68.6376	−	68.6376i	0.0931311	−	0.0931311i
$738$	50.4409	−	955.682i	0.0683481	−	1.29496i
$739$			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	0.742856	−	0.669451i	$-0.233471\pi$
$743$	54.5399	+	54.5399i	0.0734050	+	0.0734050i	−0.669451	+	0.742856i	$0.733471\pi$
$744$	−255.238	+	572.987i	−0.343062	+	0.770144i
$745$	−113.826	+	293.220i	−0.152786	+	0.393584i
$746$		−	180.739i		−	0.242278i
$747$	−21.0221	+	398.297i	−0.0281421	+	0.533196i
$748$	489.516	+	489.516i	0.654433	+	0.654433i
$749$	840.533	+	268.446i	1.12221	+	0.358405i
$750$	−49.4309	−	1208.64i	−0.0659079	−	1.61152i
$751$	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
$753$	357.982	−	137.340i	0.475408	−	0.182391i
$754$	282.764			0.375018
$755$	−37.3484	+	96.2112i	−0.0494681	+	0.127432i
$756$	−5.40671	−	1210.61i	−0.00715174	−	1.60134i
$757$	−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	$-0.780673\pi$
$761$	−1174.77			−1.54372			−0.771859	+	0.635794i	$0.780673\pi$
$762$	−2201.74	+	844.699i	−2.88942	+	1.10853i
$763$	−567.496	+	292.753i	−0.743769	+	0.383687i
$764$	−57.6245			−0.0754248
$765$	178.733	−	397.011i	0.233638	−	0.518969i
$766$			28.8236i			0.0376288i
$767$	409.169	−	409.169i	0.533467	−	0.533467i
$768$	673.550	−	258.408i	0.877018	−	0.336469i
$769$	−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	−0.623520	−	0.781807i	$-0.714298\pi$
$773$	122.356	−	122.356i	0.158287	−	0.158287i	0.781807	+	0.623520i	$0.214298\pi$
$774$	−34.3428	−	38.1701i	−0.0443706	−	0.0493153i
$775$	454.535	−	497.228i	0.586496	−	0.641584i
$776$	−1253.32			−1.61510
$777$	−35.4566	−	619.226i	−0.0456327	−	0.796944i
$778$	535.125	−	535.125i	0.687822	−	0.687822i
$779$	824.970			1.05901
$780$	−557.751	−	562.177i	−0.715065	−	0.720740i
$781$	−436.203			−0.558519
$782$	729.044	+	729.044i	0.932281	+	0.932281i
$783$	130.508	−	255.785i	0.166678	−	0.326673i
$784$	−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
$792$	41.1148	−	778.983i	0.0519126	−	0.983565i
$793$	82.5930	−	82.5930i	0.104153	−	0.104153i
$794$			1113.75i			1.40270i
$795$	392.266	−	389.178i	0.493417	−	0.489532i
$796$			781.627i			0.981944i
$797$	412.431	+	412.431i	0.517479	+	0.517479i	0.916808	−	0.399329i	$-0.130757\pi$
$797$	412.431	+	412.431i	0.517479	+	0.517479i	−0.399329	+	0.916808i	$0.630757\pi$
$798$	1692.51	−	96.9124i	2.12094	−	0.121444i
$799$		−	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
$807$	229.679	+	598.667i	0.284609	+	0.741843i
$808$	301.470	+	301.470i	0.373106	+	0.373106i
$809$	−677.677			−0.837672			−0.418836	−	0.908062i	$-0.637562\pi$
$809$	−677.677			−0.837672			−0.418836	+	0.908062i	$0.637562\pi$
$810$	−1244.29	+	398.101i	−1.53616	+	0.491483i
$811$			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
$813$	564.202	+	1470.61i	0.693976	+	1.80887i
$814$		−	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
$819$	213.404	+	473.375i	0.260567	+	0.577992i
$820$	−984.199	−	382.058i	−1.20024	−	0.465924i
$821$		−	93.5358i		−	0.113929i	−0.998376	−	0.0569646i	$-0.981858\pi$
$821$		−	93.5358i		−	0.113929i	0.998376	−	0.0569646i	$-0.0181422\pi$
$822$	−280.001	−	729.832i	−0.340634	−	0.887874i
$823$	−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
$825$	−306.262	+	779.797i	−0.371227	+	0.945209i
$826$	482.299	−	1510.13i	0.583897	−	1.82825i
$827$	−326.945	+	326.945i	−0.395338	+	0.395338i	−0.876585	−	0.481247i	$-0.840184\pi$
$827$	−326.945	+	326.945i	−0.395338	+	0.395338i	0.481247	+	0.876585i	$0.340184\pi$
$828$	100.376	−	1901.78i	0.121227	−	2.29683i
$829$	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
$837$	−648.084	−	330.670i	−0.774294	−	0.395066i
$838$	−1086.49	−	1086.49i	−1.29653	−	1.29653i
$839$			170.395i			0.203092i	0.994831	+	0.101546i	$0.0323790\pi$
$839$			170.395i			0.203092i	−0.994831	+	0.101546i	$0.967621\pi$
$840$	−775.115	−	250.933i	−0.922756	−	0.298729i
$841$	−727.888			−0.865503
$842$	−1680.99	+	1680.99i	−1.99642	+	1.99642i
$843$	282.271	+	735.750i	0.334841	+	0.872776i
$844$			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
$852$	−700.600	+	268.786i	−0.822300	+	0.315476i
$853$	−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
$855$	−399.231	−	1053.03i	−0.466937	−	1.23162i
$856$	978.063			1.14260
$857$	472.697	+	472.697i	0.551572	+	0.551572i	0.926894	−	0.375323i	$-0.122468\pi$
$857$	472.697	+	472.697i	0.551572	+	0.551572i	−0.375323	+	0.926894i	$0.622468\pi$
$858$	319.139	+	831.848i	0.371957	+	0.969520i
$859$	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
$861$	516.679	+	460.713i	0.600091	+	0.535091i
$862$	218.832	+	218.832i	0.253866	+	0.253866i
$863$	−823.471	−	823.471i	−0.954196	−	0.954196i	0.0447996	−	0.998996i	$-0.485735\pi$
$863$	−823.471	−	823.471i	−0.954196	−	0.954196i	−0.998996	+	0.0447996i	$0.985735\pi$
$864$	274.426	+	846.201i	0.317623	+	0.979399i
$865$	56.6318	+	128.497i	0.0654703	+	0.148552i
$866$	1246.13			1.43895
$867$	209.961	+	547.272i	0.242170	+	0.631225i
$868$	−553.933	−	1073.79i	−0.638171	−	1.23708i
$869$	−188.108			−0.216465
$870$	−362.441	−	365.317i	−0.416598	−	0.419904i
$871$			71.6221i			0.0822297i
$872$	−500.503	+	500.503i	−0.573971	+	0.573971i
$873$	76.6214	−	1451.71i	0.0877679	−	1.66290i
$874$	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	$-0.658659\pi$
$881$	−842.336			−0.956113			−0.478057	+	0.878329i	$0.658659\pi$
$882$	1114.14	+	884.504i	1.26320	+	1.00284i
$883$	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
$885$	−1053.09	−	4.16184i	−1.18993	−	0.00470264i
$886$	−977.170			−1.10290
$887$	−496.805	−	496.805i	−0.560095	−	0.560095i	0.369239	−	0.929334i	$-0.379618\pi$
$887$	−496.805	−	496.805i	−0.560095	−	0.560095i	−0.929334	+	0.369239i	$0.879618\pi$
$888$	−246.264	−	641.895i	−0.277324	−	0.722855i
$889$	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
$897$	292.587	+	762.638i	0.326184	+	0.850209i
$898$	335.975	−	335.975i	0.374137	−	0.374137i
$899$		−	286.592i		−	0.318790i
$900$	−11.3913	+	1441.17i	−0.0126570	+	1.60130i
$901$		−	356.418i		−	0.395581i
$902$	839.905	+	839.905i	0.931159	+	0.931159i
$903$	37.0801	−	2.12319i	0.0410632	−	0.00235126i
$904$		−	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	$0.137694\pi$
$911$			763.804i			0.838424i	−0.907888	+	0.419212i	$0.862306\pi$
$912$	−41.5203	+	15.9293i	−0.0455266	+	0.0174663i
$913$	−350.045	−	350.045i	−0.383401	−	0.383401i
$914$	86.1073			0.0942093
$915$	−212.572	−	0.840090i	−0.232319	−	0.000918131i
$916$		−	583.600i		−	0.637118i
$917$	−229.954	−	445.761i	−0.250768	−	0.486108i
$918$	−382.983	+	750.612i	−0.417192	+	0.817660i
$919$			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
$924$	1121.48	+	1000.01i	1.21373	+	1.08226i
$925$	33.0884	+	737.639i	0.0357712	+	0.797448i
$926$		−	1654.47i		−	1.78668i
$927$	−1389.31	−	73.3276i	−1.49871	−	0.0791021i
$928$	−247.779	+	247.779i	−0.267003	+	0.267003i
$929$		−	443.766i		−	0.477682i	−0.971059	−	0.238841i	$-0.923233\pi$
$929$		−	443.766i		−	0.477682i	0.971059	−	0.238841i	$-0.0767674\pi$
$930$	−925.605	+	918.317i	−0.995274	+	0.987438i
$931$	−710.785	+	999.270i	−0.763464	+	1.07333i
$932$	580.340	−	580.340i	0.622682	−	0.622682i
$933$	−829.972	+	318.420i	−0.889573	+	0.341286i
$934$	−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	$-0.280413\pi$
$941$	1197.75			1.27285			0.636423	+	0.771340i	$0.280413\pi$
$942$	−1045.39	−	2724.86i	−1.10976	−	2.89263i
$943$	770.025	+	770.025i	0.816569	+	0.816569i
$944$			41.5855i			0.0440524i
$945$	338.040	−	882.470i	0.357715	−	0.933831i
$946$	63.7283			0.0673660
$947$	−99.0939	+	99.0939i	−0.104640	+	0.104640i	−0.757488	−	0.652849i	$-0.773574\pi$
$947$	−99.0939	+	99.0939i	−0.104640	+	0.104640i	0.652849	+	0.757488i	$0.273574\pi$
$948$	−302.126	+	115.911i	−0.318698	+	0.122269i
$949$		−	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	0.535628	−	0.844454i	$-0.320075\pi$
$953$	−294.311	−	294.311i	−0.308826	−	0.308826i	−0.844454	+	0.535628i	$0.820075\pi$
$954$	−795.035	+	715.318i	−0.833370	+	0.749809i
$955$	−41.9325	−	16.2778i	−0.0439084	−	0.0170449i
$956$			2606.92i			2.72691i
$957$	127.663	+	332.758i	0.133399	+	0.347709i
$958$	−1306.11	−	1306.11i	−1.36338	−	1.36338i
$959$	538.637	+	172.028i	0.561666	+	0.179382i
$960$	1558.66	+	6.15986i	1.62360	+	0.00641652i
$961$	234.860			0.244392
$962$	555.258	+	555.258i	0.577192	+	0.577192i
$963$	−59.7937	+	1132.89i	−0.0620911	+	1.17641i
$964$	−750.124			−0.778137
$965$	−274.065	−	621.853i	−0.284005	−	0.644407i
$966$	1670.24	+	1489.33i	1.72903	+	1.54174i
$967$	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	$-0.608296\pi$
$971$	−648.040			−0.667394			−0.333697	+	0.942680i	$0.608296\pi$
$972$	1503.85	−	401.460i	1.54717	−	0.413025i
$973$	133.034	+	257.883i	0.136725	+	0.265039i
$974$	1633.85			1.67747
$975$	−247.062	−	566.641i	−0.253397	−	0.581171i
$976$			8.39425i			0.00860067i
$977$	131.673	−	131.673i	0.134773	−	0.134773i	−0.636502	−	0.771275i	$-0.719619\pi$
$977$	131.673	−	131.673i	0.134773	−	0.134773i	0.771275	+	0.636502i	$0.219619\pi$
$978$	−95.7141	−	249.482i	−0.0978672	−	0.255094i
$979$	−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	−0.996985	−	0.0775980i	$-0.975275\pi$
$983$	−903.757	+	903.757i	−0.919387	+	0.919387i	0.0775980	+	0.996985i	$0.475275\pi$
$984$	700.939	+	312.234i	0.712336	+	0.317311i
$985$	322.683	+	732.167i	0.327597	+	0.743316i
$986$	−331.931			−0.336644
$987$	−100.359	−	1752.71i	−0.101681	−	1.77579i
$988$	−934.254	+	934.254i	−0.945601	+	0.945601i
$989$	58.4260			0.0590759
$990$	665.640	−	1478.56i	0.672364	−	1.49349i
$991$	−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
$993$	1266.29	−	485.813i	1.27522	−	0.489238i
$994$	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.62.13	yes	32
3.2	odd	2	inner	105.3.k.d.62.4	yes	32
5.3	odd	4	inner	105.3.k.d.83.3	yes	32
7.6	odd	2	inner	105.3.k.d.62.14	yes	32
15.8	even	4	inner	105.3.k.d.83.14	yes	32
21.20	even	2	inner	105.3.k.d.62.3	✓	32
35.13	even	4	inner	105.3.k.d.83.4	yes	32
105.83	odd	4	inner	105.3.k.d.83.13	yes	32

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

\(f(q)\)	\(=\)	\(q+(2.28094 - 2.28094i) q^{2} +(-2.80094 + 1.07458i) q^{3} -6.40541i q^{4} +(1.80941 - 4.66112i) q^{5} +(-3.93772 + 8.83986i) q^{6} +(-3.20922 - 6.22100i) q^{7} +(-5.48661 - 5.48661i) q^{8} +(6.69054 - 6.01969i) q^{9} +O(q^{10})\)	\(q+(2.28094 - 2.28094i) q^{2} +(-2.80094 + 1.07458i) 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} +(6.88316 + 17.9412i) q^{12} +(-5.82807 - 5.82807i) q^{13} +(-21.5098 - 6.86971i) q^{14} +(-0.0592799 + 14.9999i) q^{15} +0.592330 q^{16} +(6.84147 + 6.84147i) q^{17} +(1.53016 - 28.9913i) q^{18} +25.0261 q^{19} +(-29.8564 - 11.5900i) q^{20} +(15.6738 + 13.9761i) 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} +(-12.2711 + 24.0503i) q^{27} +(-39.8481 + 20.5564i) q^{28} -10.6354 q^{29} +(34.0787 + 34.3491i) q^{30} +26.9470i q^{31} +(23.2975 - 23.2975i) q^{32} +(-12.0036 - 31.2877i) 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} +(67.6298 - 3.87246i) q^{42} +(1.25060 - 1.25060i) q^{43} +71.5513 q^{44} +(-15.9526 - 42.0775i) q^{45} +106.562 q^{46} +(-59.1134 - 59.1134i) q^{47} +(-1.65908 + 0.636508i) 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} +(-70.0965 + 26.8926i) q^{57} +(-24.2588 + 24.2588i) q^{58} +70.2066i q^{59} +(96.0805 + 0.379712i) q^{60} +14.1716i q^{61} +(61.4646 + 61.4646i) q^{62} +(-58.9200 - 22.3033i) 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} +(-69.7361 - 3.68068i) q^{72} +(51.1141 + 51.1141i) q^{73} -95.2731 q^{74} +(69.8090 + 27.4172i) q^{75} -160.302i q^{76} +(69.4914 - 35.8484i) q^{77} +(74.4687 - 28.5700i) 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} +(89.5226 - 100.397i) q^{84} +(44.2679 - 19.5099i) q^{85} -5.70508i q^{86} +(29.7891 - 11.4286i) q^{87} +(61.2879 - 61.2879i) q^{88} +70.8895i q^{89} +(-132.363 - 59.5894i) q^{90} +(-17.5529 + 54.9600i) q^{91} +(149.626 - 149.626i) q^{92} +(-28.9568 - 75.4769i) 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

Groups

Database

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