LMFDB - Embedded newform 136.3.t.b.41.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,3,Mod(41,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(16))

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

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

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

chi := DirichletCharacter("136.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	136.t (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.70573159530$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			41.2
Character	$\chi$	$=$	136.41
Dual form			136.3.t.b.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26339 + 1.89080i) q^{3} +(-0.944701 - 4.74933i) q^{5} +(-2.41180 + 12.1249i) q^{7} +(1.46519 + 3.53728i) q^{9} +O(q^{10})$	\(q+(-1.26339 + 1.89080i) q^{3} +(-0.944701 - 4.74933i) q^{5} +(-2.41180 + 12.1249i) q^{7} +(1.46519 + 3.53728i) q^{9} +(-0.164707 + 0.110054i) q^{11} +(-14.7808 + 14.7808i) q^{13} +(10.1736 + 4.21403i) q^{15} +(-15.6132 - 6.72510i) q^{17} +(-2.42331 + 5.85039i) q^{19} +(-19.8788 - 19.8788i) q^{21} +(6.97037 + 10.4319i) q^{23} +(1.43329 - 0.593689i) q^{25} +(-28.6125 - 5.69139i) q^{27} +(48.2491 - 9.59735i) q^{29} +(38.0040 + 25.3934i) q^{31} -0.450470i q^{33} +59.8638 q^{35} +(10.1181 - 15.1428i) q^{37} +(-9.27359 - 46.6215i) q^{39} +(-0.740776 + 3.72413i) q^{41} +(-22.5218 - 54.3723i) q^{43} +(15.4155 - 10.3003i) q^{45} +(-47.0089 + 47.0089i) q^{47} +(-95.9272 - 39.7344i) q^{49} +(32.4414 - 21.0251i) q^{51} +(7.00382 - 16.9087i) q^{53} +(0.678282 + 0.678282i) q^{55} +(-8.00033 - 11.9733i) q^{57} +(43.9070 - 18.1869i) q^{59} +(66.1539 + 13.1588i) q^{61} +(-46.4230 + 9.23411i) q^{63} +(84.1624 + 56.2355i) q^{65} -7.26692i q^{67} -28.5309 q^{69} +(-34.9939 + 52.3721i) q^{71} +(8.66896 + 43.5818i) q^{73} +(-0.688262 + 3.46013i) q^{75} +(-0.937156 - 2.26249i) q^{77} +(15.9172 - 10.6355i) q^{79} +(22.5443 - 22.5443i) q^{81} +(-6.01964 - 2.49342i) q^{83} +(-17.1899 + 80.5056i) q^{85} +(-42.8109 + 103.355i) q^{87} +(18.9285 + 18.9285i) q^{89} +(-143.568 - 214.865i) q^{91} +(-96.0278 + 39.7760i) q^{93} +(30.0748 + 5.98224i) q^{95} +(61.6184 - 12.2567i) q^{97} +(-0.630618 - 0.421366i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9	$ 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9} + 24 q^{11} - 48 q^{13} - 96 q^{15} - 40 q^{19} + 80 q^{21} + 48 q^{23} + 48 q^{25} + 224 q^{27} + 24 q^{29} + 88 q^{31} + 32 q^{35} - 176 q^{37} - 120 q^{39} - 352 q^{43} + 264 q^{45} - 48 q^{47} - 208 q^{49} + 400 q^{51} - 472 q^{53} - 208 q^{55} + 24 q^{57} - 576 q^{59} - 632 q^{63} - 32 q^{65} + 160 q^{69} - 160 q^{71} + 256 q^{73} + 1128 q^{75} - 208 q^{77} + 1000 q^{79} + 24 q^{81} + 312 q^{83} + 1240 q^{85} - 664 q^{87} + 720 q^{89} + 664 q^{91} - 432 q^{93} + 736 q^{95} - 288 q^{97} + 16 q^{99}+O(q^{100}) $ 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9 + 24 * q^11 - 48 * q^13 - 96 * q^15 - 40 * q^19 + 80 * q^21 + 48 * q^23 + 48 * q^25 + 224 * q^27 + 24 * q^29 + 88 * q^31 + 32 * q^35 - 176 * q^37 - 120 * q^39 - 352 * q^43 + 264 * q^45 - 48 * q^47 - 208 * q^49 + 400 * q^51 - 472 * q^53 - 208 * q^55 + 24 * q^57 - 576 * q^59 - 632 * q^63 - 32 * q^65 + 160 * q^69 - 160 * q^71 + 256 * q^73 + 1128 * q^75 - 208 * q^77 + 1000 * q^79 + 24 * q^81 + 312 * q^83 + 1240 * q^85 - 664 * q^87 + 720 * q^89 + 664 * q^91 - 432 * q^93 + 736 * q^95 - 288 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{16}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.26339	+	1.89080i	−0.421131	+	0.630266i	−0.980002	−	0.198988i	$-0.936235\pi$
$3$	−1.26339	+	1.89080i	−0.421131	+	0.630266i	0.558871	+	0.829254i	$0.311235\pi$
$4$		0			0
$5$	−0.944701	−	4.74933i	−0.188940	−	0.949866i	−0.952595	−	0.304242i	$-0.901597\pi$
$5$	−0.944701	−	4.74933i	−0.188940	−	0.949866i	0.763655	−	0.645625i	$-0.223403\pi$
$6$		0			0
$7$	−2.41180	+	12.1249i	−0.344543	+	1.73213i	0.288020	+	0.957625i	$0.407003\pi$
$7$	−2.41180	+	12.1249i	−0.344543	+	1.73213i	−0.632562	+	0.774509i	$0.717997\pi$
$8$		0			0
$9$	1.46519	+	3.53728i	0.162799	+	0.393031i
$10$		0			0
$11$	−0.164707	+	0.110054i	−0.0149734	+	0.0100049i	−0.563034	−	0.826433i	$-0.690366\pi$
$11$	−0.164707	+	0.110054i	−0.0149734	+	0.0100049i	0.548061	+	0.836438i	$0.315366\pi$
$12$		0			0
$13$	−14.7808	+	14.7808i	−1.13699	+	1.13699i	−0.147998	+	0.988988i	$0.547283\pi$
$13$	−14.7808	+	14.7808i	−1.13699	+	1.13699i	−0.988988	+	0.147998i	$0.952717\pi$
$14$		0			0
$15$	10.1736	+	4.21403i	0.678237	+	0.280935i
$16$		0			0
$17$	−15.6132	−	6.72510i	−0.918425	−	0.395594i
$17$	−15.6132	−	6.72510i	−0.918425	−	0.395594i
$18$		0			0
$19$	−2.42331	+	5.85039i	−0.127543	+	0.307916i	−0.974733	−	0.223375i	$-0.928293\pi$
$19$	−2.42331	+	5.85039i	−0.127543	+	0.307916i	0.847190	+	0.531290i	$0.178293\pi$
$20$		0			0
$21$	−19.8788	−	19.8788i	−0.946608	−	0.946608i
$22$		0			0
$23$	6.97037	+	10.4319i	0.303059	+	0.453560i	0.951475	−	0.307726i	$-0.0995680\pi$
$23$	6.97037	+	10.4319i	0.303059	+	0.453560i	−0.648416	+	0.761287i	$0.724568\pi$
$24$		0			0
$25$	1.43329	−	0.593689i	0.0573317	−	0.0237476i
$26$		0			0
$27$	−28.6125	−	5.69139i	−1.05972	−	0.210792i
$28$		0			0
$29$	48.2491	−	9.59735i	1.66376	−	0.330943i	0.728540	−	0.685003i	$-0.240199\pi$
$29$	48.2491	−	9.59735i	1.66376	−	0.330943i	0.935223	+	0.354060i	$0.115199\pi$
$30$		0			0
$31$	38.0040	+	25.3934i	1.22593	+	0.819143i	0.988346	−	0.152223i	$-0.0486430\pi$
$31$	38.0040	+	25.3934i	1.22593	+	0.819143i	0.237588	+	0.971366i	$0.423643\pi$
$32$		0			0
$33$		−	0.450470i		−	0.0136506i
$34$		0			0
$35$	59.8638			1.71039
$36$		0			0
$37$	10.1181	−	15.1428i	0.273461	−	0.409264i	−0.669165	−	0.743114i	$-0.733348\pi$
$37$	10.1181	−	15.1428i	0.273461	−	0.409264i	0.942626	+	0.333850i	$0.108348\pi$
$38$		0			0
$39$	−9.27359	−	46.6215i	−0.237784	−	1.19542i
$40$		0			0
$41$	−0.740776	+	3.72413i	−0.0180677	+	0.0908325i	−0.988767	−	0.149465i	$-0.952245\pi$
$41$	−0.740776	+	3.72413i	−0.0180677	+	0.0908325i	0.970699	+	0.240297i	$0.0772449\pi$
$42$		0			0
$43$	−22.5218	−	54.3723i	−0.523762	−	1.26447i	−0.935550	−	0.353194i	$-0.885096\pi$
$43$	−22.5218	−	54.3723i	−0.523762	−	1.26447i	0.411788	−	0.911279i	$-0.364904\pi$
$44$		0			0
$45$	15.4155	−	10.3003i	0.342568	−	0.228896i
$46$		0			0
$47$	−47.0089	+	47.0089i	−1.00019	+	1.00019i	−0.000189100		1.00000i	$0.500060\pi$
$47$	−47.0089	+	47.0089i	−1.00019	+	1.00019i	−1.00000		0.000189100i	$0.999940\pi$
$48$		0			0
$49$	−95.9272	−	39.7344i	−1.95770	−	0.810905i
$50$		0			0
$51$	32.4414	−	21.0251i	0.636107	−	0.412256i
$52$		0			0
$53$	7.00382	−	16.9087i	0.132147	−	0.319032i	−0.843931	−	0.536452i	$-0.819764\pi$
$53$	7.00382	−	16.9087i	0.132147	−	0.319032i	0.976078	+	0.217420i	$0.0697641\pi$
$54$		0			0
$55$	0.678282	+	0.678282i	0.0123324	+	0.0123324i
$56$		0			0
$57$	−8.00033	−	11.9733i	−0.140357	−	0.210059i
$58$		0			0
$59$	43.9070	−	18.1869i	0.744187	−	0.308252i	0.0218199	−	0.999762i	$-0.493054\pi$
$59$	43.9070	−	18.1869i	0.744187	−	0.308252i	0.722367	+	0.691509i	$0.243054\pi$
$60$		0			0
$61$	66.1539	+	13.1588i	1.08449	+	0.215719i	0.704808	−	0.709398i	$-0.251033\pi$
$61$	66.1539	+	13.1588i	1.08449	+	0.215719i	0.379683	+	0.925117i	$0.376033\pi$
$62$		0			0
$63$	−46.4230	+	9.23411i	−0.736873	+	0.146573i
$64$		0			0
$65$	84.1624	+	56.2355i	1.29481	+	0.865162i
$66$		0			0
$67$		−	7.26692i		−	0.108462i	−0.998528	−	0.0542308i	$-0.982729\pi$
$67$		−	7.26692i		−	0.108462i	0.998528	−	0.0542308i	$-0.0172707\pi$
$68$		0			0
$69$	−28.5309			−0.413491
$70$		0			0
$71$	−34.9939	+	52.3721i	−0.492872	+	0.737635i	−0.991631	−	0.129106i	$-0.958789\pi$
$71$	−34.9939	+	52.3721i	−0.492872	+	0.737635i	0.498759	+	0.866741i	$0.333789\pi$
$72$		0			0
$73$	8.66896	+	43.5818i	0.118753	+	0.597011i	0.993632	+	0.112670i	$0.0359404\pi$
$73$	8.66896	+	43.5818i	0.118753	+	0.597011i	−0.874880	+	0.484340i	$0.839060\pi$
$74$		0			0
$75$	−0.688262	+	3.46013i	−0.00917683	+	0.0461351i
$76$		0			0
$77$	−0.937156	−	2.26249i	−0.0121709	−	0.0293830i
$78$		0			0
$79$	15.9172	−	10.6355i	0.201484	−	0.134627i	−0.450735	−	0.892658i	$-0.648838\pi$
$79$	15.9172	−	10.6355i	0.201484	−	0.134627i	0.652219	+	0.758031i	$0.273838\pi$
$80$		0			0
$81$	22.5443	−	22.5443i	0.278324	−	0.278324i
$82$		0			0
$83$	−6.01964	−	2.49342i	−0.0725258	−	0.0300412i	0.346126	−	0.938188i	$-0.387497\pi$
$83$	−6.01964	−	2.49342i	−0.0725258	−	0.0300412i	−0.418651	+	0.908147i	$0.637497\pi$
$84$		0			0
$85$	−17.1899	+	80.5056i	−0.202234	+	0.947125i
$86$		0			0
$87$	−42.8109	+	103.355i	−0.492079	+	1.18798i
$88$		0			0
$89$	18.9285	+	18.9285i	0.212679	+	0.212679i	0.805405	−	0.592725i	$-0.201948\pi$
$89$	18.9285	+	18.9285i	0.212679	+	0.212679i	−0.592725	+	0.805405i	$0.701948\pi$
$90$		0			0
$91$	−143.568	−	214.865i	−1.57767	−	2.36115i
$92$		0			0
$93$	−96.0278	+	39.7760i	−1.03256	+	0.427699i
$94$		0			0
$95$	30.0748	+	5.98224i	0.316577	+	0.0629710i
$96$		0			0
$97$	61.6184	−	12.2567i	0.635242	−	0.126357i	0.133044	−	0.991110i	$-0.457525\pi$
$97$	61.6184	−	12.2567i	0.635242	−	0.126357i	0.502198	+	0.864753i	$0.332525\pi$
$98$		0			0
$99$	−0.630618	−	0.421366i	−0.00636988	−	0.00425622i
$100$		0			0
$101$			105.857i			1.04809i	0.851691	+	0.524045i	$0.175578\pi$
$101$			105.857i			1.04809i	−0.851691	+	0.524045i	$0.824422\pi$
$102$		0			0
$103$	−48.8235			−0.474015			−0.237008	−	0.971508i	$-0.576167\pi$
$103$	−48.8235			−0.474015			−0.237008	+	0.971508i	$0.576167\pi$
$104$		0			0
$105$	−75.6314	+	113.190i	−0.720299	+	1.07800i
$106$		0			0
$107$	17.0178	+	85.5541i	0.159045	+	0.799571i	0.975129	+	0.221638i	$0.0711405\pi$
$107$	17.0178	+	85.5541i	0.159045	+	0.799571i	−0.816084	+	0.577933i	$0.803860\pi$
$108$		0			0
$109$	−24.2219	+	121.772i	−0.222220	+	1.11717i	0.695067	+	0.718945i	$0.255375\pi$
$109$	−24.2219	+	121.772i	−0.222220	+	1.11717i	−0.917286	+	0.398228i	$0.869625\pi$
$110$		0			0
$111$	15.8488	+	38.2625i	0.142782	+	0.344707i
$112$		0			0
$113$	168.222	−	112.402i	1.48869	−	0.994712i	0.496767	−	0.867884i	$-0.334520\pi$
$113$	168.222	−	112.402i	1.48869	−	0.994712i	0.991925	−	0.126828i	$-0.0404797\pi$
$114$		0			0
$115$	42.9596	−	42.9596i	0.373562	−	0.373562i
$116$		0			0
$117$	−73.9405	−	30.6272i	−0.631970	−	0.261771i
$118$		0			0
$119$	119.197	−	173.090i	1.00166	−	1.45454i
$120$		0			0
$121$	−46.2897	+	111.753i	−0.382559	+	0.923580i
$122$		0			0
$123$	−6.10570	−	6.10570i	−0.0496398	−	0.0496398i
$124$		0			0
$125$	−71.4307	−	106.904i	−0.571445	−	0.855228i
$126$		0			0
$127$	−186.069	+	77.0725i	−1.46511	+	0.606870i	−0.965739	−	0.259516i	$-0.916437\pi$
$127$	−186.069	+	77.0725i	−1.46511	+	0.606870i	−0.499375	+	0.866386i	$0.666437\pi$
$128$		0			0
$129$	131.261	+	26.1094i	1.01753	+	0.202399i
$130$		0			0
$131$	−92.4286	+	18.3852i	−0.705562	+	0.140345i	−0.534814	−	0.844970i	$-0.679618\pi$
$131$	−92.4286	+	18.3852i	−0.705562	+	0.140345i	−0.170748	+	0.985315i	$0.554618\pi$
$132$		0			0
$133$	−65.0911	−	43.4925i	−0.489407	−	0.327011i
$134$		0			0
$135$			141.267i			1.04642i
$136$		0			0
$137$	63.7868			0.465597			0.232799	−	0.972525i	$-0.425212\pi$
$137$	63.7868			0.465597			0.232799	+	0.972525i	$0.425212\pi$
$138$		0			0
$139$	4.92308	−	7.36790i	0.0354178	−	0.0530065i	−0.813338	−	0.581791i	$-0.802352\pi$
$139$	4.92308	−	7.36790i	0.0354178	−	0.0530065i	0.848756	+	0.528785i	$0.177352\pi$
$140$		0			0
$141$	−29.4937	−	148.275i	−0.209175	−	1.05160i
$142$		0			0
$143$	0.807822	−	4.06119i	0.00564910	−	0.0284000i
$144$		0			0
$145$	−91.1620	−	220.084i	−0.628703	−	1.51782i
$146$		0			0
$147$	196.323	−	131.179i	1.33553	−	0.892375i
$148$		0			0
$149$	149.635	−	149.635i	1.00426	−	1.00426i	0.00426869	−	0.999991i	$-0.498641\pi$
$149$	149.635	−	149.635i	1.00426	−	1.00426i	0.999991	−	0.00426869i	$-0.00135877\pi$
$150$		0			0
$151$	134.734	+	55.8088i	0.892281	+	0.369595i	0.781247	−	0.624222i	$-0.214584\pi$
$151$	134.734	+	55.8088i	0.892281	+	0.369595i	0.111034	+	0.993817i	$0.464584\pi$
$152$		0			0
$153$	0.912220	−	65.0819i	0.00596222	−	0.425372i
$154$		0			0
$155$	84.6995	−	204.483i	0.546448	−	1.31924i
$156$		0			0
$157$	189.754	+	189.754i	1.20862	+	1.20862i	0.971473	+	0.237150i	$0.0762133\pi$
$157$	189.754	+	189.754i	1.20862	+	1.20862i	0.237150	+	0.971473i	$0.423787\pi$
$158$		0			0
$159$	23.1224	+	34.6051i	0.145424	+	0.217642i
$160$		0			0
$161$	−143.297	+	59.3556i	−0.890044	+	0.368668i
$162$		0			0
$163$	17.9594	+	3.57234i	0.110180	+	0.0219162i	0.249872	−	0.968279i	$-0.419611\pi$
$163$	17.9594	+	3.57234i	0.110180	+	0.0219162i	−0.139692	+	0.990195i	$0.544611\pi$
$164$		0			0
$165$	−2.13943	+	0.425559i	−0.0129662	+	0.00257915i
$166$		0			0
$167$	245.625	+	164.121i	1.47081	+	0.982763i	0.994639	+	0.103410i	$0.0329753\pi$
$167$	245.625	+	164.121i	1.47081	+	0.982763i	0.476170	+	0.879353i	$0.342025\pi$
$168$		0			0
$169$		−	267.945i		−	1.58547i
$170$		0			0
$171$	−24.2451			−0.141784
$172$		0			0
$173$	18.8843	−	28.2623i	0.109158	−	0.163366i	−0.772869	−	0.634566i	$-0.781179\pi$
$173$	18.8843	−	28.2623i	0.109158	−	0.163366i	0.882026	+	0.471200i	$0.156179\pi$
$174$		0			0
$175$	3.74163	+	18.8104i	0.0213807	+	0.107488i
$176$		0			0
$177$	−21.0840	+	105.997i	−0.119119	+	0.598851i
$178$		0			0
$179$	−31.9654	−	77.1712i	−0.178577	−	0.431124i	0.809091	−	0.587683i	$-0.199960\pi$
$179$	−31.9654	−	77.1712i	−0.178577	−	0.431124i	−0.987669	+	0.156559i	$0.949960\pi$
$180$		0			0
$181$	−187.403	+	125.218i	−1.03537	+	0.691814i	−0.952435	−	0.304740i	$-0.901430\pi$
$181$	−187.403	+	125.218i	−1.03537	+	0.691814i	−0.0829378	+	0.996555i	$0.526430\pi$
$182$		0			0
$183$	−108.459	+	108.459i	−0.592672	+	0.592672i
$184$		0			0
$185$	−81.4766	−	33.7487i	−0.440414	−	0.182425i
$186$		0			0
$187$	3.31174	−	0.610624i	0.0177098	−	0.00326537i
$188$		0			0
$189$	138.015	−	333.199i	0.730240	−	1.76296i
$190$		0			0
$191$	−186.611	−	186.611i	−0.977019	−	0.977019i	0.0227229	−	0.999742i	$-0.492766\pi$
$191$	−186.611	−	186.611i	−0.977019	−	0.977019i	−0.999742	+	0.0227229i	$0.992766\pi$
$192$		0			0
$193$	−93.3116	−	139.651i	−0.483480	−	0.723579i	0.506892	−	0.862010i	$-0.330794\pi$
$193$	−93.3116	−	139.651i	−0.483480	−	0.723579i	−0.990372	+	0.138430i	$0.955794\pi$
$194$		0			0
$195$	−212.660	+	88.0867i	−1.09057	+	0.451727i
$196$		0			0
$197$	129.207	+	25.7008i	0.655871	+	0.130461i	0.511798	−	0.859106i	$-0.328980\pi$
$197$	129.207	+	25.7008i	0.655871	+	0.130461i	0.144074	+	0.989567i	$0.453980\pi$
$198$		0			0
$199$	339.720	−	67.5744i	1.70713	−	0.339570i	0.757477	−	0.652862i	$-0.226432\pi$
$199$	339.720	−	67.5744i	1.70713	−	0.339570i	0.949657	+	0.313292i	$0.101432\pi$
$200$		0			0
$201$	13.7403	+	9.18097i	0.0683596	+	0.0456765i
$202$		0			0
$203$			608.164i			2.99588i
$204$		0			0
$205$	18.3870			0.0896925
$206$		0			0
$207$	−26.6876	+	39.9408i	−0.128926	+	0.192951i
$208$		0			0
$209$	−0.244721	−	1.23030i	−0.00117092	−	0.00588659i
$210$		0			0
$211$	12.8011	−	64.3553i	0.0606686	−	0.305002i	−0.938522	−	0.345218i	$-0.887805\pi$
$211$	12.8011	−	64.3553i	0.0606686	−	0.305002i	0.999191	+	0.0402168i	$0.0128048\pi$
$212$		0			0
$213$	−54.8141	−	132.333i	−0.257343	−	0.621281i
$214$		0			0
$215$	−236.956	+	158.329i	−1.10212	+	0.736414i
$216$		0			0
$217$	−399.552	+	399.552i	−1.84125	+	1.84125i
$218$		0			0
$219$	−93.3567	−	38.6696i	−0.426286	−	0.176574i
$220$		0			0
$221$	330.179	−	131.374i	1.49402	−	0.594452i
$222$		0			0
$223$	138.625	−	334.670i	0.621636	−	1.50076i	−0.228144	−	0.973627i	$-0.573266\pi$
$223$	138.625	−	334.670i	0.621636	−	1.50076i	0.849781	−	0.527136i	$-0.176734\pi$
$224$		0			0
$225$	4.20008	+	4.20008i	0.0186670	+	0.0186670i
$226$		0			0
$227$	64.0217	+	95.8153i	0.282034	+	0.422094i	0.945256	−	0.326329i	$-0.105812\pi$
$227$	64.0217	+	95.8153i	0.282034	+	0.422094i	−0.663222	+	0.748422i	$0.730812\pi$
$228$		0			0
$229$	−390.935	+	161.931i	−1.70714	+	0.707121i	−0.707140	+	0.707073i	$0.750015\pi$
$229$	−390.935	+	161.931i	−1.70714	+	0.707121i	−1.00000		4.72861e-5i	$0.999985\pi$
$230$		0			0
$231$	5.46192	+	1.08644i	0.0236447	+	0.00470321i
$232$		0			0
$233$	86.4696	−	17.1999i	0.371114	−	0.0738192i	−0.00600989	−	0.999982i	$-0.501913\pi$
$233$	86.4696	−	17.1999i	0.371114	−	0.0738192i	0.377124	+	0.926163i	$0.376913\pi$
$234$		0			0
$235$	267.670	+	178.851i	1.13902	+	0.761070i
$236$		0			0
$237$			43.5331i			0.183684i
$238$		0			0
$239$	33.0721			0.138377			0.0691886	−	0.997604i	$-0.477959\pi$
$239$	33.0721			0.138377			0.0691886	+	0.997604i	$0.477959\pi$
$240$		0			0
$241$	−14.0461	+	21.0215i	−0.0582825	+	0.0872260i	−0.859466	−	0.511192i	$-0.829204\pi$
$241$	−14.0461	+	21.0215i	−0.0582825	+	0.0872260i	0.801184	+	0.598418i	$0.204204\pi$
$242$		0			0
$243$	−37.0780	−	186.404i	−0.152585	−	0.767094i
$244$		0			0
$245$	−98.0891	+	493.127i	−0.400364	+	2.01276i
$246$		0			0
$247$	−50.6550	−	122.292i	−0.205081	−	0.495110i
$248$		0			0
$249$	12.3197	−	8.23177i	0.0494768	−	0.0330593i
$250$		0			0
$251$	20.7755	−	20.7755i	0.0827709	−	0.0827709i	−0.664509	−	0.747280i	$-0.731359\pi$
$251$	20.7755	−	20.7755i	0.0827709	−	0.0827709i	0.747280	+	0.664509i	$0.231359\pi$
$252$		0			0
$253$	−2.29614	−	0.951093i	−0.00907566	−	0.00375926i
$254$		0			0
$255$	−130.502	−	134.213i	−0.511774	−	0.526325i
$256$		0			0
$257$	−88.3643	+	213.330i	−0.343830	+	0.830079i	0.653491	+	0.756934i	$0.273304\pi$
$257$	−88.3643	+	213.330i	−0.343830	+	0.830079i	−0.997321	+	0.0731451i	$0.976696\pi$
$258$		0			0
$259$	159.202	+	159.202i	0.614681	+	0.614681i
$260$		0			0
$261$	104.643	+	156.609i	0.400929	+	0.600033i
$262$		0			0
$263$	−108.668	+	45.0119i	−0.413188	+	0.171148i	−0.579587	−	0.814910i	$-0.696786\pi$
$263$	−108.668	+	45.0119i	−0.413188	+	0.171148i	0.166399	+	0.986059i	$0.446786\pi$
$264$		0			0
$265$	−86.9216	−	17.2898i	−0.328006	−	0.0652444i
$266$		0			0
$267$	−59.7040	+	11.8759i	−0.223610	+	0.0444789i
$268$		0			0
$269$	−410.295	−	274.150i	−1.52526	−	1.01915i	−0.983975	−	0.178307i	$-0.942938\pi$
$269$	−410.295	−	274.150i	−1.52526	−	1.01915i	−0.541285	−	0.840839i	$-0.682062\pi$
$270$		0			0
$271$			185.365i			0.684005i	0.939699	+	0.342002i	$0.111105\pi$
$271$			185.365i			0.684005i	−0.939699	+	0.342002i	$0.888895\pi$
$272$		0			0
$273$	587.649			2.15256
$274$		0			0
$275$	−0.170736	+	0.255524i	−0.000620858	+	0.000929179i
$276$		0			0
$277$	−28.4384	−	142.970i	−0.102666	−	0.516136i	−0.997557	−	0.0698521i	$-0.977747\pi$
$277$	−28.4384	−	142.970i	−0.102666	−	0.516136i	0.894892	−	0.446284i	$-0.147253\pi$
$278$		0			0
$279$	−34.1407	+	171.637i	−0.122368	+	0.615185i
$280$		0			0
$281$	49.5544	+	119.635i	0.176350	+	0.425747i	0.987196	−	0.159513i	$-0.0509925\pi$
$281$	49.5544	+	119.635i	0.176350	+	0.425747i	−0.810846	+	0.585260i	$0.800992\pi$
$282$		0			0
$283$	209.018	−	139.661i	0.738578	−	0.493502i	−0.128478	−	0.991712i	$-0.541009\pi$
$283$	209.018	−	139.661i	0.738578	−	0.493502i	0.867056	+	0.498210i	$0.166009\pi$
$284$		0			0
$285$	−49.3074	+	49.3074i	−0.173009	+	0.173009i
$286$		0			0
$287$	−43.3683	−	17.9637i	−0.151109	−	0.0625914i
$288$		0			0
$289$	198.546	+	210.001i	0.687011	+	0.726647i
$290$		0			0
$291$	−54.6733	+	131.993i	−0.187881	+	0.453584i
$292$		0			0
$293$	−3.36051	−	3.36051i	−0.0114693	−	0.0114693i	0.701349	−	0.712818i	$-0.252582\pi$
$293$	−3.36051	−	3.36051i	−0.0114693	−	0.0114693i	−0.712818	+	0.701349i	$0.752582\pi$
$294$		0			0
$295$	−127.855	−	191.348i	−0.433406	−	0.648637i
$296$		0			0
$297$	5.33905	−	2.21151i	0.0179766	−	0.00744615i
$298$		0			0
$299$	−257.219	−	51.1641i	−0.860266	−	0.171118i
$300$		0			0
$301$	713.579	−	141.940i	2.37070	−	0.471561i
$302$		0			0
$303$	−200.154	−	133.739i	−0.660575	−	0.441382i
$304$		0			0
$305$		−	326.618i		−	1.07088i
$306$		0			0
$307$	−538.220			−1.75316			−0.876580	−	0.481256i	$-0.840181\pi$
$307$	−538.220			−1.75316			−0.876580	+	0.481256i	$0.840181\pi$
$308$		0			0
$309$	61.6833	−	92.3155i	0.199622	−	0.298756i
$310$		0			0
$311$	−92.1678	−	463.359i	−0.296360	−	1.48990i	−0.786137	−	0.618053i	$-0.787922\pi$
$311$	−92.1678	−	463.359i	−0.296360	−	1.48990i	0.489777	−	0.871848i	$-0.337078\pi$
$312$		0			0
$313$	−21.5169	+	108.173i	−0.0687441	+	0.345600i	−0.999815	−	0.0192385i	$-0.993876\pi$
$313$	−21.5169	+	108.173i	−0.0687441	+	0.345600i	0.931071	+	0.364839i	$0.118876\pi$
$314$		0			0
$315$	87.7117	+	211.755i	0.278450	+	0.672237i
$316$		0			0
$317$	−121.557	+	81.2220i	−0.383461	+	0.256221i	−0.732329	−	0.680952i	$-0.761566\pi$
$317$	−121.557	+	81.2220i	−0.383461	+	0.256221i	0.348867	+	0.937172i	$0.386566\pi$
$318$		0			0
$319$	−6.89076	+	6.89076i	−0.0216011	+	0.0216011i
$320$		0			0
$321$	−183.266	−	75.9112i	−0.570921	−	0.236483i
$322$		0			0
$323$	77.1802	−	75.0465i	0.238948	−	0.232342i
$324$		0			0
$325$	−12.4100	+	29.9604i	−0.0381847	+	0.0921859i
$326$		0			0
$327$	−199.644	−	199.644i	−0.610533	−	0.610533i
$328$		0			0
$329$	−456.604	−	683.356i	−1.38785	−	2.07707i
$330$		0			0
$331$	32.0401	−	13.2714i	0.0967979	−	0.0400950i	−0.333759	−	0.942658i	$-0.608317\pi$
$331$	32.0401	−	13.2714i	0.0967979	−	0.0400950i	0.430557	+	0.902563i	$0.358317\pi$
$332$		0			0
$333$	68.3890	+	13.6034i	0.205372	+	0.0408511i
$334$		0			0
$335$	−34.5130	+	6.86507i	−0.103024	+	0.0204927i
$336$		0			0
$337$	439.977	+	293.984i	1.30557	+	0.872355i	0.996890	−	0.0788109i	$-0.0251123\pi$
$337$	439.977	+	293.984i	1.30557	+	0.872355i	0.308681	+	0.951165i	$0.400112\pi$
$338$		0			0
$339$			460.083i			1.35718i
$340$		0			0
$341$	−9.05418			−0.0265518
$342$		0			0
$343$	376.591	−	563.608i	1.09793	−	1.64317i
$344$		0			0
$345$	26.9532	+	135.503i	0.0781252	+	0.392762i
$346$		0			0
$347$	−14.0717	+	70.7432i	−0.0405524	+	0.203871i	−0.995750	−	0.0920983i	$-0.970643\pi$
$347$	−14.0717	+	70.7432i	−0.0405524	+	0.203871i	0.955197	+	0.295969i	$0.0956426\pi$
$348$		0			0
$349$	4.08910	+	9.87195i	0.0117166	+	0.0282864i	0.929630	−	0.368495i	$-0.120127\pi$
$349$	4.08910	+	9.87195i	0.0117166	+	0.0282864i	−0.917913	+	0.396782i	$0.870127\pi$
$350$		0			0
$351$	507.040	−	338.793i	1.44456	−	0.965223i
$352$		0			0
$353$	473.984	−	473.984i	1.34273	−	1.34273i	0.449403	−	0.893329i	$-0.351637\pi$
$353$	473.984	−	473.984i	1.34273	−	1.34273i	0.893329	−	0.449403i	$-0.148363\pi$
$354$		0			0
$355$	281.791	+	116.722i	0.793778	+	0.328794i
$356$		0			0
$357$	176.685	+	444.059i	0.494916	+	1.24386i
$358$		0			0
$359$	54.8746	−	132.479i	0.152854	−	0.369022i	−0.828840	−	0.559485i	$-0.810999\pi$
$359$	54.8746	−	132.479i	0.152854	−	0.369022i	0.981694	+	0.190463i	$0.0609989\pi$
$360$		0			0
$361$	226.911	+	226.911i	0.628562	+	0.628562i
$362$		0			0
$363$	−152.821	−	228.712i	−0.420994	−	0.630062i
$364$		0			0
$365$	198.795	−	82.3435i	0.544643	−	0.225599i
$366$		0			0
$367$	279.939	+	55.6834i	0.762777	+	0.151726i	0.561125	−	0.827731i	$-0.310369\pi$
$367$	279.939	+	55.6834i	0.762777	+	0.151726i	0.201653	+	0.979457i	$0.435369\pi$
$368$		0			0
$369$	−14.2587	+	2.83623i	−0.0386414	+	0.00768625i
$370$		0			0
$371$	188.125	+	125.701i	0.507076	+	0.338817i
$372$		0			0
$373$			336.608i			0.902435i	0.892414	+	0.451217i	$0.149010\pi$
$373$			336.608i			0.902435i	−0.892414	+	0.451217i	$0.850990\pi$
$374$		0			0
$375$	292.378			0.779675
$376$		0			0
$377$	−571.305	+	855.018i	−1.51540	+	2.26795i
$378$		0			0
$379$	−102.651	−	516.061i	−0.270847	−	1.36164i	−0.841415	−	0.540389i	$-0.818277\pi$
$379$	−102.651	−	516.061i	−0.270847	−	1.36164i	0.570569	−	0.821250i	$-0.306723\pi$
$380$		0			0
$381$	89.3499	−	449.193i	0.234514	−	1.17898i
$382$		0			0
$383$	−14.3904	−	34.7415i	−0.0375728	−	0.0907088i	0.903979	−	0.427576i	$-0.140633\pi$
$383$	−14.3904	−	34.7415i	−0.0375728	−	0.0907088i	−0.941552	+	0.336868i	$0.890633\pi$
$384$		0			0
$385$	−9.86000	+	6.58824i	−0.0256104	+	0.0171123i
$386$		0			0
$387$	159.331	−	159.331i	0.411709	−	0.411709i
$388$		0			0
$389$	−372.712	−	154.382i	−0.958129	−	0.396870i	−0.151849	−	0.988404i	$-0.548523\pi$
$389$	−372.712	−	154.382i	−0.958129	−	0.396870i	−0.806280	+	0.591534i	$0.798523\pi$
$390$		0			0
$391$	−38.6744	−	209.752i	−0.0989116	−	0.536450i
$392$		0			0
$393$	82.0108	−	197.992i	0.208679	−	0.503795i
$394$		0			0
$395$	−65.5487	−	65.5487i	−0.165946	−	0.165946i
$396$		0			0
$397$	−157.159	−	235.205i	−0.395866	−	0.592455i	0.578978	−	0.815343i	$-0.303452\pi$
$397$	−157.159	−	235.205i	−0.395866	−	0.592455i	−0.974844	+	0.222888i	$0.928452\pi$
$398$		0			0
$399$	164.471	−	68.1262i	0.412208	−	0.170742i
$400$		0			0
$401$	−287.848	−	57.2565i	−0.717825	−	0.142784i	−0.177354	−	0.984147i	$-0.556754\pi$
$401$	−287.848	−	57.2565i	−0.717825	−	0.142784i	−0.540471	+	0.841363i	$0.681754\pi$
$402$		0			0
$403$	−937.065	+	186.394i	−2.32522	+	0.462516i
$404$		0			0
$405$	−128.368	−	85.7726i	−0.316958	−	0.211784i
$406$		0			0
$407$			3.60766i			0.00886402i
$408$		0			0
$409$	−328.834			−0.803994			−0.401997	−	0.915641i	$-0.631684\pi$
$409$	−328.834			−0.803994			−0.401997	+	0.915641i	$0.631684\pi$
$410$		0			0
$411$	−80.5878	+	120.608i	−0.196077	+	0.293450i
$412$		0			0
$413$	114.620	+	576.233i	0.277530	+	1.39524i
$414$		0			0
$415$	−6.15531	+	30.9448i	−0.0148321	+	0.0745658i
$416$		0			0
$417$	7.71145	+	18.6171i	0.0184927	+	0.0446453i
$418$		0			0
$419$	−191.796	+	128.154i	−0.457747	+	0.305857i	−0.762981	−	0.646421i	$-0.776265\pi$
$419$	−191.796	+	128.154i	−0.457747	+	0.305857i	0.305235	+	0.952277i	$0.401265\pi$
$420$		0			0
$421$	180.422	−	180.422i	0.428555	−	0.428555i	−0.459581	−	0.888136i	$-0.652000\pi$
$421$	180.422	−	180.422i	0.428555	−	0.428555i	0.888136	+	0.459581i	$0.152000\pi$
$422$		0			0
$423$	−235.160	−	97.4066i	−0.555935	−	0.230276i
$424$		0			0
$425$	−26.3709	−	0.369628i	−0.0620493	−	0.000869714i
$426$		0			0
$427$	−319.100	+	770.376i	−0.747307	+	1.80416i
$428$		0			0
$429$	6.65831	+	6.65831i	0.0155205	+	0.0155205i
$430$		0			0
$431$	233.097	+	348.854i	0.540828	+	0.809406i	0.996745	−	0.0806159i	$-0.0256887\pi$
$431$	233.097	+	348.854i	0.540828	+	0.809406i	−0.455917	+	0.890022i	$0.650689\pi$
$432$		0			0
$433$	236.234	−	97.8513i	0.545575	−	0.225985i	−0.0928344	−	0.995682i	$-0.529593\pi$
$433$	236.234	−	97.8513i	0.545575	−	0.225985i	0.638409	+	0.769697i	$0.279593\pi$
$434$		0			0
$435$	531.309	+	105.684i	1.22140	+	0.242951i
$436$		0			0
$437$	−77.9221	+	15.4997i	−0.178311	+	0.0354683i
$438$		0			0
$439$	−170.871	−	114.173i	−0.389229	−	0.260074i	0.345523	−	0.938410i	$-0.387701\pi$
$439$	−170.871	−	114.173i	−0.389229	−	0.260074i	−0.734752	+	0.678336i	$0.762701\pi$
$440$		0			0
$441$		−	397.539i		−	0.901450i
$442$		0			0
$443$	−257.391			−0.581017			−0.290509	−	0.956872i	$-0.593825\pi$
$443$	−257.391			−0.581017			−0.290509	+	0.956872i	$0.593825\pi$
$444$		0			0
$445$	72.0158	−	107.779i	0.161833	−	0.242201i
$446$		0			0
$447$	93.8819	+	471.976i	0.210027	+	1.05588i
$448$		0			0
$449$	82.1066	−	412.778i	0.182866	−	0.919327i	−0.774967	−	0.632001i	$-0.782234\pi$
$449$	82.1066	−	412.778i	0.182866	−	0.919327i	0.957833	−	0.287326i	$-0.0927663\pi$
$450$		0			0
$451$	−0.287844	−	0.694918i	−0.000638236	−	0.00154084i
$452$		0			0
$453$	−275.746	+	184.247i	−0.608710	+	0.406727i
$454$		0			0
$455$	−884.835	+	884.835i	−1.94469	+	1.94469i
$456$		0			0
$457$	−171.475	−	71.0272i	−0.375219	−	0.155421i	0.187101	−	0.982341i	$-0.440091\pi$
$457$	−171.475	−	71.0272i	−0.375219	−	0.155421i	−0.562319	+	0.826920i	$0.690091\pi$
$458$		0			0
$459$	408.459	+	281.283i	0.889889	+	0.612817i
$460$		0			0
$461$	−149.787	+	361.619i	−0.324919	+	0.784423i	0.674036	+	0.738699i	$0.264559\pi$
$461$	−149.787	+	361.619i	−0.324919	+	0.784423i	−0.998954	+	0.0457239i	$0.985441\pi$
$462$		0			0
$463$	567.033	+	567.033i	1.22469	+	1.22469i	0.965945	+	0.258749i	$0.0833103\pi$
$463$	567.033	+	567.033i	1.22469	+	1.22469i	0.258749	+	0.965945i	$0.416690\pi$
$464$		0			0
$465$	279.627	+	418.491i	0.601349	+	0.899982i
$466$		0			0
$467$	185.953	−	77.0243i	0.398187	−	0.164934i	−0.174599	−	0.984640i	$-0.555863\pi$
$467$	185.953	−	77.0243i	0.398187	−	0.164934i	0.572785	+	0.819705i	$0.305863\pi$
$468$		0			0
$469$	88.1110	+	17.5264i	0.187870	+	0.0373696i
$470$		0			0
$471$	−598.520	+	119.053i	−1.27074	+	0.252766i
$472$		0			0
$473$	9.69339	+	6.47691i	0.0204934	+	0.0136933i
$474$		0			0
$475$			9.82402i			0.0206821i
$476$		0			0
$477$	70.0727			0.146903
$478$		0			0
$479$	236.135	−	353.400i	0.492974	−	0.737788i	−0.498670	−	0.866792i	$-0.666178\pi$
$479$	236.135	−	353.400i	0.492974	−	0.737788i	0.991644	+	0.129004i	$0.0411780\pi$
$480$		0			0
$481$	74.2690	+	373.376i	0.154405	+	0.776249i
$482$		0			0
$483$	68.8109	−	345.936i	0.142466	−	0.716223i
$484$		0			0
$485$	−116.422	−	281.068i	−0.240045	−	0.579521i
$486$		0			0
$487$	705.933	−	471.689i	1.44955	−	0.968561i	0.452508	−	0.891761i	$-0.350530\pi$
$487$	705.933	−	471.689i	1.44955	−	0.968561i	0.997046	−	0.0768005i	$-0.0244704\pi$
$488$		0			0
$489$	−29.4443	+	29.4443i	−0.0602133	+	0.0602133i
$490$		0			0
$491$	171.856	+	71.1850i	0.350012	+	0.144980i	0.550761	−	0.834663i	$-0.314338\pi$
$491$	171.856	+	71.1850i	0.350012	+	0.144980i	−0.200749	+	0.979643i	$0.564338\pi$
$492$		0			0
$493$	−817.868	−	174.635i	−1.65896	−	0.354228i
$494$		0			0
$495$	−1.40546	+	3.39308i	−0.00283931	+	0.00685471i
$496$		0			0
$497$	−550.610	−	550.610i	−1.10787	−	1.10787i
$498$		0			0
$499$	292.679	+	438.025i	0.586531	+	0.877806i	0.999457	−	0.0329586i	$-0.0104929\pi$
$499$	292.679	+	438.025i	0.586531	+	0.877806i	−0.412925	+	0.910765i	$0.635493\pi$
$500$		0			0
$501$	−620.641	+	257.078i	−1.23880	+	0.513130i
$502$		0			0
$503$	−426.260	−	84.7883i	−0.847435	−	0.168565i	−0.247772	−	0.968818i	$-0.579698\pi$
$503$	−426.260	−	84.7883i	−0.847435	−	0.168565i	−0.599662	+	0.800253i	$0.704698\pi$
$504$		0			0
$505$	502.750	−	100.003i	0.995545	−	0.198026i
$506$		0			0
$507$	506.630	+	338.519i	0.999269	+	0.667691i
$508$		0			0
$509$		−	196.874i		−	0.386786i	−0.981121	−	0.193393i	$-0.938051\pi$
$509$		−	196.874i		−	0.386786i	0.981121	−	0.193393i	$-0.0619492\pi$
$510$		0			0
$511$	−549.334			−1.07502
$512$		0			0
$513$	102.634	−	153.603i	0.200066	−	0.299420i
$514$		0			0
$515$	46.1237	+	231.879i	0.0895605	+	0.450251i
$516$		0			0
$517$	2.56920	−	12.9162i	0.00496943	−	0.0249830i
$518$		0			0
$519$	29.5801	+	71.4127i	0.0569944	+	0.137597i
$520$		0			0
$521$	−398.527	+	266.287i	−0.764927	+	0.511108i	−0.875769	−	0.482730i	$-0.839645\pi$
$521$	−398.527	+	266.287i	−0.764927	+	0.511108i	0.110842	+	0.993838i	$0.464645\pi$
$522$		0			0
$523$	120.234	−	120.234i	0.229893	−	0.229893i	−0.582755	−	0.812648i	$-0.698025\pi$
$523$	120.234	−	120.234i	0.229893	−	0.229893i	0.812648	+	0.582755i	$0.198025\pi$
$524$		0			0
$525$	−40.2939	−	16.6903i	−0.0767503	−	0.0317910i
$526$		0			0
$527$	−422.591	−	652.054i	−0.801881	−	1.23729i
$528$		0			0
$529$	142.201	−	343.304i	0.268811	−	0.648968i
$530$		0			0
$531$	128.664	+	128.664i	0.242305	+	0.242305i
$532$		0			0
$533$	−44.0965	−	65.9950i	−0.0827326	−	0.123818i
$534$		0			0
$535$	390.248	−	161.646i	0.729436	−	0.302142i
$536$		0			0
$537$	186.300	+	37.0574i	0.346927	+	0.0690081i
$538$		0			0
$539$	20.1728	−	4.01263i	0.0374264	−	0.00744458i
$540$		0			0
$541$	56.4993	+	37.7516i	0.104435	+	0.0697812i	0.606691	−	0.794938i	$-0.292497\pi$
$541$	56.4993	+	37.7516i	0.104435	+	0.0697812i	−0.502256	+	0.864719i	$0.667497\pi$
$542$		0			0
$543$		−	512.540i		−	0.943905i
$544$		0			0
$545$	601.218			1.10315
$546$		0			0
$547$	−459.480	+	687.660i	−0.840000	+	1.25715i	0.124276	+	0.992248i	$0.460339\pi$
$547$	−459.480	+	687.660i	−0.840000	+	1.25715i	−0.964276	+	0.264901i	$0.914661\pi$
$548$		0			0
$549$	50.3815	+	253.285i	0.0917696	+	0.461357i
$550$		0			0
$551$	−60.7744	+	305.534i	−0.110298	+	0.554508i
$552$		0			0
$553$	90.5661	+	218.646i	0.163772	+	0.395381i
$554$		0			0
$555$	166.749	−	111.418i	0.300448	−	0.200753i
$556$		0			0
$557$	618.834	−	618.834i	1.11101	−	1.11101i	0.118000	−	0.993014i	$-0.462352\pi$
$557$	618.834	−	618.834i	1.11101	−	1.11101i	0.993014	−	0.118000i	$-0.0376482\pi$
$558$		0			0
$559$	1136.56	+	470.777i	2.03320	+	0.842178i
$560$		0			0
$561$	−3.02945	+	7.03329i	−0.00540010	+	0.0125371i
$562$		0			0
$563$	244.423	−	590.091i	0.434145	−	1.04812i	−0.543793	−	0.839220i	$-0.683012\pi$
$563$	244.423	−	590.091i	0.434145	−	1.04812i	0.977937	−	0.208898i	$-0.0669878\pi$
$564$		0			0
$565$	−692.756	−	692.756i	−1.22612	−	1.22612i
$566$		0			0
$567$	218.976	+	327.720i	0.386200	+	0.577990i
$568$		0			0
$569$	−30.3318	+	12.5638i	−0.0533072	+	0.0220805i	−0.409178	−	0.912455i	$-0.634184\pi$
$569$	−30.3318	+	12.5638i	−0.0533072	+	0.0220805i	0.355871	+	0.934535i	$0.384184\pi$
$570$		0			0
$571$	−331.618	−	65.9629i	−0.580767	−	0.115522i	−0.104040	−	0.994573i	$-0.533177\pi$
$571$	−331.618	−	65.9629i	−0.580767	−	0.115522i	−0.476727	+	0.879051i	$0.658177\pi$
$572$		0			0
$573$	588.605	−	117.081i	1.02723	−	0.204330i
$574$		0			0
$575$	16.1839	+	10.8137i	0.0281459	+	0.0188065i
$576$		0			0
$577$		−	889.889i		−	1.54227i	−0.636672	−	0.771135i	$-0.719689\pi$
$577$		−	889.889i		−	1.54227i	0.636672	−	0.771135i	$-0.280311\pi$
$578$		0			0
$579$	381.941			0.659656
$580$		0			0
$581$	44.7507	−	66.9742i	0.0770236	−	0.115274i
$582$		0			0
$583$	0.707290	+	3.55578i	0.00121319	+	0.00609912i
$584$		0			0
$585$	−75.6069	+	380.101i	−0.129243	+	0.649746i
$586$		0			0
$587$	−98.8591	−	238.667i	−0.168414	−	0.406588i	0.817028	−	0.576598i	$-0.195620\pi$
$587$	−98.8591	−	238.667i	−0.168414	−	0.406588i	−0.985442	+	0.170010i	$0.945620\pi$
$588$		0			0
$589$	−240.657	+	160.802i	−0.408586	+	0.273008i
$590$		0			0
$591$	−211.834	+	211.834i	−0.358433	+	0.358433i
$592$		0			0
$593$	555.337	+	230.028i	0.936487	+	0.387905i	0.798136	−	0.602478i	$-0.205820\pi$
$593$	555.337	+	230.028i	0.936487	+	0.387905i	0.138351	+	0.990383i	$0.455820\pi$
$594$		0			0
$595$	−934.667	−	402.590i	−1.57087	−	0.676622i
$596$		0			0
$597$	−301.429	+	727.715i	−0.504907	+	1.21895i
$598$		0			0
$599$	−512.903	−	512.903i	−0.856266	−	0.856266i	0.134630	−	0.990896i	$-0.457015\pi$
$599$	−512.903	−	512.903i	−0.856266	−	0.856266i	−0.990896	+	0.134630i	$0.957015\pi$
$600$		0			0
$601$	168.283	+	251.853i	0.280004	+	0.419056i	0.944639	−	0.328113i	$-0.106413\pi$
$601$	168.283	+	251.853i	0.280004	+	0.419056i	−0.664634	+	0.747169i	$0.731413\pi$
$602$		0			0
$603$	25.7051	−	10.6474i	0.0426287	−	0.0176574i
$604$		0			0
$605$	574.483	+	114.272i	0.949558	+	0.188879i
$606$		0			0
$607$	−607.168	+	120.773i	−1.00028	+	0.198967i	−0.667957	−	0.744200i	$-0.732831\pi$
$607$	−607.168	+	120.773i	−1.00028	+	0.198967i	−0.332319	+	0.943167i	$0.607831\pi$
$608$		0			0
$609$	−1149.92	−	768.350i	−1.88820	−	1.26166i
$610$		0			0
$611$		−	1389.66i		−	2.27440i
$612$		0			0
$613$	417.404			0.680921			0.340460	−	0.940259i	$-0.389417\pi$
$613$	417.404			0.680921			0.340460	+	0.940259i	$0.389417\pi$
$614$		0			0
$615$	−23.2299	+	34.7661i	−0.0377723	+	0.0565302i
$616$		0			0
$617$	119.409	+	600.310i	0.193532	+	0.972949i	0.948401	+	0.317074i	$0.102700\pi$
$617$	119.409	+	600.310i	0.193532	+	0.972949i	−0.754869	+	0.655875i	$0.772300\pi$
$618$		0			0
$619$	169.170	−	850.474i	0.273295	−	1.37395i	−0.563357	−	0.826214i	$-0.690490\pi$
$619$	169.170	−	850.474i	0.273295	−	1.37395i	0.836652	−	0.547734i	$-0.184510\pi$
$620$		0			0
$621$	−140.068	−	338.154i	−0.225552	−	0.544531i
$622$		0			0
$623$	−275.158	+	183.855i	−0.441666	+	0.295112i
$624$		0			0
$625$	−412.815	+	412.815i	−0.660504	+	0.660504i
$626$		0			0
$627$	2.63543	+	1.09163i	0.00420323	+	0.00174103i
$628$		0			0
$629$	−259.812	+	168.382i	−0.413056	+	0.267699i
$630$		0			0
$631$	246.996	−	596.302i	0.391437	−	0.945011i	−0.598191	−	0.801354i	$-0.704114\pi$
$631$	246.996	−	596.302i	0.391437	−	0.945011i	0.989627	−	0.143658i	$-0.0458865\pi$
$632$		0			0
$633$	105.510	+	105.510i	0.166683	+	0.166683i
$634$		0			0
$635$	541.823	+	810.895i	0.853264	+	1.27700i
$636$		0			0
$637$	2005.19	−	830.576i	3.14786	−	1.30389i
$638$		0			0
$639$	−236.527	−	47.0482i	−0.370152	−	0.0736278i
$640$		0			0
$641$	−149.716	+	29.7804i	−0.233567	+	0.0464593i	−0.310486	−	0.950578i	$-0.600492\pi$
$641$	−149.716	+	29.7804i	−0.233567	+	0.0464593i	0.0769191	+	0.997037i	$0.475492\pi$
$642$		0			0
$643$	−119.400	−	79.7808i	−0.185693	−	0.124076i	0.459249	−	0.888307i	$-0.348118\pi$
$643$	−119.400	−	79.7808i	−0.185693	−	0.124076i	−0.644942	+	0.764232i	$0.723118\pi$
$644$		0			0
$645$		−	648.068i		−	1.00476i
$646$		0			0
$647$	344.243			0.532061			0.266031	−	0.963965i	$-0.414288\pi$
$647$	344.243			0.532061			0.266031	+	0.963965i	$0.414288\pi$
$648$		0			0
$649$	−5.23027	+	7.82766i	−0.00805897	+	0.0120611i
$650$		0			0
$651$	−250.682	−	1260.26i	−0.385072	−	1.93589i
$652$		0			0
$653$	−184.272	+	926.399i	−0.282193	+	1.41868i	0.536233	+	0.844070i	$0.319847\pi$
$653$	−184.272	+	926.399i	−0.282193	+	1.41868i	−0.818426	+	0.574611i	$0.805153\pi$
$654$		0			0
$655$	174.635	+	421.606i	0.266618	+	0.643673i
$656$		0			0
$657$	−141.459	+	94.5200i	−0.215311	+	0.143866i
$658$		0			0
$659$	614.625	−	614.625i	0.932663	−	0.932663i	−0.0652087	−	0.997872i	$-0.520771\pi$
$659$	614.625	−	614.625i	0.932663	−	0.932663i	0.997872	+	0.0652087i	$0.0207713\pi$
$660$		0			0
$661$	−19.3671	−	8.02210i	−0.0292996	−	0.0121363i	0.367985	−	0.929832i	$-0.380048\pi$
$661$	−19.3671	−	8.02210i	−0.0292996	−	0.0121363i	−0.397285	+	0.917695i	$0.630048\pi$
$662$		0			0
$663$	−168.743	+	790.278i	−0.254515	+	1.19197i
$664$		0			0
$665$	−145.069	+	350.227i	−0.218148	+	0.526657i
$666$		0			0
$667$	436.433	+	436.433i	0.654322	+	0.654322i
$668$		0			0
$669$	457.657	+	684.931i	0.684090	+	1.02381i
$670$		0			0
$671$	−12.3442	+	5.11314i	−0.0183967	+	0.00762018i
$672$		0			0
$673$	−358.945	−	71.3987i	−0.533351	−	0.106090i	−0.0789352	−	0.996880i	$-0.525152\pi$
$673$	−358.945	−	71.3987i	−0.533351	−	0.106090i	−0.454416	+	0.890790i	$0.650152\pi$
$674$		0			0
$675$	−44.3890	+	8.82953i	−0.0657615	+	0.0130808i
$676$		0			0
$677$	465.502	+	311.038i	0.687595	+	0.459436i	0.849651	−	0.527345i	$-0.176813\pi$
$677$	465.502	+	311.038i	0.687595	+	0.459436i	−0.162056	+	0.986782i	$0.551813\pi$
$678$		0			0
$679$			776.680i			1.14386i
$680$		0			0
$681$	−262.052			−0.384805
$682$		0			0
$683$	542.968	−	812.609i	0.794975	−	1.18976i	−0.183423	−	0.983034i	$-0.558718\pi$
$683$	542.968	−	812.609i	0.794975	−	1.18976i	0.978398	−	0.206730i	$-0.0662823\pi$
$684$		0			0
$685$	−60.2595	−	302.945i	−0.0879701	−	0.442255i
$686$		0			0
$687$	187.726	−	943.762i	0.273254	−	1.37374i
$688$		0			0
$689$	146.402	+	353.446i	0.212485	+	0.512985i
$690$		0			0
$691$	−529.303	+	353.669i	−0.765996	+	0.511822i	−0.876118	−	0.482096i	$-0.839876\pi$
$691$	−529.303	+	353.669i	−0.765996	+	0.511822i	0.110123	+	0.993918i	$0.464876\pi$
$692$		0			0
$693$	6.62996	−	6.62996i	0.00956704	−	0.00956704i
$694$		0			0
$695$	−39.6435	−	16.4209i	−0.0570409	−	0.0236271i
$696$		0			0
$697$	36.6111	−	53.1640i	0.0525267	−	0.0762754i
$698$		0			0
$699$	−76.7235	+	185.227i	−0.109762	+	0.264988i
$700$		0			0
$701$	618.651	+	618.651i	0.882527	+	0.882527i	0.993791	−	0.111264i	$-0.0354899\pi$
$701$	618.651	+	618.651i	0.882527	+	0.882527i	−0.111264	+	0.993791i	$0.535490\pi$
$702$		0			0
$703$	64.0719	+	95.8904i	0.0911407	+	0.136402i
$704$		0			0
$705$	−676.344	+	280.151i	−0.959354	+	0.397377i
$706$		0			0
$707$	−1283.51	−	255.306i	−1.81543	−	0.361112i
$708$		0			0
$709$	−413.386	+	82.2277i	−0.583056	+	0.115977i	−0.477801	−	0.878468i	$-0.658566\pi$
$709$	−413.386	+	82.2277i	−0.583056	+	0.115977i	−0.105255	+	0.994445i	$0.533566\pi$
$710$		0			0
$711$	60.9425	+	40.7205i	0.0857138	+	0.0572722i
$712$		0			0
$713$			573.455i			0.804285i
$714$		0			0
$715$	−20.0511			−0.0280435
$716$		0			0
$717$	−41.7831	+	62.5328i	−0.0582748	+	0.0872145i
$718$		0			0
$719$	219.546	+	1103.73i	0.305348	+	1.53509i	0.763259	+	0.646092i	$0.223598\pi$
$719$	219.546	+	1103.73i	0.305348	+	1.53509i	−0.457911	+	0.888998i	$0.651402\pi$
$720$		0			0
$721$	117.753	−	591.982i	0.163318	−	0.821058i
$722$		0			0
$723$	−22.0016	−	53.1167i	−0.0304310	−	0.0734670i
$724$		0			0
$725$	63.4572	−	42.4008i	0.0875272	−	0.0584838i
$726$		0			0
$727$	−488.259	+	488.259i	−0.671609	+	0.671609i	−0.958087	−	0.286478i	$-0.907515\pi$
$727$	−488.259	+	488.259i	−0.671609	+	0.671609i	0.286478	+	0.958087i	$0.407515\pi$
$728$		0			0
$729$	664.396	+	275.202i	0.911380	+	0.377506i
$730$		0			0
$731$	−14.0220	+	1000.39i	−0.0191819	+	1.36852i
$732$		0			0
$733$	−172.984	+	417.620i	−0.235994	+	0.569740i	−0.996861	−	0.0791674i	$-0.974774\pi$
$733$	−172.984	+	417.620i	−0.235994	+	0.569740i	0.760867	+	0.648908i	$0.224774\pi$
$734$		0			0
$735$	−808.480	−	808.480i	−1.09997	−	1.09997i
$736$		0			0
$737$	0.799753	+	1.19692i	0.00108515	+	0.00162404i
$738$		0			0
$739$	−341.194	+	141.327i	−0.461697	+	0.191241i	−0.601393	−	0.798953i	$-0.705387\pi$
$739$	−341.194	+	141.327i	−0.461697	+	0.191241i	0.139696	+	0.990194i	$0.455387\pi$
$740$		0			0
$741$	295.227	+	58.7243i	0.398417	+	0.0792501i
$742$		0			0
$743$	607.180	−	120.776i	0.817201	−	0.162551i	0.231246	−	0.972895i	$-0.425720\pi$
$743$	607.180	−	120.776i	0.817201	−	0.162551i	0.585954	+	0.810344i	$0.300720\pi$
$744$		0			0
$745$	−852.025	−	569.305i	−1.14366	−	0.764167i
$746$		0			0
$747$		−	24.9465i		−	0.0333955i
$748$		0			0
$749$	−1078.38			−1.43976
$750$		0			0
$751$	−481.185	+	720.144i	−0.640726	+	0.958914i	0.358948	+	0.933358i	$0.383136\pi$
$751$	−481.185	+	720.144i	−0.640726	+	0.958914i	−0.999673	+	0.0255563i	$0.991864\pi$
$752$		0			0
$753$	13.0347	+	65.5299i	0.0173104	+	0.0870251i
$754$		0			0
$755$	137.771	−	692.621i	0.182478	−	0.917379i
$756$		0			0
$757$	−32.7015	−	78.9484i	−0.0431988	−	0.104291i	0.900807	−	0.434219i	$-0.142976\pi$
$757$	−32.7015	−	78.9484i	−0.0431988	−	0.104291i	−0.944006	+	0.329928i	$0.892976\pi$
$758$		0			0
$759$	4.69925	−	3.13994i	0.00619137	−	0.00413694i
$760$		0			0
$761$	271.509	−	271.509i	0.356779	−	0.356779i	−0.505845	−	0.862624i	$-0.668819\pi$
$761$	271.509	−	271.509i	0.356779	−	0.356779i	0.862624	+	0.505845i	$0.168819\pi$
$762$		0			0
$763$	−1418.06	−	587.379i	−1.85853	−	0.769828i
$764$		0			0
$765$	−309.957	+	57.1505i	−0.405173	+	0.0747065i
$766$		0			0
$767$	−380.165	+	917.799i	−0.495652	+	1.19661i
$768$		0			0
$769$	862.295	+	862.295i	1.12132	+	1.12132i	0.991543	+	0.129777i	$0.0414262\pi$
$769$	862.295	+	862.295i	1.12132	+	1.12132i	0.129777	+	0.991543i	$0.458574\pi$
$770$		0			0
$771$	−291.726	−	436.599i	−0.378374	−	0.566276i
$772$		0			0
$773$	1051.39	−	435.501i	1.36015	−	0.563391i	0.421047	−	0.907039i	$-0.361663\pi$
$773$	1051.39	−	435.501i	1.36015	−	0.563391i	0.939099	+	0.343648i	$0.111663\pi$
$774$		0			0
$775$	69.5466	+	13.8337i	0.0897376	+	0.0178499i
$776$		0			0
$777$	−502.154	+	99.8847i	−0.646273	+	0.128552i
$778$		0			0
$779$	−19.9925	−	13.3586i	−0.0256643	−	0.0171484i
$780$		0			0
$781$		−	12.4773i		−	0.0159760i
$782$		0			0
$783$	−1435.15			−1.83289
$784$		0			0
$785$	721.943	−	1080.46i	0.919673	−	1.37639i
$786$		0			0
$787$	159.912	+	803.934i	0.203192	+	1.02152i	0.938893	+	0.344210i	$0.111853\pi$
$787$	159.912	+	803.934i	0.203192	+	1.02152i	−0.735700	+	0.677307i	$0.763147\pi$
$788$		0			0
$789$	52.1823	−	262.338i	0.0661372	−	0.332494i
$790$		0			0
$791$	957.155	+	2310.78i	1.21006	+	2.92133i
$792$		0			0
$793$	−1172.31	+	783.310i	−1.47832	+	0.987781i
$794$		0			0
$795$	142.507	−	142.507i	0.179255	−	0.179255i
$796$		0			0
$797$	−821.410	−	340.239i	−1.03063	−	0.426900i	−0.197688	−	0.980265i	$-0.563343\pi$
$797$	−821.410	−	340.239i	−1.03063	−	0.426900i	−0.832939	+	0.553365i	$0.813343\pi$
$798$		0			0
$799$	1050.10	−	417.821i	1.31427	−	0.522930i
$800$		0			0
$801$	−39.2215	+	94.6890i	−0.0489656	+	0.118213i
$802$		0			0
$803$	−6.22419	−	6.22419i	−0.00775117	−	0.00775117i
$804$		0			0
$805$	417.273	+	624.492i	0.518351	+	0.775767i
$806$		0			0
$807$	1036.73	−	429.426i	1.28467	−	0.532127i
$808$		0			0
$809$	−346.111	−	68.8457i	−0.427826	−	0.0850998i	−0.0235191	−	0.999723i	$-0.507487\pi$
$809$	−346.111	−	68.8457i	−0.427826	−	0.0850998i	−0.404306	+	0.914624i	$0.632487\pi$
$810$		0			0
$811$	−452.222	+	89.9525i	−0.557610	+	0.110916i	−0.465847	−	0.884865i	$-0.654250\pi$
$811$	−452.222	+	89.9525i	−0.557610	+	0.110916i	−0.0917632	+	0.995781i	$0.529250\pi$
$812$		0			0
$813$	−350.488	−	234.189i	−0.431105	−	0.288055i
$814$		0			0
$815$		−	88.6698i		−	0.108797i
$816$		0			0
$817$	372.677			0.456153
$818$		0			0
$819$	549.682	−	822.657i	0.671162	−	1.00447i
$820$		0			0
$821$	65.9227	+	331.416i	0.0802956	+	0.403673i	0.999940	+	0.0109220i	$0.00347667\pi$
$821$	65.9227	+	331.416i	0.0802956	+	0.403673i	−0.919645	+	0.392751i	$0.871523\pi$
$822$		0			0
$823$	16.9034	−	84.9793i	0.0205388	−	0.103256i	−0.969156	−	0.246448i	$-0.920737\pi$
$823$	16.9034	−	84.9793i	0.0205388	−	0.103256i	0.989695	+	0.143192i	$0.0457367\pi$
$824$		0			0
$825$	−0.267439	−	0.645655i	−0.000324168	−	0.000782612i
$826$		0			0
$827$	275.751	−	184.251i	0.333435	−	0.222794i	−0.377570	−	0.925981i	$-0.623240\pi$
$827$	275.751	−	184.251i	0.333435	−	0.222794i	0.711005	+	0.703187i	$0.248240\pi$
$828$		0			0
$829$	−99.3933	+	99.3933i	−0.119895	+	0.119895i	−0.764509	−	0.644613i	$-0.777018\pi$
$829$	−99.3933	+	99.3933i	−0.119895	+	0.119895i	0.644613	+	0.764509i	$0.277018\pi$
$830$		0			0
$831$	306.256	+	126.855i	0.368539	+	0.152654i
$832$		0			0
$833$	1230.52	+	1265.50i	1.47721	+	1.51921i
$834$		0			0
$835$	547.425	−	1321.60i	0.655599	−	1.58276i
$836$		0			0
$837$	−942.866	−	942.866i	−1.12648	−	1.12648i
$838$		0			0
$839$	−60.3065	−	90.2550i	−0.0718790	−	0.107574i	0.793789	−	0.608194i	$-0.208106\pi$
$839$	−60.3065	−	90.2550i	−0.0718790	−	0.107574i	−0.865668	+	0.500619i	$0.833106\pi$
$840$		0			0
$841$	1458.89	−	604.290i	1.73470	−	0.718538i
$842$		0			0
$843$	−288.812	−	57.4483i	−0.342600	−	0.0681474i
$844$		0			0
$845$	−1272.56	+	253.128i	−1.50599	+	0.299559i
$846$		0			0
$847$	−1243.36	−	830.786i	−1.46796	−	0.980857i
$848$		0			0
$849$			571.657i			0.673330i
$850$		0			0
$851$	228.494			0.268501
$852$		0			0
$853$	−422.582	+	632.439i	−0.495407	+	0.741429i	−0.991956	−	0.126579i	$-0.959600\pi$
$853$	−422.582	+	632.439i	−0.495407	+	0.741429i	0.496549	+	0.868008i	$0.334600\pi$
$854$		0			0
$855$	22.9043	+	115.148i	0.0267887	+	0.134676i
$856$		0			0
$857$	170.470	−	857.011i	0.198915	−	1.00001i	−0.744304	−	0.667841i	$-0.767219\pi$
$857$	170.470	−	857.011i	0.198915	−	1.00001i	0.943219	−	0.332172i	$-0.107781\pi$
$858$		0			0
$859$	479.950	+	1158.70i	0.558731	+	1.34890i	0.910771	+	0.412911i	$0.135488\pi$
$859$	479.950	+	1158.70i	0.558731	+	1.34890i	−0.352041	+	0.935985i	$0.614512\pi$
$860$		0			0
$861$	88.7569	−	59.3055i	0.103086	−	0.0688798i
$862$		0			0
$863$	760.732	−	760.732i	0.881497	−	0.881497i	−0.112190	−	0.993687i	$-0.535786\pi$
$863$	760.732	−	760.732i	0.881497	−	0.881497i	0.993687	+	0.112190i	$0.0357864\pi$
$864$		0			0
$865$	−152.067	−	62.9882i	−0.175800	−	0.0728187i
$866$		0			0
$867$	−647.911	+	110.097i	−0.747303	+	0.126986i
$868$		0			0
$869$	−1.45120	+	3.50350i	−0.00166996	+	0.00403165i
$870$		0			0
$871$	107.411	+	107.411i	0.123319	+	0.123319i
$872$		0			0
$873$	133.638	+	200.003i	0.153079	+	0.229099i
$874$		0			0
$875$	1468.48	−	608.262i	1.67826	−	0.695157i
$876$		0			0
$877$	−293.743	−	58.4291i	−0.334940	−	0.0666238i	0.0247550	−	0.999694i	$-0.492119\pi$
$877$	−293.743	−	58.4291i	−0.334940	−	0.0666238i	−0.359695	+	0.933070i	$0.617119\pi$
$878$		0			0
$879$	10.5997	−	2.10841i	0.0120588	−	0.00239865i
$880$		0			0
$881$	−291.120	−	194.520i	−0.330443	−	0.220795i	0.379270	−	0.925286i	$-0.376175\pi$
$881$	−291.120	−	194.520i	−0.330443	−	0.220795i	−0.709713	+	0.704491i	$0.751175\pi$
$882$		0			0
$883$			953.567i			1.07992i	0.841691	+	0.539959i	$0.181560\pi$
$883$			953.567i			1.07992i	−0.841691	+	0.539959i	$0.818440\pi$
$884$		0			0
$885$	523.331			0.591335
$886$		0			0
$887$	640.230	−	958.172i	0.721793	−	1.08024i	−0.271253	−	0.962508i	$-0.587438\pi$
$887$	640.230	−	958.172i	0.721793	−	1.08024i	0.993046	−	0.117731i	$-0.0375621\pi$
$888$		0			0
$889$	−485.737	−	2441.96i	−0.546385	−	2.74687i
$890$		0			0
$891$	−1.23212	+	6.19429i	−0.00138285	+	0.00695207i
$892$		0			0
$893$	−161.103	−	388.938i	−0.180407	−	0.435541i
$894$		0			0
$895$	−336.314	+	224.718i	−0.375770	+	0.251081i
$896$		0			0
$897$	421.710	−	421.710i	0.470134	−	0.470134i
$898$		0			0
$899$	2077.37	+	860.474i	2.31075	+	0.957146i
$900$		0			0
$901$	−223.065	+	216.898i	−0.247575	+	0.240731i
$902$		0			0
$903$	−633.150	+	1528.56i	−0.701163	+	1.69276i
$904$		0			0
$905$	771.743	+	771.743i	0.852755	+	0.852755i
$906$		0			0
$907$	−310.389	−	464.530i	−0.342215	−	0.512161i	0.619945	−	0.784645i	$-0.287155\pi$
$907$	−310.389	−	464.530i	−0.342215	−	0.512161i	−0.962160	+	0.272484i	$0.912155\pi$
$908$		0			0
$909$	−374.446	+	155.100i	−0.411931	+	0.170628i
$910$		0			0
$911$	1035.74	+	206.022i	1.13693	+	0.226150i	0.727445	−	0.686166i	$-0.240708\pi$
$911$	1035.74	+	206.022i	1.13693	+	0.226150i	0.409487	+	0.912316i	$0.365708\pi$
$912$		0			0
$913$	1.26589	−	0.251801i	0.00138652	−	0.000275795i
$914$		0			0
$915$	617.569	+	412.647i	0.674939	+	0.450980i
$916$		0			0
$917$		−	1165.03i		−	1.27048i
$918$		0			0
$919$	−1159.49			−1.26169			−0.630843	−	0.775910i	$-0.717291\pi$
$919$	−1159.49			−1.26169			−0.630843	+	0.775910i	$0.717291\pi$
$920$		0			0
$921$	679.983	−	1017.67i	0.738309	−	1.10496i
$922$		0			0
$923$	−256.864	−	1291.34i	−0.278292	−	1.39907i
$924$		0			0
$925$	5.51206	−	27.7110i	0.00595898	−	0.0299578i
$926$		0			0
$927$	−71.5357	−	172.702i	−0.0771690	−	0.186302i
$928$		0			0
$929$	745.956	−	498.432i	0.802966	−	0.536525i	−0.0850284	−	0.996379i	$-0.527098\pi$
$929$	745.956	−	498.432i	0.802966	−	0.536525i	0.887995	+	0.459854i	$0.152098\pi$
$930$		0			0
$931$	464.923	−	464.923i	0.499381	−	0.499381i
$932$		0			0
$933$	992.563	+	411.133i	1.06384	+	0.440657i
$934$		0			0
$935$	−6.02866	−	15.1517i	−0.00644776	−	0.0162050i
$936$		0			0
$937$	417.604	−	1008.19i	0.445682	−	1.07597i	−0.528241	−	0.849095i	$-0.677148\pi$
$937$	417.604	−	1008.19i	0.445682	−	1.07597i	0.973923	−	0.226878i	$-0.0728518\pi$
$938$		0			0
$939$	−177.349	−	177.349i	−0.188870	−	0.188870i
$940$		0			0
$941$	−414.993	−	621.081i	−0.441013	−	0.660022i	0.542668	−	0.839948i	$-0.317414\pi$
$941$	−414.993	−	621.081i	−0.441013	−	0.660022i	−0.983680	+	0.179925i	$0.942414\pi$
$942$		0			0
$943$	−44.0132	+	18.2309i	−0.0466736	+	0.0193329i
$944$		0			0
$945$	−1712.85	−	340.708i	−1.81254	−	0.360537i
$946$		0			0
$947$	171.092	−	34.0323i	0.180667	−	0.0359369i	−0.103927	−	0.994585i	$-0.533141\pi$
$947$	171.092	−	34.0323i	0.180667	−	0.0359369i	0.284595	+	0.958648i	$0.408141\pi$
$948$		0			0
$949$	−772.308	−	516.040i	−0.813813	−	0.543772i
$950$		0			0
$951$		−	332.455i		−	0.349585i
$952$		0			0
$953$	−1285.76			−1.34917			−0.674586	−	0.738196i	$-0.735678\pi$
$953$	−1285.76			−1.34917			−0.674586	+	0.738196i	$0.735678\pi$
$954$		0			0
$955$	−709.985	+	1062.57i	−0.743439	+	1.11264i
$956$		0			0
$957$	−4.32331	−	21.7348i	−0.00451757	−	0.0227114i
$958$		0			0
$959$	−153.841	+	773.411i	−0.160418	+	0.806477i
$960$		0			0
$961$	431.716	+	1042.26i	0.449237	+	1.08455i
$962$		0			0
$963$	−277.694	+	185.549i	−0.288364	+	0.192679i
$964$		0			0
$965$	−575.096	+	575.096i	−0.595955	+	0.595955i
$966$		0			0
$967$	−241.441	−	100.008i	−0.249681	−	0.103421i	0.254333	−	0.967117i	$-0.418144\pi$
$967$	−241.441	−	100.008i	−0.249681	−	0.103421i	−0.504014	+	0.863695i	$0.668144\pi$
$968$		0			0
$969$	44.3891	+	240.745i	0.0458092	+	0.248447i
$970$		0			0
$971$	227.662	−	549.626i	0.234462	−	0.566041i	−0.762231	−	0.647305i	$-0.775896\pi$
$971$	227.662	−	549.626i	0.234462	−	0.566041i	0.996693	+	0.0812646i	$0.0258959\pi$
$972$		0			0
$973$	77.4619	+	77.4619i	0.0796114	+	0.0796114i
$974$		0			0
$975$	−40.9704	−	61.3166i	−0.0420210	−	0.0628888i
$976$		0			0
$977$	−1669.89	+	691.692i	−1.70920	+	0.707976i	−0.709209	+	0.704998i	$0.750948\pi$
$977$	−1669.89	+	691.692i	−1.70920	+	0.707976i	−0.999996	+	0.00297727i	$0.999052\pi$
$978$		0			0
$979$	−5.20081	−	1.03450i	−0.00531237	−	0.00105670i
$980$		0			0
$981$	−466.231	+	92.7390i	−0.475261	+	0.0945352i
$982$		0			0
$983$	−1327.25	−	886.843i	−1.35021	−	0.902180i	−0.350796	−	0.936452i	$-0.614089\pi$
$983$	−1327.25	−	886.843i	−1.35021	−	0.902180i	−0.999413	+	0.0342716i	$0.989089\pi$
$984$		0			0
$985$		−	637.925i		−	0.647640i
$986$		0			0
$987$	1868.96			1.89357
$988$		0			0
$989$	410.221	−	613.940i	0.414784	−	0.620768i
$990$		0			0
$991$	213.759	+	1074.64i	0.215701	+	1.08440i	0.925138	+	0.379631i	$0.123949\pi$
$991$	213.759	+	1074.64i	0.215701	+	1.08440i	−0.709437	+	0.704768i	$0.751051\pi$
$992$		0			0
$993$	−15.3856	+	77.3484i	−0.0154940	+	0.0778937i
$994$		0			0
$995$	−641.867	−	1549.60i	−0.645092	−	1.55739i
$996$		0			0
$997$	851.311	−	568.828i	0.853873	−	0.570540i	−0.0498020	−	0.998759i	$-0.515859\pi$
$997$	851.311	−	568.828i	0.853873	−	0.570540i	0.903675	+	0.428220i	$0.140859\pi$
$998$		0			0
$999$	−375.687	+	375.687i	−0.376063	+	0.376063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.b.41.2	✓	40
4.3	odd	2		272.3.bh.g.177.4		40
17.5	odd	16	inner	136.3.t.b.73.2	yes	40
68.39	even	16		272.3.bh.g.209.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.b.41.2	✓	40	1.1	even	1	trivial
136.3.t.b.73.2	yes	40	17.5	odd	16	inner
272.3.bh.g.177.4		40	4.3	odd	2
272.3.bh.g.209.4		40	68.39	even	16

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	136.t (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26339 + 1.89080i) q^{3} +(-0.944701 - 4.74933i) q^{5} +(-2.41180 + 12.1249i) q^{7} +(1.46519 + 3.53728i) q^{9} +O(q^{10})\)	\(q+(-1.26339 + 1.89080i) q^{3} +(-0.944701 - 4.74933i) q^{5} +(-2.41180 + 12.1249i) q^{7} +(1.46519 + 3.53728i) q^{9} +(-0.164707 + 0.110054i) q^{11} +(-14.7808 + 14.7808i) q^{13} +(10.1736 + 4.21403i) q^{15} +(-15.6132 - 6.72510i) q^{17} +(-2.42331 + 5.85039i) q^{19} +(-19.8788 - 19.8788i) q^{21} +(6.97037 + 10.4319i) q^{23} +(1.43329 - 0.593689i) q^{25} +(-28.6125 - 5.69139i) q^{27} +(48.2491 - 9.59735i) q^{29} +(38.0040 + 25.3934i) q^{31} -0.450470i q^{33} +59.8638 q^{35} +(10.1181 - 15.1428i) q^{37} +(-9.27359 - 46.6215i) q^{39} +(-0.740776 + 3.72413i) q^{41} +(-22.5218 - 54.3723i) q^{43} +(15.4155 - 10.3003i) q^{45} +(-47.0089 + 47.0089i) q^{47} +(-95.9272 - 39.7344i) q^{49} +(32.4414 - 21.0251i) q^{51} +(7.00382 - 16.9087i) q^{53} +(0.678282 + 0.678282i) q^{55} +(-8.00033 - 11.9733i) q^{57} +(43.9070 - 18.1869i) q^{59} +(66.1539 + 13.1588i) q^{61} +(-46.4230 + 9.23411i) q^{63} +(84.1624 + 56.2355i) q^{65} -7.26692i q^{67} -28.5309 q^{69} +(-34.9939 + 52.3721i) q^{71} +(8.66896 + 43.5818i) q^{73} +(-0.688262 + 3.46013i) q^{75} +(-0.937156 - 2.26249i) q^{77} +(15.9172 - 10.6355i) q^{79} +(22.5443 - 22.5443i) q^{81} +(-6.01964 - 2.49342i) q^{83} +(-17.1899 + 80.5056i) q^{85} +(-42.8109 + 103.355i) q^{87} +(18.9285 + 18.9285i) q^{89} +(-143.568 - 214.865i) q^{91} +(-96.0278 + 39.7760i) q^{93} +(30.0748 + 5.98224i) q^{95} +(61.6184 - 12.2567i) q^{97} +(-0.630618 - 0.421366i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9} + 24 q^{11} - 48 q^{13} - 96 q^{15} - 40 q^{19} + 80 q^{21} + 48 q^{23} + 48 q^{25} + 224 q^{27} + 24 q^{29} + 88 q^{31} + 32 q^{35} - 176 q^{37} - 120 q^{39} - 352 q^{43} + 264 q^{45} - 48 q^{47} - 208 q^{49} + 400 q^{51} - 472 q^{53} - 208 q^{55} + 24 q^{57} - 576 q^{59} - 632 q^{63} - 32 q^{65} + 160 q^{69} - 160 q^{71} + 256 q^{73} + 1128 q^{75} - 208 q^{77} + 1000 q^{79} + 24 q^{81} + 312 q^{83} + 1240 q^{85} - 664 q^{87} + 720 q^{89} + 664 q^{91} - 432 q^{93} + 736 q^{95} - 288 q^{97} + 16 q^{99}+O(q^{100}) \) 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9 + 24 * q^11 - 48 * q^13 - 96 * q^15 - 40 * q^19 + 80 * q^21 + 48 * q^23 + 48 * q^25 + 224 * q^27 + 24 * q^29 + 88 * q^31 + 32 * q^35 - 176 * q^37 - 120 * q^39 - 352 * q^43 + 264 * q^45 - 48 * q^47 - 208 * q^49 + 400 * q^51 - 472 * q^53 - 208 * q^55 + 24 * q^57 - 576 * q^59 - 632 * q^63 - 32 * q^65 + 160 * q^69 - 160 * q^71 + 256 * q^73 + 1128 * q^75 - 208 * q^77 + 1000 * q^79 + 24 * q^81 + 312 * q^83 + 1240 * q^85 - 664 * q^87 + 720 * q^89 + 664 * q^91 - 432 * q^93 + 736 * q^95 - 288 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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