LMFDB - Embedded newform 171.3.p.d.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,3,Mod(46,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("171.46");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.65941252056$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.6967728.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 $ x^6 - x^5 + 8x^4 + 5x^3 + 50x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			46.1
Root			$0.0702177 - 0.121621i$ of defining polynomial
Character	$\chi$	$=$	171.46
Dual form			171.3.p.d.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99014 - 1.14901i) q^{2} +(0.640435 + 1.10927i) q^{4} +(2.91992 - 5.05745i) q^{5} +9.38186 q^{7} +6.24860i q^{8} +O(q^{10})$	\(q+(-1.99014 - 1.14901i) q^{2} +(0.640435 + 1.10927i) q^{4} +(2.91992 - 5.05745i) q^{5} +9.38186 q^{7} +6.24860i q^{8} +(-11.6221 + 6.71002i) q^{10} +4.66273 q^{11} +(-4.96056 + 2.86398i) q^{13} +(-18.6712 - 10.7798i) q^{14} +(9.74143 - 16.8726i) q^{16} +(9.49014 - 16.4374i) q^{17} +(-3.40020 - 18.6933i) q^{19} +7.48008 q^{20} +(-9.27949 - 5.35751i) q^{22} +(-6.41006 - 11.1025i) q^{23} +(-4.55188 - 7.88409i) q^{25} +13.1629 q^{26} +(6.00848 + 10.4070i) q^{28} +(-27.7677 + 16.0317i) q^{29} -26.9378i q^{31} +(-17.1278 + 9.88874i) q^{32} +(-37.7734 + 21.8085i) q^{34} +(27.3943 - 47.4483i) q^{35} -0.140762i q^{37} +(-14.7118 + 41.1091i) q^{38} +(31.6020 + 18.2454i) q^{40} +(-10.0967 - 5.82931i) q^{41} +(-16.3988 + 28.4036i) q^{43} +(2.98618 + 5.17221i) q^{44} +29.4608i q^{46} +(5.37062 + 9.30218i) q^{47} +39.0193 q^{49} +20.9206i q^{50} +(-6.35383 - 3.66839i) q^{52} +(30.7243 - 17.7387i) q^{53} +(13.6148 - 23.5815i) q^{55} +58.6235i q^{56} +73.6821 q^{58} +(76.1002 + 43.9365i) q^{59} +(45.7649 + 79.2672i) q^{61} +(-30.9517 + 53.6099i) q^{62} -32.4825 q^{64} +33.4504i q^{65} +(17.3404 - 10.0115i) q^{67} +24.3113 q^{68} +(-109.037 + 62.9525i) q^{70} +(15.8426 + 9.14674i) q^{71} +(28.7511 - 49.7984i) q^{73} +(-0.161737 + 0.280136i) q^{74} +(18.5582 - 15.7436i) q^{76} +43.7451 q^{77} +(-81.7713 - 47.2107i) q^{79} +(-56.8884 - 98.5336i) q^{80} +(13.3959 + 23.2023i) q^{82} -81.9397 q^{83} +(-55.4209 - 95.9918i) q^{85} +(65.2718 - 37.6847i) q^{86} +29.1355i q^{88} +(-17.3556 + 10.0202i) q^{89} +(-46.5392 + 26.8694i) q^{91} +(8.21046 - 14.2209i) q^{92} -24.6835i q^{94} +(-104.469 - 37.3866i) q^{95} +(117.468 + 67.8200i) q^{97} +(-77.6539 - 44.8335i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5}+O(q^{10}) $ 6 * q + 3 * q^2 + 5 * q^4 + 2 * q^5	$ 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5} - 60 q^{10} - 26 q^{11} + 30 q^{13} - 54 q^{14} + q^{16} + 42 q^{17} + 25 q^{19} - 108 q^{20} - 39 q^{22} - 8 q^{23} - 17 q^{25} + 148 q^{26} + 32 q^{28} + 12 q^{29} - 51 q^{32} - 6 q^{34} + 38 q^{35} + 14 q^{38} - 96 q^{40} - 63 q^{41} - 34 q^{43} + 69 q^{44} - 58 q^{47} + 18 q^{49} + 162 q^{52} + 12 q^{53} - 28 q^{55} + 172 q^{58} + 147 q^{59} + 58 q^{61} + 116 q^{62} + 166 q^{64} + 201 q^{67} + 84 q^{68} - 198 q^{70} + 102 q^{71} + 7 q^{73} - 174 q^{74} - 173 q^{76} + 376 q^{77} - 134 q^{80} - 145 q^{82} - 146 q^{83} - 90 q^{85} + 270 q^{86} + 72 q^{89} - 216 q^{91} - 72 q^{92} - 558 q^{95} + 21 q^{97} - 411 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 + 5 * q^4 + 2 * q^5 - 60 * q^10 - 26 * q^11 + 30 * q^13 - 54 * q^14 + q^16 + 42 * q^17 + 25 * q^19 - 108 * q^20 - 39 * q^22 - 8 * q^23 - 17 * q^25 + 148 * q^26 + 32 * q^28 + 12 * q^29 - 51 * q^32 - 6 * q^34 + 38 * q^35 + 14 * q^38 - 96 * q^40 - 63 * q^41 - 34 * q^43 + 69 * q^44 - 58 * q^47 + 18 * q^49 + 162 * q^52 + 12 * q^53 - 28 * q^55 + 172 * q^58 + 147 * q^59 + 58 * q^61 + 116 * q^62 + 166 * q^64 + 201 * q^67 + 84 * q^68 - 198 * q^70 + 102 * q^71 + 7 * q^73 - 174 * q^74 - 173 * q^76 + 376 * q^77 - 134 * q^80 - 145 * q^82 - 146 * q^83 - 90 * q^85 + 270 * q^86 + 72 * q^89 - 216 * q^91 - 72 * q^92 - 558 * q^95 + 21 * q^97 - 411 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.99014	−	1.14901i	−0.995069	−	0.574504i	−0.0882837	−	0.996095i	$-0.528138\pi$
$2$	−1.99014	−	1.14901i	−0.995069	−	0.574504i	−0.906786	+	0.421592i	$0.861472\pi$
$3$		0			0
$3$		0			0
$4$	0.640435	+	1.10927i	0.160109	+	0.277317i
$5$	2.91992	−	5.05745i	0.583984	−	1.01149i	−0.411017	−	0.911628i	$-0.634826\pi$
$5$	2.91992	−	5.05745i	0.583984	−	1.01149i	0.995001	−	0.0998627i	$-0.0318404\pi$
$6$		0			0
$7$	9.38186			1.34027			0.670133	−	0.742241i	$-0.266237\pi$
$7$	9.38186			1.34027			0.670133	+	0.742241i	$0.266237\pi$
$8$			6.24860i			0.781075i
$9$		0			0
$10$	−11.6221	+	6.71002i	−1.16221	+	0.671002i
$11$	4.66273			0.423885			0.211942	−	0.977282i	$-0.432021\pi$
$11$	4.66273			0.423885			0.211942	+	0.977282i	$0.432021\pi$
$12$		0			0
$13$	−4.96056	+	2.86398i	−0.381581	+	0.220306i	−0.678506	−	0.734595i	$-0.737372\pi$
$13$	−4.96056	+	2.86398i	−0.381581	+	0.220306i	0.296925	+	0.954901i	$0.404039\pi$
$14$	−18.6712	−	10.7798i	−1.33366	−	0.769988i
$15$		0			0
$16$	9.74143	−	16.8726i	0.608839	−	1.05454i
$17$	9.49014	−	16.4374i	0.558243	−	0.966906i	−0.439400	−	0.898292i	$-0.644809\pi$
$17$	9.49014	−	16.4374i	0.558243	−	0.966906i	0.997643	−	0.0686144i	$-0.0218578\pi$
$18$		0			0
$19$	−3.40020	−	18.6933i	−0.178958	−	0.983857i
$19$	−3.40020	−	18.6933i	−0.178958	−	0.983857i
$20$	7.48008			0.374004
$21$		0			0
$22$	−9.27949	−	5.35751i	−0.421795	−	0.243523i
$23$	−6.41006	−	11.1025i	−0.278698	−	0.482720i	0.692363	−	0.721549i	$-0.256570\pi$
$23$	−6.41006	−	11.1025i	−0.278698	−	0.482720i	−0.971061	+	0.238830i	$0.923236\pi$
$24$		0			0
$25$	−4.55188	−	7.88409i	−0.182075	−	0.315364i
$26$	13.1629			0.506266
$27$		0			0
$28$	6.00848	+	10.4070i	0.214588	+	0.371678i
$29$	−27.7677	+	16.0317i	−0.957506	+	0.552817i	−0.895405	−	0.445253i	$-0.853114\pi$
$29$	−27.7677	+	16.0317i	−0.957506	+	0.552817i	−0.0621017	+	0.998070i	$0.519780\pi$
$30$		0			0
$31$		−	26.9378i		−	0.868960i	−0.900681	−	0.434480i	$-0.856932\pi$
$31$		−	26.9378i		−	0.868960i	0.900681	−	0.434480i	$-0.143068\pi$
$32$	−17.1278	+	9.88874i	−0.535244	+	0.309023i
$33$		0			0
$34$	−37.7734	+	21.8085i	−1.11098	+	0.641426i
$35$	27.3943	−	47.4483i	0.782694	−	1.35567i
$36$		0			0
$37$		−	0.140762i		−	0.00380438i	−0.999998	−	0.00190219i	$-0.999395\pi$
$37$		−	0.140762i		−	0.00380438i	0.999998	−	0.00190219i	$-0.000605487\pi$
$38$	−14.7118	+	41.1091i	−0.387154	+	1.08182i
$39$		0			0
$40$	31.6020	+	18.2454i	0.790050	+	0.456135i
$41$	−10.0967	−	5.82931i	−0.246260	−	0.142178i	0.371790	−	0.928317i	$-0.378744\pi$
$41$	−10.0967	−	5.82931i	−0.246260	−	0.142178i	−0.618051	+	0.786138i	$0.712077\pi$
$42$		0			0
$43$	−16.3988	+	28.4036i	−0.381368	+	0.660548i	−0.991258	−	0.131938i	$-0.957880\pi$
$43$	−16.3988	+	28.4036i	−0.381368	+	0.660548i	0.609890	+	0.792486i	$0.291214\pi$
$44$	2.98618	+	5.17221i	0.0678677	+	0.117550i
$45$		0			0
$46$			29.4608i			0.640453i
$47$	5.37062	+	9.30218i	0.114268	+	0.197919i	0.917487	−	0.397766i	$-0.130214\pi$
$47$	5.37062	+	9.30218i	0.114268	+	0.197919i	−0.803219	+	0.595684i	$0.796881\pi$
$48$		0			0
$49$	39.0193			0.796313
$50$			20.9206i			0.418411i
$51$		0			0
$52$	−6.35383	−	3.66839i	−0.122189	−	0.0705459i
$53$	30.7243	−	17.7387i	0.579703	−	0.334692i	−0.181312	−	0.983426i	$-0.558034\pi$
$53$	30.7243	−	17.7387i	0.579703	−	0.334692i	0.761016	+	0.648734i	$0.224701\pi$
$54$		0			0
$55$	13.6148	−	23.5815i	0.247542	−	0.428755i
$56$			58.6235i			1.04685i
$57$		0			0
$58$	73.6821			1.27038
$59$	76.1002	+	43.9365i	1.28983	+	0.744686i	0.978625	−	0.205655i	$-0.0659324\pi$
$59$	76.1002	+	43.9365i	1.28983	+	0.744686i	0.311210	+	0.950341i	$0.399266\pi$
$60$		0			0
$61$	45.7649	+	79.2672i	0.750244	+	1.29946i	0.947704	+	0.319151i	$0.103398\pi$
$61$	45.7649	+	79.2672i	0.750244	+	1.29946i	−0.197460	+	0.980311i	$0.563269\pi$
$62$	−30.9517	+	53.6099i	−0.499221	+	0.864676i
$63$		0			0
$64$	−32.4825			−0.507539
$65$			33.4504i			0.514621i
$66$		0			0
$67$	17.3404	−	10.0115i	0.258812	−	0.149425i	−0.364981	−	0.931015i	$-0.618924\pi$
$67$	17.3404	−	10.0115i	0.258812	−	0.149425i	0.623792	+	0.781590i	$0.285591\pi$
$68$	24.3113			0.357519
$69$		0			0
$70$	−109.037	+	62.9525i	−1.55767	+	0.899321i
$71$	15.8426	+	9.14674i	0.223135	+	0.128827i	0.607401	−	0.794395i	$-0.292212\pi$
$71$	15.8426	+	9.14674i	0.223135	+	0.128827i	−0.384266	+	0.923222i	$0.625545\pi$
$72$		0			0
$73$	28.7511	−	49.7984i	0.393851	−	0.682169i	−0.599103	−	0.800672i	$-0.704476\pi$
$73$	28.7511	−	49.7984i	0.393851	−	0.682169i	0.992954	+	0.118503i	$0.0378094\pi$
$74$	−0.161737	+	0.280136i	−0.00218563	+	0.00378563i
$75$		0			0
$76$	18.5582	−	15.7436i	0.244187	−	0.207152i
$77$	43.7451			0.568118
$78$		0			0
$79$	−81.7713	−	47.2107i	−1.03508	−	0.597603i	−0.116644	−	0.993174i	$-0.537214\pi$
$79$	−81.7713	−	47.2107i	−1.03508	−	0.597603i	−0.918436	+	0.395571i	$0.870547\pi$
$80$	−56.8884	−	98.5336i	−0.711105	−	1.23167i
$81$		0			0
$82$	13.3959	+	23.2023i	0.163364	+	0.282955i
$83$	−81.9397			−0.987226			−0.493613	−	0.869682i	$-0.664324\pi$
$83$	−81.9397			−0.987226			−0.493613	+	0.869682i	$0.664324\pi$
$84$		0			0
$85$	−55.4209	−	95.9918i	−0.652011	−	1.12932i
$86$	65.2718	−	37.6847i	0.758975	−	0.438194i
$87$		0			0
$88$			29.1355i			0.331086i
$89$	−17.3556	+	10.0202i	−0.195006	+	0.112587i	−0.594324	−	0.804226i	$-0.702580\pi$
$89$	−17.3556	+	10.0202i	−0.195006	+	0.112587i	0.399318	+	0.916813i	$0.369247\pi$
$90$		0			0
$91$	−46.5392	+	26.8694i	−0.511420	+	0.295269i
$92$	8.21046	−	14.2209i	0.0892441	−	0.154575i
$93$		0			0
$94$		−	24.6835i		−	0.262591i
$95$	−104.469	−	37.3866i	−1.09967	−	0.393543i
$96$		0			0
$97$	117.468	+	67.8200i	1.21101	+	0.699175i	0.962979	−	0.269577i	$-0.0868840\pi$
$97$	117.468	+	67.8200i	1.21101	+	0.699175i	0.248028	+	0.968753i	$0.420217\pi$
$98$	−77.6539	−	44.8335i	−0.792387	−	0.457485i
$99$		0			0
$100$	5.83037	−	10.0985i	0.0583037	−	0.100985i
$101$	51.2699	+	88.8020i	0.507622	+	0.879228i	0.999961	+	0.00882416i	$0.00280885\pi$
$101$	51.2699	+	88.8020i	0.507622	+	0.879228i	−0.492339	+	0.870404i	$0.663858\pi$
$102$		0			0
$103$		−	38.8999i		−	0.377669i	−0.982009	−	0.188835i	$-0.939529\pi$
$103$		−	38.8999i		−	0.377669i	0.982009	−	0.188835i	$-0.0604710\pi$
$104$	−17.8959	−	30.9965i	−0.172075	−	0.298043i
$105$		0			0
$106$	−81.5274			−0.769127
$107$		−	152.206i		−	1.42249i	−0.702947	−	0.711243i	$-0.748133\pi$
$107$		−	152.206i		−	1.42249i	0.702947	−	0.711243i	$-0.251867\pi$
$108$		0			0
$109$	140.866	+	81.3288i	1.29234	+	0.746136i	0.979069	−	0.203527i	$-0.0652403\pi$
$109$	140.866	+	81.3288i	1.29234	+	0.746136i	0.313275	+	0.949662i	$0.398574\pi$
$110$	−54.1907	+	31.2870i	−0.492643	+	0.284428i
$111$		0			0
$112$	91.3927	−	158.297i	0.816006	−	1.41336i
$113$			5.01487i			0.0443793i	0.999754	+	0.0221897i	$0.00706377\pi$
$113$			5.01487i			0.0443793i	−0.999754	+	0.0221897i	$0.992936\pi$
$114$		0			0
$115$	−74.8675			−0.651022
$116$	−35.5668	−	20.5345i	−0.306610	−	0.177022i
$117$		0			0
$118$	−100.967	−	174.879i	−0.855650	−	1.48203i
$119$	89.0352	−	154.213i	0.748195	−	1.29591i
$120$		0			0
$121$	−99.2589			−0.820322
$122$		−	210.337i		−	1.72407i
$123$		0			0
$124$	29.8812	−	17.2519i	0.240977	−	0.139128i
$125$	92.8315			0.742652
$126$		0			0
$127$	−145.625	+	84.0766i	−1.14665	+	0.662020i	−0.948069	−	0.318064i	$-0.896967\pi$
$127$	−145.625	+	84.0766i	−1.14665	+	0.662020i	−0.198583	+	0.980084i	$0.563634\pi$
$128$	133.156	+	76.8776i	1.04028	+	0.600606i
$129$		0			0
$130$	38.4347	−	66.5709i	0.295652	−	0.512084i
$131$	−108.056	+	187.159i	−0.824857	+	1.42869i	0.0771714	+	0.997018i	$0.475411\pi$
$131$	−108.056	+	187.159i	−0.824857	+	1.42869i	−0.902028	+	0.431677i	$0.857922\pi$
$132$		0			0
$133$	−31.9002	−	175.378i	−0.239851	−	1.31863i
$134$	−46.0131			−0.343381
$135$		0			0
$136$	102.711	+	59.3001i	0.755226	+	0.436030i
$137$	−6.48693	−	11.2357i	−0.0473499	−	0.0820123i	0.841379	−	0.540445i	$-0.181744\pi$
$137$	−6.48693	−	11.2357i	−0.0473499	−	0.0820123i	−0.888729	+	0.458433i	$0.848411\pi$
$138$		0			0
$139$	108.763	+	188.383i	0.782467	+	1.35527i	0.930500	+	0.366291i	$0.119372\pi$
$139$	108.763	+	188.383i	0.782467	+	1.35527i	−0.148033	+	0.988982i	$0.547294\pi$
$140$	70.1771			0.501265
$141$		0			0
$142$	−21.0193	−	36.4066i	−0.148023	−	0.256384i
$143$	−23.1297	+	13.3540i	−0.161746	+	0.0933844i
$144$		0			0
$145$			187.245i			1.29134i
$146$	−114.437	+	66.0704i	−0.783817	+	0.452537i
$147$		0			0
$148$	0.156143	−	0.0901491i	0.00105502	−	0.000609115i
$149$	−5.20982	+	9.02368i	−0.0349653	+	0.0605616i	−0.882978	−	0.469413i	$-0.844465\pi$
$149$	−5.20982	+	9.02368i	−0.0349653	+	0.0605616i	0.848013	+	0.529975i	$0.177799\pi$
$150$		0			0
$151$			143.558i			0.950718i	0.879792	+	0.475359i	$0.157682\pi$
$151$			143.558i			0.950718i	−0.879792	+	0.475359i	$0.842318\pi$
$152$	116.807	−	21.2465i	0.768466	−	0.139779i
$153$		0			0
$154$	−87.0589	−	50.2635i	−0.565317	−	0.326386i
$155$	−136.236	−	78.6562i	−0.878945	−	0.507459i
$156$		0			0
$157$	135.429	−	234.570i	0.862604	−	1.49407i	−0.00680261	−	0.999977i	$-0.502165\pi$
$157$	135.429	−	234.570i	0.862604	−	1.49407i	0.869407	−	0.494097i	$-0.164501\pi$
$158$	108.491	+	187.912i	0.686650	+	1.18931i
$159$		0			0
$160$			115.497i			0.721859i
$161$	−60.1383	−	104.163i	−0.373530	−	0.646973i
$162$		0			0
$163$	56.8017			0.348476			0.174238	−	0.984704i	$-0.444254\pi$
$163$	56.8017			0.348476			0.174238	+	0.984704i	$0.444254\pi$
$164$		−	14.9332i		−	0.0910561i
$165$		0			0
$166$	163.071	+	94.1493i	0.982358	+	0.567165i
$167$	29.2718	−	16.9001i	0.175280	−	0.101198i	−0.409793	−	0.912179i	$-0.634399\pi$
$167$	29.2718	−	16.9001i	0.175280	−	0.101198i	0.585073	+	0.810980i	$0.301066\pi$
$168$		0			0
$169$	−68.0953	+	117.944i	−0.402931	+	0.697896i
$170$			254.716i			1.49833i
$171$		0			0
$172$	−42.0095			−0.244241
$173$	59.2823	+	34.2267i	0.342672	+	0.197842i	0.661453	−	0.749986i	$-0.269940\pi$
$173$	59.2823	+	34.2267i	0.342672	+	0.197842i	−0.318781	+	0.947828i	$0.603273\pi$
$174$		0			0
$175$	−42.7051	−	73.9674i	−0.244029	−	0.422671i
$176$	45.4217	−	78.6726i	0.258078	−	0.447004i
$177$		0			0
$178$	46.0533			0.258727
$179$			226.861i			1.26738i	0.773587	+	0.633691i	$0.218461\pi$
$179$			226.861i			1.26738i	−0.773587	+	0.633691i	$0.781539\pi$
$180$		0			0
$181$	−184.408	+	106.468i	−1.01883	+	0.588222i	−0.913765	−	0.406243i	$-0.866839\pi$
$181$	−184.408	+	106.468i	−1.01883	+	0.588222i	−0.105066	+	0.994465i	$0.533505\pi$
$182$	123.493			0.678532
$183$		0			0
$184$	69.3754	−	40.0539i	0.377040	−	0.217684i
$185$	−0.711898	−	0.411015i	−0.00384810	−	0.00222170i
$186$		0			0
$187$	44.2500	−	76.6432i	0.236631	−	0.409857i
$188$	−6.87906	+	11.9149i	−0.0365908	+	0.0633771i
$189$		0			0
$190$	164.950	+	194.440i	0.868157	+	1.02337i
$191$	−34.8860			−0.182649			−0.0913247	−	0.995821i	$-0.529110\pi$
$191$	−34.8860			−0.182649			−0.0913247	+	0.995821i	$0.529110\pi$
$192$		0			0
$193$	32.2140	+	18.5988i	0.166912	+	0.0963667i	0.581129	−	0.813811i	$-0.302611\pi$
$193$	32.2140	+	18.5988i	0.166912	+	0.0963667i	−0.414217	+	0.910178i	$0.635945\pi$
$194$	−155.851	−	269.942i	−0.803358	−	1.39146i
$195$		0			0
$196$	24.9894	+	43.2828i	0.127497	+	0.220831i
$197$	314.378			1.59583			0.797914	−	0.602772i	$-0.205937\pi$
$197$	314.378			1.59583			0.797914	+	0.602772i	$0.205937\pi$
$198$		0			0
$199$	−153.223	−	265.390i	−0.769965	−	1.33362i	−0.937581	−	0.347766i	$-0.886940\pi$
$199$	−153.223	−	265.390i	−0.769965	−	1.33362i	0.167617	−	0.985852i	$-0.446393\pi$
$200$	49.2645	−	28.4429i	0.246323	−	0.142214i
$201$		0			0
$202$		−	235.638i		−	1.16652i
$203$	−260.513	+	150.407i	−1.28331	+	0.740921i
$204$		0			0
$205$	−58.9630	+	34.0423i	−0.287624	+	0.166060i
$206$	−44.6963	+	77.4163i	−0.216972	+	0.375807i
$207$		0			0
$208$			111.597i			0.536524i
$209$	−15.8542	−	87.1618i	−0.0758575	−	0.417042i
$210$		0			0
$211$	63.4973	+	36.6602i	0.300935	+	0.173745i	0.642863	−	0.765981i	$-0.277747\pi$
$211$	63.4973	+	36.6602i	0.300935	+	0.173745i	−0.341928	+	0.939726i	$0.611080\pi$
$212$	39.3538	+	22.7209i	0.185631	+	0.107174i
$213$		0			0
$214$	−174.886	+	302.911i	−0.817223	+	1.41547i
$215$	95.7665	+	165.872i	0.445426	+	0.771500i
$216$		0			0
$217$		−	252.726i		−	1.16464i
$218$	−186.895	−	323.711i	−0.857315	−	1.48491i
$219$		0			0
$220$	34.8776			0.158535
$221$			108.718i			0.491938i
$222$		0			0
$223$	18.0166	+	10.4019i	0.0807918	+	0.0466452i	0.539852	−	0.841760i	$-0.318480\pi$
$223$	18.0166	+	10.4019i	0.0807918	+	0.0466452i	−0.459060	+	0.888405i	$0.651814\pi$
$224$	−160.691	+	92.7748i	−0.717369	+	0.414173i
$225$		0			0
$226$	5.76212	−	9.98028i	0.0254961	−	0.0441605i
$227$		−	97.0130i		−	0.427370i	−0.976903	−	0.213685i	$-0.931453\pi$
$227$		−	97.0130i		−	0.427370i	0.976903	−	0.213685i	$-0.0685466\pi$
$228$		0			0
$229$	259.958			1.13519			0.567595	−	0.823308i	$-0.307874\pi$
$229$	259.958			1.13519			0.567595	+	0.823308i	$0.307874\pi$
$230$	148.997	+	86.0233i	0.647812	+	0.374014i
$231$		0			0
$232$	−100.176	−	173.509i	−0.431791	−	0.747884i
$233$	−184.911	+	320.275i	−0.793610	+	1.37457i	0.130109	+	0.991500i	$0.458467\pi$
$233$	−184.911	+	320.275i	−0.793610	+	1.37457i	−0.923718	+	0.383072i	$0.874866\pi$
$234$		0			0
$235$	62.7271			0.266924
$236$			112.554i			0.476923i
$237$		0			0
$238$	−354.385	+	204.604i	−1.48901	+	0.859681i
$239$	−311.812			−1.30465			−0.652327	−	0.757938i	$-0.726207\pi$
$239$	−311.812			−1.30465			−0.652327	+	0.757938i	$0.726207\pi$
$240$		0			0
$241$	−295.100	+	170.376i	−1.22448	+	0.706954i	−0.965870	−	0.259027i	$-0.916598\pi$
$241$	−295.100	+	170.376i	−1.22448	+	0.706954i	−0.258611	+	0.965982i	$0.583265\pi$
$242$	197.539	+	114.049i	0.816277	+	0.471278i
$243$		0			0
$244$	−58.6189	+	101.531i	−0.240242	+	0.416111i
$245$	113.933	−	197.338i	0.465034	−	0.805463i
$246$		0			0
$247$	70.4040	+	82.9910i	0.285037	+	0.335996i
$248$	168.323			0.678723
$249$		0			0
$250$	−184.748	−	106.664i	−0.738991	−	0.426656i
$251$	−61.1331	−	105.886i	−0.243558	−	0.421855i	0.718167	−	0.695871i	$-0.244981\pi$
$251$	−61.1331	−	105.886i	−0.243558	−	0.421855i	−0.961725	+	0.274015i	$0.911648\pi$
$252$		0			0
$253$	−29.8884	−	51.7682i	−0.118136	−	0.204617i
$254$	386.418			1.52133
$255$		0			0
$256$	−111.701	−	193.471i	−0.436331	−	0.755748i
$257$	129.449	−	74.7375i	0.503693	−	0.290807i	−0.226544	−	0.974001i	$-0.572743\pi$
$257$	129.449	−	74.7375i	0.503693	−	0.290807i	0.730237	+	0.683193i	$0.239409\pi$
$258$		0			0
$259$		−	1.32061i		−	0.00509889i
$260$	−37.1054	+	21.4228i	−0.142713	+	0.0823954i
$261$		0			0
$262$	430.094	−	248.315i	1.64158	−	0.947767i
$263$	−36.9434	+	63.9878i	−0.140469	+	0.243300i	−0.927673	−	0.373393i	$-0.878194\pi$
$263$	−36.9434	+	63.9878i	−0.140469	+	0.243300i	0.787204	+	0.616692i	$0.211528\pi$
$264$		0			0
$265$		−	207.182i		−	0.781819i
$266$	−138.024	+	385.680i	−0.518889	+	1.44992i
$267$		0			0
$268$	22.2108	+	12.8234i	0.0828762	+	0.0478486i
$269$	37.9102	+	21.8875i	0.140930	+	0.0813661i	0.568807	−	0.822471i	$-0.307405\pi$
$269$	37.9102	+	21.8875i	0.140930	+	0.0813661i	−0.427877	+	0.903837i	$0.640738\pi$
$270$		0			0
$271$	15.8330	−	27.4235i	0.0584242	−	0.101194i	−0.835334	−	0.549743i	$-0.814726\pi$
$271$	15.8330	−	27.4235i	0.0584242	−	0.101194i	0.893758	+	0.448549i	$0.148059\pi$
$272$	−184.895	−	320.248i	−0.679761	−	1.17738i
$273$		0			0
$274$			29.8141i			0.108811i
$275$	−21.2242	−	36.7614i	−0.0771789	−	0.133678i
$276$		0			0
$277$	323.770			1.16884			0.584422	−	0.811450i	$-0.301321\pi$
$277$	323.770			1.16884			0.584422	+	0.811450i	$0.301321\pi$
$278$		−	499.878i		−	1.79812i
$279$		0			0
$280$	296.485	+	171.176i	1.05888	+	0.611343i
$281$	23.7453	−	13.7094i	0.0845029	−	0.0487878i	−0.457153	−	0.889388i	$-0.651131\pi$
$281$	23.7453	−	13.7094i	0.0845029	−	0.0487878i	0.541656	+	0.840600i	$0.317798\pi$
$282$		0			0
$283$	−108.587	+	188.078i	−0.383699	+	0.664586i	−0.991588	−	0.129436i	$-0.958683\pi$
$283$	−108.587	+	188.078i	−0.383699	+	0.664586i	0.607889	+	0.794022i	$0.292017\pi$
$284$			23.4316i			0.0825055i
$285$		0			0
$286$	61.3752			0.214599
$287$	−94.7256	−	54.6898i	−0.330054	−	0.190557i
$288$		0			0
$289$	−35.6255	−	61.7051i	−0.123272	−	0.213513i
$290$	215.146	−	372.644i	0.741882	−	1.28498i
$291$		0			0
$292$	73.6529			0.252236
$293$		−	51.9721i		−	0.177379i	−0.996059	−	0.0886896i	$-0.971732\pi$
$293$		−	51.9721i		−	0.177379i	0.996059	−	0.0886896i	$-0.0282679\pi$
$294$		0			0
$295$	444.413	−	256.582i	1.50649	−	0.869770i
$296$	0.879566			0.00297151
$297$		0			0
$298$	20.7365	−	11.9723i	0.0695857	−	0.0401753i
$299$	63.5949	+	36.7165i	0.212692	+	0.122798i
$300$		0			0
$301$	−153.851	+	266.478i	−0.511134	+	0.885311i
$302$	164.950	−	285.701i	0.546191	−	0.946031i
$303$		0			0
$304$	−348.528	−	124.729i	−1.14647	−	0.410292i
$305$	534.520			1.75252
$306$		0			0
$307$	−325.035	−	187.659i	−1.05875	−	0.611268i	−0.133662	−	0.991027i	$-0.542674\pi$
$307$	−325.035	−	187.659i	−1.05875	−	0.611268i	−0.925086	+	0.379759i	$0.876007\pi$
$308$	28.0159	+	48.5250i	0.0909608	+	0.157549i
$309$		0			0
$310$	180.753	+	313.073i	0.583074	+	1.00991i
$311$	−93.0136			−0.299079			−0.149539	−	0.988756i	$-0.547779\pi$
$311$	−93.0136			−0.299079			−0.149539	+	0.988756i	$0.547779\pi$
$312$		0			0
$313$	213.267	+	369.390i	0.681365	+	1.18016i	0.974564	+	0.224108i	$0.0719467\pi$
$313$	213.267	+	369.390i	0.681365	+	1.18016i	−0.293199	+	0.956051i	$0.594720\pi$
$314$	−539.044	+	311.217i	−1.71670	+	0.991138i
$315$		0			0
$316$		−	120.941i		−	0.382726i
$317$	−515.861	+	297.833i	−1.62732	+	0.939535i	−0.642434	+	0.766341i	$0.722075\pi$
$317$	−515.861	+	297.833i	−1.62732	+	0.939535i	−0.984888	+	0.173194i	$0.944591\pi$
$318$		0			0
$319$	−129.473	+	74.7514i	−0.405872	+	0.234331i
$320$	−94.8462	+	164.279i	−0.296394	+	0.513370i
$321$		0			0
$322$			276.397i			0.858377i
$323$	−339.537	−	121.511i	−1.05120	−	0.376196i
$324$		0			0
$325$	45.1597	+	26.0730i	0.138953	+	0.0802245i
$326$	−113.043	−	65.2655i	−0.346758	−	0.200201i
$327$		0			0
$328$	36.4250	−	63.0900i	0.111052	−	0.192348i
$329$	50.3864	+	87.2718i	0.153150	+	0.265264i
$330$		0			0
$331$			30.9531i			0.0935138i	0.998906	+	0.0467569i	$0.0148886\pi$
$331$			30.9531i			0.0935138i	−0.998906	+	0.0467569i	$0.985111\pi$
$332$	−52.4771	−	90.8930i	−0.158064	−	0.273774i
$333$		0			0
$334$	−77.6734			−0.232555
$335$		−	116.931i		−	0.349048i
$336$		0			0
$337$	−354.724	−	204.800i	−1.05259	−	0.607716i	−0.129220	−	0.991616i	$-0.541247\pi$
$337$	−354.724	−	204.800i	−1.05259	−	0.607716i	−0.923374	+	0.383900i	$0.874581\pi$
$338$	271.038	−	156.484i	0.801888	−	0.462970i
$339$		0			0
$340$	70.9870	−	122.953i	0.208785	−	0.361627i
$341$		−	125.604i		−	0.368339i
$342$		0			0
$343$	−93.6372			−0.272995
$344$	−177.483	−	102.470i	−0.515938	−	0.297877i
$345$		0			0
$346$	−78.6534	−	136.232i	−0.227322	−	0.393733i
$347$	262.970	−	455.477i	0.757839	−	1.31262i	−0.186112	−	0.982529i	$-0.559589\pi$
$347$	262.970	−	455.477i	0.757839	−	1.31262i	0.943951	−	0.330087i	$-0.107078\pi$
$348$		0			0
$349$	287.557			0.823946			0.411973	−	0.911196i	$-0.364840\pi$
$349$	287.557			0.823946			0.411973	+	0.911196i	$0.364840\pi$
$350$			196.274i			0.560783i
$351$		0			0
$352$	−79.8624	+	46.1086i	−0.226882	+	0.130990i
$353$	18.5432			0.0525303			0.0262651	−	0.999655i	$-0.491639\pi$
$353$	18.5432			0.0525303			0.0262651	+	0.999655i	$0.491639\pi$
$354$		0			0
$355$	92.5184	−	53.4155i	0.260615	−	0.150466i
$356$	−22.2303	−	12.8346i	−0.0624445	−	0.0360524i
$357$		0			0
$358$	260.665	−	451.485i	0.728115	−	1.26113i
$359$	−47.7457	+	82.6979i	−0.132996	+	0.230356i	−0.924830	−	0.380380i	$-0.875793\pi$
$359$	−47.7457	+	82.6979i	−0.132996	+	0.230356i	0.791834	+	0.610736i	$0.209127\pi$
$360$		0			0
$361$	−337.877	+	127.122i	−0.935948	+	0.352138i
$362$	489.331			1.35174
$363$		0			0
$364$	−59.6108	−	34.4163i	−0.163766	−	0.0945502i
$365$	−167.902	−	290.815i	−0.460005	−	0.796752i
$366$		0			0
$367$	−249.565	−	432.259i	−0.680013	−	1.17782i	−0.974976	−	0.222309i	$-0.928641\pi$
$367$	−249.565	−	432.259i	−0.680013	−	1.17782i	0.294963	−	0.955509i	$-0.404693\pi$
$368$	−249.773			−0.678730
$369$		0			0
$370$	0.944517	+	1.63595i	0.00255275	+	0.00442149i
$371$	288.251	−	166.422i	0.776957	−	0.448576i
$372$		0			0
$373$		−	80.0714i		−	0.214669i	−0.994223	−	0.107334i	$-0.965768\pi$
$373$		−	80.0714i		−	0.214669i	0.994223	−	0.107334i	$-0.0342315\pi$
$374$	−176.127	+	101.687i	−0.470928	+	0.271891i
$375$		0			0
$376$	−58.1256	+	33.5588i	−0.154589	+	0.0892522i
$377$	91.8288	−	159.052i	0.243578	−	0.421889i
$378$		0			0
$379$		−	338.780i		−	0.893880i	−0.894564	−	0.446940i	$-0.852514\pi$
$379$		−	338.780i		−	0.893880i	0.894564	−	0.446940i	$-0.147486\pi$
$380$	−25.4338	−	139.827i	−0.0669310	−	0.367967i
$381$		0			0
$382$	69.4281	+	40.0843i	0.181749	+	0.104933i
$383$	95.7329	+	55.2714i	0.249955	+	0.144312i	0.619744	−	0.784804i	$-0.287237\pi$
$383$	95.7329	+	55.2714i	0.249955	+	0.144312i	−0.369789	+	0.929116i	$0.620570\pi$
$384$		0			0
$385$	127.732	−	221.239i	0.331772	−	0.574646i
$386$	−42.7403	−	74.0283i	−0.110726	−	0.191783i
$387$		0			0
$388$			173.737i			0.447777i
$389$	310.450	+	537.715i	0.798072	+	1.38230i	0.920870	+	0.389869i	$0.127480\pi$
$389$	310.450	+	537.715i	0.798072	+	1.38230i	−0.122799	+	0.992432i	$0.539187\pi$
$390$		0			0
$391$	−243.329			−0.622326
$392$			243.816i			0.621980i
$393$		0			0
$394$	−625.656	−	361.223i	−1.58796	−	0.916809i
$395$	−477.531	+	275.703i	−1.20894	+	0.697982i
$396$		0			0
$397$	−235.738	+	408.309i	−0.593797	+	1.02849i	0.399918	+	0.916551i	$0.369039\pi$
$397$	−235.738	+	408.309i	−0.593797	+	1.02849i	−0.993715	+	0.111936i	$0.964295\pi$
$398$			704.217i			1.76939i
$399$		0			0
$400$	−177.367			−0.443418
$401$	194.968	+	112.565i	0.486204	+	0.280710i	0.722998	−	0.690850i	$-0.242763\pi$
$401$	194.968	+	112.565i	0.486204	+	0.280710i	−0.236794	+	0.971560i	$0.576097\pi$
$402$		0			0
$403$	77.1492	+	133.626i	0.191437	+	0.331579i
$404$	−65.6701	+	113.744i	−0.162550	+	0.281544i
$405$		0			0
$406$	691.275			1.70265
$407$		−	0.656336i		−	0.00161262i
$408$		0			0
$409$	192.756	−	111.288i	0.471286	−	0.272097i	−0.245492	−	0.969399i	$-0.578949\pi$
$409$	192.756	−	111.288i	0.471286	−	0.272097i	0.716778	+	0.697302i	$0.245616\pi$
$410$	156.459			0.381608
$411$		0			0
$412$	43.1504	−	24.9129i	0.104734	−	0.0604682i
$413$	713.962	+	412.206i	1.72872	+	0.998078i
$414$		0			0
$415$	−239.258	+	414.406i	−0.576524	+	0.998569i
$416$	56.6423	−	98.1073i	0.136159	−	0.235835i
$417$		0			0
$418$	−68.5974	+	191.681i	−0.164109	+	0.458566i
$419$	−306.377			−0.731209			−0.365605	−	0.930770i	$-0.619138\pi$
$419$	−306.377			−0.731209			−0.365605	+	0.930770i	$0.619138\pi$
$420$		0			0
$421$	331.533	+	191.411i	0.787490	+	0.454658i	0.839078	−	0.544011i	$-0.183095\pi$
$421$	331.533	+	191.411i	0.787490	+	0.454658i	−0.0515881	+	0.998668i	$0.516428\pi$
$422$	−84.2456	−	145.918i	−0.199634	−	0.345776i
$423$		0			0
$424$	110.842	+	191.984i	0.261419	+	0.452792i
$425$	−172.792			−0.406569
$426$		0			0
$427$	429.360	+	743.674i	1.00553	+	1.74162i
$428$	168.837	−	97.4781i	0.394479	−	0.227752i
$429$		0			0
$430$		−	440.146i		−	1.02359i
$431$	232.981	−	134.512i	0.540560	−	0.312092i	−0.204746	−	0.978815i	$-0.565637\pi$
$431$	232.981	−	134.512i	0.540560	−	0.312092i	0.745306	+	0.666723i	$0.232303\pi$
$432$		0			0
$433$	−267.809	+	154.620i	−0.618497	+	0.357089i	−0.776284	−	0.630384i	$-0.782897\pi$
$433$	−267.809	+	154.620i	−0.618497	+	0.357089i	0.157787	+	0.987473i	$0.449564\pi$
$434$	−290.384	+	502.961i	−0.669089	+	1.15890i
$435$		0			0
$436$			208.343i			0.477852i
$437$	−185.748	+	157.576i	−0.425052	+	0.360586i
$438$		0			0
$439$	360.006	+	207.850i	0.820059	+	0.473462i	0.850437	−	0.526077i	$-0.176338\pi$
$439$	360.006	+	207.850i	0.820059	+	0.473462i	−0.0303775	+	0.999538i	$0.509671\pi$
$440$	147.352	+	85.0735i	0.334890	+	0.193349i
$441$		0			0
$442$	124.918	−	216.364i	0.282620	−	0.489512i
$443$	−174.507	−	302.256i	−0.393922	−	0.682292i	0.599041	−	0.800718i	$-0.295549\pi$
$443$	−174.507	−	302.256i	−0.393922	−	0.682292i	−0.992963	+	0.118426i	$0.962215\pi$
$444$		0			0
$445$			117.033i			0.262996i
$446$	−23.9037	−	41.4023i	−0.0535956	−	0.0928304i
$447$		0			0
$448$	−304.746			−0.680237
$449$		−	631.772i		−	1.40707i	−0.710663	−	0.703533i	$-0.751605\pi$
$449$		−	631.772i		−	1.40707i	0.710663	−	0.703533i	$-0.248395\pi$
$450$		0			0
$451$	−47.0781	−	27.1805i	−0.104386	−	0.0602673i
$452$	−5.56282	+	3.21170i	−0.0123071	+	0.00710553i
$453$		0			0
$454$	−111.469	+	193.069i	−0.245526	+	0.425263i
$455$			313.827i			0.689729i
$456$		0			0
$457$	539.986			1.18159			0.590794	−	0.806822i	$-0.298815\pi$
$457$	539.986			1.18159			0.590794	+	0.806822i	$0.298815\pi$
$458$	−517.353	−	298.694i	−1.12959	−	0.652170i
$459$		0			0
$460$	−47.9478	−	83.0480i	−0.104234	−	0.180539i
$461$	−84.8213	+	146.915i	−0.183994	+	0.318687i	−0.943237	−	0.332120i	$-0.892236\pi$
$461$	−84.8213	+	146.915i	−0.183994	+	0.318687i	0.759243	+	0.650807i	$0.225569\pi$
$462$		0			0
$463$	−462.335			−0.998564			−0.499282	−	0.866440i	$-0.666403\pi$
$463$	−462.335			−0.998564			−0.499282	+	0.866440i	$0.666403\pi$
$464$			624.686i			1.34631i
$465$		0			0
$466$	735.997	−	424.928i	1.57939	−	0.911863i
$467$	−2.60465			−0.00557741			−0.00278870	−	0.999996i	$-0.500888\pi$
$467$	−2.60465			−0.00557741			−0.00278870	+	0.999996i	$0.500888\pi$
$468$		0			0
$469$	162.685	−	93.9264i	0.346877	−	0.200269i
$470$	−124.836	−	72.0739i	−0.265608	−	0.153349i
$471$		0			0
$472$	−274.542	+	475.520i	−0.581656	+	1.00746i
$473$	−76.4633	+	132.438i	−0.161656	+	0.279996i
$474$		0			0
$475$	−131.902	+	111.897i	−0.277689	+	0.235573i
$476$	228.085			0.479170
$477$		0			0
$478$	620.550	+	358.275i	1.29822	+	0.749528i
$479$	196.128	+	339.703i	0.409452	+	0.709192i	0.994828	−	0.101570i	$-0.0323866\pi$
$479$	196.128	+	339.703i	0.409452	+	0.709192i	−0.585376	+	0.810762i	$0.699053\pi$
$480$		0			0
$481$	0.403140	+	0.698259i	0.000838129	+	0.00145168i
$482$	783.053			1.62459
$483$		0			0
$484$	−63.5689	−	110.105i	−0.131341	−	0.227489i
$485$	685.993	−	396.058i	1.41442	−	0.816615i
$486$		0			0
$487$		−	93.4189i		−	0.191825i	−0.995390	−	0.0959126i	$-0.969423\pi$
$487$		−	93.4189i		−	0.191825i	0.995390	−	0.0959126i	$-0.0305769\pi$
$488$	−495.309	+	285.967i	−1.01498	+	0.585997i
$489$		0			0
$490$	−453.487	+	261.821i	−0.925483	+	0.534328i
$491$	218.271	−	378.057i	0.444544	−	0.769973i	−0.553476	−	0.832865i	$-0.686699\pi$
$491$	218.271	−	378.057i	0.444544	−	0.769973i	0.998020	+	0.0628921i	$0.0200324\pi$
$492$		0			0
$493$			608.571i			1.23442i
$494$	−44.7566	−	246.058i	−0.0906004	−	0.498094i
$495$		0			0
$496$	−454.511	−	262.412i	−0.916354	−	0.529057i
$497$	148.633	+	85.8134i	0.299061	+	0.172663i
$498$		0			0
$499$	35.4225	−	61.3535i	0.0709869	−	0.122953i	−0.828347	−	0.560215i	$-0.810718\pi$
$499$	35.4225	−	61.3535i	0.0709869	−	0.122953i	0.899334	+	0.437262i	$0.144052\pi$
$500$	59.4526	+	102.975i	0.118905	+	0.205950i
$501$		0			0
$502$			280.970i			0.559700i
$503$	268.299	+	464.708i	0.533398	+	0.923872i	0.999239	+	0.0390040i	$0.0124185\pi$
$503$	268.299	+	464.708i	0.533398	+	0.923872i	−0.465841	+	0.884868i	$0.654248\pi$
$504$		0			0
$505$	598.816			1.18577
$506$			137.368i			0.271478i
$507$		0			0
$508$	−186.527	−	107.691i	−0.367178	−	0.211991i
$509$	−577.348	+	333.332i	−1.13428	+	0.654876i	−0.945007	−	0.327049i	$-0.893946\pi$
$509$	−577.348	+	333.332i	−1.13428	+	0.654876i	−0.189271	+	0.981925i	$0.560612\pi$
$510$		0			0
$511$	269.739	−	467.201i	0.527865	−	0.914288i
$512$		−	101.640i		−	0.198516i
$513$		0			0
$514$	−343.496			−0.668280
$515$	−196.735	−	113.585i	−0.382009	−	0.220553i
$516$		0			0
$517$	25.0417	+	43.3736i	0.0484366	+	0.0838947i
$518$	−1.51739	+	2.62820i	−0.00292933	+	0.00507375i
$519$		0			0
$520$	−209.018			−0.401957
$521$		−	928.678i		−	1.78249i	−0.453521	−	0.891245i	$-0.649832\pi$
$521$		−	928.678i		−	1.78249i	0.453521	−	0.891245i	$-0.350168\pi$
$522$		0			0
$523$	658.229	−	380.029i	1.25856	−	0.726632i	0.285768	−	0.958299i	$-0.407751\pi$
$523$	658.229	−	380.029i	1.25856	−	0.726632i	0.972795	+	0.231667i	$0.0744178\pi$
$524$	−276.812			−0.528268
$525$		0			0
$526$	147.045	−	84.8964i	0.279553	−	0.161400i
$527$	−442.787	−	255.643i	−0.840203	−	0.485091i
$528$		0			0
$529$	182.322	−	315.791i	0.344655	−	0.596959i
$530$	−238.054	+	412.321i	−0.449158	+	0.777964i
$531$		0			0
$532$	174.111	−	147.704i	0.327276	−	0.277639i
$533$	66.7801			0.125291
$534$		0			0
$535$	−769.774	−	444.429i	−1.43883	−	0.830709i
$536$	62.5577	+	108.353i	0.116712	+	0.202151i
$537$		0			0
$538$	−50.2978	−	87.1183i	−0.0934903	−	0.161930i
$539$	181.937			0.337545
$540$		0			0
$541$	−283.890	−	491.712i	−0.524750	−	0.908894i	−0.999585	−	0.0288191i	$-0.990825\pi$
$541$	−283.890	−	491.712i	−0.524750	−	0.908894i	0.474834	−	0.880075i	$-0.342508\pi$
$542$	−63.0196	+	36.3844i	−0.116272	+	0.0671299i
$543$		0			0
$544$			375.382i			0.690041i
$545$	822.633	−	474.947i	1.50942	−	0.871463i
$546$		0			0
$547$	477.215	−	275.520i	0.872422	−	0.503693i	0.00426966	−	0.999991i	$-0.498641\pi$
$547$	477.215	−	275.520i	0.872422	−	0.503693i	0.868152	+	0.496298i	$0.165308\pi$
$548$	8.30892	−	14.3915i	0.0151623	−	0.0262618i
$549$		0			0
$550$			97.5470i			0.177358i
$551$	394.100	+	464.558i	0.715246	+	0.843118i
$552$		0			0
$553$	−767.167	−	442.924i	−1.38728	−	0.800947i
$554$	−644.347	−	372.014i	−1.16308	−	0.671505i
$555$		0			0
$556$	−139.311	+	241.294i	−0.250560	+	0.433982i
$557$	−66.7590	−	115.630i	−0.119855	−	0.207594i	0.799855	−	0.600193i	$-0.204909\pi$
$557$	−66.7590	−	115.630i	−0.119855	−	0.207594i	−0.919710	+	0.392599i	$0.871576\pi$
$558$		0			0
$559$		−	187.863i		−	0.336070i
$560$	−533.719	−	924.429i	−0.953070	−	1.65077i
$561$		0			0
$562$	−63.0087			−0.112115
$563$		−	939.856i		−	1.66937i	−0.550727	−	0.834685i	$-0.685650\pi$
$563$		−	939.856i		−	1.66937i	0.550727	−	0.834685i	$-0.314350\pi$
$564$		0			0
$565$	25.3624	+	14.6430i	0.0448893	+	0.0259168i
$566$	432.206	−	249.534i	0.763614	−	0.440873i
$567$		0			0
$568$	−57.1543	+	98.9941i	−0.100624	+	0.174285i
$569$			545.726i			0.959096i	0.877516	+	0.479548i	$0.159199\pi$
$569$			545.726i			0.959096i	−0.877516	+	0.479548i	$0.840801\pi$
$570$		0			0
$571$	27.4635			0.0480973			0.0240486	−	0.999711i	$-0.492344\pi$
$571$	27.4635			0.0480973			0.0240486	+	0.999711i	$0.492344\pi$
$572$	−29.6262	−	17.1047i	−0.0517941	−	0.0299033i
$573$		0			0
$574$	125.678	+	217.681i	0.218951	+	0.379235i
$575$	−58.3557	+	101.075i	−0.101488	+	0.175783i
$576$		0			0
$577$	−90.7976			−0.157362			−0.0786808	−	0.996900i	$-0.525071\pi$
$577$	−90.7976			−0.157362			−0.0786808	+	0.996900i	$0.525071\pi$
$578$			163.736i			0.283280i
$579$		0			0
$580$	−207.705	+	119.918i	−0.358111	+	0.206756i
$581$	−768.747			−1.32314
$582$		0			0
$583$	143.259	−	82.7107i	0.245727	−	0.141871i
$584$	311.170	+	179.654i	0.532825	+	0.307627i
$585$		0			0
$586$	−59.7163	+	103.432i	−0.101905	+	0.176505i
$587$	248.332	−	430.124i	0.423053	−	0.732750i	−0.573183	−	0.819427i	$-0.694292\pi$
$587$	248.332	−	430.124i	0.423053	−	0.732750i	0.996236	+	0.0866775i	$0.0276250\pi$
$588$		0			0
$589$	−503.555	+	91.5938i	−0.854932	+	0.155507i
$590$	−1179.26			−1.99874
$591$		0			0
$592$	−2.37503	−	1.37122i	−0.00401188	−	0.00231626i
$593$	−64.8320	−	112.292i	−0.109329	−	0.189363i	0.806170	−	0.591684i	$-0.201537\pi$
$593$	−64.8320	−	112.292i	−0.109329	−	0.189363i	−0.915499	+	0.402321i	$0.868203\pi$
$594$		0			0
$595$	−519.951	−	900.582i	−0.873868	−	1.51358i
$596$	−13.3462			−0.0223930
$597$		0			0
$598$	−84.3752	−	146.142i	−0.141096	−	0.244385i
$599$	430.839	−	248.745i	0.719264	−	0.415267i	−0.0952180	−	0.995456i	$-0.530355\pi$
$599$	430.839	−	248.745i	0.719264	−	0.415267i	0.814482	+	0.580189i	$0.197021\pi$
$600$		0			0
$601$		−	718.473i		−	1.19546i	−0.801696	−	0.597731i	$-0.796069\pi$
$601$		−	718.473i		−	1.19546i	0.801696	−	0.597731i	$-0.203931\pi$
$602$	612.371	−	353.553i	1.01723	−	0.587297i
$603$		0			0
$604$	−159.245	+	91.9399i	−0.263650	+	0.152218i
$605$	−289.828	+	501.997i	−0.479055	+	0.829748i
$606$		0			0
$607$			545.141i			0.898090i	0.893509	+	0.449045i	$0.148236\pi$
$607$			545.141i			0.898090i	−0.893509	+	0.449045i	$0.851764\pi$
$608$	243.091	+	286.551i	0.399821	+	0.471301i
$609$		0			0
$610$	−1063.77	−	614.167i	−1.74388	−	1.00683i
$611$	−53.2825	−	30.7627i	−0.0872054	−	0.0503480i
$612$		0			0
$613$	−103.876	+	179.918i	−0.169455	+	0.293504i	−0.938228	−	0.346017i	$-0.887534\pi$
$613$	−103.876	+	179.918i	−0.169455	+	0.293504i	0.768774	+	0.639521i	$0.220867\pi$
$614$	431.244	+	746.936i	0.702352	+	1.21651i
$615$		0			0
$616$			273.346i			0.443743i
$617$	−398.959	−	691.018i	−0.646611	−	1.11996i	−0.983927	−	0.178572i	$-0.942852\pi$
$617$	−398.959	−	691.018i	−0.646611	−	1.11996i	0.337316	−	0.941392i	$-0.390481\pi$
$618$		0			0
$619$	−753.162			−1.21674			−0.608370	−	0.793654i	$-0.708176\pi$
$619$	−753.162			−1.21674			−0.608370	+	0.793654i	$0.708176\pi$
$620$		−	201.497i		−	0.324995i
$621$		0			0
$622$	185.110	+	106.873i	0.297604	+	0.171822i
$623$	−162.828	+	94.0086i	−0.261361	+	0.150897i
$624$		0			0
$625$	384.858	−	666.593i	0.615772	−	1.06655i
$626$		−	980.183i		−	1.56579i
$627$		0			0
$628$	346.934			0.552442
$629$	−2.31376	−	1.33585i	−0.00367848	−	0.00212377i
$630$		0			0
$631$	142.019	+	245.984i	0.225069	+	0.389831i	0.956340	−	0.292256i	$-0.0944059\pi$
$631$	142.019	+	245.984i	0.225069	+	0.389831i	−0.731271	+	0.682087i	$0.761073\pi$
$632$	295.000	−	510.956i	0.466773	−	0.808474i
$633$		0			0
$634$	1368.85			2.15906
$635$			981.988i			1.54644i
$636$		0			0
$637$	−193.558	+	111.751i	−0.303858	+	0.175433i
$638$	343.560			0.538495
$639$		0			0
$640$	777.609	−	448.953i	1.21501	−	0.701489i
$641$	−1029.31	−	594.275i	−1.60579	−	0.927106i	−0.990297	−	0.138968i	$-0.955622\pi$
$641$	−1029.31	−	594.275i	−1.60579	−	0.927106i	−0.615498	−	0.788138i	$-0.711045\pi$
$642$		0			0
$643$	−310.711	+	538.167i	−0.483220	+	0.836962i	−0.999814	−	0.0192683i	$-0.993866\pi$
$643$	−310.711	+	538.167i	−0.483220	+	0.836962i	0.516594	+	0.856230i	$0.327200\pi$
$644$	77.0294	−	133.419i	0.119611	−	0.207172i
$645$		0			0
$646$	536.109	+	631.955i	0.829890	+	0.978259i
$647$	−367.100			−0.567388			−0.283694	−	0.958915i	$-0.591560\pi$
$647$	−367.100			−0.567388			−0.283694	+	0.958915i	$0.591560\pi$
$648$		0			0
$649$	354.835	+	204.864i	0.546741	+	0.315661i
$650$	−59.9161	−	103.778i	−0.0921786	−	0.159658i
$651$		0			0
$652$	36.3778	+	63.0082i	0.0557942	+	0.0966383i
$653$	407.248			0.623656			0.311828	−	0.950139i	$-0.399059\pi$
$653$	407.248			0.623656			0.311828	+	0.950139i	$0.399059\pi$
$654$		0			0
$655$	631.032	+	1092.98i	0.963407	+	1.66867i
$656$	−196.712	+	113.572i	−0.299866	+	0.173128i
$657$		0			0
$658$		−	231.577i		−	0.351941i
$659$	186.420	−	107.630i	0.282884	−	0.163323i	−0.351845	−	0.936058i	$-0.614445\pi$
$659$	186.420	−	107.630i	0.282884	−	0.163323i	0.634728	+	0.772736i	$0.281112\pi$
$660$		0			0
$661$	570.950	−	329.638i	0.863767	−	0.498696i	−0.00150486	−	0.999999i	$-0.500479\pi$
$661$	570.950	−	329.638i	0.863767	−	0.498696i	0.865272	+	0.501303i	$0.167146\pi$
$662$	35.5653	−	61.6009i	0.0537240	−	0.0930528i
$663$		0			0
$664$		−	512.008i		−	0.771097i
$665$	−980.111	−	350.756i	−1.47385	−	0.527452i
$666$		0			0
$667$	355.985	+	205.528i	0.533711	+	0.308138i
$668$	37.4934	+	21.6468i	0.0561279	+	0.0324055i
$669$		0			0
$670$	−134.355	+	232.709i	−0.200529	+	0.347327i
$671$	213.390	+	369.602i	0.318017	+	0.550822i
$672$		0			0
$673$		−	745.165i		−	1.10723i	−0.832773	−	0.553614i	$-0.813248\pi$
$673$		−	745.165i		−	1.10723i	0.832773	−	0.553614i	$-0.186752\pi$
$674$	470.634	+	815.161i	0.698270	+	1.20944i
$675$		0			0
$676$	−174.442			−0.258051
$677$			1174.97i			1.73556i	0.496949	+	0.867780i	$0.334454\pi$
$677$			1174.97i			1.73556i	−0.496949	+	0.867780i	$0.665546\pi$
$678$		0			0
$679$	1102.07	+	636.278i	1.62307	+	0.937081i
$680$	599.814	−	346.303i	0.882080	−	0.509269i
$681$		0			0
$682$	−144.319	+	249.969i	−0.211612	+	0.366523i
$683$		−	533.368i		−	0.780919i	−0.920620	−	0.390460i	$-0.872316\pi$
$683$		−	533.368i		−	0.780919i	0.920620	−	0.390460i	$-0.127684\pi$
$684$		0			0
$685$	−75.7653			−0.110606
$686$	186.351	+	107.590i	0.271649	+	0.156837i
$687$		0			0
$688$	319.496	+	553.383i	0.464383	+	0.804335i
$689$	−101.606	+	175.987i	−0.147469	+	0.255424i
$690$		0			0
$691$	−847.914			−1.22708			−0.613541	−	0.789663i	$-0.710256\pi$
$691$	−847.914			−1.22708			−0.613541	+	0.789663i	$0.710256\pi$
$692$			87.6799i			0.126705i
$693$		0			0
$694$	−1046.69	+	604.309i	−1.50820	+	0.870762i
$695$	1270.32			1.82779
$696$		0			0
$697$	−191.638	+	110.642i	−0.274946	+	0.158740i
$698$	−572.279	−	330.405i	−0.819884	−	0.473360i
$699$		0			0
$700$	54.6997	−	94.7427i	0.0781425	−	0.135347i
$701$	−474.994	+	822.713i	−0.677594	+	1.17363i	0.298109	+	0.954532i	$0.403644\pi$
$701$	−474.994	+	822.713i	−0.677594	+	1.17363i	−0.975703	+	0.219096i	$0.929689\pi$
$702$		0			0
$703$	−2.63131	+	0.478619i	−0.00374297	+	0.000680824i
$704$	−151.457			−0.215138
$705$		0			0
$706$	−36.9035	−	21.3062i	−0.0522712	−	0.0301788i
$707$	481.007	+	833.128i	0.680349	+	1.17840i
$708$		0			0
$709$	−9.83456	−	17.0340i	−0.0138710	−	0.0240253i	0.859007	−	0.511965i	$-0.171082\pi$
$709$	−9.83456	−	17.0340i	−0.0138710	−	0.0240253i	−0.872878	+	0.487939i	$0.837749\pi$
$710$	−245.499			−0.345774
$711$		0			0
$712$	−62.6125	−	108.448i	−0.0879389	−	0.152315i
$713$	−299.078	+	172.673i	−0.419464	+	0.242178i
$714$		0			0
$715$			155.970i			0.218140i
$716$	−251.650	+	145.290i	−0.351466	+	0.202919i
$717$		0			0
$718$	190.041	−	109.720i	0.264681	−	0.152814i
$719$	165.944	−	287.423i	0.230798	−	0.399754i	−0.727245	−	0.686378i	$-0.759200\pi$
$719$	165.944	−	287.423i	0.230798	−	0.399754i	0.958043	+	0.286624i	$0.0925330\pi$
$720$		0			0
$721$		−	364.954i		−	0.506177i
$722$	818.487	+	135.234i	1.13364	+	0.187304i
$723$		0			0
$724$	−236.203	−	136.372i	−0.326248	−	0.188359i
$725$	252.790	+	145.949i	0.348676	+	0.201308i
$726$		0			0
$727$	372.720	−	645.570i	0.512682	−	0.887992i	−0.487210	−	0.873285i	$-0.661985\pi$
$727$	372.720	−	645.570i	0.512682	−	0.887992i	0.999892	−	0.0147065i	$-0.00468141\pi$
$728$	−167.896	−	290.805i	−0.230627	−	0.399458i
$729$		0			0
$730$			771.682i			1.05710i
$731$	311.254	+	539.108i	0.425792	+	0.737494i
$732$		0			0
$733$	−753.165			−1.02751			−0.513755	−	0.857937i	$-0.671746\pi$
$733$	−753.165			−1.02751			−0.513755	+	0.857937i	$0.671746\pi$
$734$			1147.01i			1.56268i
$735$		0			0
$736$	219.581	+	126.775i	0.298343	+	0.172248i
$737$	80.8536	−	46.6809i	0.109706	−	0.0633390i
$738$		0			0
$739$	−285.102	+	493.812i	−0.385795	+	0.668216i	−0.991879	−	0.127184i	$-0.959406\pi$
$739$	−285.102	+	493.812i	−0.385795	+	0.668216i	0.606084	+	0.795400i	$0.292739\pi$
$740$		−	1.05291i		−	0.00142286i
$741$		0			0
$742$	−764.879			−1.03083
$743$	790.856	+	456.601i	1.06441	+	0.614537i	0.926649	−	0.375929i	$-0.122676\pi$
$743$	790.856	+	456.601i	1.06441	+	0.614537i	0.137760	+	0.990466i	$0.456010\pi$
$744$		0			0
$745$	30.4246	+	52.6969i	0.0408383	+	0.0707341i
$746$	−92.0027	+	159.353i	−0.123328	+	0.213610i
$747$		0			0
$748$	113.357			0.151547
$749$		−	1427.97i		−	1.90651i
$750$		0			0
$751$	−340.814	+	196.769i	−0.453813	+	0.262009i	−0.709439	−	0.704767i	$-0.751052\pi$
$751$	−340.814	+	196.769i	−0.453813	+	0.262009i	0.255626	+	0.966776i	$0.417718\pi$
$752$	209.270			0.278284
$753$		0			0
$754$	−365.504	+	211.024i	−0.484753	+	0.279872i
$755$	726.040	+	419.179i	0.961643	+	0.555205i
$756$		0			0
$757$	−252.335	+	437.057i	−0.333335	+	0.577354i	−0.983164	−	0.182727i	$-0.941507\pi$
$757$	−252.335	+	437.057i	−0.333335	+	0.577354i	0.649828	+	0.760081i	$0.274841\pi$
$758$	−389.261	+	674.220i	−0.513537	+	0.889472i
$759$		0			0
$760$	233.614	−	652.783i	0.307386	−	0.858925i
$761$	564.183			0.741371			0.370685	−	0.928758i	$-0.379123\pi$
$761$	564.183			0.741371			0.370685	+	0.928758i	$0.379123\pi$
$762$		0			0
$763$	1321.58	+	763.015i	1.73209	+	1.00002i
$764$	−22.3423	−	38.6979i	−0.0292438	−	0.0506517i
$765$		0			0
$766$	−127.014	−	219.995i	−0.165815	−	0.287200i
$767$	−503.333			−0.656236
$768$		0			0
$769$	443.262	+	767.752i	0.576413	+	0.998377i	0.995887	+	0.0906095i	$0.0288815\pi$
$769$	443.262	+	767.752i	0.576413	+	0.998377i	−0.419473	+	0.907768i	$0.637785\pi$
$770$	−508.410	+	293.531i	−0.660273	+	0.381209i
$771$		0			0
$772$			47.6453i			0.0617167i
$773$	−534.516	+	308.603i	−0.691482	+	0.399228i	−0.804167	−	0.594403i	$-0.797388\pi$
$773$	−534.516	+	308.603i	−0.691482	+	0.399228i	0.112685	+	0.993631i	$0.464055\pi$
$774$		0			0
$775$	−212.380	+	122.617i	−0.274038	+	0.158216i
$776$	−423.780	+	734.008i	−0.546108	+	0.945887i
$777$		0			0
$778$		−	1426.84i		−	1.83398i
$779$	−74.6383	+	208.561i	−0.0958130	+	0.267729i
$780$		0			0
$781$	73.8699	+	42.6488i	0.0945837	+	0.0546079i
$782$	484.259	+	279.587i	0.619258	+	0.357529i
$783$		0			0
$784$	380.104	−	658.359i	0.484826	−	0.839744i
$785$	−790.883	−	1369.85i	−1.00749	−	1.74503i
$786$		0			0
$787$			81.5848i			0.103666i	0.998656	+	0.0518328i	$0.0165063\pi$
$787$			81.5848i			0.103666i	−0.998656	+	0.0518328i	$0.983494\pi$
$788$	201.339	+	348.729i	0.255506	+	0.442549i
$789$		0			0
$790$	1267.14			1.60397
$791$			47.0488i			0.0594801i
$792$		0			0
$793$	−454.039	−	262.139i	−0.572558	−	0.330567i
$794$	938.301	−	541.728i	1.18174	−	0.682277i
$795$		0			0
$796$	196.259	−	339.930i	0.246556	−	0.427048i
$797$			814.902i			1.02246i	0.859443	+	0.511231i	$0.170810\pi$
$797$			814.902i			1.02246i	−0.859443	+	0.511231i	$0.829190\pi$
$798$		0			0
$799$	203.872			0.255158
$800$	155.927	+	90.0247i	0.194909	+	0.112531i
$801$		0			0
$802$	−258.675	−	448.039i	−0.322538	−	0.558652i
$803$	134.059	−	232.196i	0.166947	−	0.289161i
$804$		0			0
$805$	−702.396			−0.872542
$806$		−	354.580i		−	0.439925i
$807$		0			0
$808$	−554.888	+	320.365i	−0.686743	+	0.396491i
$809$	−1385.45			−1.71255			−0.856275	−	0.516520i	$-0.827227\pi$
$809$	−1385.45			−1.71255			−0.856275	+	0.516520i	$0.827227\pi$
$810$		0			0
$811$	−346.960	+	200.317i	−0.427817	+	0.247000i	−0.698416	−	0.715692i	$-0.746112\pi$
$811$	−346.960	+	200.317i	−0.427817	+	0.247000i	0.270599	+	0.962692i	$0.412778\pi$
$812$	−333.683	−	192.652i	−0.410940	−	0.237256i
$813$		0			0
$814$	−0.754135	+	1.30620i	−0.000926456	+	0.00160467i
$815$	165.856	−	287.272i	0.203505	−	0.352481i
$816$		0			0
$817$	586.715	+	209.970i	0.718134	+	0.257001i
$818$	−511.482			−0.625283
$819$		0			0
$820$	−75.5239	−	43.6038i	−0.0921024	−	0.0531753i
$821$	−40.8741	−	70.7960i	−0.0497858	−	0.0862315i	0.840059	−	0.542496i	$-0.182521\pi$
$821$	−40.8741	−	70.7960i	−0.0497858	−	0.0862315i	−0.889844	+	0.456264i	$0.849187\pi$
$822$		0			0
$823$	−152.006	−	263.282i	−0.184698	−	0.319906i	0.758777	−	0.651351i	$-0.225797\pi$
$823$	−152.006	−	263.282i	−0.184698	−	0.319906i	−0.943475	+	0.331445i	$0.892464\pi$
$824$	243.070			0.294988
$825$		0			0
$826$	−947.256	−	1640.69i	−1.14680	−	1.98631i
$827$	−802.116	+	463.102i	−0.969910	+	0.559978i	−0.899209	−	0.437519i	$-0.855857\pi$
$827$	−802.116	+	463.102i	−0.969910	+	0.559978i	−0.0707015	+	0.997498i	$0.522524\pi$
$828$		0			0
$829$			982.984i			1.18575i	0.805296	+	0.592873i	$0.202006\pi$
$829$			982.984i			1.18575i	−0.805296	+	0.592873i	$0.797994\pi$
$830$	952.311	−	549.817i	1.14736	−	0.662430i
$831$		0			0
$832$	161.131	−	93.0291i	0.193667	−	0.111814i
$833$	370.299	−	641.376i	0.444536	−	0.769960i
$834$		0			0
$835$		−	197.388i		−	0.236393i
$836$	86.5320	−	73.4080i	0.103507	−	0.0878086i
$837$		0			0
$838$	609.732	+	352.029i	0.727604	+	0.420082i
$839$	−1255.14	−	724.657i	−1.49600	−	0.863716i	−0.496010	−	0.868317i	$-0.665202\pi$
$839$	−1255.14	−	724.657i	−1.49600	−	0.863716i	−0.999989	+	0.00460145i	$0.998535\pi$
$840$		0			0
$841$	93.5295	−	161.998i	0.111212	−	0.192625i
$842$	−439.865	−	761.868i	−0.522405	−	0.904832i
$843$		0			0
$844$			93.9139i			0.111272i
$845$	397.666	+	688.777i	0.470610	+	0.815121i
$846$		0			0
$847$	−931.234			−1.09945
$848$		−	691.200i		−	0.815094i
$849$		0			0
$850$	343.880	+	198.539i	0.404565	+	0.233575i
$851$	−1.56282	+	0.902294i	−0.00183645	+	0.00106028i
$852$		0			0
$853$	−291.837	+	505.476i	−0.342130	+	0.592586i	−0.984828	−	0.173533i	$-0.944482\pi$
$853$	−291.837	+	505.476i	−0.342130	+	0.592586i	0.642698	+	0.766119i	$0.277815\pi$
$854$		−	1973.35i		−	2.31072i
$855$		0			0
$856$	951.074			1.11107
$857$	197.002	+	113.739i	0.229874	+	0.132718i	0.610514	−	0.792005i	$-0.290963\pi$
$857$	197.002	+	113.739i	0.229874	+	0.132718i	−0.380640	+	0.924723i	$0.624296\pi$
$858$		0			0
$859$	−451.757	−	782.466i	−0.525910	−	0.910903i	−0.999544	−	0.0301814i	$-0.990391\pi$
$859$	−451.757	−	782.466i	−0.525910	−	0.910903i	0.473634	−	0.880722i	$-0.342942\pi$
$860$	−122.664	+	212.461i	−0.142633	+	0.247048i
$861$		0			0
$862$	−618.220			−0.717193
$863$			448.624i			0.519843i	0.965630	+	0.259921i	$0.0836967\pi$
$863$			448.624i			0.519843i	−0.965630	+	0.259921i	$0.916303\pi$
$864$		0			0
$865$	346.199	−	199.878i	0.400231	−	0.231073i
$866$	710.636			0.820596
$867$		0			0
$868$	280.341	−	161.855i	0.322973	−	0.186469i
$869$	−381.278	−	220.131i	−0.438754	−	0.253315i
$870$		0			0
$871$	−57.3453	+	99.3250i	−0.0658385	+	0.114036i
$872$	−508.191	+	880.213i	−0.582788	+	1.00942i
$873$		0			0
$874$	550.719	−	100.173i	0.630114	−	0.114614i
$875$	870.933			0.995352
$876$		0			0
$877$	−76.1813	−	43.9833i	−0.0868658	−	0.0501520i	0.455938	−	0.890012i	$-0.349304\pi$
$877$	−76.1813	−	43.9833i	−0.0868658	−	0.0501520i	−0.542804	+	0.839860i	$0.682637\pi$
$878$	−477.641	−	827.299i	−0.544011	−	0.942254i
$879$		0			0
$880$	−265.255	−	459.436i	−0.301427	−	0.522086i
$881$	−1590.01			−1.80478			−0.902388	−	0.430925i	$-0.858187\pi$
$881$	−1590.01			−1.80478			−0.902388	+	0.430925i	$0.858187\pi$
$882$		0			0
$883$	−207.973	−	360.219i	−0.235530	−	0.407949i	0.723897	−	0.689908i	$-0.242349\pi$
$883$	−207.973	−	360.219i	−0.235530	−	0.407949i	−0.959426	+	0.281959i	$0.909016\pi$
$884$	−120.597	+	69.6270i	−0.136422	+	0.0787636i
$885$		0			0
$886$			802.041i			0.905238i
$887$	483.574	−	279.192i	0.545180	−	0.314760i	−0.201996	−	0.979386i	$-0.564743\pi$
$887$	483.574	−	279.192i	0.545180	−	0.314760i	0.747175	+	0.664627i	$0.231409\pi$
$888$		0			0
$889$	−1366.23	+	788.795i	−1.53682	+	0.887283i
$890$	134.472	−	232.913i	0.151092	−	0.261700i
$891$		0			0
$892$			26.6469i			0.0298732i
$893$	155.627	−	132.024i	0.174274	−	0.147843i
$894$		0			0
$895$	1147.34	+	662.417i	1.28194	+	0.740131i
$896$	1249.25	+	721.255i	1.39425	+	0.804972i
$897$		0			0
$898$	−725.911	+	1257.31i	−0.808364	+	1.40013i
$899$	431.858	+	747.999i	0.480376	+	0.832035i
$900$		0			0
$901$		−	673.370i		−	0.747358i
$902$	62.4613	+	108.186i	0.0692475	+	0.119940i
$903$		0			0
$904$	−31.3359			−0.0346636
$905$			1243.52i			1.37405i
$906$		0			0
$907$	−333.612	−	192.611i	−0.367819	−	0.212360i	0.304686	−	0.952453i	$-0.401448\pi$
$907$	−333.612	−	192.611i	−0.367819	−	0.212360i	−0.672505	+	0.740092i	$0.734782\pi$
$908$	107.613	−	62.1306i	0.118517	−	0.0684257i
$909$		0			0
$910$	360.589	−	624.559i	0.396252	−	0.686328i
$911$		−	275.295i		−	0.302190i	−0.988519	−	0.151095i	$-0.951720\pi$
$911$		−	275.295i		−	0.302190i	0.988519	−	0.151095i	$-0.0482800\pi$
$912$		0			0
$913$	−382.063			−0.418470
$914$	−1074.65	−	620.448i	−1.17576	−	0.678827i
$915$		0			0
$916$	166.487	+	288.363i	0.181754	+	0.314807i
$917$	−1013.77	+	1755.90i	−1.10553	+	1.91483i
$918$		0			0
$919$	52.3454			0.0569591			0.0284796	−	0.999594i	$-0.490933\pi$
$919$	52.3454			0.0569591			0.0284796	+	0.999594i	$0.490933\pi$
$920$		−	467.817i		−	0.508497i
$921$		0			0
$922$	337.612	−	194.921i	0.366174	−	0.211411i
$923$	−104.784			−0.113526
$924$		0			0
$925$	−1.10978	+	0.640733i	−0.00119976	+	0.000692684i
$926$	920.111	+	531.226i	0.993640	+	0.573678i
$927$		0			0
$928$	317.066	−	549.175i	0.341666	−	0.591783i
$929$	637.608	−	1104.37i	0.686338	−	1.18877i	−0.286676	−	0.958027i	$-0.592550\pi$
$929$	637.608	−	1104.37i	0.686338	−	1.18877i	0.973014	−	0.230745i	$-0.0741162\pi$
$930$		0			0
$931$	−132.674	−	729.399i	−0.142506	−	0.783458i
$932$	−473.694			−0.508256
$933$		0			0
$934$	5.18361	+	2.99276i	0.00554991	+	0.00320424i
$935$	−258.413	−	447.584i	−0.276377	−	0.478700i
$936$		0			0
$937$	359.964	+	623.476i	0.384167	+	0.665396i	0.991653	−	0.128934i	$-0.0411555\pi$
$937$	359.964	+	623.476i	0.384167	+	0.665396i	−0.607487	+	0.794330i	$0.707822\pi$
$938$	−431.688			−0.460222
$939$		0			0
$940$	40.1727	+	69.5811i	0.0427369	+	0.0740224i
$941$	−76.8289	+	44.3572i	−0.0816461	+	0.0471384i	−0.540267	−	0.841494i	$-0.681677\pi$
$941$	−76.8289	+	44.3572i	−0.0816461	+	0.0471384i	0.458621	+	0.888632i	$0.348344\pi$
$942$		0			0
$943$			149.465i			0.158500i
$944$	1482.65	−	856.008i	1.57060	−	0.906788i
$945$		0			0
$946$	304.345	−	175.714i	0.321718	−	0.185744i
$947$	172.069	−	298.033i	0.181699	−	0.314712i	−0.760760	−	0.649033i	$-0.775174\pi$
$947$	172.069	−	298.033i	0.181699	−	0.314712i	0.942459	+	0.334321i	$0.108507\pi$
$948$		0			0
$949$			329.370i			0.347071i
$950$	391.074	−	71.1341i	0.411657	−	0.0748780i
$951$		0			0
$952$	963.618	+	556.345i	1.01220	+	0.584396i
$953$	1350.11	+	779.488i	1.41670	+	0.817931i	0.996007	−	0.0892739i	$-0.0284547\pi$
$953$	1350.11	+	779.488i	1.41670	+	0.817931i	0.420690	+	0.907204i	$0.361788\pi$
$954$		0			0
$955$	−101.864	+	176.434i	−0.106664	+	0.184748i
$956$	−199.696	−	345.883i	−0.208887	−	0.361802i
$957$		0			0
$958$		−	901.408i		−	0.940927i
$959$	−60.8595	−	105.412i	−0.0634614	−	0.109918i
$960$		0			0
$961$	235.357			0.244908
$962$		−	1.85284i		−	0.00192603i
$963$		0			0
$964$	−377.985	−	218.230i	−0.392100	−	0.226379i
$965$	188.125	−	108.614i	0.194948	−	0.112553i
$966$		0			0
$967$	645.250	−	1117.61i	0.667270	−	1.15574i	−0.311395	−	0.950281i	$-0.600796\pi$
$967$	645.250	−	1117.61i	0.667270	−	1.15574i	0.978665	−	0.205464i	$-0.0658704\pi$
$968$		−	620.229i		−	0.640733i
$969$		0			0
$970$	−1820.29			−1.87659
$971$	439.932	+	253.995i	0.453071	+	0.261581i	0.709126	−	0.705081i	$-0.249090\pi$
$971$	439.932	+	253.995i	0.453071	+	0.261581i	−0.256055	+	0.966662i	$0.582423\pi$
$972$		0			0
$973$	1020.40	+	1767.38i	1.04871	+	1.81643i
$974$	−107.339	+	185.917i	−0.110204	+	0.190879i
$975$		0			0
$976$	1783.26			1.82711
$977$		−	743.988i		−	0.761503i	−0.924677	−	0.380752i	$-0.875665\pi$
$977$		−	743.988i		−	0.761503i	0.924677	−	0.380752i	$-0.124335\pi$
$978$		0			0
$979$	−80.9244	+	46.7217i	−0.0826603	+	0.0477239i
$980$	291.868			0.297824
$981$		0			0
$982$	−868.780	+	501.590i	−0.884704	+	0.510784i
$983$	−1367.75	−	789.668i	−1.39140	−	0.803325i	−0.397929	−	0.917416i	$-0.630271\pi$
$983$	−1367.75	−	789.668i	−1.39140	−	0.803325i	−0.993470	+	0.114091i	$0.963604\pi$
$984$		0			0
$985$	917.959	−	1589.95i	0.931938	−	1.61416i
$986$	699.253	−	1211.14i	0.709182	−	1.22834i
$987$		0			0
$988$	−46.9699	+	131.247i	−0.0475404	+	0.132841i
$989$	420.470			0.425146
$990$		0			0
$991$	−1433.20	−	827.457i	−1.44621	−	0.834971i	−0.447960	−	0.894054i	$-0.647849\pi$
$991$	−1433.20	−	827.457i	−1.44621	−	0.834971i	−0.998253	+	0.0590824i	$0.981183\pi$
$992$	266.381	+	461.385i	0.268529	+	0.465106i
$993$		0			0
$994$	−197.200	−	341.561i	−0.198391	−	0.343623i
$995$	−1789.60			−1.79859
$996$		0			0
$997$	−579.476	−	1003.68i	−0.581220	−	1.00670i	−0.995335	−	0.0964779i	$-0.969242\pi$
$997$	−579.476	−	1003.68i	−0.581220	−	1.00670i	0.414115	−	0.910224i	$-0.364091\pi$
$998$	−140.991	+	81.4013i	−0.141274	+	0.0815645i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.p.d.46.1		6
3.2	odd	2		19.3.d.a.8.3	✓	6
12.11	even	2		304.3.r.b.65.3		6
19.12	odd	6	inner	171.3.p.d.145.1		6
57.2	even	18		361.3.f.i.127.3		18
57.5	odd	18		361.3.f.h.333.3		18
57.8	even	6		361.3.b.b.360.5		6
57.11	odd	6		361.3.b.b.360.2		6
57.14	even	18		361.3.f.i.333.1		18
57.17	odd	18		361.3.f.h.127.1		18
57.23	odd	18		361.3.f.i.299.3		18
57.26	odd	6		361.3.d.c.69.1		6
57.29	even	18		361.3.f.h.116.3		18
57.32	even	18		361.3.f.h.307.1		18
57.35	odd	18		361.3.f.h.262.1		18
57.41	even	18		361.3.f.i.262.3		18
57.44	odd	18		361.3.f.i.307.3		18
57.47	odd	18		361.3.f.i.116.1		18
57.50	even	6		19.3.d.a.12.3	yes	6
57.53	even	18		361.3.f.h.299.1		18
57.56	even	2		361.3.d.c.293.1		6
228.107	odd	6		304.3.r.b.145.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.d.a.8.3	✓	6	3.2	odd	2
19.3.d.a.12.3	yes	6	57.50	even	6
171.3.p.d.46.1		6	1.1	even	1	trivial
171.3.p.d.145.1		6	19.12	odd	6	inner
304.3.r.b.65.3		6	12.11	even	2
304.3.r.b.145.3		6	228.107	odd	6
361.3.b.b.360.2		6	57.11	odd	6
361.3.b.b.360.5		6	57.8	even	6
361.3.d.c.69.1		6	57.26	odd	6
361.3.d.c.293.1		6	57.56	even	2
361.3.f.h.116.3		18	57.29	even	18
361.3.f.h.127.1		18	57.17	odd	18
361.3.f.h.262.1		18	57.35	odd	18
361.3.f.h.299.1		18	57.53	even	18
361.3.f.h.307.1		18	57.32	even	18
361.3.f.h.333.3		18	57.5	odd	18
361.3.f.i.116.1		18	57.47	odd	18
361.3.f.i.127.3		18	57.2	even	18
361.3.f.i.262.3		18	57.41	even	18
361.3.f.i.299.3		18	57.23	odd	18
361.3.f.i.307.3		18	57.44	odd	18
361.3.f.i.333.1		18	57.14	even	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99014 - 1.14901i) q^{2} +(0.640435 + 1.10927i) q^{4} +(2.91992 - 5.05745i) q^{5} +9.38186 q^{7} +6.24860i q^{8} +O(q^{10})\)	\(q+(-1.99014 - 1.14901i) q^{2} +(0.640435 + 1.10927i) q^{4} +(2.91992 - 5.05745i) q^{5} +9.38186 q^{7} +6.24860i q^{8} +(-11.6221 + 6.71002i) q^{10} +4.66273 q^{11} +(-4.96056 + 2.86398i) q^{13} +(-18.6712 - 10.7798i) q^{14} +(9.74143 - 16.8726i) q^{16} +(9.49014 - 16.4374i) q^{17} +(-3.40020 - 18.6933i) q^{19} +7.48008 q^{20} +(-9.27949 - 5.35751i) q^{22} +(-6.41006 - 11.1025i) q^{23} +(-4.55188 - 7.88409i) q^{25} +13.1629 q^{26} +(6.00848 + 10.4070i) q^{28} +(-27.7677 + 16.0317i) q^{29} -26.9378i q^{31} +(-17.1278 + 9.88874i) q^{32} +(-37.7734 + 21.8085i) q^{34} +(27.3943 - 47.4483i) q^{35} -0.140762i q^{37} +(-14.7118 + 41.1091i) q^{38} +(31.6020 + 18.2454i) q^{40} +(-10.0967 - 5.82931i) q^{41} +(-16.3988 + 28.4036i) q^{43} +(2.98618 + 5.17221i) q^{44} +29.4608i q^{46} +(5.37062 + 9.30218i) q^{47} +39.0193 q^{49} +20.9206i q^{50} +(-6.35383 - 3.66839i) q^{52} +(30.7243 - 17.7387i) q^{53} +(13.6148 - 23.5815i) q^{55} +58.6235i q^{56} +73.6821 q^{58} +(76.1002 + 43.9365i) q^{59} +(45.7649 + 79.2672i) q^{61} +(-30.9517 + 53.6099i) q^{62} -32.4825 q^{64} +33.4504i q^{65} +(17.3404 - 10.0115i) q^{67} +24.3113 q^{68} +(-109.037 + 62.9525i) q^{70} +(15.8426 + 9.14674i) q^{71} +(28.7511 - 49.7984i) q^{73} +(-0.161737 + 0.280136i) q^{74} +(18.5582 - 15.7436i) q^{76} +43.7451 q^{77} +(-81.7713 - 47.2107i) q^{79} +(-56.8884 - 98.5336i) q^{80} +(13.3959 + 23.2023i) q^{82} -81.9397 q^{83} +(-55.4209 - 95.9918i) q^{85} +(65.2718 - 37.6847i) q^{86} +29.1355i q^{88} +(-17.3556 + 10.0202i) q^{89} +(-46.5392 + 26.8694i) q^{91} +(8.21046 - 14.2209i) q^{92} -24.6835i q^{94} +(-104.469 - 37.3866i) q^{95} +(117.468 + 67.8200i) q^{97} +(-77.6539 - 44.8335i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5}+O(q^{10}) \) 6 * q + 3 * q^2 + 5 * q^4 + 2 * q^5	\( 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5} - 60 q^{10} - 26 q^{11} + 30 q^{13} - 54 q^{14} + q^{16} + 42 q^{17} + 25 q^{19} - 108 q^{20} - 39 q^{22} - 8 q^{23} - 17 q^{25} + 148 q^{26} + 32 q^{28} + 12 q^{29} - 51 q^{32} - 6 q^{34} + 38 q^{35} + 14 q^{38} - 96 q^{40} - 63 q^{41} - 34 q^{43} + 69 q^{44} - 58 q^{47} + 18 q^{49} + 162 q^{52} + 12 q^{53} - 28 q^{55} + 172 q^{58} + 147 q^{59} + 58 q^{61} + 116 q^{62} + 166 q^{64} + 201 q^{67} + 84 q^{68} - 198 q^{70} + 102 q^{71} + 7 q^{73} - 174 q^{74} - 173 q^{76} + 376 q^{77} - 134 q^{80} - 145 q^{82} - 146 q^{83} - 90 q^{85} + 270 q^{86} + 72 q^{89} - 216 q^{91} - 72 q^{92} - 558 q^{95} + 21 q^{97} - 411 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 + 5 * q^4 + 2 * q^5 - 60 * q^10 - 26 * q^11 + 30 * q^13 - 54 * q^14 + q^16 + 42 * q^17 + 25 * q^19 - 108 * q^20 - 39 * q^22 - 8 * q^23 - 17 * q^25 + 148 * q^26 + 32 * q^28 + 12 * q^29 - 51 * q^32 - 6 * q^34 + 38 * q^35 + 14 * q^38 - 96 * q^40 - 63 * q^41 - 34 * q^43 + 69 * q^44 - 58 * q^47 + 18 * q^49 + 162 * q^52 + 12 * q^53 - 28 * q^55 + 172 * q^58 + 147 * q^59 + 58 * q^61 + 116 * q^62 + 166 * q^64 + 201 * q^67 + 84 * q^68 - 198 * q^70 + 102 * q^71 + 7 * q^73 - 174 * q^74 - 173 * q^76 + 376 * q^77 - 134 * q^80 - 145 * q^82 - 146 * q^83 - 90 * q^85 + 270 * q^86 + 72 * q^89 - 216 * q^91 - 72 * q^92 - 558 * q^95 + 21 * q^97 - 411 * q^98

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