LMFDB - Embedded newform 180.3.c.b.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,3,Mod(91,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("180.91");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	180.c (of order $2$, degree $1$, 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:	$4.90464475849$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.85100625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + x^{5} + 3x^{4} + 2x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + x^5 + 3x^4 + 2x^3 - 8x^2 - 8*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.4
Root			$-0.600040 - 1.28061i$ of defining polynomial
Character	$\chi$	$=$	180.91
Dual form			180.3.c.b.91.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.67986 + 1.08539i) q^{2} +(1.64388 - 3.64660i) q^{4} -2.23607 q^{5} +0.596540i q^{7} +(1.19648 + 7.91002i) q^{8} +O(q^{10})$	\(q+(-1.67986 + 1.08539i) q^{2} +(1.64388 - 3.64660i) q^{4} -2.23607 q^{5} +0.596540i q^{7} +(1.19648 + 7.91002i) q^{8} +(3.75629 - 2.42700i) q^{10} -9.27963i q^{11} -23.5117 q^{13} +(-0.647476 - 1.00210i) q^{14} +(-10.5953 - 11.9891i) q^{16} -3.97751 q^{17} -7.04756i q^{19} +(-3.67582 + 8.15404i) q^{20} +(10.0720 + 15.5885i) q^{22} -32.0793i q^{23} +5.00000 q^{25} +(39.4964 - 25.5192i) q^{26} +(2.17534 + 0.980637i) q^{28} -35.6734 q^{29} -59.2585i q^{31} +(30.8115 + 8.64000i) q^{32} +(6.68167 - 4.31713i) q^{34} -1.33390i q^{35} -5.38761 q^{37} +(7.64932 + 11.8389i) q^{38} +(-2.67541 - 17.6873i) q^{40} -40.0791 q^{41} +36.1157i q^{43} +(-33.8391 - 15.2545i) q^{44} +(34.8184 + 53.8888i) q^{46} +74.0131i q^{47} +48.6441 q^{49} +(-8.39931 + 5.42693i) q^{50} +(-38.6503 + 85.7376i) q^{52} +2.55123 q^{53} +20.7499i q^{55} +(-4.71864 + 0.713748i) q^{56} +(59.9265 - 38.7194i) q^{58} -36.4026i q^{59} -8.73223 q^{61} +(64.3183 + 99.5461i) q^{62} +(-61.1369 + 18.9284i) q^{64} +52.5737 q^{65} +69.7379i q^{67} +(-6.53853 + 14.5044i) q^{68} +(1.44780 + 2.24077i) q^{70} +59.2170i q^{71} -83.0019 q^{73} +(9.05044 - 5.84763i) q^{74} +(-25.6996 - 11.5853i) q^{76} +5.53566 q^{77} +65.8705i q^{79} +(23.6919 + 26.8085i) q^{80} +(67.3274 - 43.5013i) q^{82} -129.909i q^{83} +8.89398 q^{85} +(-39.1995 - 60.6695i) q^{86} +(73.4020 - 11.1029i) q^{88} +130.466 q^{89} -14.0256i q^{91} +(-116.980 - 52.7344i) q^{92} +(-80.3327 - 124.332i) q^{94} +15.7588i q^{95} +93.1113 q^{97} +(-81.7155 + 52.7977i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 10 q^{4} + 20 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 + 10 * q^4 + 20 * q^8	$ 8 q - 4 q^{2} + 10 q^{4} + 20 q^{8} + 10 q^{10} + 16 q^{13} + 20 q^{14} + 34 q^{16} + 40 q^{20} + 68 q^{22} + 40 q^{25} + 36 q^{26} + 28 q^{28} - 64 q^{29} + 76 q^{32} - 92 q^{34} - 112 q^{37} + 40 q^{38} - 10 q^{40} + 16 q^{41} - 172 q^{44} + 152 q^{46} - 56 q^{49} - 20 q^{50} - 128 q^{52} - 352 q^{53} - 116 q^{56} - 204 q^{58} - 176 q^{61} + 56 q^{62} - 110 q^{64} + 80 q^{65} + 184 q^{68} - 60 q^{70} - 240 q^{73} - 132 q^{74} - 24 q^{76} + 288 q^{77} + 80 q^{80} + 40 q^{82} + 160 q^{85} + 200 q^{86} + 140 q^{88} - 80 q^{89} - 144 q^{92} - 96 q^{94} + 432 q^{97} - 660 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 10 * q^4 + 20 * q^8 + 10 * q^10 + 16 * q^13 + 20 * q^14 + 34 * q^16 + 40 * q^20 + 68 * q^22 + 40 * q^25 + 36 * q^26 + 28 * q^28 - 64 * q^29 + 76 * q^32 - 92 * q^34 - 112 * q^37 + 40 * q^38 - 10 * q^40 + 16 * q^41 - 172 * q^44 + 152 * q^46 - 56 * q^49 - 20 * q^50 - 128 * q^52 - 352 * q^53 - 116 * q^56 - 204 * q^58 - 176 * q^61 + 56 * q^62 - 110 * q^64 + 80 * q^65 + 184 * q^68 - 60 * q^70 - 240 * q^73 - 132 * q^74 - 24 * q^76 + 288 * q^77 + 80 * q^80 + 40 * q^82 + 160 * q^85 + 200 * q^86 + 140 * q^88 - 80 * q^89 - 144 * q^92 - 96 * q^94 + 432 * q^97 - 660 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.67986	+	1.08539i	−0.839931	+	0.542693i
$2$	−1.67986	+	1.08539i	−0.839931	+	0.542693i
$3$		0			0
$3$		0			0
$4$	1.64388	−	3.64660i	0.410969	−	0.911649i
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$		0			0
$7$			0.596540i			0.0852199i	0.999092	+	0.0426100i	$0.0135673\pi$
$7$			0.596540i			0.0852199i	−0.999092	+	0.0426100i	$0.986433\pi$
$8$	1.19648	+	7.91002i	0.149560	+	0.988753i
$9$		0			0
$10$	3.75629	−	2.42700i	0.375629	−	0.242700i
$11$		−	9.27963i		−	0.843602i	−0.906688	−	0.421801i	$-0.861398\pi$
$11$		−	9.27963i		−	0.843602i	0.906688	−	0.421801i	$-0.138602\pi$
$12$		0			0
$13$	−23.5117			−1.80859			−0.904295	−	0.426907i	$-0.859603\pi$
$13$	−23.5117			−1.80859			−0.904295	+	0.426907i	$0.859603\pi$
$14$	−0.647476	−	1.00210i	−0.0462483	−	0.0715789i
$15$		0			0
$16$	−10.5953	−	11.9891i	−0.662209	−	0.749319i
$17$	−3.97751			−0.233971			−0.116986	−	0.993134i	$-0.537323\pi$
$17$	−3.97751			−0.233971			−0.116986	+	0.993134i	$0.537323\pi$
$18$		0			0
$19$		−	7.04756i		−	0.370924i	−0.982651	−	0.185462i	$-0.940622\pi$
$19$		−	7.04756i		−	0.370924i	0.982651	−	0.185462i	$-0.0593782\pi$
$20$	−3.67582	+	8.15404i	−0.183791	+	0.407702i
$21$		0			0
$22$	10.0720	+	15.5885i	0.457817	+	0.708568i
$23$		−	32.0793i		−	1.39475i	−0.716705	−	0.697376i	$-0.754351\pi$
$23$		−	32.0793i		−	1.39475i	0.716705	−	0.697376i	$-0.245649\pi$
$24$		0			0
$25$	5.00000			0.200000
$26$	39.4964	−	25.5192i	1.51909	−	0.981509i
$27$		0			0
$28$	2.17534	+	0.980637i	0.0776907	+	0.0350227i
$29$	−35.6734			−1.23012			−0.615059	−	0.788481i	$-0.710868\pi$
$29$	−35.6734			−1.23012			−0.615059	+	0.788481i	$0.710868\pi$
$30$		0			0
$31$		−	59.2585i		−	1.91156i	−0.294076	−	0.955782i	$-0.595012\pi$
$31$		−	59.2585i		−	1.91156i	0.294076	−	0.955782i	$-0.404988\pi$
$32$	30.8115	+	8.64000i	0.962860	+	0.270000i
$33$		0			0
$34$	6.68167	−	4.31713i	0.196520	−	0.126974i
$35$		−	1.33390i		−	0.0381115i
$36$		0			0
$37$	−5.38761			−0.145611			−0.0728055	−	0.997346i	$-0.523195\pi$
$37$	−5.38761			−0.145611			−0.0728055	+	0.997346i	$0.523195\pi$
$38$	7.64932	+	11.8389i	0.201298	+	0.311551i
$39$		0			0
$40$	−2.67541	−	17.6873i	−0.0668853	−	0.442184i
$41$	−40.0791			−0.977539			−0.488769	−	0.872413i	$-0.662554\pi$
$41$	−40.0791			−0.977539			−0.488769	+	0.872413i	$0.662554\pi$
$42$		0			0
$43$			36.1157i			0.839901i	0.907547	+	0.419950i	$0.137953\pi$
$43$			36.1157i			0.839901i	−0.907547	+	0.419950i	$0.862047\pi$
$44$	−33.8391	−	15.2545i	−0.769070	−	0.346694i
$45$		0			0
$46$	34.8184	+	53.8888i	0.756922	+	1.17150i
$47$			74.0131i			1.57475i	0.616477	+	0.787373i	$0.288559\pi$
$47$			74.0131i			1.57475i	−0.616477	+	0.787373i	$0.711441\pi$
$48$		0			0
$49$	48.6441			0.992738
$50$	−8.39931	+	5.42693i	−0.167986	+	0.108539i
$51$		0			0
$52$	−38.6503	+	85.7376i	−0.743275	+	1.64880i
$53$	2.55123			0.0481364			0.0240682	−	0.999710i	$-0.492338\pi$
$53$	2.55123			0.0481364			0.0240682	+	0.999710i	$0.492338\pi$
$54$		0			0
$55$			20.7499i			0.377270i
$56$	−4.71864	+	0.713748i	−0.0842614	+	0.0127455i
$57$		0			0
$58$	59.9265	−	38.7194i	1.03321	−	0.667576i
$59$		−	36.4026i		−	0.616993i	−0.951225	−	0.308497i	$-0.900174\pi$
$59$		−	36.4026i		−	0.616993i	0.951225	−	0.308497i	$-0.0998259\pi$
$60$		0			0
$61$	−8.73223			−0.143151			−0.0715757	−	0.997435i	$-0.522803\pi$
$61$	−8.73223			−0.143151			−0.0715757	+	0.997435i	$0.522803\pi$
$62$	64.3183	+	99.5461i	1.03739	+	1.60558i
$63$		0			0
$64$	−61.1369	+	18.9284i	−0.955264	+	0.295756i
$65$	52.5737			0.808826
$66$		0			0
$67$			69.7379i			1.04086i	0.853903	+	0.520432i	$0.174229\pi$
$67$			69.7379i			1.04086i	−0.853903	+	0.520432i	$0.825771\pi$
$68$	−6.53853	+	14.5044i	−0.0961548	+	0.213300i
$69$		0			0
$70$	1.44780	+	2.24077i	0.0206828	+	0.0320110i
$71$			59.2170i			0.834043i	0.908897	+	0.417021i	$0.136926\pi$
$71$			59.2170i			0.834043i	−0.908897	+	0.417021i	$0.863074\pi$
$72$		0			0
$73$	−83.0019			−1.13701			−0.568506	−	0.822679i	$-0.692478\pi$
$73$	−83.0019			−1.13701			−0.568506	+	0.822679i	$0.692478\pi$
$74$	9.05044	−	5.84763i	0.122303	−	0.0790220i
$75$		0			0
$76$	−25.6996	−	11.5853i	−0.338153	−	0.152438i
$77$	5.53566			0.0718917
$78$		0			0
$79$			65.8705i			0.833804i	0.908951	+	0.416902i	$0.136884\pi$
$79$			65.8705i			0.833804i	−0.908951	+	0.416902i	$0.863116\pi$
$80$	23.6919	+	26.8085i	0.296149	+	0.335106i
$81$		0			0
$82$	67.3274	−	43.5013i	0.821065	−	0.530503i
$83$		−	129.909i		−	1.56517i	−0.622542	−	0.782586i	$-0.713900\pi$
$83$		−	129.909i		−	1.56517i	0.622542	−	0.782586i	$-0.286100\pi$
$84$		0			0
$85$	8.89398			0.104635
$86$	−39.1995	−	60.6695i	−0.455808	−	0.705459i
$87$		0			0
$88$	73.4020	−	11.1029i	0.834114	−	0.126169i
$89$	130.466			1.46591			0.732956	−	0.680277i	$-0.238140\pi$
$89$	130.466			1.46591			0.732956	+	0.680277i	$0.238140\pi$
$90$		0			0
$91$		−	14.0256i		−	0.154128i
$92$	−116.980	−	52.7344i	−1.27152	−	0.573200i
$93$		0			0
$94$	−80.3327	−	124.332i	−0.854603	−	1.32268i
$95$			15.7588i			0.165882i
$96$		0			0
$97$	93.1113			0.959911			0.479955	−	0.877293i	$-0.340653\pi$
$97$	93.1113			0.959911			0.479955	+	0.877293i	$0.340653\pi$
$98$	−81.7155	+	52.7977i	−0.833831	+	0.538752i
$99$		0			0
$100$	8.21938	−	18.2330i	0.0821938	−	0.182330i
$101$	3.66081			0.0362457			0.0181228	−	0.999836i	$-0.494231\pi$
$101$	3.66081			0.0362457			0.0181228	+	0.999836i	$0.494231\pi$
$102$		0			0
$103$		−	151.417i		−	1.47007i	−0.678032	−	0.735033i	$-0.737167\pi$
$103$		−	151.417i		−	1.47007i	0.678032	−	0.735033i	$-0.262833\pi$
$104$	−28.1313	−	185.978i	−0.270493	−	1.78825i
$105$		0			0
$106$	−4.28571	+	2.76907i	−0.0404313	+	0.0261233i
$107$			82.8092i			0.773918i	0.922097	+	0.386959i	$0.126474\pi$
$107$			82.8092i			0.773918i	−0.922097	+	0.386959i	$0.873526\pi$
$108$		0			0
$109$	−7.36835			−0.0675996			−0.0337998	−	0.999429i	$-0.510761\pi$
$109$	−7.36835			−0.0675996			−0.0337998	+	0.999429i	$0.510761\pi$
$110$	−22.5216	−	34.8569i	−0.204742	−	0.316881i
$111$		0			0
$112$	7.15197	−	6.32054i	0.0638569	−	0.0564334i
$113$	−65.0370			−0.575549			−0.287774	−	0.957698i	$-0.592915\pi$
$113$	−65.0370			−0.575549			−0.287774	+	0.957698i	$0.592915\pi$
$114$		0			0
$115$			71.7315i			0.623752i
$116$	−58.6427	+	130.087i	−0.505540	+	1.12144i
$117$		0			0
$118$	39.5109	+	61.1514i	0.334838	+	0.518232i
$119$		−	2.37274i		−	0.0199390i
$120$		0			0
$121$	34.8885			0.288335
$122$	14.6689	−	9.47784i	0.120237	−	0.0776872i
$123$		0			0
$124$	−216.092	−	97.4136i	−1.74268	−	0.785593i
$125$	−11.1803			−0.0894427
$126$		0			0
$127$		−	139.469i		−	1.09818i	−0.835763	−	0.549091i	$-0.814974\pi$
$127$		−	139.469i		−	1.09818i	0.835763	−	0.549091i	$-0.185026\pi$
$128$	82.1569	−	98.1542i	0.641851	−	0.766829i
$129$		0			0
$130$	−88.3166	+	57.0628i	−0.679359	+	0.438944i
$131$		−	63.4856i		−	0.484623i	−0.970198	−	0.242312i	$-0.922094\pi$
$131$		−	63.4856i		−	0.484623i	0.970198	−	0.242312i	$-0.0779056\pi$
$132$		0			0
$133$	4.20415			0.0316101
$134$	−75.6925	−	117.150i	−0.564870	−	0.874254i
$135$		0			0
$136$	−4.75901	−	31.4622i	−0.0349927	−	0.231340i
$137$	138.157			1.00845			0.504223	−	0.863573i	$-0.331779\pi$
$137$	138.157			1.00845			0.504223	+	0.863573i	$0.331779\pi$
$138$		0			0
$139$		−	29.9578i		−	0.215523i	−0.994177	−	0.107762i	$-0.965632\pi$
$139$		−	29.9578i		−	0.215523i	0.994177	−	0.107762i	$-0.0343684\pi$
$140$	−4.86421	−	2.19277i	−0.0347443	−	0.0156626i
$141$		0			0
$142$	−64.2733	−	99.4765i	−0.452629	−	0.700539i
$143$			218.180i			1.52573i
$144$		0			0
$145$	79.7682			0.550126
$146$	139.432	−	90.0891i	0.955012	−	0.617048i
$147$		0			0
$148$	−8.85655	+	19.6464i	−0.0598416	+	0.132746i
$149$	47.3823			0.318002			0.159001	−	0.987278i	$-0.449173\pi$
$149$	47.3823			0.318002			0.159001	+	0.987278i	$0.449173\pi$
$150$		0			0
$151$			109.604i			0.725852i	0.931818	+	0.362926i	$0.118222\pi$
$151$			109.604i			0.725852i	−0.931818	+	0.362926i	$0.881778\pi$
$152$	55.7463	−	8.43227i	0.366752	−	0.0554755i
$153$		0			0
$154$	−9.29915	+	6.00833i	−0.0603841	+	0.0390151i
$155$			132.506i			0.854877i
$156$		0			0
$157$	−177.588			−1.13113			−0.565566	−	0.824703i	$-0.691342\pi$
$157$	−177.588			−1.13113			−0.565566	+	0.824703i	$0.691342\pi$
$158$	−71.4950	−	110.653i	−0.452500	−	0.700338i
$159$		0			0
$160$	−68.8967	−	19.3196i	−0.430604	−	0.120748i
$161$	19.1366			0.118861
$162$		0			0
$163$		−	96.8778i		−	0.594342i	−0.954824	−	0.297171i	$-0.903957\pi$
$163$		−	96.8778i		−	0.594342i	0.954824	−	0.297171i	$-0.0960432\pi$
$164$	−65.8850	+	146.152i	−0.401738	+	0.891173i
$165$		0			0
$166$	141.002	+	218.230i	0.849408	+	1.31464i
$167$		−	152.605i		−	0.913801i	−0.889518	−	0.456901i	$-0.848960\pi$
$167$		−	152.605i		−	0.913801i	0.889518	−	0.456901i	$-0.151040\pi$
$168$		0			0
$169$	383.799			2.27100
$170$	−14.9407	+	9.65340i	−0.0878862	+	0.0567847i
$171$		0			0
$172$	131.700	+	59.3698i	0.765695	+	0.345173i
$173$	−155.773			−0.900422			−0.450211	−	0.892922i	$-0.648651\pi$
$173$	−155.773			−0.900422			−0.450211	+	0.892922i	$0.648651\pi$
$174$		0			0
$175$			2.98270i			0.0170440i
$176$	−111.254	+	98.3209i	−0.632127	+	0.558641i
$177$		0			0
$178$	−219.165	+	141.606i	−1.23126	+	0.795540i
$179$			126.001i			0.703915i	0.936016	+	0.351957i	$0.114484\pi$
$179$			126.001i			0.703915i	−0.936016	+	0.351957i	$0.885516\pi$
$180$		0			0
$181$	−346.725			−1.91561			−0.957803	−	0.287424i	$-0.907201\pi$
$181$	−346.725			−1.91561			−0.957803	+	0.287424i	$0.907201\pi$
$182$	15.2232	+	23.5612i	0.0836442	+	0.129457i
$183$		0			0
$184$	253.748	−	38.3823i	1.37906	−	0.208599i
$185$	12.0471			0.0651192
$186$		0			0
$187$			36.9098i			0.197379i
$188$	269.896	+	121.668i	1.43562	+	0.647171i
$189$		0			0
$190$	−17.1044	−	26.4727i	−0.0900232	−	0.139330i
$191$		−	133.159i		−	0.697167i	−0.937278	−	0.348584i	$-0.886663\pi$
$191$		−	133.159i		−	0.697167i	0.937278	−	0.348584i	$-0.113337\pi$
$192$		0			0
$193$	−136.246			−0.705940			−0.352970	−	0.935635i	$-0.614828\pi$
$193$	−136.246			−0.705940			−0.352970	+	0.935635i	$0.614828\pi$
$194$	−156.414	+	101.062i	−0.806259	+	0.520937i
$195$		0			0
$196$	79.9649	−	177.386i	0.407984	−	0.905029i
$197$	−74.8945			−0.380175			−0.190087	−	0.981767i	$-0.560877\pi$
$197$	−74.8945			−0.380175			−0.190087	+	0.981767i	$0.560877\pi$
$198$		0			0
$199$			251.605i			1.26434i	0.774828	+	0.632172i	$0.217836\pi$
$199$			251.605i			1.26434i	−0.774828	+	0.632172i	$0.782164\pi$
$200$	5.98240	+	39.5501i	0.0299120	+	0.197751i
$201$		0			0
$202$	−6.14966	+	3.97339i	−0.0304439	+	0.0196703i
$203$		−	21.2806i		−	0.104831i
$204$		0			0
$205$	89.6196			0.437169
$206$	164.346	+	254.359i	0.797794	+	1.23475i
$207$		0			0
$208$	249.114	+	281.884i	1.19767	+	1.35521i
$209$	−65.3987			−0.312913
$210$		0			0
$211$			228.203i			1.08153i	0.841173	+	0.540766i	$0.181865\pi$
$211$			228.203i			1.08153i	−0.841173	+	0.540766i	$0.818135\pi$
$212$	4.19390	−	9.30331i	0.0197826	−	0.0438835i
$213$		0			0
$214$	−89.8799	−	139.108i	−0.420000	−	0.650038i
$215$		−	80.7573i		−	0.375615i
$216$		0			0
$217$	35.3500			0.162903
$218$	12.3778	−	7.99751i	0.0567790	−	0.0366858i
$219$		0			0
$220$	75.6664	+	34.1102i	0.343938	+	0.155046i
$221$	93.5179			0.423158
$222$		0			0
$223$		−	85.9549i		−	0.385448i	−0.981253	−	0.192724i	$-0.938268\pi$
$223$		−	85.9549i		−	0.385448i	0.981253	−	0.192724i	$-0.0617322\pi$
$224$	−5.15410	+	18.3803i	−0.0230094	+	0.0820549i
$225$		0			0
$226$	109.253	−	70.5902i	0.483421	−	0.312346i
$227$		−	282.357i		−	1.24386i	−0.783071	−	0.621932i	$-0.786348\pi$
$227$		−	282.357i		−	1.24386i	0.783071	−	0.621932i	$-0.213652\pi$
$228$		0			0
$229$	138.263			0.603768			0.301884	−	0.953345i	$-0.402385\pi$
$229$	138.263			0.603768			0.301884	+	0.953345i	$0.402385\pi$
$230$	−77.8563	−	120.499i	−0.338506	−	0.523909i
$231$		0			0
$232$	−42.6826	−	282.178i	−0.183977	−	1.21628i
$233$	0.522939			0.00224438			0.00112219	−	0.999999i	$-0.499643\pi$
$233$	0.522939			0.00224438			0.00112219	+	0.999999i	$0.499643\pi$
$234$		0			0
$235$		−	165.498i		−	0.704248i
$236$	−132.746	−	59.8413i	−0.562482	−	0.253565i
$237$		0			0
$238$	2.57534	+	3.98588i	0.0108208	+	0.0167474i
$239$		−	73.6928i		−	0.308338i	−0.988044	−	0.154169i	$-0.950730\pi$
$239$		−	73.6928i		−	0.308338i	0.988044	−	0.154169i	$-0.0492700\pi$
$240$		0			0
$241$	31.3705			0.130168			0.0650840	−	0.997880i	$-0.479268\pi$
$241$	31.3705			0.130168			0.0650840	+	0.997880i	$0.479268\pi$
$242$	−58.6080	+	37.8675i	−0.242182	+	0.156477i
$243$		0			0
$244$	−14.3547	+	31.8429i	−0.0588307	+	0.130504i
$245$	−108.772			−0.443966
$246$		0			0
$247$			165.700i			0.670850i
$248$	468.736	−	70.9016i	1.89006	−	0.285894i
$249$		0			0
$250$	18.7814	−	12.1350i	0.0751257	−	0.0485399i
$251$		−	78.7478i		−	0.313736i	−0.987620	−	0.156868i	$-0.949860\pi$
$251$		−	78.7478i		−	0.313736i	0.987620	−	0.156868i	$-0.0501398\pi$
$252$		0			0
$253$	−297.684			−1.17662
$254$	151.378	+	234.289i	0.595975	+	0.922397i
$255$		0			0
$256$	−31.4772	+	254.057i	−0.122958	+	0.992412i
$257$	−243.954			−0.949236			−0.474618	−	0.880192i	$-0.657414\pi$
$257$	−243.954			−0.949236			−0.474618	+	0.880192i	$0.657414\pi$
$258$		0			0
$259$		−	3.21392i		−	0.0124090i
$260$	86.4246	−	191.715i	0.332402	−	0.737366i
$261$		0			0
$262$	68.9064	+	106.647i	0.263002	+	0.407050i
$263$		−	102.737i		−	0.390635i	−0.980740	−	0.195317i	$-0.937426\pi$
$263$		−	102.737i		−	0.390635i	0.980740	−	0.195317i	$-0.0625737\pi$
$264$		0			0
$265$	−5.70472			−0.0215273
$266$	−7.06239	+	4.56312i	−0.0265503	+	0.0171546i
$267$		0			0
$268$	254.306	+	114.640i	0.948903	+	0.427763i
$269$	123.646			0.459651			0.229825	−	0.973232i	$-0.426184\pi$
$269$	123.646			0.459651			0.229825	+	0.973232i	$0.426184\pi$
$270$		0			0
$271$		−	332.371i		−	1.22646i	−0.789904	−	0.613230i	$-0.789870\pi$
$271$		−	332.371i		−	1.22646i	0.789904	−	0.613230i	$-0.210130\pi$
$272$	42.1431	+	47.6868i	0.154938	+	0.175319i
$273$		0			0
$274$	−232.085	+	149.954i	−0.847026	+	0.547277i
$275$		−	46.3981i		−	0.168720i
$276$		0			0
$277$	−125.916			−0.454571			−0.227286	−	0.973828i	$-0.572985\pi$
$277$	−125.916			−0.454571			−0.227286	+	0.973828i	$0.572985\pi$
$278$	32.5157	+	50.3249i	0.116963	+	0.181025i
$279$		0			0
$280$	10.5512	−	1.59599i	0.0376829	−	0.00569996i
$281$	−52.5628			−0.187056			−0.0935281	−	0.995617i	$-0.529814\pi$
$281$	−52.5628			−0.187056			−0.0935281	+	0.995617i	$0.529814\pi$
$282$		0			0
$283$		−	199.288i		−	0.704199i	−0.935963	−	0.352100i	$-0.885468\pi$
$283$		−	199.288i		−	0.704199i	0.935963	−	0.352100i	$-0.114532\pi$
$284$	215.941	+	97.3454i	0.760355	+	0.342766i
$285$		0			0
$286$	−236.809	−	366.512i	−0.828004	−	1.28151i
$287$		−	23.9088i		−	0.0833058i
$288$		0			0
$289$	−273.179			−0.945258
$290$	−134.000	+	86.5793i	−0.462068	+	0.298549i
$291$		0			0
$292$	−136.445	+	302.674i	−0.467276	+	1.03656i
$293$	−102.161			−0.348672			−0.174336	−	0.984686i	$-0.555778\pi$
$293$	−102.161			−0.348672			−0.174336	+	0.984686i	$0.555778\pi$
$294$		0			0
$295$			81.3987i			0.275928i
$296$	−6.44617	−	42.6161i	−0.0217776	−	0.143973i
$297$		0			0
$298$	−79.5957	+	51.4281i	−0.267100	+	0.172577i
$299$			754.238i			2.52254i
$300$		0			0
$301$	−21.5445			−0.0715763
$302$	−118.962	−	184.119i	−0.393915	−	0.609666i
$303$		0			0
$304$	−84.4939	+	74.6713i	−0.277941	+	0.245629i
$305$	19.5259			0.0640192
$306$		0			0
$307$		−	328.391i		−	1.06968i	−0.844954	−	0.534839i	$-0.820372\pi$
$307$		−	328.391i		−	1.06968i	0.844954	−	0.534839i	$-0.179628\pi$
$308$	9.09994	−	20.1863i	0.0295453	−	0.0655401i
$309$		0			0
$310$	−143.820	−	222.592i	−0.463936	−	0.718038i
$311$			95.4377i			0.306874i	0.988158	+	0.153437i	$0.0490342\pi$
$311$			95.4377i			0.306874i	−0.988158	+	0.153437i	$0.950966\pi$
$312$		0			0
$313$	550.408			1.75849			0.879246	−	0.476368i	$-0.158047\pi$
$313$	550.408			1.75849			0.879246	+	0.476368i	$0.158047\pi$
$314$	298.323	−	192.751i	0.950073	−	0.613858i
$315$		0			0
$316$	240.203	+	108.283i	0.760137	+	0.342668i
$317$	−439.394			−1.38610			−0.693051	−	0.720889i	$-0.743734\pi$
$317$	−439.394			−1.38610			−0.693051	+	0.720889i	$0.743734\pi$
$318$		0			0
$319$			331.036i			1.03773i
$320$	136.706	−	42.3251i	0.427207	−	0.132266i
$321$		0			0
$322$	−32.1468	+	20.7706i	−0.0998348	+	0.0645048i
$323$			28.0317i			0.0867855i
$324$		0			0
$325$	−117.558			−0.361718
$326$	105.150	+	162.741i	0.322545	+	0.499206i
$327$		0			0
$328$	−47.9539	−	317.026i	−0.146201	−	0.966544i
$329$	−44.1517			−0.134200
$330$		0			0
$331$		−	479.922i		−	1.44992i	−0.688794	−	0.724958i	$-0.741859\pi$
$331$		−	479.922i		−	1.44992i	0.688794	−	0.724958i	$-0.258141\pi$
$332$	−473.727	−	213.555i	−1.42689	−	0.643237i
$333$		0			0
$334$	165.635	+	256.355i	0.495913	+	0.767530i
$335$		−	155.939i		−	0.465489i
$336$		0			0
$337$	58.8437			0.174610			0.0873052	−	0.996182i	$-0.472174\pi$
$337$	58.8437			0.174610			0.0873052	+	0.996182i	$0.472174\pi$
$338$	−644.730	+	416.570i	−1.90748	+	1.23246i
$339$		0			0
$340$	14.6206	−	32.4328i	0.0430017	−	0.0953905i
$341$	−549.897			−1.61260
$342$		0			0
$343$			58.2486i			0.169821i
$344$	−285.676	+	43.2118i	−0.830454	+	0.125616i
$345$		0			0
$346$	261.677	−	169.074i	0.756293	−	0.488653i
$347$		−	12.1484i		−	0.0350099i	−0.999847	−	0.0175049i	$-0.994428\pi$
$347$		−	12.1484i		−	0.0350099i	0.999847	−	0.0175049i	$-0.00557228\pi$
$348$		0			0
$349$	−30.9277			−0.0886180			−0.0443090	−	0.999018i	$-0.514109\pi$
$349$	−30.9277			−0.0886180			−0.0443090	+	0.999018i	$0.514109\pi$
$350$	−3.23738	−	5.01052i	−0.00924965	−	0.0143158i
$351$		0			0
$352$	80.1760	−	285.919i	0.227773	−	0.812271i
$353$	288.065			0.816048			0.408024	−	0.912971i	$-0.366218\pi$
$353$	288.065			0.816048			0.408024	+	0.912971i	$0.366218\pi$
$354$		0			0
$355$		−	132.413i		−	0.372995i
$356$	214.470	−	475.757i	0.602444	−	1.33640i
$357$		0			0
$358$	−136.759	−	211.664i	−0.382010	−	0.591240i
$359$		−	663.911i		−	1.84933i	−0.380776	−	0.924667i	$-0.624343\pi$
$359$		−	663.911i		−	1.84933i	0.380776	−	0.924667i	$-0.375657\pi$
$360$		0			0
$361$	311.332			0.862415
$362$	582.450	−	376.330i	1.60898	−	1.03959i
$363$		0			0
$364$	−51.1459	−	23.0564i	−0.140511	−	0.0633418i
$365$	185.598			0.508487
$366$		0			0
$367$			6.08529i			0.0165812i	0.999966	+	0.00829059i	$0.00263901\pi$
$367$			6.08529i			0.0165812i	−0.999966	+	0.00829059i	$0.997361\pi$
$368$	−384.602	+	339.891i	−1.04511	+	0.923618i
$369$		0			0
$370$	−20.2374	+	13.0757i	−0.0546957	+	0.0353397i
$371$			1.52191i			0.00410218i
$372$		0			0
$373$	−204.741			−0.548903			−0.274451	−	0.961601i	$-0.588496\pi$
$373$	−204.741			−0.548903			−0.274451	+	0.961601i	$0.588496\pi$
$374$	−40.0614	−	62.0034i	−0.107116	−	0.165784i
$375$		0			0
$376$	−585.445	+	88.5552i	−1.55703	+	0.235519i
$377$	838.742			2.22478
$378$		0			0
$379$		−	402.331i		−	1.06156i	−0.847510	−	0.530780i	$-0.821899\pi$
$379$		−	402.331i		−	1.06156i	0.847510	−	0.530780i	$-0.178101\pi$
$380$	57.4661	+	25.9055i	0.151227	+	0.0681725i
$381$		0			0
$382$	144.529	+	223.689i	0.378348	+	0.585573i
$383$			331.751i			0.866191i	0.901348	+	0.433096i	$0.142579\pi$
$383$			331.751i			0.866191i	−0.901348	+	0.433096i	$0.857421\pi$
$384$		0			0
$385$	−12.3781			−0.0321510
$386$	228.875	−	147.880i	0.592941	−	0.383109i
$387$		0			0
$388$	153.063	−	339.540i	0.394493	−	0.875102i
$389$	623.310			1.60234			0.801169	−	0.598438i	$-0.204212\pi$
$389$	623.310			1.60234			0.801169	+	0.598438i	$0.204212\pi$
$390$		0			0
$391$			127.596i			0.326332i
$392$	58.2018	+	384.776i	0.148474	+	0.981572i
$393$		0			0
$394$	125.812	−	81.2894i	0.319321	−	0.206318i
$395$		−	147.291i		−	0.372889i
$396$		0			0
$397$	−355.449			−0.895338			−0.447669	−	0.894199i	$-0.647746\pi$
$397$	−355.449			−0.895338			−0.447669	+	0.894199i	$0.647746\pi$
$398$	−273.088	−	422.661i	−0.686151	−	1.06196i
$399$		0			0
$400$	−52.9767	−	59.9455i	−0.132442	−	0.149864i
$401$	542.927			1.35393			0.676966	−	0.736014i	$-0.263294\pi$
$401$	542.927			1.35393			0.676966	+	0.736014i	$0.263294\pi$
$402$		0			0
$403$			1393.27i			3.45724i
$404$	6.01792	−	13.3495i	0.0148958	−	0.0330433i
$405$		0			0
$406$	23.0977	+	35.7485i	0.0568908	+	0.0880505i
$407$			49.9950i			0.122838i
$408$		0			0
$409$	−108.497			−0.265273			−0.132636	−	0.991165i	$-0.542344\pi$
$409$	−108.497			−0.265273			−0.132636	+	0.991165i	$0.542344\pi$
$410$	−150.549	+	97.2718i	−0.367192	+	0.237248i
$411$		0			0
$412$	−552.156	−	248.910i	−1.34018	−	0.604151i
$413$	21.7156			0.0525801
$414$		0			0
$415$			290.486i			0.699966i
$416$	−724.431	−	203.141i	−1.74142	−	0.488320i
$417$		0			0
$418$	109.861	−	70.9828i	0.262825	−	0.169815i
$419$			172.176i			0.410921i	0.978665	+	0.205460i	$0.0658691\pi$
$419$			172.176i			0.410921i	−0.978665	+	0.205460i	$0.934131\pi$
$420$		0			0
$421$	478.522			1.13663			0.568316	−	0.822810i	$-0.307595\pi$
$421$	478.522			1.13663			0.568316	+	0.822810i	$0.307595\pi$
$422$	−247.688	−	383.350i	−0.586940	−	0.908412i
$423$		0			0
$424$	3.05250	+	20.1803i	0.00719929	+	0.0475950i
$425$	−19.8875			−0.0467942
$426$		0			0
$427$		−	5.20912i		−	0.0121993i
$428$	301.972	+	136.128i	0.705541	+	0.318056i
$429$		0			0
$430$	87.6528	+	135.661i	0.203844	+	0.315491i
$431$			290.722i			0.674530i	0.941410	+	0.337265i	$0.109502\pi$
$431$			290.722i			0.674530i	−0.941410	+	0.337265i	$0.890498\pi$
$432$		0			0
$433$	53.7726			0.124186			0.0620931	−	0.998070i	$-0.480222\pi$
$433$	53.7726			0.124186			0.0620931	+	0.998070i	$0.480222\pi$
$434$	−59.3832	+	38.3684i	−0.136828	+	0.0884065i
$435$		0			0
$436$	−12.1127	+	26.8694i	−0.0277813	+	0.0616271i
$437$	−226.081			−0.517347
$438$		0			0
$439$			328.657i			0.748650i	0.927298	+	0.374325i	$0.122126\pi$
$439$			328.657i			0.748650i	−0.927298	+	0.374325i	$0.877874\pi$
$440$	−164.132	+	24.8268i	−0.373027	+	0.0564246i
$441$		0			0
$442$	−157.097	+	101.503i	−0.355424	+	0.229645i
$443$		−	428.910i		−	0.968194i	−0.875014	−	0.484097i	$-0.839148\pi$
$443$		−	428.910i		−	0.968194i	0.875014	−	0.484097i	$-0.160852\pi$
$444$		0			0
$445$	−291.731			−0.655575
$446$	93.2942	+	144.392i	0.209180	+	0.323750i
$447$		0			0
$448$	−11.2915	−	36.4706i	−0.0252043	−	0.0814075i
$449$	−409.229			−0.911423			−0.455711	−	0.890128i	$-0.650615\pi$
$449$	−409.229			−0.911423			−0.455711	+	0.890128i	$0.650615\pi$
$450$		0			0
$451$			371.919i			0.824654i
$452$	−106.913	+	237.164i	−0.236533	+	0.524698i
$453$		0			0
$454$	306.466	+	474.321i	0.675036	+	1.04476i
$455$			31.3623i			0.0689281i
$456$		0			0
$457$	768.561			1.68175			0.840876	−	0.541228i	$-0.182040\pi$
$457$	768.561			1.68175			0.840876	+	0.541228i	$0.182040\pi$
$458$	−232.262	+	150.068i	−0.507123	+	0.327660i
$459$		0			0
$460$	261.576	+	117.918i	0.568643	+	0.256343i
$461$	316.563			0.686687			0.343343	−	0.939210i	$-0.388441\pi$
$461$	316.563			0.686687			0.343343	+	0.939210i	$0.388441\pi$
$462$		0			0
$463$		−	491.208i		−	1.06093i	−0.847708	−	0.530463i	$-0.822018\pi$
$463$		−	491.208i		−	1.06093i	0.847708	−	0.530463i	$-0.177982\pi$
$464$	377.972	+	427.692i	0.814596	+	0.921751i
$465$		0			0
$466$	−0.878466	+	0.567591i	−0.00188512	+	0.00121801i
$467$			410.393i			0.878785i	0.898295	+	0.439393i	$0.144806\pi$
$467$			410.393i			0.878785i	−0.898295	+	0.439393i	$0.855194\pi$
$468$		0			0
$469$	−41.6014			−0.0887024
$470$	179.629	+	278.014i	0.382190	+	0.591520i
$471$		0			0
$472$	287.945	−	43.5550i	0.610054	−	0.0922776i
$473$	335.141			0.708542
$474$		0			0
$475$		−	35.2378i		−	0.0741848i
$476$	−8.65243	−	3.90049i	−0.0181774	−	0.00819431i
$477$		0			0
$478$	79.9851	+	123.794i	0.167333	+	0.258983i
$479$			198.918i			0.415277i	0.978206	+	0.207638i	$0.0665778\pi$
$479$			198.918i			0.415277i	−0.978206	+	0.207638i	$0.933422\pi$
$480$		0			0
$481$	126.672			0.263351
$482$	−52.6981	+	34.0491i	−0.109332	+	0.0706413i
$483$		0			0
$484$	57.3524	−	127.224i	0.118497	−	0.262860i
$485$	−208.203			−0.429285
$486$		0			0
$487$			204.762i			0.420456i	0.977652	+	0.210228i	$0.0674206\pi$
$487$			204.762i			0.420456i	−0.977652	+	0.210228i	$0.932579\pi$
$488$	−10.4479	−	69.0721i	−0.0214097	−	0.141541i
$489$		0			0
$490$	182.721	−	118.059i	0.372901	−	0.240937i
$491$			788.598i			1.60611i	0.595908	+	0.803053i	$0.296792\pi$
$491$			788.598i			1.60611i	−0.595908	+	0.803053i	$0.703208\pi$
$492$		0			0
$493$	141.891			0.287812
$494$	−179.848	−	278.353i	−0.364066	−	0.563468i
$495$		0			0
$496$	−710.456	+	627.864i	−1.43237	+	1.26586i
$497$	−35.3253			−0.0710771
$498$		0			0
$499$		−	740.385i		−	1.48374i	−0.670545	−	0.741869i	$-0.733940\pi$
$499$		−	740.385i		−	1.48374i	0.670545	−	0.741869i	$-0.266060\pi$
$500$	−18.3791	+	40.7702i	−0.0367582	+	0.0815404i
$501$		0			0
$502$	85.4717	+	132.285i	0.170262	+	0.263517i
$503$			70.8800i			0.140914i	0.997515	+	0.0704572i	$0.0224458\pi$
$503$			70.8800i			0.140914i	−0.997515	+	0.0704572i	$0.977554\pi$
$504$		0			0
$505$	−8.18582			−0.0162095
$506$	500.068	−	323.102i	0.988277	−	0.638541i
$507$		0			0
$508$	−508.588	−	229.270i	−1.00116	−	0.451318i
$509$	−522.642			−1.02680			−0.513400	−	0.858149i	$-0.671614\pi$
$509$	−522.642			−1.02680			−0.513400	+	0.858149i	$0.671614\pi$
$510$		0			0
$511$		−	49.5139i		−	0.0968961i
$512$	−222.873	−	460.946i	−0.435299	−	0.900286i
$513$		0			0
$514$	409.809	−	264.784i	0.797293	−	0.515144i
$515$			338.578i			0.657433i
$516$		0			0
$517$	686.813			1.32846
$518$	3.48834	+	5.39894i	0.00673425	+	0.0104227i
$519$		0			0
$520$	62.9034	+	415.859i	0.120968	+	0.799729i
$521$	−304.082			−0.583650			−0.291825	−	0.956472i	$-0.594262\pi$
$521$	−304.082			−0.583650			−0.291825	+	0.956472i	$0.594262\pi$
$522$		0			0
$523$			174.416i			0.333491i	0.986000	+	0.166746i	$0.0533259\pi$
$523$			174.416i			0.333491i	−0.986000	+	0.166746i	$0.946674\pi$
$524$	−231.507	−	104.362i	−0.441806	−	0.199165i
$525$		0			0
$526$	111.509	+	172.584i	0.211995	+	0.328106i
$527$			235.701i			0.447251i
$528$		0			0
$529$	−500.081			−0.945333
$530$	9.58315	−	6.19182i	0.0180814	−	0.0116827i
$531$		0			0
$532$	6.91109	−	15.3308i	0.0129908	−	0.0288174i
$533$	942.327			1.76797
$534$		0			0
$535$		−	185.167i		−	0.346106i
$536$	−551.628	+	83.4401i	−1.02916	+	0.155672i
$537$		0			0
$538$	−207.708	+	134.204i	−0.386075	+	0.249449i
$539$		−	451.399i		−	0.837476i
$540$		0			0
$541$	−262.199			−0.484655			−0.242328	−	0.970194i	$-0.577911\pi$
$541$	−262.199			−0.484655			−0.242328	+	0.970194i	$0.577911\pi$
$542$	360.750	+	558.337i	0.665591	+	1.03014i
$543$		0			0
$544$	−122.553	−	34.3657i	−0.225281	−	0.0631722i
$545$	16.4761			0.0302314
$546$		0			0
$547$		−	146.179i		−	0.267237i	−0.991033	−	0.133619i	$-0.957340\pi$
$547$		−	146.179i		−	0.267237i	0.991033	−	0.133619i	$-0.0426598\pi$
$548$	227.113	−	503.804i	0.414440	−	0.919350i
$549$		0			0
$550$	50.3599	+	77.9425i	0.0915634	+	0.141714i
$551$			251.411i			0.456281i
$552$		0			0
$553$	−39.2944			−0.0710568
$554$	211.522	−	136.668i	0.381809	−	0.246693i
$555$		0			0
$556$	−109.244	−	49.2468i	−0.196482	−	0.0885734i
$557$	−187.700			−0.336984			−0.168492	−	0.985703i	$-0.553890\pi$
$557$	−187.700			−0.336984			−0.168492	+	0.985703i	$0.553890\pi$
$558$		0			0
$559$		−	849.142i		−	1.51904i
$560$	−15.9923	+	14.1332i	−0.0285577	+	0.0252378i
$561$		0			0
$562$	88.2982	−	57.0509i	0.157114	−	0.101514i
$563$		−	447.848i		−	0.795467i	−0.917501	−	0.397734i	$-0.869797\pi$
$563$		−	447.848i		−	0.795467i	0.917501	−	0.397734i	$-0.130203\pi$
$564$		0			0
$565$	145.427			0.257393
$566$	216.305	+	334.777i	0.382164	+	0.591479i
$567$		0			0
$568$	−468.408	+	70.8520i	−0.824662	+	0.124740i
$569$	−1078.91			−1.89615			−0.948077	−	0.318042i	$-0.896975\pi$
$569$	−1078.91			−1.89615			−0.948077	+	0.318042i	$0.896975\pi$
$570$		0			0
$571$			936.324i			1.63980i	0.572509	+	0.819899i	$0.305970\pi$
$571$			936.324i			1.63980i	−0.572509	+	0.819899i	$0.694030\pi$
$572$	795.613	+	358.660i	1.39093	+	0.627028i
$573$		0			0
$574$	25.9502	+	40.1634i	0.0452095	+	0.0699711i
$575$		−	160.396i		−	0.278950i
$576$		0			0
$577$	−544.832			−0.944250			−0.472125	−	0.881532i	$-0.656513\pi$
$577$	−544.832			−0.944250			−0.472125	+	0.881532i	$0.656513\pi$
$578$	458.904	−	296.505i	0.793951	−	0.512985i
$579$		0			0
$580$	131.129	−	290.883i	0.226084	−	0.501522i
$581$	77.4960			0.133384
$582$		0			0
$583$		−	23.6745i		−	0.0406080i
$584$	−99.3101	−	656.547i	−0.170052	−	1.12422i
$585$		0			0
$586$	171.616	−	110.884i	0.292861	−	0.189222i
$587$		−	337.889i		−	0.575619i	−0.957688	−	0.287810i	$-0.907073\pi$
$587$		−	337.889i		−	0.575619i	0.957688	−	0.287810i	$-0.0929271\pi$
$588$		0			0
$589$	−417.628			−0.709045
$590$	−88.3490	−	136.739i	−0.149744	−	0.231760i
$591$		0			0
$592$	57.0836	+	64.5926i	0.0964249	+	0.109109i
$593$	−567.269			−0.956608			−0.478304	−	0.878194i	$-0.658748\pi$
$593$	−567.269			−0.956608			−0.478304	+	0.878194i	$0.658748\pi$
$594$		0			0
$595$			5.30561i			0.00891699i
$596$	77.8906	−	172.784i	0.130689	−	0.289906i
$597$		0			0
$598$	−818.640	−	1267.02i	−1.36896	−	2.11876i
$599$		−	762.966i		−	1.27373i	−0.770974	−	0.636867i	$-0.780230\pi$
$599$		−	762.966i		−	1.27373i	0.770974	−	0.636867i	$-0.219770\pi$
$600$		0			0
$601$	−790.102			−1.31464			−0.657322	−	0.753609i	$-0.728311\pi$
$601$	−790.102			−1.31464			−0.657322	+	0.753609i	$0.728311\pi$
$602$	36.1917	−	23.3841i	0.0601192	−	0.0388440i
$603$		0			0
$604$	399.680	+	180.175i	0.661722	+	0.298302i
$605$	−78.0132			−0.128947
$606$		0			0
$607$		−	522.994i		−	0.861605i	−0.902446	−	0.430802i	$-0.858231\pi$
$607$		−	522.994i		−	0.861605i	0.902446	−	0.430802i	$-0.141769\pi$
$608$	60.8909	−	217.146i	0.100150	−	0.357148i
$609$		0			0
$610$	−32.8008	+	21.1931i	−0.0537717	+	0.0347428i
$611$		−	1740.17i		−	2.84807i
$612$		0			0
$613$	1026.91			1.67522			0.837609	−	0.546270i	$-0.183953\pi$
$613$	1026.91			1.67522			0.837609	+	0.546270i	$0.183953\pi$
$614$	356.431	+	551.652i	0.580506	+	0.898455i
$615$		0			0
$616$	6.62332	+	43.7872i	0.0107521	+	0.0710831i
$617$	479.223			0.776698			0.388349	−	0.921512i	$-0.373046\pi$
$617$	479.223			0.776698			0.388349	+	0.921512i	$0.373046\pi$
$618$		0			0
$619$		−	507.654i		−	0.820119i	−0.912059	−	0.410059i	$-0.865508\pi$
$619$		−	507.654i		−	0.820119i	0.912059	−	0.410059i	$-0.134492\pi$
$620$	483.196	+	217.823i	0.779348	+	0.351328i
$621$		0			0
$622$	−103.587	−	160.322i	−0.166538	−	0.257753i
$623$			77.8282i			0.124925i
$624$		0			0
$625$	25.0000			0.0400000
$626$	−924.609	+	597.405i	−1.47701	+	0.954321i
$627$		0			0
$628$	−291.932	+	647.591i	−0.464860	+	1.03120i
$629$	21.4293			0.0340688
$630$		0			0
$631$		−	460.186i		−	0.729297i	−0.931145	−	0.364648i	$-0.881189\pi$
$631$		−	460.186i		−	0.729297i	0.931145	−	0.364648i	$-0.118811\pi$
$632$	−521.037	+	78.8128i	−0.824426	+	0.124704i
$633$		0			0
$634$	738.122	−	476.912i	1.16423	−	0.752228i
$635$			311.862i			0.491122i
$636$		0			0
$637$	−1143.71			−1.79546
$638$	−359.302	−	556.095i	−0.563169	−	0.871622i
$639$		0			0
$640$	−183.708	+	219.479i	−0.287045	+	0.342937i
$641$	−250.774			−0.391223			−0.195612	−	0.980681i	$-0.562669\pi$
$641$	−250.774			−0.391223			−0.195612	+	0.980681i	$0.562669\pi$
$642$		0			0
$643$		−	590.355i		−	0.918126i	−0.888404	−	0.459063i	$-0.848185\pi$
$643$		−	590.355i		−	0.918126i	0.888404	−	0.459063i	$-0.151815\pi$
$644$	31.4581	−	69.7834i	0.0488480	−	0.108359i
$645$		0			0
$646$	−30.4252	−	47.0894i	−0.0470979	−	0.0728939i
$647$			319.341i			0.493572i	0.969070	+	0.246786i	$0.0793744\pi$
$647$			319.341i			0.493572i	−0.969070	+	0.246786i	$0.920626\pi$
$648$		0			0
$649$	−337.803			−0.520497
$650$	197.482	−	127.596i	0.303818	−	0.196302i
$651$		0			0
$652$	−353.274	−	159.255i	−0.541832	−	0.244256i
$653$	−88.5949			−0.135674			−0.0678369	−	0.997696i	$-0.521610\pi$
$653$	−88.5949			−0.135674			−0.0678369	+	0.997696i	$0.521610\pi$
$654$		0			0
$655$			141.958i			0.216730i
$656$	424.652	+	480.512i	0.647335	+	0.732488i
$657$		0			0
$658$	74.1688	−	47.9216i	0.112719	−	0.0728292i
$659$		−	758.423i		−	1.15087i	−0.817847	−	0.575435i	$-0.804833\pi$
$659$		−	758.423i		−	1.15087i	0.817847	−	0.575435i	$-0.195167\pi$
$660$		0			0
$661$	527.327			0.797771			0.398885	−	0.917001i	$-0.369397\pi$
$661$	527.327			0.797771			0.398885	+	0.917001i	$0.369397\pi$
$662$	520.900	+	806.203i	0.786859	+	1.21783i
$663$		0			0
$664$	1027.59	−	155.434i	1.54757	−	0.234087i
$665$	−9.40076			−0.0141365
$666$		0			0
$667$			1144.38i			1.71571i
$668$	−556.488	−	250.863i	−0.833066	−	0.375544i
$669$		0			0
$670$	169.254	+	261.956i	0.252617	+	0.390978i
$671$			81.0318i			0.120763i
$672$		0			0
$673$	120.657			0.179283			0.0896415	−	0.995974i	$-0.471428\pi$
$673$	120.657			0.179283			0.0896415	+	0.995974i	$0.471428\pi$
$674$	−98.8493	+	63.8681i	−0.146661	+	0.0947598i
$675$		0			0
$676$	630.918	−	1399.56i	0.933311	−	2.07036i
$677$	219.196			0.323776			0.161888	−	0.986809i	$-0.448242\pi$
$677$	219.196			0.323776			0.161888	+	0.986809i	$0.448242\pi$
$678$		0			0
$679$			55.5446i			0.0818035i
$680$	10.6415	+	70.3516i	0.0156492	+	0.103458i
$681$		0			0
$682$	923.751	−	596.850i	1.35447	−	0.875146i
$683$			205.502i			0.300881i	0.988619	+	0.150441i	$0.0480693\pi$
$683$			205.502i			0.300881i	−0.988619	+	0.150441i	$0.951931\pi$
$684$		0			0
$685$	−308.929			−0.450991
$686$	−63.2222	−	97.8496i	−0.0921606	−	0.142638i
$687$		0			0
$688$	432.995	−	382.659i	0.629354	−	0.556190i
$689$	−59.9837			−0.0870591
$690$		0			0
$691$		−	109.536i		−	0.158519i	−0.996854	−	0.0792593i	$-0.974744\pi$
$691$		−	109.536i		−	0.158519i	0.996854	−	0.0792593i	$-0.0252555\pi$
$692$	−256.071	+	568.042i	−0.370045	+	0.820869i
$693$		0			0
$694$	13.1857	+	20.4077i	0.0189996	+	0.0294059i
$695$			66.9876i			0.0963850i
$696$		0			0
$697$	159.415			0.228716
$698$	51.9543	−	33.5685i	0.0744331	−	0.0480924i
$699$		0			0
$700$	10.8767	+	4.90318i	0.0155381	+	0.00700455i
$701$	−168.847			−0.240865			−0.120433	−	0.992721i	$-0.538428\pi$
$701$	−168.847			−0.240865			−0.120433	+	0.992721i	$0.538428\pi$
$702$		0			0
$703$			37.9695i			0.0540106i
$704$	175.648	+	567.327i	0.249500	+	0.805863i
$705$		0			0
$706$	−483.909	+	312.661i	−0.685424	+	0.442863i
$707$			2.18382i			0.00308885i
$708$		0			0
$709$	−554.846			−0.782576			−0.391288	−	0.920268i	$-0.627970\pi$
$709$	−554.846			−0.782576			−0.391288	+	0.920268i	$0.627970\pi$
$710$	143.720	+	222.436i	0.202422	+	0.313290i
$711$		0			0
$712$	156.100	+	1031.99i	0.219242	+	1.44942i
$713$	−1900.97			−2.66616
$714$		0			0
$715$		−	487.864i		−	0.682328i
$716$	459.474	+	207.130i	0.641723	+	0.289287i
$717$		0			0
$718$	720.600	+	1115.28i	1.00362	+	1.55331i
$719$		−	377.485i		−	0.525014i	−0.964930	−	0.262507i	$-0.915451\pi$
$719$		−	377.485i		−	0.525014i	0.964930	−	0.262507i	$-0.0845494\pi$
$720$		0			0
$721$	90.3261			0.125279
$722$	−522.995	+	337.915i	−0.724369	+	0.468027i
$723$		0			0
$724$	−569.972	+	1264.37i	−0.787255	+	1.74636i
$725$	−178.367			−0.246024
$726$		0			0
$727$			173.183i			0.238216i	0.992881	+	0.119108i	$0.0380035\pi$
$727$			173.183i			0.238216i	−0.992881	+	0.119108i	$0.961997\pi$
$728$	110.943	−	16.7814i	0.152394	−	0.0230514i
$729$		0			0
$730$	−311.779	+	201.445i	−0.427094	+	0.275952i
$731$		−	143.651i		−	0.196513i
$732$		0			0
$733$	278.722			0.380249			0.190124	−	0.981760i	$-0.439111\pi$
$733$	278.722			0.380249			0.190124	+	0.981760i	$0.439111\pi$
$734$	−6.60489	−	10.2225i	−0.00899849	−	0.0139270i
$735$		0			0
$736$	277.165	−	988.412i	0.376583	−	1.34295i
$737$	647.142			0.878075
$738$		0			0
$739$			521.363i			0.705498i	0.935718	+	0.352749i	$0.114753\pi$
$739$			521.363i			0.705498i	−0.935718	+	0.352749i	$0.885247\pi$
$740$	19.8039	−	43.9308i	0.0267620	−	0.0593659i
$741$		0			0
$742$	−1.65186	−	2.55660i	−0.00222622	−	0.00344555i
$743$			1277.93i			1.71996i	0.510326	+	0.859981i	$0.329525\pi$
$743$			1277.93i			1.71996i	−0.510326	+	0.859981i	$0.670475\pi$
$744$		0			0
$745$	−105.950			−0.142215
$746$	343.936	−	222.223i	0.461041	−	0.297886i
$747$		0			0
$748$	134.595	+	60.6751i	0.179940	+	0.0811164i
$749$	−49.3989			−0.0659532
$750$		0			0
$751$			1165.31i			1.55168i	0.630930	+	0.775840i	$0.282673\pi$
$751$			1165.31i			1.55168i	−0.630930	+	0.775840i	$0.717327\pi$
$752$	887.350	−	784.194i	1.17999	−	1.04281i
$753$		0			0
$754$	−1408.97	+	910.359i	−1.86866	+	1.20737i
$755$		−	245.081i		−	0.324611i
$756$		0			0
$757$	1063.75			1.40522			0.702611	−	0.711574i	$-0.252017\pi$
$757$	1063.75			1.40522			0.702611	+	0.711574i	$0.252017\pi$
$758$	436.685	+	675.861i	0.576101	+	0.891638i
$759$		0			0
$760$	−124.653	+	18.8551i	−0.164017	+	0.0248094i
$761$	677.847			0.890732			0.445366	−	0.895349i	$-0.353074\pi$
$761$	677.847			0.890732			0.445366	+	0.895349i	$0.353074\pi$
$762$		0			0
$763$		−	4.39551i		−	0.00576083i
$764$	−485.577	−	218.897i	−0.635572	−	0.286514i
$765$		0			0
$766$	−360.078	−	557.296i	−0.470076	−	0.727541i
$767$			855.887i			1.11589i
$768$		0			0
$769$	−1289.59			−1.67697			−0.838486	−	0.544922i	$-0.816559\pi$
$769$	−1289.59			−1.67697			−0.838486	+	0.544922i	$0.816559\pi$
$770$	20.7935	−	13.4350i	0.0270046	−	0.0174481i
$771$		0			0
$772$	−223.972	+	496.836i	−0.290119	+	0.643570i
$773$	750.339			0.970684			0.485342	−	0.874324i	$-0.338695\pi$
$773$	750.339			0.970684			0.485342	+	0.874324i	$0.338695\pi$
$774$		0			0
$775$		−	296.292i		−	0.382313i
$776$	111.406	+	736.513i	0.143564	+	0.949114i
$777$		0			0
$778$	−1047.07	+	676.532i	−1.34585	+	0.869578i
$779$			282.460i			0.362593i
$780$		0			0
$781$	549.512			0.703600
$782$	−138.491	−	214.343i	−0.177098	−	0.274096i
$783$		0			0
$784$	−515.402	−	583.200i	−0.657400	−	0.743877i
$785$	397.098			0.505858
$786$		0			0
$787$			825.185i			1.04852i	0.851558	+	0.524260i	$0.175658\pi$
$787$			825.185i			1.04852i	−0.851558	+	0.524260i	$0.824342\pi$
$788$	−123.117	+	273.110i	−0.156240	+	0.346586i
$789$		0			0
$790$	159.868	+	247.429i	0.202364	+	0.313201i
$791$		−	38.7971i		−	0.0490482i
$792$		0			0
$793$	205.309			0.258902
$794$	597.106	−	385.799i	0.752022	−	0.485893i
$795$		0			0
$796$	917.500	+	413.606i	1.15264	+	0.519606i
$797$	−1113.70			−1.39737			−0.698684	−	0.715430i	$-0.746231\pi$
$797$	−1113.70			−1.39737			−0.698684	+	0.715430i	$0.746231\pi$
$798$		0			0
$799$		−	294.388i		−	0.368445i
$800$	154.058	+	43.2000i	0.192572	+	0.0540000i
$801$		0			0
$802$	−912.043	+	589.285i	−1.13721	+	0.734770i
$803$			770.226i			0.959186i
$804$		0			0
$805$	−42.7907			−0.0531561
$806$	−1512.23	−	2340.50i	−1.87622	−	2.90384i
$807$		0			0
$808$	4.38009	+	28.9571i	0.00542090	+	0.0358380i
$809$	1049.54			1.29733			0.648664	−	0.761075i	$-0.275328\pi$
$809$	1049.54			1.29733			0.648664	+	0.761075i	$0.275328\pi$
$810$		0			0
$811$		−	424.482i		−	0.523406i	−0.965148	−	0.261703i	$-0.915716\pi$
$811$		−	424.482i		−	0.523406i	0.965148	−	0.261703i	$-0.0842841\pi$
$812$	−77.6018	−	34.9827i	−0.0955688	−	0.0430821i
$813$		0			0
$814$	−54.2638	−	83.9847i	−0.0666632	−	0.103175i
$815$			216.625i			0.265798i
$816$		0			0
$817$	254.528			0.311540
$818$	182.259	−	117.761i	0.222811	−	0.143962i
$819$		0			0
$820$	147.323	−	326.807i	0.179663	−	0.398545i
$821$	1257.98			1.53225			0.766126	−	0.642690i	$-0.222182\pi$
$821$	1257.98			1.53225			0.766126	+	0.642690i	$0.222182\pi$
$822$		0			0
$823$		−	729.181i		−	0.886004i	−0.896521	−	0.443002i	$-0.853913\pi$
$823$		−	729.181i		−	0.886004i	0.896521	−	0.443002i	$-0.146087\pi$
$824$	1197.71	−	181.167i	1.45353	−	0.219863i
$825$		0			0
$826$	−36.4792	+	23.5698i	−0.0441637	+	0.0285349i
$827$		−	72.5882i		−	0.0877729i	−0.999037	−	0.0438865i	$-0.986026\pi$
$827$		−	72.5882i		−	0.0877729i	0.999037	−	0.0438865i	$-0.0139740\pi$
$828$		0			0
$829$	900.257			1.08596			0.542978	−	0.839747i	$-0.317297\pi$
$829$	900.257			1.08596			0.542978	+	0.839747i	$0.317297\pi$
$830$	−315.289	−	487.977i	−0.379867	−	0.587924i
$831$		0			0
$832$	1437.43	−	445.038i	1.72768	−	0.534901i
$833$	−193.482			−0.232272
$834$		0			0
$835$			341.235i			0.408664i
$836$	−107.507	+	238.483i	−0.128597	+	0.285266i
$837$		0			0
$838$	−186.877	−	289.232i	−0.223004	−	0.345145i
$839$			71.4721i			0.0851872i	0.999092	+	0.0425936i	$0.0135621\pi$
$839$			71.4721i			0.0851872i	−0.999092	+	0.0425936i	$0.986438\pi$
$840$		0			0
$841$	431.594			0.513191
$842$	−803.851	+	519.381i	−0.954693	+	0.616842i
$843$		0			0
$844$	832.165	+	375.138i	0.985978	+	0.444476i
$845$	−858.201			−1.01562
$846$		0			0
$847$			20.8124i			0.0245719i
$848$	−27.0312	−	30.5870i	−0.0318764	−	0.0360695i
$849$		0			0
$850$	33.4083	−	21.5857i	0.0393039	−	0.0253949i
$851$			172.831i			0.203091i
$852$		0			0
$853$	882.349			1.03441			0.517203	−	0.855862i	$-0.326973\pi$
$853$	882.349			1.03441			0.517203	+	0.855862i	$0.326973\pi$
$854$	5.65391	+	8.75061i	0.00662050	+	0.0102466i
$855$		0			0
$856$	−655.022	+	99.0796i	−0.765213	+	0.115747i
$857$	370.111			0.431868			0.215934	−	0.976408i	$-0.430720\pi$
$857$	370.111			0.431868			0.215934	+	0.976408i	$0.430720\pi$
$858$		0			0
$859$			1039.00i			1.20955i	0.796397	+	0.604774i	$0.206736\pi$
$859$			1039.00i			1.20955i	−0.796397	+	0.604774i	$0.793264\pi$
$860$	−294.489	−	132.755i	−0.342429	−	0.154366i
$861$		0			0
$862$	−315.546	−	488.373i	−0.366062	−	0.566558i
$863$			72.0666i			0.0835071i	0.999128	+	0.0417535i	$0.0132944\pi$
$863$			72.0666i			0.0835071i	−0.999128	+	0.0417535i	$0.986706\pi$
$864$		0			0
$865$	348.319			0.402681
$866$	−90.3306	+	58.3640i	−0.104308	+	0.0673950i
$867$		0			0
$868$	58.1110	−	128.907i	0.0669482	−	0.148511i
$869$	611.254			0.703399
$870$		0			0
$871$		−	1639.66i		−	1.88250i
$872$	−8.81609	−	58.2838i	−0.0101102	−	0.0668393i
$873$		0			0
$874$	379.785	−	245.385i	0.434536	−	0.280761i
$875$		−	6.66951i		−	0.00762230i
$876$		0			0
$877$	14.4444			0.0164703			0.00823514	−	0.999966i	$-0.497379\pi$
$877$	14.4444			0.0164703			0.00823514	+	0.999966i	$0.497379\pi$
$878$	−356.720	−	552.099i	−0.406287	−	0.628815i
$879$		0			0
$880$	248.772	−	219.852i	0.282696	−	0.249832i
$881$	−1589.22			−1.80388			−0.901942	−	0.431858i	$-0.857858\pi$
$881$	−1589.22			−1.80388			−0.901942	+	0.431858i	$0.857858\pi$
$882$		0			0
$883$			495.149i			0.560758i	0.959889	+	0.280379i	$0.0904601\pi$
$883$			495.149i			0.560758i	−0.959889	+	0.280379i	$0.909540\pi$
$884$	153.732	−	341.022i	0.173905	−	0.385772i
$885$		0			0
$886$	465.533	+	720.510i	0.525432	+	0.813216i
$887$		−	1384.20i		−	1.56054i	−0.625440	−	0.780272i	$-0.715081\pi$
$887$		−	1384.20i		−	1.56054i	0.625440	−	0.780272i	$-0.284919\pi$
$888$		0			0
$889$	83.1988			0.0935870
$890$	490.068	−	316.641i	0.550638	−	0.355776i
$891$		0			0
$892$	−313.443	−	141.299i	−0.351393	−	0.158407i
$893$	521.611			0.584111
$894$		0			0
$895$		−	281.746i		−	0.314800i
$896$	58.5528	+	49.0099i	0.0653491	+	0.0546985i
$897$		0			0
$898$	687.448	−	444.171i	0.765533	−	0.494623i
$899$			2113.95i			2.35145i
$900$		0			0
$901$	−10.1475			−0.0112625
$902$	−403.676	−	624.773i	−0.447534	−	0.692653i
$903$		0			0
$904$	−77.8155	−	514.444i	−0.0860791	−	0.569075i
$905$	775.300			0.856685
$906$		0			0
$907$		−	957.750i		−	1.05595i	−0.849259	−	0.527977i	$-0.822951\pi$
$907$		−	957.750i		−	1.05595i	0.849259	−	0.527977i	$-0.177049\pi$
$908$	−1029.64	−	464.160i	−1.13397	−	0.511189i
$909$		0			0
$910$	−34.0402	−	52.6844i	−0.0374068	−	0.0578949i
$911$		−	704.979i		−	0.773852i	−0.922111	−	0.386926i	$-0.873537\pi$
$911$		−	704.979i		−	0.773852i	0.922111	−	0.386926i	$-0.126463\pi$
$912$		0			0
$913$	−1205.51			−1.32038
$914$	−1291.08	+	834.185i	−1.41256	+	0.912675i
$915$		0			0
$916$	227.287	−	504.189i	0.248130	−	0.550424i
$917$	37.8717			0.0412996
$918$		0			0
$919$			607.048i			0.660553i	0.943884	+	0.330277i	$0.107142\pi$
$919$			607.048i			0.660553i	−0.943884	+	0.330277i	$0.892858\pi$
$920$	−567.398	+	85.8254i	−0.616737	+	0.0932884i
$921$		0			0
$922$	−531.782	+	343.593i	−0.576770	+	0.372660i
$923$		−	1392.29i		−	1.50844i
$924$		0			0
$925$	−26.9380			−0.0291222
$926$	533.151	+	825.163i	0.575757	+	0.891104i
$927$		0			0
$928$	−1099.15	−	308.219i	−1.18443	−	0.332132i
$929$	−1011.21			−1.08849			−0.544247	−	0.838925i	$-0.683185\pi$
$929$	−1011.21			−1.08849			−0.544247	+	0.838925i	$0.683185\pi$
$930$		0			0
$931$		−	342.822i		−	0.368230i
$932$	0.859647	−	1.90695i	0.000922368	−	0.00204608i
$933$		0			0
$934$	−445.434	−	689.403i	−0.476910	−	0.738119i
$935$		−	82.5328i		−	0.0882704i
$936$		0			0
$937$	−363.105			−0.387519			−0.193760	−	0.981049i	$-0.562068\pi$
$937$	−363.105			−0.387519			−0.193760	+	0.981049i	$0.562068\pi$
$938$	69.8846	−	45.1536i	0.0745039	−	0.0481381i
$939$		0			0
$940$	−603.505	−	272.058i	−0.642027	−	0.289424i
$941$	1106.51			1.17588			0.587942	−	0.808903i	$-0.299939\pi$
$941$	1106.51			1.17588			0.587942	+	0.808903i	$0.299939\pi$
$942$		0			0
$943$			1285.71i			1.36342i
$944$	−436.435	+	385.698i	−0.462325	+	0.408579i
$945$		0			0
$946$	−562.990	+	363.757i	−0.595127	+	0.384521i
$947$			553.561i			0.584541i	0.956336	+	0.292271i	$0.0944108\pi$
$947$			553.561i			0.584541i	−0.956336	+	0.292271i	$0.905589\pi$
$948$		0			0
$949$	1951.51			2.05639
$950$	38.2466	+	59.1947i	0.0402596	+	0.0623102i
$951$		0			0
$952$	18.7684	−	2.83894i	0.0197147	−	0.00298208i
$953$	1674.84			1.75744			0.878718	−	0.477342i	$-0.158400\pi$
$953$	1674.84			1.75744			0.878718	+	0.477342i	$0.158400\pi$
$954$		0			0
$955$			297.753i			0.311783i
$956$	−268.728	−	121.142i	−0.281096	−	0.126717i
$957$		0			0
$958$	−215.902	−	334.154i	−0.225368	−	0.348804i
$959$			82.4162i			0.0859398i
$960$		0			0
$961$	−2550.57			−2.65408
$962$	−212.791	+	137.488i	−0.221196	+	0.142919i
$963$		0			0
$964$	51.5692	−	114.396i	0.0534950	−	0.118668i
$965$	304.656			0.315706
$966$		0			0
$967$			786.720i			0.813568i	0.913524	+	0.406784i	$0.133350\pi$
$967$			786.720i			0.813568i	−0.913524	+	0.406784i	$0.866650\pi$
$968$	41.7435	+	275.969i	0.0431234	+	0.285092i
$969$		0			0
$970$	349.753	−	225.981i	0.360570	−	0.232970i
$971$			1289.75i			1.32827i	0.747612	+	0.664135i	$0.231200\pi$
$971$			1289.75i			1.32827i	−0.747612	+	0.664135i	$0.768800\pi$
$972$		0			0
$973$	17.8710			0.0183669
$974$	−222.246	−	343.972i	−0.228178	−	0.353154i
$975$		0			0
$976$	92.5210	+	104.692i	0.0947961	+	0.107266i
$977$	−495.847			−0.507520			−0.253760	−	0.967267i	$-0.581667\pi$
$977$	−495.847			−0.507520			−0.253760	+	0.967267i	$0.581667\pi$
$978$		0			0
$979$		−	1210.68i		−	1.23665i
$980$	−178.807	+	396.646i	−0.182456	+	0.404741i
$981$		0			0
$982$	−855.933	−	1324.74i	−0.871622	−	1.34902i
$983$		−	967.035i		−	0.983759i	−0.870663	−	0.491880i	$-0.836310\pi$
$983$		−	967.035i		−	0.983759i	0.870663	−	0.491880i	$-0.163690\pi$
$984$		0			0
$985$	167.469			0.170019
$986$	−238.358	+	154.007i	−0.241742	+	0.156194i
$987$		0			0
$988$	604.241	+	272.390i	0.611580	+	0.275698i
$989$	1158.57			1.17145
$990$		0			0
$991$			1203.68i			1.21461i	0.794469	+	0.607305i	$0.207749\pi$
$991$			1203.68i			1.21461i	−0.794469	+	0.607305i	$0.792251\pi$
$992$	511.994	−	1825.84i	0.516123	−	1.84057i
$993$		0			0
$994$	59.3417	−	38.3416i	0.0596999	−	0.0385730i
$995$		−	562.605i		−	0.565432i
$996$		0			0
$997$	−1274.55			−1.27838			−0.639192	−	0.769047i	$-0.720731\pi$
$997$	−1274.55			−1.27838			−0.639192	+	0.769047i	$0.720731\pi$
$998$	803.603	+	1243.74i	0.805214	+	1.24624i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.3.c.b.91.4		8
3.2	odd	2		60.3.c.a.31.5	✓	8
4.3	odd	2	inner	180.3.c.b.91.3		8
5.2	odd	4		900.3.f.f.199.3		16
5.3	odd	4		900.3.f.f.199.14		16
5.4	even	2		900.3.c.u.451.5		8
8.3	odd	2		2880.3.e.j.2431.6		8
8.5	even	2		2880.3.e.j.2431.7		8
12.11	even	2		60.3.c.a.31.6	yes	8
15.2	even	4		300.3.f.b.199.14		16
15.8	even	4		300.3.f.b.199.3		16
15.14	odd	2		300.3.c.d.151.4		8
20.3	even	4		900.3.f.f.199.4		16
20.7	even	4		900.3.f.f.199.13		16
20.19	odd	2		900.3.c.u.451.6		8
24.5	odd	2		960.3.e.c.511.1		8
24.11	even	2		960.3.e.c.511.6		8
60.23	odd	4		300.3.f.b.199.13		16
60.47	odd	4		300.3.f.b.199.4		16
60.59	even	2		300.3.c.d.151.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.5	✓	8	3.2	odd	2
60.3.c.a.31.6	yes	8	12.11	even	2
180.3.c.b.91.3		8	4.3	odd	2	inner
180.3.c.b.91.4		8	1.1	even	1	trivial
300.3.c.d.151.3		8	60.59	even	2
300.3.c.d.151.4		8	15.14	odd	2
300.3.f.b.199.3		16	15.8	even	4
300.3.f.b.199.4		16	60.47	odd	4
300.3.f.b.199.13		16	60.23	odd	4
300.3.f.b.199.14		16	15.2	even	4
900.3.c.u.451.5		8	5.4	even	2
900.3.c.u.451.6		8	20.19	odd	2
900.3.f.f.199.3		16	5.2	odd	4
900.3.f.f.199.4		16	20.3	even	4
900.3.f.f.199.13		16	20.7	even	4
900.3.f.f.199.14		16	5.3	odd	4
960.3.e.c.511.1		8	24.5	odd	2
960.3.e.c.511.6		8	24.11	even	2
2880.3.e.j.2431.6		8	8.3	odd	2
2880.3.e.j.2431.7		8	8.5	even	2

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.67986 + 1.08539i) q^{2} +(1.64388 - 3.64660i) q^{4} -2.23607 q^{5} +0.596540i q^{7} +(1.19648 + 7.91002i) q^{8} +O(q^{10})\)	\(q+(-1.67986 + 1.08539i) q^{2} +(1.64388 - 3.64660i) q^{4} -2.23607 q^{5} +0.596540i q^{7} +(1.19648 + 7.91002i) q^{8} +(3.75629 - 2.42700i) q^{10} -9.27963i q^{11} -23.5117 q^{13} +(-0.647476 - 1.00210i) q^{14} +(-10.5953 - 11.9891i) q^{16} -3.97751 q^{17} -7.04756i q^{19} +(-3.67582 + 8.15404i) q^{20} +(10.0720 + 15.5885i) q^{22} -32.0793i q^{23} +5.00000 q^{25} +(39.4964 - 25.5192i) q^{26} +(2.17534 + 0.980637i) q^{28} -35.6734 q^{29} -59.2585i q^{31} +(30.8115 + 8.64000i) q^{32} +(6.68167 - 4.31713i) q^{34} -1.33390i q^{35} -5.38761 q^{37} +(7.64932 + 11.8389i) q^{38} +(-2.67541 - 17.6873i) q^{40} -40.0791 q^{41} +36.1157i q^{43} +(-33.8391 - 15.2545i) q^{44} +(34.8184 + 53.8888i) q^{46} +74.0131i q^{47} +48.6441 q^{49} +(-8.39931 + 5.42693i) q^{50} +(-38.6503 + 85.7376i) q^{52} +2.55123 q^{53} +20.7499i q^{55} +(-4.71864 + 0.713748i) q^{56} +(59.9265 - 38.7194i) q^{58} -36.4026i q^{59} -8.73223 q^{61} +(64.3183 + 99.5461i) q^{62} +(-61.1369 + 18.9284i) q^{64} +52.5737 q^{65} +69.7379i q^{67} +(-6.53853 + 14.5044i) q^{68} +(1.44780 + 2.24077i) q^{70} +59.2170i q^{71} -83.0019 q^{73} +(9.05044 - 5.84763i) q^{74} +(-25.6996 - 11.5853i) q^{76} +5.53566 q^{77} +65.8705i q^{79} +(23.6919 + 26.8085i) q^{80} +(67.3274 - 43.5013i) q^{82} -129.909i q^{83} +8.89398 q^{85} +(-39.1995 - 60.6695i) q^{86} +(73.4020 - 11.1029i) q^{88} +130.466 q^{89} -14.0256i q^{91} +(-116.980 - 52.7344i) q^{92} +(-80.3327 - 124.332i) q^{94} +15.7588i q^{95} +93.1113 q^{97} +(-81.7155 + 52.7977i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 10 q^{4} + 20 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 + 10 * q^4 + 20 * q^8	\( 8 q - 4 q^{2} + 10 q^{4} + 20 q^{8} + 10 q^{10} + 16 q^{13} + 20 q^{14} + 34 q^{16} + 40 q^{20} + 68 q^{22} + 40 q^{25} + 36 q^{26} + 28 q^{28} - 64 q^{29} + 76 q^{32} - 92 q^{34} - 112 q^{37} + 40 q^{38} - 10 q^{40} + 16 q^{41} - 172 q^{44} + 152 q^{46} - 56 q^{49} - 20 q^{50} - 128 q^{52} - 352 q^{53} - 116 q^{56} - 204 q^{58} - 176 q^{61} + 56 q^{62} - 110 q^{64} + 80 q^{65} + 184 q^{68} - 60 q^{70} - 240 q^{73} - 132 q^{74} - 24 q^{76} + 288 q^{77} + 80 q^{80} + 40 q^{82} + 160 q^{85} + 200 q^{86} + 140 q^{88} - 80 q^{89} - 144 q^{92} - 96 q^{94} + 432 q^{97} - 660 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 10 * q^4 + 20 * q^8 + 10 * q^10 + 16 * q^13 + 20 * q^14 + 34 * q^16 + 40 * q^20 + 68 * q^22 + 40 * q^25 + 36 * q^26 + 28 * q^28 - 64 * q^29 + 76 * q^32 - 92 * q^34 - 112 * q^37 + 40 * q^38 - 10 * q^40 + 16 * q^41 - 172 * q^44 + 152 * q^46 - 56 * q^49 - 20 * q^50 - 128 * q^52 - 352 * q^53 - 116 * q^56 - 204 * q^58 - 176 * q^61 + 56 * q^62 - 110 * q^64 + 80 * q^65 + 184 * q^68 - 60 * q^70 - 240 * q^73 - 132 * q^74 - 24 * q^76 + 288 * q^77 + 80 * q^80 + 40 * q^82 + 160 * q^85 + 200 * q^86 + 140 * q^88 - 80 * q^89 - 144 * q^92 - 96 * q^94 + 432 * q^97 - 660 * q^98

Introduction

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