LMFDB - Embedded newform 441.2.u.e.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			127.2
Character	$\chi$	$=$	441.127
Dual form			441.2.u.e.316.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.10278 - 1.01265i) q^{2} +(2.14925 + 2.69508i) q^{4} +(-0.460720 - 2.01854i) q^{5} +(-2.61455 - 0.405131i) q^{7} +(-0.751559 - 3.29280i) q^{8} +O(q^{10})$	\(q+(-2.10278 - 1.01265i) q^{2} +(2.14925 + 2.69508i) q^{4} +(-0.460720 - 2.01854i) q^{5} +(-2.61455 - 0.405131i) q^{7} +(-0.751559 - 3.29280i) q^{8} +(-1.07528 + 4.71110i) q^{10} +(-2.29842 - 1.10686i) q^{11} +(3.87171 + 1.86451i) q^{13} +(5.08757 + 3.49951i) q^{14} +(-0.219952 + 0.963674i) q^{16} +(-0.678070 + 0.850272i) q^{17} -7.36179 q^{19} +(4.44993 - 5.58004i) q^{20} +(3.71221 + 4.65496i) q^{22} +(0.952254 + 1.19409i) q^{23} +(0.642583 - 0.309452i) q^{25} +(-6.25325 - 7.84133i) q^{26} +(-4.52747 - 7.91714i) q^{28} +(-5.85246 + 7.33876i) q^{29} -2.01883 q^{31} +(-2.77327 + 3.47757i) q^{32} +(2.28686 - 1.10129i) q^{34} +(0.386799 + 5.46424i) q^{35} +(1.47068 - 1.84418i) q^{37} +(15.4802 + 7.45488i) q^{38} +(-6.30040 + 3.03411i) q^{40} +(1.38192 + 6.05457i) q^{41} +(-1.19246 + 5.22449i) q^{43} +(-1.95681 - 8.57332i) q^{44} +(-0.793192 - 3.47520i) q^{46} +(-1.02275 - 0.492532i) q^{47} +(6.67174 + 2.11847i) q^{49} -1.66458 q^{50} +(3.29626 + 14.4419i) q^{52} +(7.27161 + 9.11832i) q^{53} +(-1.17532 + 5.14941i) q^{55} +(0.630975 + 8.91366i) q^{56} +(19.7380 - 9.50532i) q^{58} +(-0.983859 + 4.31057i) q^{59} +(-7.13624 + 8.94857i) q^{61} +(4.24516 + 2.04436i) q^{62} +(11.1343 - 5.36198i) q^{64} +(1.97984 - 8.67423i) q^{65} -0.688531 q^{67} -3.74889 q^{68} +(4.71998 - 11.8818i) q^{70} +(-10.2563 - 12.8610i) q^{71} +(-1.76201 + 0.848540i) q^{73} +(-4.96002 + 2.38862i) q^{74} +(-15.8223 - 19.8406i) q^{76} +(5.56090 + 3.82510i) q^{77} -5.42912 q^{79} +2.04656 q^{80} +(3.22527 - 14.1308i) q^{82} +(9.13718 - 4.40023i) q^{83} +(2.02871 + 0.976977i) q^{85} +(7.79803 - 9.77841i) q^{86} +(-1.91726 + 8.40008i) q^{88} +(-12.3348 + 5.94011i) q^{89} +(-9.36739 - 6.44341i) q^{91} +(-1.17153 + 5.13280i) q^{92} +(1.65187 + 2.07137i) q^{94} +(3.39172 + 14.8601i) q^{95} -10.2656 q^{97} +(-11.8839 - 11.2108i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 12 q^{4} - 2 q^{7}+O(q^{10}) $ 60 * q - 12 * q^4 - 2 * q^7	$ 60 q - 12 q^{4} - 2 q^{7} + 12 q^{10} - 4 q^{13} - 48 q^{19} + 6 q^{22} - 22 q^{25} + 40 q^{28} - 76 q^{31} - 12 q^{34} + 34 q^{37} + 86 q^{40} + 4 q^{43} + 8 q^{46} + 26 q^{49} + 66 q^{52} + 10 q^{55} + 42 q^{58} + 62 q^{61} - 128 q^{64} + 8 q^{67} + 96 q^{70} - 70 q^{73} + 50 q^{76} - 24 q^{79} - 36 q^{82} + 72 q^{85} - 216 q^{88} + 52 q^{91} - 38 q^{94} - 252 q^{97}+O(q^{100}) $ 60 * q - 12 * q^4 - 2 * q^7 + 12 * q^10 - 4 * q^13 - 48 * q^19 + 6 * q^22 - 22 * q^25 + 40 * q^28 - 76 * q^31 - 12 * q^34 + 34 * q^37 + 86 * q^40 + 4 * q^43 + 8 * q^46 + 26 * q^49 + 66 * q^52 + 10 * q^55 + 42 * q^58 + 62 * q^61 - 128 * q^64 + 8 * q^67 + 96 * q^70 - 70 * q^73 + 50 * q^76 - 24 * q^79 - 36 * q^82 + 72 * q^85 - 216 * q^88 + 52 * q^91 - 38 * q^94 - 252 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{3}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.10278	−	1.01265i	−1.48689	−	0.716048i	−0.498345	−	0.866979i	$-0.666059\pi$
$2$	−2.10278	−	1.01265i	−1.48689	−	0.716048i	−0.988544	+	0.150930i	$0.951773\pi$
$3$		0			0
$3$		0			0
$4$	2.14925	+	2.69508i	1.07463	+	1.34754i
$5$	−0.460720	−	2.01854i	−0.206040	−	0.902721i	−0.967172	−	0.254123i	$-0.918213\pi$
$5$	−0.460720	−	2.01854i	−0.206040	−	0.902721i	0.761132	−	0.648597i	$-0.224644\pi$
$6$		0			0
$7$	−2.61455	−	0.405131i	−0.988207	−	0.153125i
$7$	−2.61455	−	0.405131i	−0.988207	−	0.153125i
$8$	−0.751559	−	3.29280i	−0.265716	−	1.16418i
$9$		0			0
$10$	−1.07528	+	4.71110i	−0.340033	+	1.48978i
$11$	−2.29842	−	1.10686i	−0.692998	−	0.333730i	0.0540144	−	0.998540i	$-0.482798\pi$
$11$	−2.29842	−	1.10686i	−0.692998	−	0.333730i	−0.747013	+	0.664810i	$0.768513\pi$
$12$		0			0
$13$	3.87171	+	1.86451i	1.07382	+	0.517123i	0.885335	−	0.464953i	$-0.153929\pi$
$13$	3.87171	+	1.86451i	1.07382	+	0.517123i	0.188483	+	0.982077i	$0.439643\pi$
$14$	5.08757	+	3.49951i	1.35971	+	0.935284i
$15$		0			0
$16$	−0.219952	+	0.963674i	−0.0549881	+	0.240919i
$17$	−0.678070	+	0.850272i	−0.164456	+	0.206221i	−0.857230	−	0.514933i	$-0.827817\pi$
$17$	−0.678070	+	0.850272i	−0.164456	+	0.206221i	0.692774	+	0.721154i	$0.256388\pi$
$18$		0			0
$19$	−7.36179			−1.68891			−0.844455	−	0.535627i	$-0.820075\pi$
$19$	−7.36179			−1.68891			−0.844455	+	0.535627i	$0.820075\pi$
$20$	4.44993	−	5.58004i	0.995035	−	1.24773i
$21$		0			0
$22$	3.71221	+	4.65496i	0.791445	+	0.992441i
$23$	0.952254	+	1.19409i	0.198559	+	0.248985i	0.871136	−	0.491042i	$-0.163384\pi$
$23$	0.952254	+	1.19409i	0.198559	+	0.248985i	−0.672577	+	0.740027i	$0.734813\pi$
$24$		0			0
$25$	0.642583	−	0.309452i	0.128517	−	0.0618904i
$26$	−6.25325	−	7.84133i	−1.22636	−	1.53781i
$27$		0			0
$28$	−4.52747	−	7.91714i	−0.855611	−	1.49620i
$29$	−5.85246	+	7.33876i	−1.08678	+	1.36277i	−0.160017	+	0.987114i	$0.551155\pi$
$29$	−5.85246	+	7.33876i	−1.08678	+	1.36277i	−0.926758	+	0.375659i	$0.877416\pi$
$30$		0			0
$31$	−2.01883			−0.362593			−0.181296	−	0.983428i	$-0.558029\pi$
$31$	−2.01883			−0.362593			−0.181296	+	0.983428i	$0.558029\pi$
$32$	−2.77327	+	3.47757i	−0.490250	+	0.614754i
$33$		0			0
$34$	2.28686	−	1.10129i	0.392192	−	0.188870i
$35$	0.386799	+	5.46424i	0.0653810	+	0.923625i
$36$		0			0
$37$	1.47068	−	1.84418i	0.241779	−	0.303181i	−0.646105	−	0.763248i	$-0.723603\pi$
$37$	1.47068	−	1.84418i	0.241779	−	0.303181i	0.887884	+	0.460067i	$0.152175\pi$
$38$	15.4802	+	7.45488i	2.51122	+	1.20934i
$39$		0			0
$40$	−6.30040	+	3.03411i	−0.996180	+	0.479735i
$41$	1.38192	+	6.05457i	0.215819	+	0.945566i	0.960530	+	0.278178i	$0.0897304\pi$
$41$	1.38192	+	6.05457i	0.215819	+	0.945566i	−0.744710	+	0.667388i	$0.767412\pi$
$42$		0			0
$43$	−1.19246	+	5.22449i	−0.181848	+	0.796727i	0.798902	+	0.601461i	$0.205414\pi$
$43$	−1.19246	+	5.22449i	−0.181848	+	0.796727i	−0.980750	+	0.195267i	$0.937443\pi$
$44$	−1.95681	−	8.57332i	−0.294999	−	1.29248i
$45$		0			0
$46$	−0.793192	−	3.47520i	−0.116950	−	0.512390i
$47$	−1.02275	−	0.492532i	−0.149184	−	0.0718432i	0.357802	−	0.933797i	$-0.383526\pi$
$47$	−1.02275	−	0.492532i	−0.149184	−	0.0718432i	−0.506986	+	0.861954i	$0.669240\pi$
$48$		0			0
$49$	6.67174	+	2.11847i	0.953105	+	0.302639i
$50$	−1.66458			−0.235407
$51$		0			0
$52$	3.29626	+	14.4419i	0.457109	+	2.00272i
$53$	7.27161	+	9.11832i	0.998833	+	1.25250i	0.967469	+	0.252989i	$0.0814136\pi$
$53$	7.27161	+	9.11832i	0.998833	+	1.25250i	0.0313638	+	0.999508i	$0.490015\pi$
$54$		0			0
$55$	−1.17532	+	5.14941i	−0.158480	+	0.694346i
$56$	0.630975	+	8.91366i	0.0843176	+	1.19114i
$57$		0			0
$58$	19.7380	−	9.50532i	2.59173	−	1.24811i
$59$	−0.983859	+	4.31057i	−0.128088	+	0.561188i	0.869633	+	0.493700i	$0.164356\pi$
$59$	−0.983859	+	4.31057i	−0.128088	+	0.561188i	−0.997720	+	0.0674885i	$0.978501\pi$
$60$		0			0
$61$	−7.13624	+	8.94857i	−0.913702	+	1.14575i	0.0751983	+	0.997169i	$0.476041\pi$
$61$	−7.13624	+	8.94857i	−0.913702	+	1.14575i	−0.988901	+	0.148578i	$0.952530\pi$
$62$	4.24516	+	2.04436i	0.539136	+	0.259634i
$63$		0			0
$64$	11.1343	−	5.36198i	1.39178	−	0.670247i
$65$	1.97984	−	8.67423i	0.245568	−	1.07591i
$66$		0			0
$67$	−0.688531			−0.0841174			−0.0420587	−	0.999115i	$-0.513392\pi$
$67$	−0.688531			−0.0841174			−0.0420587	+	0.999115i	$0.513392\pi$
$68$	−3.74889			−0.454620
$69$		0			0
$70$	4.71998	−	11.8818i	0.564146	−	1.42014i
$71$	−10.2563	−	12.8610i	−1.21720	−	1.52632i	−0.778444	−	0.627714i	$-0.783991\pi$
$71$	−10.2563	−	12.8610i	−1.21720	−	1.52632i	−0.438755	−	0.898607i	$-0.644581\pi$
$72$		0			0
$73$	−1.76201	+	0.848540i	−0.206228	+	0.0993141i	−0.534147	−	0.845392i	$-0.679367\pi$
$73$	−1.76201	+	0.848540i	−0.206228	+	0.0993141i	0.327919	+	0.944706i	$0.393653\pi$
$74$	−4.96002	+	2.38862i	−0.576590	+	0.277671i
$75$		0			0
$76$	−15.8223	−	19.8406i	−1.81495	−	2.27587i
$77$	5.56090	+	3.82510i	0.633723	+	0.435910i
$78$		0			0
$79$	−5.42912			−0.610824			−0.305412	−	0.952220i	$-0.598794\pi$
$79$	−5.42912			−0.610824			−0.305412	+	0.952220i	$0.598794\pi$
$80$	2.04656			0.228812
$81$		0			0
$82$	3.22527	−	14.1308i	0.356171	−	1.56049i
$83$	9.13718	−	4.40023i	1.00294	−	0.482989i	0.141002	−	0.990009i	$-0.454968\pi$
$83$	9.13718	−	4.40023i	1.00294	−	0.482989i	0.861934	+	0.507021i	$0.169253\pi$
$84$		0			0
$85$	2.02871	+	0.976977i	0.220045	+	0.105968i
$86$	7.79803	−	9.77841i	0.840883	−	1.05443i
$87$		0			0
$88$	−1.91726	+	8.40008i	−0.204381	+	0.895452i
$89$	−12.3348	+	5.94011i	−1.30748	+	0.629650i	−0.952305	−	0.305149i	$-0.901294\pi$
$89$	−12.3348	+	5.94011i	−1.30748	+	0.629650i	−0.355177	+	0.934799i	$0.615579\pi$
$90$		0			0
$91$	−9.36739	−	6.44341i	−0.981969	−	0.675453i
$92$	−1.17153	+	5.13280i	−0.122140	+	0.535131i
$93$		0			0
$94$	1.65187	+	2.07137i	0.170377	+	0.213646i
$95$	3.39172	+	14.8601i	0.347983	+	1.52461i
$96$		0			0
$97$	−10.2656			−1.04232			−0.521158	−	0.853460i	$-0.674500\pi$
$97$	−10.2656			−1.04232			−0.521158	+	0.853460i	$0.674500\pi$
$98$	−11.8839	−	11.2108i	−1.20046	−	1.13246i
$99$		0			0
$100$	2.21507	+	1.06672i	0.221507	+	0.106672i
$101$	−1.37390	−	6.01945i	−0.136708	−	0.598957i	−0.996145	−	0.0877163i	$-0.972043\pi$
$101$	−1.37390	−	6.01945i	−0.136708	−	0.598957i	0.859437	−	0.511241i	$-0.170814\pi$
$102$		0			0
$103$	−0.377481	−	1.65385i	−0.0371943	−	0.162959i	0.952920	−	0.303222i	$-0.0980623\pi$
$103$	−0.377481	−	1.65385i	−0.0371943	−	0.162959i	−0.990114	+	0.140263i	$0.955205\pi$
$104$	3.22965	−	14.1500i	0.316693	−	1.38752i
$105$		0			0
$106$	−6.05698	−	26.5374i	−0.588306	−	2.57754i
$107$	9.24497	−	4.45214i	0.893745	−	0.430405i	0.0701192	−	0.997539i	$-0.477662\pi$
$107$	9.24497	−	4.45214i	0.893745	−	0.430405i	0.823626	+	0.567134i	$0.191948\pi$
$108$		0			0
$109$	−8.90798	−	4.28986i	−0.853230	−	0.410894i	−0.0444545	−	0.999011i	$-0.514155\pi$
$109$	−8.90798	−	4.28986i	−0.853230	−	0.410894i	−0.808775	+	0.588118i	$0.799869\pi$
$110$	7.68596	−	9.63789i	0.732827	−	0.918936i
$111$		0			0
$112$	0.965491	−	2.43046i	0.0912303	−	0.229657i
$113$	−11.2235	+	5.40495i	−1.05582	+	0.508455i	−0.879510	−	0.475881i	$-0.842129\pi$
$113$	−11.2235	+	5.40495i	−1.05582	+	0.508455i	−0.176307	+	0.984335i	$0.556415\pi$
$114$		0			0
$115$	1.97160	−	2.47231i	0.183853	−	0.230544i
$116$	−32.3569			−3.00427
$117$		0			0
$118$	6.43391	−	8.06787i	0.592290	−	0.742708i
$119$	2.11732	−	1.94837i	0.194094	−	0.178607i
$120$		0			0
$121$	−2.80081	−	3.51210i	−0.254619	−	0.319282i
$122$	24.0677	−	11.5904i	2.17898	−	1.04934i
$123$		0			0
$124$	−4.33898	−	5.44091i	−0.389652	−	0.488608i
$125$	−7.37523	−	9.24825i	−0.659661	−	0.827189i
$126$		0			0
$127$	2.76122	−	3.46246i	0.245018	−	0.307243i	−0.644081	−	0.764957i	$-0.722760\pi$
$127$	2.76122	−	3.46246i	0.245018	−	0.307243i	0.889100	+	0.457714i	$0.151332\pi$
$128$	−19.9467			−1.76306
$129$		0			0
$130$	−12.9471	+	16.2351i	−1.13553	+	1.42391i
$131$	2.92738	−	12.8257i	0.255766	−	1.12058i	−0.669962	−	0.742395i	$-0.733690\pi$
$131$	2.92738	−	12.8257i	0.255766	−	1.12058i	0.925728	−	0.378189i	$-0.123453\pi$
$132$		0			0
$133$	19.2478	+	2.98249i	1.66899	+	0.258614i
$134$	1.44783	+	0.697238i	0.125073	+	0.0602321i
$135$		0			0
$136$	3.30938	+	1.59371i	0.283777	+	0.136660i
$137$	3.03307	−	13.2887i	0.259133	−	1.13533i	−0.663049	−	0.748576i	$-0.730738\pi$
$137$	3.03307	−	13.2887i	0.259133	−	1.13533i	0.922181	−	0.386758i	$-0.126405\pi$
$138$		0			0
$139$	−3.65063	−	15.9944i	−0.309642	−	1.35663i	−0.855087	−	0.518484i	$-0.826496\pi$
$139$	−3.65063	−	15.9944i	−0.309642	−	1.35663i	0.545445	−	0.838147i	$-0.316361\pi$
$140$	−13.8952	+	12.7865i	−1.17436	+	1.08065i
$141$		0			0
$142$	8.54312	+	37.4299i	0.716923	+	3.14104i
$143$	−6.83503	−	8.57086i	−0.571574	−	0.716731i
$144$		0			0
$145$	17.5100	+	8.43235i	1.45412	+	0.700269i
$146$	4.56439			0.377752
$147$		0			0
$148$	8.13107			0.668370
$149$	17.8218	+	8.58252i	1.46002	+	0.703108i	0.984302	−	0.176491i	$-0.0564747\pi$
$149$	17.8218	+	8.58252i	1.46002	+	0.703108i	0.475716	+	0.879599i	$0.342189\pi$
$150$		0			0
$151$	7.86955	+	9.86810i	0.640415	+	0.803054i	0.991055	−	0.133456i	$-0.0426074\pi$
$151$	7.86955	+	9.86810i	0.640415	+	0.803054i	−0.350640	+	0.936510i	$0.614036\pi$
$152$	5.53282	+	24.2409i	0.448771	+	1.96619i
$153$		0			0
$154$	−7.81988	−	13.6746i	−0.630144	−	1.10193i
$155$	0.930116	+	4.07510i	0.0747087	+	0.327320i
$156$		0			0
$157$	2.66644	−	11.6824i	0.212805	−	0.932361i	−0.749845	−	0.661613i	$-0.769872\pi$
$157$	2.66644	−	11.6824i	0.212805	−	0.932361i	0.962650	−	0.270748i	$-0.0872709\pi$
$158$	11.4162	+	5.49777i	0.908228	+	0.437379i
$159$		0			0
$160$	8.29734	+	3.99579i	0.655962	+	0.315895i
$161$	−2.00595	−	3.50779i	−0.158091	−	0.276453i
$162$		0			0
$163$	−5.62831	+	24.6592i	−0.440843	+	1.93146i	−0.0868231	+	0.996224i	$0.527671\pi$
$163$	−5.62831	+	24.6592i	−0.440843	+	1.93146i	−0.354020	+	0.935238i	$0.615186\pi$
$164$	−13.3475	+	16.7372i	−1.04226	+	1.30695i
$165$		0			0
$166$	−23.6694			−1.83710
$167$	−6.65515	+	8.34529i	−0.514991	+	0.645778i	−0.969537	−	0.244945i	$-0.921230\pi$
$167$	−6.65515	+	8.34529i	−0.514991	+	0.645778i	0.454546	+	0.890723i	$0.349801\pi$
$168$		0			0
$169$	3.40832	+	4.27390i	0.262178	+	0.328761i
$170$	−3.27661	−	4.10873i	−0.251304	−	0.315125i
$171$		0			0
$172$	−16.6433	+	8.01498i	−1.26904	+	0.611137i
$173$	−11.4047	−	14.3011i	−0.867085	−	1.08729i	−0.995424	−	0.0955593i	$-0.969536\pi$
$173$	−11.4047	−	14.3011i	−0.867085	−	1.08729i	0.128339	−	0.991730i	$-0.459035\pi$
$174$		0			0
$175$	−1.80543	+	0.548747i	−0.136478	+	0.0414813i
$176$	1.57219	−	1.97147i	0.118509	−	0.148605i
$177$		0			0
$178$	31.9525			2.39494
$179$	7.49256	−	9.39537i	0.560020	−	0.702243i	−0.418542	−	0.908198i	$-0.637459\pi$
$179$	7.49256	−	9.39537i	0.560020	−	0.702243i	0.978561	+	0.205955i	$0.0660300\pi$
$180$		0			0
$181$	−17.8207	+	8.58199i	−1.32460	+	0.637894i	−0.956457	−	0.291874i	$-0.905721\pi$
$181$	−17.8207	+	8.58199i	−1.32460	+	0.637894i	−0.368144	+	0.929769i	$0.620007\pi$
$182$	13.1727	+	23.0349i	0.976423	+	1.70746i
$183$		0			0
$184$	3.21621	−	4.03301i	0.237103	−	0.297317i
$185$	−4.40013	−	2.11899i	−0.323504	−	0.155791i
$186$		0			0
$187$	2.49962	−	1.20375i	0.182790	−	0.0880271i
$188$	−0.870743	−	3.81498i	−0.0635055	−	0.278236i
$189$		0			0
$190$	7.91597	−	34.6821i	0.574285	−	2.51611i
$191$	0.713721	+	3.12701i	0.0516430	+	0.226263i	0.994163	−	0.107886i	$-0.0344082\pi$
$191$	0.713721	+	3.12701i	0.0516430	+	0.226263i	−0.942520	+	0.334149i	$0.891551\pi$
$192$		0			0
$193$	3.94362	+	17.2781i	0.283868	+	1.24371i	0.892789	+	0.450476i	$0.148746\pi$
$193$	3.94362	+	17.2781i	0.283868	+	1.24371i	−0.608921	+	0.793231i	$0.708397\pi$
$194$	21.5863	+	10.3954i	1.54981	+	0.746348i
$195$		0			0
$196$	8.62981	+	22.5340i	0.616415	+	1.60957i
$197$	13.5219			0.963396			0.481698	−	0.876337i	$-0.340020\pi$
$197$	13.5219			0.963396			0.481698	+	0.876337i	$0.340020\pi$
$198$		0			0
$199$	−0.904590	−	3.96327i	−0.0641247	−	0.280949i	0.932692	−	0.360673i	$-0.117453\pi$
$199$	−0.904590	−	3.96327i	−0.0641247	−	0.280949i	−0.996817	+	0.0797246i	$0.974596\pi$
$200$	−1.50190	−	1.88332i	−0.106200	−	0.133171i
$201$		0			0
$202$	−3.20656	+	14.0488i	−0.225613	+	0.988473i
$203$	18.2747	−	16.8165i	1.28263	−	1.18029i
$204$		0			0
$205$	11.5848	−	5.57892i	0.809114	−	0.389649i
$206$	−0.881006	+	3.85994i	−0.0613826	+	0.268935i
$207$		0			0
$208$	−2.64838	+	3.32096i	−0.183632	+	0.230267i
$209$	16.9204	+	8.14846i	1.17041	+	0.563641i
$210$		0			0
$211$	−11.2881	+	5.43607i	−0.777106	+	0.374234i	−0.780015	−	0.625761i	$-0.784788\pi$
$211$	−11.2881	+	5.43607i	−0.777106	+	0.374234i	0.00290876	+	0.999996i	$0.499074\pi$
$212$	−8.94603	+	39.1951i	−0.614416	+	2.69193i
$213$		0			0
$214$	−23.9486			−1.63709
$215$	11.0953			0.756690
$216$		0			0
$217$	5.27834	+	0.817891i	0.358317	+	0.0555221i
$218$	14.3874	+	18.0413i	0.974439	+	1.22191i
$219$		0			0
$220$	−16.4041	+	7.89980i	−1.10596	+	0.532604i
$221$	−4.21063	+	2.02773i	−0.283238	+	0.136400i
$222$		0			0
$223$	−15.5875	−	19.5461i	−1.04382	−	1.30891i	−0.949637	−	0.313351i	$-0.898548\pi$
$223$	−15.5875	−	19.5461i	−1.04382	−	1.30891i	−0.0941808	−	0.995555i	$-0.530023\pi$
$224$	8.65973	−	7.96875i	0.578602	−	0.532434i
$225$		0			0
$226$	29.0738			1.93396
$227$	−24.3586			−1.61673			−0.808367	−	0.588679i	$-0.799648\pi$
$227$	−24.3586			−1.61673			−0.808367	+	0.588679i	$0.799648\pi$
$228$		0			0
$229$	1.56665	−	6.86396i	0.103527	−	0.453583i	−0.896419	−	0.443208i	$-0.853840\pi$
$229$	1.56665	−	6.86396i	0.103527	−	0.453583i	0.999946	−	0.0103751i	$-0.00330256\pi$
$230$	−6.64941	+	3.20219i	−0.438449	+	0.211146i
$231$		0			0
$232$	28.5635	+	13.7555i	1.87529	+	0.903090i
$233$	2.87702	−	3.60767i	0.188480	−	0.236347i	−0.678609	−	0.734500i	$-0.737417\pi$
$233$	2.87702	−	3.60767i	0.188480	−	0.236347i	0.867089	+	0.498153i	$0.165988\pi$
$234$		0			0
$235$	−0.522996	+	2.29139i	−0.0341165	+	0.149474i
$236$	−13.7319	+	6.61292i	−0.893869	+	0.430464i
$237$		0			0
$238$	−6.42526	+	1.95291i	−0.416488	+	0.126588i
$239$	−2.25948	+	9.89942i	−0.146153	+	0.640340i	0.847779	+	0.530349i	$0.177939\pi$
$239$	−2.25948	+	9.89942i	−0.146153	+	0.640340i	−0.993933	+	0.109991i	$0.964918\pi$
$240$		0			0
$241$	5.11364	+	6.41230i	0.329399	+	0.413053i	0.918760	−	0.394817i	$-0.129192\pi$
$241$	5.11364	+	6.41230i	0.329399	+	0.413053i	−0.589361	+	0.807870i	$0.700621\pi$
$242$	2.33297	+	10.2214i	0.149969	+	0.657057i
$243$		0			0
$244$	−39.4547			−2.52583
$245$	1.20243	−	14.4432i	0.0768202	−	0.922744i
$246$		0			0
$247$	−28.5027	−	13.7262i	−1.81358	−	0.873375i
$248$	1.51727	+	6.64760i	0.0963468	+	0.422123i
$249$		0			0
$250$	6.14329	+	26.9155i	0.388536	+	1.70229i
$251$	−4.07743	+	17.8644i	−0.257365	+	1.12759i	0.666692	+	0.745333i	$0.267710\pi$
$251$	−4.07743	+	17.8644i	−0.257365	+	1.12759i	−0.924057	+	0.382255i	$0.875147\pi$
$252$		0			0
$253$	−0.866988	−	3.79852i	−0.0545071	−	0.238811i
$254$	−9.31247	+	4.48465i	−0.584317	+	0.281392i
$255$		0			0
$256$	19.6750	+	9.47500i	1.22969	+	0.592187i
$257$	13.4172	−	16.8247i	0.836943	−	1.04949i	−0.161098	−	0.986938i	$-0.551504\pi$
$257$	13.4172	−	16.8247i	0.836943	−	1.04949i	0.998041	−	0.0625555i	$-0.0199250\pi$
$258$		0			0
$259$	−4.59231	+	4.22587i	−0.285352	+	0.262583i
$260$	27.6329	−	13.3073i	1.71372	−	0.825283i
$261$		0			0
$262$	−19.1435	+	24.0052i	−1.18269	+	1.48304i
$263$	−7.67583			−0.473312			−0.236656	−	0.971594i	$-0.576051\pi$
$263$	−7.67583			−0.473312			−0.236656	+	0.971594i	$0.576051\pi$
$264$		0			0
$265$	15.0556	−	18.8791i	0.924855	−	1.15973i
$266$	−37.4536	−	25.7627i	−2.29643	−	1.57961i
$267$		0			0
$268$	−1.47983	−	1.85564i	−0.0903948	−	0.113351i
$269$	−0.107810	+	0.0519187i	−0.00657330	+	0.00316554i	−0.437168	−	0.899380i	$-0.644018\pi$
$269$	−0.107810	+	0.0519187i	−0.00657330	+	0.00316554i	0.430594	+	0.902546i	$0.358304\pi$
$270$		0			0
$271$	−6.48968	−	8.13780i	−0.394220	−	0.494336i	0.544624	−	0.838681i	$-0.316673\pi$
$271$	−6.48968	−	8.13780i	−0.394220	−	0.494336i	−0.938843	+	0.344345i	$0.888101\pi$
$272$	−0.670243	−	0.840458i	−0.0406394	−	0.0509602i
$273$		0			0
$274$	−19.8347	+	24.8719i	−1.19826	+	1.50256i
$275$	−1.81944			−0.109717
$276$		0			0
$277$	3.75641	−	4.71039i	0.225701	−	0.283020i	−0.656068	−	0.754702i	$-0.727782\pi$
$277$	3.75641	−	4.71039i	0.225701	−	0.283020i	0.881769	+	0.471682i	$0.156353\pi$
$278$	−8.52023	+	37.3296i	−0.511010	+	2.23888i
$279$		0			0
$280$	17.7019	−	5.38035i	1.05789	−	0.321537i
$281$	−7.96048	−	3.83357i	−0.474883	−	0.228691i	0.181104	−	0.983464i	$-0.442033\pi$
$281$	−7.96048	−	3.83357i	−0.474883	−	0.228691i	−0.655987	+	0.754773i	$0.727747\pi$
$282$		0			0
$283$	1.36334	+	0.656550i	0.0810422	+	0.0390279i	0.473966	−	0.880543i	$-0.342822\pi$
$283$	1.36334	+	0.656550i	0.0810422	+	0.0390279i	−0.392924	+	0.919571i	$0.628536\pi$
$284$	12.6180	−	55.2831i	0.748741	−	3.28045i
$285$		0			0
$286$	5.69333	+	24.9441i	0.336653	+	1.47498i
$287$	−1.16019	−	16.3898i	−0.0684841	−	0.967462i
$288$		0			0
$289$	3.51967	+	15.4207i	0.207039	+	0.907099i
$290$	−28.2806	−	35.4628i	−1.66069	−	2.08244i
$291$		0			0
$292$	−6.07388	−	2.92503i	−0.355447	−	0.171174i
$293$	−23.4300			−1.36880			−0.684399	−	0.729108i	$-0.739935\pi$
$293$	−23.4300			−1.36880			−0.684399	+	0.729108i	$0.739935\pi$
$294$		0			0
$295$	9.15436			0.532987
$296$	−7.17780	−	3.45665i	−0.417201	−	0.200914i
$297$		0			0
$298$	−28.7843	−	36.0943i	−1.66743	−	2.09089i
$299$	1.46045	+	6.39865i	0.0844600	+	0.370044i
$300$		0			0
$301$	5.23434	−	13.1766i	0.301702	−	0.759486i
$302$	−6.55504	−	28.7195i	−0.377200	−	1.65262i
$303$		0			0
$304$	1.61924	−	7.09437i	0.0928699	−	0.406890i
$305$	21.3509	+	10.2820i	1.22255	+	0.588748i
$306$		0			0
$307$	29.9200	+	14.4087i	1.70763	+	0.822349i	0.992343	+	0.123515i	$0.0394166\pi$
$307$	29.9200	+	14.4087i	1.70763	+	0.822349i	0.715283	+	0.698835i	$0.246298\pi$
$308$	1.64284	+	23.2081i	0.0936098	+	1.32241i
$309$		0			0
$310$	2.17081	−	9.51092i	0.123293	−	0.540184i
$311$	−14.5599	+	18.2576i	−0.825618	+	1.03529i	0.173112	+	0.984902i	$0.444618\pi$
$311$	−14.5599	+	18.2576i	−0.825618	+	1.03529i	−0.998730	+	0.0503900i	$0.983954\pi$
$312$		0			0
$313$	3.50921			0.198353			0.0991763	−	0.995070i	$-0.468379\pi$
$313$	3.50921			0.198353			0.0991763	+	0.995070i	$0.468379\pi$
$314$	−17.4371	+	21.8655i	−0.984034	+	1.23394i
$315$		0			0
$316$	−11.6685	−	14.6319i	−0.656407	−	0.823108i
$317$	11.0121	+	13.8087i	0.618499	+	0.775573i	0.988132	−	0.153605i	$-0.0490882\pi$
$317$	11.0121	+	13.8087i	0.618499	+	0.775573i	−0.369633	+	0.929178i	$0.620517\pi$
$318$		0			0
$319$	21.5744	−	10.3897i	1.20793	−	0.581710i
$320$	−15.9532	−	20.0046i	−0.891809	−	1.11829i
$321$		0			0
$322$	0.665928	+	9.40743i	0.0371107	+	0.524256i
$323$	4.99180	−	6.25952i	0.277751	−	0.348289i
$324$		0			0
$325$	3.06487			0.170008
$326$	36.8062	−	46.1535i	2.03851	−	2.55620i
$327$		0			0
$328$	18.8979	−	9.10074i	1.04346	−	0.502504i
$329$	2.47450	+	1.70210i	0.136424	+	0.0938398i
$330$		0			0
$331$	12.4627	−	15.6278i	0.685013	−	0.858979i	−0.310792	−	0.950478i	$-0.600594\pi$
$331$	12.4627	−	15.6278i	0.685013	−	0.858979i	0.995805	+	0.0914989i	$0.0291658\pi$
$332$	31.4971	+	15.1682i	1.72863	+	0.832463i
$333$		0			0
$334$	22.4451	−	10.8090i	1.22814	−	0.591442i
$335$	0.317220	+	1.38983i	0.0173316	+	0.0759346i
$336$		0			0
$337$	−4.54804	+	19.9263i	−0.247747	+	1.08545i	0.686023	+	0.727580i	$0.259355\pi$
$337$	−4.54804	+	19.9263i	−0.247747	+	1.08545i	−0.933770	+	0.357872i	$0.883502\pi$
$338$	−2.83900	−	12.4385i	−0.154421	−	0.676564i
$339$		0			0
$340$	1.72719	+	7.56731i	0.0936699	+	0.410395i
$341$	4.64011	+	2.23456i	0.251276	+	0.121008i
$342$		0			0
$343$	−16.5853	−	8.24177i	−0.895524	−	0.445014i
$344$	18.0994			0.975853
$345$		0			0
$346$	9.49970	+	41.6209i	0.510707	+	2.23755i
$347$	18.3391	+	22.9965i	0.984494	+	1.23452i	0.972094	+	0.234593i	$0.0753758\pi$
$347$	18.3391	+	22.9965i	0.984494	+	1.23452i	0.0124001	+	0.999923i	$0.496053\pi$
$348$		0			0
$349$	3.75843	−	16.4667i	0.201184	−	0.881445i	−0.769033	−	0.639209i	$-0.779262\pi$
$349$	3.75843	−	16.4667i	0.201184	−	0.881445i	0.970217	−	0.242236i	$-0.0778808\pi$
$350$	4.35212	+	0.674371i	0.232630	+	0.0360467i
$351$		0			0
$352$	10.2233	−	4.92329i	0.544904	−	0.262412i
$353$	6.71717	−	29.4298i	0.357519	−	1.56639i	−0.401833	−	0.915713i	$-0.631627\pi$
$353$	6.71717	−	29.4298i	0.357519	−	1.56639i	0.759352	−	0.650680i	$-0.225516\pi$
$354$		0			0
$355$	−21.2352	+	26.6281i	−1.12705	+	1.41327i
$356$	−42.5195	−	20.4763i	−2.25353	−	1.08524i
$357$		0			0
$358$	−25.2694	+	12.1691i	−1.33553	+	0.643156i
$359$	1.25242	−	5.48722i	0.0661003	−	0.289604i	−0.931064	−	0.364855i	$-0.881119\pi$
$359$	1.25242	−	5.48722i	0.0661003	−	0.289604i	0.997165	+	0.0752506i	$0.0239757\pi$
$360$		0			0
$361$	35.1959			1.85242
$362$	46.1635			2.42630
$363$		0			0
$364$	−2.76739	−	39.0944i	−0.145051	−	2.04910i
$365$	2.52461	+	3.16576i	0.132144	+	0.165703i
$366$		0			0
$367$	−11.0045	+	5.29950i	−0.574431	+	0.276631i	−0.698462	−	0.715647i	$-0.746132\pi$
$367$	−11.0045	+	5.29950i	−0.574431	+	0.276631i	0.124031	+	0.992278i	$0.460418\pi$
$368$	−1.36016	+	0.655020i	−0.0709034	+	0.0341453i
$369$		0			0
$370$	7.10671	+	8.91154i	0.369460	+	0.463289i
$371$	−15.3179	−	26.7862i	−0.795265	−	1.39067i
$372$		0			0
$373$	−7.32099			−0.379067			−0.189533	−	0.981874i	$-0.560697\pi$
$373$	−7.32099			−0.379067			−0.189533	+	0.981874i	$0.560697\pi$
$374$	−6.47512			−0.334820
$375$		0			0
$376$	−0.853148	+	3.73789i	−0.0439978	+	0.192767i
$377$	−36.3422	+	17.5015i	−1.87172	+	0.901373i
$378$		0			0
$379$	15.4937	+	7.46137i	0.795858	+	0.383265i	0.787200	−	0.616698i	$-0.211530\pi$
$379$	15.4937	+	7.46137i	0.795858	+	0.383265i	0.00865769	+	0.999963i	$0.497244\pi$
$380$	−32.7594	+	41.0790i	−1.68052	+	2.10731i
$381$		0			0
$382$	1.66576	−	7.29817i	0.0852277	−	0.373407i
$383$	−29.6246	+	14.2664i	−1.51374	+	0.728981i	−0.992248	−	0.124272i	$-0.960340\pi$
$383$	−29.6246	+	14.2664i	−1.51374	+	0.728981i	−0.521497	+	0.853253i	$0.674626\pi$
$384$		0			0
$385$	5.15911	−	12.9872i	0.262933	−	0.661890i
$386$	9.20405	−	40.3256i	0.468474	−	2.05252i
$387$		0			0
$388$	−22.0634	−	27.6666i	−1.12010	−	1.40456i
$389$	−0.271461	−	1.18935i	−0.0137636	−	0.0603023i	0.967580	−	0.252566i	$-0.0812744\pi$
$389$	−0.271461	−	1.18935i	−0.0137636	−	0.0603023i	−0.981343	+	0.192263i	$0.938417\pi$
$390$		0			0
$391$	−1.66100			−0.0840001
$392$	1.96148	−	23.5608i	0.0990699	−	1.19000i
$393$		0			0
$394$	−28.4336	−	13.6929i	−1.43246	−	0.689838i
$395$	2.50130	+	10.9589i	0.125854	+	0.551403i
$396$		0			0
$397$	−0.0786519	−	0.344596i	−0.00394742	−	0.0172948i	0.972916	−	0.231160i	$-0.0742519\pi$
$397$	−0.0786519	−	0.344596i	−0.00394742	−	0.0172948i	−0.976863	+	0.213865i	$0.931395\pi$
$398$	−2.11123	+	9.24991i	−0.105826	+	0.463656i
$399$		0			0
$400$	0.156873	+	0.687306i	0.00784365	+	0.0343653i
$401$	−7.35492	+	3.54194i	−0.367287	+	0.176876i	−0.608419	−	0.793616i	$-0.708196\pi$
$401$	−7.35492	+	3.54194i	−0.367287	+	0.176876i	0.241131	+	0.970492i	$0.422482\pi$
$402$		0			0
$403$	−7.81632	−	3.76414i	−0.389359	−	0.187505i
$404$	13.2700	−	16.6401i	0.660208	−	0.827874i
$405$		0			0
$406$	−55.4569	+	16.8557i	−2.75228	+	0.836532i
$407$	−5.42148	+	2.61085i	−0.268733	+	0.129415i
$408$		0			0
$409$	13.7984	−	17.3027i	0.682289	−	0.855563i	−0.313274	−	0.949663i	$-0.601426\pi$
$409$	13.7984	−	17.3027i	0.682289	−	0.855563i	0.995563	+	0.0940997i	$0.0299973\pi$
$410$	−30.0097			−1.48207
$411$		0			0
$412$	3.64595	−	4.57188i	0.179623	−	0.225241i
$413$	4.31869	−	10.8716i	0.212509	−	0.534957i
$414$		0			0
$415$	−13.0918	−	16.4165i	−0.642649	−	0.805856i
$416$	−17.2213	+	8.29333i	−0.844343	+	0.406614i
$417$		0			0
$418$	−27.3285	−	34.2688i	−1.33668	−	1.67614i
$419$	21.6012	+	27.0871i	1.05529	+	1.32329i	0.944161	+	0.329483i	$0.106875\pi$
$419$	21.6012	+	27.0871i	1.05529	+	1.32329i	0.111127	+	0.993806i	$0.464554\pi$
$420$		0			0
$421$	7.43023	−	9.31722i	0.362127	−	0.454094i	−0.567074	−	0.823667i	$-0.691925\pi$
$421$	7.43023	−	9.31722i	0.362127	−	0.454094i	0.929202	+	0.369573i	$0.120496\pi$
$422$	29.2412			1.42344
$423$		0			0
$424$	24.5597	−	30.7969i	1.19272	−	1.49563i
$425$	−0.172598	+	0.756201i	−0.00837223	+	0.0366811i
$426$		0			0
$427$	22.2834	−	20.5054i	1.07837	−	0.992324i
$428$	31.8686	+	15.3471i	1.54043	+	0.741831i
$429$		0			0
$430$	−23.3309	−	11.2356i	−1.12511	−	0.541827i
$431$	−0.813999	+	3.56636i	−0.0392089	+	0.171786i	−0.990741	−	0.135763i	$-0.956651\pi$
$431$	−0.813999	+	3.56636i	−0.0392089	+	0.171786i	0.951532	+	0.307548i	$0.0995086\pi$
$432$		0			0
$433$	0.956841	+	4.19219i	0.0459828	+	0.201464i	0.992701	−	0.120598i	$-0.0384812\pi$
$433$	0.956841	+	4.19219i	0.0459828	+	0.201464i	−0.946719	+	0.322062i	$0.895624\pi$
$434$	−10.2709	−	7.06493i	−0.493021	−	0.339127i
$435$		0			0
$436$	−7.58400	−	33.2277i	−0.363208	−	1.59132i
$437$	−7.01029	−	8.79063i	−0.335348	−	0.420513i
$438$		0			0
$439$	−28.5132	−	13.7312i	−1.36086	−	0.655356i	−0.396032	−	0.918237i	$-0.629613\pi$
$439$	−28.5132	−	13.7312i	−1.36086	−	0.655356i	−0.964828	+	0.262881i	$0.915327\pi$
$440$	17.8393			0.850454
$441$		0			0
$442$	10.9074			0.518812
$443$	6.79416	+	3.27189i	0.322800	+	0.155452i	0.588265	−	0.808668i	$-0.299811\pi$
$443$	6.79416	+	3.27189i	0.322800	+	0.155452i	−0.265465	+	0.964121i	$0.585525\pi$
$444$		0			0
$445$	17.6732	+	22.1615i	0.837792	+	1.05056i
$446$	12.9838	+	56.8859i	0.614802	+	2.69362i
$447$		0			0
$448$	−31.2834	+	9.50832i	−1.47800	+	0.449226i
$449$	5.61518	+	24.6017i	0.264997	+	1.16103i	0.915754	+	0.401740i	$0.131594\pi$
$449$	5.61518	+	24.6017i	0.264997	+	1.16103i	−0.650757	+	0.759286i	$0.725548\pi$
$450$		0			0
$451$	3.52534	−	15.4455i	0.166002	−	0.727301i
$452$	−38.6888	−	18.6316i	−1.81977	−	0.876355i
$453$		0			0
$454$	51.2207	+	24.6666i	2.40390	+	1.15766i
$455$	−8.69058	+	21.8771i	−0.407421	+	1.02561i
$456$		0			0
$457$	−4.16130	+	18.2319i	−0.194658	+	0.852851i	0.779396	+	0.626532i	$0.215526\pi$
$457$	−4.16130	+	18.2319i	−0.194658	+	0.852851i	−0.974053	+	0.226319i	$0.927331\pi$
$458$	−10.2451	+	12.8469i	−0.478721	+	0.600298i
$459$		0			0
$460$	10.9005			0.508240
$461$	12.0851	−	15.1543i	0.562861	−	0.705805i	−0.416223	−	0.909263i	$-0.636646\pi$
$461$	12.0851	−	15.1543i	0.562861	−	0.705805i	0.979084	+	0.203458i	$0.0652179\pi$
$462$		0			0
$463$	1.02031	+	1.27943i	0.0474177	+	0.0594599i	0.804975	−	0.593309i	$-0.202179\pi$
$463$	1.02031	+	1.27943i	0.0474177	+	0.0594599i	−0.757557	+	0.652769i	$0.773607\pi$
$464$	−5.78491	−	7.25405i	−0.268558	−	0.336761i
$465$		0			0
$466$	−9.70304	+	4.67274i	−0.449485	+	0.216460i
$467$	8.58342	+	10.7633i	0.397193	+	0.498065i	0.939706	−	0.341983i	$-0.111098\pi$
$467$	8.58342	+	10.7633i	0.397193	+	0.498065i	−0.542513	+	0.840047i	$0.682527\pi$
$468$		0			0
$469$	1.80020	+	0.278945i	0.0831254	+	0.0128805i
$470$	3.42011	−	4.28869i	0.157758	−	0.197822i
$471$		0			0
$472$	14.9332			0.687358
$473$	8.52353	−	10.6882i	0.391912	−	0.491442i
$474$		0			0
$475$	−4.73056	+	2.27812i	−0.217053	+	0.104527i
$476$	9.80166	+	1.51879i	0.449259	+	0.0696137i
$477$		0			0
$478$	14.7758	−	18.5282i	0.675829	−	0.847462i
$479$	−9.13433	−	4.39886i	−0.417358	−	0.200989i	0.213406	−	0.976964i	$-0.431544\pi$
$479$	−9.13433	−	4.39886i	−0.417358	−	0.200989i	−0.630764	+	0.775974i	$0.717259\pi$
$480$		0			0
$481$	9.13254	−	4.39800i	0.416408	−	0.200532i
$482$	−4.25947	−	18.6620i	−0.194014	−	0.850029i
$483$		0			0
$484$	3.44574	−	15.0968i	0.156625	−	0.686218i
$485$	4.72957	+	20.7216i	0.214759	+	0.940920i
$486$		0			0
$487$	−4.71606	−	20.6624i	−0.213705	−	0.936303i	−0.962024	−	0.272964i	$-0.911996\pi$
$487$	−4.71606	−	20.6624i	−0.213705	−	0.936303i	0.748319	−	0.663339i	$-0.230861\pi$
$488$	34.8291	+	16.7728i	1.57664	+	0.759270i
$489$		0			0
$490$	−17.1543	+	29.1533i	−0.774952	+	1.31701i
$491$	−20.9336			−0.944719			−0.472359	−	0.881406i	$-0.656598\pi$
$491$	−20.9336			−0.944719			−0.472359	+	0.881406i	$0.656598\pi$
$492$		0			0
$493$	−2.27157	−	9.95238i	−0.102306	−	0.448233i
$494$	46.0351	+	57.7262i	2.07122	+	2.59722i
$495$		0			0
$496$	0.444047	−	1.94550i	0.0199383	−	0.0873554i
$497$	21.6052	+	37.7809i	0.969127	+	1.69470i
$498$		0			0
$499$	−5.42774	+	2.61386i	−0.242979	+	0.117013i	−0.551411	−	0.834234i	$-0.685910\pi$
$499$	−5.42774	+	2.61386i	−0.242979	+	0.117013i	0.308432	+	0.951247i	$0.400196\pi$
$500$	9.07351	−	39.7536i	0.405780	−	1.77784i
$501$		0			0
$502$	26.6642	−	33.4358i	1.19008	−	1.49231i
$503$	2.71280	+	1.30641i	0.120958	+	0.0582501i	0.493384	−	0.869812i	$-0.335760\pi$
$503$	2.71280	+	1.30641i	0.120958	+	0.0582501i	−0.372426	+	0.928062i	$0.621474\pi$
$504$		0			0
$505$	−11.5175	+	5.54655i	−0.512524	+	0.246818i
$506$	−2.02347	+	8.86541i	−0.0899543	+	0.394115i
$507$		0			0
$508$	15.2661			0.677326
$509$	−18.1230			−0.803288			−0.401644	−	0.915796i	$-0.631561\pi$
$509$	−18.1230			−0.803288			−0.401644	+	0.915796i	$0.631561\pi$
$510$		0			0
$511$	4.95063	−	1.50470i	0.219003	−	0.0665642i
$512$	−6.90429	−	8.65770i	−0.305129	−	0.382620i
$513$		0			0
$514$	−45.2509	+	21.7917i	−1.99593	+	0.961190i
$515$	−3.16446	+	1.52392i	−0.139443	+	0.0671521i
$516$		0			0
$517$	1.80555	+	2.26409i	0.0794080	+	0.0995745i
$518$	13.9359	−	4.23571i	0.612309	−	0.186106i
$519$		0			0
$520$	−30.0504			−1.31780
$521$	5.81614			0.254810			0.127405	−	0.991851i	$-0.459335\pi$
$521$	5.81614			0.254810			0.127405	+	0.991851i	$0.459335\pi$
$522$		0			0
$523$	−6.78820	+	29.7410i	−0.296827	+	1.30049i	0.577995	+	0.816041i	$0.303835\pi$
$523$	−6.78820	+	29.7410i	−0.296827	+	1.30049i	−0.874822	+	0.484445i	$0.839022\pi$
$524$	40.8579	−	19.6761i	1.78488	−	0.859555i
$525$		0			0
$526$	16.1406	+	7.77289i	0.703762	+	0.338914i
$527$	1.36891	−	1.71656i	0.0596306	−	0.0747744i
$528$		0			0
$529$	4.59892	−	20.1492i	0.199953	−	0.876052i
$530$	−50.7763	+	24.4526i	−2.20558	+	1.06215i
$531$		0			0
$532$	33.3302	+	58.2843i	1.44505	+	2.52694i
$533$	−5.93847	+	26.0181i	−0.257224	+	1.12697i
$534$		0			0
$535$	−13.2462	−	16.6102i	−0.572683	−	0.718121i
$536$	0.517472	+	2.26719i	0.0223514	+	0.0979277i
$537$		0			0
$538$	0.279276			0.0120405
$539$	−12.9896	−	12.2538i	−0.559501	−	0.527808i
$540$		0			0
$541$	7.60542	+	3.66258i	0.326982	+	0.157466i	0.590172	−	0.807278i	$-0.299060\pi$
$541$	7.60542	+	3.66258i	0.326982	+	0.157466i	−0.263189	+	0.964744i	$0.584774\pi$
$542$	5.40566	+	23.6837i	0.232193	+	1.01730i
$543$		0			0
$544$	−1.07641	−	4.71607i	−0.0461508	−	0.202200i
$545$	−4.55519	+	19.9576i	−0.195123	+	0.854889i
$546$		0			0
$547$	7.90340	+	34.6270i	0.337925	+	1.48055i	0.803376	+	0.595472i	$0.203035\pi$
$547$	7.90340	+	34.6270i	0.337925	+	1.48055i	−0.465451	+	0.885074i	$0.654108\pi$
$548$	42.3330	−	20.3865i	1.80838	−	0.870868i
$549$		0			0
$550$	3.82589	+	1.84245i	0.163136	+	0.0785623i
$551$	43.0846	−	54.0264i	1.83547	−	2.30160i
$552$		0			0
$553$	14.1947	+	2.19950i	0.603620	+	0.0935325i
$554$	−12.6689	+	6.10100i	−0.538248	+	0.259207i
$555$		0			0
$556$	35.2601	−	44.2148i	1.49536	−	1.87513i
$557$	−29.8289			−1.26389			−0.631946	−	0.775012i	$-0.717744\pi$
$557$	−29.8289			−1.26389			−0.631946	+	0.775012i	$0.717744\pi$
$558$		0			0
$559$	−14.3580	+	18.0043i	−0.607278	+	0.761502i
$560$	−5.35082	−	0.829123i	−0.226114	−	0.0350369i
$561$		0			0
$562$	12.8571	+	16.1223i	0.542344	+	0.680078i
$563$	1.70372	−	0.820469i	0.0718033	−	0.0345786i	−0.397637	−	0.917543i	$-0.630170\pi$
$563$	1.70372	−	0.820469i	0.0718033	−	0.0345786i	0.469441	+	0.882964i	$0.344456\pi$
$564$		0			0
$565$	16.0810	+	20.1649i	0.676533	+	0.848346i
$566$	−2.20195	−	2.76116i	−0.0925550	−	0.116060i
$567$		0			0
$568$	−34.6404	+	43.4377i	−1.45348	+	1.82261i
$569$	−23.1906			−0.972203			−0.486101	−	0.873902i	$-0.661581\pi$
$569$	−23.1906			−0.972203			−0.486101	+	0.873902i	$0.661581\pi$
$570$		0			0
$571$	4.94909	−	6.20596i	0.207113	−	0.259711i	−0.667416	−	0.744685i	$-0.732600\pi$
$571$	4.94909	−	6.20596i	0.207113	−	0.259711i	0.874529	+	0.484974i	$0.161171\pi$
$572$	8.40892	−	36.8419i	0.351595	−	1.54044i
$573$		0			0
$574$	−14.1575	+	35.6391i	−0.590921	+	1.48755i
$575$	0.981415	+	0.472625i	0.0409279	+	0.0197098i
$576$		0			0
$577$	4.92134	+	2.36999i	0.204878	+	0.0986640i	0.533509	−	0.845794i	$-0.320873\pi$
$577$	4.92134	+	2.36999i	0.204878	+	0.0986640i	−0.328631	+	0.944458i	$0.606587\pi$
$578$	8.21459	−	35.9905i	0.341682	−	1.49701i
$579$		0			0
$580$	14.9075	+	65.3139i	0.618999	+	2.71201i
$581$	−25.6723	+	7.80288i	−1.06507	+	0.323718i
$582$		0			0
$583$	−6.62050	−	29.0063i	−0.274193	−	1.20132i
$584$	4.11832	+	5.16421i	0.170417	+	0.213697i
$585$		0			0
$586$	49.2682	+	23.7263i	2.03525	+	0.980125i
$587$	−11.0440			−0.455835			−0.227917	−	0.973680i	$-0.573192\pi$
$587$	−11.0440			−0.455835			−0.227917	+	0.973680i	$0.573192\pi$
$588$		0			0
$589$	14.8622			0.612387
$590$	−19.2496	−	9.27012i	−0.792493	−	0.381645i
$591$		0			0
$592$	1.45371	+	1.82289i	0.0597470	+	0.0749203i
$593$	−1.80306	−	7.89970i	−0.0740426	−	0.324402i	0.924319	−	0.381621i	$-0.124634\pi$
$593$	−1.80306	−	7.89970i	−0.0740426	−	0.324402i	−0.998362	+	0.0572187i	$0.981777\pi$
$594$		0			0
$595$	−4.90837	−	3.37625i	−0.201223	−	0.138413i
$596$	15.1730	+	66.4771i	0.621509	+	2.72301i
$597$		0			0
$598$	3.40856	−	14.9339i	0.139386	−	0.610691i
$599$	−7.67886	−	3.69794i	−0.313750	−	0.151094i	0.270381	−	0.962753i	$-0.412850\pi$
$599$	−7.67886	−	3.69794i	−0.313750	−	0.151094i	−0.584131	+	0.811659i	$0.698565\pi$
$600$		0			0
$601$	−20.7260	−	9.98111i	−0.845431	−	0.407138i	−0.0395513	−	0.999218i	$-0.512593\pi$
$601$	−20.7260	−	9.98111i	−0.845431	−	0.407138i	−0.805880	+	0.592079i	$0.798307\pi$
$602$	−24.3499	+	22.4069i	−0.992426	+	0.913238i
$603$		0			0
$604$	−9.68164	+	42.4181i	−0.393941	+	1.72597i
$605$	−5.79895	+	7.27166i	−0.235761	+	0.295635i
$606$		0			0
$607$	−6.96194			−0.282577			−0.141288	−	0.989968i	$-0.545124\pi$
$607$	−6.96194			−0.282577			−0.141288	+	0.989968i	$0.545124\pi$
$608$	20.4162	−	25.6011i	0.827988	−	1.03826i
$609$		0			0
$610$	−34.4842	−	43.2418i	−1.39622	−	1.75081i
$611$	−3.04147	−	3.81388i	−0.123045	−	0.154293i
$612$		0			0
$613$	−19.8410	+	9.55490i	−0.801369	+	0.385919i	−0.789300	−	0.614008i	$-0.789556\pi$
$613$	−19.8410	+	9.55490i	−0.801369	+	0.385919i	−0.0120692	+	0.999927i	$0.503842\pi$
$614$	−48.3243	−	60.5967i	−1.95021	−	2.44549i
$615$		0			0
$616$	8.41591	−	21.1857i	0.339087	−	0.853596i
$617$	16.9852	−	21.2987i	0.683797	−	0.857455i	−0.311900	−	0.950115i	$-0.600966\pi$
$617$	16.9852	−	21.2987i	0.683797	−	0.857455i	0.995698	+	0.0926600i	$0.0295369\pi$
$618$		0			0
$619$	−6.64138			−0.266940			−0.133470	−	0.991053i	$-0.542612\pi$
$619$	−6.64138			−0.266940			−0.133470	+	0.991053i	$0.542612\pi$
$620$	−8.98366	+	11.2652i	−0.360792	+	0.452419i
$621$		0			0
$622$	49.1048	−	23.6476i	1.96892	−	0.948183i
$623$	34.6564	−	10.5335i	1.38848	−	0.422016i
$624$		0			0
$625$	−13.0467	+	16.3600i	−0.521867	+	0.654401i
$626$	−7.37910	−	3.55359i	−0.294928	−	0.142030i
$627$		0			0
$628$	37.2160	−	17.9223i	1.48508	−	0.715176i
$629$	0.570828	+	2.50096i	0.0227604	+	0.0997199i
$630$		0			0
$631$	2.52355	−	11.0564i	0.100461	−	0.440149i	−0.899533	−	0.436852i	$-0.856093\pi$
$631$	2.52355	−	11.0564i	0.100461	−	0.440149i	0.999995	−	0.00329705i	$-0.00104949\pi$
$632$	4.08030	+	17.8770i	0.162306	+	0.711108i
$633$		0			0
$634$	−9.17263	−	40.1879i	−0.364292	−	1.59607i
$635$	−8.26127	−	3.97842i	−0.327839	−	0.157879i
$636$		0			0
$637$	21.8811	+	20.6416i	0.866960	+	0.817852i
$638$	−55.8872			−2.21259
$639$		0			0
$640$	9.18985	+	40.2634i	0.363261	+	1.59155i
$641$	−4.94734	−	6.20376i	−0.195408	−	0.245034i	0.674468	−	0.738304i	$-0.264373\pi$
$641$	−4.94734	−	6.20376i	−0.195408	−	0.245034i	−0.869876	+	0.493270i	$0.835801\pi$
$642$		0			0
$643$	0.213255	−	0.934333i	0.00840998	−	0.0368465i	−0.970549	−	0.240904i	$-0.922556\pi$
$643$	0.213255	−	0.934333i	0.00840998	−	0.0368465i	0.978959	+	0.204058i	$0.0654131\pi$
$644$	5.14247	−	12.9453i	0.202642	−	0.510117i
$645$		0			0
$646$	−16.8353	+	8.10747i	−0.662378	+	0.318984i
$647$	6.77369	−	29.6775i	0.266301	−	1.16674i	−0.647979	−	0.761659i	$-0.724385\pi$
$647$	6.77369	−	29.6775i	0.266301	−	1.16674i	0.914280	−	0.405083i	$-0.132757\pi$
$648$		0			0
$649$	7.03251	−	8.81848i	0.276050	−	0.346156i
$650$	−6.44475	−	3.10363i	−0.252784	−	0.121734i
$651$		0			0
$652$	−78.5552	+	37.8302i	−3.07646	+	1.48155i
$653$	11.1654	−	48.9189i	0.436937	−	1.91435i	0.0332553	−	0.999447i	$-0.489413\pi$
$653$	11.1654	−	48.9189i	0.436937	−	1.91435i	0.403682	−	0.914899i	$-0.367730\pi$
$654$		0			0
$655$	−27.2379			−1.06427
$656$	−6.13859			−0.239672
$657$		0			0
$658$	−3.47971	−	6.08493i	−0.135653	−	0.237215i
$659$	4.38993	+	5.50480i	0.171008	+	0.214437i	0.859949	−	0.510381i	$-0.170496\pi$
$659$	4.38993	+	5.50480i	0.171008	+	0.214437i	−0.688941	+	0.724817i	$0.741924\pi$
$660$		0			0
$661$	38.0908	−	18.3436i	1.48156	−	0.713482i	0.493817	−	0.869566i	$-0.335601\pi$
$661$	38.0908	−	18.3436i	1.48156	−	0.713482i	0.987744	+	0.156084i	$0.0498871\pi$
$662$	−42.0317	+	20.2414i	−1.63361	+	0.786705i
$663$		0			0
$664$	−21.3562	−	26.7798i	−0.828781	−	1.03926i
$665$	−2.84753	−	40.2265i	−0.110423	−	1.55992i
$666$		0			0
$667$	−14.3362			−0.555098
$668$	−36.7948			−1.42363
$669$		0			0
$670$	0.740362	−	3.24374i	0.0286027	−	0.125317i
$671$	26.3069	−	12.6687i	1.01556	−	0.489070i
$672$		0			0
$673$	−20.1257	−	9.69202i	−0.775788	−	0.373600i	0.00371918	−	0.999993i	$-0.498816\pi$
$673$	−20.1257	−	9.69202i	−0.775788	−	0.373600i	−0.779507	+	0.626393i	$0.784530\pi$
$674$	29.7417	−	37.2950i	1.14561	−	1.43655i
$675$		0			0
$676$	−4.19314	+	18.3714i	−0.161275	+	0.706591i
$677$	12.1420	−	5.84727i	0.466655	−	0.224729i	−0.185754	−	0.982596i	$-0.559473\pi$
$677$	12.1420	−	5.84727i	0.466655	−	0.224729i	0.652409	+	0.757867i	$0.273759\pi$
$678$		0			0
$679$	26.8400	+	4.15892i	1.03002	+	0.159605i
$680$	1.69229	−	7.41439i	0.0648962	−	0.284329i
$681$		0			0
$682$	−7.49432	−	9.39758i	−0.286972	−	0.359852i
$683$	3.31624	+	14.5294i	0.126892	+	0.555952i	0.997905	+	0.0646920i	$0.0206065\pi$
$683$	3.31624	+	14.5294i	0.126892	+	0.555952i	−0.871013	+	0.491260i	$0.836536\pi$
$684$		0			0
$685$	−28.2213			−1.07828
$686$	26.5293	+	34.1257i	1.01289	+	1.30292i
$687$		0			0
$688$	−4.77242	−	2.29828i	−0.181947	−	0.0876210i
$689$	11.1523	+	48.8615i	0.424869	+	1.86147i
$690$		0			0
$691$	10.0258	+	43.9260i	0.381400	+	1.67102i	0.693099	+	0.720843i	$0.256245\pi$
$691$	10.0258	+	43.9260i	0.381400	+	1.67102i	−0.311698	+	0.950181i	$0.600898\pi$
$692$	14.0308	−	61.4732i	0.533373	−	2.33686i
$693$		0			0
$694$	−15.2758	−	66.9275i	−0.579860	−	2.54053i
$695$	−30.6036	+	14.7379i	−1.16086	+	0.559041i
$696$		0			0
$697$	−6.08507	−	2.93042i	−0.230489	−	0.110997i
$698$	−24.5781	+	30.8200i	−0.930295	+	1.16655i
$699$		0			0
$700$	−5.35925	−	3.68639i	−0.202561	−	0.139332i
$701$	0.561563	−	0.270435i	0.0212100	−	0.0102142i	−0.423249	−	0.906014i	$-0.639110\pi$
$701$	0.561563	−	0.270435i	0.0212100	−	0.0102142i	0.444459	+	0.895799i	$0.353396\pi$
$702$		0			0
$703$	−10.8268	+	13.5764i	−0.408342	+	0.512045i
$704$	−31.5261			−1.18819
$705$		0			0
$706$	−43.9267	+	55.0824i	−1.65320	+	2.07305i
$707$	1.15346	+	16.2947i	0.0433805	+	0.612827i
$708$		0			0
$709$	13.0832	+	16.4058i	0.491350	+	0.616134i	0.964254	−	0.264980i	$-0.0853655\pi$
$709$	13.0832	+	16.4058i	0.491350	+	0.616134i	−0.472904	+	0.881114i	$0.656794\pi$
$710$	71.6179	−	34.4893i	2.68777	−	1.29436i
$711$		0			0
$712$	28.8299	+	36.1515i	1.08044	+	1.35483i
$713$	−1.92244	−	2.41066i	−0.0719960	−	0.0902801i
$714$		0			0
$715$	−14.1516	+	17.7456i	−0.529241	+	0.663647i
$716$	41.4246			1.54811
$717$		0			0
$718$	−8.19018	+	10.2702i	−0.305655	+	0.383279i
$719$	−8.11305	+	35.5456i	−0.302566	+	1.32563i	0.563674	+	0.825997i	$0.309387\pi$
$719$	−8.11305	+	35.5456i	−0.302566	+	1.32563i	−0.866239	+	0.499629i	$0.833470\pi$
$720$		0			0
$721$	0.316916	+	4.47701i	0.0118026	+	0.166732i
$722$	−74.0092	−	35.6410i	−2.75434	−	1.32642i
$723$		0			0
$724$	−61.4303	−	29.5833i	−2.28304	−	1.09945i
$725$	−1.48970	+	6.52682i	−0.0553262	+	0.242400i
$726$		0			0
$727$	−7.91990	−	34.6994i	−0.293733	−	1.28693i	−0.879286	−	0.476294i	$-0.841980\pi$
$727$	−7.91990	−	34.6994i	−0.293733	−	1.28693i	0.585553	−	0.810634i	$-0.300877\pi$
$728$	−14.1767	+	35.6875i	−0.525423	+	1.32267i
$729$		0			0
$730$	−2.10290	−	9.21343i	−0.0778320	−	0.341004i
$731$	−3.63367	−	4.55648i	−0.134396	−	0.168527i
$732$		0			0
$733$	−9.46081	−	4.55608i	−0.349443	−	0.168283i	0.250925	−	0.968006i	$-0.419265\pi$
$733$	−9.46081	−	4.55608i	−0.349443	−	0.168283i	−0.600368	+	0.799724i	$0.704979\pi$
$734$	28.5066			1.05220
$735$		0			0
$736$	−6.79339			−0.250408
$737$	1.58253	+	0.762106i	0.0582932	+	0.0280725i
$738$		0			0
$739$	6.25172	+	7.83941i	0.229973	+	0.288377i	0.883407	−	0.468606i	$-0.155244\pi$
$739$	6.25172	+	7.83941i	0.229973	+	0.288377i	−0.653434	+	0.756984i	$0.726672\pi$
$740$	−3.74614	−	16.4129i	−0.137711	−	0.603351i
$741$		0			0
$742$	5.08517	+	71.8371i	0.186682	+	2.63722i
$743$	−4.14282	−	18.1509i	−0.151985	−	0.665891i	−0.992307	−	0.123803i	$-0.960491\pi$
$743$	−4.14282	−	18.1509i	−0.151985	−	0.665891i	0.840322	−	0.542088i	$-0.182366\pi$
$744$		0			0
$745$	9.11336	−	39.9282i	0.333888	−	1.46286i
$746$	15.3944	+	7.41357i	0.563630	+	0.271430i
$747$		0			0
$748$	8.61651	+	4.14949i	0.315051	+	0.151721i
$749$	−25.9751	+	7.89492i	−0.949111	+	0.288474i
$750$		0			0
$751$	9.22995	−	40.4391i	0.336806	−	1.47564i	−0.468860	−	0.883272i	$-0.655335\pi$
$751$	9.22995	−	40.4391i	0.336806	−	1.47564i	0.805666	−	0.592370i	$-0.201808\pi$
$752$	0.699598	−	0.877268i	0.0255117	−	0.0319907i
$753$		0			0
$754$	94.1425			3.42847
$755$	16.2935	−	20.4315i	0.592983	−	0.743577i
$756$		0			0
$757$	20.2613	+	25.4068i	0.736408	+	0.923426i	0.999141	−	0.0414423i	$-0.0131953\pi$
$757$	20.2613	+	25.4068i	0.736408	+	0.923426i	−0.262733	+	0.964869i	$0.584624\pi$
$758$	−25.0241	−	31.3792i	−0.908917	−	1.13975i
$759$		0			0
$760$	46.3822	−	22.3365i	1.68246	−	0.810229i
$761$	−3.42302	−	4.29234i	−0.124084	−	0.155597i	0.715909	−	0.698194i	$-0.246013\pi$
$761$	−3.42302	−	4.29234i	−0.124084	−	0.155597i	−0.839993	+	0.542597i	$0.817441\pi$
$762$		0			0
$763$	21.5524	+	14.8249i	0.780249	+	0.536699i
$764$	−6.89358	+	8.64427i	−0.249401	+	0.312739i
$765$		0			0
$766$	76.7408			2.77276
$767$	−11.8463	+	14.8548i	−0.427746	+	0.536377i
$768$		0			0
$769$	−6.21257	+	2.99182i	−0.224031	+	0.107888i	−0.542533	−	0.840035i	$-0.682535\pi$
$769$	−6.21257	+	2.99182i	−0.224031	+	0.107888i	0.318502	+	0.947922i	$0.396820\pi$
$770$	−23.9999	+	22.0849i	−0.864897	+	0.795885i
$771$		0			0
$772$	−38.0900	+	47.7634i	−1.37089	+	1.71904i
$773$	17.5683	+	8.46043i	0.631887	+	0.304301i	0.722275	−	0.691606i	$-0.243097\pi$
$773$	17.5683	+	8.46043i	0.631887	+	0.304301i	−0.0903883	+	0.995907i	$0.528811\pi$
$774$		0			0
$775$	−1.29727	+	0.624731i	−0.0465992	+	0.0224410i
$776$	7.71522	+	33.8026i	0.276960	+	1.21344i
$777$		0			0
$778$	−0.633565	+	2.77583i	−0.0227144	+	0.0995183i
$779$	−10.1734	−	44.5725i	−0.364499	−	1.59697i
$780$		0			0
$781$	9.33794	+	40.9122i	0.334138	+	1.46395i
$782$	3.49271	+	1.68200i	0.124899	+	0.0601482i
$783$		0			0
$784$	−3.50898	+	5.96342i	−0.125321	+	0.212979i
$785$	−24.8100			−0.885508
$786$		0			0
$787$	5.99224	+	26.2537i	0.213600	+	0.935844i	0.962097	+	0.272706i	$0.0879185\pi$
$787$	5.99224	+	26.2537i	0.213600	+	0.935844i	−0.748497	+	0.663138i	$0.769224\pi$
$788$	29.0620	+	36.4426i	1.03529	+	1.29821i
$789$		0			0
$790$	5.83781	−	25.5771i	0.207700	−	0.909994i
$791$	31.5341	−	9.58452i	1.12122	−	0.340786i
$792$		0			0
$793$	−44.3142	+	21.3406i	−1.57364	+	0.757826i
$794$	−0.183566	+	0.804257i	−0.00651452	+	0.0285420i
$795$		0			0
$796$	8.73712	−	10.9560i	0.309679	−	0.388325i
$797$	26.1627	+	12.5993i	0.926729	+	0.446289i	0.835469	−	0.549538i	$-0.185196\pi$
$797$	26.1627	+	12.5993i	0.926729	+	0.446289i	0.0912605	+	0.995827i	$0.470910\pi$
$798$		0			0
$799$	1.11229	−	0.535648i	0.0393498	−	0.0189499i
$800$	−0.705917	+	3.09282i	−0.0249579	+	0.109348i
$801$		0			0
$802$	19.0525			0.672767
$803$	4.98905			0.176060
$804$		0			0
$805$	−6.15645	+	5.66521i	−0.216986	+	0.199673i
$806$	12.6243	+	15.8303i	0.444671	+	0.557599i
$807$		0			0
$808$	−18.7882	+	9.04794i	−0.660968	+	0.318305i
$809$	−9.13429	+	4.39884i	−0.321144	+	0.154655i	−0.587510	−	0.809217i	$-0.699892\pi$
$809$	−9.13429	+	4.39884i	−0.321144	+	0.154655i	0.266365	+	0.963872i	$0.414177\pi$
$810$		0			0
$811$	9.79229	+	12.2791i	0.343854	+	0.431179i	0.923446	−	0.383727i	$-0.125360\pi$
$811$	9.79229	+	12.2791i	0.343854	+	0.431179i	−0.579593	+	0.814906i	$0.696788\pi$
$812$	84.5988	+	13.1088i	2.96884	+	0.460029i
$813$		0			0
$814$	14.0440			0.492244
$815$	52.3689			1.83440
$816$		0			0
$817$	8.77860	−	38.4616i	0.307124	−	1.34560i
$818$	−46.5366	+	22.4108i	−1.62711	+	0.783576i
$819$		0			0
$820$	39.9342	+	19.2313i	1.39456	+	0.671586i
$821$	24.7347	−	31.0163i	0.863247	−	1.08248i	−0.132576	−	0.991173i	$-0.542325\pi$
$821$	24.7347	−	31.0163i	0.863247	−	1.08248i	0.995823	−	0.0913046i	$-0.0291037\pi$
$822$		0			0
$823$	2.16615	−	9.49052i	0.0755072	−	0.330819i	−0.923040	−	0.384704i	$-0.874303\pi$
$823$	2.16615	−	9.49052i	0.0755072	−	0.330819i	0.998547	+	0.0538855i	$0.0171606\pi$
$824$	−5.16210	+	2.48593i	−0.179830	+	0.0866016i
$825$		0			0
$826$	−20.0903	+	18.4873i	−0.699032	+	0.643255i
$827$	5.07374	−	22.2295i	0.176431	−	0.772996i	−0.806828	−	0.590786i	$-0.798818\pi$
$827$	5.07374	−	22.2295i	0.176431	−	0.772996i	0.983260	−	0.182210i	$-0.0583252\pi$
$828$		0			0
$829$	−30.9275	−	38.7818i	−1.07416	−	1.34695i	−0.934183	−	0.356793i	$-0.883870\pi$
$829$	−30.9275	−	38.7818i	−1.07416	−	1.34695i	−0.139972	−	0.990155i	$-0.544701\pi$
$830$	10.9049	+	47.7777i	0.378516	+	1.65839i
$831$		0			0
$832$	53.1061			1.84112
$833$	−6.32518	+	4.23632i	−0.219154	+	0.146780i
$834$		0			0
$835$	19.9115	+	9.58887i	0.689066	+	0.331837i
$836$	14.4056	+	63.1150i	0.498227	+	2.18288i
$837$		0			0
$838$	−17.9930	−	78.8325i	−0.621558	−	2.72322i
$839$	−3.97284	+	17.4061i	−0.137158	+	0.600926i	0.858894	+	0.512153i	$0.171152\pi$
$839$	−3.97284	+	17.4061i	−0.137158	+	0.600926i	−0.996052	+	0.0887735i	$0.971705\pi$
$840$		0			0
$841$	−13.1529	−	57.6267i	−0.453549	−	1.98713i
$842$	−25.0592	+	12.0679i	−0.863597	+	0.415886i
$843$		0			0
$844$	−38.9116	−	18.7389i	−1.33939	−	0.645018i
$845$	7.05677	−	8.84891i	0.242760	−	0.304412i
$846$		0			0
$847$	5.89999	+	10.3173i	0.202726	+	0.354505i
$848$	−10.3865	+	5.00187i	−0.356674	+	0.171765i
$849$		0			0
$850$	1.12870	−	1.41534i	0.0387140	−	0.0485459i
$851$	3.60257			0.123495
$852$		0			0
$853$	−19.6325	+	24.6183i	−0.672203	+	0.842916i	−0.994610	−	0.103685i	$-0.966937\pi$
$853$	−19.6325	+	24.6183i	−0.672203	+	0.842916i	0.322407	+	0.946601i	$0.395508\pi$
$854$	−67.6217	+	20.5531i	−2.31397	+	0.703311i
$855$		0			0
$856$	−21.6081	−	27.0957i	−0.738551	−	0.926113i
$857$	30.7632	−	14.8148i	1.05085	−	0.506063i	0.172962	−	0.984928i	$-0.444666\pi$
$857$	30.7632	−	14.8148i	1.05085	−	0.506063i	0.877888	+	0.478865i	$0.158952\pi$
$858$		0			0
$859$	9.09305	+	11.4023i	0.310251	+	0.389042i	0.912372	−	0.409363i	$-0.134249\pi$
$859$	9.09305	+	11.4023i	0.310251	+	0.389042i	−0.602121	+	0.798405i	$0.705678\pi$
$860$	23.8465	+	29.9026i	0.813159	+	1.01967i
$861$		0			0
$862$	5.32312	−	6.67498i	0.181306	−	0.227351i
$863$	−12.4444			−0.423614			−0.211807	−	0.977312i	$-0.567935\pi$
$863$	−12.4444			−0.423614			−0.211807	+	0.977312i	$0.567935\pi$
$864$		0			0
$865$	−23.6130	+	29.6097i	−0.802865	+	1.00676i
$866$	2.23318	−	9.78420i	0.0758865	−	0.332481i
$867$		0			0
$868$	9.14019	+	15.9834i	0.310238	+	0.542511i
$869$	12.4784	+	6.00927i	0.423300	+	0.203850i
$870$		0			0
$871$	−2.66579	−	1.28378i	−0.0903268	−	0.0434991i
$872$	−7.43075	+	32.5562i	−0.251637	+	1.10249i
$873$		0			0
$874$	5.83931	+	25.5837i	0.197518	+	0.865381i
$875$	15.5362	+	27.1679i	0.525218	+	0.918444i
$876$		0			0
$877$	3.87769	+	16.9893i	0.130940	+	0.573686i	0.997245	+	0.0741715i	$0.0236312\pi$
$877$	3.87769	+	16.9893i	0.130940	+	0.573686i	−0.866305	+	0.499515i	$0.833512\pi$
$878$	46.0521	+	57.7475i	1.55418	+	1.94888i
$879$		0			0
$880$	−4.70384	−	2.26525i	−0.158566	−	0.0763615i
$881$	−11.8517			−0.399292			−0.199646	−	0.979868i	$-0.563979\pi$
$881$	−11.8517			−0.399292			−0.199646	+	0.979868i	$0.563979\pi$
$882$		0			0
$883$	3.33150			0.112114			0.0560569	−	0.998428i	$-0.482147\pi$
$883$	3.33150			0.112114			0.0560569	+	0.998428i	$0.482147\pi$
$884$	−14.5146	−	6.98987i	−0.488179	−	0.235095i
$885$		0			0
$886$	−10.9733	−	13.7601i	−0.368657	−	0.462281i
$887$	0.883870	+	3.87249i	0.0296774	+	0.130025i	0.987597	−	0.157013i	$-0.0501864\pi$
$887$	0.883870	+	3.87249i	0.0296774	+	0.130025i	−0.957919	+	0.287038i	$0.907329\pi$
$888$		0			0
$889$	−8.62209	+	7.93411i	−0.289176	+	0.266102i
$890$	−14.7211	−	64.4976i	−0.493454	−	2.16196i
$891$		0			0
$892$	19.1768	−	84.0192i	0.642088	−	2.81317i
$893$	7.52930	+	3.62592i	0.251958	+	0.121337i
$894$		0			0
$895$	−22.4169	−	10.7954i	−0.749316	−	0.360851i
$896$	52.1517	+	8.08104i	1.74227	+	0.269968i
$897$		0			0
$898$	13.1053	−	57.4181i	0.437330	−	1.91607i
$899$	11.8151	−	14.8157i	0.394057	−	0.494132i
$900$		0			0
$901$	−12.6837			−0.422556
$902$	−23.0538	+	28.9086i	−0.767609	+	0.962551i
$903$		0			0
$904$	26.2325	+	32.8945i	0.872480	+	1.09405i
$905$	25.5335	+	32.0180i	0.848761	+	1.06431i
$906$		0			0
$907$	20.9862	−	10.1064i	0.696836	−	0.335579i	−0.0517091	−	0.998662i	$-0.516467\pi$
$907$	20.9862	−	10.1064i	0.696836	−	0.335579i	0.748545	+	0.663083i	$0.230753\pi$
$908$	−52.3527	−	65.6482i	−1.73738	−	2.17861i
$909$		0			0
$910$	40.4281	−	37.2023i	1.34018	−	1.23324i
$911$	−3.44994	+	4.32609i	−0.114302	+	0.143330i	−0.835691	−	0.549200i	$-0.814932\pi$
$911$	−3.44994	+	4.32609i	−0.114302	+	0.143330i	0.721389	+	0.692530i	$0.243504\pi$
$912$		0			0
$913$	−25.8715			−0.856221
$914$	27.2127	−	34.1237i	0.900117	−	1.12871i
$915$		0			0
$916$	21.8660	−	10.5301i	0.722474	−	0.347925i
$917$	−12.8499	+	32.3474i	−0.424339	+	1.06821i
$918$		0			0
$919$	−14.6394	+	18.3572i	−0.482908	+	0.605548i	−0.962279	−	0.272065i	$-0.912294\pi$
$919$	−14.6394	+	18.3572i	−0.482908	+	0.605548i	0.479371	+	0.877613i	$0.340865\pi$
$920$	−9.62258	−	4.63399i	−0.317247	−	0.152778i
$921$		0			0
$922$	−40.7583	+	19.6282i	−1.34230	+	0.646419i
$923$	−15.7299	−	68.9170i	−0.517755	−	2.26843i
$924$		0			0
$925$	0.374352	−	1.64014i	0.0123086	−	0.0539276i
$926$	−0.849878	−	3.72356i	−0.0279287	−	0.122364i
$927$		0			0
$928$	−9.29059	−	40.7047i	−0.304979	−	1.33620i
$929$	−27.9139	−	13.4426i	−0.915826	−	0.441039i	−0.0842471	−	0.996445i	$-0.526848\pi$
$929$	−27.9139	−	13.4426i	−0.915826	−	0.441039i	−0.831579	+	0.555406i	$0.812563\pi$
$930$		0			0
$931$	−49.1159	−	15.5957i	−1.60971	−	0.511129i
$932$	15.9064			0.521032
$933$		0			0
$934$	−7.14967	−	31.3247i	−0.233944	−	1.02498i
$935$	−3.58145	−	4.49100i	−0.117126	−	0.146871i
$936$		0			0
$937$	6.82365	−	29.8964i	0.222919	−	0.976672i	−0.732349	−	0.680930i	$-0.761576\pi$
$937$	6.82365	−	29.8964i	0.222919	−	0.976672i	0.955268	−	0.295742i	$-0.0955669\pi$
$938$	−3.50295	−	2.40952i	−0.114375	−	0.0786737i
$939$		0			0
$940$	−7.29953	+	3.51527i	−0.238085	+	0.114655i
$941$	−0.558228	+	2.44576i	−0.0181977	+	0.0797295i	−0.983211	−	0.182470i	$-0.941591\pi$
$941$	−0.558228	+	2.44576i	−0.0181977	+	0.0797295i	0.965014	+	0.262200i	$0.0844479\pi$
$942$		0			0
$943$	−5.91376	+	7.41562i	−0.192579	+	0.241486i
$944$	−3.93758	−	1.89624i	−0.128157	−	0.0617173i
$945$		0			0
$946$	−28.7464	+	13.8435i	−0.934627	+	0.450093i
$947$	2.60141	−	11.3975i	0.0845343	−	0.370369i	−0.914912	−	0.403654i	$-0.867740\pi$
$947$	2.60141	−	11.3975i	0.0845343	−	0.370369i	0.999446	+	0.0332852i	$0.0105970\pi$
$948$		0			0
$949$	−8.40410			−0.272809
$950$	12.2543			0.397580
$951$		0			0
$952$	−8.00688	−	5.50758i	−0.259505	−	0.178502i
$953$	−7.28722	−	9.13788i	−0.236056	−	0.296005i	0.649667	−	0.760219i	$-0.274908\pi$
$953$	−7.28722	−	9.13788i	−0.236056	−	0.296005i	−0.885723	+	0.464214i	$0.846337\pi$
$954$		0			0
$955$	5.98319	−	2.88135i	0.193612	−	0.0932384i
$956$	−31.5359	+	15.1869i	−1.01994	+	0.491179i
$957$		0			0
$958$	14.7530	+	18.4997i	0.476648	+	0.597697i
$959$	−13.3138	+	33.5153i	−0.429925	+	1.08227i
$960$		0			0
$961$	−26.9243			−0.868526
$962$	−23.6573			−0.762743
$963$		0			0
$964$	−6.29114	+	27.5633i	−0.202624	+	0.887754i
$965$	33.0598	−	15.9207i	1.06423	−	0.512507i
$966$		0			0
$967$	22.8417	+	11.0000i	0.734538	+	0.353735i	0.763467	−	0.645847i	$-0.223495\pi$
$967$	22.8417	+	11.0000i	0.734538	+	0.353735i	−0.0289292	+	0.999581i	$0.509210\pi$
$968$	−9.45967	+	11.8620i	−0.304045	+	0.381261i
$969$		0			0
$970$	11.0384	−	48.3623i	0.354421	−	1.55282i
$971$	−47.4046	+	22.8288i	−1.52129	+	0.732613i	−0.993183	−	0.116568i	$-0.962811\pi$
$971$	−47.4046	+	22.8288i	−1.52129	+	0.732613i	−0.528103	+	0.849180i	$0.677097\pi$
$972$		0			0
$973$	3.06490	+	43.2973i	0.0982562	+	1.38805i
$974$	−11.0068	+	48.2242i	−0.352682	+	1.54520i
$975$		0			0
$976$	−7.05387	−	8.84527i	−0.225789	−	0.283130i
$977$	−5.99781	−	26.2781i	−0.191887	−	0.840711i	−0.975594	−	0.219581i	$-0.929531\pi$
$977$	−5.99781	−	26.2781i	−0.191887	−	0.840711i	0.783707	−	0.621130i	$-0.213326\pi$
$978$		0			0
$979$	34.9253			1.11622
$980$	41.5099	−	27.8015i	1.32599	−	0.888086i
$981$		0			0
$982$	44.0187	+	21.1983i	1.40469	+	0.676464i
$983$	0.146991	+	0.644012i	0.00468830	+	0.0205408i	0.977218	−	0.212238i	$-0.0680753\pi$
$983$	0.146991	+	0.644012i	0.00468830	+	0.0205408i	−0.972530	+	0.232779i	$0.925218\pi$
$984$		0			0
$985$	−6.22981	−	27.2946i	−0.198498	−	0.869677i
$986$	−5.30163	+	23.2279i	−0.168838	+	0.739729i
$987$		0			0
$988$	−24.2664	−	106.318i	−0.772016	−	3.38242i
$989$	−7.37402	+	3.55114i	−0.234480	+	0.112920i
$990$		0			0
$991$	38.1266	+	18.3608i	1.21113	+	0.583249i	0.926828	−	0.375485i	$-0.122524\pi$
$991$	38.1266	+	18.3608i	1.21113	+	0.583249i	0.284302	+	0.958735i	$0.408238\pi$
$992$	5.59877	−	7.02063i	0.177761	−	0.222905i
$993$		0			0
$994$	−7.17242	−	101.323i	−0.227495	−	3.21378i
$995$	−7.58327	+	3.65191i	−0.240406	+	0.115773i
$996$		0			0
$997$	−10.2660	+	12.8732i	−0.325128	+	0.407697i	−0.917353	−	0.398075i	$-0.869678\pi$
$997$	−10.2660	+	12.8732i	−0.325128	+	0.407697i	0.592225	+	0.805773i	$0.298250\pi$
$998$	14.0603			0.445070
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.e.127.2	✓	60
3.2	odd	2	inner	441.2.u.e.127.9	yes	60
49.22	even	7	inner	441.2.u.e.316.2	yes	60
147.71	odd	14	inner	441.2.u.e.316.9	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.u.e.127.2	✓	60	1.1	even	1	trivial
441.2.u.e.127.9	yes	60	3.2	odd	2	inner
441.2.u.e.316.2	yes	60	49.22	even	7	inner
441.2.u.e.316.9	yes	60	147.71	odd	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.10278 - 1.01265i) q^{2} +(2.14925 + 2.69508i) q^{4} +(-0.460720 - 2.01854i) q^{5} +(-2.61455 - 0.405131i) q^{7} +(-0.751559 - 3.29280i) q^{8} +O(q^{10})\)	\(q+(-2.10278 - 1.01265i) q^{2} +(2.14925 + 2.69508i) q^{4} +(-0.460720 - 2.01854i) q^{5} +(-2.61455 - 0.405131i) q^{7} +(-0.751559 - 3.29280i) q^{8} +(-1.07528 + 4.71110i) q^{10} +(-2.29842 - 1.10686i) q^{11} +(3.87171 + 1.86451i) q^{13} +(5.08757 + 3.49951i) q^{14} +(-0.219952 + 0.963674i) q^{16} +(-0.678070 + 0.850272i) q^{17} -7.36179 q^{19} +(4.44993 - 5.58004i) q^{20} +(3.71221 + 4.65496i) q^{22} +(0.952254 + 1.19409i) q^{23} +(0.642583 - 0.309452i) q^{25} +(-6.25325 - 7.84133i) q^{26} +(-4.52747 - 7.91714i) q^{28} +(-5.85246 + 7.33876i) q^{29} -2.01883 q^{31} +(-2.77327 + 3.47757i) q^{32} +(2.28686 - 1.10129i) q^{34} +(0.386799 + 5.46424i) q^{35} +(1.47068 - 1.84418i) q^{37} +(15.4802 + 7.45488i) q^{38} +(-6.30040 + 3.03411i) q^{40} +(1.38192 + 6.05457i) q^{41} +(-1.19246 + 5.22449i) q^{43} +(-1.95681 - 8.57332i) q^{44} +(-0.793192 - 3.47520i) q^{46} +(-1.02275 - 0.492532i) q^{47} +(6.67174 + 2.11847i) q^{49} -1.66458 q^{50} +(3.29626 + 14.4419i) q^{52} +(7.27161 + 9.11832i) q^{53} +(-1.17532 + 5.14941i) q^{55} +(0.630975 + 8.91366i) q^{56} +(19.7380 - 9.50532i) q^{58} +(-0.983859 + 4.31057i) q^{59} +(-7.13624 + 8.94857i) q^{61} +(4.24516 + 2.04436i) q^{62} +(11.1343 - 5.36198i) q^{64} +(1.97984 - 8.67423i) q^{65} -0.688531 q^{67} -3.74889 q^{68} +(4.71998 - 11.8818i) q^{70} +(-10.2563 - 12.8610i) q^{71} +(-1.76201 + 0.848540i) q^{73} +(-4.96002 + 2.38862i) q^{74} +(-15.8223 - 19.8406i) q^{76} +(5.56090 + 3.82510i) q^{77} -5.42912 q^{79} +2.04656 q^{80} +(3.22527 - 14.1308i) q^{82} +(9.13718 - 4.40023i) q^{83} +(2.02871 + 0.976977i) q^{85} +(7.79803 - 9.77841i) q^{86} +(-1.91726 + 8.40008i) q^{88} +(-12.3348 + 5.94011i) q^{89} +(-9.36739 - 6.44341i) q^{91} +(-1.17153 + 5.13280i) q^{92} +(1.65187 + 2.07137i) q^{94} +(3.39172 + 14.8601i) q^{95} -10.2656 q^{97} +(-11.8839 - 11.2108i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 12 q^{4} - 2 q^{7}+O(q^{10}) \) 60 * q - 12 * q^4 - 2 * q^7	\( 60 q - 12 q^{4} - 2 q^{7} + 12 q^{10} - 4 q^{13} - 48 q^{19} + 6 q^{22} - 22 q^{25} + 40 q^{28} - 76 q^{31} - 12 q^{34} + 34 q^{37} + 86 q^{40} + 4 q^{43} + 8 q^{46} + 26 q^{49} + 66 q^{52} + 10 q^{55} + 42 q^{58} + 62 q^{61} - 128 q^{64} + 8 q^{67} + 96 q^{70} - 70 q^{73} + 50 q^{76} - 24 q^{79} - 36 q^{82} + 72 q^{85} - 216 q^{88} + 52 q^{91} - 38 q^{94} - 252 q^{97}+O(q^{100}) \) 60 * q - 12 * q^4 - 2 * q^7 + 12 * q^10 - 4 * q^13 - 48 * q^19 + 6 * q^22 - 22 * q^25 + 40 * q^28 - 76 * q^31 - 12 * q^34 + 34 * q^37 + 86 * q^40 + 4 * q^43 + 8 * q^46 + 26 * q^49 + 66 * q^52 + 10 * q^55 + 42 * q^58 + 62 * q^61 - 128 * q^64 + 8 * q^67 + 96 * q^70 - 70 * q^73 + 50 * q^76 - 24 * q^79 - 36 * q^82 + 72 * q^85 - 216 * q^88 + 52 * q^91 - 38 * q^94 - 252 * q^97

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