LMFDB - Embedded newform 950.2.bb.d.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			193.3
Character	$\chi$	$=$	950.193
Dual form			950.2.bb.d.507.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0871557 - 0.996195i) q^{2} +(0.368687 - 0.790651i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-0.819776 - 0.298374i) q^{6} +(1.54311 + 0.413475i) q^{7} +(0.258819 + 0.965926i) q^{8} +(1.43916 + 1.71513i) q^{9} +O(q^{10})$	\(q+(-0.0871557 - 0.996195i) q^{2} +(0.368687 - 0.790651i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-0.819776 - 0.298374i) q^{6} +(1.54311 + 0.413475i) q^{7} +(0.258819 + 0.965926i) q^{8} +(1.43916 + 1.71513i) q^{9} +(-2.93639 + 5.08598i) q^{11} +(-0.225790 + 0.842661i) q^{12} +(-3.19946 + 1.49193i) q^{13} +(0.277411 - 1.57327i) q^{14} +(0.939693 - 0.342020i) q^{16} +(3.13283 - 0.274087i) q^{17} +(1.58317 - 1.58317i) q^{18} +(-3.75846 + 2.20771i) q^{19} +(0.895838 - 1.06762i) q^{21} +(5.32255 + 2.48194i) q^{22} +(-5.28921 + 7.55377i) q^{23} +(0.859133 + 0.151488i) q^{24} +(1.76510 + 3.05725i) q^{26} +(4.41465 - 1.18290i) q^{27} +(-1.59146 - 0.139235i) q^{28} +(-1.62212 + 1.36112i) q^{29} +(-7.02169 + 4.05397i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(2.93863 + 4.19679i) q^{33} +(-0.546087 - 3.09702i) q^{34} +(-1.71513 - 1.43916i) q^{36} +(3.18153 + 3.18153i) q^{37} +(2.52688 + 3.55174i) q^{38} +3.07971i q^{39} +(-2.16409 - 5.94578i) q^{41} +(-1.14163 - 0.799380i) q^{42} +(6.53300 - 4.57446i) q^{43} +(2.00861 - 5.51861i) q^{44} +(7.98601 + 4.61073i) q^{46} +(0.622339 - 7.11337i) q^{47} +(0.0760335 - 0.869067i) q^{48} +(-3.85196 - 2.22393i) q^{49} +(0.938324 - 2.57802i) q^{51} +(2.89178 - 2.02484i) q^{52} +(5.18480 + 3.63043i) q^{53} +(-1.56316 - 4.29476i) q^{54} +1.59754i q^{56} +(0.359835 + 3.78558i) q^{57} +(1.49732 + 1.49732i) q^{58} +(1.57918 + 1.32509i) q^{59} +(-0.597908 - 3.39091i) q^{61} +(4.65053 + 6.64164i) q^{62} +(1.51162 + 3.24169i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(3.92470 - 3.29322i) q^{66} +(14.6514 + 1.28183i) q^{67} +(-3.03764 + 0.813932i) q^{68} +(4.02234 + 6.96689i) q^{69} +(8.81302 + 1.55397i) q^{71} +(-1.28420 + 1.83403i) q^{72} +(-14.0860 - 6.56842i) q^{73} +(2.89213 - 3.44671i) q^{74} +(3.31799 - 2.82682i) q^{76} +(-6.63409 + 6.63409i) q^{77} +(3.06799 - 0.268414i) q^{78} +(7.18374 - 2.61467i) q^{79} +(-0.474004 + 2.68821i) q^{81} +(-5.73454 + 2.67406i) q^{82} +(-0.677291 + 2.52768i) q^{83} +(-0.696838 + 1.20696i) q^{84} +(-5.12644 - 6.10945i) q^{86} +(0.478117 + 1.78436i) q^{87} +(-5.67267 - 1.51999i) q^{88} +(10.3108 + 3.75284i) q^{89} +(-5.55398 + 0.979317i) q^{91} +(3.89716 - 8.35748i) q^{92} +(0.616476 + 7.04635i) q^{93} -7.14054 q^{94} -0.872387 q^{96} +(-0.768732 - 8.78664i) q^{97} +(-1.87974 + 4.03113i) q^{98} +(-12.9491 + 2.28327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{6}+O(q^{10}) $ 96 * q - 12 * q^6	$ 96 q - 12 q^{6} + 12 q^{26} - 72 q^{31} + 12 q^{36} - 24 q^{41} + 12 q^{51} - 72 q^{61} - 36 q^{66} + 168 q^{71} - 12 q^{76} + 12 q^{81} - 48 q^{86} - 72 q^{91}+O(q^{100}) $ 96 * q - 12 * q^6 + 12 * q^26 - 72 * q^31 + 12 * q^36 - 24 * q^41 + 12 * q^51 - 72 * q^61 - 36 * q^66 + 168 * q^71 - 12 * q^76 + 12 * q^81 - 48 * q^86 - 72 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$3$	0.368687	−	0.790651i	0.212861	−	0.456483i	−0.770667	−	0.637238i	$-0.780077\pi$
$3$	0.368687	−	0.790651i	0.212861	−	0.456483i	0.983528	+	0.180756i	$0.0578544\pi$
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$		0			0
$5$		0			0
$6$	−0.819776	−	0.298374i	−0.334672	−	0.121811i
$7$	1.54311	+	0.413475i	0.583240	+	0.156279i	0.538362	−	0.842714i	$-0.319043\pi$
$7$	1.54311	+	0.413475i	0.583240	+	0.156279i	0.0448783	+	0.998992i	$0.485710\pi$
$8$	0.258819	+	0.965926i	0.0915064	+	0.341506i
$9$	1.43916	+	1.71513i	0.479721	+	0.571709i
$10$		0			0
$11$	−2.93639	+	5.08598i	−0.885355	+	1.53348i	−0.0400491	+	0.999198i	$0.512751\pi$
$11$	−2.93639	+	5.08598i	−0.885355	+	1.53348i	−0.845306	+	0.534282i	$0.820582\pi$
$12$	−0.225790	+	0.842661i	−0.0651801	+	0.243255i
$13$	−3.19946	+	1.49193i	−0.887369	+	0.413787i	−0.812197	−	0.583383i	$-0.801729\pi$
$13$	−3.19946	+	1.49193i	−0.887369	+	0.413787i	−0.0751725	+	0.997171i	$0.523951\pi$
$14$	0.277411	−	1.57327i	0.0741411	−	0.420475i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	3.13283	−	0.274087i	0.759822	−	0.0664758i	0.299342	−	0.954146i	$-0.403233\pi$
$17$	3.13283	−	0.274087i	0.759822	−	0.0664758i	0.460480	+	0.887670i	$0.347677\pi$
$18$	1.58317	−	1.58317i	0.373157	−	0.373157i
$19$	−3.75846	+	2.20771i	−0.862250	+	0.506483i
$19$	−3.75846	+	2.20771i	−0.862250	+	0.506483i
$20$		0			0
$21$	0.895838	−	1.06762i	0.195488	−	0.232973i
$22$	5.32255	+	2.48194i	1.13477	+	0.529152i
$23$	−5.28921	+	7.55377i	−1.10288	+	1.57507i	−0.326054	+	0.945351i	$0.605719\pi$
$23$	−5.28921	+	7.55377i	−1.10288	+	1.57507i	−0.776822	+	0.629720i	$0.783170\pi$
$24$	0.859133	+	0.151488i	0.175370	+	0.0309224i
$25$		0			0
$26$	1.76510	+	3.05725i	0.346166	+	0.599576i
$27$	4.41465	−	1.18290i	0.849600	−	0.227650i
$28$	−1.59146	−	0.139235i	−0.300759	−	0.0263130i
$29$	−1.62212	+	1.36112i	−0.301220	+	0.252754i	−0.780852	−	0.624716i	$-0.785215\pi$
$29$	−1.62212	+	1.36112i	−0.301220	+	0.252754i	0.479632	+	0.877470i	$0.340770\pi$
$30$		0			0
$31$	−7.02169	+	4.05397i	−1.26113	+	0.728115i	−0.973294	−	0.229564i	$-0.926270\pi$
$31$	−7.02169	+	4.05397i	−1.26113	+	0.728115i	−0.287839	+	0.957679i	$0.592937\pi$
$32$	−0.422618	−	0.906308i	−0.0747091	−	0.160214i
$33$	2.93863	+	4.19679i	0.511549	+	0.730568i
$34$	−0.546087	−	3.09702i	−0.0936532	−	0.531134i
$35$		0			0
$36$	−1.71513	−	1.43916i	−0.285855	−	0.239861i
$37$	3.18153	+	3.18153i	0.523040	+	0.523040i	0.918488	−	0.395448i	$-0.129411\pi$
$37$	3.18153	+	3.18153i	0.523040	+	0.523040i	−0.395448	+	0.918488i	$0.629411\pi$
$38$	2.52688	+	3.55174i	0.409914	+	0.576169i
$39$			3.07971i			0.493148i
$40$		0			0
$41$	−2.16409	−	5.94578i	−0.337973	−	0.928574i	−0.985969	−	0.166930i	$-0.946615\pi$
$41$	−2.16409	−	5.94578i	−0.337973	−	0.928574i	0.647995	−	0.761644i	$-0.275608\pi$
$42$	−1.14163	−	0.799380i	−0.176158	−	0.123347i
$43$	6.53300	−	4.57446i	0.996273	−	0.697598i	0.0428024	−	0.999084i	$-0.486371\pi$
$43$	6.53300	−	4.57446i	0.996273	−	0.697598i	0.953471	+	0.301486i	$0.0974825\pi$
$44$	2.00861	−	5.51861i	0.302809	−	0.831962i
$45$		0			0
$46$	7.98601	+	4.61073i	1.17747	+	0.679815i
$47$	0.622339	−	7.11337i	0.0907775	−	1.03759i	−0.805055	−	0.593200i	$-0.797864\pi$
$47$	0.622339	−	7.11337i	0.0907775	−	1.03759i	0.895833	−	0.444391i	$-0.146580\pi$
$48$	0.0760335	−	0.869067i	0.0109745	−	0.125439i
$49$	−3.85196	−	2.22393i	−0.550279	−	0.317704i
$50$		0			0
$51$	0.938324	−	2.57802i	0.131392	−	0.360996i
$52$	2.89178	−	2.02484i	0.401017	−	0.280795i
$53$	5.18480	+	3.63043i	0.712187	+	0.498678i	0.872639	−	0.488365i	$-0.162407\pi$
$53$	5.18480	+	3.63043i	0.712187	+	0.498678i	−0.160453	+	0.987044i	$0.551295\pi$
$54$	−1.56316	−	4.29476i	−0.212720	−	0.584442i
$55$		0			0
$56$			1.59754i			0.213481i
$57$	0.359835	+	3.78558i	0.0476613	+	0.501413i
$58$	1.49732	+	1.49732i	0.196608	+	0.196608i
$59$	1.57918	+	1.32509i	0.205592	+	0.172512i	0.739770	−	0.672860i	$-0.234934\pi$
$59$	1.57918	+	1.32509i	0.205592	+	0.172512i	−0.534178	+	0.845372i	$0.679379\pi$
$60$		0			0
$61$	−0.597908	−	3.39091i	−0.0765543	−	0.434161i	−0.998862	−	0.0477037i	$-0.984810\pi$
$61$	−0.597908	−	3.39091i	−0.0765543	−	0.434161i	0.922307	−	0.386458i	$-0.126301\pi$
$62$	4.65053	+	6.64164i	0.590618	+	0.843489i
$63$	1.51162	+	3.24169i	0.190447	+	0.408414i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$		0			0
$66$	3.92470	−	3.29322i	0.483098	−	0.405367i
$67$	14.6514	+	1.28183i	1.78995	+	0.156600i	0.933253	−	0.359220i	$-0.116957\pi$
$67$	14.6514	+	1.28183i	1.78995	+	0.156600i	0.856697	+	0.515821i	$0.172513\pi$
$68$	−3.03764	+	0.813932i	−0.368367	+	0.0987038i
$69$	4.02234	+	6.96689i	0.484233	+	0.838716i
$70$		0			0
$71$	8.81302	+	1.55397i	1.04591	+	0.184423i	0.670098	−	0.742272i	$-0.266252\pi$
$71$	8.81302	+	1.55397i	1.04591	+	0.184423i	0.375814	+	0.926695i	$0.377363\pi$
$72$	−1.28420	+	1.83403i	−0.151345	+	0.216143i
$73$	−14.0860	−	6.56842i	−1.64864	−	0.768775i	−0.999970	−	0.00770911i	$-0.997546\pi$
$73$	−14.0860	−	6.56842i	−1.64864	−	0.768775i	−0.648674	−	0.761066i	$-0.724676\pi$
$74$	2.89213	−	3.44671i	0.336204	−	0.400672i
$75$		0			0
$76$	3.31799	−	2.82682i	0.380600	−	0.324258i
$77$	−6.63409	+	6.63409i	−0.756025	+	0.756025i
$78$	3.06799	−	0.268414i	0.347381	−	0.0303919i
$79$	7.18374	−	2.61467i	0.808234	−	0.294173i	0.0953400	−	0.995445i	$-0.469606\pi$
$79$	7.18374	−	2.61467i	0.808234	−	0.294173i	0.712894	+	0.701272i	$0.247384\pi$
$80$		0			0
$81$	−0.474004	+	2.68821i	−0.0526671	+	0.298690i
$82$	−5.73454	+	2.67406i	−0.633274	+	0.295300i
$83$	−0.677291	+	2.52768i	−0.0743423	+	0.277449i	−0.993083	−	0.117411i	$-0.962540\pi$
$83$	−0.677291	+	2.52768i	−0.0743423	+	0.277449i	0.918741	+	0.394861i	$0.129207\pi$
$84$	−0.696838	+	1.20696i	−0.0760313	+	0.131690i
$85$		0			0
$86$	−5.12644	−	6.10945i	−0.552798	−	0.658799i
$87$	0.478117	+	1.78436i	0.0512596	+	0.191303i
$88$	−5.67267	−	1.51999i	−0.604709	−	0.162031i
$89$	10.3108	+	3.75284i	1.09295	+	0.397800i	0.824712	−	0.565553i	$-0.191337\pi$
$89$	10.3108	+	3.75284i	1.09295	+	0.397800i	0.268236	+	0.963353i	$0.413559\pi$
$90$		0			0
$91$	−5.55398	+	0.979317i	−0.582216	+	0.102660i
$92$	3.89716	−	8.35748i	0.406307	−	0.871327i
$93$	0.616476	+	7.04635i	0.0639256	+	0.730673i
$94$	−7.14054			−0.736490
$95$		0			0
$96$	−0.872387			−0.0890376
$97$	−0.768732	−	8.78664i	−0.0780529	−	0.892149i	−0.929769	−	0.368144i	$-0.879993\pi$
$97$	−0.768732	−	8.78664i	−0.0780529	−	0.892149i	0.851716	−	0.524004i	$-0.175562\pi$
$98$	−1.87974	+	4.03113i	−0.189883	+	0.407205i
$99$	−12.9491	+	2.28327i	−1.30143	+	0.229477i
$100$		0			0
$101$	−0.202646	−	0.0737571i	−0.0201640	−	0.00733911i	0.331918	−	0.943308i	$-0.392304\pi$
$101$	−0.202646	−	0.0737571i	−0.0201640	−	0.00733911i	−0.352082	+	0.935969i	$0.614526\pi$
$102$	−2.64999	−	0.710064i	−0.262388	−	0.0703068i
$103$	0.887819	+	3.31338i	0.0874794	+	0.326477i	0.995772	−	0.0918576i	$-0.0292805\pi$
$103$	0.887819	+	3.31338i	0.0874794	+	0.326477i	−0.908293	+	0.418335i	$0.862614\pi$
$104$	−2.26917	−	2.70430i	−0.222511	−	0.265178i
$105$		0			0
$106$	3.16473	−	5.48148i	0.307386	−	0.532408i
$107$	−1.50619	+	5.62119i	−0.145609	+	0.543421i	0.854118	+	0.520079i	$0.174097\pi$
$107$	−1.50619	+	5.62119i	−0.145609	+	0.543421i	−0.999728	+	0.0233423i	$0.992569\pi$
$108$	−4.14217	+	1.93153i	−0.398581	+	0.185861i
$109$	0.0199076	−	0.112901i	0.00190680	−	0.0108140i	−0.983840	−	0.179053i	$-0.942697\pi$
$109$	0.0199076	−	0.112901i	0.00190680	−	0.0108140i	0.985746	+	0.168239i	$0.0538079\pi$
$110$		0			0
$111$	3.68846	−	1.34249i	0.350094	−	0.127424i
$112$	1.59146	−	0.139235i	0.150379	−	0.0131565i
$113$	13.3173	−	13.3173i	1.25278	−	1.25278i	0.298314	−	0.954468i	$-0.403576\pi$
$113$	13.3173	−	13.3173i	1.25278	−	1.25278i	0.954468	−	0.298314i	$-0.0964243\pi$
$114$	3.73982	−	0.688401i	0.350266	−	0.0644746i
$115$		0			0
$116$	1.36112	−	1.62212i	0.126377	−	0.150610i
$117$	−7.16339	−	3.34035i	−0.662256	−	0.308815i
$118$	1.18241	−	1.68866i	0.108850	−	0.155454i
$119$	4.94762	+	0.872398i	0.453547	+	0.0799726i
$120$		0			0
$121$	−11.7448	−	20.3426i	−1.06771	−	1.84932i
$122$	−3.32589	+	0.891170i	−0.301112	+	0.0806828i
$123$	−5.49890	−	0.481092i	−0.495819	−	0.0433786i
$124$	6.21105	−	5.21169i	0.557769	−	0.468023i
$125$		0			0
$126$	3.09760	−	1.78840i	0.275957	−	0.159324i
$127$	−4.24253	−	9.09814i	−0.376464	−	0.807330i	−0.999680	−	0.0252802i	$-0.991952\pi$
$127$	−4.24253	−	9.09814i	−0.376464	−	0.807330i	0.623216	−	0.782049i	$-0.285826\pi$
$128$	0.573576	+	0.819152i	0.0506975	+	0.0724035i
$129$	−1.20817	−	6.85186i	−0.106373	−	0.603273i
$130$		0			0
$131$	4.56150	+	3.82756i	0.398540	+	0.334415i	0.819929	−	0.572465i	$-0.194013\pi$
$131$	4.56150	+	3.82756i	0.398540	+	0.334415i	−0.421389	+	0.906880i	$0.638457\pi$
$132$	−3.62275	−	3.62275i	−0.315320	−	0.315320i
$133$	−6.71254	+	1.85271i	−0.582051	+	0.160650i
$134$		−	14.7073i		−	1.27052i
$135$		0			0
$136$	1.07558	+	2.95514i	0.0922304	+	0.253401i
$137$	−0.113302	−	0.0793352i	−0.00968008	−	0.00677807i	0.568726	−	0.822527i	$-0.307436\pi$
$137$	−0.113302	−	0.0793352i	−0.00968008	−	0.00677807i	−0.578406	+	0.815749i	$0.696325\pi$
$138$	6.58981	−	4.61424i	0.560962	−	0.392790i
$139$	−6.65401	+	18.2817i	−0.564386	+	1.55064i	0.248753	+	0.968567i	$0.419979\pi$
$139$	−6.65401	+	18.2817i	−0.564386	+	1.55064i	−0.813139	+	0.582070i	$0.802243\pi$
$140$		0			0
$141$	−5.39474	−	3.11466i	−0.454319	−	0.262301i
$142$	0.779954	−	8.91492i	0.0654523	−	0.748123i
$143$	1.80693	−	20.6533i	0.151103	−	1.72711i
$144$	1.93898	+	1.11947i	0.161582	+	0.0932892i
$145$		0			0
$146$	−5.31575	+	14.6049i	−0.439934	+	1.20871i
$147$	−3.17851	+	2.22562i	−0.262159	+	0.183566i
$148$	−3.68566	−	2.58073i	−0.302959	−	0.212134i
$149$	5.67849	+	15.6015i	0.465200	+	1.27813i	0.921527	+	0.388315i	$0.126943\pi$
$149$	5.67849	+	15.6015i	0.465200	+	1.27813i	−0.456326	+	0.889812i	$0.650835\pi$
$150$		0			0
$151$			5.72726i			0.466077i	0.972467	+	0.233039i	$0.0748669\pi$
$151$			5.72726i			0.466077i	−0.972467	+	0.233039i	$0.925133\pi$
$152$	−3.10525	−	3.05900i	−0.251869	−	0.248117i
$153$	4.97874	+	4.97874i	0.402507	+	0.402507i
$154$	7.18705	+	6.03065i	0.579149	+	0.485964i
$155$		0			0
$156$	−0.534786	−	3.03292i	−0.0428171	−	0.242828i
$157$	−0.806342	−	1.15158i	−0.0643531	−	0.0919057i	0.785686	−	0.618626i	$-0.212310\pi$
$157$	−0.806342	−	1.15158i	−0.0643531	−	0.0919057i	−0.850039	+	0.526720i	$0.823422\pi$
$158$	−3.23082	−	6.92852i	−0.257030	−	0.551204i
$159$	4.78197	−	2.76087i	0.379235	−	0.218951i
$160$		0			0
$161$	−11.2851	+	9.46934i	−0.889392	+	0.746289i
$162$	2.71929	+	0.237907i	0.213648	+	0.0186918i
$163$	0.419400	−	0.112378i	0.0328499	−	0.00880212i	−0.242357	−	0.970187i	$-0.577920\pi$
$163$	0.419400	−	0.112378i	0.0328499	−	0.00880212i	0.275207	+	0.961385i	$0.411254\pi$
$164$	3.16368	+	5.47966i	0.247042	+	0.427889i
$165$		0			0
$166$	2.57710	+	0.454411i	0.200021	+	0.0352692i
$167$	−5.64249	+	8.05831i	−0.436629	+	0.623571i	−0.975810	−	0.218619i	$-0.929845\pi$
$167$	−5.64249	+	8.05831i	−0.436629	+	0.623571i	0.539181	+	0.842190i	$0.318734\pi$
$168$	1.26310	+	0.588993i	0.0974502	+	0.0454418i
$169$	−0.345577	+	0.411843i	−0.0265828	+	0.0316802i
$170$		0			0
$171$	−9.19554	−	3.26898i	−0.703201	−	0.249985i
$172$	−5.63940	+	5.63940i	−0.430000	+	0.430000i
$173$	−1.13024	+	0.0988834i	−0.0859307	+	0.00751796i	−0.130040	−	0.991509i	$-0.541511\pi$
$173$	−1.13024	+	0.0988834i	−0.0859307	+	0.00751796i	0.0441093	+	0.999027i	$0.485955\pi$
$174$	1.73590	−	0.631815i	0.131598	−	0.0478978i
$175$		0			0
$176$	−1.01980	+	5.78356i	−0.0768702	+	0.435952i
$177$	1.62991	−	0.760038i	0.122511	−	0.0571279i
$178$	2.83991	−	10.5987i	0.212860	−	0.794406i
$179$	−5.06603	+	8.77462i	−0.378653	+	0.655846i	−0.990867	−	0.134846i	$-0.956946\pi$
$179$	−5.06603	+	8.77462i	−0.378653	+	0.655846i	0.612214	+	0.790692i	$0.290279\pi$
$180$		0			0
$181$	3.50396	+	4.17586i	0.260448	+	0.310389i	0.880383	−	0.474264i	$-0.157286\pi$
$181$	3.50396	+	4.17586i	0.260448	+	0.310389i	−0.619935	+	0.784653i	$0.712841\pi$
$182$	1.45965	+	5.44750i	0.108197	+	0.403795i
$183$	−2.90147	−	0.777445i	−0.214482	−	0.0574704i
$184$	−8.66533	−	3.15392i	−0.638817	−	0.232510i
$185$		0			0
$186$	6.96581	−	1.22826i	0.510758	−	0.0900604i
$187$	−7.80520	+	16.7383i	−0.570773	+	1.22403i
$188$	0.622339	+	7.11337i	0.0453887	+	0.518796i
$189$	7.30139			0.531098
$190$		0			0
$191$	18.8349			1.36284			0.681422	−	0.731891i	$-0.261362\pi$
$191$	18.8349			1.36284			0.681422	+	0.731891i	$0.261362\pi$
$192$	0.0760335	+	0.869067i	0.00548725	+	0.0627195i
$193$	2.31910	−	4.97332i	0.166932	−	0.357988i	−0.804990	−	0.593288i	$-0.797830\pi$
$193$	2.31910	−	4.97332i	0.166932	−	0.357988i	0.971923	+	0.235300i	$0.0756074\pi$
$194$	−8.68621	+	1.53161i	−0.623633	+	0.109963i
$195$		0			0
$196$	4.17962	+	1.52126i	0.298544	+	0.108661i
$197$	−0.103648	−	0.0277724i	−0.00738461	−	0.00197870i	0.255125	−	0.966908i	$-0.417883\pi$
$197$	−0.103648	−	0.0277724i	−0.00738461	−	0.00197870i	−0.262509	+	0.964929i	$0.584550\pi$
$198$	3.40316	+	12.7008i	0.241852	+	0.902605i
$199$	−11.0756	−	13.1994i	−0.785130	−	0.935682i	0.214023	−	0.976829i	$-0.431343\pi$
$199$	−11.0756	−	13.1994i	−0.785130	−	0.935682i	−0.999153	+	0.0411466i	$0.986899\pi$
$200$		0			0
$201$	6.41524	−	11.1115i	0.452496	−	0.783747i
$202$	−0.0558147	+	0.208303i	−0.00392711	+	0.0146562i
$203$	−3.06590	+	1.42965i	−0.215184	+	0.100342i
$204$	−0.476400	+	2.70180i	−0.0333546	+	0.189164i
$205$		0			0
$206$	3.22340	−	1.17322i	0.224585	−	0.0817422i
$207$	−20.5677	+	1.79944i	−1.42956	+	0.125070i
$208$	−2.49623	+	2.49623i	−0.173083	+	0.173083i
$209$	−0.192060	−	25.5981i	−0.0132851	−	1.77066i
$210$		0			0
$211$	−4.54348	+	5.41471i	−0.312786	+	0.372764i	−0.899418	−	0.437090i	$-0.856009\pi$
$211$	−4.54348	+	5.41471i	−0.312786	+	0.372764i	0.586632	+	0.809854i	$0.300454\pi$
$212$	−5.73645	−	2.67495i	−0.393981	−	0.183716i
$213$	4.47789	−	6.39509i	0.306820	−	0.438184i
$214$	5.73108	+	1.01054i	0.391768	+	0.0690793i
$215$		0			0
$216$	2.28519	+	3.95807i	0.155488	+	0.269312i
$217$	−12.5114	+	3.35243i	−0.849332	+	0.227578i
$218$	−0.114207	−	0.00999180i	−0.00773506	−	0.000676730i
$219$	−10.3867	+	8.71544i	−0.701865	+	0.588935i
$220$		0			0
$221$	−9.61442	+	5.55089i	−0.646736	+	0.373393i
$222$	−1.65885	−	3.55742i	−0.111335	−	0.238759i
$223$	−1.83330	−	2.61822i	−0.122767	−	0.175329i	0.753064	−	0.657947i	$-0.228575\pi$
$223$	−1.83330	−	2.61822i	−0.122767	−	0.175329i	−0.875831	+	0.482618i	$0.839686\pi$
$224$	−0.277411	−	1.57327i	−0.0185353	−	0.105119i
$225$		0			0
$226$	−14.4273	−	12.1059i	−0.959687	−	0.805273i
$227$	−14.5907	−	14.5907i	−0.968422	−	0.968422i	0.0310946	−	0.999516i	$-0.490101\pi$
$227$	−14.5907	−	14.5907i	−0.968422	−	0.968422i	−0.999516	+	0.0310946i	$0.990101\pi$
$228$	−1.01173	−	3.66559i	−0.0670033	−	0.242759i
$229$			1.51821i			0.100326i	0.998741	+	0.0501631i	$0.0159741\pi$
$229$			1.51821i			0.100326i	−0.998741	+	0.0501631i	$0.984026\pi$
$230$		0			0
$231$	2.79935	+	7.69115i	0.184184	+	0.506041i
$232$	−1.73458	−	1.21456i	−0.113881	−	0.0797400i
$233$	9.65169	−	6.75818i	0.632303	−	0.442743i	−0.212984	−	0.977056i	$-0.568318\pi$
$233$	9.65169	−	6.75818i	0.632303	−	0.442743i	0.845287	+	0.534312i	$0.179429\pi$
$234$	−2.70330	+	7.42727i	−0.176720	+	0.485536i
$235$		0			0
$236$	−1.78529	−	1.03074i	−0.116212	−	0.0670952i
$237$	0.581260	−	6.64383i	0.0377569	−	0.431563i
$238$	0.437865	−	5.00482i	0.0283826	−	0.324415i
$239$	−4.25407	−	2.45609i	−0.275173	−	0.158871i	0.356063	−	0.934462i	$-0.384119\pi$
$239$	−4.25407	−	2.45609i	−0.275173	−	0.158871i	−0.631236	+	0.775591i	$0.717452\pi$
$240$		0			0
$241$	−0.750889	+	2.06305i	−0.0483690	+	0.132893i	−0.961525	−	0.274718i	$-0.911416\pi$
$241$	−0.750889	+	2.06305i	−0.0483690	+	0.132893i	0.913156	+	0.407610i	$0.133638\pi$
$242$	−19.2415	+	13.4731i	−1.23689	+	0.866081i
$243$	13.1822	+	9.23027i	0.845638	+	0.592122i
$244$	1.17765	+	3.23557i	0.0753913	+	0.207136i
$245$		0			0
$246$			5.51991i			0.351937i
$247$	8.73127	−	12.6708i	0.555558	−	0.806226i
$248$	−5.73319	−	5.73319i	−0.364058	−	0.364058i
$249$	1.74881	+	1.46742i	0.110826	+	0.0929942i
$250$		0			0
$251$	1.14631	+	6.50103i	0.0723542	+	0.410341i	0.999376	+	0.0353327i	$0.0112491\pi$
$251$	1.14631	+	6.50103i	0.0723542	+	0.410341i	−0.927021	+	0.375008i	$0.877640\pi$
$252$	−2.05157	−	2.92995i	−0.129237	−	0.184569i
$253$	−22.8871	−	49.0816i	−1.43890	−	3.08574i
$254$	−8.69376	+	5.01934i	−0.545495	+	0.314942i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−11.5381	−	1.00946i	−0.719729	−	0.0629681i	−0.278594	−	0.960409i	$-0.589868\pi$
$257$	−11.5381	−	1.00946i	−0.719729	−	0.0629681i	−0.441135	+	0.897441i	$0.645424\pi$
$258$	−6.72049	+	1.80075i	−0.418400	+	0.112110i
$259$	3.59396	+	6.22492i	0.223318	+	0.386798i
$260$		0			0
$261$	−4.66899	−	0.823269i	−0.289003	−	0.0509591i
$262$	3.41543	−	4.87774i	0.211006	−	0.301348i
$263$	28.6638	+	13.3662i	1.76749	+	0.824193i	0.977460	+	0.211122i	$0.0677116\pi$
$263$	28.6638	+	13.3662i	1.76749	+	0.824193i	0.790028	+	0.613071i	$0.210066\pi$
$264$	−3.29322	+	3.92470i	−0.202684	+	0.241549i
$265$		0			0
$266$	2.43070	+	6.52553i	0.149035	+	0.400106i
$267$	6.76866	−	6.76866i	0.414235	−	0.414235i
$268$	−14.6514	+	1.28183i	−0.894975	+	0.0783001i
$269$	23.2995	−	8.48031i	1.42059	−	0.517054i	0.486374	−	0.873751i	$-0.338319\pi$
$269$	23.2995	−	8.48031i	1.42059	−	0.517054i	0.934220	+	0.356697i	$0.116097\pi$
$270$		0			0
$271$	−4.77391	+	27.0742i	−0.289995	+	1.64464i	0.396884	+	0.917869i	$0.370091\pi$
$271$	−4.77391	+	27.0742i	−0.289995	+	1.64464i	−0.686879	+	0.726772i	$0.741020\pi$
$272$	2.85015	−	1.32905i	0.172816	−	0.0805853i
$273$	−1.27338	+	4.75232i	−0.0770686	+	0.287624i
$274$	−0.0691584	+	0.119786i	−0.00417801	+	0.00723653i
$275$		0			0
$276$	−5.17102	−	6.16258i	−0.311259	−	0.370944i
$277$	−1.87621	−	7.00209i	−0.112730	−	0.420715i	0.886377	−	0.462964i	$-0.153214\pi$
$277$	−1.87621	−	7.00209i	−0.112730	−	0.420715i	−0.999107	+	0.0422495i	$0.986548\pi$
$278$	18.7921	+	5.03533i	1.12708	+	0.301999i
$279$	−17.0584	−	6.20877i	−1.02126	−	0.371709i
$280$		0			0
$281$	22.8174	−	4.02333i	1.36117	−	0.240012i	0.555079	−	0.831798i	$-0.312688\pi$
$281$	22.8174	−	4.02333i	1.36117	−	0.240012i	0.806095	+	0.591786i	$0.201577\pi$
$282$	−2.63262	+	5.64567i	−0.156770	+	0.336195i
$283$	−0.151740	−	1.73439i	−0.00901998	−	0.103099i	0.990350	−	0.138588i	$-0.0442565\pi$
$283$	−0.151740	−	1.73439i	−0.00901998	−	0.103099i	−0.999370	+	0.0354895i	$0.988701\pi$
$284$	−8.94897			−0.531024
$285$		0			0
$286$	−20.7321			−1.22592
$287$	−0.880991	−	10.0698i	−0.0520033	−	0.594400i
$288$	0.946217	−	2.02917i	0.0557564	−	0.119570i
$289$	−7.00226	+	1.23469i	−0.411898	+	0.0726287i
$290$		0			0
$291$	−7.23059	−	2.63172i	−0.423865	−	0.154274i
$292$	15.0126	+	4.02262i	0.878547	+	0.235406i
$293$	6.16018	+	22.9901i	0.359882	+	1.34310i	0.874229	+	0.485515i	$0.161368\pi$
$293$	6.16018	+	22.9901i	0.359882	+	1.34310i	−0.514347	+	0.857582i	$0.671966\pi$
$294$	2.49418	+	2.97244i	0.145463	+	0.173356i
$295$		0			0
$296$	−2.24968	+	3.89656i	−0.130760	+	0.226483i
$297$	−6.94693	+	25.9263i	−0.403102	+	1.50440i
$298$	15.0473	−	7.01665i	0.871664	−	0.406464i
$299$	5.65289	−	32.0591i	0.326915	−	1.85403i
$300$		0			0
$301$	11.9725	−	4.35765i	0.690086	−	0.251171i
$302$	5.70546	−	0.499163i	0.328312	−	0.0287236i
$303$	−0.133029	+	0.133029i	−0.00764232	+	0.00764232i
$304$	−2.77672	+	3.36004i	−0.159256	+	0.192711i
$305$		0			0
$306$	4.52587	−	5.39372i	0.258727	−	0.308339i
$307$	−15.2323	−	7.10295i	−0.869355	−	0.405387i	−0.0638386	−	0.997960i	$-0.520334\pi$
$307$	−15.2323	−	7.10295i	−0.869355	−	0.405387i	−0.805517	+	0.592573i	$0.798112\pi$
$308$	5.38131	−	7.68530i	0.306629	−	0.437911i
$309$	2.94706	+	0.519646i	0.167652	+	0.0295616i
$310$		0			0
$311$	2.69548	+	4.66871i	0.152847	+	0.264738i	0.932273	−	0.361756i	$-0.117823\pi$
$311$	2.69548	+	4.66871i	0.152847	+	0.264738i	−0.779426	+	0.626494i	$0.784489\pi$
$312$	−2.97477	+	0.797087i	−0.168413	+	0.0451262i
$313$	−26.6685	−	2.33319i	−1.50739	−	0.131880i	−0.696704	−	0.717359i	$-0.745351\pi$
$313$	−26.6685	−	2.33319i	−1.50739	−	0.131880i	−0.810687	+	0.585479i	$0.800906\pi$
$314$	−1.07692	+	0.903640i	−0.0607739	+	0.0509953i
$315$		0			0
$316$	−6.62057	+	3.82239i	−0.372436	+	0.215026i
$317$	6.47229	+	13.8799i	0.363520	+	0.779571i	0.999966	+	0.00824972i	$0.00262600\pi$
$317$	6.47229	+	13.8799i	0.363520	+	0.779571i	−0.636446	+	0.771321i	$0.719596\pi$
$318$	−3.16714	−	4.52315i	−0.177605	−	0.253646i
$319$	−2.15945	−	12.2469i	−0.120906	−	0.685692i
$320$		0			0
$321$	3.88909	+	3.26333i	0.217068	+	0.182141i
$322$	10.4169	+	10.4169i	0.580509	+	0.580509i
$323$	−11.1695	+	7.94651i	−0.621487	+	0.442156i
$324$		−	2.72968i		−	0.151649i
$325$		0			0
$326$	−0.148503	−	0.408010i	−0.00822484	−	0.0225976i
$327$	−0.0819259	−	0.0573651i	−0.00453051	−	0.00317230i
$328$	5.18307	−	3.62923i	0.286187	−	0.200391i
$329$	3.90153	−	10.7194i	0.215099	−	0.590978i
$330$		0			0
$331$	20.2224	+	11.6754i	1.11152	+	0.641739i	0.939224	−	0.343306i	$-0.111547\pi$
$331$	20.2224	+	11.6754i	1.11152	+	0.641739i	0.172300	+	0.985044i	$0.444880\pi$
$332$	0.228074	−	2.60689i	0.0125172	−	0.143072i
$333$	−0.877989	+	10.0355i	−0.0481135	+	0.549940i
$334$	8.51942	+	4.91869i	0.466162	+	0.269139i
$335$		0			0
$336$	0.476665	−	1.30963i	0.0260042	−	0.0714460i
$337$	10.4767	−	7.33590i	0.570705	−	0.399612i	−0.252298	−	0.967650i	$-0.581186\pi$
$337$	10.4767	−	7.33590i	0.570705	−	0.399612i	0.823002	+	0.568038i	$0.192297\pi$
$338$	0.440394	+	0.308368i	0.0239543	+	0.0167730i
$339$	−5.61941	−	15.4392i	−0.305204	−	0.838542i
$340$		0			0
$341$		−	47.6162i		−	2.57856i
$342$	−2.45510	+	9.44546i	−0.132757	+	0.510752i
$343$	−12.9319	−	12.9319i	−0.698256	−	0.698256i
$344$	6.10945	+	5.12644i	0.329399	+	0.276399i
$345$		0			0
$346$	0.197014	+	1.11732i	0.0105915	+	0.0600677i
$347$	14.9853	+	21.4012i	0.804452	+	1.14888i	0.986204	+	0.165532i	$0.0529342\pi$
$347$	14.9853	+	21.4012i	0.804452	+	1.14888i	−0.181752	+	0.983344i	$0.558177\pi$
$348$	−0.780704	−	1.67423i	−0.0418501	−	0.0897479i
$349$	−23.0986	+	13.3360i	−1.23644	+	0.713858i	−0.968364	−	0.249541i	$-0.919720\pi$
$349$	−23.0986	+	13.3360i	−1.23644	+	0.713858i	−0.268074	+	0.963398i	$0.586387\pi$
$350$		0			0
$351$	−12.3597	+	10.3710i	−0.659711	+	0.553563i
$352$	5.85043	+	0.511847i	0.311829	+	0.0272815i
$353$	−19.8562	+	5.32045i	−1.05684	+	0.283179i	−0.745075	−	0.666981i	$-0.767586\pi$
$353$	−19.8562	+	5.32045i	−1.05684	+	0.283179i	−0.311764	+	0.950160i	$0.600920\pi$
$354$	−0.899201	−	1.55746i	−0.0477920	−	0.0827782i
$355$		0			0
$356$	−10.8059	−	1.90537i	−0.572710	−	0.100984i
$357$	2.51388	−	3.59020i	0.133049	−	0.190013i
$358$	9.18276	+	4.28199i	0.485324	+	0.226310i
$359$	−16.0811	+	19.1647i	−0.848729	+	1.01148i	0.151008	+	0.988533i	$0.451748\pi$
$359$	−16.0811	+	19.1647i	−0.848729	+	1.01148i	−0.999737	+	0.0229434i	$0.992696\pi$
$360$		0			0
$361$	9.25203	−	16.5952i	0.486949	−	0.873430i
$362$	3.85458	−	3.85458i	0.202592	−	0.202592i
$363$	−20.4140	+	1.78599i	−1.07146	+	0.0937404i
$364$	5.29955	−	1.92888i	0.277772	−	0.101101i
$365$		0			0
$366$	−0.521608	+	2.95818i	−0.0272649	+	0.154627i
$367$	32.3581	−	15.0888i	1.68908	−	0.787631i	0.691193	−	0.722670i	$-0.257085\pi$
$367$	32.3581	−	15.0888i	1.68908	−	0.787631i	0.997888	−	0.0649615i	$-0.0206925\pi$
$368$	−2.38669	+	8.90724i	−0.124415	+	0.464322i
$369$	7.08330	−	12.2686i	0.368742	−	0.638679i
$370$		0			0
$371$	6.49961	+	7.74594i	0.337443	+	0.402149i
$372$	−1.83070	−	6.83225i	−0.0949172	−	0.354236i
$373$	25.5104	+	6.83550i	1.32088	+	0.353929i	0.849307	−	0.527899i	$-0.177020\pi$
$373$	25.5104	+	6.83550i	1.32088	+	0.353929i	0.471573	+	0.881827i	$0.343687\pi$
$374$	17.3549	+	6.31666i	0.897400	+	0.326627i
$375$		0			0
$376$	7.03206	−	1.23994i	0.362651	−	0.0639451i
$377$	3.15920	−	6.77494i	0.162707	−	0.348927i
$378$	−0.636358	−	7.27360i	−0.0327307	−	0.374114i
$379$	2.36562			0.121514			0.0607568	−	0.998153i	$-0.480649\pi$
$379$	2.36562			0.121514			0.0607568	+	0.998153i	$0.480649\pi$
$380$		0			0
$381$	−8.75762			−0.448667
$382$	−1.64157	−	18.7632i	−0.0839899	−	0.960009i
$383$	−14.0616	+	30.1551i	−0.718512	+	1.54085i	0.118065	+	0.993006i	$0.462331\pi$
$383$	−14.0616	+	30.1551i	−0.718512	+	1.54085i	−0.836577	+	0.547849i	$0.815447\pi$
$384$	0.859133	−	0.151488i	0.0438425	−	0.00773061i
$385$		0			0
$386$	−5.15652	−	1.87682i	−0.262460	−	0.0955276i
$387$	17.2478	+	4.62154i	0.876757	+	0.234926i
$388$	2.28284	+	8.51967i	0.115894	+	0.432521i
$389$	15.0503	+	17.9363i	0.763081	+	0.909405i	0.998039	−	0.0626007i	$-0.0199395\pi$
$389$	15.0503	+	17.9363i	0.763081	+	0.909405i	−0.234957	+	0.972006i	$0.575495\pi$
$390$		0			0
$391$	−14.4998	+	25.1144i	−0.733285	+	1.27009i
$392$	1.15119	−	4.29630i	0.0581438	−	0.216996i
$393$	4.70803	−	2.19539i	0.237489	−	0.110743i
$394$	−0.0186332	+	0.105674i	−0.000938726	+	0.00532378i
$395$		0			0
$396$	12.3558	−	4.49716i	0.620904	−	0.225991i
$397$	−8.33986	+	0.729643i	−0.418565	+	0.0366197i	−0.294493	−	0.955654i	$-0.595151\pi$
$397$	−8.33986	+	0.729643i	−0.418565	+	0.0366197i	−0.124072	+	0.992273i	$0.539595\pi$
$398$	−12.1839	+	12.1839i	−0.610723	+	0.610723i
$399$	−1.00998	+	5.99035i	−0.0505622	+	0.299893i
$400$		0			0
$401$	19.9355	−	23.7582i	0.995533	−	1.18643i	0.0130807	−	0.999914i	$-0.495836\pi$
$401$	19.9355	−	23.7582i	0.995533	−	1.18643i	0.982452	−	0.186515i	$-0.0597194\pi$
$402$	−11.6284	−	5.42240i	−0.579970	−	0.270445i
$403$	16.4173	−	23.4464i	0.817806	−	1.16795i
$404$	0.212375	+	0.0374475i	0.0105661	+	0.00186308i
$405$		0			0
$406$	1.69142	+	2.92963i	0.0839438	+	0.145395i
$407$	−25.5234	+	6.83897i	−1.26515	+	0.338995i
$408$	2.73304	+	0.239110i	0.135305	+	0.0118377i
$409$	22.3950	−	18.7916i	1.10736	−	0.929185i	0.109461	−	0.993991i	$-0.465087\pi$
$409$	22.3950	−	18.7916i	1.10736	−	0.929185i	0.997898	+	0.0648064i	$0.0206430\pi$
$410$		0			0
$411$	−0.104500	+	0.0603329i	−0.00515458	+	0.00297600i
$412$	−1.44969	−	3.10888i	−0.0714213	−	0.153163i
$413$	1.88896	+	2.69771i	0.0929494	+	0.132746i
$414$	3.58519	+	20.3326i	0.176203	+	0.999294i
$415$		0			0
$416$	2.70430	+	2.26917i	0.132589	+	0.111255i
$417$	12.0012	+	12.0012i	0.587703	+	0.587703i
$418$	−25.4840	+	2.42235i	−1.24646	+	0.118481i
$419$		−	14.2136i		−	0.694381i	−0.937795	−	0.347191i	$-0.887136\pi$
$419$		−	14.2136i		−	0.694381i	0.937795	−	0.347191i	$-0.112864\pi$
$420$		0			0
$421$	−6.44556	−	17.7090i	−0.314137	−	0.863086i	−0.991810	−	0.127722i	$-0.959234\pi$
$421$	−6.44556	−	17.7090i	−0.314137	−	0.863086i	0.677673	−	0.735364i	$-0.262989\pi$
$422$	5.79010	+	4.05427i	0.281858	+	0.197359i
$423$	13.0960	−	9.16991i	0.636749	−	0.445856i
$424$	−2.16481	+	5.94775i	−0.105132	+	0.288849i
$425$		0			0
$426$	−6.76103	−	3.90348i	−0.327573	−	0.189124i
$427$	0.479417	−	5.47976i	0.0232006	−	0.265184i
$428$	0.507202	−	5.79734i	0.0245165	−	0.280225i
$429$	−15.6633	−	9.04323i	−0.756233	−	0.436611i
$430$		0			0
$431$	5.30439	−	14.5737i	0.255503	−	0.701990i	−0.743928	−	0.668260i	$-0.767039\pi$
$431$	5.30439	−	14.5737i	0.255503	−	0.701990i	0.999431	−	0.0337297i	$-0.0107385\pi$
$432$	3.74384	−	2.62146i	0.180126	−	0.126125i
$433$	14.3698	+	10.0618i	0.690567	+	0.483540i	0.865415	−	0.501055i	$-0.167055\pi$
$433$	14.3698	+	10.0618i	0.690567	+	0.483540i	−0.174848	+	0.984595i	$0.555944\pi$
$434$	4.43012	+	12.1717i	0.212653	+	0.584258i
$435$		0			0
$436$			0.114643i			0.00549040i
$437$	3.20274	−	40.0676i	0.153208	−	1.91669i
$438$	9.58753	+	9.58753i	0.458110	+	0.458110i
$439$	1.16663	+	0.978918i	0.0556801	+	0.0467212i	0.670203	−	0.742178i	$-0.266207\pi$
$439$	1.16663	+	0.978918i	0.0556801	+	0.0467212i	−0.614523	+	0.788899i	$0.710651\pi$
$440$		0			0
$441$	−1.72927	−	9.80719i	−0.0823463	−	0.467009i
$442$	6.36772	+	9.09404i	0.302881	+	0.432559i
$443$	−4.43369	−	9.50807i	−0.210651	−	0.451742i	0.772385	−	0.635154i	$-0.219063\pi$
$443$	−4.43369	−	9.50807i	−0.210651	−	0.451742i	−0.983036	+	0.183412i	$0.941286\pi$
$444$	−3.39931	+	1.96259i	−0.161324	+	0.0931404i
$445$		0			0
$446$	−2.44847	+	2.05451i	−0.115939	+	0.0972840i
$447$	14.4290	+	1.26237i	0.682466	+	0.0597080i
$448$	−1.54311	+	0.413475i	−0.0729050	+	0.0195348i
$449$	7.68035	+	13.3028i	0.362458	+	0.627796i	0.988365	−	0.152102i	$-0.0486043\pi$
$449$	7.68035	+	13.3028i	0.362458	+	0.627796i	−0.625907	+	0.779898i	$0.715271\pi$
$450$		0			0
$451$	36.5947	+	6.45263i	1.72318	+	0.303843i
$452$	−10.8024	+	15.4275i	−0.508103	+	0.725646i
$453$	4.52826	+	2.11156i	0.212756	+	0.0992099i
$454$	−13.2636	+	15.8069i	−0.622490	+	0.741854i
$455$		0			0
$456$	−3.56346	+	1.32735i	−0.166874	+	0.0621591i
$457$	22.0892	−	22.0892i	1.03329	−	1.03329i	0.0338614	−	0.999427i	$-0.489220\pi$
$457$	22.0892	−	22.0892i	1.03329	−	1.03329i	0.999427	−	0.0338614i	$-0.0107805\pi$
$458$	1.51243	−	0.132321i	0.0706714	−	0.00618294i
$459$	13.5061	−	4.91582i	0.630411	−	0.229451i
$460$		0			0
$461$	−0.811244	+	4.60079i	−0.0377834	+	0.214280i	−0.997854	−	0.0654773i	$-0.979143\pi$
$461$	−0.811244	+	4.60079i	−0.0377834	+	0.214280i	0.960071	+	0.279758i	$0.0902541\pi$
$462$	7.41791	−	3.45903i	0.345112	−	0.160929i
$463$	0.787091	−	2.93746i	0.0365792	−	0.136515i	−0.945221	−	0.326430i	$-0.894154\pi$
$463$	0.787091	−	2.93746i	0.0365792	−	0.136515i	0.981801	+	0.189914i	$0.0608210\pi$
$464$	−1.05876	+	1.83383i	−0.0491519	+	0.0851335i
$465$		0			0
$466$	−7.57367	−	9.02594i	−0.350843	−	0.418119i
$467$	8.81814	+	32.9097i	0.408055	+	1.52288i	0.798351	+	0.602192i	$0.205706\pi$
$467$	8.81814	+	32.9097i	0.408055	+	1.52288i	−0.390297	+	0.920689i	$0.627628\pi$
$468$	7.63461	+	2.04569i	0.352910	+	0.0945620i
$469$	22.0786	+	8.03597i	1.01950	+	0.371067i
$470$		0			0
$471$	−1.20778	+	0.212965i	−0.0556516	+	0.00981289i
$472$	−0.871216	+	1.86833i	−0.0401010	+	0.0859968i
$473$	4.08214	+	46.6591i	0.187697	+	2.14539i
$474$	−6.66921			−0.306327
$475$		0			0
$476$	−5.02394			−0.230272
$477$	1.23511	+	14.1174i	0.0565518	+	0.646390i
$478$	−2.07598	+	4.45195i	−0.0949530	+	0.203627i
$479$	5.18333	−	0.913961i	0.236832	−	0.0417600i	−0.0539720	−	0.998542i	$-0.517188\pi$
$479$	5.18333	−	0.913961i	0.236832	−	0.0417600i	0.290805	+	0.956782i	$0.406077\pi$
$480$		0			0
$481$	−14.9258	−	5.43254i	−0.680557	−	0.247702i
$482$	2.12065	+	0.568225i	0.0965928	+	0.0258820i
$483$	3.32627	+	12.4138i	0.151351	+	0.564848i
$484$	15.0988	+	17.9941i	0.686309	+	0.817911i
$485$		0			0
$486$	8.04624	−	13.9365i	0.364985	−	0.632173i
$487$	−2.96185	+	11.0538i	−0.134214	+	0.500895i	0.865786	+	0.500415i	$0.166819\pi$
$487$	−2.96185	+	11.0538i	−0.134214	+	0.500895i	−1.00000		0.000479587i	$0.999847\pi$
$488$	3.12061	−	1.45517i	0.141264	−	0.0658723i
$489$	0.0657755	−	0.373031i	0.00297447	−	0.0168691i
$490$		0			0
$491$	−11.5892	+	4.21814i	−0.523015	+	0.190362i	−0.590017	−	0.807391i	$-0.700879\pi$
$491$	−11.5892	+	4.21814i	−0.523015	+	0.190362i	0.0670020	+	0.997753i	$0.478657\pi$
$492$	5.49890	−	0.481092i	0.247910	−	0.0216893i
$493$	−4.70875	+	4.70875i	−0.212072	+	0.212072i
$494$	−13.3836	−	7.59371i	−0.602157	−	0.341657i
$495$		0			0
$496$	−5.21169	+	6.21105i	−0.234012	+	0.278884i
$497$	12.9569	+	6.04191i	0.581197	+	0.271017i
$498$	1.30942	−	1.87005i	0.0586766	−	0.0837988i
$499$	12.7161	+	2.24220i	0.569253	+	0.100375i	0.450864	−	0.892593i	$-0.351116\pi$
$499$	12.7161	+	2.24220i	0.569253	+	0.100375i	0.118389	+	0.992967i	$0.462227\pi$
$500$		0			0
$501$	4.29100	+	7.43223i	0.191708	+	0.332048i
$502$	6.37638	−	1.70855i	0.284592	−	0.0762562i
$503$	−30.8765	−	2.70134i	−1.37672	−	0.120447i	−0.625356	−	0.780340i	$-0.715046\pi$
$503$	−30.8765	−	2.70134i	−1.37672	−	0.120447i	−0.751360	+	0.659893i	$0.770602\pi$
$504$	−2.73999	+	2.29913i	−0.122049	+	0.102411i
$505$		0			0
$506$	−46.9001	+	27.0778i	−2.08496	+	1.20375i
$507$	0.198214	+	0.425072i	0.00880300	+	0.0188781i
$508$	5.75796	+	8.22321i	0.255468	+	0.364846i
$509$	2.47413	+	14.0315i	0.109664	+	0.621934i	0.989255	+	0.146203i	$0.0467053\pi$
$509$	2.47413	+	14.0315i	0.109664	+	0.621934i	−0.879591	+	0.475731i	$0.842184\pi$
$510$		0			0
$511$	−19.0204	−	15.9600i	−0.841412	−	0.706029i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−13.9808	+	14.1922i	−0.617267	+	0.626599i
$514$			11.5822i			0.510869i
$515$		0			0
$516$	2.37963	+	6.53797i	0.104757	+	0.287818i
$517$	34.3510	+	24.0528i	1.51076	+	1.05784i
$518$	5.88800	−	4.12282i	0.258704	−	0.181146i
$519$	−0.338523	+	0.930084i	−0.0148595	+	0.0408262i
$520$		0			0
$521$	1.08961	+	0.629085i	0.0477366	+	0.0275607i	0.523678	−	0.851916i	$-0.324559\pi$
$521$	1.08961	+	0.629085i	0.0477366	+	0.0275607i	−0.475942	+	0.879477i	$0.657893\pi$
$522$	−0.413207	+	4.72298i	−0.0180856	+	0.206719i
$523$	2.77013	−	31.6628i	0.121129	−	1.38452i	−0.655803	−	0.754932i	$-0.727670\pi$
$523$	2.77013	−	31.6628i	0.121129	−	1.38452i	0.776932	−	0.629584i	$-0.216775\pi$
$524$	−5.15685	−	2.97731i	−0.225278	−	0.130064i
$525$		0			0
$526$	10.8171	−	29.7197i	0.471647	−	1.29584i
$527$	−20.8866	+	14.6249i	−0.909834	+	0.637073i
$528$	4.19679	+	2.93863i	0.182642	+	0.127887i
$529$	−21.2173	−	58.2941i	−0.922491	−	2.53452i
$530$		0			0
$531$			4.61552i			0.200296i
$532$	6.28885	−	2.99018i	0.272656	−	0.129641i
$533$	15.7946	+	15.7946i	0.684139	+	0.684139i
$534$	−7.33283	−	6.15298i	−0.317323	−	0.266265i
$535$		0			0
$536$	2.55390	+	14.4839i	0.110312	+	0.625609i
$537$	5.06989	+	7.24055i	0.218782	+	0.312453i
$538$	−10.4787	−	22.4717i	−0.451770	−	0.968824i
$539$	22.6217	−	13.0606i	0.974385	−	0.562562i
$540$		0			0
$541$	−7.76016	+	6.51155i	−0.333635	+	0.279953i	−0.794179	−	0.607684i	$-0.792099\pi$
$541$	−7.76016	+	6.51155i	−0.333635	+	0.279953i	0.460544	+	0.887637i	$0.347654\pi$
$542$	27.3872	+	2.39607i	1.17638	+	0.102920i
$543$	4.59351	−	1.23083i	0.197127	−	0.0528199i
$544$	−1.57240	−	2.72347i	−0.0674159	−	0.116768i
$545$		0			0
$546$	4.84522	+	0.854344i	0.207356	+	0.0365625i
$547$	10.9716	−	15.6691i	0.469111	−	0.669960i	−0.512972	−	0.858405i	$-0.671456\pi$
$547$	10.9716	−	15.6691i	0.469111	−	0.669960i	0.982084	+	0.188445i	$0.0603446\pi$
$548$	0.125358	+	0.0584552i	0.00535501	+	0.00249708i
$549$	4.95535	−	5.90556i	0.211489	−	0.252043i
$550$		0			0
$551$	3.09171	−	8.69689i	0.131711	−	0.370500i
$552$	−5.68845	+	5.68845i	−0.242116	+	0.242116i
$553$	12.1664	−	1.06442i	0.517368	−	0.0452638i
$554$	−6.81193	+	2.47934i	−0.289411	+	0.105337i
$555$		0			0
$556$	3.37833	−	19.1595i	0.143273	−	0.812542i
$557$	13.3573	−	6.22861i	0.565967	−	0.263915i	−0.118506	−	0.992953i	$-0.537810\pi$
$557$	13.3573	−	6.22861i	0.565967	−	0.263915i	0.684472	+	0.729039i	$0.260033\pi$
$558$	−4.69840	+	17.5347i	−0.198899	+	0.742301i
$559$	−14.0773	+	24.3826i	−0.595405	+	1.03127i
$560$		0			0
$561$	10.3565	+	12.3424i	0.437251	+	0.521096i
$562$	−5.99669	−	22.3799i	−0.252955	−	0.944041i
$563$	21.2672	+	5.69853i	0.896305	+	0.240164i	0.677429	−	0.735588i	$-0.263094\pi$
$563$	21.2672	+	5.69853i	0.896305	+	0.240164i	0.218877	+	0.975753i	$0.429761\pi$
$564$	5.85364	+	2.13055i	0.246483	+	0.0897124i
$565$		0			0
$566$	−1.71457	+	0.302324i	−0.0720686	+	0.0127076i
$567$	−1.84295	+	3.95221i	−0.0773965	+	0.165977i
$568$	0.779954	+	8.91492i	0.0327262	+	0.374062i
$569$	−13.6775			−0.573390			−0.286695	−	0.958022i	$-0.592557\pi$
$569$	−13.6775			−0.573390			−0.286695	+	0.958022i	$0.592557\pi$
$570$		0			0
$571$	12.6607			0.529836			0.264918	−	0.964271i	$-0.414655\pi$
$571$	12.6607			0.529836			0.264918	+	0.964271i	$0.414655\pi$
$572$	1.80693	+	20.6533i	0.0755514	+	0.863556i
$573$	6.94417	−	14.8918i	0.290097	−	0.622115i
$574$	−9.95467	+	1.75528i	−0.415500	+	0.0732639i
$575$		0			0
$576$	−2.10392	−	0.765763i	−0.0876632	−	0.0319068i
$577$	−1.11184	−	0.297916i	−0.0462864	−	0.0124024i	0.235602	−	0.971850i	$-0.424294\pi$
$577$	−1.11184	−	0.297916i	−0.0462864	−	0.0124024i	−0.281888	+	0.959447i	$0.590961\pi$
$578$	1.84028	+	6.86801i	0.0765454	+	0.285671i
$579$	−3.07714	−	3.66719i	−0.127882	−	0.152403i
$580$		0			0
$581$	−2.09027	+	3.62045i	−0.0867189	+	0.150202i
$582$	−1.99152	+	7.43245i	−0.0825511	+	0.308085i
$583$	−33.6889	+	15.7094i	−1.39525	+	0.650617i
$584$	2.69888	−	15.3061i	0.111680	−	0.633370i
$585$		0			0
$586$	22.3657	−	8.14046i	0.923920	−	0.336279i
$587$	21.6556	−	1.89462i	0.893824	−	0.0781994i	0.369019	−	0.929422i	$-0.379694\pi$
$587$	21.6556	−	1.89462i	0.893824	−	0.0781994i	0.524805	+	0.851223i	$0.324138\pi$
$588$	2.74375	−	2.74375i	0.113150	−	0.113150i
$589$	17.4407	−	30.7386i	0.718633	−	1.26656i
$590$		0			0
$591$	−0.0601719	+	0.0717100i	−0.00247514	+	0.00294976i
$592$	4.07780	+	1.90151i	0.167597	+	0.0781516i
$593$	−1.58329	+	2.26117i	−0.0650179	+	0.0928552i	−0.850344	−	0.526227i	$-0.823606\pi$
$593$	−1.58329	+	2.26117i	−0.0650179	+	0.0928552i	0.785326	+	0.619082i	$0.212495\pi$
$594$	26.4331	+	4.66087i	1.08456	+	0.191238i
$595$		0			0
$596$	−8.30140	−	14.3784i	−0.340039	−	0.588964i
$597$	−14.5196	+	3.89051i	−0.594247	+	0.159228i
$598$	−32.4298	−	2.83724i	−1.32615	−	0.116023i
$599$	−31.8340	+	26.7119i	−1.30070	+	1.09142i	−0.310678	+	0.950515i	$0.600556\pi$
$599$	−31.8340	+	26.7119i	−1.30070	+	1.09142i	−0.990023	+	0.140903i	$0.954999\pi$
$600$		0			0
$601$	39.3324	−	22.7086i	1.60440	−	0.926301i	0.613808	−	0.789455i	$-0.289637\pi$
$601$	39.3324	−	22.7086i	1.60440	−	0.926301i	0.990592	−	0.136846i	$-0.0436966\pi$
$602$	−5.38455	−	11.5472i	−0.219458	−	0.470629i
$603$	18.8872	+	26.9737i	0.769147	+	1.09846i
$604$	−0.994528	−	5.64025i	−0.0404668	−	0.229498i
$605$		0			0
$606$	0.144117	+	0.120929i	0.00585436	+	0.00491239i
$607$	7.32036	+	7.32036i	0.297124	+	0.297124i	0.839886	−	0.542762i	$-0.182621\pi$
$607$	7.32036	+	7.32036i	0.297124	+	0.297124i	−0.542762	+	0.839886i	$0.682621\pi$
$608$	3.58926	+	2.47330i	0.145564	+	0.100306i
$609$			2.95115i			0.119587i
$610$		0			0
$611$	8.62151	+	23.6874i	0.348789	+	0.958289i
$612$	−5.76765	−	4.03855i	−0.233144	−	0.163249i
$613$	17.9758	−	12.5868i	0.726037	−	0.508377i	−0.151159	−	0.988510i	$-0.548300\pi$
$613$	17.9758	−	12.5868i	0.726037	−	0.508377i	0.877196	+	0.480133i	$0.159412\pi$
$614$	−5.74834	+	15.7934i	−0.231984	+	0.637371i
$615$		0			0
$616$	−8.12507	−	4.69101i	−0.327368	−	0.189006i
$617$	1.49682	−	17.1087i	0.0602597	−	0.688771i	−0.904644	−	0.426168i	$-0.859863\pi$
$617$	1.49682	−	17.1087i	0.0602597	−	0.688771i	0.964904	−	0.262603i	$-0.0845811\pi$
$618$	0.260815	−	2.98113i	0.0104915	−	0.119919i
$619$	−8.18034	−	4.72292i	−0.328795	−	0.189830i	0.326511	−	0.945193i	$-0.394127\pi$
$619$	−8.18034	−	4.72292i	−0.328795	−	0.189830i	−0.655306	+	0.755363i	$0.727460\pi$
$620$		0			0
$621$	−14.4146	+	39.6039i	−0.578440	+	1.58925i
$622$	4.41602	−	3.09213i	0.177066	−	0.123983i
$623$	14.3591	+	10.0543i	0.575283	+	0.402818i
$624$	1.05332	+	2.89398i	0.0421666	+	0.115852i
$625$		0			0
$626$			26.7703i			1.06996i
$627$	−20.3100	−	9.28584i	−0.811104	−	0.370841i
$628$	0.994061	+	0.994061i	0.0396673	+	0.0396673i
$629$	10.8392	+	9.09515i	0.432186	+	0.362648i
$630$		0			0
$631$	−3.18194	−	18.0457i	−0.126671	−	0.718387i	−0.980301	−	0.197507i	$-0.936715\pi$
$631$	−3.18194	−	18.0457i	−0.126671	−	0.718387i	0.853630	−	0.520879i	$-0.174396\pi$
$632$	4.38487	+	6.26224i	0.174421	+	0.249098i
$633$	2.60603	+	5.58864i	0.103580	+	0.222129i
$634$	13.2630	−	7.65737i	0.526739	−	0.304113i
$635$		0			0
$636$	−4.22990	+	3.54931i	−0.167727	+	0.140739i
$637$	15.6421	+	1.36851i	0.619763	+	0.0542222i
$638$	−12.0120	+	3.21862i	−0.475561	+	0.127426i
$639$	10.0181	+	17.3519i	0.396310	+	0.686430i
$640$		0			0
$641$	8.91860	+	1.57259i	0.352263	+	0.0621135i	0.346980	−	0.937873i	$-0.387207\pi$
$641$	8.91860	+	1.57259i	0.352263	+	0.0621135i	0.00528330	+	0.999986i	$0.498318\pi$
$642$	2.91196	−	4.15871i	0.114926	−	0.164131i
$643$	−19.2214	−	8.96307i	−0.758017	−	0.353469i	0.00488111	−	0.999988i	$-0.498446\pi$
$643$	−19.2214	−	8.96307i	−0.758017	−	0.353469i	−0.762898	+	0.646519i	$0.776224\pi$
$644$	9.46934	−	11.2851i	0.373144	−	0.444696i
$645$		0			0
$646$	8.88976	+	10.4344i	0.349763	+	0.410536i
$647$	−7.11127	+	7.11127i	−0.279573	+	0.279573i	−0.832938	−	0.553366i	$-0.813343\pi$
$647$	−7.11127	+	7.11127i	−0.279573	+	0.279573i	0.553366	+	0.832938i	$0.313343\pi$
$648$	−2.71929	+	0.237907i	−0.106824	+	0.00934588i
$649$	−11.3765	+	4.14070i	−0.446565	+	0.162537i
$650$		0			0
$651$	−1.96220	+	11.1282i	−0.0769046	+	0.436148i
$652$	−0.393514	+	0.183499i	−0.0154112	+	0.00718636i
$653$	7.42215	−	27.6999i	0.290451	−	1.08398i	−0.654312	−	0.756225i	$-0.727042\pi$
$653$	7.42215	−	27.6999i	0.290451	−	1.08398i	0.944763	−	0.327754i	$-0.106292\pi$
$654$	−0.0500065	+	0.0866139i	−0.00195541	+	0.00338687i
$655$		0			0
$656$	−4.06715	−	4.84704i	−0.158796	−	0.189245i
$657$	−9.00641	−	33.6124i	−0.351373	−	1.31134i
$658$	−11.0186	−	2.95243i	−0.429551	−	0.115098i
$659$	−25.6411	−	9.33261i	−0.998837	−	0.363547i	−0.209701	−	0.977766i	$-0.567249\pi$
$659$	−25.6411	−	9.33261i	−0.998837	−	0.363547i	−0.789136	+	0.614219i	$0.789471\pi$
$660$		0			0
$661$	−34.1344	+	6.01881i	−1.32767	+	0.234105i	−0.792104	−	0.610387i	$-0.791014\pi$
$661$	−34.1344	+	6.01881i	−1.32767	+	0.234105i	−0.535569	+	0.844491i	$0.679903\pi$
$662$	9.86848	−	21.1630i	0.383550	−	0.822525i
$663$	0.844107	+	9.64819i	0.0327824	+	0.374705i
$664$	−2.61685			−0.101554
$665$		0			0
$666$	10.0738			0.390352
$667$	−1.70186	−	19.4524i	−0.0658964	−	0.753199i
$668$	4.15746	−	8.91570i	0.160857	−	0.344959i
$669$	−2.74601	+	0.484195i	−0.106167	+	0.0187201i
$670$		0			0
$671$	19.0018	+	6.91608i	0.733555	+	0.266992i
$672$	−1.34619	−	0.360710i	−0.0519303	−	0.0139147i
$673$	6.26245	+	23.3718i	0.241400	+	0.900915i	0.975159	+	0.221506i	$0.0710972\pi$
$673$	6.26245	+	23.3718i	0.241400	+	0.900915i	−0.733759	+	0.679409i	$0.762236\pi$
$674$	−8.22109	−	9.79752i	−0.316665	−	0.377386i
$675$		0			0
$676$	0.268811	−	0.465595i	0.0103389	−	0.0179075i
$677$	6.84243	−	25.5363i	0.262976	−	0.981439i	−0.700502	−	0.713651i	$-0.747040\pi$
$677$	6.84243	−	25.5363i	0.262976	−	0.981439i	0.963478	−	0.267789i	$-0.0862929\pi$
$678$	−14.8907	+	6.94364i	−0.571873	+	0.266669i
$679$	2.44682	−	13.8766i	0.0939003	−	0.532535i
$680$		0			0
$681$	−16.9156	+	6.15678i	−0.648207	+	0.235928i
$682$	−47.4350	+	4.15003i	−1.81638	+	0.158913i
$683$	14.8588	−	14.8588i	0.568555	−	0.568555i	−0.363168	−	0.931724i	$-0.618305\pi$
$683$	14.8588	−	14.8588i	0.568555	−	0.568555i	0.931724	+	0.363168i	$0.118305\pi$
$684$	9.62350	+	1.62253i	0.367964	+	0.0620390i
$685$		0			0
$686$	−11.7556	+	14.0098i	−0.448830	+	0.534895i
$687$	1.20038	+	0.559744i	0.0457972	+	0.0213556i
$688$	4.57446	−	6.53300i	0.174399	−	0.249068i
$689$	−22.0049	−	3.88006i	−0.838319	−	0.147818i
$690$		0			0
$691$	−0.635975	−	1.10154i	−0.0241936	−	0.0419046i	0.853675	−	0.520806i	$-0.174368\pi$
$691$	−0.635975	−	1.10154i	−0.0241936	−	0.0419046i	−0.877869	+	0.478901i	$0.841035\pi$
$692$	1.09590	−	0.293646i	0.0416599	−	0.0111627i
$693$	−20.9259	−	1.83078i	−0.794908	−	0.0695454i
$694$	20.0137	−	16.7935i	0.759710	−	0.637472i
$695$		0			0
$696$	−1.59981	+	0.923652i	−0.0606407	+	0.0350109i
$697$	−8.40936	−	18.0339i	−0.318527	−	0.683084i
$698$	15.2984	+	21.8484i	0.579053	+	0.826973i
$699$	−1.78492	−	10.1228i	−0.0675118	−	0.382878i
$700$		0			0
$701$	−23.6853	−	19.8743i	−0.894581	−	0.750643i	0.0745424	−	0.997218i	$-0.476250\pi$
$701$	−23.6853	−	19.8743i	−0.894581	−	0.750643i	−0.969124	+	0.246575i	$0.920695\pi$
$702$	11.4088	+	11.4088i	0.430596	+	0.430596i
$703$	−18.9815	−	4.93375i	−0.715902	−	0.186080i
$704$		−	5.87278i		−	0.221339i
$705$		0			0
$706$	7.03079	+	19.3169i	0.264607	+	0.727002i
$707$	−0.282208	−	0.197604i	−0.0106135	−	0.00743167i
$708$	−1.47316	+	1.03152i	−0.0553649	+	0.0387669i
$709$	−10.8177	+	29.7215i	−0.406269	+	1.11621i	0.552867	+	0.833269i	$0.313534\pi$
$709$	−10.8177	+	29.7215i	−0.406269	+	1.11621i	−0.959136	+	0.282945i	$0.908689\pi$
$710$		0			0
$711$	14.8231	+	8.55810i	0.555909	+	0.320954i
$712$	−0.956323	+	10.9308i	−0.0358397	+	0.409650i
$713$	6.51638	−	74.4826i	0.244040	−	2.78939i
$714$	−3.79563	−	2.19141i	−0.142048	−	0.0820115i
$715$		0			0
$716$	3.46537	−	9.52102i	0.129507	−	0.355817i
$717$	−3.51033	+	2.45796i	−0.131096	+	0.0917942i
$718$	20.4934	+	14.3496i	0.764806	+	0.535523i
$719$	7.60833	+	20.9037i	0.283743	+	0.779577i	0.996908	+	0.0785810i	$0.0250389\pi$
$719$	7.60833	+	20.9037i	0.283743	+	0.779577i	−0.713165	+	0.700996i	$0.752739\pi$
$720$		0			0
$721$			5.48000i			0.204086i
$722$	−17.3384	−	7.77046i	−0.645268	−	0.289187i
$723$	1.35431	+	1.35431i	0.0503674	+	0.0503674i
$724$	−4.17586	−	3.50396i	−0.155195	−	0.130224i
$725$		0			0
$726$	3.55840	+	20.1807i	0.132064	+	0.748975i
$727$	13.4317	+	19.1825i	0.498156	+	0.711440i	0.986962	−	0.160952i	$-0.0514564\pi$
$727$	13.4317	+	19.1825i	0.498156	+	0.711440i	−0.488806	+	0.872392i	$0.662568\pi$
$728$	−2.38342	−	5.11127i	−0.0883356	−	0.189436i
$729$	5.06611	−	2.92492i	0.187634	−	0.108330i
$730$		0			0
$731$	19.2129	−	16.1216i	0.710617	−	0.596278i
$732$	2.99239	+	0.261800i	0.110602	+	0.00967641i
$733$	−31.7757	+	8.51429i	−1.17366	+	0.314482i	−0.792411	−	0.609988i	$-0.791174\pi$
$733$	−31.7757	+	8.51429i	−1.17366	+	0.314482i	−0.381254	+	0.924471i	$0.624508\pi$
$734$	−17.8516	−	30.9199i	−0.658916	−	1.14128i
$735$		0			0
$736$	9.08136	+	1.60129i	0.334743	+	0.0590243i
$737$	−49.5415	+	70.7526i	−1.82488	+	2.60621i
$738$	−12.8393	−	5.98706i	−0.472621	−	0.220387i
$739$	−5.53195	+	6.59272i	−0.203496	+	0.242517i	−0.858134	−	0.513425i	$-0.828376\pi$
$739$	−5.53195	+	6.59272i	−0.203496	+	0.242517i	0.654638	+	0.755942i	$0.272821\pi$
$740$		0			0
$741$	−6.79910	−	11.5750i	−0.249771	−	0.425217i
$742$	7.14998	−	7.14998i	0.262484	−	0.262484i
$743$	−29.6084	+	2.59040i	−1.08623	+	0.0950326i	−0.616177	−	0.787607i	$-0.711320\pi$
$743$	−29.6084	+	2.59040i	−1.08623	+	0.0950326i	−0.470050	+	0.882640i	$0.655764\pi$
$744$	−6.64670	+	2.41920i	−0.243680	+	0.0886922i
$745$		0			0
$746$	4.58611	−	26.0091i	0.167909	−	0.952261i
$747$	−5.31004	+	2.47611i	−0.194284	+	0.0905961i
$748$	4.78005	−	17.8394i	0.174776	−	0.652272i
$749$	−4.64844	+	8.05134i	−0.169850	+	0.294189i
$750$		0			0
$751$	−9.51283	−	11.3369i	−0.347128	−	0.413691i	0.564026	−	0.825757i	$-0.309252\pi$
$751$	−9.51283	−	11.3369i	−0.347128	−	0.413691i	−0.911154	+	0.412066i	$0.864807\pi$
$752$	−1.84811	−	6.89723i	−0.0673935	−	0.251516i
$753$	5.56267	+	1.49051i	0.202715	+	0.0543173i
$754$	−7.02450	−	2.55671i	−0.255817	−	0.0931098i
$755$		0			0
$756$	−7.19046	+	1.26787i	−0.261515	+	0.0461121i
$757$	−5.64902	+	12.1144i	−0.205317	+	0.440304i	−0.981821	−	0.189808i	$-0.939213\pi$
$757$	−5.64902	+	12.1144i	−0.205317	+	0.440304i	0.776504	+	0.630112i	$0.216991\pi$
$758$	−0.206177	−	2.35661i	−0.00748869	−	0.0855961i
$759$	−47.2446			−1.71487
$760$		0			0
$761$	19.2257			0.696929			0.348465	−	0.937322i	$-0.386703\pi$
$761$	19.2257			0.696929			0.348465	+	0.937322i	$0.386703\pi$
$762$	0.763277	+	8.72430i	0.0276506	+	0.316048i
$763$	0.0774014	−	0.165988i	0.00280212	−	0.00600916i
$764$	−18.5487	+	3.27064i	−0.671070	+	0.118328i
$765$		0			0
$766$	31.2659	+	11.3799i	1.12968	+	0.411171i
$767$	−7.02946	−	1.88354i	−0.253819	−	0.0680106i
$768$	−0.225790	−	0.842661i	−0.00814751	−	0.0304069i
$769$	−4.89090	−	5.82875i	−0.176371	−	0.210190i	0.670616	−	0.741805i	$-0.266030\pi$
$769$	−4.89090	−	5.82875i	−0.176371	−	0.210190i	−0.846986	+	0.531615i	$0.821585\pi$
$770$		0			0
$771$	−5.05208	+	8.75046i	−0.181946	+	0.315140i
$772$	−1.42026	+	5.30047i	−0.0511162	+	0.190768i
$773$	−40.0666	+	18.6833i	−1.44109	+	0.671993i	−0.976891	−	0.213736i	$-0.931437\pi$
$773$	−40.0666	+	18.6833i	−1.44109	+	0.671993i	−0.464203	+	0.885729i	$0.653659\pi$
$774$	3.10071	−	17.5850i	0.111453	−	0.632080i
$775$		0			0
$776$	8.28828	−	3.01669i	0.297532	−	0.108293i
$777$	6.24679	−	0.546523i	0.224102	−	0.0196064i
$778$	16.5563	−	16.5563i	0.593572	−	0.593572i
$779$	21.2602	+	17.5693i	0.761725	+	0.629485i
$780$		0			0
$781$	−33.7819	+	40.2597i	−1.20881	+	1.44061i
$782$	26.2825	+	12.2557i	0.939861	+	0.438265i
$783$	−5.55102	+	7.92768i	−0.198377	+	0.283312i
$784$	−4.38028	−	0.772362i	−0.156439	−	0.0275844i
$785$		0			0
$786$	−2.59737	−	4.49877i	−0.0926450	−	0.160466i
$787$	−1.28166	+	0.343419i	−0.0456862	+	0.0122416i	−0.281590	−	0.959535i	$-0.590862\pi$
$787$	−1.28166	+	0.343419i	−0.0456862	+	0.0122416i	0.235904	+	0.971776i	$0.424195\pi$
$788$	0.106896	+	0.00935218i	0.00380801	+	0.000333158i
$789$	21.1359	−	17.7352i	0.752459	−	0.631388i
$790$		0			0
$791$	26.0563	−	15.0436i	0.926456	−	0.534890i
$792$	−5.55693	−	11.9169i	−0.197457	−	0.423448i
$793$	6.97198	+	9.95702i	0.247582	+	0.353584i
$794$	1.45373	+	8.24453i	0.0515910	+	0.292587i
$795$		0			0
$796$	13.1994	+	11.0756i	0.467841	+	0.392565i
$797$	12.3561	+	12.3561i	0.437676	+	0.437676i	0.891229	−	0.453553i	$-0.149844\pi$
$797$	12.3561	+	12.3561i	0.437676	+	0.437676i	−0.453553	+	0.891229i	$0.649844\pi$
$798$	6.05558	+	0.484042i	0.214365	+	0.0171349i
$799$		−	22.4555i		−	0.794419i
$800$		0			0
$801$	8.40239	+	23.0854i	0.296884	+	0.815682i
$802$	−25.4053	−	17.7890i	−0.897093	−	0.628151i
$803$	74.7689	−	52.3538i	2.63854	−	1.84752i
$804$	−4.38828	+	12.0567i	−0.154763	+	0.425207i
$805$		0			0
$806$	−24.7880	−	14.3114i	−0.873121	−	0.504097i
$807$	1.88523	−	21.5483i	0.0663634	−	0.758537i
$808$	0.0187953	−	0.214831i	0.000661215	−	0.00755772i
$809$	−0.351332	−	0.202842i	−0.0123522	−	0.00713154i	0.493811	−	0.869569i	$-0.335603\pi$
$809$	−0.351332	−	0.202842i	−0.0123522	−	0.00713154i	−0.506163	+	0.862438i	$0.668937\pi$
$810$		0			0
$811$	−5.86165	+	16.1048i	−0.205831	+	0.565515i	−0.999057	−	0.0434117i	$-0.986177\pi$
$811$	−5.86165	+	16.1048i	−0.205831	+	0.565515i	0.793227	+	0.608926i	$0.208400\pi$
$812$	2.77106	−	1.94032i	0.0972452	−	0.0680918i
$813$	19.6462	+	13.7564i	0.689021	+	0.482458i
$814$	9.03745	+	24.8302i	0.316763	+	0.870298i
$815$		0			0
$816$		−	2.74348i		−	0.0960409i
$817$	−14.4549	+	31.6159i	−0.505714	+	1.10610i
$818$	−20.6719	−	20.6719i	−0.722777	−	0.722777i
$819$	−9.67275	−	8.11640i	−0.337993	−	0.283610i
$820$		0			0
$821$	−7.50653	−	42.5717i	−0.261980	−	1.48576i	−0.777499	−	0.628884i	$-0.783512\pi$
$821$	−7.50653	−	42.5717i	−0.261980	−	1.48576i	0.515520	−	0.856878i	$-0.327599\pi$
$822$	0.0692110	+	0.0988436i	0.00241401	+	0.00344757i
$823$	5.37261	+	11.5216i	0.187278	+	0.401618i	0.977420	−	0.211305i	$-0.0677713\pi$
$823$	5.37261	+	11.5216i	0.187278	+	0.401618i	−0.790143	+	0.612923i	$0.789994\pi$
$824$	−2.97070	+	1.71513i	−0.103489	+	0.0597495i
$825$		0			0
$826$	2.52281	−	2.11689i	0.0877798	−	0.0736560i
$827$	−19.0327	−	1.66515i	−0.661833	−	0.0579029i	−0.248710	−	0.968578i	$-0.580006\pi$
$827$	−19.0327	−	1.66515i	−0.661833	−	0.0579029i	−0.413123	+	0.910675i	$0.635562\pi$
$828$	19.9428	−	5.34365i	0.693060	−	0.185705i
$829$	18.6219	+	32.2541i	0.646766	+	1.12023i	0.983891	+	0.178772i	$0.0572124\pi$
$829$	18.6219	+	32.2541i	0.646766	+	1.12023i	−0.337124	+	0.941460i	$0.609454\pi$
$830$		0			0
$831$	−6.22794	−	1.09815i	−0.216045	−	0.0380946i
$832$	2.02484	−	2.89178i	0.0701989	−	0.100254i
$833$	−12.6771	−	5.91141i	−0.439234	−	0.204818i
$834$	10.9096	−	13.0015i	0.377768	−	0.450207i
$835$		0			0
$836$	4.63421	+	25.1759i	0.160278	+	0.870727i
$837$	−26.2029	+	26.2029i	−0.905703	+	0.905703i
$838$	−14.1595	+	1.23880i	−0.489133	+	0.0427936i
$839$	36.8447	−	13.4104i	1.27202	−	0.462978i	0.384235	−	0.923235i	$-0.374465\pi$
$839$	36.8447	−	13.4104i	1.27202	−	0.462978i	0.887785	+	0.460258i	$0.152243\pi$
$840$		0			0
$841$	−4.25717	+	24.1436i	−0.146799	+	0.832539i
$842$	−17.0799	+	7.96448i	−0.588611	+	0.274474i
$843$	5.23143	−	19.5240i	0.180180	−	0.672441i
$844$	3.53420	−	6.12142i	0.121652	−	0.210708i
$845$		0			0
$846$	−10.2764	−	12.2469i	−0.353310	−	0.421059i
$847$	−9.71234	−	36.2470i	−0.333720	−	1.24546i
$848$	6.11380	+	1.63819i	0.209949	+	0.0562556i
$849$	−1.42724	−	0.519474i	−0.0489828	−	0.0178283i
$850$		0			0
$851$	−40.8603	+	7.20477i	−1.40067	+	0.246976i
$852$	−3.29937	+	7.07551i	−0.113034	+	0.242403i
$853$	−3.01705	−	34.4851i	−0.103302	−	1.18075i	−0.854062	−	0.520171i	$-0.825868\pi$
$853$	−3.01705	−	34.4851i	−0.103302	−	1.18075i	0.750760	−	0.660575i	$-0.229687\pi$
$854$	−5.50069			−0.188230
$855$		0			0
$856$	−5.81949			−0.198906
$857$	−3.29342	−	37.6440i	−0.112501	−	1.28589i	−0.817186	−	0.576373i	$-0.804467\pi$
$857$	−3.29342	−	37.6440i	−0.112501	−	1.28589i	0.704685	−	0.709520i	$-0.251088\pi$
$858$	−7.64367	+	16.3919i	−0.260950	+	0.559610i
$859$	28.5980	−	5.04259i	0.975750	−	0.172051i	0.337033	−	0.941493i	$-0.390577\pi$
$859$	28.5980	−	5.04259i	0.975750	−	0.172051i	0.638717	+	0.769442i	$0.279465\pi$
$860$		0			0
$861$	−8.28649	−	3.01603i	−0.282403	−	0.102786i
$862$	−14.9805	−	4.01402i	−0.510239	−	0.136718i
$863$	−5.31886	−	19.8503i	−0.181056	−	0.675710i	−0.995440	−	0.0953846i	$-0.969592\pi$
$863$	−5.31886	−	19.8503i	−0.181056	−	0.675710i	0.814384	−	0.580326i	$-0.197075\pi$
$864$	−2.93779	−	3.50112i	−0.0999455	−	0.119110i
$865$		0			0
$866$	8.77112	−	15.1920i	0.298055	−	0.516246i
$867$	−1.60543	+	5.99156i	−0.0545234	+	0.203484i
$868$	11.7392	−	5.47409i	0.398455	−	0.185803i
$869$	−7.79613	+	44.2140i	−0.264466	+	1.49986i
$870$		0			0
$871$	−48.7888	+	17.7577i	−1.65315	+	0.601696i
$872$	0.114207	−	0.00999180i	0.00386753	−	0.000338365i
$873$	13.9639	−	13.9639i	0.472606	−	0.472606i
$874$	−40.1943	+	0.301573i	−1.35959	+	0.0102009i
$875$		0			0
$876$	8.71544	−	10.3867i	0.294467	−	0.350933i
$877$	−33.1320	−	15.4497i	−1.11879	−	0.521699i	−0.226883	−	0.973922i	$-0.572853\pi$
$877$	−33.1320	−	15.4497i	−1.11879	−	0.521699i	−0.891905	+	0.452223i	$0.850631\pi$
$878$	0.873514	−	1.24751i	0.0294797	−	0.0421013i
$879$	20.4483	+	3.60559i	0.689705	+	0.121614i
$880$		0			0
$881$	−10.6439	−	18.4358i	−0.358602	−	0.621117i	0.629126	−	0.777304i	$-0.283413\pi$
$881$	−10.6439	−	18.4358i	−0.358602	−	0.621117i	−0.987728	+	0.156187i	$0.950080\pi$
$882$	−9.61916	+	2.57745i	−0.323894	+	0.0867871i
$883$	−33.8438	−	2.96095i	−1.13893	−	0.0996438i	−0.497955	−	0.867203i	$-0.665916\pi$
$883$	−33.8438	−	2.96095i	−1.13893	−	0.0996438i	−0.640979	+	0.767559i	$0.721471\pi$
$884$	8.50445	−	7.13608i	0.286036	−	0.240012i
$885$		0			0
$886$	−9.08547	+	5.24550i	−0.305232	+	0.176226i
$887$	−8.63817	−	18.5246i	−0.290042	−	0.621996i	0.706257	−	0.707955i	$-0.250382\pi$
$887$	−8.63817	−	18.5246i	−0.290042	−	0.621996i	−0.996299	+	0.0859594i	$0.972604\pi$
$888$	2.25139	+	3.21532i	0.0755518	+	0.107899i
$889$	−2.78484	−	15.7936i	−0.0934005	−	0.529700i
$890$		0			0
$891$	−12.2803	−	10.3044i	−0.411406	−	0.345211i
$892$	2.26009	+	2.26009i	0.0756735	+	0.0756735i
$893$	13.3652	+	28.1092i	0.447250	+	0.940640i
$894$		−	14.4841i		−	0.484420i
$895$		0			0
$896$	0.546392	+	1.50120i	0.0182537	+	0.0501516i
$897$	−23.2634	−	16.2892i	−0.776743	−	0.543881i
$898$	12.5827	−	8.81053i	0.419892	−	0.294011i
$899$	5.87208	−	16.1334i	0.195845	−	0.538079i
$900$		0			0
$901$	17.2381	+	9.95243i	0.574285	+	0.331564i
$902$	3.23864	−	37.0178i	0.107835	−	1.23256i
$903$	0.968737	−	11.0727i	0.0322376	−	0.368477i
$904$	16.3102	+	9.41672i	0.542470	+	0.313195i
$905$		0			0
$906$	1.70886	−	4.69506i	0.0567732	−	0.155983i
$907$	−38.9548	+	27.2764i	−1.29347	+	0.905699i	−0.998755	−	0.0498853i	$-0.984114\pi$
$907$	−38.9548	+	27.2764i	−1.29347	+	0.905699i	−0.294717	+	0.955584i	$0.595226\pi$
$908$	16.9027	+	11.8354i	0.560937	+	0.392772i
$909$	−0.165138	−	0.453713i	−0.00547728	−	0.0150487i
$910$		0			0
$911$		−	20.9070i		−	0.692679i	−0.938109	−	0.346339i	$-0.887425\pi$
$911$		−	20.9070i		−	0.692679i	0.938109	−	0.346339i	$-0.112575\pi$
$912$	1.63288	+	3.43421i	0.0540700	+	0.113718i
$913$	−10.8670	−	10.8670i	−0.359644	−	0.359644i
$914$	−23.9303	−	20.0799i	−0.791545	−	0.664185i
$915$		0			0
$916$	−0.263635	−	1.49515i	−0.00871073	−	0.0494010i
$917$	5.45630	+	7.79240i	0.180183	+	0.257328i
$918$	−6.07425	−	13.0263i	−0.200480	−	0.429931i
$919$	−5.76753	+	3.32988i	−0.190253	+	0.109843i	−0.592101	−	0.805864i	$-0.701701\pi$
$919$	−5.76753	+	3.32988i	−0.190253	+	0.109843i	0.401848	+	0.915706i	$0.368368\pi$
$920$		0			0
$921$	−11.2319	+	9.42470i	−0.370104	+	0.310554i
$922$	4.65399	+	0.407171i	0.153271	+	0.0134095i
$923$	−30.5153	+	8.17654i	−1.00442	+	0.269134i
$924$	−4.09238	−	7.08821i	−0.134629	−	0.233185i
$925$		0			0
$926$	−2.99488	−	0.528079i	−0.0984180	−	0.0173538i
$927$	−4.40516	+	6.29123i	−0.144685	+	0.206631i
$928$	1.91913	+	0.894906i	0.0629986	+	0.0293767i
$929$	−20.5474	+	24.4875i	−0.674140	+	0.803408i	−0.989341	−	0.145616i	$-0.953483\pi$
$929$	−20.5474	+	24.4875i	−0.674140	+	0.803408i	0.315202	+	0.949025i	$0.397928\pi$
$930$		0			0
$931$	19.3872	−	0.145460i	0.635390	−	0.00476726i
$932$	−8.33151	+	8.33151i	−0.272908	+	0.272908i
$933$	4.68511	−	0.409894i	0.153384	−	0.0134193i
$934$	32.0160	−	11.6529i	1.04759	−	0.381293i
$935$		0			0
$936$	1.37250	−	7.78385i	0.0448617	−	0.254423i
$937$	37.0145	−	17.2601i	1.20921	−	0.563864i	0.289771	−	0.957096i	$-0.406421\pi$
$937$	37.0145	−	17.2601i	1.20921	−	0.563864i	0.919439	+	0.393232i	$0.128643\pi$
$938$	6.08111	−	22.6950i	0.198555	−	0.741018i
$939$	−11.6770	+	20.2252i	−0.381066	+	0.660026i
$940$		0			0
$941$	32.5431	+	38.7834i	1.06088	+	1.26430i	0.963114	+	0.269093i	$0.0867238\pi$
$941$	32.5431	+	38.7834i	1.06088	+	1.26430i	0.0977614	+	0.995210i	$0.468832\pi$
$942$	0.317419	+	1.18462i	0.0103421	+	0.0385972i
$943$	56.3594	+	15.1014i	1.83531	+	0.491771i
$944$	1.93715	+	0.705065i	0.0630489	+	0.0229479i
$945$		0			0
$946$	46.1258	−	8.13321i	1.49968	−	0.264434i
$947$	12.2732	−	26.3201i	0.398827	−	0.855287i	−0.599658	−	0.800256i	$-0.704697\pi$
$947$	12.2732	−	26.3201i	0.398827	−	0.855287i	0.998485	−	0.0550304i	$-0.0175256\pi$
$948$	0.581260	+	6.64383i	0.0188784	+	0.215781i
$949$	54.8672			1.78107
$950$		0			0
$951$	13.3604			0.433240
$952$	0.437865	+	5.00482i	0.0141913	+	0.162207i
$953$	−8.27657	+	17.7492i	−0.268105	+	0.574952i	−0.993559	−	0.113318i	$-0.963852\pi$
$953$	−8.27657	+	17.7492i	−0.268105	+	0.574952i	0.725454	+	0.688270i	$0.241630\pi$
$954$	13.9560	−	2.46082i	0.451843	−	0.0796720i
$955$		0			0
$956$	4.61594	+	1.68006i	0.149290	+	0.0543372i
$957$	−10.4791	−	2.80788i	−0.338743	−	0.0907658i
$958$	−1.36224	−	5.08395i	−0.0440120	−	0.164255i
$959$	−0.142035	−	0.169271i	−0.00458655	−	0.00546603i
$960$		0			0
$961$	17.3694	−	30.0847i	0.560304	−	0.970474i
$962$	−4.11100	+	15.3425i	−0.132544	+	0.494661i
$963$	−11.8087	+	5.50650i	−0.380531	+	0.177444i
$964$	0.381237	−	2.16210i	0.0122788	−	0.0696366i
$965$		0			0
$966$	12.0767	−	4.39555i	0.388560	−	0.141424i
$967$	−40.3701	+	3.53192i	−1.29821	+	0.113579i	−0.715221	−	0.698898i	$-0.753674\pi$
$967$	−40.3701	+	3.53192i	−1.29821	+	0.113579i	−0.582993	+	0.812477i	$0.698119\pi$
$968$	16.6096	−	16.6096i	0.533854	−	0.533854i
$969$	2.16488	+	11.7609i	0.0695459	+	0.377816i
$970$		0			0
$971$	−0.0689715	+	0.0821970i	−0.00221340	+	0.00263783i	−0.767150	−	0.641468i	$-0.778326\pi$
$971$	−0.0689715	+	0.0821970i	−0.00221340	+	0.00263783i	0.764937	+	0.644106i	$0.222770\pi$
$972$	−14.5847	−	6.80098i	−0.467806	−	0.218142i
$973$	−17.8269	+	25.4594i	−0.571504	+	0.816192i
$974$	11.2699	+	1.98718i	0.361110	+	0.0636734i
$975$		0			0
$976$	−1.72161	−	2.98191i	−0.0551074	−	0.0954487i
$977$	−36.2839	+	9.72224i	−1.16083	+	0.311042i	−0.787295	−	0.616576i	$-0.788519\pi$
$977$	−36.2839	+	9.72224i	−1.16083	+	0.311042i	−0.373530	+	0.927618i	$0.621853\pi$
$978$	−0.377345	−	0.0330134i	−0.0120661	−	0.00105565i
$979$	−49.3635	+	41.4209i	−1.57767	+	1.32382i
$980$		0			0
$981$	0.222290	−	0.128339i	0.00709719	−	0.00409756i
$982$	5.21215	+	11.1775i	0.166326	+	0.356688i
$983$	15.8557	+	22.6442i	0.505717	+	0.722238i	0.988115	−	0.153713i	$-0.0491232\pi$
$983$	15.8557	+	22.6442i	0.505717	+	0.722238i	−0.482399	+	0.875952i	$0.660234\pi$
$984$	−0.958522	−	5.43605i	−0.0305566	−	0.173295i
$985$		0			0
$986$	5.10123	+	4.28044i	0.162456	+	0.136317i
$987$	−7.03684	−	7.03684i	−0.223985	−	0.223985i
$988$	−6.39836	+	13.9945i	−0.203559	+	0.445225i
$989$			73.5441i			2.33857i
$990$		0			0
$991$	−13.8824	−	38.1416i	−0.440990	−	1.21161i	−0.938842	−	0.344348i	$-0.888100\pi$
$991$	−13.8824	−	38.1416i	−0.440990	−	1.21161i	0.497853	−	0.867262i	$-0.334122\pi$
$992$	6.64164	+	4.65053i	0.210872	+	0.147654i
$993$	16.6869	−	11.6843i	0.529543	−	0.370790i
$994$	4.88965	−	13.4342i	0.155090	−	0.426107i
$995$		0			0
$996$	−1.97706	−	1.14145i	−0.0626454	−	0.0361683i
$997$	2.42815	−	27.7539i	0.0769003	−	0.878975i	−0.855560	−	0.517703i	$-0.826787\pi$
$997$	2.42815	−	27.7539i	0.0769003	−	0.878975i	0.932461	−	0.361272i	$-0.117657\pi$
$998$	1.12538	−	12.8632i	0.0356233	−	0.407177i
$999$	17.8088	+	10.2819i	0.563444	+	0.325305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.d.193.3	✓	96
5.2	odd	4	inner	950.2.bb.d.307.6	yes	96
5.3	odd	4	inner	950.2.bb.d.307.3	yes	96
5.4	even	2	inner	950.2.bb.d.193.6	yes	96
19.13	odd	18	inner	950.2.bb.d.393.6	yes	96
95.13	even	36	inner	950.2.bb.d.507.6	yes	96
95.32	even	36	inner	950.2.bb.d.507.3	yes	96
95.89	odd	18	inner	950.2.bb.d.393.3	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.d.193.3	✓	96	1.1	even	1	trivial
950.2.bb.d.193.6	yes	96	5.4	even	2	inner
950.2.bb.d.307.3	yes	96	5.3	odd	4	inner
950.2.bb.d.307.6	yes	96	5.2	odd	4	inner
950.2.bb.d.393.3	yes	96	95.89	odd	18	inner
950.2.bb.d.393.6	yes	96	19.13	odd	18	inner
950.2.bb.d.507.3	yes	96	95.32	even	36	inner
950.2.bb.d.507.6	yes	96	95.13	even	36	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(0.368687 - 0.790651i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-0.819776 - 0.298374i) q^{6} +(1.54311 + 0.413475i) q^{7} +(0.258819 + 0.965926i) q^{8} +(1.43916 + 1.71513i) q^{9} +O(q^{10})\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(0.368687 - 0.790651i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-0.819776 - 0.298374i) q^{6} +(1.54311 + 0.413475i) q^{7} +(0.258819 + 0.965926i) q^{8} +(1.43916 + 1.71513i) q^{9} +(-2.93639 + 5.08598i) q^{11} +(-0.225790 + 0.842661i) q^{12} +(-3.19946 + 1.49193i) q^{13} +(0.277411 - 1.57327i) q^{14} +(0.939693 - 0.342020i) q^{16} +(3.13283 - 0.274087i) q^{17} +(1.58317 - 1.58317i) q^{18} +(-3.75846 + 2.20771i) q^{19} +(0.895838 - 1.06762i) q^{21} +(5.32255 + 2.48194i) q^{22} +(-5.28921 + 7.55377i) q^{23} +(0.859133 + 0.151488i) q^{24} +(1.76510 + 3.05725i) q^{26} +(4.41465 - 1.18290i) q^{27} +(-1.59146 - 0.139235i) q^{28} +(-1.62212 + 1.36112i) q^{29} +(-7.02169 + 4.05397i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(2.93863 + 4.19679i) q^{33} +(-0.546087 - 3.09702i) q^{34} +(-1.71513 - 1.43916i) q^{36} +(3.18153 + 3.18153i) q^{37} +(2.52688 + 3.55174i) q^{38} +3.07971i q^{39} +(-2.16409 - 5.94578i) q^{41} +(-1.14163 - 0.799380i) q^{42} +(6.53300 - 4.57446i) q^{43} +(2.00861 - 5.51861i) q^{44} +(7.98601 + 4.61073i) q^{46} +(0.622339 - 7.11337i) q^{47} +(0.0760335 - 0.869067i) q^{48} +(-3.85196 - 2.22393i) q^{49} +(0.938324 - 2.57802i) q^{51} +(2.89178 - 2.02484i) q^{52} +(5.18480 + 3.63043i) q^{53} +(-1.56316 - 4.29476i) q^{54} +1.59754i q^{56} +(0.359835 + 3.78558i) q^{57} +(1.49732 + 1.49732i) q^{58} +(1.57918 + 1.32509i) q^{59} +(-0.597908 - 3.39091i) q^{61} +(4.65053 + 6.64164i) q^{62} +(1.51162 + 3.24169i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(3.92470 - 3.29322i) q^{66} +(14.6514 + 1.28183i) q^{67} +(-3.03764 + 0.813932i) q^{68} +(4.02234 + 6.96689i) q^{69} +(8.81302 + 1.55397i) q^{71} +(-1.28420 + 1.83403i) q^{72} +(-14.0860 - 6.56842i) q^{73} +(2.89213 - 3.44671i) q^{74} +(3.31799 - 2.82682i) q^{76} +(-6.63409 + 6.63409i) q^{77} +(3.06799 - 0.268414i) q^{78} +(7.18374 - 2.61467i) q^{79} +(-0.474004 + 2.68821i) q^{81} +(-5.73454 + 2.67406i) q^{82} +(-0.677291 + 2.52768i) q^{83} +(-0.696838 + 1.20696i) q^{84} +(-5.12644 - 6.10945i) q^{86} +(0.478117 + 1.78436i) q^{87} +(-5.67267 - 1.51999i) q^{88} +(10.3108 + 3.75284i) q^{89} +(-5.55398 + 0.979317i) q^{91} +(3.89716 - 8.35748i) q^{92} +(0.616476 + 7.04635i) q^{93} -7.14054 q^{94} -0.872387 q^{96} +(-0.768732 - 8.78664i) q^{97} +(-1.87974 + 4.03113i) q^{98} +(-12.9491 + 2.28327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{6}+O(q^{10}) \) 96 * q - 12 * q^6	\( 96 q - 12 q^{6} + 12 q^{26} - 72 q^{31} + 12 q^{36} - 24 q^{41} + 12 q^{51} - 72 q^{61} - 36 q^{66} + 168 q^{71} - 12 q^{76} + 12 q^{81} - 48 q^{86} - 72 q^{91}+O(q^{100}) \) 96 * q - 12 * q^6 + 12 * q^26 - 72 * q^31 + 12 * q^36 - 24 * q^41 + 12 * q^51 - 72 * q^61 - 36 * q^66 + 168 * q^71 - 12 * q^76 + 12 * q^81 - 48 * q^86 - 72 * q^91

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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