LMFDB - Embedded newform 525.2.bc.e.157.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(82,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("525.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.2
Character	$\chi$	$=$	525.157
Dual form			525.2.bc.e.418.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.602389 + 2.24814i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-2.95923 - 1.70851i) q^{4} -2.32745i q^{6} +(-0.519864 + 2.59417i) q^{7} +(2.33208 - 2.33208i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.602389 + 2.24814i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-2.95923 - 1.70851i) q^{4} -2.32745i q^{6} +(-0.519864 + 2.59417i) q^{7} +(2.33208 - 2.33208i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-1.76389 + 3.05515i) q^{11} +(3.30060 + 0.884392i) q^{12} +(-4.49057 - 4.49057i) q^{13} +(-5.51892 - 2.73143i) q^{14} +(0.421011 + 0.729213i) q^{16} +(-0.481759 - 1.79795i) q^{17} +(0.602389 + 2.24814i) q^{18} +(-0.0699116 - 0.121090i) q^{19} +(-0.169272 - 2.64033i) q^{21} +(-5.80587 - 5.80587i) q^{22} +(3.72112 + 0.997072i) q^{23} +(-1.64903 + 2.85621i) q^{24} +(12.8005 - 7.39038i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(5.97058 - 6.78857i) q^{28} -2.01969i q^{29} +(-4.56612 - 2.63625i) q^{31} +(4.47838 - 1.19998i) q^{32} +(0.913058 - 3.40758i) q^{33} +4.33225 q^{34} -3.41703 q^{36} +(1.50406 - 5.61323i) q^{37} +(0.314343 - 0.0842279i) q^{38} +(5.49980 + 3.17531i) q^{39} +0.903323i q^{41} +(6.03781 + 1.20996i) q^{42} +(-2.38469 + 2.38469i) q^{43} +(10.4395 - 6.02727i) q^{44} +(-4.48312 + 7.76500i) q^{46} +(2.38655 + 0.639474i) q^{47} +(-0.595400 - 0.595400i) q^{48} +(-6.45948 - 2.69723i) q^{49} +(0.930686 + 1.61200i) q^{51} +(5.61644 + 20.9608i) q^{52} +(0.726718 + 2.71215i) q^{53} +(-1.16373 - 2.01563i) q^{54} +(4.83746 + 7.26219i) q^{56} +(0.0988699 + 0.0988699i) q^{57} +(4.54056 + 1.21664i) q^{58} +(3.15338 - 5.46181i) q^{59} +(-8.69243 + 5.01858i) q^{61} +(8.67726 - 8.67726i) q^{62} +(0.846872 + 2.50655i) q^{63} +12.4749i q^{64} +(7.11071 + 4.10537i) q^{66} +(-10.3615 + 2.77634i) q^{67} +(-1.64618 + 6.14364i) q^{68} -3.85239 q^{69} -5.09892 q^{71} +(0.853601 - 3.18568i) q^{72} +(-9.04441 + 2.42344i) q^{73} +(11.7133 + 6.76269i) q^{74} +0.477780i q^{76} +(-7.00861 - 6.16411i) q^{77} +(-10.4516 + 10.4516i) q^{78} +(7.30150 - 4.21552i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-2.03080 - 0.544151i) q^{82} +(-7.37852 - 7.37852i) q^{83} +(-4.01013 + 8.10256i) q^{84} +(-3.92463 - 6.79765i) q^{86} +(0.522735 + 1.95087i) q^{87} +(3.01132 + 11.2384i) q^{88} +(1.75399 + 3.03799i) q^{89} +(13.9838 - 9.31484i) q^{91} +(-9.30816 - 9.30816i) q^{92} +(5.09285 + 1.36462i) q^{93} +(-2.87526 + 4.98010i) q^{94} +(-4.01520 + 2.31818i) q^{96} +(8.70237 - 8.70237i) q^{97} +(9.95489 - 12.8971i) q^{98} +3.52778i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{7} + 24 q^{8}+O(q^{10}) $ 32 * q - 8 * q^7 + 24 * q^8	$ 32 q - 8 q^{7} + 24 q^{8} - 8 q^{11} - 8 q^{21} + 8 q^{22} + 8 q^{23} + 24 q^{26} + 24 q^{28} + 24 q^{31} - 24 q^{32} + 36 q^{33} - 32 q^{36} - 4 q^{37} - 12 q^{38} - 16 q^{42} - 40 q^{43} - 40 q^{46} + 60 q^{47} - 8 q^{51} + 108 q^{52} + 24 q^{53} - 48 q^{56} - 16 q^{57} - 4 q^{58} - 24 q^{61} - 4 q^{63} + 72 q^{66} - 8 q^{67} - 132 q^{68} - 16 q^{71} - 12 q^{72} - 36 q^{73} - 60 q^{77} - 80 q^{78} + 16 q^{81} - 12 q^{82} - 16 q^{86} + 24 q^{87} + 32 q^{88} - 24 q^{91} + 56 q^{92} + 24 q^{93} + 72 q^{98}+O(q^{100}) $ 32 * q - 8 * q^7 + 24 * q^8 - 8 * q^11 - 8 * q^21 + 8 * q^22 + 8 * q^23 + 24 * q^26 + 24 * q^28 + 24 * q^31 - 24 * q^32 + 36 * q^33 - 32 * q^36 - 4 * q^37 - 12 * q^38 - 16 * q^42 - 40 * q^43 - 40 * q^46 + 60 * q^47 - 8 * q^51 + 108 * q^52 + 24 * q^53 - 48 * q^56 - 16 * q^57 - 4 * q^58 - 24 * q^61 - 4 * q^63 + 72 * q^66 - 8 * q^67 - 132 * q^68 - 16 * q^71 - 12 * q^72 - 36 * q^73 - 60 * q^77 - 80 * q^78 + 16 * q^81 - 12 * q^82 - 16 * q^86 + 24 * q^87 + 32 * q^88 - 24 * q^91 + 56 * q^92 + 24 * q^93 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.602389	+	2.24814i	−0.425953	+	1.58968i	0.335880	+	0.941905i	$0.390966\pi$
$2$	−0.602389	+	2.24814i	−0.425953	+	1.58968i	−0.761833	+	0.647774i	$0.775700\pi$
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	−2.95923	−	1.70851i	−1.47962	−	0.854257i
$5$		0			0
$5$		0			0
$6$		−	2.32745i		−	0.950178i
$7$	−0.519864	+	2.59417i	−0.196490	+	0.980506i
$7$	−0.519864	+	2.59417i	−0.196490	+	0.980506i
$8$	2.33208	−	2.33208i	0.824516	−	0.824516i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	−1.76389	+	3.05515i	−0.531834	+	0.921163i	0.467476	+	0.884006i	$0.345163\pi$
$11$	−1.76389	+	3.05515i	−0.531834	+	0.921163i	−0.999309	+	0.0371569i	$0.988170\pi$
$12$	3.30060	+	0.884392i	0.952800	+	0.255302i
$13$	−4.49057	−	4.49057i	−1.24546	−	1.24546i	−0.957704	−	0.287756i	$-0.907091\pi$
$13$	−4.49057	−	4.49057i	−1.24546	−	1.24546i	−0.287756	−	0.957704i	$-0.592909\pi$
$14$	−5.51892	−	2.73143i	−1.47499	−	0.730005i
$15$		0			0
$16$	0.421011	+	0.729213i	0.105253	+	0.182303i
$17$	−0.481759	−	1.79795i	−0.116844	−	0.436066i	0.882575	−	0.470172i	$-0.155808\pi$
$17$	−0.481759	−	1.79795i	−0.116844	−	0.436066i	−0.999418	+	0.0341060i	$0.989142\pi$
$18$	0.602389	+	2.24814i	0.141984	+	0.529893i
$19$	−0.0699116	−	0.121090i	−0.0160388	−	0.0277800i	0.857895	−	0.513826i	$-0.171772\pi$
$19$	−0.0699116	−	0.121090i	−0.0160388	−	0.0277800i	−0.873933	+	0.486046i	$0.838439\pi$
$20$		0			0
$21$	−0.169272	−	2.64033i	−0.0369382	−	0.576167i
$22$	−5.80587	−	5.80587i	−1.23782	−	1.23782i
$23$	3.72112	+	0.997072i	0.775908	+	0.207904i	0.624980	−	0.780641i	$-0.285107\pi$
$23$	3.72112	+	0.997072i	0.775908	+	0.207904i	0.150928	+	0.988545i	$0.451774\pi$
$24$	−1.64903	+	2.85621i	−0.336607	+	0.583021i
$25$		0			0
$26$	12.8005	−	7.39038i	2.51039	−	1.44937i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	5.97058	−	6.78857i	1.12833	−	1.28292i
$29$		−	2.01969i		−	0.375047i	−0.982260	−	0.187524i	$-0.939954\pi$
$29$		−	2.01969i		−	0.375047i	0.982260	−	0.187524i	$-0.0600462\pi$
$30$		0			0
$31$	−4.56612	−	2.63625i	−0.820100	−	0.473485i	0.0303510	−	0.999539i	$-0.490337\pi$
$31$	−4.56612	−	2.63625i	−0.820100	−	0.473485i	−0.850451	+	0.526054i	$0.823671\pi$
$32$	4.47838	−	1.19998i	0.791673	−	0.212128i
$33$	0.913058	−	3.40758i	0.158943	−	0.593183i
$34$	4.33225			0.742975
$35$		0			0
$36$	−3.41703			−0.569505
$37$	1.50406	−	5.61323i	0.247266	−	0.922810i	−0.724965	−	0.688786i	$-0.758144\pi$
$37$	1.50406	−	5.61323i	0.247266	−	0.922810i	0.972231	−	0.234024i	$-0.0751893\pi$
$38$	0.314343	−	0.0842279i	0.0509931	−	0.0136636i
$39$	5.49980	+	3.17531i	0.880673	+	0.508457i
$40$		0			0
$41$			0.903323i			0.141075i	0.997509	+	0.0705377i	$0.0224715\pi$
$41$			0.903323i			0.141075i	−0.997509	+	0.0705377i	$0.977529\pi$
$42$	6.03781	+	1.20996i	0.931655	+	0.186700i
$43$	−2.38469	+	2.38469i	−0.363663	+	0.363663i	−0.865159	−	0.501497i	$-0.832783\pi$
$43$	−2.38469	+	2.38469i	−0.363663	+	0.363663i	0.501497	+	0.865159i	$0.332783\pi$
$44$	10.4395	−	6.02727i	1.57382	−	0.908645i
$45$		0			0
$46$	−4.48312	+	7.76500i	−0.661001	+	1.14489i
$47$	2.38655	+	0.639474i	0.348114	+	0.0932768i	0.428639	−	0.903476i	$-0.358993\pi$
$47$	2.38655	+	0.639474i	0.348114	+	0.0932768i	−0.0805254	+	0.996753i	$0.525660\pi$
$48$	−0.595400	−	0.595400i	−0.0859386	−	0.0859386i
$49$	−6.45948	−	2.69723i	−0.922783	−	0.385319i
$50$		0			0
$51$	0.930686	+	1.61200i	0.130322	+	0.225725i
$52$	5.61644	+	20.9608i	0.778860	+	2.90675i
$53$	0.726718	+	2.71215i	0.0998224	+	0.372542i	0.997706	−	0.0676898i	$-0.0215628\pi$
$53$	0.726718	+	2.71215i	0.0998224	+	0.372542i	−0.897884	+	0.440232i	$0.854896\pi$
$54$	−1.16373	−	2.01563i	−0.158363	−	0.274293i
$55$		0			0
$56$	4.83746	+	7.26219i	0.646433	+	0.970451i
$57$	0.0988699	+	0.0988699i	0.0130956	+	0.0130956i
$58$	4.54056	+	1.21664i	0.596205	+	0.159753i
$59$	3.15338	−	5.46181i	0.410535	−	0.711067i	−0.584414	−	0.811456i	$-0.698675\pi$
$59$	3.15338	−	5.46181i	0.410535	−	0.711067i	0.994948	+	0.100389i	$0.0320087\pi$
$60$		0			0
$61$	−8.69243	+	5.01858i	−1.11295	+	0.642563i	−0.939592	−	0.342296i	$-0.888795\pi$
$61$	−8.69243	+	5.01858i	−1.11295	+	0.642563i	−0.173359	+	0.984859i	$0.555462\pi$
$62$	8.67726	−	8.67726i	1.10201	−	1.10201i
$63$	0.846872	+	2.50655i	0.106696	+	0.315796i
$64$			12.4749i			1.55937i
$65$		0			0
$66$	7.11071	+	4.10537i	0.875268	+	0.505336i
$67$	−10.3615	+	2.77634i	−1.26585	+	0.339184i	−0.828441	−	0.560077i	$-0.810772\pi$
$67$	−10.3615	+	2.77634i	−1.26585	+	0.339184i	−0.437412	+	0.899261i	$0.644105\pi$
$68$	−1.64618	+	6.14364i	−0.199629	+	0.745025i
$69$	−3.85239			−0.463773
$70$		0			0
$71$	−5.09892			−0.605130			−0.302565	−	0.953129i	$-0.597843\pi$
$71$	−5.09892			−0.605130			−0.302565	+	0.953129i	$0.597843\pi$
$72$	0.853601	−	3.18568i	0.100598	−	0.375436i
$73$	−9.04441	+	2.42344i	−1.05857	+	0.283643i	−0.745788	−	0.666183i	$-0.767927\pi$
$73$	−9.04441	+	2.42344i	−1.05857	+	0.283643i	−0.312780	+	0.949826i	$0.601260\pi$
$74$	11.7133	+	6.76269i	1.36165	+	0.786147i
$75$		0			0
$76$			0.477780i			0.0548051i
$77$	−7.00861	−	6.16411i	−0.798705	−	0.702465i
$78$	−10.4516	+	10.4516i	−1.18341	+	1.18341i
$79$	7.30150	−	4.21552i	0.821483	−	0.474284i	−0.0294445	−	0.999566i	$-0.509374\pi$
$79$	7.30150	−	4.21552i	0.821483	−	0.474284i	0.850928	+	0.525283i	$0.176040\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−2.03080	−	0.544151i	−0.224264	−	0.0600915i
$83$	−7.37852	−	7.37852i	−0.809898	−	0.809898i	0.174720	−	0.984618i	$-0.444098\pi$
$83$	−7.37852	−	7.37852i	−0.809898	−	0.809898i	−0.984618	+	0.174720i	$0.944098\pi$
$84$	−4.01013	+	8.10256i	−0.437541	+	0.884061i
$85$		0			0
$86$	−3.92463	−	6.79765i	−0.423203	−	0.733010i
$87$	0.522735	+	1.95087i	0.0560431	+	0.209156i
$88$	3.01132	+	11.2384i	0.321008	+	1.19802i
$89$	1.75399	+	3.03799i	0.185922	+	0.322027i	0.943887	−	0.330269i	$-0.107139\pi$
$89$	1.75399	+	3.03799i	0.185922	+	0.322027i	−0.757965	+	0.652296i	$0.773806\pi$
$90$		0			0
$91$	13.9838	−	9.31484i	1.46590	−	0.976460i
$92$	−9.30816	−	9.30816i	−0.970443	−	0.970443i
$93$	5.09285	+	1.36462i	0.528104	+	0.141505i
$94$	−2.87526	+	4.98010i	−0.296560	+	0.513658i
$95$		0			0
$96$	−4.01520	+	2.31818i	−0.409800	+	0.236598i
$97$	8.70237	−	8.70237i	0.883592	−	0.883592i	−0.110306	−	0.993898i	$-0.535183\pi$
$97$	8.70237	−	8.70237i	0.883592	−	0.883592i	0.993898	+	0.110306i	$0.0351831\pi$
$98$	9.95489	−	12.8971i	1.00560	−	1.30280i
$99$			3.52778i			0.354556i
$100$		0			0
$101$	−1.24483	−	0.718705i	−0.123866	−	0.0715138i	0.436787	−	0.899565i	$-0.356116\pi$
$101$	−1.24483	−	0.718705i	−0.123866	−	0.0715138i	−0.560653	+	0.828051i	$0.689450\pi$
$102$	−4.18463	+	1.12127i	−0.414341	+	0.111022i
$103$	1.60502	−	5.99000i	0.158147	−	0.590212i	−0.840668	−	0.541550i	$-0.817838\pi$
$103$	1.60502	−	5.99000i	0.158147	−	0.590212i	0.998815	−	0.0486620i	$-0.0154957\pi$
$104$	−20.9448			−2.05380
$105$		0			0
$106$	−6.53507			−0.634742
$107$	−4.64750	+	17.3447i	−0.449291	+	1.67678i	0.255061	+	0.966925i	$0.417905\pi$
$107$	−4.64750	+	17.3447i	−0.449291	+	1.67678i	−0.704352	+	0.709851i	$0.748762\pi$
$108$	3.30060	−	0.884392i	0.317600	−	0.0851006i
$109$	−11.0263	−	6.36604i	−1.05613	−	0.609756i	−0.131770	−	0.991280i	$-0.542066\pi$
$109$	−11.0263	−	6.36604i	−1.05613	−	0.609756i	−0.924359	+	0.381524i	$0.875399\pi$
$110$		0			0
$111$			5.81124i			0.551579i
$112$	−2.11057	+	0.713086i	−0.199431	+	0.0673803i
$113$	−11.1631	+	11.1631i	−1.05013	+	1.05013i	−0.0514580	+	0.998675i	$0.516387\pi$
$113$	−11.1631	+	11.1631i	−1.05013	+	1.05013i	−0.998675	+	0.0514580i	$0.983613\pi$
$114$	−0.281832	+	0.162716i	−0.0263960	+	0.0152397i
$115$		0			0
$116$	−3.45067	+	5.97674i	−0.320387	+	0.554926i
$117$	−6.13423	−	1.64366i	−0.567110	−	0.151957i
$118$	10.3794	+	10.3794i	0.955499	+	0.955499i
$119$	4.91464	−	0.315078i	0.450524	−	0.0288832i
$120$		0			0
$121$	−0.722631	−	1.25163i	−0.0656938	−	0.113785i
$122$	−6.04627	−	22.5650i	−0.547403	−	2.04294i
$123$	−0.233797	−	0.872543i	−0.0210808	−	0.0786745i
$124$	9.00815	+	15.6026i	0.808955	+	1.40115i
$125$		0			0
$126$	−6.14524	+	0.393972i	−0.547462	+	0.0350978i
$127$	4.84282	+	4.84282i	0.429731	+	0.429731i	0.888537	−	0.458806i	$-0.151723\pi$
$127$	4.84282	+	4.84282i	0.429731	+	0.429731i	−0.458806	+	0.888537i	$0.651723\pi$
$128$	−19.0887	−	5.11481i	−1.68722	−	0.452089i
$129$	1.68623	−	2.92064i	0.148465	−	0.257148i
$130$		0			0
$131$	2.49109	−	1.43823i	0.217648	−	0.125659i	−0.387213	−	0.921990i	$-0.626562\pi$
$131$	2.49109	−	1.43823i	0.217648	−	0.125659i	0.604861	+	0.796331i	$0.293229\pi$
$132$	−8.52384	+	8.52384i	−0.741905	+	0.741905i
$133$	0.350474	−	0.118412i	0.0303900	−	0.0102677i
$134$		−	24.9665i		−	2.15678i
$135$		0			0
$136$	−5.31646	−	3.06946i	−0.455883	−	0.263204i
$137$	−19.8248	+	5.31203i	−1.69375	+	0.453838i	−0.971352	−	0.237645i	$-0.923625\pi$
$137$	−19.8248	+	5.31203i	−1.69375	+	0.453838i	−0.722393	+	0.691482i	$0.756958\pi$
$138$	2.32064	−	8.66073i	0.197546	−	0.737250i
$139$	−10.4910			−0.889832			−0.444916	−	0.895572i	$-0.646766\pi$
$139$	−10.4910			−0.889832			−0.444916	+	0.895572i	$0.646766\pi$
$140$		0			0
$141$	−2.47074			−0.208074
$142$	3.07153	−	11.4631i	0.257757	−	0.961963i
$143$	21.6402	−	5.79849i	1.80965	−	0.484894i
$144$	0.729213	+	0.421011i	0.0607678	+	0.0350843i
$145$		0			0
$146$		−	21.7930i		−	1.80360i
$147$	6.93748	+	0.933491i	0.572194	+	0.0769930i
$148$	−14.0411	+	14.0411i	−1.15418	+	1.15418i
$149$	−11.4119	+	6.58864i	−0.934896	+	0.539763i	−0.888357	−	0.459154i	$-0.848153\pi$
$149$	−11.4119	+	6.58864i	−0.934896	+	0.539763i	−0.0465396	+	0.998916i	$0.514819\pi$
$150$		0			0
$151$	2.10520	−	3.64631i	0.171319	−	0.296732i	−0.767563	−	0.640974i	$-0.778531\pi$
$151$	2.10520	−	3.64631i	0.171319	−	0.296732i	0.938881	+	0.344242i	$0.111864\pi$
$152$	−0.445432	−	0.119353i	−0.0361293	−	0.00968083i
$153$	−1.31619	−	1.31619i	−0.106408	−	0.106408i
$154$	18.0797	−	12.0432i	1.45690	−	0.970468i
$155$		0			0
$156$	−10.8501	−	18.7930i	−0.868706	−	1.50464i
$157$	0.250229	+	0.933866i	0.0199704	+	0.0745306i	0.975192	−	0.221361i	$-0.0710499\pi$
$157$	0.250229	+	0.933866i	0.0199704	+	0.0745306i	−0.955222	+	0.295892i	$0.904383\pi$
$158$	5.07877	+	18.9542i	0.404045	+	1.50792i
$159$	−1.40391	−	2.43165i	−0.111337	−	0.192842i
$160$		0			0
$161$	−4.52106	+	9.13490i	−0.356309	+	0.719931i
$162$	1.64576	+	1.64576i	0.129303	+	0.129303i
$163$	−9.91429	−	2.65652i	−0.776547	−	0.208075i	−0.151285	−	0.988490i	$-0.548341\pi$
$163$	−9.91429	−	2.65652i	−0.776547	−	0.208075i	−0.625262	+	0.780415i	$0.715008\pi$
$164$	1.54334	−	2.67314i	0.120515	−	0.208737i
$165$		0			0
$166$	21.0327	−	12.1432i	1.63246	−	0.942499i
$167$	−5.80633	+	5.80633i	−0.449307	+	0.449307i	−0.895124	−	0.445817i	$-0.852913\pi$
$167$	−5.80633	+	5.80633i	−0.449307	+	0.449307i	0.445817	+	0.895124i	$0.352913\pi$
$168$	−6.55223	−	5.76271i	−0.505515	−	0.444603i
$169$			27.3304i			2.10234i
$170$		0			0
$171$	−0.121090	−	0.0699116i	−0.00926001	−	0.00534627i
$172$	11.1312	−	2.98258i	0.848742	−	0.227420i
$173$	−1.16854	+	4.36106i	−0.0888426	+	0.331565i	−0.996014	−	0.0891961i	$-0.971570\pi$
$173$	−1.16854	+	4.36106i	−0.0888426	+	0.331565i	0.907172	+	0.420761i	$0.138237\pi$
$174$	−4.70074			−0.356362
$175$		0			0
$176$	−2.97048			−0.223908
$177$	−1.63231	+	6.09186i	−0.122692	+	0.457892i
$178$	−7.88643	+	2.11316i	−0.591113	+	0.158388i
$179$	−12.7668	−	7.37089i	−0.954232	−	0.550926i	−0.0598390	−	0.998208i	$-0.519059\pi$
$179$	−12.7668	−	7.37089i	−0.954232	−	0.550926i	−0.894393	+	0.447282i	$0.852392\pi$
$180$		0			0
$181$			6.11772i			0.454727i	0.973810	+	0.227363i	$0.0730105\pi$
$181$			6.11772i			0.454727i	−0.973810	+	0.227363i	$0.926989\pi$
$182$	12.5174	+	37.0488i	0.927853	+	2.74624i
$183$	7.09734	−	7.09734i	0.524650	−	0.524650i
$184$	11.0032	−	6.35271i	0.811168	−	0.468328i
$185$		0			0
$186$	−6.13575	+	10.6274i	−0.449895	+	0.779241i
$187$	6.34277	+	1.69954i	0.463829	+	0.124283i
$188$	−5.96980	−	5.96980i	−0.435393	−	0.435393i
$189$	−1.46676	−	2.20196i	−0.106691	−	0.160169i
$190$		0			0
$191$	11.2238	+	19.4402i	0.812124	+	1.40664i	0.911375	+	0.411578i	$0.135022\pi$
$191$	11.2238	+	19.4402i	0.812124	+	1.40664i	−0.0992508	+	0.995062i	$0.531645\pi$
$192$	−3.22875	−	12.0499i	−0.233015	−	0.869624i
$193$	−4.64744	−	17.3445i	−0.334530	−	1.24848i	−0.904378	−	0.426733i	$-0.859664\pi$
$193$	−4.64744	−	17.3445i	−0.334530	−	1.24848i	0.569848	−	0.821750i	$-0.307002\pi$
$194$	14.3220	+	24.8064i	1.02826	+	1.78100i
$195$		0			0
$196$	14.5069	+	19.0179i	1.03620	+	1.35842i
$197$	12.1280	+	12.1280i	0.864085	+	0.864085i	0.991810	−	0.127724i	$-0.0407673\pi$
$197$	12.1280	+	12.1280i	0.864085	+	0.864085i	−0.127724	+	0.991810i	$0.540767\pi$
$198$	−7.93097	−	2.12510i	−0.563630	−	0.151024i
$199$	−3.39732	+	5.88433i	−0.240830	+	0.417129i	−0.960951	−	0.276719i	$-0.910753\pi$
$199$	−3.39732	+	5.88433i	−0.240830	+	0.417129i	0.720121	+	0.693848i	$0.244086\pi$
$200$		0			0
$201$	9.28983	−	5.36348i	0.655254	−	0.378311i
$202$	2.36563	−	2.36563i	0.166445	−	0.166445i
$203$	5.23943	+	1.04996i	0.367736	+	0.0736931i
$204$		−	6.36036i		−	0.445314i
$205$		0			0
$206$	12.4995	+	7.21662i	0.870885	+	0.502805i
$207$	3.72112	−	0.997072i	0.258636	−	0.0693013i
$208$	1.38400	−	5.16516i	0.0959632	−	0.358140i
$209$	0.493266			0.0341199
$210$		0			0
$211$	2.53741			0.174683			0.0873414	−	0.996178i	$-0.472163\pi$
$211$	2.53741			0.174683			0.0873414	+	0.996178i	$0.472163\pi$
$212$	2.48322	−	9.26749i	0.170548	−	0.636494i
$213$	4.92518	−	1.31970i	0.337468	−	0.0904242i
$214$	−36.1938	−	20.8965i	−2.47416	−	1.42846i
$215$		0			0
$216$			3.29806i			0.224405i
$217$	9.21266	−	10.4748i	0.625396	−	0.711078i
$218$	20.9539	−	20.9539i	1.41918	−	1.41918i
$219$	8.10900	−	4.68173i	0.547955	−	0.316362i
$220$		0			0
$221$	−5.91044	+	10.2372i	−0.397579	+	0.688627i
$222$	−13.0645	−	3.50063i	−0.876833	−	0.234947i
$223$	7.81577	+	7.81577i	0.523383	+	0.523383i	0.918591	−	0.395209i	$-0.129328\pi$
$223$	7.81577	+	7.81577i	0.523383	+	0.523383i	−0.395209	+	0.918591i	$0.629328\pi$
$224$	0.784806	+	12.2415i	0.0524370	+	0.817921i
$225$		0			0
$226$	−18.3717	−	31.8207i	−1.22207	−	2.11668i
$227$	−6.35498	−	23.7171i	−0.421795	−	1.57416i	−0.770824	−	0.637049i	$-0.780155\pi$
$227$	−6.35498	−	23.7171i	−0.421795	−	1.57416i	0.349029	−	0.937112i	$-0.386512\pi$
$228$	−0.123658	−	0.461500i	−0.00818948	−	0.0305636i
$229$	3.69144	+	6.39377i	0.243937	+	0.422512i	0.961832	−	0.273640i	$-0.0882275\pi$
$229$	3.69144	+	6.39377i	0.243937	+	0.422512i	−0.717895	+	0.696151i	$0.754894\pi$
$230$		0			0
$231$	8.36519	+	4.14011i	0.550389	+	0.272399i
$232$	−4.71009	−	4.71009i	−0.309232	−	0.309232i
$233$	7.04458	+	1.88759i	0.461505	+	0.123660i	0.482078	−	0.876128i	$-0.339882\pi$
$233$	7.04458	+	1.88759i	0.461505	+	0.123660i	−0.0205724	+	0.999788i	$0.506549\pi$
$234$	7.39038	−	12.8005i	0.483124	−	0.836796i
$235$		0			0
$236$	−18.6632	+	10.7752i	−1.21487	+	0.701404i
$237$	−5.96165	+	5.96165i	−0.387251	+	0.387251i
$238$	−2.25218	+	11.2386i	−0.145987	+	0.728492i
$239$			9.88581i			0.639460i	0.947509	+	0.319730i	$0.103592\pi$
$239$			9.88581i			0.639460i	−0.947509	+	0.319730i	$0.896408\pi$
$240$		0			0
$241$	−2.91713	−	1.68420i	−0.187909	−	0.108489i	0.403095	−	0.915158i	$-0.367935\pi$
$241$	−2.91713	−	1.68420i	−0.187909	−	0.108489i	−0.591003	+	0.806669i	$0.701268\pi$
$242$	3.24916	−	0.870610i	0.208864	−	0.0559649i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	34.2972			2.19565
$245$		0			0
$246$	2.10244			0.134047
$247$	−0.229822	+	0.857708i	−0.0146232	+	0.0545746i
$248$	−16.7965	+	4.50062i	−1.06658	+	0.285789i
$249$	9.03681	+	5.21740i	0.572684	+	0.330639i
$250$		0			0
$251$			4.93770i			0.311665i	0.987784	+	0.155832i	$0.0498060\pi$
$251$			4.93770i			0.311665i	−0.987784	+	0.155832i	$0.950194\pi$
$252$	1.77639	−	8.86437i	0.111902	−	0.558403i
$253$	−9.60986	+	9.60986i	−0.604167	+	0.604167i
$254$	−13.8046	+	7.97010i	−0.866179	+	0.500089i
$255$		0			0
$256$	10.5227	−	18.2259i	0.657670	−	1.13912i
$257$	19.8010	+	5.30566i	1.23515	+	0.330958i	0.816584	−	0.577227i	$-0.195865\pi$
$257$	19.8010	+	5.30566i	1.23515	+	0.330958i	0.418569	+	0.908185i	$0.362532\pi$
$258$	5.55026	+	5.55026i	0.345544	+	0.345544i
$259$	13.7798	+	6.81991i	0.856235	+	0.423769i
$260$		0			0
$261$	−1.00985	−	1.74910i	−0.0625079	−	0.108267i
$262$	1.73275	+	6.46671i	0.107050	+	0.399515i
$263$	0.900371	+	3.36023i	0.0555192	+	0.207201i	0.988114	−	0.153726i	$-0.0491272\pi$
$263$	0.900371	+	3.36023i	0.0555192	+	0.207201i	−0.932594	+	0.360926i	$0.882461\pi$
$264$	−5.81743	−	10.0761i	−0.358038	−	0.620140i
$265$		0			0
$266$	0.0550865	+	0.859247i	0.00337757	+	0.0526838i
$267$	−2.48051	−	2.48051i	−0.151805	−	0.151805i
$268$	35.4054	+	9.48684i	2.16273	+	0.579501i
$269$	9.35542	−	16.2041i	0.570410	−	0.987979i	−0.426114	−	0.904670i	$-0.640118\pi$
$269$	9.35542	−	16.2041i	0.570410	−	0.987979i	0.996524	−	0.0833095i	$-0.0265490\pi$
$270$		0			0
$271$	6.07958	−	3.51005i	0.369308	−	0.213220i	−0.303848	−	0.952721i	$-0.598272\pi$
$271$	6.07958	−	3.51005i	0.369308	−	0.213220i	0.673156	+	0.739500i	$0.264938\pi$
$272$	1.10826	−	1.10826i	0.0671982	−	0.0671982i
$273$	−11.0965	+	12.6167i	−0.671588	+	0.763599i
$274$		−	47.7689i		−	2.88582i
$275$		0			0
$276$	11.4001	+	6.58186i	0.686206	+	0.396181i
$277$	−7.53340	+	2.01857i	−0.452638	+	0.121284i	−0.477934	−	0.878396i	$-0.658614\pi$
$277$	−7.53340	+	2.01857i	−0.452638	+	0.121284i	0.0252953	+	0.999680i	$0.491947\pi$
$278$	6.31964	−	23.5852i	0.379027	−	1.41455i
$279$	−5.27250			−0.315657
$280$		0			0
$281$	−3.11841			−0.186029			−0.0930143	−	0.995665i	$-0.529650\pi$
$281$	−3.11841			−0.186029			−0.0930143	+	0.995665i	$0.529650\pi$
$282$	1.48834	−	5.55457i	0.0886296	−	0.330770i
$283$	30.3411	−	8.12988i	1.80359	−	0.483271i	0.809063	−	0.587721i	$-0.199975\pi$
$283$	30.3411	−	8.12988i	1.80359	−	0.483271i	0.994530	+	0.104450i	$0.0333082\pi$
$284$	15.0889	+	8.71157i	0.895361	+	0.516937i
$285$		0			0
$286$			52.1434i			3.08330i
$287$	−2.34338	−	0.469605i	−0.138325	−	0.0277199i
$288$	3.27840	−	3.27840i	0.193182	−	0.193182i
$289$	11.7219	−	6.76765i	0.689524	−	0.398097i
$290$		0			0
$291$	−6.15350	+	10.6582i	−0.360725	+	0.624794i
$292$	30.9050	+	8.28097i	1.80858	+	0.484607i
$293$	1.77405	+	1.77405i	0.103641	+	0.103641i	0.757026	−	0.653385i	$-0.226652\pi$
$293$	1.77405	+	1.77405i	0.103641	+	0.103641i	−0.653385	+	0.757026i	$0.726652\pi$
$294$	−6.27768	+	15.0341i	−0.366122	+	0.876808i
$295$		0			0
$296$	−9.58292	−	16.5981i	−0.556996	−	0.964746i
$297$	−0.913058	−	3.40758i	−0.0529810	−	0.197728i
$298$	−7.93785	−	29.6245i	−0.459827	−	1.71610i
$299$	−12.2325	−	21.1874i	−0.707426	−	1.22530i
$300$		0			0
$301$	−4.94660	−	7.42603i	−0.285117	−	0.428029i
$302$	6.92929	+	6.92929i	0.398736	+	0.398736i
$303$	1.38843	+	0.372029i	0.0797633	+	0.0213725i
$304$	0.0588671	−	0.101961i	0.00337626	−	0.00584786i
$305$		0			0
$306$	3.75184	−	2.16613i	0.214478	−	0.123829i
$307$	−10.6518	+	10.6518i	−0.607929	+	0.607929i	−0.942404	−	0.334476i	$-0.891441\pi$
$307$	−10.6518	+	10.6518i	−0.607929	+	0.607929i	0.334476	+	0.942404i	$0.391441\pi$
$308$	10.2087	+	30.2153i	0.581692	+	1.72168i
$309$			6.20130i			0.352780i
$310$		0			0
$311$	−16.1465	−	9.32219i	−0.915584	−	0.528613i	−0.0333607	−	0.999443i	$-0.510621\pi$
$311$	−16.1465	−	9.32219i	−0.915584	−	0.528613i	−0.882224	+	0.470831i	$0.843954\pi$
$312$	20.2311	−	5.42090i	1.14536	−	0.306898i
$313$	5.31635	−	19.8409i	0.300498	−	1.12147i	−0.636254	−	0.771479i	$-0.719517\pi$
$313$	5.31635	−	19.8409i	0.300498	−	1.12147i	0.936752	−	0.349994i	$-0.113816\pi$
$314$	−2.25020			−0.126986
$315$		0			0
$316$	−28.8091			−1.62064
$317$	7.55924	−	28.2115i	0.424569	−	1.58451i	−0.340292	−	0.940320i	$-0.610526\pi$
$317$	7.55924	−	28.2115i	0.424569	−	1.58451i	0.764862	−	0.644195i	$-0.222807\pi$
$318$	6.31239	−	1.69140i	0.353981	−	0.0948490i
$319$	6.17047	+	3.56252i	0.345480	+	0.199463i
$320$		0			0
$321$		−	17.9566i		−	1.00224i
$322$	−17.8131	−	15.6667i	−0.992688	−	0.873074i
$323$	−0.184034	+	0.184034i	−0.0102399	+	0.0102399i
$324$	−2.95923	+	1.70851i	−0.164402	+	0.0949174i
$325$		0			0
$326$	11.9445	−	20.6885i	0.661545	−	1.14583i
$327$	12.2983	+	3.29531i	0.680095	+	0.182231i
$328$	2.10662	+	2.10662i	0.116319	+	0.116319i
$329$	−2.89959	+	5.85868i	−0.159859	+	0.323000i
$330$		0			0
$331$	11.8275	+	20.4858i	0.650098	+	1.12600i	0.983099	+	0.183076i	$0.0586054\pi$
$331$	11.8275	+	20.4858i	0.650098	+	1.12600i	−0.333001	+	0.942926i	$0.608061\pi$
$332$	9.22846	+	34.4411i	0.506477	+	1.89020i
$333$	−1.50406	−	5.61323i	−0.0824220	−	0.307603i
$334$	−9.55580	−	16.5511i	−0.522870	−	0.905638i
$335$		0			0
$336$	1.85410	−	1.23504i	0.101149	−	0.0673772i
$337$	8.38731	+	8.38731i	0.456886	+	0.456886i	0.897632	−	0.440746i	$-0.145286\pi$
$337$	8.38731	+	8.38731i	0.456886	+	0.456886i	−0.440746	+	0.897632i	$0.645286\pi$
$338$	−61.4428	−	16.4635i	−3.34205	−	0.895499i
$339$	7.89348	−	13.6719i	0.428715	−	0.742556i
$340$		0			0
$341$	16.1083	−	9.30013i	0.872313	−	0.503630i
$342$	0.230115	−	0.230115i	0.0124432	−	0.0124432i
$343$	10.3551	−	15.3548i	0.559125	−	0.829083i
$344$			11.1226i			0.599691i
$345$		0			0
$346$	−9.10037	−	5.25410i	−0.489239	−	0.282462i
$347$	10.5150	−	2.81748i	0.564473	−	0.151250i	0.0347126	−	0.999397i	$-0.488948\pi$
$347$	10.5150	−	2.81748i	0.564473	−	0.151250i	0.529761	+	0.848147i	$0.322282\pi$
$348$	1.78620	−	6.66619i	0.0957503	−	0.357345i
$349$	−5.13321			−0.274775			−0.137387	−	0.990517i	$-0.543870\pi$
$349$	−5.13321			−0.274775			−0.137387	+	0.990517i	$0.543870\pi$
$350$		0			0
$351$	6.35062			0.338971
$352$	−4.23326	+	15.7988i	−0.225634	+	0.842076i
$353$	−20.8591	+	5.58918i	−1.11022	+	0.297482i	−0.766919	−	0.641744i	$-0.778211\pi$
$353$	−20.8591	+	5.58918i	−1.11022	+	0.297482i	−0.343299	+	0.939226i	$0.611544\pi$
$354$	−12.7121	−	7.33933i	−0.675640	−	0.390081i
$355$		0			0
$356$		−	11.9868i		−	0.635301i
$357$	−4.66563	+	1.57634i	−0.246931	+	0.0834290i
$358$	24.2614	−	24.2614i	1.28225	−	1.28225i
$359$	−3.58984	+	2.07260i	−0.189465	+	0.109388i	−0.591732	−	0.806135i	$-0.701556\pi$
$359$	−3.58984	+	2.07260i	−0.189465	+	0.109388i	0.402267	+	0.915522i	$0.368222\pi$
$360$		0			0
$361$	9.49022	−	16.4376i	0.499486	−	0.865134i
$362$	−13.7535	−	3.68525i	−0.722869	−	0.193692i
$363$	1.02196	+	1.02196i	0.0536387	+	0.0536387i
$364$	−57.2959	+	3.67325i	−3.00312	+	0.192530i
$365$		0			0
$366$	11.6805	+	20.2312i	0.610549	+	1.05750i
$367$	−0.879473	−	3.28224i	−0.0459081	−	0.171331i	0.939166	−	0.343465i	$-0.111601\pi$
$367$	−0.879473	−	3.28224i	−0.0459081	−	0.171331i	−0.985074	+	0.172133i	$0.944934\pi$
$368$	0.839557	+	3.13327i	0.0437650	+	0.163333i
$369$	0.451661	+	0.782300i	0.0235126	+	0.0407249i
$370$		0			0
$371$	−7.41358	+	0.475286i	−0.384894	+	0.0246756i
$372$	−12.7394	−	12.7394i	−0.660509	−	0.660509i
$373$	−34.6439	−	9.28280i	−1.79379	−	0.480645i	−0.800812	−	0.598916i	$-0.795598\pi$
$373$	−34.6439	−	9.28280i	−1.79379	−	0.480645i	−0.992981	+	0.118271i	$0.962265\pi$
$374$	−7.64163	+	13.2357i	−0.395139	+	0.684401i
$375$		0			0
$376$	7.05693	−	4.07432i	0.363934	−	0.210117i
$377$	−9.06957	+	9.06957i	−0.467107	+	0.467107i
$378$	5.83388	−	1.97105i	0.300062	−	0.101380i
$379$		−	8.02575i		−	0.412255i	−0.978525	−	0.206128i	$-0.933914\pi$
$379$		−	8.02575i		−	0.412255i	0.978525	−	0.206128i	$-0.0660862\pi$
$380$		0			0
$381$	−5.93122	−	3.42439i	−0.303866	−	0.175437i
$382$	−50.4654	+	13.5222i	−2.58203	+	0.691853i
$383$	−8.49599	+	31.7075i	−0.434125	+	1.62018i	0.309028	+	0.951053i	$0.399996\pi$
$383$	−8.49599	+	31.7075i	−0.434125	+	1.62018i	−0.743152	+	0.669122i	$0.766670\pi$
$384$	19.7621			1.00848
$385$		0			0
$386$	41.7925			2.12718
$387$	−0.872859	+	3.25755i	−0.0443699	+	0.165591i
$388$	−40.6205	+	10.8842i	−2.06219	+	0.552562i
$389$	13.4380	+	7.75844i	0.681334	+	0.393369i	0.800358	−	0.599523i	$-0.204643\pi$
$389$	13.4380	+	7.75844i	0.681334	+	0.393369i	−0.119023	+	0.992891i	$0.537976\pi$
$390$		0			0
$391$		−	7.17073i		−	0.362640i
$392$	−21.3542	+	8.77387i	−1.07855	+	0.443148i
$393$	−2.03397	+	2.03397i	−0.102600	+	0.102600i
$394$	−34.5713	+	19.9598i	−1.74168	+	1.00556i
$395$		0			0
$396$	6.02727	−	10.4395i	0.302882	−	0.524606i
$397$	−20.3268	−	5.44656i	−1.02017	−	0.273355i	−0.290299	−	0.956936i	$-0.593755\pi$
$397$	−20.3268	−	5.44656i	−1.02017	−	0.273355i	−0.729875	+	0.683581i	$0.760422\pi$
$398$	−11.1823	−	11.1823i	−0.560519	−	0.560519i
$399$	−0.307885	+	0.205087i	−0.0154135	+	0.0102672i
$400$		0			0
$401$	−9.34890	−	16.1928i	−0.466862	−	0.808628i	0.532422	−	0.846479i	$-0.321282\pi$
$401$	−9.34890	−	16.1928i	−0.466862	−	0.808628i	−0.999283	+	0.0378510i	$0.987949\pi$
$402$	6.46180	+	24.1158i	0.322285	+	1.20279i
$403$	8.66622	+	32.3428i	0.431695	+	1.61111i
$404$	2.45584	+	4.25363i	0.122182	+	0.211626i
$405$		0			0
$406$	−5.51665	+	11.1465i	−0.273787	+	0.553193i
$407$	14.4963	+	14.4963i	0.718553	+	0.718553i
$408$	5.92974	+	1.58887i	0.293566	+	0.0786608i
$409$	−11.9001	+	20.6115i	−0.588421	+	1.01918i	0.406018	+	0.913865i	$0.366917\pi$
$409$	−11.9001	+	20.6115i	−0.588421	+	1.01918i	−0.994439	+	0.105310i	$0.966416\pi$
$410$		0			0
$411$	17.7744	−	10.2621i	0.876747	−	0.506190i
$412$	−14.9836	+	14.9836i	−0.738190	+	0.738190i
$413$	12.5296	+	11.0198i	0.616539	+	0.542249i
$414$			8.96625i			0.440667i
$415$		0			0
$416$	−25.4991	−	14.7219i	−1.25019	−	0.721800i
$417$	10.1335	−	2.71526i	0.496239	−	0.132967i
$418$	−0.297138	+	1.10893i	−0.0145335	+	0.0542397i
$419$	−9.72005			−0.474856			−0.237428	−	0.971405i	$-0.576304\pi$
$419$	−9.72005			−0.474856			−0.237428	+	0.971405i	$0.576304\pi$
$420$		0			0
$421$	13.0095			0.634043			0.317022	−	0.948418i	$-0.397317\pi$
$421$	13.0095			0.634043			0.317022	+	0.948418i	$0.397317\pi$
$422$	−1.52851	+	5.70448i	−0.0744067	+	0.277690i
$423$	2.38655	−	0.639474i	0.116038	−	0.0310923i
$424$	8.01972	+	4.63019i	0.389472	+	0.224862i
$425$		0			0
$426$			11.8675i			0.574981i
$427$	−8.50018	−	25.1586i	−0.411353	−	1.21751i
$428$	43.3867	−	43.3867i	2.09718	−	2.09718i
$429$	−19.4021	+	11.2018i	−0.936743	+	0.540829i
$430$		0			0
$431$	−6.60239	+	11.4357i	−0.318026	+	0.550837i	−0.980076	−	0.198622i	$-0.936353\pi$
$431$	−6.60239	+	11.4357i	−0.318026	+	0.550837i	0.662050	+	0.749460i	$0.269687\pi$
$432$	−0.813332	−	0.217932i	−0.0391314	−	0.0104852i
$433$	13.9321	+	13.9321i	0.669535	+	0.669535i	0.957608	−	0.288074i	$-0.0930148\pi$
$433$	13.9321	+	13.9321i	0.669535	+	0.669535i	−0.288074	+	0.957608i	$0.593015\pi$
$434$	17.9993	+	27.0213i	0.863995	+	1.29706i
$435$		0			0
$436$	21.7529	+	37.6772i	1.04178	+	1.80441i
$437$	−0.139414	−	0.520299i	−0.00666906	−	0.0248893i
$438$	5.64044	+	21.0504i	0.269511	+	1.00583i
$439$	−6.30838	−	10.9264i	−0.301083	−	0.521490i	0.675299	−	0.737544i	$-0.264015\pi$
$439$	−6.30838	−	10.9264i	−0.301083	−	0.521490i	−0.976381	+	0.216054i	$0.930681\pi$
$440$		0			0
$441$	−6.94269	+	0.893868i	−0.330604	+	0.0425652i
$442$	−19.4543	−	19.4543i	−0.925346	−	0.925346i
$443$	18.4828	+	4.95246i	0.878146	+	0.235299i	0.669607	−	0.742716i	$-0.266463\pi$
$443$	18.4828	+	4.95246i	0.878146	+	0.235299i	0.208539	+	0.978014i	$0.433129\pi$
$444$	9.92859	−	17.1968i	0.471190	−	0.816125i
$445$		0			0
$446$	−22.2791	+	12.8629i	−1.05495	+	0.609074i
$447$	9.31775	−	9.31775i	0.440714	−	0.440714i
$448$	−32.3622	−	6.48527i	−1.52897	−	0.306400i
$449$		−	22.2412i		−	1.04963i	−0.851217	−	0.524814i	$-0.824135\pi$
$449$		−	22.2412i		−	1.04963i	0.851217	−	0.524814i	$-0.175865\pi$
$450$		0			0
$451$	−2.75979	−	1.59336i	−0.129953	−	0.0750286i
$452$	52.1064	−	13.9619i	2.45088	−	0.656711i
$453$	−1.08973	+	4.06693i	−0.0512000	+	0.191081i
$454$	57.1477			2.68207
$455$		0			0
$456$	0.461145			0.0215951
$457$	2.74748	−	10.2537i	0.128522	−	0.479650i	−0.871419	−	0.490540i	$-0.836800\pi$
$457$	2.74748	−	10.2537i	0.128522	−	0.479650i	0.999941	+	0.0108896i	$0.00346635\pi$
$458$	−16.5978	+	4.44737i	−0.775564	+	0.207812i
$459$	1.61200	+	0.930686i	0.0752415	+	0.0434407i
$460$		0			0
$461$		−	6.43806i		−	0.299851i	−0.988697	−	0.149925i	$-0.952097\pi$
$461$		−	6.43806i		−	0.299851i	0.988697	−	0.149925i	$-0.0479033\pi$
$462$	−14.3467	+	16.3122i	−0.667467	+	0.758912i
$463$	10.4584	−	10.4584i	0.486041	−	0.486041i	−0.421014	−	0.907054i	$-0.638326\pi$
$463$	10.4584	−	10.4584i	0.486041	−	0.486041i	0.907054	+	0.421014i	$0.138326\pi$
$464$	1.47279	−	0.850314i	0.0683724	−	0.0394748i
$465$		0			0
$466$	−8.48714	+	14.7002i	−0.393159	+	0.680972i
$467$	−10.0867	−	2.70272i	−0.466756	−	0.125067i	0.0177729	−	0.999842i	$-0.494342\pi$
$467$	−10.0867	−	2.70272i	−0.466756	−	0.125067i	−0.484529	+	0.874775i	$0.661009\pi$
$468$	15.3444	+	15.3444i	0.709295	+	0.709295i
$469$	−1.81578	−	28.3227i	−0.0838447	−	1.30782i
$470$		0			0
$471$	−0.483404	−	0.837281i	−0.0222741	−	0.0385799i
$472$	−5.38345	−	20.0913i	−0.247794	−	0.924778i
$473$	−3.07926	−	11.4919i	−0.141584	−	0.528400i
$474$	−9.81143	−	16.9939i	−0.450654	−	0.780555i
$475$		0			0
$476$	−15.0819	−	7.46434i	−0.691277	−	0.342127i
$477$	1.98543	+	1.98543i	0.0909066	+	0.0909066i
$478$	−22.2247	−	5.95510i	−1.01654	−	0.272380i
$479$	−15.3074	+	26.5132i	−0.699412	+	1.21142i	0.269258	+	0.963068i	$0.413222\pi$
$479$	−15.3074	+	26.5132i	−0.699412	+	1.21142i	−0.968670	+	0.248350i	$0.920112\pi$
$480$		0			0
$481$	−31.9607	+	18.4525i	−1.45728	+	0.841362i
$482$	5.54358	−	5.54358i	0.252503	−	0.252503i
$483$	2.00272	−	9.99377i	0.0911268	−	0.454732i
$484$			4.93850i			0.224477i
$485$		0			0
$486$	−2.01563	−	1.16373i	−0.0914309	−	0.0527877i
$487$	17.3396	−	4.64613i	0.785733	−	0.210536i	0.156422	−	0.987690i	$-0.450004\pi$
$487$	17.3396	−	4.64613i	0.785733	−	0.210536i	0.629311	+	0.777154i	$0.283337\pi$
$488$	−8.56773	+	31.9752i	−0.387843	+	1.44745i
$489$	10.2640			0.464155
$490$		0			0
$491$	5.26968			0.237817			0.118909	−	0.992905i	$-0.462060\pi$
$491$	5.26968			0.237817			0.118909	+	0.992905i	$0.462060\pi$
$492$	−0.798891	+	2.98150i	−0.0360168	+	0.134417i
$493$	−3.63130	+	0.973004i	−0.163546	+	0.0438219i
$494$	−1.78981	−	1.03335i	−0.0805273	−	0.0464925i
$495$		0			0
$496$		−	4.43957i		−	0.199343i
$497$	2.65074	−	13.2275i	0.118902	−	0.593334i
$498$	−17.1731	+	17.1731i	−0.769547	+	0.769547i
$499$	31.1135	−	17.9634i	1.39283	−	0.804150i	0.399202	−	0.916863i	$-0.369287\pi$
$499$	31.1135	−	17.9634i	1.39283	−	0.804150i	0.993628	+	0.112713i	$0.0359540\pi$
$500$		0			0
$501$	4.10569	−	7.11127i	0.183429	−	0.317708i
$502$	−11.1007	−	2.97441i	−0.495447	−	0.132755i
$503$	−2.39146	−	2.39146i	−0.106630	−	0.106630i	0.651779	−	0.758409i	$-0.274023\pi$
$503$	−2.39146	−	2.39146i	−0.106630	−	0.106630i	−0.758409	+	0.651779i	$0.774023\pi$
$504$	7.82046	+	3.87051i	0.348351	+	0.172406i
$505$		0			0
$506$	−15.8155	−	27.3932i	−0.703085	−	1.21778i
$507$	−7.07364	−	26.3992i	−0.314151	−	1.17243i
$508$	−6.05701	−	22.6051i	−0.268736	−	1.00294i
$509$	16.3136	+	28.2560i	0.723087	+	1.25242i	0.959756	+	0.280834i	$0.0906110\pi$
$509$	16.3136	+	28.2560i	0.723087	+	1.25242i	−0.236669	+	0.971590i	$0.576056\pi$
$510$		0			0
$511$	−1.58497	−	24.7226i	−0.0701151	−	1.09367i
$512$	6.68782	+	6.68782i	0.295563	+	0.295563i
$513$	0.135059	+	0.0361889i	0.00596299	+	0.00159778i
$514$	−23.8558	+	41.3194i	−1.05223	+	1.82252i
$515$		0			0
$516$	−9.97992	+	5.76191i	−0.439341	+	0.253654i
$517$	−6.16330	+	6.16330i	−0.271062	+	0.271062i
$518$	−23.6329	+	26.8707i	−1.03837	+	1.18063i
$519$		−	4.51490i		−	0.198182i
$520$		0			0
$521$	5.77709	+	3.33540i	0.253099	+	0.146127i	0.621182	−	0.783666i	$-0.286653\pi$
$521$	5.77709	+	3.33540i	0.253099	+	0.146127i	−0.368084	+	0.929793i	$0.619986\pi$
$522$	4.54056	−	1.21664i	0.198735	−	0.0532509i
$523$	−5.72338	+	21.3599i	−0.250266	+	0.934005i	0.720397	+	0.693562i	$0.243960\pi$
$523$	−5.72338	+	21.3599i	−0.250266	+	0.934005i	−0.970663	+	0.240444i	$0.922707\pi$
$524$	−9.82896			−0.429380
$525$		0			0
$526$	−8.09666			−0.353031
$527$	−2.54007	+	9.47969i	−0.110647	+	0.412942i
$528$	2.86926	−	0.768816i	0.124868	−	0.0334584i
$529$	−7.06598	−	4.07955i	−0.307217	−	0.177372i
$530$		0			0
$531$		−	6.30675i		−	0.273690i
$532$	−1.23944	−	0.248380i	−0.0537367	−	0.0107686i
$533$	4.05643	−	4.05643i	0.175704	−	0.175704i
$534$	7.07078	−	4.08232i	0.305983	−	0.176659i
$535$		0			0
$536$	−17.6891	+	30.6384i	−0.764053	+	1.32338i
$537$	14.2395	+	3.81545i	0.614478	+	0.164649i
$538$	30.7935	+	30.7935i	1.32760	+	1.32760i
$539$	19.6343	−	14.9771i	0.845709	−	0.645108i
$540$		0			0
$541$	−7.12948	−	12.3486i	−0.306520	−	0.530909i	0.671078	−	0.741386i	$-0.265831\pi$
$541$	−7.12948	−	12.3486i	−0.306520	−	0.530909i	−0.977599	+	0.210478i	$0.932498\pi$
$542$	4.22882	+	15.7822i	0.181644	+	0.677903i
$543$	−1.58338	−	5.90927i	−0.0679495	−	0.253591i
$544$	−4.31499	−	7.47379i	−0.185004	−	0.320436i
$545$		0			0
$546$	−21.6798	−	32.5466i	−0.927811	−	1.39287i
$547$	11.2527	+	11.2527i	0.481132	+	0.481132i	0.905493	−	0.424361i	$-0.139501\pi$
$547$	11.2527	+	11.2527i	0.481132	+	0.481132i	−0.424361	+	0.905493i	$0.639501\pi$
$548$	67.7418	+	18.1514i	2.89379	+	0.775388i
$549$	−5.01858	+	8.69243i	−0.214188	+	0.370984i
$550$		0			0
$551$	−0.244565	+	0.141200i	−0.0104188	+	0.00601532i
$552$	−8.98409	+	8.98409i	−0.382388	+	0.382388i
$553$	7.14002	+	21.1329i	0.303625	+	0.898661i
$554$		−	18.1521i		−	0.771211i
$555$		0			0
$556$	31.0452	+	17.9240i	1.31661	+	0.760145i
$557$	13.5980	−	3.64356i	0.576164	−	0.154383i	0.0410418	−	0.999157i	$-0.486932\pi$
$557$	13.5980	−	3.64356i	0.576164	−	0.154383i	0.535122	+	0.844775i	$0.320266\pi$
$558$	3.17610	−	11.8534i	0.134455	−	0.501793i
$559$	21.4173			0.905854
$560$		0			0
$561$	−6.56652			−0.277239
$562$	1.87849	−	7.01063i	0.0792395	−	0.295726i
$563$	−33.9375	+	9.09354i	−1.43030	+	0.383247i	−0.889125	−	0.457665i	$-0.848686\pi$
$563$	−33.9375	+	9.09354i	−1.43030	+	0.383247i	−0.541172	+	0.840912i	$0.682019\pi$
$564$	7.31149	+	4.22129i	0.307869	+	0.177748i
$565$		0			0
$566$			73.1086i			3.07299i
$567$	1.98669	+	1.74730i	0.0834331	+	0.0733798i
$568$	−11.8911	+	11.8911i	−0.498939	+	0.498939i
$569$	22.1757	−	12.8031i	0.929652	−	0.536735i	0.0429507	−	0.999077i	$-0.486324\pi$
$569$	22.1757	−	12.8031i	0.929652	−	0.536735i	0.886702	+	0.462342i	$0.152991\pi$
$570$		0			0
$571$	−15.1850	+	26.3013i	−0.635474	+	1.10067i	0.350941	+	0.936398i	$0.385862\pi$
$571$	−15.1850	+	26.3013i	−0.635474	+	1.10067i	−0.986415	+	0.164275i	$0.947471\pi$
$572$	−73.9453	−	19.8136i	−3.09181	−	0.828448i
$573$	−15.8728	−	15.8728i	−0.663096	−	0.663096i
$574$	2.46736	−	4.98537i	0.102986	−	0.208085i
$575$		0			0
$576$	6.23747	+	10.8036i	0.259895	+	0.450151i
$577$	−5.93273	−	22.1412i	−0.246983	−	0.921752i	−0.972376	−	0.233418i	$-0.925009\pi$
$577$	−5.93273	−	22.1412i	−0.246983	−	0.921752i	0.725394	−	0.688334i	$-0.241658\pi$
$578$	8.15351	+	30.4293i	0.339141	+	1.26569i
$579$	8.97817	+	15.5506i	0.373120	+	0.646263i
$580$		0			0
$581$	22.9770	−	15.3053i	0.953247	−	0.634973i
$582$	−20.2543	−	20.2543i	−0.839569	−	0.839569i
$583$	−9.56788	−	2.56370i	−0.396261	−	0.106178i
$584$	−15.4406	+	26.7440i	−0.638938	+	1.10667i
$585$		0			0
$586$	−5.05699	+	2.91966i	−0.208902	+	0.120610i
$587$	−3.26809	+	3.26809i	−0.134888	+	0.134888i	−0.771327	−	0.636439i	$-0.780407\pi$
$587$	−3.26809	+	3.26809i	−0.134888	+	0.134888i	0.636439	+	0.771327i	$0.280407\pi$
$588$	−18.9347	−	14.6152i	−0.780855	−	0.602720i
$589$			0.737218i			0.0303765i
$590$		0			0
$591$	−14.8537	−	8.57580i	−0.611001	−	0.352761i
$592$	4.72647	−	1.26645i	0.194257	−	0.0520509i
$593$	3.38581	−	12.6360i	0.139038	−	0.518899i	−0.860910	−	0.508757i	$-0.830105\pi$
$593$	3.38581	−	12.6360i	0.139038	−	0.518899i	0.999949	−	0.0101415i	$-0.00322821\pi$
$594$	8.21074			0.336891
$595$		0			0
$596$	45.0272			1.84438
$597$	1.75858	−	6.56312i	0.0719740	−	0.268610i
$598$	55.0011	−	14.7375i	2.24916	−	0.602661i
$599$	1.72270	+	0.994603i	0.0703877	+	0.0406384i	0.534781	−	0.844991i	$-0.320394\pi$
$599$	1.72270	+	0.994603i	0.0703877	+	0.0406384i	−0.464393	+	0.885629i	$0.653728\pi$
$600$		0			0
$601$		−	28.1436i		−	1.14800i	−0.818855	−	0.574001i	$-0.805391\pi$
$601$		−	28.1436i		−	1.14800i	0.818855	−	0.574001i	$-0.194609\pi$
$602$	19.6746	−	6.64731i	0.801876	−	0.270924i
$603$	−7.58511	+	7.58511i	−0.308890	+	0.308890i
$604$	−12.4595	+	7.19352i	−0.506972	+	0.292700i
$605$		0			0
$606$	−1.67275	+	2.89729i	−0.0679509	+	0.117694i
$607$	42.8022	+	11.4688i	1.73729	+	0.465505i	0.981841	−	0.189706i	$-0.0607535\pi$
$607$	42.8022	+	11.4688i	1.73729	+	0.465505i	0.755446	+	0.655211i	$0.227420\pi$
$608$	−0.458396	−	0.458396i	−0.0185904	−	0.0185904i
$609$	−5.33266	+	0.341877i	−0.216090	+	0.0138536i
$610$		0			0
$611$	−7.84536	−	13.5886i	−0.317389	−	0.549734i
$612$	1.64618	+	6.14364i	0.0665430	+	0.248342i
$613$	−4.91551	−	18.3450i	−0.198536	−	0.740946i	−0.991323	−	0.131447i	$-0.958038\pi$
$613$	−4.91551	−	18.3450i	−0.198536	−	0.740946i	0.792787	−	0.609498i	$-0.208629\pi$
$614$	−17.5302	−	30.3632i	−0.707462	−	1.22536i
$615$		0			0
$616$	−30.7199	+	1.96946i	−1.23774	+	0.0793516i
$617$	−8.02128	−	8.02128i	−0.322924	−	0.322924i	0.526963	−	0.849888i	$-0.323330\pi$
$617$	−8.02128	−	8.02128i	−0.322924	−	0.322924i	−0.849888	+	0.526963i	$0.823330\pi$
$618$	−13.9414	−	3.73560i	−0.560807	−	0.150268i
$619$	15.2997	−	26.4998i	0.614945	−	1.06512i	−0.375449	−	0.926843i	$-0.622512\pi$
$619$	15.2997	−	26.4998i	0.614945	−	1.06512i	0.990394	−	0.138273i	$-0.0441552\pi$
$620$		0			0
$621$	−3.33627	+	1.92619i	−0.133880	+	0.0772955i
$622$	30.6841	−	30.6841i	1.23032	−	1.23032i
$623$	−8.79292	+	2.97080i	−0.352281	+	0.119023i
$624$			5.34737i			0.214066i
$625$		0			0
$626$	41.4027	+	23.9038i	1.65478	+	0.955390i
$627$	−0.476458	+	0.127667i	−0.0190279	+	0.00509851i
$628$	0.855038	−	3.19105i	0.0341197	−	0.127337i
$629$	−10.8169			−0.431298
$630$		0			0
$631$	6.68706			0.266207			0.133104	−	0.991102i	$-0.457506\pi$
$631$	6.68706			0.266207			0.133104	+	0.991102i	$0.457506\pi$
$632$	7.19675	−	26.8587i	0.286272	−	1.06838i
$633$	−2.45095	+	0.656731i	−0.0974167	+	0.0261027i
$634$	58.8699	+	33.9885i	2.33802	+	1.34986i
$635$		0			0
$636$			9.59441i			0.380443i
$637$	16.8946	+	41.1189i	0.669390	+	1.62919i
$638$	−11.7261	+	11.7261i	−0.464240	+	0.464240i
$639$	−4.41579	+	2.54946i	−0.174686	+	0.100855i
$640$		0			0
$641$	−24.4639	+	42.3726i	−0.966264	+	1.67362i	−0.260085	+	0.965586i	$0.583751\pi$
$641$	−24.4639	+	42.3726i	−0.966264	+	1.67362i	−0.706179	+	0.708033i	$0.749583\pi$
$642$	40.3690	+	10.8168i	1.59324	+	0.426906i
$643$	−3.55117	−	3.55117i	−0.140044	−	0.140044i	0.633609	−	0.773653i	$-0.281573\pi$
$643$	−3.55117	−	3.55117i	−0.140044	−	0.140044i	−0.773653	+	0.633609i	$0.781573\pi$
$644$	28.9860	−	19.3080i	1.14221	−	0.760842i
$645$		0			0
$646$	−0.302875	−	0.524594i	−0.0119164	−	0.0206399i
$647$	7.51337	+	28.0403i	0.295381	+	1.10238i	0.940914	+	0.338645i	$0.109969\pi$
$647$	7.51337	+	28.0403i	0.295381	+	1.10238i	−0.645533	+	0.763732i	$0.723365\pi$
$648$	−0.853601	−	3.18568i	−0.0335326	−	0.125145i
$649$	11.1244	+	19.2681i	0.436672	+	0.756338i
$650$		0			0
$651$	−6.18766	+	12.5023i	−0.242514	+	0.490005i
$652$	24.8000	+	24.8000i	0.971242	+	0.971242i
$653$	9.80085	+	2.62613i	0.383537	+	0.102768i	0.445436	−	0.895314i	$-0.353049\pi$
$653$	9.80085	+	2.62613i	0.383537	+	0.102768i	−0.0618985	+	0.998082i	$0.519716\pi$
$654$	−14.8167	+	25.6632i	−0.579377	+	1.00351i
$655$		0			0
$656$	−0.658715	+	0.380309i	−0.0257185	+	0.0148486i
$657$	−6.62097	+	6.62097i	−0.258309	+	0.258309i
$658$	−11.4245	−	10.0479i	−0.445373	−	0.391708i
$659$			19.2380i			0.749405i	0.927145	+	0.374703i	$0.122255\pi$
$659$			19.2380i			0.749405i	−0.927145	+	0.374703i	$0.877745\pi$
$660$		0			0
$661$	16.0842	+	9.28623i	0.625604	+	0.361193i	0.779048	−	0.626965i	$-0.215703\pi$
$661$	16.0842	+	9.28623i	0.625604	+	0.361193i	−0.153444	+	0.988157i	$0.549036\pi$
$662$	−53.1798	+	14.2495i	−2.06689	+	0.553822i
$663$	3.05947	−	11.4181i	0.118820	−	0.443442i
$664$	−34.4146			−1.33555
$665$		0			0
$666$	13.5254			0.524098
$667$	2.01378	−	7.51552i	0.0779738	−	0.291002i
$668$	27.1025	−	7.26209i	1.04863	−	0.280979i
$669$	−9.57233	−	5.52659i	−0.370088	−	0.213670i
$670$		0			0
$671$		−	35.4089i		−	1.36695i
$672$	−3.92640	−	11.6213i	−0.151464	−	0.448300i
$673$	−11.7627	+	11.7627i	−0.453420	+	0.453420i	−0.896488	−	0.443068i	$-0.853890\pi$
$673$	−11.7627	+	11.7627i	−0.453420	+	0.453420i	0.443068	+	0.896488i	$0.353890\pi$
$674$	−23.9083	+	13.8035i	−0.920913	+	0.531690i
$675$		0			0
$676$	46.6944	−	80.8771i	1.79594	−	3.11066i
$677$	−48.0456	−	12.8738i	−1.84654	−	0.494780i	−0.847209	−	0.531259i	$-0.821719\pi$
$677$	−48.0456	−	12.8738i	−1.84654	−	0.494780i	−0.999334	+	0.0364792i	$0.988386\pi$
$678$	25.9815	+	25.9815i	0.997813	+	0.997813i
$679$	18.0514	+	27.0995i	0.692750	+	1.03998i
$680$		0			0
$681$	12.2769	+	21.2642i	0.470451	+	0.814846i
$682$	11.2046	+	41.8161i	0.429046	+	1.60122i
$683$	−11.7226	−	43.7494i	−0.448553	−	1.67402i	−0.706380	−	0.707833i	$-0.749673\pi$
$683$	−11.7226	−	43.7494i	−0.448553	−	1.67402i	0.257827	−	0.966191i	$-0.416994\pi$
$684$	0.238890	+	0.413769i	0.00913418	+	0.0158209i
$685$		0			0
$686$	28.2821	+	32.5294i	1.07981	+	1.24198i
$687$	−5.22049	−	5.22049i	−0.199174	−	0.199174i
$688$	−2.74293	−	0.734967i	−0.104573	−	0.0280204i
$689$	8.91571	−	15.4425i	0.339662	−	0.588311i
$690$		0			0
$691$	−17.7216	+	10.2316i	−0.674161	+	0.389227i	−0.797652	−	0.603119i	$-0.793925\pi$
$691$	−17.7216	+	10.2316i	−0.674161	+	0.389227i	0.123490	+	0.992346i	$0.460591\pi$
$692$	10.9089	−	10.9089i	0.414695	−	0.414695i
$693$	−9.15169	−	1.83397i	−0.347644	−	0.0696666i
$694$			25.3364i			0.961756i
$695$		0			0
$696$	5.76866	+	3.33054i	0.218660	+	0.126244i
$697$	1.62413	−	0.435184i	0.0615182	−	0.0164838i
$698$	3.09219	−	11.5402i	0.117041	−	0.436803i
$699$	−7.29308			−0.275850
$700$		0			0
$701$	−24.5198			−0.926099			−0.463049	−	0.886332i	$-0.653245\pi$
$701$	−24.5198			−0.926099			−0.463049	+	0.886332i	$0.653245\pi$
$702$	−3.82554	+	14.2771i	−0.144386	+	0.538855i
$703$	−0.784860	+	0.210303i	−0.0296015	+	0.00793171i
$704$	−38.1128	−	22.0045i	−1.43643	−	0.829324i
$705$		0			0
$706$		−	50.2611i		−	1.89160i
$707$	2.51159	−	2.85569i	0.0944581	−	0.107399i
$708$	15.2384	−	15.2384i	0.572694	−	0.572694i
$709$	−8.72879	+	5.03957i	−0.327817	+	0.189265i	−0.654871	−	0.755740i	$-0.727277\pi$
$709$	−8.72879	+	5.03957i	−0.327817	+	0.189265i	0.327055	+	0.945005i	$0.393944\pi$
$710$		0			0
$711$	4.21552	−	7.30150i	0.158095	−	0.273828i
$712$	11.1753	+	2.99441i	0.418812	+	0.112220i
$713$	−14.3626	−	14.3626i	−0.537883	−	0.537883i
$714$	−0.733329	−	11.4386i	−0.0274442	−	0.428078i
$715$		0			0
$716$	25.1865	+	43.6244i	0.941265	+	1.63032i
$717$	−2.55864	−	9.54896i	−0.0955540	−	0.356612i
$718$	−2.49702	−	9.31900i	−0.0931879	−	0.347782i
$719$	1.67817	+	2.90667i	0.0625851	+	0.108401i	0.895620	−	0.444820i	$-0.146732\pi$
$719$	1.67817	+	2.90667i	0.0625851	+	0.108401i	−0.833035	+	0.553220i	$0.813399\pi$
$720$		0			0
$721$	14.7047	+	7.27767i	0.547632	+	0.271035i
$722$	31.2372	+	31.2372i	1.16253	+	1.16253i
$723$	3.25363	+	0.871808i	0.121004	+	0.0324229i
$724$	10.4522	−	18.1038i	0.388454	−	0.672821i
$725$		0			0
$726$	−2.91312	+	1.68189i	−0.108116	+	0.0624208i
$727$	−23.0330	+	23.0330i	−0.854247	+	0.854247i	−0.990653	−	0.136406i	$-0.956445\pi$
$727$	−23.0330	+	23.0330i	−0.854247	+	0.854247i	0.136406	+	0.990653i	$0.456445\pi$
$728$	10.8884	−	54.3344i	0.403552	−	2.01377i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	5.43640	+	3.13871i	0.201073	+	0.116089i
$732$	−33.1286	+	8.87677i	−1.22447	+	0.328095i
$733$	−12.4202	+	46.3528i	−0.458751	+	1.71208i	0.218071	+	0.975933i	$0.430024\pi$
$733$	−12.4202	+	46.3528i	−0.458751	+	1.71208i	−0.676821	+	0.736147i	$0.736643\pi$
$734$	7.90873			0.291917
$735$		0			0
$736$	17.8611			0.658367
$737$	9.79434	−	36.5530i	0.360779	−	1.34645i
$738$	−2.03080	+	0.544151i	−0.0747548	+	0.0200305i
$739$	−16.4664	−	9.50689i	−0.605727	−	0.349717i	0.165564	−	0.986199i	$-0.447055\pi$
$739$	−16.4664	−	9.50689i	−0.605727	−	0.349717i	−0.771291	+	0.636482i	$0.780389\pi$
$740$		0			0
$741$		−	0.887964i		−	0.0326202i
$742$	3.39735	−	16.9531i	0.124720	−	0.622368i
$743$	2.50371	−	2.50371i	0.0918524	−	0.0918524i	−0.659688	−	0.751540i	$-0.729311\pi$
$743$	2.50371	−	2.50371i	0.0918524	−	0.0918524i	0.751540	+	0.659688i	$0.229311\pi$
$744$	15.0594	−	8.69452i	0.552103	−	0.318757i
$745$		0			0
$746$	41.7382	−	72.2926i	1.52814	−	2.64682i
$747$	−10.0792	−	2.70073i	−0.368780	−	0.0988144i
$748$	−15.8660	−	15.8660i	−0.580120	−	0.580120i
$749$	−42.5791	−	21.0733i	−1.55581	−	0.770002i
$750$		0			0
$751$	−12.4684	−	21.5959i	−0.454978	−	0.788046i	0.543708	−	0.839274i	$-0.317020\pi$
$751$	−12.4684	−	21.5959i	−0.454978	−	0.788046i	−0.998687	+	0.0512283i	$0.983686\pi$
$752$	0.538452	+	2.00953i	0.0196353	+	0.0732800i
$753$	−1.27797	−	4.76945i	−0.0465718	−	0.173808i
$754$	−14.9263	−	25.8531i	−0.543584	−	0.941515i
$755$		0			0
$756$	0.578407	+	9.02208i	0.0210365	+	0.328130i
$757$	0.224148	+	0.224148i	0.00814681	+	0.00814681i	0.711168	−	0.703022i	$-0.248166\pi$
$757$	0.224148	+	0.224148i	0.00814681	+	0.00814681i	−0.703022	+	0.711168i	$0.748166\pi$
$758$	18.0431	+	4.83462i	0.655353	+	0.175601i
$759$	6.79520	−	11.7696i	0.246650	−	0.427211i
$760$		0			0
$761$	−12.1337	+	7.00541i	−0.439847	+	0.253946i	−0.703533	−	0.710663i	$-0.748395\pi$
$761$	−12.1337	+	7.00541i	−0.439847	+	0.253946i	0.263685	+	0.964609i	$0.415062\pi$
$762$	11.2714	−	11.2714i	0.408321	−	0.408321i
$763$	22.2468	−	25.2947i	0.805389	−	0.915730i
$764$		−	76.7039i		−	2.77505i
$765$		0			0
$766$	−66.1651	−	38.2004i	−2.39064	−	1.38024i
$767$	−38.6871	+	10.3662i	−1.39691	+	0.374301i
$768$	−5.44696	+	20.3283i	−0.196550	+	0.733535i
$769$	−49.1264			−1.77154			−0.885772	−	0.464120i	$-0.846371\pi$
$769$	−49.1264			−1.77154			−0.885772	+	0.464120i	$0.846371\pi$
$770$		0			0
$771$	−20.4995			−0.738272
$772$	−15.8804	+	59.2666i	−0.571549	+	2.13305i
$773$	22.4052	−	6.00345i	0.805858	−	0.215929i	0.167704	−	0.985837i	$-0.446365\pi$
$773$	22.4052	−	6.00345i	0.805858	−	0.215929i	0.638154	+	0.769908i	$0.279698\pi$
$774$	−6.79765	−	3.92463i	−0.244337	−	0.141068i
$775$		0			0
$776$		−	40.5893i		−	1.45707i
$777$	−15.0754	−	3.02106i	−0.540826	−	0.108380i
$778$	−25.5370	+	25.5370i	−0.915546	+	0.915546i
$779$	0.109384	−	0.0631527i	0.00391908	−	0.00226268i
$780$		0			0
$781$	8.99394	−	15.5780i	0.321829	−	0.557423i
$782$	16.1208	+	4.31957i	0.576480	+	0.154467i
$783$	1.42814	+	1.42814i	0.0510375	+	0.0510375i
$784$	−0.752658	−	5.84591i	−0.0268806	−	0.208782i
$785$		0			0
$786$	−3.34742	−	5.79789i	−0.119398	−	0.206804i
$787$	−3.76964	−	14.0685i	−0.134373	−	0.501488i	−1.00000		0.000797382i	$-0.999746\pi$
$787$	−3.76964	−	14.0685i	−0.134373	−	0.501488i	0.865626	−	0.500690i	$-0.166920\pi$
$788$	−15.1687	−	56.6105i	−0.540364	−	2.01667i
$789$	−1.73938	−	3.01270i	−0.0619237	−	0.107255i
$790$		0			0
$791$	−23.1557	−	34.7622i	−0.823321	−	1.23600i
$792$	8.22708	+	8.22708i	0.292337	+	0.292337i
$793$	61.5702	+	16.4977i	2.18642	+	0.585850i
$794$	24.4893	−	42.4167i	0.869093	−	1.50531i
$795$		0			0
$796$	20.1069	−	11.6087i	0.712671	−	0.411461i
$797$	38.0535	−	38.0535i	1.34792	−	1.34792i	0.460013	−	0.887912i	$-0.347845\pi$
$797$	38.0535	−	38.0535i	1.34792	−	1.34792i	0.887912	−	0.460013i	$-0.152155\pi$
$798$	−0.275599	−	0.815711i	−0.00975609	−	0.0288759i
$799$		−	4.59896i		−	0.162700i
$800$		0			0
$801$	3.03799	+	1.75399i	0.107342	+	0.0619740i
$802$	42.0354	−	11.2633i	1.48432	−	0.397722i
$803$	8.54938	−	31.9067i	0.301701	−	1.12596i
$804$	−36.6543			−1.29270
$805$		0			0
$806$	−77.9317			−2.74503
$807$	−4.84272	+	18.0733i	−0.170472	+	0.636210i
$808$	−4.57913	+	1.22698i	−0.161093	+	0.0431648i
$809$	15.3437	+	8.85869i	0.539456	+	0.311455i	0.744858	−	0.667222i	$-0.232517\pi$
$809$	15.3437	+	8.85869i	0.539456	+	0.311455i	−0.205402	+	0.978678i	$0.565850\pi$
$810$		0			0
$811$			27.9256i			0.980600i	0.871554	+	0.490300i	$0.163113\pi$
$811$			27.9256i			0.980600i	−0.871554	+	0.490300i	$0.836887\pi$
$812$	−13.7108	−	12.0587i	−0.481156	−	0.423179i
$813$	−4.96396	+	4.96396i	−0.174094	+	0.174094i
$814$	−41.3221	+	23.8573i	−1.44834	+	0.836199i
$815$		0			0
$816$	−0.783659	+	1.35734i	−0.0274336	+	0.0475163i
$817$	0.455481	+	0.122046i	0.0159353	+	0.00426984i
$818$	−39.1693	−	39.1693i	−1.36952	−	1.36952i
$819$	7.45291	−	15.0588i	0.260426	−	0.526197i
$820$		0			0
$821$	9.80771	+	16.9874i	0.342291	+	0.592866i	0.984858	−	0.173364i	$-0.0554637\pi$
$821$	9.80771	+	16.9874i	0.342291	+	0.592866i	−0.642566	+	0.766230i	$0.722130\pi$
$822$	12.3635	+	46.1412i	0.431227	+	1.60936i
$823$	13.0933	+	48.8650i	0.456405	+	1.70333i	0.683924	+	0.729553i	$0.260272\pi$
$823$	13.0933	+	48.8650i	0.456405	+	1.70333i	−0.227519	+	0.973774i	$0.573061\pi$
$824$	−10.2261	−	17.7122i	−0.356245	−	0.617034i
$825$		0			0
$826$	−32.3218	+	21.5301i	−1.12462	+	0.749127i
$827$	−18.2487	−	18.2487i	−0.634570	−	0.634570i	0.314641	−	0.949211i	$-0.398116\pi$
$827$	−18.2487	−	18.2487i	−0.634570	−	0.634570i	−0.949211	+	0.314641i	$0.898116\pi$
$828$	−12.7152	−	3.40702i	−0.441883	−	0.118402i
$829$	20.5574	−	35.6064i	0.713988	−	1.23666i	−0.249361	−	0.968411i	$-0.580221\pi$
$829$	20.5574	−	35.6064i	0.713988	−	1.23666i	0.963349	−	0.268252i	$-0.0864460\pi$
$830$		0			0
$831$	6.75426	−	3.89958i	0.234303	−	0.135275i
$832$	56.0196	−	56.0196i	1.94213	−	1.94213i
$833$	−1.73757	+	12.9132i	−0.0602034	+	0.447417i
$834$			24.4172i			0.845499i
$835$		0			0
$836$	−1.45969	−	0.842752i	−0.0504844	−	0.0291472i
$837$	5.09285	−	1.36462i	0.176035	−	0.0471683i
$838$	5.85525	−	21.8521i	0.202266	−	0.754868i
$839$	−46.0286			−1.58908			−0.794541	−	0.607210i	$-0.792289\pi$
$839$	−46.0286			−1.58908			−0.794541	+	0.607210i	$0.792289\pi$
$840$		0			0
$841$	24.9208			0.859339
$842$	−7.83676	+	29.2472i	−0.270073	+	1.00793i
$843$	3.01215	−	0.807103i	0.103744	−	0.0277981i
$844$	−7.50880	−	4.33521i	−0.258464	−	0.149224i
$845$		0			0
$846$			5.75052i			0.197707i
$847$	3.62263	−	1.22395i	0.124475	−	0.0420555i
$848$	−1.67178	+	1.67178i	−0.0574091	+	0.0574091i
$849$	−27.2031	+	15.7057i	−0.933609	+	0.539019i
$850$		0			0
$851$	11.1936	−	19.3879i	0.383711	−	0.664608i
$852$	−16.8295	−	4.50944i	−0.576568	−	0.154491i
$853$	−22.9994	−	22.9994i	−0.787484	−	0.787484i	0.193597	−	0.981081i	$-0.437984\pi$
$853$	−22.9994	−	22.9994i	−0.787484	−	0.787484i	−0.981081	+	0.193597i	$0.937984\pi$
$854$	61.6807	−	3.95436i	2.11067	−	0.135315i
$855$		0			0
$856$	29.6109	+	51.2876i	1.01208	+	1.75298i
$857$	−2.22400	−	8.30009i	−0.0759705	−	0.283526i	0.917481	−	0.397779i	$-0.130219\pi$
$857$	−2.22400	−	8.30009i	−0.0759705	−	0.283526i	−0.993452	+	0.114254i	$0.963552\pi$
$858$	−13.4957	−	50.3666i	−0.460735	−	1.71949i
$859$	1.33433	+	2.31112i	0.0455266	+	0.0788544i	0.887891	−	0.460054i	$-0.152170\pi$
$859$	1.33433	+	2.31112i	0.0455266	+	0.0788544i	−0.842364	+	0.538909i	$0.818837\pi$
$860$		0			0
$861$	2.38507	−	0.152907i	0.0812830	−	0.00521107i
$862$	−21.7319	−	21.7319i	−0.740190	−	0.740190i
$863$	0.515877	+	0.138229i	0.0175607	+	0.00470537i	0.267589	−	0.963533i	$-0.413773\pi$
$863$	0.515877	+	0.138229i	0.0175607	+	0.00470537i	−0.250028	+	0.968239i	$0.580440\pi$
$864$	−2.31818	+	4.01520i	−0.0788660	+	0.136600i
$865$		0			0
$866$	−39.7140	+	22.9289i	−1.34954	+	0.779155i
$867$	−9.57090	+	9.57090i	−0.325045	+	0.325045i
$868$	−45.1588	+	15.2575i	−1.53279	+	0.517873i
$869$			29.7429i			1.00896i
$870$		0			0
$871$	58.9962	+	34.0615i	1.99901	+	1.15413i
$872$	−40.5604	+	10.8681i	−1.37355	+	0.368041i
$873$	3.18529	−	11.8877i	0.107806	−	0.402336i
$874$	1.25369			0.0424067
$875$		0			0
$876$	−31.9952			−1.08102
$877$	−10.7066	+	39.9574i	−0.361535	+	1.34927i	0.510523	+	0.859864i	$0.329452\pi$
$877$	−10.7066	+	39.9574i	−0.361535	+	1.34927i	−0.872058	+	0.489402i	$0.837215\pi$
$878$	28.3643	−	7.60019i	0.957249	−	0.256494i
$879$	−2.17276	−	1.25444i	−0.0732854	−	0.0423113i
$880$		0			0
$881$		−	23.0542i		−	0.776715i	−0.921509	−	0.388358i	$-0.873043\pi$
$881$		−	23.0542i		−	0.776715i	0.921509	−	0.388358i	$-0.126957\pi$
$882$	2.17265	−	16.1466i	0.0731571	−	0.543686i
$883$	7.73430	−	7.73430i	0.260280	−	0.260280i	−0.564888	−	0.825168i	$-0.691081\pi$
$883$	7.73430	−	7.73430i	0.260280	−	0.260280i	0.825168	+	0.564888i	$0.191081\pi$
$884$	34.9807	−	20.1961i	1.17653	−	0.679269i
$885$		0			0
$886$	−22.2677	+	38.5688i	−0.748098	+	1.29574i
$887$	49.6024	+	13.2909i	1.66549	+	0.446265i	0.963888	−	0.266308i	$-0.0858039\pi$
$887$	49.6024	+	13.2909i	1.66549	+	0.446265i	0.701597	+	0.712574i	$0.252471\pi$
$888$	13.5523	+	13.5523i	0.454785	+	0.454785i
$889$	−15.0807	+	10.0455i	−0.505791	+	0.336916i
$890$		0			0
$891$	1.76389	+	3.05515i	0.0590926	+	0.102351i
$892$	−9.77533	−	36.4820i	−0.327302	−	1.22151i
$893$	−0.0894132	−	0.333695i	−0.00299210	−	0.0111667i
$894$	15.3347	+	26.5606i	0.512871	+	0.888318i
$895$		0			0
$896$	23.1922	−	46.8605i	0.774798	−	1.56550i
$897$	17.2994	+	17.2994i	0.577611	+	0.577611i
$898$	50.0015	+	13.3979i	1.66857	+	0.447092i
$899$	−5.32442	+	9.22216i	−0.177579	+	0.307576i
$900$		0			0
$901$	4.52620	−	2.61320i	0.150790	−	0.0870584i
$902$	5.24458	−	5.24458i	0.174625	−	0.174625i
$903$	6.70005	+	5.89272i	0.222964	+	0.196097i
$904$			52.0664i			1.73170i
$905$		0			0
$906$	−8.48661	−	4.89974i	−0.281949	−	0.162783i
$907$	−13.5581	+	3.63289i	−0.450191	+	0.120628i	−0.476789	−	0.879018i	$-0.658199\pi$
$907$	−13.5581	+	3.63289i	−0.450191	+	0.120628i	0.0265979	+	0.999646i	$0.491533\pi$
$908$	−21.7152	+	81.0421i	−0.720643	+	2.68948i
$909$	−1.43741			−0.0476759
$910$		0			0
$911$	42.2471			1.39971			0.699854	−	0.714286i	$-0.253248\pi$
$911$	42.2471			1.39971			0.699854	+	0.714286i	$0.253248\pi$
$912$	−0.0304719	+	0.113723i	−0.00100902	+	0.00376573i
$913$	35.5574	−	9.52758i	1.17678	−	0.315317i
$914$	21.3969	+	12.3535i	0.707745	+	0.408617i
$915$		0			0
$916$		−	25.2275i		−	0.833541i
$917$	2.43600	+	7.21001i	0.0804437	+	0.238096i
$918$	−3.06337	+	3.06337i	−0.101106	+	0.101106i
$919$	3.66062	−	2.11346i	0.120753	−	0.0697166i	−0.438407	−	0.898777i	$-0.644457\pi$
$919$	3.66062	−	2.11346i	0.120753	−	0.0697166i	0.559160	+	0.829060i	$0.311124\pi$
$920$		0			0
$921$	7.53194	−	13.0457i	0.248186	−	0.429870i
$922$	14.4737	+	3.87822i	0.476666	+	0.127722i
$923$	22.8970	+	22.8970i	0.753665	+	0.753665i
$924$	−17.6811	−	26.5436i	−0.581666	−	0.873220i
$925$		0			0
$926$	17.2119	+	29.8119i	0.565618	+	0.979679i
$927$	−1.60502	−	5.99000i	−0.0527156	−	0.196737i
$928$	−2.42359	−	9.04495i	−0.0795581	−	0.296915i
$929$	3.81103	+	6.60089i	0.125036	+	0.216568i	0.921747	−	0.387792i	$-0.126762\pi$
$929$	3.81103	+	6.60089i	0.125036	+	0.216568i	−0.796711	+	0.604360i	$0.793429\pi$
$930$		0			0
$931$	0.124983	+	0.970749i	0.00409617	+	0.0318150i
$932$	−17.6216	−	17.6216i	−0.577214	−	0.577214i
$933$	18.0091	+	4.82552i	0.589591	+	0.157980i
$934$	12.1522	−	21.0483i	0.397633	−	0.688720i
$935$		0			0
$936$	−18.1387	+	10.4724i	−0.592882	+	0.342300i
$937$	−31.1453	+	31.1453i	−1.01747	+	1.01747i	−0.0176276	+	0.999845i	$0.505611\pi$
$937$	−31.1453	+	31.1453i	−1.01747	+	1.01747i	−0.999845	+	0.0176276i	$0.994389\pi$
$938$	64.7674	+	12.9792i	2.11473	+	0.423785i
$939$			20.5408i			0.670324i
$940$		0			0
$941$	35.5296	+	20.5130i	1.15823	+	0.668706i	0.950880	−	0.309561i	$-0.100182\pi$
$941$	35.5296	+	20.5130i	1.15823	+	0.668706i	0.207352	+	0.978266i	$0.433515\pi$
$942$	2.17353	−	0.582395i	0.0708173	−	0.0189754i
$943$	−0.900678	+	3.36137i	−0.0293301	+	0.109461i
$944$	5.31043			0.172840
$945$		0			0
$946$	27.6905			0.900295
$947$	−13.8565	+	51.7131i	−0.450276	+	1.68045i	0.251343	+	0.967898i	$0.419128\pi$
$947$	−13.8565	+	51.7131i	−0.450276	+	1.68045i	−0.701618	+	0.712553i	$0.747539\pi$
$948$	27.8275	−	7.45635i	0.903795	−	0.242171i
$949$	51.4972	+	29.7319i	1.67167	+	0.965139i
$950$		0			0
$951$			29.2067i			0.947091i
$952$	10.7266	−	12.1961i	0.347650	−	0.395279i
$953$	−35.5644	+	35.5644i	−1.15204	+	1.15204i	−0.165900	+	0.986143i	$0.553053\pi$
$953$	−35.5644	+	35.5644i	−1.15204	+	1.15204i	−0.986143	+	0.165900i	$0.946947\pi$
$954$	−5.65954	+	3.26753i	−0.183234	+	0.105790i
$955$		0			0
$956$	16.8900	−	29.2544i	0.546263	−	0.946155i
$957$	−6.88226	−	1.84410i	−0.222472	−	0.0596112i
$958$	−50.3845	−	50.3845i	−1.62785	−	1.62785i
$959$	−3.47416	−	54.1905i	−0.112186	−	1.74990i
$960$		0			0
$961$	−1.60035	−	2.77188i	−0.0516241	−	0.0894156i
$962$	−22.2312	−	82.9679i	−0.716762	−	2.67499i
$963$	4.64750	+	17.3447i	0.149764	+	0.558925i
$964$	5.75497	+	9.96790i	0.185355	+	0.321044i
$965$		0			0
$966$	21.2610	+	10.5225i	0.684063	+	0.338557i
$967$	5.89078	+	5.89078i	0.189435	+	0.189435i	0.795452	−	0.606017i	$-0.207234\pi$
$967$	5.89078	+	5.89078i	0.189435	+	0.189435i	−0.606017	+	0.795452i	$0.707234\pi$
$968$	−4.60415	−	1.23368i	−0.147983	−	0.0396519i
$969$	0.130131	−	0.225394i	0.00418043	−	0.00724071i
$970$		0			0
$971$	−2.71844	+	1.56949i	−0.0872389	+	0.0503674i	−0.542985	−	0.839742i	$-0.682706\pi$
$971$	−2.71844	+	1.56949i	−0.0872389	+	0.0503674i	0.455746	+	0.890110i	$0.349373\pi$
$972$	2.41620	−	2.41620i	0.0774998	−	0.0774998i
$973$	5.45387	−	27.2154i	0.174843	−	0.872485i
$974$			41.7807i			1.33874i
$975$		0			0
$976$	−7.31922	−	4.22576i	−0.234283	−	0.135263i
$977$	28.5027	−	7.63727i	0.911882	−	0.244338i	0.227770	−	0.973715i	$-0.426857\pi$
$977$	28.5027	−	7.63727i	0.911882	−	0.244338i	0.684112	+	0.729377i	$0.260190\pi$
$978$	−6.18293	+	23.0750i	−0.197708	+	0.737858i
$979$	−12.3754			−0.395518
$980$		0			0
$981$	−12.7321			−0.406504
$982$	−3.17439	+	11.8470i	−0.101299	+	0.378053i
$983$	−52.8361	+	14.1574i	−1.68521	+	0.451551i	−0.969147	−	0.246484i	$-0.920725\pi$
$983$	−52.8361	+	14.1574i	−1.68521	+	0.451551i	−0.716064	+	0.698035i	$0.754058\pi$
$984$	−2.58008	−	1.48961i	−0.0822498	−	0.0474869i
$985$		0			0
$986$		−	8.74982i		−	0.278651i
$987$	1.28445	−	6.40952i	0.0408844	−	0.204017i
$988$	2.14550	−	2.14550i	0.0682575	−	0.0682575i
$989$	−11.2515	+	6.49603i	−0.357775	+	0.206562i
$990$		0			0
$991$	−24.3059	+	42.0991i	−0.772104	+	1.33732i	0.164304	+	0.986410i	$0.447462\pi$
$991$	−24.3059	+	42.0991i	−0.772104	+	1.33732i	−0.936408	+	0.350913i	$0.885871\pi$
$992$	−23.6123	−	6.32689i	−0.749690	−	0.200879i
$993$	−16.7266	−	16.7266i	−0.530803	−	0.530803i
$994$	28.1405	+	13.9273i	0.892563	+	0.441748i
$995$		0			0
$996$	−17.8280	−	30.8790i	−0.564902	−	0.978439i
$997$	2.81774	+	10.5159i	0.0892387	+	0.333043i	0.996083	−	0.0884222i	$-0.0281825\pi$
$997$	2.81774	+	10.5159i	0.0892387	+	0.333043i	−0.906844	+	0.421466i	$0.861516\pi$
$998$	21.6418	+	80.7685i	0.685061	+	2.55668i
$999$	2.90562	+	5.03269i	0.0919298	+	0.159227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bc.e.157.2		32
5.2	odd	4		105.2.u.a.73.2	yes	32
5.3	odd	4	inner	525.2.bc.e.493.7		32
5.4	even	2		105.2.u.a.52.7	✓	32
7.5	odd	6	inner	525.2.bc.e.82.7		32
15.2	even	4		315.2.bz.d.73.7		32
15.14	odd	2		315.2.bz.d.262.2		32
35.2	odd	12		735.2.v.b.313.7		32
35.4	even	6		735.2.m.c.97.13		32
35.9	even	6		735.2.v.b.607.2		32
35.12	even	12		105.2.u.a.103.7	yes	32
35.17	even	12		735.2.m.c.538.13		32
35.19	odd	6		105.2.u.a.82.2	yes	32
35.24	odd	6		735.2.m.c.97.14		32
35.27	even	4		735.2.v.b.178.2		32
35.32	odd	12		735.2.m.c.538.14		32
35.33	even	12	inner	525.2.bc.e.418.2		32
35.34	odd	2		735.2.v.b.472.7		32
105.47	odd	12		315.2.bz.d.208.2		32
105.89	even	6		315.2.bz.d.82.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.u.a.52.7	✓	32	5.4	even	2
105.2.u.a.73.2	yes	32	5.2	odd	4
105.2.u.a.82.2	yes	32	35.19	odd	6
105.2.u.a.103.7	yes	32	35.12	even	12
315.2.bz.d.73.7		32	15.2	even	4
315.2.bz.d.82.7		32	105.89	even	6
315.2.bz.d.208.2		32	105.47	odd	12
315.2.bz.d.262.2		32	15.14	odd	2
525.2.bc.e.82.7		32	7.5	odd	6	inner
525.2.bc.e.157.2		32	1.1	even	1	trivial
525.2.bc.e.418.2		32	35.33	even	12	inner
525.2.bc.e.493.7		32	5.3	odd	4	inner
735.2.m.c.97.13		32	35.4	even	6
735.2.m.c.97.14		32	35.24	odd	6
735.2.m.c.538.13		32	35.17	even	12
735.2.m.c.538.14		32	35.32	odd	12
735.2.v.b.178.2		32	35.27	even	4
735.2.v.b.313.7		32	35.2	odd	12
735.2.v.b.472.7		32	35.34	odd	2
735.2.v.b.607.2		32	35.9	even	6

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.602389 + 2.24814i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-2.95923 - 1.70851i) q^{4} -2.32745i q^{6} +(-0.519864 + 2.59417i) q^{7} +(2.33208 - 2.33208i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.602389 + 2.24814i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-2.95923 - 1.70851i) q^{4} -2.32745i q^{6} +(-0.519864 + 2.59417i) q^{7} +(2.33208 - 2.33208i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-1.76389 + 3.05515i) q^{11} +(3.30060 + 0.884392i) q^{12} +(-4.49057 - 4.49057i) q^{13} +(-5.51892 - 2.73143i) q^{14} +(0.421011 + 0.729213i) q^{16} +(-0.481759 - 1.79795i) q^{17} +(0.602389 + 2.24814i) q^{18} +(-0.0699116 - 0.121090i) q^{19} +(-0.169272 - 2.64033i) q^{21} +(-5.80587 - 5.80587i) q^{22} +(3.72112 + 0.997072i) q^{23} +(-1.64903 + 2.85621i) q^{24} +(12.8005 - 7.39038i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(5.97058 - 6.78857i) q^{28} -2.01969i q^{29} +(-4.56612 - 2.63625i) q^{31} +(4.47838 - 1.19998i) q^{32} +(0.913058 - 3.40758i) q^{33} +4.33225 q^{34} -3.41703 q^{36} +(1.50406 - 5.61323i) q^{37} +(0.314343 - 0.0842279i) q^{38} +(5.49980 + 3.17531i) q^{39} +0.903323i q^{41} +(6.03781 + 1.20996i) q^{42} +(-2.38469 + 2.38469i) q^{43} +(10.4395 - 6.02727i) q^{44} +(-4.48312 + 7.76500i) q^{46} +(2.38655 + 0.639474i) q^{47} +(-0.595400 - 0.595400i) q^{48} +(-6.45948 - 2.69723i) q^{49} +(0.930686 + 1.61200i) q^{51} +(5.61644 + 20.9608i) q^{52} +(0.726718 + 2.71215i) q^{53} +(-1.16373 - 2.01563i) q^{54} +(4.83746 + 7.26219i) q^{56} +(0.0988699 + 0.0988699i) q^{57} +(4.54056 + 1.21664i) q^{58} +(3.15338 - 5.46181i) q^{59} +(-8.69243 + 5.01858i) q^{61} +(8.67726 - 8.67726i) q^{62} +(0.846872 + 2.50655i) q^{63} +12.4749i q^{64} +(7.11071 + 4.10537i) q^{66} +(-10.3615 + 2.77634i) q^{67} +(-1.64618 + 6.14364i) q^{68} -3.85239 q^{69} -5.09892 q^{71} +(0.853601 - 3.18568i) q^{72} +(-9.04441 + 2.42344i) q^{73} +(11.7133 + 6.76269i) q^{74} +0.477780i q^{76} +(-7.00861 - 6.16411i) q^{77} +(-10.4516 + 10.4516i) q^{78} +(7.30150 - 4.21552i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-2.03080 - 0.544151i) q^{82} +(-7.37852 - 7.37852i) q^{83} +(-4.01013 + 8.10256i) q^{84} +(-3.92463 - 6.79765i) q^{86} +(0.522735 + 1.95087i) q^{87} +(3.01132 + 11.2384i) q^{88} +(1.75399 + 3.03799i) q^{89} +(13.9838 - 9.31484i) q^{91} +(-9.30816 - 9.30816i) q^{92} +(5.09285 + 1.36462i) q^{93} +(-2.87526 + 4.98010i) q^{94} +(-4.01520 + 2.31818i) q^{96} +(8.70237 - 8.70237i) q^{97} +(9.95489 - 12.8971i) q^{98} +3.52778i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{7} + 24 q^{8}+O(q^{10}) \) 32 * q - 8 * q^7 + 24 * q^8	\( 32 q - 8 q^{7} + 24 q^{8} - 8 q^{11} - 8 q^{21} + 8 q^{22} + 8 q^{23} + 24 q^{26} + 24 q^{28} + 24 q^{31} - 24 q^{32} + 36 q^{33} - 32 q^{36} - 4 q^{37} - 12 q^{38} - 16 q^{42} - 40 q^{43} - 40 q^{46} + 60 q^{47} - 8 q^{51} + 108 q^{52} + 24 q^{53} - 48 q^{56} - 16 q^{57} - 4 q^{58} - 24 q^{61} - 4 q^{63} + 72 q^{66} - 8 q^{67} - 132 q^{68} - 16 q^{71} - 12 q^{72} - 36 q^{73} - 60 q^{77} - 80 q^{78} + 16 q^{81} - 12 q^{82} - 16 q^{86} + 24 q^{87} + 32 q^{88} - 24 q^{91} + 56 q^{92} + 24 q^{93} + 72 q^{98}+O(q^{100}) \) 32 * q - 8 * q^7 + 24 * q^8 - 8 * q^11 - 8 * q^21 + 8 * q^22 + 8 * q^23 + 24 * q^26 + 24 * q^28 + 24 * q^31 - 24 * q^32 + 36 * q^33 - 32 * q^36 - 4 * q^37 - 12 * q^38 - 16 * q^42 - 40 * q^43 - 40 * q^46 + 60 * q^47 - 8 * q^51 + 108 * q^52 + 24 * q^53 - 48 * q^56 - 16 * q^57 - 4 * q^58 - 24 * q^61 - 4 * q^63 + 72 * q^66 - 8 * q^67 - 132 * q^68 - 16 * q^71 - 12 * q^72 - 36 * q^73 - 60 * q^77 - 80 * q^78 + 16 * q^81 - 12 * q^82 - 16 * q^86 + 24 * q^87 + 32 * q^88 - 24 * q^91 + 56 * q^92 + 24 * q^93 + 72 * q^98

Introduction

L-functions

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