LMFDB - Embedded newform 925.2.bb.e.576.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(151,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.151"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			576.7
Character	$\chi$	$=$	925.576
Dual form			925.2.bb.e.326.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.138747 + 0.381204i) q^{2} +(-2.85950 + 1.04077i) q^{3} +(1.40602 + 1.17979i) q^{4} -1.23446i q^{6} +(0.311866 - 1.76868i) q^{7} +(-1.34746 + 0.777958i) q^{8} +(4.79540 - 4.02382i) q^{9} +(-0.401914 - 0.696135i) q^{11} +(-5.24842 - 1.91027i) q^{12} +(-0.619185 + 0.737916i) q^{13} +(0.630958 + 0.364284i) q^{14} +(0.527835 + 2.99350i) q^{16} +(4.16945 + 4.96895i) q^{17} +(0.868548 + 2.38632i) q^{18} +(1.57597 + 4.32995i) q^{19} +(0.949014 + 5.38213i) q^{21} +(0.321134 - 0.0566245i) q^{22} +(2.01842 + 1.16533i) q^{23} +(3.04339 - 3.62697i) q^{24} +(-0.195387 - 0.338419i) q^{26} +(-4.96003 + 8.59103i) q^{27} +(2.52517 - 2.11887i) q^{28} +(-8.39549 + 4.84714i) q^{29} -5.05958i q^{31} +(-4.27892 - 0.754490i) q^{32} +(1.87379 + 1.57230i) q^{33} +(-2.47268 + 0.899982i) q^{34} +11.4897 q^{36} +(-5.87563 + 1.57385i) q^{37} -1.86926 q^{38} +(1.00256 - 2.75450i) q^{39} +(1.50630 + 1.26393i) q^{41} +(-2.18336 - 0.384985i) q^{42} -8.69915i q^{43} +(0.256195 - 1.45296i) q^{44} +(-0.724279 + 0.607742i) q^{46} +(1.25173 - 2.16806i) q^{47} +(-4.62490 - 8.01056i) q^{48} +(3.54687 + 1.29096i) q^{49} +(-17.0941 - 9.86927i) q^{51} +(-1.74118 + 0.307017i) q^{52} +(1.54232 + 8.74695i) q^{53} +(-2.58674 - 3.08276i) q^{54} +(0.955732 + 2.62585i) q^{56} +(-9.01299 - 10.7413i) q^{57} +(-0.682900 - 3.87292i) q^{58} +(-3.73942 + 0.659360i) q^{59} +(-1.10354 + 1.31515i) q^{61} +(1.92873 + 0.702001i) q^{62} +(-5.62133 - 9.73643i) q^{63} +(-2.15838 + 3.73842i) q^{64} +(-0.859348 + 0.496145i) q^{66} +(-2.17053 + 12.3097i) q^{67} +11.9055i q^{68} +(-6.98451 - 1.23156i) q^{69} +(-12.4371 + 4.52672i) q^{71} +(-3.33126 + 9.15255i) q^{72} -2.72964 q^{73} +(0.215268 - 2.45818i) q^{74} +(-2.89259 + 7.94734i) q^{76} +(-1.35658 + 0.493756i) q^{77} +(0.910926 + 0.764357i) q^{78} +(-8.15046 - 1.43715i) q^{79} +(1.98082 - 11.2338i) q^{81} +(-0.690810 + 0.398839i) q^{82} +(0.555832 - 0.466399i) q^{83} +(-5.01546 + 8.68704i) q^{84} +(3.31615 + 1.20698i) q^{86} +(18.9621 - 22.5982i) q^{87} +(1.08313 + 0.625343i) q^{88} +(-4.75128 + 0.837778i) q^{89} +(1.11204 + 1.32527i) q^{91} +(1.46309 + 4.01980i) q^{92} +(5.26588 + 14.4679i) q^{93} +(0.652799 + 0.777976i) q^{94} +(13.0208 - 2.29592i) q^{96} +(4.98157 + 2.87611i) q^{97} +(-0.984235 + 1.17297i) q^{98} +(-4.72845 - 1.72102i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} + 6 q^{9} - 30 q^{11} + 36 q^{14} + 18 q^{19} - 24 q^{21} - 96 q^{24} + 48 q^{26} + 18 q^{29} + 54 q^{34} + 24 q^{36} + 36 q^{39} + 72 q^{41} + 84 q^{44} - 18 q^{46} + 6 q^{49} - 18 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) $ 96 * q + 12 * q^4 + 6 * q^9 - 30 * q^11 + 36 * q^14 + 18 * q^19 - 24 * q^21 - 96 * q^24 + 48 * q^26 + 18 * q^29 + 54 * q^34 + 24 * q^36 + 36 * q^39 + 72 * q^41 + 84 * q^44 - 18 * q^46 + 6 * q^49 - 18 * q^51 - 24 * q^54 + 90 * q^56 - 18 * q^59 - 144 * q^61 - 66 * q^64 - 36 * q^66 + 6 * q^69 - 30 * q^71 + 6 * q^74 - 54 * q^76 - 60 * q^79 - 18 * q^81 - 48 * q^84 - 72 * q^86 - 108 * q^89 - 54 * q^91 - 6 * q^94 + 24 * q^96 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.138747	+	0.381204i	−0.0981088	+	0.269552i	−0.979032	−	0.203708i	$-0.934701\pi$
$2$	−0.138747	+	0.381204i	−0.0981088	+	0.269552i	0.880923	+	0.473260i	$0.156923\pi$
$3$	−2.85950	+	1.04077i	−1.65093	+	0.600890i	−0.988900	−	0.148584i	$-0.952528\pi$
$3$	−2.85950	+	1.04077i	−1.65093	+	0.600890i	−0.662033	+	0.749475i	$0.730306\pi$
$4$	1.40602	+	1.17979i	0.703012	+	0.589897i
$5$		0			0
$5$		0			0
$6$		−	1.23446i		−	0.503965i
$7$	0.311866	−	1.76868i	0.117874	−	0.668499i	−0.867412	−	0.497590i	$-0.834218\pi$
$7$	0.311866	−	1.76868i	0.117874	−	0.668499i	0.985287	−	0.170909i	$-0.0546704\pi$
$8$	−1.34746	+	0.777958i	−0.476400	+	0.275050i
$9$	4.79540	−	4.02382i	1.59847	−	1.34127i
$10$		0			0
$11$	−0.401914	−	0.696135i	−0.121182	−	0.209893i	0.799052	−	0.601261i	$-0.205335\pi$
$11$	−0.401914	−	0.696135i	−0.121182	−	0.209893i	−0.920234	+	0.391369i	$0.872002\pi$
$12$	−5.24842	−	1.91027i	−1.51509	−	0.551447i
$13$	−0.619185	+	0.737916i	−0.171731	+	0.204661i	−0.845044	−	0.534696i	$-0.820426\pi$
$13$	−0.619185	+	0.737916i	−0.171731	+	0.204661i	0.673313	+	0.739357i	$0.264871\pi$
$14$	0.630958	+	0.364284i	0.168631	+	0.0973589i
$15$		0			0
$16$	0.527835	+	2.99350i	0.131959	+	0.748375i
$17$	4.16945	+	4.96895i	1.01124	+	1.20515i	0.978619	+	0.205680i	$0.0659406\pi$
$17$	4.16945	+	4.96895i	1.01124	+	1.20515i	0.0326197	+	0.999468i	$0.489615\pi$
$18$	0.868548	+	2.38632i	0.204719	+	0.562460i
$19$	1.57597	+	4.32995i	0.361553	+	0.993359i	0.978481	+	0.206339i	$0.0661550\pi$
$19$	1.57597	+	4.32995i	0.361553	+	0.993359i	−0.616927	+	0.787020i	$0.711623\pi$
$20$		0			0
$21$	0.949014	+	5.38213i	0.207092	+	1.17448i
$22$	0.321134	−	0.0566245i	0.0684659	−	0.0120724i
$23$	2.01842	+	1.16533i	0.420869	+	0.242989i	0.695449	−	0.718575i	$-0.255205\pi$
$23$	2.01842	+	1.16533i	0.420869	+	0.242989i	−0.274580	+	0.961564i	$0.588539\pi$
$24$	3.04339	−	3.62697i	0.621229	−	0.740352i
$25$		0			0
$26$	−0.195387	−	0.338419i	−0.0383185	−	0.0663695i
$27$	−4.96003	+	8.59103i	−0.954559	+	1.65334i
$28$	2.52517	−	2.11887i	0.477213	−	0.400429i
$29$	−8.39549	+	4.84714i	−1.55900	+	0.900092i	−0.561652	+	0.827374i	$0.689834\pi$
$29$	−8.39549	+	4.84714i	−1.55900	+	0.900092i	−0.997353	+	0.0727177i	$0.976833\pi$
$30$		0			0
$31$		−	5.05958i		−	0.908728i	−0.890816	−	0.454364i	$-0.849867\pi$
$31$		−	5.05958i		−	0.908728i	0.890816	−	0.454364i	$-0.150133\pi$
$32$	−4.27892	−	0.754490i	−0.756414	−	0.133376i
$33$	1.87379	+	1.57230i	0.326185	+	0.273702i
$34$	−2.47268	+	0.899982i	−0.424061	+	0.154346i
$35$		0			0
$36$	11.4897			1.91495
$37$	−5.87563	+	1.57385i	−0.965947	+	0.258739i
$37$	−5.87563	+	1.57385i	−0.965947	+	0.258739i
$38$	−1.86926			−0.303233
$39$	1.00256	−	2.75450i	0.160538	−	0.441073i
$40$		0			0
$41$	1.50630	+	1.26393i	0.235244	+	0.197393i	0.752787	−	0.658264i	$-0.228709\pi$
$41$	1.50630	+	1.26393i	0.235244	+	0.197393i	−0.517543	+	0.855657i	$0.673153\pi$
$42$	−2.18336	−	0.384985i	−0.336900	−	0.0594045i
$43$		−	8.69915i		−	1.32661i	−0.748350	−	0.663304i	$-0.769154\pi$
$43$		−	8.69915i		−	1.32661i	0.748350	−	0.663304i	$-0.230846\pi$
$44$	0.256195	−	1.45296i	0.0386229	−	0.219041i
$45$		0			0
$46$	−0.724279	+	0.607742i	−0.106789	+	0.0896067i
$47$	1.25173	−	2.16806i	0.182584	−	0.316244i	−0.760176	−	0.649717i	$-0.774887\pi$
$47$	1.25173	−	2.16806i	0.182584	−	0.316244i	0.942760	+	0.333473i	$0.108221\pi$
$48$	−4.62490	−	8.01056i	−0.667546	−	1.15622i
$49$	3.54687	+	1.29096i	0.506696	+	0.184422i
$50$		0			0
$51$	−17.0941	−	9.86927i	−2.39365	−	1.38197i
$52$	−1.74118	+	0.307017i	−0.241458	+	0.0425756i
$53$	1.54232	+	8.74695i	0.211854	+	1.20149i	0.886282	+	0.463145i	$0.153279\pi$
$53$	1.54232	+	8.74695i	0.211854	+	1.20149i	−0.674428	+	0.738341i	$0.735610\pi$
$54$	−2.58674	−	3.08276i	−0.352011	−	0.419511i
$55$		0			0
$56$	0.955732	+	2.62585i	0.127715	+	0.350894i
$57$	−9.01299	−	10.7413i	−1.19380	−	1.42272i
$58$	−0.682900	−	3.87292i	−0.0896692	−	0.508539i
$59$	−3.73942	+	0.659360i	−0.486831	+	0.0858414i	−0.411676	−	0.911330i	$-0.635056\pi$
$59$	−3.73942	+	0.659360i	−0.486831	+	0.0858414i	−0.0751552	+	0.997172i	$0.523945\pi$
$60$		0			0
$61$	−1.10354	+	1.31515i	−0.141294	+	0.168387i	−0.832050	−	0.554700i	$-0.812833\pi$
$61$	−1.10354	+	1.31515i	−0.141294	+	0.168387i	0.690757	+	0.723087i	$0.257277\pi$
$62$	1.92873	+	0.702001i	0.244949	+	0.0891543i
$63$	−5.62133	−	9.73643i	−0.708221	−	1.22667i
$64$	−2.15838	+	3.73842i	−0.269797	+	0.467303i
$65$		0			0
$66$	−0.859348	+	0.496145i	−0.105778	+	0.0610712i
$67$	−2.17053	+	12.3097i	−0.265172	+	1.50387i	0.503372	+	0.864070i	$0.332093\pi$
$67$	−2.17053	+	12.3097i	−0.265172	+	1.50387i	−0.768544	+	0.639797i	$0.779019\pi$
$68$			11.9055i			1.44376i
$69$	−6.98451	−	1.23156i	−0.840836	−	0.148262i
$70$		0			0
$71$	−12.4371	+	4.52672i	−1.47601	+	0.537223i	−0.949725	−	0.313086i	$-0.898637\pi$
$71$	−12.4371	+	4.52672i	−1.47601	+	0.537223i	−0.526283	+	0.850309i	$0.676415\pi$
$72$	−3.33126	+	9.15255i	−0.392592	+	1.07864i
$73$	−2.72964			−0.319480			−0.159740	−	0.987159i	$-0.551066\pi$
$73$	−2.72964			−0.319480			−0.159740	+	0.987159i	$0.551066\pi$
$74$	0.215268	−	2.45818i	0.0250244	−	0.285757i
$75$		0			0
$76$	−2.89259	+	7.94734i	−0.331803	+	0.911622i
$77$	−1.35658	+	0.493756i	−0.154597	+	0.0562688i
$78$	0.910926	+	0.764357i	0.103142	+	0.0865464i
$79$	−8.15046	−	1.43715i	−0.916999	−	0.161692i	−0.304819	−	0.952410i	$-0.598596\pi$
$79$	−8.15046	−	1.43715i	−0.916999	−	0.161692i	−0.612180	+	0.790719i	$0.709707\pi$
$80$		0			0
$81$	1.98082	−	11.2338i	0.220091	−	1.24820i
$82$	−0.690810	+	0.398839i	−0.0762872	+	0.0440444i
$83$	0.555832	−	0.466399i	0.0610105	−	0.0511939i	−0.611772	−	0.791034i	$-0.709543\pi$
$83$	0.555832	−	0.466399i	0.0610105	−	0.0511939i	0.672783	+	0.739840i	$0.265099\pi$
$84$	−5.01546	+	8.68704i	−0.547232	+	0.947834i
$85$		0			0
$86$	3.31615	+	1.20698i	0.357590	+	0.130152i
$87$	18.9621	−	22.5982i	2.03295	−	2.42278i
$88$	1.08313	+	0.625343i	0.115462	+	0.0666618i
$89$	−4.75128	+	0.837778i	−0.503634	+	0.0888043i	−0.419693	−	0.907666i	$-0.637862\pi$
$89$	−4.75128	+	0.837778i	−0.503634	+	0.0888043i	−0.0839418	+	0.996471i	$0.526751\pi$
$90$		0			0
$91$	1.11204	+	1.32527i	0.116573	+	0.138926i
$92$	1.46309	+	4.01980i	0.152537	+	0.419093i
$93$	5.26588	+	14.4679i	0.546046	+	1.50025i
$94$	0.652799	+	0.777976i	0.0673311	+	0.0802421i
$95$		0			0
$96$	13.0208	−	2.29592i	1.32893	−	0.234327i
$97$	4.98157	+	2.87611i	0.505802	+	0.292025i	0.731106	−	0.682263i	$-0.239004\pi$
$97$	4.98157	+	2.87611i	0.505802	+	0.292025i	−0.225304	+	0.974288i	$0.572338\pi$
$98$	−0.984235	+	1.17297i	−0.0994227	+	0.118487i
$99$	−4.72845	−	1.72102i	−0.475227	−	0.172969i
$100$		0			0
$101$	−4.94450	+	8.56413i	−0.491996	+	0.852163i	−0.999958	−	0.00921726i	$-0.997066\pi$
$101$	−4.94450	+	8.56413i	−0.491996	+	0.852163i	0.507961	+	0.861380i	$0.330399\pi$
$102$	6.13395	−	5.14700i	0.607352	−	0.509629i
$103$	13.8852	−	8.01661i	1.36815	−	0.789900i	0.377456	−	0.926028i	$-0.376799\pi$
$103$	13.8852	−	8.01661i	1.36815	−	0.789900i	0.990691	+	0.136128i	$0.0434657\pi$
$104$	0.260261	−	1.47601i	0.0255207	−	0.144735i
$105$		0			0
$106$	−3.54836	−	0.625672i	−0.344648	−	0.0607707i
$107$	−9.05075	−	7.59448i	−0.874969	−	0.734186i	0.0901690	−	0.995926i	$-0.471259\pi$
$107$	−9.05075	−	7.59448i	−0.874969	−	0.734186i	−0.965138	+	0.261740i	$0.915704\pi$
$108$	−17.1096	+	6.22737i	−1.64637	+	0.599229i
$109$	3.91897	−	10.7673i	0.375369	−	1.03132i	−0.597884	−	0.801582i	$-0.703992\pi$
$109$	3.91897	−	10.7673i	0.375369	−	1.03132i	0.973253	−	0.229735i	$-0.0737860\pi$
$110$		0			0
$111$	15.1633	−	10.6156i	1.43924	−	1.00759i
$112$	5.45916			0.515843
$113$	−5.50132	+	15.1148i	−0.517521	+	1.42188i	0.355723	+	0.934592i	$0.384235\pi$
$113$	−5.50132	+	15.1148i	−0.517521	+	1.42188i	−0.873243	+	0.487285i	$0.837987\pi$
$114$	5.34514	−	1.94547i	0.500618	−	0.182210i
$115$		0			0
$116$	−17.5229	−	3.08976i	−1.62696	−	0.286877i
$117$			6.03009i			0.557482i
$118$	0.267482	−	1.51696i	0.0246237	−	0.139648i
$119$	10.0888	−	5.82477i	0.924839	−	0.533956i
$120$		0			0
$121$	5.17693	−	8.96671i	0.470630	−	0.815155i
$122$	−0.348226	−	0.603145i	−0.0315269	−	0.0546062i
$123$	−5.62272	−	2.04650i	−0.506983	−	0.184527i
$124$	5.96926	−	7.11389i	0.536056	−	0.638846i
$125$		0			0
$126$	4.49150	−	0.791973i	0.400135	−	0.0705546i
$127$	−0.389870	−	2.21106i	−0.0345953	−	0.196200i	0.962612	−	0.270884i	$-0.0873161\pi$
$127$	−0.389870	−	2.21106i	−0.0345953	−	0.196200i	−0.997207	+	0.0746845i	$0.976205\pi$
$128$	−6.71137	−	7.99830i	−0.593207	−	0.706956i
$129$	9.05384	+	24.8752i	0.797146	+	2.19014i
$130$		0			0
$131$	7.71599	+	9.19555i	0.674149	+	0.803419i	0.989342	−	0.145608i	$-0.0465139\pi$
$131$	7.71599	+	9.19555i	0.674149	+	0.803419i	−0.315193	+	0.949027i	$0.602069\pi$
$132$	0.779607	+	4.42137i	0.0678561	+	0.384831i
$133$	8.14980	−	1.43703i	0.706677	−	0.124606i
$134$	−4.39134	−	2.53534i	−0.379354	−	0.219020i
$135$		0			0
$136$	−9.48380	−	3.45182i	−0.813229	−	0.295991i
$137$	9.14384	+	15.8376i	0.781211	+	1.35310i	0.931237	+	0.364415i	$0.118731\pi$
$137$	9.14384	+	15.8376i	0.781211	+	1.35310i	−0.150026	+	0.988682i	$0.547936\pi$
$138$	1.43855	−	2.49165i	0.122458	−	0.212103i
$139$	8.43096	−	7.07442i	0.715105	−	0.600044i	−0.210922	−	0.977503i	$-0.567646\pi$
$139$	8.43096	−	7.07442i	0.715105	−	0.600044i	0.926026	+	0.377459i	$0.123202\pi$
$140$		0			0
$141$	−1.32286	+	7.50233i	−0.111405	+	0.631810i
$142$		−	5.36913i		−	0.450567i
$143$	0.762548	+	0.134458i	0.0637675	+	0.0112439i
$144$	14.5765	+	12.2311i	1.21471	+	1.01926i
$145$		0			0
$146$	0.378729	−	1.04055i	0.0313439	−	0.0861165i
$147$	−11.4859			−0.947339
$148$	−10.1181	−	4.71916i	−0.831701	−	0.387913i
$149$	9.75416			0.799092			0.399546	−	0.916713i	$-0.369168\pi$
$149$	9.75416			0.799092			0.399546	+	0.916713i	$0.369168\pi$
$150$		0			0
$151$	−16.7537	+	6.09785i	−1.36340	+	0.496236i	−0.917103	−	0.398650i	$-0.869479\pi$
$151$	−16.7537	+	6.09785i	−1.36340	+	0.496236i	−0.446294	+	0.894886i	$0.647256\pi$
$152$	−5.49208	−	4.60840i	−0.445467	−	0.373791i
$153$	39.9883	+	7.05101i	3.23286	+	0.570041i
$154$		−	0.585642i		−	0.0471924i
$155$		0			0
$156$	4.65936	−	2.69008i	0.373048	−	0.215379i
$157$	−1.22447	+	1.02745i	−0.0977231	+	0.0819994i	−0.690340	−	0.723485i	$-0.742539\pi$
$157$	−1.22447	+	1.02745i	−0.0977231	+	0.0819994i	0.592617	+	0.805484i	$0.298095\pi$
$158$	1.67870	−	2.90759i	0.133550	−	0.231315i
$159$	−13.5139	−	23.4067i	−1.07172	−	1.85627i
$160$		0			0
$161$	2.69058	−	3.20651i	0.212048	−	0.252708i
$162$	4.00753	+	2.31375i	0.314861	+	0.181785i
$163$	−4.58162	+	0.807863i	−0.358860	+	0.0632767i	−0.350172	−	0.936686i	$-0.613877\pi$
$163$	−4.58162	+	0.807863i	−0.358860	+	0.0632767i	−0.00868851	+	0.999962i	$0.502766\pi$
$164$	0.626708	+	3.55424i	0.0489376	+	0.277539i
$165$		0			0
$166$	0.100673	+	0.276597i	0.00781374	+	0.0214681i
$167$	4.35935	+	11.9772i	0.337337	+	0.926825i	0.986147	+	0.165875i	$0.0530447\pi$
$167$	4.35935	+	11.9772i	0.337337	+	0.926825i	−0.648810	+	0.760950i	$0.724733\pi$
$168$	−5.46583	−	6.51392i	−0.421698	−	0.502560i
$169$	2.09630	+	11.8887i	0.161254	+	0.914514i
$170$		0			0
$171$	24.9803	+	14.4224i	1.91029	+	1.10291i
$172$	10.2632	−	12.2312i	0.782562	−	0.932621i
$173$	−19.0279	−	6.92557i	−1.44666	−	0.526542i	−0.505004	−	0.863117i	$-0.668509\pi$
$173$	−19.0279	−	6.92557i	−1.44666	−	0.526542i	−0.941657	+	0.336575i	$0.890731\pi$
$174$	5.98358	+	10.3639i	0.453614	+	0.785683i
$175$		0			0
$176$	1.87174	−	1.57057i	0.141087	−	0.118386i
$177$	10.0066	−	5.77732i	0.752144	−	0.434250i
$178$	0.339860	−	1.92744i	0.0254736	−	0.144468i
$179$			1.15180i			0.0860896i	0.999073	+	0.0430448i	$0.0137058\pi$
$179$			1.15180i			0.0860896i	−0.999073	+	0.0430448i	$0.986294\pi$
$180$		0			0
$181$	12.8650	+	10.7950i	0.956250	+	0.802389i	0.980339	−	0.197321i	$-0.0632240\pi$
$181$	12.8650	+	10.7950i	0.956250	+	0.802389i	−0.0240888	+	0.999710i	$0.507668\pi$
$182$	−0.659491	+	0.240035i	−0.0488847	+	0.0177926i
$183$	1.78680	−	4.90919i	0.132084	−	0.362898i
$184$	−3.62632			−0.267336
$185$		0			0
$186$	−6.24583			−0.457967
$187$	1.78330	−	4.89959i	0.130408	−	0.358293i
$188$	4.31782	−	1.57156i	0.314910	−	0.114618i
$189$	13.6479	+	11.4520i	0.992741	+	0.833009i
$190$		0			0
$191$		−	8.38059i		−	0.606398i	−0.952927	−	0.303199i	$-0.901945\pi$
$191$		−	8.38059i		−	0.606398i	0.952927	−	0.303199i	$-0.0980547\pi$
$192$	2.28104	−	12.9364i	0.164620	−	0.933604i
$193$	5.66918	−	3.27310i	0.408076	−	0.235603i	−0.281887	−	0.959448i	$-0.590960\pi$
$193$	5.66918	−	3.27310i	0.408076	−	0.235603i	0.689963	+	0.723845i	$0.257627\pi$
$194$	−1.78756	+	1.49994i	−0.128340	+	0.107690i
$195$		0			0
$196$	3.46392	+	5.99969i	0.247423	+	0.428549i
$197$	−2.73633	−	0.995942i	−0.194955	−	0.0709580i	0.242697	−	0.970102i	$-0.421968\pi$
$197$	−2.73633	−	0.995942i	−0.194955	−	0.0709580i	−0.437653	+	0.899144i	$0.644190\pi$
$198$	1.31212	−	1.56372i	0.0932480	−	0.111129i
$199$	−7.93604	−	4.58187i	−0.562571	−	0.324800i	0.191606	−	0.981472i	$-0.438630\pi$
$199$	−7.93604	−	4.58187i	−0.562571	−	0.324800i	−0.754177	+	0.656671i	$0.771964\pi$
$200$		0			0
$201$	−6.60495	−	37.4585i	−0.465877	−	2.64212i
$202$	−2.57865	−	3.07311i	−0.181433	−	0.216223i
$203$	5.95478	+	16.3606i	0.417944	+	1.14829i
$204$	−12.3910	−	34.0439i	−0.867541	−	2.38355i
$205$		0			0
$206$	1.12944	+	6.40536i	0.0786917	+	0.446283i
$207$	14.3682	−	2.53350i	0.998659	−	0.176091i
$208$	−2.53578	−	1.46403i	−0.175825	−	0.101512i
$209$	2.38082	−	2.83736i	0.164685	−	0.196264i
$210$		0			0
$211$	5.64904	+	9.78442i	0.388896	+	0.673587i	0.992301	−	0.123847i	$-0.0395233\pi$
$211$	5.64904	+	9.78442i	0.388896	+	0.673587i	−0.603405	+	0.797435i	$0.706190\pi$
$212$	−8.15105	+	14.1180i	−0.559817	+	0.969631i
$213$	30.8525	−	25.8883i	2.11398	−	1.77384i
$214$	4.15081	−	2.39647i	0.283744	−	0.163819i
$215$		0			0
$216$		−	15.4348i		−	1.05020i
$217$	−8.94880	−	1.57791i	−0.607484	−	0.107116i
$218$	3.56078	+	2.98785i	0.241167	+	0.202363i
$219$	7.80541	−	2.84094i	0.527441	−	0.191973i
$220$		0			0
$221$	−6.24833			−0.420308
$222$	1.94285	+	7.25321i	0.130395	+	0.486803i
$223$	17.5376			1.17440			0.587202	−	0.809441i	$-0.300230\pi$
$223$	17.5376			1.17440			0.587202	+	0.809441i	$0.300230\pi$
$224$	−2.66890	+	7.33276i	−0.178324	+	0.489940i
$225$		0			0
$226$	−4.99851	−	4.19425i	−0.332496	−	0.278997i
$227$	17.7806	+	3.13521i	1.18014	+	0.208091i	0.729098	−	0.684410i	$-0.239940\pi$
$227$	17.7806	+	3.13521i	1.18014	+	0.208091i	0.451046	+	0.892501i	$0.351051\pi$
$228$		−	25.7359i		−	1.70440i
$229$	−1.79675	+	10.1899i	−0.118733	+	0.673367i	0.866101	+	0.499868i	$0.166618\pi$
$229$	−1.79675	+	10.1899i	−0.118733	+	0.673367i	−0.984834	+	0.173498i	$0.944493\pi$
$230$		0			0
$231$	3.36527	−	2.82379i	0.221418	−	0.185792i
$232$	7.54174	−	13.0627i	0.495139	−	0.857607i
$233$	7.00549	+	12.1339i	0.458945	+	0.794916i	0.998905	−	0.0467742i	$-0.0148941\pi$
$233$	7.00549	+	12.1339i	0.458945	+	0.794916i	−0.539960	+	0.841690i	$0.681561\pi$
$234$	−2.29869	−	0.836656i	−0.150270	−	0.0546939i
$235$		0			0
$236$	−6.03562	−	3.48467i	−0.392885	−	0.226832i
$237$	24.8020	−	4.37326i	1.61106	−	0.284074i
$238$	0.820636	+	4.65406i	0.0531940	+	0.301678i
$239$	4.76612	+	5.68005i	0.308295	+	0.367412i	0.897838	−	0.440325i	$-0.145137\pi$
$239$	4.76612	+	5.68005i	0.308295	+	0.367412i	−0.589543	+	0.807737i	$0.700692\pi$
$240$		0			0
$241$	2.48441	+	6.82587i	0.160035	+	0.439693i	0.993631	−	0.112682i	$-0.0359440\pi$
$241$	2.48441	+	6.82587i	0.160035	+	0.439693i	−0.833596	+	0.552375i	$0.813722\pi$
$242$	2.69986	+	3.21757i	0.173554	+	0.206833i
$243$	0.859861	+	4.87651i	0.0551601	+	0.312828i
$244$	−3.10320	+	0.547178i	−0.198662	+	0.0350295i
$245$		0			0
$246$	1.56027	−	1.85946i	0.0994791	−	0.118555i
$247$	−4.17096	−	1.51811i	−0.265392	−	0.0965948i
$248$	3.93614	+	6.81760i	0.249945	+	0.432918i
$249$	−1.10399	+	1.91216i	−0.0699623	+	0.121178i
$250$		0			0
$251$	0.716785	−	0.413836i	0.0452431	−	0.0261211i	−0.477208	−	0.878790i	$-0.658351\pi$
$251$	0.716785	−	0.413836i	0.0452431	−	0.0261211i	0.522451	+	0.852669i	$0.325018\pi$
$252$	3.58325	−	20.3216i	0.225724	−	1.28014i
$253$		−	1.87345i		−	0.117783i
$254$	0.896958	+	0.158158i	0.0562802	+	0.00992371i
$255$		0			0
$256$	−4.13268	+	1.50417i	−0.258293	+	0.0940109i
$257$	5.47478	−	15.0418i	0.341508	−	0.938285i	−0.643450	−	0.765488i	$-0.722498\pi$
$257$	5.47478	−	15.0418i	0.341508	−	0.938285i	0.984958	−	0.172796i	$-0.0552802\pi$
$258$	−10.7387			−0.668563
$259$	0.951227	+	10.8829i	0.0591064	+	0.676234i
$260$		0			0
$261$	−20.7557	+	57.0259i	−1.28475	+	3.52981i
$262$	−4.57595	+	1.66551i	−0.282703	+	0.102896i
$263$	−11.7430	−	9.85352i	−0.724102	−	0.607594i	0.204415	−	0.978884i	$-0.434471\pi$
$263$	−11.7430	−	9.85352i	−0.724102	−	0.607594i	−0.928517	+	0.371291i	$0.878915\pi$
$264$	−3.74804	−	0.660881i	−0.230676	−	0.0406744i
$265$		0			0
$266$	−0.582958	+	3.30612i	−0.0357434	+	0.202711i
$267$	12.7143	−	7.34063i	0.778105	−	0.449239i
$268$	−17.5747	+	14.7469i	−1.07355	+	0.900811i
$269$	1.73271	−	3.00115i	0.105645	−	0.182983i	−0.808356	−	0.588694i	$-0.799642\pi$
$269$	1.73271	−	3.00115i	0.105645	−	0.182983i	0.914002	+	0.405710i	$0.132976\pi$
$270$		0			0
$271$	9.00650	+	3.27810i	0.547106	+	0.199130i	0.600760	−	0.799429i	$-0.294865\pi$
$271$	9.00650	+	3.27810i	0.547106	+	0.199130i	−0.0536543	+	0.998560i	$0.517087\pi$
$272$	−12.6738	+	15.1040i	−0.768461	+	0.915816i
$273$	−4.55918	−	2.63224i	−0.275934	−	0.159311i
$274$	−7.30603	+	1.28825i	−0.441374	+	0.0778261i
$275$		0			0
$276$	−8.36740	−	9.97188i	−0.503658	−	0.600237i
$277$	−3.33544	−	9.16404i	−0.200407	−	0.550614i	0.798255	−	0.602319i	$-0.205757\pi$
$277$	−3.33544	−	9.16404i	−0.200407	−	0.550614i	−0.998662	+	0.0517054i	$0.983534\pi$
$278$	1.52703	+	4.19547i	0.0915849	+	0.251627i
$279$	−20.3588	−	24.2627i	−1.21885	−	1.45257i
$280$		0			0
$281$	8.72852	−	1.53907i	0.520700	−	0.0918135i	0.0928798	−	0.995677i	$-0.470393\pi$
$281$	8.72852	−	1.53907i	0.520700	−	0.0918135i	0.427820	+	0.903864i	$0.359282\pi$
$282$	−2.67637	−	1.54521i	−0.159376	−	0.0920157i
$283$	−13.6131	+	16.2235i	−0.809214	+	0.964384i	−0.999851	−	0.0172765i	$-0.994500\pi$
$283$	−13.6131	+	16.2235i	−0.809214	+	0.964384i	0.190636	+	0.981661i	$0.438945\pi$
$284$	−22.8274	−	8.30849i	−1.35456	−	0.493018i
$285$		0			0
$286$	−0.157057	+	0.272031i	−0.00928698	+	0.0160855i
$287$	2.70526	−	2.26998i	0.159686	−	0.133993i
$288$	−23.5551	+	13.5995i	−1.38800	+	0.801360i
$289$	−4.35418	+	24.6938i	−0.256129	+	1.45258i
$290$		0			0
$291$	−17.2382	−	3.03956i	−1.01052	−	0.178182i
$292$	−3.83794	−	3.22041i	−0.224598	−	0.188460i
$293$	−0.211381	+	0.0769364i	−0.0123490	+	0.00449467i	−0.348187	−	0.937425i	$-0.613203\pi$
$293$	−0.211381	+	0.0769364i	−0.0123490	+	0.00449467i	0.335838	+	0.941920i	$0.390980\pi$
$294$	1.59363	−	4.37846i	0.0929423	−	0.255357i
$295$		0			0
$296$	6.69280	−	6.69169i	0.389011	−	0.388947i
$297$	7.97402			0.462700
$298$	−1.35336	+	3.71832i	−0.0783980	+	0.215397i
$299$	−2.10969	+	0.767866i	−0.122007	+	0.0444068i
$300$		0			0
$301$	−15.3860	−	2.71297i	−0.886836	−	0.156373i
$302$		−	7.23263i		−	0.416191i
$303$	5.22549	−	29.6352i	0.300197	−	1.70250i
$304$	−12.1299	+	7.00318i	−0.695695	+	0.401660i
$305$		0			0
$306$	−8.23612	+	14.2654i	−0.470828	+	0.815498i
$307$	4.07607	+	7.05996i	0.232634	+	0.402933i	0.958582	−	0.284816i	$-0.0919323\pi$
$307$	4.07607	+	7.05996i	0.232634	+	0.402933i	−0.725949	+	0.687749i	$0.758599\pi$
$308$	−2.48992	−	0.906257i	−0.141876	−	0.0516388i
$309$	−31.3612	+	37.3748i	−1.78408	+	2.12618i
$310$		0			0
$311$	13.7812	−	2.42999i	0.781459	−	0.137792i	0.231334	−	0.972874i	$-0.425691\pi$
$311$	13.7812	−	2.42999i	0.781459	−	0.137792i	0.550125	+	0.835082i	$0.314580\pi$
$312$	0.791979	+	4.49153i	0.0448370	+	0.254283i
$313$	−14.5358	−	17.3231i	−0.821611	−	0.979158i	0.178377	−	0.983962i	$-0.442915\pi$
$313$	−14.5358	−	17.3231i	−0.821611	−	0.979158i	−0.999988	+	0.00480401i	$0.998471\pi$
$314$	−0.221777	−	0.609327i	−0.0125156	−	0.0343863i
$315$		0			0
$316$	−9.76420	−	11.6365i	−0.549279	−	0.654606i
$317$	−0.972720	−	5.51657i	−0.0546334	−	0.309842i	0.945229	−	0.326407i	$-0.105838\pi$
$317$	−0.972720	−	5.51657i	−0.0546334	−	0.309842i	−0.999863	+	0.0165653i	$0.994727\pi$
$318$	10.7977	−	1.90393i	0.605506	−	0.106767i
$319$	6.74853	+	3.89626i	0.377845	+	0.218149i
$320$		0			0
$321$	33.7848	+	12.2966i	1.88568	+	0.686332i
$322$	0.849024	+	1.47055i	0.0473143	+	0.0819507i
$323$	−14.9444	+	25.8844i	−0.831528	+	1.44025i
$324$	16.0386	−	13.4580i	0.891035	−	0.747667i
$325$		0			0
$326$	0.327725	−	1.85862i	0.0181510	−	0.102939i
$327$			34.8678i			1.92819i
$328$	−3.01296	−	0.531266i	−0.166363	−	0.0293343i
$329$	−3.44424	−	2.89006i	−0.189887	−	0.159334i
$330$		0			0
$331$	8.16552	−	22.4346i	0.448818	−	1.23312i	−0.484730	−	0.874664i	$-0.661082\pi$
$331$	8.16552	−	22.4346i	0.448818	−	1.23312i	0.933548	−	0.358453i	$-0.116696\pi$
$332$	1.33177			0.0730902
$333$	−21.8431	+	31.1897i	−1.19699	+	1.70918i
$334$	−5.17061			−0.282923
$335$		0			0
$336$	−15.6105	+	5.68175i	−0.851621	+	0.309965i
$337$	10.9802	+	9.21347i	0.598129	+	0.501890i	0.890844	−	0.454310i	$-0.150114\pi$
$337$	10.9802	+	9.21347i	0.598129	+	0.501890i	−0.292715	+	0.956200i	$0.594559\pi$
$338$	−4.82287	−	0.850402i	−0.262329	−	0.0462558i
$339$		−	48.9462i		−	2.65840i
$340$		0			0
$341$	−3.52215	+	2.03352i	−0.190735	+	0.110121i
$342$	−8.96382	+	7.52154i	−0.484708	+	0.406718i
$343$	9.67533	−	16.7582i	0.522418	−	0.904855i
$344$	6.76757	+	11.7218i	0.364883	+	0.631996i
$345$		0			0
$346$	5.28011	−	6.29259i	0.283860	−	0.338292i
$347$	−18.5439	−	10.7063i	−0.995488	−	0.574745i	−0.0885777	−	0.996069i	$-0.528232\pi$
$347$	−18.5439	−	10.7063i	−0.995488	−	0.574745i	−0.906910	+	0.421324i	$0.861565\pi$
$348$	53.3224	−	9.40218i	2.85838	−	0.504010i
$349$	−2.33228	−	13.2270i	−0.124844	−	0.708025i	−0.981400	−	0.191972i	$-0.938512\pi$
$349$	−2.33228	−	13.2270i	−0.124844	−	0.708025i	0.856557	−	0.516053i	$-0.172599\pi$
$350$		0			0
$351$	−3.26828	−	8.97953i	−0.174448	−	0.479292i
$352$	1.19453	+	3.28195i	0.0636687	+	0.174928i
$353$	1.27057	+	1.51420i	0.0676254	+	0.0805928i	0.798797	−	0.601601i	$-0.205470\pi$
$353$	1.27057	+	1.51420i	0.0676254	+	0.0805928i	−0.731171	+	0.682194i	$0.761026\pi$
$354$	0.813951	+	4.61615i	0.0432610	+	0.245345i
$355$		0			0
$356$	−7.66881	−	4.42759i	−0.406446	−	0.234662i
$357$	−22.7867	+	27.1561i	−1.20600	+	1.43725i
$358$	−0.439071	−	0.159809i	−0.0232056	−	0.00844615i
$359$	11.2420	+	19.4717i	0.593330	+	1.02768i	0.993780	+	0.111359i	$0.0355202\pi$
$359$	11.2420	+	19.4717i	0.593330	+	1.02768i	−0.400451	+	0.916318i	$0.631146\pi$
$360$		0			0
$361$	−1.70994	+	1.43481i	−0.0899970	+	0.0755165i
$362$	−5.90009	+	3.40642i	−0.310102	+	0.179038i
$363$	−5.47113	+	31.0283i	−0.287160	+	1.62856i
$364$			3.17534i			0.166433i
$365$		0			0
$366$	1.62349	+	1.36227i	0.0848612	+	0.0712070i
$367$	−14.9160	+	5.42899i	−0.778611	+	0.283391i	−0.700593	−	0.713561i	$-0.747081\pi$
$367$	−14.9160	+	5.42899i	−0.778611	+	0.283391i	−0.0780174	+	0.996952i	$0.524859\pi$
$368$	−2.42304	+	6.65724i	−0.126309	+	0.347032i
$369$	12.3091			0.640787
$370$		0			0
$371$	15.9516			0.828164
$372$	−9.66516	+	26.5548i	−0.501115	+	1.37680i
$373$	24.9041	−	9.06435i	1.28949	−	0.469334i	0.395927	−	0.918282i	$-0.370423\pi$
$373$	24.9041	−	9.06435i	1.28949	−	0.469334i	0.893558	+	0.448948i	$0.148201\pi$
$374$	1.62031	+	1.35960i	0.0837844	+	0.0703035i
$375$		0			0
$376$			3.89517i			0.200878i
$377$	1.62158	−	9.19645i	0.0835158	−	0.473641i
$378$	−6.25915	+	3.61372i	−0.321936	+	0.185870i
$379$	22.0851	−	18.5316i	1.13444	−	0.951906i	0.135195	−	0.990819i	$-0.456834\pi$
$379$	22.0851	−	18.5316i	1.13444	−	0.951906i	0.999243	+	0.0389130i	$0.0123895\pi$
$380$		0			0
$381$	3.41604	+	5.91676i	0.175009	+	0.303125i
$382$	3.19471	+	1.16278i	0.163456	+	0.0594930i
$383$	2.72116	−	3.24296i	0.139045	−	0.165707i	−0.692028	−	0.721870i	$-0.743283\pi$
$383$	2.72116	−	3.24296i	0.139045	−	0.165707i	0.831073	+	0.556163i	$0.187727\pi$
$384$	27.5156	+	15.8861i	1.40415	+	0.810685i
$385$		0			0
$386$	0.461138	+	2.61524i	0.0234713	+	0.133112i
$387$	−35.0038	−	41.7159i	−1.77934	−	2.12054i
$388$	3.61099	+	9.92111i	0.183320	+	0.503668i
$389$	−3.67317	−	10.0919i	−0.186237	−	0.511682i	0.811076	−	0.584941i	$-0.198882\pi$
$389$	−3.67317	−	10.0919i	−0.186237	−	0.511682i	−0.997313	+	0.0732588i	$0.976660\pi$
$390$		0			0
$391$	2.62519	+	14.8882i	0.132762	+	0.752929i
$392$	−5.78358	+	1.01980i	−0.292115	+	0.0515078i
$393$	−31.6343	−	18.2641i	−1.59574	−	0.921302i
$394$	0.759314	−	0.904915i	0.0382537	−	0.0455890i
$395$		0			0
$396$	−4.61787	−	7.99839i	−0.232057	−	0.401934i
$397$	16.1531	−	27.9779i	0.810700	−	1.40417i	−0.101676	−	0.994818i	$-0.532420\pi$
$397$	16.1531	−	27.9779i	0.810700	−	1.40417i	0.912375	−	0.409355i	$-0.134246\pi$
$398$	2.84773	−	2.38953i	0.142744	−	0.119776i
$399$	−21.8087	+	12.5913i	−1.09180	+	0.630352i
$400$		0			0
$401$		−	4.27679i		−	0.213573i	−0.994282	−	0.106786i	$-0.965944\pi$
$401$		−	4.27679i		−	0.213573i	0.994282	−	0.106786i	$-0.0340561\pi$
$402$	15.1958	+	2.67942i	0.757896	+	0.133637i
$403$	3.73355	+	3.13282i	0.185981	+	0.156057i
$404$	−17.0560	+	6.20787i	−0.848567	+	0.308853i
$405$		0			0
$406$	−7.06294			−0.350528
$407$	3.45711	+	3.45768i	0.171362	+	0.171391i
$408$	30.7115			1.52045
$409$	9.55320	−	26.2472i	0.472375	−	1.29784i	−0.443463	−	0.896293i	$-0.646250\pi$
$409$	9.55320	−	26.2472i	0.472375	−	1.29784i	0.915838	−	0.401548i	$-0.131528\pi$
$410$		0			0
$411$	−42.6301	−	35.7709i	−2.10279	−	1.76445i
$412$	28.9808	+	5.11010i	1.42778	+	0.251757i
$413$			6.81947i			0.335564i
$414$	−1.02776	+	5.82873i	−0.0505118	+	0.286466i
$415$		0			0
$416$	3.20620	−	2.69032i	0.157197	−	0.131904i
$417$	−16.7455	+	29.0040i	−0.820029	+	1.42033i
$418$	0.751279	+	1.30125i	0.0367463	+	0.0636464i
$419$	27.4357	+	9.98578i	1.34032	+	0.487837i	0.909914	−	0.414797i	$-0.136147\pi$
$419$	27.4357	+	9.98578i	1.34032	+	0.487837i	0.430408	+	0.902634i	$0.358370\pi$
$420$		0			0
$421$	−1.75178	−	1.01139i	−0.0853766	−	0.0492922i	0.456704	−	0.889619i	$-0.349030\pi$
$421$	−1.75178	−	1.01139i	−0.0853766	−	0.0492922i	−0.542081	+	0.840327i	$0.682363\pi$
$422$	−4.51365	+	0.795878i	−0.219721	+	0.0387427i
$423$	−2.72133	−	15.4334i	−0.132316	−	0.750399i
$424$	−8.88298	−	10.5863i	−0.431395	−	0.514117i
$425$		0			0
$426$	5.58804	+	15.3530i	0.270741	+	0.743856i
$427$	1.98192	+	2.36196i	0.0959118	+	0.114303i
$428$	−3.76565	−	21.3560i	−0.182019	−	1.03228i
$429$	−2.32045	+	0.409157i	−0.112032	+	0.0197543i
$430$		0			0
$431$	−0.140774	+	0.167768i	−0.00678084	+	0.00808109i	−0.769424	−	0.638738i	$-0.779457\pi$
$431$	−0.140774	+	0.167768i	−0.00678084	+	0.00808109i	0.762643	+	0.646819i	$0.223901\pi$
$432$	−28.3353	−	10.3132i	−1.36328	−	0.496195i
$433$	6.79454	+	11.7685i	0.326525	+	0.565558i	0.981820	−	0.189815i	$-0.0607890\pi$
$433$	6.79454	+	11.7685i	0.326525	+	0.565558i	−0.655295	+	0.755373i	$0.727456\pi$
$434$	1.84312	−	3.19238i	0.0884728	−	0.153239i
$435$		0			0
$436$	18.2133	−	10.5155i	0.872260	−	0.503599i
$437$	−1.86487	+	10.5762i	−0.0892087	+	0.505927i
$438$			3.36962i			0.161007i
$439$	7.42186	+	1.30867i	0.354226	+	0.0624596i	0.347930	−	0.937521i	$-0.386885\pi$
$439$	7.42186	+	1.30867i	0.354226	+	0.0624596i	0.00629609	+	0.999980i	$0.497996\pi$
$440$		0			0
$441$	22.2032	−	8.08131i	1.05730	−	0.384824i
$442$	0.866936	−	2.38189i	0.0412359	−	0.113295i
$443$	−13.6578			−0.648902			−0.324451	−	0.945902i	$-0.605180\pi$
$443$	−13.6578			−0.648902			−0.324451	+	0.945902i	$0.605180\pi$
$444$	33.8442	+	2.96381i	1.60618	+	0.140656i
$445$		0			0
$446$	−2.43328	+	6.68539i	−0.115219	+	0.316563i
$447$	−27.8920	+	10.1519i	−1.31925	+	0.480167i
$448$	5.93895	+	4.98337i	0.280589	+	0.235442i
$449$	6.70947	+	1.18306i	0.316639	+	0.0558321i	0.329709	−	0.944083i	$-0.393049\pi$
$449$	6.70947	+	1.18306i	0.316639	+	0.0558321i	−0.0130699	+	0.999915i	$0.504160\pi$
$450$		0			0
$451$	0.274466	−	1.55658i	0.0129241	−	0.0732963i
$452$	−25.5673	+	14.7613i	−1.20258	+	0.694312i
$453$	41.5607	−	34.8736i	1.95269	−	1.63850i
$454$	−3.66216	+	6.34305i	−0.171874	+	0.297694i
$455$		0			0
$456$	20.5009	+	7.46172i	0.960043	+	0.349427i
$457$	−14.0045	+	16.6899i	−0.655102	+	0.780720i	−0.986674	−	0.162710i	$-0.947977\pi$
$457$	−14.0045	+	16.6899i	−0.655102	+	0.780720i	0.331572	+	0.943430i	$0.392421\pi$
$458$	−3.63513	−	2.09874i	−0.169859	−	0.0980679i
$459$	−63.3690	+	11.1737i	−2.95781	+	0.521542i
$460$		0			0
$461$	−0.244773	−	0.291709i	−0.0114002	−	0.0135863i	0.760314	−	0.649555i	$-0.225045\pi$
$461$	−0.244773	−	0.291709i	−0.0114002	−	0.0135863i	−0.771714	+	0.635969i	$0.780601\pi$
$462$	0.609521	+	1.67464i	0.0283575	+	0.0779115i
$463$	2.80442	+	7.70509i	0.130333	+	0.358086i	0.987644	−	0.156712i	$-0.0500893\pi$
$463$	2.80442	+	7.70509i	0.130333	+	0.358086i	−0.857312	+	0.514798i	$0.827867\pi$
$464$	−18.9414	−	22.5734i	−0.879330	−	1.04794i
$465$		0			0
$466$	−5.59747	+	0.986985i	−0.259298	+	0.0457212i
$467$	−22.2386	−	12.8394i	−1.02908	−	0.594138i	−0.112357	−	0.993668i	$-0.535840\pi$
$467$	−22.2386	−	12.8394i	−1.02908	−	0.594138i	−0.916720	+	0.399530i	$0.869173\pi$
$468$	−7.11426	+	8.47845i	−0.328857	+	0.391916i
$469$	21.0950	+	7.67795i	0.974076	+	0.354535i
$470$		0			0
$471$	2.43202	−	4.21239i	0.112062	−	0.194096i
$472$	4.52577	−	3.79757i	0.208315	−	0.174797i
$473$	−6.05578	+	3.49631i	−0.278445	+	0.160760i
$474$	−1.77409	+	10.0614i	−0.0814868	+	0.462135i
$475$		0			0
$476$	21.0571	+	3.71294i	0.965152	+	0.170182i
$477$	42.5922	+	35.7391i	1.95016	+	1.63638i
$478$	−2.82654	+	1.02878i	−0.129283	+	0.0470551i
$479$	−1.01456	+	2.78748i	−0.0463563	+	0.127363i	−0.960711	−	0.277552i	$-0.910477\pi$
$479$	−1.01456	+	2.78748i	−0.0463563	+	0.127363i	0.914354	+	0.404915i	$0.132699\pi$
$480$		0			0
$481$	2.47673	−	5.31023i	0.112929	−	0.242125i
$482$	−2.94675			−0.134221
$483$	−4.35647	+	11.9693i	−0.198226	+	0.544622i
$484$	17.8577	−	6.49969i	0.811716	−	0.295440i
$485$		0			0
$486$	−1.97825	−	0.348818i	−0.0897351	−	0.0158227i
$487$		−	34.6469i		−	1.57000i	−0.619495	−	0.785000i	$-0.712663\pi$
$487$		−	34.6469i		−	1.57000i	0.619495	−	0.785000i	$-0.287337\pi$
$488$	0.463848	−	2.63061i	0.0209974	−	0.119082i
$489$	12.2603	−	7.07851i	0.554432	−	0.320101i
$490$		0			0
$491$	−12.8267	+	22.2166i	−0.578863	+	1.00262i	0.416747	+	0.909023i	$0.363170\pi$
$491$	−12.8267	+	22.2166i	−0.578863	+	1.00262i	−0.995610	+	0.0935978i	$0.970163\pi$
$492$	−5.49122	−	9.51108i	−0.247563	−	0.428792i
$493$	−59.0898	−	21.5069i	−2.66127	−	0.968623i
$494$	1.15742	−	1.37935i	0.0520746	−	0.0620601i
$495$		0			0
$496$	15.1459	−	2.67062i	0.680069	−	0.119915i
$497$	4.12763	+	23.4089i	0.185149	+	1.05003i
$498$	−0.575749	−	0.686151i	−0.0257999	−	0.0307471i
$499$	−1.87592	−	5.15405i	−0.0839778	−	0.230727i	0.890595	−	0.454796i	$-0.150288\pi$
$499$	−1.87592	−	5.15405i	−0.0839778	−	0.230727i	−0.974573	+	0.224069i	$0.928066\pi$
$500$		0			0
$501$	−24.9311	−	29.7118i	−1.11384	−	1.32742i
$502$	0.0583042	+	0.330660i	0.00260225	+	0.0147581i
$503$	−23.7543	+	4.18852i	−1.05915	+	0.186757i	−0.675980	−	0.736920i	$-0.736279\pi$
$503$	−23.7543	+	4.18852i	−1.05915	+	0.186757i	−0.383172	+	0.923677i	$0.625168\pi$
$504$	15.1491	+	8.74631i	0.674792	+	0.389592i
$505$		0			0
$506$	0.714168	+	0.259936i	0.0317486	+	0.0115556i
$507$	−18.3678	−	31.8139i	−0.815742	−	1.41291i
$508$	2.06043	−	3.56877i	0.0914168	−	0.158338i
$509$	15.4148	−	12.9346i	0.683250	−	0.573315i	−0.233704	−	0.972308i	$-0.575085\pi$
$509$	15.4148	−	12.9346i	0.683250	−	0.573315i	0.916954	+	0.398993i	$0.130640\pi$
$510$		0			0
$511$	−0.851284	+	4.82787i	−0.0376586	+	0.213572i
$512$		−	22.6662i		−	1.00171i
$513$	−45.0156	−	7.93747i	−1.98749	−	0.350448i
$514$	4.97440	+	4.17402i	0.219411	+	0.184108i
$515$		0			0
$516$	−16.6177	+	45.6568i	−0.731554	+	2.00993i
$517$	−2.01235			−0.0885030
$518$	−4.28060	−	1.14736i	−0.188079	−	0.0504123i
$519$	61.6181			2.70473
$520$		0			0
$521$	20.5522	−	7.48040i	0.900410	−	0.327722i	0.149993	−	0.988687i	$-0.452075\pi$
$521$	20.5522	−	7.48040i	0.900410	−	0.327722i	0.750417	+	0.660965i	$0.229853\pi$
$522$	−18.8587	−	15.8243i	−0.825423	−	0.692612i
$523$	28.2762	+	4.98587i	1.23643	+	0.218017i	0.753387	−	0.657578i	$-0.228419\pi$
$523$	28.2762	+	4.98587i	1.23643	+	0.218017i	0.483047	+	0.875594i	$0.339530\pi$
$524$			22.0324i			0.962491i
$525$		0			0
$526$	5.38550	−	3.10932i	0.234819	−	0.135573i
$527$	25.1408	−	21.0957i	1.09515	−	0.918941i
$528$	−3.71762	+	6.43910i	−0.161789	+	0.280226i
$529$	−8.78399	−	15.2143i	−0.381913	−	0.661492i
$530$		0			0
$531$	−15.2788	+	18.2086i	−0.663046	+	0.790187i
$532$	13.1542	+	7.59459i	0.570307	+	0.329267i
$533$	−1.86535	+	0.328912i	−0.0807974	+	0.0142468i
$534$	1.03420	+	5.86524i	0.0447542	+	0.253814i
$535$		0			0
$536$	−6.65170	−	18.2754i	−0.287310	−	0.789377i
$537$	−1.19876	−	3.29357i	−0.0517304	−	0.142128i
$538$	0.903641	+	1.07692i	0.0389587	+	0.0464292i
$539$	−0.526857	−	2.98795i	−0.0226933	−	0.128700i
$540$		0			0
$541$	6.90596	+	3.98716i	0.296911	+	0.171421i	0.641054	−	0.767496i	$-0.278497\pi$
$541$	6.90596	+	3.98716i	0.296911	+	0.171421i	−0.344144	+	0.938917i	$0.611831\pi$
$542$	−2.49925	+	2.97849i	−0.107352	+	0.127937i
$543$	−48.0227	−	17.4788i	−2.06085	−	0.750089i
$544$	−14.0917	−	24.4076i	−0.604177	−	1.04647i
$545$		0			0
$546$	1.63599	−	1.37276i	0.0700140	−	0.0587487i
$547$	−23.3631	+	13.4887i	−0.998932	+	0.576734i	−0.907932	−	0.419117i	$-0.862340\pi$
$547$	−23.3631	+	13.4887i	−0.998932	+	0.576734i	−0.0910002	+	0.995851i	$0.529006\pi$
$548$	−5.82864	+	33.0559i	−0.248987	+	1.41208i
$549$			10.7471i			0.458674i
$550$		0			0
$551$	−34.2190	−	28.7131i	−1.45778	−	1.22322i
$552$	10.3695	−	3.77418i	0.441354	−	0.160640i
$553$	−5.08371	+	13.9674i	−0.216181	+	0.593953i
$554$	3.95615			0.168081
$555$		0			0
$556$	20.2005			0.856691
$557$	−12.5591	+	34.5058i	−0.532146	+	1.46206i	0.324367	+	0.945931i	$0.394849\pi$
$557$	−12.5591	+	34.5058i	−0.532146	+	1.46206i	−0.856512	+	0.516127i	$0.827373\pi$
$558$	12.0738	−	4.39449i	0.511123	−	0.186034i
$559$	6.41924	+	5.38639i	0.271505	+	0.227820i
$560$		0			0
$561$			15.8664i			0.669879i
$562$	−0.624354	+	3.54089i	−0.0263368	+	0.149363i
$563$	26.9217	−	15.5433i	1.13462	−	0.655070i	0.189524	−	0.981876i	$-0.439306\pi$
$563$	26.9217	−	15.5433i	1.13462	−	0.655070i	0.945092	+	0.326806i	$0.105972\pi$
$564$	−10.7112	+	8.98775i	−0.451022	+	0.378452i
$565$		0			0
$566$	−4.29567	−	7.44032i	−0.180560	−	0.312740i
$567$	−19.2512	−	7.00688i	−0.808476	−	0.294261i
$568$	13.2369	−	15.7751i	0.555407	−	0.661908i
$569$	−1.08438	−	0.626070i	−0.0454598	−	0.0262462i	0.477098	−	0.878850i	$-0.341689\pi$
$569$	−1.08438	−	0.626070i	−0.0454598	−	0.0262462i	−0.522558	+	0.852604i	$0.675022\pi$
$570$		0			0
$571$	0.709326	+	4.02279i	0.0296844	+	0.168349i	0.996046	−	0.0888384i	$-0.0283155\pi$
$571$	0.709326	+	4.02279i	0.0296844	+	0.168349i	−0.966362	+	0.257187i	$0.917204\pi$
$572$	0.913528	+	1.08870i	0.0381965	+	0.0455209i
$573$	8.72229	+	23.9643i	0.364379	+	1.00112i
$574$	0.489979	+	1.34621i	0.0204513	+	0.0561896i
$575$		0			0
$576$	4.69244	+	26.6121i	0.195518	+	1.10884i
$577$	5.31998	−	0.938057i	0.221474	−	0.0390518i	−0.0618100	−	0.998088i	$-0.519687\pi$
$577$	5.31998	−	0.938057i	0.221474	−	0.0390518i	0.283284	+	0.959036i	$0.408576\pi$
$578$	−8.80925	−	5.08602i	−0.366416	−	0.211551i
$579$	−12.8045	+	15.2598i	−0.532135	+	0.634174i
$580$		0			0
$581$	−0.651566	−	1.12854i	−0.0270315	−	0.0468199i
$582$	3.55043	−	6.14953i	0.147170	−	0.254906i
$583$	5.46918	−	4.58918i	0.226510	−	0.190065i
$584$	3.67809	−	2.12355i	0.152200	−	0.0878729i
$585$		0			0
$586$		−	0.0912540i		−	0.00376967i
$587$	16.2624	+	2.86751i	0.671222	+	0.118355i	0.498865	−	0.866680i	$-0.333750\pi$
$587$	16.2624	+	2.86751i	0.671222	+	0.118355i	0.172358	+	0.985034i	$0.444862\pi$
$588$	−16.1494	−	13.5510i	−0.665990	−	0.558832i
$589$	21.9078	−	7.97377i	0.902693	−	0.328553i
$590$		0			0
$591$	8.86108			0.364496
$592$	−7.81268	−	16.7580i	−0.321099	−	0.688748i
$593$	39.9907			1.64222			0.821112	−	0.570768i	$-0.193354\pi$
$593$	39.9907			1.64222			0.821112	+	0.570768i	$0.193354\pi$
$594$	−1.10637	+	3.03973i	−0.0453949	+	0.124722i
$595$		0			0
$596$	13.7146	+	11.5079i	0.561771	+	0.471382i
$597$	27.4618	+	4.84225i	1.12394	+	0.198180i
$598$		−	0.910762i		−	0.0372438i
$599$	1.81733	−	10.3066i	0.0742541	−	0.421116i	−0.924908	−	0.380191i	$-0.875858\pi$
$599$	1.81733	−	10.3066i	0.0742541	−	0.421116i	0.999162	−	0.0409251i	$-0.0130305\pi$
$600$		0			0
$601$	−11.3561	+	9.52890i	−0.463225	+	0.388692i	−0.844316	−	0.535846i	$-0.819993\pi$
$601$	−11.3561	+	9.52890i	−0.463225	+	0.388692i	0.381091	+	0.924537i	$0.375548\pi$
$602$	3.16896	−	5.48880i	0.129157	−	0.223707i
$603$	39.1233	+	67.7636i	1.59323	+	2.75955i
$604$	−30.7503	−	11.1922i	−1.25121	−	0.455404i
$605$		0			0
$606$	10.5720	+	6.10377i	0.429460	+	0.247949i
$607$	−6.61955	+	1.16721i	−0.268679	+	0.0473754i	−0.306365	−	0.951914i	$-0.599113\pi$
$607$	−6.61955	+	1.16721i	−0.268679	+	0.0473754i	0.0376853	+	0.999290i	$0.488002\pi$
$608$	−3.47657	−	19.7166i	−0.140993	−	0.799613i
$609$	−34.0554	−	40.5856i	−1.37999	−	1.64461i
$610$		0			0
$611$	0.824794	+	2.26610i	0.0333676	+	0.0916767i
$612$	47.9057	+	57.0918i	1.93647	+	2.30780i
$613$	3.18089	+	18.0397i	0.128475	+	0.728617i	0.979183	+	0.202979i	$0.0650623\pi$
$613$	3.18089	+	18.0397i	0.128475	+	0.728617i	−0.850708	+	0.525638i	$0.823827\pi$
$614$	−3.25683	+	0.574266i	−0.131435	+	0.0231755i
$615$		0			0
$616$	1.44382	−	1.72068i	0.0581734	−	0.0693283i
$617$	3.64931	+	1.32824i	0.146916	+	0.0534730i	0.414431	−	0.910081i	$-0.363980\pi$
$617$	3.64931	+	1.32824i	0.146916	+	0.0534730i	−0.267516	+	0.963554i	$0.586203\pi$
$618$	−9.89615	−	17.1406i	−0.398082	−	0.689498i
$619$	−15.3029	+	26.5053i	−0.615074	+	1.06534i	0.375297	+	0.926904i	$0.377541\pi$
$619$	−15.3029	+	26.5053i	−0.615074	+	1.06534i	−0.990372	+	0.138435i	$0.955793\pi$
$620$		0			0
$621$	−20.0228	+	11.5602i	−0.803489	+	0.463894i
$622$	−0.985773	+	5.59059i	−0.0395259	+	0.224162i
$623$			8.66477i			0.347147i
$624$	8.77479	+	1.54723i	0.351273	+	0.0619389i
$625$		0			0
$626$	8.62042	−	3.13758i	0.344541	−	0.125403i
$627$	−3.85492	+	10.5913i	−0.153951	+	0.422976i
$628$	−2.93381			−0.117072
$629$	−32.3185	−	22.6336i	−1.28862	−	0.902462i
$630$		0			0
$631$	15.2339	−	41.8548i	0.606452	−	1.66621i	−0.131463	−	0.991321i	$-0.541967\pi$
$631$	15.2339	−	41.8548i	0.606452	−	1.66621i	0.737915	−	0.674893i	$-0.235810\pi$
$632$	12.1005	−	4.40421i	0.481331	−	0.175190i
$633$	−26.3368	−	22.0992i	−1.04679	−	0.878364i
$634$	2.23790	+	0.394602i	0.0888784	+	0.0156717i
$635$		0			0
$636$	8.61426	−	48.8539i	0.341578	−	1.93718i
$637$	−3.14879	+	1.81795i	−0.124760	+	0.0720300i
$638$	−2.42161	+	2.03197i	−0.0958724	+	0.0804465i
$639$	−41.4260	+	71.7519i	−1.63879	+	2.83846i
$640$		0			0
$641$	−19.2279	−	6.99839i	−0.759457	−	0.276420i	−0.0668775	−	0.997761i	$-0.521304\pi$
$641$	−19.2279	−	6.99839i	−0.759457	−	0.276420i	−0.692580	+	0.721341i	$0.743526\pi$
$642$	−9.37506	+	11.1728i	−0.370004	+	0.440954i
$643$	11.7364	+	6.77603i	0.462840	+	0.267221i	0.713237	−	0.700922i	$-0.247228\pi$
$643$	11.7364	+	6.77603i	0.462840	+	0.267221i	−0.250398	+	0.968143i	$0.580561\pi$
$644$	7.56604	−	1.33410i	0.298144	−	0.0525708i
$645$		0			0
$646$	−7.79376	−	9.28824i	−0.306641	−	0.365441i
$647$	−4.85094	−	13.3279i	−0.190710	−	0.523972i	0.807078	−	0.590445i	$-0.201048\pi$
$647$	−4.85094	−	13.3279i	−0.190710	−	0.523972i	−0.997788	+	0.0664728i	$0.978825\pi$
$648$	6.07033	+	16.6781i	0.238465	+	0.655177i
$649$	1.96193	+	2.33813i	0.0770124	+	0.0917798i
$650$		0			0
$651$	27.2313	−	4.80162i	1.06728	−	0.188190i
$652$	−7.39498	−	4.26949i	−0.289610	−	0.167206i
$653$	−19.0492	+	22.7020i	−0.745453	+	0.888397i	−0.996836	−	0.0794913i	$-0.974670\pi$
$653$	−19.0492	+	22.7020i	−0.745453	+	0.888397i	0.251382	+	0.967888i	$0.419115\pi$
$654$	−13.2917	−	4.83779i	−0.519748	−	0.189173i
$655$		0			0
$656$	−2.98851	+	5.17624i	−0.116682	+	0.202098i
$657$	−13.0897	+	10.9836i	−0.510678	+	0.428510i
$658$	1.57958	−	0.911970i	0.0615784	−	0.0355523i
$659$	8.14954	−	46.2183i	0.317461	−	1.80041i	−0.240615	−	0.970621i	$-0.577349\pi$
$659$	8.14954	−	46.2183i	0.317461	−	1.80041i	0.558076	−	0.829790i	$-0.311540\pi$
$660$		0			0
$661$	23.7868	+	4.19425i	0.925199	+	0.163138i	0.615897	−	0.787827i	$-0.288794\pi$
$661$	23.7868	+	4.19425i	0.925199	+	0.163138i	0.309302	+	0.950964i	$0.399905\pi$
$662$	7.41921	+	6.22546i	0.288356	+	0.241959i
$663$	17.8671	−	6.50309i	0.693901	−	0.252559i
$664$	−0.386124	+	1.06087i	−0.0149845	+	0.0411697i
$665$		0			0
$666$	−8.85896	−	12.6541i	−0.343278	−	0.490338i
$667$	−22.5941			−0.874849
$668$	−8.00129	+	21.9834i	−0.309579	+	0.850562i
$669$	−50.1487	+	18.2526i	−1.93886	+	0.705688i
$670$		0			0
$671$	1.35905	+	0.239636i	0.0524654	+	0.00925106i
$672$		−	23.7457i		−	0.916012i
$673$	5.36863	−	30.4470i	0.206946	−	1.17365i	−0.687403	−	0.726276i	$-0.741249\pi$
$673$	5.36863	−	30.4470i	0.206946	−	1.17365i	0.894349	−	0.447370i	$-0.147639\pi$
$674$	−5.03568	+	2.90735i	−0.193967	+	0.111987i
$675$		0			0
$676$	−11.0788	+	19.1890i	−0.426106	+	0.738037i
$677$	8.82007	+	15.2768i	0.338983	+	0.587135i	0.984242	−	0.176829i	$-0.0565838\pi$
$677$	8.82007	+	15.2768i	0.338983	+	0.587135i	−0.645259	+	0.763964i	$0.723250\pi$
$678$	18.6585	+	6.79114i	0.716575	+	0.260812i
$679$	6.64051	−	7.91386i	0.254840	−	0.303706i
$680$		0			0
$681$	−54.1068	+	9.54049i	−2.07338	+	0.365592i
$682$	−0.286496	−	1.62480i	−0.0109705	−	0.0622169i
$683$	−3.55277	−	4.23402i	−0.135943	−	0.162010i	0.693778	−	0.720189i	$-0.255945\pi$
$683$	−3.55277	−	4.23402i	−0.135943	−	0.162010i	−0.829721	+	0.558179i	$0.811500\pi$
$684$	18.1075	+	49.7499i	0.692357	+	1.90223i
$685$		0			0
$686$	5.04585	+	6.01341i	0.192652	+	0.229593i
$687$	−5.46755	−	31.0080i	−0.208600	−	1.18303i
$688$	26.0409	−	4.59171i	0.992800	−	0.175057i
$689$	−7.40950	−	4.27788i	−0.282280	−	0.162974i
$690$		0			0
$691$	−22.6364	−	8.23899i	−0.861130	−	0.313426i	−0.126560	−	0.991959i	$-0.540394\pi$
$691$	−22.6364	−	8.23899i	−0.861130	−	0.313426i	−0.734570	+	0.678533i	$0.762616\pi$
$692$	−18.5829	−	32.1865i	−0.706414	−	1.22355i
$693$	−4.51858	+	7.82640i	−0.171647	+	0.297301i
$694$	6.65419	−	5.58353i	0.252590	−	0.211948i
$695$		0			0
$696$	−7.97032	+	45.2020i	−0.302114	+	1.71338i
$697$			12.7546i			0.483115i
$698$	5.36578	+	0.946131i	0.203098	+	0.0358116i
$699$	−32.6608	−	27.4057i	−1.23535	−	1.03658i
$700$		0			0
$701$	−4.40745	+	12.1094i	−0.166467	+	0.457365i	−0.994676	−	0.103056i	$-0.967138\pi$
$701$	−4.40745	+	12.1094i	−0.166467	+	0.457365i	0.828209	+	0.560420i	$0.189360\pi$
$702$	3.87650			0.146309
$703$	−16.0745	−	22.9608i	−0.606262	−	0.865984i
$704$	3.46993			0.130778
$705$		0			0
$706$	−0.753506	+	0.274254i	−0.0283586	+	0.0103217i
$707$	13.6052	+	11.4161i	0.511676	+	0.429347i
$708$	20.8856	+	3.68269i	0.784929	+	0.138404i
$709$			1.71517i			0.0644146i	0.999481	+	0.0322073i	$0.0102537\pi$
$709$			1.71517i			0.0644146i	−0.999481	+	0.0322073i	$0.989746\pi$
$710$		0			0
$711$	−44.8675	+	25.9043i	−1.68266	+	0.971486i
$712$	5.75041	−	4.82517i	0.215506	−	0.180831i
$713$	5.89610	−	10.2124i	0.220811	−	0.382456i
$714$	−7.19043	−	12.4542i	−0.269095	−	0.466086i
$715$		0			0
$716$	−1.35889	+	1.61946i	−0.0507840	+	0.0605220i
$717$	−19.5404	−	11.2816i	−0.729748	−	0.421320i
$718$	−8.98248	+	1.58385i	−0.335223	+	0.0591089i
$719$	−0.0690262	−	0.391467i	−0.00257424	−	0.0145993i	0.983494	−	0.180943i	$-0.0579150\pi$
$719$	−0.0690262	−	0.391467i	−0.00257424	−	0.0145993i	−0.986068	+	0.166344i	$0.946804\pi$
$720$		0			0
$721$	−9.84852	−	27.0586i	−0.366778	−	1.00771i
$722$	−0.309707	−	0.850913i	−0.0115261	−	0.0316677i
$723$	−14.2084	−	16.9329i	−0.528415	−	0.629740i
$724$	5.35261	+	30.3562i	0.198928	+	1.12818i
$725$		0			0
$726$	−11.0690	−	6.39069i	−0.410809	−	0.237181i
$727$	−28.5791	+	34.0593i	−1.05994	+	1.26319i	−0.0964811	+	0.995335i	$0.530759\pi$
$727$	−28.5791	+	34.0593i	−1.05994	+	1.26319i	−0.963460	+	0.267853i	$0.913686\pi$
$728$	−2.52943	−	0.920638i	−0.0937470	−	0.0341211i
$729$	9.57652	+	16.5870i	0.354686	+	0.614334i
$730$		0			0
$731$	43.2256	−	36.2706i	1.59876	−	1.34152i
$732$	8.30411	−	4.79438i	0.306929	−	0.177205i
$733$	−2.88933	+	16.3862i	−0.106720	+	0.605238i	0.883800	+	0.467865i	$0.154977\pi$
$733$	−2.88933	+	16.3862i	−0.106720	+	0.605238i	−0.990519	+	0.137372i	$0.956134\pi$
$734$		−	6.43930i		−	0.237679i
$735$		0			0
$736$	−7.75742	−	6.50925i	−0.285942	−	0.239934i
$737$	9.44156	−	3.43645i	0.347784	−	0.126583i
$738$	−1.70785	+	4.69228i	−0.0628669	+	0.172725i
$739$	−2.89588			−0.106527			−0.0532634	−	0.998580i	$-0.516962\pi$
$739$	−2.89588			−0.106527			−0.0532634	+	0.998580i	$0.516962\pi$
$740$		0			0
$741$	13.5069			0.496187
$742$	−2.21323	+	6.08080i	−0.0812503	+	0.223233i
$743$	−25.2611	+	9.19428i	−0.926739	+	0.337306i	−0.760916	−	0.648850i	$-0.775250\pi$
$743$	−25.2611	+	9.19428i	−0.926739	+	0.337306i	−0.165823	+	0.986156i	$0.553028\pi$
$744$	−18.3510	−	15.3983i	−0.672779	−	0.564529i
$745$		0			0
$746$			10.7512i			0.393629i
$747$	0.788734	−	4.47313i	0.0288583	−	0.163663i
$748$	8.28786	−	4.78500i	0.303034	−	0.174957i
$749$	−16.2549	+	13.6394i	−0.593939	+	0.498374i
$750$		0			0
$751$	14.5769	+	25.2479i	0.531918	+	0.921309i	0.999306	+	0.0372569i	$0.0118620\pi$
$751$	14.5769	+	25.2479i	0.531918	+	0.921309i	−0.467387	+	0.884053i	$0.654805\pi$
$752$	7.15079	+	2.60268i	0.260763	+	0.0949098i
$753$	−1.61894	+	1.92937i	−0.0589974	+	0.0703103i
$754$	3.28073	+	1.89413i	0.119477	+	0.0689802i
$755$		0			0
$756$	5.67834	+	32.2035i	0.206519	+	1.17123i
$757$	20.5151	+	24.4489i	0.745634	+	0.888612i	0.996849	−	0.0793195i	$-0.0252747\pi$
$757$	20.5151	+	24.4489i	0.745634	+	0.888612i	−0.251216	+	0.967931i	$0.580830\pi$
$758$	4.00009	+	10.9901i	0.145290	+	0.399180i
$759$	1.94984	+	5.35714i	0.0707747	+	0.194452i
$760$		0			0
$761$	−3.89898	−	22.1122i	−0.141338	−	0.801568i	−0.970235	−	0.242166i	$-0.922142\pi$
$761$	−3.89898	−	22.1122i	−0.141338	−	0.801568i	0.828897	−	0.559402i	$-0.188969\pi$
$762$	−2.72946	+	0.481277i	−0.0988778	+	0.0174348i
$763$	−17.8217	−	10.2894i	−0.645189	−	0.372500i
$764$	9.88737	−	11.7833i	0.357712	−	0.426305i
$765$		0			0
$766$	0.858674	+	1.48727i	0.0310252	+	0.0537372i
$767$	1.82884	−	3.16764i	0.0660356	−	0.114377i
$768$	10.2519	−	8.60237i	0.369934	−	0.310411i
$769$	6.35195	−	3.66730i	0.229057	−	0.132246i	−0.381080	−	0.924542i	$-0.624448\pi$
$769$	6.35195	−	3.66730i	0.229057	−	0.132246i	0.610137	+	0.792296i	$0.291114\pi$
$770$		0			0
$771$			48.7102i			1.75425i
$772$	11.8326	+	2.08640i	0.425864	+	0.0750913i
$773$	36.3314	+	30.4856i	1.30675	+	1.09649i	0.988937	+	0.148338i	$0.0473923\pi$
$773$	36.3314	+	30.4856i	1.30675	+	1.09649i	0.317811	+	0.948154i	$0.397052\pi$
$774$	20.7589	−	7.55563i	0.746164	−	0.271581i
$775$		0			0
$776$	−8.94997			−0.321285
$777$	−14.0467	−	30.1298i	−0.503923	−	1.08090i
$778$	4.35673			0.156196
$779$	−3.09888	+	8.51411i	−0.111029	+	0.305050i
$780$		0			0
$781$	8.14983	+	6.83852i	0.291624	+	0.244702i
$782$	−6.03968	−	1.06496i	−0.215979	−	0.0380828i
$783$		−	96.1679i		−	3.43676i
$784$	−1.99231	+	11.2990i	−0.0711541	+	0.403535i
$785$		0			0
$786$	11.3515	−	9.52505i	0.404895	−	0.339747i
$787$	7.10871	−	12.3126i	0.253398	−	0.438898i	−0.711061	−	0.703130i	$-0.751785\pi$
$787$	7.10871	−	12.3126i	0.253398	−	0.438898i	0.964459	+	0.264232i	$0.0851184\pi$
$788$	−2.67234	−	4.62862i	−0.0951980	−	0.164888i
$789$	43.8343	+	15.9544i	1.56054	+	0.567991i
$790$		0			0
$791$	25.0175	+	14.4439i	0.889520	+	0.513565i
$792$	7.71029	−	1.35953i	0.273973	−	0.0483089i
$793$	−0.287173	−	1.62864i	−0.0101978	−	0.0578346i
$794$	8.42411	+	10.0395i	0.298961	+	0.356287i
$795$		0			0
$796$	−5.75259	−	15.8051i	−0.203895	−	0.560197i
$797$	−27.8445	−	33.1838i	−0.986303	−	1.17543i	−0.984492	−	0.175431i	$-0.943868\pi$
$797$	−27.8445	−	33.1838i	−0.986303	−	1.17543i	−0.00181088	−	0.999998i	$-0.500576\pi$
$798$	−1.77395	−	10.0606i	−0.0627972	−	0.356140i
$799$	15.9920	−	2.81982i	0.565756	−	0.0997581i
$800$		0			0
$801$	−19.4132	+	23.1357i	−0.685931	+	0.817461i
$802$	1.63033	+	0.593392i	0.0575690	+	0.0209534i
$803$	1.09708	+	1.90020i	0.0387151	+	0.0670566i
$804$	34.9066	−	60.4601i	1.23106	−	2.13226i
$805$		0			0
$806$	−1.71226	+	0.988575i	−0.0603118	+	0.0348211i
$807$	−1.83118	+	10.3851i	−0.0644606	+	0.365574i
$808$		−	15.3865i		−	0.541293i
$809$	0.512621	+	0.0903888i	0.0180228	+	0.00317790i	0.182652	−	0.983178i	$-0.441532\pi$
$809$	0.512621	+	0.0903888i	0.0180228	+	0.00317790i	−0.164630	+	0.986355i	$0.552643\pi$
$810$		0			0
$811$	40.9174	−	14.8927i	1.43680	−	0.522954i	0.497931	−	0.867217i	$-0.334093\pi$
$811$	40.9174	−	14.8927i	1.43680	−	0.522954i	0.938873	+	0.344263i	$0.111871\pi$
$812$	−10.9296	+	30.0288i	−0.383554	+	1.05381i
$813$	−29.1658			−1.02289
$814$	−1.79774	+	0.838120i	−0.0630109	+	0.0293761i
$815$		0			0
$816$	20.5208	−	56.3805i	0.718372	−	1.97371i
$817$	37.6669	−	13.7096i	1.31780	−	0.479639i
$818$	8.68006	+	7.28343i	0.303491	+	0.254659i
$819$	10.6653	+	1.88058i	0.372676	+	0.0657129i
$820$		0			0
$821$	3.17102	−	17.9837i	0.110669	−	0.627637i	−0.878134	−	0.478414i	$-0.841212\pi$
$821$	3.17102	−	17.9837i	0.110669	−	0.627637i	0.988804	−	0.149223i	$-0.0476771\pi$
$822$	19.5508	−	11.2877i	0.681913	−	0.393703i
$823$	−5.26394	+	4.41697i	−0.183489	+	0.153966i	−0.729906	−	0.683548i	$-0.760436\pi$
$823$	−5.26394	+	4.41697i	−0.183489	+	0.153966i	0.546416	+	0.837514i	$0.315992\pi$
$824$	−12.4732	+	21.6042i	−0.434523	+	0.752616i
$825$		0			0
$826$	−2.59961	−	0.946181i	−0.0904520	−	0.0329218i
$827$	6.98918	−	8.32938i	0.243038	−	0.289641i	−0.630712	−	0.776017i	$-0.717237\pi$
$827$	6.98918	−	8.32938i	0.243038	−	0.289641i	0.873750	+	0.486376i	$0.161682\pi$
$828$	23.1910	+	13.3893i	0.805944	+	0.465312i
$829$	−39.4462	+	6.95543i	−1.37002	+	0.241572i	−0.809769	−	0.586748i	$-0.800408\pi$
$829$	−39.4462	+	6.95543i	−1.37002	+	0.241572i	−0.560255	+	0.828320i	$0.689297\pi$
$830$		0			0
$831$	19.0754	+	22.7331i	0.661717	+	0.788604i
$832$	−1.42221	−	3.90748i	−0.0493061	−	0.135467i
$833$	8.37379	+	23.0068i	0.290135	+	0.797139i
$834$	−8.73306	−	10.4077i	−0.302401	−	0.360387i
$835$		0			0
$836$	6.69499	−	1.18051i	0.231551	−	0.0408287i
$837$	43.4670	+	25.0957i	1.50244	+	0.867434i
$838$	−7.61324	+	9.07311i	−0.262995	+	0.313425i
$839$	9.24284	+	3.36412i	0.319098	+	0.116142i	0.496603	−	0.867978i	$-0.334580\pi$
$839$	9.24284	+	3.36412i	0.319098	+	0.116142i	−0.177505	+	0.984120i	$0.556803\pi$
$840$		0			0
$841$	32.4896	−	56.2736i	1.12033	−	1.94047i
$842$	0.628601	−	0.527459i	0.0216630	−	0.0181774i
$843$	−23.3574	+	13.4854i	−0.804471	+	0.464462i
$844$	−3.60092	+	20.4218i	−0.123949	+	0.702948i
$845$		0			0
$846$	6.26086	+	1.10396i	0.215253	+	0.0379549i
$847$	−14.2447	−	11.9528i	−0.489455	−	0.410702i
$848$	−25.3699	+	9.23389i	−0.871206	+	0.317093i
$849$	22.0417	−	60.5591i	0.756469	−	2.07838i
$850$		0			0
$851$	−13.6935	−	3.67038i	−0.469408	−	0.125819i
$852$	73.9222			2.53253
$853$	14.2889	−	39.2583i	0.489241	−	1.34418i	−0.412128	−	0.911126i	$-0.635214\pi$
$853$	14.2889	−	39.2583i	0.489241	−	1.34418i	0.901369	−	0.433052i	$-0.142564\pi$
$854$	−1.17537	+	0.427801i	−0.0402204	+	0.0146390i
$855$		0			0
$856$	18.1037	+	3.19218i	0.618773	+	0.109106i
$857$		−	22.3532i		−	0.763572i	−0.924251	−	0.381786i	$-0.875309\pi$
$857$		−	22.3532i		−	0.763572i	0.924251	−	0.381786i	$-0.124691\pi$
$858$	0.165982	−	0.941333i	0.00566654	−	0.0321366i
$859$	−10.1552	+	5.86311i	−0.346491	+	0.200047i	−0.663139	−	0.748496i	$-0.730776\pi$
$859$	−10.1552	+	5.86311i	−0.346491	+	0.200047i	0.316648	+	0.948543i	$0.397443\pi$
$860$		0			0
$861$	−5.37315	+	9.30657i	−0.183116	+	0.317167i
$862$	−0.0444218	−	0.0769408i	−0.00151301	−	0.00262061i
$863$	−17.7138	−	6.44728i	−0.602983	−	0.219468i	0.0224469	−	0.999748i	$-0.492854\pi$
$863$	−17.7138	−	6.44728i	−0.602983	−	0.219468i	−0.625430	+	0.780280i	$0.715077\pi$
$864$	27.7054	−	33.0181i	0.942559	−	1.12330i
$865$		0			0
$866$	−5.42892	+	0.957264i	−0.184482	+	0.0325292i
$867$	−13.2499	−	75.1436i	−0.449989	−	2.55201i
$868$	−10.7206	−	12.7763i	−0.363881	−	0.433656i
$869$	2.27533	+	6.25143i	0.0771854	+	0.212065i
$870$		0			0
$871$	−7.73955	−	9.22364i	−0.262245	−	0.312531i
$872$	3.09582	+	17.5573i	0.104838	+	0.594565i
$873$	35.4616	−	6.25283i	1.20019	−	0.211626i
$874$	−3.77294	−	2.17831i	−0.127622	−	0.0736823i
$875$		0			0
$876$	14.3263	+	5.21435i	0.484041	+	0.176177i
$877$	21.7882	+	37.7383i	0.735735	+	1.27433i	0.954400	+	0.298531i	$0.0964965\pi$
$877$	21.7882	+	37.7383i	0.735735	+	1.27433i	−0.218665	+	0.975800i	$0.570170\pi$
$878$	−1.52863	+	2.64767i	−0.0515888	+	0.0893544i
$879$	0.524371	−	0.439999i	0.0176866	−	0.0148408i
$880$		0			0
$881$	5.57697	−	31.6286i	0.187893	−	1.06559i	−0.734289	−	0.678837i	$-0.762484\pi$
$881$	5.57697	−	31.6286i	0.187893	−	1.06559i	0.922182	−	0.386757i	$-0.126405\pi$
$882$			9.58521i			0.322751i
$883$	46.3909	+	8.17997i	1.56118	+	0.275278i	0.886463	−	0.462799i	$-0.153155\pi$
$883$	46.3909	+	8.17997i	1.56118	+	0.275278i	0.674716	+	0.738077i	$0.264266\pi$
$884$	−8.78530	−	7.37174i	−0.295482	−	0.247938i
$885$		0			0
$886$	1.89498	−	5.20641i	0.0636630	−	0.174913i
$887$	14.8997			0.500281			0.250141	−	0.968210i	$-0.419523\pi$
$887$	14.8997			0.500281			0.250141	+	0.968210i	$0.419523\pi$
$888$	−12.1735	+	26.1006i	−0.408517	+	0.875878i
$889$	−4.03225			−0.135237
$890$		0			0
$891$	−8.61635	+	3.13609i	−0.288659	+	0.105063i
$892$	24.6582	+	20.6907i	0.825619	+	0.692777i
$893$	11.3603	+	2.00312i	0.380157	+	0.0670320i
$894$		−	12.0411i		−	0.402714i
$895$		0			0
$896$	−16.2395	+	9.37588i	−0.542524	+	0.313226i
$897$	5.23349	−	4.39142i	0.174741	−	0.146625i
$898$	−1.38190	+	2.39353i	−0.0461148	+	0.0798731i
$899$	24.5245	+	42.4777i	0.817938	+	1.41671i
$900$		0			0
$901$	−37.0325	+	44.1337i	−1.23373	+	1.47031i
$902$	0.555292	+	0.320598i	0.0184892	+	0.0106747i
$903$	46.8199	−	8.25562i	1.55807	−	0.274730i
$904$	−4.34582	−	24.6463i	−0.144540	−	0.819725i
$905$		0			0
$906$	7.52753	+	20.6817i	0.250085	+	0.687104i
$907$	−6.30664	−	17.3274i	−0.209409	−	0.575346i	0.789872	−	0.613272i	$-0.210147\pi$
$907$	−6.30664	−	17.3274i	−0.209409	−	0.575346i	−0.999281	+	0.0379264i	$0.987925\pi$
$908$	21.3011	+	25.3857i	0.706902	+	0.842453i
$909$	10.7496	+	60.9642i	0.356543	+	2.02205i
$910$		0			0
$911$	29.9054	+	17.2659i	0.990810	+	0.572045i	0.905516	−	0.424311i	$-0.139484\pi$
$911$	29.9054	+	17.2659i	0.990810	+	0.572045i	0.0852940	+	0.996356i	$0.472817\pi$
$912$	27.3966	−	32.6500i	0.907192	−	1.08115i
$913$	−0.548073	−	0.199482i	−0.0181386	−	0.00660190i
$914$	−4.41917	−	7.65423i	−0.146173	−	0.253179i
$915$		0			0
$916$	−14.5482	+	12.2074i	−0.480687	+	0.403345i
$917$	18.6704	−	10.7793i	0.616550	−	0.355965i
$918$	4.53281	−	25.7068i	0.149605	−	0.848451i
$919$			16.9978i			0.560706i	0.959897	+	0.280353i	$0.0904515\pi$
$919$			16.9978i			0.560706i	−0.959897	+	0.280353i	$0.909549\pi$
$920$		0			0
$921$	−19.0033	−	15.9457i	−0.626181	−	0.525429i
$922$	0.145162	−	0.0528347i	0.00478066	−	0.00174002i
$923$	4.36051	−	11.9804i	0.143528	−	0.394339i
$924$	8.06313			0.265258
$925$		0			0
$926$	−3.32632			−0.109310
$927$	34.3276	−	94.3142i	1.12747	−	3.09769i
$928$	39.5808	−	14.4062i	1.29930	−	0.472908i
$929$	31.1560	+	26.1430i	1.02219	+	0.857723i	0.989902	−	0.141755i	$-0.0452746\pi$
$929$	31.1560	+	26.1430i	1.02219	+	0.857723i	0.0322928	+	0.999478i	$0.489719\pi$
$930$		0			0
$931$			17.3923i			0.570010i
$932$	−4.46558	+	25.3255i	−0.146275	+	0.829566i
$933$	−36.8782	+	21.2916i	−1.20734	+	0.697057i
$934$	7.97997	−	6.69599i	0.261113	−	0.219100i
$935$		0			0
$936$	−4.69115	−	8.12532i	−0.153335	−	0.265584i
$937$	−3.84156	−	1.39821i	−0.125498	−	0.0456776i	0.278508	−	0.960434i	$-0.410160\pi$
$937$	−3.84156	−	1.39821i	−0.125498	−	0.0456776i	−0.404006	+	0.914756i	$0.632382\pi$
$938$	−5.85373	+	6.97620i	−0.191131	+	0.227781i
$939$	59.5945	+	34.4069i	1.94479	+	1.12283i
$940$		0			0
$941$	0.261499	+	1.48304i	0.00852463	+	0.0483456i	0.988773	−	0.149423i	$-0.0477416\pi$
$941$	0.261499	+	1.48304i	0.00852463	+	0.0483456i	−0.980249	+	0.197769i	$0.936631\pi$
$942$	1.26834	+	1.51155i	0.0413248	+	0.0492490i
$943$	1.56743	+	4.30648i	0.0510426	+	0.140238i
$944$	−3.94759	−	10.8459i	−0.128483	−	0.353004i
$945$		0			0
$946$	−0.492585	−	2.79359i	−0.0160153	−	0.0908274i
$947$	17.5708	−	3.09820i	0.570973	−	0.100678i	0.119295	−	0.992859i	$-0.461937\pi$
$947$	17.5708	−	3.09820i	0.570973	−	0.100678i	0.451678	+	0.892181i	$0.350826\pi$
$948$	40.0317	+	23.1123i	1.30017	+	0.750653i
$949$	1.69015	−	2.01425i	0.0548647	−	0.0653852i
$950$		0			0
$951$	8.52299	+	14.7623i	0.276377	+	0.478699i
$952$	−9.06285	+	15.6973i	−0.293729	+	0.508753i
$953$	21.0267	−	17.6435i	0.681123	−	0.571530i	−0.235212	−	0.971944i	$-0.575578\pi$
$953$	21.0267	−	17.6435i	0.681123	−	0.571530i	0.916334	+	0.400415i	$0.131134\pi$
$954$	−19.5334	+	11.2776i	−0.632417	+	0.365126i
$955$		0			0
$956$			13.6093i			0.440157i
$957$	−23.3525	−	4.11768i	−0.754880	−	0.133106i
$958$	−0.921830	−	0.773507i	−0.0297830	−	0.0249909i
$959$	30.8633	−	11.2333i	0.996629	−	0.362743i
$960$		0			0
$961$	5.40061			0.174213
$962$	1.68064	+	1.68092i	0.0541860	+	0.0541950i
$963$	−73.9608			−2.38335
$964$	−4.55998	+	12.5284i	−0.146867	+	0.403514i
$965$		0			0
$966$	−3.95830	−	3.32141i	−0.127356	−	0.106864i
$967$	−0.515395	−	0.0908781i	−0.0165740	−	0.00292244i	0.165355	−	0.986234i	$-0.447123\pi$
$967$	−0.515395	−	0.0908781i	−0.0165740	−	0.00292244i	−0.181929	+	0.983312i	$0.558234\pi$
$968$			16.1097i			0.517786i
$969$	15.7936	−	89.5702i	0.507365	−	2.87741i
$970$		0			0
$971$	−23.5867	+	19.7916i	−0.756934	+	0.635143i	−0.937327	−	0.348452i	$-0.886708\pi$
$971$	−23.5867	+	19.7916i	−0.756934	+	0.635143i	0.180393	+	0.983595i	$0.442263\pi$
$972$	−4.54429	+	7.87095i	−0.145758	+	0.252461i
$973$	−9.88306	−	17.1180i	−0.316836	−	0.548777i
$974$	13.2075	+	4.80715i	0.423197	+	0.154031i
$975$		0			0
$976$	−4.51938	−	2.60926i	−0.144662	−	0.0835205i
$977$	29.8543	−	5.26411i	0.955123	−	0.168414i	0.325697	−	0.945474i	$-0.394401\pi$
$977$	29.8543	−	5.26411i	0.955123	−	0.168414i	0.629426	+	0.777060i	$0.283290\pi$
$978$	0.997272	+	5.65581i	0.0318892	+	0.180853i
$979$	2.49281	+	2.97081i	0.0796705	+	0.0949476i
$980$		0			0
$981$	−24.5325	−	67.4025i	−0.783263	−	2.15200i
$982$	−6.68938	−	7.97209i	−0.213467	−	0.254400i
$983$	−7.25467	−	41.1433i	−0.231388	−	1.31227i	−0.850088	−	0.526640i	$-0.823452\pi$
$983$	−7.25467	−	41.1433i	−0.231388	−	1.31227i	0.618700	−	0.785627i	$-0.287660\pi$
$984$	9.16849	−	1.61665i	0.292281	−	0.0515370i
$985$		0			0
$986$	16.3970	−	19.5412i	0.522188	−	0.622320i
$987$	12.8567	+	4.67945i	0.409233	+	0.148949i
$988$	−4.07342	−	7.05537i	−0.129593	−	0.224461i
$989$	10.1374	−	17.5585i	0.322351	−	0.558328i
$990$		0			0
$991$	−28.7917	+	16.6229i	−0.914598	+	0.528043i	−0.881908	−	0.471422i	$-0.843741\pi$
$991$	−28.7917	+	16.6229i	−0.914598	+	0.528043i	−0.0326900	+	0.999466i	$0.510407\pi$
$992$	−3.81740	+	21.6496i	−0.121203	+	0.687375i
$993$			72.6501i			2.30548i
$994$	−9.49628	−	1.67445i	−0.301204	−	0.0531103i
$995$		0			0
$996$	−3.80819	+	1.38607i	−0.120667	+	0.0439192i
$997$	2.94764	−	8.09857i	0.0933526	−	0.256484i	−0.884224	−	0.467062i	$-0.845312\pi$
$997$	2.94764	−	8.09857i	0.0933526	−	0.256484i	0.977577	+	0.210578i	$0.0675346\pi$
$998$	2.22502			0.0704319
$999$	15.6223	−	58.2840i	0.494269	−	1.84403i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bb.e.576.7		96
5.2	odd	4		185.2.v.a.169.7	yes	96
5.3	odd	4		185.2.v.a.169.10	yes	96
5.4	even	2	inner	925.2.bb.e.576.10		96
37.30	even	18	inner	925.2.bb.e.326.7		96
185.67	odd	36		185.2.v.a.104.10	yes	96
185.104	even	18	inner	925.2.bb.e.326.10		96
185.178	odd	36		185.2.v.a.104.7	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.v.a.104.7	✓	96	185.178	odd	36
185.2.v.a.104.10	yes	96	185.67	odd	36
185.2.v.a.169.7	yes	96	5.2	odd	4
185.2.v.a.169.10	yes	96	5.3	odd	4
925.2.bb.e.326.7		96	37.30	even	18	inner
925.2.bb.e.326.10		96	185.104	even	18	inner
925.2.bb.e.576.7		96	1.1	even	1	trivial
925.2.bb.e.576.10		96	5.4	even	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.138747 + 0.381204i) q^{2} +(-2.85950 + 1.04077i) q^{3} +(1.40602 + 1.17979i) q^{4} -1.23446i q^{6} +(0.311866 - 1.76868i) q^{7} +(-1.34746 + 0.777958i) q^{8} +(4.79540 - 4.02382i) q^{9} +(-0.401914 - 0.696135i) q^{11} +(-5.24842 - 1.91027i) q^{12} +(-0.619185 + 0.737916i) q^{13} +(0.630958 + 0.364284i) q^{14} +(0.527835 + 2.99350i) q^{16} +(4.16945 + 4.96895i) q^{17} +(0.868548 + 2.38632i) q^{18} +(1.57597 + 4.32995i) q^{19} +(0.949014 + 5.38213i) q^{21} +(0.321134 - 0.0566245i) q^{22} +(2.01842 + 1.16533i) q^{23} +(3.04339 - 3.62697i) q^{24} +(-0.195387 - 0.338419i) q^{26} +(-4.96003 + 8.59103i) q^{27} +(2.52517 - 2.11887i) q^{28} +(-8.39549 + 4.84714i) q^{29} -5.05958i q^{31} +(-4.27892 - 0.754490i) q^{32} +(1.87379 + 1.57230i) q^{33} +(-2.47268 + 0.899982i) q^{34} +11.4897 q^{36} +(-5.87563 + 1.57385i) q^{37} -1.86926 q^{38} +(1.00256 - 2.75450i) q^{39} +(1.50630 + 1.26393i) q^{41} +(-2.18336 - 0.384985i) q^{42} -8.69915i q^{43} +(0.256195 - 1.45296i) q^{44} +(-0.724279 + 0.607742i) q^{46} +(1.25173 - 2.16806i) q^{47} +(-4.62490 - 8.01056i) q^{48} +(3.54687 + 1.29096i) q^{49} +(-17.0941 - 9.86927i) q^{51} +(-1.74118 + 0.307017i) q^{52} +(1.54232 + 8.74695i) q^{53} +(-2.58674 - 3.08276i) q^{54} +(0.955732 + 2.62585i) q^{56} +(-9.01299 - 10.7413i) q^{57} +(-0.682900 - 3.87292i) q^{58} +(-3.73942 + 0.659360i) q^{59} +(-1.10354 + 1.31515i) q^{61} +(1.92873 + 0.702001i) q^{62} +(-5.62133 - 9.73643i) q^{63} +(-2.15838 + 3.73842i) q^{64} +(-0.859348 + 0.496145i) q^{66} +(-2.17053 + 12.3097i) q^{67} +11.9055i q^{68} +(-6.98451 - 1.23156i) q^{69} +(-12.4371 + 4.52672i) q^{71} +(-3.33126 + 9.15255i) q^{72} -2.72964 q^{73} +(0.215268 - 2.45818i) q^{74} +(-2.89259 + 7.94734i) q^{76} +(-1.35658 + 0.493756i) q^{77} +(0.910926 + 0.764357i) q^{78} +(-8.15046 - 1.43715i) q^{79} +(1.98082 - 11.2338i) q^{81} +(-0.690810 + 0.398839i) q^{82} +(0.555832 - 0.466399i) q^{83} +(-5.01546 + 8.68704i) q^{84} +(3.31615 + 1.20698i) q^{86} +(18.9621 - 22.5982i) q^{87} +(1.08313 + 0.625343i) q^{88} +(-4.75128 + 0.837778i) q^{89} +(1.11204 + 1.32527i) q^{91} +(1.46309 + 4.01980i) q^{92} +(5.26588 + 14.4679i) q^{93} +(0.652799 + 0.777976i) q^{94} +(13.0208 - 2.29592i) q^{96} +(4.98157 + 2.87611i) q^{97} +(-0.984235 + 1.17297i) q^{98} +(-4.72845 - 1.72102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} + 6 q^{9} - 30 q^{11} + 36 q^{14} + 18 q^{19} - 24 q^{21} - 96 q^{24} + 48 q^{26} + 18 q^{29} + 54 q^{34} + 24 q^{36} + 36 q^{39} + 72 q^{41} + 84 q^{44} - 18 q^{46} + 6 q^{49} - 18 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) \) 96 * q + 12 * q^4 + 6 * q^9 - 30 * q^11 + 36 * q^14 + 18 * q^19 - 24 * q^21 - 96 * q^24 + 48 * q^26 + 18 * q^29 + 54 * q^34 + 24 * q^36 + 36 * q^39 + 72 * q^41 + 84 * q^44 - 18 * q^46 + 6 * q^49 - 18 * q^51 - 24 * q^54 + 90 * q^56 - 18 * q^59 - 144 * q^61 - 66 * q^64 - 36 * q^66 + 6 * q^69 - 30 * q^71 + 6 * q^74 - 54 * q^76 - 60 * q^79 - 18 * q^81 - 48 * q^84 - 72 * q^86 - 108 * q^89 - 54 * q^91 - 6 * q^94 + 24 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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