LMFDB - Embedded newform 875.2.bb.b.768.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(82,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([27, 50]))

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

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

chi := DirichletCharacter("875.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not 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:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			768.14
Character	$\chi$	$=$	875.768
Dual form			875.2.bb.b.507.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.35892 - 0.882496i) q^{2} +(2.55023 - 0.978941i) q^{3} +(0.254403 - 0.571398i) q^{4} +(2.60166 - 3.58087i) q^{6} +(-0.156130 + 2.64114i) q^{7} +(0.348409 + 2.19977i) q^{8} +(3.31591 - 2.98566i) q^{9} +(2.62811 - 2.91881i) q^{11} +(0.0894203 - 1.70624i) q^{12} +(0.0441012 + 0.0865535i) q^{13} +(2.11863 + 3.72689i) q^{14} +(3.25179 + 3.61148i) q^{16} +(2.60462 - 2.10918i) q^{17} +(1.87124 - 6.98356i) q^{18} +(-5.56832 + 2.47917i) q^{19} +(2.18736 + 6.88836i) q^{21} +(0.995562 - 6.28573i) q^{22} +(-2.85640 - 4.39848i) q^{23} +(3.04197 + 5.26884i) q^{24} +(0.136313 + 0.0787005i) q^{26} +(1.81310 - 3.55840i) q^{27} +(1.46942 + 0.761125i) q^{28} +(-2.51245 - 3.45809i) q^{29} +(-0.701840 - 0.0737664i) q^{31} +(3.30346 + 0.885159i) q^{32} +(3.84493 - 10.0164i) q^{33} +(1.67814 - 5.16477i) q^{34} +(-0.862422 - 2.65426i) q^{36} +(-7.70713 - 0.403914i) q^{37} +(-5.37906 + 8.28302i) q^{38} +(0.197199 + 0.177559i) q^{39} +(-0.124652 - 0.0405019i) q^{41} +(9.05139 + 7.43042i) q^{42} +(8.25770 + 8.25770i) q^{43} +(-0.999203 - 2.24425i) q^{44} +(-7.76327 - 3.45643i) q^{46} +(1.70482 - 2.10528i) q^{47} +(11.8282 + 6.02679i) q^{48} +(-6.95125 - 0.824720i) q^{49} +(4.57761 - 7.92865i) q^{51} +(0.0606759 - 0.00317989i) q^{52} +(-4.21462 - 10.9795i) q^{53} +(-0.676413 - 6.43564i) q^{54} +(-5.86430 + 0.576749i) q^{56} +(-11.7735 + 11.7735i) q^{57} +(-6.46598 - 2.48206i) q^{58} +(5.04772 - 1.07293i) q^{59} +(-1.48307 + 6.97731i) q^{61} +(-1.01885 + 0.519128i) q^{62} +(7.36783 + 9.22393i) q^{63} +(-3.97346 + 1.29105i) q^{64} +(-3.61445 - 17.0046i) q^{66} +(-0.351262 - 0.433773i) q^{67} +(-0.542557 - 2.02485i) q^{68} +(-11.5903 - 8.42087i) q^{69} +(0.818370 - 0.594581i) q^{71} +(7.72305 + 6.25400i) q^{72} +(-0.111673 - 2.13084i) q^{73} +(-10.8299 + 6.25262i) q^{74} +3.81243i q^{76} +(7.29866 + 7.39691i) q^{77} +(0.424673 + 0.0672616i) q^{78} +(-15.3675 + 1.61519i) q^{79} +(-0.258873 + 2.46301i) q^{81} +(-0.205136 + 0.0549659i) q^{82} +(-10.6837 + 1.69214i) q^{83} +(4.49246 + 0.502566i) q^{84} +(18.5090 + 3.93420i) q^{86} +(-9.79260 - 6.35939i) q^{87} +(7.33636 + 4.76429i) q^{88} +(0.981714 + 0.208670i) q^{89} +(-0.235485 + 0.102964i) q^{91} +(-3.23996 + 0.513159i) q^{92} +(-1.86207 + 0.498939i) q^{93} +(0.458824 - 4.36542i) q^{94} +(9.29110 - 0.976534i) q^{96} +(11.1837 + 1.77133i) q^{97} +(-10.1740 + 5.01371i) q^{98} -17.5251i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) $ 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.35892	−	0.882496i	0.960904	−	0.624019i	0.0340422	−	0.999420i	$-0.489162\pi$
$2$	1.35892	−	0.882496i	0.960904	−	0.624019i	0.926862	+	0.375402i	$0.122495\pi$
$3$	2.55023	−	0.978941i	1.47238	−	0.565192i	0.515808	−	0.856704i	$-0.327492\pi$
$3$	2.55023	−	0.978941i	1.47238	−	0.565192i	0.956567	+	0.291512i	$0.0941583\pi$
$4$	0.254403	−	0.571398i	0.127201	−	0.285699i
$5$		0			0
$5$		0			0
$6$	2.60166	−	3.58087i	1.06212	−	1.46189i
$7$	−0.156130	+	2.64114i	−0.0590114	+	0.998257i
$7$	−0.156130	+	2.64114i	−0.0590114	+	0.998257i
$8$	0.348409	+	2.19977i	0.123181	+	0.777736i
$9$	3.31591	−	2.98566i	1.10530	−	0.995219i
$10$		0			0
$11$	2.62811	−	2.91881i	0.792404	−	0.880054i	−0.202664	−	0.979248i	$-0.564960\pi$
$11$	2.62811	−	2.91881i	0.792404	−	0.880054i	0.995068	+	0.0991947i	$0.0316267\pi$
$12$	0.0894203	−	1.70624i	0.0258134	−	0.492549i
$13$	0.0441012	+	0.0865535i	0.0122315	+	0.0240056i	0.897041	−	0.441946i	$-0.145712\pi$
$13$	0.0441012	+	0.0865535i	0.0122315	+	0.0240056i	−0.884810	+	0.465952i	$0.845712\pi$
$14$	2.11863	+	3.72689i	0.566227	+	0.996054i
$15$		0			0
$16$	3.25179	+	3.61148i	0.812948	+	0.902871i
$17$	2.60462	−	2.10918i	0.631712	−	0.511550i	−0.259142	−	0.965839i	$-0.583440\pi$
$17$	2.60462	−	2.10918i	0.631712	−	0.511550i	0.890854	+	0.454289i	$0.150107\pi$
$18$	1.87124	−	6.98356i	0.441055	−	1.64604i
$19$	−5.56832	+	2.47917i	−1.27746	+	0.568762i	−0.929526	−	0.368757i	$-0.879783\pi$
$19$	−5.56832	+	2.47917i	−1.27746	+	0.568762i	−0.347934	+	0.937519i	$0.613117\pi$
$20$		0			0
$21$	2.18736	+	6.88836i	0.477320	+	1.50316i
$22$	0.995562	−	6.28573i	0.212254	−	1.34012i
$23$	−2.85640	−	4.39848i	−0.595601	−	0.917146i	−0.999997	−	0.00256149i	$-0.999185\pi$
$23$	−2.85640	−	4.39848i	−0.595601	−	0.917146i	0.404395	−	0.914584i	$-0.367482\pi$
$24$	3.04197	+	5.26884i	0.620939	+	1.07550i
$25$		0			0
$26$	0.136313	+	0.0787005i	0.0267332	+	0.0154344i
$27$	1.81310	−	3.55840i	0.348930	−	0.684814i
$28$	1.46942	+	0.761125i	0.277695	+	0.143839i
$29$	−2.51245	−	3.45809i	−0.466550	−	0.642152i	0.509301	−	0.860589i	$-0.329904\pi$
$29$	−2.51245	−	3.45809i	−0.466550	−	0.642152i	−0.975851	+	0.218437i	$0.929904\pi$
$30$		0			0
$31$	−0.701840	−	0.0737664i	−0.126054	−	0.0132488i	0.0412913	−	0.999147i	$-0.486853\pi$
$31$	−0.701840	−	0.0737664i	−0.126054	−	0.0132488i	−0.167345	+	0.985898i	$0.553520\pi$
$32$	3.30346	+	0.885159i	0.583975	+	0.156475i
$33$	3.84493	−	10.0164i	0.669317	−	1.74363i
$34$	1.67814	−	5.16477i	0.287798	−	0.885751i
$35$		0			0
$36$	−0.862422	−	2.65426i	−0.143737	−	0.442377i
$37$	−7.70713	−	0.403914i	−1.26704	−	0.0664030i	−0.593066	−	0.805154i	$-0.702083\pi$
$37$	−7.70713	−	0.403914i	−1.26704	−	0.0664030i	−0.673978	+	0.738751i	$0.735416\pi$
$38$	−5.37906	+	8.28302i	−0.872599	+	1.34368i
$39$	0.197199	+	0.177559i	0.0315771	+	0.0284322i
$40$		0			0
$41$	−0.124652	−	0.0405019i	−0.0194674	−	0.00632534i	0.299267	−	0.954169i	$-0.403258\pi$
$41$	−0.124652	−	0.0405019i	−0.0194674	−	0.00632534i	−0.318735	+	0.947844i	$0.603258\pi$
$42$	9.05139	+	7.43042i	1.39666	+	1.14654i
$43$	8.25770	+	8.25770i	1.25929	+	1.25929i	0.951434	+	0.307854i	$0.0996108\pi$
$43$	8.25770	+	8.25770i	1.25929	+	1.25929i	0.307854	+	0.951434i	$0.400389\pi$
$44$	−0.999203	−	2.24425i	−0.150636	−	0.338333i
$45$		0			0
$46$	−7.76327	−	3.45643i	−1.14463	−	0.509623i
$47$	1.70482	−	2.10528i	0.248674	−	0.307087i	−0.637490	−	0.770459i	$-0.720027\pi$
$47$	1.70482	−	2.10528i	0.248674	−	0.307087i	0.886164	+	0.463372i	$0.153361\pi$
$48$	11.8282	+	6.02679i	1.70726	+	0.869893i
$49$	−6.95125	−	0.824720i	−0.993035	−	0.117817i
$50$		0			0
$51$	4.57761	−	7.92865i	0.640993	−	1.11023i
$52$	0.0606759	−	0.00317989i	0.00841424	−	0.000440972i
$53$	−4.21462	−	10.9795i	−0.578922	−	1.50814i	−0.839868	−	0.542791i	$-0.817368\pi$
$53$	−4.21462	−	10.9795i	−0.578922	−	1.50814i	0.260945	−	0.965354i	$-0.415966\pi$
$54$	−0.676413	−	6.43564i	−0.0920482	−	0.875780i
$55$		0			0
$56$	−5.86430	+	0.576749i	−0.783649	+	0.0770713i
$57$	−11.7735	+	11.7735i	−1.55944	+	1.55944i
$58$	−6.46598	−	2.48206i	−0.849025	−	0.325910i
$59$	5.04772	−	1.07293i	0.657157	−	0.139683i	0.132748	−	0.991150i	$-0.457620\pi$
$59$	5.04772	−	1.07293i	0.657157	−	0.139683i	0.524409	+	0.851467i	$0.324286\pi$
$60$		0			0
$61$	−1.48307	+	6.97731i	−0.189888	+	0.893354i	0.775259	+	0.631644i	$0.217620\pi$
$61$	−1.48307	+	6.97731i	−0.189888	+	0.893354i	−0.965147	+	0.261709i	$0.915714\pi$
$62$	−1.01885	+	0.519128i	−0.129394	+	0.0659293i
$63$	7.36783	+	9.22393i	0.928260	+	1.16211i
$64$	−3.97346	+	1.29105i	−0.496682	+	0.161382i
$65$		0			0
$66$	−3.61445	−	17.0046i	−0.444908	−	2.09313i
$67$	−0.351262	−	0.433773i	−0.0429135	−	0.0529938i	0.755237	−	0.655451i	$-0.227522\pi$
$67$	−0.351262	−	0.433773i	−0.0429135	−	0.0529938i	−0.798151	+	0.602458i	$0.794188\pi$
$68$	−0.542557	−	2.02485i	−0.0657947	−	0.245549i
$69$	−11.5903	−	8.42087i	−1.39531	−	1.01375i
$70$		0			0
$71$	0.818370	−	0.594581i	0.0971227	−	0.0705637i	−0.538164	−	0.842840i	$-0.680882\pi$
$71$	0.818370	−	0.594581i	0.0971227	−	0.0705637i	0.635287	+	0.772276i	$0.280882\pi$
$72$	7.72305	+	6.25400i	0.910170	+	0.737041i
$73$	−0.111673	−	2.13084i	−0.0130703	−	0.249396i	−0.997349	−	0.0727716i	$-0.976816\pi$
$73$	−0.111673	−	2.13084i	−0.0130703	−	0.249396i	0.984278	−	0.176624i	$-0.0565178\pi$
$74$	−10.8299	+	6.25262i	−1.25894	+	0.726852i
$75$		0			0
$76$			3.81243i			0.437316i
$77$	7.29866	+	7.39691i	0.831759	+	0.842956i
$78$	0.424673	+	0.0672616i	0.0480848	+	0.00761588i
$79$	−15.3675	+	1.61519i	−1.72898	+	0.181723i	−0.916167	−	0.400797i	$-0.868733\pi$
$79$	−15.3675	+	1.61519i	−1.72898	+	0.181723i	−0.812816	+	0.582521i	$0.802067\pi$
$80$		0			0
$81$	−0.258873	+	2.46301i	−0.0287636	+	0.273668i
$82$	−0.205136	+	0.0549659i	−0.0226534	+	0.00606997i
$83$	−10.6837	+	1.69214i	−1.17269	+	0.185736i	−0.712232	−	0.701944i	$-0.752316\pi$
$83$	−10.6837	+	1.69214i	−1.17269	+	0.185736i	−0.460461	+	0.887680i	$0.652316\pi$
$84$	4.49246	+	0.502566i	0.490168	+	0.0548345i
$85$		0			0
$86$	18.5090	+	3.93420i	1.99587	+	0.424236i
$87$	−9.79260	−	6.35939i	−1.04988	−	0.681798i
$88$	7.33636	+	4.76429i	0.782058	+	0.507875i
$89$	0.981714	+	0.208670i	0.104061	+	0.0221190i	0.259648	−	0.965703i	$-0.416393\pi$
$89$	0.981714	+	0.208670i	0.104061	+	0.0221190i	−0.155587	+	0.987822i	$0.549727\pi$
$90$		0			0
$91$	−0.235485	+	0.102964i	−0.0246856	+	0.0107936i
$92$	−3.23996	+	0.513159i	−0.337789	+	0.0535005i
$93$	−1.86207	+	0.498939i	−0.193087	+	0.0517376i
$94$	0.458824	−	4.36542i	0.0473241	−	0.450259i
$95$		0			0
$96$	9.29110	−	0.976534i	0.948269	−	0.0996670i
$97$	11.1837	+	1.77133i	1.13554	+	0.179851i	0.695773	−	0.718262i	$-0.255062\pi$
$97$	11.1837	+	1.77133i	1.13554	+	0.179851i	0.439764	+	0.898113i	$0.355062\pi$
$98$	−10.1740	+	5.01371i	−1.02773	+	0.506461i
$99$		−	17.5251i		−	1.76134i
$100$		0			0
$101$	−10.1623	+	5.86718i	−1.01118	+	0.583807i	−0.911538	−	0.411216i	$-0.865104\pi$
$101$	−10.1623	+	5.86718i	−1.01118	+	0.583807i	−0.0996449	+	0.995023i	$0.531771\pi$
$102$	−0.776377	−	14.8141i	−0.0768727	−	1.46682i
$103$	7.82705	+	6.33822i	0.771222	+	0.624523i	0.931996	−	0.362468i	$-0.118066\pi$
$103$	7.82705	+	6.33822i	0.771222	+	0.624523i	−0.160774	+	0.986991i	$0.551399\pi$
$104$	−0.175032	+	0.127168i	−0.0171633	+	0.0124699i
$105$		0			0
$106$	−15.4167	−	11.2009i	−1.49740	−	1.08792i
$107$	−0.292999	−	1.09349i	−0.0283253	−	0.105711i	0.950316	−	0.311287i	$-0.100760\pi$
$107$	−0.292999	−	1.09349i	−0.0283253	−	0.105711i	−0.978641	+	0.205576i	$0.934093\pi$
$108$	−1.57201	−	1.94126i	−0.151266	−	0.186798i
$109$	0.608654	+	2.86349i	0.0582985	+	0.274273i	0.997636	−	0.0687217i	$-0.0218921\pi$
$109$	0.608654	+	2.86349i	0.0582985	+	0.274273i	−0.939337	+	0.342995i	$0.888559\pi$
$110$		0			0
$111$	−20.0504	+	6.51476i	−1.90310	+	0.618353i
$112$	−10.0461	+	8.02458i	−0.949271	+	0.758252i
$113$	4.16270	−	2.12100i	0.391594	−	0.199527i	−0.247097	−	0.968991i	$-0.579477\pi$
$113$	4.16270	−	2.12100i	0.391594	−	0.199527i	0.638690	+	0.769464i	$0.279477\pi$
$114$	−5.60924	+	26.3894i	−0.525353	+	2.47159i
$115$		0			0
$116$	−2.61512	+	0.555861i	−0.242808	+	0.0516104i
$117$	0.404655	+	0.155332i	0.0374103	+	0.0143605i
$118$	5.91261	−	5.91261i	0.544300	−	0.544300i
$119$	5.16397	+	7.20846i	0.473381	+	0.660798i
$120$		0			0
$121$	−0.462683	−	4.40213i	−0.0420621	−	0.400194i
$122$	4.14206	+	10.7904i	0.375005	+	0.976921i
$123$	−0.357541	+	0.0187379i	−0.0322383	+	0.00168954i
$124$	−0.220700	+	0.382263i	−0.0198194	+	0.0343283i
$125$		0			0
$126$	18.1524	+	6.03254i	1.61714	+	0.537422i
$127$	14.7555	+	7.51832i	1.30934	+	0.667143i	0.962628	−	0.270829i	$-0.0872976\pi$
$127$	14.7555	+	7.51832i	1.30934	+	0.667143i	0.346713	+	0.937971i	$0.387298\pi$
$128$	−8.56482	+	10.5767i	−0.757030	+	0.934854i
$129$	29.1428	+	12.9752i	2.56588	+	1.14240i
$130$		0			0
$131$	−0.163724	−	0.367729i	−0.0143046	−	0.0321287i	0.906252	−	0.422738i	$-0.138931\pi$
$131$	−0.163724	−	0.367729i	−0.0143046	−	0.0321287i	−0.920557	+	0.390609i	$0.872264\pi$
$132$	−4.74518	−	4.74518i	−0.413015	−	0.413015i
$133$	−5.67847	−	15.0938i	−0.492386	−	1.30880i
$134$	−0.860142	−	0.279477i	−0.0743049	−	0.0241431i
$135$		0			0
$136$	5.54717	+	4.99470i	0.475666	+	0.428292i
$137$	6.89895	−	10.6234i	0.589417	−	0.907623i	−0.410574	−	0.911827i	$-0.634672\pi$
$137$	6.89895	−	10.6234i	0.589417	−	0.907623i	0.999991	+	0.00420463i	$0.00133838\pi$
$138$	−23.1818	−	1.21491i	−1.97336	−	0.103420i
$139$	4.44619	+	13.6840i	0.377121	+	1.16066i	0.942036	+	0.335511i	$0.108909\pi$
$139$	4.44619	+	13.6840i	0.377121	+	1.16066i	−0.564915	+	0.825149i	$0.691091\pi$
$140$		0			0
$141$	2.28674	−	7.03788i	0.192579	−	0.592696i
$142$	0.587388	−	1.53020i	0.0492925	−	0.128411i
$143$	0.368536	+	0.0987488i	0.0308185	+	0.00825779i
$144$	21.5653	+	2.26661i	1.79711	+	0.188884i
$145$		0			0
$146$	−2.03221	−	2.79710i	−0.168187	−	0.231489i
$147$	−18.5346	+	4.70164i	−1.52871	+	0.387785i
$148$	−2.19151	+	4.30108i	−0.180141	+	0.353547i
$149$	9.24670	+	5.33859i	0.757519	+	0.437354i	0.828404	−	0.560131i	$-0.189249\pi$
$149$	9.24670	+	5.33859i	0.757519	+	0.437354i	−0.0708851	+	0.997484i	$0.522582\pi$
$150$		0			0
$151$	−10.4396	−	18.0820i	−0.849565	−	1.47149i	−0.881597	−	0.472003i	$-0.843531\pi$
$151$	−10.4396	−	18.0820i	−0.849565	−	1.47149i	0.0320315	−	0.999487i	$-0.489802\pi$
$152$	−7.39366	−	11.3852i	−0.599705	−	0.923465i
$153$	2.33939	−	14.7703i	0.189128	−	1.19411i
$154$	16.4461	+	3.61081i	1.32526	+	0.290967i
$155$		0			0
$156$	0.151625	−	0.0675076i	0.0121397	−	0.00540494i
$157$	3.09395	−	11.5468i	0.246924	−	0.921533i	−0.725483	−	0.688241i	$-0.758383\pi$
$157$	3.09395	−	11.5468i	0.246924	−	0.921533i	0.972407	−	0.233293i	$-0.0749500\pi$
$158$	−19.4579	+	15.7567i	−1.54799	+	1.25354i
$159$	−21.4965	−	23.8743i	−1.70478	−	1.89335i
$160$		0			0
$161$	12.0630	−	6.85743i	0.950695	−	0.540441i
$162$	1.82181	+	3.57550i	0.143135	+	0.280918i
$163$	0.758967	−	14.4820i	0.0594469	−	1.13431i	−0.792222	−	0.610234i	$-0.791076\pi$
$163$	0.758967	−	14.4820i	0.0594469	−	1.13431i	0.851668	−	0.524081i	$-0.175591\pi$
$164$	−0.0548546	+	0.0609222i	−0.00428342	+	0.00475722i
$165$		0			0
$166$	−13.0251	+	11.7278i	−1.01094	+	0.910257i
$167$	0.261681	+	1.65219i	0.0202495	+	0.127850i	0.995742	−	0.0921813i	$-0.0293839\pi$
$167$	0.261681	+	1.65219i	0.0202495	+	0.127850i	−0.975493	+	0.220032i	$0.929384\pi$
$168$	−14.3907	+	7.21164i	−1.11027	+	0.556390i
$169$	7.63566	−	10.5096i	0.587359	−	0.808430i
$170$		0			0
$171$	−11.0621	+	24.8458i	−0.845937	+	1.90001i
$172$	6.81921	−	2.61765i	0.519960	−	0.199594i
$173$	0.235876	−	0.153180i	0.0179333	−	0.0116460i	−0.535641	−	0.844446i	$-0.679930\pi$
$173$	0.235876	−	0.153180i	0.0179333	−	0.0116460i	0.553575	+	0.832800i	$0.313263\pi$
$174$	−18.9195			−1.43429
$175$		0			0
$176$	19.0873			1.43876
$177$	11.8225	−	7.67763i	0.888634	−	0.577086i
$178$	1.51822	−	0.582792i	0.113796	−	0.0436821i
$179$	5.33375	−	11.9798i	0.398663	−	0.895412i	−0.596988	−	0.802250i	$-0.703636\pi$
$179$	5.33375	−	11.9798i	0.398663	−	0.895412i	0.995651	−	0.0931620i	$-0.0296975\pi$
$180$		0			0
$181$	−13.5383	+	18.6338i	−1.00629	+	1.38504i	−0.0849076	+	0.996389i	$0.527060\pi$
$181$	−13.5383	+	18.6338i	−1.00629	+	1.38504i	−0.921384	+	0.388653i	$0.872940\pi$
$182$	−0.229142	+	0.347735i	−0.0169851	+	0.0257758i
$183$	3.04820	+	19.2456i	0.225330	+	1.42268i
$184$	8.68043	−	7.81590i	0.639930	−	0.576196i
$185$		0			0
$186$	−2.09009	+	2.32129i	−0.153253	+	0.170205i
$187$	0.688927	−	13.1455i	0.0503793	−	0.961295i
$188$	−0.769242	−	1.50972i	−0.0561027	−	0.110108i
$189$	9.11516	+	5.34421i	0.663030	+	0.388734i
$190$		0			0
$191$	2.70749	+	3.00698i	0.195907	+	0.217577i	0.833093	−	0.553133i	$-0.186568\pi$
$191$	2.70749	+	3.00698i	0.195907	+	0.217577i	−0.637185	+	0.770711i	$0.719901\pi$
$192$	−8.86936	+	7.18227i	−0.640091	+	0.518335i
$193$	0.795745	−	2.96976i	0.0572790	−	0.213768i	−0.931355	−	0.364114i	$-0.881372\pi$
$193$	0.795745	−	2.96976i	0.0572790	−	0.213768i	0.988634	+	0.150346i	$0.0480386\pi$
$194$	16.7611	−	7.46250i	1.20337	−	0.535776i
$195$		0			0
$196$	−2.23966	+	3.76212i	−0.159976	+	0.268723i
$197$	1.97286	−	12.4561i	0.140560	−	0.887464i	−0.812120	−	0.583490i	$-0.801687\pi$
$197$	1.97286	−	12.4561i	0.140560	−	0.887464i	0.952681	−	0.303973i	$-0.0983134\pi$
$198$	−15.4658	−	23.8153i	−1.09911	−	1.69248i
$199$	−2.17496	−	3.76715i	−0.154179	−	0.267046i	0.778581	−	0.627545i	$-0.215940\pi$
$199$	−2.17496	−	3.76715i	−0.154179	−	0.267046i	−0.932760	+	0.360498i	$0.882607\pi$
$200$		0			0
$201$	−1.32044	−	0.762355i	−0.0931365	−	0.0537724i
$202$	−8.63198	+	16.9412i	−0.607344	+	1.19198i
$203$	9.52558	−	6.09583i	0.668564	−	0.427843i
$204$	−3.36586	−	4.63270i	−0.235657	−	0.324354i
$205$		0			0
$206$	16.2298	+	1.70582i	1.13078	+	0.118850i
$207$	−22.6039	−	6.05670i	−1.57108	−	0.420970i
$208$	−0.169178	+	0.440725i	−0.0117304	+	0.0305588i
$209$	−7.39789	+	22.7684i	−0.511723	+	1.57492i
$210$		0			0
$211$	2.05986	+	6.33961i	0.141807	+	0.436437i	0.996587	−	0.0825543i	$-0.0263078\pi$
$211$	2.05986	+	6.33961i	0.141807	+	0.436437i	−0.854780	+	0.518991i	$0.826308\pi$
$212$	−7.34585	−	0.384980i	−0.504515	−	0.0264405i
$213$	1.50497	−	2.31745i	0.103119	−	0.158789i
$214$	−1.36316	−	1.22740i	−0.0931838	−	0.0839031i
$215$		0			0
$216$	8.45936	+	2.74861i	0.575586	+	0.187019i
$217$	0.304405	−	1.84214i	0.0206644	−	0.125053i
$218$	3.35413	+	3.35413i	0.227171	+	0.227171i
$219$	−2.37076	−	5.32481i	−0.160201	−	0.359817i
$220$		0			0
$221$	0.297423	+	0.132421i	0.0200069	+	0.00890762i
$222$	−21.4977	+	26.5474i	−1.44283	+	1.78175i
$223$	13.7309	+	6.99626i	0.919491	+	0.468504i	0.848633	−	0.528982i	$-0.177426\pi$
$223$	13.7309	+	6.99626i	0.919491	+	0.468504i	0.0708583	+	0.997486i	$0.477426\pi$
$224$	−2.85360	+	8.58670i	−0.190664	+	0.573723i
$225$		0			0
$226$	3.78502	−	6.55584i	0.251776	−	0.436088i
$227$	13.2319	−	0.693452i	0.878229	−	0.0460260i	0.392110	−	0.919918i	$-0.371745\pi$
$227$	13.2319	−	0.693452i	0.878229	−	0.0460260i	0.486119	+	0.873892i	$0.338412\pi$
$228$	3.73215	+	9.72258i	0.247168	+	0.643893i
$229$	0.433550	+	4.12495i	0.0286498	+	0.272584i	0.999464	+	0.0327499i	$0.0104265\pi$
$229$	0.433550	+	4.12495i	0.0286498	+	0.272584i	−0.970814	+	0.239834i	$0.922907\pi$
$230$		0			0
$231$	25.8544	+	11.7189i	1.70109	+	0.771044i
$232$	6.73164	−	6.73164i	0.441954	−	0.441954i
$233$	24.0569	+	9.23458i	1.57602	+	0.604977i	0.980177	−	0.198124i	$-0.0634848\pi$
$233$	24.0569	+	9.23458i	1.57602	+	0.604977i	0.595843	+	0.803101i	$0.296818\pi$
$234$	0.686975	−	0.146021i	0.0449090	−	0.00954570i
$235$		0			0
$236$	0.671086	−	3.15721i	0.0436840	−	0.205517i
$237$	−37.6096	+	19.1630i	−2.44300	+	1.24477i
$238$	13.3789	+	5.23857i	0.867224	+	0.339566i
$239$	0.618920	−	0.201099i	0.0400346	−	0.0130080i	−0.288931	−	0.957350i	$-0.593300\pi$
$239$	0.618920	−	0.201099i	0.0400346	−	0.0130080i	0.328966	+	0.944342i	$0.393300\pi$
$240$		0			0
$241$	0.238703	+	1.12301i	0.0153762	+	0.0723393i	0.985167	−	0.171600i	$-0.0548936\pi$
$241$	0.238703	+	1.12301i	0.0153762	+	0.0723393i	−0.969791	+	0.243939i	$0.921560\pi$
$242$	−4.51361	−	5.57385i	−0.290146	−	0.358300i
$243$	4.85188	+	18.1075i	0.311248	+	1.16159i
$244$	3.60952	+	2.62247i	0.231076	+	0.167887i
$245$		0			0
$246$	−0.469334	+	0.340991i	−0.0299237	+	0.0217408i
$247$	−0.460151	−	0.372623i	−0.0292787	−	0.0237094i
$248$	−0.0822585	−	1.56959i	−0.00522342	−	0.0996688i
$249$	−25.5895	+	14.7741i	−1.62167	+	0.936270i
$250$		0			0
$251$			13.8492i			0.874153i	0.899424	+	0.437076i	$0.143986\pi$
$251$			13.8492i			0.874153i	−0.899424	+	0.437076i	$0.856014\pi$
$252$	7.14493	−	1.86337i	0.450088	−	0.117381i
$253$	−20.3452	−	3.22237i	−1.27909	−	0.202589i
$254$	26.6865	−	2.80487i	1.67446	−	0.175993i
$255$		0			0
$256$	−1.43165	+	13.6212i	−0.0894778	+	0.851325i
$257$	−0.352213	+	0.0943752i	−0.0219704	+	0.00588696i	−0.269788	−	0.962920i	$-0.586953\pi$
$257$	−0.352213	+	0.0943752i	−0.0219704	+	0.00588696i	0.247817	+	0.968807i	$0.420287\pi$
$258$	51.0535	−	8.08608i	3.17845	−	0.503417i
$259$	2.27010	−	20.2925i	0.141057	−	1.26092i
$260$		0			0
$261$	−18.6557	−	3.96540i	−1.15476	−	0.245452i
$262$	−0.547007	−	0.355231i	−0.0337942	−	0.0219462i
$263$	−24.9486	−	16.2018i	−1.53839	−	0.999045i	−0.986243	−	0.165301i	$-0.947141\pi$
$263$	−24.9486	−	16.2018i	−1.53839	−	0.999045i	−0.552151	−	0.833744i	$-0.686193\pi$
$264$	23.3734	+	4.96816i	1.43853	+	0.305769i
$265$		0			0
$266$	−21.0368	−	15.5001i	−1.28985	−	0.950371i
$267$	2.70787	−	0.428885i	0.165719	−	0.0262473i
$268$	−0.337219	+	0.0903576i	−0.0205989	+	0.00551947i
$269$	−2.16638	+	20.6117i	−0.132087	+	1.25672i	0.704825	+	0.709381i	$0.251026\pi$
$269$	−2.16638	+	20.6117i	−0.132087	+	1.25672i	−0.836911	+	0.547338i	$0.815641\pi$
$270$		0			0
$271$	−5.57572	+	0.586032i	−0.338701	+	0.0355989i	−0.272352	−	0.962198i	$-0.587802\pi$
$271$	−5.57572	+	0.586032i	−0.338701	+	0.0355989i	−0.0663487	+	0.997796i	$0.521135\pi$
$272$	16.0869	+	2.54792i	0.975413	+	0.154490i
$273$	−0.499746	+	0.493108i	−0.0302460	+	0.0298443i
$274$		−	20.5248i		−	1.23995i
$275$		0			0
$276$	−7.76028	+	4.48040i	−0.467114	+	0.269688i
$277$	−0.309378	−	5.90329i	−0.0185887	−	0.354694i	−0.992050	−	0.125843i	$-0.959836\pi$
$277$	−0.309378	−	5.90329i	−0.0185887	−	0.354694i	0.973461	−	0.228851i	$-0.0734969\pi$
$278$	18.1181	+	14.6717i	1.08665	+	0.879953i
$279$	−2.54748	+	1.85085i	−0.152514	+	0.110808i
$280$		0			0
$281$	−6.92124	−	5.02858i	−0.412887	−	0.299980i	0.361883	−	0.932224i	$-0.382134\pi$
$281$	−6.92124	−	5.02858i	−0.412887	−	0.299980i	−0.774769	+	0.632244i	$0.782134\pi$
$282$	−3.10338	−	11.5820i	−0.184804	−	0.689697i
$283$	9.49677	+	11.7275i	0.564525	+	0.697130i	0.976855	−	0.213905i	$-0.0686182\pi$
$283$	9.49677	+	11.7275i	0.564525	+	0.697130i	−0.412330	+	0.911035i	$0.635285\pi$
$284$	−0.131547	−	0.618878i	−0.00780585	−	0.0367236i
$285$		0			0
$286$	0.587957	−	0.191039i	0.0347666	−	0.0112964i
$287$	0.126433	−	0.322900i	0.00746312	−	0.0190602i
$288$	13.5968	−	6.92789i	0.801196	−	0.408230i
$289$	−1.19910	+	5.64132i	−0.0705353	+	0.331843i
$290$		0			0
$291$	30.2551	−	6.43093i	1.77359	−	0.376988i
$292$	−1.24597	−	0.478282i	−0.0729147	−	0.0279893i
$293$	−7.80680	+	7.80680i	−0.456078	+	0.456078i	−0.897366	−	0.441288i	$-0.854522\pi$
$293$	−7.80680	+	7.80680i	−0.456078	+	0.456078i	0.441288	+	0.897366i	$0.354522\pi$
$294$	−21.0380	+	22.7459i	−1.22696	+	1.32657i
$295$		0			0
$296$	−1.79672	−	17.0946i	−0.104432	−	0.993605i
$297$	−5.62128	−	14.6439i	−0.326180	−	0.849727i
$298$	17.2768	−	0.905441i	1.00082	−	0.0524508i
$299$	0.254733	−	0.441210i	0.0147316	−	0.0255158i
$300$		0			0
$301$	−23.0990	+	20.5205i	−1.33141	+	1.18278i
$302$	−30.1439	−	15.3591i	−1.73459	−	0.883817i
$303$	−20.1725	+	24.9109i	−1.15888	+	1.43109i
$304$	−27.0605	−	12.0481i	−1.55203	−	0.691007i
$305$		0			0
$306$	−9.85570	−	22.1363i	−0.563413	−	1.26545i
$307$	−8.14095	−	8.14095i	−0.464628	−	0.464628i	0.435541	−	0.900169i	$-0.356557\pi$
$307$	−8.14095	−	8.14095i	−0.464628	−	0.464628i	−0.900169	+	0.435541i	$0.856557\pi$
$308$	6.08338	−	2.28864i	0.346632	−	0.130407i
$309$	26.1655	+	8.50169i	1.48850	+	0.483644i
$310$		0			0
$311$	−21.3562	−	19.2292i	−1.21100	−	1.09039i	−0.993442	−	0.114339i	$-0.963525\pi$
$311$	−21.3562	−	19.2292i	−1.21100	−	1.09039i	−0.217556	−	0.976048i	$-0.569808\pi$
$312$	−0.321882	+	0.495655i	−0.0182230	+	0.0280610i
$313$	9.50493	+	0.498133i	0.537251	+	0.0281561i	0.319032	−	0.947744i	$-0.396642\pi$
$313$	9.50493	+	0.498133i	0.537251	+	0.0281561i	0.218218	+	0.975900i	$0.429975\pi$
$314$	−5.98554	−	18.4216i	−0.337783	−	1.03959i
$315$		0			0
$316$	−2.98662	+	9.19189i	−0.168011	+	0.517084i
$317$	2.79733	−	7.28729i	0.157114	−	0.409295i	−0.832317	−	0.554299i	$-0.812986\pi$
$317$	2.79733	−	7.28729i	0.157114	−	0.409295i	0.989431	+	0.145004i	$0.0463196\pi$
$318$	−50.2810	−	13.4728i	−2.81962	−	0.755515i
$319$	−16.6965	−	1.75487i	−0.934824	−	0.0982540i
$320$		0			0
$321$	−1.81768	−	2.50182i	−0.101453	−	0.139638i
$322$	10.3410	−	19.9642i	0.576281	−	1.11256i
$323$	−9.27431	+	18.2019i	−0.516036	+	1.01278i
$324$	1.34150	+	0.774516i	0.0745278	+	0.0430287i
$325$		0			0
$326$	−11.7489	−	20.3497i	−0.650711	−	1.12706i
$327$	4.35540	+	6.70673i	0.240854	+	0.370883i
$328$	0.0456650	−	0.288317i	0.00252143	−	0.0159197i
$329$	5.29417	+	4.83138i	0.291877	+	0.266362i
$330$		0			0
$331$	0.945325	−	0.420886i	0.0519597	−	0.0231340i	−0.380592	−	0.924743i	$-0.624280\pi$
$331$	0.945325	−	0.420886i	0.0519597	−	0.0231340i	0.432552	+	0.901609i	$0.357613\pi$
$332$	−1.75109	+	6.53515i	−0.0961035	+	0.358663i
$333$	−26.7621	+	21.6715i	−1.46655	+	1.18759i
$334$	1.81366	+	2.01427i	0.0992388	+	0.110216i
$335$		0			0
$336$	−17.7644	+	30.2991i	−0.969125	+	1.65295i
$337$	0.849753	+	1.66773i	0.0462890	+	0.0908472i	0.912992	−	0.407977i	$-0.133765\pi$
$337$	0.849753	+	1.66773i	0.0462890	+	0.0908472i	−0.866703	+	0.498824i	$0.833765\pi$
$338$	1.10162	−	21.0202i	0.0599202	−	1.14335i
$339$	8.53950	−	9.48407i	0.463802	−	0.515104i
$340$		0			0
$341$	−2.05982	+	1.85467i	−0.111545	+	0.100436i
$342$	6.89381	+	43.5258i	0.372774	+	2.35361i
$343$	3.26350	−	18.2305i	0.176212	−	0.984352i
$344$	−15.2880	+	21.0421i	−0.824272	+	1.13451i
$345$		0			0
$346$	0.185357	−	0.416319i	0.00996486	−	0.0223814i
$347$	1.85615	−	0.712508i	0.0996431	−	0.0382494i	−0.308036	−	0.951375i	$-0.599672\pi$
$347$	1.85615	−	0.712508i	0.0996431	−	0.0382494i	0.407679	+	0.913125i	$0.366338\pi$
$348$	−6.12500	+	3.97762i	−0.328335	+	0.213223i
$349$	−4.37015			−0.233929			−0.116964	−	0.993136i	$-0.537316\pi$
$349$	−4.37015			−0.233929			−0.116964	+	0.993136i	$0.537316\pi$
$350$		0			0
$351$	0.387952			0.0207073
$352$	11.2654	−	7.31587i	0.600450	−	0.389937i
$353$	−17.4347	+	6.69256i	−0.927957	+	0.356209i	−0.774955	−	0.632017i	$-0.782227\pi$
$353$	−17.4347	+	6.69256i	−0.927957	+	0.356209i	−0.153002	+	0.988226i	$0.548894\pi$
$354$	9.29042	−	20.8666i	0.493780	−	1.10905i
$355$		0			0
$356$	0.368984	−	0.507863i	0.0195561	−	0.0269167i
$357$	20.2260	+	13.3280i	1.07047	+	0.705393i
$358$	−3.32396	−	20.9867i	−0.175677	−	1.10918i
$359$	12.4207	−	11.1836i	0.655539	−	0.590250i	−0.272761	−	0.962082i	$-0.587937\pi$
$359$	12.4207	−	11.1836i	0.655539	−	0.590250i	0.928300	+	0.371832i	$0.121270\pi$
$360$		0			0
$361$	12.1464	−	13.4899i	0.639282	−	0.709995i
$362$	−1.95321	+	37.2694i	−0.102658	+	1.95884i
$363$	−5.48937	−	10.7735i	−0.288117	−	0.565462i
$364$	−0.00107477	+	0.160750i	−5.63332e−5	+	0.00842560i
$365$		0			0
$366$	21.1264	+	23.4633i	1.10430	+	1.22644i
$367$	−7.50742	+	6.07938i	−0.391884	+	0.317341i	−0.804931	−	0.593368i	$-0.797798\pi$
$367$	−7.50742	+	6.07938i	−0.391884	+	0.317341i	0.413047	+	0.910710i	$0.364464\pi$
$368$	6.59659	−	24.6188i	0.343871	−	1.28334i
$369$	−0.534260	+	0.237868i	−0.0278125	+	0.0123829i
$370$		0			0
$371$	29.6563	−	9.41718i	1.53968	−	0.488916i
$372$	−0.188622	+	1.19091i	−0.00977959	+	0.0617459i
$373$	−2.67853	−	4.12458i	−0.138689	−	0.213563i	0.762500	−	0.646988i	$-0.223972\pi$
$373$	−2.67853	−	4.12458i	−0.138689	−	0.213563i	−0.901190	+	0.433425i	$0.857305\pi$
$374$	−10.6647	−	18.4717i	−0.551456	−	0.955150i
$375$		0			0
$376$	5.22511	+	3.01672i	0.269465	+	0.155575i
$377$	0.188508	−	0.369967i	0.00970865	−	0.0190543i
$378$	17.1030	−	0.781708i	0.879686	−	0.0402067i
$379$	−7.39900	−	10.1839i	−0.380061	−	0.523109i	0.575540	−	0.817774i	$-0.304792\pi$
$379$	−7.39900	−	10.1839i	−0.380061	−	0.523109i	−0.955601	+	0.294665i	$0.904792\pi$
$380$		0			0
$381$	44.9900	+	4.72864i	2.30491	+	0.242255i
$382$	6.33292	+	1.69690i	0.324020	+	0.0868210i
$383$	6.42601	−	16.7403i	0.328354	−	0.855391i	−0.665672	−	0.746245i	$-0.731855\pi$
$383$	6.42601	−	16.7403i	0.328354	−	0.855391i	0.994026	−	0.109146i	$-0.0348117\pi$
$384$	−11.4883	+	35.3574i	−0.586260	+	1.80432i
$385$		0			0
$386$	−1.53944	−	4.73792i	−0.0783556	−	0.241154i
$387$	52.0365	+	2.72712i	2.64516	+	0.138627i
$388$	3.85731	−	5.93974i	0.195825	−	0.301544i
$389$	8.86329	+	7.98055i	0.449387	+	0.404630i	0.862506	−	0.506047i	$-0.168894\pi$
$389$	8.86329	+	7.98055i	0.449387	+	0.404630i	−0.413119	+	0.910677i	$0.635561\pi$
$390$		0			0
$391$	−16.7170	−	5.43168i	−0.845415	−	0.274692i
$392$	−0.607684	−	15.5785i	−0.0306927	−	0.786832i
$393$	−0.777518	−	0.777518i	−0.0392206	−	0.0392206i
$394$	−8.31153	−	18.6680i	−0.418729	−	0.940480i
$395$		0			0
$396$	−10.0138	−	4.45844i	−0.503213	−	0.224045i
$397$	23.6125	−	29.1590i	1.18508	−	1.46345i	0.330750	−	0.943719i	$-0.392698\pi$
$397$	23.6125	−	29.1590i	1.18508	−	1.46345i	0.854329	−	0.519732i	$-0.173968\pi$
$398$	−6.28010	−	3.19987i	−0.314793	−	0.160395i
$399$	−29.2573	−	32.9337i	−1.46470	−	1.64875i
$400$		0			0
$401$	0.106730	−	0.184861i	0.00532982	−	0.00923152i	−0.863348	−	0.504609i	$-0.831637\pi$
$401$	0.106730	−	0.184861i	0.00532982	−	0.00923152i	0.868678	+	0.495377i	$0.164970\pi$
$402$	−2.46715	+	0.129298i	−0.123050	+	0.00644879i
$403$	−0.0245673	−	0.0639999i	−0.00122378	−	0.00318806i
$404$	0.767189	+	7.29932i	0.0381691	+	0.363155i
$405$		0			0
$406$	7.56499	−	16.6900i	0.375444	−	0.828313i
$407$	−21.4341	+	21.4341i	−1.06245	+	1.06245i
$408$	19.0361	+	7.30726i	0.942426	+	0.361763i
$409$	−31.2443	+	6.64117i	−1.54493	+	0.328385i	−0.900011	−	0.435867i	$-0.856442\pi$
$409$	−31.2443	+	6.64117i	−1.54493	+	0.328385i	−0.644918	+	0.764252i	$0.723109\pi$
$410$		0			0
$411$	7.19417	−	33.8459i	0.354862	−	1.66950i
$412$	5.61287	−	2.85990i	0.276526	−	0.140897i
$413$	2.04565	+	13.4992i	0.100660	+	0.664255i
$414$	−36.0620	+	11.7173i	−1.77235	+	0.575872i
$415$		0			0
$416$	0.0690729	+	0.324962i	0.00338658	+	0.0159326i
$417$	24.7346	+	30.5447i	1.21126	+	1.49578i
$418$	10.0398	+	37.4691i	0.491063	+	1.83267i
$419$	8.57555	+	6.23050i	0.418943	+	0.304380i	0.777212	−	0.629238i	$-0.216633\pi$
$419$	8.57555	+	6.23050i	0.418943	+	0.304380i	−0.358269	+	0.933618i	$0.616633\pi$
$420$		0			0
$421$	7.12732	−	5.17830i	0.347364	−	0.252375i	−0.400398	−	0.916341i	$-0.631128\pi$
$421$	7.12732	−	5.17830i	0.347364	−	0.252375i	0.747762	+	0.663966i	$0.231128\pi$
$422$	8.39388	+	6.79723i	0.408608	+	0.330884i
$423$	−0.632612	−	12.0710i	−0.0307586	−	0.586910i
$424$	22.6839	−	13.0965i	1.10163	−	0.636024i
$425$		0			0
$426$		−	4.47737i		−	0.216929i
$427$	−18.1965	−	5.00637i	−0.880591	−	0.242275i
$428$	−0.699356	−	0.110767i	−0.0338047	−	0.00535413i
$429$	1.03652	−	0.108943i	0.0500436	−	0.00525980i
$430$		0			0
$431$	−0.640581	+	6.09472i	−0.0308557	+	0.293572i	0.968202	+	0.250170i	$0.0804864\pi$
$431$	−0.640581	+	6.09472i	−0.0308557	+	0.293572i	−0.999058	+	0.0434025i	$0.986180\pi$
$432$	18.7469	−	5.02322i	0.901961	−	0.241680i
$433$	−35.2854	+	5.58866i	−1.69571	+	0.268574i	−0.928097	−	0.372339i	$-0.878556\pi$
$433$	−35.2854	+	5.58866i	−1.69571	+	0.268574i	−0.767613	+	0.640913i	$0.778556\pi$
$434$	−1.21202	−	2.77197i	−0.0581787	−	0.133059i
$435$		0			0
$436$	1.79104	+	0.380697i	0.0857751	+	0.0182321i
$437$	26.8100	+	17.4106i	1.28249	+	0.832861i
$438$	−7.92080	−	5.14383i	−0.378470	−	0.245782i
$439$	25.5065	+	5.42157i	1.21736	+	0.258757i	0.771431	−	0.636312i	$-0.219541\pi$
$439$	25.5065	+	5.42157i	1.21736	+	0.258757i	0.445926	+	0.895070i	$0.352874\pi$
$440$		0			0
$441$	−25.5120	+	18.0194i	−1.21486	+	0.858064i
$442$	0.521037	−	0.0825241i	0.0247832	−	0.00392527i
$443$	32.7161	−	8.76626i	1.55439	−	0.416498i	0.623508	−	0.781817i	$-0.285707\pi$
$443$	32.7161	−	8.76626i	1.55439	−	0.416498i	0.930882	+	0.365319i	$0.119040\pi$
$444$	−1.37835	+	13.1141i	−0.0654135	+	0.622368i
$445$		0			0
$446$	24.8335	−	2.61010i	1.17590	−	0.123592i
$447$	28.8074	+	4.56264i	1.36254	+	0.215805i
$448$	−2.78948	−	10.6960i	−0.131791	−	0.505340i
$449$		−	17.8247i		−	0.841199i	−0.907246	−	0.420600i	$-0.861820\pi$
$449$		−	17.8247i		−	0.841199i	0.907246	−	0.420600i	$-0.138180\pi$
$450$		0			0
$451$	−0.445816	+	0.257392i	−0.0209927	+	0.0121201i
$452$	−0.152933	−	2.91814i	−0.00719338	−	0.137258i
$453$	−44.3247	−	35.8934i	−2.08255	−	1.68642i
$454$	17.3691	−	12.6194i	0.815173	−	0.592258i
$455$		0			0
$456$	−30.0010	−	21.7970i	−1.40493	−	1.02074i
$457$	−2.20826	−	8.24133i	−0.103298	−	0.385513i	0.894849	−	0.446370i	$-0.147283\pi$
$457$	−2.20826	−	8.24133i	−0.103298	−	0.385513i	−0.998147	+	0.0608568i	$0.980617\pi$
$458$	4.22941	+	5.22289i	0.197627	+	0.244050i
$459$	−2.78288	−	13.0924i	−0.129893	−	0.611101i
$460$		0			0
$461$	25.2246	−	8.19596i	1.17483	−	0.381724i	0.344384	−	0.938829i	$-0.388088\pi$
$461$	25.2246	−	8.19596i	1.17483	−	0.381724i	0.830442	+	0.557105i	$0.188088\pi$
$462$	45.4760	−	6.89134i	2.11573	−	0.320614i
$463$	20.3912	−	10.3899i	0.947661	−	0.482857i	0.0893575	−	0.996000i	$-0.471519\pi$
$463$	20.3912	−	10.3899i	0.947661	−	0.482857i	0.858304	+	0.513142i	$0.171519\pi$
$464$	4.31887	−	20.3187i	0.200498	−	0.943271i
$465$		0			0
$466$	40.8410	−	8.68102i	1.89192	−	0.402140i
$467$	−8.32450	−	3.19548i	−0.385212	−	0.147869i	0.158052	−	0.987431i	$-0.449479\pi$
$467$	−8.32450	−	3.19548i	−0.385212	−	0.147869i	−0.543264	+	0.839562i	$0.682812\pi$
$468$	0.191702	−	0.191702i	0.00886142	−	0.00886142i
$469$	1.20050	−	0.860009i	0.0554338	−	0.0397115i
$470$		0			0
$471$	−3.41334	−	32.4757i	−0.157278	−	1.49640i
$472$	4.11886	+	10.7300i	0.189586	+	0.493888i
$473$	45.8047	−	2.40053i	2.10610	−	0.110376i
$474$	−34.1972	+	59.2314i	−1.57073	+	2.72059i
$475$		0			0
$476$	5.43263	−	1.11683i	0.249004	−	0.0511899i
$477$	−46.7562	−	23.8235i	−2.14082	−	1.09080i
$478$	0.663596	−	0.819472i	0.0303522	−	0.0374818i
$479$	2.18656	+	0.973518i	0.0999064	+	0.0444812i	0.456081	−	0.889938i	$-0.349253\pi$
$479$	2.18656	+	0.973518i	0.0999064	+	0.0444812i	−0.356175	+	0.934419i	$0.615919\pi$
$480$		0			0
$481$	−0.304934	−	0.684892i	−0.0139038	−	0.0312284i
$482$	1.31543	+	1.31543i	0.0599161	+	0.0599161i
$483$	24.0503	−	29.2970i	1.09433	−	1.33306i
$484$	−2.63308	−	0.855538i	−0.119685	−	0.0388881i
$485$		0			0
$486$	22.5731	+	20.3249i	1.02394	+	0.921957i
$487$	−2.63929	+	4.06415i	−0.119598	+	0.184164i	−0.893399	−	0.449264i	$-0.851686\pi$
$487$	−2.63929	+	4.06415i	−0.119598	+	0.184164i	0.773801	+	0.633428i	$0.218353\pi$
$488$	−15.8652	−	0.831460i	−0.718184	−	0.0376384i
$489$	−12.2414	−	37.6753i	−0.553577	−	1.70374i
$490$		0			0
$491$	−9.20020	+	28.3153i	−0.415199	+	1.27785i	0.496874	+	0.867823i	$0.334481\pi$
$491$	−9.20020	+	28.3153i	−0.415199	+	1.27785i	−0.912073	+	0.410029i	$0.865519\pi$
$492$	−0.0802525	+	0.209065i	−0.00361806	+	0.00942537i
$493$	−13.8377	−	3.70780i	−0.623218	−	0.166991i
$494$	−0.954148	−	0.100285i	−0.0429291	−	0.00451203i
$495$		0			0
$496$	−2.01583	−	2.77456i	−0.0905136	−	0.124581i
$497$	1.44260	+	2.25426i	0.0647094	+	0.101117i
$498$	−21.7361	+	42.6595i	−0.974018	+	1.91162i
$499$	33.6862	+	19.4488i	1.50800	+	0.870646i	0.999957	+	0.00931623i	$0.00296549\pi$
$499$	33.6862	+	19.4488i	1.50800	+	0.870646i	0.508046	+	0.861330i	$0.330368\pi$
$500$		0			0
$501$	2.28474	+	3.95729i	0.102075	+	0.176799i
$502$	12.2218	+	18.8200i	0.545488	+	0.839977i
$503$	−5.93752	+	37.4880i	−0.264741	+	1.67151i	0.393979	+	0.919120i	$0.371098\pi$
$503$	−5.93752	+	37.4880i	−0.264741	+	1.67151i	−0.658719	+	0.752389i	$0.728902\pi$
$504$	−17.7235	+	19.4212i	−0.789467	+	0.865090i
$505$		0			0
$506$	−30.4914	+	13.5756i	−1.35551	+	0.603510i
$507$	9.18442	−	34.2767i	0.407894	−	1.52228i
$508$	8.04979	−	6.51859i	0.357152	−	0.289216i
$509$	6.94597	+	7.71429i	0.307875	+	0.341930i	0.877149	−	0.480218i	$-0.159442\pi$
$509$	6.94597	+	7.71429i	0.307875	+	0.341930i	−0.569274	+	0.822148i	$0.692776\pi$
$510$		0			0
$511$	5.64528	+	0.0377441i	0.249733	+	0.00166970i
$512$	−2.28214	−	4.47894i	−0.100857	−	0.197943i
$513$	−1.27400	+	24.3093i	−0.0562483	+	1.07328i
$514$	−0.395345	+	0.439075i	−0.0174379	+	0.0193668i
$515$		0			0
$516$	14.8280	−	13.3512i	0.652768	−	0.587755i
$517$	−1.66446	−	10.5090i	−0.0732027	−	0.462184i
$518$	−14.8232	−	29.5794i	−0.651293	−	1.29964i
$519$	0.451584	−	0.621552i	0.0198223	−	0.0272831i
$520$		0			0
$521$	−4.89041	+	10.9840i	−0.214253	+	0.481219i	−0.988416	−	0.151766i	$-0.951504\pi$
$521$	−4.89041	+	10.9840i	−0.214253	+	0.481219i	0.774164	+	0.632985i	$0.218171\pi$
$522$	−28.8512	+	11.0749i	−1.26278	+	0.484737i
$523$	20.1088	−	13.0588i	0.879298	−	0.571023i	−0.0241556	−	0.999708i	$-0.507690\pi$
$523$	20.1088	−	13.0588i	0.879298	−	0.571023i	0.903454	+	0.428685i	$0.141023\pi$
$524$	−0.251771			−0.0109987
$525$		0			0
$526$	−48.2012			−2.10167
$527$	−1.98361	+	1.28817i	−0.0864074	+	0.0561136i
$528$	48.6769	−	18.6853i	2.11839	−	0.813175i
$529$	−1.83261	+	4.11611i	−0.0796787	+	0.178961i
$530$		0			0
$531$	13.5344	−	18.6285i	0.587342	−	0.808407i
$532$	−10.0692	−	0.595233i	−0.436554	−	0.0258066i
$533$	−0.00199173	−	0.0125753i	−8.62712e−5	−	0.000544695i
$534$	3.30130	−	2.97251i	0.142861	−	0.128633i
$535$		0			0
$536$	0.831817	−	0.923827i	0.0359290	−	0.0399032i
$537$	1.87477	−	35.7727i	0.0809021	−	1.54370i
$538$	15.2458	+	29.9216i	0.657294	+	1.29001i
$539$	−20.6758	+	18.1219i	−0.890570	+	0.780565i
$540$		0			0
$541$	−12.8091	−	14.2259i	−0.550705	−	0.611620i	0.401954	−	0.915660i	$-0.368331\pi$
$541$	−12.8091	−	14.2259i	−0.550705	−	0.611620i	−0.952659	+	0.304040i	$0.901664\pi$
$542$	−7.05982	+	5.71693i	−0.303245	+	0.245563i
$543$	−16.2843	+	60.7737i	−0.698825	+	2.60805i
$544$	10.4712	−	4.66208i	0.448949	−	0.199885i
$545$		0			0
$546$	−0.243952	+	1.11112i	−0.0104402	+	0.0475516i
$547$	−1.95187	+	12.3236i	−0.0834558	+	0.526919i	0.910174	+	0.414226i	$0.135948\pi$
$547$	−1.95187	+	12.3236i	−0.0834558	+	0.526919i	−0.993630	+	0.112693i	$0.964052\pi$
$548$	−4.31510	−	6.64468i	−0.184332	−	0.283847i
$549$	15.9141	+	27.5641i	0.679199	+	1.17641i
$550$		0			0
$551$	22.5633	+	13.0269i	0.961230	+	0.554967i
$552$	14.4858	−	28.4300i	0.616556	−	1.21006i
$553$	−1.86663	−	40.8400i	−0.0793770	−	1.73669i
$554$	−5.63005	−	7.74910i	−0.239198	−	0.329228i
$555$		0			0
$556$	8.95012	+	0.940695i	0.379570	+	0.0398944i
$557$	21.9963	+	5.89390i	0.932014	+	0.249732i	0.692713	−	0.721213i	$-0.256415\pi$
$557$	21.9963	+	5.89390i	0.932014	+	0.249732i	0.239301	+	0.970946i	$0.423082\pi$
$558$	−1.82846	+	4.76331i	−0.0774050	+	0.201647i
$559$	−0.350558	+	1.07891i	−0.0148270	+	0.0456329i
$560$		0			0
$561$	−11.1118	−	34.1985i	−0.469139	−	1.44386i
$562$	−13.8431	−	0.725488i	−0.583937	−	0.0306029i
$563$	15.8945	−	24.4754i	0.669874	−	1.03152i	−0.326397	−	0.945233i	$-0.605835\pi$
$563$	15.8945	−	24.4754i	0.669874	−	1.03152i	0.996271	−	0.0862825i	$-0.0274988\pi$
$564$	−3.43967	−	3.09710i	−0.144836	−	0.130411i
$565$		0			0
$566$	23.2549	+	7.55597i	0.977476	+	0.317601i
$567$	−6.46474	−	1.06827i	−0.271494	−	0.0448631i
$568$	1.59307	+	1.59307i	0.0668436	+	0.0668436i
$569$	−0.645950	−	1.45083i	−0.0270796	−	0.0608218i	0.899499	−	0.436922i	$-0.143931\pi$
$569$	−0.645950	−	1.45083i	−0.0270796	−	0.0608218i	−0.926579	+	0.376100i	$0.877265\pi$
$570$		0			0
$571$	3.28341	+	1.46187i	0.137406	+	0.0611773i	0.474288	−	0.880370i	$-0.342706\pi$
$571$	3.28341	+	1.46187i	0.137406	+	0.0611773i	−0.336882	+	0.941547i	$0.609372\pi$
$572$	0.150181	−	0.185458i	0.00627940	−	0.00775441i
$573$	9.84838	+	5.01800i	0.411422	+	0.209630i
$574$	−0.113145	−	0.550374i	−0.00472258	−	0.0229722i
$575$		0			0
$576$	−9.32098	+	16.1444i	−0.388374	+	0.672683i
$577$	−22.3066	+	1.16904i	−0.928634	+	0.0486677i	−0.510652	−	0.859788i	$-0.670596\pi$
$577$	−22.3066	+	1.16904i	−0.928634	+	0.0486677i	−0.417982	+	0.908455i	$0.637263\pi$
$578$	3.34896	+	8.72433i	0.139298	+	0.362884i
$579$	−0.877889	−	8.35256i	−0.0364838	−	0.347121i
$580$		0			0
$581$	−2.80113	−	28.4815i	−0.116210	−	1.18161i
$582$	35.4392	−	35.4392i	1.46900	−	1.46900i
$583$	−43.1234	−	16.5535i	−1.78599	−	0.685577i
$584$	4.64845	−	0.988058i	0.192354	−	0.0408861i
$585$		0			0
$586$	−3.71938	+	17.4983i	−0.153646	+	0.722848i
$587$	−38.6684	+	19.7026i	−1.59602	+	0.813211i	−0.596070	+	0.802933i	$0.703272\pi$
$587$	−38.6684	+	19.7026i	−1.59602	+	0.813211i	−0.999947	+	0.0102788i	$0.996728\pi$
$588$	−2.02875	+	11.7868i	−0.0836644	+	0.486078i
$589$	4.09095	−	1.32923i	0.168565	−	0.0547699i
$590$		0			0
$591$	−7.16259	−	33.6973i	−0.294630	−	1.38612i
$592$	−23.6033	−	29.1476i	−0.970088	−	1.19796i
$593$	−3.34701	−	12.4912i	−0.137445	−	0.512953i	−0.999976	−	0.00694789i	$-0.997788\pi$
$593$	−3.34701	−	12.4912i	−0.137445	−	0.512953i	0.862531	−	0.506005i	$-0.168878\pi$
$594$	−20.5621	−	14.9392i	−0.843673	−	0.612964i
$595$		0			0
$596$	5.40284	−	3.92539i	0.221309	−	0.160790i
$597$	−9.23448	−	7.47793i	−0.377942	−	0.306051i
$598$	−0.0432035	−	0.824371i	−0.00176672	−	0.0337110i
$599$	−19.9444	+	11.5149i	−0.814905	+	0.470485i	−0.848656	−	0.528945i	$-0.822588\pi$
$599$	−19.9444	+	11.5149i	−0.814905	+	0.470485i	0.0337516	+	0.999430i	$0.489255\pi$
$600$		0			0
$601$		−	14.0409i		−	0.572740i	−0.958119	−	0.286370i	$-0.907551\pi$
$601$		−	14.0409i		−	0.572740i	0.958119	−	0.286370i	$-0.0924486\pi$
$602$	−13.2806	+	48.2705i	−0.541276	+	1.96736i
$603$	−2.45985	−	0.389602i	−0.100173	−	0.0158658i
$604$	−12.9879	+	1.36508i	−0.528469	+	0.0555443i
$605$		0			0
$606$	−5.42907	+	51.6542i	−0.220541	+	2.09831i
$607$	38.2415	−	10.2468i	1.55218	−	0.415904i	0.622000	−	0.783017i	$-0.286320\pi$
$607$	38.2415	−	10.2468i	1.55218	−	0.415904i	0.930176	+	0.367113i	$0.119654\pi$
$608$	−20.5892	+	3.26100i	−0.835001	+	0.132251i
$609$	18.3249	−	24.8707i	0.742564	−	1.00781i
$610$		0			0
$611$	0.257404	+	0.0547130i	0.0104135	+	0.00221345i
$612$	−7.84459	−	5.09433i	−0.317099	−	0.205926i
$613$	3.25467	+	2.11361i	0.131455	+	0.0853679i	0.608691	−	0.793407i	$-0.291695\pi$
$613$	3.25467	+	2.11361i	0.131455	+	0.0853679i	−0.477236	+	0.878775i	$0.658361\pi$
$614$	−18.2473	−	3.87858i	−0.736400	−	0.156527i
$615$		0			0
$616$	−13.7286	+	18.6325i	−0.553140	+	0.750725i
$617$	−27.5463	+	4.36290i	−1.10897	+	0.175644i	−0.683943	−	0.729536i	$-0.739736\pi$
$617$	−27.5463	+	4.36290i	−1.10897	+	0.175644i	−0.425029	+	0.905180i	$0.639736\pi$
$618$	43.0597	−	11.5378i	1.73211	−	0.464118i
$619$	2.82187	−	26.8483i	0.113421	−	1.07913i	−0.778721	−	0.627370i	$-0.784131\pi$
$619$	2.82187	−	26.8483i	0.113421	−	1.07913i	0.892142	−	0.451755i	$-0.149202\pi$
$620$		0			0
$621$	−20.8305	+	2.18937i	−0.835898	+	0.0878564i
$622$	−45.9911	−	7.28427i	−1.84408	−	0.292073i
$623$	−0.704401	+	2.56027i	−0.0282212	+	0.102575i
$624$			1.28957i			0.0516239i
$625$		0			0
$626$	13.3561	−	7.71114i	0.533816	−	0.308199i
$627$	3.42258	+	65.3067i	0.136685	+	2.60810i
$628$	−5.81069	−	4.70541i	−0.231872	−	0.187766i
$629$	−20.9260	+	15.2037i	−0.834376	+	0.606209i
$630$		0			0
$631$	8.70119	+	6.32178i	0.346389	+	0.251666i	0.747353	−	0.664428i	$-0.231325\pi$
$631$	8.70119	+	6.32178i	0.346389	+	0.251666i	−0.400964	+	0.916094i	$0.631325\pi$
$632$	−8.90724	−	33.2423i	−0.354311	−	1.32231i
$633$	11.4592	+	14.1510i	0.455464	+	0.562451i
$634$	−2.62964	−	12.3715i	−0.104436	−	0.491335i
$635$		0			0
$636$	−19.1105	+	6.20937i	−0.757780	+	0.246217i
$637$	−0.235176	−	0.638026i	−0.00931801	−	0.0252795i
$638$	−24.2379	+	12.3498i	−0.959589	+	0.488935i
$639$	0.938426	−	4.41495i	0.0371236	−	0.174653i
$640$		0			0
$641$	−29.4673	+	6.26346i	−1.16389	+	0.247392i	−0.749056	−	0.662506i	$-0.769493\pi$
$641$	−29.4673	+	6.26346i	−1.16389	+	0.247392i	−0.414831	+	0.909898i	$0.636159\pi$
$642$	−4.67792	−	1.79569i	−0.184623	−	0.0708701i
$643$	20.4056	−	20.4056i	0.804720	−	0.804720i	−0.179110	−	0.983829i	$-0.557322\pi$
$643$	20.4056	−	20.4056i	0.804720	−	0.804720i	0.983829	+	0.179110i	$0.0573217\pi$
$644$	−0.849471	−	8.63730i	−0.0334739	−	0.340357i
$645$		0			0
$646$	3.45998	+	32.9195i	0.136131	+	1.29520i
$647$	6.86034	+	17.8718i	0.269708	+	0.702613i	0.999814	+	0.0192794i	$0.00613721\pi$
$647$	6.86034	+	17.8718i	0.269708	+	0.702613i	−0.730106	+	0.683334i	$0.760529\pi$
$648$	−5.50825	+	0.288675i	−0.216384	+	0.0113402i
$649$	10.1343	−	17.5531i	0.397805	−	0.689019i
$650$		0			0
$651$	−1.02704	−	4.99588i	−0.0402531	−	0.195804i
$652$	−8.08188	−	4.11792i	−0.316511	−	0.161270i
$653$	−7.59612	+	9.38043i	−0.297259	+	0.367084i	−0.903791	−	0.427975i	$-0.859227\pi$
$653$	−7.59612	+	9.38043i	−0.297259	+	0.367084i	0.606531	+	0.795060i	$0.292560\pi$
$654$	11.8373	+	5.27031i	0.462876	+	0.206086i
$655$		0			0
$656$	−0.259071	−	0.581883i	−0.0101150	−	0.0227187i
$657$	−6.73225	−	6.73225i	−0.262650	−	0.262650i
$658$	11.4580	+	1.89339i	0.446681	+	0.0738120i
$659$	−15.5052	−	5.03793i	−0.603995	−	0.196250i	−0.00897383	−	0.999960i	$-0.502856\pi$
$659$	−15.5052	−	5.03793i	−0.603995	−	0.196250i	−0.595022	+	0.803710i	$0.702856\pi$
$660$		0			0
$661$	10.4225	+	9.38450i	0.405390	+	0.365015i	0.846455	−	0.532460i	$-0.178732\pi$
$661$	10.4225	+	9.38450i	0.405390	+	0.365015i	−0.441065	+	0.897475i	$0.645399\pi$
$662$	0.913195	−	1.40620i	0.0354923	−	0.0546534i
$663$	0.888130	+	0.0465449i	0.0344921	+	0.00180766i
$664$	−7.44463	−	22.9122i	−0.288908	−	0.889166i
$665$		0			0
$666$	−17.2426	+	53.0674i	−0.668138	+	2.05632i
$667$	−8.03376	+	20.9287i	−0.311069	+	0.810361i
$668$	1.01063	+	0.270798i	0.0391025	+	0.0104775i
$669$	41.8660	+	4.40029i	1.61863	+	0.170125i
$670$		0			0
$671$	16.4678	+	22.6659i	0.635731	+	0.875008i
$672$	1.12855	+	24.6916i	0.0435347	+	0.952498i
$673$	0.128682	−	0.252552i	0.00496031	−	0.00973515i	−0.888513	−	0.458851i	$-0.848261\pi$
$673$	0.128682	−	0.252552i	0.00496031	−	0.00973515i	0.893473	+	0.449116i	$0.148261\pi$
$674$	2.62652	+	1.51642i	0.101170	+	0.0584103i
$675$		0			0
$676$	−4.06262	−	7.03667i	−0.156255	−	0.270641i
$677$	18.2427	+	28.0912i	0.701123	+	1.07963i	0.992407	+	0.122998i	$0.0392508\pi$
$677$	18.2427	+	28.0912i	0.701123	+	1.07963i	−0.291284	+	0.956637i	$0.594083\pi$
$678$	3.23488	−	20.4242i	0.124235	−	0.784387i
$679$	−6.42445	+	29.2613i	−0.246548	+	1.12295i
$680$		0			0
$681$	33.0654	−	14.7217i	1.26707	−	0.564136i
$682$	−1.16240	+	4.33814i	−0.0445106	+	0.166116i
$683$	17.5831	−	14.2385i	0.672798	−	0.544821i	−0.230907	−	0.972976i	$-0.574169\pi$
$683$	17.5831	−	14.2385i	0.672798	−	0.544821i	0.903706	+	0.428155i	$0.140836\pi$
$684$	11.3826	+	12.6417i	0.435225	+	0.483367i
$685$		0			0
$686$	−11.6535	−	27.6538i	−0.444931	−	1.05583i
$687$	5.14374	+	10.0951i	0.196246	+	0.385154i
$688$	−2.97020	+	56.6749i	−0.113238	+	2.16071i
$689$	0.764441	−	0.848997i	0.0291229	−	0.0323442i
$690$		0			0
$691$	21.1493	−	19.0429i	0.804557	−	0.724427i	−0.160338	−	0.987062i	$-0.551258\pi$
$691$	21.1493	−	19.0429i	0.804557	−	0.724427i	0.964895	+	0.262636i	$0.0845917\pi$
$692$	−0.0275190	−	0.173748i	−0.00104612	−	0.00660492i
$693$	46.2863	+	2.73619i	1.75827	+	0.103939i
$694$	1.89358	−	2.60628i	0.0718792	−	0.0989332i
$695$		0			0
$696$	10.5773	−	23.7571i	0.400933	−	0.900511i
$697$	−0.410097	+	0.157421i	−0.0155335	+	0.00596276i
$698$	−5.93870	+	3.85664i	−0.224783	+	0.145976i
$699$	70.3907			2.66242
$700$		0			0
$701$	29.7376			1.12317			0.561587	−	0.827418i	$-0.310191\pi$
$701$	29.7376			1.12317			0.561587	+	0.827418i	$0.310191\pi$
$702$	0.527197	−	0.342366i	0.0198978	−	0.0129218i
$703$	43.9171	−	16.8582i	1.65637	−	0.635819i
$704$	−6.67433	+	14.9908i	−0.251548	+	0.564986i
$705$		0			0
$706$	−17.7863	+	24.4807i	−0.669396	+	0.921345i
$707$	−13.9094	−	27.7560i	−0.523118	−	1.04387i
$708$	−1.37930	−	8.70856i	−0.0518373	−	0.327288i
$709$	6.43362	−	5.79286i	0.241620	−	0.217555i	−0.539420	−	0.842037i	$-0.681356\pi$
$709$	6.43362	−	5.79286i	0.241620	−	0.217555i	0.781039	+	0.624482i	$0.214690\pi$
$710$		0			0
$711$	−46.1349	+	51.2380i	−1.73020	+	1.92158i
$712$	−0.116987	+	2.23225i	−0.00438428	+	0.0836570i
$713$	1.68028	+	3.29773i	0.0629269	+	0.123501i
$714$	39.2475	+	0.262407i	1.46880	+	0.00982033i
$715$		0			0
$716$	−5.48831	−	6.09539i	−0.205108	−	0.227795i
$717$	1.38152	−	1.11873i	0.0515939	−	0.0417799i
$718$	7.00926	−	26.1589i	0.261583	−	0.976242i
$719$	24.7026	−	10.9983i	0.921251	−	0.410167i	0.109377	−	0.994000i	$-0.465114\pi$
$719$	24.7026	−	10.9983i	0.921251	−	0.410167i	0.811874	+	0.583833i	$0.198448\pi$
$720$		0			0
$721$	−17.9622	+	19.6828i	−0.668946	+	0.733024i
$722$	4.60121	−	29.0509i	0.171239	−	1.08116i
$723$	1.70811	+	2.63025i	0.0635251	+	0.0978201i
$724$	7.20316	+	12.4762i	0.267703	+	0.463676i
$725$		0			0
$726$	−16.9672	−	9.79602i	−0.629712	−	0.363565i
$727$	7.90873	−	15.5218i	0.293318	−	0.575670i	−0.696575	−	0.717484i	$-0.745294\pi$
$727$	7.90873	−	15.5218i	0.293318	−	0.575670i	0.989893	+	0.141814i	$0.0452936\pi$
$728$	−0.308542	−	0.482140i	−0.0114353	−	0.0178693i
$729$	25.7325	+	35.4177i	0.953055	+	1.31177i
$730$		0			0
$731$	38.9251	+	4.09119i	1.43970	+	0.151318i
$732$	11.7724	+	3.15439i	0.435119	+	0.116590i
$733$	−16.4531	+	42.8618i	−0.607709	+	1.58314i	0.191113	+	0.981568i	$0.438790\pi$
$733$	−16.4531	+	42.8618i	−0.607709	+	1.58314i	−0.798822	+	0.601567i	$0.794543\pi$
$734$	−4.83698	+	14.8867i	−0.178536	+	0.549477i
$735$		0			0
$736$	−5.54266	−	17.0586i	−0.204305	−	0.628787i
$737$	−2.18925	−	0.114734i	−0.0806422	−	0.00422628i
$738$	−0.516102	+	0.794727i	−0.0189980	+	0.0292543i
$739$	18.2915	+	16.4697i	0.672864	+	0.605849i	0.933066	−	0.359705i	$-0.117123\pi$
$739$	18.2915	+	16.4697i	0.672864	+	0.605849i	−0.260202	+	0.965554i	$0.583789\pi$
$740$		0			0
$741$	−1.53827	−	0.499813i	−0.0565096	−	0.0183611i
$742$	31.9901	−	38.9688i	1.17439	−	1.43059i
$743$	−10.2323	−	10.2323i	−0.375388	−	0.375388i	0.494047	−	0.869435i	$-0.335517\pi$
$743$	−10.2323	−	10.2323i	−0.375388	−	0.375388i	−0.869435	+	0.494047i	$0.835517\pi$
$744$	−1.74631	−	3.92228i	−0.0640229	−	0.143798i
$745$		0			0
$746$	−7.27985	−	3.24120i	−0.266534	−	0.118669i
$747$	−30.3742	+	37.5090i	−1.11133	+	1.37238i
$748$	−7.33605	−	3.73790i	−0.268233	−	0.136671i
$749$	2.93380	−	0.603126i	0.107199	−	0.0220377i
$750$		0			0
$751$	5.60583	−	9.70959i	0.204560	−	0.354308i	−0.745433	−	0.666581i	$-0.767757\pi$
$751$	5.60583	−	9.70959i	0.204560	−	0.354308i	0.949992	+	0.312273i	$0.101090\pi$
$752$	13.1469	−	0.689001i	0.479419	−	0.0251253i
$753$	13.5575	+	35.3186i	0.494064	+	1.28708i
$754$	−0.0703268	−	0.669115i	−0.00256115	−	0.0243677i
$755$		0			0
$756$	5.37259	−	3.84880i	0.195399	−	0.139979i
$757$	−34.2009	+	34.2009i	−1.24305	+	1.24305i	−0.284326	+	0.958728i	$0.591770\pi$
$757$	−34.2009	+	34.2009i	−1.24305	+	1.24305i	−0.958728	+	0.284326i	$0.908230\pi$
$758$	−19.0419	−	7.30949i	−0.691632	−	0.265493i
$759$	−55.0395	+	11.6990i	−1.99781	+	0.424647i
$760$		0			0
$761$	−3.57175	+	16.8038i	−0.129476	+	0.609135i	0.864784	+	0.502144i	$0.167455\pi$
$761$	−3.57175	+	16.8038i	−0.129476	+	0.609135i	−0.994260	+	0.106992i	$0.965878\pi$
$762$	65.3109	−	33.2776i	2.36597	−	1.20552i
$763$	−7.65792	+	1.16047i	−0.277235	+	0.0420117i
$764$	2.40697	−	0.782073i	0.0870812	−	0.0282944i
$765$		0			0
$766$	−6.04081	−	28.4198i	−0.218263	−	1.02685i
$767$	0.315476	+	0.389580i	0.0113912	+	0.0140669i
$768$	9.68333	+	36.1387i	0.349417	+	1.30404i
$769$	−15.2142	−	11.0538i	−0.548638	−	0.398609i	0.278645	−	0.960394i	$-0.410115\pi$
$769$	−15.2142	−	11.0538i	−0.548638	−	0.398609i	−0.827283	+	0.561785i	$0.810115\pi$
$770$		0			0
$771$	−0.805836	+	0.585474i	−0.0290215	+	0.0210853i
$772$	−1.49448	−	1.21020i	−0.0537873	−	0.0435561i
$773$	1.69120	+	32.2701i	0.0608283	+	1.16067i	0.843107	+	0.537745i	$0.180724\pi$
$773$	1.69120	+	32.2701i	0.0608283	+	1.16067i	−0.782279	+	0.622928i	$0.785943\pi$
$774$	73.1203	−	42.2160i	2.62825	−	1.51742i
$775$		0			0
$776$			25.2188i			0.905302i
$777$	−14.0759	−	53.9730i	−0.504971	−	1.93627i
$778$	19.0873	+	3.02314i	0.684314	+	0.108385i
$779$	0.794514	−	0.0835068i	0.0284664	−	0.00299194i
$780$		0			0
$781$	0.415297	−	3.95129i	0.0148605	−	0.141388i
$782$	−27.5106	+	7.37143i	−0.983776	+	0.263602i
$783$	−16.8606	+	2.67045i	−0.602548	+	0.0954343i
$784$	−19.6256	−	27.7861i	−0.700913	−	0.992362i
$785$		0			0
$786$	−1.74274	−	0.370432i	−0.0621616	−	0.0132129i
$787$	11.1430	+	7.23632i	0.397204	+	0.257947i	0.727750	−	0.685843i	$-0.240566\pi$
$787$	11.1430	+	7.23632i	0.397204	+	0.257947i	−0.330546	+	0.943790i	$0.607233\pi$
$788$	−6.61551	−	4.29616i	−0.235668	−	0.153045i
$789$	−79.4852	−	16.8951i	−2.82975	−	0.601481i
$790$		0			0
$791$	4.95194	+	11.3254i	0.176071	+	0.402686i
$792$	38.5512	−	6.10592i	1.36986	−	0.216964i
$793$	−0.669316	+	0.179343i	−0.0237681	+	0.00636865i
$794$	6.35491	−	60.4629i	0.225527	−	2.14575i
$795$		0			0
$796$	−2.70586	+	0.284397i	−0.0959066	+	0.0100802i
$797$	−37.9724	−	6.01424i	−1.34505	−	0.213035i	−0.557959	−	0.829869i	$-0.688415\pi$
$797$	−37.9724	−	6.01424i	−1.34505	−	0.213035i	−0.787094	+	0.616833i	$0.788415\pi$
$798$	−68.8223	−	18.9350i	−2.43628	−	0.670290i
$799$		−	9.07923i		−	0.321200i
$800$		0			0
$801$	3.87829	−	2.23913i	0.137033	−	0.0791159i
$802$	−0.0181017	−	0.345401i	−0.000639192	−	0.0121965i
$803$	−6.51300	−	5.27412i	−0.229839	−	0.186120i
$804$	−0.771531	+	0.560550i	−0.0272098	+	0.0197691i
$805$		0			0
$806$	−0.0898647	−	0.0652905i	−0.00316535	−	0.00229976i
$807$	14.6529	+	54.6854i	0.515807	+	1.92502i
$808$	−16.4471	−	20.3104i	−0.578606	−	0.714519i
$809$	0.240260	+	1.13033i	0.00844708	+	0.0397404i	0.982169	−	0.187999i	$-0.0602000\pi$
$809$	0.240260	+	1.13033i	0.00844708	+	0.0397404i	−0.973722	+	0.227739i	$0.926867\pi$
$810$		0			0
$811$	11.7589	−	3.82070i	0.412911	−	0.134163i	−0.0951926	−	0.995459i	$-0.530347\pi$
$811$	11.7589	−	3.82070i	0.412911	−	0.134163i	0.508104	+	0.861296i	$0.330347\pi$
$812$	−1.05981	−	6.99369i	−0.0371920	−	0.245430i
$813$	−13.6457	+	6.95282i	−0.478575	+	0.243846i
$814$	−10.2118	+	48.0428i	−0.357924	+	1.68390i
$815$		0			0
$816$	43.5196	−	9.25038i	1.52349	−	0.323828i
$817$	−66.4538	−	25.5092i	−2.32492	−	0.892454i
$818$	−36.5978	+	36.5978i	−1.27961	+	1.27961i
$819$	−0.473433	+	1.04450i	−0.0165431	+	0.0364977i
$820$		0			0
$821$	3.87750	+	36.8920i	0.135326	+	1.28754i	0.825710	+	0.564095i	$0.190775\pi$
$821$	3.87750	+	36.8920i	0.135326	+	1.28754i	−0.690384	+	0.723443i	$0.742558\pi$
$822$	−20.0925	−	52.3428i	−0.700807	−	1.82567i
$823$	−50.2235	+	2.63210i	−1.75068	+	0.0917494i	−0.900532	−	0.434790i	$-0.856823\pi$
$823$	−50.2235	+	2.63210i	−1.75068	+	0.0917494i	−0.850151	+	0.526539i	$0.823489\pi$
$824$	−11.2156	+	19.4260i	−0.390714	+	0.676737i
$825$		0			0
$826$	14.6929	+	16.5392i	0.511232	+	0.575472i
$827$	17.5564	+	8.94542i	0.610495	+	0.311063i	0.731765	−	0.681557i	$-0.238697\pi$
$827$	17.5564	+	8.94542i	0.610495	+	0.311063i	−0.121270	+	0.992620i	$0.538697\pi$
$828$	−9.21129	+	11.3750i	−0.320114	+	0.395308i
$829$	−20.7157	−	9.22321i	−0.719485	−	0.320335i	0.0141306	−	0.999900i	$-0.495502\pi$
$829$	−20.7157	−	9.22321i	−0.719485	−	0.320335i	−0.733615	+	0.679565i	$0.762169\pi$
$830$		0			0
$831$	−6.56796	−	14.7519i	−0.227840	−	0.511737i
$832$	−0.286979	−	0.286979i	−0.00994922	−	0.00994922i
$833$	−19.8448	+	12.5133i	−0.687582	+	0.433561i
$834$	60.5681	+	19.6798i	2.09730	+	0.681454i
$835$		0			0
$836$	11.1278	+	10.0195i	0.384862	+	0.346531i
$837$	−1.53499	+	2.36368i	−0.0530571	+	0.0817008i
$838$	17.1519	+	0.898893i	0.592503	+	0.0310518i
$839$	5.77620	+	17.7773i	0.199417	+	0.613742i	0.999897	+	0.0143819i	$0.00457805\pi$
$839$	5.77620	+	17.7773i	0.199417	+	0.613742i	−0.800480	+	0.599360i	$0.795422\pi$
$840$		0			0
$841$	3.31550	−	10.2041i	0.114328	−	0.351864i
$842$	5.11566	−	13.3267i	0.176297	−	0.459270i
$843$	−22.5734	−	6.04853i	−0.777470	−	0.208323i
$844$	4.14647	+	0.435812i	0.142728	+	0.0150013i
$845$		0			0
$846$	−11.5122	−	15.8452i	−0.395799	−	0.544770i
$847$	11.6989	−	0.534707i	0.401978	−	0.0183727i
$848$	25.9471	−	50.9240i	0.891025	−	1.74874i
$849$	35.6995	+	20.6111i	1.22520	+	0.707372i
$850$		0			0
$851$	20.2381	+	35.0534i	0.693752	+	1.20161i
$852$	−0.941319	−	1.44950i	−0.0322491	−	0.0496592i
$853$	5.30806	−	33.5138i	0.181744	−	1.14749i	−0.713084	−	0.701079i	$-0.752702\pi$
$853$	5.30806	−	33.5138i	0.181744	−	1.14749i	0.894828	−	0.446410i	$-0.147298\pi$
$854$	−29.1458	+	9.25507i	−0.997348	+	0.316702i
$855$		0			0
$856$	2.30334	−	1.02551i	0.0787264	−	0.0350513i
$857$	−2.31682	+	8.64649i	−0.0791410	+	0.295358i	−0.994140	−	0.108097i	$-0.965524\pi$
$857$	−2.31682	+	8.64649i	−0.0791410	+	0.295358i	0.914999	+	0.403455i	$0.132191\pi$
$858$	1.31241	−	1.06277i	0.0448049	−	0.0362823i
$859$	15.4543	+	17.1638i	0.527295	+	0.585621i	0.946675	−	0.322190i	$-0.104419\pi$
$859$	15.4543	+	17.1638i	0.527295	+	0.585621i	−0.419380	+	0.907811i	$0.637752\pi$
$860$		0			0
$861$	0.00633321	−	0.947241i	0.000215835	−	0.0322819i
$862$	4.50806	+	8.84757i	0.153545	+	0.301349i
$863$	−0.192954	+	3.68178i	−0.00656823	+	0.125329i	0.993377	+	0.114897i	$0.0366539\pi$
$863$	−0.192954	+	3.68178i	−0.00656823	+	0.125329i	−0.999946	+	0.0104318i	$0.996679\pi$
$864$	9.13923	−	10.1501i	0.310923	−	0.345315i
$865$		0			0
$866$	−43.0183	+	38.7338i	−1.46182	+	1.31623i
$867$	2.46454	+	15.5605i	0.0837003	+	0.528463i
$868$	−0.975154	−	0.642582i	−0.0330989	−	0.0218107i
$869$	−35.6731	+	49.0998i	−1.21013	+	1.66560i
$870$		0			0
$871$	0.0220535	−	0.0495329i	0.000747253	−	0.00167836i
$872$	−6.08696	+	2.33657i	−0.206131	+	0.0791261i
$873$	42.3729	−	27.5173i	1.43410	−	0.931318i
$874$	51.7975			1.75208
$875$		0			0
$876$	−3.64571			−0.123177
$877$	−25.2117	+	16.3727i	−0.851339	+	0.552866i	−0.894942	−	0.446183i	$-0.852783\pi$
$877$	−25.2117	+	16.3727i	−0.851339	+	0.552866i	0.0436027	+	0.999049i	$0.486116\pi$
$878$	39.4459	−	15.1418i	1.33123	−	0.511013i
$879$	−12.2667	+	27.5515i	−0.413746	+	0.929290i
$880$		0			0
$881$	−26.3597	+	36.2810i	−0.888079	+	1.22234i	0.0860376	+	0.996292i	$0.472579\pi$
$881$	−26.3597	+	36.2810i	−0.888079	+	1.22234i	−0.974117	+	0.226045i	$0.927421\pi$
$882$	−18.7669	+	47.0012i	−0.631915	+	1.58261i
$883$	−4.53057	−	28.6049i	−0.152466	−	0.962631i	−0.938708	−	0.344713i	$-0.887976\pi$
$883$	−4.53057	−	28.6049i	−0.152466	−	0.962631i	0.786242	−	0.617918i	$-0.212024\pi$
$884$	0.151331	−	0.136259i	0.00508980	−	0.00458287i
$885$		0			0
$886$	36.7226	−	40.7845i	1.23372	−	1.37018i
$887$	1.26056	−	24.0529i	0.0423254	−	0.807616i	−0.892183	−	0.451674i	$-0.850827\pi$
$887$	1.26056	−	24.0529i	0.0423254	−	0.807616i	0.934508	−	0.355942i	$-0.115840\pi$
$888$	−21.3167	−	41.8363i	−0.715341	−	1.40394i
$889$	−22.1607	+	37.7976i	−0.743246	+	1.26769i
$890$		0			0
$891$	6.50871	+	7.22865i	0.218050	+	0.242169i
$892$	7.49083	−	6.06596i	0.250812	−	0.203103i
$893$	−4.27364	+	15.9494i	−0.143012	+	0.533728i
$894$	43.1735	−	19.2221i	1.44394	−	0.642883i
$895$		0			0
$896$	−26.5972	−	24.2722i	−0.888552	−	0.810878i
$897$	0.217708	−	1.37455i	0.00726906	−	0.0458950i
$898$	−15.7302	−	24.2224i	−0.524924	−	0.808312i
$899$	1.50825	+	2.61236i	0.0503029	+	0.0871271i
$900$		0			0
$901$	−34.1351	−	19.7079i	−1.13720	−	0.656565i
$902$	−0.378683	+	0.743207i	−0.0126088	+	0.0247461i
$903$	−38.8195	+	74.9445i	−1.29183	+	2.49400i
$904$	6.11603	+	8.41800i	0.203416	+	0.279978i
$905$		0			0
$906$	−91.9096	−	9.66009i	−3.05349	−	0.320935i
$907$	−3.49857	−	0.937438i	−0.116168	−	0.0311271i	0.200267	−	0.979741i	$-0.435819\pi$
$907$	−3.49857	−	0.937438i	−0.116168	−	0.0311271i	−0.316435	+	0.948614i	$0.602486\pi$
$908$	2.96998	−	7.73707i	0.0985623	−	0.256764i
$909$	−16.1797	+	49.7961i	−0.536648	+	1.65163i
$910$		0			0
$911$	2.97054	+	9.14238i	0.0984183	+	0.302900i	0.988129	−	0.153623i	$-0.0490943\pi$
$911$	2.97054	+	9.14238i	0.0984183	+	0.302900i	−0.889711	+	0.456524i	$0.849094\pi$
$912$	−80.8049	−	4.23481i	−2.67572	−	0.140228i
$913$	−23.1390	+	35.6309i	−0.765788	+	1.17921i
$914$	−10.2738	−	9.25056i	−0.339827	−	0.305981i
$915$		0			0
$916$	2.46728	+	0.801669i	0.0815213	+	0.0264879i
$917$	0.996787	−	0.375004i	0.0329168	−	0.0123837i
$918$	−15.3357	−	15.3357i	−0.506154	−	0.506154i
$919$	−2.99431	−	6.72533i	−0.0987732	−	0.221848i	0.857400	−	0.514651i	$-0.172079\pi$
$919$	−2.99431	−	6.72533i	−0.0987732	−	0.221848i	−0.956173	+	0.292803i	$0.905412\pi$
$920$		0			0
$921$	−28.7308	−	12.7918i	−0.946712	−	0.421503i
$922$	27.0454	−	33.3983i	0.890693	−	1.09991i
$923$	0.0875541	+	0.0446111i	0.00288188	+	0.00146839i
$924$	13.2736	−	11.7918i	0.436668	−	0.387923i
$925$		0			0
$926$	18.5411	−	32.1142i	0.609300	−	1.05534i
$927$	44.8776	−	2.35193i	1.47397	−	0.0772476i
$928$	−5.23882	−	13.6476i	−0.171973	−	0.448004i
$929$	−6.12235	−	58.2502i	−0.200868	−	1.91113i	−0.376062	−	0.926595i	$-0.622722\pi$
$929$	−6.12235	−	58.2502i	−0.200868	−	1.91113i	0.175194	−	0.984534i	$-0.443945\pi$
$930$		0			0
$931$	40.7514	−	12.6411i	1.33557	−	0.414294i
$932$	11.3968	−	11.3968i	0.373313	−	0.373313i
$933$	−73.2874	−	28.1324i	−2.39932	−	0.921013i
$934$	−14.1324	+	3.00393i	−0.462425	+	0.0982914i
$935$		0			0
$936$	−0.200710	+	0.944266i	−0.00656041	+	0.0308643i
$937$	4.14402	−	2.11148i	0.135379	−	0.0689791i	−0.384989	−	0.922921i	$-0.625795\pi$
$937$	4.14402	−	2.11148i	0.135379	−	0.0689791i	0.520368	+	0.853942i	$0.325795\pi$
$938$	0.872432	−	2.22812i	0.0284859	−	0.0727507i
$939$	24.7274	−	8.03442i	0.806948	−	0.262193i
$940$		0			0
$941$	−6.07308	−	28.5716i	−0.197977	−	0.931408i	−0.959159	−	0.282869i	$-0.908714\pi$
$941$	−6.07308	−	28.5716i	−0.197977	−	0.931408i	0.761182	−	0.648539i	$-0.224619\pi$
$942$	−33.2981	−	41.1198i	−1.08491	−	1.33976i
$943$	0.177910	+	0.663969i	0.00579355	+	0.0216218i
$944$	20.2890	+	14.7408i	0.660350	+	0.479773i
$945$		0			0
$946$	60.1267	−	43.6846i	1.95489	−	1.42031i
$947$	−4.73472	−	3.83410i	−0.153858	−	0.124592i	0.549301	−	0.835625i	$-0.314894\pi$
$947$	−4.73472	−	3.83410i	−0.153858	−	0.124592i	−0.703158	+	0.711033i	$0.748228\pi$
$948$	1.38174	+	26.3651i	0.0448768	+	0.856300i
$949$	0.179507	−	0.103638i	0.00582703	−	0.00336424i
$950$		0			0
$951$		−	21.3227i		−	0.691435i
$952$	−14.0578	+	13.8710i	−0.455615	+	0.449563i
$953$	−5.50713	−	0.872243i	−0.178393	−	0.0282547i	0.0665986	−	0.997780i	$-0.478785\pi$
$953$	−5.50713	−	0.872243i	−0.178393	−	0.0282547i	−0.244992	+	0.969525i	$0.578785\pi$
$954$	−84.5622	+	8.88785i	−2.73780	+	0.287755i
$955$		0			0
$956$	0.0425472	−	0.404809i	0.00137607	−	0.0130925i
$957$	−44.2978	+	11.8696i	−1.43194	+	0.383688i
$958$	3.83049	−	0.606690i	0.123758	−	0.0196013i
$959$	26.9809	+	19.8797i	0.871259	+	0.641950i
$960$		0			0
$961$	−29.8354	−	6.34172i	−0.962433	−	0.204572i
$962$	−1.01880	−	0.661614i	−0.0328473	−	0.0213313i
$963$	−4.23634	−	2.75111i	−0.136514	−	0.0886533i
$964$	0.702411	+	0.149302i	0.0226231	+	0.00480869i
$965$		0			0
$966$	6.82809	−	61.0366i	0.219690	−	1.96382i
$967$	58.4215	−	9.25305i	1.87871	−	0.297558i	0.891016	−	0.453972i	$-0.149993\pi$
$967$	58.4215	−	9.25305i	1.87871	−	0.297558i	0.987692	+	0.156414i	$0.0499934\pi$
$968$	9.52247	−	2.55154i	0.306064	−	0.0820095i
$969$	−5.83307	+	55.4979i	−0.187385	+	1.78285i
$970$		0			0
$971$	−52.4895	+	5.51687i	−1.68447	+	0.177045i	−0.897822	−	0.440359i	$-0.854851\pi$
$971$	−52.4895	+	5.51687i	−1.68447	+	0.177045i	−0.786647	+	0.617404i	$0.788185\pi$
$972$	11.5809	+	1.83423i	0.371458	+	0.0588331i
$973$	−36.8355	+	9.60655i	−1.18089	+	0.307972i
$974$			7.85203i			0.251595i
$975$		0			0
$976$	−30.0211	+	17.3327i	−0.960952	+	0.554806i
$977$	−0.689886	−	13.1638i	−0.0220714	−	0.421148i	−0.987212	−	0.159415i	$-0.949039\pi$
$977$	−0.689886	−	13.1638i	−0.0220714	−	0.421148i	0.965140	−	0.261733i	$-0.0842940\pi$
$978$	−49.8835	−	40.3949i	−1.59510	−	1.29168i
$979$	3.18912	−	2.31703i	0.101925	−	0.0740525i
$980$		0			0
$981$	10.5677	+	7.67785i	0.337399	+	0.245135i
$982$	12.4858	+	46.5975i	0.398436	+	1.48699i
$983$	33.7893	+	41.7263i	1.07771	+	1.33086i	0.940299	+	0.340350i	$0.110546\pi$
$983$	33.7893	+	41.7263i	1.07771	+	1.33086i	0.137413	+	0.990514i	$0.456121\pi$
$984$	−0.165789	−	0.779978i	−0.00528518	−	0.0248648i
$985$		0			0
$986$	−22.0765	+	7.17309i	−0.703059	+	0.228438i
$987$	18.2310	+	7.13844i	0.580299	+	0.227219i
$988$	−0.329979	+	0.168133i	−0.0104980	+	0.00534902i
$989$	12.7340	−	59.9086i	0.404917	−	1.90498i
$990$		0			0
$991$	−10.3254	+	2.19474i	−0.327998	+	0.0697182i	−0.368968	−	0.929442i	$-0.620289\pi$
$991$	−10.3254	+	2.19474i	−0.327998	+	0.0697182i	0.0409694	+	0.999160i	$0.486955\pi$
$992$	−2.25320	−	0.864924i	−0.0715393	−	0.0274614i
$993$	1.99877	−	1.99877i	0.0634291	−	0.0634291i
$994$	3.94976	+	1.79028i	0.125279	+	0.0567843i
$995$		0			0
$996$	1.93185	+	18.3803i	0.0612131	+	0.582404i
$997$	21.4543	+	55.8904i	0.679465	+	1.77007i	0.636867	+	0.770974i	$0.280230\pi$
$997$	21.4543	+	55.8904i	0.679465	+	1.77007i	0.0425978	+	0.999092i	$0.486437\pi$
$998$	62.9405	−	3.29857i	1.99235	−	0.104414i
$999$	−15.4110	+	26.6927i	−0.487584	+	0.844520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.b.768.14		288
5.2	odd	4		175.2.x.a.117.14	yes	288
5.3	odd	4		875.2.bb.c.607.5		288
5.4	even	2		875.2.bb.a.768.5		288
7.3	odd	6	inner	875.2.bb.b.143.14		288
25.3	odd	20		875.2.bb.a.257.5		288
25.4	even	10		875.2.bb.c.243.14		288
25.21	even	5		175.2.x.a.103.5	yes	288
25.22	odd	20	inner	875.2.bb.b.257.14		288
35.3	even	12		875.2.bb.c.857.14		288
35.17	even	12		175.2.x.a.17.5	yes	288
35.24	odd	6		875.2.bb.a.143.5		288
175.3	even	60		875.2.bb.a.507.5		288
175.122	even	60	inner	875.2.bb.b.507.14		288
175.129	odd	30		875.2.bb.c.493.5		288
175.171	odd	30		175.2.x.a.3.14	✓	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.14	✓	288	175.171	odd	30
175.2.x.a.17.5	yes	288	35.17	even	12
175.2.x.a.103.5	yes	288	25.21	even	5
175.2.x.a.117.14	yes	288	5.2	odd	4
875.2.bb.a.143.5		288	35.24	odd	6
875.2.bb.a.257.5		288	25.3	odd	20
875.2.bb.a.507.5		288	175.3	even	60
875.2.bb.a.768.5		288	5.4	even	2
875.2.bb.b.143.14		288	7.3	odd	6	inner
875.2.bb.b.257.14		288	25.22	odd	20	inner
875.2.bb.b.507.14		288	175.122	even	60	inner
875.2.bb.b.768.14		288	1.1	even	1	trivial
875.2.bb.c.243.14		288	25.4	even	10
875.2.bb.c.493.5		288	175.129	odd	30
875.2.bb.c.607.5		288	5.3	odd	4
875.2.bb.c.857.14		288	35.3	even	12

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.35892 - 0.882496i) q^{2} +(2.55023 - 0.978941i) q^{3} +(0.254403 - 0.571398i) q^{4} +(2.60166 - 3.58087i) q^{6} +(-0.156130 + 2.64114i) q^{7} +(0.348409 + 2.19977i) q^{8} +(3.31591 - 2.98566i) q^{9} +(2.62811 - 2.91881i) q^{11} +(0.0894203 - 1.70624i) q^{12} +(0.0441012 + 0.0865535i) q^{13} +(2.11863 + 3.72689i) q^{14} +(3.25179 + 3.61148i) q^{16} +(2.60462 - 2.10918i) q^{17} +(1.87124 - 6.98356i) q^{18} +(-5.56832 + 2.47917i) q^{19} +(2.18736 + 6.88836i) q^{21} +(0.995562 - 6.28573i) q^{22} +(-2.85640 - 4.39848i) q^{23} +(3.04197 + 5.26884i) q^{24} +(0.136313 + 0.0787005i) q^{26} +(1.81310 - 3.55840i) q^{27} +(1.46942 + 0.761125i) q^{28} +(-2.51245 - 3.45809i) q^{29} +(-0.701840 - 0.0737664i) q^{31} +(3.30346 + 0.885159i) q^{32} +(3.84493 - 10.0164i) q^{33} +(1.67814 - 5.16477i) q^{34} +(-0.862422 - 2.65426i) q^{36} +(-7.70713 - 0.403914i) q^{37} +(-5.37906 + 8.28302i) q^{38} +(0.197199 + 0.177559i) q^{39} +(-0.124652 - 0.0405019i) q^{41} +(9.05139 + 7.43042i) q^{42} +(8.25770 + 8.25770i) q^{43} +(-0.999203 - 2.24425i) q^{44} +(-7.76327 - 3.45643i) q^{46} +(1.70482 - 2.10528i) q^{47} +(11.8282 + 6.02679i) q^{48} +(-6.95125 - 0.824720i) q^{49} +(4.57761 - 7.92865i) q^{51} +(0.0606759 - 0.00317989i) q^{52} +(-4.21462 - 10.9795i) q^{53} +(-0.676413 - 6.43564i) q^{54} +(-5.86430 + 0.576749i) q^{56} +(-11.7735 + 11.7735i) q^{57} +(-6.46598 - 2.48206i) q^{58} +(5.04772 - 1.07293i) q^{59} +(-1.48307 + 6.97731i) q^{61} +(-1.01885 + 0.519128i) q^{62} +(7.36783 + 9.22393i) q^{63} +(-3.97346 + 1.29105i) q^{64} +(-3.61445 - 17.0046i) q^{66} +(-0.351262 - 0.433773i) q^{67} +(-0.542557 - 2.02485i) q^{68} +(-11.5903 - 8.42087i) q^{69} +(0.818370 - 0.594581i) q^{71} +(7.72305 + 6.25400i) q^{72} +(-0.111673 - 2.13084i) q^{73} +(-10.8299 + 6.25262i) q^{74} +3.81243i q^{76} +(7.29866 + 7.39691i) q^{77} +(0.424673 + 0.0672616i) q^{78} +(-15.3675 + 1.61519i) q^{79} +(-0.258873 + 2.46301i) q^{81} +(-0.205136 + 0.0549659i) q^{82} +(-10.6837 + 1.69214i) q^{83} +(4.49246 + 0.502566i) q^{84} +(18.5090 + 3.93420i) q^{86} +(-9.79260 - 6.35939i) q^{87} +(7.33636 + 4.76429i) q^{88} +(0.981714 + 0.208670i) q^{89} +(-0.235485 + 0.102964i) q^{91} +(-3.23996 + 0.513159i) q^{92} +(-1.86207 + 0.498939i) q^{93} +(0.458824 - 4.36542i) q^{94} +(9.29110 - 0.976534i) q^{96} +(11.1837 + 1.77133i) q^{97} +(-10.1740 + 5.01371i) q^{98} -17.5251i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) \) 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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