LMFDB - Embedded newform 875.2.bb.b.143.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] 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("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [288,2] 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:	$6.98691017686$
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			143.5
Character	$\chi$	$=$	875.143
Dual form			875.2.bb.b.257.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0830157 - 1.58403i) q^{2} +(1.52315 + 1.23343i) q^{3} +(-0.513230 + 0.0539426i) q^{4} +(1.82734 - 2.51512i) q^{6} +(-2.08368 - 1.63042i) q^{7} +(-0.368222 - 2.32486i) q^{8} +(0.174924 + 0.822951i) q^{9} +(-2.03775 - 0.433137i) q^{11} +(-0.848262 - 0.550868i) q^{12} +(-0.992394 - 1.94768i) q^{13} +(-2.40967 + 3.43597i) q^{14} +(-4.66165 + 0.990865i) q^{16} +(-4.72957 - 1.81551i) q^{17} +(1.28906 - 0.345403i) q^{18} +(0.785987 - 7.47816i) q^{19} +(-1.16276 - 5.05345i) q^{21} +(-0.516939 + 3.26382i) q^{22} +(2.00560 - 0.105109i) q^{23} +(2.30669 - 3.99530i) q^{24} +(-3.00281 + 1.73368i) q^{26} +(1.92076 - 3.76970i) q^{27} +(1.15736 + 0.724382i) q^{28} +(4.12547 + 5.67823i) q^{29} +(2.58369 + 5.80306i) q^{31} +(0.738117 + 2.75469i) q^{32} +(-2.56957 - 3.17315i) q^{33} +(-2.48320 + 7.64252i) q^{34} +(-0.134168 - 0.412927i) q^{36} +(1.44212 - 2.22067i) q^{37} +(-11.9109 - 0.624225i) q^{38} +(0.890754 - 4.19067i) q^{39} +(8.47974 + 2.75523i) q^{41} +(-7.90831 + 2.26137i) q^{42} +(0.986332 + 0.986332i) q^{43} +(1.06920 + 0.112377i) q^{44} +(-0.332993 - 3.16821i) q^{46} +(-0.941527 - 2.45276i) q^{47} +(-8.32258 - 4.24056i) q^{48} +(1.68344 + 6.79456i) q^{49} +(-4.96456 - 8.59887i) q^{51} +(0.614389 + 0.946077i) q^{52} +(5.81286 - 7.17828i) q^{53} +(-6.13079 - 2.72960i) q^{54} +(-3.02325 + 5.44463i) q^{56} +(10.4209 - 10.4209i) q^{57} +(8.65203 - 7.00627i) q^{58} +(7.04085 + 7.81965i) q^{59} +(-6.37468 - 5.73979i) q^{61} +(8.97777 - 4.57440i) q^{62} +(0.977274 - 1.99997i) q^{63} +(-4.76284 + 1.54754i) q^{64} +(-4.81306 + 4.33370i) q^{66} +(1.17677 - 3.06559i) q^{67} +(2.52529 + 0.676649i) q^{68} +(3.18448 + 2.31366i) q^{69} +(5.41526 - 3.93442i) q^{71} +(1.84884 - 0.709703i) q^{72} +(-6.94515 + 4.51023i) q^{73} +(-3.63734 - 2.10002i) q^{74} +3.88041i q^{76} +(3.53982 + 4.22492i) q^{77} +(-6.71211 - 1.06309i) q^{78} +(-1.08662 + 2.44058i) q^{79} +(9.88106 - 4.39933i) q^{81} +(3.66043 - 13.6609i) q^{82} +(-2.88395 + 0.456772i) q^{83} +(0.869359 + 2.53086i) q^{84} +(1.48050 - 1.64427i) q^{86} +(-0.719940 + 13.7373i) q^{87} +(-0.256640 + 4.89698i) q^{88} +(-8.47306 + 9.41028i) q^{89} +(-1.10772 + 5.67637i) q^{91} +(-1.02366 + 0.162132i) q^{92} +(-3.22229 + 12.0258i) q^{93} +(-3.80710 + 1.69503i) q^{94} +(-2.27344 + 5.10623i) q^{96} +(-3.33125 - 0.527619i) q^{97} +(10.6231 - 3.23068i) q^{98} -1.75274i 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 $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.0830157	−	1.58403i	−0.0587010	−	1.12008i	−0.856161	−	0.516709i	$-0.827157\pi$
$2$	−0.0830157	−	1.58403i	−0.0587010	−	1.12008i	0.797460	−	0.603372i	$-0.206177\pi$
$3$	1.52315	+	1.23343i	0.879393	+	0.712119i	0.958605	−	0.284739i	$-0.0919070\pi$
$3$	1.52315	+	1.23343i	0.879393	+	0.712119i	−0.0792117	+	0.996858i	$0.525240\pi$
$4$	−0.513230	+	0.0539426i	−0.256615	+	0.0269713i
$5$		0			0
$5$		0			0
$6$	1.82734	−	2.51512i	0.746010	−	1.02679i
$7$	−2.08368	−	1.63042i	−0.787557	−	0.616242i
$7$	−2.08368	−	1.63042i	−0.787557	−	0.616242i
$8$	−0.368222	−	2.32486i	−0.130186	−	0.821963i
$9$	0.174924	+	0.822951i	0.0583079	+	0.274317i
$10$		0			0
$11$	−2.03775	−	0.433137i	−0.614405	−	0.130596i	−0.109811	−	0.993953i	$-0.535025\pi$
$11$	−2.03775	−	0.433137i	−0.614405	−	0.130596i	−0.504594	+	0.863357i	$0.668358\pi$
$12$	−0.848262	−	0.550868i	−0.244872	−	0.159022i
$13$	−0.992394	−	1.94768i	−0.275241	−	0.540190i	0.711462	−	0.702724i	$-0.248033\pi$
$13$	−0.992394	−	1.94768i	−0.275241	−	0.540190i	−0.986703	+	0.162534i	$0.948033\pi$
$14$	−2.40967	+	3.43597i	−0.644011	+	0.918302i
$15$		0			0
$16$	−4.66165	+	0.990865i	−1.16541	+	0.247716i
$17$	−4.72957	−	1.81551i	−1.14709	−	0.440326i	−0.290780	−	0.956790i	$-0.593915\pi$
$17$	−4.72957	−	1.81551i	−1.14709	−	0.440326i	−0.856309	+	0.516464i	$0.827248\pi$
$18$	1.28906	−	0.345403i	0.303835	−	0.0814123i
$19$	0.785987	−	7.47816i	0.180318	−	1.71561i	−0.413076	−	0.910696i	$-0.635546\pi$
$19$	0.785987	−	7.47816i	0.180318	−	1.71561i	0.593394	−	0.804912i	$-0.297788\pi$
$20$		0			0
$21$	−1.16276	−	5.05345i	−0.253735	−	1.10275i
$22$	−0.516939	+	3.26382i	−0.110212	+	0.695850i
$23$	2.00560	−	0.105109i	0.418196	−	0.0219167i	0.157922	−	0.987452i	$-0.449520\pi$
$23$	2.00560	−	0.105109i	0.418196	−	0.0219167i	0.260274	+	0.965535i	$0.416187\pi$
$24$	2.30669	−	3.99530i	0.470851	−	0.815537i
$25$		0			0
$26$	−3.00281	+	1.73368i	−0.588900	+	0.340002i
$27$	1.92076	−	3.76970i	0.369650	−	0.725479i
$28$	1.15736	+	0.724382i	0.218720	+	0.136895i
$29$	4.12547	+	5.67823i	0.766081	+	1.05442i	0.996684	+	0.0813721i	$0.0259302\pi$
$29$	4.12547	+	5.67823i	0.766081	+	1.05442i	−0.230603	+	0.973048i	$0.574070\pi$
$30$		0			0
$31$	2.58369	+	5.80306i	0.464045	+	1.04226i	0.982348	+	0.187064i	$0.0598972\pi$
$31$	2.58369	+	5.80306i	0.464045	+	1.04226i	−0.518303	+	0.855197i	$0.673436\pi$
$32$	0.738117	+	2.75469i	0.130482	+	0.486965i
$33$	−2.56957	−	3.17315i	−0.447304	−	0.552374i
$34$	−2.48320	+	7.64252i	−0.425866	+	1.31068i
$35$		0			0
$36$	−0.134168	−	0.412927i	−0.0223614	−	0.0688212i
$37$	1.44212	−	2.22067i	0.237083	−	0.365076i	−0.700023	−	0.714120i	$-0.746827\pi$
$37$	1.44212	−	2.22067i	0.237083	−	0.365076i	0.937106	+	0.349044i	$0.113494\pi$
$38$	−11.9109	−	0.624225i	−1.93221	−	0.101263i
$39$	0.890754	−	4.19067i	0.142635	−	0.671044i
$40$		0			0
$41$	8.47974	+	2.75523i	1.32431	+	0.430295i	0.883974	−	0.467536i	$-0.154858\pi$
$41$	8.47974	+	2.75523i	1.32431	+	0.430295i	0.440339	+	0.897832i	$0.354858\pi$
$42$	−7.90831	+	2.26137i	−1.22028	+	0.348936i
$43$	0.986332	+	0.986332i	0.150414	+	0.150414i	0.778303	−	0.627889i	$-0.216081\pi$
$43$	0.986332	+	0.986332i	0.150414	+	0.150414i	−0.627889	+	0.778303i	$0.716081\pi$
$44$	1.06920	+	0.112377i	0.161188	+	0.0169415i
$45$		0			0
$46$	−0.332993	−	3.16821i	−0.0490971	−	0.467128i
$47$	−0.941527	−	2.45276i	−0.137336	−	0.357772i	0.847614	−	0.530614i	$-0.178038\pi$
$47$	−0.941527	−	2.45276i	−0.137336	−	0.357772i	−0.984950	+	0.172842i	$0.944705\pi$
$48$	−8.32258	−	4.24056i	−1.20126	−	0.612073i
$49$	1.68344	+	6.79456i	0.240492	+	0.970651i
$50$		0			0
$51$	−4.96456	−	8.59887i	−0.695178	−	1.20408i
$52$	0.614389	+	0.946077i	0.0852005	+	0.131197i
$53$	5.81286	−	7.17828i	0.798458	−	0.986013i	−0.201521	−	0.979484i	$-0.564588\pi$
$53$	5.81286	−	7.17828i	0.798458	−	0.986013i	0.999979	−	0.00652896i	$-0.00207825\pi$
$54$	−6.13079	−	2.72960i	−0.834295	−	0.371452i
$55$		0			0
$56$	−3.02325	+	5.44463i	−0.403999	+	0.727569i
$57$	10.4209	−	10.4209i	1.38029	−	1.38029i
$58$	8.65203	−	7.00627i	1.13607	−	0.919969i
$59$	7.04085	+	7.81965i	0.916640	+	1.01803i	0.999769	+	0.0214933i	$0.00684204\pi$
$59$	7.04085	+	7.81965i	0.916640	+	1.01803i	−0.0831288	+	0.996539i	$0.526491\pi$
$60$		0			0
$61$	−6.37468	−	5.73979i	−0.816194	−	0.734904i	0.151112	−	0.988517i	$-0.451715\pi$
$61$	−6.37468	−	5.73979i	−0.816194	−	0.734904i	−0.967306	+	0.253612i	$0.918381\pi$
$62$	8.97777	−	4.57440i	1.14018	−	0.580949i
$63$	0.977274	−	1.99997i	0.123125	−	0.251972i
$64$	−4.76284	+	1.54754i	−0.595355	+	0.193443i
$65$		0			0
$66$	−4.81306	+	4.33370i	−0.592447	+	0.533442i
$67$	1.17677	−	3.06559i	0.143765	−	0.374521i	−0.842724	−	0.538345i	$-0.819050\pi$
$67$	1.17677	−	3.06559i	0.143765	−	0.374521i	0.986490	+	0.163824i	$0.0523829\pi$
$68$	2.52529	+	0.676649i	0.306236	+	0.0820558i
$69$	3.18448	+	2.31366i	0.383366	+	0.278532i
$70$		0			0
$71$	5.41526	−	3.93442i	0.642673	−	0.466930i	−0.218094	−	0.975928i	$-0.569984\pi$
$71$	5.41526	−	3.93442i	0.642673	−	0.466930i	0.860768	+	0.508998i	$0.169984\pi$
$72$	1.84884	−	0.709703i	0.217888	−	0.0836393i
$73$	−6.94515	+	4.51023i	−0.812868	+	0.527883i	−0.882844	−	0.469666i	$-0.844374\pi$
$73$	−6.94515	+	4.51023i	−0.812868	+	0.527883i	0.0699760	+	0.997549i	$0.477708\pi$
$74$	−3.63734	−	2.10002i	−0.422832	−	0.244122i
$75$		0			0
$76$			3.88041i			0.445114i
$77$	3.53982	+	4.22492i	0.403400	+	0.481474i
$78$	−6.71211	−	1.06309i	−0.759996	−	0.120372i
$79$	−1.08662	+	2.44058i	−0.122254	+	0.274586i	−0.964297	−	0.264824i	$-0.914686\pi$
$79$	−1.08662	+	2.44058i	−0.122254	+	0.274586i	0.842043	+	0.539410i	$0.181353\pi$
$80$		0			0
$81$	9.88106	−	4.39933i	1.09790	−	0.488814i
$82$	3.66043	−	13.6609i	0.404227	−	1.50860i
$83$	−2.88395	+	0.456772i	−0.316554	+	0.0501373i	−0.312690	−	0.949855i	$-0.601230\pi$
$83$	−2.88395	+	0.456772i	−0.316554	+	0.0501373i	−0.00386431	+	0.999993i	$0.501230\pi$
$84$	0.869359	+	2.53086i	0.0948548	+	0.276139i
$85$		0			0
$86$	1.48050	−	1.64427i	0.159647	−	0.177306i
$87$	−0.719940	+	13.7373i	−0.0771857	+	1.47279i
$88$	−0.256640	+	4.89698i	−0.0273579	+	0.522020i
$89$	−8.47306	+	9.41028i	−0.898142	+	0.997488i	0.101854	+	0.994799i	$0.467523\pi$
$89$	−8.47306	+	9.41028i	−0.898142	+	0.997488i	−0.999996	+	0.00268884i	$0.999144\pi$
$90$		0			0
$91$	−1.10772	+	5.67637i	−0.116120	+	0.595045i
$92$	−1.02366	+	0.162132i	−0.106724	+	0.0169035i
$93$	−3.22229	+	12.0258i	−0.334136	+	1.24701i
$94$	−3.80710	+	1.69503i	−0.392672	+	0.174829i
$95$		0			0
$96$	−2.27344	+	5.10623i	−0.232032	+	0.521152i
$97$	−3.33125	−	0.527619i	−0.338237	−	0.0535716i	−0.0149946	−	0.999888i	$-0.504773\pi$
$97$	−3.33125	−	0.527619i	−0.338237	−	0.0535716i	−0.323243	+	0.946316i	$0.604773\pi$
$98$	10.6231	−	3.23068i	1.07309	−	0.326348i
$99$		−	1.75274i		−	0.176157i
$100$		0			0
$101$	−2.45915	−	1.41979i	−0.244695	−	0.141275i	0.372638	−	0.927977i	$-0.378453\pi$
$101$	−2.45915	−	1.41979i	−0.244695	−	0.141275i	−0.617333	+	0.786702i	$0.711787\pi$
$102$	−13.2088	+	8.57788i	−1.30786	+	0.849337i
$103$	−6.81372	+	2.61554i	−0.671375	+	0.257717i	−0.670087	−	0.742282i	$-0.733743\pi$
$103$	−6.81372	+	2.61554i	−0.671375	+	0.257717i	−0.00128815	+	0.999999i	$0.500410\pi$
$104$	−4.16268	+	3.02436i	−0.408184	+	0.296563i
$105$		0			0
$106$	−11.8532	−	8.61186i	−1.15129	−	0.836458i
$107$	11.2003	+	3.00110i	1.08277	+	0.290127i	0.755730	−	0.654883i	$-0.227282\pi$
$107$	11.2003	+	3.00110i	1.08277	+	0.290127i	0.327040	+	0.945011i	$0.393949\pi$
$108$	−0.782443	+	2.03833i	−0.0752906	+	0.196139i
$109$	7.26460	−	6.54107i	0.695822	−	0.626521i	−0.243362	−	0.969936i	$-0.578250\pi$
$109$	7.26460	−	6.54107i	0.695822	−	0.626521i	0.939184	+	0.343415i	$0.111584\pi$
$110$		0			0
$111$	4.93560	−	1.60367i	0.468467	−	0.152214i
$112$	11.3289	+	5.53582i	1.07048	+	0.523086i
$113$	−8.16704	+	4.16132i	−0.768291	+	0.391464i	−0.793775	−	0.608212i	$-0.791887\pi$
$113$	−8.16704	+	4.16132i	−0.768291	+	0.391464i	0.0254843	+	0.999675i	$0.491887\pi$
$114$	−17.3722	−	15.6420i	−1.62706	−	1.46501i
$115$		0			0
$116$	−2.42361	−	2.69170i	−0.225027	−	0.249918i
$117$	1.42926	−	1.15739i	0.132135	−	0.107001i
$118$	11.8021	−	11.8021i	1.08647	−	1.08647i
$119$	6.89485	+	11.4941i	0.632050	+	1.05367i
$120$		0			0
$121$	−6.08418	−	2.70885i	−0.553107	−	0.246259i
$122$	−8.56282	+	10.5742i	−0.775241	+	0.957343i
$123$	9.51757	+	14.6558i	0.858170	+	1.32147i
$124$	−1.63906	−	2.83893i	−0.147192	−	0.254944i
$125$		0			0
$126$	−3.24914	−	1.38201i	−0.289457	−	0.123119i
$127$	−2.18980	−	1.11576i	−0.194313	−	0.0990074i	0.354127	−	0.935197i	$-0.384778\pi$
$127$	−2.18980	−	1.11576i	−0.194313	−	0.0990074i	−0.548440	+	0.836190i	$0.684778\pi$
$128$	4.89078	+	12.7409i	0.432288	+	1.12615i
$129$	0.285768	+	2.71890i	0.0251605	+	0.239386i
$130$		0			0
$131$	5.54090	+	0.582372i	0.484111	+	0.0508821i	0.343441	−	0.939174i	$-0.388408\pi$
$131$	5.54090	+	0.582372i	0.484111	+	0.0508821i	0.140670	+	0.990056i	$0.455074\pi$
$132$	1.48995	+	1.48995i	0.129683	+	0.129683i
$133$	−13.8303	+	14.3006i	−1.19924	+	1.24002i
$134$	−4.95369	−	1.60955i	−0.427934	−	0.139044i
$135$		0			0
$136$	−2.47928	+	11.6641i	−0.212597	+	1.00019i
$137$	9.06922	+	0.475298i	0.774836	+	0.0406074i	0.435655	−	0.900114i	$-0.356517\pi$
$137$	9.06922	+	0.475298i	0.774836	+	0.0406074i	0.339181	+	0.940721i	$0.389850\pi$
$138$	3.40056	−	5.23640i	0.289475	−	0.445752i
$139$	−5.50579	−	16.9451i	−0.466995	−	1.43726i	−0.856456	−	0.516220i	$-0.827339\pi$
$139$	−5.50579	−	16.9451i	−0.466995	−	1.43726i	0.389461	−	0.921043i	$-0.372661\pi$
$140$		0			0
$141$	1.59121	−	4.89724i	0.134004	−	0.412422i
$142$	−6.68181	−	8.25134i	−0.560725	−	0.692437i
$143$	1.17864	+	4.39874i	0.0985627	+	0.367841i
$144$	−1.63087	−	3.66299i	−0.135906	−	0.305249i
$145$		0			0
$146$	7.72092	+	10.6269i	0.638988	+	0.879491i
$147$	−5.81644	+	12.4256i	−0.479732	+	1.02484i
$148$	−0.620350	+	1.21751i	−0.0509925	+	0.100078i
$149$	12.6781	−	7.31970i	1.03863	−	0.599653i	0.119185	−	0.992872i	$-0.461972\pi$
$149$	12.6781	−	7.31970i	1.03863	−	0.599653i	0.919445	+	0.393219i	$0.128638\pi$
$150$		0			0
$151$	−8.05257	+	13.9475i	−0.655309	+	1.13503i	0.326508	+	0.945195i	$0.394128\pi$
$151$	−8.05257	+	13.9475i	−0.655309	+	1.13503i	−0.981816	+	0.189833i	$0.939205\pi$
$152$	−17.6751	+	0.926314i	−1.43364	+	0.0751340i
$153$	0.666764	−	4.20978i	0.0539047	−	0.340341i
$154$	6.39855	−	5.95794i	0.515610	−	0.480104i
$155$		0			0
$156$	−0.231106	+	2.19882i	−0.0185033	+	0.176047i
$157$	−4.14906	+	1.11174i	−0.331131	+	0.0887263i	−0.420554	−	0.907267i	$-0.638164\pi$
$157$	−4.14906	+	1.11174i	−0.331131	+	0.0887263i	0.0894230	+	0.995994i	$0.471498\pi$
$158$	3.95616	+	1.51863i	0.314736	+	0.120816i
$159$	17.7078	−	3.76390i	1.40432	−	0.298497i
$160$		0			0
$161$	−4.35040	−	3.05096i	−0.342859	−	0.240449i
$162$	−7.78897	−	15.2867i	−0.611959	−	1.20104i
$163$	12.7929	+	8.30781i	1.00202	+	0.650718i	0.937785	−	0.347217i	$-0.112873\pi$
$163$	12.7929	+	8.30781i	1.00202	+	0.650718i	0.0642326	+	0.997935i	$0.479540\pi$
$164$	−4.50068	−	0.956649i	−0.351444	−	0.0747017i
$165$		0			0
$166$	0.962956	+	4.53035i	0.0747399	+	0.351623i
$167$	2.64539	+	16.7023i	0.204706	+	1.29246i	0.849289	+	0.527929i	$0.177031\pi$
$167$	2.64539	+	16.7023i	0.204706	+	1.29246i	−0.644583	+	0.764535i	$0.722969\pi$
$168$	−11.3204	+	4.56405i	−0.873390	+	0.352124i
$169$	4.83258	−	6.65148i	0.371737	−	0.511652i
$170$		0			0
$171$	6.29165	−	0.661279i	0.481135	−	0.0505693i
$172$	−0.559420	−	0.453010i	−0.0426554	−	0.0345417i
$173$	−0.981067	−	18.7199i	−0.0745892	−	1.42325i	−0.737904	−	0.674906i	$-0.764184\pi$
$173$	−0.981067	−	18.7199i	−0.0745892	−	1.42325i	0.663315	−	0.748340i	$-0.269149\pi$
$174$	21.8201			1.65418
$175$		0			0
$176$	9.92847			0.748387
$177$	1.07933	+	20.5949i	0.0811276	+	1.54801i
$178$	15.6096	+	12.6404i	1.16999	+	0.947439i
$179$	−9.75542	+	1.02534i	−0.729155	+	0.0766372i	−0.461829	−	0.886969i	$-0.652807\pi$
$179$	−9.75542	+	1.02534i	−0.729155	+	0.0766372i	−0.267326	+	0.963606i	$0.586140\pi$
$180$		0			0
$181$	0.493376	−	0.679074i	0.0366723	−	0.0504751i	−0.790287	−	0.612737i	$-0.790069\pi$
$181$	0.493376	−	0.679074i	0.0366723	−	0.0504751i	0.826959	+	0.562262i	$0.190069\pi$
$182$	9.08353	+	1.28343i	0.673316	+	0.0951344i
$183$	−2.63002	−	16.6053i	−0.194416	−	1.22750i
$184$	−0.982870	−	4.62404i	−0.0724582	−	0.340889i
$185$		0			0
$186$	19.3167	+	4.10589i	1.41637	+	0.301059i
$187$	8.85132	+	5.74811i	0.647272	+	0.420344i
$188$	0.615528	+	1.20804i	0.0448920	+	0.0881055i
$189$	−10.1485	+	4.72320i	−0.738192	+	0.343562i
$190$		0			0
$191$	2.66133	−	0.565683i	0.192567	−	0.0409314i	−0.110618	−	0.993863i	$-0.535283\pi$
$191$	2.66133	−	0.565683i	0.192567	−	0.0409314i	0.303185	+	0.952932i	$0.401950\pi$
$192$	−9.16332	−	3.51747i	−0.661305	−	0.253851i
$193$	−6.77095	+	1.81427i	−0.487384	+	0.130594i	−0.494139	−	0.869383i	$-0.664517\pi$
$193$	−6.77095	+	1.81427i	−0.487384	+	0.130594i	0.00675479	+	0.999977i	$0.497850\pi$
$194$	−0.559220	+	5.32062i	−0.0401496	+	0.381998i
$195$		0			0
$196$	−1.23051	−	3.39636i	−0.0878935	−	0.242597i
$197$	2.31863	−	14.6392i	0.165195	−	1.04300i	−0.756190	−	0.654352i	$-0.772942\pi$
$197$	2.31863	−	14.6392i	0.165195	−	1.04300i	0.921385	−	0.388650i	$-0.127058\pi$
$198$	−2.77639	+	0.145505i	−0.197310	+	0.0103406i
$199$	10.5072	−	18.1990i	0.744835	−	1.29009i	−0.205437	−	0.978670i	$-0.565862\pi$
$199$	10.5072	−	18.1990i	0.744835	−	1.29009i	0.950272	−	0.311422i	$-0.100805\pi$
$200$		0			0
$201$	5.57358	−	3.21791i	0.393130	−	0.226974i
$202$	−2.04485	+	4.01325i	−0.143875	+	0.282371i
$203$	0.661748	−	18.5579i	0.0464456	−	1.30251i
$204$	3.01181	+	4.14540i	0.210869	+	0.290236i
$205$		0			0
$206$	4.70875	+	10.5760i	0.328074	+	0.736867i
$207$	0.437326	+	1.63212i	0.0303963	+	0.113440i
$208$	6.55609	+	8.09610i	0.454583	+	0.561363i
$209$	−4.84072	+	14.8982i	−0.334839	+	1.03053i
$210$		0			0
$211$	−7.71478	−	23.7437i	−0.531108	−	1.63458i	−0.751912	−	0.659263i	$-0.770868\pi$
$211$	−7.71478	−	23.7437i	−0.531108	−	1.63458i	0.220805	−	0.975318i	$-0.429132\pi$
$212$	−2.59612	+	3.99767i	−0.178302	+	0.274561i
$213$	13.1011	+	0.686599i	0.897672	+	0.0470450i
$214$	3.82405	−	17.9907i	0.261407	−	1.22982i
$215$		0			0
$216$	−9.47131	−	3.07741i	−0.644441	−	0.209392i
$217$	4.07787	−	16.3042i	0.276824	−	1.10680i
$218$	−10.9644	−	10.9644i	−0.742600	−	0.742600i
$219$	−16.1416	−	1.69655i	−1.09075	−	0.114642i
$220$		0			0
$221$	1.15756	+	11.0134i	0.0778656	+	0.740842i
$222$	−2.95001	−	7.68503i	−0.197992	−	0.515786i
$223$	11.6067	+	5.91390i	0.777241	+	0.396024i	0.797153	−	0.603778i	$-0.206339\pi$
$223$	11.6067	+	5.91390i	0.777241	+	0.396024i	−0.0199118	+	0.999802i	$0.506339\pi$
$224$	2.95331	−	6.94333i	0.197326	−	0.463921i
$225$		0			0
$226$	7.26966	+	12.5914i	0.483571	+	0.837569i
$227$	1.68692	+	2.59763i	0.111965	+	0.172411i	0.890211	−	0.455549i	$-0.150557\pi$
$227$	1.68692	+	2.59763i	0.111965	+	0.172411i	−0.778246	+	0.627960i	$0.783890\pi$
$228$	−4.78620	+	5.91047i	−0.316974	+	0.391430i
$229$	−0.487685	−	0.217131i	−0.0322271	−	0.0143484i	0.390560	−	0.920578i	$-0.372281\pi$
$229$	−0.487685	−	0.217131i	−0.0322271	−	0.0143484i	−0.422787	+	0.906229i	$0.638948\pi$
$230$		0			0
$231$	0.180576	+	10.8013i	0.0118810	+	0.710674i
$232$	11.6820	−	11.6820i	0.766961	−	0.766961i
$233$	19.2882	−	15.6193i	1.26361	−	1.02325i	0.265360	−	0.964149i	$-0.414509\pi$
$233$	19.2882	−	15.6193i	1.26361	−	1.02325i	0.998252	−	0.0591038i	$-0.0188243\pi$
$234$	−1.95199	−	2.16791i	−0.127606	−	0.141721i
$235$		0			0
$236$	−4.03538	−	3.63348i	−0.262681	−	0.236519i
$237$	−4.66535	+	2.37712i	−0.303047	+	0.154410i
$238$	17.6347	−	11.8759i	1.14309	−	0.769799i
$239$	25.9462	−	8.43043i	1.67832	−	0.545320i	0.693736	−	0.720229i	$-0.255963\pi$
$239$	25.9462	−	8.43043i	1.67832	−	0.545320i	0.984585	+	0.174910i	$0.0559633\pi$
$240$		0			0
$241$	14.2251	−	12.8083i	0.916319	−	0.825057i	−0.0686763	−	0.997639i	$-0.521878\pi$
$241$	14.2251	−	12.8083i	0.916319	−	0.825057i	0.984995	+	0.172582i	$0.0552109\pi$
$242$	−3.78583	+	9.86243i	−0.243362	+	0.633981i
$243$	8.21660	+	2.20163i	0.527095	+	0.141235i
$244$	3.58129	+	2.60196i	0.229269	+	0.166574i
$245$		0			0
$246$	22.4251	−	16.2928i	1.42977	−	1.03879i
$247$	−15.3451	+	5.89043i	−0.976386	+	0.374799i
$248$	12.5400	−	8.14354i	0.796288	−	0.517116i
$249$	−4.95609	−	2.86140i	−0.314079	−	0.181334i
$250$		0			0
$251$			7.49714i			0.473215i	0.971605	+	0.236608i	$0.0760356\pi$
$251$			7.49714i			0.473215i	−0.971605	+	0.236608i	$0.923964\pi$
$252$	−0.393683	+	1.07916i	−0.0247997	+	0.0679806i
$253$	−4.13244	−	0.654514i	−0.259804	−	0.0411489i
$254$	−1.58561	+	3.56134i	−0.0994900	+	0.223458i
$255$		0			0
$256$	10.6261	−	4.73103i	0.664130	−	0.295690i
$257$	−3.54307	+	13.2229i	−0.221011	+	0.824824i	0.762953	+	0.646454i	$0.223749\pi$
$257$	−3.54307	+	13.2229i	−0.221011	+	0.824824i	−0.983964	+	0.178369i	$0.942918\pi$
$258$	4.28311	−	0.678378i	0.266655	−	0.0422340i
$259$	−6.62555	+	2.27590i	−0.411691	+	0.141417i
$260$		0			0
$261$	−3.95126	+	4.38832i	−0.244577	+	0.271630i
$262$	0.462516	−	8.82533i	0.0285743	−	0.545231i
$263$	−1.02406	+	19.5402i	−0.0631462	+	1.20490i	0.764865	+	0.644190i	$0.222805\pi$
$263$	−1.02406	+	19.5402i	−0.0631462	+	1.20490i	−0.828012	+	0.560711i	$0.810528\pi$
$264$	−6.43097	+	7.14231i	−0.395799	+	0.439579i
$265$		0			0
$266$	23.8008	+	20.7205i	1.45932	+	1.27046i
$267$	−24.5127	+	3.88242i	−1.50015	+	0.237600i
$268$	−0.438587	+	1.63683i	−0.0267910	+	0.0999853i
$269$	−8.43550	+	3.75573i	−0.514321	+	0.228991i	−0.647450	−	0.762108i	$-0.724164\pi$
$269$	−8.43550	+	3.75573i	−0.514321	+	0.228991i	0.133128	+	0.991099i	$0.457498\pi$
$270$		0			0
$271$	0.449933	−	1.01057i	0.0273315	−	0.0613875i	−0.899364	−	0.437201i	$-0.855970\pi$
$271$	0.449933	−	1.01057i	0.0273315	−	0.0613875i	0.926695	+	0.375813i	$0.122637\pi$
$272$	23.8465	+	3.77692i	1.44591	+	0.229010i
$273$	−8.68860	+	7.27970i	−0.525858	+	0.440588i
$274$		−	14.4054i		−	0.870263i
$275$		0			0
$276$	−1.75918	−	1.01566i	−0.105890	−	0.0611356i
$277$	16.3045	−	10.5883i	0.979643	−	0.636188i	0.0477267	−	0.998860i	$-0.484802\pi$
$277$	16.3045	−	10.5883i	0.979643	−	0.636188i	0.931917	+	0.362673i	$0.118136\pi$
$278$	−26.3845	+	10.1281i	−1.58244	+	0.607441i
$279$	−4.32369	+	3.14135i	−0.258853	+	0.188067i
$280$		0			0
$281$	−1.38801	−	1.00845i	−0.0828017	−	0.0601589i	0.545614	−	0.838036i	$-0.316296\pi$
$281$	−1.38801	−	1.00845i	−0.0828017	−	0.0601589i	−0.628416	+	0.777878i	$0.716296\pi$
$282$	−7.88949	−	2.11398i	−0.469812	−	0.125886i
$283$	−9.46043	+	24.6453i	−0.562364	+	1.46501i	0.297618	+	0.954685i	$0.403808\pi$
$283$	−9.46043	+	24.6453i	−0.562364	+	1.46501i	−0.859982	+	0.510324i	$0.829525\pi$
$284$	−2.56704	+	2.31137i	−0.152326	+	0.137155i
$285$		0			0
$286$	6.86990	−	2.23217i	0.406226	−	0.131991i
$287$	−13.1769	−	19.5666i	−0.777805	−	1.15498i
$288$	−2.13786	+	1.08929i	−0.125975	+	0.0641873i
$289$	6.43928	+	5.79795i	0.378781	+	0.341056i
$290$		0			0
$291$	−4.42323	−	4.91250i	−0.259294	−	0.287976i
$292$	3.32116	−	2.68943i	0.194356	−	0.157387i
$293$	−4.33790	+	4.33790i	−0.253423	+	0.253423i	−0.822372	−	0.568950i	$-0.807350\pi$
$293$	−4.33790	+	4.33790i	−0.253423	+	0.253423i	0.568950	+	0.822372i	$0.307350\pi$
$294$	20.1654	+	8.18193i	1.17607	+	0.477180i
$295$		0			0
$296$	−5.69377	−	2.53503i	−0.330944	−	0.147346i
$297$	−5.54683	+	6.84976i	−0.321860	+	0.397463i
$298$	−12.6471	−	19.4749i	−0.732629	−	1.12815i
$299$	−2.19506	−	3.80196i	−0.126944	−	0.219873i
$300$		0			0
$301$	−0.447061	−	3.66334i	−0.0257682	−	0.211151i
$302$	22.7617	+	11.5977i	1.30979	+	0.667372i
$303$	−1.99446	−	5.19574i	−0.114579	−	0.298488i
$304$	3.74585	+	35.6394i	0.214839	+	2.04406i
$305$		0			0
$306$	−6.72379	−	0.706699i	−0.384373	−	0.0403993i
$307$	12.5574	+	12.5574i	0.716687	+	0.716687i	0.967925	−	0.251239i	$-0.0808379\pi$
$307$	12.5574	+	12.5574i	0.716687	+	0.716687i	−0.251239	+	0.967925i	$0.580838\pi$
$308$	−2.04465	−	1.97740i	−0.116504	−	0.112673i
$309$	−13.6044	−	4.42034i	−0.773928	−	0.251464i
$310$		0			0
$311$	−1.32225	+	6.22068i	−0.0749777	+	0.352743i	−0.999604	−	0.0281326i	$-0.991044\pi$
$311$	−1.32225	+	6.22068i	−0.0749777	+	0.352743i	0.924626	+	0.380875i	$0.124377\pi$
$312$	−10.0707	−	0.527784i	−0.570142	−	0.0298799i
$313$	4.16011	−	6.40601i	0.235143	−	0.362089i	−0.701325	−	0.712842i	$-0.747408\pi$
$313$	4.16011	−	6.40601i	0.235143	−	0.362089i	0.936468	+	0.350753i	$0.114074\pi$
$314$	2.10547	+	6.47997i	0.118818	+	0.365686i
$315$		0			0
$316$	0.426032	−	1.31119i	0.0239662	−	0.0737603i
$317$	8.88140	+	10.9676i	0.498829	+	0.616003i	0.962921	−	0.269785i	$-0.0869525\pi$
$317$	8.88140	+	10.9676i	0.498829	+	0.616003i	−0.464092	+	0.885787i	$0.653619\pi$
$318$	−7.43217	−	27.7372i	−0.416775	−	1.55543i
$319$	−5.94723	−	13.3577i	−0.332981	−	0.747888i
$320$		0			0
$321$	13.3581	+	18.3858i	0.745575	+	1.02620i
$322$	−4.47168	+	7.14446i	−0.249197	+	0.398145i
$323$	−17.2941	+	33.9415i	−0.962268	+	1.88856i
$324$	−4.83394	+	2.79088i	−0.268552	+	0.155049i
$325$		0			0
$326$	12.0978	−	20.9541i	0.670037	−	1.16054i
$327$	19.1330	−	1.00272i	1.05806	−	0.0554505i
$328$	3.28311	−	20.7288i	0.181280	−	1.14455i
$329$	−2.03720	+	6.64586i	−0.112314	+	0.366398i
$330$		0			0
$331$	1.07624	−	10.2397i	0.0591554	−	0.562826i	−0.924299	−	0.381670i	$-0.875349\pi$
$331$	1.07624	−	10.2397i	0.0591554	−	0.562826i	0.983454	−	0.181157i	$-0.0579841\pi$
$332$	1.45549	−	0.389997i	0.0798802	−	0.0214038i
$333$	2.07976	+	0.798347i	0.113970	+	0.0437491i
$334$	26.2374	−	5.57694i	1.43565	−	0.305156i
$335$		0			0
$336$	10.4277	+	22.4053i	0.568876	+	1.22231i
$337$	−11.6695	−	22.9028i	−0.635681	−	1.24759i	−0.954056	−	0.299629i	$-0.903137\pi$
$337$	−11.6695	−	22.9028i	−0.635681	−	1.24759i	0.318375	−	0.947965i	$-0.396863\pi$
$338$	−10.9374	−	7.10280i	−0.594914	−	0.386341i
$339$	−17.5723	−	3.73512i	−0.954398	−	0.202864i
$340$		0			0
$341$	−2.75139	−	12.9443i	−0.148996	−	0.700973i
$342$	−1.56980	−	9.91130i	−0.0848848	−	0.535942i
$343$	7.57025	−	16.9024i	0.408755	−	0.912644i
$344$	1.92990	−	2.65628i	0.104053	−	0.143217i
$345$		0			0
$346$	−29.5715	+	3.10809i	−1.58977	+	0.167092i
$347$	−3.54647	−	2.87187i	−0.190384	−	0.154170i	0.529389	−	0.848379i	$-0.322421\pi$
$347$	−3.54647	−	2.87187i	−0.190384	−	0.154170i	−0.719774	+	0.694209i	$0.755754\pi$
$348$	−0.371530	−	7.08921i	−0.0199161	−	0.380022i
$349$	35.4204			1.89601			0.948005	−	0.318256i	$-0.103097\pi$
$349$	35.4204			1.89601			0.948005	+	0.318256i	$0.103097\pi$
$350$		0			0
$351$	−9.24834			−0.493640
$352$	−0.310939	−	5.93307i	−0.0165731	−	0.316234i
$353$	8.31018	+	6.72945i	0.442306	+	0.358173i	0.824454	−	0.565929i	$-0.191482\pi$
$353$	8.31018	+	6.72945i	0.442306	+	0.358173i	−0.382148	+	0.924101i	$0.624816\pi$
$354$	32.5334	−	3.41940i	1.72913	−	0.181739i
$355$		0			0
$356$	3.84101	−	5.28670i	0.203573	−	0.280194i
$357$	−3.67525	+	26.0116i	−0.194515	+	1.37668i
$358$	2.43402	+	15.3678i	0.128642	+	0.812214i
$359$	0.793602	+	3.73360i	0.0418847	+	0.197052i	0.994115	−	0.108328i	$-0.0345498\pi$
$359$	0.793602	+	3.73360i	0.0418847	+	0.197052i	−0.952230	+	0.305380i	$0.901216\pi$
$360$		0			0
$361$	−36.7204	−	7.80515i	−1.93265	−	0.410797i
$362$	−1.11663	−	0.725151i	−0.0586890	−	0.0381131i
$363$	−5.92598	−	11.6304i	−0.311033	−	0.610437i
$364$	0.262315	−	2.97304i	0.0137490	−	0.155829i
$365$		0			0
$366$	−26.0850	+	5.54453i	−1.36348	+	0.289817i
$367$	7.77350	+	2.98397i	0.405773	+	0.155762i	0.552690	−	0.833387i	$-0.313601\pi$
$367$	7.77350	+	2.98397i	0.405773	+	0.155762i	−0.146916	+	0.989149i	$0.546935\pi$
$368$	−9.24526	+	2.47726i	−0.481943	+	0.129136i
$369$	−0.784116	+	7.46037i	−0.0408195	+	0.388371i
$370$		0			0
$371$	−23.8158	+	5.47982i	−1.23645	+	0.284498i
$372$	1.00507	−	6.34579i	0.0521107	−	0.329014i
$373$	17.4072	−	0.912274i	0.901312	−	0.0472358i	0.403952	−	0.914780i	$-0.367636\pi$
$373$	17.4072	−	0.912274i	0.901312	−	0.0472358i	0.497360	+	0.867544i	$0.334303\pi$
$374$	8.37041	−	14.4980i	0.432824	−	0.749672i
$375$		0			0
$376$	−5.35564	+	3.09208i	−0.276196	+	0.159462i
$377$	6.96529	−	13.6702i	0.358731	−	0.704049i
$378$	8.32419	+	15.6834i	0.428150	+	0.806667i
$379$	6.41691	+	8.83212i	0.329614	+	0.453675i	0.941372	−	0.337370i	$-0.109537\pi$
$379$	6.41691	+	8.83212i	0.329614	+	0.453675i	−0.611758	+	0.791045i	$0.709537\pi$
$380$		0			0
$381$	−1.95919	−	4.40042i	−0.100372	−	0.225440i
$382$	−1.11699	−	4.16868i	−0.0571504	−	0.213288i
$383$	10.4424	+	12.8953i	0.533582	+	0.658919i	0.970646	−	0.240511i	$-0.0773152\pi$
$383$	10.4424	+	12.8953i	0.533582	+	0.658919i	−0.437064	+	0.899430i	$0.643982\pi$
$384$	−8.26557	+	25.4388i	−0.421800	+	1.29817i
$385$		0			0
$386$	3.43596	+	10.5748i	0.174886	+	0.538244i
$387$	−0.639170	+	0.984236i	−0.0324909	+	0.0500315i
$388$	1.73816	+	0.0910931i	0.0882417	+	0.00462455i
$389$	−3.99680	+	18.8035i	−0.202646	+	0.953373i	0.752810	+	0.658238i	$0.228698\pi$
$389$	−3.99680	+	18.8035i	−0.202646	+	0.953373i	−0.955456	+	0.295135i	$0.904635\pi$
$390$		0			0
$391$	−9.67645	−	3.14407i	−0.489359	−	0.159002i
$392$	15.1765	−	6.41568i	0.766531	−	0.324041i
$393$	7.72133	+	7.72133i	0.389490	+	0.389490i
$394$	−23.3815	−	2.45750i	−1.17794	−	0.123807i
$395$		0			0
$396$	0.0945471	+	0.899556i	0.00475117	+	0.0452044i
$397$	−0.436005	−	1.13583i	−0.0218825	−	0.0570058i	0.922204	−	0.386704i	$-0.126386\pi$
$397$	−0.436005	−	1.13583i	−0.0218825	−	0.0570058i	−0.944086	+	0.329698i	$0.893053\pi$
$398$	−29.7001	−	15.1329i	−1.48873	−	0.758546i
$399$	−38.7044	+	4.72336i	−1.93765	+	0.236464i
$400$		0			0
$401$	2.37174	+	4.10797i	0.118439	+	0.205142i	0.919149	−	0.393910i	$-0.128878\pi$
$401$	2.37174	+	4.10797i	0.118439	+	0.205142i	−0.800710	+	0.599052i	$0.795544\pi$
$402$	−5.55997	−	8.56160i	−0.277306	−	0.427014i
$403$	8.73849	−	10.7911i	0.435295	−	0.537545i
$404$	1.33870	+	0.596027i	0.0666027	+	0.0296534i
$405$		0			0
$406$	−29.4512	+	0.492364i	−1.46164	+	0.0244356i
$407$	−3.90054	+	3.90054i	−0.193342	+	0.193342i
$408$	−18.1631	+	14.7082i	−0.899210	+	0.728166i
$409$	−16.5891	−	18.4241i	−0.820280	−	0.911014i	0.177038	−	0.984204i	$-0.443349\pi$
$409$	−16.5891	−	18.4241i	−0.820280	−	0.911014i	−0.997318	+	0.0731905i	$0.976682\pi$
$410$		0			0
$411$	13.2276	+	11.9102i	0.652468	+	0.587485i
$412$	3.35591	−	1.70992i	0.165334	−	0.0842419i
$413$	−1.92153	−	27.7732i	−0.0945522	−	1.36663i
$414$	2.54904	−	0.828232i	0.125278	−	0.0407054i
$415$		0			0
$416$	4.63276	−	4.17136i	0.227140	−	0.204518i
$417$	12.5143	−	32.6010i	0.612829	−	1.59648i
$418$	24.0011	+	6.43108i	1.17393	+	0.314554i
$419$	−19.6973	−	14.3109i	−0.962276	−	0.699135i	−0.00859807	−	0.999963i	$-0.502737\pi$
$419$	−19.6973	−	14.3109i	−0.962276	−	0.699135i	−0.953678	+	0.300828i	$0.902737\pi$
$420$		0			0
$421$	−6.00083	+	4.35986i	−0.292463	+	0.212486i	−0.724335	−	0.689448i	$-0.757853\pi$
$421$	−6.00083	+	4.35986i	−0.292463	+	0.212486i	0.431872	+	0.901935i	$0.357853\pi$
$422$	−36.9703	+	14.1916i	−1.79969	+	0.690835i
$423$	1.85381	−	1.20388i	0.0901352	−	0.0585345i
$424$	−18.8290	−	10.8709i	−0.914415	−	0.527938i
$425$		0			0
$426$		−	20.8096i		−	1.00823i
$427$	3.92451	+	22.3533i	0.189920	+	1.08175i
$428$	−5.91019	−	0.936083i	−0.285680	−	0.0452473i
$429$	−3.63027	+	8.15371i	−0.175271	+	0.393665i
$430$		0			0
$431$	16.4910	−	7.34228i	0.794345	−	0.353665i	0.0308873	−	0.999523i	$-0.490167\pi$
$431$	16.4910	−	7.34228i	0.794345	−	0.353665i	0.763458	+	0.645858i	$0.223500\pi$
$432$	−5.21865	+	19.4763i	−0.251082	+	0.937052i
$433$	−24.9324	+	3.94891i	−1.19818	+	0.189773i	−0.723460	−	0.690366i	$-0.757449\pi$
$433$	−24.9324	+	3.94891i	−1.19818	+	0.189773i	−0.474717	+	0.880139i	$0.657449\pi$
$434$	−26.1650	−	5.10597i	−1.25596	−	0.245095i
$435$		0			0
$436$	−3.37556	+	3.74894i	−0.161660	+	0.179542i
$437$	0.790352	−	15.0808i	0.0378077	−	0.721413i
$438$	−1.34739	+	25.7096i	−0.0643805	+	1.22845i
$439$	−18.6654	+	20.7300i	−0.890849	+	0.989388i	−0.999989	−	0.00463865i	$-0.998523\pi$
$439$	−18.6654	+	20.7300i	−0.890849	+	0.989388i	0.109141	+	0.994026i	$0.465190\pi$
$440$		0			0
$441$	−5.29712	+	2.57392i	−0.252244	+	0.122568i
$442$	17.3495	−	2.74789i	0.825232	−	0.130704i
$443$	−7.92554	+	29.5785i	−0.376554	+	1.40532i	0.474507	+	0.880252i	$0.342626\pi$
$443$	−7.92554	+	29.5785i	−0.376554	+	1.40532i	−0.851061	+	0.525066i	$0.824040\pi$
$444$	−2.44659	+	1.08929i	−0.116110	+	0.0516955i
$445$		0			0
$446$	8.40428	−	18.8763i	0.397954	−	0.893820i
$447$	28.3390	+	4.48846i	1.34039	+	0.212297i
$448$	12.4474	+	4.54087i	0.588084	+	0.214536i
$449$			30.4224i			1.43572i	0.696187	+	0.717861i	$0.254879\pi$
$449$			30.4224i			1.43572i	−0.696187	+	0.717861i	$0.745121\pi$
$450$		0			0
$451$	−16.0862	−	9.28737i	−0.757469	−	0.437325i
$452$	3.96710	−	2.57626i	0.186597	−	0.121177i
$453$	−29.4685	+	11.3119i	−1.38455	+	0.531478i
$454$	3.97469	−	2.88778i	0.186541	−	0.135530i
$455$		0			0
$456$	−28.0645	−	20.3900i	−1.31424	−	0.954851i
$457$	−38.9922	−	10.4479i	−1.82398	−	0.488733i	−0.826710	−	0.562628i	$-0.809790\pi$
$457$	−38.9922	−	10.4479i	−1.82398	−	0.488733i	−0.997266	+	0.0738955i	$0.976457\pi$
$458$	−0.303458	+	0.790535i	−0.0141797	+	0.0369393i
$459$	−15.9283	+	14.3419i	−0.743469	+	0.669423i
$460$		0			0
$461$	16.9923	−	5.52114i	0.791411	−	0.257145i	0.114706	−	0.993399i	$-0.463407\pi$
$461$	16.9923	−	5.52114i	0.791411	−	0.257145i	0.676705	+	0.736255i	$0.263407\pi$
$462$	17.0946	−	1.18272i	0.795315	−	0.0550249i
$463$	30.4814	−	15.5311i	1.41659	−	0.721790i	0.432866	−	0.901458i	$-0.357502\pi$
$463$	30.4814	−	15.5311i	1.41659	−	0.721790i	0.983727	+	0.179668i	$0.0575024\pi$
$464$	−24.8579	−	22.3821i	−1.15400	−	1.03906i
$465$		0			0
$466$	−26.3427	−	29.2565i	−1.22030	−	1.35528i
$467$	−5.18944	+	4.20233i	−0.240139	+	0.194460i	−0.741833	−	0.670584i	$-0.766043\pi$
$467$	−5.18944	+	4.20233i	−0.240139	+	0.194460i	0.501695	+	0.865045i	$0.332710\pi$
$468$	−0.671104	+	0.671104i	−0.0310218	+	0.0310218i
$469$	−7.45022	+	4.46907i	−0.344019	+	0.206363i
$470$		0			0
$471$	−7.69091	−	3.42421i	−0.354378	−	0.157779i
$472$	15.5870	−	19.2484i	0.717451	−	0.885978i
$473$	−1.58268	−	2.43712i	−0.0727718	−	0.112059i
$474$	4.15273	+	7.19274i	0.190741	+	0.330374i
$475$		0			0
$476$	−4.15867	−	5.52721i	−0.190612	−	0.253339i
$477$	6.92419	+	3.52805i	0.317037	+	0.161538i
$478$	−15.5080	−	40.3998i	−0.709321	−	1.84785i
$479$	−0.529424	−	5.03713i	−0.0241900	−	0.230153i	−0.999937	−	0.0112499i	$-0.996419\pi$
$479$	−0.529424	−	5.03713i	−0.0241900	−	0.230153i	0.975747	−	0.218903i	$-0.0702477\pi$
$480$		0			0
$481$	−5.75631	−	0.605013i	−0.262465	−	0.0275862i
$482$	−21.4697	−	21.4697i	−0.977920	−	0.977920i
$483$	−2.86319	−	10.0130i	−0.130280	−	0.455606i
$484$	3.26870	+	1.06207i	0.148577	+	0.0482758i
$485$		0			0
$486$	2.80535	−	13.1981i	0.127253	−	0.598680i
$487$	−18.7766	−	0.984042i	−0.850851	−	0.0445912i	−0.378076	−	0.925774i	$-0.623414\pi$
$487$	−18.7766	−	0.984042i	−0.850851	−	0.0445912i	−0.472775	+	0.881183i	$0.656748\pi$
$488$	−10.9969	+	16.9338i	−0.497807	+	0.766556i
$489$	9.23849	+	28.4332i	0.417779	+	1.28579i
$490$		0			0
$491$	−8.10726	+	24.9516i	−0.365876	+	1.12605i	0.583555	+	0.812073i	$0.301661\pi$
$491$	−8.10726	+	24.9516i	−0.365876	+	1.12605i	−0.949431	+	0.313976i	$0.898339\pi$
$492$	−5.67527	−	7.00838i	−0.255861	−	0.315962i
$493$	−9.20282	−	34.3454i	−0.414474	−	1.54684i
$494$	10.6045	+	23.8182i	0.477121	+	1.07163i
$495$		0			0
$496$	−17.7943	−	24.4918i	−0.798989	−	1.09971i
$497$	−17.6984	−	0.631101i	−0.793884	−	0.0283088i
$498$	−4.12112	+	8.08815i	−0.184672	+	0.362439i
$499$	2.61768	−	1.51132i	0.117183	−	0.0676558i	−0.440263	−	0.897869i	$-0.645115\pi$
$499$	2.61768	−	1.51132i	0.117183	−	0.0676558i	0.557446	+	0.830213i	$0.311781\pi$
$500$		0			0
$501$	−16.5717	+	28.7031i	−0.740370	+	1.28236i
$502$	11.8757	−	0.622380i	0.530039	−	0.0277782i
$503$	2.19511	−	13.8594i	0.0978750	−	0.617958i	−0.889178	−	0.457562i	$-0.848723\pi$
$503$	2.19511	−	13.8594i	0.0978750	−	0.617958i	0.987053	−	0.160396i	$-0.0512772\pi$
$504$	−5.00950	−	1.53560i	−0.223141	−	0.0684009i
$505$		0			0
$506$	−0.693715	+	6.60026i	−0.0308394	+	0.293417i
$507$	15.5649	−	4.17060i	0.691260	−	0.185223i
$508$	1.18405	+	0.454516i	0.0525339	+	0.0201659i
$509$	22.1880	−	4.71620i	0.983465	−	0.209042i	0.312003	−	0.950081i	$-0.399000\pi$
$509$	22.1880	−	4.71620i	0.983465	−	0.209042i	0.671462	+	0.741039i	$0.265667\pi$
$510$		0			0
$511$	21.8251	+	1.92565i	0.965483	+	0.0851858i
$512$	4.01531	+	7.88049i	0.177453	+	0.348272i
$513$	−26.6808	−	17.3267i	−1.17798	−	0.764992i
$514$	21.2397	+	4.51464i	0.936843	+	0.199132i
$515$		0			0
$516$	−0.293330	−	1.38001i	−0.0129131	−	0.0607514i
$517$	0.856215	+	5.40593i	0.0376563	+	0.237752i
$518$	4.15513	+	10.3062i	0.182566	+	0.452827i
$519$	21.5953	−	29.7233i	0.947927	−	1.30471i
$520$		0			0
$521$	−41.7780	+	4.39105i	−1.83033	+	0.192375i	−0.956080	−	0.293105i	$-0.905311\pi$
$521$	−41.7780	+	4.39105i	−1.83033	+	0.192375i	−0.874248	+	0.485480i	$0.838645\pi$
$522$	7.27927	+	5.89463i	0.318605	+	0.258001i
$523$	1.38297	+	26.3887i	0.0604732	+	1.15390i	0.845339	+	0.534231i	$0.179399\pi$
$523$	1.38297	+	26.3887i	0.0604732	+	1.15390i	−0.784865	+	0.619666i	$0.787268\pi$
$524$	−2.87517			−0.125602
$525$		0			0
$526$	31.0374			1.35329
$527$	−1.68421	−	32.1367i	−0.0733655	−	1.39990i
$528$	15.1226	+	12.2460i	0.658126	+	0.532940i
$529$	−18.8626	+	1.98254i	−0.820114	+	0.0861975i
$530$		0			0
$531$	−5.20358	+	7.16212i	−0.225816	+	0.310809i
$532$	6.32672	−	8.08554i	0.274298	−	0.350553i
$533$	−3.04892	−	19.2501i	−0.132063	−	0.833815i
$534$	8.18483	+	38.5066i	0.354192	+	1.66634i
$535$		0			0
$536$	−7.56039	−	1.60701i	−0.326559	−	0.0694123i
$537$	−16.1237	−	10.4708i	−0.695788	−	0.451850i
$538$	6.64948	+	13.0503i	0.286679	+	0.562640i
$539$	−0.487457	−	14.5748i	−0.0209963	−	0.627780i
$540$		0			0
$541$	4.85225	−	1.03138i	0.208615	−	0.0443424i	−0.102419	−	0.994741i	$-0.532658\pi$
$541$	4.85225	−	1.03138i	0.208615	−	0.0443424i	0.311033	+	0.950399i	$0.399325\pi$
$542$	−1.63812	−	0.628817i	−0.0703634	−	0.0270100i
$543$	1.58907	−	0.425791i	0.0681937	−	0.0182724i
$544$	1.51020	−	14.3685i	0.0647491	−	0.616046i
$545$		0			0
$546$	12.2526	+	13.1587i	0.524362	+	0.563141i
$547$	−2.72171	+	17.1842i	−0.116372	+	0.734743i	0.858638	+	0.512582i	$0.171311\pi$
$547$	−2.72171	+	17.1842i	−0.116372	+	0.734743i	−0.975010	+	0.222161i	$0.928689\pi$
$548$	−4.68023	+	0.245281i	−0.199930	+	0.0104779i
$549$	3.60848	−	6.25007i	0.154006	−	0.266747i
$550$		0			0
$551$	45.7053	−	26.3880i	1.94711	−	1.12416i
$552$	4.20635	−	8.25542i	0.179034	−	0.351374i
$553$	6.24333	−	3.31374i	0.265493	−	0.140915i
$554$	−18.1257	−	24.9479i	−0.770088	−	1.05994i
$555$		0			0
$556$	3.73980	+	8.39972i	0.158603	+	0.356228i
$557$	2.83348	+	10.5747i	0.120058	+	0.448064i	0.999615	−	0.0277296i	$-0.00882774\pi$
$557$	2.83348	+	10.5747i	0.120058	+	0.448064i	−0.879557	+	0.475793i	$0.842161\pi$
$558$	5.33493	+	6.58809i	0.225846	+	0.278896i
$559$	0.942233	−	2.89989i	0.0398522	−	0.122652i
$560$		0			0
$561$	6.39205	+	19.6727i	0.269872	+	0.830582i
$562$	−1.48219	+	2.28237i	−0.0625224	+	0.0962760i
$563$	1.98954	+	0.104267i	0.0838491	+	0.00439434i	0.0942144	−	0.995552i	$-0.469966\pi$
$563$	1.98954	+	0.104267i	0.0838491	+	0.00439434i	−0.0103653	+	0.999946i	$0.503299\pi$
$564$	−0.552486	+	2.59924i	−0.0232639	+	0.109448i
$565$		0			0
$566$	39.8243	+	12.9397i	1.67394	+	0.543896i
$567$	−27.7617	−	6.94351i	−1.16588	−	0.291600i
$568$	−11.1410	−	11.1410i	−0.467466	−	0.467466i
$569$	31.7588	+	3.33799i	1.33140	+	0.139936i	0.743357	−	0.668895i	$-0.233232\pi$
$569$	31.7588	+	3.33799i	1.33140	+	0.139936i	0.588042	+	0.808831i	$0.299899\pi$
$570$		0			0
$571$	1.54321	+	14.6827i	0.0645815	+	0.614452i	0.978169	+	0.207810i	$0.0666336\pi$
$571$	1.54321	+	14.6827i	0.0645815	+	0.614452i	−0.913588	+	0.406642i	$0.866700\pi$
$572$	−0.842191	−	2.19398i	−0.0352138	−	0.0917351i
$573$	4.75134	+	2.42093i	0.198490	+	0.101136i
$574$	−29.9003	+	22.4969i	−1.24801	+	0.939004i
$575$		0			0
$576$	−2.10668	−	3.64889i	−0.0877785	−	0.152037i
$577$	4.42257	+	6.81017i	0.184114	+	0.283511i	0.918661	−	0.395047i	$-0.129272\pi$
$577$	4.42257	+	6.81017i	0.184114	+	0.283511i	−0.734547	+	0.678558i	$0.762605\pi$
$578$	8.64959	−	10.6814i	0.359776	−	0.444286i
$579$	−12.5510	−	5.58805i	−0.521601	−	0.232232i
$580$		0			0
$581$	6.75395	+	3.75028i	0.280201	+	0.155588i
$582$	−7.41437	+	7.41437i	−0.307335	+	0.307335i
$583$	−14.9543	+	12.1098i	−0.619346	+	0.501536i
$584$	13.0430	+	14.4858i	0.539725	+	0.599425i
$585$		0			0
$586$	7.23150	+	6.51127i	0.298730	+	0.268978i
$587$	−6.22031	+	3.16940i	−0.256739	+	0.130815i	−0.577624	−	0.816303i	$-0.696020\pi$
$587$	−6.22031	+	3.16940i	−0.256739	+	0.130815i	0.320884	+	0.947118i	$0.396020\pi$
$588$	2.31490	−	6.69092i	0.0954650	−	0.275929i
$589$	45.4270	−	14.7601i	1.87179	−	0.608181i
$590$		0			0
$591$	21.5880	−	19.4379i	0.888013	−	0.799570i
$592$	−4.52228	+	11.7809i	−0.185865	+	0.484194i
$593$	8.18799	+	2.19397i	0.336240	+	0.0900954i	0.422989	−	0.906135i	$-0.360981\pi$
$593$	8.18799	+	2.19397i	0.336240	+	0.0900954i	−0.0867484	+	0.996230i	$0.527648\pi$
$594$	11.3107	+	8.21773i	0.464085	+	0.337177i
$595$		0			0
$596$	−6.11193	+	4.44058i	−0.250355	+	0.181893i
$597$	38.4512	−	14.7600i	1.57370	−	0.604087i
$598$	−5.84022	+	3.79268i	−0.238824	+	0.155094i
$599$	20.6751	+	11.9368i	0.844762	+	0.487723i	0.858880	−	0.512177i	$-0.171161\pi$
$599$	20.6751	+	11.9368i	0.844762	+	0.487723i	−0.0141183	+	0.999900i	$0.504494\pi$
$600$		0			0
$601$			9.32470i			0.380362i	0.981749	+	0.190181i	$0.0609075\pi$
$601$			9.32470i			0.380362i	−0.981749	+	0.190181i	$0.939092\pi$
$602$	−5.76574	+	1.01228i	−0.234994	+	0.0412573i
$603$	2.72868	+	0.432180i	0.111120	+	0.0175997i
$604$	3.38046	−	7.59263i	0.137549	−	0.308940i
$605$		0			0
$606$	−8.06467	+	3.59062i	−0.327605	+	0.145859i
$607$	−5.76957	+	21.5323i	−0.234180	+	0.873971i	0.744337	+	0.667804i	$0.232766\pi$
$607$	−5.76957	+	21.5323i	−0.234180	+	0.873971i	−0.978517	+	0.206167i	$0.933901\pi$
$608$	21.1802	−	3.35461i	0.858969	−	0.136047i
$609$	23.8977	−	27.4503i	0.968384	−	1.11234i
$610$		0			0
$611$	−3.84284	+	4.26790i	−0.155465	+	0.172661i
$612$	−0.115116	+	2.19655i	−0.00465330	+	0.0887903i
$613$	1.08016	−	20.6108i	0.0436274	−	0.832461i	−0.885938	−	0.463804i	$-0.846484\pi$
$613$	1.08016	−	20.6108i	0.0436274	−	0.832461i	0.929565	−	0.368657i	$-0.120182\pi$
$614$	18.8488	−	20.9338i	0.760677	−	0.844818i
$615$		0			0
$616$	8.51891	−	9.78531i	0.343237	−	0.394261i
$617$	−11.9685	+	1.89563i	−0.481835	+	0.0763151i	−0.392627	−	0.919698i	$-0.628434\pi$
$617$	−11.9685	+	1.89563i	−0.481835	+	0.0763151i	−0.0892079	+	0.996013i	$0.528434\pi$
$618$	−5.87259	+	21.9168i	−0.236230	+	0.881624i
$619$	−14.7437	+	6.56430i	−0.592597	+	0.263841i	−0.681048	−	0.732239i	$-0.738475\pi$
$619$	−14.7437	+	6.56430i	−0.592597	+	0.263841i	0.0884500	+	0.996081i	$0.471809\pi$
$620$		0			0
$621$	3.45604	−	7.76240i	0.138686	−	0.311494i
$622$	9.96354	+	1.57807i	0.399502	+	0.0632749i
$623$	32.9979	−	5.79335i	1.32203	−	0.232106i
$624$			20.4181i			0.817376i
$625$		0			0
$626$	−10.4927	−	6.05796i	−0.419372	−	0.242125i
$627$	−25.7490	+	16.7216i	−1.02831	+	0.667795i
$628$	2.06945	−	0.794388i	0.0825801	−	0.0316995i
$629$	−10.8523	+	7.88463i	−0.432708	+	0.314381i
$630$		0			0
$631$	32.3943	+	23.5358i	1.28960	+	0.936947i	0.999797	−	0.0201409i	$-0.00641148\pi$
$631$	32.3943	+	23.5358i	1.28960	+	0.936947i	0.289799	+	0.957087i	$0.406411\pi$
$632$	6.07412	+	1.62756i	0.241616	+	0.0647407i
$633$	17.5352	−	45.6809i	0.696963	−	1.81565i
$634$	16.6358	−	14.9789i	0.660691	−	0.594889i
$635$		0			0
$636$	−8.88511	+	2.88695i	−0.352318	+	0.114475i
$637$	11.5630	−	10.0217i	0.458143	−	0.397074i
$638$	−20.6654	+	10.5295i	−0.818149	+	0.416868i
$639$	4.18509	+	3.76827i	0.165560	+	0.149071i
$640$		0			0
$641$	−24.6903	−	27.4213i	−0.975207	−	1.08308i	−0.996524	−	0.0833043i	$-0.973453\pi$
$641$	−24.6903	−	27.4213i	−0.975207	−	1.08308i	0.0213172	−	0.999773i	$-0.493214\pi$
$642$	28.0148	−	22.6860i	1.10566	−	0.895344i
$643$	15.3835	−	15.3835i	0.606667	−	0.606667i	−0.335406	−	0.942074i	$-0.608874\pi$
$643$	15.3835	−	15.3835i	0.606667	−	0.606667i	0.942074	+	0.335406i	$0.108874\pi$
$644$	2.39733	+	1.33117i	0.0944681	+	0.0524555i
$645$		0			0
$646$	55.2002	+	24.5767i	2.17182	+	0.966958i
$647$	22.1547	−	27.3587i	0.870990	−	1.07558i	−0.125519	−	0.992091i	$-0.540060\pi$
$647$	22.1547	−	27.3587i	0.870990	−	1.07558i	0.996508	−	0.0834914i	$-0.0266071\pi$
$648$	−13.8663	−	21.3522i	−0.544718	−	0.838793i
$649$	−10.9605	−	18.9842i	−0.430238	−	0.745193i
$650$		0			0
$651$	26.3213	−	19.8041i	1.03161	−	0.776184i
$652$	−7.01384	−	3.57373i	−0.274683	−	0.139958i
$653$	11.1096	+	28.9416i	0.434754	+	1.13257i	0.959598	+	0.281374i	$0.0907902\pi$
$653$	11.1096	+	28.9416i	0.434754	+	1.13257i	−0.524844	+	0.851198i	$0.675876\pi$
$654$	−3.17668	−	30.2241i	−0.124218	−	1.18186i
$655$		0			0
$656$	−42.2597	−	4.44167i	−1.64996	−	0.173418i
$657$	−4.92657	−	4.92657i	−0.192204	−	0.192204i
$658$	10.6964	+	2.67528i	0.416989	+	0.104293i
$659$	−6.75492	−	2.19481i	−0.263134	−	0.0854976i	0.174479	−	0.984661i	$-0.444176\pi$
$659$	−6.75492	−	2.19481i	−0.263134	−	0.0854976i	−0.437613	+	0.899163i	$0.644176\pi$
$660$		0			0
$661$	−0.998752	+	4.69876i	−0.0388469	+	0.182760i	−0.993293	−	0.115622i	$-0.963114\pi$
$661$	−0.998752	+	4.69876i	−0.0388469	+	0.182760i	0.954446	+	0.298383i	$0.0964472\pi$
$662$	−16.3094	−	0.854740i	−0.633884	−	0.0332204i
$663$	−11.8211	+	18.2029i	−0.459093	+	0.706941i
$664$	2.12387	+	6.53659i	0.0824220	+	0.253669i
$665$		0			0
$666$	1.09196	−	3.36069i	0.0423124	−	0.130224i
$667$	8.87088	+	10.9546i	0.343482	+	0.424165i
$668$	−2.25866	−	8.42942i	−0.0873901	−	0.326144i
$669$	10.3844	+	23.3238i	0.401484	+	0.901749i
$670$		0			0
$671$	10.5039	+	14.4574i	0.405498	+	0.558120i
$672$	13.0624	−	6.93307i	0.503894	−	0.267449i
$673$	5.97729	−	11.7311i	0.230408	−	0.452201i	−0.746638	−	0.665231i	$-0.768333\pi$
$673$	5.97729	−	11.7311i	0.230408	−	0.452201i	0.977046	+	0.213030i	$0.0683332\pi$
$674$	−35.3100	+	20.3863i	−1.36009	+	0.785249i
$675$		0			0
$676$	−2.12143	+	3.67442i	−0.0815934	+	0.141324i
$677$	−47.3857	+	2.48338i	−1.82118	+	0.0954440i	−0.932077	−	0.362261i	$-0.882005\pi$
$677$	−47.3857	+	2.48338i	−1.82118	+	0.0954440i	−0.889104	+	0.457706i	$0.848671\pi$
$678$	−4.45777	+	28.1453i	−0.171200	+	1.08091i
$679$	6.08102	+	6.53074i	0.233368	+	0.250627i
$680$		0			0
$681$	−0.634543	+	6.03727i	−0.0243157	+	0.231349i
$682$	−20.2758	+	5.43288i	−0.776400	+	0.208036i
$683$	−16.6665	−	6.39766i	−0.637725	−	0.244800i	0.0179550	−	0.999839i	$-0.494284\pi$
$683$	−16.6665	−	6.39766i	−0.637725	−	0.244800i	−0.655680	+	0.755039i	$0.727618\pi$
$684$	−3.19339	+	0.678776i	−0.122102	+	0.0259537i
$685$		0			0
$686$	−27.4024	−	10.5884i	−1.04623	−	0.404266i
$687$	−0.475004	−	0.932248i	−0.0181225	−	0.0355675i
$688$	−5.57526	−	3.62062i	−0.212555	−	0.138035i
$689$	−19.7497	−	4.19792i	−0.752403	−	0.159928i
$690$		0			0
$691$	1.63598	+	7.69670i	0.0622357	+	0.292796i	0.998248	−	0.0591718i	$-0.0188460\pi$
$691$	1.63598	+	7.69670i	0.0622357	+	0.292796i	−0.936012	+	0.351968i	$0.885513\pi$
$692$	1.51331	+	9.55468i	0.0575275	+	0.363214i
$693$	−2.85770	+	3.65214i	−0.108555	+	0.138733i
$694$	−4.25473	+	5.85614i	−0.161507	+	0.222296i
$695$		0			0
$696$	32.2024	−	3.38461i	1.22063	−	0.128293i
$697$	−35.1033	−	28.4261i	−1.32963	−	1.07672i
$698$	−2.94045	−	56.1071i	−0.111298	−	2.12368i
$699$	48.6441			1.83989
$700$		0			0
$701$	21.0860			0.796406			0.398203	−	0.917297i	$-0.369634\pi$
$701$	21.0860			0.796406			0.398203	+	0.917297i	$0.369634\pi$
$702$	0.767757	+	14.6497i	0.0289771	+	0.552917i
$703$	−15.4730	−	12.5298i	−0.583577	−	0.472571i
$704$	10.3758	−	1.09054i	0.391052	−	0.0411012i
$705$		0			0
$706$	9.96981	−	13.7223i	0.375219	−	0.516444i
$707$	2.80922	+	6.96785i	0.105652	+	0.262053i
$708$	−1.66489	−	10.5117i	−0.0625703	−	0.395054i
$709$	−0.596764	−	2.80755i	−0.0224119	−	0.105440i	0.965520	−	0.260329i	$-0.0838312\pi$
$709$	−0.596764	−	2.80755i	−0.0224119	−	0.105440i	−0.987932	+	0.154890i	$0.950498\pi$
$710$		0			0
$711$	−2.19855	−	0.467316i	−0.0824521	−	0.0175257i
$712$	24.9976	+	16.2336i	0.936824	+	0.608381i
$713$	5.79180	+	11.3671i	0.216905	+	0.425699i
$714$	41.5084	+	3.66234i	1.55341	+	0.137060i
$715$		0			0
$716$	4.95146	−	1.05247i	0.185045	−	0.0393325i
$717$	49.9184	+	19.1619i	1.86424	+	0.715613i
$718$	5.84827	−	1.56704i	0.218256	−	0.0584814i
$719$	−0.593697	+	5.64865i	−0.0221412	+	0.210659i	0.977858	+	0.209270i	$0.0671088\pi$
$719$	−0.593697	+	5.64865i	−0.0221412	+	0.210659i	−0.999999	+	0.00138897i	$0.999558\pi$
$720$		0			0
$721$	18.4620	+	5.65929i	0.687562	+	0.210763i
$722$	−9.31526	+	58.8143i	−0.346678	+	2.18884i
$723$	37.4651	−	1.96346i	1.39334	−	0.0730220i
$724$	−0.216584	+	0.375135i	−0.00804929	+	0.0139418i
$725$		0			0
$726$	−17.9310	+	10.3525i	−0.665481	+	0.384216i
$727$	18.9408	−	37.1735i	0.702477	−	1.37869i	−0.213294	−	0.976988i	$-0.568419\pi$
$727$	18.9408	−	37.1735i	0.702477	−	1.37869i	0.915771	−	0.401701i	$-0.131581\pi$
$728$	13.6047	+	0.485123i	0.504223	+	0.0179799i
$729$	−9.27315	−	12.7634i	−0.343450	−	0.472718i
$730$		0			0
$731$	−2.87423	−	6.45562i	−0.106307	−	0.238770i
$732$	2.24553	+	8.38045i	0.0829973	+	0.309750i
$733$	−21.7630	−	26.8750i	−0.803834	−	0.992652i	−0.999927	−	0.0120672i	$-0.996159\pi$
$733$	−21.7630	−	26.8750i	−0.803834	−	0.992652i	0.196093	−	0.980585i	$-0.437175\pi$
$734$	4.08138	−	12.5612i	0.150647	−	0.463642i
$735$		0			0
$736$	1.76991	+	5.44722i	0.0652397	+	0.200787i
$737$	−3.72578	+	5.73720i	−0.137241	+	0.211333i
$738$	11.8826	+	0.622739i	0.437404	+	0.0229233i
$739$	−1.72889	+	8.13381i	−0.0635984	+	0.299207i	−0.998438	−	0.0558621i	$-0.982209\pi$
$739$	−1.72889	+	8.13381i	−0.0635984	+	0.299207i	0.934840	+	0.355069i	$0.115543\pi$
$740$		0			0
$741$	−30.6384	−	9.95501i	−1.12553	−	0.365706i
$742$	10.6573	+	37.2701i	0.391242	+	1.36823i
$743$	10.0390	+	10.0390i	0.368295	+	0.368295i	0.866855	−	0.498560i	$-0.166138\pi$
$743$	10.0390	+	10.0390i	0.368295	+	0.368295i	−0.498560	+	0.866855i	$0.666138\pi$
$744$	29.1447	+	3.06324i	1.06850	+	0.112304i
$745$		0			0
$746$	−2.89015	−	27.4979i	−0.105816	−	1.00677i
$747$	−0.880372	−	2.29345i	−0.0322111	−	0.0839128i
$748$	−4.85283	−	2.47264i	−0.177437	−	0.0904086i
$749$	−18.4447	−	24.5145i	−0.673954	−	0.895740i
$750$		0			0
$751$	19.9959	+	34.6339i	0.729661	+	1.26381i	0.957026	+	0.290000i	$0.0936555\pi$
$751$	19.9959	+	34.6339i	0.729661	+	1.26381i	−0.227365	+	0.973810i	$0.573011\pi$
$752$	6.81943	+	10.5010i	0.248679	+	0.382932i
$753$	−9.24716	+	11.4193i	−0.336985	+	0.416142i
$754$	−22.2322	−	9.89842i	−0.809650	−	0.360479i
$755$		0			0
$756$	4.95371	−	2.97152i	0.180165	−	0.108073i
$757$	12.1964	−	12.1964i	0.443287	−	0.443287i	−0.449828	−	0.893115i	$-0.648515\pi$
$757$	12.1964	−	12.1964i	0.443287	−	0.443287i	0.893115	+	0.449828i	$0.148515\pi$
$758$	13.4577	−	10.8978i	0.488805	−	0.395826i
$759$	−5.48704	−	6.09398i	−0.199167	−	0.221197i
$760$		0			0
$761$	7.43933	+	6.69840i	0.269676	+	0.242817i	0.792862	−	0.609401i	$-0.208590\pi$
$761$	7.43933	+	6.69840i	0.269676	+	0.242817i	−0.523186	+	0.852218i	$0.675257\pi$
$762$	−6.80777	+	3.46873i	−0.246619	+	0.125659i
$763$	−25.8018	+	1.78513i	−0.934088	+	0.0646261i
$764$	−1.33536	+	0.433884i	−0.0483116	+	0.0156974i
$765$		0			0
$766$	19.5597	−	17.6116i	0.706721	−	0.636334i
$767$	8.24291	−	21.4735i	0.297634	−	0.775364i
$768$	22.0205	+	5.90038i	0.794597	+	0.212912i
$769$	−33.7752	−	24.5391i	−1.21796	−	0.884902i	−0.222034	−	0.975039i	$-0.571270\pi$
$769$	−33.7752	−	24.5391i	−1.21796	−	0.884902i	−0.995929	+	0.0901368i	$0.971270\pi$
$770$		0			0
$771$	−21.7061	+	15.7704i	−0.781728	+	0.567959i
$772$	3.37719	−	1.29638i	0.121548	−	0.0466578i
$773$	−23.9689	+	15.5656i	−0.862100	+	0.559854i	−0.898246	−	0.439492i	$-0.855158\pi$
$773$	−23.9689	+	15.5656i	−0.862100	+	0.559854i	0.0361462	+	0.999347i	$0.488492\pi$
$774$	1.61213	+	0.930761i	0.0579466	+	0.0334555i
$775$		0			0
$776$			7.93899i			0.284993i
$777$	−12.8989	−	4.70558i	−0.462745	−	0.168812i
$778$	30.1171	+	4.77008i	1.07975	+	0.171016i
$779$	27.2690	−	61.2473i	0.977015	−	2.19441i
$780$		0			0
$781$	−12.7391	+	5.67181i	−0.455841	+	0.202953i
$782$	−4.17702	+	15.5888i	−0.149370	+	0.557456i
$783$	29.3293	−	4.64530i	1.04814	−	0.166009i
$784$	−14.5801	−	30.0058i	−0.520718	−	1.07164i
$785$		0			0
$786$	11.5899	−	12.8719i	0.413397	−	0.459124i
$787$	−1.80727	+	34.4848i	−0.0644222	+	1.22925i	0.754870	+	0.655874i	$0.227700\pi$
$787$	−1.80727	+	34.4848i	−0.0644222	+	1.22925i	−0.819293	+	0.573375i	$0.805634\pi$
$788$	−0.400310	+	7.63836i	−0.0142604	+	0.272105i
$789$	−25.6612	+	28.4996i	−0.913563	+	1.01461i
$790$		0			0
$791$	23.8022	+	4.64488i	0.846309	+	0.165153i
$792$	−4.07487	+	0.645396i	−0.144794	+	0.0229332i
$793$	−4.85309	+	18.1120i	−0.172338	+	0.643175i
$794$	−1.76300	+	0.784939i	−0.0625666	+	0.0278564i
$795$		0			0
$796$	−4.41090	+	9.90705i	−0.156340	+	0.351146i
$797$	−46.4194	−	7.35212i	−1.64426	−	0.260425i	−0.735433	−	0.677597i	$-0.763021\pi$
$797$	−46.4194	−	7.35212i	−1.64426	−	0.260425i	−0.908828	+	0.417172i	$0.863021\pi$
$798$	10.6950	+	60.9170i	0.378600	+	2.15644i
$799$			13.3099i			0.470869i
$800$		0			0
$801$	−9.22634	−	5.32683i	−0.325997	−	0.188214i
$802$	6.31027	−	4.09794i	0.222824	−	0.144703i
$803$	16.1060	−	6.18253i	0.568370	−	0.218177i
$804$	−2.68694	+	1.95218i	−0.0947612	+	0.0688480i
$805$		0			0
$806$	−17.8190	−	12.9462i	−0.627646	−	0.456012i
$807$	−17.4810	−	4.68401i	−0.615359	−	0.164885i
$808$	−2.39531	+	6.23999i	−0.0842667	+	0.219522i
$809$	24.0985	−	21.6984i	0.847259	−	0.762875i	−0.126135	−	0.992013i	$-0.540257\pi$
$809$	24.0985	−	21.6984i	0.847259	−	0.762875i	0.973394	+	0.229138i	$0.0735907\pi$
$810$		0			0
$811$	−8.85993	+	2.87877i	−0.311114	+	0.101087i	−0.460413	−	0.887705i	$-0.652299\pi$
$811$	−8.85993	+	2.87877i	−0.311114	+	0.101087i	0.149298	+	0.988792i	$0.452299\pi$
$812$	0.661432	+	9.56015i	0.0232117	+	0.335495i
$813$	1.93178	−	0.984289i	0.0677503	−	0.0345205i
$814$	6.50239	+	5.85478i	0.227909	+	0.205210i
$815$		0			0
$816$	31.6634	+	35.1658i	1.10844	+	1.23105i
$817$	8.15120	−	6.60071i	0.285174	−	0.230930i
$818$	−27.8073	+	27.8073i	−0.972258	+	0.972258i
$819$	−4.86514	+	0.0813352i	−0.170002	+	0.00284208i
$820$		0			0
$821$	−33.9829	−	15.1302i	−1.18601	−	0.528047i	−0.283610	−	0.958940i	$-0.591532\pi$
$821$	−33.9829	−	15.1302i	−1.18601	−	0.528047i	−0.902403	+	0.430893i	$0.858199\pi$
$822$	17.7680	−	21.9417i	0.619731	−	0.765304i
$823$	−16.2420	−	25.0106i	−0.566162	−	0.871813i	0.433406	−	0.901199i	$-0.357312\pi$
$823$	−16.2420	−	25.0106i	−0.566162	−	0.871813i	−0.999568	+	0.0293856i	$0.990645\pi$
$824$	8.58974	+	14.8779i	0.299238	+	0.518295i
$825$		0			0
$826$	−43.8342	+	5.34938i	−1.52519	+	0.186129i
$827$	−25.7867	−	13.1390i	−0.896691	−	0.456887i	−0.0560176	−	0.998430i	$-0.517840\pi$
$827$	−25.7867	−	13.1390i	−0.896691	−	0.456887i	−0.840673	+	0.541543i	$0.817840\pi$
$828$	−0.312490	−	0.814064i	−0.0108598	−	0.0282907i
$829$	−0.985667	−	9.37799i	−0.0342336	−	0.325711i	−0.998214	−	0.0597381i	$-0.980973\pi$
$829$	−0.985667	−	9.37799i	−0.0342336	−	0.325711i	0.963980	−	0.265973i	$-0.0856932\pi$
$830$		0			0
$831$	37.8941	+	3.98283i	1.31453	+	0.138163i
$832$	7.74074	+	7.74074i	0.268362	+	0.268362i
$833$	4.37365	−	35.1916i	0.151538	−	1.21932i
$834$	−52.6799	−	17.1167i	−1.82416	−	0.592704i
$835$		0			0
$836$	1.68075	−	7.90732i	0.0581300	−	0.273480i
$837$	26.8385	+	1.40654i	0.927673	+	0.0486173i
$838$	−21.0338	+	32.3892i	−0.726601	+	1.11887i
$839$	−16.9096	−	52.0423i	−0.583784	−	1.79670i	−0.604101	−	0.796907i	$-0.706468\pi$
$839$	−16.9096	−	52.0423i	−0.583784	−	1.79670i	0.0203179	−	0.999794i	$-0.493532\pi$
$840$		0			0
$841$	−6.26123	+	19.2701i	−0.215905	+	0.664486i
$842$	7.40433	+	9.14358i	0.255170	+	0.315109i
$843$	−0.870306	−	3.24803i	−0.0299749	−	0.111868i
$844$	5.24025	+	11.7698i	0.180377	+	0.405133i
$845$		0			0
$846$	−2.06088	−	2.83656i	−0.0708544	−	0.0975228i
$847$	8.26091	+	15.5642i	0.283848	+	0.534791i
$848$	−19.9848	+	39.2224i	−0.686282	+	1.34690i
$849$	−44.8078	+	25.8698i	−1.53780	+	0.887849i
$850$		0			0
$851$	2.65890	−	4.60535i	0.0911460	−	0.157870i
$852$	−6.76091	+	0.354324i	−0.231625	+	0.0121389i
$853$	−9.03599	+	57.0510i	−0.309386	+	1.95339i	−0.00773601	+	0.999970i	$0.502462\pi$
$853$	−9.03599	+	57.0510i	−0.309386	+	1.95339i	−0.301650	+	0.953419i	$0.597538\pi$
$854$	35.0826	−	8.07223i	1.20050	−	0.276226i
$855$		0			0
$856$	2.85296	−	27.1441i	0.0975123	−	0.927768i
$857$	−13.6104	+	3.64690i	−0.464923	+	0.124576i	−0.483674	−	0.875248i	$-0.660698\pi$
$857$	−13.6104	+	3.64690i	−0.464923	+	0.124576i	0.0187505	+	0.999824i	$0.494031\pi$
$858$	13.2171	+	5.07358i	0.451226	+	0.173209i
$859$	20.5048	−	4.35843i	0.699615	−	0.148708i	0.155646	−	0.987813i	$-0.450254\pi$
$859$	20.5048	−	4.35843i	0.699615	−	0.148708i	0.543969	+	0.839105i	$0.316921\pi$
$860$		0			0
$861$	4.06354	−	46.0556i	0.138485	−	1.56957i
$862$	−12.9994	−	25.5128i	−0.442763	−	0.868971i
$863$	12.8270	+	8.32996i	0.436637	+	0.283555i	0.744180	−	0.667979i	$-0.232840\pi$
$863$	12.8270	+	8.32996i	0.436637	+	0.283555i	−0.307544	+	0.951534i	$0.599507\pi$
$864$	11.8021	+	2.50861i	0.401516	+	0.0853448i
$865$		0			0
$866$	8.32500	+	39.1660i	0.282895	+	1.33092i
$867$	2.65667	+	16.7735i	0.0902252	+	0.569659i
$868$	−1.21339	+	8.58779i	−0.0411851	+	0.291489i
$869$	3.27136	−	4.50263i	0.110973	−	0.152741i
$870$		0			0
$871$	−7.13862	+	0.750299i	−0.241883	+	0.0254229i
$872$	−17.8821	−	14.4806i	−0.605564	−	0.490376i
$873$	−0.148511	−	2.83375i	−0.00502632	−	0.0959080i
$874$	−23.9541			−0.810261
$875$		0			0
$876$	8.37585			0.282994
$877$	0.783299	+	14.9462i	0.0264501	+	0.504699i	0.979445	+	0.201712i	$0.0646505\pi$
$877$	0.783299	+	14.9462i	0.0264501	+	0.504699i	−0.952995	+	0.302987i	$0.902016\pi$
$878$	34.3865	+	27.8456i	1.16049	+	0.939745i
$879$	−11.9578	+	1.25681i	−0.403326	+	0.0423912i
$880$		0			0
$881$	−10.0697	+	13.8597i	−0.339257	+	0.466947i	−0.944224	−	0.329303i	$-0.893186\pi$
$881$	−10.0697	+	13.8597i	−0.339257	+	0.466947i	0.604967	+	0.796250i	$0.293186\pi$
$882$	4.51692	+	8.17714i	0.152093	+	0.275339i
$883$	4.27148	+	26.9691i	0.143747	+	0.907581i	0.949143	+	0.314845i	$0.101952\pi$
$883$	4.27148	+	26.9691i	0.143747	+	0.907581i	−0.805397	+	0.592736i	$0.798048\pi$
$884$	−1.18818	−	5.58997i	−0.0399630	−	0.188011i
$885$		0			0
$886$	47.5113	+	10.0988i	1.59617	+	0.339277i
$887$	26.6089	+	17.2800i	0.893439	+	0.580206i	0.907666	−	0.419693i	$-0.137862\pi$
$887$	26.6089	+	17.2800i	0.893439	+	0.580206i	−0.0142273	+	0.999899i	$0.504529\pi$
$888$	−5.54572	−	10.8841i	−0.186102	−	0.365246i
$889$	2.74368	+	5.89517i	0.0920200	+	0.197718i
$890$		0			0
$891$	−22.0406	+	4.68488i	−0.738389	+	0.156949i
$892$	−6.27591	−	2.40909i	−0.210133	−	0.0806625i
$893$	−19.0822	+	5.11306i	−0.638561	+	0.171102i
$894$	4.75729	−	45.2626i	0.159108	−	1.51381i
$895$		0			0
$896$	10.5823	−	34.5220i	0.353529	−	1.15330i
$897$	1.34602	−	8.49842i	0.0449422	−	0.283754i
$898$	48.1901	−	2.52554i	1.60813	−	0.0842783i
$899$	−22.2922	+	38.6112i	−0.743485	+	1.28775i
$900$		0			0
$901$	−40.5246	+	23.3969i	−1.35007	+	0.779463i
$902$	−13.3761	+	26.2521i	−0.445376	+	0.874099i
$903$	3.83751	−	6.13125i	0.127704	−	0.204035i
$904$	12.6818	+	17.4550i	0.421790	+	0.580544i
$905$		0			0
$906$	20.3648	+	45.7400i	0.676574	+	1.51961i
$907$	−3.31110	−	12.3572i	−0.109943	−	0.410314i	0.888916	−	0.458071i	$-0.151459\pi$
$907$	−3.31110	−	12.3572i	−0.109943	−	0.410314i	−0.998859	+	0.0477567i	$0.984793\pi$
$908$	−1.00590	−	1.24218i	−0.0333819	−	0.0412233i
$909$	0.738256	−	2.27212i	0.0244864	−	0.0753614i
$910$		0			0
$911$	−2.87409	−	8.84554i	−0.0952228	−	0.293066i	0.892089	−	0.451860i	$-0.149239\pi$
$911$	−2.87409	−	8.84554i	−0.0952228	−	0.293066i	−0.987312	+	0.158794i	$0.949239\pi$
$912$	−38.2531	+	58.9046i	−1.26669	+	1.95052i
$913$	6.07461	+	0.318357i	0.201040	+	0.0105361i
$914$	−13.3129	+	62.6323i	−0.440351	+	2.07169i
$915$		0			0
$916$	0.262007	+	0.0851313i	0.00865696	+	0.00281282i
$917$	−10.5960	−	10.2475i	−0.349909	−	0.338402i
$918$	24.0404	+	24.0404i	0.793450	+	0.793450i
$919$	48.3968	+	5.08671i	1.59646	+	0.167795i	0.860581	−	0.509313i	$-0.170101\pi$
$919$	48.3968	+	5.08671i	1.59646	+	0.167795i	0.735883	+	0.677108i	$0.236767\pi$
$920$		0			0
$921$	3.63822	+	34.6154i	0.119883	+	1.14062i
$922$	−10.1563	−	26.4581i	−0.334480	−	0.871350i
$923$	−13.0371	−	6.64272i	−0.429121	−	0.218648i
$924$	−0.675327	−	5.53381i	−0.0222166	−	0.182049i
$925$		0			0
$926$	−27.1322	−	46.9943i	−0.891619	−	1.54433i
$927$	−3.34434	−	5.14984i	−0.109843	−	0.169143i
$928$	−12.5967	+	15.5556i	−0.413506	+	0.510637i
$929$	0.431385	+	0.192065i	0.0141533	+	0.00630145i	0.413801	−	0.910367i	$-0.364201\pi$
$929$	0.431385	+	0.192065i	0.0141533	+	0.00630145i	−0.399648	+	0.916669i	$0.630868\pi$
$930$		0			0
$931$	52.1340	−	7.24862i	1.70862	−	0.237564i
$932$	−9.05674	+	9.05674i	−0.296663	+	0.296663i
$933$	−9.68674	+	7.84416i	−0.317129	+	0.256806i
$934$	7.08743	+	7.87139i	0.231908	+	0.257560i
$935$		0			0
$936$	−3.21705	−	2.89665i	−0.105153	−	0.0946799i
$937$	−30.8727	+	15.7304i	−1.00857	+	0.513890i	−0.878565	−	0.477624i	$-0.841498\pi$
$937$	−30.8727	+	15.7304i	−1.00857	+	0.513890i	−0.130002	+	0.991514i	$0.541498\pi$
$938$	7.69765	+	11.4304i	0.251337	+	0.373216i
$939$	14.2378	−	4.62615i	0.464634	−	0.150969i
$940$		0			0
$941$	−8.33164	+	7.50184i	−0.271604	+	0.244553i	−0.793665	−	0.608355i	$-0.791830\pi$
$941$	−8.33164	+	7.50184i	−0.271604	+	0.244553i	0.522062	+	0.852908i	$0.325163\pi$
$942$	−4.78560	+	12.4669i	−0.155923	+	0.406194i
$943$	17.2966	+	4.63460i	0.563253	+	0.150923i
$944$	−40.5702	−	29.4760i	−1.32045	−	0.959362i
$945$		0			0
$946$	−3.72909	+	2.70934i	−0.121243	+	0.0880883i
$947$	53.5143	−	20.5422i	1.73898	−	0.667532i	0.738999	−	0.673706i	$-0.235299\pi$
$947$	53.5143	−	20.5422i	1.73898	−	0.667532i	0.999981	+	0.00617413i	$0.00196530\pi$
$948$	2.26617	−	1.47167i	0.0736018	−	0.0477976i
$949$	15.6768	+	9.05102i	0.508892	+	0.293809i
$950$		0			0
$951$			27.6599i			0.896934i
$952$	24.1835	−	20.2620i	0.783791	−	0.656695i
$953$	−17.0778	−	2.70486i	−0.553204	−	0.0876189i	−0.126427	−	0.991976i	$-0.540351\pi$
$953$	−17.0778	−	2.70486i	−0.553204	−	0.0876189i	−0.426777	+	0.904357i	$0.640351\pi$
$954$	5.01373	−	11.2610i	0.162326	−	0.364589i
$955$		0			0
$956$	−12.8616	+	5.72636i	−0.415974	+	0.185204i
$957$	7.41718	−	27.6813i	0.239764	−	0.894810i
$958$	−7.93504	+	1.25679i	−0.256370	+	0.0406050i
$959$	−18.1224	−	15.7770i	−0.585203	−	0.509467i
$960$		0			0
$961$	−6.25705	+	6.94916i	−0.201840	+	0.224166i
$962$	−0.480497	+	9.16843i	−0.0154918	+	0.295602i
$963$	−0.510569	+	9.74223i	−0.0164528	+	0.313939i
$964$	−6.60983	+	7.34096i	−0.212888	+	0.236436i
$965$		0			0
$966$	−15.6232	+	5.36663i	−0.502669	+	0.172668i
$967$	−13.9567	+	2.21053i	−0.448819	+	0.0710859i	−0.376753	−	0.926314i	$-0.622959\pi$
$967$	−13.9567	+	2.21053i	−0.448819	+	0.0710859i	−0.0720662	+	0.997400i	$0.522959\pi$
$968$	−4.05738	+	15.1423i	−0.130409	+	0.486693i
$969$	−68.2059	+	30.3672i	−2.19109	+	0.975535i
$970$		0			0
$971$	−4.23795	+	9.51858i	−0.136002	+	0.305466i	−0.968689	−	0.248279i	$-0.920135\pi$
$971$	−4.23795	+	9.51858i	−0.136002	+	0.305466i	0.832686	+	0.553745i	$0.186802\pi$
$972$	−4.33576	−	0.686717i	−0.139070	−	0.0220265i
$973$	−16.1553	+	44.2849i	−0.517917	+	1.41971i
$974$			29.8245i			0.955640i
$975$		0			0
$976$	35.4039	+	20.4405i	1.13325	+	0.654283i
$977$	20.8965	−	13.5703i	0.668538	−	0.434154i	−0.165240	−	0.986253i	$-0.552840\pi$
$977$	20.8965	−	13.5703i	0.668538	−	0.434154i	0.833778	+	0.552100i	$0.186173\pi$
$978$	44.2722	−	16.9945i	1.41567	−	0.543424i
$979$	21.3419	−	15.5058i	0.682091	−	0.495568i
$980$		0			0
$981$	6.65373	+	4.83422i	0.212437	+	0.154345i
$982$	40.1972	+	10.7708i	1.28274	+	0.343710i
$983$	−4.18853	+	10.9115i	−0.133593	+	0.348022i	−0.984017	−	0.178077i	$-0.943013\pi$
$983$	−4.18853	+	10.9115i	−0.133593	+	0.348022i	0.850423	+	0.526099i	$0.176346\pi$
$984$	30.5681	−	27.5236i	0.974475	−	0.877421i
$985$		0			0
$986$	−53.6403	+	17.4288i	−1.70826	+	0.555046i
$987$	−11.3001	+	7.60993i	−0.359687	+	0.242227i
$988$	7.55782	−	3.85090i	0.240446	−	0.122513i
$989$	2.08186	+	1.87451i	0.0661993	+	0.0596061i
$990$		0			0
$991$	−7.21705	−	8.01534i	−0.229257	−	0.254616i	0.617531	−	0.786547i	$-0.288133\pi$
$991$	−7.21705	−	8.01534i	−0.229257	−	0.254616i	−0.846788	+	0.531931i	$0.821467\pi$
$992$	−14.0786	+	11.4006i	−0.446995	+	0.361969i
$993$	14.2692	−	14.2692i	0.452820	−	0.452820i
$994$	0.469562	+	28.0873i	0.0148936	+	0.890876i
$995$		0			0
$996$	2.69796	+	1.20121i	0.0854882	+	0.0380618i
$997$	−7.79493	+	9.62594i	−0.246868	+	0.304856i	−0.885485	−	0.464668i	$-0.846174\pi$
$997$	−7.79493	+	9.62594i	−0.246868	+	0.304856i	0.638617	+	0.769525i	$0.279507\pi$
$998$	−2.61129	−	4.02103i	−0.0826588	−	0.127283i
$999$	−5.60130	−	9.70173i	−0.177217	−	0.306949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.b.143.5		288
5.2	odd	4		175.2.x.a.17.14	yes	288
5.3	odd	4		875.2.bb.c.857.5		288
5.4	even	2		875.2.bb.a.143.14		288
7.5	odd	6	inner	875.2.bb.b.768.5		288
25.3	odd	20		875.2.bb.a.507.14		288
25.4	even	10		875.2.bb.c.493.14		288
25.21	even	5		175.2.x.a.3.5	✓	288
25.22	odd	20	inner	875.2.bb.b.507.5		288
35.12	even	12		175.2.x.a.117.5	yes	288
35.19	odd	6		875.2.bb.a.768.14		288
35.33	even	12		875.2.bb.c.607.14		288
175.47	even	60	inner	875.2.bb.b.257.5		288
175.54	odd	30		875.2.bb.c.243.5		288
175.96	odd	30		175.2.x.a.103.14	yes	288
175.103	even	60		875.2.bb.a.257.14		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.5	✓	288	25.21	even	5
175.2.x.a.17.14	yes	288	5.2	odd	4
175.2.x.a.103.14	yes	288	175.96	odd	30
175.2.x.a.117.5	yes	288	35.12	even	12
875.2.bb.a.143.14		288	5.4	even	2
875.2.bb.a.257.14		288	175.103	even	60
875.2.bb.a.507.14		288	25.3	odd	20
875.2.bb.a.768.14		288	35.19	odd	6
875.2.bb.b.143.5		288	1.1	even	1	trivial
875.2.bb.b.257.5		288	175.47	even	60	inner
875.2.bb.b.507.5		288	25.22	odd	20	inner
875.2.bb.b.768.5		288	7.5	odd	6	inner
875.2.bb.c.243.5		288	175.54	odd	30
875.2.bb.c.493.14		288	25.4	even	10
875.2.bb.c.607.14		288	35.33	even	12
875.2.bb.c.857.5		288	5.3	odd	4

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

\(f(q)\)	\(=\)	\(q+(-0.0830157 - 1.58403i) q^{2} +(1.52315 + 1.23343i) q^{3} +(-0.513230 + 0.0539426i) q^{4} +(1.82734 - 2.51512i) q^{6} +(-2.08368 - 1.63042i) q^{7} +(-0.368222 - 2.32486i) q^{8} +(0.174924 + 0.822951i) q^{9} +(-2.03775 - 0.433137i) q^{11} +(-0.848262 - 0.550868i) q^{12} +(-0.992394 - 1.94768i) q^{13} +(-2.40967 + 3.43597i) q^{14} +(-4.66165 + 0.990865i) q^{16} +(-4.72957 - 1.81551i) q^{17} +(1.28906 - 0.345403i) q^{18} +(0.785987 - 7.47816i) q^{19} +(-1.16276 - 5.05345i) q^{21} +(-0.516939 + 3.26382i) q^{22} +(2.00560 - 0.105109i) q^{23} +(2.30669 - 3.99530i) q^{24} +(-3.00281 + 1.73368i) q^{26} +(1.92076 - 3.76970i) q^{27} +(1.15736 + 0.724382i) q^{28} +(4.12547 + 5.67823i) q^{29} +(2.58369 + 5.80306i) q^{31} +(0.738117 + 2.75469i) q^{32} +(-2.56957 - 3.17315i) q^{33} +(-2.48320 + 7.64252i) q^{34} +(-0.134168 - 0.412927i) q^{36} +(1.44212 - 2.22067i) q^{37} +(-11.9109 - 0.624225i) q^{38} +(0.890754 - 4.19067i) q^{39} +(8.47974 + 2.75523i) q^{41} +(-7.90831 + 2.26137i) q^{42} +(0.986332 + 0.986332i) q^{43} +(1.06920 + 0.112377i) q^{44} +(-0.332993 - 3.16821i) q^{46} +(-0.941527 - 2.45276i) q^{47} +(-8.32258 - 4.24056i) q^{48} +(1.68344 + 6.79456i) q^{49} +(-4.96456 - 8.59887i) q^{51} +(0.614389 + 0.946077i) q^{52} +(5.81286 - 7.17828i) q^{53} +(-6.13079 - 2.72960i) q^{54} +(-3.02325 + 5.44463i) q^{56} +(10.4209 - 10.4209i) q^{57} +(8.65203 - 7.00627i) q^{58} +(7.04085 + 7.81965i) q^{59} +(-6.37468 - 5.73979i) q^{61} +(8.97777 - 4.57440i) q^{62} +(0.977274 - 1.99997i) q^{63} +(-4.76284 + 1.54754i) q^{64} +(-4.81306 + 4.33370i) q^{66} +(1.17677 - 3.06559i) q^{67} +(2.52529 + 0.676649i) q^{68} +(3.18448 + 2.31366i) q^{69} +(5.41526 - 3.93442i) q^{71} +(1.84884 - 0.709703i) q^{72} +(-6.94515 + 4.51023i) q^{73} +(-3.63734 - 2.10002i) q^{74} +3.88041i q^{76} +(3.53982 + 4.22492i) q^{77} +(-6.71211 - 1.06309i) q^{78} +(-1.08662 + 2.44058i) q^{79} +(9.88106 - 4.39933i) q^{81} +(3.66043 - 13.6609i) q^{82} +(-2.88395 + 0.456772i) q^{83} +(0.869359 + 2.53086i) q^{84} +(1.48050 - 1.64427i) q^{86} +(-0.719940 + 13.7373i) q^{87} +(-0.256640 + 4.89698i) q^{88} +(-8.47306 + 9.41028i) q^{89} +(-1.10772 + 5.67637i) q^{91} +(-1.02366 + 0.162132i) q^{92} +(-3.22229 + 12.0258i) q^{93} +(-3.80710 + 1.69503i) q^{94} +(-2.27344 + 5.10623i) q^{96} +(-3.33125 - 0.527619i) q^{97} +(10.6231 - 3.23068i) q^{98} -1.75274i 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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