LMFDB - Embedded newform 875.2.bb.a.257.14

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			257.14
Character	$\chi$	$=$	875.257
Dual form			875.2.bb.a.143.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(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 $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.0830157	−	1.58403i	0.0587010	−	1.12008i	−0.797460	−	0.603372i	$-0.793823\pi$
$2$	0.0830157	−	1.58403i	0.0587010	−	1.12008i	0.856161	−	0.516709i	$-0.172843\pi$
$3$	−1.52315	+	1.23343i	−0.879393	+	0.712119i	−0.958605	−	0.284739i	$-0.908093\pi$
$3$	−1.52315	+	1.23343i	−0.879393	+	0.712119i	0.0792117	+	0.996858i	$0.474760\pi$
$4$	−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	−0.504594	−	0.863357i	$-0.668358\pi$
$11$	−2.03775	+	0.433137i	−0.614405	+	0.130596i	−0.109811	+	0.993953i	$0.535025\pi$
$12$	0.848262	−	0.550868i	0.244872	−	0.159022i
$13$	0.992394	−	1.94768i	0.275241	−	0.540190i	−0.711462	−	0.702724i	$-0.751967\pi$
$13$	0.992394	−	1.94768i	0.275241	−	0.540190i	0.986703	+	0.162534i	$0.0519667\pi$
$14$	−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	$-0.406085\pi$
$17$	4.72957	−	1.81551i	1.14709	−	0.440326i	0.856309	+	0.516464i	$0.172752\pi$
$18$	−1.28906	−	0.345403i	−0.303835	−	0.0814123i
$19$	0.785987	+	7.47816i	0.180318	+	1.71561i	0.593394	+	0.804912i	$0.297788\pi$
$19$	0.785987	+	7.47816i	0.180318	+	1.71561i	−0.413076	+	0.910696i	$0.635546\pi$
$20$		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	$-0.550480\pi$
$23$	−2.00560	−	0.105109i	−0.418196	−	0.0219167i	−0.260274	+	0.965535i	$0.583813\pi$
$24$	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	−0.230603	−	0.973048i	$-0.574070\pi$
$29$	4.12547	−	5.67823i	0.766081	−	1.05442i	0.996684	−	0.0813721i	$-0.0259302\pi$
$30$		0			0
$31$	2.58369	−	5.80306i	0.464045	−	1.04226i	−0.518303	−	0.855197i	$-0.673436\pi$
$31$	2.58369	−	5.80306i	0.464045	−	1.04226i	0.982348	−	0.187064i	$-0.0598972\pi$
$32$	−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	$-0.253173\pi$
$37$	−1.44212	−	2.22067i	−0.237083	−	0.365076i	−0.937106	+	0.349044i	$0.886506\pi$
$38$	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	0.440339	−	0.897832i	$-0.354858\pi$
$41$	8.47974	−	2.75523i	1.32431	−	0.430295i	0.883974	+	0.467536i	$0.154858\pi$
$42$	7.90831	+	2.26137i	1.22028	+	0.348936i
$43$	−0.986332	+	0.986332i	−0.150414	+	0.150414i	−0.778303	−	0.627889i	$-0.783919\pi$
$43$	−0.986332	+	0.986332i	−0.150414	+	0.150414i	0.627889	+	0.778303i	$0.283919\pi$
$44$	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	$-0.821962\pi$
$47$	0.941527	−	2.45276i	0.137336	−	0.357772i	0.984950	+	0.172842i	$0.0552949\pi$
$48$	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	−0.999979	−	0.00652896i	$-0.997922\pi$
$53$	−5.81286	−	7.17828i	−0.798458	−	0.986013i	0.201521	−	0.979484i	$-0.435412\pi$
$54$	−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	−0.0831288	−	0.996539i	$-0.526491\pi$
$59$	7.04085	−	7.81965i	0.916640	−	1.01803i	0.999769	−	0.0214933i	$-0.00684204\pi$
$60$		0			0
$61$	−6.37468	+	5.73979i	−0.816194	+	0.734904i	−0.967306	−	0.253612i	$-0.918381\pi$
$61$	−6.37468	+	5.73979i	−0.816194	+	0.734904i	0.151112	+	0.988517i	$0.451715\pi$
$62$	−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	$-0.180950\pi$
$67$	−1.17677	−	3.06559i	−0.143765	−	0.374521i	−0.986490	+	0.163824i	$0.947617\pi$
$68$	−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	0.860768	−	0.508998i	$-0.169984\pi$
$71$	5.41526	+	3.93442i	0.642673	+	0.466930i	−0.218094	+	0.975928i	$0.569984\pi$
$72$	−1.84884	−	0.709703i	−0.217888	−	0.0836393i
$73$	6.94515	+	4.51023i	0.812868	+	0.527883i	0.882844	−	0.469666i	$-0.155626\pi$
$73$	6.94515	+	4.51023i	0.812868	+	0.527883i	−0.0699760	+	0.997549i	$0.522292\pi$
$74$	−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	0.842043	−	0.539410i	$-0.181353\pi$
$79$	−1.08662	−	2.44058i	−0.122254	−	0.274586i	−0.964297	+	0.264824i	$0.914686\pi$
$80$		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	$-0.398770\pi$
$83$	2.88395	+	0.456772i	0.316554	+	0.0501373i	0.00386431	+	0.999993i	$0.498770\pi$
$84$	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	−0.999996	−	0.00268884i	$-0.999144\pi$
$89$	−8.47306	−	9.41028i	−0.898142	−	0.997488i	0.101854	−	0.994799i	$-0.467523\pi$
$90$		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	$-0.495227\pi$
$97$	3.33125	−	0.527619i	0.338237	−	0.0535716i	0.323243	+	0.946316i	$0.395227\pi$
$98$	−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	−0.617333	−	0.786702i	$-0.711787\pi$
$101$	−2.45915	+	1.41979i	−0.244695	+	0.141275i	0.372638	+	0.927977i	$0.378453\pi$
$102$	13.2088	+	8.57788i	1.30786	+	0.849337i
$103$	6.81372	+	2.61554i	0.671375	+	0.257717i	0.670087	−	0.742282i	$-0.266257\pi$
$103$	6.81372	+	2.61554i	0.671375	+	0.257717i	0.00128815	+	0.999999i	$0.499590\pi$
$104$	−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	$-0.772718\pi$
$107$	−11.2003	+	3.00110i	−1.08277	+	0.290127i	−0.327040	+	0.945011i	$0.606051\pi$
$108$	0.782443	+	2.03833i	0.0752906	+	0.196139i
$109$	7.26460	+	6.54107i	0.695822	+	0.626521i	0.939184	−	0.343415i	$-0.111584\pi$
$109$	7.26460	+	6.54107i	0.695822	+	0.626521i	−0.243362	+	0.969936i	$0.578250\pi$
$110$		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	$-0.208113\pi$
$113$	8.16704	+	4.16132i	0.768291	+	0.391464i	−0.0254843	+	0.999675i	$0.508113\pi$
$114$	−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	$-0.615222\pi$
$127$	2.18980	−	1.11576i	0.194313	−	0.0990074i	0.548440	+	0.836190i	$0.315222\pi$
$128$	−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	0.140670	−	0.990056i	$-0.455074\pi$
$131$	5.54090	−	0.582372i	0.484111	−	0.0508821i	0.343441	+	0.939174i	$0.388408\pi$
$132$	−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	$-0.643483\pi$
$137$	−9.06922	+	0.475298i	−0.774836	+	0.0406074i	−0.339181	+	0.940721i	$0.610150\pi$
$138$	−3.40056	−	5.23640i	−0.289475	−	0.445752i
$139$	−5.50579	+	16.9451i	−0.466995	+	1.43726i	0.389461	+	0.921043i	$0.372661\pi$
$139$	−5.50579	+	16.9451i	−0.466995	+	1.43726i	−0.856456	+	0.516220i	$0.827339\pi$
$140$		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	0.919445	−	0.393219i	$-0.128638\pi$
$149$	12.6781	+	7.31970i	1.03863	+	0.599653i	0.119185	+	0.992872i	$0.461972\pi$
$150$		0			0
$151$	−8.05257	−	13.9475i	−0.655309	−	1.13503i	−0.981816	−	0.189833i	$-0.939205\pi$
$151$	−8.05257	−	13.9475i	−0.655309	−	1.13503i	0.326508	−	0.945195i	$-0.394128\pi$
$152$	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	$-0.361836\pi$
$157$	4.14906	+	1.11174i	0.331131	+	0.0887263i	−0.0894230	+	0.995994i	$0.528502\pi$
$158$	−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	$-0.887127\pi$
$163$	−12.7929	+	8.30781i	−1.00202	+	0.650718i	−0.0642326	+	0.997935i	$0.520460\pi$
$164$	−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	0.644583	+	0.764535i	$0.277031\pi$
$167$	−2.64539	+	16.7023i	−0.204706	+	1.29246i	−0.849289	+	0.527929i	$0.822969\pi$
$168$	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	−0.663315	−	0.748340i	$-0.730851\pi$
$173$	0.981067	−	18.7199i	0.0745892	−	1.42325i	0.737904	−	0.674906i	$-0.235816\pi$
$174$	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	−0.267326	−	0.963606i	$-0.586140\pi$
$179$	−9.75542	−	1.02534i	−0.729155	−	0.0766372i	−0.461829	+	0.886969i	$0.652807\pi$
$180$		0			0
$181$	0.493376	+	0.679074i	0.0366723	+	0.0504751i	0.826959	−	0.562262i	$-0.190069\pi$
$181$	0.493376	+	0.679074i	0.0366723	+	0.0504751i	−0.790287	+	0.612737i	$0.790069\pi$
$182$	−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	0.303185	−	0.952932i	$-0.401950\pi$
$191$	2.66133	+	0.565683i	0.192567	+	0.0409314i	−0.110618	+	0.993863i	$0.535283\pi$
$192$	9.16332	−	3.51747i	0.661305	−	0.253851i
$193$	6.77095	+	1.81427i	0.487384	+	0.130594i	0.494139	−	0.869383i	$-0.335483\pi$
$193$	6.77095	+	1.81427i	0.487384	+	0.130594i	−0.00675479	+	0.999977i	$0.502150\pi$
$194$	−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	−0.921385	−	0.388650i	$-0.872942\pi$
$197$	−2.31863	−	14.6392i	−0.165195	−	1.04300i	0.756190	−	0.654352i	$-0.227058\pi$
$198$	2.77639	+	0.145505i	0.197310	+	0.0103406i
$199$	10.5072	+	18.1990i	0.744835	+	1.29009i	0.950272	+	0.311422i	$0.100805\pi$
$199$	10.5072	+	18.1990i	0.744835	+	1.29009i	−0.205437	+	0.978670i	$0.565862\pi$
$200$		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	0.220805	+	0.975318i	$0.429132\pi$
$211$	−7.71478	+	23.7437i	−0.531108	+	1.63458i	−0.751912	+	0.659263i	$0.770868\pi$
$212$	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	$-0.793661\pi$
$223$	−11.6067	+	5.91390i	−0.777241	+	0.396024i	0.0199118	+	0.999802i	$0.493661\pi$
$224$	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	$-0.849443\pi$
$227$	−1.68692	+	2.59763i	−0.111965	+	0.172411i	0.778246	+	0.627960i	$0.216110\pi$
$228$	4.78620	+	5.91047i	0.316974	+	0.391430i
$229$	−0.487685	+	0.217131i	−0.0322271	+	0.0143484i	−0.422787	−	0.906229i	$-0.638948\pi$
$229$	−0.487685	+	0.217131i	−0.0322271	+	0.0143484i	0.390560	+	0.920578i	$0.372281\pi$
$230$		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	−0.998252	−	0.0591038i	$-0.981176\pi$
$233$	−19.2882	−	15.6193i	−1.26361	−	1.02325i	−0.265360	−	0.964149i	$-0.585491\pi$
$234$	−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	0.984585	−	0.174910i	$-0.0559633\pi$
$239$	25.9462	+	8.43043i	1.67832	+	0.545320i	0.693736	+	0.720229i	$0.255963\pi$
$240$		0			0
$241$	14.2251	+	12.8083i	0.916319	+	0.825057i	0.984995	−	0.172582i	$-0.0552109\pi$
$241$	14.2251	+	12.8083i	0.916319	+	0.825057i	−0.0686763	+	0.997639i	$0.521878\pi$
$242$	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	$-0.923964\pi$
$251$		−	7.49714i		−	0.473215i	0.971605	−	0.236608i	$-0.0760356\pi$
$252$	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	0.983964	+	0.178369i	$0.0570822\pi$
$257$	3.54307	+	13.2229i	0.221011	+	0.824824i	−0.762953	+	0.646454i	$0.776251\pi$
$258$	−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	0.828012	+	0.560711i	$0.189472\pi$
$263$	1.02406	+	19.5402i	0.0631462	+	1.20490i	−0.764865	+	0.644190i	$0.777195\pi$
$264$	−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	0.133128	−	0.991099i	$-0.457498\pi$
$269$	−8.43550	−	3.75573i	−0.514321	−	0.228991i	−0.647450	+	0.762108i	$0.724164\pi$
$270$		0			0
$271$	0.449933	+	1.01057i	0.0273315	+	0.0613875i	0.926695	−	0.375813i	$-0.122637\pi$
$271$	0.449933	+	1.01057i	0.0273315	+	0.0613875i	−0.899364	+	0.437201i	$0.855970\pi$
$272$	−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	$-0.515198\pi$
$277$	−16.3045	−	10.5883i	−0.979643	−	0.636188i	−0.931917	+	0.362673i	$0.881864\pi$
$278$	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	−0.628416	−	0.777878i	$-0.716296\pi$
$281$	−1.38801	+	1.00845i	−0.0828017	+	0.0601589i	0.545614	+	0.838036i	$0.316296\pi$
$282$	7.88949	−	2.11398i	0.469812	−	0.125886i
$283$	9.46043	+	24.6453i	0.562364	+	1.46501i	0.859982	+	0.510324i	$0.170475\pi$
$283$	9.46043	+	24.6453i	0.562364	+	1.46501i	−0.297618	+	0.954685i	$0.596192\pi$
$284$	−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	$-0.192650\pi$
$293$	4.33790	+	4.33790i	0.253423	+	0.253423i	−0.568950	+	0.822372i	$0.692650\pi$
$294$	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	$-0.919162\pi$
$307$	−12.5574	+	12.5574i	−0.716687	+	0.716687i	0.251239	+	0.967925i	$0.419162\pi$
$308$	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	0.924626	−	0.380875i	$-0.124377\pi$
$311$	−1.32225	−	6.22068i	−0.0749777	−	0.352743i	−0.999604	+	0.0281326i	$0.991044\pi$
$312$	10.0707	−	0.527784i	0.570142	−	0.0298799i
$313$	−4.16011	−	6.40601i	−0.235143	−	0.362089i	0.701325	−	0.712842i	$-0.252592\pi$
$313$	−4.16011	−	6.40601i	−0.235143	−	0.362089i	−0.936468	+	0.350753i	$0.885926\pi$
$314$	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	$-0.913048\pi$
$317$	−8.88140	+	10.9676i	−0.498829	+	0.616003i	0.464092	+	0.885787i	$0.346381\pi$
$318$	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	0.983454	+	0.181157i	$0.0579841\pi$
$331$	1.07624	+	10.2397i	0.0591554	+	0.562826i	−0.924299	+	0.381670i	$0.875349\pi$
$332$	−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	−0.318375	−	0.947965i	$-0.603137\pi$
$337$	11.6695	−	22.9028i	0.635681	−	1.24759i	0.954056	−	0.299629i	$-0.0968628\pi$
$338$	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	$-0.677579\pi$
$347$	3.54647	−	2.87187i	0.190384	−	0.154170i	0.719774	+	0.694209i	$0.244246\pi$
$348$	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	$-0.808518\pi$
$353$	−8.31018	+	6.72945i	−0.442306	+	0.358173i	0.382148	+	0.924101i	$0.375184\pi$
$354$	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	−0.952230	−	0.305380i	$-0.901216\pi$
$359$	0.793602	−	3.73360i	0.0418847	−	0.197052i	0.994115	+	0.108328i	$0.0345498\pi$
$360$		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	$-0.686399\pi$
$367$	−7.77350	+	2.98397i	−0.405773	+	0.155762i	0.146916	+	0.989149i	$0.453065\pi$
$368$	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	$-0.632364\pi$
$373$	−17.4072	−	0.912274i	−0.901312	−	0.0472358i	−0.497360	+	0.867544i	$0.665697\pi$
$374$	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	−0.611758	−	0.791045i	$-0.709537\pi$
$379$	6.41691	−	8.83212i	0.329614	−	0.453675i	0.941372	+	0.337370i	$0.109537\pi$
$380$		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	$-0.922685\pi$
$383$	−10.4424	+	12.8953i	−0.533582	+	0.658919i	0.437064	+	0.899430i	$0.356018\pi$
$384$	−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	−0.955456	−	0.295135i	$-0.904635\pi$
$389$	−3.99680	−	18.8035i	−0.202646	−	0.953373i	0.752810	−	0.658238i	$-0.228698\pi$
$390$		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	$-0.873614\pi$
$397$	0.436005	−	1.13583i	0.0218825	−	0.0570058i	0.944086	+	0.329698i	$0.106947\pi$
$398$	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	−0.800710	−	0.599052i	$-0.795544\pi$
$401$	2.37174	−	4.10797i	0.118439	−	0.205142i	0.919149	+	0.393910i	$0.128878\pi$
$402$	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	−0.997318	−	0.0731905i	$-0.976682\pi$
$409$	−16.5891	+	18.4241i	−0.820280	+	0.911014i	0.177038	+	0.984204i	$0.443349\pi$
$410$		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	−0.953678	−	0.300828i	$-0.902737\pi$
$419$	−19.6973	+	14.3109i	−0.962276	+	0.699135i	−0.00859807	+	0.999963i	$0.502737\pi$
$420$		0			0
$421$	−6.00083	−	4.35986i	−0.292463	−	0.212486i	0.431872	−	0.901935i	$-0.357853\pi$
$421$	−6.00083	−	4.35986i	−0.292463	−	0.212486i	−0.724335	+	0.689448i	$0.757853\pi$
$422$	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	0.763458	−	0.645858i	$-0.223500\pi$
$431$	16.4910	+	7.34228i	0.794345	+	0.353665i	0.0308873	+	0.999523i	$0.490167\pi$
$432$	5.21865	+	19.4763i	0.251082	+	0.937052i
$433$	24.9324	+	3.94891i	1.19818	+	0.189773i	0.723460	−	0.690366i	$-0.242551\pi$
$433$	24.9324	+	3.94891i	1.19818	+	0.189773i	0.474717	+	0.880139i	$0.342551\pi$
$434$	−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	0.109141	−	0.994026i	$-0.465190\pi$
$439$	−18.6654	−	20.7300i	−0.890849	−	0.989388i	−0.999989	+	0.00463865i	$0.998523\pi$
$440$		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	0.851061	+	0.525066i	$0.175960\pi$
$443$	7.92554	+	29.5785i	0.376554	+	1.40532i	−0.474507	+	0.880252i	$0.657374\pi$
$444$	−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	$-0.745121\pi$
$449$		−	30.4224i		−	1.43572i	0.696187	−	0.717861i	$-0.254879\pi$
$450$		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	$-0.190210\pi$
$457$	38.9922	−	10.4479i	1.82398	−	0.488733i	0.997266	+	0.0738955i	$0.0235431\pi$
$458$	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	0.676705	−	0.736255i	$-0.263407\pi$
$461$	16.9923	+	5.52114i	0.791411	+	0.257145i	0.114706	+	0.993399i	$0.463407\pi$
$462$	−17.0946	−	1.18272i	−0.795315	−	0.0550249i
$463$	−30.4814	−	15.5311i	−1.41659	−	0.721790i	−0.432866	−	0.901458i	$-0.642498\pi$
$463$	−30.4814	−	15.5311i	−1.41659	−	0.721790i	−0.983727	+	0.179668i	$0.942498\pi$
$464$	−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	$-0.233957\pi$
$467$	5.18944	+	4.20233i	0.240139	+	0.194460i	−0.501695	+	0.865045i	$0.667290\pi$
$468$	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	0.975747	+	0.218903i	$0.0702477\pi$
$479$	−0.529424	+	5.03713i	−0.0241900	+	0.230153i	−0.999937	+	0.0112499i	$0.996419\pi$
$480$		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	$-0.376586\pi$
$487$	18.7766	−	0.984042i	0.850851	−	0.0445912i	0.472775	+	0.881183i	$0.343252\pi$
$488$	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	−0.949431	−	0.313976i	$-0.898339\pi$
$491$	−8.10726	−	24.9516i	−0.365876	−	1.12605i	0.583555	−	0.812073i	$-0.301661\pi$
$492$	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	0.557446	−	0.830213i	$-0.311781\pi$
$499$	2.61768	+	1.51132i	0.117183	+	0.0676558i	−0.440263	+	0.897869i	$0.645115\pi$
$500$		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	−0.987053	−	0.160396i	$-0.948723\pi$
$503$	−2.19511	−	13.8594i	−0.0978750	−	0.617958i	0.889178	−	0.457562i	$-0.151277\pi$
$504$	−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	0.671462	−	0.741039i	$-0.265667\pi$
$509$	22.1880	+	4.71620i	0.983465	+	0.209042i	0.312003	+	0.950081i	$0.399000\pi$
$510$		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	−0.874248	−	0.485480i	$-0.838645\pi$
$521$	−41.7780	−	4.39105i	−1.83033	−	0.192375i	−0.956080	+	0.293105i	$0.905311\pi$
$522$	−7.27927	+	5.89463i	−0.318605	+	0.258001i
$523$	−1.38297	+	26.3887i	−0.0604732	+	1.15390i	0.784865	+	0.619666i	$0.212732\pi$
$523$	−1.38297	+	26.3887i	−0.0604732	+	1.15390i	−0.845339	+	0.534231i	$0.820601\pi$
$524$	−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	0.311033	−	0.950399i	$-0.399325\pi$
$541$	4.85225	+	1.03138i	0.208615	+	0.0443424i	−0.102419	+	0.994741i	$0.532658\pi$
$542$	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	0.975010	+	0.222161i	$0.0713110\pi$
$547$	2.72171	+	17.1842i	0.116372	+	0.734743i	−0.858638	+	0.512582i	$0.828689\pi$
$548$	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	$-0.991172\pi$
$557$	−2.83348	+	10.5747i	−0.120058	+	0.448064i	0.879557	+	0.475793i	$0.157839\pi$
$558$	−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	$-0.530034\pi$
$563$	−1.98954	+	0.104267i	−0.0838491	+	0.00439434i	0.0103653	+	0.999946i	$0.496701\pi$
$564$	−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	0.588042	−	0.808831i	$-0.299899\pi$
$569$	31.7588	−	3.33799i	1.33140	−	0.139936i	0.743357	+	0.668895i	$0.233232\pi$
$570$		0			0
$571$	1.54321	−	14.6827i	0.0645815	−	0.614452i	−0.913588	−	0.406642i	$-0.866700\pi$
$571$	1.54321	−	14.6827i	0.0645815	−	0.614452i	0.978169	−	0.207810i	$-0.0666336\pi$
$572$	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	$-0.870728\pi$
$577$	−4.42257	+	6.81017i	−0.184114	+	0.283511i	0.734547	+	0.678558i	$0.237395\pi$
$578$	−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	$-0.303980\pi$
$587$	6.22031	+	3.16940i	0.256739	+	0.130815i	−0.320884	+	0.947118i	$0.603980\pi$
$588$	−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	$-0.639019\pi$
$593$	−8.18799	+	2.19397i	−0.336240	+	0.0900954i	0.0867484	+	0.996230i	$0.472352\pi$
$594$	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	−0.0141183	−	0.999900i	$-0.504494\pi$
$599$	20.6751	−	11.9368i	0.844762	−	0.487723i	0.858880	+	0.512177i	$0.171161\pi$
$600$		0			0
$601$		−	9.32470i		−	0.380362i	−0.981749	−	0.190181i	$-0.939092\pi$
$601$		−	9.32470i		−	0.380362i	0.981749	−	0.190181i	$-0.0609075\pi$
$602$	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	0.978517	+	0.206167i	$0.0660989\pi$
$607$	5.76957	+	21.5323i	0.234180	+	0.873971i	−0.744337	+	0.667804i	$0.767234\pi$
$608$	−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	−0.929565	−	0.368657i	$-0.879818\pi$
$613$	−1.08016	−	20.6108i	−0.0436274	−	0.832461i	0.885938	−	0.463804i	$-0.153516\pi$
$614$	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	$-0.371566\pi$
$617$	11.9685	+	1.89563i	0.481835	+	0.0763151i	0.0892079	+	0.996013i	$0.471566\pi$
$618$	5.87259	+	21.9168i	0.236230	+	0.881624i
$619$	−14.7437	−	6.56430i	−0.592597	−	0.263841i	0.0884500	−	0.996081i	$-0.471809\pi$
$619$	−14.7437	−	6.56430i	−0.592597	−	0.263841i	−0.681048	+	0.732239i	$0.738475\pi$
$620$		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	0.289799	−	0.957087i	$-0.406411\pi$
$631$	32.3943	−	23.5358i	1.28960	−	0.936947i	0.999797	+	0.0201409i	$0.00641148\pi$
$632$	−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	0.0213172	+	0.999773i	$0.493214\pi$
$641$	−24.6903	+	27.4213i	−0.975207	+	1.08308i	−0.996524	+	0.0833043i	$0.973453\pi$
$642$	−28.0148	−	22.6860i	−1.10566	−	0.895344i
$643$	−15.3835	−	15.3835i	−0.606667	−	0.606667i	0.335406	−	0.942074i	$-0.391126\pi$
$643$	−15.3835	−	15.3835i	−0.606667	−	0.606667i	−0.942074	+	0.335406i	$0.891126\pi$
$644$	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	−0.996508	−	0.0834914i	$-0.973393\pi$
$647$	−22.1547	−	27.3587i	−0.870990	−	1.07558i	0.125519	−	0.992091i	$-0.459940\pi$
$648$	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	0.524844	+	0.851198i	$0.324124\pi$
$653$	−11.1096	+	28.9416i	−0.434754	+	1.13257i	−0.959598	+	0.281374i	$0.909210\pi$
$654$	−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	−0.437613	−	0.899163i	$-0.644176\pi$
$659$	−6.75492	+	2.19481i	−0.263134	+	0.0854976i	0.174479	+	0.984661i	$0.444176\pi$
$660$		0			0
$661$	−0.998752	−	4.69876i	−0.0388469	−	0.182760i	0.954446	−	0.298383i	$-0.0964472\pi$
$661$	−0.998752	−	4.69876i	−0.0388469	−	0.182760i	−0.993293	+	0.115622i	$0.963114\pi$
$662$	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	$-0.231667\pi$
$673$	−5.97729	−	11.7311i	−0.230408	−	0.452201i	−0.977046	+	0.213030i	$0.931667\pi$
$674$	−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	$-0.117995\pi$
$677$	47.3857	+	2.48338i	1.82118	+	0.0954440i	0.889104	+	0.457706i	$0.151329\pi$
$678$	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	$-0.505716\pi$
$683$	16.6665	−	6.39766i	0.637725	−	0.244800i	0.655680	+	0.755039i	$0.272382\pi$
$684$	−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	−0.936012	−	0.351968i	$-0.885513\pi$
$691$	1.63598	−	7.69670i	0.0622357	−	0.292796i	0.998248	+	0.0591718i	$0.0188460\pi$
$692$	−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	−0.987932	−	0.154890i	$-0.950498\pi$
$709$	−0.596764	+	2.80755i	−0.0224119	+	0.105440i	0.965520	+	0.260329i	$0.0838312\pi$
$710$		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	−0.999999	−	0.00138897i	$-0.999558\pi$
$719$	−0.593697	−	5.64865i	−0.0221412	−	0.210659i	0.977858	−	0.209270i	$-0.0671088\pi$
$720$		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	−0.915771	−	0.401701i	$-0.868419\pi$
$727$	−18.9408	−	37.1735i	−0.702477	−	1.37869i	0.213294	−	0.976988i	$-0.431581\pi$
$728$	−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	−0.196093	−	0.980585i	$-0.562825\pi$
$733$	21.7630	−	26.8750i	0.803834	−	0.992652i	0.999927	−	0.0120672i	$-0.00384120\pi$
$734$	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	0.934840	−	0.355069i	$-0.115543\pi$
$739$	−1.72889	−	8.13381i	−0.0635984	−	0.299207i	−0.998438	+	0.0558621i	$0.982209\pi$
$740$		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	$-0.833862\pi$
$743$	−10.0390	+	10.0390i	−0.368295	+	0.368295i	0.498560	+	0.866855i	$0.333862\pi$
$744$	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	−0.227365	−	0.973810i	$-0.573011\pi$
$751$	19.9959	−	34.6339i	0.729661	−	1.26381i	0.957026	−	0.290000i	$-0.0936555\pi$
$752$	−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	$-0.351485\pi$
$757$	−12.1964	−	12.1964i	−0.443287	−	0.443287i	−0.893115	+	0.449828i	$0.851485\pi$
$758$	−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	−0.523186	−	0.852218i	$-0.675257\pi$
$761$	7.43933	−	6.69840i	0.269676	−	0.242817i	0.792862	+	0.609401i	$0.208590\pi$
$762$	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	−0.995929	−	0.0901368i	$-0.971270\pi$
$769$	−33.7752	+	24.5391i	−1.21796	+	0.884902i	−0.222034	+	0.975039i	$0.571270\pi$
$770$		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	$-0.144842\pi$
$773$	23.9689	+	15.5656i	0.862100	+	0.559854i	−0.0361462	+	0.999347i	$0.511508\pi$
$774$	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	0.819293	+	0.573375i	$0.194366\pi$
$787$	1.80727	+	34.4848i	0.0644222	+	1.22925i	−0.754870	+	0.655874i	$0.772300\pi$
$788$	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	$-0.236979\pi$
$797$	46.4194	−	7.35212i	1.64426	−	0.260425i	0.908828	+	0.417172i	$0.136979\pi$
$798$	−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	0.973394	−	0.229138i	$-0.0735907\pi$
$809$	24.0985	+	21.6984i	0.847259	+	0.762875i	−0.126135	+	0.992013i	$0.540257\pi$
$810$		0			0
$811$	−8.85993	−	2.87877i	−0.311114	−	0.101087i	0.149298	−	0.988792i	$-0.452299\pi$
$811$	−8.85993	−	2.87877i	−0.311114	−	0.101087i	−0.460413	+	0.887705i	$0.652299\pi$
$812$	−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	−0.902403	−	0.430893i	$-0.858199\pi$
$821$	−33.9829	+	15.1302i	−1.18601	+	0.528047i	−0.283610	+	0.958940i	$0.591532\pi$
$822$	−17.7680	−	21.9417i	−0.619731	−	0.765304i
$823$	16.2420	−	25.0106i	0.566162	−	0.871813i	−0.433406	−	0.901199i	$-0.642688\pi$
$823$	16.2420	−	25.0106i	0.566162	−	0.871813i	0.999568	+	0.0293856i	$0.00935509\pi$
$824$	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	$-0.482160\pi$
$827$	25.7867	−	13.1390i	0.896691	−	0.456887i	0.840673	+	0.541543i	$0.182160\pi$
$828$	0.312490	−	0.814064i	0.0108598	−	0.0282907i
$829$	−0.985667	+	9.37799i	−0.0342336	+	0.325711i	0.963980	+	0.265973i	$0.0856932\pi$
$829$	−0.985667	+	9.37799i	−0.0342336	+	0.325711i	−0.998214	+	0.0597381i	$0.980973\pi$
$830$		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	0.0203179	+	0.999794i	$0.493532\pi$
$839$	−16.9096	+	52.0423i	−0.583784	+	1.79670i	−0.604101	+	0.796907i	$0.706468\pi$
$840$		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	0.301650	+	0.953419i	$0.402462\pi$
$853$	9.03599	+	57.0510i	0.309386	+	1.95339i	0.00773601	+	0.999970i	$0.497538\pi$
$854$	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	$-0.339302\pi$
$857$	13.6104	+	3.64690i	0.464923	+	0.124576i	−0.0187505	+	0.999824i	$0.505969\pi$
$858$	−13.2171	+	5.07358i	−0.451226	+	0.173209i
$859$	20.5048	+	4.35843i	0.699615	+	0.148708i	0.543969	−	0.839105i	$-0.316921\pi$
$859$	20.5048	+	4.35843i	0.699615	+	0.148708i	0.155646	+	0.987813i	$0.450254\pi$
$860$		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	$-0.767160\pi$
$863$	−12.8270	+	8.32996i	−0.436637	+	0.283555i	0.307544	+	0.951534i	$0.400493\pi$
$864$	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	0.952995	+	0.302987i	$0.0979838\pi$
$877$	−0.783299	+	14.9462i	−0.0264501	+	0.504699i	−0.979445	+	0.201712i	$0.935350\pi$
$878$	−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	0.604967	−	0.796250i	$-0.293186\pi$
$881$	−10.0697	−	13.8597i	−0.339257	−	0.466947i	−0.944224	+	0.329303i	$0.893186\pi$
$882$	−4.51692	+	8.17714i	−0.152093	+	0.275339i
$883$	−4.27148	+	26.9691i	−0.143747	+	0.907581i	0.805397	+	0.592736i	$0.201952\pi$
$883$	−4.27148	+	26.9691i	−0.143747	+	0.907581i	−0.949143	+	0.314845i	$0.898048\pi$
$884$	−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	$-0.862138\pi$
$887$	−26.6089	+	17.2800i	−0.893439	+	0.580206i	0.0142273	+	0.999899i	$0.495471\pi$
$888$	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	$-0.848541\pi$
$907$	3.31110	−	12.3572i	0.109943	−	0.410314i	0.998859	+	0.0477567i	$0.0152072\pi$
$908$	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	−0.987312	−	0.158794i	$-0.949239\pi$
$911$	−2.87409	+	8.84554i	−0.0952228	+	0.293066i	0.892089	+	0.451860i	$0.149239\pi$
$912$	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	0.735883	−	0.677108i	$-0.236767\pi$
$919$	48.3968	−	5.08671i	1.59646	−	0.167795i	0.860581	+	0.509313i	$0.170101\pi$
$920$		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	−0.399648	−	0.916669i	$-0.630868\pi$
$929$	0.431385	−	0.192065i	0.0141533	−	0.00630145i	0.413801	+	0.910367i	$0.364201\pi$
$930$		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	$-0.158502\pi$
$937$	30.8727	+	15.7304i	1.00857	+	0.513890i	0.130002	+	0.991514i	$0.458502\pi$
$938$	−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	0.522062	−	0.852908i	$-0.325163\pi$
$941$	−8.33164	−	7.50184i	−0.271604	−	0.244553i	−0.793665	+	0.608355i	$0.791830\pi$
$942$	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	$-0.764701\pi$
$947$	−53.5143	−	20.5422i	−1.73898	−	0.667532i	−0.999981	+	0.00617413i	$0.998035\pi$
$948$	−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	$-0.459649\pi$
$953$	17.0778	−	2.70486i	0.553204	−	0.0876189i	0.426777	+	0.904357i	$0.359649\pi$
$954$	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	$-0.377041\pi$
$967$	13.9567	+	2.21053i	0.448819	+	0.0710859i	0.0720662	+	0.997400i	$0.477041\pi$
$968$	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	0.832686	−	0.553745i	$-0.186802\pi$
$971$	−4.23795	−	9.51858i	−0.136002	−	0.305466i	−0.968689	+	0.248279i	$0.920135\pi$
$972$	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	$-0.447160\pi$
$977$	−20.8965	−	13.5703i	−0.668538	−	0.434154i	−0.833778	+	0.552100i	$0.813827\pi$
$978$	−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	$-0.0569875\pi$
$983$	4.18853	+	10.9115i	0.133593	+	0.348022i	−0.850423	+	0.526099i	$0.823654\pi$
$984$	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	−0.846788	−	0.531931i	$-0.821467\pi$
$991$	−7.21705	+	8.01534i	−0.229257	+	0.254616i	0.617531	+	0.786547i	$0.288133\pi$
$992$	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	$-0.153826\pi$
$997$	7.79493	+	9.62594i	0.246868	+	0.304856i	−0.638617	+	0.769525i	$0.720493\pi$
$998$	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.a.257.14		288
5.2	odd	4		175.2.x.a.103.14	yes	288
5.3	odd	4		875.2.bb.c.243.5		288
5.4	even	2		875.2.bb.b.257.5		288
7.3	odd	6	inner	875.2.bb.a.507.14		288
25.6	even	5		875.2.bb.c.607.14		288
25.8	odd	20	inner	875.2.bb.a.768.14		288
25.17	odd	20		875.2.bb.b.768.5		288
25.19	even	10		175.2.x.a.117.5	yes	288
35.3	even	12		875.2.bb.c.493.14		288
35.17	even	12		175.2.x.a.3.5	✓	288
35.24	odd	6		875.2.bb.b.507.5		288
175.17	even	60		875.2.bb.b.143.5		288
175.31	odd	30		875.2.bb.c.857.5		288
175.94	odd	30		175.2.x.a.17.14	yes	288
175.108	even	60	inner	875.2.bb.a.143.14		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.5	✓	288	35.17	even	12
175.2.x.a.17.14	yes	288	175.94	odd	30
175.2.x.a.103.14	yes	288	5.2	odd	4
175.2.x.a.117.5	yes	288	25.19	even	10
875.2.bb.a.143.14		288	175.108	even	60	inner
875.2.bb.a.257.14		288	1.1	even	1	trivial
875.2.bb.a.507.14		288	7.3	odd	6	inner
875.2.bb.a.768.14		288	25.8	odd	20	inner
875.2.bb.b.143.5		288	175.17	even	60
875.2.bb.b.257.5		288	5.4	even	2
875.2.bb.b.507.5		288	35.24	odd	6
875.2.bb.b.768.5		288	25.17	odd	20
875.2.bb.c.243.5		288	5.3	odd	4
875.2.bb.c.493.14		288	35.3	even	12
875.2.bb.c.607.14		288	25.6	even	5
875.2.bb.c.857.5		288	175.31	odd	30

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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