LMFDB - Embedded newform 875.2.bb.c.857.5

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 = [288,8] 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			857.5
Character	$\chi$	$=$	875.857
Dual form			875.2.bb.c.243.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.58403 + 0.0830157i) q^{2} +(-1.23343 + 1.52315i) q^{3} +(0.513230 - 0.0539426i) q^{4} +(1.82734 - 2.51512i) q^{6} +(-1.63042 + 2.08368i) q^{7} +(2.32486 - 0.368222i) q^{8} +(-0.174924 - 0.822951i) q^{9} +(-2.03775 - 0.433137i) q^{11} +(-0.550868 + 0.848262i) q^{12} +(1.94768 - 0.992394i) q^{13} +(2.40967 - 3.43597i) q^{14} +(-4.66165 + 0.990865i) q^{16} +(-1.81551 + 4.72957i) q^{17} +(0.345403 + 1.28906i) q^{18} +(-0.785987 + 7.47816i) q^{19} +(-1.16276 - 5.05345i) q^{21} +(3.26382 + 0.516939i) q^{22} +(0.105109 + 2.00560i) q^{23} +(-2.30669 + 3.99530i) q^{24} +(-3.00281 + 1.73368i) q^{26} +(-3.76970 - 1.92076i) q^{27} +(-0.724382 + 1.15736i) q^{28} +(-4.12547 - 5.67823i) q^{29} +(2.58369 + 5.80306i) q^{31} +(2.75469 - 0.738117i) q^{32} +(3.17315 - 2.56957i) q^{33} +(2.48320 - 7.64252i) q^{34} +(-0.134168 - 0.412927i) q^{36} +(-2.22067 - 1.44212i) q^{37} +(0.624225 - 11.9109i) q^{38} +(-0.890754 + 4.19067i) q^{39} +(8.47974 + 2.75523i) q^{41} +(2.26137 + 7.90831i) q^{42} +(-0.986332 + 0.986332i) q^{43} +(-1.06920 - 0.112377i) q^{44} +(-0.332993 - 3.16821i) q^{46} +(-2.45276 + 0.941527i) q^{47} +(4.24056 - 8.32258i) q^{48} +(-1.68344 - 6.79456i) q^{49} +(-4.96456 - 8.59887i) q^{51} +(0.946077 - 0.614389i) q^{52} +(7.17828 + 5.81286i) q^{53} +(6.13079 + 2.72960i) q^{54} +(-3.02325 + 5.44463i) q^{56} +(-10.4209 - 10.4209i) q^{57} +(7.00627 + 8.65203i) q^{58} +(-7.04085 - 7.81965i) q^{59} +(-6.37468 - 5.73979i) q^{61} +(-4.57440 - 8.97777i) q^{62} +(1.99997 + 0.977274i) q^{63} +(4.76284 - 1.54754i) q^{64} +(-4.81306 + 4.33370i) q^{66} +(-3.06559 - 1.17677i) q^{67} +(-0.676649 + 2.52529i) q^{68} +(-3.18448 - 2.31366i) q^{69} +(5.41526 - 3.93442i) q^{71} +(-0.709703 - 1.84884i) q^{72} +(-4.51023 - 6.94515i) q^{73} +(3.63734 + 2.10002i) q^{74} +3.88041i q^{76} +(4.22492 - 3.53982i) q^{77} +(1.06309 - 6.71211i) q^{78} +(1.08662 - 2.44058i) q^{79} +(9.88106 - 4.39933i) q^{81} +(-13.6609 - 3.66043i) q^{82} +(-0.456772 - 2.88395i) q^{83} +(-0.869359 - 2.53086i) q^{84} +(1.48050 - 1.64427i) q^{86} +(13.7373 + 0.719940i) q^{87} +(-4.89698 - 0.256640i) q^{88} +(8.47306 - 9.41028i) q^{89} +(-1.10772 + 5.67637i) q^{91} +(0.162132 + 1.02366i) q^{92} +(-12.0258 - 3.22229i) q^{93} +(3.80710 - 1.69503i) q^{94} +(-2.27344 + 5.10623i) q^{96} +(-0.527619 + 3.33125i) q^{97} +(3.23068 + 10.6231i) q^{98} +1.75274i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) $ 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.58403	+	0.0830157i	−1.12008	+	0.0587010i	−0.603372	−	0.797460i	$-0.706177\pi$
$2$	−1.58403	+	0.0830157i	−1.12008	+	0.0587010i	−0.516709	+	0.856161i	$0.672843\pi$
$3$	−1.23343	+	1.52315i	−0.712119	+	0.879393i	−0.996858	−	0.0792117i	$-0.974760\pi$
$3$	−1.23343	+	1.52315i	−0.712119	+	0.879393i	0.284739	+	0.958605i	$0.408093\pi$
$4$	0.513230	−	0.0539426i	0.256615	−	0.0269713i
$5$		0			0
$5$		0			0
$6$	1.82734	−	2.51512i	0.746010	−	1.02679i
$7$	−1.63042	+	2.08368i	−0.616242	+	0.787557i
$7$	−1.63042	+	2.08368i	−0.616242	+	0.787557i
$8$	2.32486	−	0.368222i	0.821963	−	0.130186i
$9$	−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	$0.668358\pi$
$12$	−0.550868	+	0.848262i	−0.159022	+	0.244872i
$13$	1.94768	−	0.992394i	0.540190	−	0.275241i	−0.162534	−	0.986703i	$-0.551967\pi$
$13$	1.94768	−	0.992394i	0.540190	−	0.275241i	0.702724	+	0.711462i	$0.251967\pi$
$14$	2.40967	−	3.43597i	0.644011	−	0.918302i
$15$		0			0
$16$	−4.66165	+	0.990865i	−1.16541	+	0.247716i
$17$	−1.81551	+	4.72957i	−0.440326	+	1.14709i	0.516464	+	0.856309i	$0.327248\pi$
$17$	−1.81551	+	4.72957i	−0.440326	+	1.14709i	−0.956790	+	0.290780i	$0.906085\pi$
$18$	0.345403	+	1.28906i	0.0814123	+	0.303835i
$19$	−0.785987	+	7.47816i	−0.180318	+	1.71561i	0.413076	+	0.910696i	$0.364454\pi$
$19$	−0.785987	+	7.47816i	−0.180318	+	1.71561i	−0.593394	+	0.804912i	$0.702212\pi$
$20$		0			0
$21$	−1.16276	−	5.05345i	−0.253735	−	1.10275i
$22$	3.26382	+	0.516939i	0.695850	+	0.110212i
$23$	0.105109	+	2.00560i	0.0219167	+	0.418196i	0.987452	+	0.157922i	$0.0504796\pi$
$23$	0.105109	+	2.00560i	0.0219167	+	0.418196i	−0.965535	+	0.260274i	$0.916187\pi$
$24$	−2.30669	+	3.99530i	−0.470851	+	0.815537i
$25$		0			0
$26$	−3.00281	+	1.73368i	−0.588900	+	0.340002i
$27$	−3.76970	−	1.92076i	−0.725479	−	0.369650i
$28$	−0.724382	+	1.15736i	−0.136895	+	0.218720i
$29$	−4.12547	−	5.67823i	−0.766081	−	1.05442i	−0.996684	−	0.0813721i	$-0.974070\pi$
$29$	−4.12547	−	5.67823i	−0.766081	−	1.05442i	0.230603	−	0.973048i	$-0.425930\pi$
$30$		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	$0.673436\pi$
$32$	2.75469	−	0.738117i	0.486965	−	0.130482i
$33$	3.17315	−	2.56957i	0.552374	−	0.447304i
$34$	2.48320	−	7.64252i	0.425866	−	1.31068i
$35$		0			0
$36$	−0.134168	−	0.412927i	−0.0223614	−	0.0688212i
$37$	−2.22067	−	1.44212i	−0.365076	−	0.237083i	0.349044	−	0.937106i	$-0.386506\pi$
$37$	−2.22067	−	1.44212i	−0.365076	−	0.237083i	−0.714120	+	0.700023i	$0.753173\pi$
$38$	0.624225	−	11.9109i	0.101263	−	1.93221i
$39$	−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	$0.354858\pi$
$42$	2.26137	+	7.90831i	0.348936	+	1.22028i
$43$	−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
$47$	−2.45276	+	0.941527i	−0.357772	+	0.137336i	−0.530614	−	0.847614i	$-0.678038\pi$
$47$	−2.45276	+	0.941527i	−0.357772	+	0.137336i	0.172842	+	0.984950i	$0.444705\pi$
$48$	4.24056	−	8.32258i	0.612073	−	1.20126i
$49$	−1.68344	−	6.79456i	−0.240492	−	0.970651i
$50$		0			0
$51$	−4.96456	−	8.59887i	−0.695178	−	1.20408i
$52$	0.946077	−	0.614389i	0.131197	−	0.0852005i
$53$	7.17828	+	5.81286i	0.986013	+	0.798458i	0.979484	−	0.201521i	$-0.0645884\pi$
$53$	7.17828	+	5.81286i	0.986013	+	0.798458i	0.00652896	+	0.999979i	$0.497922\pi$
$54$	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
$58$	7.00627	+	8.65203i	0.919969	+	1.13607i
$59$	−7.04085	−	7.81965i	−0.916640	−	1.01803i	−0.999769	−	0.0214933i	$-0.993158\pi$
$59$	−7.04085	−	7.81965i	−0.916640	−	1.01803i	0.0831288	−	0.996539i	$-0.473509\pi$
$60$		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	$0.918381\pi$
$62$	−4.57440	−	8.97777i	−0.580949	−	1.14018i
$63$	1.99997	+	0.977274i	0.251972	+	0.123125i
$64$	4.76284	−	1.54754i	0.595355	−	0.193443i
$65$		0			0
$66$	−4.81306	+	4.33370i	−0.592447	+	0.533442i
$67$	−3.06559	−	1.17677i	−0.374521	−	0.143765i	0.163824	−	0.986490i	$-0.447617\pi$
$67$	−3.06559	−	1.17677i	−0.374521	−	0.143765i	−0.538345	+	0.842724i	$0.680950\pi$
$68$	−0.676649	+	2.52529i	−0.0820558	+	0.306236i
$69$	−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	$0.169984\pi$
$72$	−0.709703	−	1.84884i	−0.0836393	−	0.217888i
$73$	−4.51023	−	6.94515i	−0.527883	−	0.812868i	0.469666	−	0.882844i	$-0.344374\pi$
$73$	−4.51023	−	6.94515i	−0.527883	−	0.812868i	−0.997549	+	0.0699760i	$0.977708\pi$
$74$	3.63734	+	2.10002i	0.422832	+	0.244122i
$75$		0			0
$76$			3.88041i			0.445114i
$77$	4.22492	−	3.53982i	0.481474	−	0.403400i
$78$	1.06309	−	6.71211i	0.120372	−	0.759996i
$79$	1.08662	−	2.44058i	0.122254	−	0.274586i	−0.842043	−	0.539410i	$-0.818647\pi$
$79$	1.08662	−	2.44058i	0.122254	−	0.274586i	0.964297	+	0.264824i	$0.0853138\pi$
$80$		0			0
$81$	9.88106	−	4.39933i	1.09790	−	0.488814i
$82$	−13.6609	−	3.66043i	−1.50860	−	0.404227i
$83$	−0.456772	−	2.88395i	−0.0501373	−	0.316554i	−0.999993	−	0.00386431i	$-0.998770\pi$
$83$	−0.456772	−	2.88395i	−0.0501373	−	0.316554i	0.949855	−	0.312690i	$-0.101230\pi$
$84$	−0.869359	−	2.53086i	−0.0948548	−	0.276139i
$85$		0			0
$86$	1.48050	−	1.64427i	0.159647	−	0.177306i
$87$	13.7373	+	0.719940i	1.47279	+	0.0771857i
$88$	−4.89698	−	0.256640i	−0.522020	−	0.0273579i
$89$	8.47306	−	9.41028i	0.898142	−	0.997488i	−0.101854	−	0.994799i	$-0.532477\pi$
$89$	8.47306	−	9.41028i	0.898142	−	0.997488i	0.999996	−	0.00268884i	$-0.000855885\pi$
$90$		0			0
$91$	−1.10772	+	5.67637i	−0.116120	+	0.595045i
$92$	0.162132	+	1.02366i	0.0169035	+	0.106724i
$93$	−12.0258	−	3.22229i	−1.24701	−	0.334136i
$94$	3.80710	−	1.69503i	0.392672	−	0.174829i
$95$		0			0
$96$	−2.27344	+	5.10623i	−0.232032	+	0.521152i
$97$	−0.527619	+	3.33125i	−0.0535716	+	0.338237i	0.946316	+	0.323243i	$0.104773\pi$
$97$	−0.527619	+	3.33125i	−0.0535716	+	0.338237i	−0.999888	+	0.0149946i	$0.995227\pi$
$98$	3.23068	+	10.6231i	0.326348	+	1.07309i
$99$			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	$0.711787\pi$
$102$	8.57788	+	13.2088i	0.849337	+	1.30786i
$103$	−2.61554	−	6.81372i	−0.257717	−	0.671375i	−0.999999	−	0.00128815i	$-0.999590\pi$
$103$	−2.61554	−	6.81372i	−0.257717	−	0.671375i	0.742282	−	0.670087i	$-0.233743\pi$
$104$	4.16268	−	3.02436i	0.408184	−	0.296563i
$105$		0			0
$106$	−11.8532	−	8.61186i	−1.15129	−	0.836458i
$107$	3.00110	−	11.2003i	0.290127	−	1.08277i	−0.654883	−	0.755730i	$-0.727282\pi$
$107$	3.00110	−	11.2003i	0.290127	−	1.08277i	0.945011	−	0.327040i	$-0.106051\pi$
$108$	−2.03833	−	0.782443i	−0.196139	−	0.0752906i
$109$	−7.26460	+	6.54107i	−0.695822	+	0.626521i	−0.939184	−	0.343415i	$-0.888416\pi$
$109$	−7.26460	+	6.54107i	−0.695822	+	0.626521i	0.243362	+	0.969936i	$0.421750\pi$
$110$		0			0
$111$	4.93560	−	1.60367i	0.468467	−	0.152214i
$112$	5.53582	−	11.3289i	0.523086	−	1.07048i
$113$	−4.16132	−	8.16704i	−0.391464	−	0.768291i	0.608212	−	0.793775i	$-0.291887\pi$
$113$	−4.16132	−	8.16704i	−0.391464	−	0.768291i	−0.999675	+	0.0254843i	$0.991887\pi$
$114$	17.3722	+	15.6420i	1.62706	+	1.46501i
$115$		0			0
$116$	−2.42361	−	2.69170i	−0.225027	−	0.249918i
$117$	−1.15739	−	1.42926i	−0.107001	−	0.132135i
$118$	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
$122$	10.5742	+	8.56282i	0.957343	+	0.775241i
$123$	−14.6558	+	9.51757i	−1.32147	+	0.858170i
$124$	1.63906	+	2.83893i	0.147192	+	0.254944i
$125$		0			0
$126$	−3.24914	−	1.38201i	−0.289457	−	0.123119i
$127$	−1.11576	+	2.18980i	−0.0990074	+	0.194313i	−0.935197	−	0.354127i	$-0.884778\pi$
$127$	−1.11576	+	2.18980i	−0.0990074	+	0.194313i	0.836190	+	0.548440i	$0.184778\pi$
$128$	−12.7409	+	4.89078i	−1.12615	+	0.432288i
$129$	−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
$133$	−14.3006	−	13.8303i	−1.24002	−	1.19924i
$134$	4.95369	+	1.60955i	0.427934	+	0.139044i
$135$		0			0
$136$	−2.47928	+	11.6641i	−0.212597	+	1.00019i
$137$	0.475298	−	9.06922i	0.0406074	−	0.774836i	−0.900114	−	0.435655i	$-0.856517\pi$
$137$	0.475298	−	9.06922i	0.0406074	−	0.774836i	0.940721	−	0.339181i	$-0.110150\pi$
$138$	5.23640	+	3.40056i	0.445752	+	0.289475i
$139$	5.50579	+	16.9451i	0.466995	+	1.43726i	0.856456	+	0.516220i	$0.172661\pi$
$139$	5.50579	+	16.9451i	0.466995	+	1.43726i	−0.389461	+	0.921043i	$0.627339\pi$
$140$		0			0
$141$	1.59121	−	4.89724i	0.134004	−	0.412422i
$142$	−8.25134	+	6.68181i	−0.692437	+	0.560725i
$143$	−4.39874	+	1.17864i	−0.367841	+	0.0985627i
$144$	1.63087	+	3.66299i	0.135906	+	0.305249i
$145$		0			0
$146$	7.72092	+	10.6269i	0.638988	+	0.879491i
$147$	12.4256	+	5.81644i	1.02484	+	0.479732i
$148$	−1.21751	−	0.620350i	−0.100078	−	0.0509925i
$149$	−12.6781	+	7.31970i	−1.03863	+	0.599653i	−0.919445	−	0.393219i	$-0.871362\pi$
$149$	−12.6781	+	7.31970i	−1.03863	+	0.599653i	−0.119185	+	0.992872i	$0.538028\pi$
$150$		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	$0.939205\pi$
$152$	0.926314	+	17.6751i	0.0751340	+	1.43364i
$153$	4.20978	+	0.666764i	0.340341	+	0.0539047i
$154$	−6.39855	+	5.95794i	−0.515610	+	0.480104i
$155$		0			0
$156$	−0.231106	+	2.19882i	−0.0185033	+	0.176047i
$157$	1.11174	+	4.14906i	0.0887263	+	0.331131i	0.995994	−	0.0894230i	$-0.0285023\pi$
$157$	1.11174	+	4.14906i	0.0887263	+	0.331131i	−0.907267	+	0.420554i	$0.861836\pi$
$158$	−1.51863	+	3.95616i	−0.120816	+	0.314736i
$159$	−17.7078	+	3.76390i	−1.40432	+	0.298497i
$160$		0			0
$161$	−4.35040	−	3.05096i	−0.342859	−	0.240449i
$162$	−15.2867	+	7.78897i	−1.20104	+	0.611959i
$163$	−8.30781	+	12.7929i	−0.650718	+	1.00202i	0.347217	+	0.937785i	$0.387127\pi$
$163$	−8.30781	+	12.7929i	−0.650718	+	1.00202i	−0.997935	+	0.0642326i	$0.979540\pi$
$164$	4.50068	+	0.956649i	0.351444	+	0.0747017i
$165$		0			0
$166$	0.962956	+	4.53035i	0.0747399	+	0.351623i
$167$	16.7023	−	2.64539i	1.29246	−	0.204706i	0.527929	−	0.849289i	$-0.322969\pi$
$167$	16.7023	−	2.64539i	1.29246	−	0.204706i	0.764535	+	0.644583i	$0.222969\pi$
$168$	−4.56405	−	11.3204i	−0.352124	−	0.873390i
$169$	−4.83258	+	6.65148i	−0.371737	+	0.511652i
$170$		0			0
$171$	6.29165	−	0.661279i	0.481135	−	0.0505693i
$172$	−0.453010	+	0.559420i	−0.0345417	+	0.0426554i
$173$	18.7199	−	0.981067i	1.42325	−	0.0745892i	0.674906	−	0.737904i	$-0.264184\pi$
$173$	18.7199	−	0.981067i	1.42325	−	0.0745892i	0.748340	+	0.663315i	$0.230851\pi$
$174$	−21.8201			−1.65418
$175$		0			0
$176$	9.92847			0.748387
$177$	20.5949	−	1.07933i	1.54801	−	0.0811276i
$178$	−12.6404	+	15.6096i	−0.947439	+	1.16999i
$179$	9.75542	−	1.02534i	0.729155	−	0.0766372i	0.267326	−	0.963606i	$-0.413860\pi$
$179$	9.75542	−	1.02534i	0.729155	−	0.0766372i	0.461829	+	0.886969i	$0.347193\pi$
$180$		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	$0.190069\pi$
$182$	1.28343	−	9.08353i	0.0951344	−	0.673316i
$183$	16.6053	−	2.63002i	1.22750	−	0.194416i
$184$	0.982870	+	4.62404i	0.0724582	+	0.340889i
$185$		0			0
$186$	19.3167	+	4.10589i	1.41637	+	0.301059i
$187$	5.74811	−	8.85132i	0.420344	−	0.647272i
$188$	−1.20804	+	0.615528i	−0.0881055	+	0.0448920i
$189$	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	$0.401950\pi$
$192$	−3.51747	+	9.16332i	−0.253851	+	0.661305i
$193$	−1.81427	−	6.77095i	−0.130594	−	0.487384i	0.869383	−	0.494139i	$-0.164517\pi$
$193$	−1.81427	−	6.77095i	−0.130594	−	0.487384i	−0.999977	+	0.00675479i	$0.997850\pi$
$194$	0.559220	−	5.32062i	0.0401496	−	0.381998i
$195$		0			0
$196$	−1.23051	−	3.39636i	−0.0878935	−	0.242597i
$197$	−14.6392	−	2.31863i	−1.04300	−	0.165195i	−0.388650	−	0.921385i	$-0.627058\pi$
$197$	−14.6392	−	2.31863i	−1.04300	−	0.165195i	−0.654352	+	0.756190i	$0.727058\pi$
$198$	−0.145505	−	2.77639i	−0.0103406	−	0.197310i
$199$	−10.5072	+	18.1990i	−0.744835	+	1.29009i	0.205437	+	0.978670i	$0.434138\pi$
$199$	−10.5072	+	18.1990i	−0.744835	+	1.29009i	−0.950272	+	0.311422i	$0.899195\pi$
$200$		0			0
$201$	5.57358	−	3.21791i	0.393130	−	0.226974i
$202$	4.01325	+	2.04485i	0.282371	+	0.143875i
$203$	18.5579	+	0.661748i	1.30251	+	0.0464456i
$204$	−3.01181	−	4.14540i	−0.210869	−	0.290236i
$205$		0			0
$206$	4.70875	+	10.5760i	0.328074	+	0.736867i
$207$	1.63212	−	0.437326i	0.113440	−	0.0303963i
$208$	−8.09610	+	6.55609i	−0.561363	+	0.454583i
$209$	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	$-0.429132\pi$
$212$	3.99767	+	2.59612i	0.274561	+	0.178302i
$213$	−0.686599	+	13.1011i	−0.0470450	+	0.897672i
$214$	−3.82405	+	17.9907i	−0.261407	+	1.22982i
$215$		0			0
$216$	−9.47131	−	3.07741i	−0.644441	−	0.209392i
$217$	−16.3042	−	4.07787i	−1.10680	−	0.276824i
$218$	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
$222$	−7.68503	+	2.95001i	−0.515786	+	0.197992i
$223$	−5.91390	+	11.6067i	−0.396024	+	0.777241i	−0.999802	−	0.0199118i	$-0.993661\pi$
$223$	−5.91390	+	11.6067i	−0.396024	+	0.777241i	0.603778	+	0.797153i	$0.293661\pi$
$224$	−2.95331	+	6.94333i	−0.197326	+	0.463921i
$225$		0			0
$226$	7.26966	+	12.5914i	0.483571	+	0.837569i
$227$	2.59763	−	1.68692i	0.172411	−	0.111965i	−0.455549	−	0.890211i	$-0.650557\pi$
$227$	2.59763	−	1.68692i	0.172411	−	0.111965i	0.627960	+	0.778246i	$0.283890\pi$
$228$	−5.91047	−	4.78620i	−0.391430	−	0.316974i
$229$	0.487685	+	0.217131i	0.0322271	+	0.0143484i	0.422787	−	0.906229i	$-0.361052\pi$
$229$	0.487685	+	0.217131i	0.0322271	+	0.0143484i	−0.390560	+	0.920578i	$0.627719\pi$
$230$		0			0
$231$	0.180576	+	10.8013i	0.0118810	+	0.710674i
$232$	−11.6820	−	11.6820i	−0.766961	−	0.766961i
$233$	15.6193	+	19.2882i	1.02325	+	1.26361i	0.964149	+	0.265360i	$0.0854909\pi$
$233$	15.6193	+	19.2882i	1.02325	+	1.26361i	0.0591038	+	0.998252i	$0.481176\pi$
$234$	1.95199	+	2.16791i	0.127606	+	0.141721i
$235$		0			0
$236$	−4.03538	−	3.63348i	−0.262681	−	0.236519i
$237$	2.37712	+	4.66535i	0.154410	+	0.303047i
$238$	11.8759	+	17.6347i	0.769799	+	1.14309i
$239$	−25.9462	+	8.43043i	−1.67832	+	0.545320i	−0.984585	−	0.174910i	$-0.944037\pi$
$239$	−25.9462	+	8.43043i	−1.67832	+	0.545320i	−0.693736	+	0.720229i	$0.744037\pi$
$240$		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	$0.0552109\pi$
$242$	9.86243	+	3.78583i	0.633981	+	0.243362i
$243$	−2.20163	+	8.21660i	−0.141235	+	0.527095i
$244$	−3.58129	−	2.60196i	−0.229269	−	0.166574i
$245$		0			0
$246$	22.4251	−	16.2928i	1.42977	−	1.03879i
$247$	5.89043	+	15.3451i	0.374799	+	0.976386i
$248$	8.14354	+	12.5400i	0.517116	+	0.796288i
$249$	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	$0.923964\pi$
$252$	1.07916	+	0.393683i	0.0679806	+	0.0247997i
$253$	0.654514	−	4.13244i	0.0411489	−	0.259804i
$254$	1.58561	−	3.56134i	0.0994900	−	0.223458i
$255$		0			0
$256$	10.6261	−	4.73103i	0.664130	−	0.295690i
$257$	13.2229	+	3.54307i	0.824824	+	0.221011i	0.646454	−	0.762953i	$-0.276251\pi$
$257$	13.2229	+	3.54307i	0.824824	+	0.221011i	0.178369	+	0.983964i	$0.442918\pi$
$258$	0.678378	+	4.28311i	0.0422340	+	0.266655i
$259$	6.62555	−	2.27590i	0.411691	−	0.141417i
$260$		0			0
$261$	−3.95126	+	4.38832i	−0.244577	+	0.271630i
$262$	−8.82533	−	0.462516i	−0.545231	−	0.0285743i
$263$	−19.5402	−	1.02406i	−1.20490	−	0.0631462i	−0.560711	−	0.828012i	$-0.689472\pi$
$263$	−19.5402	−	1.02406i	−1.20490	−	0.0631462i	−0.644190	+	0.764865i	$0.722805\pi$
$264$	6.43097	−	7.14231i	0.395799	−	0.439579i
$265$		0			0
$266$	23.8008	+	20.7205i	1.45932	+	1.27046i
$267$	3.88242	+	24.5127i	0.237600	+	1.50015i
$268$	−1.63683	−	0.438587i	−0.0999853	−	0.0267910i
$269$	8.43550	−	3.75573i	0.514321	−	0.228991i	−0.133128	−	0.991099i	$-0.542502\pi$
$269$	8.43550	−	3.75573i	0.514321	−	0.228991i	0.647450	+	0.762108i	$0.275836\pi$
$270$		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	$0.122637\pi$
$272$	3.77692	−	23.8465i	0.229010	−	1.44591i
$273$	−7.27970	−	8.68860i	−0.440588	−	0.525858i
$274$			14.4054i			0.870263i
$275$		0			0
$276$	−1.75918	−	1.01566i	−0.105890	−	0.0611356i
$277$	−10.5883	−	16.3045i	−0.636188	−	0.979643i	−0.998860	−	0.0477267i	$-0.984802\pi$
$277$	−10.5883	−	16.3045i	−0.636188	−	0.979643i	0.362673	−	0.931917i	$-0.381864\pi$
$278$	−10.1281	−	26.3845i	−0.607441	−	1.58244i
$279$	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	$0.716296\pi$
$282$	−2.11398	+	7.88949i	−0.125886	+	0.469812i
$283$	−24.6453	−	9.46043i	−1.46501	−	0.562364i	−0.510324	−	0.859982i	$-0.670475\pi$
$283$	−24.6453	−	9.46043i	−1.46501	−	0.562364i	−0.954685	+	0.297618i	$0.903808\pi$
$284$	2.56704	−	2.31137i	0.152326	−	0.137155i
$285$		0			0
$286$	6.86990	−	2.23217i	0.406226	−	0.131991i
$287$	−19.5666	+	13.1769i	−1.15498	+	0.777805i
$288$	−1.08929	−	2.13786i	−0.0641873	−	0.125975i
$289$	−6.43928	−	5.79795i	−0.378781	−	0.341056i
$290$		0			0
$291$	−4.42323	−	4.91250i	−0.259294	−	0.287976i
$292$	−2.68943	−	3.32116i	−0.157387	−	0.194356i
$293$	−4.33790	−	4.33790i	−0.253423	−	0.253423i	0.568950	−	0.822372i	$-0.307350\pi$
$293$	−4.33790	−	4.33790i	−0.253423	−	0.253423i	−0.822372	+	0.568950i	$0.807350\pi$
$294$	−20.1654	−	8.18193i	−1.17607	−	0.477180i
$295$		0			0
$296$	−5.69377	−	2.53503i	−0.330944	−	0.147346i
$297$	6.84976	+	5.54683i	0.397463	+	0.321860i
$298$	19.4749	−	12.6471i	1.12815	−	0.732629i
$299$	2.19506	+	3.80196i	0.126944	+	0.219873i
$300$		0			0
$301$	−0.447061	−	3.66334i	−0.0257682	−	0.211151i
$302$	11.5977	−	22.7617i	0.667372	−	1.30979i
$303$	5.19574	−	1.99446i	0.298488	−	0.114579i
$304$	−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	−0.251239	−	0.967925i	$-0.580838\pi$
$307$	12.5574	−	12.5574i	0.716687	−	0.716687i	0.967925	+	0.251239i	$0.0808379\pi$
$308$	1.97740	−	2.04465i	0.112673	−	0.116504i
$309$	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	$0.124377\pi$
$312$	−0.527784	+	10.0707i	−0.0298799	+	0.570142i
$313$	6.40601	+	4.16011i	0.362089	+	0.235143i	0.712842	−	0.701325i	$-0.247408\pi$
$313$	6.40601	+	4.16011i	0.362089	+	0.235143i	−0.350753	+	0.936468i	$0.614074\pi$
$314$	−2.10547	−	6.47997i	−0.118818	−	0.365686i
$315$		0			0
$316$	0.426032	−	1.31119i	0.0239662	−	0.0737603i
$317$	10.9676	−	8.88140i	0.616003	−	0.498829i	−0.269785	−	0.962921i	$-0.586952\pi$
$317$	10.9676	−	8.88140i	0.616003	−	0.498829i	0.885787	+	0.464092i	$0.153619\pi$
$318$	27.7372	−	7.43217i	1.55543	−	0.416775i
$319$	5.94723	+	13.3577i	0.332981	+	0.747888i
$320$		0			0
$321$	13.3581	+	18.3858i	0.745575	+	1.02620i
$322$	7.14446	+	4.47168i	0.398145	+	0.249197i
$323$	−33.9415	−	17.2941i	−1.88856	−	0.962268i
$324$	4.83394	−	2.79088i	0.268552	−	0.155049i
$325$		0			0
$326$	12.0978	−	20.9541i	0.670037	−	1.16054i
$327$	−1.00272	−	19.1330i	−0.0554505	−	1.05806i
$328$	20.7288	+	3.28311i	1.14455	+	0.181280i
$329$	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	$-0.0579841\pi$
$332$	−0.389997	−	1.45549i	−0.0214038	−	0.0798802i
$333$	−0.798347	+	2.07976i	−0.0437491	+	0.113970i
$334$	−26.2374	+	5.57694i	−1.43565	+	0.305156i
$335$		0			0
$336$	10.4277	+	22.4053i	0.568876	+	1.22231i
$337$	−22.9028	+	11.6695i	−1.24759	+	0.635681i	−0.947965	−	0.318375i	$-0.896863\pi$
$337$	−22.9028	+	11.6695i	−1.24759	+	0.635681i	−0.299629	+	0.954056i	$0.596863\pi$
$338$	7.10280	−	10.9374i	0.386341	−	0.594914i
$339$	17.5723	+	3.73512i	0.954398	+	0.202864i
$340$		0			0
$341$	−2.75139	−	12.9443i	−0.148996	−	0.700973i
$342$	−9.91130	+	1.56980i	−0.535942	+	0.0848848i
$343$	16.9024	+	7.57025i	0.912644	+	0.408755i
$344$	−1.92990	+	2.65628i	−0.104053	+	0.143217i
$345$		0			0
$346$	−29.5715	+	3.10809i	−1.58977	+	0.167092i
$347$	−2.87187	+	3.54647i	−0.154170	+	0.190384i	−0.848379	−	0.529389i	$-0.822421\pi$
$347$	−2.87187	+	3.54647i	−0.154170	+	0.190384i	0.694209	+	0.719774i	$0.255754\pi$
$348$	7.08921	−	0.371530i	0.380022	−	0.0199161i
$349$	−35.4204			−1.89601			−0.948005	−	0.318256i	$-0.896903\pi$
$349$	−35.4204			−1.89601			−0.948005	+	0.318256i	$0.896903\pi$
$350$		0			0
$351$	−9.24834			−0.493640
$352$	−5.93307	+	0.310939i	−0.316234	+	0.0165731i
$353$	−6.72945	+	8.31018i	−0.358173	+	0.442306i	−0.924101	−	0.382148i	$-0.875184\pi$
$353$	−6.72945	+	8.31018i	−0.358173	+	0.442306i	0.565929	+	0.824454i	$0.308518\pi$
$354$	−32.5334	+	3.41940i	−1.72913	+	0.181739i
$355$		0			0
$356$	3.84101	−	5.28670i	0.203573	−	0.280194i
$357$	26.0116	+	3.67525i	1.37668	+	0.194515i
$358$	−15.3678	+	2.43402i	−0.812214	+	0.128642i
$359$	−0.793602	−	3.73360i	−0.0418847	−	0.197052i	0.952230	−	0.305380i	$-0.0987836\pi$
$359$	−0.793602	−	3.73360i	−0.0418847	−	0.197052i	−0.994115	+	0.108328i	$0.965450\pi$
$360$		0			0
$361$	−36.7204	−	7.80515i	−1.93265	−	0.410797i
$362$	−0.725151	+	1.11663i	−0.0381131	+	0.0586890i
$363$	11.6304	−	5.92598i	0.610437	−	0.311033i
$364$	−0.262315	+	2.97304i	−0.0137490	+	0.155829i
$365$		0			0
$366$	−26.0850	+	5.54453i	−1.36348	+	0.289817i
$367$	2.98397	−	7.77350i	0.155762	−	0.405773i	−0.833387	−	0.552690i	$-0.813601\pi$
$367$	2.98397	−	7.77350i	0.155762	−	0.405773i	0.989149	+	0.146916i	$0.0469348\pi$
$368$	−2.47726	−	9.24526i	−0.129136	−	0.481943i
$369$	0.784116	−	7.46037i	0.0408195	−	0.388371i
$370$		0			0
$371$	−23.8158	+	5.47982i	−1.23645	+	0.284498i
$372$	−6.34579	−	1.00507i	−0.329014	−	0.0521107i
$373$	0.912274	+	17.4072i	0.0472358	+	0.901312i	0.914780	+	0.403952i	$0.132364\pi$
$373$	0.912274	+	17.4072i	0.0472358	+	0.901312i	−0.867544	+	0.497360i	$0.834303\pi$
$374$	−8.37041	+	14.4980i	−0.432824	+	0.749672i
$375$		0			0
$376$	−5.35564	+	3.09208i	−0.276196	+	0.159462i
$377$	−13.6702	−	6.96529i	−0.704049	−	0.358731i
$378$	−15.6834	+	8.32419i	−0.806667	+	0.428150i
$379$	−6.41691	−	8.83212i	−0.329614	−	0.453675i	0.611758	−	0.791045i	$-0.290463\pi$
$379$	−6.41691	−	8.83212i	−0.329614	−	0.453675i	−0.941372	+	0.337370i	$0.890463\pi$
$380$		0			0
$381$	−1.95919	−	4.40042i	−0.100372	−	0.225440i
$382$	−4.16868	+	1.11699i	−0.213288	+	0.0571504i
$383$	−12.8953	+	10.4424i	−0.658919	+	0.533582i	−0.899430	−	0.437064i	$-0.856018\pi$
$383$	−12.8953	+	10.4424i	−0.658919	+	0.533582i	0.240511	+	0.970646i	$0.422685\pi$
$384$	8.26557	−	25.4388i	0.421800	−	1.29817i
$385$		0			0
$386$	3.43596	+	10.5748i	0.174886	+	0.538244i
$387$	0.984236	+	0.639170i	0.0500315	+	0.0324909i
$388$	−0.0910931	+	1.73816i	−0.00462455	+	0.0882417i
$389$	3.99680	−	18.8035i	0.202646	−	0.953373i	−0.752810	−	0.658238i	$-0.771302\pi$
$389$	3.99680	−	18.8035i	0.202646	−	0.953373i	0.955456	−	0.295135i	$-0.0953646\pi$
$390$		0			0
$391$	−9.67645	−	3.14407i	−0.489359	−	0.159002i
$392$	−6.41568	−	15.1765i	−0.324041	−	0.766531i
$393$	−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
$397$	−1.13583	+	0.436005i	−0.0570058	+	0.0218825i	−0.386704	−	0.922204i	$-0.626386\pi$
$397$	−1.13583	+	0.436005i	−0.0570058	+	0.0218825i	0.329698	+	0.944086i	$0.393053\pi$
$398$	15.1329	−	29.7001i	0.758546	−	1.48873i
$399$	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	$0.795544\pi$
$402$	−8.56160	+	5.55997i	−0.427014	+	0.277306i
$403$	10.7911	+	8.73849i	0.537545	+	0.435295i
$404$	−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
$408$	−14.7082	−	18.1631i	−0.728166	−	0.899210i
$409$	16.5891	+	18.4241i	0.820280	+	0.911014i	0.997318	−	0.0731905i	$-0.0233181\pi$
$409$	16.5891	+	18.4241i	0.820280	+	0.911014i	−0.177038	+	0.984204i	$0.556651\pi$
$410$		0			0
$411$	13.2276	+	11.9102i	0.652468	+	0.587485i
$412$	−1.70992	−	3.35591i	−0.0842419	−	0.165334i
$413$	27.7732	−	1.92153i	1.36663	−	0.0945522i
$414$	−2.54904	+	0.828232i	−0.125278	+	0.0407054i
$415$		0			0
$416$	4.63276	−	4.17136i	0.227140	−	0.204518i
$417$	−32.6010	−	12.5143i	−1.59648	−	0.612829i
$418$	−6.43108	+	24.0011i	−0.314554	+	1.17393i
$419$	19.6973	+	14.3109i	0.962276	+	0.699135i	0.953678	−	0.300828i	$-0.0972631\pi$
$419$	19.6973	+	14.3109i	0.962276	+	0.699135i	0.00859807	+	0.999963i	$0.497263\pi$
$420$		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	$0.357853\pi$
$422$	14.1916	+	36.9703i	0.690835	+	1.79969i
$423$	1.20388	+	1.85381i	0.0585345	+	0.0901352i
$424$	18.8290	+	10.8709i	0.914415	+	0.527938i
$425$		0			0
$426$		−	20.8096i		−	1.00823i
$427$	22.3533	−	3.92451i	1.08175	−	0.189920i
$428$	0.936083	−	5.91019i	0.0452473	−	0.285680i
$429$	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	$0.223500\pi$
$432$	19.4763	+	5.21865i	0.937052	+	0.251082i
$433$	−3.94891	−	24.9324i	−0.189773	−	1.19818i	−0.880139	−	0.474717i	$-0.842551\pi$
$433$	−3.94891	−	24.9324i	−0.189773	−	1.19818i	0.690366	−	0.723460i	$-0.257449\pi$
$434$	26.1650	+	5.10597i	1.25596	+	0.245095i
$435$		0			0
$436$	−3.37556	+	3.74894i	−0.161660	+	0.179542i
$437$	−15.0808	−	0.790352i	−0.721413	−	0.0378077i
$438$	−25.7096	−	1.34739i	−1.22845	−	0.0643805i
$439$	18.6654	−	20.7300i	0.890849	−	0.989388i	−0.109141	−	0.994026i	$-0.534810\pi$
$439$	18.6654	−	20.7300i	0.890849	−	0.989388i	0.999989	+	0.00463865i	$0.00147653\pi$
$440$		0			0
$441$	−5.29712	+	2.57392i	−0.252244	+	0.122568i
$442$	−2.74789	−	17.3495i	−0.130704	−	0.825232i
$443$	−29.5785	−	7.92554i	−1.40532	−	0.376554i	−0.525066	−	0.851061i	$-0.675960\pi$
$443$	−29.5785	−	7.92554i	−1.40532	−	0.376554i	−0.880252	+	0.474507i	$0.842626\pi$
$444$	2.44659	−	1.08929i	0.116110	−	0.0516955i
$445$		0			0
$446$	8.40428	−	18.8763i	0.397954	−	0.893820i
$447$	4.48846	−	28.3390i	0.212297	−	1.34039i
$448$	−4.54087	+	12.4474i	−0.214536	+	0.588084i
$449$		−	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
$452$	−2.57626	−	3.96710i	−0.121177	−	0.186597i
$453$	−11.3119	−	29.4685i	−0.531478	−	1.38455i
$454$	−3.97469	+	2.88778i	−0.186541	+	0.135530i
$455$		0			0
$456$	−28.0645	−	20.3900i	−1.31424	−	0.954851i
$457$	−10.4479	+	38.9922i	−0.488733	+	1.82398i	0.0738955	+	0.997266i	$0.476457\pi$
$457$	−10.4479	+	38.9922i	−0.488733	+	1.82398i	−0.562628	+	0.826710i	$0.690210\pi$
$458$	−0.790535	−	0.303458i	−0.0369393	−	0.0141797i
$459$	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	$0.263407\pi$
$462$	−1.18272	−	17.0946i	−0.0550249	−	0.795315i
$463$	15.5311	+	30.4814i	0.721790	+	1.41659i	0.901458	+	0.432866i	$0.142498\pi$
$463$	15.5311	+	30.4814i	0.721790	+	1.41659i	−0.179668	+	0.983727i	$0.557502\pi$
$464$	24.8579	+	22.3821i	1.15400	+	1.03906i
$465$		0			0
$466$	−26.3427	−	29.2565i	−1.22030	−	1.35528i
$467$	4.20233	+	5.18944i	0.194460	+	0.240139i	0.865045	−	0.501695i	$-0.167290\pi$
$467$	4.20233	+	5.18944i	0.194460	+	0.240139i	−0.670584	+	0.741833i	$0.733957\pi$
$468$	−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
$472$	−19.2484	−	15.5870i	−0.885978	−	0.717451i
$473$	2.43712	−	1.58268i	0.112059	−	0.0727718i
$474$	−4.15273	−	7.19274i	−0.190741	−	0.330374i
$475$		0			0
$476$	−4.15867	−	5.52721i	−0.190612	−	0.253339i
$477$	3.52805	−	6.92419i	0.161538	−	0.317037i
$478$	40.3998	−	15.5080i	1.84785	−	0.709321i
$479$	0.529424	+	5.03713i	0.0241900	+	0.230153i	0.999937	+	0.0112499i	$0.00358104\pi$
$479$	0.529424	+	5.03713i	0.0241900	+	0.230153i	−0.975747	+	0.218903i	$0.929752\pi$
$480$		0			0
$481$	−5.75631	−	0.605013i	−0.262465	−	0.0275862i
$482$	−21.4697	+	21.4697i	−0.977920	+	0.977920i
$483$	10.0130	−	2.86319i	0.455606	−	0.130280i
$484$	−3.26870	−	1.06207i	−0.148577	−	0.0482758i
$485$		0			0
$486$	2.80535	−	13.1981i	0.127253	−	0.598680i
$487$	−0.984042	+	18.7766i	−0.0445912	+	0.850851i	0.881183	+	0.472775i	$0.156748\pi$
$487$	−0.984042	+	18.7766i	−0.0445912	+	0.850851i	−0.925774	+	0.378076i	$0.876586\pi$
$488$	−16.9338	−	10.9969i	−0.766556	−	0.497807i
$489$	−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	$0.898339\pi$
$492$	−7.00838	+	5.67527i	−0.315962	+	0.255861i
$493$	34.3454	−	9.20282i	1.54684	−	0.414474i
$494$	−10.6045	−	23.8182i	−0.477121	−	1.07163i
$495$		0			0
$496$	−17.7943	−	24.4918i	−0.798989	−	1.09971i
$497$	−0.631101	+	17.6984i	−0.0283088	+	0.793884i
$498$	−8.08815	−	4.12112i	−0.362439	−	0.184672i
$499$	−2.61768	+	1.51132i	−0.117183	+	0.0676558i	−0.557446	−	0.830213i	$-0.688219\pi$
$499$	−2.61768	+	1.51132i	−0.117183	+	0.0676558i	0.440263	+	0.897869i	$0.354885\pi$
$500$		0			0
$501$	−16.5717	+	28.7031i	−0.740370	+	1.28236i
$502$	−0.622380	−	11.8757i	−0.0277782	−	0.530039i
$503$	13.8594	+	2.19511i	0.617958	+	0.0978750i	0.457562	−	0.889178i	$-0.348723\pi$
$503$	13.8594	+	2.19511i	0.617958	+	0.0978750i	0.160396	+	0.987053i	$0.448723\pi$
$504$	5.00950	+	1.53560i	0.223141	+	0.0684009i
$505$		0			0
$506$	−0.693715	+	6.60026i	−0.0308394	+	0.293417i
$507$	−4.17060	−	15.5649i	−0.185223	−	0.691260i
$508$	−0.454516	+	1.18405i	−0.0201659	+	0.0525339i
$509$	−22.1880	+	4.71620i	−0.983465	+	0.209042i	−0.671462	−	0.741039i	$-0.734333\pi$
$509$	−22.1880	+	4.71620i	−0.983465	+	0.209042i	−0.312003	+	0.950081i	$0.601000\pi$
$510$		0			0
$511$	21.8251	+	1.92565i	0.965483	+	0.0851858i
$512$	7.88049	−	4.01531i	0.348272	−	0.177453i
$513$	17.3267	−	26.6808i	0.764992	−	1.17798i
$514$	−21.2397	−	4.51464i	−0.936843	−	0.199132i
$515$		0			0
$516$	−0.293330	−	1.38001i	−0.0129131	−	0.0607514i
$517$	5.40593	−	0.856215i	0.237752	−	0.0376563i
$518$	−10.3062	+	4.15513i	−0.452827	+	0.182566i
$519$	−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	$0.838645\pi$
$522$	5.89463	−	7.27927i	0.258001	−	0.318605i
$523$	−26.3887	+	1.38297i	−1.15390	+	0.0604732i	−0.619666	−	0.784865i	$-0.712732\pi$
$523$	−26.3887	+	1.38297i	−1.15390	+	0.0604732i	−0.534231	+	0.845339i	$0.679399\pi$
$524$	2.87517			0.125602
$525$		0			0
$526$	31.0374			1.35329
$527$	−32.1367	+	1.68421i	−1.39990	+	0.0733655i
$528$	−12.2460	+	15.1226i	−0.532940	+	0.658126i
$529$	18.8626	−	1.98254i	0.820114	−	0.0861975i
$530$		0			0
$531$	−5.20358	+	7.16212i	−0.225816	+	0.310809i
$532$	−8.08554	−	6.32672i	−0.350553	−	0.274298i
$533$	19.2501	−	3.04892i	0.833815	−	0.132063i
$534$	−8.18483	−	38.5066i	−0.354192	−	1.66634i
$535$		0			0
$536$	−7.56039	−	1.60701i	−0.326559	−	0.0694123i
$537$	−10.4708	+	16.1237i	−0.451850	+	0.695788i
$538$	−13.0503	+	6.64948i	−0.562640	+	0.286679i
$539$	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	$0.399325\pi$
$542$	−0.628817	+	1.63812i	−0.0270100	+	0.0703634i
$543$	0.425791	+	1.58907i	0.0182724	+	0.0681937i
$544$	−1.51020	+	14.3685i	−0.0647491	+	0.616046i
$545$		0			0
$546$	12.2526	+	13.1587i	0.524362	+	0.563141i
$547$	17.1842	+	2.72171i	0.734743	+	0.116372i	0.512582	−	0.858638i	$-0.328689\pi$
$547$	17.1842	+	2.72171i	0.734743	+	0.116372i	0.222161	+	0.975010i	$0.428689\pi$
$548$	−0.245281	−	4.68023i	−0.0104779	−	0.199930i
$549$	−3.60848	+	6.25007i	−0.154006	+	0.266747i
$550$		0			0
$551$	45.7053	−	26.3880i	1.94711	−	1.12416i
$552$	−8.25542	−	4.20635i	−0.351374	−	0.179034i
$553$	3.31374	+	6.24333i	0.140915	+	0.265493i
$554$	18.1257	+	24.9479i	0.770088	+	1.05994i
$555$		0			0
$556$	3.73980	+	8.39972i	0.158603	+	0.356228i
$557$	10.5747	−	2.83348i	0.448064	−	0.120058i	−0.0277296	−	0.999615i	$-0.508828\pi$
$557$	10.5747	−	2.83348i	0.448064	−	0.120058i	0.475793	+	0.879557i	$0.342161\pi$
$558$	−6.58809	+	5.33493i	−0.278896	+	0.225846i
$559$	−0.942233	+	2.89989i	−0.0398522	+	0.122652i
$560$		0			0
$561$	6.39205	+	19.6727i	0.269872	+	0.830582i
$562$	2.28237	+	1.48219i	0.0962760	+	0.0625224i
$563$	−0.104267	+	1.98954i	−0.00439434	+	0.0838491i	−0.999946	−	0.0103653i	$-0.996701\pi$
$563$	−0.104267	+	1.98954i	−0.00439434	+	0.0838491i	0.995552	+	0.0942144i	$0.0300339\pi$
$564$	0.552486	−	2.59924i	0.0232639	−	0.109448i
$565$		0			0
$566$	39.8243	+	12.9397i	1.67394	+	0.543896i
$567$	−6.94351	+	27.7617i	−0.291600	+	1.16588i
$568$	11.1410	−	11.1410i	0.467466	−	0.467466i
$569$	−31.7588	−	3.33799i	−1.33140	−	0.139936i	−0.588042	−	0.808831i	$-0.700101\pi$
$569$	−31.7588	−	3.33799i	−1.33140	−	0.139936i	−0.743357	+	0.668895i	$0.766768\pi$
$570$		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	$0.866700\pi$
$572$	−2.19398	+	0.842191i	−0.0917351	+	0.0352138i
$573$	−2.42093	+	4.75134i	−0.101136	+	0.198490i
$574$	29.9003	−	22.4969i	1.24801	−	0.939004i
$575$		0			0
$576$	−2.10668	−	3.64889i	−0.0877785	−	0.152037i
$577$	6.81017	−	4.42257i	0.283511	−	0.184114i	−0.395047	−	0.918661i	$-0.629272\pi$
$577$	6.81017	−	4.42257i	0.283511	−	0.184114i	0.678558	+	0.734547i	$0.262605\pi$
$578$	10.6814	+	8.64959i	0.444286	+	0.359776i
$579$	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
$583$	−12.1098	−	14.9543i	−0.501536	−	0.619346i
$584$	−13.0430	−	14.4858i	−0.539725	−	0.599425i
$585$		0			0
$586$	7.23150	+	6.51127i	0.298730	+	0.268978i
$587$	3.16940	+	6.22031i	0.130815	+	0.256739i	0.947118	−	0.320884i	$-0.103980\pi$
$587$	3.16940	+	6.22031i	0.130815	+	0.256739i	−0.816303	+	0.577624i	$0.803980\pi$
$588$	6.69092	+	2.31490i	0.275929	+	0.0954650i
$589$	−45.4270	+	14.7601i	−1.87179	+	0.608181i
$590$		0			0
$591$	21.5880	−	19.4379i	0.888013	−	0.799570i
$592$	11.7809	+	4.52228i	0.484194	+	0.185865i
$593$	−2.19397	+	8.18799i	−0.0900954	+	0.336240i	−0.996230	−	0.0867484i	$-0.972352\pi$
$593$	−2.19397	+	8.18799i	−0.0900954	+	0.336240i	0.906135	+	0.422989i	$0.139019\pi$
$594$	−11.3107	−	8.21773i	−0.464085	−	0.337177i
$595$		0			0
$596$	−6.11193	+	4.44058i	−0.250355	+	0.181893i
$597$	−14.7600	−	38.4512i	−0.604087	−	1.57370i
$598$	−3.79268	−	5.84022i	−0.155094	−	0.238824i
$599$	−20.6751	−	11.9368i	−0.844762	−	0.487723i	0.0141183	−	0.999900i	$-0.495506\pi$
$599$	−20.6751	−	11.9368i	−0.844762	−	0.487723i	−0.858880	+	0.512177i	$0.828839\pi$
$600$		0			0
$601$			9.32470i			0.380362i	0.981749	+	0.190181i	$0.0609075\pi$
$601$			9.32470i			0.380362i	−0.981749	+	0.190181i	$0.939092\pi$
$602$	1.01228	+	5.76574i	0.0412573	+	0.234994i
$603$	−0.432180	+	2.72868i	−0.0175997	+	0.111120i
$604$	−3.38046	+	7.59263i	−0.137549	+	0.308940i
$605$		0			0
$606$	−8.06467	+	3.59062i	−0.327605	+	0.145859i
$607$	21.5323	+	5.76957i	0.873971	+	0.234180i	0.667804	−	0.744337i	$-0.267234\pi$
$607$	21.5323	+	5.76957i	0.873971	+	0.234180i	0.206167	+	0.978517i	$0.433901\pi$
$608$	3.35461	+	21.1802i	0.136047	+	0.858969i
$609$	−23.8977	+	27.4503i	−0.968384	+	1.11234i
$610$		0			0
$611$	−3.84284	+	4.26790i	−0.155465	+	0.172661i
$612$	2.19655	+	0.115116i	0.0887903	+	0.00465330i
$613$	20.6108	+	1.08016i	0.832461	+	0.0436274i	0.463804	−	0.885938i	$-0.346484\pi$
$613$	20.6108	+	1.08016i	0.832461	+	0.0436274i	0.368657	+	0.929565i	$0.379818\pi$
$614$	−18.8488	+	20.9338i	−0.760677	+	0.844818i
$615$		0			0
$616$	8.51891	−	9.78531i	0.343237	−	0.394261i
$617$	1.89563	+	11.9685i	0.0763151	+	0.481835i	0.996013	+	0.0892079i	$0.0284335\pi$
$617$	1.89563	+	11.9685i	0.0763151	+	0.481835i	−0.919698	+	0.392627i	$0.871566\pi$
$618$	−21.9168	−	5.87259i	−0.881624	−	0.236230i
$619$	14.7437	−	6.56430i	0.592597	−	0.263841i	−0.0884500	−	0.996081i	$-0.528191\pi$
$619$	14.7437	−	6.56430i	0.592597	−	0.263841i	0.681048	+	0.732239i	$0.261525\pi$
$620$		0			0
$621$	3.45604	−	7.76240i	0.138686	−	0.311494i
$622$	1.57807	−	9.96354i	0.0632749	−	0.399502i
$623$	5.79335	+	32.9979i	0.232106	+	1.32203i
$624$		−	20.4181i		−	0.817376i
$625$		0			0
$626$	−10.4927	−	6.05796i	−0.419372	−	0.242125i
$627$	16.7216	+	25.7490i	0.667795	+	1.02831i
$628$	0.794388	+	2.06945i	0.0316995	+	0.0825801i
$629$	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	$0.406411\pi$
$632$	1.62756	−	6.07412i	0.0647407	−	0.241616i
$633$	45.6809	+	17.5352i	1.81565	+	0.696963i
$634$	−16.6358	+	14.9789i	−0.660691	+	0.594889i
$635$		0			0
$636$	−8.88511	+	2.88695i	−0.352318	+	0.114475i
$637$	−10.0217	−	11.5630i	−0.397074	−	0.458143i
$638$	−10.5295	−	20.6654i	−0.416868	−	0.818149i
$639$	−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	$-0.493214\pi$
$642$	−22.6860	−	28.0148i	−0.895344	−	1.10566i
$643$	15.3835	+	15.3835i	0.606667	+	0.606667i	0.942074	−	0.335406i	$-0.108874\pi$
$643$	15.3835	+	15.3835i	0.606667	+	0.606667i	−0.335406	+	0.942074i	$0.608874\pi$
$644$	−2.39733	−	1.33117i	−0.0944681	−	0.0524555i
$645$		0			0
$646$	55.2002	+	24.5767i	2.17182	+	0.966958i
$647$	−27.3587	−	22.1547i	−1.07558	−	0.870990i	−0.0834914	−	0.996508i	$-0.526607\pi$
$647$	−27.3587	−	22.1547i	−1.07558	−	0.870990i	−0.992091	+	0.125519i	$0.959940\pi$
$648$	21.3522	−	13.8663i	0.838793	−	0.544718i
$649$	10.9605	+	18.9842i	0.430238	+	0.745193i
$650$		0			0
$651$	26.3213	−	19.8041i	1.03161	−	0.776184i
$652$	−3.57373	+	7.01384i	−0.139958	+	0.274683i
$653$	−28.9416	+	11.1096i	−1.13257	+	0.434754i	−0.851198	−	0.524844i	$-0.824124\pi$
$653$	−28.9416	+	11.1096i	−1.13257	+	0.434754i	−0.281374	+	0.959598i	$0.590790\pi$
$654$	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
$658$	−2.67528	+	10.6964i	−0.104293	+	0.416989i
$659$	6.75492	+	2.19481i	0.263134	+	0.0854976i	0.437613	−	0.899163i	$-0.355824\pi$
$659$	6.75492	+	2.19481i	0.263134	+	0.0854976i	−0.174479	+	0.984661i	$0.555824\pi$
$660$		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	$0.0964472\pi$
$662$	−0.854740	+	16.3094i	−0.0332204	+	0.633884i
$663$	−18.2029	−	11.8211i	−0.706941	−	0.459093i
$664$	−2.12387	−	6.53659i	−0.0824220	−	0.253669i
$665$		0			0
$666$	1.09196	−	3.36069i	0.0423124	−	0.130224i
$667$	10.9546	−	8.87088i	0.424165	−	0.343482i
$668$	8.42942	−	2.25866i	0.326144	−	0.0873901i
$669$	−10.3844	−	23.3238i	−0.401484	−	0.901749i
$670$		0			0
$671$	10.5039	+	14.4574i	0.405498	+	0.558120i
$672$	−6.93307	−	13.0624i	−0.267449	−	0.503894i
$673$	11.7311	+	5.97729i	0.452201	+	0.230408i	0.665231	−	0.746638i	$-0.268333\pi$
$673$	11.7311	+	5.97729i	0.452201	+	0.230408i	−0.213030	+	0.977046i	$0.568333\pi$
$674$	35.3100	−	20.3863i	1.36009	−	0.785249i
$675$		0			0
$676$	−2.12143	+	3.67442i	−0.0815934	+	0.141324i
$677$	2.48338	+	47.3857i	0.0954440	+	1.82118i	0.457706	+	0.889104i	$0.348671\pi$
$677$	2.48338	+	47.3857i	0.0954440	+	1.82118i	−0.362261	+	0.932077i	$0.617995\pi$
$678$	−28.1453	−	4.45777i	−1.08091	−	0.171200i
$679$	−6.08102	−	6.53074i	−0.233368	−	0.250627i
$680$		0			0
$681$	−0.634543	+	6.03727i	−0.0243157	+	0.231349i
$682$	5.43288	+	20.2758i	0.208036	+	0.776400i
$683$	6.39766	−	16.6665i	0.244800	−	0.637725i	−0.755039	−	0.655680i	$-0.772382\pi$
$683$	6.39766	−	16.6665i	0.244800	−	0.637725i	0.999839	+	0.0179550i	$0.00571555\pi$
$684$	3.19339	−	0.678776i	0.122102	−	0.0259537i
$685$		0			0
$686$	−27.4024	−	10.5884i	−1.04623	−	0.404266i
$687$	−0.932248	+	0.475004i	−0.0355675	+	0.0181225i
$688$	3.62062	−	5.57526i	0.138035	−	0.212555i
$689$	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	$0.885513\pi$
$692$	9.55468	−	1.51331i	0.363214	−	0.0575275i
$693$	−3.65214	−	2.85770i	−0.138733	−	0.108555i
$694$	4.25473	−	5.85614i	0.161507	−	0.222296i
$695$		0			0
$696$	32.2024	−	3.38461i	1.22063	−	0.128293i
$697$	−28.4261	+	35.1033i	−1.07672	+	1.32963i
$698$	56.1071	−	2.94045i	2.12368	−	0.111298i
$699$	−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	$0.369634\pi$
$702$	14.6497	−	0.767757i	0.552917	−	0.0289771i
$703$	12.5298	−	15.4730i	0.472571	−	0.583577i
$704$	−10.3758	+	1.09054i	−0.391052	+	0.0411012i
$705$		0			0
$706$	9.96981	−	13.7223i	0.375219	−	0.516444i
$707$	6.96785	−	2.80922i	0.262053	−	0.105652i
$708$	10.5117	−	1.66489i	0.395054	−	0.0625703i
$709$	0.596764	+	2.80755i	0.0224119	+	0.105440i	0.987932	−	0.154890i	$-0.0495022\pi$
$709$	0.596764	+	2.80755i	0.0224119	+	0.105440i	−0.965520	+	0.260329i	$0.916169\pi$
$710$		0			0
$711$	−2.19855	−	0.467316i	−0.0824521	−	0.0175257i
$712$	16.2336	−	24.9976i	0.608381	−	0.936824i
$713$	−11.3671	+	5.79180i	−0.425699	+	0.216905i
$714$	−41.5084	−	3.66234i	−1.55341	−	0.137060i
$715$		0			0
$716$	4.95146	−	1.05247i	0.185045	−	0.0393325i
$717$	19.1619	−	49.9184i	0.715613	−	1.86424i
$718$	1.56704	+	5.84827i	0.0584814	+	0.218256i
$719$	0.593697	−	5.64865i	0.0221412	−	0.210659i	−0.977858	−	0.209270i	$-0.932891\pi$
$719$	0.593697	−	5.64865i	0.0221412	−	0.210659i	0.999999	−	0.00138897i	$-0.000442124\pi$
$720$		0			0
$721$	18.4620	+	5.65929i	0.687562	+	0.210763i
$722$	58.8143	+	9.31526i	2.18884	+	0.346678i
$723$	1.96346	+	37.4651i	0.0730220	+	1.39334i
$724$	0.216584	−	0.375135i	0.00804929	−	0.0139418i
$725$		0			0
$726$	−17.9310	+	10.3525i	−0.665481	+	0.384216i
$727$	−37.1735	−	18.9408i	−1.37869	−	0.702477i	−0.401701	−	0.915771i	$-0.631581\pi$
$727$	−37.1735	−	18.9408i	−1.37869	−	0.702477i	−0.976988	+	0.213294i	$0.931581\pi$
$728$	−0.485123	+	13.6047i	−0.0179799	+	0.504223i
$729$	9.27315	+	12.7634i	0.343450	+	0.472718i
$730$		0			0
$731$	−2.87423	−	6.45562i	−0.106307	−	0.238770i
$732$	8.38045	−	2.24553i	0.309750	−	0.0829973i
$733$	26.8750	−	21.7630i	0.992652	−	0.803834i	0.0120672	−	0.999927i	$-0.496159\pi$
$733$	26.8750	−	21.7630i	0.992652	−	0.803834i	0.980585	+	0.196093i	$0.0628255\pi$
$734$	−4.08138	+	12.5612i	−0.150647	+	0.463642i
$735$		0			0
$736$	1.76991	+	5.44722i	0.0652397	+	0.200787i
$737$	5.73720	+	3.72578i	0.211333	+	0.137241i
$738$	−0.622739	+	11.8826i	−0.0229233	+	0.437404i
$739$	1.72889	−	8.13381i	0.0635984	−	0.299207i	−0.934840	−	0.355069i	$-0.884457\pi$
$739$	1.72889	−	8.13381i	0.0635984	−	0.299207i	0.998438	+	0.0558621i	$0.0177907\pi$
$740$		0			0
$741$	−30.6384	−	9.95501i	−1.12553	−	0.365706i
$742$	37.2701	−	10.6573i	1.36823	−	0.391242i
$743$	−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
$747$	−2.29345	+	0.880372i	−0.0839128	+	0.0322111i
$748$	2.47264	−	4.85283i	0.0904086	−	0.177437i
$749$	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	$0.573011\pi$
$752$	10.5010	−	6.81943i	0.382932	−	0.248679i
$753$	−11.4193	−	9.24716i	−0.416142	−	0.336985i
$754$	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	$0.851485\pi$
$758$	10.8978	+	13.4577i	0.395826	+	0.488805i
$759$	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	$0.675257\pi$
$762$	3.46873	+	6.80777i	0.125659	+	0.246619i
$763$	−1.78513	−	25.8018i	−0.0646261	−	0.934088i
$764$	1.33536	−	0.433884i	0.0483116	−	0.0156974i
$765$		0			0
$766$	19.5597	−	17.6116i	0.706721	−	0.636334i
$767$	−21.4735	−	8.24291i	−0.775364	−	0.297634i
$768$	−5.90038	+	22.0205i	−0.212912	+	0.794597i
$769$	33.7752	+	24.5391i	1.21796	+	0.884902i	0.995929	−	0.0901368i	$-0.0287304\pi$
$769$	33.7752	+	24.5391i	1.21796	+	0.884902i	0.222034	+	0.975039i	$0.428730\pi$
$770$		0			0
$771$	−21.7061	+	15.7704i	−0.781728	+	0.567959i
$772$	−1.29638	−	3.37719i	−0.0466578	−	0.121548i
$773$	−15.5656	−	23.9689i	−0.559854	−	0.862100i	0.439492	−	0.898246i	$-0.355158\pi$
$773$	−15.5656	−	23.9689i	−0.559854	−	0.862100i	−0.999347	+	0.0361462i	$0.988492\pi$
$774$	−1.61213	−	0.930761i	−0.0579466	−	0.0334555i
$775$		0			0
$776$			7.93899i			0.284993i
$777$	−4.70558	+	12.8989i	−0.168812	+	0.462745i
$778$	−4.77008	+	30.1171i	−0.171016	+	1.07975i
$779$	−27.2690	+	61.2473i	−0.977015	+	2.19441i
$780$		0			0
$781$	−12.7391	+	5.67181i	−0.455841	+	0.202953i
$782$	15.5888	+	4.17702i	0.557456	+	0.149370i
$783$	4.64530	+	29.3293i	0.166009	+	1.04814i
$784$	14.5801	+	30.0058i	0.520718	+	1.07164i
$785$		0			0
$786$	11.5899	−	12.8719i	0.413397	−	0.459124i
$787$	34.4848	+	1.80727i	1.22925	+	0.0644222i	0.655874	−	0.754870i	$-0.272300\pi$
$787$	34.4848	+	1.80727i	1.22925	+	0.0644222i	0.573375	+	0.819293i	$0.305634\pi$
$788$	−7.63836	−	0.400310i	−0.272105	−	0.0142604i
$789$	25.6612	−	28.4996i	0.913563	−	1.01461i
$790$		0			0
$791$	23.8022	+	4.64488i	0.846309	+	0.165153i
$792$	0.645396	+	4.07487i	0.0229332	+	0.144794i
$793$	−18.1120	−	4.85309i	−0.643175	−	0.172338i
$794$	1.76300	−	0.784939i	0.0625666	−	0.0278564i
$795$		0			0
$796$	−4.41090	+	9.90705i	−0.156340	+	0.351146i
$797$	−7.35212	+	46.4194i	−0.260425	+	1.64426i	0.417172	+	0.908828i	$0.363021\pi$
$797$	−7.35212	+	46.4194i	−0.260425	+	1.64426i	−0.677597	+	0.735433i	$0.736979\pi$
$798$	−60.9170	+	10.6950i	−2.15644	+	0.378600i
$799$		−	13.3099i		−	0.470869i
$800$		0			0
$801$	−9.22634	−	5.32683i	−0.325997	−	0.188214i
$802$	−4.09794	−	6.31027i	−0.144703	−	0.222824i
$803$	6.18253	+	16.1060i	0.218177	+	0.568370i
$804$	2.68694	−	1.95218i	0.0947612	−	0.0688480i
$805$		0			0
$806$	−17.8190	−	12.9462i	−0.627646	−	0.456012i
$807$	−4.68401	+	17.4810i	−0.164885	+	0.615359i
$808$	−6.23999	−	2.39531i	−0.219522	−	0.0842667i
$809$	−24.0985	+	21.6984i	−0.847259	+	0.762875i	−0.973394	−	0.229138i	$-0.926409\pi$
$809$	−24.0985	+	21.6984i	−0.847259	+	0.762875i	0.126135	+	0.992013i	$0.459743\pi$
$810$		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	$0.452299\pi$
$812$	9.56015	−	0.661432i	0.335495	−	0.0232117i
$813$	0.984289	+	1.93178i	0.0345205	+	0.0677503i
$814$	−6.50239	−	5.85478i	−0.227909	−	0.205210i
$815$		0			0
$816$	31.6634	+	35.1658i	1.10844	+	1.23105i
$817$	−6.60071	−	8.15120i	−0.230930	−	0.285174i
$818$	−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	$0.858199\pi$
$822$	−21.9417	−	17.7680i	−0.765304	−	0.619731i
$823$	25.0106	−	16.2420i	0.871813	−	0.566162i	−0.0293856	−	0.999568i	$-0.509355\pi$
$823$	25.0106	−	16.2420i	0.871813	−	0.566162i	0.901199	+	0.433406i	$0.142688\pi$
$824$	−8.58974	−	14.8779i	−0.299238	−	0.518295i
$825$		0			0
$826$	−43.8342	+	5.34938i	−1.52519	+	0.186129i
$827$	−13.1390	+	25.7867i	−0.456887	+	0.896691i	0.541543	+	0.840673i	$0.317840\pi$
$827$	−13.1390	+	25.7867i	−0.456887	+	0.896691i	−0.998430	+	0.0560176i	$0.982160\pi$
$828$	0.814064	−	0.312490i	0.0282907	−	0.0108598i
$829$	0.985667	+	9.37799i	0.0342336	+	0.325711i	0.998214	+	0.0597381i	$0.0190266\pi$
$829$	0.985667	+	9.37799i	0.0342336	+	0.325711i	−0.963980	+	0.265973i	$0.914307\pi$
$830$		0			0
$831$	37.8941	+	3.98283i	1.31453	+	0.138163i
$832$	7.74074	−	7.74074i	0.268362	−	0.268362i
$833$	35.1916	+	4.37365i	1.21932	+	0.151538i
$834$	52.6799	+	17.1167i	1.82416	+	0.592704i
$835$		0			0
$836$	1.68075	−	7.90732i	0.0581300	−	0.273480i
$837$	1.40654	−	26.8385i	0.0486173	−	0.927673i
$838$	−32.3892	−	21.0338i	−1.11887	−	0.726601i
$839$	16.9096	+	52.0423i	0.583784	+	1.79670i	0.604101	+	0.796907i	$0.293532\pi$
$839$	16.9096	+	52.0423i	0.583784	+	1.79670i	−0.0203179	+	0.999794i	$0.506468\pi$
$840$		0			0
$841$	−6.26123	+	19.2701i	−0.215905	+	0.664486i
$842$	9.14358	−	7.40433i	0.315109	−	0.255170i
$843$	3.24803	−	0.870306i	0.111868	−	0.0299749i
$844$	−5.24025	−	11.7698i	−0.180377	−	0.405133i
$845$		0			0
$846$	−2.06088	−	2.83656i	−0.0708544	−	0.0975228i
$847$	15.5642	−	8.26091i	0.534791	−	0.283848i
$848$	−39.2224	−	19.9848i	−1.34690	−	0.686282i
$849$	44.8078	−	25.8698i	1.53780	−	0.887849i
$850$		0			0
$851$	2.65890	−	4.60535i	0.0911460	−	0.157870i
$852$	0.354324	+	6.76091i	0.0121389	+	0.231625i
$853$	−57.0510	−	9.03599i	−1.95339	−	0.309386i	−0.999970	−	0.00773601i	$-0.997538\pi$
$853$	−57.0510	−	9.03599i	−1.95339	−	0.309386i	−0.953419	−	0.301650i	$-0.902462\pi$
$854$	−35.0826	+	8.07223i	−1.20050	+	0.276226i
$855$		0			0
$856$	2.85296	−	27.1441i	0.0975123	−	0.927768i
$857$	3.64690	+	13.6104i	0.124576	+	0.464923i	0.999824	−	0.0187505i	$-0.00596883\pi$
$857$	3.64690	+	13.6104i	0.124576	+	0.464923i	−0.875248	+	0.483674i	$0.839302\pi$
$858$	−5.07358	+	13.2171i	−0.173209	+	0.451226i
$859$	−20.5048	+	4.35843i	−0.699615	+	0.148708i	−0.543969	−	0.839105i	$-0.683079\pi$
$859$	−20.5048	+	4.35843i	−0.699615	+	0.148708i	−0.155646	+	0.987813i	$0.549746\pi$
$860$		0			0
$861$	4.06354	−	46.0556i	0.138485	−	1.56957i
$862$	−25.5128	+	12.9994i	−0.868971	+	0.442763i
$863$	−8.32996	+	12.8270i	−0.283555	+	0.436637i	−0.951534	−	0.307544i	$-0.900493\pi$
$863$	−8.32996	+	12.8270i	−0.283555	+	0.436637i	0.667979	+	0.744180i	$0.267160\pi$
$864$	−11.8021	−	2.50861i	−0.401516	−	0.0853448i
$865$		0			0
$866$	8.32500	+	39.1660i	0.282895	+	1.33092i
$867$	16.7735	−	2.65667i	0.569659	−	0.0902252i
$868$	−8.58779	−	1.21339i	−0.291489	−	0.0411851i
$869$	−3.27136	+	4.50263i	−0.110973	+	0.152741i
$870$		0			0
$871$	−7.13862	+	0.750299i	−0.241883	+	0.0254229i
$872$	−14.4806	+	17.8821i	−0.490376	+	0.605564i
$873$	2.83375	−	0.148511i	0.0959080	−	0.00502632i
$874$	23.9541			0.810261
$875$		0			0
$876$	8.37585			0.282994
$877$	14.9462	−	0.783299i	0.504699	−	0.0264501i	0.201712	−	0.979445i	$-0.435350\pi$
$877$	14.9462	−	0.783299i	0.504699	−	0.0264501i	0.302987	+	0.952995i	$0.402016\pi$
$878$	−27.8456	+	34.3865i	−0.939745	+	1.16049i
$879$	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	$0.293186\pi$
$882$	8.17714	−	4.51692i	0.275339	−	0.152093i
$883$	−26.9691	+	4.27148i	−0.907581	+	0.143747i	−0.592736	−	0.805397i	$-0.701952\pi$
$883$	−26.9691	+	4.27148i	−0.907581	+	0.143747i	−0.314845	+	0.949143i	$0.601952\pi$
$884$	1.18818	+	5.58997i	0.0399630	+	0.188011i
$885$		0			0
$886$	47.5113	+	10.0988i	1.59617	+	0.339277i
$887$	17.2800	−	26.6089i	0.580206	−	0.893439i	−0.419693	−	0.907666i	$-0.637862\pi$
$887$	17.2800	−	26.6089i	0.580206	−	0.893439i	0.999899	+	0.0142273i	$0.00452884\pi$
$888$	10.8841	−	5.54572i	0.365246	−	0.186102i
$889$	−2.74368	−	5.89517i	−0.0920200	−	0.197718i
$890$		0			0
$891$	−22.0406	+	4.68488i	−0.738389	+	0.156949i
$892$	−2.40909	+	6.27591i	−0.0806625	+	0.210133i
$893$	−5.11306	−	19.0822i	−0.171102	−	0.638561i
$894$	−4.75729	+	45.2626i	−0.159108	+	1.51381i
$895$		0			0
$896$	10.5823	−	34.5220i	0.353529	−	1.15330i
$897$	−8.49842	−	1.34602i	−0.283754	−	0.0449422i
$898$	2.52554	+	48.1901i	0.0842783	+	1.60813i
$899$	22.2922	−	38.6112i	0.743485	−	1.28775i
$900$		0			0
$901$	−40.5246	+	23.3969i	−1.35007	+	0.779463i
$902$	26.2521	+	13.3761i	0.874099	+	0.445376i
$903$	6.13125	+	3.83751i	0.204035	+	0.127704i
$904$	−12.6818	−	17.4550i	−0.421790	−	0.580544i
$905$		0			0
$906$	20.3648	+	45.7400i	0.676574	+	1.51961i
$907$	−12.3572	+	3.31110i	−0.410314	+	0.109943i	−0.458071	−	0.888916i	$-0.651459\pi$
$907$	−12.3572	+	3.31110i	−0.410314	+	0.109943i	0.0477567	+	0.998859i	$0.484793\pi$
$908$	1.24218	−	1.00590i	0.0412233	−	0.0333819i
$909$	−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	$0.949239\pi$
$912$	58.9046	+	38.2531i	1.95052	+	1.26669i
$913$	−0.318357	+	6.07461i	−0.0105361	+	0.201040i
$914$	13.3129	−	62.6323i	0.440351	−	2.07169i
$915$		0			0
$916$	0.262007	+	0.0851313i	0.00865696	+	0.00281282i
$917$	−10.2475	+	10.5960i	−0.338402	+	0.349909i
$918$	−24.0404	+	24.0404i	−0.793450	+	0.793450i
$919$	−48.3968	−	5.08671i	−1.59646	−	0.167795i	−0.735883	−	0.677108i	$-0.763233\pi$
$919$	−48.3968	−	5.08671i	−1.59646	−	0.167795i	−0.860581	+	0.509313i	$0.829899\pi$
$920$		0			0
$921$	3.63822	+	34.6154i	0.119883	+	1.14062i
$922$	−26.4581	+	10.1563i	−0.871350	+	0.334480i
$923$	6.64272	−	13.0371i	0.218648	−	0.429121i
$924$	0.675327	+	5.53381i	0.0222166	+	0.182049i
$925$		0			0
$926$	−27.1322	−	46.9943i	−0.891619	−	1.54433i
$927$	−5.14984	+	3.34434i	−0.169143	+	0.109843i
$928$	−15.5556	−	12.5967i	−0.510637	−	0.413506i
$929$	−0.431385	−	0.192065i	−0.0141533	−	0.00630145i	0.399648	−	0.916669i	$-0.369132\pi$
$929$	−0.431385	−	0.192065i	−0.0141533	−	0.00630145i	−0.413801	+	0.910367i	$0.635799\pi$
$930$		0			0
$931$	52.1340	−	7.24862i	1.70862	−	0.237564i
$932$	9.05674	+	9.05674i	0.296663	+	0.296663i
$933$	−7.84416	−	9.68674i	−0.256806	−	0.317129i
$934$	−7.08743	−	7.87139i	−0.231908	−	0.257560i
$935$		0			0
$936$	−3.21705	−	2.89665i	−0.105153	−	0.0946799i
$937$	15.7304	+	30.8727i	0.513890	+	1.00857i	0.991514	+	0.130002i	$0.0414983\pi$
$937$	15.7304	+	30.8727i	0.513890	+	1.00857i	−0.477624	+	0.878565i	$0.658502\pi$
$938$	−11.4304	+	7.69765i	−0.373216	+	0.251337i
$939$	−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	$0.325163\pi$
$942$	12.4669	+	4.78560i	0.406194	+	0.155923i
$943$	−4.63460	+	17.2966i	−0.150923	+	0.563253i
$944$	40.5702	+	29.4760i	1.32045	+	0.959362i
$945$		0			0
$946$	−3.72909	+	2.70934i	−0.121243	+	0.0880883i
$947$	−20.5422	−	53.5143i	−0.667532	−	1.73898i	−0.673706	−	0.738999i	$-0.735299\pi$
$947$	−20.5422	−	53.5143i	−0.667532	−	1.73898i	0.00617413	−	0.999981i	$-0.498035\pi$
$948$	1.47167	+	2.26617i	0.0477976	+	0.0736018i
$949$	−15.6768	−	9.05102i	−0.508892	−	0.293809i
$950$		0			0
$951$			27.6599i			0.896934i
$952$	−20.2620	−	24.1835i	−0.656695	−	0.783791i
$953$	2.70486	−	17.0778i	0.0876189	−	0.553204i	−0.904357	−	0.426777i	$-0.859649\pi$
$953$	2.70486	−	17.0778i	0.0876189	−	0.553204i	0.991976	−	0.126427i	$-0.0403510\pi$
$954$	−5.01373	+	11.2610i	−0.162326	+	0.364589i
$955$		0			0
$956$	−12.8616	+	5.72636i	−0.415974	+	0.185204i
$957$	−27.6813	−	7.41718i	−0.894810	−	0.239764i
$958$	−1.25679	−	7.93504i	−0.0406050	−	0.256370i
$959$	18.1224	+	15.7770i	0.585203	+	0.509467i
$960$		0			0
$961$	−6.25705	+	6.94916i	−0.201840	+	0.224166i
$962$	9.16843	+	0.480497i	0.295602	+	0.0154918i
$963$	−9.74223	−	0.510569i	−0.313939	−	0.0164528i
$964$	6.60983	−	7.34096i	0.212888	−	0.236436i
$965$		0			0
$966$	−15.6232	+	5.36663i	−0.502669	+	0.172668i
$967$	2.21053	+	13.9567i	0.0710859	+	0.448819i	0.997400	+	0.0720662i	$0.0229593\pi$
$967$	2.21053	+	13.9567i	0.0710859	+	0.448819i	−0.926314	+	0.376753i	$0.877041\pi$
$968$	−15.1423	−	4.05738i	−0.486693	−	0.130409i
$969$	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	$0.186802\pi$
$972$	−0.686717	+	4.33576i	−0.0220265	+	0.139070i
$973$	−44.2849	−	16.1553i	−1.41971	−	0.517917i
$974$		−	29.8245i		−	0.955640i
$975$		0			0
$976$	35.4039	+	20.4405i	1.13325	+	0.654283i
$977$	−13.5703	−	20.8965i	−0.434154	−	0.668538i	0.552100	−	0.833778i	$-0.313827\pi$
$977$	−13.5703	−	20.8965i	−0.434154	−	0.668538i	−0.986253	+	0.165240i	$0.947160\pi$
$978$	16.9945	+	44.2722i	0.543424	+	1.41567i
$979$	−21.3419	+	15.5058i	−0.682091	+	0.495568i
$980$		0			0
$981$	6.65373	+	4.83422i	0.212437	+	0.154345i
$982$	10.7708	−	40.1972i	0.343710	−	1.28274i
$983$	−10.9115	−	4.18853i	−0.348022	−	0.133593i	0.178077	−	0.984017i	$-0.443013\pi$
$983$	−10.9115	−	4.18853i	−0.348022	−	0.133593i	−0.526099	+	0.850423i	$0.676346\pi$
$984$	−30.5681	+	27.5236i	−0.974475	+	0.877421i
$985$		0			0
$986$	−53.6403	+	17.4288i	−1.70826	+	0.555046i
$987$	7.60993	+	11.3001i	0.242227	+	0.359687i
$988$	3.85090	+	7.55782i	0.122513	+	0.240446i
$989$	−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	$0.821467\pi$
$992$	11.4006	+	14.0786i	0.361969	+	0.446995i
$993$	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
$997$	9.62594	+	7.79493i	0.304856	+	0.246868i	0.769525	−	0.638617i	$-0.220493\pi$
$997$	9.62594	+	7.79493i	0.304856	+	0.246868i	−0.464668	+	0.885485i	$0.653826\pi$
$998$	4.02103	−	2.61129i	0.127283	−	0.0826588i
$999$	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.c.857.5		288
5.2	odd	4		875.2.bb.b.143.5		288
5.3	odd	4		875.2.bb.a.143.14		288
5.4	even	2		175.2.x.a.17.14	yes	288
7.5	odd	6	inner	875.2.bb.c.607.14		288
25.3	odd	20	inner	875.2.bb.c.493.14		288
25.4	even	10		875.2.bb.b.507.5		288
25.21	even	5		875.2.bb.a.507.14		288
25.22	odd	20		175.2.x.a.3.5	✓	288
35.12	even	12		875.2.bb.b.768.5		288
35.19	odd	6		175.2.x.a.117.5	yes	288
35.33	even	12		875.2.bb.a.768.14		288
175.47	even	60		175.2.x.a.103.14	yes	288
175.54	odd	30		875.2.bb.b.257.5		288
175.96	odd	30		875.2.bb.a.257.14		288
175.103	even	60	inner	875.2.bb.c.243.5		288

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

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+(-1.58403 + 0.0830157i) q^{2} +(-1.23343 + 1.52315i) q^{3} +(0.513230 - 0.0539426i) q^{4} +(1.82734 - 2.51512i) q^{6} +(-1.63042 + 2.08368i) q^{7} +(2.32486 - 0.368222i) q^{8} +(-0.174924 - 0.822951i) q^{9} +(-2.03775 - 0.433137i) q^{11} +(-0.550868 + 0.848262i) q^{12} +(1.94768 - 0.992394i) q^{13} +(2.40967 - 3.43597i) q^{14} +(-4.66165 + 0.990865i) q^{16} +(-1.81551 + 4.72957i) q^{17} +(0.345403 + 1.28906i) q^{18} +(-0.785987 + 7.47816i) q^{19} +(-1.16276 - 5.05345i) q^{21} +(3.26382 + 0.516939i) q^{22} +(0.105109 + 2.00560i) q^{23} +(-2.30669 + 3.99530i) q^{24} +(-3.00281 + 1.73368i) q^{26} +(-3.76970 - 1.92076i) q^{27} +(-0.724382 + 1.15736i) q^{28} +(-4.12547 - 5.67823i) q^{29} +(2.58369 + 5.80306i) q^{31} +(2.75469 - 0.738117i) q^{32} +(3.17315 - 2.56957i) q^{33} +(2.48320 - 7.64252i) q^{34} +(-0.134168 - 0.412927i) q^{36} +(-2.22067 - 1.44212i) q^{37} +(0.624225 - 11.9109i) q^{38} +(-0.890754 + 4.19067i) q^{39} +(8.47974 + 2.75523i) q^{41} +(2.26137 + 7.90831i) q^{42} +(-0.986332 + 0.986332i) q^{43} +(-1.06920 - 0.112377i) q^{44} +(-0.332993 - 3.16821i) q^{46} +(-2.45276 + 0.941527i) q^{47} +(4.24056 - 8.32258i) q^{48} +(-1.68344 - 6.79456i) q^{49} +(-4.96456 - 8.59887i) q^{51} +(0.946077 - 0.614389i) q^{52} +(7.17828 + 5.81286i) q^{53} +(6.13079 + 2.72960i) q^{54} +(-3.02325 + 5.44463i) q^{56} +(-10.4209 - 10.4209i) q^{57} +(7.00627 + 8.65203i) q^{58} +(-7.04085 - 7.81965i) q^{59} +(-6.37468 - 5.73979i) q^{61} +(-4.57440 - 8.97777i) q^{62} +(1.99997 + 0.977274i) q^{63} +(4.76284 - 1.54754i) q^{64} +(-4.81306 + 4.33370i) q^{66} +(-3.06559 - 1.17677i) q^{67} +(-0.676649 + 2.52529i) q^{68} +(-3.18448 - 2.31366i) q^{69} +(5.41526 - 3.93442i) q^{71} +(-0.709703 - 1.84884i) q^{72} +(-4.51023 - 6.94515i) q^{73} +(3.63734 + 2.10002i) q^{74} +3.88041i q^{76} +(4.22492 - 3.53982i) q^{77} +(1.06309 - 6.71211i) q^{78} +(1.08662 - 2.44058i) q^{79} +(9.88106 - 4.39933i) q^{81} +(-13.6609 - 3.66043i) q^{82} +(-0.456772 - 2.88395i) q^{83} +(-0.869359 - 2.53086i) q^{84} +(1.48050 - 1.64427i) q^{86} +(13.7373 + 0.719940i) q^{87} +(-4.89698 - 0.256640i) q^{88} +(8.47306 - 9.41028i) q^{89} +(-1.10772 + 5.67637i) q^{91} +(0.162132 + 1.02366i) q^{92} +(-12.0258 - 3.22229i) q^{93} +(3.80710 - 1.69503i) q^{94} +(-2.27344 + 5.10623i) q^{96} +(-0.527619 + 3.33125i) q^{97} +(3.23068 + 10.6231i) q^{98} +1.75274i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) \) 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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