LMFDB - Embedded newform 750.2.l.c.293.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			293.6
Character	$\chi$	$=$	750.293
Dual form			750.2.l.c.407.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156434 + 0.987688i) q^{2} +(-1.66195 + 0.487767i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-0.741748 - 1.56519i) q^{6} +(-0.104631 + 0.104631i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(2.52417 - 1.62129i) q^{9} +O(q^{10})$	\(q+(0.156434 + 0.987688i) q^{2} +(-1.66195 + 0.487767i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-0.741748 - 1.56519i) q^{6} +(-0.104631 + 0.104631i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(2.52417 - 1.62129i) q^{9} +(1.81255 - 2.49477i) q^{11} +(1.42988 - 0.977465i) q^{12} +(-4.49023 - 0.711182i) q^{13} +(-0.119711 - 0.0869753i) q^{14} +(0.809017 - 0.587785i) q^{16} +(3.30481 - 1.68388i) q^{17} +(1.99620 + 2.23946i) q^{18} +(3.32698 + 1.08100i) q^{19} +(0.122857 - 0.224928i) q^{21} +(2.74760 + 1.39997i) q^{22} +(4.88306 - 0.773401i) q^{23} +(1.18911 + 1.25937i) q^{24} -4.54620i q^{26} +(-3.40423 + 3.92571i) q^{27} +(0.0671775 - 0.131843i) q^{28} +(0.509399 + 1.56777i) q^{29} +(2.45755 - 7.56355i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.79551 + 5.03028i) q^{33} +(2.18014 + 3.00070i) q^{34} +(-1.89962 + 2.32195i) q^{36} +(-1.31491 + 8.30199i) q^{37} +(-0.547238 + 3.45513i) q^{38} +(7.80943 - 1.00823i) q^{39} +(-1.27149 - 1.75005i) q^{41} +(0.241378 + 0.0861576i) q^{42} +(2.77052 + 2.77052i) q^{43} +(-0.952916 + 2.93277i) q^{44} +(1.52776 + 4.70196i) q^{46} +(2.43413 - 4.77725i) q^{47} +(-1.05784 + 1.37148i) q^{48} +6.97810i q^{49} +(-4.67109 + 4.41051i) q^{51} +(4.49023 - 0.711182i) q^{52} +(10.2880 + 5.24200i) q^{53} +(-4.40992 - 2.74820i) q^{54} +(0.140729 + 0.0457256i) q^{56} +(-6.05656 - 0.173781i) q^{57} +(-1.46878 + 0.748381i) q^{58} +(10.4207 - 7.57107i) q^{59} +(11.8153 + 8.58430i) q^{61} +(7.85487 + 1.24409i) q^{62} +(-0.0944693 + 0.433745i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-5.24923 - 0.986496i) q^{66} +(-1.64885 - 3.23605i) q^{67} +(-2.62271 + 2.62271i) q^{68} +(-7.73817 + 3.66715i) q^{69} +(-4.79465 + 1.55788i) q^{71} +(-2.59053 - 1.51300i) q^{72} +(-1.68322 - 10.6274i) q^{73} -8.40547 q^{74} -3.49819 q^{76} +(0.0713809 + 0.450681i) q^{77} +(2.21748 + 7.55556i) q^{78} +(-8.57556 + 2.78637i) q^{79} +(3.74283 - 8.18481i) q^{81} +(1.52960 - 1.52960i) q^{82} +(-4.59112 - 9.01058i) q^{83} +(-0.0473370 + 0.251884i) q^{84} +(-2.30301 + 3.16982i) q^{86} +(-1.61130 - 2.35709i) q^{87} +(-3.04574 - 0.482397i) q^{88} +(-6.13326 - 4.45607i) q^{89} +(0.544231 - 0.395407i) q^{91} +(-4.40507 + 2.24450i) q^{92} +(-0.395073 + 13.7690i) q^{93} +(5.09921 + 1.65683i) q^{94} +(-1.52008 - 0.830274i) q^{96} +(8.26018 + 4.20877i) q^{97} +(-6.89219 + 1.09162i) q^{98} +(0.530447 - 9.23588i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{19}{20}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$3$	−1.66195	+	0.487767i	−0.959528	+	0.281612i
$3$	−1.66195	+	0.487767i	−0.959528	+	0.281612i
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$		0			0
$5$		0			0
$6$	−0.741748	−	1.56519i	−0.302817	−	0.638985i
$7$	−0.104631	+	0.104631i	−0.0395470	+	0.0395470i	−0.726604	−	0.687057i	$-0.758902\pi$
$7$	−0.104631	+	0.104631i	−0.0395470	+	0.0395470i	0.687057	+	0.726604i	$0.258902\pi$
$8$	−0.453990	−	0.891007i	−0.160510	−	0.315018i
$9$	2.52417	−	1.62129i	0.841389	−	0.540430i
$10$		0			0
$11$	1.81255	−	2.49477i	0.546506	−	0.752200i	−0.443027	−	0.896508i	$-0.646096\pi$
$11$	1.81255	−	2.49477i	0.546506	−	0.752200i	0.989533	+	0.144308i	$0.0460955\pi$
$12$	1.42988	−	0.977465i	0.412771	−	0.282170i
$13$	−4.49023	−	0.711182i	−1.24536	−	0.197246i	−0.501252	−	0.865301i	$-0.667127\pi$
$13$	−4.49023	−	0.711182i	−1.24536	−	0.197246i	−0.744112	+	0.668055i	$0.767127\pi$
$14$	−0.119711	−	0.0869753i	−0.0319942	−	0.0232451i
$15$		0			0
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	3.30481	−	1.68388i	0.801533	−	0.408402i	−0.00470771	−	0.999989i	$-0.501499\pi$
$17$	3.30481	−	1.68388i	0.801533	−	0.408402i	0.806241	+	0.591587i	$0.201499\pi$
$18$	1.99620	+	2.23946i	0.470508	+	0.527847i
$19$	3.32698	+	1.08100i	0.763262	+	0.247999i	0.664678	−	0.747130i	$-0.268569\pi$
$19$	3.32698	+	1.08100i	0.763262	+	0.247999i	0.0985837	+	0.995129i	$0.468569\pi$
$20$		0			0
$21$	0.122857	−	0.224928i	0.0268095	−	0.0490834i
$22$	2.74760	+	1.39997i	0.585790	+	0.298475i
$23$	4.88306	−	0.773401i	1.01819	−	0.161265i	0.375042	−	0.927008i	$-0.377628\pi$
$23$	4.88306	−	0.773401i	1.01819	−	0.161265i	0.643147	+	0.765743i	$0.277628\pi$
$24$	1.18911	+	1.25937i	0.242727	+	0.257067i
$25$		0			0
$26$		−	4.54620i		−	0.891583i
$27$	−3.40423	+	3.92571i	−0.655145	+	0.755504i
$28$	0.0671775	−	0.131843i	0.0126954	−	0.0249161i
$29$	0.509399	+	1.56777i	0.0945931	+	0.291128i	0.987147	−	0.159812i	$-0.0510889\pi$
$29$	0.509399	+	1.56777i	0.0945931	+	0.291128i	−0.892554	+	0.450940i	$0.851089\pi$
$30$		0			0
$31$	2.45755	−	7.56355i	0.441388	−	1.35845i	−0.445008	−	0.895527i	$-0.646799\pi$
$31$	2.45755	−	7.56355i	0.441388	−	1.35845i	0.886396	−	0.462927i	$-0.153201\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−1.79551	+	5.03028i	−0.312559	+	0.875660i
$34$	2.18014	+	3.00070i	0.373890	+	0.514616i
$35$		0			0
$36$	−1.89962	+	2.32195i	−0.316603	+	0.386992i
$37$	−1.31491	+	8.30199i	−0.216169	+	1.36484i	0.605941	+	0.795510i	$0.292797\pi$
$37$	−1.31491	+	8.30199i	−0.216169	+	1.36484i	−0.822110	+	0.569329i	$0.807203\pi$
$38$	−0.547238	+	3.45513i	−0.0887737	+	0.560495i
$39$	7.80943	−	1.00823i	1.25051	−	0.161447i
$40$		0			0
$41$	−1.27149	−	1.75005i	−0.198573	−	0.273312i	0.698105	−	0.715995i	$-0.254027\pi$
$41$	−1.27149	−	1.75005i	−0.198573	−	0.273312i	−0.896678	+	0.442683i	$0.854027\pi$
$42$	0.241378	+	0.0861576i	0.0372454	+	0.0132944i
$43$	2.77052	+	2.77052i	0.422501	+	0.422501i	0.886064	−	0.463563i	$-0.153429\pi$
$43$	2.77052	+	2.77052i	0.422501	+	0.422501i	−0.463563	+	0.886064i	$0.653429\pi$
$44$	−0.952916	+	2.93277i	−0.143657	+	0.442132i
$45$		0			0
$46$	1.52776	+	4.70196i	0.225256	+	0.693266i
$47$	2.43413	−	4.77725i	0.355054	−	0.696833i	−0.642533	−	0.766258i	$-0.722116\pi$
$47$	2.43413	−	4.77725i	0.355054	−	0.696833i	0.997587	+	0.0694250i	$0.0221165\pi$
$48$	−1.05784	+	1.37148i	−0.152687	+	0.197956i
$49$			6.97810i			0.996872i
$50$		0			0
$51$	−4.67109	+	4.41051i	−0.654083	+	0.617595i
$52$	4.49023	−	0.711182i	0.622682	−	0.0986232i
$53$	10.2880	+	5.24200i	1.41317	+	0.720045i	0.983154	−	0.182778i	$-0.0585089\pi$
$53$	10.2880	+	5.24200i	1.41317	+	0.720045i	0.430013	+	0.902823i	$0.358509\pi$
$54$	−4.40992	−	2.74820i	−0.600114	−	0.373983i
$55$		0			0
$56$	0.140729	+	0.0457256i	0.0188057	+	0.00611035i
$57$	−6.05656	−	0.173781i	−0.802211	−	0.0230178i
$58$	−1.46878	+	0.748381i	−0.192860	+	0.0982673i
$59$	10.4207	−	7.57107i	1.35666	−	0.985670i	0.358009	−	0.933718i	$-0.383456\pi$
$59$	10.4207	−	7.57107i	1.35666	−	0.985670i	0.998650	−	0.0519515i	$-0.0165441\pi$
$60$		0			0
$61$	11.8153	+	8.58430i	1.51279	+	1.09911i	0.964920	+	0.262544i	$0.0845614\pi$
$61$	11.8153	+	8.58430i	1.51279	+	1.09911i	0.547871	+	0.836563i	$0.315439\pi$
$62$	7.85487	+	1.24409i	0.997570	+	0.158000i
$63$	−0.0944693	+	0.433745i	−0.0119020	+	0.0546468i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$		0			0
$66$	−5.24923	−	0.986496i	−0.646136	−	0.121429i
$67$	−1.64885	−	3.23605i	−0.201439	−	0.395346i	0.768083	−	0.640350i	$-0.221211\pi$
$67$	−1.64885	−	3.23605i	−0.201439	−	0.395346i	−0.969522	+	0.245004i	$0.921211\pi$
$68$	−2.62271	+	2.62271i	−0.318050	+	0.318050i
$69$	−7.73817	+	3.66715i	−0.931567	+	0.441473i
$70$		0			0
$71$	−4.79465	+	1.55788i	−0.569020	+	0.184886i	−0.579376	−	0.815061i	$-0.696704\pi$
$71$	−4.79465	+	1.55788i	−0.569020	+	0.184886i	0.0103558	+	0.999946i	$0.496704\pi$
$72$	−2.59053	−	1.51300i	−0.305297	−	0.178309i
$73$	−1.68322	−	10.6274i	−0.197006	−	1.24385i	−0.865797	−	0.500396i	$-0.833188\pi$
$73$	−1.68322	−	10.6274i	−0.197006	−	1.24385i	0.668791	−	0.743451i	$-0.266812\pi$
$74$	−8.40547			−0.977116
$75$		0			0
$76$	−3.49819			−0.401270
$77$	0.0713809	+	0.450681i	0.00813461	+	0.0513599i
$78$	2.21748	+	7.55556i	0.251081	+	0.855499i
$79$	−8.57556	+	2.78637i	−0.964826	+	0.313491i	−0.748725	−	0.662880i	$-0.769334\pi$
$79$	−8.57556	+	2.78637i	−0.964826	+	0.313491i	−0.216100	+	0.976371i	$0.569334\pi$
$80$		0			0
$81$	3.74283	−	8.18481i	0.415871	−	0.909424i
$82$	1.52960	−	1.52960i	0.168916	−	0.168916i
$83$	−4.59112	−	9.01058i	−0.503941	−	0.989039i	−0.993147	−	0.116871i	$-0.962714\pi$
$83$	−4.59112	−	9.01058i	−0.503941	−	0.989039i	0.489206	−	0.872168i	$-0.337286\pi$
$84$	−0.0473370	+	0.251884i	−0.00516489	+	0.0274828i
$85$		0			0
$86$	−2.30301	+	3.16982i	−0.248340	+	0.341810i
$87$	−1.61130	−	2.35709i	−0.172750	−	0.252707i
$88$	−3.04574	−	0.482397i	−0.324676	−	0.0514237i
$89$	−6.13326	−	4.45607i	−0.650124	−	0.472343i	0.213189	−	0.977011i	$-0.431615\pi$
$89$	−6.13326	−	4.45607i	−0.650124	−	0.472343i	−0.863314	+	0.504668i	$0.831615\pi$
$90$		0			0
$91$	0.544231	−	0.395407i	0.0570509	−	0.0414499i
$92$	−4.40507	+	2.24450i	−0.459261	+	0.234005i
$93$	−0.395073	+	13.7690i	−0.0409672	+	1.42778i
$94$	5.09921	+	1.65683i	0.525944	+	0.170889i
$95$		0			0
$96$	−1.52008	−	0.830274i	−0.155143	−	0.0847395i
$97$	8.26018	+	4.20877i	0.838694	+	0.427336i	0.819913	−	0.572487i	$-0.194021\pi$
$97$	8.26018	+	4.20877i	0.838694	+	0.427336i	0.0187810	+	0.999824i	$0.494021\pi$
$98$	−6.89219	+	1.09162i	−0.696217	+	0.110270i
$99$	0.530447	−	9.23588i	0.0533120	−	0.928241i
$100$		0			0
$101$			4.19074i			0.416994i	0.978023	+	0.208497i	$0.0668571\pi$
$101$			4.19074i			0.416994i	−0.978023	+	0.208497i	$0.933143\pi$
$102$	−5.08693	−	3.92362i	−0.503681	−	0.388496i
$103$	7.94553	−	15.5940i	0.782896	−	1.53652i	−0.0598493	−	0.998207i	$-0.519062\pi$
$103$	7.94553	−	15.5940i	0.782896	−	1.53652i	0.842745	−	0.538312i	$-0.180938\pi$
$104$	1.40485	+	4.32369i	0.137757	+	0.423973i
$105$		0			0
$106$	−3.56807	+	10.9814i	−0.346561	+	1.06661i
$107$	−0.457779	−	0.457779i	−0.0442552	−	0.0442552i	0.684633	−	0.728888i	$-0.259963\pi$
$107$	−0.457779	−	0.457779i	−0.0442552	−	0.0442552i	−0.728888	+	0.684633i	$0.759963\pi$
$108$	2.02450	−	4.78554i	0.194808	−	0.460489i
$109$	0.0442666	+	0.0609277i	0.00423997	+	0.00583582i	0.811132	−	0.584864i	$-0.198852\pi$
$109$	0.0442666	+	0.0609277i	0.00423997	+	0.00583582i	−0.806892	+	0.590699i	$0.798852\pi$
$110$		0			0
$111$	−1.86413	−	14.4389i	−0.176935	−	1.37048i
$112$	−0.0231478	+	0.146149i	−0.00218726	+	0.0138098i
$113$	2.67766	−	16.9061i	0.251893	−	1.59039i	−0.459881	−	0.887980i	$-0.652108\pi$
$113$	2.67766	−	16.9061i	0.251893	−	1.59039i	0.711774	−	0.702408i	$-0.247892\pi$
$114$	−0.775813	−	6.00918i	−0.0726615	−	0.562811i
$115$		0			0
$116$	−0.968935	−	1.33363i	−0.0899634	−	0.123824i
$117$	−12.4871	+	5.48482i	−1.15443	+	0.507072i
$118$	9.10802	+	9.10802i	0.838461	+	0.838461i
$119$	−0.169600	+	0.521974i	−0.0155472	+	0.0478493i
$120$		0			0
$121$	0.460680	+	1.41783i	0.0418800	+	0.128893i
$122$	−6.63030	+	13.0127i	−0.600279	+	1.17811i
$123$	2.96676	+	2.28831i	0.267504	+	0.206330i
$124$			7.95279i			0.714181i
$125$		0			0
$126$	−0.443183	−	0.0254535i	−0.0394819	−	0.00226758i
$127$	8.80705	−	1.39490i	0.781499	−	0.123777i	0.247078	−	0.968996i	$-0.420530\pi$
$127$	8.80705	−	1.39490i	0.781499	−	0.123777i	0.534421	+	0.845218i	$0.320530\pi$
$128$	−0.891007	−	0.453990i	−0.0787546	−	0.0401275i
$129$	−5.95584	−	3.25310i	−0.524383	−	0.286420i
$130$		0			0
$131$	1.60573	+	0.521733i	0.140293	+	0.0455840i	0.378322	−	0.925674i	$-0.376501\pi$
$131$	1.60573	+	0.521733i	0.140293	+	0.0455840i	−0.238029	+	0.971258i	$0.576501\pi$
$132$	0.153190	−	5.33893i	0.0133335	−	0.464694i
$133$	−0.461214	+	0.235000i	−0.0399923	+	0.0203771i
$134$	2.93827	−	2.13478i	0.253828	−	0.184417i
$135$		0			0
$136$	−3.00070	−	2.18014i	−0.257308	−	0.186945i
$137$	−14.4460	−	2.28802i	−1.23420	−	0.195479i	−0.494959	−	0.868916i	$-0.664817\pi$
$137$	−14.4460	−	2.28802i	−1.23420	−	0.195479i	−0.739244	+	0.673438i	$0.764817\pi$
$138$	−4.83252	−	7.06923i	−0.411371	−	0.601773i
$139$	10.4809	−	14.4257i	0.888977	−	1.22357i	−0.0848764	−	0.996391i	$-0.527050\pi$
$139$	10.4809	−	14.4257i	0.888977	−	1.22357i	0.973853	−	0.227180i	$-0.0729505\pi$
$140$		0			0
$141$	−1.71522	+	9.12684i	−0.144448	+	0.768619i
$142$	−2.28874	−	4.49191i	−0.192067	−	0.376953i
$143$	−9.91301	+	9.91301i	−0.828967	+	0.828967i
$144$	1.08912	−	2.79532i	0.0907603	−	0.232943i
$145$		0			0
$146$	10.2333	−	3.32499i	0.846912	−	0.275178i
$147$	−3.40369	−	11.5973i	−0.280732	−	0.956527i
$148$	−1.31491	−	8.30199i	−0.108085	−	0.682419i
$149$	−15.4486			−1.26560			−0.632800	−	0.774316i	$-0.718094\pi$
$149$	−15.4486			−1.26560			−0.632800	+	0.774316i	$0.718094\pi$
$150$		0			0
$151$	−7.09145			−0.577094			−0.288547	−	0.957466i	$-0.593172\pi$
$151$	−7.09145			−0.577094			−0.288547	+	0.957466i	$0.593172\pi$
$152$	−0.547238	−	3.45513i	−0.0443869	−	0.280248i
$153$	5.61182	−	9.60845i	0.453689	−	0.776797i
$154$	−0.433966	+	0.141004i	−0.0349700	+	0.0113624i
$155$		0			0
$156$	−7.11565	+	3.37213i	−0.569708	+	0.269987i
$157$	5.10830	−	5.10830i	0.407687	−	0.407687i	−0.473244	−	0.880931i	$-0.656917\pi$
$157$	5.10830	−	5.10830i	0.407687	−	0.407687i	0.880931	+	0.473244i	$0.156917\pi$
$158$	−4.09358	−	8.03409i	−0.325667	−	0.639158i
$159$	−19.6551	−	3.69380i	−1.55875	−	0.292938i
$160$		0			0
$161$	−0.430000	+	0.591844i	−0.0338887	+	0.0466439i
$162$	8.66955	+	2.41637i	0.681145	+	0.189848i
$163$	−2.11572	−	0.335098i	−0.165716	−	0.0262469i	0.0730249	−	0.997330i	$-0.476735\pi$
$163$	−2.11572	−	0.335098i	−0.165716	−	0.0262469i	−0.238741	+	0.971083i	$0.576735\pi$
$164$	1.75005	+	1.27149i	0.136656	+	0.0992863i
$165$		0			0
$166$	8.18143	−	5.94416i	0.635002	−	0.461356i
$167$	3.73873	−	1.90498i	0.289312	−	0.147412i	−0.303312	−	0.952891i	$-0.598092\pi$
$167$	3.73873	−	1.90498i	0.289312	−	0.147412i	0.592623	+	0.805480i	$0.298092\pi$
$168$	−0.256188	−	0.00735081i	−0.0197654	−	0.000567128i
$169$	7.29261	+	2.36951i	0.560970	+	0.182270i
$170$		0			0
$171$	10.1505	−	2.66537i	0.776226	−	0.203826i
$172$	−3.49106	−	1.77878i	−0.266191	−	0.135631i
$173$	0.107360	−	0.0170042i	0.00816244	−	0.00129280i	−0.152352	−	0.988326i	$-0.548685\pi$
$173$	0.107360	−	0.0170042i	0.00816244	−	0.00129280i	0.160514	+	0.987034i	$0.448685\pi$
$174$	2.07601	−	1.96020i	0.157382	−	0.148602i
$175$		0			0
$176$		−	3.08370i		−	0.232443i
$177$	−13.6258	+	17.6656i	−1.02417	+	1.32783i
$178$	3.44176	−	6.75483i	0.257971	−	0.506296i
$179$	0.495650	+	1.52545i	0.0370466	+	0.114018i	0.967870	−	0.251452i	$-0.0809082\pi$
$179$	0.495650	+	1.52545i	0.0370466	+	0.114018i	−0.930823	+	0.365470i	$0.880908\pi$
$180$		0			0
$181$	−3.90297	+	12.0121i	−0.290105	+	0.892852i	0.694717	+	0.719284i	$0.255530\pi$
$181$	−3.90297	+	12.0121i	−0.290105	+	0.892852i	−0.984822	+	0.173568i	$0.944470\pi$
$182$	0.475675	+	0.475675i	0.0352594	+	0.0352594i
$183$	−23.8236	−	8.50359i	−1.76109	−	0.628603i
$184$	−2.90597	−	3.99972i	−0.214231	−	0.294864i
$185$		0			0
$186$	−13.6612	+	1.76373i	−1.00169	+	0.129323i
$187$	1.78924	−	11.2968i	0.130843	−	0.826107i
$188$	−0.838744	+	5.29562i	−0.0611717	+	0.386223i
$189$	−0.0545633	−	0.766943i	−0.00396889	−	0.0557869i
$190$		0			0
$191$	12.2687	+	16.8865i	0.887734	+	1.22186i	0.974218	+	0.225608i	$0.0724369\pi$
$191$	12.2687	+	16.8865i	0.887734	+	1.22186i	−0.0864840	+	0.996253i	$0.527563\pi$
$192$	0.582259	−	1.63125i	0.0420209	−	0.117725i
$193$	−4.75446	−	4.75446i	−0.342233	−	0.342233i	0.514973	−	0.857206i	$-0.327802\pi$
$193$	−4.75446	−	4.75446i	−0.342233	−	0.342233i	−0.857206	+	0.514973i	$0.827802\pi$
$194$	−2.86478	+	8.81688i	−0.205679	+	0.633015i
$195$		0			0
$196$	−2.15635	−	6.63657i	−0.154025	−	0.474041i
$197$	1.96506	−	3.85665i	0.140005	−	0.274775i	−0.810348	−	0.585948i	$-0.800722\pi$
$197$	1.96506	−	3.85665i	0.140005	−	0.274775i	0.950353	+	0.311174i	$0.100722\pi$
$198$	9.20515	−	0.920894i	0.654182	−	0.0654451i
$199$			0.610848i			0.0433019i	0.999766	+	0.0216509i	$0.00689224\pi$
$199$			0.610848i			0.0433019i	−0.999766	+	0.0216509i	$0.993108\pi$
$200$		0			0
$201$	4.31874	+	4.57390i	0.304621	+	0.322618i
$202$	−4.13914	+	0.655576i	−0.291229	+	0.0461261i
$203$	−0.217337	−	0.110739i	−0.0152541	−	0.00777235i
$204$	3.07954	−	5.63809i	0.215611	−	0.394745i
$205$		0			0
$206$	16.6449	+	5.40827i	1.15971	+	0.376812i
$207$	11.0718	−	9.86905i	0.769540	−	0.685947i
$208$	−4.05069	+	2.06393i	−0.280865	+	0.143108i
$209$	8.72718	−	6.34067i	0.603671	−	0.438593i
$210$		0			0
$211$	3.67523	+	2.67021i	0.253013	+	0.183825i	0.707061	−	0.707152i	$-0.250020\pi$
$211$	3.67523	+	2.67021i	0.253013	+	0.183825i	−0.454048	+	0.890977i	$0.650020\pi$
$212$	−11.4044	−	1.80627i	−0.783254	−	0.124055i
$213$	7.20859	−	4.92778i	0.493925	−	0.337646i
$214$	0.380531	−	0.523756i	0.0260125	−	0.0358032i
$215$		0			0
$216$	5.04332	+	1.25096i	0.343155	+	0.0851168i
$217$	0.534249	+	1.04852i	0.0362672	+	0.0711783i
$218$	−0.0532528	+	0.0532528i	−0.00360673	+	0.00360673i
$219$	7.98114	+	16.8413i	0.539316	+	1.13803i
$220$		0			0
$221$	−16.0369	+	5.21070i	−1.07876	+	0.350509i
$222$	13.9695	−	4.09991i	0.937571	−	0.275168i
$223$	3.05224	+	19.2711i	0.204393	+	1.29049i	0.849986	+	0.526805i	$0.176610\pi$
$223$	3.05224	+	19.2711i	0.204393	+	1.29049i	−0.645593	+	0.763681i	$0.723390\pi$
$224$	−0.147971			−0.00988675
$225$		0			0
$226$	17.1168			1.13859
$227$	−1.89042	−	11.9356i	−0.125471	−	0.792194i	−0.967520	−	0.252793i	$-0.918651\pi$
$227$	−1.89042	−	11.9356i	−0.125471	−	0.792194i	0.842049	−	0.539401i	$-0.181349\pi$
$228$	5.81383	−	1.70630i	0.385030	−	0.113003i
$229$	−5.88719	+	1.91287i	−0.389037	+	0.126406i	−0.497003	−	0.867749i	$-0.665566\pi$
$229$	−5.88719	+	1.91287i	−0.389037	+	0.126406i	0.107966	+	0.994155i	$0.465566\pi$
$230$		0			0
$231$	−0.338459	−	0.714193i	−0.0222690	−	0.0469905i
$232$	1.16563	−	1.16563i	0.0765274	−	0.0765274i
$233$	3.43912	+	6.74965i	0.225304	+	0.442184i	0.975792	−	0.218700i	$-0.0701816\pi$
$233$	3.43912	+	6.74965i	0.225304	+	0.442184i	−0.750488	+	0.660884i	$0.770182\pi$
$234$	−7.37071	−	11.4754i	−0.481838	−	0.750168i
$235$		0			0
$236$	−7.57107	+	10.4207i	−0.492835	+	0.678329i
$237$	12.8931	−	8.81368i	0.837494	−	0.572510i
$238$	−0.542079	−	0.0858568i	−0.0351377	−	0.00556527i
$239$	13.6576	+	9.92281i	0.883435	+	0.641853i	0.934158	−	0.356859i	$-0.116152\pi$
$239$	13.6576	+	9.92281i	0.883435	+	0.641853i	−0.0507228	+	0.998713i	$0.516152\pi$
$240$		0			0
$241$	−7.96740	+	5.78866i	−0.513225	+	0.372880i	−0.814046	−	0.580801i	$-0.802740\pi$
$241$	−7.96740	+	5.78866i	−0.513225	+	0.372880i	0.300820	+	0.953681i	$0.402740\pi$
$242$	−1.32830	+	0.676805i	−0.0853866	+	0.0435066i
$243$	−2.22813	+	15.4284i	−0.142934	+	0.989732i
$244$	−13.8897	−	4.51303i	−0.889196	−	0.288917i
$245$		0			0
$246$	−1.79603	+	3.28821i	−0.114511	+	0.209648i
$247$	−14.1701	−	7.22003i	−0.901622	−	0.459399i
$248$	−7.85487	+	1.24409i	−0.498785	+	0.0789998i
$249$	12.0253	+	12.7357i	0.762071	+	0.807095i
$250$		0			0
$251$		−	0.308302i		−	0.0194599i	−0.999953	−	0.00972993i	$-0.996903\pi$
$251$		−	0.308302i		−	0.0194599i	0.999953	−	0.00972993i	$-0.00309718\pi$
$252$	−0.0441891	−	0.441709i	−0.00278365	−	0.0278250i
$253$	6.92136	−	13.5839i	0.435142	−	0.854014i
$254$	2.75545	+	8.48041i	0.172892	+	0.532108i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	5.10907	+	5.10907i	0.318695	+	0.318695i	0.848266	−	0.529571i	$-0.177647\pi$
$257$	5.10907	+	5.10907i	0.318695	+	0.318695i	−0.529571	+	0.848266i	$0.677647\pi$
$258$	2.28135	−	6.39141i	0.142031	−	0.397912i
$259$	−0.731069	−	1.00623i	−0.0454264	−	0.0625241i
$260$		0			0
$261$	3.82762	+	3.13143i	0.236924	+	0.193831i
$262$	−0.264118	+	1.66758i	−0.0163173	+	0.103023i
$263$	−0.817350	+	5.16055i	−0.0504000	+	0.318213i	0.949589	+	0.313498i	$0.101501\pi$
$263$	−0.817350	+	5.16055i	−0.0504000	+	0.318213i	−0.999989	+	0.00471508i	$0.998499\pi$
$264$	5.29716	−	0.683889i	0.326018	−	0.0420904i
$265$		0			0
$266$	−0.304257	−	0.418773i	−0.0186552	−	0.0256766i
$267$	12.3667	+	4.41418i	0.756830	+	0.270143i
$268$	2.56814	+	2.56814i	0.156874	+	0.156874i
$269$	−0.702217	+	2.16120i	−0.0428149	+	0.131771i	−0.970179	−	0.242389i	$-0.922069\pi$
$269$	−0.702217	+	2.16120i	−0.0428149	+	0.131771i	0.927364	+	0.374160i	$0.122069\pi$
$270$		0			0
$271$	−5.82840	−	17.9380i	−0.354050	−	1.08965i	−0.956558	−	0.291541i	$-0.905832\pi$
$271$	−5.82840	−	17.9380i	−0.354050	−	1.08965i	0.602508	−	0.798113i	$-0.294168\pi$
$272$	1.68388	−	3.30481i	0.102100	−	0.200383i
$273$	−0.711619	+	0.922605i	−0.0430691	+	0.0558386i
$274$		−	14.6260i		−	0.883592i
$275$		0			0
$276$	6.22623	−	5.87890i	0.374775	−	0.353868i
$277$	16.3654	−	2.59202i	0.983299	−	0.155739i	0.355973	−	0.934496i	$-0.384149\pi$
$277$	16.3654	−	2.59202i	0.983299	−	0.155739i	0.627326	+	0.778757i	$0.284149\pi$
$278$	15.8877	+	8.09517i	0.952878	+	0.485516i
$279$	−6.05945	−	23.0761i	−0.362770	−	1.38153i
$280$		0			0
$281$	−23.8171	−	7.73865i	−1.42081	−	0.461649i	−0.504951	−	0.863148i	$-0.668489\pi$
$281$	−23.8171	−	7.73865i	−1.42081	−	0.461649i	−0.915859	+	0.401499i	$0.868489\pi$
$282$	−9.28279	−	0.266351i	−0.552782	−	0.0158610i
$283$	−23.8762	+	12.1655i	−1.41929	+	0.723165i	−0.984173	−	0.177209i	$-0.943293\pi$
$283$	−23.8762	+	12.1655i	−1.41929	+	0.723165i	−0.435117	+	0.900374i	$0.643293\pi$
$284$	4.07857	−	2.96325i	0.242019	−	0.175837i
$285$		0			0
$286$	−11.3417	−	8.24023i	−0.670649	−	0.487255i
$287$	0.316148	+	0.0500729i	0.0186616	+	0.00295571i
$288$	2.93128	+	0.638430i	0.172727	+	0.0376198i
$289$	−1.90607	+	2.62348i	−0.112122	+	0.154322i
$290$		0			0
$291$	−15.7809	−	2.96573i	−0.925094	−	0.173854i
$292$	4.88489	+	9.58715i	0.285867	+	0.561045i
$293$	−1.78525	+	1.78525i	−0.104296	+	0.104296i	−0.757329	−	0.653033i	$-0.773496\pi$
$293$	−1.78525	+	1.78525i	−0.104296	+	0.104296i	0.653033	+	0.757329i	$0.273496\pi$
$294$	10.9220	−	5.17600i	0.636986	−	0.301870i
$295$		0			0
$296$	7.99408	−	2.59743i	0.464646	−	0.150973i
$297$	3.62338	+	15.6083i	0.210250	+	0.905687i
$298$	−2.41669	−	15.2584i	−0.139995	−	0.883896i
$299$	−22.4761			−1.29983
$300$		0			0
$301$	−0.579767			−0.0334172
$302$	−1.10935	−	7.00414i	−0.0638357	−	0.403043i
$303$	−2.04410	−	6.96480i	−0.117431	−	0.400117i
$304$	3.32698	−	1.08100i	0.190815	−	0.0619997i
$305$		0			0
$306$	10.3680	+	4.03963i	0.592701	+	0.230931i
$307$	−18.1356	+	18.1356i	−1.03505	+	1.03505i	−0.0356889	+	0.999363i	$0.511363\pi$
$307$	−18.1356	+	18.1356i	−1.03505	+	1.03505i	−0.999363	+	0.0356889i	$0.988637\pi$
$308$	−0.207155	−	0.406565i	−0.0118038	−	0.0231662i
$309$	−5.59885	+	29.7920i	−0.318508	+	1.69481i
$310$		0			0
$311$	6.19053	−	8.52054i	0.351033	−	0.483155i	−0.596590	−	0.802546i	$-0.703478\pi$
$311$	6.19053	−	8.52054i	0.351033	−	0.483155i	0.947623	+	0.319391i	$0.103478\pi$
$312$	−4.44375	−	6.50052i	−0.251578	−	0.368020i
$313$	17.4862	+	2.76954i	0.988377	+	0.156543i	0.629633	−	0.776893i	$-0.283205\pi$
$313$	17.4862	+	2.76954i	0.988377	+	0.156543i	0.358744	+	0.933436i	$0.383205\pi$
$314$	5.84453	+	4.24630i	0.329826	+	0.239632i
$315$		0			0
$316$	7.29480	−	5.29999i	0.410365	−	0.298147i
$317$	4.53776	−	2.31211i	0.254866	−	0.129861i	−0.321890	−	0.946777i	$-0.604318\pi$
$317$	4.53776	−	2.31211i	0.254866	−	0.129861i	0.576756	+	0.816916i	$0.304318\pi$
$318$	0.573599	−	19.9909i	0.0321659	−	1.12103i
$319$	4.83453	+	1.57084i	0.270682	+	0.0879499i
$320$		0			0
$321$	0.984096	+	0.537517i	0.0549269	+	0.0300013i
$322$	−0.651824	−	0.332121i	−0.0363248	−	0.0185084i
$323$	12.8153	−	2.02974i	0.713063	−	0.112938i
$324$	−1.03040	+	8.94082i	−0.0572445	+	0.496712i
$325$		0			0
$326$		−	2.14210i		−	0.118640i
$327$	−0.103287	−	0.0796671i	−0.00571181	−	0.00440560i
$328$	−0.982063	+	1.92741i	−0.0542254	+	0.106423i
$329$	0.245164	+	0.754537i	0.0135163	+	0.0415990i
$330$		0			0
$331$	−4.54014	+	13.9731i	−0.249548	+	0.768031i	0.745307	+	0.666722i	$0.232303\pi$
$331$	−4.54014	+	13.9731i	−0.249548	+	0.768031i	−0.994855	+	0.101309i	$0.967697\pi$
$332$	7.15083	+	7.15083i	0.392453	+	0.392453i
$333$	10.1409	+	23.0874i	0.555717	+	1.26518i
$334$	2.46639	+	3.39470i	0.134955	+	0.185750i
$335$		0			0
$336$	−0.0328164	−	0.254184i	−0.00179028	−	0.0138669i
$337$	−3.87373	+	24.4578i	−0.211015	+	1.33230i	0.623720	+	0.781648i	$0.285621\pi$
$337$	−3.87373	+	24.4578i	−0.211015	+	1.33230i	−0.834735	+	0.550651i	$0.814379\pi$
$338$	−1.19952	+	7.57350i	−0.0652455	+	0.411944i
$339$	3.79608	+	29.4031i	0.206175	+	1.59696i
$340$		0			0
$341$	−14.4149	−	19.8403i	−0.780608	−	1.07441i
$342$	4.22044	+	9.60854i	0.228215	+	0.519571i
$343$	−1.46255	−	1.46255i	−0.0789703	−	0.0789703i
$344$	1.21076	−	3.72634i	0.0652799	−	0.200911i
$345$		0			0
$346$	0.0335897	+	0.103378i	0.00180579	+	0.00555765i
$347$	−14.5067	+	28.4710i	−0.778760	+	1.52840i	0.0687565	+	0.997633i	$0.478097\pi$
$347$	−14.5067	+	28.4710i	−0.778760	+	1.52840i	−0.847516	+	0.530769i	$0.821903\pi$
$348$	2.26082	+	1.74381i	0.121193	+	0.0934778i
$349$			27.0969i			1.45047i	0.688504	+	0.725233i	$0.258268\pi$
$349$			27.0969i			1.45047i	−0.688504	+	0.725233i	$0.741732\pi$
$350$		0			0
$351$	18.0777	−	15.2063i	0.964914	−	0.811652i
$352$	3.04574	−	0.482397i	0.162338	−	0.0257118i
$353$	−5.52827	−	2.81680i	−0.294240	−	0.149923i	0.300639	−	0.953738i	$-0.402800\pi$
$353$	−5.52827	−	2.81680i	−0.294240	−	0.149923i	−0.594879	+	0.803815i	$0.702800\pi$
$354$	−19.5797	−	10.6945i	−1.04065	−	0.568406i
$355$		0			0
$356$	7.21008	+	2.34270i	0.382133	+	0.124163i
$357$	0.0272647	−	0.950221i	0.00144300	−	0.0502910i
$358$	−1.42914	+	0.728181i	−0.0755321	+	0.0384855i
$359$	27.6886	−	20.1169i	1.46135	−	1.06173i	0.478338	−	0.878176i	$-0.341239\pi$
$359$	27.6886	−	20.1169i	1.46135	−	1.06173i	0.983009	−	0.183555i	$-0.0587606\pi$
$360$		0			0
$361$	−5.47109	−	3.97498i	−0.287952	−	0.209209i
$362$	−12.4748	−	1.97581i	−0.655659	−	0.103846i
$363$	−1.45720	−	2.13165i	−0.0764829	−	0.111883i
$364$	−0.395407	+	0.544231i	−0.0207250	+	0.0285255i
$365$		0			0
$366$	4.67207	−	24.8605i	0.244213	−	1.29948i
$367$	−5.51668	−	10.8271i	−0.287968	−	0.565170i	0.701024	−	0.713138i	$-0.252727\pi$
$367$	−5.51668	−	10.8271i	−0.287968	−	0.565170i	−0.988992	+	0.147968i	$0.952727\pi$
$368$	3.49589	−	3.49589i	0.182236	−	0.182236i
$369$	−6.04678	−	2.35597i	−0.314783	−	0.122647i
$370$		0			0
$371$	−1.62493	+	0.527971i	−0.0843621	+	0.0274109i
$372$	−3.87911	−	13.2171i	−0.201122	−	0.685277i
$373$	4.00874	+	25.3102i	0.207565	+	1.31051i	0.842814	+	0.538205i	$0.180897\pi$
$373$	4.00874	+	25.3102i	0.207565	+	1.31051i	−0.635249	+	0.772307i	$0.719103\pi$
$374$	11.4377			0.591427
$375$		0			0
$376$	−5.36163			−0.276505
$377$	−1.17235	−	7.40192i	−0.0603790	−	0.381218i
$378$	0.748965	−	0.173868i	0.0385226	−	0.00894279i
$379$	6.14399	−	1.99630i	0.315596	−	0.102543i	−0.146936	−	0.989146i	$-0.546941\pi$
$379$	6.14399	−	1.99630i	0.315596	−	0.102543i	0.462532	+	0.886603i	$0.346941\pi$
$380$		0			0
$381$	−13.9565	+	6.61404i	−0.715013	+	0.338848i
$382$	−14.7593	+	14.7593i	−0.755152	+	0.755152i
$383$	0.124507	+	0.244359i	0.00636200	+	0.0124861i	0.894166	−	0.447736i	$-0.147770\pi$
$383$	0.124507	+	0.244359i	0.00636200	+	0.0124861i	−0.887804	+	0.460222i	$0.847770\pi$
$384$	1.70225	+	0.319907i	0.0868677	+	0.0163252i
$385$		0			0
$386$	3.95216	−	5.43968i	0.201160	−	0.276873i
$387$	11.4851	+	2.50144i	0.583819	+	0.127155i
$388$	−9.15648	−	1.45024i	−0.464850	−	0.0736250i
$389$	−22.1354	−	16.0823i	−1.12231	−	0.815407i	−0.137754	−	0.990467i	$-0.543988\pi$
$389$	−22.1354	−	16.0823i	−1.12231	−	0.815407i	−0.984558	+	0.175059i	$0.943988\pi$
$390$		0			0
$391$	14.8353	−	10.7784i	0.750251	−	0.545089i
$392$	6.21754	−	3.16799i	0.314033	−	0.160008i
$393$	−2.92313	−	0.0838734i	−0.147452	−	0.00423085i
$394$	4.11657	+	1.33755i	0.207390	+	0.0673850i
$395$		0			0
$396$	2.34956	+	8.94776i	0.118070	+	0.449642i
$397$	−1.05681	−	0.538470i	−0.0530396	−	0.0270250i	0.427270	−	0.904124i	$-0.359476\pi$
$397$	−1.05681	−	0.538470i	−0.0530396	−	0.0270250i	−0.480309	+	0.877099i	$0.659476\pi$
$398$	−0.603327	+	0.0955577i	−0.0302421	+	0.00478987i
$399$	0.651890	−	0.615524i	0.0326353	−	0.0308147i
$400$		0			0
$401$			4.37934i			0.218694i	0.994004	+	0.109347i	$0.0348759\pi$
$401$			4.37934i			0.218694i	−0.994004	+	0.109347i	$0.965124\pi$
$402$	−3.84199	+	4.98109i	−0.191621	+	0.248434i
$403$	−16.4140	+	32.2143i	−0.817639	+	1.60471i
$404$	−1.29501	−	3.98563i	−0.0644291	−	0.198292i
$405$		0			0
$406$	0.0753765	−	0.231985i	0.00374087	−	0.0115132i
$407$	18.3282	+	18.3282i	0.908494	+	0.908494i
$408$	6.05042	+	2.15964i	0.299540	+	0.106918i
$409$	−19.0597	−	26.2334i	−0.942440	−	1.29716i	−0.954805	−	0.297234i	$-0.903936\pi$
$409$	−19.0597	−	26.2334i	−0.942440	−	1.29716i	0.0123647	−	0.999924i	$-0.496064\pi$
$410$		0			0
$411$	25.1245	−	3.24369i	1.23930	−	0.160000i
$412$	−2.73784	+	17.2861i	−0.134884	+	0.851623i
$413$	−0.298159	+	1.88250i	−0.0146715	+	0.0926320i
$414$	11.4796	+	9.39158i	0.564189	+	0.461571i
$415$		0			0
$416$	−2.67219	−	3.67795i	−0.131015	−	0.180326i
$417$	−10.3823	+	29.0870i	−0.508425	+	1.42440i
$418$	7.62783	+	7.62783i	0.373089	+	0.373089i
$419$	9.10066	−	28.0089i	0.444596	−	1.36833i	−0.438330	−	0.898814i	$-0.644430\pi$
$419$	9.10066	−	28.0089i	0.444596	−	1.36833i	0.882926	−	0.469512i	$-0.155570\pi$
$420$		0			0
$421$	1.83346	+	5.64281i	0.0893574	+	0.275014i	0.985742	−	0.168263i	$-0.0538158\pi$
$421$	1.83346	+	5.64281i	0.0893574	+	0.275014i	−0.896385	+	0.443277i	$0.853816\pi$
$422$	−2.06240	+	4.04770i	−0.100396	+	0.197039i
$423$	−1.60116	−	16.0050i	−0.0778509	−	0.778190i
$424$		−	11.5465i		−	0.560748i
$425$		0			0
$426$	5.99479	+	6.34897i	0.290448	+	0.307608i
$427$	−2.13444	+	0.338062i	−0.103293	+	0.0163600i
$428$	0.576835	+	0.293912i	0.0278824	+	0.0142068i
$429$	11.6397	−	21.3102i	0.561970	−	1.02887i
$430$		0			0
$431$	−16.7496	−	5.44228i	−0.806801	−	0.262146i	−0.123559	−	0.992337i	$-0.539431\pi$
$431$	−16.7496	−	5.44228i	−0.806801	−	0.262146i	−0.683242	+	0.730192i	$0.739431\pi$
$432$	−0.446605	+	5.17692i	−0.0214873	+	0.249075i
$433$	8.08290	−	4.11844i	0.388439	−	0.197920i	−0.248854	−	0.968541i	$-0.580054\pi$
$433$	8.08290	−	4.11844i	0.388439	−	0.197920i	0.637293	+	0.770621i	$0.280054\pi$
$434$	−0.952038	+	0.691696i	−0.0456993	+	0.0332025i
$435$		0			0
$436$	−0.0609277	−	0.0442666i	−0.00291791	−	0.00211998i
$437$	17.0819	+	2.70551i	0.817138	+	0.129422i
$438$	−15.3854	+	10.5174i	−0.735142	+	0.502542i
$439$	−16.9822	+	23.3740i	−0.810517	+	1.11558i	0.180726	+	0.983533i	$0.442155\pi$
$439$	−16.9822	+	23.3740i	−0.810517	+	1.11558i	−0.991243	+	0.132048i	$0.957845\pi$
$440$		0			0
$441$	11.3135	+	17.6139i	0.538740	+	0.838757i
$442$	−7.65526	−	15.0243i	−0.364124	−	0.714633i
$443$	−12.4501	+	12.4501i	−0.591523	+	0.591523i	−0.938043	−	0.346520i	$-0.887363\pi$
$443$	−12.4501	+	12.4501i	−0.591523	+	0.591523i	0.346520	+	0.938043i	$0.387363\pi$
$444$	6.23474	+	13.1561i	0.295888	+	0.624362i
$445$		0			0
$446$	−18.5563	+	6.02932i	−0.878668	+	0.285497i
$447$	25.6748	−	7.53532i	1.21438	−	0.356408i
$448$	−0.0231478	−	0.146149i	−0.00109363	−	0.00690491i
$449$	12.8503			0.606444			0.303222	−	0.952920i	$-0.401938\pi$
$449$	12.8503			0.606444			0.303222	+	0.952920i	$0.401938\pi$
$450$		0			0
$451$	−6.67060			−0.314106
$452$	2.67766	+	16.9061i	0.125946	+	0.795194i
$453$	11.7856	−	3.45897i	0.553738	−	0.162517i
$454$	11.4929	−	3.73428i	0.539390	−	0.175259i
$455$		0			0
$456$	2.59478	+	5.47533i	0.121512	+	0.256406i
$457$	10.9813	−	10.9813i	0.513683	−	0.513683i	−0.401970	−	0.915653i	$-0.631674\pi$
$457$	10.9813	−	10.9813i	0.513683	−	0.513683i	0.915653	+	0.401970i	$0.131674\pi$
$458$	−2.81027	−	5.51547i	−0.131316	−	0.257721i
$459$	−4.63989	+	18.7060i	−0.216571	+	0.873123i
$460$		0			0
$461$	6.59561	−	9.07808i	0.307188	−	0.422808i	−0.627314	−	0.778767i	$-0.715846\pi$
$461$	6.59561	−	9.07808i	0.307188	−	0.422808i	0.934502	+	0.355958i	$0.115846\pi$
$462$	0.652454	−	0.446017i	0.0303549	−	0.0207506i
$463$	1.27477	+	0.201904i	0.0592438	+	0.00938330i	0.185986	−	0.982552i	$-0.440452\pi$
$463$	1.27477	+	0.201904i	0.0592438	+	0.00938330i	−0.126742	+	0.991936i	$0.540452\pi$
$464$	1.33363	+	0.968935i	0.0619120	+	0.0449817i
$465$		0			0
$466$	−6.12855	+	4.45265i	−0.283900	+	0.206265i
$467$	32.6024	−	16.6117i	1.50866	−	0.768700i	0.512705	−	0.858565i	$-0.328644\pi$
$467$	32.6024	−	16.6117i	1.50866	−	0.768700i	0.995954	+	0.0898651i	$0.0286436\pi$
$468$	10.1810	−	9.07510i	0.470619	−	0.419497i
$469$	0.511114	+	0.166071i	0.0236010	+	0.00766845i
$470$		0			0
$471$	−5.99809	+	10.9814i	−0.276377	+	0.505997i
$472$	−11.4768	−	5.84771i	−0.528261	−	0.269162i
$473$	11.9335	−	1.89008i	0.548704	−	0.0869062i
$474$	10.7221	+	11.3556i	0.492482	+	0.521578i
$475$		0			0
$476$		−	0.548836i		−	0.0251559i
$477$	34.4675	−	3.44816i	1.57816	−	0.157881i
$478$	−7.66413	+	15.0417i	−0.350549	+	0.687991i
$479$	8.59259	+	26.4453i	0.392605	+	1.20832i	0.930811	+	0.365502i	$0.119103\pi$
$479$	8.59259	+	26.4453i	0.392605	+	1.20832i	−0.538205	+	0.842814i	$0.680897\pi$
$480$		0			0
$481$	11.8084	−	36.3427i	0.538419	−	1.65708i
$482$	−6.96376	−	6.96376i	−0.317191	−	0.317191i
$483$	0.425957	−	1.19336i	0.0193817	−	0.0542996i
$484$	−0.876264	−	1.20607i	−0.0398302	−	0.0548216i
$485$		0			0
$486$	−15.5870	+	0.212837i	−0.707041	+	0.00965449i
$487$	1.49720	−	9.45297i	0.0678448	−	0.428355i	−0.930264	−	0.366890i	$-0.880423\pi$
$487$	1.49720	−	9.45297i	0.0678448	−	0.428355i	0.998109	−	0.0614653i	$-0.0195774\pi$
$488$	2.28464	−	14.4247i	0.103421	−	0.652974i
$489$	3.67968	−	0.475064i	0.166401	−	0.0214831i
$490$		0			0
$491$	6.14271	+	8.45471i	0.277216	+	0.381556i	0.924809	−	0.380431i	$-0.124224\pi$
$491$	6.14271	+	8.45471i	0.277216	+	0.381556i	−0.647593	+	0.761986i	$0.724224\pi$
$492$	−3.52869	−	1.25953i	−0.159085	−	0.0567840i
$493$	4.32341	+	4.32341i	0.194716	+	0.194716i
$494$	4.91445	−	15.1251i	0.221111	−	0.680511i
$495$		0			0
$496$	−2.45755	−	7.56355i	−0.110347	−	0.339613i
$497$	0.338668	−	0.664674i	0.0151913	−	0.0298147i
$498$	−10.6978	+	13.8695i	−0.479379	+	0.621509i
$499$		−	15.0118i		−	0.672022i	−0.941858	−	0.336011i	$-0.890922\pi$
$499$		−	15.0118i		−	0.672022i	0.941858	−	0.336011i	$-0.109078\pi$
$500$		0			0
$501$	−5.28441	+	4.98961i	−0.236090	+	0.222920i
$502$	0.304507	−	0.0482291i	0.0135908	−	0.00215257i
$503$	−9.89345	−	5.04097i	−0.441127	−	0.224766i	0.219297	−	0.975658i	$-0.429624\pi$
$503$	−9.89345	−	5.04097i	−0.441127	−	0.224766i	−0.660424	+	0.750893i	$0.729624\pi$
$504$	0.429358	−	0.112744i	0.0191251	−	0.00502200i
$505$		0			0
$506$	14.4994	+	4.71115i	0.644578	+	0.209436i
$507$	−13.2757	−	0.380921i	−0.589596	−	0.0169173i
$508$	−7.94495	+	4.04816i	−0.352500	+	0.179608i
$509$	−31.3045	+	22.7440i	−1.38755	+	1.00811i	−0.391416	+	0.920214i	$0.628015\pi$
$509$	−31.3045	+	22.7440i	−1.38755	+	1.00811i	−0.996130	+	0.0878971i	$0.971985\pi$
$510$		0			0
$511$	1.28808	+	0.935846i	0.0569814	+	0.0413994i
$512$	0.987688	+	0.156434i	0.0436501	+	0.00691349i
$513$	−15.5695	+	9.38079i	−0.687411	+	0.414172i
$514$	−4.24694	+	5.84540i	−0.187324	+	0.257830i
$515$		0			0
$516$	6.66961	+	1.25343i	0.293613	+	0.0551791i
$517$	−7.50612	−	14.7316i	−0.330119	−	0.647895i
$518$	0.879477	−	0.879477i	0.0386420	−	0.0386420i
$519$	−0.170133	+	0.0806269i	−0.00746802	+	0.00353913i
$520$		0			0
$521$	20.0378	−	6.51069i	0.877874	−	0.285239i	0.164800	−	0.986327i	$-0.447302\pi$
$521$	20.0378	−	6.51069i	0.877874	−	0.285239i	0.713074	+	0.701089i	$0.247302\pi$
$522$	−2.49410	+	4.27036i	−0.109164	+	0.186909i
$523$	1.81949	+	11.4878i	0.0795606	+	0.502326i	0.995000	+	0.0998710i	$0.0318430\pi$
$523$	1.81949	+	11.4878i	0.0795606	+	0.502326i	−0.915440	+	0.402455i	$0.868157\pi$
$524$	−1.68836			−0.0737565
$525$		0			0
$526$	−5.22487			−0.227815
$527$	−4.61442	−	29.1343i	−0.201007	−	1.26911i
$528$	1.50413	+	5.12496i	0.0654587	+	0.223035i
$529$	1.37184	−	0.445739i	0.0596454	−	0.0193800i
$530$		0			0
$531$	14.0286	−	36.0056i	0.608791	−	1.56251i
$532$	0.366021	−	0.366021i	0.0158690	−	0.0158690i
$533$	4.46465	+	8.76237i	0.193386	+	0.379541i
$534$	−2.42525	+	12.9050i	−0.104951	+	0.558453i
$535$		0			0
$536$	−2.13478	+	2.93827i	−0.0922084	+	0.126914i
$537$	−1.56781	−	2.29347i	−0.0676560	−	0.0989704i
$538$	−2.24445	−	0.355485i	−0.0967649	−	0.0153261i
$539$	17.4087	+	12.6482i	0.749847	+	0.544796i
$540$		0			0
$541$	−13.9722	+	10.1514i	−0.600713	+	0.436443i	−0.846132	−	0.532974i	$-0.821074\pi$
$541$	−13.9722	+	10.1514i	−0.600713	+	0.436443i	0.245419	+	0.969417i	$0.421074\pi$
$542$	16.8054	−	8.56276i	0.721852	−	0.367802i
$543$	0.627438	−	21.8673i	0.0269259	−	0.938414i
$544$	3.52754	+	1.14617i	0.151242	+	0.0491415i
$545$		0			0
$546$	−1.02257	−	0.558531i	−0.0437619	−	0.0239029i
$547$	−4.99544	−	2.54530i	−0.213590	−	0.108829i	0.343923	−	0.938998i	$-0.388244\pi$
$547$	−4.99544	−	2.54530i	−0.213590	−	0.108829i	−0.557512	+	0.830169i	$0.688244\pi$
$548$	14.4460	−	2.28802i	0.617101	−	0.0977393i
$549$	43.7414	+	2.51221i	1.86684	+	0.107219i
$550$		0			0
$551$			5.76660i			0.245666i
$552$	6.78051	+	5.22991i	0.288598	+	0.222600i
$553$	0.605732	−	1.18882i	0.0257583	−	0.0505536i
$554$	5.12021	+	15.7584i	0.217537	+	0.669510i
$555$		0			0
$556$	−5.51012	+	16.9584i	−0.233681	+	0.719197i
$557$	−0.714899	−	0.714899i	−0.0302913	−	0.0302913i	0.691799	−	0.722090i	$-0.256818\pi$
$557$	−0.714899	−	0.714899i	−0.0302913	−	0.0302913i	−0.722090	+	0.691799i	$0.756818\pi$
$558$	21.8440	−	9.59474i	0.924732	−	0.406178i
$559$	−10.4699	−	14.4106i	−0.442830	−	0.609504i
$560$		0			0
$561$	2.53659	+	19.6475i	0.107095	+	0.829520i
$562$	3.91756	−	24.7345i	0.165252	−	1.04336i
$563$	−0.262374	+	1.65657i	−0.0110578	+	0.0698159i	−0.992600	−	0.121429i	$-0.961252\pi$
$563$	−0.262374	+	1.65657i	−0.0110578	+	0.0698159i	0.981542	+	0.191245i	$0.0612524\pi$
$564$	−1.18908	−	9.21017i	−0.0500692	−	0.387818i
$565$		0			0
$566$	−15.7508	−	21.6791i	−0.662055	−	0.911241i
$567$	0.464771	+	1.24801i	0.0195185	+	0.0524114i
$568$	3.56480	+	3.56480i	0.149576	+	0.149576i
$569$	−3.81378	+	11.7376i	−0.159882	+	0.492066i	−0.998623	−	0.0524648i	$-0.983292\pi$
$569$	−3.81378	+	11.7376i	−0.159882	+	0.492066i	0.838741	+	0.544531i	$0.183292\pi$
$570$		0			0
$571$	−1.99738	−	6.14731i	−0.0835879	−	0.257257i	0.900524	−	0.434806i	$-0.143183\pi$
$571$	−1.99738	−	6.14731i	−0.0835879	−	0.257257i	−0.984112	+	0.177549i	$0.943183\pi$
$572$	6.36454	−	12.4911i	0.266115	−	0.522280i
$573$	−28.6267	−	22.0802i	−1.19590	−	0.922413i
$574$			0.320088i			0.0133602i
$575$		0			0
$576$	−0.172016	+	2.99506i	−0.00716735	+	0.124794i
$577$	−32.3673	+	5.12648i	−1.34747	+	0.213418i	−0.788124	−	0.615516i	$-0.788947\pi$
$577$	−32.3673	+	5.12648i	−1.34747	+	0.213418i	−0.559346	+	0.828935i	$0.688947\pi$
$578$	−2.88935	−	1.47220i	−0.120181	−	0.0612354i
$579$	10.2207	+	5.58261i	0.424760	+	0.232005i
$580$		0			0
$581$	1.42317	+	0.462415i	0.0590429	+	0.0191842i
$582$	0.460539	−	16.0506i	0.0190900	−	0.665318i
$583$	31.7252	−	16.1648i	1.31392	−	0.669477i
$584$	−8.70495	+	6.32451i	−0.360213	+	0.261710i
$585$		0			0
$586$	−2.04255	−	1.48400i	−0.0843770	−	0.0613035i
$587$	−25.8604	−	4.09589i	−1.06737	−	0.169056i	−0.402056	−	0.915615i	$-0.631704\pi$
$587$	−25.8604	−	4.09589i	−1.06737	−	0.169056i	−0.665319	+	0.746559i	$0.731704\pi$
$588$	6.82086	+	9.97786i	0.281287	+	0.411480i
$589$	16.3524	−	22.5072i	0.673790	−	0.927392i
$590$		0			0
$591$	−1.38469	+	7.36805i	−0.0569585	+	0.303081i
$592$	3.81600	+	7.48933i	0.156837	+	0.307810i
$593$	28.6751	−	28.6751i	1.17754	−	1.17754i	0.197176	−	0.980368i	$-0.436823\pi$
$593$	28.6751	−	28.6751i	1.17754	−	1.17754i	0.980368	−	0.197176i	$-0.0631772\pi$
$594$	−14.8493	+	6.02045i	−0.609276	+	0.247022i
$595$		0			0
$596$	14.6925	−	4.77388i	0.601828	−	0.195546i
$597$	−0.297951	−	1.01520i	−0.0121943	−	0.0415494i
$598$	−3.51603	−	22.1994i	−0.143781	−	0.907799i
$599$	−23.8130			−0.972971			−0.486486	−	0.873689i	$-0.661721\pi$
$599$	−23.8130			−0.972971			−0.486486	+	0.873689i	$0.661721\pi$
$600$		0			0
$601$	−24.9278			−1.01683			−0.508413	−	0.861113i	$-0.669768\pi$
$601$	−24.9278			−1.01683			−0.508413	+	0.861113i	$0.669768\pi$
$602$	−0.0906956	−	0.572630i	−0.00369648	−	0.0233386i
$603$	−9.40854	−	5.49506i	−0.383145	−	0.223776i
$604$	6.74437	−	2.19138i	0.274424	−	0.0891659i
$605$		0			0
$606$	6.55929	−	3.10847i	0.266453	−	0.126273i
$607$	−12.2020	+	12.2020i	−0.495265	+	0.495265i	−0.909960	−	0.414695i	$-0.863888\pi$
$607$	−12.2020	+	12.2020i	−0.495265	+	0.495265i	0.414695	+	0.909960i	$0.363888\pi$
$608$	1.58815	+	3.11691i	0.0644079	+	0.126408i
$609$	0.415219	+	0.0780327i	0.0168255	+	0.00316205i
$610$		0			0
$611$	−14.3273	+	19.7198i	−0.579620	+	0.797778i
$612$	−2.36798	+	10.8723i	−0.0957200	+	0.439488i
$613$	−1.82779	−	0.289494i	−0.0738239	−	0.0116926i	0.119413	−	0.992845i	$-0.461899\pi$
$613$	−1.82779	−	0.289494i	−0.0738239	−	0.0116926i	−0.193237	+	0.981152i	$0.561899\pi$
$614$	−20.7493	−	15.0753i	−0.837375	−	0.608388i
$615$		0			0
$616$	0.369154	−	0.268206i	0.0148736	−	0.0108063i
$617$	3.92556	−	2.00017i	0.158037	−	0.0805239i	−0.373183	−	0.927758i	$-0.621734\pi$
$617$	3.92556	−	2.00017i	0.158037	−	0.0805239i	0.531220	+	0.847234i	$0.321734\pi$
$618$	−30.3011	−	0.869429i	−1.21889	−	0.0349736i
$619$	4.50152	+	1.46263i	0.180931	+	0.0587882i	0.398082	−	0.917350i	$-0.369676\pi$
$619$	4.50152	+	1.46263i	0.180931	+	0.0587882i	−0.217150	+	0.976138i	$0.569676\pi$
$620$		0			0
$621$	−13.5869	+	21.8023i	−0.545224	+	0.874897i
$622$	9.38405	+	4.78141i	0.376266	+	0.191717i
$623$	1.10798	−	0.175486i	0.0443902	−	0.00703072i
$624$	5.72534	−	5.40595i	0.229197	−	0.216411i
$625$		0			0
$626$			17.7041i			0.707599i
$627$	−11.4114	+	14.7947i	−0.455727	+	0.590844i
$628$	−3.27973	+	6.43684i	−0.130876	+	0.256858i
$629$	9.63406	+	29.6506i	0.384135	+	1.18225i
$630$		0			0
$631$	9.68700	−	29.8135i	0.385633	−	1.18686i	−0.550387	−	0.834910i	$-0.685520\pi$
$631$	9.68700	−	29.8135i	0.385633	−	1.18686i	0.936020	−	0.351947i	$-0.114480\pi$
$632$	6.37589	+	6.37589i	0.253619	+	0.253619i
$633$	−7.41050	−	2.64511i	−0.294541	−	0.105134i
$634$	2.99350	+	4.12020i	0.118887	+	0.163634i
$635$		0			0
$636$	19.8345	−	2.56073i	0.786490	−	0.101540i
$637$	4.96270	−	31.3333i	0.196629	−	1.24147i
$638$	−0.795208	+	5.02075i	−0.0314826	+	0.198773i
$639$	−9.57672	+	11.7059i	−0.378849	+	0.463076i
$640$		0			0
$641$	17.3534	+	23.8849i	0.685419	+	0.943398i	0.999983	−	0.00583804i	$-0.00185832\pi$
$641$	17.3534	+	23.8849i	0.685419	+	0.943398i	−0.314564	+	0.949236i	$0.601858\pi$
$642$	−0.376953	+	1.05607i	−0.0148771	+	0.0416796i
$643$	−23.8141	−	23.8141i	−0.939135	−	0.939135i	0.0591164	−	0.998251i	$-0.481172\pi$
$643$	−23.8141	−	23.8141i	−0.939135	−	0.939135i	−0.998251	+	0.0591164i	$0.981172\pi$
$644$	0.226064	−	0.695754i	0.00890818	−	0.0274166i
$645$		0			0
$646$	4.00951	+	12.3400i	0.157752	+	0.485511i
$647$	−16.4252	+	32.2362i	−0.645740	+	1.26734i	0.303514	+	0.952827i	$0.401840\pi$
$647$	−16.4252	+	32.2362i	−0.645740	+	1.26734i	−0.949254	+	0.314509i	$0.898160\pi$
$648$	−8.99193	+	0.380938i	−0.353237	+	0.0149647i
$649$		−	39.7202i		−	1.55915i
$650$		0			0
$651$	−1.39933	−	1.48200i	−0.0548441	−	0.0580843i
$652$	2.11572	−	0.335098i	0.0828581	−	0.0131234i
$653$	−14.2513	−	7.26139i	−0.557696	−	0.284160i	0.152337	−	0.988329i	$-0.451320\pi$
$653$	−14.2513	−	7.26139i	−0.557696	−	0.284160i	−0.710033	+	0.704168i	$0.751320\pi$
$654$	0.0625286	−	0.114478i	0.00244506	−	0.00447646i
$655$		0			0
$656$	−2.05731	−	0.668459i	−0.0803243	−	0.0260990i
$657$	−21.4789	−	24.0964i	−0.837971	−	0.940091i
$658$	−0.706895	+	0.360181i	−0.0275576	+	0.0140413i
$659$	9.25834	−	6.72658i	0.360654	−	0.262030i	−0.392671	−	0.919679i	$-0.628449\pi$
$659$	9.25834	−	6.72658i	0.360654	−	0.262030i	0.753325	+	0.657649i	$0.228449\pi$
$660$		0			0
$661$	5.86553	+	4.26156i	0.228143	+	0.165755i	0.695984	−	0.718057i	$-0.254968\pi$
$661$	5.86553	+	4.26156i	0.228143	+	0.165755i	−0.467842	+	0.883812i	$0.654968\pi$
$662$	−14.5113	−	2.29836i	−0.563998	−	0.0893285i
$663$	24.1109	−	16.4822i	0.936390	−	0.640115i
$664$	−5.94416	+	8.18143i	−0.230678	+	0.317501i
$665$		0			0
$666$	−21.2168	+	13.6277i	−0.822135	+	0.528063i
$667$	3.69994	+	7.26155i	0.143262	+	0.281168i
$668$	−2.96707	+	2.96707i	−0.114800	+	0.114800i
$669$	−14.4725	−	30.5388i	−0.559538	−	1.18070i
$670$		0			0
$671$	42.8316	−	13.9168i	1.65350	−	0.537254i
$672$	0.245921	−	0.0721755i	0.00948661	−	0.00278423i
$673$	3.38928	+	21.3991i	0.130647	+	0.824874i	0.962778	+	0.270294i	$0.0871210\pi$
$673$	3.38928	+	21.3991i	0.130647	+	0.824874i	−0.832131	+	0.554580i	$0.812879\pi$
$674$	−24.7626			−0.953821
$675$		0			0
$676$	−7.66790			−0.294919
$677$	−0.271360	−	1.71330i	−0.0104292	−	0.0658476i	0.981925	−	0.189271i	$-0.0606126\pi$
$677$	−0.271360	−	1.71330i	−0.0104292	−	0.0658476i	−0.992354	+	0.123424i	$0.960613\pi$
$678$	−28.4473	+	8.34901i	−1.09251	+	0.320642i
$679$	−1.30465	+	0.423905i	−0.0500677	+	0.0162680i
$680$		0			0
$681$	8.96358	+	18.9143i	0.343485	+	0.724799i
$682$	17.3411	−	17.3411i	0.664025	−	0.664025i
$683$	5.65426	+	11.0971i	0.216354	+	0.424619i	0.973519	−	0.228604i	$-0.0734162\pi$
$683$	5.65426	+	11.0971i	0.216354	+	0.424619i	−0.757165	+	0.653224i	$0.773416\pi$
$684$	−8.83003	+	5.67159i	−0.337624	+	0.216859i
$685$		0			0
$686$	1.21575	−	1.67334i	0.0464176	−	0.0638883i
$687$	8.85120	−	6.05067i	0.337694	−	0.230847i
$688$	3.86987	+	0.612927i	0.147537	+	0.0233676i
$689$	−42.4675	−	30.8544i	−1.61788	−	1.17546i
$690$		0			0
$691$	−30.9813	+	22.5093i	−1.17859	+	0.856293i	−0.992011	−	0.126148i	$-0.959738\pi$
$691$	−30.9813	+	22.5093i	−1.17859	+	0.856293i	−0.186574	+	0.982441i	$0.559738\pi$
$692$	−0.0968510	+	0.0493481i	−0.00368172	+	0.00187593i
$693$	0.910863	+	1.02187i	0.0346008	+	0.0388175i
$694$	−30.3898	−	9.87425i	−1.15358	−	0.374821i
$695$		0			0
$696$	−1.36867	+	2.50578i	−0.0518792	+	0.0949813i
$697$	−7.14889	−	3.64254i	−0.270784	−	0.137971i
$698$	−26.7633	+	4.23889i	−1.01301	+	0.160445i
$699$	−9.00790	−	9.54010i	−0.340710	−	0.360840i
$700$		0			0
$701$		−	22.4631i		−	0.848418i	−0.905564	−	0.424209i	$-0.860552\pi$
$701$		−	22.4631i		−	0.848418i	0.905564	−	0.424209i	$-0.139448\pi$
$702$	17.8471	+	15.4763i	0.673594	+	0.584115i
$703$	−13.3491	+	26.1991i	−0.503472	+	0.988119i
$704$	0.952916	+	2.93277i	0.0359144	+	0.110533i
$705$		0			0
$706$	1.91730	−	5.90085i	0.0721587	−	0.222082i
$707$	−0.438483	−	0.438483i	−0.0164909	−	0.0164909i
$708$	7.49989	−	21.0116i	0.281863	−	0.789664i
$709$	23.3849	+	32.1865i	0.878238	+	1.20879i	0.976906	+	0.213670i	$0.0685418\pi$
$709$	23.3849	+	32.1865i	0.878238	+	1.20879i	−0.0986680	+	0.995120i	$0.531458\pi$
$710$		0			0
$711$	−17.1286	+	20.9367i	−0.642374	+	0.785188i
$712$	−1.18595	+	7.48779i	−0.0444453	+	0.280617i
$713$	6.15069	−	38.8339i	0.230345	−	1.45434i
$714$	0.942787	−	0.121718i	0.0352829	−	0.00455519i
$715$		0			0
$716$	−0.942782	−	1.29763i	−0.0352334	−	0.0484946i
$717$	−27.5383	−	9.82952i	−1.02844	−	0.367090i
$718$	24.2007	+	24.2007i	0.903162	+	0.903162i
$719$	3.27225	−	10.0709i	0.122034	−	0.375583i	−0.871315	−	0.490724i	$-0.836732\pi$
$719$	3.27225	−	10.0709i	0.122034	−	0.375583i	0.993349	+	0.115142i	$0.0367322\pi$
$720$		0			0
$721$	0.800268	+	2.46297i	0.0298036	+	0.0917259i
$722$	3.07017	−	6.02555i	0.114260	−	0.224248i
$723$	10.4179	−	13.5067i	0.387447	−	0.502320i
$724$		−	12.6303i		−	0.469400i
$725$		0			0
$726$	1.87745	−	1.77272i	0.0696788	−	0.0657918i
$727$	12.8632	−	2.03732i	0.477068	−	0.0755602i	0.0867303	−	0.996232i	$-0.472358\pi$
$727$	12.8632	−	2.03732i	0.477068	−	0.0755602i	0.390338	+	0.920672i	$0.372358\pi$
$728$	−0.599386	−	0.305402i	−0.0222147	−	0.0113190i
$729$	−3.82242	−	26.7281i	−0.141571	−	0.989928i
$730$		0			0
$731$	13.8213	+	4.49080i	0.511198	+	0.166098i
$732$	25.2853	+	0.725511i	0.934571	+	0.0268157i
$733$	38.5339	−	19.6340i	1.42328	−	0.725199i	0.438458	−	0.898752i	$-0.355525\pi$
$733$	38.5339	−	19.6340i	1.42328	−	0.725199i	0.984824	+	0.173553i	$0.0555249\pi$
$734$	9.83080	−	7.14249i	0.362861	−	0.263634i
$735$		0			0
$736$	3.99972	+	2.90597i	0.147432	+	0.107115i
$737$	−11.0618	−	1.75202i	−0.407467	−	0.0645364i
$738$	1.38104	−	6.34089i	0.0508367	−	0.233411i
$739$	7.30628	−	10.0562i	0.268766	−	0.369924i	−0.653207	−	0.757180i	$-0.726577\pi$
$739$	7.30628	−	10.0562i	0.268766	−	0.369924i	0.921973	+	0.387255i	$0.126577\pi$
$740$		0			0
$741$	27.0717	+	5.08763i	0.994504	+	0.186899i
$742$	−0.775666	−	1.52233i	−0.0284756	−	0.0558865i
$743$	5.87728	−	5.87728i	0.215616	−	0.215616i	−0.591032	−	0.806648i	$-0.701279\pi$
$743$	5.87728	−	5.87728i	0.215616	−	0.215616i	0.806648	+	0.591032i	$0.201279\pi$
$744$	12.4476	−	5.89897i	0.456351	−	0.216267i
$745$		0			0
$746$	−24.3715	+	7.91878i	−0.892304	+	0.289927i
$747$	−26.1975	−	15.3007i	−0.958517	−	0.559822i
$748$	1.78924	+	11.2968i	0.0654213	+	0.413054i
$749$	0.0957962			0.00350032
$750$		0			0
$751$	−30.0007			−1.09474			−0.547371	−	0.836890i	$-0.684371\pi$
$751$	−30.0007			−1.09474			−0.547371	+	0.836890i	$0.684371\pi$
$752$	−0.838744	−	5.29562i	−0.0305858	−	0.193111i
$753$	0.150380	+	0.512383i	0.00548014	+	0.0186723i
$754$	7.12739	−	2.31583i	0.259564	−	0.0843376i
$755$		0			0
$756$	0.288891	+	0.712545i	0.0105069	+	0.0259150i
$757$	0.751496	−	0.751496i	0.0273136	−	0.0273136i	−0.693318	−	0.720632i	$-0.743852\pi$
$757$	0.751496	−	0.751496i	0.0273136	−	0.0273136i	0.720632	+	0.693318i	$0.243852\pi$
$758$	2.93286	+	5.75606i	0.106526	+	0.209069i
$759$	−4.87717	+	25.9518i	−0.177030	+	0.941992i
$760$		0			0
$761$	26.8487	−	36.9541i	0.973266	−	1.33959i	0.0328857	−	0.999459i	$-0.489530\pi$
$761$	26.8487	−	36.9541i	0.973266	−	1.33959i	0.940380	−	0.340126i	$-0.110470\pi$
$762$	−8.71589	−	12.7500i	−0.315743	−	0.461884i
$763$	−0.0110066	−	0.00174328i	−0.000398467	−	6.31110e-5i
$764$	−16.8865	−	12.2687i	−0.610931	−	0.443867i
$765$		0			0
$766$	−0.221873	+	0.161200i	−0.00801659	+	0.00582440i
$767$	−52.1757	+	26.5848i	−1.88395	+	0.959922i
$768$	−0.0496773	+	1.73134i	−0.00179258	+	0.0624743i
$769$	−40.4186	−	13.1328i	−1.45753	−	0.473580i	−0.530216	−	0.847863i	$-0.677889\pi$
$769$	−40.4186	−	13.1328i	−1.45753	−	0.473580i	−0.927315	+	0.374283i	$0.877889\pi$
$770$		0			0
$771$	−10.9831	−	5.99899i	−0.395545	−	0.216048i
$772$	5.99097	+	3.05255i	0.215620	+	0.109864i
$773$	−45.3851	+	7.18830i	−1.63239	+	0.258545i	−0.904288	−	0.426923i	$-0.859597\pi$
$773$	−45.3851	+	7.18830i	−1.63239	+	0.258545i	−0.728102	+	0.685469i	$0.759597\pi$
$774$	−0.673979	+	11.7350i	−0.0242257	+	0.421805i
$775$		0			0
$776$		−	9.27062i		−	0.332796i
$777$	1.70581	+	1.31571i	0.0611955	+	0.0472010i
$778$	12.4216	−	24.3788i	0.445336	−	0.874021i
$779$	−2.33840	−	7.19686i	−0.0837819	−	0.257854i
$780$		0			0
$781$	−4.80402	+	14.7853i	−0.171901	+	0.529058i
$782$	12.9665	+	12.9665i	0.463681	+	0.463681i
$783$	−7.88873	−	3.33730i	−0.281920	−	0.119265i
$784$	4.10163	+	5.64541i	0.146487	+	0.201622i
$785$		0			0
$786$	−0.374437	−	2.90026i	−0.0133557	−	0.103449i
$787$	−3.38594	+	21.3780i	−0.120696	+	0.762043i	0.850888	+	0.525347i	$0.176064\pi$
$787$	−3.38594	+	21.3780i	−0.120696	+	0.762043i	−0.971584	+	0.236696i	$0.923936\pi$
$788$	−0.677114	+	4.27513i	−0.0241212	+	0.152295i
$789$	−1.15875	−	8.97526i	−0.0412525	−	0.319528i
$790$		0			0
$791$	1.48874	+	2.04907i	0.0529335	+	0.0728567i
$792$	−8.47005	+	3.72037i	−0.300970	+	0.132198i
$793$	−46.9482	−	46.9482i	−1.66718	−	1.66718i
$794$	0.366520	−	1.12803i	0.0130073	−	0.0400323i
$795$		0			0
$796$	−0.188762	−	0.580951i	−0.00669050	−	0.0205913i
$797$	10.1366	−	19.8941i	0.359055	−	0.704685i	−0.638853	−	0.769328i	$-0.720591\pi$
$797$	10.1366	−	19.8941i	0.359055	−	0.704685i	0.997908	+	0.0646433i	$0.0205910\pi$
$798$	0.709924	+	0.547575i	0.0251310	+	0.0193839i
$799$		−	19.8867i		−	0.703539i
$800$		0			0
$801$	−22.7060	−	1.30408i	−0.802276	−	0.0460773i
$802$	−4.32542	+	0.685079i	−0.152736	+	0.0241910i
$803$	−29.5639	−	15.0636i	−1.04329	−	0.531581i
$804$	−5.52078	−	3.01547i	−0.194703	−	0.106348i
$805$		0			0
$806$	−34.3854	−	11.1725i	−1.21117	−	0.393534i
$807$	0.112888	−	3.93433i	0.00397384	−	0.138495i
$808$	3.73397	−	1.90255i	0.131361	−	0.0669316i
$809$	10.1700	−	7.38891i	0.357557	−	0.259780i	−0.394476	−	0.918906i	$-0.629074\pi$
$809$	10.1700	−	7.38891i	0.357557	−	0.259780i	0.752032	+	0.659126i	$0.229074\pi$
$810$		0			0
$811$	20.5014	+	14.8951i	0.719902	+	0.523039i	0.886353	−	0.463010i	$-0.153231\pi$
$811$	20.5014	+	14.8951i	0.719902	+	0.523039i	−0.166451	+	0.986050i	$0.553231\pi$
$812$	0.240920	+	0.0381580i	0.00845465	+	0.00133908i
$813$	18.4361	+	26.9691i	0.646581	+	0.945849i
$814$	−15.2354	+	20.9697i	−0.533999	+	0.734987i
$815$		0			0
$816$	−1.18656	+	6.31377i	−0.0415378	+	0.221026i
$817$	6.22253	+	12.2124i	0.217699	+	0.427258i
$818$	22.9288	−	22.9288i	0.801687	−	0.801687i
$819$	0.732660	−	1.88043i	0.0256012	−	0.0657075i
$820$		0			0
$821$	−23.8661	+	7.75457i	−0.832933	+	0.270636i	−0.694280	−	0.719705i	$-0.744277\pi$
$821$	−23.8661	+	7.75457i	−0.832933	+	0.270636i	−0.138653	+	0.990341i	$0.544277\pi$
$822$	7.13410	+	24.3078i	0.248830	+	0.847831i
$823$	−6.78412	−	42.8332i	−0.236479	−	1.49307i	−0.764933	−	0.644110i	$-0.777228\pi$
$823$	−6.78412	−	42.8332i	−0.236479	−	1.49307i	0.528454	−	0.848962i	$-0.322772\pi$
$824$	−17.5015			−0.609695
$825$		0			0
$826$	−1.90597			−0.0663172
$827$	−0.349392	−	2.20597i	−0.0121495	−	0.0767091i	0.980869	−	0.194671i	$-0.0623639\pi$
$827$	−0.349392	−	2.20597i	−0.0121495	−	0.0767091i	−0.993018	+	0.117962i	$0.962364\pi$
$828$	−7.48016	+	12.8074i	−0.259953	+	0.445088i
$829$	8.12669	−	2.64052i	0.282251	−	0.0917091i	−0.164470	−	0.986382i	$-0.552591\pi$
$829$	8.12669	−	2.64052i	0.282251	−	0.0917091i	0.446722	+	0.894673i	$0.352591\pi$
$830$		0			0
$831$	−25.9341	+	12.2903i	−0.899645	+	0.426345i
$832$	3.21465	−	3.21465i	0.111448	−	0.111448i
$833$	11.7503	+	23.0613i	0.407124	+	0.799026i
$834$	−30.3531	−	5.70430i	−1.05104	−	0.197524i
$835$		0			0
$836$	−6.34067	+	8.72718i	−0.219296	+	0.301836i
$837$	21.3263	+	35.3957i	0.737143	+	1.22345i
$838$	29.0878	+	4.60705i	1.00482	+	0.159148i
$839$	0.581684	+	0.422618i	0.0200819	+	0.0145904i	0.597781	−	0.801659i	$-0.296049\pi$
$839$	0.581684	+	0.422618i	0.0200819	+	0.0145904i	−0.577699	+	0.816250i	$0.696049\pi$
$840$		0			0
$841$	21.2631	−	15.4485i	0.733210	−	0.532708i
$842$	−5.28652	+	2.69362i	−0.182186	+	0.0928282i
$843$	43.3576	+	1.24406i	1.49331	+	0.0428477i
$844$	−4.32049	−	1.40381i	−0.148718	−	0.0483213i
$845$		0			0
$846$	15.5575	−	4.08518i	0.534877	−	0.140451i
$847$	−0.196551	−	0.100148i	−0.00675357	−	0.00344111i
$848$	11.4044	−	1.80627i	0.391627	−	0.0620276i
$849$	33.7471	−	31.8645i	1.15820	−	1.09359i
$850$		0			0
$851$			41.5561i			1.42452i
$852$	−5.33301	+	6.91418i	−0.182706	+	0.236876i
$853$	−18.0934	+	35.5102i	−0.619505	+	1.21585i	0.341647	+	0.939828i	$0.389015\pi$
$853$	−18.0934	+	35.5102i	−0.619505	+	1.21585i	−0.961152	+	0.276019i	$0.910985\pi$
$854$	−0.667799	−	2.05527i	−0.0228516	−	0.0703300i
$855$		0			0
$856$	−0.200057	+	0.615712i	−0.00683780	+	0.0210446i
$857$	−24.3570	−	24.3570i	−0.832018	−	0.832018i	0.155774	−	0.987793i	$-0.450213\pi$
$857$	−24.3570	−	24.3570i	−0.832018	−	0.832018i	−0.987793	+	0.155774i	$0.950213\pi$
$858$	22.8687	+	8.16275i	0.780723	+	0.278672i
$859$	−12.1583	−	16.7344i	−0.414835	−	0.570971i	0.549555	−	0.835458i	$-0.314797\pi$
$859$	−12.1583	−	16.7344i	−0.414835	−	0.570971i	−0.964389	+	0.264487i	$0.914797\pi$
$860$		0			0
$861$	−0.549846	+	0.0709877i	−0.0187387	+	0.00241925i
$862$	2.75506	−	17.3948i	0.0938378	−	0.592468i
$863$	−9.03734	+	57.0595i	−0.307634	+	1.94233i	0.0260968	+	0.999659i	$0.491692\pi$
$863$	−9.03734	+	57.0595i	−0.307634	+	1.94233i	−0.333731	+	0.942668i	$0.608308\pi$
$864$	−5.18305	+	0.368742i	−0.176331	+	0.0125449i
$865$		0			0
$866$	5.33218	+	7.33912i	0.181195	+	0.249393i
$867$	1.88815	−	5.28981i	0.0641248	−	0.179651i
$868$	−0.832112	−	0.832112i	−0.0282437	−	0.0282437i
$869$	−8.59232	+	26.4445i	−0.291475	+	0.897067i
$870$		0			0
$871$	5.10228	+	15.7032i	0.172884	+	0.532083i
$872$	0.0341904	−	0.0671024i	0.00115783	−	0.00227237i
$873$	27.6737	−	2.76851i	0.936614	−	0.0936999i
$874$			17.2948i			0.585006i
$875$		0			0
$876$	−12.7948	−	13.5507i	−0.432295	−	0.457835i
$877$	−39.1633	+	6.20286i	−1.32245	+	0.209456i	−0.777432	−	0.628967i	$-0.783478\pi$
$877$	−39.1633	+	6.20286i	−1.32245	+	0.209456i	−0.545020	+	0.838423i	$0.683478\pi$
$878$	−25.7429	−	13.1166i	−0.868779	−	0.442665i
$879$	2.09622	−	3.83779i	0.0707037	−	0.129446i
$880$		0			0
$881$	17.2013	+	5.58904i	0.579526	+	0.188299i	0.584088	−	0.811690i	$-0.301452\pi$
$881$	17.2013	+	5.58904i	0.579526	+	0.188299i	−0.00456226	+	0.999990i	$0.501452\pi$
$882$	−15.6272	+	13.9297i	−0.526196	+	0.469036i
$883$	43.8739	−	22.3549i	1.47647	−	0.752301i	0.484037	−	0.875048i	$-0.339170\pi$
$883$	43.8739	−	22.3549i	1.47647	−	0.752301i	0.992438	+	0.122746i	$0.0391702\pi$
$884$	13.6418	−	9.91133i	0.458823	−	0.333354i
$885$		0			0
$886$	−14.2445	−	10.3492i	−0.478552	−	0.347689i
$887$	−9.93256	−	1.57316i	−0.333503	−	0.0528216i	−0.0125625	−	0.999921i	$-0.503999\pi$
$887$	−9.93256	−	1.57316i	−0.333503	−	0.0528216i	−0.320940	+	0.947099i	$0.603999\pi$
$888$	−12.0188	+	8.21606i	−0.403326	+	0.275713i
$889$	−0.775544	+	1.06745i	−0.0260109	+	0.0358010i
$890$		0			0
$891$	−13.6351	−	24.1729i	−0.456793	−	0.809823i
$892$	−8.85794	−	17.3847i	−0.296586	−	0.582082i
$893$	13.2625	−	13.2625i	0.443813	−	0.443813i
$894$	11.4590	+	24.1800i	0.383246	+	0.808699i
$895$		0			0
$896$	0.140729	−	0.0457256i	0.00470143	−	0.00152759i
$897$	37.3542	−	10.9631i	1.24722	−	0.366047i
$898$	2.01023	+	12.6921i	0.0670823	+	0.423541i
$899$	13.1098			0.437236
$900$		0			0
$901$	42.8268			1.42677
$902$	−1.04351	−	6.58847i	−0.0347451	−	0.219372i
$903$	0.963546	−	0.282791i	0.0320648	−	0.00941071i
$904$	−16.2790	+	5.28938i	−0.541433	+	0.175922i
$905$		0			0
$906$	5.26007	+	11.0994i	0.174754	+	0.368754i
$907$	22.2868	−	22.2868i	0.740021	−	0.740021i	−0.232561	−	0.972582i	$-0.574710\pi$
$907$	22.2868	−	22.2868i	0.740021	−	0.740021i	0.972582	+	0.232561i	$0.0747104\pi$
$908$	5.48620	+	10.7673i	0.182066	+	0.357324i
$909$	6.79440	+	10.5781i	0.225356	+	0.350854i
$910$		0			0
$911$	−3.12524	+	4.30152i	−0.103544	+	0.142516i	−0.857645	−	0.514243i	$-0.828073\pi$
$911$	−3.12524	+	4.30152i	−0.103544	+	0.142516i	0.754101	+	0.656759i	$0.228073\pi$
$912$	−5.00200	+	3.41936i	−0.165633	+	0.113226i
$913$	−30.8009	−	4.87839i	−1.01936	−	0.161451i
$914$	12.5639	+	9.12823i	0.415578	+	0.301935i
$915$		0			0
$916$	5.00795	−	3.63849i	0.165467	−	0.120219i
$917$	−0.222600	+	0.113420i	−0.00735089	+	0.00374546i
$918$	−19.2016	−	1.65649i	−0.633746	−	0.0546723i
$919$	21.4823	+	6.98001i	0.708635	+	0.230249i	0.641089	−	0.767467i	$-0.278483\pi$
$919$	21.4823	+	6.98001i	0.708635	+	0.230249i	0.0675461	+	0.997716i	$0.478483\pi$
$920$		0			0
$921$	21.2945	−	38.9864i	0.701678	−	1.28464i
$922$	9.99809	+	5.09428i	0.329270	+	0.167771i
$923$	22.6370	−	3.58534i	0.745105	−	0.118013i
$924$	0.542592	+	0.574649i	0.0178500	+	0.0189045i
$925$		0			0
$926$			1.29066i			0.0424139i
$927$	−5.22653	−	52.2438i	−0.171662	−	1.71591i
$928$	−0.748381	+	1.46878i	−0.0245668	+	0.0482151i
$929$	14.5401	+	44.7499i	0.477046	+	1.46820i	0.843178	+	0.537634i	$0.180682\pi$
$929$	14.5401	+	44.7499i	0.477046	+	1.46820i	−0.366132	+	0.930563i	$0.619318\pi$
$930$		0			0
$931$	−7.54334	+	23.2160i	−0.247223	+	0.760874i
$932$	−5.35655	−	5.35655i	−0.175460	−	0.175460i
$933$	−6.13233	+	17.1803i	−0.200763	+	0.562456i
$934$	21.5074	+	29.6023i	0.703743	+	0.968618i
$935$		0			0
$936$	10.5560	+	8.63604i	0.345035	+	0.282278i
$937$	−5.23090	+	33.0266i	−0.170886	+	1.07893i	0.741905	+	0.670505i	$0.233923\pi$
$937$	−5.23090	+	33.0266i	−0.170886	+	1.07893i	−0.912791	+	0.408427i	$0.866077\pi$
$938$	−0.0840705	+	0.530801i	−0.00274500	+	0.0173313i
$939$	−30.4121	+	3.92634i	−0.992460	+	0.128131i
$940$		0			0
$941$	3.42075	+	4.70826i	0.111513	+	0.153485i	0.861126	−	0.508392i	$-0.169760\pi$
$941$	3.42075	+	4.70826i	0.111513	+	0.153485i	−0.749612	+	0.661877i	$0.769760\pi$
$942$	−11.7845	−	4.20637i	−0.383960	−	0.137051i
$943$	−7.56223	−	7.56223i	−0.246260	−	0.246260i
$944$	3.98035	−	12.2503i	0.129549	−	0.398712i
$945$		0			0
$946$	3.73363	+	11.4909i	0.121391	+	0.373602i
$947$	−7.66387	+	15.0412i	−0.249042	+	0.488773i	−0.981357	−	0.192193i	$-0.938440\pi$
$947$	−7.66387	+	15.0412i	−0.249042	+	0.488773i	0.732315	+	0.680966i	$0.238440\pi$
$948$	−9.53845	+	12.3665i	−0.309795	+	0.401645i
$949$			48.9166i			1.58790i
$950$		0			0
$951$	−6.41377	+	6.05598i	−0.207981	+	0.196379i
$952$	0.542079	−	0.0858568i	0.0175689	−	0.00278264i
$953$	−15.8844	−	8.09351i	−0.514547	−	0.262175i	0.177380	−	0.984142i	$-0.443238\pi$
$953$	−15.8844	−	8.09351i	−0.514547	−	0.262175i	−0.691927	+	0.721968i	$0.743238\pi$
$954$	8.79761	+	33.5037i	0.284833	+	1.08472i
$955$		0			0
$956$	−16.0554	−	5.21673i	−0.519270	−	0.168721i
$957$	−8.80096	−	0.252526i	−0.284495	−	0.00816301i
$958$	−24.7755	+	12.6238i	−0.800460	+	0.407855i
$959$	1.75090	−	1.27210i	0.0565396	−	0.0410784i
$960$		0			0
$961$	−26.0882	−	18.9542i	−0.841556	−	0.611426i
$962$	37.7425	+	5.97782i	1.21687	+	0.192733i
$963$	−1.89770	−	0.413318i	−0.0611527	−	0.0133190i
$964$	5.78866	−	7.96740i	0.186440	−	0.256613i
$965$		0			0
$966$	1.24530	+	0.234031i	0.0400668	+	0.00752982i
$967$	18.3163	+	35.9477i	0.589011	+	1.15600i	0.972598	+	0.232495i	$0.0746889\pi$
$967$	18.3163	+	35.9477i	0.589011	+	1.15600i	−0.383586	+	0.923505i	$0.625311\pi$
$968$	1.05415	−	1.05415i	0.0338816	−	0.0338816i
$969$	−20.3084	+	9.62422i	−0.652399	+	0.309175i
$970$		0			0
$971$	−25.6210	+	8.32477i	−0.822217	+	0.267155i	−0.689764	−	0.724035i	$-0.742286\pi$
$971$	−25.6210	+	8.32477i	−0.822217	+	0.267155i	−0.132454	+	0.991189i	$0.542286\pi$
$972$	−2.64856	−	15.3618i	−0.0849526	−	0.492730i
$973$	0.412752	+	2.60601i	0.0132322	+	0.0835449i
$974$	9.57080			0.306668
$975$		0			0
$976$	14.6045			0.467478
$977$	1.79808	+	11.3526i	0.0575256	+	0.363202i	0.999613	+	0.0278335i	$0.00886083\pi$
$977$	1.79808	+	11.3526i	0.0575256	+	0.363202i	−0.942087	+	0.335369i	$0.891139\pi$
$978$	1.04484	+	3.56006i	0.0334104	+	0.113838i
$979$	−22.2337	+	7.22418i	−0.710593	+	0.230886i
$980$		0			0
$981$	0.210518	+	0.0820227i	0.00672131	+	0.00261878i
$982$	−7.38969	+	7.38969i	−0.235814	+	0.235814i
$983$	14.5645	+	28.5844i	0.464535	+	0.911702i	0.997834	+	0.0657754i	$0.0209521\pi$
$983$	14.5645	+	28.5844i	0.464535	+	0.911702i	−0.533299	+	0.845927i	$0.679048\pi$
$984$	0.692016	−	3.68228i	0.0220607	−	0.117387i
$985$		0			0
$986$	−3.59385	+	4.94651i	−0.114451	+	0.157529i
$987$	−0.775489	−	1.13442i	−0.0246841	−	0.0361090i
$988$	15.7077	+	2.48785i	0.499728	+	0.0791491i
$989$	15.6713	+	11.3859i	0.498320	+	0.362051i
$990$		0			0
$991$	12.7382	−	9.25484i	0.404642	−	0.293990i	−0.366787	−	0.930305i	$-0.619542\pi$
$991$	12.7382	−	9.25484i	0.404642	−	0.293990i	0.771429	+	0.636315i	$0.219542\pi$
$992$	7.08598	−	3.61049i	0.224980	−	0.114633i
$993$	0.729868	−	25.4371i	0.0231617	−	0.807223i
$994$	0.709470	+	0.230521i	0.0225030	+	0.00731167i
$995$		0			0
$996$	−15.3723	−	8.39640i	−0.487089	−	0.266050i
$997$	8.15491	+	4.15513i	0.258269	+	0.131594i	0.578331	−	0.815802i	$-0.303704\pi$
$997$	8.15491	+	4.15513i	0.258269	+	0.131594i	−0.320063	+	0.947396i	$0.603704\pi$
$998$	14.8270	−	2.34837i	0.469341	−	0.0743363i
$999$	−28.1150	−	33.4238i	−0.889518	−	1.05748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.c.293.6		80
3.2	odd	2	inner	750.2.l.c.293.3		80
5.2	odd	4		150.2.l.a.137.3	yes	80
5.3	odd	4		750.2.l.b.707.8		80
5.4	even	2		750.2.l.a.293.5		80
15.2	even	4		150.2.l.a.137.10	yes	80
15.8	even	4		750.2.l.b.707.1		80
15.14	odd	2		750.2.l.a.293.8		80
25.2	odd	20	inner	750.2.l.c.407.3		80
25.11	even	5		150.2.l.a.23.10	yes	80
25.14	even	10		750.2.l.b.593.1		80
25.23	odd	20		750.2.l.a.407.8		80
75.2	even	20	inner	750.2.l.c.407.6		80
75.11	odd	10		150.2.l.a.23.3	✓	80
75.14	odd	10		750.2.l.b.593.8		80
75.23	even	20		750.2.l.a.407.5		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.23.3	✓	80	75.11	odd	10
150.2.l.a.23.10	yes	80	25.11	even	5
150.2.l.a.137.3	yes	80	5.2	odd	4
150.2.l.a.137.10	yes	80	15.2	even	4
750.2.l.a.293.5		80	5.4	even	2
750.2.l.a.293.8		80	15.14	odd	2
750.2.l.a.407.5		80	75.23	even	20
750.2.l.a.407.8		80	25.23	odd	20
750.2.l.b.593.1		80	25.14	even	10
750.2.l.b.593.8		80	75.14	odd	10
750.2.l.b.707.1		80	15.8	even	4
750.2.l.b.707.8		80	5.3	odd	4
750.2.l.c.293.3		80	3.2	odd	2	inner
750.2.l.c.293.6		80	1.1	even	1	trivial
750.2.l.c.407.3		80	25.2	odd	20	inner
750.2.l.c.407.6		80	75.2	even	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.156434 + 0.987688i) q^{2} +(-1.66195 + 0.487767i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-0.741748 - 1.56519i) q^{6} +(-0.104631 + 0.104631i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(2.52417 - 1.62129i) q^{9} +O(q^{10})\)	\(q+(0.156434 + 0.987688i) q^{2} +(-1.66195 + 0.487767i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-0.741748 - 1.56519i) q^{6} +(-0.104631 + 0.104631i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(2.52417 - 1.62129i) q^{9} +(1.81255 - 2.49477i) q^{11} +(1.42988 - 0.977465i) q^{12} +(-4.49023 - 0.711182i) q^{13} +(-0.119711 - 0.0869753i) q^{14} +(0.809017 - 0.587785i) q^{16} +(3.30481 - 1.68388i) q^{17} +(1.99620 + 2.23946i) q^{18} +(3.32698 + 1.08100i) q^{19} +(0.122857 - 0.224928i) q^{21} +(2.74760 + 1.39997i) q^{22} +(4.88306 - 0.773401i) q^{23} +(1.18911 + 1.25937i) q^{24} -4.54620i q^{26} +(-3.40423 + 3.92571i) q^{27} +(0.0671775 - 0.131843i) q^{28} +(0.509399 + 1.56777i) q^{29} +(2.45755 - 7.56355i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.79551 + 5.03028i) q^{33} +(2.18014 + 3.00070i) q^{34} +(-1.89962 + 2.32195i) q^{36} +(-1.31491 + 8.30199i) q^{37} +(-0.547238 + 3.45513i) q^{38} +(7.80943 - 1.00823i) q^{39} +(-1.27149 - 1.75005i) q^{41} +(0.241378 + 0.0861576i) q^{42} +(2.77052 + 2.77052i) q^{43} +(-0.952916 + 2.93277i) q^{44} +(1.52776 + 4.70196i) q^{46} +(2.43413 - 4.77725i) q^{47} +(-1.05784 + 1.37148i) q^{48} +6.97810i q^{49} +(-4.67109 + 4.41051i) q^{51} +(4.49023 - 0.711182i) q^{52} +(10.2880 + 5.24200i) q^{53} +(-4.40992 - 2.74820i) q^{54} +(0.140729 + 0.0457256i) q^{56} +(-6.05656 - 0.173781i) q^{57} +(-1.46878 + 0.748381i) q^{58} +(10.4207 - 7.57107i) q^{59} +(11.8153 + 8.58430i) q^{61} +(7.85487 + 1.24409i) q^{62} +(-0.0944693 + 0.433745i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-5.24923 - 0.986496i) q^{66} +(-1.64885 - 3.23605i) q^{67} +(-2.62271 + 2.62271i) q^{68} +(-7.73817 + 3.66715i) q^{69} +(-4.79465 + 1.55788i) q^{71} +(-2.59053 - 1.51300i) q^{72} +(-1.68322 - 10.6274i) q^{73} -8.40547 q^{74} -3.49819 q^{76} +(0.0713809 + 0.450681i) q^{77} +(2.21748 + 7.55556i) q^{78} +(-8.57556 + 2.78637i) q^{79} +(3.74283 - 8.18481i) q^{81} +(1.52960 - 1.52960i) q^{82} +(-4.59112 - 9.01058i) q^{83} +(-0.0473370 + 0.251884i) q^{84} +(-2.30301 + 3.16982i) q^{86} +(-1.61130 - 2.35709i) q^{87} +(-3.04574 - 0.482397i) q^{88} +(-6.13326 - 4.45607i) q^{89} +(0.544231 - 0.395407i) q^{91} +(-4.40507 + 2.24450i) q^{92} +(-0.395073 + 13.7690i) q^{93} +(5.09921 + 1.65683i) q^{94} +(-1.52008 - 0.830274i) q^{96} +(8.26018 + 4.20877i) q^{97} +(-6.89219 + 1.09162i) q^{98} +(0.530447 - 9.23588i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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