LMFDB - Embedded newform 375.2.l.c.257.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,2,Mod(32,375)] 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("375.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.l (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [64,0,10,-20,0,-6,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			257.4
Character	$\chi$	$=$	375.257
Dual form			375.2.l.c.143.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0231951 - 0.0455229i) q^{2} +(1.39036 + 1.03290i) q^{3} +(1.17404 - 1.61592i) q^{4} +(0.0147712 - 0.0872517i) q^{6} +(-1.44136 - 1.44136i) q^{7} +(-0.201718 - 0.0319491i) q^{8} +(0.866221 + 2.87222i) q^{9} +(2.86751 + 0.931709i) q^{11} +(3.30143 - 1.03405i) q^{12} +(2.79268 + 1.42294i) q^{13} +(-0.0321825 + 0.0990475i) q^{14} +(-1.23123 - 3.78934i) q^{16} +(0.952042 - 6.01096i) q^{17} +(0.110660 - 0.106054i) q^{18} +(1.91085 + 2.63007i) q^{19} +(-0.515229 - 3.49280i) q^{21} +(-0.0240979 - 0.152148i) q^{22} +(-5.12542 + 2.61153i) q^{23} +(-0.247462 - 0.252776i) q^{24} -0.160136i q^{26} +(-1.76237 + 4.88816i) q^{27} +(-4.02134 + 0.636918i) q^{28} +(-0.976916 - 0.709771i) q^{29} +(-0.0161330 + 0.0117213i) q^{31} +(-0.432772 + 0.432772i) q^{32} +(3.02451 + 4.25727i) q^{33} +(-0.295719 + 0.0960849i) q^{34} +(5.65826 + 1.97235i) q^{36} +(-1.24327 + 2.44005i) q^{37} +(0.0754058 - 0.147992i) q^{38} +(2.41308 + 4.86298i) q^{39} +(-10.1904 + 3.31106i) q^{41} +(-0.147052 + 0.104471i) q^{42} +(3.91319 - 3.91319i) q^{43} +(4.87212 - 3.53981i) q^{44} +(0.237769 + 0.172749i) q^{46} +(-3.63479 + 0.575694i) q^{47} +(2.20216 - 6.54030i) q^{48} -2.84495i q^{49} +(7.53242 - 7.37405i) q^{51} +(5.57807 - 2.84217i) q^{52} +(0.635421 + 4.01189i) q^{53} +(0.263401 - 0.0331531i) q^{54} +(0.244699 + 0.336799i) q^{56} +(-0.0598219 + 5.63047i) q^{57} +(-0.00965120 + 0.0609353i) q^{58} +(-1.33548 - 4.11017i) q^{59} +(-3.99489 + 12.2950i) q^{61} +(0.000907794 + 0.000462544i) q^{62} +(2.89137 - 5.38845i) q^{63} +(-7.54893 - 2.45280i) q^{64} +(0.123650 - 0.236432i) q^{66} +(0.920343 + 0.145768i) q^{67} +(-8.59551 - 8.59551i) q^{68} +(-9.82366 - 1.66309i) q^{69} +(-5.79154 + 7.97137i) q^{71} +(-0.0829678 - 0.607055i) q^{72} +(-0.0177571 - 0.0348503i) q^{73} +0.139916 q^{74} +6.49339 q^{76} +(-2.79018 - 5.47604i) q^{77} +(0.165405 - 0.222648i) q^{78} +(-6.00647 + 8.26720i) q^{79} +(-7.49932 + 4.97596i) q^{81} +(0.387096 + 0.387096i) q^{82} +(2.17217 + 0.344039i) q^{83} +(-6.24900 - 3.26811i) q^{84} +(-0.268906 - 0.0873730i) q^{86} +(-0.625143 - 1.99590i) q^{87} +(-0.548661 - 0.279557i) q^{88} +(4.18096 - 12.8677i) q^{89} +(-1.97429 - 6.07624i) q^{91} +(-1.79740 + 11.3483i) q^{92} +(-0.0345377 - 0.000366951i) q^{93} +(0.110516 + 0.152113i) q^{94} +(-1.04872 + 0.154699i) q^{96} +(0.838657 + 5.29507i) q^{97} +(-0.129510 + 0.0659889i) q^{98} +(-0.192183 + 9.04318i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 10 q^{3} - 20 q^{4} - 6 q^{6} + 20 q^{7} - 10 q^{9} + 10 q^{12} + 20 q^{13} - 8 q^{16} + 10 q^{18} - 6 q^{21} - 20 q^{22} + 10 q^{27} - 40 q^{28} - 12 q^{31} + 10 q^{33} + 20 q^{34} - 22 q^{36} + 20 q^{37}+ \cdots - 120 q^{97}+O(q^{100}) $ 64 * q + 10 * q^3 - 20 * q^4 - 6 * q^6 + 20 * q^7 - 10 * q^9 + 10 * q^12 + 20 * q^13 - 8 * q^16 + 10 * q^18 - 6 * q^21 - 20 * q^22 + 10 * q^27 - 40 * q^28 - 12 * q^31 + 10 * q^33 + 20 * q^34 - 22 * q^36 + 20 * q^37 + 30 * q^39 - 90 * q^42 + 20 * q^43 - 12 * q^46 - 100 * q^48 - 16 * q^51 - 20 * q^52 + 120 * q^54 - 70 * q^57 + 20 * q^58 - 12 * q^61 + 20 * q^63 - 100 * q^64 - 30 * q^66 + 60 * q^67 - 80 * q^69 + 150 * q^72 + 60 * q^73 - 64 * q^76 + 80 * q^78 - 60 * q^79 + 14 * q^81 + 60 * q^82 - 130 * q^84 + 60 * q^87 - 20 * q^88 - 12 * q^91 + 20 * q^93 + 260 * q^94 + 42 * q^96 - 120 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$-1$

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 $

$2$	−0.0231951	−	0.0455229i	−0.0164014	−	0.0321896i	0.882660	−	0.470011i	$-0.155750\pi$
$2$	−0.0231951	−	0.0455229i	−0.0164014	−	0.0321896i	−0.899062	+	0.437822i	$0.855750\pi$
$3$	1.39036	+	1.03290i	0.802727	+	0.596347i
$3$	1.39036	+	1.03290i	0.802727	+	0.596347i
$4$	1.17404	−	1.61592i	0.587018	−	0.807961i
$5$		0			0
$5$		0			0
$6$	0.0147712	−	0.0872517i	0.00603031	−	0.0356203i
$7$	−1.44136	−	1.44136i	−0.544784	−	0.544784i	0.380144	−	0.924927i	$-0.375875\pi$
$7$	−1.44136	−	1.44136i	−0.544784	−	0.544784i	−0.924927	+	0.380144i	$0.875875\pi$
$8$	−0.201718	−	0.0319491i	−0.0713182	−	0.0112957i
$9$	0.866221	+	2.87222i	0.288740	+	0.957407i
$10$		0			0
$11$	2.86751	+	0.931709i	0.864586	+	0.280921i	0.707542	−	0.706671i	$-0.249804\pi$
$11$	2.86751	+	0.931709i	0.864586	+	0.280921i	0.157043	+	0.987592i	$0.449804\pi$
$12$	3.30143	−	1.03405i	0.953040	−	0.298505i
$13$	2.79268	+	1.42294i	0.774551	+	0.394653i	0.796139	−	0.605114i	$-0.206872\pi$
$13$	2.79268	+	1.42294i	0.774551	+	0.394653i	−0.0215884	+	0.999767i	$0.506872\pi$
$14$	−0.0321825	+	0.0990475i	−0.00860113	+	0.0264716i
$15$		0			0
$16$	−1.23123	−	3.78934i	−0.307808	−	0.947334i
$17$	0.952042	−	6.01096i	0.230904	−	1.45787i	−0.551017	−	0.834494i	$-0.685760\pi$
$17$	0.952042	−	6.01096i	0.230904	−	1.45787i	0.781921	−	0.623377i	$-0.214240\pi$
$18$	0.110660	−	0.106054i	0.0260828	−	0.0249972i
$19$	1.91085	+	2.63007i	0.438380	+	0.603378i	0.969851	−	0.243698i	$-0.0783606\pi$
$19$	1.91085	+	2.63007i	0.438380	+	0.603378i	−0.531471	+	0.847076i	$0.678361\pi$
$20$		0			0
$21$	−0.515229	−	3.49280i	−0.112432	−	0.762192i
$22$	−0.0240979	−	0.152148i	−0.00513769	−	0.0324381i
$23$	−5.12542	+	2.61153i	−1.06872	+	0.544542i	−0.897647	−	0.440716i	$-0.854725\pi$
$23$	−5.12542	+	2.61153i	−1.06872	+	0.544542i	−0.171077	+	0.985258i	$0.554725\pi$
$24$	−0.247462	−	0.252776i	−0.0505129	−	0.0515978i
$25$		0			0
$26$		−	0.160136i		−	0.0314053i
$27$	−1.76237	+	4.88816i	−0.339168	+	0.940726i
$28$	−4.02134	+	0.636918i	−0.759962	+	0.120366i
$29$	−0.976916	−	0.709771i	−0.181409	−	0.131801i	0.493375	−	0.869817i	$-0.335763\pi$
$29$	−0.976916	−	0.709771i	−0.181409	−	0.131801i	−0.674784	+	0.738016i	$0.735763\pi$
$30$		0			0
$31$	−0.0161330	+	0.0117213i	−0.00289757	+	0.00210521i	−0.589233	−	0.807963i	$-0.700570\pi$
$31$	−0.0161330	+	0.0117213i	−0.00289757	+	0.00210521i	0.586336	+	0.810068i	$0.300570\pi$
$32$	−0.432772	+	0.432772i	−0.0765040	+	0.0765040i
$33$	3.02451	+	4.25727i	0.526500	+	0.741096i
$34$	−0.295719	+	0.0960849i	−0.0507154	+	0.0164784i
$35$		0			0
$36$	5.65826	+	1.97235i	0.943044	+	0.328725i
$37$	−1.24327	+	2.44005i	−0.204392	+	0.401142i	−0.970334	−	0.241767i	$-0.922273\pi$
$37$	−1.24327	+	2.44005i	−0.204392	+	0.401142i	0.765942	+	0.642910i	$0.222273\pi$
$38$	0.0754058	−	0.147992i	0.0122324	−	0.0240075i
$39$	2.41308	+	4.86298i	0.386402	+	0.778700i
$40$		0			0
$41$	−10.1904	+	3.31106i	−1.59147	+	0.517100i	−0.964979	−	0.262328i	$-0.915510\pi$
$41$	−10.1904	+	3.31106i	−1.59147	+	0.517100i	−0.626491	+	0.779428i	$0.715510\pi$
$42$	−0.147052	+	0.104471i	−0.0226906	+	0.0161202i
$43$	3.91319	−	3.91319i	0.596755	−	0.596755i	−0.342692	−	0.939448i	$-0.611339\pi$
$43$	3.91319	−	3.91319i	0.596755	−	0.596755i	0.939448	+	0.342692i	$0.111339\pi$
$44$	4.87212	−	3.53981i	0.734500	−	0.533646i
$45$		0			0
$46$	0.237769	+	0.172749i	0.0350571	+	0.0254705i
$47$	−3.63479	+	0.575694i	−0.530188	+	0.0839735i	−0.415789	−	0.909461i	$-0.636494\pi$
$47$	−3.63479	+	0.575694i	−0.530188	+	0.0839735i	−0.114399	+	0.993435i	$0.536494\pi$
$48$	2.20216	−	6.54030i	0.317855	−	0.944011i
$49$		−	2.84495i		−	0.406422i
$50$		0			0
$51$	7.53242	−	7.37405i	1.05475	−	1.03257i
$52$	5.57807	−	2.84217i	0.773540	−	0.394138i
$53$	0.635421	+	4.01189i	0.0872818	+	0.551075i	0.992117	+	0.125314i	$0.0399938\pi$
$53$	0.635421	+	4.01189i	0.0872818	+	0.551075i	−0.904835	+	0.425762i	$0.860006\pi$
$54$	0.263401	−	0.0331531i	0.0358444	−	0.00451156i
$55$		0			0
$56$	0.244699	+	0.336799i	0.0326993	+	0.0450067i
$57$	−0.0598219	+	5.63047i	−0.00792360	+	0.745775i
$58$	−0.00965120	+	0.0609353i	−0.00126726	+	0.00800119i
$59$	−1.33548	−	4.11017i	−0.173864	−	0.535099i	0.825716	−	0.564087i	$-0.190772\pi$
$59$	−1.33548	−	4.11017i	−0.173864	−	0.535099i	−0.999580	+	0.0289879i	$0.990772\pi$
$60$		0			0
$61$	−3.99489	+	12.2950i	−0.511493	+	1.57421i	0.278081	+	0.960558i	$0.410302\pi$
$61$	−3.99489	+	12.2950i	−0.511493	+	1.57421i	−0.789574	+	0.613656i	$0.789698\pi$
$62$	0.000907794	0	0.000462544i	0.000115290	0	5.87432e-5i
$63$	2.89137	−	5.38845i	0.364279	−	0.678881i
$64$	−7.54893	−	2.45280i	−0.943617	−	0.306600i
$65$		0			0
$66$	0.123650	−	0.236432i	0.0152202	−	0.0291028i
$67$	0.920343	+	0.145768i	0.112438	+	0.0178084i	0.212400	−	0.977183i	$-0.431872\pi$
$67$	0.920343	+	0.145768i	0.112438	+	0.0178084i	−0.0999620	+	0.994991i	$0.531872\pi$
$68$	−8.59551	−	8.59551i	−1.04236	−	1.04236i
$69$	−9.82366	−	1.66309i	−1.18263	−	0.200212i
$70$		0			0
$71$	−5.79154	+	7.97137i	−0.687329	+	0.946028i	−0.999993	−	0.00383630i	$-0.998779\pi$
$71$	−5.79154	+	7.97137i	−0.687329	+	0.946028i	0.312663	+	0.949864i	$0.398779\pi$
$72$	−0.0829678	−	0.607055i	−0.00977785	−	0.0715421i
$73$	−0.0177571	−	0.0348503i	−0.00207831	−	0.00407891i	0.889965	−	0.456029i	$-0.150729\pi$
$73$	−0.0177571	−	0.0348503i	−0.00207831	−	0.00407891i	−0.892043	+	0.451950i	$0.850729\pi$
$74$	0.139916			0.0162649
$75$		0			0
$76$	6.49339			0.744843
$77$	−2.79018	−	5.47604i	−0.317971	−	0.624053i
$78$	0.165405	−	0.222648i	0.0187285	−	0.0252099i
$79$	−6.00647	+	8.26720i	−0.675781	+	0.930133i	−0.999874	−	0.0158924i	$-0.994941\pi$
$79$	−6.00647	+	8.26720i	−0.675781	+	0.930133i	0.324093	+	0.946025i	$0.394941\pi$
$80$		0			0
$81$	−7.49932	+	4.97596i	−0.833258	+	0.552884i
$82$	0.387096	+	0.387096i	0.0427476	+	0.0427476i
$83$	2.17217	+	0.344039i	0.238427	+	0.0377632i	0.274504	−	0.961586i	$-0.411486\pi$
$83$	2.17217	+	0.344039i	0.238427	+	0.0377632i	−0.0360772	+	0.999349i	$0.511486\pi$
$84$	−6.24900	−	3.26811i	−0.681822	−	0.356580i
$85$		0			0
$86$	−0.268906	−	0.0873730i	−0.0289969	−	0.00942167i
$87$	−0.625143	−	1.99590i	−0.0670224	−	0.213983i
$88$	−0.548661	−	0.279557i	−0.0584875	−	0.0298009i
$89$	4.18096	−	12.8677i	0.443181	−	1.36397i	−0.441285	−	0.897367i	$-0.645477\pi$
$89$	4.18096	−	12.8677i	0.443181	−	1.36397i	0.884466	−	0.466604i	$-0.154523\pi$
$90$		0			0
$91$	−1.97429	−	6.07624i	−0.206962	−	0.636963i
$92$	−1.79740	+	11.3483i	−0.187392	+	1.18314i
$93$	−0.0345377		0.000366951i	−0.00358139		3.80511e-5i
$94$	0.110516	+	0.152113i	0.0113989	+	0.0156892i
$95$		0			0
$96$	−1.04872	+	0.154699i	−0.107035	+	0.0157889i
$97$	0.838657	+	5.29507i	0.0851527	+	0.537633i	0.992979	+	0.118287i	$0.0377404\pi$
$97$	0.838657	+	5.29507i	0.0851527	+	0.537633i	−0.907827	+	0.419346i	$0.862260\pi$
$98$	−0.129510	+	0.0659889i	−0.0130825	+	0.00666588i
$99$	−0.192183	+	9.04318i	−0.0193151	+	0.908874i
$100$		0			0
$101$		−	12.2476i		−	1.21869i	−0.792907	−	0.609343i	$-0.791433\pi$
$101$		−	12.2476i		−	1.21869i	0.792907	−	0.609343i	$-0.208567\pi$
$102$	−0.510403	−	0.171856i	−0.0505374	−	0.0170163i
$103$	−16.5959	+	2.62854i	−1.63525	+	0.258998i	−0.905383	−	0.424596i	$-0.860416\pi$
$103$	−16.5959	+	2.62854i	−1.63525	+	0.258998i	−0.729863	+	0.683593i	$0.760416\pi$
$104$	−0.517874	−	0.376257i	−0.0507817	−	0.0368951i
$105$		0			0
$106$	0.167894	−	0.121982i	0.0163073	−	0.0118480i
$107$	3.55622	−	3.55622i	0.343793	−	0.343793i	−0.513998	−	0.857791i	$-0.671836\pi$
$107$	3.55622	−	3.55622i	0.343793	−	0.343793i	0.857791	+	0.513998i	$0.171836\pi$
$108$	5.82980	+	8.58672i	0.560972	+	0.826257i
$109$	9.79911	−	3.18392i	0.938585	−	0.304965i	0.200516	−	0.979690i	$-0.435738\pi$
$109$	9.79911	−	3.18392i	0.938585	−	0.304965i	0.738069	+	0.674726i	$0.235738\pi$
$110$		0			0
$111$	−4.24894	+	2.10838i	−0.403291	+	0.200119i
$112$	−3.68716	+	7.23645i	−0.348404	+	0.683781i
$113$	3.97267	−	7.79680i	0.373717	−	0.733462i	−0.625176	−	0.780483i	$-0.714973\pi$
$113$	3.97267	−	7.79680i	0.373717	−	0.733462i	0.998894	+	0.0470217i	$0.0149730\pi$
$114$	0.257703	−	0.127876i	0.0241361	−	0.0119767i
$115$		0			0
$116$	−2.29387	+	0.745324i	−0.212980	+	0.0692016i
$117$	−1.66793	+	9.25379i	−0.154200	+	0.855513i
$118$	−0.156130	+	0.156130i	−0.0143730	+	0.0143730i
$119$	−10.0362	+	7.29173i	−0.920017	+	0.668432i
$120$		0			0
$121$	−1.54468	−	1.12228i	−0.140425	−	0.102025i
$122$	0.652366	−	0.103325i	0.0590624	−	0.00935457i
$123$	−17.5883	−	5.92211i	−1.58589	−	0.533979i
$124$			0.0398309i			0.00357692i
$125$		0			0
$126$	−0.312364	−	0.00663826i	−0.0278276	−	0.000591383i
$127$	−3.11066	+	1.58496i	−0.276026	+	0.140642i	−0.586524	−	0.809932i	$-0.699504\pi$
$127$	−3.11066	+	1.58496i	−0.276026	+	0.140642i	0.310498	+	0.950574i	$0.399504\pi$
$128$	0.254925	+	1.60954i	0.0225324	+	0.142264i
$129$	9.48270	−	1.39881i	0.834905	−	0.123158i
$130$		0			0
$131$	4.58971	+	6.31720i	0.401005	+	0.551936i	0.960996	−	0.276563i	$-0.0891953\pi$
$131$	4.58971	+	6.31720i	0.401005	+	0.551936i	−0.559991	+	0.828499i	$0.689195\pi$
$132$	10.4303	+	0.110818i	0.907841	+	0.00964550i
$133$	1.03664	−	6.54511i	0.0898884	−	0.567533i
$134$	−0.0147116	−	0.0452778i	−0.00127089	−	0.00391140i
$135$		0			0
$136$	−0.384089	+	1.18210i	−0.0329353	+	0.101365i
$137$	−8.83454	−	4.50142i	−0.754786	−	0.384583i	0.0338629	−	0.999426i	$-0.489219\pi$
$137$	−8.83454	−	4.50142i	−0.754786	−	0.384583i	−0.788649	+	0.614844i	$0.789219\pi$
$138$	0.152152	+	0.485777i	0.0129520	+	0.0413521i
$139$	4.81723	+	1.56521i	0.408592	+	0.132760i	0.506100	−	0.862475i	$-0.331087\pi$
$139$	4.81723	+	1.56521i	0.408592	+	0.132760i	−0.0975070	+	0.995235i	$0.531087\pi$
$140$		0			0
$141$	−5.64831	−	2.95396i	−0.475674	−	0.248768i
$142$	0.497215	+	0.0787512i	0.0417254	+	0.00660865i
$143$	6.68226	+	6.68226i	0.558799	+	0.558799i
$144$	9.81730	−	6.81877i	0.818108	−	0.568231i
$145$		0			0
$146$	−0.00117461	+	0.00161671i	−9.72113e−5	+	0.000133800i
$147$	2.93856	−	3.95552i	0.242368	−	0.326245i
$148$	2.48329	+	4.87374i	0.204125	+	0.400619i
$149$	2.08572			0.170869			0.0854344	−	0.996344i	$-0.472772\pi$
$149$	2.08572			0.170869			0.0854344	+	0.996344i	$0.472772\pi$
$150$		0			0
$151$	3.13158			0.254844			0.127422	−	0.991849i	$-0.459330\pi$
$151$	3.13158			0.254844			0.127422	+	0.991849i	$0.459330\pi$
$152$	−0.301426	−	0.591583i	−0.0244489	−	0.0479837i
$153$	18.0895	−	2.47234i	1.46245	−	0.199877i
$154$	−0.184567	+	0.254035i	−0.0148728	+	0.0204707i
$155$		0			0
$156$	10.6912	+	1.80996i	0.855984	+	0.144913i
$157$	−4.55824	−	4.55824i	−0.363787	−	0.363787i	0.501418	−	0.865205i	$-0.332812\pi$
$157$	−4.55824	−	4.55824i	−0.363787	−	0.363787i	−0.865205	+	0.501418i	$0.832812\pi$
$158$	0.515668	+	0.0816737i	0.0410243	+	0.00649761i
$159$	−3.26043	+	6.23431i	−0.258569	+	0.494413i
$160$		0			0
$161$	11.1517	+	3.62342i	0.878881	+	0.285566i
$162$	0.400467	+	0.225973i	0.0314637	+	0.0177541i
$163$	16.2906	+	8.30047i	1.27598	+	0.650143i	0.954905	−	0.296912i	$-0.0959568\pi$
$163$	16.2906	+	8.30047i	1.27598	+	0.650143i	0.321072	+	0.947055i	$0.395957\pi$
$164$	−6.61347	+	20.3542i	−0.516425	+	1.58939i
$165$		0			0
$166$	−0.0347221	−	0.106864i	−0.00269496	−	0.00829423i
$167$	0.197736	−	1.24845i	0.0153012	−	0.0966082i	−0.978856	−	0.204551i	$-0.934426\pi$
$167$	0.197736	−	1.24845i	0.0153012	−	0.0966082i	0.994157	+	0.107943i	$0.0344265\pi$
$168$	−0.00766063	+	0.721024i	−0.000591031	+	0.0556282i
$169$	−1.86690	−	2.56957i	−0.143608	−	0.197659i
$170$		0			0
$171$	−5.89891	+	7.76662i	−0.451101	+	0.593928i
$172$	−1.72918	−	10.9176i	−0.131849	−	0.832461i
$173$	1.84621	−	0.940691i	0.140365	−	0.0715194i	−0.382398	−	0.923998i	$-0.624902\pi$
$173$	1.84621	−	0.940691i	0.140365	−	0.0715194i	0.522762	+	0.852478i	$0.324902\pi$
$174$	−0.0763589	+	0.0747534i	−0.00578876	+	0.00566704i
$175$		0			0
$176$		−	12.0131i		−	0.905521i
$177$	2.38861	−	7.09405i	0.179539	−	0.533221i
$178$	−0.682752	+	0.108137i	−0.0511744	+	0.00810523i
$179$	4.10633	+	2.98343i	0.306922	+	0.222992i	0.730575	−	0.682833i	$-0.239252\pi$
$179$	4.10633	+	2.98343i	0.306922	+	0.222992i	−0.423653	+	0.905825i	$0.639252\pi$
$180$		0			0
$181$	0.846389	−	0.614938i	0.0629116	−	0.0457080i	−0.555885	−	0.831259i	$-0.687621\pi$
$181$	0.846389	−	0.614938i	0.0629116	−	0.0457080i	0.618797	+	0.785551i	$0.287621\pi$
$182$	−0.230814	+	0.230814i	−0.0171091	+	0.0171091i
$183$	−18.2539	+	12.9682i	−1.34937	+	0.958636i
$184$	1.11733	−	0.363042i	0.0823705	−	0.0267638i
$185$		0			0
$186$	0.000784400		0.00158077i	5.75150e−5		0.000115908i
$187$	8.33045	−	16.3494i	0.609183	−	1.19559i
$188$	−3.33709	+	6.54942i	−0.243383	+	0.477665i
$189$	9.58581	−	4.50539i	0.697265	−	0.327719i
$190$		0			0
$191$	18.0007	−	5.84879i	1.30249	−	0.423204i	0.426041	−	0.904704i	$-0.359908\pi$
$191$	18.0007	−	5.84879i	1.30249	−	0.423204i	0.876446	+	0.481500i	$0.159908\pi$
$192$	−7.96226	−	11.2076i	−0.574627	−	0.808839i
$193$	7.84492	−	7.84492i	0.564690	−	0.564690i	−0.365946	−	0.930636i	$-0.619255\pi$
$193$	7.84492	−	7.84492i	0.564690	−	0.564690i	0.930636	+	0.365946i	$0.119255\pi$
$194$	0.221594	−	0.160998i	0.0159095	−	0.0115590i
$195$		0			0
$196$	−4.59722	−	3.34008i	−0.328373	−	0.238577i
$197$	24.8793	−	3.94049i	1.77257	−	0.280748i	0.817244	−	0.576291i	$-0.195501\pi$
$197$	24.8793	−	3.94049i	1.77257	−	0.280748i	0.955329	+	0.295543i	$0.0955007\pi$
$198$	0.416130	−	0.201009i	0.0295730	−	0.0142851i
$199$		−	16.1153i		−	1.14238i	−0.820817	−	0.571191i	$-0.806482\pi$
$199$		−	16.1153i		−	1.14238i	0.820817	−	0.571191i	$-0.193518\pi$
$200$		0			0
$201$	1.12905	+	1.15330i	0.0796368	+	0.0813472i
$202$	−0.557548	+	0.284085i	−0.0392290	+	0.0199882i
$203$	0.385053	+	2.43113i	0.0270254	+	0.170632i
$204$	−3.07255	−	20.8292i	−0.215121	−	1.45834i
$205$		0			0
$206$	0.504603	+	0.694526i	0.0351573	+	0.0483899i
$207$	−11.9406	−	12.4592i	−0.829932	−	0.865973i
$208$	1.95357	−	12.3344i	0.135456	−	0.855236i
$209$	3.02893	+	9.32209i	0.209515	+	0.644822i
$210$		0			0
$211$	4.91691	−	15.1327i	0.338494	−	1.04178i	−0.626481	−	0.779436i	$-0.715506\pi$
$211$	4.91691	−	15.1327i	0.338494	−	1.04178i	0.964975	−	0.262341i	$-0.0844944\pi$
$212$	7.22891	+	3.68331i	0.496484	+	0.252971i
$213$	−16.2860	+	5.10100i	−1.11590	+	0.349515i
$214$	−0.244376	−	0.0794027i	−0.0167052	−	0.00542786i
$215$		0			0
$216$	0.511674	−	0.929725i	0.0348150	−	0.0632598i
$217$	0.0401481	+	0.00635884i	0.00272543	+	0.000431666i
$218$	−0.372233	−	0.372233i	−0.0252108	−	0.0252108i
$219$	0.0113081	−	0.0667959i	0.000764134	−	0.00451365i
$220$		0			0
$221$	11.2120	−	15.4320i	0.754201	−	1.03807i
$222$	0.194534	+	0.144520i	0.0130563	+	0.00969953i
$223$	9.88171	+	19.3939i	0.661728	+	1.29871i	0.940969	+	0.338494i	$0.109917\pi$
$223$	9.88171	+	19.3939i	0.661728	+	1.29871i	−0.279240	+	0.960221i	$0.590083\pi$
$224$	1.24756			0.0833563
$225$		0			0
$226$	−0.447080			−0.0297393
$227$	9.73935	+	19.1146i	0.646423	+	1.26868i	0.948917	+	0.315526i	$0.102181\pi$
$227$	9.73935	+	19.1146i	0.646423	+	1.26868i	−0.302493	+	0.953151i	$0.597819\pi$
$228$	9.02818	+	6.70705i	0.597906	+	0.444185i
$229$	−6.79217	+	9.34861i	−0.448839	+	0.617774i	−0.972148	−	0.234369i	$-0.924697\pi$
$229$	−6.79217	+	9.34861i	−0.448839	+	0.617774i	0.523309	+	0.852143i	$0.324697\pi$
$230$		0			0
$231$	1.77686	−	10.4957i	0.116909	−	0.690565i
$232$	0.174385	+	0.174385i	0.0114490	+	0.0114490i
$233$	14.4364	+	2.28650i	0.945759	+	0.149793i	0.610219	−	0.792233i	$-0.291081\pi$
$233$	14.4364	+	2.28650i	0.945759	+	0.149793i	0.335540	+	0.942026i	$0.391081\pi$
$234$	0.459947	−	0.138713i	0.0300677	−	0.00906798i
$235$		0			0
$236$	−8.20961	−	2.66746i	−0.534400	−	0.173637i
$237$	−16.8904	+	5.29031i	−1.09715	+	0.343642i
$238$	0.564731	+	0.287745i	0.0366061	+	0.0186517i
$239$	−1.25167	+	3.85226i	−0.0809640	+	0.249182i	−0.983342	−	0.181763i	$-0.941820\pi$
$239$	−1.25167	+	3.85226i	−0.0809640	+	0.249182i	0.902378	+	0.430945i	$0.141820\pi$
$240$		0			0
$241$	−0.611740	−	1.88274i	−0.0394057	−	0.121278i	0.929419	−	0.369027i	$-0.120309\pi$
$241$	−0.611740	−	1.88274i	−0.0394057	−	0.121278i	−0.968824	+	0.247749i	$0.920309\pi$
$242$	−0.0152603	+	0.0963496i	−0.000980967	+	0.00619358i
$243$	−15.5665	−	0.827690i	−0.998589	−	0.0530963i
$244$	15.1776	+	20.8902i	0.971648	+	1.33736i
$245$		0			0
$246$	0.138371	+	0.938036i	0.00882222	+	0.0598070i
$247$	1.59398	+	10.0640i	0.101422	+	0.640355i
$248$	0.00362881	−	0.00184897i	0.000230429	−	0.000117410i
$249$	2.66475	+	2.72199i	0.168872	+	0.172499i
$250$		0			0
$251$			27.0328i			1.70629i	0.521671	+	0.853147i	$0.325309\pi$
$251$			27.0328i			1.70629i	−0.521671	+	0.853147i	$0.674691\pi$
$252$	−5.31274	−	10.9985i	−0.334671	−	0.692839i
$253$	−17.1304	+	2.71318i	−1.07698	+	0.170576i
$254$	0.144304	+	0.104843i	0.00905443	+	0.00657843i
$255$		0			0
$256$	−12.7757	+	9.28206i	−0.798479	+	0.580129i
$257$	−8.81239	+	8.81239i	−0.549701	+	0.549701i	−0.926354	−	0.376653i	$-0.877075\pi$
$257$	−8.81239	+	8.81239i	−0.549701	+	0.549701i	0.376653	+	0.926354i	$0.377075\pi$
$258$	−0.283630	−	0.399234i	−0.0176580	−	0.0248553i
$259$	5.30900	−	1.72500i	0.329885	−	0.107186i
$260$		0			0
$261$	1.19240	−	3.42074i	0.0738074	−	0.211738i
$262$	0.181119	−	0.355465i	0.0111895	−	0.0219607i
$263$	1.63641	−	3.21164i	0.100906	−	0.198038i	−0.835035	−	0.550198i	$-0.814552\pi$
$263$	1.63641	−	3.21164i	0.100906	−	0.198038i	0.935940	+	0.352159i	$0.114552\pi$
$264$	−0.474083	−	0.955400i	−0.0291778	−	0.0588008i
$265$		0			0
$266$	−0.321997	+	0.104623i	−0.0197429	+	0.00641487i
$267$	19.1041	−	13.5722i	1.16915	−	0.830607i
$268$	1.31607	−	1.31607i	0.0803915	−	0.0803915i
$269$	10.9791	−	7.97680i	0.669409	−	0.486354i	−0.200418	−	0.979710i	$-0.564230\pi$
$269$	10.9791	−	7.97680i	0.669409	−	0.486354i	0.869827	+	0.493356i	$0.164230\pi$
$270$		0			0
$271$	6.66756	+	4.84427i	0.405026	+	0.294268i	0.771585	−	0.636126i	$-0.219464\pi$
$271$	6.66756	+	4.84427i	0.405026	+	0.294268i	−0.366559	+	0.930395i	$0.619464\pi$
$272$	−23.9497	+	3.79326i	−1.45217	+	0.230000i
$273$	3.53119	−	10.4874i	0.213717	−	0.634728i
$274$			0.506585i			0.0306039i
$275$		0			0
$276$	−14.2207	+	13.9217i	−0.855988	+	0.837990i
$277$	−17.2075	+	8.76768i	−1.03390	+	0.526799i	−0.886718	−	0.462311i	$-0.847020\pi$
$277$	−17.2075	+	8.76768i	−1.03390	+	0.526799i	−0.147182	+	0.989109i	$0.547020\pi$
$278$	−0.0404830	−	0.255600i	−0.00242801	−	0.0153299i
$279$	−0.0476409	−	0.0361843i	−0.00285219	−	0.00216630i
$280$		0			0
$281$	−6.10119	−	8.39756i	−0.363966	−	0.500957i	0.587282	−	0.809382i	$-0.300198\pi$
$281$	−6.10119	−	8.39756i	−0.363966	−	0.500957i	−0.951248	+	0.308426i	$0.900198\pi$
$282$	−0.00345987	+	0.325645i	−0.000206032	+	0.0193919i
$283$	1.50821	−	9.52247i	0.0896539	−	0.566052i	−0.901442	−	0.432900i	$-0.857490\pi$
$283$	1.50821	−	9.52247i	0.0896539	−	0.566052i	0.991096	−	0.133152i	$-0.0425098\pi$
$284$	6.08164	+	18.7174i	0.360879	+	1.11067i
$285$		0			0
$286$	0.149200	−	0.459192i	0.00882241	−	0.0271526i
$287$	19.4605	+	9.91560i	1.14871	+	0.585299i
$288$	−1.61789	−	0.868141i	−0.0953353	−	0.0511557i
$289$	−19.0573	−	6.19208i	−1.12102	−	0.364240i
$290$		0			0
$291$	−4.30326	+	8.22833i	−0.252262	+	0.482353i
$292$	−0.0771628	−	0.0122214i	−0.00451561	−	0.000715202i
$293$	7.74605	+	7.74605i	0.452529	+	0.452529i	0.896193	−	0.443664i	$-0.146322\pi$
$293$	7.74605	+	7.74605i	0.452529	+	0.452529i	−0.443664	+	0.896193i	$0.646322\pi$
$294$	−0.248227	−	0.0420233i	−0.0144769	−	0.00245085i
$295$		0			0
$296$	0.328748	−	0.452482i	0.0191081	−	0.0263000i
$297$	−9.60794	+	12.3748i	−0.557509	+	0.718059i
$298$	−0.0483784	−	0.0949480i	−0.00280249	−	0.00550019i
$299$	−18.0297			−1.04269
$300$		0			0
$301$	−11.2806			−0.650205
$302$	−0.0726372	−	0.142558i	−0.00417980	−	0.00820332i
$303$	12.6506	−	17.0287i	0.726760	−	0.978272i
$304$	7.61350	−	10.4791i	0.436664	−	0.601017i
$305$		0			0
$306$	−0.532135	−	0.766140i	−0.0304201	−	0.0437973i
$307$	17.8437	+	17.8437i	1.01839	+	1.01839i	0.999828	+	0.0185640i	$0.00590944\pi$
$307$	17.8437	+	17.8437i	1.01839	+	1.01839i	0.0185640	+	0.999828i	$0.494091\pi$
$308$	−12.1246	−	1.92035i	−0.690865	−	0.109422i
$309$	−25.7894	−	13.4874i	−1.46711	−	0.767270i
$310$		0			0
$311$	−4.51681	−	1.46760i	−0.256125	−	0.0832199i	0.178140	−	0.984005i	$-0.442992\pi$
$311$	−4.51681	−	1.46760i	−0.256125	−	0.0832199i	−0.434265	+	0.900785i	$0.642992\pi$
$312$	−0.331395	−	1.05805i	−0.0187616	−	0.0599002i
$313$	−24.0613	−	12.2599i	−1.36003	−	0.692968i	−0.386660	−	0.922222i	$-0.626371\pi$
$313$	−24.0613	−	12.2599i	−1.36003	−	0.692968i	−0.973367	+	0.229254i	$0.926371\pi$
$314$	−0.101776	+	0.313233i	−0.00574353	+	0.0176768i
$315$		0			0
$316$	6.30734	+	19.4120i	0.354815	+	1.09201i
$317$	0.606678	−	3.83042i	0.0340745	−	0.215138i	−0.964776	−	0.263073i	$-0.915264\pi$
$317$	0.606678	−	3.83042i	0.0340745	−	0.215138i	0.998850	+	0.0479351i	$0.0152641\pi$
$318$	0.359430	+	0.00381882i	0.0201558	+	0.000214149i
$319$	−2.14001	−	2.94547i	−0.119818	−	0.164915i
$320$		0			0
$321$	8.61767	−	1.27121i	0.480992	−	0.0709518i
$322$	−0.0937170	−	0.591706i	−0.00522264	−	0.0329745i
$323$	17.6284	−	8.98213i	0.980872	−	0.499779i
$324$	−0.763718	+	17.9603i	−0.0424288	+	0.997793i
$325$		0			0
$326$		−	0.934125i		−	0.0517364i
$327$	16.9130	+	5.69473i	0.935292	+	0.314919i
$328$	2.16137	−	0.342328i	0.119342	−	0.0189019i
$329$	6.06883	+	4.40926i	0.334585	+	0.243090i
$330$		0			0
$331$	14.0789	−	10.2289i	0.773845	−	0.562232i	−0.129280	−	0.991608i	$-0.541267\pi$
$331$	14.0789	−	10.2289i	0.773845	−	0.562232i	0.903126	+	0.429377i	$0.141267\pi$
$332$	3.10615	−	3.10615i	0.170472	−	0.170472i
$333$	−8.08532	−	1.45732i	−0.443073	−	0.0798607i
$334$	−0.0614197	+	0.0199565i	−0.00336074	+	0.00109197i
$335$		0			0
$336$	−12.6010	+	6.25282i	−0.687444	+	0.341119i
$337$	6.33712	−	12.4373i	0.345205	−	0.677503i	−0.651497	−	0.758651i	$-0.725859\pi$
$337$	6.33712	−	12.4373i	0.345205	−	0.677503i	0.996702	+	0.0811484i	$0.0258588\pi$
$338$	−0.0736713	+	0.144588i	−0.00400719	+	0.00786455i
$339$	13.5768	−	6.73701i	0.737391	−	0.365904i
$340$		0			0
$341$	−0.0571823	+	0.0185797i	−0.00309659	+	0.00100614i
$342$	0.490385	+	0.0883883i	0.0265170	+	0.00477949i
$343$	−14.1901	+	14.1901i	−0.766195	+	0.766195i
$344$	−0.914384	+	0.664339i	−0.0493003	+	0.0358188i
$345$		0			0
$346$	−0.0856460	−	0.0622255i	−0.00460436	−	0.00334526i
$347$	−16.0196	+	2.53725i	−0.859977	+	0.136207i	−0.570820	−	0.821075i	$-0.693375\pi$
$347$	−16.0196	+	2.53725i	−0.859977	+	0.136207i	−0.289156	+	0.957282i	$0.593375\pi$
$348$	−3.95916	−	1.33308i	−0.212233	−	0.0714604i
$349$		−	3.27425i		−	0.175267i	−0.996153	−	0.0876333i	$-0.972070\pi$
$349$		−	3.27425i		−	0.175267i	0.996153	−	0.0876333i	$-0.0279304\pi$
$350$		0			0
$351$	−11.8773	+	11.1433i	−0.633963	+	0.594786i
$352$	−1.64419	+	0.837759i	−0.0876358	+	0.0446527i
$353$	−4.57504	−	28.8857i	−0.243505	−	1.53743i	−0.741919	−	0.670490i	$-0.766084\pi$
$353$	−4.57504	−	28.8857i	−0.243505	−	1.53743i	0.498414	−	0.866939i	$-0.333916\pi$
$354$	−0.378346	+	0.0558104i	−0.0201089	+	0.00296629i
$355$		0			0
$356$	−15.8846	−	21.8632i	−0.841881	−	1.15875i
$357$	−21.4856	−	0.228277i	−1.13714	−	0.0120817i
$358$	0.0405675	−	0.256133i	0.00214406	−	0.0135371i
$359$	−8.54970	−	26.3133i	−0.451236	−	1.38876i	−0.875498	−	0.483222i	$-0.839466\pi$
$359$	−8.54970	−	26.3133i	−0.451236	−	1.38876i	0.424262	−	0.905540i	$-0.360534\pi$
$360$		0			0
$361$	2.60544	−	8.01873i	0.137129	−	0.422038i
$362$	−0.0476258	−	0.0242666i	−0.00250316	−	0.00127542i
$363$	−0.988464	−	3.15588i	−0.0518809	−	0.165640i
$364$	−12.1366	−	3.94343i	−0.636132	−	0.206692i
$365$		0			0
$366$	1.01375	+	0.530172i	0.0529896	+	0.0277126i
$367$	−5.42920	−	0.859901i	−0.283402	−	0.0448865i	0.0131151	−	0.999914i	$-0.495825\pi$
$367$	−5.42920	−	0.859901i	−0.283402	−	0.0448865i	−0.296517	+	0.955028i	$0.595825\pi$
$368$	16.2065	+	16.2065i	0.844825	+	0.844825i
$369$	−18.3372	−	26.4009i	−0.954597	−	1.37438i
$370$		0			0
$371$	4.86671	−	6.69846i	0.252667	−	0.347767i
$372$	−0.0411415	+	0.0553794i	−0.00213309	+	0.00287129i
$373$	3.41888	+	6.70992i	0.177023	+	0.347427i	0.962420	−	0.271565i	$-0.0875413\pi$
$373$	3.41888	+	6.70992i	0.177023	+	0.347427i	−0.785397	+	0.618992i	$0.787541\pi$
$374$	−0.937499			−0.0484769
$375$		0			0
$376$	0.751596			0.0387606
$377$	−1.71825	−	3.37226i	−0.0884945	−	0.173680i
$378$	−0.427442	−	0.331871i	−0.0219853	−	0.0170696i
$379$	−13.4955	+	18.5749i	−0.693216	+	0.954130i	0.306781	+	0.951780i	$0.400748\pi$
$379$	−13.4955	+	18.5749i	−0.693216	+	0.954130i	−0.999997	+	0.00234966i	$0.999252\pi$
$380$		0			0
$381$	−5.96205	−	1.00934i	−0.305445	−	0.0517100i
$382$	−0.683782	−	0.683782i	−0.0349853	−	0.0349853i
$383$	−7.62404	−	1.20753i	−0.389570	−	0.0617019i	−0.0414229	−	0.999142i	$-0.513189\pi$
$383$	−7.62404	−	1.20753i	−0.389570	−	0.0617019i	−0.348147	+	0.937440i	$0.613189\pi$
$384$	−1.30806	+	2.50115i	−0.0667515	+	0.127636i
$385$		0			0
$386$	−0.539087	−	0.175160i	−0.0274388	−	0.00891542i
$387$	14.6292	+	7.84986i	0.743645	+	0.399031i
$388$	9.54104	+	4.86140i	0.484373	+	0.246800i
$389$	5.38913	−	16.5860i	0.273240	−	0.840945i	−0.716440	−	0.697649i	$-0.754230\pi$
$389$	5.38913	−	16.5860i	0.273240	−	0.840945i	0.989680	−	0.143297i	$-0.0457703\pi$
$390$		0			0
$391$	10.8182	+	33.2950i	0.547099	+	1.68380i
$392$	−0.0908935	+	0.573879i	−0.00459082	+	0.0289853i
$393$	−0.143687	+	13.5239i	−0.00724806	+	0.682192i
$394$	−0.756459	−	1.04118i	−0.0381098	−	0.0524537i
$395$		0			0
$396$	14.3874	+	10.9276i	0.722996	+	0.549131i
$397$	−1.62336	−	10.2495i	−0.0814741	−	0.514407i	−0.994348	−	0.106167i	$-0.966142\pi$
$397$	−1.62336	−	10.2495i	−0.0814741	−	0.514407i	0.912874	−	0.408241i	$-0.133858\pi$
$398$	−0.733615	+	0.373795i	−0.0367728	+	0.0187367i
$399$	8.20178	−	8.02933i	0.410602	−	0.401969i
$400$		0			0
$401$			14.7017i			0.734168i	0.930188	+	0.367084i	$0.119644\pi$
$401$			14.7017i			0.734168i	−0.930188	+	0.367084i	$0.880356\pi$
$402$	0.0263130	−	0.0781483i	0.00131238	−	0.00389768i
$403$	−0.0617331	+	0.00977756i	−0.00307514	+	0.000487055i
$404$	−19.7912	−	14.3792i	−0.984651	−	0.715391i
$405$		0			0
$406$	0.101741	−	0.0739189i	0.00504930	−	0.00366853i
$407$	−5.83850	+	5.83850i	−0.289404	+	0.289404i
$408$	−1.75502	+	1.24683i	−0.0868865	+	0.0617271i
$409$	4.73536	−	1.53861i	0.234148	−	0.0760794i	−0.189593	−	0.981863i	$-0.560717\pi$
$409$	4.73536	−	1.53861i	0.234148	−	0.0760794i	0.423741	+	0.905783i	$0.360717\pi$
$410$		0			0
$411$	−7.63369	−	15.3838i	−0.376542	−	0.758829i
$412$	−15.2367	+	29.9037i	−0.750659	+	1.47325i
$413$	−3.99934	+	7.84915i	−0.196795	+	0.386231i
$414$	−0.290214	+	0.832565i	−0.0142632	+	0.0409183i
$415$		0			0
$416$	−1.82440	+	0.592785i	−0.0894488	+	0.0290637i
$417$	5.08099	+	7.15195i	0.248817	+	0.350233i
$418$	0.354112	−	0.354112i	0.0173202	−	0.0173202i
$419$	−19.7469	+	14.3470i	−0.964699	+	0.700895i	−0.954237	−	0.299051i	$-0.903330\pi$
$419$	−19.7469	+	14.3470i	−0.964699	+	0.700895i	−0.0104616	+	0.999945i	$0.503330\pi$
$420$		0			0
$421$	−2.27800	−	1.65506i	−0.111023	−	0.0806628i	0.530889	−	0.847442i	$-0.321858\pi$
$421$	−2.27800	−	1.65506i	−0.111023	−	0.0806628i	−0.641911	+	0.766779i	$0.721858\pi$
$422$	−0.802932	+	0.127172i	−0.0390861	+	0.00619063i
$423$	−4.80205	−	9.94124i	−0.233484	−	0.483360i
$424$		−	0.829573i		−	0.0402876i
$425$		0			0
$426$	0.609968	+	0.623068i	0.0295530	+	0.0301877i
$427$	23.4796	−	11.9635i	1.13626	−	0.578953i
$428$	−1.57144	−	9.92171i	−0.0759586	−	0.479584i
$429$	2.38864	+	16.1929i	0.115325	+	0.781801i
$430$		0			0
$431$	12.9674	+	17.8481i	0.624617	+	0.859712i	0.997679	−	0.0680947i	$-0.0216920\pi$
$431$	12.9674	+	17.8481i	0.624617	+	0.859712i	−0.373062	+	0.927807i	$0.621692\pi$
$432$	20.6927	+	0.659759i	0.995580	+	0.0317427i
$433$	6.30865	−	39.8312i	0.303174	−	1.91417i	−0.0923805	−	0.995724i	$-0.529448\pi$
$433$	6.30865	−	39.8312i	0.303174	−	1.91417i	0.395555	−	0.918442i	$-0.370552\pi$
$434$	−0.000641766	−	0.00197515i	−3.08058e−5	−	9.48104e-5i
$435$		0			0
$436$	6.35954	−	19.5726i	0.304567	−	0.937360i
$437$	−16.6624	−	8.48993i	−0.797072	−	0.406129i
$438$	−0.00330304	+	0.00103456i	−0.000157825	+	4.94330e-5i
$439$	12.3771	+	4.02156i	0.590727	+	0.191939i	0.589100	−	0.808060i	$-0.299482\pi$
$439$	12.3771	+	4.02156i	0.590727	+	0.191939i	0.00162635	+	0.999999i	$0.499482\pi$
$440$		0			0
$441$	8.17133	−	2.46436i	0.389111	−	0.117350i
$442$	−0.962572	−	0.152456i	−0.0457849	−	0.00725162i
$443$	−20.7027	−	20.7027i	−0.983613	−	0.983613i	0.0162549	−	0.999868i	$-0.494826\pi$
$443$	−20.7027	−	20.7027i	−0.983613	−	0.983613i	−0.999868	+	0.0162549i	$0.994826\pi$
$444$	−1.58142	+	9.34127i	−0.0750509	+	0.443317i
$445$		0			0
$446$	0.653662	−	0.899688i	0.0309518	−	0.0426015i
$447$	2.89991	+	2.15435i	0.137161	+	0.101897i
$448$	7.34538	+	14.4161i	0.347037	+	0.681097i
$449$	27.3773			1.29201			0.646007	−	0.763332i	$-0.276438\pi$
$449$	27.3773			1.29201			0.646007	+	0.763332i	$0.276438\pi$
$450$		0			0
$451$	−32.3059			−1.52123
$452$	−7.93497	−	15.5733i	−0.373230	−	0.732504i
$453$	4.35403	+	3.23462i	0.204570	+	0.151976i
$454$	0.644245	−	0.886727i	0.0302359	−	0.0416162i
$455$		0			0
$456$	0.191956	−	1.13386i	0.00898914	−	0.0530978i
$457$	9.58199	+	9.58199i	0.448227	+	0.448227i	0.894765	−	0.446538i	$-0.147343\pi$
$457$	9.58199	+	9.58199i	0.448227	+	0.448227i	−0.446538	+	0.894765i	$0.647343\pi$
$458$	0.583121	+	0.0923573i	0.0272475	+	0.00431557i
$459$	27.7046	+	15.2472i	1.29314	+	0.711680i
$460$		0			0
$461$	−27.6032	−	8.96881i	−1.28561	−	0.417719i	−0.415056	−	0.909796i	$-0.636238\pi$
$461$	−27.6032	−	8.96881i	−1.28561	−	0.417719i	−0.870552	+	0.492077i	$0.836238\pi$
$462$	−0.519008	+	0.162561i	−0.0241464	+	0.00756300i
$463$	−6.38255	−	3.25207i	−0.296622	−	0.151137i	0.299346	−	0.954145i	$-0.403232\pi$
$463$	−6.38255	−	3.25207i	−0.296622	−	0.151137i	−0.595968	+	0.803008i	$0.703232\pi$
$464$	−1.48675	+	4.57576i	−0.0690208	+	0.212424i
$465$		0			0
$466$	−0.230765	−	0.710222i	−0.0106900	−	0.0329004i
$467$	1.33507	−	8.42928i	0.0617795	−	0.390061i	−0.937352	−	0.348385i	$-0.886730\pi$
$467$	1.33507	−	8.42928i	0.0617795	−	0.390061i	0.999131	−	0.0416760i	$-0.0132697\pi$
$468$	12.9952	+	13.5595i	0.600703	+	0.626789i
$469$	−1.11644	−	1.53665i	−0.0515525	−	0.0709560i
$470$		0			0
$471$	−1.62939	−	11.0458i	−0.0750783	−	0.508965i
$472$	0.138074	+	0.871764i	0.00635537	+	0.0401262i
$473$	14.8670	−	7.57513i	0.683587	−	0.348305i
$474$	0.632604	+	0.646191i	0.0290565	+	0.0296805i
$475$		0			0
$476$			24.7785i			1.13572i
$477$	−10.9726	+	5.30025i	−0.502402	+	0.242682i
$478$	0.204399	−	0.0323735i	0.00934897	−	0.00148073i
$479$	11.8446	+	8.60560i	0.541193	+	0.393200i	0.824528	−	0.565821i	$-0.191441\pi$
$479$	11.8446	+	8.60560i	0.541193	+	0.393200i	−0.283335	+	0.959021i	$0.591441\pi$
$480$		0			0
$481$	−6.94411	+	5.04519i	−0.316624	+	0.230041i
$482$	−0.0715186	+	0.0715186i	−0.00325758	+	0.00325758i
$483$	11.7623	+	16.5566i	0.535205	+	0.753349i
$484$	−3.62702	+	1.17849i	−0.164865	+	0.0535677i
$485$		0			0
$486$	0.323387	+	0.727829i	0.0146691	+	0.0330150i
$487$	5.68806	−	11.1635i	0.257751	−	0.505864i	−0.725477	−	0.688246i	$-0.758381\pi$
$487$	5.68806	−	11.1635i	0.257751	−	0.505864i	0.983228	+	0.182382i	$0.0583808\pi$
$488$	1.19866	−	2.35250i	0.0542606	−	0.106492i
$489$	14.0763	+	28.3673i	0.636550	+	1.28281i
$490$		0			0
$491$	34.7580	−	11.2936i	1.56861	−	0.509672i	0.609518	−	0.792772i	$-0.291363\pi$
$491$	34.7580	−	11.2936i	1.56861	−	0.509672i	0.959090	+	0.283101i	$0.0913631\pi$
$492$	−30.2190	+	21.4686i	−1.36238	+	0.967880i
$493$	−5.19647	+	5.19647i	−0.234037	+	0.234037i
$494$	0.421169	−	0.305997i	0.0189493	−	0.0137675i
$495$		0			0
$496$	0.0642794	+	0.0467017i	0.00288623	+	0.00209697i
$497$	19.8373	−	3.14193i	0.889826	−	0.140935i
$498$	0.0621035	−	0.184444i	0.00278293	−	0.00826513i
$499$			8.39246i			0.375698i	0.982198	+	0.187849i	$0.0601515\pi$
$499$			8.39246i			0.375698i	−0.982198	+	0.187849i	$0.939848\pi$
$500$		0			0
$501$	1.56446	−	1.53156i	0.0698948	−	0.0684251i
$502$	1.23061	−	0.627027i	0.0549248	−	0.0279856i
$503$	5.88019	+	37.1261i	0.262185	+	1.65537i	0.670042	+	0.742323i	$0.266276\pi$
$503$	5.88019	+	37.1261i	0.262185	+	1.65537i	−0.407857	+	0.913046i	$0.633724\pi$
$504$	−0.755399	+	0.994573i	−0.0336482	+	0.0443018i
$505$		0			0
$506$	0.520852	+	0.716891i	0.0231547	+	0.0318697i
$507$	0.0584458	−	5.50096i	0.00259567	−	0.244306i
$508$	−1.09085	+	6.88738i	−0.0483988	+	0.305578i
$509$	−4.05260	−	12.4726i	−0.179628	−	0.552839i	0.820186	−	0.572096i	$-0.193870\pi$
$509$	−4.05260	−	12.4726i	−0.179628	−	0.552839i	−0.999815	+	0.0192578i	$0.993870\pi$
$510$		0			0
$511$	−0.0246374	+	0.0758262i	−0.00108990	+	0.00335436i
$512$	3.62285	+	1.84593i	0.160109	+	0.0815794i
$513$	−16.2238	+	4.70541i	−0.716298	+	0.207749i
$514$	0.605569	+	0.196761i	0.0267105	+	0.00867877i
$515$		0			0
$516$	8.87266	−	16.9655i	0.390597	−	0.746867i
$517$	−10.9592	−	1.73576i	−0.481983	−	0.0763386i
$518$	−0.201670	−	0.201670i	−0.00886086	−	0.00886086i
$519$	3.53855	+	0.599055i	0.155325	+	0.0262956i
$520$		0			0
$521$	−10.1668	+	13.9934i	−0.445415	+	0.613061i	−0.971405	−	0.237430i	$-0.923695\pi$
$521$	−10.1668	+	13.9934i	−0.445415	+	0.613061i	0.525990	+	0.850491i	$0.323695\pi$
$522$	−0.183380	+	0.0250630i	−0.00802631	+	0.00109698i
$523$	5.13521	+	10.0784i	0.224547	+	0.440698i	0.975604	−	0.219540i	$-0.0704555\pi$
$523$	5.13521	+	10.0784i	0.224547	+	0.440698i	−0.751057	+	0.660238i	$0.770455\pi$
$524$	15.5966			0.681340
$525$		0			0
$526$	−0.184160			−0.00802976
$527$	0.0550970	+	0.108134i	0.00240006	+	0.00471039i
$528$	12.4084	−	16.7026i	0.540005	−	0.726886i
$529$	5.93077	−	8.16301i	0.257860	−	0.354913i
$530$		0			0
$531$	10.6485	−	7.39610i	0.462106	−	0.320963i
$532$	−9.35933	−	9.35933i	−0.405778	−	0.405778i
$533$	−33.1699	−	5.25360i	−1.43675	−	0.227559i
$534$	−1.06097	−	0.554867i	−0.0459126	−	0.0240114i
$535$		0			0
$536$	−0.180993	−	0.0588082i	−0.00781770	−	0.00254013i
$537$	2.62771	+	8.38949i	0.113394	+	0.362033i
$538$	−0.617789	−	0.314779i	−0.0266348	−	0.0135711i
$539$	2.65067	−	8.15791i	0.114172	−	0.351386i
$540$		0			0
$541$	−9.85115	−	30.3187i	−0.423534	−	1.30350i	−0.904391	−	0.426705i	$-0.859674\pi$
$541$	−9.85115	−	30.3187i	−0.423534	−	1.30350i	0.480857	−	0.876799i	$-0.340326\pi$
$542$	0.0658705	−	0.415890i	0.00282938	−	0.0178640i
$543$	1.81196	+	0.0192515i	0.0777586	+	0.000826159i
$544$	2.18936	+	3.01339i	0.0938679	+	0.129198i
$545$		0			0
$546$	−0.559325	+	0.0825069i	−0.0239369	+	0.00353097i
$547$	−2.95981	−	18.6875i	−0.126552	−	0.799020i	−0.966559	−	0.256444i	$-0.917449\pi$
$547$	−2.95981	−	18.6875i	−0.126552	−	0.799020i	0.840007	−	0.542576i	$-0.182551\pi$
$548$	−17.6460	+	8.99110i	−0.753801	+	0.384081i
$549$	−38.7744	−	0.824023i	−1.65485	−	0.0351685i
$550$		0			0
$551$		−	3.92562i		−	0.167237i
$552$	1.92848	+	0.649332i	0.0820815	+	0.0276374i
$553$	20.5735	−	3.25853i	0.874876	−	0.138567i
$554$	0.798260	+	0.579970i	0.0339148	+	0.0246406i
$555$		0			0
$556$	8.18487	−	5.94666i	0.347116	−	0.252194i
$557$	27.8152	−	27.8152i	1.17857	−	1.17857i	0.198459	−	0.980109i	$-0.436406\pi$
$557$	27.8152	−	27.8152i	1.17857	−	1.17857i	0.980109	−	0.198459i	$-0.0635936\pi$
$558$	−0.000542180		0.00300805i	−2.29523e−5		0.000127341i
$559$	16.4965	−	5.36005i	0.697729	−	0.226706i
$560$		0			0
$561$	28.4697	−	14.1271i	1.20199	−	0.596446i
$562$	−0.240764	+	0.472526i	−0.0101560	+	0.0199323i
$563$	−18.6793	+	36.6601i	−0.787237	+	1.54504i	0.0503464	+	0.998732i	$0.483967\pi$
$563$	−18.6793	+	36.6601i	−0.787237	+	1.54504i	−0.837584	+	0.546309i	$0.816033\pi$
$564$	−11.4047	+	5.65917i	−0.480224	+	0.238294i
$565$		0			0
$566$	−0.468474	+	0.152216i	−0.0196914	+	0.00639813i
$567$	17.9814	+	3.63708i	0.755148	+	0.152743i
$568$	1.42294	−	1.42294i	0.0597052	−	0.0597052i
$569$	7.49851	−	5.44798i	0.314354	−	0.228391i	−0.419409	−	0.907798i	$-0.637763\pi$
$569$	7.49851	−	5.44798i	0.314354	−	0.228391i	0.733762	+	0.679406i	$0.237763\pi$
$570$		0			0
$571$	6.86662	+	4.98889i	0.287359	+	0.208779i	0.722121	−	0.691767i	$-0.243167\pi$
$571$	6.86662	+	4.98889i	0.287359	+	0.208779i	−0.434762	+	0.900545i	$0.643167\pi$
$572$	18.6432	−	2.95280i	0.779513	−	0.123463i
$573$	31.0688	+	10.4611i	1.29792	+	0.437017i
$574$		−	1.11589i		−	0.0465763i
$575$		0			0
$576$	0.505937	−	23.8069i	0.0210807	−	0.991953i
$577$	−23.4083	+	11.9271i	−0.974498	+	0.496532i	−0.867343	−	0.497711i	$-0.834174\pi$
$577$	−23.4083	+	11.9271i	−0.974498	+	0.496532i	−0.107155	+	0.994242i	$0.534174\pi$
$578$	0.160153	+	1.01117i	0.00666150	+	0.0420590i
$579$	19.0103	−	2.80425i	0.790043	−	0.116540i
$580$		0			0
$581$	−2.63501	−	3.62677i	−0.109318	−	0.150464i
$582$	0.474392	+	0.00504025i	0.0196642	+	0.000208925i
$583$	−1.91584	+	12.0961i	−0.0793460	+	0.500971i
$584$	0.00246850	+	0.00759726i	0.000102147	+	0.000314377i
$585$		0			0
$586$	0.172952	−	0.532293i	0.00714460	−	0.0219888i
$587$	−29.1195	−	14.8371i	−1.20189	−	0.612395i	−0.265759	−	0.964040i	$-0.585622\pi$
$587$	−29.1195	−	14.8371i	−1.20189	−	0.612395i	−0.936133	+	0.351645i	$0.885622\pi$
$588$	−2.94183	−	9.39240i	−0.121319	−	0.387336i
$589$	−0.0616556	−	0.0200331i	−0.00254047	−	0.000825450i
$590$		0			0
$591$	38.6613	+	20.2192i	1.59032	+	0.831705i
$592$	10.7769	+	1.70690i	0.442929	+	0.0701531i
$593$	4.77949	+	4.77949i	0.196270	+	0.196270i	0.798399	−	0.602129i	$-0.205681\pi$
$593$	4.77949	+	4.77949i	0.196270	+	0.196270i	−0.602129	+	0.798399i	$0.705681\pi$
$594$	0.786194	+	0.150347i	0.0322579	+	0.00616880i
$595$		0			0
$596$	2.44871	−	3.37036i	0.100303	−	0.138055i
$597$	16.6455	−	22.4061i	0.681256	−	0.917021i
$598$	0.418201	+	0.820766i	0.0171015	+	0.0335636i
$599$	−26.7065			−1.09120			−0.545598	−	0.838047i	$-0.683697\pi$
$599$	−26.7065			−1.09120			−0.545598	+	0.838047i	$0.683697\pi$
$600$		0			0
$601$	12.6263			0.515039			0.257520	−	0.966273i	$-0.417095\pi$
$601$	12.6263			0.515039			0.257520	+	0.966273i	$0.417095\pi$
$602$	0.261655	+	0.513527i	0.0106643	+	0.0209298i
$603$	0.378542	+	2.76970i	0.0154154	+	0.112791i
$604$	3.67658	−	5.06038i	0.149598	−	0.205904i
$605$		0			0
$606$	−1.06863	−	0.180912i	−0.0434100	−	0.00734905i
$607$	−27.3885	−	27.3885i	−1.11167	−	1.11167i	−0.992925	−	0.118742i	$-0.962114\pi$
$607$	−27.3885	−	27.3885i	−1.11167	−	1.11167i	−0.118742	−	0.992925i	$-0.537886\pi$
$608$	−1.96518	−	0.311254i	−0.0796987	−	0.0126230i
$609$	−1.97576	+	3.77787i	−0.0800617	+	0.153087i
$610$		0			0
$611$	−10.9700	−	3.56436i	−0.443798	−	0.144199i
$612$	17.2426	−	32.1338i	0.696991	−	1.29893i
$613$	30.2547	+	15.4155i	1.22198	+	0.622628i	0.941429	−	0.337212i	$-0.109484\pi$
$613$	30.2547	+	15.4155i	1.22198	+	0.622628i	0.280547	+	0.959840i	$0.409484\pi$
$614$	0.398410	−	1.22618i	0.0160785	−	0.0494846i
$615$		0			0
$616$	0.387877	+	1.19376i	0.0156280	+	0.0480981i
$617$	−2.87470	+	18.1501i	−0.115731	+	0.730697i	0.859767	+	0.510687i	$0.170609\pi$
$617$	−2.87470	+	18.1501i	−0.115731	+	0.730697i	−0.975498	+	0.220010i	$0.929391\pi$
$618$	−0.0157973	+	1.48685i	−0.000635459	+	0.0598099i
$619$	1.95042	+	2.68452i	0.0783938	+	0.107900i	0.846413	−	0.532527i	$-0.178757\pi$
$619$	1.95042	+	2.68452i	0.0783938	+	0.107900i	−0.768019	+	0.640427i	$0.778757\pi$
$620$		0			0
$621$	−3.73270	−	29.6563i	−0.149788	−	1.19007i
$622$	0.0379583	+	0.239659i	0.00152199	+	0.00960946i
$623$	−24.5733	+	12.5207i	−0.984507	+	0.501631i
$624$	15.4564	−	15.1314i	0.618752	−	0.605742i
$625$		0			0
$626$			1.37971i			0.0551443i
$627$	−5.41750	+	16.0897i	−0.216354	+	0.642560i
$628$	−12.7173	+	2.01422i	−0.507476	+	0.0803763i
$629$	13.4834	+	9.79627i	0.537619	+	0.390603i
$630$		0			0
$631$	16.0880	−	11.6886i	0.640454	−	0.465317i	−0.219552	−	0.975601i	$-0.570460\pi$
$631$	16.0880	−	11.6886i	0.640454	−	0.465317i	0.860006	+	0.510284i	$0.170460\pi$
$632$	1.47575	−	1.47575i	0.0587020	−	0.0587020i
$633$	22.4669	−	15.9612i	0.892979	−	0.634402i
$634$	−0.188444	+	0.0612291i	−0.00748405	+	0.00243172i
$635$		0			0
$636$	6.24630	+	12.5879i	0.247682	+	0.499143i
$637$	4.04820	−	7.94505i	0.160396	−	0.314794i
$638$	−0.0844488	+	0.165740i	−0.00334336	+	0.00656171i
$639$	−27.9123	−	9.72963i	−1.10419	−	0.384898i
$640$		0			0
$641$	−39.9060	+	12.9663i	−1.57619	+	0.512136i	−0.961072	−	0.276296i	$-0.910893\pi$
$641$	−39.9060	+	12.9663i	−1.57619	+	0.512136i	−0.615121	+	0.788433i	$0.710893\pi$
$642$	−0.257757	−	0.362816i	−0.0101728	−	0.0143192i
$643$	18.4566	−	18.4566i	0.727857	−	0.727857i	−0.242335	−	0.970193i	$-0.577913\pi$
$643$	18.4566	−	18.4566i	0.727857	−	0.727857i	0.970193	+	0.242335i	$0.0779133\pi$
$644$	18.9477	−	13.7663i	0.746645	−	0.542469i
$645$		0			0
$646$	−0.817785	−	0.594156i	−0.0321753	−	0.0233768i
$647$	0.715984	−	0.113401i	0.0281482	−	0.00445824i	−0.142344	−	0.989817i	$-0.545464\pi$
$647$	0.715984	−	0.113401i	0.0281482	−	0.00445824i	0.170493	+	0.985359i	$0.445464\pi$
$648$	1.67173	−	0.764146i	0.0656717	−	0.0300185i
$649$		−	13.0302i		−	0.511481i
$650$		0			0
$651$	0.0492524	+	0.0503102i	0.00193035	+	0.00197181i
$652$	32.5386	−	16.5793i	1.27431	−	0.649294i
$653$	−3.58799	−	22.6537i	−0.140409	−	0.886507i	−0.952845	−	0.303457i	$-0.901859\pi$
$653$	−3.58799	−	22.6537i	−0.140409	−	0.886507i	0.812436	−	0.583050i	$-0.198141\pi$
$654$	−0.133058	−	0.902019i	−0.00520299	−	0.0352717i
$655$		0			0
$656$	25.0934	+	34.5381i	0.979733	+	1.34849i
$657$	0.0847161	−	0.0811904i	0.00330509	−	0.00316754i
$658$	0.0599554	−	0.378544i	0.00233731	−	0.0147572i
$659$	6.79306	+	20.9069i	0.264620	+	0.814416i	0.991781	+	0.127949i	$0.0408395\pi$
$659$	6.79306	+	20.9069i	0.264620	+	0.814416i	−0.727161	+	0.686467i	$0.759161\pi$
$660$		0			0
$661$	−3.85456	+	11.8631i	−0.149925	+	0.461421i	−0.997611	−	0.0690762i	$-0.977995\pi$
$661$	−3.85456	+	11.8631i	−0.149925	+	0.461421i	0.847687	+	0.530497i	$0.177995\pi$
$662$	−0.792210	−	0.403651i	−0.0307901	−	0.0156884i
$663$	31.5285	−	9.87516i	1.22447	−	0.383520i
$664$	−0.427176	−	0.138798i	−0.0165776	−	0.00538640i
$665$		0			0
$666$	0.121198	+	0.401870i	0.00469633	+	0.0155721i
$667$	6.86070	+	1.08663i	0.265647	+	0.0420744i
$668$	−1.78525	−	1.78525i	−0.0690736	−	0.0690736i
$669$	−6.29291	+	37.1715i	−0.243298	+	1.43713i
$670$		0			0
$671$	−22.9107	+	31.5339i	−0.884459	+	1.21735i
$672$	1.73456	+	1.28861i	0.0669123	+	0.0497093i
$673$	−5.83674	−	11.4552i	−0.224990	−	0.441567i	0.750724	−	0.660616i	$-0.229705\pi$
$673$	−5.83674	−	11.4552i	−0.224990	−	0.441567i	−0.975714	+	0.219048i	$0.929705\pi$
$674$	−0.713172			−0.0274704
$675$		0			0
$676$	−6.34403			−0.244001
$677$	−13.0973	−	25.7050i	−0.503371	−	0.987922i	−0.993235	−	0.116123i	$-0.962953\pi$
$677$	−13.0973	−	25.7050i	−0.503371	−	0.987922i	0.489863	−	0.871799i	$-0.337047\pi$
$678$	−0.621603	−	0.461790i	−0.0238725	−	0.0177349i
$679$	6.42331	−	8.84092i	0.246504	−	0.339283i
$680$		0			0
$681$	−6.20225	+	36.6360i	−0.237671	+	1.40389i
$682$	0.00217215	+	0.00217215i	8.31758e−5	+	8.31758e-5i
$683$	20.5763	+	3.25897i	0.787331	+	0.124701i	0.537137	−	0.843495i	$-0.319506\pi$
$683$	20.5763	+	3.25897i	0.787331	+	0.124701i	0.250194	+	0.968196i	$0.419506\pi$
$684$	5.62471	+	18.6505i	0.215066	+	0.713119i
$685$		0			0
$686$	0.975118	+	0.316835i	0.0372302	+	0.0120968i
$687$	−19.0998	+	5.98232i	−0.728703	+	0.228240i
$688$	−19.6464	−	10.0103i	−0.749013	−	0.381641i
$689$	−3.93416	+	12.1081i	−0.149880	+	0.461282i
$690$		0			0
$691$	−3.21593	−	9.89763i	−0.122340	−	0.376524i	0.871067	−	0.491164i	$-0.163428\pi$
$691$	−3.21593	−	9.89763i	−0.122340	−	0.376524i	−0.993407	+	0.114640i	$0.963428\pi$
$692$	0.647434	−	4.08774i	0.0246117	−	0.155392i
$693$	13.3115	−	12.7575i	0.505662	−	0.484617i
$694$	0.487079	+	0.670407i	0.0184893	+	0.0254483i
$695$		0			0
$696$	0.0623358	+	0.422583i	0.00236283	+	0.0160179i
$697$	10.2009	+	64.4062i	0.386388	+	2.43956i
$698$	−0.149053	+	0.0759465i	−0.00564175	+	0.00287462i
$699$	17.7101	+	18.0905i	0.669857	+	0.684244i
$700$		0			0
$701$		−	29.3464i		−	1.10840i	−0.832384	−	0.554199i	$-0.813025\pi$
$701$		−	29.3464i		−	1.10840i	0.832384	−	0.554199i	$-0.186975\pi$
$702$	0.782771	+	0.282219i	0.0295438	+	0.0106517i
$703$	−8.79321	+	1.39271i	−0.331642	+	0.0525270i
$704$	−19.3613	−	14.0668i	−0.729707	−	0.530163i
$705$		0			0
$706$	−1.20884	+	0.878275i	−0.0454953	+	0.0330543i
$707$	−17.6533	+	17.6533i	−0.663920	+	0.663920i
$708$	−8.65911	−	12.1885i	−0.325429	−	0.458071i
$709$	−18.4297	+	5.98817i	−0.692141	+	0.224890i	−0.633903	−	0.773412i	$-0.718548\pi$
$709$	−18.4297	+	5.98817i	−0.692141	+	0.224890i	−0.0582380	+	0.998303i	$0.518548\pi$
$710$		0			0
$711$	−28.9482	−	10.0907i	−1.08564	−	0.378431i
$712$	−1.25449	+	2.46207i	−0.0470139	+	0.0922700i
$713$	0.0520778	−	0.102208i	0.00195033	−	0.00382774i
$714$	0.487969	+	0.983383i	0.0182618	+	0.0368022i
$715$		0			0
$716$	9.64197	−	3.13287i	0.360337	−	0.117081i
$717$	−5.71929	+	4.06318i	−0.213591	+	0.151742i
$718$	−0.999546	+	0.999546i	−0.0373027	+	0.0373027i
$719$	23.3742	−	16.9824i	0.871712	−	0.633336i	−0.0593341	−	0.998238i	$-0.518898\pi$
$719$	23.3742	−	16.9824i	0.871712	−	0.633336i	0.931046	+	0.364903i	$0.118898\pi$
$720$		0			0
$721$	27.7094	+	20.1321i	1.03195	+	0.749758i
$722$	−0.425469	+	0.0673877i	−0.0158343	+	0.00250791i
$723$	1.09415	−	3.24957i	0.0406919	−	0.120853i
$724$		−	2.08966i		−	0.0776615i
$725$		0			0
$726$	−0.120737	+	0.118199i	−0.00448097	+	0.00438676i
$727$	−23.3536	+	11.8992i	−0.866136	+	0.441318i	−0.829826	−	0.558022i	$-0.811560\pi$
$727$	−23.3536	+	11.8992i	−0.866136	+	0.441318i	−0.0363101	+	0.999341i	$0.511560\pi$
$728$	0.204121	+	1.28877i	0.00756521	+	0.0477649i
$729$	−20.7881	−	17.2294i	−0.769931	−	0.638128i
$730$		0			0
$731$	−19.7965	−	27.2475i	−0.732199	−	1.00779i
$732$	−0.475156	+	44.7220i	−0.0175623	+	1.65297i
$733$	−6.31509	+	39.8719i	−0.233253	+	1.47270i	0.541640	+	0.840610i	$0.317804\pi$
$733$	−6.31509	+	39.8719i	−0.233253	+	1.47270i	−0.774893	+	0.632092i	$0.782196\pi$
$734$	0.0867856	+	0.267099i	0.00320332	+	0.00985879i
$735$		0			0
$736$	1.08794	−	3.34834i	0.0401020	−	0.123421i
$737$	2.50327	+	1.27548i	0.0922093	+	0.0469830i
$738$	−0.776514	+	1.44713i	−0.0285839	+	0.0532698i
$739$	15.4065	+	5.00589i	0.566739	+	0.184145i	0.578351	−	0.815788i	$-0.303696\pi$
$739$	15.4065	+	5.00589i	0.566739	+	0.184145i	−0.0116122	+	0.999933i	$0.503696\pi$
$740$		0			0
$741$	−8.17891	+	15.6390i	−0.300460	+	0.574513i
$742$	−0.417817	−	0.0661757i	−0.0153385	−	0.00242939i
$743$	−3.57440	−	3.57440i	−0.131132	−	0.131132i	0.638494	−	0.769626i	$-0.279558\pi$
$743$	−3.57440	−	3.57440i	−0.131132	−	0.131132i	−0.769626	+	0.638494i	$0.779558\pi$
$744$	0.00695516	+	0.00117747i	0.000254989	+	4.31681e-5i
$745$		0			0
$746$	0.226154	−	0.311274i	0.00828009	−	0.0113966i
$747$	0.893427	+	6.53698i	0.0326888	+	0.239176i
$748$	−16.6392	−	32.6562i	−0.608388	−	1.19403i
$749$	−10.2516			−0.374585
$750$		0			0
$751$	5.81393			0.212153			0.106077	−	0.994358i	$-0.466171\pi$
$751$	5.81393			0.212153			0.106077	+	0.994358i	$0.466171\pi$
$752$	6.65676	+	13.0646i	0.242747	+	0.476418i
$753$	−27.9222	+	37.5854i	−1.01754	+	1.36969i
$754$	−0.113660	+	0.156440i	−0.00413926	+	0.00569720i
$755$		0			0
$756$	3.97373	−	20.7794i	0.144523	−	0.755740i
$757$	3.51235	+	3.51235i	0.127658	+	0.127658i	0.768049	−	0.640391i	$-0.221228\pi$
$757$	3.51235	+	3.51235i	0.127658	+	0.127658i	−0.640391	+	0.768049i	$0.721228\pi$
$758$	1.15861	+	0.183506i	0.0420827	+	0.00666525i
$759$	−26.6199	−	13.9217i	−0.966240	−	0.505326i
$760$		0			0
$761$	16.5920	+	5.39106i	0.601459	+	0.195426i	0.593891	−	0.804546i	$-0.297591\pi$
$761$	16.5920	+	5.39106i	0.601459	+	0.195426i	0.00756785	+	0.999971i	$0.497591\pi$
$762$	0.0923422	+	0.294822i	0.00334520	+	0.0106803i
$763$	−18.7133	−	9.53488i	−0.677465	−	0.345186i
$764$	11.6823	−	35.9545i	0.422651	−	1.30079i
$765$		0			0
$766$	0.121870	+	0.375077i	0.00440334	+	0.0135521i
$767$	2.11898	−	13.3787i	0.0765119	−	0.483077i
$768$	−27.3503	−	0.290587i	−0.986918	−	0.0104857i
$769$	2.97500	+	4.09474i	0.107281	+	0.147660i	0.859282	−	0.511502i	$-0.170911\pi$
$769$	2.97500	+	4.09474i	0.107281	+	0.147660i	−0.752000	+	0.659163i	$0.770911\pi$
$770$		0			0
$771$	−21.3548	+	3.15007i	−0.769073	+	0.113447i
$772$	−3.46656	−	21.8870i	−0.124764	−	0.787731i
$773$	4.71165	−	2.40071i	0.169466	−	0.0863474i	−0.367200	−	0.930142i	$-0.619683\pi$
$773$	4.71165	−	2.40071i	0.169466	−	0.0863474i	0.536666	+	0.843795i	$0.319683\pi$
$774$	0.0180224	−	0.848043i	0.000647801	−	0.0304823i
$775$		0			0
$776$		−	1.09491i		−	0.0393049i
$777$	9.16320	+	3.08531i	0.328728	+	0.110685i
$778$	−0.880046	+	0.139386i	−0.0315512	+	0.00499722i
$779$	−28.1806	−	20.4744i	−1.00968	−	0.733572i
$780$		0			0
$781$	−24.0343	+	17.4619i	−0.860014	+	0.624837i
$782$	1.26476	−	1.26476i	0.0452275	−	0.0452275i
$783$	5.19116	−	3.52444i	0.185517	−	0.125953i
$784$	−10.7805	+	3.50279i	−0.385017	+	0.125100i
$785$		0			0
$786$	0.618982	−	0.307148i	0.0220783	−	0.0109556i
$787$	−14.6311	+	28.7152i	−0.521543	+	1.02359i	0.468585	+	0.883418i	$0.344764\pi$
$787$	−14.6311	+	28.7152i	−0.521543	+	1.02359i	−0.990128	+	0.140167i	$0.955236\pi$
$788$	22.8416	−	44.8292i	0.813699	−	1.59697i
$789$	5.59253	−	2.77509i	0.199099	−	0.0987959i
$790$		0			0
$791$	−16.9641	+	5.51196i	−0.603173	+	0.195983i
$792$	0.327688	−	1.81804i	0.0116439	−	0.0646011i
$793$	−28.6515	+	28.6515i	−1.01745	+	1.01745i
$794$	−0.428933	+	0.311638i	−0.0152223	+	0.0110596i
$795$		0			0
$796$	−26.0410	−	18.9199i	−0.923000	−	0.670599i
$797$	−27.1310	+	4.29713i	−0.961030	+	0.152212i	−0.617188	−	0.786816i	$-0.711728\pi$
$797$	−27.1310	+	4.29713i	−0.961030	+	0.152212i	−0.343841	+	0.939028i	$0.611728\pi$
$798$	−0.555759	−	0.187128i	−0.0196737	−	0.00662425i
$799$			22.3966i			0.792336i
$800$		0			0
$801$	40.5805	+	0.862405i	1.43384	+	0.0304716i
$802$	0.669264	−	0.341007i	0.0236325	−	0.0120414i
$803$	−0.0184483	−	0.116478i	−0.000651025	−	0.00411041i
$804$	3.18918	−	0.470440i	0.112474	−	0.0165912i
$805$		0			0
$806$	0.00187701	+	0.00258348i	6.61147e−5	+	9.09991e-5i
$807$	23.5042	+	0.249724i	0.827388	+	0.00879072i
$808$	−0.391301	+	2.47057i	−0.0137659	+	0.0869145i
$809$	−1.47285	−	4.53298i	−0.0517828	−	0.159371i	0.921821	−	0.387616i	$-0.126701\pi$
$809$	−1.47285	−	4.53298i	−0.0517828	−	0.159371i	−0.973604	+	0.228245i	$0.926701\pi$
$810$		0			0
$811$	−17.2310	+	53.0316i	−0.605062	+	1.86219i	−0.108700	+	0.994075i	$0.534669\pi$
$811$	−17.2310	+	53.0316i	−0.605062	+	1.86219i	−0.496363	+	0.868115i	$0.665331\pi$
$812$	4.38058	+	2.23202i	0.153728	+	0.0783284i
$813$	4.26667	+	13.6222i	0.149639	+	0.477753i
$814$	0.401210	+	0.130361i	0.0140624	+	0.00456915i
$815$		0			0
$816$	−37.2169	−	19.4637i	−1.30285	−	0.681367i
$817$	17.7695	+	2.81441i	0.621675	+	0.0984636i
$818$	−0.179879	−	0.179879i	−0.00628932	−	0.00628932i
$819$	15.7421	−	10.9340i	0.550075	−	0.382064i
$820$		0			0
$821$	11.9603	−	16.4619i	0.417416	−	0.574524i	−0.547591	−	0.836746i	$-0.684455\pi$
$821$	11.9603	−	16.4619i	0.417416	−	0.574524i	0.965008	+	0.262222i	$0.0844552\pi$
$822$	−0.523253	+	0.704337i	−0.0182506	+	0.0245666i
$823$	−12.2207	−	23.9846i	−0.425989	−	0.836050i	−0.999854	−	0.0170998i	$-0.994557\pi$
$823$	−12.2207	−	23.9846i	−0.425989	−	0.836050i	0.573865	−	0.818950i	$-0.305443\pi$
$824$	3.43168			0.119548
$825$		0			0
$826$	0.450081			0.0156603
$827$	8.46369	+	16.6109i	0.294311	+	0.577618i	0.990057	−	0.140670i	$-0.0449257\pi$
$827$	8.46369	+	16.6109i	0.294311	+	0.577618i	−0.695745	+	0.718289i	$0.744926\pi$
$828$	−34.1518	+	4.66762i	−1.18686	+	0.162211i
$829$	−20.7919	+	28.6176i	−0.722132	+	0.993930i	0.277318	+	0.960778i	$0.410554\pi$
$829$	−20.7919	+	28.6176i	−0.722132	+	0.993930i	−0.999450	+	0.0331514i	$0.989446\pi$
$830$		0			0
$831$	−32.9809	−	5.58347i	−1.14409	−	0.193688i
$832$	−17.5916	−	17.5916i	−0.609879	−	0.609879i
$833$	−17.1009	−	2.70851i	−0.592510	−	0.0938444i
$834$	0.207724	−	0.397192i	0.00719289	−	0.0137536i
$835$		0			0
$836$	18.6198	+	6.04995i	0.643981	+	0.209242i
$837$	−0.0288633	−	0.0995178i	−0.000997662	−	0.00343984i
$838$	1.11115	+	0.566157i	0.0383839	+	0.0195576i
$839$	−8.42816	+	25.9392i	−0.290972	+	0.895520i	0.693572	+	0.720387i	$0.256036\pi$
$839$	−8.42816	+	25.9392i	−0.290972	+	0.895520i	−0.984545	+	0.175134i	$0.943964\pi$
$840$		0			0
$841$	−8.51090	−	26.1939i	−0.293479	−	0.903237i
$842$	−0.0225049	+	0.142090i	−0.000775570	+	0.00489676i
$843$	0.191006	−	17.9776i	0.00657859	−	0.619182i
$844$	−18.6806	−	25.7117i	−0.643013	−	0.885032i
$845$		0			0
$846$	−0.341170	+	0.449191i	−0.0117297	+	0.0154435i
$847$	0.608837	+	3.84405i	0.0209199	+	0.132083i
$848$	14.4201	−	7.34738i	0.495187	−	0.252310i
$849$	11.9328	−	11.6819i	0.409531	−	0.400920i
$850$		0			0
$851$		−	15.7531i		−	0.540011i
$852$	−10.8775	+	32.3057i	−0.372658	+	1.10677i
$853$	47.8254	−	7.57479i	1.63751	−	0.259356i	0.731260	−	0.682099i	$-0.238933\pi$
$853$	47.8254	−	7.57479i	1.63751	−	0.259356i	0.906250	+	0.422743i	$0.138933\pi$
$854$	−1.08922	−	0.791367i	−0.0372725	−	0.0270800i
$855$		0			0
$856$	−0.830973	+	0.603737i	−0.0284021	+	0.0206353i
$857$	−27.4824	+	27.4824i	−0.938780	+	0.938780i	−0.998231	−	0.0594514i	$-0.981065\pi$
$857$	−27.4824	+	27.4824i	−0.938780	+	0.938780i	0.0594514	+	0.998231i	$0.481065\pi$
$858$	0.681744	−	0.484334i	0.0232743	−	0.0165349i
$859$	−28.7211	+	9.33206i	−0.979953	+	0.318406i	−0.754827	−	0.655924i	$-0.772279\pi$
$859$	−28.7211	+	9.33206i	−0.979953	+	0.318406i	−0.225126	+	0.974330i	$0.572279\pi$
$860$		0			0
$861$	16.8153	+	33.8871i	0.573062	+	1.15487i
$862$	0.511717	−	1.00430i	0.0174291	−	0.0342066i
$863$	16.3635	−	32.1153i	0.557021	−	1.09322i	−0.425131	−	0.905132i	$-0.639772\pi$
$863$	16.3635	−	32.1153i	0.557021	−	1.09322i	0.982153	−	0.188085i	$-0.0602279\pi$
$864$	−1.35275	−	2.87816i	−0.0460216	−	0.0979170i
$865$		0			0
$866$	−1.95956	+	0.636700i	−0.0665886	+	0.0216360i
$867$	−20.1007	−	28.2936i	−0.682655	−	0.960899i
$868$	0.0574107	−	0.0574107i	0.00194865	−	0.00194865i
$869$	−24.9262	+	18.1100i	−0.845564	+	0.614338i
$870$		0			0
$871$	2.36280	+	1.71668i	0.0800606	+	0.0581674i
$872$	−2.07838	+	0.329184i	−0.0703830	+	0.0111476i
$873$	−14.4822	+	6.99551i	−0.490147	+	0.236762i
$874$			0.955447i			0.0323185i
$875$		0			0
$876$	−0.0946608	−	0.0966939i	−0.00319829	−	0.00326698i
$877$	36.9183	−	18.8108i	1.24664	−	0.635195i	0.298915	−	0.954280i	$-0.403375\pi$
$877$	36.9183	−	18.8108i	1.24664	−	0.635195i	0.947726	+	0.319085i	$0.103375\pi$
$878$	−0.104015	−	0.656722i	−0.00351032	−	0.0221633i
$879$	2.76890	+	18.7707i	0.0933927	+	0.633122i
$880$		0			0
$881$	−7.72042	−	10.6262i	−0.260107	−	0.358007i	0.658912	−	0.752220i	$-0.271017\pi$
$881$	−7.72042	−	10.6262i	−0.260107	−	0.358007i	−0.919019	+	0.394213i	$0.871017\pi$
$882$	−0.301719	−	0.314822i	−0.0101594	−	0.0106006i
$883$	−1.28990	+	8.14408i	−0.0434084	+	0.274070i	−0.999840	−	0.0178865i	$-0.994306\pi$
$883$	−1.28990	+	8.14408i	−0.0434084	+	0.274070i	0.956432	+	0.291957i	$0.0943063\pi$
$884$	−11.7736	−	36.2354i	−0.395989	−	1.21873i
$885$		0			0
$886$	−0.462245	+	1.42265i	−0.0155294	+	0.0477947i
$887$	7.79789	+	3.97322i	0.261827	+	0.133408i	0.579977	−	0.814633i	$-0.303061\pi$
$887$	7.79789	+	3.97322i	0.261827	+	0.133408i	−0.318150	+	0.948040i	$0.603061\pi$
$888$	0.924450	−	0.289550i	0.0310225	−	0.00971667i
$889$	6.76808	+	2.19908i	0.226994	+	0.0737548i
$890$		0			0
$891$	−26.1405	+	7.28140i	−0.875740	+	0.243936i
$892$	42.9406	+	6.80112i	1.43776	+	0.227718i
$893$	−8.45966	−	8.45966i	−0.283092	−	0.283092i
$894$	0.0308085	−	0.181982i	0.00103039	−	0.00608640i
$895$		0			0
$896$	1.95248	−	2.68736i	0.0652279	−	0.0897785i
$897$	−25.0679	−	18.6230i	−0.836992	−	0.621803i
$898$	−0.635018	−	1.24629i	−0.0211908	−	0.0415893i
$899$	0.0240800			0.000803114
$900$		0			0
$901$	24.7202			0.823551
$902$	0.749338	+	1.47066i	0.0249502	+	0.0489676i
$903$	−15.6842	−	11.6518i	−0.521937	−	0.387748i
$904$	−1.05046	+	1.44584i	−0.0349378	+	0.0480878i
$905$		0			0
$906$	0.0462571	−	0.273235i	0.00153679	−	0.00907763i
$907$	22.7174	+	22.7174i	0.754317	+	0.754317i	0.975282	−	0.220964i	$-0.0709205\pi$
$907$	22.7174	+	22.7174i	0.754317	+	0.754317i	−0.220964	+	0.975282i	$0.570920\pi$
$908$	42.3220	+	6.70314i	1.40450	+	0.222452i
$909$	35.1780	−	10.6092i	1.16678	−	0.351884i
$910$		0			0
$911$	32.0727	+	10.4210i	1.06262	+	0.345265i	0.787607	−	0.616177i	$-0.211320\pi$
$911$	32.0727	+	10.4210i	1.06262	+	0.345265i	0.275008	+	0.961442i	$0.411320\pi$
$912$	21.4094	−	6.70573i	0.708937	−	0.222049i
$913$	5.90818	+	3.01037i	0.195532	+	0.0996286i
$914$	0.213945	−	0.658455i	0.00707667	−	0.0217798i
$915$		0			0
$916$	7.13239	+	21.9512i	0.235661	+	0.725289i
$917$	2.48993	−	15.7208i	0.0822248	−	0.519147i
$918$	0.0514874	−	1.61486i	0.00169934	−	0.0532982i
$919$	−21.7602	−	29.9504i	−0.717804	−	0.987972i	−0.999594	−	0.0284959i	$-0.990928\pi$
$919$	−21.7602	−	29.9504i	−0.717804	−	0.987972i	0.281790	−	0.959476i	$-0.409072\pi$
$920$		0			0
$921$	6.37839	+	43.2400i	0.210175	+	1.42481i
$922$	0.231971	+	1.46461i	0.00763956	+	0.0482343i
$923$	−27.5167	+	14.0205i	−0.905724	+	0.461490i
$924$	−14.8741	−	15.1936i	−0.489322	−	0.499832i
$925$		0			0
$926$			0.365984i			0.0120270i
$927$	−21.9255	−	45.3903i	−0.720127	−	1.49081i
$928$	0.729951	−	0.115613i	0.0239618	−	0.00379518i
$929$	21.0087	+	15.2637i	0.689272	+	0.500785i	0.876421	−	0.481546i	$-0.159925\pi$
$929$	21.0087	+	15.2637i	0.689272	+	0.500785i	−0.187149	+	0.982332i	$0.559925\pi$
$930$		0			0
$931$	7.48241	−	5.43629i	0.245226	−	0.178167i
$932$	20.6436	−	20.6436i	0.676205	−	0.676205i
$933$	−4.76411	−	6.70592i	−0.155970	−	0.219542i
$934$	−0.414692	+	0.134742i	−0.0135692	+	0.00440888i
$935$		0			0
$936$	0.632102	−	1.81337i	0.0206609	−	0.0592719i
$937$	11.4061	−	22.3857i	0.372621	−	0.731310i	−0.626210	−	0.779655i	$-0.715395\pi$
$937$	11.4061	−	22.3857i	0.372621	−	0.731310i	0.998831	+	0.0483450i	$0.0153947\pi$
$938$	−0.0440569	+	0.0864664i	−0.00143851	+	0.00282323i
$939$	−20.7907	−	41.8987i	−0.678480	−	1.36731i
$940$		0			0
$941$	−37.5058	+	12.1864i	−1.22265	+	0.397264i	−0.848047	−	0.529920i	$-0.822222\pi$
$941$	−37.5058	+	12.1864i	−1.22265	+	0.397264i	−0.374606	+	0.927184i	$0.622222\pi$
$942$	−0.465045	+	0.330384i	−0.0151520	+	0.0107645i
$943$	43.5831	−	43.5831i	1.41926	−	1.41926i
$944$	−13.9305	+	10.1211i	−0.453401	+	0.329415i
$945$		0			0
$946$	−0.689684	−	0.501085i	−0.0224236	−	0.0162917i
$947$	−27.4747	+	4.35156i	−0.892808	+	0.141407i	−0.585949	−	0.810348i	$-0.699278\pi$
$947$	−27.4747	+	4.35156i	−0.892808	+	0.141407i	−0.306859	+	0.951755i	$0.599278\pi$
$948$	−11.2812	+	33.5046i	−0.366397	+	1.08818i
$949$		−	0.122593i		−	0.00397954i
$950$		0			0
$951$	4.79995	−	4.69903i	0.155649	−	0.152377i
$952$	2.25745	−	1.15023i	0.0731644	−	0.0372791i
$953$	1.49150	+	9.41698i	0.0483145	+	0.305046i	0.999998	−	0.00203511i	$-0.000647795\pi$
$953$	1.49150	+	9.41698i	0.0483145	+	0.305046i	−0.951683	+	0.307081i	$0.900648\pi$
$954$	0.495794	+	0.376566i	0.0160519	+	0.0121918i
$955$		0			0
$956$	4.75543	+	6.54529i	0.153802	+	0.211690i
$957$	0.0669960	−	6.30571i	0.00216567	−	0.203835i
$958$	0.117016	−	0.738808i	0.00378060	−	0.0238698i
$959$	6.24559	+	19.2220i	0.201681	+	0.620709i
$960$		0			0
$961$	−9.57940	+	29.4824i	−0.309013	+	0.951044i
$962$	0.390741	+	0.199093i	0.0125980	+	0.00641900i
$963$	13.2947	+	7.13379i	0.428417	+	0.229883i
$964$	−3.76057	−	1.22188i	−0.121120	−	0.0393542i
$965$		0			0
$966$	0.480874	−	0.919486i	0.0154719	−	0.0295840i
$967$	−61.1082	−	9.67859i	−1.96511	−	0.311242i	−0.998484	−	0.0550419i	$-0.982471\pi$
$967$	−61.1082	−	9.67859i	−1.96511	−	0.311242i	−0.966624	−	0.256201i	$-0.917529\pi$
$968$	0.275735	+	0.275735i	0.00886245	+	0.00886245i
$969$	33.7876	+	5.72004i	1.08541	+	0.183754i
$970$		0			0
$971$	15.4537	−	21.2702i	0.495933	−	0.682594i	−0.485535	−	0.874217i	$-0.661375\pi$
$971$	15.4537	−	21.2702i	0.495933	−	0.682594i	0.981469	+	0.191623i	$0.0613752\pi$
$972$	−19.6131	+	24.1825i	−0.629090	+	0.775653i
$973$	−4.68734	−	9.19942i	−0.150269	−	0.294920i
$974$	−0.640128			−0.0205110
$975$		0			0
$976$	51.5085			1.64875
$977$	8.85510	+	17.3791i	0.283300	+	0.556007i	0.988176	−	0.153323i	$-0.0489976\pi$
$977$	8.85510	+	17.3791i	0.283300	+	0.556007i	−0.704876	+	0.709330i	$0.748998\pi$
$978$	0.964861	−	1.29877i	0.0308528	−	0.0415302i
$979$	23.9779	−	33.0027i	0.766336	−	1.05477i
$980$		0			0
$981$	17.6331	+	25.3873i	0.562983	+	0.810553i
$982$	−1.32033	−	1.32033i	−0.0421335	−	0.0421335i
$983$	54.7775	+	8.67590i	1.74713	+	0.276718i	0.946562	−	0.322523i	$-0.104531\pi$
$983$	54.7775	+	8.67590i	1.74713	+	0.276718i	0.800569	+	0.599241i	$0.204531\pi$
$984$	3.35868	+	1.75653i	0.107071	+	0.0559961i
$985$		0			0
$986$	0.357091	+	0.116026i	0.0113721	+	0.00369502i
$987$	3.88353	+	12.3990i	0.123614	+	0.394664i
$988$	18.1340	+	9.23973i	0.576919	+	0.293955i
$989$	−9.83731	+	30.2761i	−0.312808	+	0.962725i
$990$		0			0
$991$	−8.12909	−	25.0188i	−0.258229	−	0.794748i	−0.993176	−	0.116623i	$-0.962793\pi$
$991$	−8.12909	−	25.0188i	−0.258229	−	0.794748i	0.734947	−	0.678124i	$-0.237207\pi$
$992$	0.00190925	−	0.0120546i	6.06189e−5	−	0.000382733i
$993$	30.1402	+	0.320230i	0.956471	+	0.0101622i
$994$	−0.603158	−	0.830176i	−0.0191310	−	0.0263316i
$995$		0			0
$996$	7.52703	−	1.11032i	0.238503	−	0.0351820i
$997$	−3.96330	−	25.0233i	−0.125519	−	0.792496i	−0.967478	−	0.252955i	$-0.918598\pi$
$997$	−3.96330	−	25.0233i	−0.125519	−	0.792496i	0.841959	−	0.539541i	$-0.181402\pi$
$998$	0.382049	−	0.194664i	0.0120935	−	0.00616197i
$999$	−9.73626	−	10.3776i	−0.308042	−	0.328332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.l.c.257.4		64
3.2	odd	2	inner	375.2.l.c.257.5		64
5.2	odd	4		375.2.l.a.368.5		64
5.3	odd	4		375.2.l.b.368.4		64
5.4	even	2		75.2.l.a.47.5	yes	64
15.2	even	4		375.2.l.a.368.4		64
15.8	even	4		375.2.l.b.368.5		64
15.14	odd	2		75.2.l.a.47.4	yes	64
25.6	even	5		375.2.l.b.107.5		64
25.8	odd	20	inner	375.2.l.c.143.5		64
25.17	odd	20		75.2.l.a.8.4	✓	64
25.19	even	10		375.2.l.a.107.4		64
75.8	even	20	inner	375.2.l.c.143.4		64
75.17	even	20		75.2.l.a.8.5	yes	64
75.44	odd	10		375.2.l.a.107.5		64
75.56	odd	10		375.2.l.b.107.4		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.l.a.8.4	✓	64	25.17	odd	20
75.2.l.a.8.5	yes	64	75.17	even	20
75.2.l.a.47.4	yes	64	15.14	odd	2
75.2.l.a.47.5	yes	64	5.4	even	2
375.2.l.a.107.4		64	25.19	even	10
375.2.l.a.107.5		64	75.44	odd	10
375.2.l.a.368.4		64	15.2	even	4
375.2.l.a.368.5		64	5.2	odd	4
375.2.l.b.107.4		64	75.56	odd	10
375.2.l.b.107.5		64	25.6	even	5
375.2.l.b.368.4		64	5.3	odd	4
375.2.l.b.368.5		64	15.8	even	4
375.2.l.c.143.4		64	75.8	even	20	inner
375.2.l.c.143.5		64	25.8	odd	20	inner
375.2.l.c.257.4		64	1.1	even	1	trivial
375.2.l.c.257.5		64	3.2	odd	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0231951 - 0.0455229i) q^{2} +(1.39036 + 1.03290i) q^{3} +(1.17404 - 1.61592i) q^{4} +(0.0147712 - 0.0872517i) q^{6} +(-1.44136 - 1.44136i) q^{7} +(-0.201718 - 0.0319491i) q^{8} +(0.866221 + 2.87222i) q^{9} +(2.86751 + 0.931709i) q^{11} +(3.30143 - 1.03405i) q^{12} +(2.79268 + 1.42294i) q^{13} +(-0.0321825 + 0.0990475i) q^{14} +(-1.23123 - 3.78934i) q^{16} +(0.952042 - 6.01096i) q^{17} +(0.110660 - 0.106054i) q^{18} +(1.91085 + 2.63007i) q^{19} +(-0.515229 - 3.49280i) q^{21} +(-0.0240979 - 0.152148i) q^{22} +(-5.12542 + 2.61153i) q^{23} +(-0.247462 - 0.252776i) q^{24} -0.160136i q^{26} +(-1.76237 + 4.88816i) q^{27} +(-4.02134 + 0.636918i) q^{28} +(-0.976916 - 0.709771i) q^{29} +(-0.0161330 + 0.0117213i) q^{31} +(-0.432772 + 0.432772i) q^{32} +(3.02451 + 4.25727i) q^{33} +(-0.295719 + 0.0960849i) q^{34} +(5.65826 + 1.97235i) q^{36} +(-1.24327 + 2.44005i) q^{37} +(0.0754058 - 0.147992i) q^{38} +(2.41308 + 4.86298i) q^{39} +(-10.1904 + 3.31106i) q^{41} +(-0.147052 + 0.104471i) q^{42} +(3.91319 - 3.91319i) q^{43} +(4.87212 - 3.53981i) q^{44} +(0.237769 + 0.172749i) q^{46} +(-3.63479 + 0.575694i) q^{47} +(2.20216 - 6.54030i) q^{48} -2.84495i q^{49} +(7.53242 - 7.37405i) q^{51} +(5.57807 - 2.84217i) q^{52} +(0.635421 + 4.01189i) q^{53} +(0.263401 - 0.0331531i) q^{54} +(0.244699 + 0.336799i) q^{56} +(-0.0598219 + 5.63047i) q^{57} +(-0.00965120 + 0.0609353i) q^{58} +(-1.33548 - 4.11017i) q^{59} +(-3.99489 + 12.2950i) q^{61} +(0.000907794 + 0.000462544i) q^{62} +(2.89137 - 5.38845i) q^{63} +(-7.54893 - 2.45280i) q^{64} +(0.123650 - 0.236432i) q^{66} +(0.920343 + 0.145768i) q^{67} +(-8.59551 - 8.59551i) q^{68} +(-9.82366 - 1.66309i) q^{69} +(-5.79154 + 7.97137i) q^{71} +(-0.0829678 - 0.607055i) q^{72} +(-0.0177571 - 0.0348503i) q^{73} +0.139916 q^{74} +6.49339 q^{76} +(-2.79018 - 5.47604i) q^{77} +(0.165405 - 0.222648i) q^{78} +(-6.00647 + 8.26720i) q^{79} +(-7.49932 + 4.97596i) q^{81} +(0.387096 + 0.387096i) q^{82} +(2.17217 + 0.344039i) q^{83} +(-6.24900 - 3.26811i) q^{84} +(-0.268906 - 0.0873730i) q^{86} +(-0.625143 - 1.99590i) q^{87} +(-0.548661 - 0.279557i) q^{88} +(4.18096 - 12.8677i) q^{89} +(-1.97429 - 6.07624i) q^{91} +(-1.79740 + 11.3483i) q^{92} +(-0.0345377 - 0.000366951i) q^{93} +(0.110516 + 0.152113i) q^{94} +(-1.04872 + 0.154699i) q^{96} +(0.838657 + 5.29507i) q^{97} +(-0.129510 + 0.0659889i) q^{98} +(-0.192183 + 9.04318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 10 q^{3} - 20 q^{4} - 6 q^{6} + 20 q^{7} - 10 q^{9} + 10 q^{12} + 20 q^{13} - 8 q^{16} + 10 q^{18} - 6 q^{21} - 20 q^{22} + 10 q^{27} - 40 q^{28} - 12 q^{31} + 10 q^{33} + 20 q^{34} - 22 q^{36} + 20 q^{37}+ \cdots - 120 q^{97}+O(q^{100}) \) 64 * q + 10 * q^3 - 20 * q^4 - 6 * q^6 + 20 * q^7 - 10 * q^9 + 10 * q^12 + 20 * q^13 - 8 * q^16 + 10 * q^18 - 6 * q^21 - 20 * q^22 + 10 * q^27 - 40 * q^28 - 12 * q^31 + 10 * q^33 + 20 * q^34 - 22 * q^36 + 20 * q^37 + 30 * q^39 - 90 * q^42 + 20 * q^43 - 12 * q^46 - 100 * q^48 - 16 * q^51 - 20 * q^52 + 120 * q^54 - 70 * q^57 + 20 * q^58 - 12 * q^61 + 20 * q^63 - 100 * q^64 - 30 * q^66 + 60 * q^67 - 80 * q^69 + 150 * q^72 + 60 * q^73 - 64 * q^76 + 80 * q^78 - 60 * q^79 + 14 * q^81 + 60 * q^82 - 130 * q^84 + 60 * q^87 - 20 * q^88 - 12 * q^91 + 20 * q^93 + 260 * q^94 + 42 * q^96 - 120 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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