LMFDB - Embedded newform 875.2.bb.a.82.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [288,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			82.7
Character	$\chi$	$=$	875.82
Dual form			875.2.bb.a.843.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.596349 - 0.228917i) q^{2} +(0.0491972 - 0.00257832i) q^{3} +(-1.18306 - 1.06523i) q^{4} +(-0.0299289 - 0.00972449i) q^{6} +(-1.82620 - 1.91442i) q^{7} +(1.04166 + 2.04438i) q^{8} +(-2.98115 + 0.313332i) q^{9} +(-0.367849 + 3.49985i) q^{11} +(-0.0609498 - 0.0493562i) q^{12} +(0.577852 + 0.0915228i) q^{13} +(0.650809 + 1.55971i) q^{14} +(0.179610 + 1.70887i) q^{16} +(0.00169324 - 0.00260736i) q^{17} +(1.84953 + 0.495581i) q^{18} +(4.41097 + 4.89888i) q^{19} +(-0.0947799 - 0.0894755i) q^{21} +(1.02054 - 2.00293i) q^{22} +(1.59759 - 4.16186i) q^{23} +(0.0565180 + 0.0978920i) q^{24} +(-0.323650 - 0.186860i) q^{26} +(-0.291831 + 0.0462215i) q^{27} +(0.121204 + 4.21020i) q^{28} +(7.69230 - 2.49938i) q^{29} +(0.916502 + 4.31180i) q^{31} +(1.47178 - 5.49276i) q^{32} +(-0.00907344 + 0.173131i) q^{33} +(-0.00160663 + 0.00116728i) q^{34} +(3.86066 + 2.80493i) q^{36} +(-0.765883 + 0.945787i) q^{37} +(-1.50904 - 3.93119i) q^{38} +(0.0286647 + 0.00301278i) q^{39} +(-2.00472 - 2.75926i) q^{41} +(0.0360394 + 0.0750553i) q^{42} +(6.51520 - 6.51520i) q^{43} +(4.16335 - 3.74869i) q^{44} +(-1.90544 + 2.11621i) q^{46} +(0.0629228 - 0.0408626i) q^{47} +(0.0132423 + 0.0836086i) q^{48} +(-0.329993 + 6.99222i) q^{49} +(7.65801e-5 - 0.000132641i) q^{51} +(-0.586142 - 0.723824i) q^{52} +(0.259564 + 4.95277i) q^{53} +(0.184614 + 0.0392409i) q^{54} +(2.01151 - 5.72762i) q^{56} +(0.229638 + 0.229638i) q^{57} +(-5.15944 - 0.270395i) q^{58} +(-0.931010 - 0.414512i) q^{59} +(3.41172 + 7.66284i) q^{61} +(0.440489 - 2.78114i) q^{62} +(6.04403 + 5.13497i) q^{63} +(-0.115113 + 0.158439i) q^{64} +(0.0450436 - 0.101170i) q^{66} +(1.65377 + 1.07397i) q^{67} +(-0.00478065 + 0.00128097i) q^{68} +(0.0678664 - 0.208871i) q^{69} +(2.56775 + 7.90273i) q^{71} +(-3.74593 - 5.76822i) q^{72} +(-5.67738 + 4.59745i) q^{73} +(0.673240 - 0.388695i) q^{74} -10.4944i q^{76} +(7.37195 - 5.68721i) q^{77} +(-0.0164045 - 0.00835850i) q^{78} +(-2.35530 + 11.0808i) q^{79} +(8.78197 - 1.86667i) q^{81} +(0.563871 + 2.10440i) q^{82} +(13.4652 - 6.86085i) q^{83} +(0.0168181 + 0.206818i) q^{84} +(-5.37677 + 2.39389i) q^{86} +(0.371995 - 0.142796i) q^{87} +(-7.53820 + 2.89365i) q^{88} +(-1.15239 + 0.513075i) q^{89} +(-0.880061 - 1.27339i) q^{91} +(-6.32340 + 3.22193i) q^{92} +(0.0562065 + 0.209766i) q^{93} +(-0.0468781 + 0.00996424i) q^{94} +(0.0582454 - 0.274023i) q^{96} +(12.6048 + 6.42245i) q^{97} +(1.79743 - 4.09426i) q^{98} -10.5489i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.596349	−	0.228917i	−0.421682	−	0.161869i	0.138268	−	0.990395i	$-0.455846\pi$
$2$	−0.596349	−	0.228917i	−0.421682	−	0.161869i	−0.559950	+	0.828526i	$0.689180\pi$
$3$	0.0491972	−	0.00257832i	0.0284040	−	0.00148859i	−0.0381287	−	0.999273i	$-0.512140\pi$
$3$	0.0491972	−	0.00257832i	0.0284040	−	0.00148859i	0.0665327	+	0.997784i	$0.478806\pi$
$4$	−1.18306	−	1.06523i	−0.591530	−	0.532616i
$5$		0			0
$5$		0			0
$6$	−0.0299289	−	0.00972449i	−0.0122184	−	0.00397001i
$7$	−1.82620	−	1.91442i	−0.690238	−	0.723582i
$7$	−1.82620	−	1.91442i	−0.690238	−	0.723582i
$8$	1.04166	+	2.04438i	0.368284	+	0.722797i
$9$	−2.98115	+	0.313332i	−0.993717	+	0.104444i
$10$		0			0
$11$	−0.367849	+	3.49985i	−0.110911	+	1.05525i	0.787568	+	0.616228i	$0.211340\pi$
$11$	−0.367849	+	3.49985i	−0.110911	+	1.05525i	−0.898479	+	0.439017i	$0.855327\pi$
$12$	−0.0609498	−	0.0493562i	−0.0175947	−	0.0142479i
$13$	0.577852	+	0.0915228i	0.160267	+	0.0253839i	0.236052	−	0.971740i	$-0.424146\pi$
$13$	0.577852	+	0.0915228i	0.160267	+	0.0253839i	−0.0757850	+	0.997124i	$0.524146\pi$
$14$	0.650809	+	1.55971i	0.173936	+	0.416850i
$15$		0			0
$16$	0.179610	+	1.70887i	0.0449024	+	0.427218i
$17$	0.00169324	−	0.00260736i	0.000410671	−	0.000632378i	−0.838465	−	0.544955i	$-0.816547\pi$
$17$	0.00169324	−	0.00260736i	0.000410671	−	0.000632378i	0.838876	+	0.544323i	$0.183213\pi$
$18$	1.84953	+	0.495581i	0.435939	+	0.116810i
$19$	4.41097	+	4.89888i	1.01195	+	1.12388i	0.992273	+	0.124074i	$0.0395960\pi$
$19$	4.41097	+	4.89888i	1.01195	+	1.12388i	0.0196734	+	0.999806i	$0.493737\pi$
$20$		0			0
$21$	−0.0947799	−	0.0894755i	−0.0206827	−	0.0195252i
$22$	1.02054	−	2.00293i	0.217580	−	0.427025i
$23$	1.59759	−	4.16186i	0.333121	−	0.867809i	−0.660059	−	0.751214i	$-0.729469\pi$
$23$	1.59759	−	4.16186i	0.333121	−	0.867809i	0.993180	−	0.116595i	$-0.0371979\pi$
$24$	0.0565180	+	0.0978920i	0.0115367	+	0.0199821i
$25$		0			0
$26$	−0.323650	−	0.186860i	−0.0634731	−	0.0366462i
$27$	−0.291831	+	0.0462215i	−0.0561629	+	0.00889533i
$28$	0.121204	+	4.21020i	0.0229054	+	0.795653i
$29$	7.69230	−	2.49938i	1.42842	−	0.464123i	0.510156	−	0.860082i	$-0.329588\pi$
$29$	7.69230	−	2.49938i	1.42842	−	0.464123i	0.918268	+	0.395959i	$0.129588\pi$
$30$		0			0
$31$	0.916502	+	4.31180i	0.164609	+	0.774423i	0.980547	+	0.196284i	$0.0628875\pi$
$31$	0.916502	+	4.31180i	0.164609	+	0.774423i	−0.815938	+	0.578139i	$0.803779\pi$
$32$	1.47178	−	5.49276i	0.260176	−	0.970991i
$33$	−0.00907344	+	0.173131i	−0.00157948	+	0.0301383i
$34$	−0.00160663	+	0.00116728i	−0.000275535	+	0.000200188i
$35$		0			0
$36$	3.86066	+	2.80493i	0.643443	+	0.467488i
$37$	−0.765883	+	0.945787i	−0.125910	+	0.155486i	−0.836203	−	0.548420i	$-0.815229\pi$
$37$	−0.765883	+	0.945787i	−0.125910	+	0.155486i	0.710292	+	0.703907i	$0.248563\pi$
$38$	−1.50904	−	3.93119i	−0.244799	−	0.637723i
$39$	0.0286647	+	0.00301278i	0.00459003	+	0.000482431i
$40$		0			0
$41$	−2.00472	−	2.75926i	−0.313085	−	0.430924i	0.623255	−	0.782018i	$-0.285810\pi$
$41$	−2.00472	−	2.75926i	−0.313085	−	0.430924i	−0.936340	+	0.351094i	$0.885810\pi$
$42$	0.0360394	+	0.0750553i	0.00556100	+	0.0115813i
$43$	6.51520	−	6.51520i	0.993558	−	0.993558i	−0.00642125	−	0.999979i	$-0.502044\pi$
$43$	6.51520	−	6.51520i	0.993558	−	0.993558i	0.999979	+	0.00642125i	$0.00204396\pi$
$44$	4.16335	−	3.74869i	0.627648	−	0.565137i
$45$		0			0
$46$	−1.90544	+	2.11621i	−0.280942	+	0.312018i
$47$	0.0629228	−	0.0408626i	0.00917824	−	0.00596042i	−0.540042	−	0.841638i	$-0.681592\pi$
$47$	0.0629228	−	0.0408626i	0.00917824	−	0.00596042i	0.549220	+	0.835678i	$0.314925\pi$
$48$	0.0132423	+	0.0836086i	0.00191136	+	0.0120679i
$49$	−0.329993	+	6.99222i	−0.0471419	+	0.998888i
$50$		0			0
$51$	7.65801e−5	0	0.000132641i	1.07234e−5	0	1.85734e-5i
$52$	−0.586142	−	0.723824i	−0.0812832	−	0.100376i
$53$	0.259564	+	4.95277i	0.0356538	+	0.680315i	0.956738	+	0.290951i	$0.0939718\pi$
$53$	0.259564	+	4.95277i	0.0356538	+	0.680315i	−0.921084	+	0.389364i	$0.872695\pi$
$54$	0.184614	+	0.0392409i	0.0251228	+	0.00534001i
$55$		0			0
$56$	2.01151	−	5.72762i	0.268800	−	0.765386i
$57$	0.229638	+	0.229638i	0.0304163	+	0.0304163i
$58$	−5.15944	−	0.270395i	−0.677468	−	0.0355046i
$59$	−0.931010	−	0.414512i	−0.121207	−	0.0539649i	0.345237	−	0.938515i	$-0.387798\pi$
$59$	−0.931010	−	0.414512i	−0.121207	−	0.0539649i	−0.466444	+	0.884551i	$0.654465\pi$
$60$		0			0
$61$	3.41172	+	7.66284i	0.436826	+	0.981127i	0.989070	+	0.147445i	$0.0471048\pi$
$61$	3.41172	+	7.66284i	0.436826	+	0.981127i	−0.552245	+	0.833682i	$0.686229\pi$
$62$	0.440489	−	2.78114i	0.0559422	−	0.353205i
$63$	6.04403	+	5.13497i	0.761476	+	0.646945i
$64$	−0.115113	+	0.158439i	−0.0143891	+	0.0198048i
$65$		0			0
$66$	0.0450436	−	0.101170i	0.00554449	−	0.0124531i
$67$	1.65377	+	1.07397i	0.202040	+	0.131206i	0.641693	−	0.766961i	$-0.278232\pi$
$67$	1.65377	+	1.07397i	0.202040	+	0.131206i	−0.439654	+	0.898167i	$0.644899\pi$
$68$	−0.00478065	+	0.00128097i	−0.000579739	+	0.000155341i
$69$	0.0678664	−	0.208871i	0.00817015	−	0.0251451i
$70$		0			0
$71$	2.56775	+	7.90273i	0.304736	+	0.937882i	0.979776	+	0.200100i	$0.0641266\pi$
$71$	2.56775	+	7.90273i	0.304736	+	0.937882i	−0.675039	+	0.737782i	$0.735873\pi$
$72$	−3.74593	−	5.76822i	−0.441462	−	0.679791i
$73$	−5.67738	+	4.59745i	−0.664487	+	0.538091i	−0.901154	−	0.433500i	$-0.857278\pi$
$73$	−5.67738	+	4.59745i	−0.664487	+	0.538091i	0.236666	+	0.971591i	$0.423945\pi$
$74$	0.673240	−	0.388695i	0.0782626	−	0.0451849i
$75$		0			0
$76$		−	10.4944i		−	1.20379i
$77$	7.37195	−	5.68721i	0.840112	−	0.648118i
$78$	−0.0164045	−	0.00835850i	−0.00185744	−	0.000946414i
$79$	−2.35530	+	11.0808i	−0.264992	+	1.24669i	0.621303	+	0.783570i	$0.286603\pi$
$79$	−2.35530	+	11.0808i	−0.264992	+	1.24669i	−0.886296	+	0.463120i	$0.846730\pi$
$80$		0			0
$81$	8.78197	−	1.86667i	0.975774	−	0.207407i
$82$	0.563871	+	2.10440i	0.0622692	+	0.232392i
$83$	13.4652	−	6.86085i	1.47800	−	0.753076i	0.485371	−	0.874308i	$-0.338684\pi$
$83$	13.4652	−	6.86085i	1.47800	−	0.753076i	0.992624	+	0.121232i	$0.0386844\pi$
$84$	0.0168181	+	0.206818i	0.00183501	+	0.0225657i
$85$		0			0
$86$	−5.37677	+	2.39389i	−0.579792	+	0.258140i
$87$	0.371995	−	0.142796i	0.0398821	−	0.0153093i
$88$	−7.53820	+	2.89365i	−0.803575	+	0.308464i
$89$	−1.15239	+	0.513075i	−0.122153	+	0.0543859i	−0.466903	−	0.884309i	$-0.654630\pi$
$89$	−1.15239	+	0.513075i	−0.122153	+	0.0543859i	0.344750	+	0.938694i	$0.387964\pi$
$90$		0			0
$91$	−0.880061	−	1.27339i	−0.0922554	−	0.133488i
$92$	−6.32340	+	3.22193i	−0.659260	+	0.335910i
$93$	0.0562065	+	0.209766i	0.00582835	+	0.0217517i
$94$	−0.0468781	+	0.00996424i	−0.00483510	+	0.00102773i
$95$		0			0
$96$	0.0582454	−	0.274023i	0.00594464	−	0.0279674i
$97$	12.6048	+	6.42245i	1.27982	+	0.652101i	0.955819	−	0.293955i	$-0.0949717\pi$
$97$	12.6048	+	6.42245i	1.27982	+	0.652101i	0.324002	+	0.946057i	$0.394972\pi$
$98$	1.79743	−	4.09426i	0.181568	−	0.413583i
$99$		−	10.5489i		−	1.06020i
$100$		0			0
$101$	−9.59110	+	5.53743i	−0.954351	+	0.550995i	−0.894430	−	0.447209i	$-0.852418\pi$
$101$	−9.59110	+	5.53743i	−0.954351	+	0.550995i	−0.0599208	+	0.998203i	$0.519085\pi$
$102$	−7.60321e−5	0	6.15695e-5i	−7.52830e−6	0	6.09629e-6i
$103$	4.99114	+	7.68569i	0.491792	+	0.757293i	0.994224	−	0.107323i	$-0.0342280\pi$
$103$	4.99114	+	7.68569i	0.491792	+	0.757293i	−0.502432	+	0.864617i	$0.667561\pi$
$104$	0.414820	+	1.27669i	0.0406765	+	0.125189i
$105$		0			0
$106$	0.978982	−	3.01300i	0.0950871	−	0.292648i
$107$	−16.7396	+	4.48536i	−1.61828	+	0.433617i	−0.950495	−	0.310739i	$-0.899424\pi$
$107$	−16.7396	+	4.48536i	−1.61828	+	0.433617i	−0.667784	+	0.744355i	$0.732757\pi$
$108$	0.394491	+	0.256185i	0.0379599	+	0.0246514i
$109$	1.10392	−	2.47944i	0.105736	−	0.237487i	−0.852927	−	0.522030i	$-0.825175\pi$
$109$	1.10392	−	2.47944i	0.105736	−	0.237487i	0.958663	+	0.284542i	$0.0918416\pi$
$110$		0			0
$111$	−0.0352408	+	0.0485048i	−0.00334491	+	0.00460387i
$112$	2.94349	−	3.46459i	0.278134	−	0.327373i
$113$	−2.16659	+	13.6793i	−0.203815	+	1.28684i	0.647451	+	0.762107i	$0.275835\pi$
$113$	−2.16659	+	13.6793i	−0.203815	+	1.28684i	−0.851267	+	0.524733i	$0.824165\pi$
$114$	−0.0843764	−	0.189513i	−0.00790258	−	0.0177495i
$115$		0			0
$116$	−11.7629	−	5.23717i	−1.09216	−	0.486259i
$117$	−1.75134	−	0.0917840i	−0.161912	−	0.00848543i
$118$	0.460317	+	0.460317i	0.0423757	+	0.0423757i
$119$	−0.00808377	+	0.00151999i	−0.000741038	+	0.000139337i
$120$		0			0
$121$	−1.35404	−	0.287810i	−0.123094	−	0.0261645i
$122$	−0.280420	−	5.35073i	−0.0253880	−	0.484432i
$123$	−0.105741	−	0.130579i	−0.00953434	−	0.0117739i
$124$	3.50880	−	6.07742i	0.315099	−	0.545768i
$125$		0			0
$126$	−2.42887	−	4.44581i	−0.216381	−	0.396064i
$127$	0.945529	+	5.96983i	0.0839021	+	0.529737i	0.993462	+	0.114164i	$0.0364189\pi$
$127$	0.945529	+	5.96983i	0.0839021	+	0.529737i	−0.909560	+	0.415573i	$0.863581\pi$
$128$	−9.43332	+	6.12607i	−0.833795	+	0.541473i
$129$	0.303731	−	0.337328i	0.0267420	−	0.0297000i
$130$		0			0
$131$	10.8977	−	9.81230i	0.952133	−	0.857304i	−0.0377361	−	0.999288i	$-0.512015\pi$
$131$	10.8977	−	9.81230i	0.952133	−	0.857304i	0.989869	+	0.141983i	$0.0453480\pi$
$132$	0.195160	−	0.195160i	0.0169865	−	0.0169865i
$133$	1.32319	−	17.3908i	0.114735	−	1.50797i
$134$	−0.740372	−	1.01903i	−0.0639584	−	0.0880312i
$135$		0			0
$136$	0.00709422		0.000745632i	0.000608324		6.39375e-5i
$137$	3.54693	+	9.24006i	0.303034	+	0.789432i	0.997550	+	0.0699541i	$0.0222853\pi$
$137$	3.54693	+	9.24006i	0.303034	+	0.789432i	−0.694516	+	0.719477i	$0.744381\pi$
$138$	−0.0882861	+	0.109024i	−0.00751541	+	0.00928076i
$139$	−14.6696	−	10.6581i	−1.24426	−	0.904005i	−0.246382	−	0.969173i	$-0.579242\pi$
$139$	−14.6696	−	10.6581i	−1.24426	−	0.904005i	−0.997874	+	0.0651678i	$0.979242\pi$
$140$		0			0
$141$	0.00299027	−	0.00217256i	0.000251826	−	0.000182962i
$142$	0.277792	−	5.30058i	0.0233118	−	0.444815i
$143$	−0.532879	+	1.98873i	−0.0445616	+	0.166306i
$144$	−1.07089	−	5.03813i	−0.0892406	−	0.419844i
$145$		0			0
$146$	4.43813	−	1.44204i	0.367302	−	0.119344i
$147$	0.00179341	+	0.344848i	0.000147918	+	0.0284426i
$148$	1.91357	−	0.303080i	0.157295	−	0.0249130i
$149$	5.99122	+	3.45903i	0.490820	+	0.283375i	0.724914	−	0.688839i	$-0.241879\pi$
$149$	5.99122	+	3.45903i	0.490820	+	0.283375i	−0.234095	+	0.972214i	$0.575213\pi$
$150$		0			0
$151$	−3.27178	−	5.66690i	−0.266254	−	0.461166i	0.701637	−	0.712534i	$-0.252453\pi$
$151$	−3.27178	−	5.66690i	−0.266254	−	0.461166i	−0.967891	+	0.251369i	$0.919119\pi$
$152$	−5.42042	+	14.1207i	−0.439654	+	1.14534i
$153$	−0.00423084	+	0.00830348i	−0.000342043	+	0.000671297i
$154$	−5.69815	+	1.70400i	−0.459170	+	0.137312i
$155$		0			0
$156$	−0.0307028	−	0.0340989i	−0.00245819	−	0.00273010i
$157$	23.0449	+	6.17486i	1.83918	+	0.492807i	0.998790	−	0.0491717i	$-0.0156581\pi$
$157$	23.0449	+	6.17486i	1.83918	+	0.492807i	0.840392	+	0.541979i	$0.182325\pi$
$158$	3.94117	−	6.06887i	0.313542	−	0.482813i
$159$	0.0255396	+	0.242993i	0.00202542	+	0.0192706i
$160$		0			0
$161$	−10.8851	+	4.54194i	−0.857863	+	0.357955i
$162$	−5.66443	−	0.897157i	−0.445039	−	0.0704873i
$163$	−10.6566	−	8.62952i	−0.834687	−	0.675916i	0.113532	−	0.993534i	$-0.463784\pi$
$163$	−10.6566	−	8.62952i	−0.834687	−	0.675916i	−0.948219	+	0.317618i	$0.897117\pi$
$164$	−0.567549	+	5.39987i	−0.0443181	+	0.421659i
$165$		0			0
$166$	−9.60050	+	1.00905i	−0.745144	+	0.0783178i
$167$	2.17131	+	4.26144i	0.168021	+	0.329760i	0.959629	−	0.281270i	$-0.0907556\pi$
$167$	2.17131	+	4.26144i	0.168021	+	0.329760i	−0.791608	+	0.611030i	$0.790756\pi$
$168$	0.0841932	−	0.286969i	0.00649564	−	0.0221402i
$169$	−12.0382	−	3.91145i	−0.926015	−	0.300881i
$170$		0			0
$171$	−14.6848	−	13.2222i	−1.12297	−	1.01113i
$172$	−14.6481	+	0.767673i	−1.11691	+	0.0585345i
$173$	−16.5720	−	6.36138i	−1.25994	−	0.483647i	−0.365493	−	0.930814i	$-0.619100\pi$
$173$	−16.5720	−	6.36138i	−1.25994	−	0.483647i	−0.894451	+	0.447167i	$0.852433\pi$
$174$	−0.254527			−0.0192957
$175$		0			0
$176$	−6.04687			−0.455800
$177$	−0.0468718	−	0.0179924i	−0.00352310	−	0.00135239i
$178$	0.804675	−	0.0421712i	0.0603130	−	0.00316087i
$179$	−3.49351	−	3.14557i	−0.261117	−	0.235111i	0.528165	−	0.849142i	$-0.322880\pi$
$179$	−3.49351	−	3.14557i	−0.261117	−	0.235111i	−0.789282	+	0.614031i	$0.789547\pi$
$180$		0			0
$181$	23.4101	+	7.60642i	1.74006	+	0.565380i	0.994842	−	0.101438i	$-0.0323444\pi$
$181$	23.4101	+	7.60642i	1.74006	+	0.565380i	0.745220	+	0.666818i	$0.232344\pi$
$182$	0.233323	+	0.960845i	0.0172950	+	0.0712226i
$183$	0.187604	+	0.368194i	0.0138681	+	0.0272177i
$184$	10.1726	−	1.06918i	0.749933	−	0.0788211i
$185$		0			0
$186$	0.0145002	−	0.137960i	0.00106321	−	0.0101157i
$187$	0.00850252	+	0.00688521i	0.000621766	+	0.000503496i
$188$	−0.117970	−	0.0186846i	−0.00860382	−	0.00136271i
$189$	0.621429	+	0.474277i	0.0452023	+	0.0344986i
$190$		0			0
$191$	0.283233	+	2.69478i	0.0204940	+	0.194988i	0.999979	−	0.00653111i	$-0.00207893\pi$
$191$	0.283233	+	2.69478i	0.0204940	+	0.194988i	−0.979485	+	0.201519i	$0.935412\pi$
$192$	−0.00525471	+	0.00809154i	−0.000379226	+	0.000583957i
$193$	−7.27372	−	1.94899i	−0.523574	−	0.140291i	−0.0126547	−	0.999920i	$-0.504028\pi$
$193$	−7.27372	−	1.94899i	−0.523574	−	0.140291i	−0.510919	+	0.859629i	$0.670695\pi$
$194$	−6.04663	−	6.71546i	−0.434123	−	0.482142i
$195$		0			0
$196$	7.83874	−	7.92070i	0.559910	−	0.565764i
$197$	−8.91567	+	17.4980i	−0.635215	+	1.24668i	0.319056	+	0.947736i	$0.396634\pi$
$197$	−8.91567	+	17.4980i	−0.635215	+	1.24668i	−0.954271	+	0.298944i	$0.903366\pi$
$198$	−2.41481	+	6.29079i	−0.171613	+	0.447067i
$199$	6.20257	+	10.7432i	0.439689	+	0.761563i	0.997665	−	0.0682937i	$-0.0217555\pi$
$199$	6.20257	+	10.7432i	0.439689	+	0.761563i	−0.557977	+	0.829857i	$0.688422\pi$
$200$		0			0
$201$	0.0841298	+	0.0485723i	0.00593406	+	0.00342603i
$202$	6.98725	−	1.10667i	0.491621	−	0.0778652i
$203$	−18.8325	−	10.1619i	−1.32178	−	0.713226i
$204$	−0.000231892	0	7.53463e-5i	−1.62357e−5	0	5.27529e-6i
$205$		0			0
$206$	−1.21708	−	5.72590i	−0.0847979	−	0.398943i
$207$	−3.45861	+	12.9077i	−0.240390	+	0.897149i
$208$	−0.0526129	+	1.00391i	−0.00364805	+	0.0696089i
$209$	−18.7679	+	13.6357i	−1.29821	+	0.943202i
$210$		0			0
$211$	18.7799	+	13.6444i	1.29286	+	0.939319i	0.999859	−	0.0167927i	$-0.00534553\pi$
$211$	18.7799	+	13.6444i	1.29286	+	0.939319i	0.293003	+	0.956112i	$0.405346\pi$
$212$	4.96877	−	6.13593i	0.341257	−	0.421417i
$213$	0.146702	+	0.382172i	0.0100519	+	0.0261860i
$214$	11.0094	+	1.15714i	0.752588	+	0.0791002i
$215$		0			0
$216$	−0.398484	−	0.548466i	−0.0271134	−	0.0373184i
$217$	6.58088	−	9.62878i	0.446739	−	0.653644i
$218$	−1.22591	+	1.22591i	−0.0830288	+	0.0830288i
$219$	−0.267458	+	0.240820i	−0.0180731	+	0.0162731i
$220$		0			0
$221$	0.00121708	−	0.00135170i	8.18694e−5	−	9.09251e-5i
$222$	0.0321194	−	0.0208585i	0.00215571	−	0.00139993i
$223$	−4.15501	−	26.2337i	−0.278240	−	1.75674i	−0.590779	−	0.806833i	$-0.701180\pi$
$223$	−4.15501	−	26.2337i	−0.278240	−	1.75674i	0.312539	−	0.949905i	$-0.398820\pi$
$224$	−13.2032	+	7.21327i	−0.882176	+	0.481957i
$225$		0			0
$226$	4.42346	−	7.66166i	0.294244	−	0.509646i
$227$	−11.7451	−	14.5040i	−0.779551	−	0.962665i	0.220368	−	0.975417i	$-0.429274\pi$
$227$	−11.7451	−	14.5040i	−0.779551	−	0.962665i	−0.999919	+	0.0127517i	$0.995941\pi$
$228$	−0.0270578	−	0.516295i	−0.00179195	−	0.0341924i
$229$	−8.83466	−	1.87787i	−0.583811	−	0.124093i	−0.0934678	−	0.995622i	$-0.529795\pi$
$229$	−8.83466	−	1.87787i	−0.583811	−	0.124093i	−0.490343	+	0.871529i	$0.663129\pi$
$230$		0			0
$231$	0.348016	−	0.298802i	0.0228978	−	0.0196597i
$232$	13.1225	+	13.1225i	0.861532	+	0.861532i
$233$	0.127164	+	0.00666441i	0.00833082	+	0.000436600i	0.0565009	−	0.998403i	$-0.482006\pi$
$233$	0.127164	+	0.00666441i	0.00833082	+	0.000436600i	−0.0481701	+	0.998839i	$0.515339\pi$
$234$	1.02340	+	0.455647i	0.0669017	+	0.0297866i
$235$		0			0
$236$	0.659889	+	1.48214i	0.0429551	+	0.0964788i
$237$	−0.0873044	+	0.551218i	−0.00567103	+	0.0358055i
$238$	0.00516870		0.000944066i	0.000335037		6.11947e-5i
$239$	10.3096	−	14.1899i	0.666871	−	0.917870i	−0.332813	−	0.942993i	$-0.607998\pi$
$239$	10.3096	−	14.1899i	0.666871	−	0.917870i	0.999684	+	0.0251232i	$0.00799782\pi$
$240$		0			0
$241$	0.647399	−	1.45408i	0.0417026	−	0.0936657i	−0.891493	−	0.453035i	$-0.850341\pi$
$241$	0.647399	−	1.45408i	0.0417026	−	0.0936657i	0.933196	+	0.359369i	$0.117008\pi$
$242$	0.741595	+	0.481597i	0.0476715	+	0.0309582i
$243$	1.28344	−	0.343896i	0.0823326	−	0.0220610i
$244$	4.12644	−	12.6999i	0.264168	−	0.813027i
$245$		0			0
$246$	0.0331667	+	0.102077i	0.00211463	+	0.00650816i
$247$	2.10053	+	3.23453i	0.133654	+	0.205809i
$248$	−7.86028	+	6.36513i	−0.499128	+	0.404186i
$249$	0.644760	−	0.372252i	0.0408600	−	0.0235905i
$250$		0			0
$251$		−	16.8292i		−	1.06225i	−0.847294	−	0.531124i	$-0.821770\pi$
$251$		−	16.8292i		−	1.06225i	0.847294	−	0.531124i	$-0.178230\pi$
$252$	−1.68052	−	12.5133i	−0.105863	−	0.788262i
$253$	13.9782	+	7.12227i	0.878805	+	0.447773i
$254$	0.802730	−	3.77655i	0.0503678	−	0.236962i
$255$		0			0
$256$	7.41103	−	1.57526i	0.463189	−	0.0984539i
$257$	−4.99329	−	18.6352i	−0.311473	−	1.16243i	−0.927229	−	0.374496i	$-0.877816\pi$
$257$	−4.99329	−	18.6352i	−0.311473	−	1.16243i	0.615756	−	0.787937i	$-0.288851\pi$
$258$	−0.258350	+	0.131636i	−0.0160841	+	0.00819528i
$259$	3.20929	−	0.260975i	0.199415	−	0.0162162i
$260$		0			0
$261$	−22.1488	+	9.86127i	−1.37097	+	0.610397i
$262$	−8.74500	+	3.35689i	−0.540268	+	0.207389i
$263$	−15.7161	+	6.03286i	−0.969098	+	0.372002i	−0.790868	−	0.611987i	$-0.790371\pi$
$263$	−15.7161	+	6.03286i	−0.969098	+	0.372002i	−0.178230	+	0.983989i	$0.557037\pi$
$264$	−0.363398	+	0.161795i	−0.0223656	+	0.00995780i
$265$		0			0
$266$	−4.77012	+	10.0681i	−0.292475	+	0.617313i
$267$	−0.0553713	+	0.0282131i	−0.00338867	+	0.00172661i
$268$	−0.812480	−	3.03222i	−0.0496301	−	0.185222i
$269$	−23.4861	+	4.99213i	−1.43197	+	0.304376i	−0.857642	−	0.514247i	$-0.828072\pi$
$269$	−23.4861	+	4.99213i	−1.43197	+	0.304376i	−0.574332	+	0.818622i	$0.694738\pi$
$270$		0			0
$271$	−0.519589	+	2.44447i	−0.0315628	+	0.148491i	−0.991107	−	0.133066i	$-0.957518\pi$
$271$	−0.519589	+	2.44447i	−0.0315628	+	0.148491i	0.959544	+	0.281558i	$0.0908510\pi$
$272$	0.00475977	+	0.00242522i	0.000288603	+	0.000147051i
$273$	−0.0465797	−	0.0603782i	−0.00281913	−	0.00365425i
$274$		−	6.32225i		−	0.381941i
$275$		0			0
$276$	−0.302787	+	0.174814i	−0.0182256	+	0.0105226i
$277$	−21.4095	+	17.3370i	−1.28637	+	1.04168i	−0.289959	+	0.957039i	$0.593642\pi$
$277$	−21.4095	+	17.3370i	−1.28637	+	1.04168i	−0.996411	+	0.0846428i	$0.973025\pi$
$278$	6.30836	+	9.71403i	0.378351	+	0.582609i
$279$	−4.08326	−	12.5670i	−0.244458	−	0.752365i
$280$		0			0
$281$	2.24129	−	6.89798i	0.133704	−	0.411499i	−0.861682	−	0.507449i	$-0.830589\pi$
$281$	2.24129	−	6.89798i	0.133704	−	0.411499i	0.995386	+	0.0959494i	$0.0305887\pi$
$282$	−0.00228058		0.000611079i	−0.000135806		3.63892e-5i
$283$	6.80370	+	4.41837i	0.404438	+	0.262645i	0.730789	−	0.682604i	$-0.239152\pi$
$283$	6.80370	+	4.41837i	0.404438	+	0.262645i	−0.326351	+	0.945249i	$0.605819\pi$
$284$	5.38044	−	12.0847i	0.319270	−	0.717093i
$285$		0			0
$286$	0.773036	−	1.06399i	0.0457106	−	0.0629152i
$287$	−1.62136	+	8.87683i	−0.0957059	+	0.523983i
$288$	−2.66654	+	16.8359i	−0.157128	+	0.992065i
$289$	6.91452	+	15.5303i	0.406736	+	0.913545i
$290$		0			0
$291$	0.636679	+	0.283468i	0.0373228	+	0.0166172i
$292$	11.6140	+	0.608666i	0.679661	+	0.0356195i
$293$	22.2968	+	22.2968i	1.30259	+	1.30259i	0.926638	+	0.375956i	$0.122686\pi$
$293$	22.2968	+	22.2968i	1.30259	+	1.30259i	0.375956	+	0.926638i	$0.377314\pi$
$294$	0.0778721	−	0.206060i	0.00454159	−	0.0120177i
$295$		0			0
$296$	−2.73134	−	0.580564i	−0.158756	−	0.0337446i
$297$	−0.0544186	−	1.03837i	−0.00315769	−	0.0602523i
$298$	−2.78102	−	3.43428i	−0.161100	−	0.198942i
$299$	1.30408	−	2.25873i	0.0754167	−	0.130626i
$300$		0			0
$301$	−24.3709	−	0.574763i	−1.40471	−	0.0331288i
$302$	0.653876	+	4.12841i	0.0376264	+	0.237563i
$303$	−0.457578	+	0.297155i	−0.0262872	+	0.0170711i
$304$	−7.57931	+	8.41767i	−0.434703	+	0.482787i
$305$		0			0
$306$	0.00442386	−	0.00398326i	0.000252895	−	0.000227708i
$307$	15.2811	−	15.2811i	0.872140	−	0.872140i	−0.120566	−	0.992705i	$-0.538471\pi$
$307$	15.2811	−	15.2811i	0.872140	−	0.872140i	0.992705	+	0.120566i	$0.0384708\pi$
$308$	−14.7797	−	1.12452i	−0.842150	−	0.0640757i
$309$	0.265366	+	0.365246i	0.0150962	+	0.0207781i
$310$		0			0
$311$	9.75391	+	1.02518i	0.553093	+	0.0581325i	0.376953	−	0.926233i	$-0.376972\pi$
$311$	9.75391	+	1.02518i	0.553093	+	0.0581325i	0.176141	+	0.984365i	$0.443639\pi$
$312$	0.0236997	+	0.0617398i	0.00134173	+	0.00349533i
$313$	11.1352	−	13.7509i	0.629400	−	0.777245i	−0.358299	−	0.933607i	$-0.616643\pi$
$313$	11.1352	−	13.7509i	0.629400	−	0.777245i	0.987700	+	0.156362i	$0.0499766\pi$
$314$	−12.3293	−	8.95773i	−0.695780	−	0.505514i
$315$		0			0
$316$	14.5901	−	10.6003i	0.820759	−	0.596316i
$317$	1.11718	−	21.3171i	0.0627473	−	1.19729i	−0.767929	−	0.640535i	$-0.778713\pi$
$317$	1.11718	−	21.3171i	0.0627473	−	1.19729i	0.830676	−	0.556755i	$-0.187954\pi$
$318$	0.0403947	−	0.150755i	0.00226522	−	0.00845393i
$319$	5.91785	+	27.8413i	0.331336	+	1.55881i
$320$		0			0
$321$	−0.811977	+	0.263827i	−0.0453201	+	0.0147254i
$322$	7.53102	−	0.216804i	0.419687	−	0.0120820i
$323$	0.0202420	−	0.00320601i	0.00112629	−	0.000178387i
$324$	−12.3780	−	7.14646i	−0.687669	−	0.397026i
$325$		0			0
$326$	4.37959	+	7.58567i	0.242563	+	0.420131i
$327$	0.0479169	−	0.124828i	0.00264981	−	0.00690300i
$328$	3.55273	−	6.97263i	0.196167	−	0.384999i
$329$	−0.193138	−	0.0458374i	−0.0106480	−	0.00252710i
$330$		0			0
$331$	−6.39481	−	7.10215i	−0.351490	−	0.390370i	0.541309	−	0.840824i	$-0.317929\pi$
$331$	−6.39481	−	7.10215i	−0.351490	−	0.390370i	−0.892800	+	0.450454i	$0.851262\pi$
$332$	−23.2385	−	6.22675i	−1.27538	−	0.341737i
$333$	1.98687	−	3.05951i	0.108880	−	0.167660i
$334$	−0.319344	−	3.03835i	−0.0174737	−	0.166251i
$335$		0			0
$336$	0.135879	−	0.178037i	0.00741280	−	0.00971273i
$337$	7.46859	+	1.18291i	0.406840	+	0.0644372i	0.356501	−	0.934295i	$-0.383970\pi$
$337$	7.46859	+	1.18291i	0.406840	+	0.0644372i	0.0503394	+	0.998732i	$0.483970\pi$
$338$	6.28357	+	5.08833i	0.341781	+	0.276769i
$339$	−0.0713205	+	0.678569i	−0.00387360	+	0.0368548i
$340$		0			0
$341$	−15.4278	+	1.62153i	−0.835463	+	0.0878107i
$342$	5.73045	+	11.2466i	0.309867	+	0.608148i
$343$	13.9887	−	12.1374i	0.755317	−	0.655360i
$344$	20.1062	+	6.53289i	1.08405	+	0.352230i
$345$		0			0
$346$	8.42645	+	7.58721i	0.453009	+	0.407891i
$347$	3.44467	−	0.180528i	0.184920	−	0.00969123i	0.0403487	−	0.999186i	$-0.487153\pi$
$347$	3.44467	−	0.180528i	0.184920	−	0.00969123i	0.144571	+	0.989494i	$0.453820\pi$
$348$	−0.592204	−	0.227326i	−0.0317455	−	0.0121859i
$349$	5.03213			0.269364			0.134682	−	0.990889i	$-0.456999\pi$
$349$	5.03213			0.269364			0.134682	+	0.990889i	$0.456999\pi$
$350$		0			0
$351$	−0.172866			−0.00922688
$352$	18.6825	+	7.17152i	0.995778	+	0.382243i
$353$	6.66875	−	0.349494i	0.354942	−	0.0186017i	0.125968	−	0.992034i	$-0.459796\pi$
$353$	6.66875	−	0.349494i	0.354942	−	0.0186017i	0.228974	+	0.973433i	$0.426463\pi$
$354$	0.0238332	+	0.0214595i	0.00126672	+	0.00114056i
$355$		0			0
$356$	1.90989	+	0.620560i	0.101224	+	0.0328896i
$357$	−0.000393780	0	9.56218e-5i	−2.08410e−5	0	5.06084e-6i
$358$	1.36327	+	2.67558i	0.0720513	+	0.141409i
$359$	3.98990	−	0.419355i	0.210579	−	0.0221327i	0.00134837	−	0.999999i	$-0.499571\pi$
$359$	3.98990	−	0.419355i	0.210579	−	0.0221327i	0.209230	+	0.977866i	$0.432904\pi$
$360$		0			0
$361$	−2.55632	+	24.3217i	−0.134543	+	1.28009i
$362$	−12.2194	−	9.89505i	−0.642236	−	0.520072i
$363$	−0.0673570	−	0.0106683i	−0.00353532	−	0.000559940i
$364$	−0.315292	+	2.44397i	−0.0165258	+	0.128099i
$365$		0			0
$366$	−0.0275917	−	0.262518i	−0.00144224	−	0.0137220i
$367$	−11.8537	+	18.2531i	−0.618758	+	0.952803i	0.380845	+	0.924639i	$0.375633\pi$
$367$	−11.8537	+	18.2531i	−0.618758	+	0.952803i	−0.999603	+	0.0281648i	$0.991034\pi$
$368$	7.39904	+	1.98257i	0.385701	+	0.103348i
$369$	6.84094	+	7.59764i	0.356125	+	0.395517i
$370$		0			0
$371$	9.00766	−	9.54166i	0.467654	−	0.495378i
$372$	0.156954	−	0.308039i	0.00813766	−	0.0159711i
$373$	−1.32186	+	3.44356i	−0.0684432	+	0.178301i	−0.963536	−	0.267580i	$-0.913776\pi$
$373$	−1.32186	+	3.44356i	−0.0684432	+	0.178301i	0.895092	+	0.445881i	$0.147109\pi$
$374$	−0.00349433	−	0.00605235i	−0.000180687	−	0.000312960i
$375$		0			0
$376$	0.149083	+	0.0860731i	0.00768837	+	0.00443888i
$377$	4.67376	−	0.740251i	0.240711	−	0.0381249i
$378$	−0.262018	−	0.425090i	−0.0134768	−	0.0218643i
$379$	4.03502	−	1.31106i	0.207265	−	0.0673446i	−0.203544	−	0.979066i	$-0.565246\pi$
$379$	4.03502	−	1.31106i	0.207265	−	0.0673446i	0.410810	+	0.911721i	$0.365246\pi$
$380$		0			0
$381$	0.0619095	+	0.291261i	0.00317172	+	0.0149218i
$382$	0.447976	−	1.67187i	0.0229204	−	0.0855402i
$383$	−0.0476437	+	0.909095i	−0.00243448	+	0.0464526i	−0.999577	−	0.0290955i	$-0.990737\pi$
$383$	−0.0476437	+	0.909095i	−0.00243448	+	0.0464526i	0.997142	+	0.0755481i	$0.0240706\pi$
$384$	−0.448298	+	0.325708i	−0.0228771	+	0.0166212i
$385$		0			0
$386$	3.89152	+	2.82735i	0.198073	+	0.143908i
$387$	−17.3814	+	21.4642i	−0.883545	+	1.09109i
$388$	−8.07081	−	21.0252i	−0.409733	−	1.06739i
$389$	9.71731	+	1.02133i	0.492687	+	0.0517835i	0.347615	−	0.937638i	$-0.386992\pi$
$389$	9.71731	+	1.02133i	0.492687	+	0.0517835i	0.145073	+	0.989421i	$0.453658\pi$
$390$		0			0
$391$	−0.00814638	−	0.0112125i	−0.000411980	−	0.000567042i
$392$	−14.6385	+	6.60891i	−0.739355	+	0.333800i
$393$	0.510835	−	0.510835i	0.0257682	−	0.0257682i
$394$	9.32243	−	8.39395i	0.469657	−	0.422881i
$395$		0			0
$396$	−11.2370	+	12.4799i	−0.564680	+	0.627140i
$397$	5.29843	−	3.44084i	0.265921	−	0.172691i	−0.404791	−	0.914409i	$-0.632656\pi$
$397$	5.29843	−	3.44084i	0.265921	−	0.172691i	0.670711	+	0.741718i	$0.265989\pi$
$398$	−1.23960	−	7.82654i	−0.0621357	−	0.392309i
$399$	0.0202584	−	0.858989i	0.00101419	−	0.0430033i
$400$		0			0
$401$	−1.84234	+	3.19103i	−0.0920023	+	0.159353i	−0.908354	−	0.418203i	$-0.862660\pi$
$401$	−1.84234	+	3.19103i	−0.0920023	+	0.159353i	0.816351	+	0.577556i	$0.195993\pi$
$402$	−0.0390516	−	0.0482248i	−0.00194772	−	0.00240523i
$403$	0.134975	+	2.57547i	0.00672356	+	0.128293i
$404$	17.2455	+	3.66565i	0.857996	+	0.182373i
$405$		0			0
$406$	8.90452	+	10.3711i	0.441924	+	0.514710i
$407$	−3.02839	−	3.02839i	−0.150112	−	0.150112i
$408$	0.000350938	0	1.83919e-5i	1.73740e−5	0	9.10534e-7i
$409$	28.0200	+	12.4753i	1.38550	+	0.616864i	0.957899	−	0.287104i	$-0.0926925\pi$
$409$	28.0200	+	12.4753i	1.38550	+	0.616864i	0.427600	+	0.903968i	$0.359359\pi$
$410$		0			0
$411$	0.198323	+	0.445440i	0.00978254	+	0.0219719i
$412$	2.28222	−	14.4094i	0.112437	−	0.709898i
$413$	0.906659	+	2.53932i	0.0446138	+	0.124952i
$414$	5.01733	−	6.90577i	0.246589	−	0.339400i
$415$		0			0
$416$	1.35318	−	3.03930i	0.0663453	−	0.149014i
$417$	−0.749181	−	0.486524i	−0.0366876	−	0.0238252i
$418$	14.3137	−	3.83534i	0.700105	−	0.187593i
$419$	−1.92150	+	5.91378i	−0.0938716	+	0.288907i	−0.986958	−	0.160978i	$-0.948535\pi$
$419$	−1.92150	+	5.91378i	−0.0938716	+	0.288907i	0.893086	+	0.449885i	$0.148535\pi$
$420$		0			0
$421$	8.85803	+	27.2622i	0.431714	+	1.32868i	0.896417	+	0.443212i	$0.146161\pi$
$421$	8.85803	+	27.2622i	0.431714	+	1.32868i	−0.464703	+	0.885467i	$0.653839\pi$
$422$	−8.07594	−	12.4358i	−0.393130	−	0.605368i
$423$	−0.174779	+	0.141533i	−0.00849804	+	0.00688158i
$424$	−9.85496	+	5.68977i	−0.478599	+	0.276319i
$425$		0			0
$426$		−	0.261490i		−	0.0126692i
$427$	8.43941	−	20.5253i	0.408412	−	0.993291i
$428$	24.5819	+	12.5251i	1.18821	+	0.605425i
$429$	−0.0210886	+	0.0992140i	−0.00101817	+	0.00479010i
$430$		0			0
$431$	−6.49460	+	1.38047i	−0.312834	+	0.0664949i	−0.361653	−	0.932313i	$-0.617788\pi$
$431$	−6.49460	+	1.38047i	−0.312834	+	0.0664949i	0.0488191	+	0.998808i	$0.484454\pi$
$432$	−0.131402	−	0.490400i	−0.00632210	−	0.0235944i
$433$	−17.9987	+	9.17080i	−0.864963	+	0.440721i	−0.829406	−	0.558647i	$-0.811321\pi$
$433$	−17.9987	+	9.17080i	−0.864963	+	0.440721i	−0.0355575	+	0.999368i	$0.511321\pi$
$434$	−6.12869	+	4.23564i	−0.294186	+	0.203317i
$435$		0			0
$436$	−3.94719	+	1.75740i	−0.189036	+	0.0841642i
$437$	27.4354	−	10.5315i	1.31241	−	0.503788i
$438$	0.214626	−	0.0823871i	0.0102552	−	0.00393661i
$439$	9.03790	−	4.02393i	0.431356	−	0.192052i	−0.179561	−	0.983747i	$-0.557468\pi$
$439$	9.03790	−	4.02393i	0.431356	−	0.192052i	0.610917	+	0.791695i	$0.290801\pi$
$440$		0			0
$441$	−1.20712	−	20.9483i	−0.0574821	−	0.997536i
$442$	−0.00103523		0.000527475i	−4.92408e−5		2.50894e-5i
$443$	2.07463	+	7.74261i	0.0985685	+	0.367863i	0.997536	−	0.0701521i	$-0.0223485\pi$
$443$	2.07463	+	7.74261i	0.0985685	+	0.367863i	−0.898968	+	0.438015i	$0.855682\pi$
$444$	0.0933609	−	0.0198445i	0.00443071	−	0.000941777i
$445$		0			0
$446$	−3.52750	+	16.5956i	−0.167032	+	0.785823i
$447$	0.303670	+	0.154727i	0.0143631	+	0.00731835i
$448$	0.513536	−	0.0689673i	0.0242623	−	0.00325840i
$449$			3.52087i			0.166160i	0.996543	+	0.0830800i	$0.0264757\pi$
$449$			3.52087i			0.166160i	−0.996543	+	0.0830800i	$0.973524\pi$
$450$		0			0
$451$	10.3944	−	6.00124i	0.489455	−	0.282587i
$452$	17.1348	−	13.8755i	0.805955	−	0.652650i
$453$	−0.175574	−	0.270360i	−0.00824917	−	0.0127026i
$454$	3.68397	+	11.3381i	0.172897	+	0.532123i
$455$		0			0
$456$	−0.230262	+	0.708674i	−0.0107830	+	0.0331867i
$457$	−2.99554	+	0.802653i	−0.140125	+	0.0375465i	−0.328200	−	0.944608i	$-0.606442\pi$
$457$	−2.99554	+	0.802653i	−0.140125	+	0.0375465i	0.188075	+	0.982155i	$0.439775\pi$
$458$	4.83866	+	3.14226i	0.226096	+	0.146828i
$459$	−0.000373624	0	0.000839173i	−1.74393e−5	0	3.91692e-5i
$460$		0			0
$461$	14.6393	−	20.1493i	0.681821	−	0.938446i	−0.318133	−	0.948046i	$-0.603056\pi$
$461$	14.6393	−	20.1493i	0.681821	−	0.938446i	0.999954	+	0.00960024i	$0.00305590\pi$
$462$	−0.275940	+	0.0985236i	−0.0128379	+	0.00458373i
$463$	1.63929	−	10.3501i	0.0761842	−	0.481008i	−0.919867	−	0.392230i	$-0.871704\pi$
$463$	1.63929	−	10.3501i	0.0761842	−	0.481008i	0.996051	−	0.0887782i	$-0.0282962\pi$
$464$	5.65273	+	12.6962i	0.262421	+	0.589408i
$465$		0			0
$466$	−0.0743087	−	0.0330844i	−0.00344229	−	0.00153260i
$467$	18.7791	+	0.984172i	0.868994	+	0.0455421i	0.481620	−	0.876380i	$-0.340049\pi$
$467$	18.7791	+	0.984172i	0.868994	+	0.0455421i	0.387375	+	0.921922i	$0.373382\pi$
$468$	1.97417	+	1.97417i	0.0912562	+	0.0912562i
$469$	−0.964083	−	5.12728i	−0.0445172	−	0.236756i
$470$		0			0
$471$	1.14966	+	0.244369i	0.0529738	+	0.0112599i
$472$	−0.122378	−	2.33512i	−0.00563292	−	0.107483i
$473$	20.4056	+	25.1988i	0.938252	+	1.15864i
$474$	0.178247	−	0.308733i	0.00818715	−	0.0141806i
$475$		0			0
$476$	0.0111827	+	0.00681286i	0.000512560	+	0.000312267i
$477$	−2.32566	−	14.6836i	−0.106485	−	0.672317i
$478$	−9.39641	+	6.10210i	−0.429782	+	0.279104i
$479$	25.9607	−	28.8323i	1.18618	−	1.31738i	0.249010	−	0.968501i	$-0.419895\pi$
$479$	25.9607	−	28.8323i	1.18618	−	1.31738i	0.937167	−	0.348881i	$-0.113438\pi$
$480$		0			0
$481$	−0.529129	+	0.476430i	−0.0241262	+	0.0217233i
$482$	−0.718939	+	0.718939i	−0.0327468	+	0.0327468i
$483$	−0.523804	+	0.251516i	−0.0238339	+	0.0114444i
$484$	1.29533	+	1.78286i	0.0588784	+	0.0810392i
$485$		0			0
$486$	−0.844100	−	0.0887185i	−0.0382892	−	0.00402435i
$487$	−12.0414	−	31.3690i	−0.545649	−	1.42146i	−0.878161	−	0.478366i	$-0.841229\pi$
$487$	−12.0414	−	31.3690i	−0.545649	−	1.42146i	0.332512	−	0.943099i	$-0.392104\pi$
$488$	−12.1119	+	14.9570i	−0.548280	+	0.677069i
$489$	−0.546523	−	0.397072i	−0.0247146	−	0.0179562i
$490$		0			0
$491$	−2.90556	+	2.11101i	−0.131126	+	0.0952686i	−0.651415	−	0.758722i	$-0.725824\pi$
$491$	−2.90556	+	2.11101i	−0.131126	+	0.0952686i	0.520289	+	0.853990i	$0.325824\pi$
$492$	−0.0139993	+	0.267122i	−0.000631135	+	0.0120428i
$493$	0.00650812	−	0.0242886i	0.000293111	−	0.00109391i
$494$	−0.512210	−	2.40976i	−0.0230454	−	0.108420i
$495$		0			0
$496$	−7.20371	+	2.34063i	−0.323456	+	0.105097i
$497$	10.4399	−	19.3477i	0.468294	−	0.867864i
$498$	−0.469716	+	0.0743958i	−0.0210485	+	0.00333375i
$499$	29.9009	+	17.2633i	1.33855	+	0.772812i	0.986592	−	0.163204i	$-0.0521828\pi$
$499$	29.9009	+	17.2633i	1.33855	+	0.772812i	0.351958	+	0.936016i	$0.385516\pi$
$500$		0			0
$501$	0.117810	+	0.204053i	0.00526335	+	0.00911640i
$502$	−3.85248	+	10.0360i	−0.171944	+	0.447931i
$503$	−2.11060	+	4.14229i	−0.0941072	+	0.184696i	−0.933262	−	0.359198i	$-0.883050\pi$
$503$	−2.11060	+	4.14229i	−0.0941072	+	0.184696i	0.839154	+	0.543893i	$0.183050\pi$
$504$	−4.20198	+	17.7052i	−0.187171	+	0.788652i
$505$		0			0
$506$	−6.70550	−	7.44721i	−0.298096	−	0.331069i
$507$	−0.602331	−	0.161394i	−0.0267504	−	0.00716776i
$508$	5.24064	−	8.06988i	0.232516	−	0.358043i
$509$	−0.986814	−	9.38891i	−0.0437398	−	0.416156i	−0.994381	−	0.105863i	$-0.966240\pi$
$509$	−0.986814	−	9.38891i	−0.0437398	−	0.416156i	0.950641	−	0.310293i	$-0.100427\pi$
$510$		0			0
$511$	19.1695	+	2.47302i	0.848008	+	0.109400i
$512$	17.4388	+	2.76203i	0.770692	+	0.122066i
$513$	−1.51369	−	1.22576i	−0.0668311	−	0.0541188i
$514$	−1.28817	+	12.2561i	−0.0568188	+	0.540595i
$515$		0			0
$516$	−0.718665	+	0.0755347i	−0.0316375	+	0.00332523i
$517$	0.119867	+	0.235252i	0.00527174	+	0.0103464i
$518$	−1.97360	−	0.579028i	−0.0867148	−	0.0254410i
$519$	−0.831697	−	0.270235i	−0.0365074	−	0.0118620i
$520$		0			0
$521$	−13.5338	−	12.1859i	−0.592926	−	0.533873i	0.317117	−	0.948386i	$-0.397285\pi$
$521$	−13.5338	−	12.1859i	−0.592926	−	0.533873i	−0.910043	+	0.414514i	$0.863952\pi$
$522$	15.4658	−	0.810528i	0.676920	−	0.0354759i
$523$	38.2614	+	14.6872i	1.67306	+	0.642226i	0.995632	−	0.0933662i	$-0.0297627\pi$
$523$	38.2614	+	14.6872i	1.67306	+	0.642226i	0.677424	+	0.735592i	$0.263096\pi$
$524$	−23.3450			−1.01983
$525$		0			0
$526$	10.7533			0.468867
$527$	0.0127943	+	0.00491127i	0.000557328	+	0.000213938i
$528$	−0.297489	+	0.0155907i	−0.0129466	+	0.000678500i
$529$	2.32351	+	2.09210i	0.101022	+	0.0909608i
$530$		0			0
$531$	2.90536	+	0.944009i	0.126082	+	0.0409665i
$532$	−20.0906	+	19.1648i	−0.871040	+	0.830901i
$533$	−0.905897	−	1.77792i	−0.0392388	−	0.0770104i
$534$	0.0394790	−	0.00414941i	0.00170843	−	0.000179563i
$535$		0			0
$536$	−0.472931	+	4.49964i	−0.0204275	+	0.194355i
$537$	−0.179981	−	0.145746i	−0.00776675	−	0.00628939i
$538$	15.1487	+	2.39932i	0.653107	+	0.103442i
$539$	−24.3503	−	3.72701i	−1.04884	−	0.160534i
$540$		0			0
$541$	2.36398	+	22.4918i	0.101635	+	0.966996i	0.919900	+	0.392154i	$0.128270\pi$
$541$	2.36398	+	22.4918i	0.101635	+	0.966996i	−0.818264	+	0.574842i	$0.805063\pi$
$542$	0.869437	−	1.33882i	0.0373455	−	0.0575071i
$543$	1.17133	+	0.313856i	0.0502664	+	0.0134688i
$544$	−0.0118295	−	0.0131380i	−0.000507186	−	0.000563288i
$545$		0			0
$546$	0.0139562	+	0.0466693i	0.000597269	+	0.00199726i
$547$	−0.875256	+	1.71779i	−0.0374232	+	0.0734473i	−0.908961	−	0.416881i	$-0.863123\pi$
$547$	−0.875256	+	1.71779i	−0.0374232	+	0.0734473i	0.871538	+	0.490328i	$0.163123\pi$
$548$	5.64658	−	14.7099i	0.241210	−	0.628374i
$549$	−12.5719	−	21.7751i	−0.536554	−	0.929339i
$550$		0			0
$551$	46.1747	+	26.6590i	1.96711	+	1.13571i
$552$	0.497706	−	0.0788289i	0.0211838	−	0.00335518i
$553$	25.5146	−	15.7268i	1.08499	−	0.668770i
$554$	16.7362	−	5.43794i	0.711055	−	0.231036i
$555$		0			0
$556$	6.00167	+	28.2356i	0.254528	+	1.19746i
$557$	1.52355	−	5.68596i	0.0645548	−	0.240922i	−0.926108	−	0.377259i	$-0.876867\pi$
$557$	1.52355	−	5.68596i	0.0645548	−	0.240922i	0.990662	+	0.136338i	$0.0435332\pi$
$558$	−0.441746	+	8.42902i	−0.0187006	+	0.356829i
$559$	4.36111	−	3.16853i	0.184455	−	0.134015i
$560$		0			0
$561$	0.000436053	0	0.000316811i	1.84102e−5	0	1.33758e-5i
$562$	−2.91566	+	3.60053i	−0.122989	+	0.151879i
$563$	−5.70009	−	14.8493i	−0.240230	−	0.625821i	0.759464	−	0.650549i	$-0.225461\pi$
$563$	−5.70009	−	14.8493i	−0.240230	−	0.625821i	−0.999694	+	0.0247281i	$0.992128\pi$
$564$	−0.00585195		0.000615065i	−0.000246412		2.58989e-5i
$565$		0			0
$566$	−3.04594	−	4.19237i	−0.128030	−	0.176219i
$567$	−19.6112	−	13.4035i	−0.823593	−	0.562892i
$568$	−13.4814	+	13.4814i	−0.565669	+	0.565669i
$569$	−18.8462	+	16.9692i	−0.790072	+	0.711384i	−0.961798	−	0.273761i	$-0.911732\pi$
$569$	−18.8462	+	16.9692i	−0.790072	+	0.711384i	0.171726	+	0.985145i	$0.445066\pi$
$570$		0			0
$571$	18.0577	−	20.0552i	0.755693	−	0.839282i	−0.235477	−	0.971880i	$-0.575665\pi$
$571$	18.0577	−	20.0552i	0.755693	−	0.839282i	0.991170	+	0.132598i	$0.0423319\pi$
$572$	2.74889	−	1.78515i	0.114937	−	0.0746409i
$573$	0.0208823	+	0.131846i	0.000872370	+	0.00550793i
$574$	2.99895	−	4.92253i	0.125174	−	0.205462i
$575$		0			0
$576$	0.293524	−	0.508398i	0.0122302	−	0.0211833i
$577$	−11.1065	−	13.7154i	−0.462370	−	0.570979i	0.491623	−	0.870808i	$-0.336404\pi$
$577$	−11.1065	−	13.7154i	−0.462370	−	0.570979i	−0.953993	+	0.299829i	$0.903070\pi$
$578$	−0.568326	−	10.8443i	−0.0236392	−	0.451063i
$579$	−0.362872	−	0.0771308i	−0.0150804	−	0.00320545i
$580$		0			0
$581$	−37.7246	−	13.2487i	−1.56508	−	0.549649i
$582$	−0.314792	−	0.314792i	−0.0130485	−	0.0130485i
$583$	−17.4295	−	0.913439i	−0.721854	−	0.0378308i
$584$	−15.3129	−	6.81772i	−0.633651	−	0.282119i
$585$		0			0
$586$	−8.19256	−	18.4008i	−0.338431	−	0.760129i
$587$	−3.52976	+	22.2860i	−0.145689	+	0.919842i	0.801227	+	0.598360i	$0.204181\pi$
$587$	−3.52976	+	22.2860i	−0.145689	+	0.919842i	−0.946916	+	0.321482i	$0.895819\pi$
$588$	0.365222	−	0.409887i	0.0150615	−	0.0169035i
$589$	−17.0803	+	23.5091i	−0.703784	+	0.968675i
$590$		0			0
$591$	−0.393511	+	0.883839i	−0.0161869	+	0.0363563i
$592$	−1.75379	−	1.13892i	−0.0720803	−	0.0468095i
$593$	−28.9916	+	7.76827i	−1.19054	+	0.319005i	−0.799100	−	0.601199i	$-0.794690\pi$
$593$	−28.9916	+	7.76827i	−1.19054	+	0.319005i	−0.391441	+	0.920203i	$0.628023\pi$
$594$	−0.205248	+	0.631687i	−0.00842141	+	0.0259184i
$595$		0			0
$596$	−3.40330	−	10.4743i	−0.139405	−	0.429043i
$597$	0.332848	+	0.512542i	0.0136226	+	0.0209769i
$598$	−1.29475	+	1.04846i	−0.0529461	+	0.0428749i
$599$	−0.212550	+	0.122716i	−0.00868454	+	0.00501402i	−0.504336	−	0.863508i	$-0.668263\pi$
$599$	−0.212550	+	0.122716i	−0.00868454	+	0.00501402i	0.495651	+	0.868522i	$0.334929\pi$
$600$		0			0
$601$			0.0516122i			0.00210530i	0.999999	+	0.00105265i	$0.000335070\pi$
$601$			0.0516122i			0.00210530i	−0.999999	+	0.00105265i	$0.999665\pi$
$602$	14.4020	+	5.92166i	0.586980	+	0.241349i
$603$	−5.26664	−	2.68349i	−0.214474	−	0.109280i
$604$	−2.16584	+	10.1895i	−0.0881270	+	0.414605i
$605$		0			0
$606$	0.340900	−	0.0724605i	0.0138481	−	0.00294351i
$607$	−4.21905	−	15.7457i	−0.171246	−	0.639099i	−0.997161	−	0.0753037i	$-0.976007\pi$
$607$	−4.21905	−	15.7457i	−0.171246	−	0.639099i	0.825915	−	0.563795i	$-0.190659\pi$
$608$	33.4003	−	17.0183i	1.35456	−	0.690184i
$609$	−0.952708	−	0.451381i	−0.0386057	−	0.0182909i
$610$		0			0
$611$	0.0401000	−	0.0178537i	0.00162227	−	0.000722282i
$612$	0.0138505	−	0.00531670i	0.000559872	−	0.000214915i
$613$	−21.9866	+	8.43988i	−0.888032	+	0.340883i	−0.759257	−	0.650791i	$-0.774438\pi$
$613$	−21.9866	+	8.43988i	−0.888032	+	0.340883i	−0.128774	+	0.991674i	$0.541104\pi$
$614$	−12.6110	+	5.61477i	−0.508938	+	0.226594i
$615$		0			0
$616$	19.3059	+	9.14690i	0.777857	+	0.368539i
$617$	−36.9814	+	18.8430i	−1.48882	+	0.758590i	−0.993893	−	0.110347i	$-0.964804\pi$
$617$	−36.9814	+	18.8430i	−1.48882	+	0.758590i	−0.494924	+	0.868937i	$0.664804\pi$
$618$	−0.0746401	−	0.278560i	−0.00300246	−	0.0112053i
$619$	32.6605	−	6.94219i	1.31273	−	0.279030i	0.502216	−	0.864742i	$-0.332518\pi$
$619$	32.6605	−	6.94219i	1.31273	−	0.279030i	0.810519	+	0.585712i	$0.199185\pi$
$620$		0			0
$621$	−0.273859	+	1.28840i	−0.0109896	+	0.0517019i
$622$	−5.58205	−	2.84420i	−0.223820	−	0.114042i
$623$	3.08673	+	1.26917i	0.123667	+	0.0508482i
$624$			0.0495254i			0.00198260i
$625$		0			0
$626$	−9.78828	+	5.65127i	−0.391218	+	0.225870i
$627$	−0.888173	+	0.719228i	−0.0354702	+	0.0287232i
$628$	−20.6858	−	31.8534i	−0.825455	−	1.27109i
$629$	0.00116918	+	0.00359838i	4.66184e−5	+	0.000143477i
$630$		0			0
$631$	−7.10523	+	21.8676i	−0.282855	+	0.870537i	0.704179	+	0.710023i	$0.251315\pi$
$631$	−7.10523	+	21.8676i	−0.282855	+	0.870537i	−0.987034	+	0.160514i	$0.948685\pi$
$632$	−25.1068	+	6.72736i	−0.998696	+	0.267600i
$633$	0.959098	+	0.622846i	0.0381207	+	0.0247559i
$634$	−5.54608	+	12.4567i	−0.220263	+	0.494719i
$635$		0			0
$636$	0.228629	−	0.314681i	0.00906575	−	0.0124779i
$637$	−0.830635	+	4.01027i	−0.0329110	+	0.158893i
$638$	2.84424	−	17.9578i	0.112605	−	0.710957i
$639$	−10.1310	−	22.7547i	−0.400778	−	0.900161i
$640$		0			0
$641$	24.0230	+	10.6957i	0.948853	+	0.422456i	0.822014	−	0.569467i	$-0.192850\pi$
$641$	24.0230	+	10.6957i	0.948853	+	0.422456i	0.126839	+	0.991923i	$0.459517\pi$
$642$	0.544616	+	0.0285421i	0.0214943	+	0.00112647i
$643$	−18.6442	−	18.6442i	−0.735254	−	0.735254i	0.236402	−	0.971655i	$-0.424032\pi$
$643$	−18.6442	−	18.6442i	−0.735254	−	0.735254i	−0.971655	+	0.236402i	$0.924032\pi$
$644$	17.7159	+	6.22174i	0.698105	+	0.245171i
$645$		0			0
$646$	−0.0128052	−	0.00272183i	−0.000503813	−	0.000107089i
$647$	0.776781	+	14.8219i	0.0305384	+	0.582707i	0.970452	+	0.241295i	$0.0775720\pi$
$647$	0.776781	+	14.8219i	0.0305384	+	0.582707i	−0.939913	+	0.341413i	$0.889095\pi$
$648$	12.9640	+	16.0092i	0.509275	+	0.628902i
$649$	1.79320	−	3.10592i	0.0703894	−	0.121918i
$650$		0			0
$651$	0.298935	−	0.490677i	0.0117162	−	0.0192311i
$652$	3.41492	+	21.5610i	0.133739	+	0.844393i
$653$	2.07418	−	1.34699i	0.0811689	−	0.0527117i	−0.503416	−	0.864044i	$-0.667924\pi$
$653$	2.07418	−	1.34699i	0.0811689	−	0.0527117i	0.584585	+	0.811332i	$0.301257\pi$
$654$	−0.0571504	+	0.0634719i	−0.00223476	+	0.00248195i
$655$		0			0
$656$	4.35516	−	3.92140i	0.170040	−	0.153105i
$657$	15.4846	−	15.4846i	0.604112	−	0.604112i
$658$	0.104684	+	0.0715475i	0.00408102	+	0.00278921i
$659$	−20.7720	−	28.5901i	−0.809161	−	1.11371i	−0.991452	−	0.130470i	$-0.958352\pi$
$659$	−20.7720	−	28.5901i	−0.809161	−	1.11371i	0.182292	−	0.983245i	$-0.441648\pi$
$660$		0			0
$661$	−12.7496	−	1.34004i	−0.495903	−	0.0521215i	−0.146724	−	0.989178i	$-0.546873\pi$
$661$	−12.7496	−	1.34004i	−0.495903	−	0.0521215i	−0.349179	+	0.937056i	$0.613539\pi$
$662$	2.18773	+	5.69924i	0.0850286	+	0.221507i
$663$	5.63916e−5	0	6.96378e-5i	2.19007e−6	0	2.70451e-6i
$664$	28.0524	+	20.3812i	1.08864	+	0.790945i
$665$		0			0
$666$	−1.88524	+	1.36971i	−0.0730516	+	0.0530751i
$667$	1.88706	−	36.0073i	0.0730673	−	1.39421i
$668$	1.97063	−	7.35449i	0.0762460	−	0.284554i
$669$	−0.272054	−	1.27991i	−0.0105182	−	0.0494842i
$670$		0			0
$671$	−28.0738	+	9.12174i	−1.08378	+	0.352141i
$672$	−0.630962	+	0.388915i	−0.0243399	+	0.0150027i
$673$	−29.4878	+	4.67041i	−1.13667	+	0.180031i	−0.696277	−	0.717773i	$-0.745161\pi$
$673$	−29.4878	+	4.67041i	−1.13667	+	0.180031i	−0.440394	+	0.897804i	$0.645161\pi$
$674$	−4.18310	−	2.41511i	−0.161127	−	0.0930267i
$675$		0			0
$676$	10.0753	+	17.4510i	0.387512	+	0.671191i
$677$	−16.3200	+	42.5152i	−0.627230	+	1.63399i	0.138149	+	0.990411i	$0.455885\pi$
$677$	−16.3200	+	42.5152i	−0.627230	+	1.63399i	−0.765379	+	0.643579i	$0.777449\pi$
$678$	0.197868	−	0.388337i	0.00759907	−	0.0149140i
$679$	−10.7236	−	35.8595i	−0.411533	−	1.37616i
$680$		0			0
$681$	−0.615223	−	0.683274i	−0.0235754	−	0.0261831i
$682$	9.57155	+	2.56469i	0.366514	+	0.0982071i
$683$	−18.7286	+	28.8396i	−0.716631	+	1.10352i	0.273295	+	0.961930i	$0.411886\pi$
$683$	−18.7286	+	28.8396i	−0.716631	+	1.10352i	−0.989926	+	0.141585i	$0.954780\pi$
$684$	3.28822	+	31.2854i	0.125728	+	1.19623i
$685$		0			0
$686$	−11.1206	+	4.03590i	−0.424586	+	0.154092i
$687$	−0.439482	−	0.0696072i	−0.0167673	−	0.00265568i
$688$	12.3038	+	9.96345i	0.469079	+	0.379853i
$689$	−0.303302	+	2.88573i	−0.0115549	+	0.109937i
$690$		0			0
$691$	−29.6140	+	3.11256i	−1.12657	+	0.118407i	−0.649432	−	0.760420i	$-0.724993\pi$
$691$	−29.6140	+	3.11256i	−1.12657	+	0.118407i	−0.477140	+	0.878827i	$0.658326\pi$
$692$	12.8293	+	25.1789i	0.487697	+	0.957159i
$693$	−20.1949	+	19.2643i	−0.767141	+	0.731791i
$694$	−2.09555	−	0.680886i	−0.0795460	−	0.0258461i
$695$		0			0
$696$	0.679422	+	0.611755i	0.0257534	+	0.0231885i
$697$	−0.0105889		0.000554939i	−0.000401082		2.10198e-5i
$698$	−3.00090	−	1.15194i	−0.113586	−	0.0436015i
$699$	0.00627332			0.000237279
$700$		0			0
$701$	−45.8591			−1.73208			−0.866038	−	0.499979i	$-0.833341\pi$
$701$	−45.8591			−1.73208			−0.866038	+	0.499979i	$0.833341\pi$
$702$	0.103088	+	0.0395718i	0.00389081	+	0.00149354i
$703$	−8.01159	+	0.419870i	−0.302163	+	0.0158357i
$704$	−0.512168	−	0.461159i	−0.0193031	−	0.0173806i
$705$		0			0
$706$	−4.05690	−	1.31817i	−0.152684	−	0.0496099i
$707$	28.1162	+	8.24894i	1.05742	+	0.310233i
$708$	0.0362861	+	0.0712155i	0.00136372	+	0.00267644i
$709$	−23.4280	+	2.46238i	−0.879856	+	0.0924766i	−0.533673	−	0.845691i	$-0.679189\pi$
$709$	−23.4280	+	2.46238i	−0.879856	+	0.0924766i	−0.346182	+	0.938167i	$0.612522\pi$
$710$		0			0
$711$	3.54954	−	33.7716i	0.133118	−	1.26653i
$712$	−2.24932	−	1.82146i	−0.0842968	−	0.0682622i
$713$	19.4093	+	3.07414i	0.726885	+	0.115127i
$714$	0.000256720	0	3.31189e-5i	9.60749e−6	0	1.23944e-6i
$715$		0			0
$716$	0.782269	+	7.44279i	0.0292348	+	0.278150i
$717$	0.470616	−	0.724686i	0.0175755	−	0.0270639i
$718$	−2.47537	−	0.663273i	−0.0923799	−	0.0247531i
$719$	−23.8551	−	26.4938i	−0.889645	−	0.988051i	0.110338	−	0.993894i	$-0.464807\pi$
$719$	−23.8551	−	26.4938i	−0.889645	−	0.988051i	−0.999983	+	0.00584290i	$0.998140\pi$
$720$		0			0
$721$	5.59880	−	23.5907i	0.208510	−	0.878565i
$722$	7.09211	−	13.9191i	0.263941	−	0.518013i
$723$	0.0281011	−	0.0732060i	0.00104509	−	0.00272256i
$724$	−19.5930	−	33.9361i	−0.728169	−	1.26123i
$725$		0			0
$726$	0.0377261	+	0.0217812i	0.00140015	+	0.000808375i
$727$	−33.9484	+	5.37689i	−1.25907	+	0.199418i	−0.750077	−	0.661350i	$-0.769984\pi$
$727$	−33.9484	+	5.37689i	−1.25907	+	0.199418i	−0.508998	+	0.860768i	$0.669984\pi$
$728$	1.68657	−	3.12562i	0.0625083	−	0.115843i
$729$	−25.5540	+	8.30299i	−0.946443	+	0.307518i
$730$		0			0
$731$	−0.00595568	−	0.0280193i	−0.000220279	−	0.00103633i
$732$	0.170265	−	0.635438i	0.00629318	−	0.0234865i
$733$	−0.231075	+	4.40918i	−0.00853496	+	0.162857i	0.991037	+	0.133590i	$0.0426505\pi$
$733$	−0.231075	+	4.40918i	−0.00853496	+	0.162857i	−0.999572	+	0.0292667i	$0.990683\pi$
$734$	11.2474	−	8.17169i	0.415148	−	0.301623i
$735$		0			0
$736$	−20.5088	−	14.9005i	−0.755965	−	0.549240i
$737$	−4.36707	+	5.39288i	−0.160863	+	0.198649i
$738$	−2.34036	−	6.09685i	−0.0861498	−	0.224428i
$739$	−9.96776	−	1.04765i	−0.366670	−	0.0385386i	−0.0805980	−	0.996747i	$-0.525683\pi$
$739$	−9.96776	−	1.04765i	−0.366670	−	0.0385386i	−0.286072	+	0.958208i	$0.592350\pi$
$740$		0			0
$741$	0.111680	+	0.153714i	0.00410267	+	0.00564683i
$742$	−7.55595	+	3.62815i	−0.277388	+	0.133194i
$743$	6.77097	−	6.77097i	0.248403	−	0.248403i	−0.571912	−	0.820315i	$-0.693798\pi$
$743$	6.77097	−	6.77097i	0.248403	−	0.248403i	0.820315	+	0.571912i	$0.193798\pi$
$744$	−0.370292	+	0.333413i	−0.0135756	+	0.0122235i
$745$		0			0
$746$	1.57658	−	1.75096i	0.0577225	−	0.0641074i
$747$	−37.9920	+	24.6723i	−1.39006	+	0.902713i
$748$	−0.00272465	−	0.0172028i	−9.96232e−5	−	0.000628996i
$749$	39.1567	+	23.8554i	1.43076	+	0.871659i
$750$		0			0
$751$	15.4883	−	26.8266i	0.565177	−	0.978916i	−0.431856	−	0.901943i	$-0.642141\pi$
$751$	15.4883	−	26.8266i	0.565177	−	0.978916i	0.997033	−	0.0769731i	$-0.0245255\pi$
$752$	0.0811304	+	0.100188i	0.00295852	+	0.00365347i
$753$	−0.0433909	−	0.827948i	−0.00158125	−	0.0301721i
$754$	−2.95665	−	0.628455i	−0.107675	−	0.0228870i
$755$		0			0
$756$	−0.229973	−	1.22307i	−0.00836403	−	0.0444824i
$757$	4.48925	+	4.48925i	0.163164	+	0.163164i	0.783967	−	0.620803i	$-0.213193\pi$
$757$	4.48925	+	4.48925i	0.163164	+	0.163164i	−0.620803	+	0.783967i	$0.713193\pi$
$758$	−2.70640	−	0.141837i	−0.0983010	−	0.00515174i
$759$	0.706054	+	0.314355i	0.0256281	+	0.0114104i
$760$		0			0
$761$	−18.9521	−	42.5670i	−0.687012	−	1.54305i	−0.832700	−	0.553724i	$-0.813206\pi$
$761$	−18.9521	−	42.5670i	−0.687012	−	1.54305i	0.145688	−	0.989331i	$-0.453460\pi$
$762$	0.0297549	−	0.187865i	0.00107791	−	0.00680564i
$763$	−6.76266	+	2.41459i	−0.244825	+	0.0874141i
$764$	2.53549	−	3.48980i	0.0917308	−	0.126257i
$765$		0			0
$766$	0.236519	−	0.531231i	0.00854579	−	0.0191942i
$767$	−0.500049	−	0.324736i	−0.0180557	−	0.0117255i
$768$	0.360540	−	0.0966065i	0.0130099	−	0.00348599i
$769$	−3.45276	+	10.6265i	−0.124510	+	0.383201i	−0.993811	−	0.111081i	$-0.964569\pi$
$769$	−3.45276	+	10.6265i	−0.124510	+	0.383201i	0.869302	+	0.494282i	$0.164569\pi$
$770$		0			0
$771$	−0.293704	−	0.903926i	−0.0105775	−	0.0325541i
$772$	6.52913	+	10.0540i	0.234989	+	0.361851i
$773$	7.46682	−	6.04651i	0.268563	−	0.217478i	−0.485573	−	0.874196i	$-0.661389\pi$
$773$	7.46682	−	6.04651i	0.268563	−	0.217478i	0.754136	+	0.656718i	$0.228056\pi$
$774$	15.2789	−	8.82126i	0.549188	−	0.317074i
$775$		0			0
$776$			32.4590i			1.16521i
$777$	0.157215	−	0.0211138i	0.00564006	−	0.000757453i
$778$	−5.56110	−	2.83352i	−0.199375	−	0.101587i
$779$	4.67453	−	21.9919i	0.167482	−	0.787942i
$780$		0			0
$781$	−28.6029	+	6.07974i	−1.02349	+	0.217550i
$782$	0.00229135	+	0.00855142i	8.19383e−5	+	0.000305798i
$783$	−2.12933	+	1.08495i	−0.0760959	+	0.0387728i
$784$	−12.0081	+	0.691954i	−0.428860	+	0.0247126i
$785$		0			0
$786$	−0.421575	+	0.187697i	−0.0150371	+	0.00669493i
$787$	17.2641	−	6.62709i	0.615400	−	0.236230i	−0.0306434	−	0.999530i	$-0.509756\pi$
$787$	17.2641	−	6.62709i	0.615400	−	0.236230i	0.646044	+	0.763300i	$0.276422\pi$
$788$	29.1872	−	11.2039i	1.03975	−	0.399123i
$789$	−0.757635	+	0.337321i	−0.0269725	+	0.0120089i
$790$		0			0
$791$	30.1445	−	20.8334i	1.07182	−	0.740749i
$792$	21.5659	−	10.9884i	0.766309	−	0.390454i
$793$	1.27014	+	4.74024i	0.0451042	+	0.168331i
$794$	−3.94738	+	0.839041i	−0.140087	+	0.0297765i
$795$		0			0
$796$	4.10596	−	19.3170i	0.145532	−	0.684673i
$797$	−20.8503	−	10.6238i	−0.738556	−	0.376313i	0.0438861	−	0.999037i	$-0.486026\pi$
$797$	−20.8503	−	10.6238i	−0.738556	−	0.376313i	−0.782442	+	0.622724i	$0.786026\pi$
$798$	−0.208718	+	0.507620i	−0.00738854	+	0.0179695i
$799$		0	0.000233253i		0	8.25188e-6i
$800$		0			0
$801$	3.27467	−	1.89063i	0.115705	−	0.0668023i
$802$	1.82916	−	1.48122i	0.0645899	−	0.0523039i
$803$	−14.0020	−	21.5612i	−0.494119	−	0.760877i
$804$	−0.0477898	−	0.147082i	−0.00168542	−	0.00518718i
$805$		0			0
$806$	0.509076	−	1.56677i	0.0179314	−	0.0551873i
$807$	−1.14258	+	0.306154i	−0.0402207	+	0.0107771i
$808$	−21.3113	−	13.8397i	−0.749729	−	0.486880i
$809$	8.98201	−	20.1739i	0.315791	−	0.709277i	−0.684005	−	0.729477i	$-0.739764\pi$
$809$	8.98201	−	20.1739i	0.315791	−	0.709277i	0.999796	+	0.0201997i	$0.00643019\pi$
$810$		0			0
$811$	11.7193	−	16.1302i	0.411519	−	0.566408i	−0.552069	−	0.833799i	$-0.686161\pi$
$811$	11.7193	−	16.1302i	0.411519	−	0.566408i	0.963588	+	0.267391i	$0.0861614\pi$
$812$	11.4552	+	32.0832i	0.401999	+	1.12590i
$813$	−0.0192597	+	0.121601i	−0.000675467	+	0.00426473i
$814$	1.11273	+	2.49922i	0.0390010	+	0.0875977i
$815$		0			0
$816$	0.000240420	0	0.000107042i	8.41639e−6	0	3.74722e-6i
$817$	60.6555	+	3.17882i	2.12207	+	0.111213i
$818$	−13.8539	−	13.8539i	−0.484389	−	0.484389i
$819$	3.02259	+	3.52042i	0.105618	+	0.123013i
$820$		0			0
$821$	39.4208	+	8.37915i	1.37580	+	0.292434i	0.835708	−	0.549174i	$-0.185058\pi$
$821$	39.4208	+	8.37915i	1.37580	+	0.292434i	0.540088	+	0.841609i	$0.318391\pi$
$822$	−0.0163008	−	0.311037i	−0.000568554	−	0.0108487i
$823$	−1.15373	−	1.42474i	−0.0402165	−	0.0496633i	0.756641	−	0.653831i	$-0.226839\pi$
$823$	−1.15373	−	1.42474i	−0.0402165	−	0.0496633i	−0.796857	+	0.604167i	$0.793506\pi$
$824$	−10.5134	+	18.2097i	−0.366251	+	0.634365i
$825$		0			0
$826$	0.0406087	−	1.72187i	0.00141296	−	0.0599116i
$827$	−3.13808	−	19.8131i	−0.109122	−	0.688968i	−0.980228	−	0.197873i	$-0.936597\pi$
$827$	−3.13808	−	19.8131i	−0.109122	−	0.688968i	0.871106	−	0.491095i	$-0.163403\pi$
$828$	17.8415	−	11.5864i	0.620034	−	0.402655i
$829$	−7.42726	+	8.24881i	−0.257959	+	0.286493i	−0.858188	−	0.513336i	$-0.828410\pi$
$829$	−7.42726	+	8.24881i	−0.257959	+	0.286493i	0.600229	+	0.799829i	$0.295076\pi$
$830$		0			0
$831$	−1.00859	+	0.908134i	−0.0349874	+	0.0315028i
$832$	−0.0810188	+	0.0810188i	−0.00280882	+	0.00280882i
$833$	0.0176725	+	0.0126999i	0.000612315	+	0.000440026i
$834$	0.335400	+	0.461638i	0.0116139	+	0.0159852i
$835$		0			0
$836$	36.7288	+	3.86035i	1.27029	+	0.133513i
$837$	−0.466762	−	1.21596i	−0.0161337	−	0.0420296i
$838$	2.49965	−	3.08681i	0.0863490	−	0.106632i
$839$	14.2530	+	10.3554i	0.492069	+	0.357509i	0.805980	−	0.591943i	$-0.201639\pi$
$839$	14.2530	+	10.3554i	0.492069	+	0.357509i	−0.313910	+	0.949453i	$0.601639\pi$
$840$		0			0
$841$	29.4630	−	21.4062i	1.01597	−	0.738143i
$842$	0.958304	−	18.2855i	0.0330253	−	0.630161i
$843$	0.0924801	−	0.345140i	0.00318518	−	0.0118873i
$844$	−7.68331	−	36.1471i	−0.264470	−	1.24424i
$845$		0			0
$846$	0.136629	−	0.0443933i	0.00469739	−	0.00152627i
$847$	1.92176	+	3.11779i	0.0660323	+	0.107129i
$848$	−8.41703	+	1.33313i	−0.289042	+	0.0457798i
$849$	0.346115	+	0.199830i	0.0118786	+	0.00685813i
$850$		0			0
$851$	2.71267	+	4.69848i	0.0929891	+	0.161062i
$852$	0.233545	−	0.608404i	0.00800110	−	0.0208436i
$853$	−13.8589	+	27.1996i	−0.474519	+	0.931297i	0.522388	+	0.852708i	$0.325041\pi$
$853$	−13.8589	+	27.1996i	−0.474519	+	0.931297i	−0.996907	+	0.0785886i	$0.974959\pi$
$854$	−9.73142	+	10.3083i	−0.333002	+	0.352744i
$855$		0			0
$856$	−26.6068	−	29.5499i	−0.909402	−	1.00999i
$857$	26.1571	+	7.00877i	0.893509	+	0.239415i	0.676227	−	0.736694i	$-0.263614\pi$
$857$	26.1571	+	7.00877i	0.893509	+	0.239415i	0.217283	+	0.976109i	$0.430281\pi$
$858$	0.0352879	−	0.0543386i	0.00120471	−	0.00185509i
$859$	−0.100406	−	0.955297i	−0.00342580	−	0.0325943i	0.992675	−	0.120812i	$-0.0385497\pi$
$859$	−0.100406	−	0.955297i	−0.00342580	−	0.0325943i	−0.996101	+	0.0882173i	$0.971883\pi$
$860$		0			0
$861$	−0.0568791	+	0.440896i	−0.00193844	+	0.0150257i
$862$	4.18906	+	0.663482i	0.142680	+	0.0225983i
$863$	−15.6555	−	12.6776i	−0.532921	−	0.431551i	0.324712	−	0.945813i	$-0.394732\pi$
$863$	−15.6555	−	12.6776i	−0.532921	−	0.431551i	−0.857633	+	0.514262i	$0.828066\pi$
$864$	−0.175628	+	1.67098i	−0.00597497	+	0.0568481i
$865$		0			0
$866$	12.8329	−	1.34879i	0.436078	−	0.0458337i
$867$	0.380217	+	0.746218i	0.0129128	+	0.0253429i
$868$	−18.0425	+	4.38127i	−0.612402	+	0.148710i
$869$	−37.9149	−	12.3193i	−1.28617	−	0.417903i
$870$		0			0
$871$	0.857341	+	0.771953i	0.0290499	+	0.0261566i
$872$	6.21883	−	0.325915i	0.210596	−	0.0110369i
$873$	−39.5891	−	15.1968i	−1.33989	−	0.514335i
$874$	−18.7719			−0.634969
$875$		0			0
$876$	0.572948			0.0193581
$877$	48.6569	+	18.6776i	1.64303	+	0.630699i	0.991755	−	0.128146i	$-0.0409027\pi$
$877$	48.6569	+	18.6776i	1.64303	+	0.630699i	0.651271	+	0.758845i	$0.274236\pi$
$878$	−6.31089	+	0.330740i	−0.212982	+	0.0111619i
$879$	1.15443	+	1.03945i	0.0389379	+	0.0350599i
$880$		0			0
$881$	−1.59813	−	0.519265i	−0.0538425	−	0.0174945i	0.281972	−	0.959423i	$-0.409012\pi$
$881$	−1.59813	−	0.519265i	−0.0538425	−	0.0174945i	−0.335814	+	0.941928i	$0.609012\pi$
$882$	−4.07554	+	12.7688i	−0.137231	+	0.429948i
$883$	5.52102	+	10.8356i	0.185797	+	0.364647i	0.965051	−	0.262061i	$-0.0844020\pi$
$883$	5.52102	+	10.8356i	0.185797	+	0.364647i	−0.779254	+	0.626708i	$0.784402\pi$
$884$	−0.00287975		0.000302674i	−9.68564e−5		1.01800e-5i
$885$		0			0
$886$	0.535213	−	5.09221i	0.0179808	−	0.171076i
$887$	−12.8570	−	10.4114i	−0.431696	−	0.349580i	0.388712	−	0.921359i	$-0.372920\pi$
$887$	−12.8570	−	10.4114i	−0.431696	−	0.349580i	−0.820408	+	0.571779i	$0.806253\pi$
$888$	−0.135871	−	0.0215199i	−0.00455954	−	0.000722160i
$889$	9.70203	−	12.7122i	0.325396	−	0.426355i
$890$		0			0
$891$	3.30261	+	31.4223i	0.110642	+	1.05269i
$892$	−23.0294	+	35.4621i	−0.771080	+	1.18736i
$893$	0.477732	+	0.128008i	0.0159867	+	0.00428362i
$894$	−0.145673	−	0.161787i	−0.00487204	−	0.00541095i
$895$		0			0
$896$	28.9550	+	6.87189i	0.967318	+	0.229574i
$897$	0.0583332	−	0.114485i	0.00194769	−	0.00382256i
$898$	0.805985	−	2.09966i	0.0268961	−	0.0700667i
$899$	17.8268	+	30.8770i	0.594558	+	1.02981i
$900$		0			0
$901$	0.0133532	+	0.00770945i	0.000444858	+	0.000256839i
$902$	−7.57250	+	1.19937i	−0.252137	+	0.0399345i
$903$	−1.20046	+	0.0345590i	−0.0399488	+	0.00115005i
$904$	−30.2225	+	9.81989i	−1.00519	+	0.326605i
$905$		0			0
$906$	0.0428132	+	0.201420i	0.00142237	+	0.00669175i
$907$	0.331257	−	1.23627i	0.0109992	−	0.0410496i	−0.960208	−	0.279285i	$-0.909902\pi$
$907$	0.331257	−	1.23627i	0.0109992	−	0.0410496i	0.971207	+	0.238236i	$0.0765691\pi$
$908$	−1.55496	+	29.6704i	−0.0516032	+	0.984647i
$909$	26.8575	−	19.5131i	0.890807	−	0.647209i
$910$		0			0
$911$	−31.4927	−	22.8808i	−1.04340	−	0.758075i	−0.0724537	−	0.997372i	$-0.523083\pi$
$911$	−31.4927	−	22.8808i	−1.04340	−	0.758075i	−0.970946	+	0.239297i	$0.923083\pi$
$912$	−0.351177	+	0.433668i	−0.0116286	+	0.0143602i
$913$	19.0588	+	49.6499i	0.630755	+	1.64317i
$914$	1.97013	+	0.207069i	0.0651660	+	0.00684922i
$915$		0			0
$916$	8.45158	+	11.6326i	0.279248	+	0.384352i
$917$	−38.6861	−	2.94347i	−1.27753	−	0.0972019i
$918$	0.000414911	0	0.000414911i	1.36941e−5	0	1.36941e-5i
$919$	−11.4703	+	10.3279i	−0.378372	+	0.340687i	−0.836271	−	0.548317i	$-0.815269\pi$
$919$	−11.4703	+	10.3279i	−0.378372	+	0.340687i	0.457899	+	0.889004i	$0.348602\pi$
$920$		0			0
$921$	0.712389	−	0.791188i	0.0234740	−	0.0260705i
$922$	−13.3426	+	8.66481i	−0.439417	+	0.285360i
$923$	0.760502	+	4.80162i	0.0250322	+	0.158047i
$924$	−0.730018	−	0.0172168i	−0.0240158	−	0.000566390i
$925$		0			0
$926$	−3.34689	+	5.79698i	−0.109986	+	0.190501i
$927$	−17.2875	−	21.3483i	−0.567797	−	0.701171i
$928$	−2.40711	−	45.9305i	−0.0790174	−	1.50774i
$929$	11.5873	+	2.46296i	0.380168	+	0.0808072i	0.394032	−	0.919097i	$-0.371080\pi$
$929$	11.5873	+	2.46296i	0.380168	+	0.0808072i	−0.0138641	+	0.999904i	$0.504413\pi$
$930$		0			0
$931$	−35.7096	+	29.2259i	−1.17034	+	0.957840i
$932$	−0.143344	−	0.143344i	−0.00469539	−	0.00469539i
$933$	0.482508	+	0.0252872i	0.0157966	+	0.000827865i
$934$	−10.9736	−	4.88577i	−0.359067	−	0.159867i
$935$		0			0
$936$	−1.63667	−	3.67602i	−0.0534962	−	0.120154i
$937$	2.80906	−	17.7357i	0.0917681	−	0.579401i	−0.898363	−	0.439254i	$-0.855243\pi$
$937$	2.80906	−	17.7357i	0.0917681	−	0.579401i	0.990131	−	0.140146i	$-0.0447573\pi$
$938$	−0.598792	+	3.27834i	−0.0195512	+	0.107042i
$939$	0.512368	−	0.705214i	0.0167205	−	0.0230138i
$940$		0			0
$941$	13.8674	−	31.1468i	0.452065	−	1.01536i	−0.533460	−	0.845825i	$-0.679108\pi$
$941$	13.8674	−	31.1468i	0.452065	−	1.01536i	0.985525	−	0.169530i	$-0.0542249\pi$
$942$	−0.629661	−	0.408907i	−0.0205155	−	0.0133229i
$943$	−14.6864	+	3.93521i	−0.478255	+	0.128148i
$944$	0.541130	−	1.66543i	0.0176123	−	0.0542050i
$945$		0			0
$946$	−6.40043	−	19.6985i	−0.208096	−	0.640453i
$947$	15.2875	+	23.5407i	0.496777	+	0.764970i	0.994762	−	0.102216i	$-0.0325933\pi$
$947$	15.2875	+	23.5407i	0.496777	+	0.764970i	−0.497985	+	0.867186i	$0.665927\pi$
$948$	0.690462	−	0.559125i	0.0224252	−	0.0181595i
$949$	−3.70146	+	2.13704i	−0.120154	+	0.0693712i
$950$		0			0
$951$		−	1.05162i		−	0.0341013i
$952$	−0.0115280	−	0.0149430i	−0.000373625	−	0.000484305i
$953$	−27.0986	−	13.8074i	−0.877809	−	0.447266i	−0.0438152	−	0.999040i	$-0.513951\pi$
$953$	−27.0986	−	13.8074i	−0.877809	−	0.447266i	−0.833994	+	0.551774i	$0.813951\pi$
$954$	−1.97443	+	9.28895i	−0.0639244	+	0.300741i
$955$		0			0
$956$	−27.3124	+	5.80544i	−0.883347	+	0.187761i
$957$	0.362926	+	1.35446i	0.0117317	+	0.0437834i
$958$	−22.0819	+	11.2513i	−0.713432	+	0.363512i
$959$	11.2119	−	23.6645i	0.362053	−	0.764166i
$960$		0			0
$961$	10.5682	−	4.70528i	0.340911	−	0.151783i
$962$	0.424608	−	0.162992i	0.0136899	−	0.00525506i
$963$	48.4979	−	18.6166i	1.56282	−	0.599912i
$964$	−2.31485	+	1.03064i	−0.0745563	+	0.0331946i
$965$		0			0
$966$	0.369946	−	0.0300835i	0.0119028	−	0.000967921i
$967$	17.7365	−	9.03721i	0.570368	−	0.290617i	−0.144924	−	0.989443i	$-0.546294\pi$
$967$	17.7365	−	9.03721i	0.570368	−	0.290617i	0.715292	+	0.698826i	$0.246294\pi$
$968$	−0.822060	−	3.06797i	−0.0264220	−	0.0986083i
$969$	0.000987583	0	0.000209917i	3.17257e−5	0	6.74351e-6i
$970$		0			0
$971$	0.137281	−	0.645855i	0.00440555	−	0.0207265i	−0.975890	−	0.218263i	$-0.929961\pi$
$971$	0.137281	−	0.645855i	0.00440555	−	0.0207265i	0.980295	+	0.197537i	$0.0632942\pi$
$972$	−1.88472	−	0.960310i	−0.0604523	−	0.0308020i
$973$	6.38556	+	47.5474i	0.204712	+	1.52430i
$974$			21.4633i			0.687730i
$975$		0			0
$976$	−12.4820	+	7.20651i	−0.399540	+	0.230675i
$977$	−15.2947	+	12.3854i	−0.489321	+	0.396244i	−0.841981	−	0.539507i	$-0.818611\pi$
$977$	−15.2947	+	12.3854i	−0.489321	+	0.396244i	0.352660	+	0.935751i	$0.385277\pi$
$978$	0.235022	+	0.361902i	0.00751517	+	0.0115723i
$979$	−1.37178	−	4.22192i	−0.0438424	−	0.134933i
$980$		0			0
$981$	−2.51406	+	7.73748i	−0.0802678	+	0.247039i
$982$	2.21597	−	0.593768i	0.0707145	−	0.0189479i
$983$	13.1523	+	8.54122i	0.419494	+	0.272423i	0.737078	−	0.675807i	$-0.236205\pi$
$983$	13.1523	+	8.54122i	0.419494	+	0.272423i	−0.317584	+	0.948230i	$0.602872\pi$
$984$	0.156807	−	0.352194i	0.00499882	−	0.0112275i
$985$		0			0
$986$	−0.00944118	+	0.0129947i	−0.000300669	+	0.000413835i
$987$	−0.00962002	−	0.00175710i	−0.000306208	−	5.59292e-5i
$988$	0.960476	−	6.06421i	0.0305568	−	0.192928i
$989$	−16.7068	−	37.5240i	−0.531244	−	1.19319i
$990$		0			0
$991$	−19.2192	−	8.55695i	−0.610519	−	0.271821i	0.0780982	−	0.996946i	$-0.475115\pi$
$991$	−19.2192	−	8.55695i	−0.610519	−	0.271821i	−0.688617	+	0.725125i	$0.741782\pi$
$992$	25.0326	+	1.31190i	0.794785	+	0.0416529i
$993$	−0.332918	−	0.332918i	−0.0105648	−	0.0105648i
$994$	−10.6548	+	9.14811i	−0.337951	+	0.290160i
$995$		0			0
$996$	−1.15933	−	0.246422i	−0.0367346	−	0.00780819i
$997$	0.681112	+	12.9964i	0.0215710	+	0.411600i	0.987979	+	0.154587i	$0.0494048\pi$
$997$	0.681112	+	12.9964i	0.0215710	+	0.411600i	−0.966408	+	0.257012i	$0.917262\pi$
$998$	−13.8795	−	17.1398i	−0.439349	−	0.542550i
$999$	0.179793	−	0.311410i	0.00568839	−	0.00985259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.82.7		288
5.2	odd	4		175.2.x.a.138.12	yes	288
5.3	odd	4		875.2.bb.c.418.7		288
5.4	even	2		875.2.bb.b.82.12		288
7.3	odd	6	inner	875.2.bb.a.332.12		288
25.2	odd	20		875.2.bb.b.593.7		288
25.11	even	5		875.2.bb.c.782.7		288
25.14	even	10		175.2.x.a.152.12	yes	288
25.23	odd	20	inner	875.2.bb.a.593.12		288
35.3	even	12		875.2.bb.c.668.7		288
35.17	even	12		175.2.x.a.38.12	✓	288
35.24	odd	6		875.2.bb.b.332.7		288
175.52	even	60		875.2.bb.b.843.12		288
175.73	even	60	inner	875.2.bb.a.843.7		288
175.136	odd	30		875.2.bb.c.157.7		288
175.164	odd	30		175.2.x.a.52.12	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.38.12	✓	288	35.17	even	12
175.2.x.a.52.12	yes	288	175.164	odd	30
175.2.x.a.138.12	yes	288	5.2	odd	4
175.2.x.a.152.12	yes	288	25.14	even	10
875.2.bb.a.82.7		288	1.1	even	1	trivial
875.2.bb.a.332.12		288	7.3	odd	6	inner
875.2.bb.a.593.12		288	25.23	odd	20	inner
875.2.bb.a.843.7		288	175.73	even	60	inner
875.2.bb.b.82.12		288	5.4	even	2
875.2.bb.b.332.7		288	35.24	odd	6
875.2.bb.b.593.7		288	25.2	odd	20
875.2.bb.b.843.12		288	175.52	even	60
875.2.bb.c.157.7		288	175.136	odd	30
875.2.bb.c.418.7		288	5.3	odd	4
875.2.bb.c.668.7		288	35.3	even	12
875.2.bb.c.782.7		288	25.11	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.596349 - 0.228917i) q^{2} +(0.0491972 - 0.00257832i) q^{3} +(-1.18306 - 1.06523i) q^{4} +(-0.0299289 - 0.00972449i) q^{6} +(-1.82620 - 1.91442i) q^{7} +(1.04166 + 2.04438i) q^{8} +(-2.98115 + 0.313332i) q^{9} +(-0.367849 + 3.49985i) q^{11} +(-0.0609498 - 0.0493562i) q^{12} +(0.577852 + 0.0915228i) q^{13} +(0.650809 + 1.55971i) q^{14} +(0.179610 + 1.70887i) q^{16} +(0.00169324 - 0.00260736i) q^{17} +(1.84953 + 0.495581i) q^{18} +(4.41097 + 4.89888i) q^{19} +(-0.0947799 - 0.0894755i) q^{21} +(1.02054 - 2.00293i) q^{22} +(1.59759 - 4.16186i) q^{23} +(0.0565180 + 0.0978920i) q^{24} +(-0.323650 - 0.186860i) q^{26} +(-0.291831 + 0.0462215i) q^{27} +(0.121204 + 4.21020i) q^{28} +(7.69230 - 2.49938i) q^{29} +(0.916502 + 4.31180i) q^{31} +(1.47178 - 5.49276i) q^{32} +(-0.00907344 + 0.173131i) q^{33} +(-0.00160663 + 0.00116728i) q^{34} +(3.86066 + 2.80493i) q^{36} +(-0.765883 + 0.945787i) q^{37} +(-1.50904 - 3.93119i) q^{38} +(0.0286647 + 0.00301278i) q^{39} +(-2.00472 - 2.75926i) q^{41} +(0.0360394 + 0.0750553i) q^{42} +(6.51520 - 6.51520i) q^{43} +(4.16335 - 3.74869i) q^{44} +(-1.90544 + 2.11621i) q^{46} +(0.0629228 - 0.0408626i) q^{47} +(0.0132423 + 0.0836086i) q^{48} +(-0.329993 + 6.99222i) q^{49} +(7.65801e-5 - 0.000132641i) q^{51} +(-0.586142 - 0.723824i) q^{52} +(0.259564 + 4.95277i) q^{53} +(0.184614 + 0.0392409i) q^{54} +(2.01151 - 5.72762i) q^{56} +(0.229638 + 0.229638i) q^{57} +(-5.15944 - 0.270395i) q^{58} +(-0.931010 - 0.414512i) q^{59} +(3.41172 + 7.66284i) q^{61} +(0.440489 - 2.78114i) q^{62} +(6.04403 + 5.13497i) q^{63} +(-0.115113 + 0.158439i) q^{64} +(0.0450436 - 0.101170i) q^{66} +(1.65377 + 1.07397i) q^{67} +(-0.00478065 + 0.00128097i) q^{68} +(0.0678664 - 0.208871i) q^{69} +(2.56775 + 7.90273i) q^{71} +(-3.74593 - 5.76822i) q^{72} +(-5.67738 + 4.59745i) q^{73} +(0.673240 - 0.388695i) q^{74} -10.4944i q^{76} +(7.37195 - 5.68721i) q^{77} +(-0.0164045 - 0.00835850i) q^{78} +(-2.35530 + 11.0808i) q^{79} +(8.78197 - 1.86667i) q^{81} +(0.563871 + 2.10440i) q^{82} +(13.4652 - 6.86085i) q^{83} +(0.0168181 + 0.206818i) q^{84} +(-5.37677 + 2.39389i) q^{86} +(0.371995 - 0.142796i) q^{87} +(-7.53820 + 2.89365i) q^{88} +(-1.15239 + 0.513075i) q^{89} +(-0.880061 - 1.27339i) q^{91} +(-6.32340 + 3.22193i) q^{92} +(0.0562065 + 0.209766i) q^{93} +(-0.0468781 + 0.00996424i) q^{94} +(0.0582454 - 0.274023i) q^{96} +(12.6048 + 6.42245i) q^{97} +(1.79743 - 4.09426i) q^{98} -10.5489i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

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