LMFDB - Embedded newform 1295.2.j.a.186.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1295,2,Mod(186,1295)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1295, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1295.186"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1295 = 5 \cdot 7 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1295.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$10.3406270618$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			186.7
Character	$\chi$	$=$	1295.186
Dual form			1295.2.j.a.926.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.439861 - 0.761862i) q^{2} +(0.702103 - 1.21608i) q^{3} +(0.613044 - 1.06182i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.23531 q^{6} +(-1.97238 - 1.76344i) q^{7} -2.83806 q^{8} +(0.514102 + 0.890450i) q^{9} +(-0.439861 + 0.761862i) q^{10} +(-1.30938 + 2.26792i) q^{11} +(-0.860841 - 1.49102i) q^{12} -1.85392 q^{13} +(-0.475927 + 2.27835i) q^{14} -1.40421 q^{15} +(0.0222650 + 0.0385641i) q^{16} +(-0.331250 + 0.573741i) q^{17} +(0.452267 - 0.783349i) q^{18} +(0.727697 + 1.26041i) q^{19} -1.22609 q^{20} +(-3.52930 + 1.16045i) q^{21} +2.30379 q^{22} +(-2.25885 - 3.91244i) q^{23} +(-1.99261 + 3.45131i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.815469 + 1.41243i) q^{26} +5.65643 q^{27} +(-3.08162 + 1.01325i) q^{28} -10.4288 q^{29} +(0.617656 + 1.06981i) q^{30} +(-1.32525 + 2.29541i) q^{31} +(-2.81848 + 4.88174i) q^{32} +(1.83864 + 3.18463i) q^{33} +0.582816 q^{34} +(-0.540997 + 2.58985i) q^{35} +1.26067 q^{36} +(-0.500000 - 0.866025i) q^{37} +(0.640171 - 1.10881i) q^{38} +(-1.30165 + 2.25452i) q^{39} +(1.41903 + 2.45783i) q^{40} -5.51742 q^{41} +(2.43650 + 2.17840i) q^{42} +4.15401 q^{43} +(1.60542 + 2.78067i) q^{44} +(0.514102 - 0.890450i) q^{45} +(-1.98716 + 3.44186i) q^{46} +(-1.35151 - 2.34088i) q^{47} +0.0625294 q^{48} +(0.780546 + 6.95635i) q^{49} +0.879722 q^{50} +(0.465143 + 0.805652i) q^{51} +(-1.13654 + 1.96854i) q^{52} +(5.93698 - 10.2831i) q^{53} +(-2.48804 - 4.30942i) q^{54} +2.61877 q^{55} +(5.59773 + 5.00476i) q^{56} +2.04367 q^{57} +(4.58724 + 7.94533i) q^{58} +(-4.47424 + 7.74961i) q^{59} +(-0.860841 + 1.49102i) q^{60} +(-3.25753 - 5.64221i) q^{61} +2.33171 q^{62} +(0.556255 - 2.66289i) q^{63} +5.04801 q^{64} +(0.926962 + 1.60555i) q^{65} +(1.61750 - 2.80159i) q^{66} +(0.610021 - 1.05659i) q^{67} +(0.406142 + 0.703458i) q^{68} -6.34378 q^{69} +(2.21107 - 0.727010i) q^{70} +11.7319 q^{71} +(-1.45905 - 2.52715i) q^{72} +(1.15865 - 2.00685i) q^{73} +(-0.439861 + 0.761862i) q^{74} +(0.702103 + 1.21608i) q^{75} +1.78444 q^{76} +(6.58194 - 2.16417i) q^{77} +2.29017 q^{78} +(-2.61787 - 4.53428i) q^{79} +(0.0222650 - 0.0385641i) q^{80} +(2.42909 - 4.20731i) q^{81} +(2.42690 + 4.20351i) q^{82} -11.5498 q^{83} +(-0.931424 + 4.45890i) q^{84} +0.662500 q^{85} +(-1.82719 - 3.16478i) q^{86} +(-7.32212 + 12.6823i) q^{87} +(3.71611 - 6.43649i) q^{88} +(-3.80066 - 6.58293i) q^{89} -0.904534 q^{90} +(3.65664 + 3.26929i) q^{91} -5.53910 q^{92} +(1.86093 + 3.22323i) q^{93} +(-1.18895 + 2.05933i) q^{94} +(0.727697 - 1.26041i) q^{95} +(3.95772 + 6.85498i) q^{96} -0.968186 q^{97} +(4.95644 - 3.65450i) q^{98} -2.69262 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 3 q^{2} + q^{3} - 11 q^{4} - 19 q^{5} - 8 q^{6} - 18 q^{8} - 12 q^{9} + 3 q^{10} + 13 q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - 2 q^{15} + 5 q^{16} + 2 q^{17} + 11 q^{18} + 12 q^{19} + 22 q^{20}+ \cdots - 142 q^{99}+O(q^{100}) $ 38 * q + 3 * q^2 + q^3 - 11 * q^4 - 19 * q^5 - 8 * q^6 - 18 * q^8 - 12 * q^9 + 3 * q^10 + 13 * q^11 + 4 * q^12 - 6 * q^13 - q^14 - 2 * q^15 + 5 * q^16 + 2 * q^17 + 11 * q^18 + 12 * q^19 + 22 * q^20 - 8 * q^21 - 20 * q^22 + 16 * q^23 - 15 * q^24 - 19 * q^25 + 3 * q^26 - 14 * q^27 + 27 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^31 + 16 * q^32 + 2 * q^33 - 28 * q^34 + 10 * q^36 - 19 * q^37 - 2 * q^38 + 45 * q^39 + 9 * q^40 - 36 * q^41 + 29 * q^42 - 74 * q^43 - q^44 - 12 * q^45 + 29 * q^46 - 2 * q^47 - 70 * q^48 + 6 * q^49 - 6 * q^50 + 43 * q^51 - 40 * q^52 + 10 * q^53 + 38 * q^54 - 26 * q^55 + 21 * q^56 + 24 * q^57 + 13 * q^58 + 28 * q^59 + 4 * q^60 - 22 * q^61 - 20 * q^62 - 27 * q^63 - 14 * q^64 + 3 * q^65 - 34 * q^66 + 61 * q^67 + 17 * q^68 - 40 * q^69 + 5 * q^70 - 34 * q^71 - 17 * q^72 - 16 * q^73 + 3 * q^74 + q^75 - 90 * q^76 + 5 * q^77 + 106 * q^78 + 63 * q^79 + 5 * q^80 + 5 * q^81 - 37 * q^82 - 48 * q^83 + 40 * q^84 - 4 * q^85 + 19 * q^86 - 32 * q^87 + 58 * q^88 + 16 * q^89 - 22 * q^90 - 11 * q^91 + 14 * q^92 + 31 * q^93 + 12 * q^95 - 40 * q^96 - 48 * q^97 + 66 * q^98 - 142 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1295\mathbb{Z}\right)^\times$.

$n$	$556$	$631$	$1037$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	−0.439861	−	0.761862i	−0.311029	−	0.538718i	0.667557	−	0.744559i	$-0.267340\pi$
$2$	−0.439861	−	0.761862i	−0.311029	−	0.538718i	−0.978585	+	0.205841i	$0.934007\pi$
$3$	0.702103	−	1.21608i	0.405360	−	0.702103i	−0.589004	−	0.808130i	$-0.700480\pi$
$3$	0.702103	−	1.21608i	0.405360	−	0.702103i	0.994363	+	0.106027i	$0.0338130\pi$
$4$	0.613044	−	1.06182i	0.306522	−	0.530912i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.23531			−0.504314
$7$	−1.97238	−	1.76344i	−0.745489	−	0.666518i
$7$	−1.97238	−	1.76344i	−0.745489	−	0.666518i
$8$	−2.83806			−1.00341
$9$	0.514102	+	0.890450i	0.171367	+	0.296817i
$10$	−0.439861	+	0.761862i	−0.139096	+	0.240922i
$11$	−1.30938	+	2.26792i	−0.394794	+	0.683803i	−0.993075	−	0.117483i	$-0.962517\pi$
$11$	−1.30938	+	2.26792i	−0.394794	+	0.683803i	0.598281	+	0.801286i	$0.295851\pi$
$12$	−0.860841	−	1.49102i	−0.248503	−	0.430420i
$13$	−1.85392			−0.514186			−0.257093	−	0.966387i	$-0.582765\pi$
$13$	−1.85392			−0.514186			−0.257093	+	0.966387i	$0.582765\pi$
$14$	−0.475927	+	2.27835i	−0.127197	+	0.608914i
$15$	−1.40421			−0.362565
$16$	0.0222650	+	0.0385641i	0.00556625	+	0.00964103i
$17$	−0.331250	+	0.573741i	−0.0803399	+	0.139153i	−0.903396	−	0.428807i	$-0.858934\pi$
$17$	−0.331250	+	0.573741i	−0.0803399	+	0.139153i	0.823056	+	0.567960i	$0.192267\pi$
$18$	0.452267	−	0.783349i	0.106600	−	0.184637i
$19$	0.727697	+	1.26041i	0.166945	+	0.289157i	0.937344	−	0.348404i	$-0.113276\pi$
$19$	0.727697	+	1.26041i	0.166945	+	0.289157i	−0.770399	+	0.637562i	$0.779943\pi$
$20$	−1.22609			−0.274162
$21$	−3.52930	+	1.16045i	−0.770156	+	0.253231i
$22$	2.30379			0.491169
$23$	−2.25885	−	3.91244i	−0.471003	−	0.815801i	0.528447	−	0.848966i	$-0.322774\pi$
$23$	−2.25885	−	3.91244i	−0.471003	−	0.815801i	−0.999450	+	0.0331656i	$0.989441\pi$
$24$	−1.99261	+	3.45131i	−0.406740	+	0.704495i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.815469	+	1.41243i	0.159927	+	0.277001i
$27$	5.65643			1.08858
$28$	−3.08162	+	1.01325i	−0.582371	+	0.191486i
$29$	−10.4288			−1.93659			−0.968293	−	0.249818i	$-0.919629\pi$
$29$	−10.4288			−1.93659			−0.968293	+	0.249818i	$0.919629\pi$
$30$	0.617656	+	1.06981i	0.112768	+	0.195320i
$31$	−1.32525	+	2.29541i	−0.238023	+	0.412267i	−0.960147	−	0.279496i	$-0.909833\pi$
$31$	−1.32525	+	2.29541i	−0.238023	+	0.412267i	0.722124	+	0.691763i	$0.243166\pi$
$32$	−2.81848	+	4.88174i	−0.498241	+	0.862978i
$33$	1.83864	+	3.18463i	0.320067	+	0.554372i
$34$	0.582816			0.0999521
$35$	−0.540997	+	2.58985i	−0.0914451	+	0.437765i
$36$	1.26067			0.210111
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$38$	0.640171	−	1.10881i	0.103849	−	0.179873i
$39$	−1.30165	+	2.25452i	−0.208430	+	0.361012i
$40$	1.41903	+	2.45783i	0.224369	+	0.388618i
$41$	−5.51742			−0.861677			−0.430838	−	0.902429i	$-0.641782\pi$
$41$	−5.51742			−0.861677			−0.430838	+	0.902429i	$0.641782\pi$
$42$	2.43650	+	2.17840i	0.375960	+	0.336135i
$43$	4.15401			0.633480			0.316740	−	0.948512i	$-0.397412\pi$
$43$	4.15401			0.633480			0.316740	+	0.948512i	$0.397412\pi$
$44$	1.60542	+	2.78067i	0.242026	+	0.419202i
$45$	0.514102	−	0.890450i	0.0766378	−	0.132740i
$46$	−1.98716	+	3.44186i	−0.292991	+	0.507475i
$47$	−1.35151	−	2.34088i	−0.197138	−	0.341453i	0.750461	−	0.660914i	$-0.229831\pi$
$47$	−1.35151	−	2.34088i	−0.197138	−	0.341453i	−0.947599	+	0.319461i	$0.896498\pi$
$48$	0.0625294			0.00902534
$49$	0.780546	+	6.95635i	0.111507	+	0.993764i
$50$	0.879722			0.124412
$51$	0.465143	+	0.805652i	0.0651331	+	0.112814i
$52$	−1.13654	+	1.96854i	−0.157609	+	0.272987i
$53$	5.93698	−	10.2831i	0.815507	−	1.41250i	−0.0934570	−	0.995623i	$-0.529792\pi$
$53$	5.93698	−	10.2831i	0.815507	−	1.41250i	0.908964	−	0.416876i	$-0.136875\pi$
$54$	−2.48804	−	4.30942i	−0.338580	−	0.586438i
$55$	2.61877			0.353114
$56$	5.59773	+	5.00476i	0.748028	+	0.668789i
$57$	2.04367			0.270691
$58$	4.58724	+	7.94533i	0.602334	+	1.04327i
$59$	−4.47424	+	7.74961i	−0.582496	+	1.00891i	0.412686	+	0.910873i	$0.364591\pi$
$59$	−4.47424	+	7.74961i	−0.582496	+	1.00891i	−0.995182	+	0.0980398i	$0.968743\pi$
$60$	−0.860841	+	1.49102i	−0.111134	+	0.192490i
$61$	−3.25753	−	5.64221i	−0.417084	−	0.722411i	0.578561	−	0.815639i	$-0.303615\pi$
$61$	−3.25753	−	5.64221i	−0.417084	−	0.722411i	−0.995645	+	0.0932285i	$0.970281\pi$
$62$	2.33171			0.296128
$63$	0.556255	−	2.66289i	0.0700815	−	0.335493i
$64$	5.04801			0.631001
$65$	0.926962	+	1.60555i	0.114975	+	0.199143i
$66$	1.61750	−	2.80159i	0.199100	−	0.344851i
$67$	0.610021	−	1.05659i	0.0745259	−	0.129083i	−0.826354	−	0.563151i	$-0.809589\pi$
$67$	0.610021	−	1.05659i	0.0745259	−	0.129083i	0.900880	+	0.434068i	$0.142922\pi$
$68$	0.406142	+	0.703458i	0.0492519	+	0.0853068i
$69$	−6.34378			−0.763702
$70$	2.21107	−	0.727010i	0.264274	−	0.0868943i
$71$	11.7319			1.39231			0.696157	−	0.717889i	$-0.254892\pi$
$71$	11.7319			1.39231			0.696157	+	0.717889i	$0.254892\pi$
$72$	−1.45905	−	2.52715i	−0.171951	−	0.297828i
$73$	1.15865	−	2.00685i	0.135610	−	0.234884i	−0.790220	−	0.612823i	$-0.790034\pi$
$73$	1.15865	−	2.00685i	0.135610	−	0.234884i	0.925830	+	0.377939i	$0.123367\pi$
$74$	−0.439861	+	0.761862i	−0.0511328	+	0.0885647i
$75$	0.702103	+	1.21608i	0.0810719	+	0.140421i
$76$	1.78444			0.204689
$77$	6.58194	−	2.16417i	0.750082	−	0.246630i
$78$	2.29017			0.259311
$79$	−2.61787	−	4.53428i	−0.294533	−	0.510146i	0.680343	−	0.732894i	$-0.261831\pi$
$79$	−2.61787	−	4.53428i	−0.294533	−	0.510146i	−0.974876	+	0.222747i	$0.928497\pi$
$80$	0.0222650	−	0.0385641i	0.00248930	−	0.00431160i
$81$	2.42909	−	4.20731i	0.269899	−	0.467479i
$82$	2.42690	+	4.20351i	0.268006	+	0.464201i
$83$	−11.5498			−1.26776			−0.633880	−	0.773431i	$-0.718539\pi$
$83$	−11.5498			−1.26776			−0.633880	+	0.773431i	$0.718539\pi$
$84$	−0.931424	+	4.45890i	−0.101627	+	0.486506i
$85$	0.662500			0.0718582
$86$	−1.82719	−	3.16478i	−0.197031	−	0.341267i
$87$	−7.32212	+	12.6823i	−0.785014	+	1.35968i
$88$	3.71611	−	6.43649i	0.396139	−	0.686132i
$89$	−3.80066	−	6.58293i	−0.402869	−	0.697789i	0.591202	−	0.806523i	$-0.298654\pi$
$89$	−3.80066	−	6.58293i	−0.402869	−	0.697789i	−0.994071	+	0.108734i	$0.965320\pi$
$90$	−0.904534			−0.0953462
$91$	3.65664	+	3.26929i	0.383320	+	0.342714i
$92$	−5.53910			−0.577491
$93$	1.86093	+	3.22323i	0.192969	+	0.334233i
$94$	−1.18895	+	2.05933i	−0.122631	+	0.212403i
$95$	0.727697	−	1.26041i	0.0746601	−	0.129315i
$96$	3.95772	+	6.85498i	0.403933	+	0.699633i
$97$	−0.968186			−0.0983044			−0.0491522	−	0.998791i	$-0.515652\pi$
$97$	−0.968186			−0.0983044			−0.0491522	+	0.998791i	$0.515652\pi$
$98$	4.95644	−	3.65450i	0.500676	−	0.369160i
$99$	−2.69262			−0.270619
$100$	0.613044	+	1.06182i	0.0613044	+	0.106182i
$101$	−0.393610	+	0.681753i	−0.0391657	+	0.0678370i	−0.884944	−	0.465698i	$-0.845803\pi$
$101$	−0.393610	+	0.681753i	−0.0391657	+	0.0678370i	0.845778	+	0.533535i	$0.179137\pi$
$102$	0.409197	−	0.708750i	0.0405165	−	0.0701767i
$103$	0.357596	+	0.619375i	0.0352350	+	0.0610288i	0.883105	−	0.469175i	$-0.155449\pi$
$103$	0.357596	+	0.619375i	0.0352350	+	0.0610288i	−0.847870	+	0.530204i	$0.822115\pi$
$104$	5.26155			0.515938
$105$	2.76963	+	2.47624i	0.270288	+	0.241656i
$106$	−10.4458			−1.01458
$107$	−1.45707	−	2.52372i	−0.140861	−	0.243978i	0.786960	−	0.617004i	$-0.211654\pi$
$107$	−1.45707	−	2.52372i	−0.140861	−	0.243978i	−0.927821	+	0.373026i	$0.878320\pi$
$108$	3.46764	−	6.00613i	0.333674	−	0.577940i
$109$	8.31381	−	14.3999i	0.796319	−	1.37926i	−0.125679	−	0.992071i	$-0.540111\pi$
$109$	8.31381	−	14.3999i	0.796319	−	1.37926i	0.921998	−	0.387194i	$-0.126556\pi$
$110$	−1.15189	−	1.99514i	−0.109829	−	0.190229i
$111$	−1.40421			−0.133281
$112$	0.0240906	−	0.115326i	0.00227635	−	0.0108973i
$113$	8.86284			0.833746			0.416873	−	0.908965i	$-0.363126\pi$
$113$	8.86284			0.833746			0.416873	+	0.908965i	$0.363126\pi$
$114$	−0.898932	−	1.55700i	−0.0841927	−	0.145826i
$115$	−2.25885	+	3.91244i	−0.210639	+	0.364837i
$116$	−6.39334	+	11.0736i	−0.593606	+	1.02816i
$117$	−0.953106	−	1.65083i	−0.0881146	−	0.152619i
$118$	7.87218			0.724692
$119$	1.66511	−	0.547495i	0.152640	−	0.0501888i
$120$	3.98523			0.363800
$121$	2.07103	+	3.58713i	0.188276	+	0.326103i
$122$	−2.86572	+	4.96358i	−0.259450	+	0.449381i
$123$	−3.87380	+	6.70962i	−0.349289	+	0.604986i
$124$	1.62488	+	2.81437i	0.145918	+	0.252738i
$125$	1.00000			0.0894427
$126$	−2.27343	+	0.747514i	−0.202533	+	0.0665938i
$127$	−17.2232			−1.52831			−0.764157	−	0.645030i	$-0.776845\pi$
$127$	−17.2232			−1.52831			−0.764157	+	0.645030i	$0.776845\pi$
$128$	3.41653	+	5.91760i	0.301981	+	0.523047i
$129$	2.91654	−	5.05160i	0.256787	−	0.444769i
$130$	0.815469	−	1.41243i	0.0715214	−	0.123879i
$131$	−9.32803	−	16.1566i	−0.814994	−	1.41161i	−0.909332	−	0.416070i	$-0.863407\pi$
$131$	−9.32803	−	16.1566i	−0.814994	−	1.41161i	0.0943388	−	0.995540i	$-0.469926\pi$
$132$	4.50868			0.392430
$133$	0.787363	−	3.76925i	0.0682730	−	0.326835i
$134$	−1.07330			−0.0927188
$135$	−2.82822	−	4.89861i	−0.243414	−	0.421605i
$136$	0.940108	−	1.62831i	0.0806136	−	0.139627i
$137$	−4.37814	+	7.58316i	−0.374050	+	0.647873i	−0.990184	−	0.139768i	$-0.955364\pi$
$137$	−4.37814	+	7.58316i	−0.374050	+	0.647873i	0.616134	+	0.787641i	$0.288698\pi$
$138$	2.79038	+	4.83309i	0.237533	+	0.411420i
$139$	8.49623			0.720640			0.360320	−	0.932829i	$-0.382667\pi$
$139$	8.49623			0.720640			0.360320	+	0.932829i	$0.382667\pi$
$140$	2.41831	+	2.16214i	0.204384	+	0.182734i
$141$	−3.79560			−0.319647
$142$	−5.16039	−	8.93805i	−0.433050	−	0.750065i
$143$	2.42750	−	4.20455i	0.202997	−	0.351602i
$144$	−0.0228930	+	0.0396518i	−0.00190775	+	0.00330431i
$145$	5.21442	+	9.03163i	0.433034	+	0.750036i
$146$	−2.03859			−0.168715
$147$	9.00749	+	3.93487i	0.742925	+	0.324542i
$148$	−1.22609			−0.100784
$149$	8.22355	+	14.2436i	0.673700	+	1.16688i	0.976847	+	0.213939i	$0.0686292\pi$
$149$	8.22355	+	14.2436i	0.673700	+	1.16688i	−0.303147	+	0.952944i	$0.598037\pi$
$150$	0.617656	−	1.06981i	0.0504314	−	0.0873498i
$151$	1.91486	−	3.31664i	0.155829	−	0.269904i	−0.777531	−	0.628844i	$-0.783528\pi$
$151$	1.91486	−	3.31664i	0.155829	−	0.269904i	0.933361	+	0.358940i	$0.116862\pi$
$152$	−2.06525	−	3.57711i	−0.167514	−	0.290142i
$153$	−0.681184			−0.0550705
$154$	−4.54394	−	4.06259i	−0.366161	−	0.327373i
$155$	2.65051			0.212894
$156$	1.59593	+	2.76424i	0.127777	+	0.221316i
$157$	0.684531	−	1.18564i	0.0546315	−	0.0946245i	−0.837416	−	0.546566i	$-0.815935\pi$
$157$	0.684531	−	1.18564i	0.0546315	−	0.0946245i	0.892048	+	0.451941i	$0.149268\pi$
$158$	−2.30300	+	3.98891i	−0.183217	+	0.317340i
$159$	−8.33674	−	14.4397i	−0.661147	−	1.14514i
$160$	5.63695			0.445640
$161$	−2.44406	+	11.7002i	−0.192619	+	0.922102i
$162$	−4.27386			−0.335786
$163$	1.87951	+	3.25541i	0.147215	+	0.254983i	0.930197	−	0.367061i	$-0.119636\pi$
$163$	1.87951	+	3.25541i	0.147215	+	0.254983i	−0.782982	+	0.622044i	$0.786302\pi$
$164$	−3.38242	+	5.85853i	−0.264123	+	0.457474i
$165$	1.83864	−	3.18463i	0.143138	−	0.247923i
$166$	5.08033	+	8.79939i	0.394310	+	0.682965i
$167$	−22.0658			−1.70751			−0.853753	−	0.520678i	$-0.825679\pi$
$167$	−22.0658			−1.70751			−0.853753	+	0.520678i	$0.825679\pi$
$168$	10.0164	−	3.29342i	0.772779	−	0.254093i
$169$	−9.56297			−0.735613
$170$	−0.291408	−	0.504733i	−0.0223500	−	0.0387113i
$171$	−0.748220	+	1.29596i	−0.0572178	+	0.0991042i
$172$	2.54659	−	4.41083i	0.194176	−	0.336322i
$173$	−6.75775	−	11.7048i	−0.513782	−	0.889897i	−0.999872	−	0.0159882i	$-0.994911\pi$
$173$	−6.75775	−	11.7048i	−0.513782	−	0.889897i	0.486090	−	0.873909i	$-0.338423\pi$
$174$	12.8829			0.976647
$175$	2.51337	−	0.826408i	0.189993	−	0.0624706i
$176$	−0.116614			−0.00879009
$177$	6.28276	+	10.8821i	0.472241	+	0.817945i
$178$	−3.34352	+	5.79115i	−0.250608	+	0.434065i
$179$	−11.5292	+	19.9692i	−0.861734	+	1.49257i	0.00852038	+	0.999964i	$0.497288\pi$
$179$	−11.5292	+	19.9692i	−0.861734	+	1.49257i	−0.870254	+	0.492603i	$0.836045\pi$
$180$	−0.630334	−	1.09177i	−0.0469823	−	0.0813758i
$181$	−0.407733			−0.0303066			−0.0151533	−	0.999885i	$-0.504824\pi$
$181$	−0.407733			−0.0303066			−0.0151533	+	0.999885i	$0.504824\pi$
$182$	0.882332	−	4.22389i	0.0654028	−	0.313095i
$183$	−9.14849			−0.676276
$184$	6.41076	+	11.1038i	0.472607	+	0.818580i
$185$	−0.500000	+	0.866025i	−0.0367607	+	0.0636715i
$186$	1.63710	−	2.83554i	0.120038	−	0.207912i
$187$	−0.867466	−	1.50249i	−0.0634354	−	0.109873i
$188$	−3.31414			−0.241709
$189$	−11.1566	−	9.97479i	−0.811524	−	0.725559i
$190$	−1.28034			−0.0928858
$191$	8.30734	+	14.3887i	0.601098	+	1.04113i	0.992655	+	0.120978i	$0.0386032\pi$
$191$	8.30734	+	14.3887i	0.601098	+	1.04113i	−0.391557	+	0.920154i	$0.628064\pi$
$192$	3.54423	−	6.13878i	0.255782	−	0.443028i
$193$	10.5661	−	18.3011i	0.760567	−	1.31734i	−0.181991	−	0.983300i	$-0.558254\pi$
$193$	10.5661	−	18.3011i	0.760567	−	1.31734i	0.942559	−	0.334041i	$-0.108412\pi$
$194$	0.425867	+	0.737624i	0.0305755	+	0.0529583i
$195$	2.60329			0.186426
$196$	7.86492	+	3.43575i	0.561780	+	0.245410i
$197$	−15.7226			−1.12019			−0.560095	−	0.828428i	$-0.689235\pi$
$197$	−15.7226			−1.12019			−0.560095	+	0.828428i	$0.689235\pi$
$198$	1.18438	+	2.05141i	0.0841703	+	0.145787i
$199$	1.60196	−	2.77467i	0.113560	−	0.196691i	−0.803643	−	0.595111i	$-0.797108\pi$
$199$	1.60196	−	2.77467i	0.113560	−	0.196691i	0.917203	+	0.398420i	$0.130441\pi$
$200$	1.41903	−	2.45783i	0.100341	−	0.173795i
$201$	−0.856595	−	1.48367i	−0.0604196	−	0.104650i
$202$	0.692536			0.0487266
$203$	20.5696	+	18.3906i	1.44370	+	1.29077i
$204$	1.14061			0.0798589
$205$	2.75871	+	4.77823i	0.192677	+	0.333726i
$206$	0.314585	−	0.544878i	0.0219182	−	0.0379635i
$207$	2.32256	−	4.02279i	0.161429	−	0.279603i
$208$	−0.0412776	−	0.0714950i	−0.00286209	−	0.00495729i
$209$	−3.81133			−0.263636
$210$	0.668300	−	3.19927i	0.0461171	−	0.220771i
$211$	−7.07225			−0.486874			−0.243437	−	0.969917i	$-0.578275\pi$
$211$	−7.07225			−0.486874			−0.243437	+	0.969917i	$0.578275\pi$
$212$	−7.27926	−	12.6080i	−0.499942	−	0.865924i
$213$	8.23697	−	14.2669i	0.564388	−	0.977549i
$214$	−1.28182	+	2.22018i	−0.0876234	+	0.151768i
$215$	−2.07700	−	3.59748i	−0.141651	−	0.245346i
$216$	−16.0533			−1.09229
$217$	6.66172	−	2.19040i	0.452227	−	0.148694i
$218$	−14.6277			−0.990713
$219$	−1.62699	−	2.81803i	−0.109942	−	0.190425i
$220$	1.60542	−	2.78067i	0.108237	−	0.187473i
$221$	0.614112	−	1.06367i	0.0413096	−	0.0715504i
$222$	0.617656	+	1.06981i	0.0414544	+	0.0718011i
$223$	2.44022			0.163409			0.0817045	−	0.996657i	$-0.473964\pi$
$223$	2.44022			0.163409			0.0817045	+	0.996657i	$0.473964\pi$
$224$	14.1678	−	4.65842i	0.946624	−	0.311254i
$225$	−1.02820			−0.0685469
$226$	−3.89842	−	6.75226i	−0.259319	−	0.449154i
$227$	−6.84179	+	11.8503i	−0.454106	+	0.786534i	−0.998636	−	0.0522067i	$-0.983375\pi$
$227$	−6.84179	+	11.8503i	−0.454106	+	0.786534i	0.544530	+	0.838741i	$0.316708\pi$
$228$	1.25286	−	2.17002i	0.0829728	−	0.143713i
$229$	−3.85637	−	6.67942i	−0.254836	−	0.441389i	0.710015	−	0.704187i	$-0.248688\pi$
$229$	−3.85637	−	6.67942i	−0.254836	−	0.441389i	−0.964851	+	0.262798i	$0.915355\pi$
$230$	3.97432			0.262059
$231$	1.98940	−	9.52363i	0.130893	−	0.626609i
$232$	29.5977			1.94318
$233$	4.66288	+	8.07634i	0.305475	+	0.529099i	0.977367	−	0.211551i	$-0.0678513\pi$
$233$	4.66288	+	8.07634i	0.305475	+	0.529099i	−0.671892	+	0.740649i	$0.734518\pi$
$234$	−0.838468	+	1.45227i	−0.0548124	+	0.0949378i
$235$	−1.35151	+	2.34088i	−0.0881628	+	0.152702i
$236$	5.48581	+	9.50171i	0.357096	+	0.618508i
$237$	−7.35206			−0.477567
$238$	−1.14953	−	1.02776i	−0.0745131	−	0.0666199i
$239$	−21.9382			−1.41907			−0.709533	−	0.704672i	$-0.751094\pi$
$239$	−21.9382			−1.41907			−0.709533	+	0.704672i	$0.751094\pi$
$240$	−0.0312647	−	0.0541520i	−0.00201813	−	0.00349550i
$241$	0.757292	−	1.31167i	0.0487815	−	0.0844920i	−0.840604	−	0.541651i	$-0.817800\pi$
$241$	0.757292	−	1.31167i	0.0487815	−	0.0844920i	0.889385	+	0.457159i	$0.151133\pi$
$242$	1.82193	−	3.15568i	0.117118	−	0.202855i
$243$	5.07370	+	8.78790i	0.325478	+	0.563744i
$244$	−7.98804			−0.511382
$245$	5.63410	−	4.15415i	0.359949	−	0.265399i
$246$	6.81574			0.434556
$247$	−1.34909	−	2.33670i	−0.0858408	−	0.148681i
$248$	3.76115	−	6.51451i	0.238833	−	0.413672i
$249$	−8.10918	+	14.0455i	−0.513899	+	0.890099i
$250$	−0.439861	−	0.761862i	−0.0278193	−	0.0481844i
$251$	−28.9786			−1.82911			−0.914556	−	0.404459i	$-0.867460\pi$
$251$	−28.9786			−1.82911			−0.914556	+	0.404459i	$0.867460\pi$
$252$	−2.48651	−	2.22312i	−0.156636	−	0.140043i
$253$	11.8308			0.743796
$254$	7.57583	+	13.1217i	0.475350	+	0.823330i
$255$	0.465143	−	0.805652i	0.0291284	−	0.0504519i
$256$	8.05361	−	13.9493i	0.503350	−	0.871828i
$257$	−12.7759	−	22.1286i	−0.796941	−	1.38034i	−0.921599	−	0.388143i	$-0.873117\pi$
$257$	−12.7759	−	22.1286i	−0.796941	−	1.38034i	0.124658	−	0.992200i	$-0.460217\pi$
$258$	−5.13150			−0.319473
$259$	−0.540997	+	2.58985i	−0.0336159	+	0.160925i
$260$	2.27307			0.140970
$261$	−5.36148	−	9.28636i	−0.331867	−	0.574811i
$262$	−8.20608	+	14.2133i	−0.506973	+	0.878103i
$263$	9.46488	−	16.3937i	0.583630	−	1.01088i	−0.411415	−	0.911448i	$-0.634965\pi$
$263$	9.46488	−	16.3937i	0.583630	−	1.01088i	0.995045	−	0.0994282i	$-0.0317014\pi$
$264$	−5.21819	−	9.03817i	−0.321157	−	0.556261i
$265$	−11.8740			−0.729411
$266$	−3.21798	+	1.05809i	−0.197307	+	0.0648754i
$267$	−10.6738			−0.653227
$268$	−0.747939	−	1.29547i	−0.0456877	−	0.0791334i
$269$	10.7211	−	18.5694i	0.653676	−	1.13220i	−0.328548	−	0.944487i	$-0.606559\pi$
$269$	10.7211	−	18.5694i	0.653676	−	1.13220i	0.982224	−	0.187712i	$-0.0601072\pi$
$270$	−2.48804	+	4.30942i	−0.151418	+	0.262263i
$271$	−15.0866	−	26.1307i	−0.916444	−	1.58733i	−0.804773	−	0.593583i	$-0.797713\pi$
$271$	−15.0866	−	26.1307i	−0.916444	−	1.58733i	−0.111672	−	0.993745i	$-0.535620\pi$
$272$	−0.0295011			−0.00178877
$273$	6.54305	−	2.15138i	0.396003	−	0.130208i
$274$	7.70310			0.465361
$275$	−1.30938	−	2.26792i	−0.0789588	−	0.136761i
$276$	−3.88902	+	6.73598i	−0.234091	+	0.405458i
$277$	5.93458	−	10.2790i	0.356574	−	0.617605i	−0.630812	−	0.775936i	$-0.717278\pi$
$277$	5.93458	−	10.2790i	0.356574	−	0.617605i	0.987386	+	0.158331i	$0.0506113\pi$
$278$	−3.73716	−	6.47295i	−0.224140	−	0.388222i
$279$	−2.72526			−0.163157
$280$	1.53538	−	7.35016i	0.0917566	−	0.439256i
$281$	−1.92744			−0.114981			−0.0574907	−	0.998346i	$-0.518310\pi$
$281$	−1.92744			−0.114981			−0.0574907	+	0.998346i	$0.518310\pi$
$282$	1.66954	+	2.89172i	0.0994195	+	0.172200i
$283$	9.09434	−	15.7519i	0.540603	−	0.936351i	−0.458267	−	0.888815i	$-0.651530\pi$
$283$	9.09434	−	15.7519i	0.540603	−	0.936351i	0.998870	−	0.0475365i	$-0.0151370\pi$
$284$	7.19215	−	12.4572i	0.426775	−	0.739197i
$285$	−1.02184	−	1.76987i	−0.0605284	−	0.104838i
$286$	−4.27105			−0.252552
$287$	10.8824	+	9.72965i	0.642370	+	0.574323i
$288$	−5.79593			−0.341529
$289$	8.28055	+	14.3423i	0.487091	+	0.843666i
$290$	4.58724	−	7.94533i	0.269372	−	0.466566i
$291$	−0.679766	+	1.17739i	−0.0398486	+	0.0690198i
$292$	−1.42061	−	2.46057i	−0.0831350	−	0.143994i
$293$	23.8905			1.39570			0.697850	−	0.716244i	$-0.254140\pi$
$293$	23.8905			1.39570			0.697850	+	0.716244i	$0.254140\pi$
$294$	−0.964218	−	8.59326i	−0.0562344	−	0.501169i
$295$	8.94848			0.521000
$296$	1.41903	+	2.45783i	0.0824795	+	0.142859i
$297$	−7.40643	+	12.8283i	−0.429765	+	0.744375i
$298$	7.23444	−	12.5304i	0.419080	−	0.725868i
$299$	4.18774	+	7.25337i	0.242183	+	0.419473i
$300$	1.72168			0.0994013
$301$	−8.19327	−	7.32535i	−0.472252	−	0.422226i
$302$	−3.36909			−0.193870
$303$	0.552710	+	0.957322i	0.0317524	+	0.0549967i
$304$	−0.0324044	+	0.0561260i	−0.00185852	+	0.00321905i
$305$	−3.25753	+	5.64221i	−0.186526	+	0.323072i
$306$	0.299627	+	0.518968i	0.0171285	+	0.0296675i
$307$	5.64062			0.321927			0.160964	−	0.986960i	$-0.448540\pi$
$307$	5.64062			0.321927			0.160964	+	0.986960i	$0.448540\pi$
$308$	1.73705	−	8.31559i	0.0989778	−	0.473825i
$309$	1.00428			0.0571314
$310$	−1.16586	−	2.01932i	−0.0662161	−	0.114690i
$311$	7.58710	−	13.1412i	0.430225	−	0.745171i	−0.566668	−	0.823946i	$-0.691768\pi$
$311$	7.58710	−	13.1412i	0.430225	−	0.745171i	0.996892	+	0.0787753i	$0.0251010\pi$
$312$	3.69415	−	6.39846i	0.209140	−	0.362242i
$313$	−16.2025	−	28.0635i	−0.915819	−	1.58624i	−0.805698	−	0.592326i	$-0.798210\pi$
$313$	−16.2025	−	28.0635i	−0.915819	−	1.58624i	−0.110120	−	0.993918i	$-0.535124\pi$
$314$	−1.20439			−0.0679679
$315$	−2.58426	+	0.849716i	−0.145607	+	0.0478761i
$316$	−6.41947			−0.361124
$317$	1.15803	+	2.00577i	0.0650416	+	0.112655i	0.896712	−	0.442614i	$-0.145949\pi$
$317$	1.15803	+	2.00577i	0.0650416	+	0.112655i	−0.831671	+	0.555269i	$0.812615\pi$
$318$	−7.33402	+	12.7029i	−0.411271	+	0.712343i
$319$	13.6553	−	23.6517i	0.764552	−	1.32424i
$320$	−2.52401	−	4.37171i	−0.141096	−	0.244386i
$321$	−4.09206			−0.228397
$322$	9.98896	−	3.28441i	0.556663	−	0.183033i
$323$	−0.964197			−0.0536494
$324$	−2.97828	−	5.15854i	−0.165460	−	0.286585i
$325$	0.926962	−	1.60555i	0.0514186	−	0.0890596i
$326$	1.65345	−	2.86386i	0.0915761	−	0.158614i
$327$	−11.6743	−	20.2205i	−0.645591	−	1.11820i
$328$	15.6588			0.864612
$329$	−1.46232	+	7.00042i	−0.0806206	+	0.385945i
$330$	−3.23499			−0.178081
$331$	−0.882606	−	1.52872i	−0.0485124	−	0.0840260i	0.840750	−	0.541424i	$-0.182115\pi$
$331$	−0.882606	−	1.52872i	−0.0485124	−	0.0840260i	−0.889262	+	0.457398i	$0.848781\pi$
$332$	−7.08056	+	12.2639i	−0.388596	+	0.673069i
$333$	0.514102	−	0.890450i	0.0281726	−	0.0487964i
$334$	9.70591	+	16.8111i	0.531084	+	0.919864i
$335$	−1.22004			−0.0666580
$336$	−0.123332	−	0.110267i	−0.00672829	−	0.00601555i
$337$	−13.8878			−0.756517			−0.378258	−	0.925700i	$-0.623477\pi$
$337$	−13.8878			−0.756517			−0.378258	+	0.925700i	$0.623477\pi$
$338$	4.20638	+	7.28566i	0.228797	+	0.396288i
$339$	6.22263	−	10.7779i	0.337967	−	0.585376i
$340$	0.406142	−	0.703458i	0.0220261	−	0.0381504i
$341$	−3.47053	−	6.01113i	−0.187940	−	0.325521i
$342$	1.31645			0.0711856
$343$	10.7276	−	15.0970i	0.579235	−	0.815161i
$344$	−11.7893			−0.635638
$345$	3.17189	+	5.49388i	0.170769	+	0.295780i
$346$	−5.94494	+	10.2969i	−0.319602	+	0.553567i
$347$	4.01321	−	6.95108i	0.215440	−	0.373154i	−0.737968	−	0.674835i	$-0.764215\pi$
$347$	4.01321	−	6.95108i	0.215440	−	0.373154i	0.953409	+	0.301682i	$0.0975480\pi$
$348$	8.97757	+	15.5496i	0.481248	+	0.833546i
$349$	−16.2924			−0.872115			−0.436057	−	0.899919i	$-0.643626\pi$
$349$	−16.2924			−0.872115			−0.436057	+	0.899919i	$0.643626\pi$
$350$	−1.73514	−	1.55134i	−0.0927474	−	0.0829226i
$351$	−10.4866			−0.559733
$352$	−7.38093	−	12.7841i	−0.393405	−	0.681397i
$353$	6.74041	−	11.6747i	0.358756	−	0.621383i	−0.628998	−	0.777407i	$-0.716534\pi$
$353$	6.74041	−	11.6747i	0.358756	−	0.621383i	0.987753	+	0.156024i	$0.0498678\pi$
$354$	5.52708	−	9.57318i	0.293761	−	0.508809i
$355$	−5.86593	−	10.1601i	−0.311331	−	0.539241i
$356$	−9.31988			−0.493953
$357$	0.503282	−	2.40930i	0.0266365	−	0.127514i
$358$	20.2850			1.07210
$359$	15.8408	+	27.4371i	0.836045	+	1.44807i	0.893177	+	0.449706i	$0.148471\pi$
$359$	15.8408	+	27.4371i	0.836045	+	1.44807i	−0.0571320	+	0.998367i	$0.518196\pi$
$360$	−1.45905	+	2.52715i	−0.0768988	+	0.133193i
$361$	8.44092	−	14.6201i	0.444259	−	0.769479i
$362$	0.179346	+	0.310637i	0.00942622	+	0.0163267i
$363$	5.81631			0.305277
$364$	5.71309	−	1.87849i	0.299447	−	0.0984595i
$365$	−2.31731			−0.121293
$366$	4.02407	+	6.96989i	0.210341	+	0.364322i
$367$	−13.8643	+	24.0137i	−0.723711	+	1.25351i	0.235791	+	0.971804i	$0.424232\pi$
$367$	−13.8643	+	24.0137i	−0.723711	+	1.25351i	−0.959502	+	0.281701i	$0.909101\pi$
$368$	0.100587	−	0.174221i	0.00524344	−	0.00908191i
$369$	−2.83652	−	4.91299i	−0.147663	−	0.255760i
$370$	0.879722			0.0457346
$371$	−29.8437	+	9.81273i	−1.54941	+	0.509452i
$372$	4.56333			0.236598
$373$	−8.76014	−	15.1730i	−0.453583	−	0.785629i	0.545023	−	0.838421i	$-0.316521\pi$
$373$	−8.76014	−	15.1730i	−0.453583	−	0.785629i	−0.998605	+	0.0527928i	$0.983188\pi$
$374$	−0.763129	+	1.32178i	−0.0394605	+	0.0683475i
$375$	0.702103	−	1.21608i	0.0362565	−	0.0627980i
$376$	3.83567	+	6.64357i	0.197810	+	0.342616i
$377$	19.3343			0.995765
$378$	−2.69205	+	12.8873i	−0.138464	+	0.662852i
$379$	22.4681			1.15411			0.577054	−	0.816706i	$-0.304202\pi$
$379$	22.4681			1.15411			0.577054	+	0.816706i	$0.304202\pi$
$380$	−0.892220	−	1.54537i	−0.0457699	−	0.0792759i
$381$	−12.0925	+	20.9448i	−0.619517	+	1.07303i
$382$	7.30815	−	12.6581i	0.373918	−	0.647644i
$383$	14.4317	+	24.9964i	0.737423	+	1.27725i	0.953652	+	0.300911i	$0.0972908\pi$
$383$	14.4317	+	24.9964i	0.737423	+	1.27725i	−0.216229	+	0.976343i	$0.569376\pi$
$384$	9.59502			0.489644
$385$	−5.16520	−	4.61804i	−0.263243	−	0.235357i
$386$	−18.5905			−0.946233
$387$	2.13558	+	3.69894i	0.108558	+	0.188028i
$388$	−0.593541	+	1.02804i	−0.0301325	+	0.0521910i
$389$	3.06791	−	5.31377i	0.155549	−	0.269419i	−0.777710	−	0.628623i	$-0.783619\pi$
$389$	3.06791	−	5.31377i	0.155549	−	0.269419i	0.933259	+	0.359205i	$0.116952\pi$
$390$	−1.14509	−	1.98335i	−0.0579838	−	0.100431i
$391$	2.99297			0.151361
$392$	−2.21524	−	19.7425i	−0.111886	−	0.997149i
$393$	−26.1970			−1.32146
$394$	6.91577	+	11.9785i	0.348411	+	0.603466i
$395$	−2.61787	+	4.53428i	−0.131719	+	0.228144i
$396$	−1.65070	+	2.85909i	−0.0829507	+	0.143675i
$397$	9.41263	+	16.3031i	0.472406	+	0.818231i	0.999501	−	0.0315748i	$-0.0100522\pi$
$397$	9.41263	+	16.3031i	0.472406	+	0.818231i	−0.527095	+	0.849806i	$0.676719\pi$
$398$	−2.81855			−0.141281
$399$	−4.03089	−	3.60390i	−0.201797	−	0.180421i
$400$	−0.0445300			−0.00222650
$401$	17.7968	+	30.8250i	0.888732	+	1.53933i	0.841375	+	0.540451i	$0.181746\pi$
$401$	17.7968	+	30.8250i	0.888732	+	1.53933i	0.0473566	+	0.998878i	$0.484920\pi$
$402$	−0.753566	+	1.30521i	−0.0375845	+	0.0650982i
$403$	2.45692	−	4.25551i	0.122388	−	0.211982i
$404$	0.482601	+	0.835890i	0.0240103	+	0.0415871i
$405$	−4.85819			−0.241405
$406$	4.96336	−	23.7605i	0.246327	−	1.17921i
$407$	2.61877			0.129807
$408$	−1.32011	−	2.28649i	−0.0653550	−	0.113198i
$409$	9.99241	−	17.3074i	0.494093	−	0.855794i	−0.505884	−	0.862601i	$-0.668834\pi$
$409$	9.99241	−	17.3074i	0.494093	−	0.855794i	0.999977	+	0.00680784i	$0.00216702\pi$
$410$	2.42690	−	4.20351i	0.119856	−	0.207597i
$411$	6.14782	+	10.6483i	0.303249	+	0.525243i
$412$	0.876889			0.0432012
$413$	22.4909	−	7.39509i	1.10670	−	0.363889i
$414$	−4.08641			−0.200836
$415$	5.77492	+	10.0025i	0.283480	+	0.491001i
$416$	5.22524	−	9.05038i	0.256188	−	0.443731i
$417$	5.96523	−	10.3321i	0.292118	−	0.505964i
$418$	1.67646	+	2.90371i	0.0819983	+	0.142025i
$419$	5.57361			0.272288			0.136144	−	0.990689i	$-0.456529\pi$
$419$	5.57361			0.272288			0.136144	+	0.990689i	$0.456529\pi$
$420$	4.32723	−	1.42281i	0.211147	−	0.0694261i
$421$	15.7722			0.768691			0.384346	−	0.923189i	$-0.374427\pi$
$421$	15.7722			0.768691			0.384346	+	0.923189i	$0.374427\pi$
$422$	3.11081	+	5.38808i	0.151432	+	0.262287i
$423$	1.38963	−	2.40690i	0.0675660	−	0.117028i
$424$	−16.8495	+	29.1842i	−0.818285	+	1.41731i
$425$	−0.331250	−	0.573741i	−0.0160680	−	0.0278305i
$426$	−14.4925			−0.702164
$427$	−3.52463	+	16.8730i	−0.170569	+	0.816543i
$428$	−3.57300			−0.172707
$429$	−3.40871	−	5.90405i	−0.164574	−	0.285050i
$430$	−1.82719	+	3.16478i	−0.0881148	+	0.152619i
$431$	−2.86121	+	4.95576i	−0.137820	+	0.238711i	−0.926671	−	0.375873i	$-0.877343\pi$
$431$	−2.86121	+	4.95576i	−0.137820	+	0.238711i	0.788851	+	0.614584i	$0.210676\pi$
$432$	0.125941	+	0.218135i	0.00605932	+	0.0104950i
$433$	−3.41219			−0.163979			−0.0819896	−	0.996633i	$-0.526127\pi$
$433$	−3.41219			−0.163979			−0.0819896	+	0.996633i	$0.526127\pi$
$434$	−4.59901	−	4.11184i	−0.220760	−	0.197374i
$435$	14.6442			0.702137
$436$	−10.1935	−	17.6556i	−0.488179	−	0.845550i
$437$	3.28751	−	5.69414i	0.157263	−	0.272388i
$438$	−1.43130	+	2.47908i	−0.0683901	+	0.118455i
$439$	10.7229	+	18.5726i	0.511776	+	0.886423i	0.999907	+	0.0136520i	$0.00434570\pi$
$439$	10.7229	+	18.5726i	0.511776	+	0.886423i	−0.488130	+	0.872771i	$0.662321\pi$
$440$	−7.43222			−0.354317
$441$	−5.79300	+	4.27131i	−0.275857	+	0.203396i
$442$	−1.08050			−0.0513940
$443$	−15.9251	−	27.5831i	−0.756624	−	1.31051i	−0.944563	−	0.328330i	$-0.893514\pi$
$443$	−15.9251	−	27.5831i	−0.756624	−	1.31051i	0.187940	−	0.982181i	$-0.439819\pi$
$444$	−0.860841	+	1.49102i	−0.0408537	+	0.0707607i
$445$	−3.80066	+	6.58293i	−0.180168	+	0.312061i
$446$	−1.07336	−	1.85911i	−0.0508249	−	0.0880314i
$447$	23.0951			1.09236
$448$	−9.95659	−	8.90187i	−0.470404	−	0.420574i
$449$	−14.2049			−0.670370			−0.335185	−	0.942152i	$-0.608799\pi$
$449$	−14.2049			−0.670370			−0.335185	+	0.942152i	$0.608799\pi$
$450$	0.452267	+	0.783349i	0.0213201	+	0.0369274i
$451$	7.22442	−	12.5131i	0.340185	−	0.589217i
$452$	5.43331	−	9.41078i	0.255562	−	0.442646i
$453$	−2.68886	−	4.65725i	−0.126334	−	0.218817i
$454$	12.0378			0.564960
$455$	1.00297	−	4.80139i	0.0470198	−	0.225092i
$456$	−5.80007			−0.271613
$457$	−7.97473	−	13.8126i	−0.373042	−	0.646128i	0.616990	−	0.786971i	$-0.288352\pi$
$457$	−7.97473	−	13.8126i	−0.373042	−	0.646128i	−0.990032	+	0.140843i	$0.955019\pi$
$458$	−3.39253	+	5.87604i	−0.158523	+	0.274569i
$459$	−1.87369	+	3.24533i	−0.0874564	+	0.151479i
$460$	2.76955	+	4.79700i	0.129131	+	0.223661i
$461$	−29.2431			−1.36199			−0.680993	−	0.732290i	$-0.738452\pi$
$461$	−29.2431			−1.36199			−0.680993	+	0.732290i	$0.738452\pi$
$462$	−8.13075	+	2.67343i	−0.378277	+	0.124379i
$463$	−11.6477			−0.541313			−0.270657	−	0.962676i	$-0.587241\pi$
$463$	−11.6477			−0.541313			−0.270657	+	0.962676i	$0.587241\pi$
$464$	−0.232198	−	0.402179i	−0.0107795	−	0.0186707i
$465$	1.86093	−	3.22323i	0.0862986	−	0.149474i
$466$	4.10204	−	7.10494i	0.190023	−	0.329130i
$467$	−3.10678	−	5.38110i	−0.143765	−	0.249008i	0.785147	−	0.619310i	$-0.212587\pi$
$467$	−3.10678	−	5.38110i	−0.143765	−	0.249008i	−0.928911	+	0.370302i	$0.879254\pi$
$468$	−2.33718			−0.108036
$469$	−3.06642	+	1.00825i	−0.141594	+	0.0465568i
$470$	2.37791			0.109685
$471$	−0.961223	−	1.66489i	−0.0442908	−	0.0767139i
$472$	12.6982	−	21.9939i	0.584481	−	1.01235i
$473$	−5.43919	+	9.42095i	−0.250094	+	0.433176i
$474$	3.23388	+	5.60125i	0.148537	+	0.257274i
$475$	−1.45539			−0.0667780
$476$	0.439442	−	2.10369i	0.0201418	−	0.0964225i
$477$	12.2088			0.559004
$478$	9.64977	+	16.7139i	0.441370	+	0.764476i
$479$	0.177807	−	0.307971i	0.00812422	−	0.0140716i	−0.861935	−	0.507019i	$-0.830747\pi$
$479$	0.177807	−	0.307971i	0.00812422	−	0.0140716i	0.870059	+	0.492948i	$0.164081\pi$
$480$	3.95772	−	6.85498i	0.180644	−	0.312885i
$481$	0.926962	+	1.60555i	0.0422658	+	0.0732066i
$482$	−1.33241			−0.0606898
$483$	12.5123	+	11.1869i	0.569331	+	0.509021i
$484$	5.07854			0.230843
$485$	0.484093	+	0.838473i	0.0219815	+	0.0380731i
$486$	4.46344	−	7.73091i	0.202466	−	0.350681i
$487$	0.242738	−	0.420435i	0.0109995	−	0.0190517i	−0.860473	−	0.509496i	$-0.829832\pi$
$487$	0.242738	−	0.420435i	0.0109995	−	0.0190517i	0.871473	+	0.490444i	$0.163165\pi$
$488$	9.24508	+	16.0129i	0.418505	+	0.724872i
$489$	5.27845			0.238700
$490$	−5.64311	−	2.46516i	−0.254930	−	0.111364i
$491$	20.6425			0.931584			0.465792	−	0.884894i	$-0.345769\pi$
$491$	20.6425			0.931584			0.465792	+	0.884894i	$0.345769\pi$
$492$	4.74962	+	8.22659i	0.214130	+	0.370883i
$493$	3.45455	−	5.98345i	0.155585	−	0.269481i
$494$	−1.18683	+	2.05565i	−0.0533979	+	0.0924879i
$495$	1.34631	+	2.33188i	0.0605122	+	0.104810i
$496$	−0.118027			−0.00529958
$497$	−23.1396	−	20.6884i	−1.03795	−	0.928003i
$498$	14.2677			0.639349
$499$	−6.15178	−	10.6552i	−0.275391	−	0.476992i	0.694842	−	0.719162i	$-0.255474\pi$
$499$	−6.15178	−	10.6552i	−0.275391	−	0.476992i	−0.970234	+	0.242170i	$0.922141\pi$
$500$	0.613044	−	1.06182i	0.0274162	−	0.0474862i
$501$	−15.4925	+	26.8338i	−0.692154	+	1.19885i
$502$	12.7466	+	22.0777i	0.568907	+	0.985375i
$503$	−16.4357			−0.732830			−0.366415	−	0.930451i	$-0.619415\pi$
$503$	−16.4357			−0.732830			−0.366415	+	0.930451i	$0.619415\pi$
$504$	−1.57869	+	7.55746i	−0.0703202	+	0.336636i
$505$	0.787221			0.0350309
$506$	−5.20391	−	9.01343i	−0.231342	−	0.400696i
$507$	−6.71419	+	11.6293i	−0.298188	+	0.516476i
$508$	−10.5586	+	18.2880i	−0.468462	+	0.811401i
$509$	−6.54492	−	11.3361i	−0.290099	−	0.502466i	0.683734	−	0.729731i	$-0.260355\pi$
$509$	−6.54492	−	11.3361i	−0.290099	−	0.502466i	−0.973833	+	0.227266i	$0.927021\pi$
$510$	−0.818394			−0.0362391
$511$	−5.82426	+	1.91504i	−0.257650	+	0.0847164i
$512$	−0.503772			−0.0222638
$513$	4.11617	+	7.12941i	0.181733	+	0.314771i
$514$	−11.2393	+	19.4670i	−0.495743	+	0.858653i
$515$	0.357596	−	0.619375i	0.0157576	−	0.0272929i
$516$	−3.57594	−	6.19371i	−0.157422	−	0.272663i
$517$	7.07858			0.311315
$518$	2.21107	−	0.727010i	0.0971489	−	0.0319430i
$519$	−18.9786			−0.833066
$520$	−2.63078	−	4.55664i	−0.115367	−	0.199822i
$521$	18.2775	−	31.6575i	0.800750	−	1.38694i	−0.118373	−	0.992969i	$-0.537768\pi$
$521$	18.2775	−	31.6575i	0.800750	−	1.38694i	0.919123	−	0.393971i	$-0.128899\pi$
$522$	−4.71661	+	8.16942i	−0.206441	+	0.357566i
$523$	17.3150	+	29.9905i	0.757132	+	1.31139i	0.944307	+	0.329065i	$0.106733\pi$
$523$	17.3150	+	29.9905i	0.757132	+	1.31139i	−0.187175	+	0.982327i	$0.559933\pi$
$524$	−22.8740			−0.999254
$525$	0.759671	−	3.63668i	0.0331548	−	0.158718i
$526$	−16.6529			−0.726103
$527$	−0.877980	−	1.52071i	−0.0382454	−	0.0662430i
$528$	−0.0818749	+	0.141811i	−0.00356315	+	0.00617155i
$529$	1.29520	−	2.24335i	0.0563129	−	0.0975369i
$530$	5.22289	+	9.04631i	0.226868	+	0.392947i
$531$	−9.20085			−0.399283
$532$	−3.51959	−	3.14676i	−0.152594	−	0.136429i
$533$	10.2289			0.443062
$534$	4.69500	+	8.13197i	0.203172	+	0.351905i
$535$	−1.45707	+	2.52372i	−0.0629947	+	0.109110i
$536$	−1.73128	+	2.99866i	−0.0747798	+	0.129522i
$537$	16.1894	+	28.0409i	0.698624	+	1.21005i
$538$	−18.8631			−0.813248
$539$	−16.7985	−	7.33831i	−0.723561	−	0.316083i
$540$	−6.93528			−0.298447
$541$	21.6094	+	37.4286i	0.929061	+	1.60918i	0.784896	+	0.619627i	$0.212716\pi$
$541$	21.6094	+	37.4286i	0.929061	+	1.60918i	0.144164	+	0.989554i	$0.453951\pi$
$542$	−13.2720	+	22.9878i	−0.570081	+	0.987410i
$543$	−0.286271	+	0.495836i	−0.0122851	+	0.0212784i
$544$	−1.86724	−	3.23415i	−0.0800572	−	0.138663i
$545$	−16.6276			−0.712249
$546$	−4.51709	−	4.03859i	−0.193314	−	0.172836i
$547$	11.9097			0.509220			0.254610	−	0.967044i	$-0.418053\pi$
$547$	11.9097			0.509220			0.254610	+	0.967044i	$0.418053\pi$
$548$	5.36799	+	9.29763i	0.229309	+	0.397175i
$549$	3.34940	−	5.80134i	0.142949	−	0.247595i
$550$	−1.15189	+	1.99514i	−0.0491169	+	0.0850730i
$551$	−7.58903	−	13.1446i	−0.323303	−	0.559978i
$552$	18.0041			0.766303
$553$	−2.83251	+	13.5598i	−0.120451	+	0.576620i
$554$	−10.4416			−0.443620
$555$	0.702103	+	1.21608i	0.0298026	+	0.0516197i
$556$	5.20856	−	9.02149i	0.220892	−	0.382597i
$557$	−3.62644	+	6.28118i	−0.153657	+	0.266142i	−0.932569	−	0.360991i	$-0.882438\pi$
$557$	−3.62644	+	6.28118i	−0.153657	+	0.266142i	0.778912	+	0.627133i	$0.215772\pi$
$558$	1.19874	+	2.07627i	0.0507466	+	0.0878956i
$559$	−7.70122			−0.325727
$560$	−0.111921	+	0.0368000i	−0.00472951	+	0.00155508i
$561$	−2.43620			−0.102857
$562$	0.847806	+	1.46844i	0.0357625	+	0.0619425i
$563$	14.7154	−	25.4879i	0.620181	−	1.07419i	−0.369270	−	0.929322i	$-0.620392\pi$
$563$	14.7154	−	25.4879i	0.620181	−	1.07419i	0.989452	−	0.144863i	$-0.0462743\pi$
$564$	−2.32687	+	4.03026i	−0.0979789	+	0.169704i
$565$	−4.43142	−	7.67545i	−0.186431	−	0.322908i
$566$	−16.0010			−0.672572
$567$	−12.2104	+	4.01485i	−0.512790	+	0.168608i
$568$	−33.2957			−1.39706
$569$	11.3003	+	19.5727i	0.473733	+	0.820529i	0.999548	−	0.0300697i	$-0.00957292\pi$
$569$	11.3003	+	19.5727i	0.473733	+	0.820529i	−0.525815	+	0.850599i	$0.676240\pi$
$570$	−0.898932	+	1.55700i	−0.0376521	+	0.0652154i
$571$	11.3991	−	19.7439i	0.477038	−	0.826255i	−0.522615	−	0.852569i	$-0.675044\pi$
$571$	11.3991	−	19.7439i	0.477038	−	0.826255i	0.999654	+	0.0263139i	$0.00837694\pi$
$572$	−2.97633	−	5.15515i	−0.124446	−	0.215548i
$573$	23.3304			0.974643
$574$	2.62589	−	12.5706i	0.109603	−	0.524687i
$575$	4.51770			0.188401
$576$	2.59519	+	4.49500i	0.108133	+	0.187292i
$577$	−13.9292	+	24.1260i	−0.579879	+	1.00438i	0.415614	+	0.909541i	$0.363567\pi$
$577$	−13.9292	+	24.1260i	−0.579879	+	1.00438i	−0.995493	+	0.0948387i	$0.969766\pi$
$578$	7.28458	−	12.6173i	0.302999	−	0.524809i
$579$	−14.8370	−	25.6985i	−0.616606	−	1.06799i
$580$	12.7867			0.530938
$581$	22.7807	+	20.3675i	0.945101	+	0.844985i
$582$	1.19601			0.0495763
$583$	15.5476	+	26.9292i	0.643914	+	1.11529i
$584$	−3.28833	+	5.69555i	−0.136072	+	0.235684i
$585$	−0.953106	+	1.65083i	−0.0394061	+	0.0682533i
$586$	−10.5085	−	18.2013i	−0.434103	−	0.751889i
$587$	−30.0899			−1.24194			−0.620972	−	0.783833i	$-0.713262\pi$
$587$	−30.0899			−1.24194			−0.620972	+	0.783833i	$0.713262\pi$
$588$	9.70013	−	7.15212i	0.400026	−	0.294948i
$589$	−3.85753			−0.158947
$590$	−3.93609	−	6.81750i	−0.162046	−	0.280672i
$591$	−11.0389	+	19.1199i	−0.454080	+	0.786489i
$592$	0.0222650	−	0.0385641i	0.000915087	−	0.00158498i
$593$	5.79895	+	10.0441i	0.238134	+	0.412461i	0.960179	−	0.279386i	$-0.0901308\pi$
$593$	5.79895	+	10.0441i	0.238134	+	0.412461i	−0.722045	+	0.691847i	$0.756797\pi$
$594$	13.0312			0.534677
$595$	−1.30670	−	1.16828i	−0.0535695	−	0.0478948i
$596$	20.1656			0.826016
$597$	−2.24948	−	3.89621i	−0.0920649	−	0.159461i
$598$	3.68404	−	6.38095i	0.150652	−	0.260937i
$599$	5.29699	−	9.17466i	0.216429	−	0.374867i	−0.737284	−	0.675582i	$-0.763892\pi$
$599$	5.29699	−	9.17466i	0.216429	−	0.374867i	0.953714	+	0.300716i	$0.0972256\pi$
$600$	−1.99261	−	3.45131i	−0.0813481	−	0.140899i
$601$	19.9386			0.813312			0.406656	−	0.913581i	$-0.366695\pi$
$601$	19.9386			0.813312			0.406656	+	0.913581i	$0.366695\pi$
$602$	−1.97700	+	9.46428i	−0.0805767	+	0.385735i
$603$	1.25445			0.0510852
$604$	−2.34779	−	4.06649i	−0.0955302	−	0.165463i
$605$	2.07103	−	3.58713i	0.0841994	−	0.145838i
$606$	0.486232	−	0.842178i	0.0197518	−	0.0342111i
$607$	9.83370	+	17.0325i	0.399138	+	0.691327i	0.993620	−	0.112782i	$-0.0359762\pi$
$607$	9.83370	+	17.0325i	0.399138	+	0.691327i	−0.594482	+	0.804109i	$0.702643\pi$
$608$	−8.20398			−0.332715
$609$	36.8064	−	12.1021i	1.49147	−	0.490403i
$610$	5.73145			0.232059
$611$	2.50560	+	4.33982i	0.101366	+	0.175570i
$612$	−0.417596	+	0.723298i	−0.0168803	+	0.0292376i
$613$	8.52884	−	14.7724i	0.344477	−	0.596651i	−0.640782	−	0.767723i	$-0.721390\pi$
$613$	8.52884	−	14.7724i	0.344477	−	0.596651i	0.985259	+	0.171072i	$0.0547230\pi$
$614$	−2.48109	−	4.29737i	−0.100129	−	0.173428i
$615$	7.74760			0.312414
$616$	−18.6800	+	6.14205i	−0.752637	+	0.247470i
$617$	15.0250			0.604886			0.302443	−	0.953168i	$-0.402198\pi$
$617$	15.0250			0.604886			0.302443	+	0.953168i	$0.402198\pi$
$618$	−0.441743	−	0.765121i	−0.0177695	−	0.0307777i
$619$	−4.43422	+	7.68030i	−0.178226	+	0.308697i	−0.941273	−	0.337646i	$-0.890369\pi$
$619$	−4.43422	+	7.68030i	−0.178226	+	0.308697i	0.763047	+	0.646343i	$0.223703\pi$
$620$	1.62488	−	2.81437i	0.0652567	−	0.113028i
$621$	−12.7770	−	22.1305i	−0.512724	−	0.888065i
$622$	−13.3491			−0.535249
$623$	−4.11228	+	19.6863i	−0.164755	+	0.788713i
$624$	−0.115925			−0.00464070
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−14.2537	+	24.6881i	−0.569692	+	0.986735i
$627$	−2.67595	+	4.63488i	−0.106867	+	0.185099i
$628$	−0.839295	−	1.45370i	−0.0334915	−	0.0580090i
$629$	0.662500			0.0264156
$630$	1.78408	+	1.59509i	0.0710795	+	0.0635500i
$631$	4.20432			0.167371			0.0836856	−	0.996492i	$-0.473331\pi$
$631$	4.20432			0.167371			0.0836856	+	0.996492i	$0.473331\pi$
$632$	7.42967	+	12.8686i	0.295536	+	0.511884i
$633$	−4.96545	+	8.60041i	−0.197359	+	0.341836i
$634$	1.01875	−	1.76452i	0.0404596	−	0.0700781i
$635$	8.61162	+	14.9158i	0.341742	+	0.591914i
$636$	−20.4432			−0.810624
$637$	−1.44707	−	12.8965i	−0.0573352	−	0.510979i
$638$	−24.0258			−0.951191
$639$	6.03137	+	10.4466i	0.238597	+	0.413262i
$640$	3.41653	−	5.91760i	0.135050	−	0.233914i
$641$	−13.9285	+	24.1248i	−0.550141	+	0.952873i	0.448123	+	0.893972i	$0.352093\pi$
$641$	−13.9285	+	24.1248i	−0.550141	+	0.952873i	−0.998264	+	0.0589006i	$0.981241\pi$
$642$	1.79994	+	3.11759i	0.0710379	+	0.123041i
$643$	−18.4951			−0.729374			−0.364687	−	0.931130i	$-0.618824\pi$
$643$	−18.4951			−0.729374			−0.364687	+	0.931130i	$0.618824\pi$
$644$	10.9252	+	9.76788i	0.430513	+	0.384908i
$645$	−5.83309			−0.229678
$646$	0.424113	+	0.734585i	0.0166865	+	0.0289019i
$647$	−7.55419	+	13.0842i	−0.296986	+	0.514395i	−0.975445	−	0.220243i	$-0.929315\pi$
$647$	−7.55419	+	13.0842i	−0.296986	+	0.514395i	0.678459	+	0.734638i	$0.262648\pi$
$648$	−6.89392	+	11.9406i	−0.270819	+	0.469072i
$649$	−11.7170	−	20.2944i	−0.459932	−	0.796625i
$650$	−1.63094			−0.0639707
$651$	2.01351	−	9.63906i	0.0789158	−	0.377785i
$652$	4.60890			0.180498
$653$	9.94990	+	17.2337i	0.389369	+	0.674408i	0.992365	−	0.123337i	$-0.0393596\pi$
$653$	9.94990	+	17.2337i	0.389369	+	0.674408i	−0.602995	+	0.797745i	$0.706026\pi$
$654$	−10.2702	+	17.7884i	−0.401595	+	0.695583i
$655$	−9.32803	+	16.1566i	−0.364476	+	0.631291i
$656$	−0.122846	−	0.212775i	−0.00479631	−	0.00830746i
$657$	2.38266			0.0929565
$658$	5.97657	−	1.96512i	0.232991	−	0.0766084i
$659$	−22.9674			−0.894683			−0.447342	−	0.894363i	$-0.647629\pi$
$659$	−22.9674			−0.894683			−0.447342	+	0.894363i	$0.647629\pi$
$660$	−2.25434	−	3.90463i	−0.0877501	−	0.151988i
$661$	−4.65685	+	8.06591i	−0.181131	+	0.313728i	−0.942266	−	0.334866i	$-0.891309\pi$
$661$	−4.65685	+	8.06591i	−0.181131	+	0.313728i	0.761135	+	0.648593i	$0.224642\pi$
$662$	−0.776448	+	1.34485i	−0.0301775	+	0.0522690i
$663$	−0.862340	−	1.49362i	−0.0334905	−	0.0580073i
$664$	32.7792			1.27208
$665$	−3.65795	+	1.20275i	−0.141849	+	0.0466406i
$666$	−0.904534			−0.0350500
$667$	23.5572	+	40.8022i	0.912137	+	1.57987i
$668$	−13.5273	+	23.4300i	−0.523388	+	0.906535i
$669$	1.71329	−	2.96750i	0.0662394	−	0.114730i
$670$	0.536649	+	0.929503i	0.0207326	+	0.0359098i
$671$	17.0614			0.658649
$672$	4.28223	−	20.4998i	0.165191	−	0.790797i
$673$	29.2926			1.12915			0.564573	−	0.825383i	$-0.309041\pi$
$673$	29.2926			1.12915			0.564573	+	0.825383i	$0.309041\pi$
$674$	6.10870	+	10.5806i	0.235299	+	0.407549i
$675$	−2.82822	+	4.89861i	−0.108858	+	0.188548i
$676$	−5.86252	+	10.1542i	−0.225482	+	0.390546i
$677$	−7.00452	−	12.1322i	−0.269206	−	0.466278i	0.699451	−	0.714680i	$-0.253428\pi$
$677$	−7.00452	−	12.1322i	−0.269206	−	0.466278i	−0.968657	+	0.248403i	$0.920094\pi$
$678$	−10.9484			−0.420470
$679$	1.90963	+	1.70734i	0.0732848	+	0.0655217i
$680$	−1.88022			−0.0721030
$681$	9.60729	+	16.6403i	0.368152	+	0.637658i
$682$	−3.05310	+	5.28813i	−0.116909	+	0.202493i
$683$	−4.16162	+	7.20814i	−0.159240	+	0.275812i	−0.934595	−	0.355714i	$-0.884238\pi$
$683$	−4.16162	+	7.20814i	−0.159240	+	0.275812i	0.775355	+	0.631526i	$0.217571\pi$
$684$	0.917384	+	1.58896i	0.0350771	+	0.0607552i
$685$	8.75628			0.334560
$686$	−16.2205	−	1.53235i	−0.619300	−	0.0585056i
$687$	−10.8303			−0.413201
$688$	0.0924891	+	0.160196i	0.00352611	+	0.00610741i
$689$	−11.0067	+	19.0642i	−0.419322	+	0.726287i
$690$	2.79038	−	4.83309i	0.106228	−	0.183992i
$691$	13.3190	+	23.0691i	0.506678	+	0.877592i	0.999970	+	0.00772809i	$0.00245995\pi$
$691$	13.3190	+	23.0691i	0.506678	+	0.877592i	−0.493292	+	0.869864i	$0.664207\pi$
$692$	−16.5712			−0.629943
$693$	5.31087	+	4.74829i	0.201743	+	0.180372i
$694$	−7.06102			−0.268033
$695$	−4.24811	−	7.35795i	−0.161140	−	0.279103i
$696$	20.7806	−	35.9931i	0.787688	−	1.36432i
$697$	1.82765	−	3.16557i	0.0692270	−	0.119905i
$698$	7.16641	+	12.4126i	0.271253	+	0.469824i
$699$	13.0953			0.495310
$700$	0.663310	−	3.17539i	0.0250707	−	0.120018i
$701$	24.1312			0.911423			0.455711	−	0.890128i	$-0.349385\pi$
$701$	24.1312			0.911423			0.455711	+	0.890128i	$0.349385\pi$
$702$	4.61265	+	7.98934i	0.174093	+	0.301538i
$703$	0.727697	−	1.26041i	0.0274456	−	0.0475372i
$704$	−6.60978	+	11.4485i	−0.249116	+	0.431481i
$705$	1.89780	+	3.28708i	0.0714753	+	0.123799i
$706$	−11.8594			−0.446333
$707$	1.97858	−	0.650566i	0.0744122	−	0.0244670i
$708$	15.4064			0.579009
$709$	−8.85706	−	15.3409i	−0.332634	−	0.576139i	0.650394	−	0.759597i	$-0.274604\pi$
$709$	−8.85706	−	15.3409i	−0.332634	−	0.576139i	−0.983027	+	0.183459i	$0.941271\pi$
$710$	−5.16039	+	8.93805i	−0.193666	+	0.335439i
$711$	2.69170	−	4.66216i	0.100947	−	0.174845i
$712$	10.7865	+	18.6828i	0.404241	+	0.700166i
$713$	11.9742			0.448437
$714$	−2.05693	+	0.676327i	−0.0769787	+	0.0253109i
$715$	−4.85499			−0.181566
$716$	14.1358	+	24.4840i	0.528281	+	0.915009i
$717$	−15.4029	+	26.6786i	−0.575232	+	0.996331i
$718$	13.9355	−	24.1370i	0.520068	−	0.900784i
$719$	18.7593	+	32.4920i	0.699603	+	1.21175i	0.968604	+	0.248609i	$0.0799733\pi$
$719$	18.7593	+	32.4920i	0.699603	+	1.21175i	−0.269001	+	0.963140i	$0.586693\pi$
$720$	0.0457859			0.00170634
$721$	0.386917	−	1.85224i	0.0144095	−	0.0689811i
$722$	−14.8513			−0.552709
$723$	−1.06339	−	1.84185i	−0.0395481	−	0.0684993i
$724$	−0.249959	+	0.432941i	−0.00928964	+	0.0160901i
$725$	5.21442	−	9.03163i	0.193659	−	0.335426i
$726$	−2.55837	−	4.43123i	−0.0949500	−	0.164458i
$727$	−37.0709			−1.37488			−0.687442	−	0.726239i	$-0.741267\pi$
$727$	−37.0709			−1.37488			−0.687442	+	0.726239i	$0.741267\pi$
$728$	−10.3778	−	9.27844i	−0.384626	−	0.343882i
$729$	28.8236			1.06754
$730$	1.01929	+	1.76547i	0.0377257	+	0.0653429i
$731$	−1.37601	+	2.38333i	−0.0508937	+	0.0881505i
$732$	−5.60843	+	9.71409i	−0.207294	+	0.359043i
$733$	−0.986951	−	1.70945i	−0.0364539	−	0.0631400i	0.847223	−	0.531238i	$-0.178273\pi$
$733$	−0.986951	−	1.70945i	−0.0364539	−	0.0631400i	−0.883677	+	0.468098i	$0.844940\pi$
$734$	24.3935			0.900381
$735$	−1.09605	−	9.76815i	−0.0404284	−	0.360304i
$736$	25.4660			0.938691
$737$	1.59750	+	2.76695i	0.0588447	+	0.101922i
$738$	−2.49535	+	4.32207i	−0.0918550	+	0.159098i
$739$	11.2373	−	19.4636i	0.413371	−	0.715980i	−0.581885	−	0.813271i	$-0.697685\pi$
$739$	11.2373	−	19.4636i	0.413371	−	0.715980i	0.995256	+	0.0972915i	$0.0310179\pi$
$740$	0.613044	+	1.06182i	0.0225360	+	0.0390334i
$741$	−3.78881			−0.139186
$742$	20.6030	+	18.4205i	0.756361	+	0.676239i
$743$	29.4497			1.08040			0.540202	−	0.841535i	$-0.318348\pi$
$743$	29.4497			1.08040			0.540202	+	0.841535i	$0.318348\pi$
$744$	−5.28144	−	9.14772i	−0.193627	−	0.335372i
$745$	8.22355	−	14.2436i	0.301288	−	0.521846i
$746$	−7.70649	+	13.3480i	−0.282155	+	0.488706i
$747$	−5.93779	−	10.2846i	−0.217253	−	0.376292i
$748$	−2.12718			−0.0777774
$749$	−1.57654	+	7.54720i	−0.0576056	+	0.275769i
$750$	−1.23531			−0.0451072
$751$	−1.12342	−	1.94582i	−0.0409942	−	0.0710040i	0.844800	−	0.535082i	$-0.179719\pi$
$751$	−1.12342	−	1.94582i	−0.0409942	−	0.0710040i	−0.885795	+	0.464078i	$0.846386\pi$
$752$	0.0601828	−	0.104240i	0.00219464	−	0.00380123i
$753$	−20.3460	+	35.2402i	−0.741448	+	1.28423i
$754$	−8.50439	−	14.7300i	−0.309712	−	0.536436i
$755$	−3.82972			−0.139378
$756$	−17.4310	+	5.73138i	−0.633958	+	0.208448i
$757$	30.1017			1.09406			0.547032	−	0.837112i	$-0.315757\pi$
$757$	30.1017			1.09406			0.547032	+	0.837112i	$0.315757\pi$
$758$	−9.88283	−	17.1176i	−0.358961	−	0.621738i
$759$	8.30644	−	14.3872i	0.301505	−	0.522222i
$760$	−2.06525	+	3.57711i	−0.0749144	+	0.129756i
$761$	0.502376	+	0.870141i	0.0182111	+	0.0315426i	0.874987	−	0.484146i	$-0.160870\pi$
$761$	0.502376	+	0.870141i	0.0182111	+	0.0315426i	−0.856776	+	0.515688i	$0.827536\pi$
$762$	21.2761			0.770751
$763$	−41.7915	+	13.7412i	−1.51295	+	0.497465i
$764$	20.3711			0.736999
$765$	0.340592	+	0.589923i	0.0123141	+	0.0213287i
$766$	12.6958	−	21.9899i	0.458720	−	0.794526i
$767$	8.29490	−	14.3672i	0.299511	−	0.518769i
$768$	−11.3089	−	19.5876i	−0.408076	−	0.706808i
$769$	−34.7250			−1.25222			−0.626108	−	0.779737i	$-0.715353\pi$
$769$	−34.7250			−1.25222			−0.626108	+	0.779737i	$0.715353\pi$
$770$	−1.24634	+	5.96646i	−0.0449150	+	0.215016i
$771$	−35.8801			−1.29219
$772$	−12.9550	−	22.4388i	−0.466261	−	0.807588i
$773$	−3.03951	+	5.26458i	−0.109324	+	0.189354i	−0.915496	−	0.402326i	$-0.868202\pi$
$773$	−3.03951	+	5.26458i	−0.109324	+	0.189354i	0.806173	+	0.591680i	$0.201535\pi$
$774$	1.87872	−	3.25404i	0.0675292	−	0.116964i
$775$	−1.32525	−	2.29541i	−0.0476045	−	0.0824534i
$776$	2.74777			0.0986392
$777$	2.76963	+	2.47624i	0.0993598	+	0.0888345i
$778$	−5.39781			−0.193521
$779$	−4.01501	−	6.95420i	−0.143853	−	0.249160i
$780$	1.59593	−	2.76424i	0.0571436	−	0.0989756i
$781$	−15.3615	+	26.6069i	−0.549677	+	0.952069i
$782$	−1.31649	−	2.28023i	−0.0470777	−	0.0815410i
$783$	−58.9900			−2.10813
$784$	−0.250887	+	0.184984i	−0.00896024	+	0.00660658i
$785$	−1.36906			−0.0488639
$786$	11.5230	+	19.9585i	0.411013	+	0.711895i
$787$	−1.18813	+	2.05790i	−0.0423522	+	0.0733562i	−0.886424	−	0.462873i	$-0.846818\pi$
$787$	−1.18813	+	2.05790i	−0.0423522	+	0.0733562i	0.844072	+	0.536229i	$0.180152\pi$
$788$	−9.63866	+	16.6947i	−0.343363	+	0.594722i
$789$	−13.2907	−	23.0201i	−0.473160	−	0.819537i
$790$	4.60599			0.163874
$791$	−17.4809	−	15.6291i	−0.621548	−	0.555707i
$792$	7.64184			0.271541
$793$	6.03921	+	10.4602i	0.214459	+	0.371454i
$794$	8.28050	−	14.3422i	0.293864	−	0.508987i
$795$	−8.33674	+	14.4397i	−0.295674	+	0.512122i
$796$	−1.96414	−	3.40199i	−0.0696170	−	0.120580i
$797$	−42.8422			−1.51755			−0.758774	−	0.651354i	$-0.774201\pi$
$797$	−42.8422			−1.51755			−0.758774	+	0.651354i	$0.774201\pi$
$798$	−0.972639	+	4.65620i	−0.0344310	+	0.164828i
$799$	1.79075			0.0633522
$800$	−2.81848	−	4.88174i	−0.0996481	−	0.172596i
$801$	3.90785	−	6.76859i	0.138077	−	0.239156i
$802$	15.6563	−	27.1175i	0.552843	−	0.957551i
$803$	3.03424	+	5.25546i	0.107076	+	0.185461i
$804$	−2.10052			−0.0740797
$805$	11.3547	−	3.73346i	0.400199	−	0.131587i
$806$	−4.32281			−0.152265
$807$	−15.0546	−	26.0753i	−0.529947	−	0.917896i
$808$	1.11709	−	1.93486i	0.0392991	−	0.0680681i
$809$	22.6653	−	39.2575i	0.796871	−	1.38022i	−0.124773	−	0.992185i	$-0.539820\pi$
$809$	22.6653	−	39.2575i	0.796871	−	1.38022i	0.921644	−	0.388036i	$-0.126846\pi$
$810$	2.13693	+	3.70127i	0.0750840	+	0.130049i
$811$	13.4410			0.471977			0.235988	−	0.971756i	$-0.424167\pi$
$811$	13.4410			0.471977			0.235988	+	0.971756i	$0.424167\pi$
$812$	32.1377	−	10.5670i	1.12781	−	0.370829i
$813$	−42.3693			−1.48596
$814$	−1.15189	−	1.99514i	−0.0403739	−	0.0699296i
$815$	1.87951	−	3.25541i	0.0658364	−	0.114032i
$816$	−0.0207128	+	0.0358757i	−0.000725094	+	0.00125590i
$817$	3.02286	+	5.23574i	0.105756	+	0.183176i
$818$	−17.5811			−0.614708
$819$	−1.03125	+	4.93680i	−0.0360349	+	0.172506i
$820$	6.76485			0.236239
$821$	7.65142	+	13.2526i	0.267036	+	0.462520i	0.968095	−	0.250583i	$-0.0806223\pi$
$821$	7.65142	+	13.2526i	0.267036	+	0.462520i	−0.701059	+	0.713103i	$0.747289\pi$
$822$	5.40837	−	9.36758i	0.188639	−	0.326732i
$823$	−20.5304	+	35.5598i	−0.715646	+	1.23954i	0.247064	+	0.968999i	$0.420534\pi$
$823$	−20.5304	+	35.5598i	−0.715646	+	1.23954i	−0.962710	+	0.270536i	$0.912799\pi$
$824$	−1.01488	−	1.75782i	−0.0353550	−	0.0612367i
$825$	−3.67729			−0.128027
$826$	−15.5269	−	13.8821i	−0.540250	−	0.483021i
$827$	18.9159			0.657769			0.328884	−	0.944370i	$-0.393327\pi$
$827$	18.9159			0.657769			0.328884	+	0.944370i	$0.393327\pi$
$828$	−2.84766	−	4.93229i	−0.0989630	−	0.171409i
$829$	−17.2297	+	29.8426i	−0.598411	+	1.03648i	0.394645	+	0.918834i	$0.370868\pi$
$829$	−17.2297	+	29.8426i	−0.598411	+	1.03648i	−0.993056	+	0.117644i	$0.962466\pi$
$830$	5.08033	−	8.79939i	0.176341	−	0.305431i
$831$	−8.33338	−	14.4338i	−0.289082	−	0.500704i
$832$	−9.35863			−0.324452
$833$	−4.24970	−	1.85646i	−0.147243	−	0.0643224i
$834$	−10.4955			−0.363429
$835$	11.0329	+	19.1096i	0.381810	+	0.661314i
$836$	−2.33652	+	4.04697i	−0.0808101	+	0.139967i
$837$	−7.49621	+	12.9838i	−0.259107	+	0.448786i
$838$	−2.45161	−	4.24632i	−0.0846896	−	0.146687i
$839$	1.24446			0.0429634			0.0214817	−	0.999769i	$-0.493162\pi$
$839$	1.24446			0.0429634			0.0214817	+	0.999769i	$0.493162\pi$
$840$	−7.86037	−	7.02771i	−0.271209	−	0.242479i
$841$	79.7606			2.75036
$842$	−6.93759	−	12.0163i	−0.239085	−	0.414108i
$843$	−1.35326	+	2.34392i	−0.0466088	+	0.0807288i
$844$	−4.33560	+	7.50948i	−0.149238	+	0.258487i
$845$	4.78148	+	8.28177i	0.164488	+	0.284902i
$846$	−2.44497			−0.0840599
$847$	2.24084	−	10.7273i	0.0769962	−	0.368595i
$848$	0.528748			0.0181573
$849$	−12.7703	−	22.1189i	−0.438277	−	0.759118i
$850$	−0.291408	+	0.504733i	−0.00999521	+	0.0173122i
$851$	−2.25885	+	3.91244i	−0.0774324	+	0.134117i
$852$	−10.0993	−	17.4924i	−0.345995	−	0.599281i
$853$	38.3071			1.31161			0.655804	−	0.754931i	$-0.272330\pi$
$853$	38.3071			1.31161			0.655804	+	0.754931i	$0.272330\pi$
$854$	14.4053	−	4.73651i	0.492938	−	0.162080i
$855$	1.49644			0.0511772
$856$	4.13526	+	7.16249i	0.141340	+	0.244809i
$857$	−5.97339	+	10.3462i	−0.204047	+	0.353420i	−0.949829	−	0.312770i	$-0.898743\pi$
$857$	−5.97339	+	10.3462i	−0.204047	+	0.353420i	0.745782	+	0.666191i	$0.232076\pi$
$858$	−2.99872	+	5.19393i	−0.102374	+	0.177318i
$859$	−6.26427	−	10.8500i	−0.213734	−	0.370198i	0.739146	−	0.673545i	$-0.235229\pi$
$859$	−6.26427	−	10.8500i	−0.213734	−	0.370198i	−0.952880	+	0.303347i	$0.901896\pi$
$860$	−5.09318			−0.173676
$861$	19.4726	−	6.40268i	0.663625	−	0.218203i
$862$	5.03414			0.171464
$863$	−17.4475	−	30.2200i	−0.593921	−	1.02870i	−0.993698	−	0.112089i	$-0.964246\pi$
$863$	−17.4475	−	30.2200i	−0.593921	−	1.02870i	0.399777	−	0.916612i	$-0.369088\pi$
$864$	−15.9425	+	27.6132i	−0.542375	+	0.939421i
$865$	−6.75775	+	11.7048i	−0.229770	+	0.397974i
$866$	1.50089	+	2.59961i	0.0510023	+	0.0883385i
$867$	23.2552			0.789788
$868$	1.75811	−	8.41638i	0.0596740	−	0.285671i
$869$	13.7112			0.465119
$870$	−6.44143	−	11.1569i	−0.218385	−	0.378254i
$871$	−1.13093	+	1.95883i	−0.0383202	+	0.0663725i
$872$	−23.5951	+	40.8680i	−0.799032	+	1.38396i
$873$	−0.497746	−	0.862121i	−0.0168461	−	0.0291784i
$874$	−5.78420			−0.195653
$875$	−1.97238	−	1.76344i	−0.0666785	−	0.0596152i
$876$	−3.98966			−0.134798
$877$	−12.9390	−	22.4110i	−0.436919	−	0.756767i	0.560531	−	0.828134i	$-0.310597\pi$
$877$	−12.9390	−	22.4110i	−0.436919	−	0.756767i	−0.997450	+	0.0713670i	$0.977264\pi$
$878$	9.43318	−	16.3387i	0.318354	−	0.551406i
$879$	16.7736	−	29.0528i	0.565761	−	0.979926i
$880$	0.0583069	+	0.100990i	0.00196552	+	0.00340439i
$881$	43.0360			1.44992			0.724960	−	0.688790i	$-0.241858\pi$
$881$	43.0360			1.44992			0.724960	+	0.688790i	$0.241858\pi$
$882$	5.80226	+	2.53468i	0.195372	+	0.0853472i
$883$	−26.8171			−0.902467			−0.451233	−	0.892406i	$-0.649016\pi$
$883$	−26.8171			−0.902467			−0.451233	+	0.892406i	$0.649016\pi$
$884$	−0.752956	−	1.30416i	−0.0253246	−	0.0438636i
$885$	6.28276	−	10.8821i	0.211193	−	0.365796i
$886$	−14.0097	+	24.2654i	−0.470663	+	0.815213i
$887$	21.9851	+	38.0793i	0.738186	+	1.27858i	0.953311	+	0.301990i	$0.0976509\pi$
$887$	21.9851	+	38.0793i	0.738186	+	1.27858i	−0.215125	+	0.976587i	$0.569016\pi$
$888$	3.98523			0.133735
$889$	33.9707	+	30.3722i	1.13934	+	1.01865i
$890$	6.68704			0.224150
$891$	6.36123	+	11.0180i	0.213109	+	0.369116i
$892$	1.49596	−	2.59108i	0.0500885	−	0.0867558i
$893$	1.96698	−	3.40691i	0.0658224	−	0.114008i
$894$	−10.1587	−	17.5953i	−0.339756	−	0.588475i
$895$	23.0584			0.770758
$896$	3.69666	−	17.6966i	0.123497	−	0.591201i
$897$	11.7609			0.392685
$898$	6.24818	+	10.8222i	0.208504	+	0.361140i
$899$	13.8209	−	23.9384i	0.460951	−	0.798391i
$900$	−0.630334	+	1.09177i	−0.0210111	+	0.0363924i
$901$	3.93325	+	6.81258i	0.131035	+	0.226960i
$902$	−12.7110			−0.423229
$903$	−14.6607	+	4.82051i	−0.487879	+	0.160417i
$904$	−25.1533			−0.836586
$905$	0.203867	+	0.353107i	0.00677676	+	0.0117377i
$906$	−2.36545	+	4.09708i	−0.0785869	+	0.136116i
$907$	9.75714	−	16.8999i	0.323980	−	0.561150i	−0.657325	−	0.753607i	$-0.728312\pi$
$907$	9.75714	−	16.8999i	0.323980	−	0.561150i	0.981305	+	0.192457i	$0.0616455\pi$
$908$	8.38864	+	14.5296i	0.278387	+	0.482180i
$909$	−0.809423			−0.0268469
$910$	−4.09916	+	1.34782i	−0.135886	+	0.0446798i
$911$	−16.7608			−0.555311			−0.277655	−	0.960681i	$-0.589557\pi$
$911$	−16.7608			−0.555311			−0.277655	+	0.960681i	$0.589557\pi$
$912$	0.0455024	+	0.0788125i	0.00150674	+	0.00260974i
$913$	15.1232	−	26.1941i	0.500504	−	0.866898i
$914$	−7.01555	+	12.1513i	−0.232054	+	0.401929i
$915$	4.57425	+	7.92283i	0.151220	+	0.261921i
$916$	−9.45650			−0.312451
$917$	−10.0929	+	48.3164i	−0.333296	+	1.59555i
$918$	3.29666			0.108806
$919$	−6.21207	−	10.7596i	−0.204917	−	0.354927i	0.745189	−	0.666853i	$-0.232359\pi$
$919$	−6.21207	−	10.7596i	−0.204917	−	0.354927i	−0.950106	+	0.311926i	$0.899026\pi$
$920$	6.41076	−	11.1038i	0.211356	−	0.366080i
$921$	3.96030	−	6.85943i	0.130496	−	0.226026i
$922$	12.8629	+	22.2792i	0.423617	+	0.733726i
$923$	−21.7500			−0.715909
$924$	−8.89282	−	7.95080i	−0.292552	−	0.261562i
$925$	1.00000			0.0328798
$926$	5.12336	+	8.87392i	0.168364	+	0.291615i
$927$	−0.367682	+	0.636843i	−0.0120763	+	0.0209167i
$928$	29.3934	−	50.9109i	0.964886	−	1.67123i
$929$	−19.7297	−	34.1728i	−0.647310	−	1.12117i	−0.983763	−	0.179474i	$-0.942560\pi$
$929$	−19.7297	−	34.1728i	−0.647310	−	1.12117i	0.336453	−	0.941700i	$-0.390773\pi$
$930$	−3.27420			−0.107365
$931$	−8.19983	+	6.04592i	−0.268739	+	0.198147i
$932$	11.4342			0.374540
$933$	−10.6539	−	18.4530i	−0.348791	−	0.604125i
$934$	−2.73310	+	4.73387i	−0.0894299	+	0.154897i
$935$	−0.867466	+	1.50249i	−0.0283692	+	0.0491368i
$936$	2.70497	+	4.68515i	0.0884148	+	0.153139i
$937$	−7.43644			−0.242938			−0.121469	−	0.992595i	$-0.538761\pi$
$937$	−7.43644			−0.242938			−0.121469	+	0.992595i	$0.538761\pi$
$938$	2.11695	+	1.89270i	0.0691208	+	0.0617988i
$939$	−45.5033			−1.48494
$940$	1.65707	+	2.87013i	0.0540477	+	0.0936133i
$941$	5.07920	−	8.79743i	0.165577	−	0.286788i	−0.771283	−	0.636492i	$-0.780385\pi$
$941$	5.07920	−	8.79743i	0.165577	−	0.286788i	0.936860	+	0.349704i	$0.113718\pi$
$942$	−0.845609	+	1.46464i	−0.0275514	+	0.0477205i
$943$	12.4630	+	21.5866i	0.405852	+	0.702956i
$944$	−0.398476			−0.0129693
$945$	−3.06011	+	14.6493i	−0.0995454	+	0.476542i
$946$	9.56995			0.311146
$947$	−26.1578	−	45.3067i	−0.850015	−	1.47227i	−0.881194	−	0.472756i	$-0.843259\pi$
$947$	−26.1578	−	45.3067i	−0.850015	−	1.47227i	0.0311782	−	0.999514i	$-0.490074\pi$
$948$	−4.50714	+	7.80659i	−0.146385	+	0.253546i
$949$	−2.14806	+	3.72054i	−0.0697288	+	0.120774i
$950$	0.640171	+	1.10881i	0.0207699	+	0.0359745i
$951$	3.25223			0.105461
$952$	−4.72568	+	1.55383i	−0.153160	+	0.0503598i
$953$	16.5930			0.537499			0.268750	−	0.963210i	$-0.413390\pi$
$953$	16.5930			0.537499			0.268750	+	0.963210i	$0.413390\pi$
$954$	−5.37020	−	9.30145i	−0.173867	−	0.301146i
$955$	8.30734	−	14.3887i	0.268819	−	0.465608i
$956$	−13.4491	+	23.2945i	−0.434975	+	0.753399i
$957$	−19.1749	−	33.2119i	−0.619837	−	1.07359i
$958$	−0.312842			−0.0101075
$959$	22.0078	−	7.23627i	0.710670	−	0.233671i
$960$	−7.08845			−0.228779
$961$	11.9874	+	20.7628i	0.386690	+	0.669768i
$962$	0.815469	−	1.41243i	0.0262918	−	0.0455387i
$963$	1.49817	−	2.59490i	0.0482778	−	0.0836195i
$964$	−0.928507	−	1.60822i	−0.0299052	−	0.0517973i
$965$	−21.1323			−0.680272
$966$	3.01918	−	14.4534i	0.0971404	−	0.465029i
$967$	13.1962			0.424360			0.212180	−	0.977231i	$-0.431944\pi$
$967$	13.1962			0.424360			0.212180	+	0.977231i	$0.431944\pi$
$968$	−5.87772	−	10.1805i	−0.188917	−	0.327214i
$969$	−0.676966	+	1.17254i	−0.0217473	+	0.0376674i
$970$	0.425867	−	0.737624i	0.0136738	−	0.0236837i
$971$	−2.25638	−	3.90817i	−0.0724107	−	0.125419i	0.827547	−	0.561397i	$-0.189736\pi$
$971$	−2.25638	−	3.90817i	−0.0724107	−	0.125419i	−0.899957	+	0.435978i	$0.856403\pi$
$972$	12.4416			0.399065
$973$	−16.7578	−	14.9826i	−0.537229	−	0.480320i
$974$	−0.427084			−0.0136847
$975$	−1.30165	−	2.25452i	−0.0416860	−	0.0722023i
$976$	0.145058	−	0.251248i	0.00464319	−	0.00804224i
$977$	22.4927	−	38.9584i	0.719604	−	1.24639i	−0.241553	−	0.970388i	$-0.577657\pi$
$977$	22.4927	−	38.9584i	0.719604	−	1.24639i	0.961157	−	0.276003i	$-0.0890099\pi$
$978$	−2.32178	−	4.02145i	−0.0742425	−	0.128592i
$979$	19.9061			0.636200
$980$	−0.957019	−	8.52910i	−0.0305708	−	0.272452i
$981$	17.0966			0.545852
$982$	−9.07985	−	15.7268i	−0.289750	−	0.501861i
$983$	−12.0221	+	20.8229i	−0.383446	+	0.664148i	−0.991552	−	0.129708i	$-0.958596\pi$
$983$	−12.0221	+	20.8229i	−0.383446	+	0.664148i	0.608106	+	0.793856i	$0.291929\pi$
$984$	10.9941	−	19.0423i	0.350479	−	0.607047i
$985$	7.86131	+	13.6162i	0.250482	+	0.433848i
$986$	−6.07809			−0.193566
$987$	7.48635	+	6.69332i	0.238293	+	0.213051i
$988$	−3.30822			−0.105248
$989$	−9.38328	−	16.2523i	−0.298371	−	0.516794i
$990$	1.18438	−	2.05141i	0.0376421	−	0.0651980i
$991$	21.1894	−	36.7012i	0.673105	−	1.16585i	−0.303914	−	0.952699i	$-0.598294\pi$
$991$	21.1894	−	36.7012i	0.673105	−	1.16585i	0.977019	−	0.213152i	$-0.0683731\pi$
$992$	−7.47039	−	12.9391i	−0.237185	−	0.410817i
$993$	−2.47872			−0.0786599
$994$	−5.58350	+	26.7293i	−0.177098	+	0.847801i
$995$	−3.20391			−0.101571
$996$	9.94258	+	17.2210i	0.315043	+	0.545670i
$997$	−10.2027	+	17.6716i	−0.323122	+	0.559664i	−0.981130	−	0.193347i	$-0.938066\pi$
$997$	−10.2027	+	17.6716i	−0.323122	+	0.559664i	0.658009	+	0.753010i	$0.271399\pi$
$998$	−5.41186	+	9.37361i	−0.171309	+	0.296717i
$999$	−2.82822	−	4.89861i	−0.0894808	−	0.154985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1295.2.j.a.186.7	✓	38
7.2	even	3	inner	1295.2.j.a.926.7	yes	38
7.3	odd	6		9065.2.a.s.1.13		19
7.4	even	3		9065.2.a.r.1.13		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1295.2.j.a.186.7	✓	38	1.1	even	1	trivial
1295.2.j.a.926.7	yes	38	7.2	even	3	inner
9065.2.a.r.1.13		19	7.4	even	3
9065.2.a.s.1.13		19	7.3	odd	6

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:	\( N \)	\(=\)	\( 1295 = 5 \cdot 7 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1295.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.439861 - 0.761862i) q^{2} +(0.702103 - 1.21608i) q^{3} +(0.613044 - 1.06182i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.23531 q^{6} +(-1.97238 - 1.76344i) q^{7} -2.83806 q^{8} +(0.514102 + 0.890450i) q^{9} +(-0.439861 + 0.761862i) q^{10} +(-1.30938 + 2.26792i) q^{11} +(-0.860841 - 1.49102i) q^{12} -1.85392 q^{13} +(-0.475927 + 2.27835i) q^{14} -1.40421 q^{15} +(0.0222650 + 0.0385641i) q^{16} +(-0.331250 + 0.573741i) q^{17} +(0.452267 - 0.783349i) q^{18} +(0.727697 + 1.26041i) q^{19} -1.22609 q^{20} +(-3.52930 + 1.16045i) q^{21} +2.30379 q^{22} +(-2.25885 - 3.91244i) q^{23} +(-1.99261 + 3.45131i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.815469 + 1.41243i) q^{26} +5.65643 q^{27} +(-3.08162 + 1.01325i) q^{28} -10.4288 q^{29} +(0.617656 + 1.06981i) q^{30} +(-1.32525 + 2.29541i) q^{31} +(-2.81848 + 4.88174i) q^{32} +(1.83864 + 3.18463i) q^{33} +0.582816 q^{34} +(-0.540997 + 2.58985i) q^{35} +1.26067 q^{36} +(-0.500000 - 0.866025i) q^{37} +(0.640171 - 1.10881i) q^{38} +(-1.30165 + 2.25452i) q^{39} +(1.41903 + 2.45783i) q^{40} -5.51742 q^{41} +(2.43650 + 2.17840i) q^{42} +4.15401 q^{43} +(1.60542 + 2.78067i) q^{44} +(0.514102 - 0.890450i) q^{45} +(-1.98716 + 3.44186i) q^{46} +(-1.35151 - 2.34088i) q^{47} +0.0625294 q^{48} +(0.780546 + 6.95635i) q^{49} +0.879722 q^{50} +(0.465143 + 0.805652i) q^{51} +(-1.13654 + 1.96854i) q^{52} +(5.93698 - 10.2831i) q^{53} +(-2.48804 - 4.30942i) q^{54} +2.61877 q^{55} +(5.59773 + 5.00476i) q^{56} +2.04367 q^{57} +(4.58724 + 7.94533i) q^{58} +(-4.47424 + 7.74961i) q^{59} +(-0.860841 + 1.49102i) q^{60} +(-3.25753 - 5.64221i) q^{61} +2.33171 q^{62} +(0.556255 - 2.66289i) q^{63} +5.04801 q^{64} +(0.926962 + 1.60555i) q^{65} +(1.61750 - 2.80159i) q^{66} +(0.610021 - 1.05659i) q^{67} +(0.406142 + 0.703458i) q^{68} -6.34378 q^{69} +(2.21107 - 0.727010i) q^{70} +11.7319 q^{71} +(-1.45905 - 2.52715i) q^{72} +(1.15865 - 2.00685i) q^{73} +(-0.439861 + 0.761862i) q^{74} +(0.702103 + 1.21608i) q^{75} +1.78444 q^{76} +(6.58194 - 2.16417i) q^{77} +2.29017 q^{78} +(-2.61787 - 4.53428i) q^{79} +(0.0222650 - 0.0385641i) q^{80} +(2.42909 - 4.20731i) q^{81} +(2.42690 + 4.20351i) q^{82} -11.5498 q^{83} +(-0.931424 + 4.45890i) q^{84} +0.662500 q^{85} +(-1.82719 - 3.16478i) q^{86} +(-7.32212 + 12.6823i) q^{87} +(3.71611 - 6.43649i) q^{88} +(-3.80066 - 6.58293i) q^{89} -0.904534 q^{90} +(3.65664 + 3.26929i) q^{91} -5.53910 q^{92} +(1.86093 + 3.22323i) q^{93} +(-1.18895 + 2.05933i) q^{94} +(0.727697 - 1.26041i) q^{95} +(3.95772 + 6.85498i) q^{96} -0.968186 q^{97} +(4.95644 - 3.65450i) q^{98} -2.69262 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 3 q^{2} + q^{3} - 11 q^{4} - 19 q^{5} - 8 q^{6} - 18 q^{8} - 12 q^{9} + 3 q^{10} + 13 q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - 2 q^{15} + 5 q^{16} + 2 q^{17} + 11 q^{18} + 12 q^{19} + 22 q^{20}+ \cdots - 142 q^{99}+O(q^{100}) \) 38 * q + 3 * q^2 + q^3 - 11 * q^4 - 19 * q^5 - 8 * q^6 - 18 * q^8 - 12 * q^9 + 3 * q^10 + 13 * q^11 + 4 * q^12 - 6 * q^13 - q^14 - 2 * q^15 + 5 * q^16 + 2 * q^17 + 11 * q^18 + 12 * q^19 + 22 * q^20 - 8 * q^21 - 20 * q^22 + 16 * q^23 - 15 * q^24 - 19 * q^25 + 3 * q^26 - 14 * q^27 + 27 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^31 + 16 * q^32 + 2 * q^33 - 28 * q^34 + 10 * q^36 - 19 * q^37 - 2 * q^38 + 45 * q^39 + 9 * q^40 - 36 * q^41 + 29 * q^42 - 74 * q^43 - q^44 - 12 * q^45 + 29 * q^46 - 2 * q^47 - 70 * q^48 + 6 * q^49 - 6 * q^50 + 43 * q^51 - 40 * q^52 + 10 * q^53 + 38 * q^54 - 26 * q^55 + 21 * q^56 + 24 * q^57 + 13 * q^58 + 28 * q^59 + 4 * q^60 - 22 * q^61 - 20 * q^62 - 27 * q^63 - 14 * q^64 + 3 * q^65 - 34 * q^66 + 61 * q^67 + 17 * q^68 - 40 * q^69 + 5 * q^70 - 34 * q^71 - 17 * q^72 - 16 * q^73 + 3 * q^74 + q^75 - 90 * q^76 + 5 * q^77 + 106 * q^78 + 63 * q^79 + 5 * q^80 + 5 * q^81 - 37 * q^82 - 48 * q^83 + 40 * q^84 - 4 * q^85 + 19 * q^86 - 32 * q^87 + 58 * q^88 + 16 * q^89 - 22 * q^90 - 11 * q^91 + 14 * q^92 + 31 * q^93 + 12 * q^95 - 40 * q^96 - 48 * q^97 + 66 * q^98 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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