LMFDB - Embedded newform 425.2.k.c.86.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(86,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("425.86");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.7
Character	$\chi$	$=$	425.86
Dual form			425.2.k.c.341.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.762747 + 0.554168i) q^{2} +(-0.324602 + 0.999022i) q^{3} +(-0.343353 + 1.05673i) q^{4} +(-1.44286 + 1.70826i) q^{5} +(-0.306037 - 0.941886i) q^{6} -2.98759 q^{7} +(-0.906403 - 2.78962i) q^{8} +(1.53437 + 1.11479i) q^{9} +(0.153870 - 2.10256i) q^{10} +(-0.890676 + 0.647114i) q^{11} +(-0.944246 - 0.686035i) q^{12} +(-0.236263 - 0.171655i) q^{13} +(2.27877 - 1.65563i) q^{14} +(-1.23824 - 1.99595i) q^{15} +(0.439455 + 0.319283i) q^{16} +(-0.309017 - 0.951057i) q^{17} -1.78812 q^{18} +(-0.0608886 - 0.187396i) q^{19} +(-1.30977 - 2.11125i) q^{20} +(0.969777 - 2.98467i) q^{21} +(0.320751 - 0.987169i) q^{22} +(4.69845 - 3.41362i) q^{23} +3.08111 q^{24} +(-0.836327 - 4.92956i) q^{25} +0.275335 q^{26} +(-4.16121 + 3.02330i) q^{27} +(1.02580 - 3.15708i) q^{28} +(0.315623 - 0.971387i) q^{29} +(2.05056 + 0.836214i) q^{30} +(3.00543 + 9.24977i) q^{31} +5.35423 q^{32} +(-0.357366 - 1.09986i) q^{33} +(0.762747 + 0.554168i) q^{34} +(4.31066 - 5.10359i) q^{35} +(-1.70486 + 1.23866i) q^{36} +(-6.10089 - 4.43255i) q^{37} +(0.150291 + 0.109193i) q^{38} +(0.248179 - 0.180312i) q^{39} +(6.07322 + 2.47665i) q^{40} +(-7.49579 - 5.44601i) q^{41} +(0.914313 + 2.81397i) q^{42} -6.74894 q^{43} +(-0.378010 - 1.16340i) q^{44} +(-4.11823 + 1.01263i) q^{45} +(-1.69201 + 5.20746i) q^{46} +(-2.54046 + 7.81874i) q^{47} +(-0.461618 + 0.335385i) q^{48} +1.92568 q^{49} +(3.36971 + 3.29654i) q^{50} +1.05043 q^{51} +(0.262515 - 0.190728i) q^{52} +(4.04225 - 12.4408i) q^{53} +(1.49854 - 4.61203i) q^{54} +(0.179677 - 2.45520i) q^{55} +(2.70796 + 8.33424i) q^{56} +0.206977 q^{57} +(0.297572 + 0.915831i) q^{58} +(-4.42688 - 3.21631i) q^{59} +(2.53434 - 0.623171i) q^{60} +(-2.13763 + 1.55308i) q^{61} +(-7.41831 - 5.38972i) q^{62} +(-4.58407 - 3.33052i) q^{63} +(-4.96284 + 3.60571i) q^{64} +(0.634125 - 0.155926i) q^{65} +(0.882088 + 0.640874i) q^{66} +(0.607795 + 1.87060i) q^{67} +1.11111 q^{68} +(1.88516 + 5.80192i) q^{69} +(-0.459699 + 6.28158i) q^{70} +(-3.79117 + 11.6680i) q^{71} +(1.71907 - 5.29076i) q^{72} +(-7.08602 + 5.14830i) q^{73} +7.10982 q^{74} +(5.19621 + 0.764635i) q^{75} +0.218933 q^{76} +(2.66097 - 1.93331i) q^{77} +(-0.0893741 + 0.275065i) q^{78} +(-0.893899 + 2.75114i) q^{79} +(-1.17949 + 0.290025i) q^{80} +(0.0886289 + 0.272772i) q^{81} +8.73539 q^{82} +(0.182744 + 0.562427i) q^{83} +(2.82102 + 2.04959i) q^{84} +(2.07052 + 0.844356i) q^{85} +(5.14773 - 3.74005i) q^{86} +(0.867986 + 0.630629i) q^{87} +(2.61251 + 1.89810i) q^{88} +(6.00901 - 4.36580i) q^{89} +(2.58000 - 3.05457i) q^{90} +(0.705856 + 0.512834i) q^{91} +(1.99406 + 6.13708i) q^{92} -10.2163 q^{93} +(-2.39517 - 7.37156i) q^{94} +(0.407975 + 0.166372i) q^{95} +(-1.73800 + 5.34900i) q^{96} +(-5.84338 + 17.9841i) q^{97} +(-1.46881 + 1.06715i) q^{98} -2.08802 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) $ 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.762747	+	0.554168i	−0.539344	+	0.391856i	−0.823841	−	0.566821i	$-0.808173\pi$
$2$	−0.762747	+	0.554168i	−0.539344	+	0.391856i	0.284498	+	0.958677i	$0.408173\pi$
$3$	−0.324602	+	0.999022i	−0.187409	+	0.576786i	−0.999982	−	0.00607434i	$-0.998066\pi$
$3$	−0.324602	+	0.999022i	−0.187409	+	0.576786i	0.812572	+	0.582860i	$0.198066\pi$
$4$	−0.343353	+	1.05673i	−0.171677	+	0.528366i
$5$	−1.44286	+	1.70826i	−0.645265	+	0.763959i
$5$	−1.44286	+	1.70826i	−0.645265	+	0.763959i
$6$	−0.306037	−	0.941886i	−0.124939	−	0.384523i
$7$	−2.98759			−1.12920			−0.564601	−	0.825364i	$-0.690970\pi$
$7$	−2.98759			−1.12920			−0.564601	+	0.825364i	$0.690970\pi$
$8$	−0.906403	−	2.78962i	−0.320462	−	0.986280i
$9$	1.53437	+	1.11479i	0.511457	+	0.371595i
$10$	0.153870	−	2.10256i	0.0486579	−	0.664887i
$11$	−0.890676	+	0.647114i	−0.268549	+	0.195112i	−0.713907	−	0.700240i	$-0.753076\pi$
$11$	−0.890676	+	0.647114i	−0.268549	+	0.195112i	0.445358	+	0.895352i	$0.353076\pi$
$12$	−0.944246	−	0.686035i	−0.272580	−	0.198041i
$13$	−0.236263	−	0.171655i	−0.0655275	−	0.0476085i	0.554539	−	0.832158i	$-0.312895\pi$
$13$	−0.236263	−	0.171655i	−0.0655275	−	0.0476085i	−0.620067	+	0.784549i	$0.712895\pi$
$14$	2.27877	−	1.65563i	0.609028	−	0.442485i
$15$	−1.23824	−	1.99595i	−0.319712	−	0.515353i
$16$	0.439455	+	0.319283i	0.109864	+	0.0798206i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	−1.78812			−0.421463
$19$	−0.0608886	−	0.187396i	−0.0139688	−	0.0429915i	0.943829	−	0.330434i	$-0.107195\pi$
$19$	−0.0608886	−	0.187396i	−0.0139688	−	0.0429915i	−0.957798	+	0.287442i	$0.907195\pi$
$20$	−1.30977	−	2.11125i	−0.292873	−	0.472090i
$21$	0.969777	−	2.98467i	0.211623	−	0.651308i
$22$	0.320751	−	0.987169i	0.0683843	−	0.210465i
$23$	4.69845	−	3.41362i	0.979694	−	0.711790i	0.0220540	−	0.999757i	$-0.492979\pi$
$23$	4.69845	−	3.41362i	0.979694	−	0.711790i	0.957640	+	0.287967i	$0.0929794\pi$
$24$	3.08111			0.628930
$25$	−0.836327	−	4.92956i	−0.167265	−	0.985912i
$26$	0.275335			0.0539975
$27$	−4.16121	+	3.02330i	−0.800826	+	0.581834i
$28$	1.02580	−	3.15708i	0.193858	−	0.596632i
$29$	0.315623	−	0.971387i	0.0586097	−	0.180382i	−0.917465	−	0.397815i	$-0.869768\pi$
$29$	0.315623	−	0.971387i	0.0586097	−	0.180382i	0.976075	+	0.217433i	$0.0697685\pi$
$30$	2.05056	+	0.836214i	0.374379	+	0.152671i
$31$	3.00543	+	9.24977i	0.539792	+	1.66131i	0.733062	+	0.680162i	$0.238091\pi$
$31$	3.00543	+	9.24977i	0.539792	+	1.66131i	−0.193270	+	0.981146i	$0.561909\pi$
$32$	5.35423			0.946504
$33$	−0.357366	−	1.09986i	−0.0622095	−	0.191461i
$34$	0.762747	+	0.554168i	0.130810	+	0.0950391i
$35$	4.31066	−	5.10359i	0.728635	−	0.862664i
$36$	−1.70486	+	1.23866i	−0.284144	+	0.206443i
$37$	−6.10089	−	4.43255i	−1.00298	−	0.728707i	−0.0402547	−	0.999189i	$-0.512817\pi$
$37$	−6.10089	−	4.43255i	−1.00298	−	0.728707i	−0.962725	+	0.270482i	$0.912817\pi$
$38$	0.150291	+	0.109193i	0.0243805	+	0.0177135i
$39$	0.248179	−	0.180312i	0.0397404	−	0.0288731i
$40$	6.07322	+	2.47665i	0.960260	+	0.391593i
$41$	−7.49579	−	5.44601i	−1.17065	−	0.850524i	−0.179559	−	0.983747i	$-0.557467\pi$
$41$	−7.49579	−	5.44601i	−1.17065	−	0.850524i	−0.991086	+	0.133224i	$0.957467\pi$
$42$	0.914313	+	2.81397i	0.141082	+	0.434204i
$43$	−6.74894			−1.02920			−0.514602	−	0.857429i	$-0.672060\pi$
$43$	−6.74894			−1.02920			−0.514602	+	0.857429i	$0.672060\pi$
$44$	−0.378010	−	1.16340i	−0.0569872	−	0.175388i
$45$	−4.11823	+	1.01263i	−0.613909	+	0.150955i
$46$	−1.69201	+	5.20746i	−0.249473	+	0.767798i
$47$	−2.54046	+	7.81874i	−0.370564	+	1.14048i	0.575858	+	0.817550i	$0.304668\pi$
$47$	−2.54046	+	7.81874i	−0.370564	+	1.14048i	−0.946423	+	0.322931i	$0.895332\pi$
$48$	−0.461618	+	0.335385i	−0.0666289	+	0.0484087i
$49$	1.92568			0.275097
$50$	3.36971	+	3.29654i	0.476549	+	0.466201i
$51$	1.05043			0.147090
$52$	0.262515	−	0.190728i	0.0364043	−	0.0264493i
$53$	4.04225	−	12.4408i	0.555246	−	1.70887i	−0.140045	−	0.990145i	$-0.544725\pi$
$53$	4.04225	−	12.4408i	0.555246	−	1.70887i	0.695292	−	0.718728i	$-0.255275\pi$
$54$	1.49854	−	4.61203i	0.203925	−	0.627617i
$55$	0.179677	−	2.45520i	0.0242276	−	0.331059i
$56$	2.70796	+	8.33424i	0.361866	+	1.11371i
$57$	0.206977			0.0274148
$58$	0.297572	+	0.915831i	0.0390731	+	0.120255i
$59$	−4.42688	−	3.21631i	−0.576330	−	0.418728i	0.261069	−	0.965320i	$-0.415925\pi$
$59$	−4.42688	−	3.21631i	−0.576330	−	0.418728i	−0.837399	+	0.546592i	$0.815925\pi$
$60$	2.53434	−	0.623171i	0.327182	−	0.0804510i
$61$	−2.13763	+	1.55308i	−0.273695	+	0.198851i	−0.716163	−	0.697933i	$-0.754103\pi$
$61$	−2.13763	+	1.55308i	−0.273695	+	0.198851i	0.442468	+	0.896784i	$0.354103\pi$
$62$	−7.41831	−	5.38972i	−0.942127	−	0.684495i
$63$	−4.58407	−	3.33052i	−0.577539	−	0.419606i
$64$	−4.96284	+	3.60571i	−0.620354	+	0.450714i
$65$	0.634125	−	0.155926i	0.0786536	−	0.0193402i
$66$	0.882088	+	0.640874i	0.108577	+	0.0788861i
$67$	0.607795	+	1.87060i	0.0742540	+	0.228530i	0.981294	−	0.192513i	$-0.0616639\pi$
$67$	0.607795	+	1.87060i	0.0742540	+	0.228530i	−0.907040	+	0.421044i	$0.861664\pi$
$68$	1.11111			0.134742
$69$	1.88516	+	5.80192i	0.226947	+	0.698470i
$70$	−0.459699	+	6.28158i	−0.0549446	+	0.750792i
$71$	−3.79117	+	11.6680i	−0.449930	+	1.38474i	0.427056	+	0.904225i	$0.359551\pi$
$71$	−3.79117	+	11.6680i	−0.449930	+	1.38474i	−0.876986	+	0.480516i	$0.840449\pi$
$72$	1.71907	−	5.29076i	0.202595	−	0.623522i
$73$	−7.08602	+	5.14830i	−0.829356	+	0.602562i	−0.919377	−	0.393378i	$-0.871307\pi$
$73$	−7.08602	+	5.14830i	−0.829356	+	0.602562i	0.0900211	+	0.995940i	$0.471307\pi$
$74$	7.10982			0.826499
$75$	5.19621	+	0.764635i	0.600007	+	0.0882925i
$76$	0.218933			0.0251134
$77$	2.66097	−	1.93331i	0.303246	−	0.220321i
$78$	−0.0893741	+	0.275065i	−0.0101196	+	0.0311450i
$79$	−0.893899	+	2.75114i	−0.100571	+	0.309527i	−0.988666	−	0.150135i	$-0.952029\pi$
$79$	−0.893899	+	2.75114i	−0.100571	+	0.309527i	0.888094	+	0.459662i	$0.152029\pi$
$80$	−1.17949	+	0.290025i	−0.131871	+	0.0324258i
$81$	0.0886289	+	0.272772i	0.00984765	+	0.0303080i
$82$	8.73539			0.964663
$83$	0.182744	+	0.562427i	0.0200587	+	0.0617344i	0.960585	−	0.277987i	$-0.0896672\pi$
$83$	0.182744	+	0.562427i	0.0200587	+	0.0617344i	−0.940526	+	0.339721i	$0.889667\pi$
$84$	2.82102	+	2.04959i	0.307798	+	0.223629i
$85$	2.07052	+	0.844356i	0.224580	+	0.0915833i
$86$	5.14773	−	3.74005i	0.555094	−	0.403299i
$87$	0.867986	+	0.630629i	0.0930579	+	0.0676105i
$88$	2.61251	+	1.89810i	0.278495	+	0.202338i
$89$	6.00901	−	4.36580i	0.636953	−	0.462774i	−0.221849	−	0.975081i	$-0.571209\pi$
$89$	6.00901	−	4.36580i	0.636953	−	0.462774i	0.858802	+	0.512307i	$0.171209\pi$
$90$	2.58000	−	3.05457i	0.271956	−	0.321980i
$91$	0.705856	+	0.512834i	0.0739938	+	0.0537596i
$92$	1.99406	+	6.13708i	0.207895	+	0.639835i
$93$	−10.2163			−1.05938
$94$	−2.39517	−	7.37156i	−0.247043	−	0.760319i
$95$	0.407975	+	0.166372i	0.0418573	+	0.0170694i
$96$	−1.73800	+	5.34900i	−0.177383	+	0.545930i
$97$	−5.84338	+	17.9841i	−0.593306	+	1.82601i	−0.0303195	+	0.999540i	$0.509652\pi$
$97$	−5.84338	+	17.9841i	−0.593306	+	1.82601i	−0.562986	+	0.826466i	$0.690348\pi$
$98$	−1.46881	+	1.06715i	−0.148372	+	0.107799i
$99$	−2.08802			−0.209854
$100$	5.49638	+	0.808806i	0.549638	+	0.0808806i
$101$	15.0028			1.49284			0.746420	−	0.665476i	$-0.231771\pi$
$101$	15.0028			1.49284			0.746420	+	0.665476i	$0.231771\pi$
$102$	−0.801216	+	0.582117i	−0.0793322	+	0.0576382i
$103$	−0.822546	+	2.53154i	−0.0810479	+	0.249440i	−0.983367	−	0.181628i	$-0.941863\pi$
$103$	−0.822546	+	2.53154i	−0.0810479	+	0.249440i	0.902319	+	0.431068i	$0.141863\pi$
$104$	−0.264703	+	0.814672i	−0.0259563	+	0.0798852i
$105$	3.69935	+	5.96308i	0.361019	+	0.581937i
$106$	3.81107	+	11.7293i	0.370164	+	1.13925i
$107$	−18.4353			−1.78220			−0.891102	−	0.453803i	$-0.850067\pi$
$107$	−18.4353			−1.78220			−0.891102	+	0.453803i	$0.850067\pi$
$108$	−1.76605	−	5.43535i	−0.169938	−	0.523017i
$109$	−3.85676	−	2.80210i	−0.369411	−	0.268393i	0.387556	−	0.921846i	$-0.373319\pi$
$109$	−3.85676	−	2.80210i	−0.369411	−	0.268393i	−0.756967	+	0.653454i	$0.773319\pi$
$110$	1.22355	+	1.97227i	0.116661	+	0.188049i
$111$	6.40858	−	4.65611i	0.608276	−	0.441938i
$112$	−1.31291	−	0.953885i	−0.124058	−	0.0901336i
$113$	4.58330	+	3.32996i	0.431160	+	0.313256i	0.782113	−	0.623137i	$-0.214142\pi$
$113$	4.58330	+	3.32996i	0.431160	+	0.313256i	−0.350952	+	0.936393i	$0.614142\pi$
$114$	−0.157871	+	0.114700i	−0.0147860	+	0.0107427i
$115$	−0.947823	+	12.9516i	−0.0883849	+	1.20774i
$116$	0.918127	+	0.667058i	0.0852459	+	0.0619348i
$117$	−0.171156	−	0.526765i	−0.0158234	−	0.0486995i
$118$	5.15896			0.474921
$119$	0.923215	+	2.84136i	0.0846310	+	0.260467i
$120$	−4.44561	+	5.26335i	−0.405827	+	0.480476i
$121$	−3.02464	+	9.30888i	−0.274967	+	0.846262i
$122$	0.769803	−	2.36921i	0.0696947	−	0.214498i
$123$	7.87383	−	5.72067i	0.709960	−	0.515816i
$124$	−10.8065			−0.970449
$125$	9.62769	+	5.68398i	0.861126	+	0.508391i
$126$	5.34216			0.475917
$127$	−10.8208	+	7.86176i	−0.960190	+	0.697619i	−0.953195	−	0.302357i	$-0.902227\pi$
$127$	−10.8208	+	7.86176i	−0.960190	+	0.697619i	−0.00699486	+	0.999976i	$0.502227\pi$
$128$	−1.52188	+	4.68387i	−0.134516	+	0.413999i
$129$	2.19072	−	6.74234i	0.192882	−	0.593630i
$130$	−0.397268	+	0.470344i	−0.0348427	+	0.0412519i
$131$	−5.18237	−	15.9497i	−0.452786	−	1.39353i	−0.873715	−	0.486438i	$-0.838296\pi$
$131$	−5.18237	−	15.9497i	−0.452786	−	1.39353i	0.420929	−	0.907094i	$-0.361704\pi$
$132$	1.28496			0.111841
$133$	0.181910	+	0.559861i	0.0157736	+	0.0485461i
$134$	−1.50022	−	1.08998i	−0.129599	−	0.0941595i
$135$	0.839446	−	11.4706i	0.0722480	−	0.987235i
$136$	−2.37299	+	1.72408i	−0.203483	+	0.147839i
$137$	−12.7264	−	9.24625i	−1.08729	−	0.789960i	−0.108348	−	0.994113i	$-0.534556\pi$
$137$	−12.7264	−	9.24625i	−1.08729	−	0.789960i	−0.978939	+	0.204153i	$0.934556\pi$
$138$	−4.65314	−	3.38071i	−0.396102	−	0.287785i
$139$	1.44142	−	1.04726i	0.122260	−	0.0888271i	−0.524975	−	0.851118i	$-0.675925\pi$
$139$	1.44142	−	1.04726i	0.122260	−	0.0888271i	0.647235	+	0.762291i	$0.275925\pi$
$140$	3.91305	+	6.30755i	0.330713	+	0.533085i
$141$	−6.98645	−	5.07596i	−0.588366	−	0.427473i
$142$	−3.57435	−	11.0007i	−0.299952	−	0.923159i
$143$	0.321514			0.0268864
$144$	0.318355	+	0.979796i	0.0265296	+	0.0816497i
$145$	1.20399	+	1.94074i	0.0999857	+	0.161170i
$146$	2.55182	−	7.85369i	0.211190	−	0.649976i
$147$	−0.625080	+	1.92380i	−0.0515557	+	0.158672i
$148$	6.77878	−	4.92507i	0.557213	−	0.404839i
$149$	17.3523			1.42155			0.710777	−	0.703417i	$-0.248343\pi$
$149$	17.3523			1.42155			0.710777	+	0.703417i	$0.248343\pi$
$150$	−4.38713	+	2.29635i	−0.358208	+	0.187496i
$151$	12.2796			0.999301			0.499650	−	0.866227i	$-0.333462\pi$
$151$	12.2796			0.999301			0.499650	+	0.866227i	$0.333462\pi$
$152$	−0.467574	+	0.339712i	−0.0379252	+	0.0275543i
$153$	0.586078	−	1.80376i	0.0473816	−	0.145826i
$154$	−0.958271	+	2.94925i	−0.0772196	+	0.237658i
$155$	−20.1375	−	8.21203i	−1.61748	−	0.659606i
$156$	0.105329	+	0.324169i	0.00843307	+	0.0259543i
$157$	3.26062			0.260225			0.130113	−	0.991499i	$-0.458466\pi$
$157$	3.26062			0.260225			0.130113	+	0.991499i	$0.458466\pi$
$158$	−0.842774	−	2.59379i	−0.0670475	−	0.206351i
$159$	11.1165	+	8.07661i	0.881595	+	0.640516i
$160$	−7.72539	+	9.14644i	−0.610746	+	0.723090i
$161$	−14.0370	+	10.1985i	−1.10627	+	0.803754i
$162$	−0.218763	−	0.158941i	−0.0171876	−	0.0124875i
$163$	6.03600	+	4.38541i	0.472776	+	0.343492i	0.798522	−	0.601965i	$-0.205615\pi$
$163$	6.03600	+	4.38541i	0.472776	+	0.343492i	−0.325746	+	0.945457i	$0.605615\pi$
$164$	8.32868	−	6.05114i	0.650360	−	0.472515i
$165$	2.39448	+	0.976465i	0.186410	+	0.0760177i
$166$	−0.451067	−	0.327719i	−0.0350096	−	0.0254359i
$167$	3.87712	+	11.9325i	0.300021	+	0.923368i	0.981489	+	0.191520i	$0.0613418\pi$
$167$	3.87712	+	11.9325i	0.300021	+	0.923368i	−0.681468	+	0.731848i	$0.738658\pi$
$168$	−9.20510			−0.710189
$169$	−3.99087	−	12.2826i	−0.306990	−	0.944817i
$170$	−2.04720	+	0.503387i	−0.157013	+	0.0386081i
$171$	0.115481	−	0.355412i	0.00883102	−	0.0271791i
$172$	2.31727	−	7.13182i	0.176690	−	0.543796i
$173$	13.5928	−	9.87572i	1.03344	−	0.750837i	0.0644442	−	0.997921i	$-0.479473\pi$
$173$	13.5928	−	9.87572i	1.03344	−	0.750837i	0.968994	+	0.247085i	$0.0794725\pi$
$174$	−1.01153			−0.0766837
$175$	2.49860	+	14.7275i	0.188876	+	1.11329i
$176$	−0.598024			−0.0450778
$177$	4.65014	−	3.37853i	0.349526	−	0.253946i
$178$	−2.16397	+	6.66000i	−0.162196	+	0.499188i
$179$	−1.35029	+	4.15577i	−0.100926	+	0.310617i	−0.988753	−	0.149560i	$-0.952214\pi$
$179$	−1.35029	+	4.15577i	−0.100926	+	0.310617i	0.887827	+	0.460177i	$0.152214\pi$
$180$	0.343924	−	4.69956i	0.0256346	−	0.350284i
$181$	0.474695	+	1.46096i	0.0352838	+	0.108592i	0.967147	−	0.254217i	$-0.0818177\pi$
$181$	0.474695	+	1.46096i	0.0352838	+	0.108592i	−0.931863	+	0.362809i	$0.881818\pi$
$182$	−0.822586			−0.0609741
$183$	−0.857681	−	2.63967i	−0.0634016	−	0.195130i
$184$	−13.7814	−	10.0128i	−1.01598	−	0.738152i
$185$	16.3747	−	4.02638i	1.20389	−	0.296025i
$186$	7.79245	−	5.66155i	0.571370	−	0.415125i
$187$	0.890676	+	0.647114i	0.0651327	+	0.0473217i
$188$	−7.39004	−	5.36918i	−0.538974	−	0.391588i
$189$	12.4320	−	9.03237i	0.904294	−	0.657008i
$190$	−0.403379	+	0.0991872i	−0.0292642	+	0.00719580i
$191$	−13.5352	−	9.83392i	−0.979374	−	0.711557i	−0.0218057	−	0.999762i	$-0.506942\pi$
$191$	−13.5352	−	9.83392i	−0.979374	−	0.711557i	−0.957569	+	0.288205i	$0.906942\pi$
$192$	−1.99124	−	6.12841i	−0.143705	−	0.442280i
$193$	−14.5964			−1.05068			−0.525338	−	0.850894i	$-0.676061\pi$
$193$	−14.5964			−1.05068			−0.525338	+	0.850894i	$0.676061\pi$
$194$	−5.50918	−	16.9555i	−0.395536	−	1.21734i
$195$	−0.0500653	+	0.684119i	−0.00358525	+	0.0489908i
$196$	−0.661189	+	2.03493i	−0.0472278	+	0.145352i
$197$	−0.388632	+	1.19609i	−0.0276889	+	0.0852176i	−0.963946	−	0.266098i	$-0.914266\pi$
$197$	−0.388632	+	1.19609i	−0.0276889	+	0.0852176i	0.936257	+	0.351316i	$0.114266\pi$
$198$	1.59263	−	1.15712i	0.113184	−	0.0822326i
$199$	−6.04347			−0.428410			−0.214205	−	0.976789i	$-0.568716\pi$
$199$	−6.04347			−0.428410			−0.214205	+	0.976789i	$0.568716\pi$
$200$	−12.9936	+	6.80120i	−0.918783	+	0.480918i
$201$	−2.06606			−0.145729
$202$	−11.4434	+	8.31410i	−0.805153	+	0.584978i
$203$	−0.942951	+	2.90211i	−0.0661822	+	0.203688i
$204$	−0.360670	+	1.11003i	−0.0252520	+	0.0777175i
$205$	20.1186	−	4.94697i	1.40514	−	0.345511i
$206$	−0.775503	−	2.38675i	−0.0540318	−	0.166293i
$207$	11.0146			0.765570
$208$	−0.0490204	−	0.150869i	−0.00339895	−	0.0104609i
$209$	0.175498	+	0.127507i	0.0121395	+	0.00881985i
$210$	−6.12622	−	2.49826i	−0.422749	−	0.172397i
$211$	2.17852	−	1.58279i	0.149976	−	0.108964i	−0.510267	−	0.860016i	$-0.670453\pi$
$211$	2.17852	−	1.58279i	0.149976	−	0.108964i	0.660243	+	0.751052i	$0.270453\pi$
$212$	11.7587	+	8.54316i	0.807588	+	0.586747i
$213$	−10.4260	−	7.57494i	−0.714378	−	0.519026i
$214$	14.0614	−	10.2162i	0.961221	−	0.698368i
$215$	9.73775	−	11.5290i	0.664109	−	0.786268i
$216$	12.2056	+	8.86788i	0.830486	+	0.603383i
$217$	−8.97899	−	27.6345i	−0.609534	−	1.87595i
$218$	4.49457			0.304411
$219$	−2.84313	−	8.75024i	−0.192121	−	0.591286i
$220$	2.53280	+	1.03287i	0.170761	+	0.0696362i
$221$	−0.0902444	+	0.277744i	−0.00607049	+	0.0186831i
$222$	−2.30786	+	7.10286i	−0.154893	+	0.476713i
$223$	2.45270	−	1.78199i	0.164245	−	0.119331i	−0.502627	−	0.864504i	$-0.667633\pi$
$223$	2.45270	−	1.78199i	0.164245	−	0.119331i	0.666872	+	0.745173i	$0.267633\pi$
$224$	−15.9962			−1.06879
$225$	4.21217	−	8.49610i	0.280811	−	0.566407i
$226$	−5.34126			−0.355295
$227$	14.0255	−	10.1901i	0.930906	−	0.676343i	−0.0153085	−	0.999883i	$-0.504873\pi$
$227$	14.0255	−	10.1901i	0.930906	−	0.676343i	0.946214	+	0.323540i	$0.104873\pi$
$228$	−0.0710662	+	0.218719i	−0.00470648	+	0.0144850i
$229$	−4.89542	+	15.0665i	−0.323498	+	0.995626i	0.648615	+	0.761116i	$0.275348\pi$
$229$	−4.89542	+	15.0665i	−0.323498	+	0.995626i	−0.972114	+	0.234509i	$0.924652\pi$
$230$	−6.45439	−	10.4040i	−0.425590	−	0.686021i
$231$	1.06766	+	3.28593i	0.0702471	+	0.216198i
$232$	−2.99588			−0.196689
$233$	4.27931	+	13.1704i	0.280347	+	0.862820i	0.987755	+	0.156014i	$0.0498645\pi$
$233$	4.27931	+	13.1704i	0.280347	+	0.862820i	−0.707408	+	0.706806i	$0.750135\pi$
$234$	0.422466	+	0.306939i	0.0276174	+	0.0200652i
$235$	−9.69094	−	15.6211i	−0.632167	−	1.01901i
$236$	4.91876	−	3.57369i	0.320184	−	0.232628i
$237$	−2.45829	−	1.78605i	−0.159683	−	0.116016i
$238$	−2.27877	−	1.65563i	−0.147711	−	0.107318i
$239$	−15.1994	+	11.0430i	−0.983165	+	0.714311i	−0.958414	−	0.285382i	$-0.907879\pi$
$239$	−15.1994	+	11.0430i	−0.983165	+	0.714311i	−0.0247516	+	0.999694i	$0.507879\pi$
$240$	0.0931228	−	1.27248i	0.00601105	−	0.0821382i
$241$	−20.4696	−	14.8721i	−1.31857	−	0.957994i	−0.999949	−	0.0101100i	$-0.996782\pi$
$241$	−20.4696	−	14.8721i	−1.31857	−	0.957994i	−0.318616	−	0.947884i	$-0.603218\pi$
$242$	−2.85165	−	8.77648i	−0.183311	−	0.564174i
$243$	−15.7319			−1.00920
$244$	−0.907226	−	2.79215i	−0.0580792	−	0.178749i
$245$	−2.77848	+	3.28957i	−0.177511	+	0.210163i
$246$	−2.83553	+	8.72685i	−0.180787	+	0.556404i
$247$	−0.0177817	+	0.0547265i	−0.00113142	+	0.00348216i
$248$	23.0792	−	16.7680i	1.46553	−	1.06477i
$249$	−0.621197			−0.0393667
$250$	−10.4934	+	0.999917i	−0.663659	+	0.0632403i
$251$	−21.2449			−1.34096			−0.670482	−	0.741926i	$-0.733913\pi$
$251$	−21.2449			−1.34096			−0.670482	+	0.741926i	$0.733913\pi$
$252$	5.09343	−	3.70059i	0.320856	−	0.233115i
$253$	−1.97579	+	6.08087i	−0.124217	+	0.382301i
$254$	3.89679	−	11.9931i	0.244506	−	0.752512i
$255$	−1.51563	+	1.79442i	−0.0949122	+	0.112371i
$256$	−5.22611	−	16.0843i	−0.326632	−	1.00527i
$257$	5.82085			0.363095			0.181547	−	0.983382i	$-0.441889\pi$
$257$	5.82085			0.363095			0.181547	+	0.983382i	$0.441889\pi$
$258$	2.06543	+	6.35672i	0.128588	+	0.395752i
$259$	18.2269	+	13.2426i	1.13257	+	0.822858i
$260$	−0.0529574	+	0.723638i	−0.00328428	+	0.0448782i
$261$	1.56717	−	1.13862i	0.0970055	−	0.0704786i
$262$	12.7917	+	9.29368i	0.790271	+	0.574166i
$263$	−2.11070	−	1.53351i	−0.130151	−	0.0945603i	0.520805	−	0.853676i	$-0.325632\pi$
$263$	−2.11070	−	1.53351i	−0.130151	−	0.0945603i	−0.650956	+	0.759115i	$0.725632\pi$
$264$	−2.74428	+	1.99383i	−0.168898	+	0.122712i
$265$	15.4197	+	24.8555i	0.947227	+	1.52686i
$266$	−0.449009	−	0.326224i	−0.0275305	−	0.0200021i
$267$	2.41099	+	7.42028i	0.147550	+	0.454114i
$268$	−2.18541			−0.133495
$269$	−0.188821	−	0.581130i	−0.0115126	−	0.0354321i	0.945135	−	0.326679i	$-0.105930\pi$
$269$	−0.188821	−	0.581130i	−0.0115126	−	0.0354321i	−0.956648	+	0.291247i	$0.905930\pi$
$270$	5.71638	+	9.21439i	0.347888	+	0.560770i
$271$	1.89464	−	5.83109i	0.115091	−	0.354213i	−0.876875	−	0.480718i	$-0.840376\pi$
$271$	1.89464	−	5.83109i	0.115091	−	0.354213i	0.991966	+	0.126505i	$0.0403760\pi$
$272$	0.167857	−	0.516610i	0.0101778	−	0.0313241i
$273$	−0.741455	+	0.538699i	−0.0448749	+	0.0326035i
$274$	14.8310			0.895972
$275$	3.93488	+	3.84944i	0.237282	+	0.232130i
$276$	−6.77836			−0.408009
$277$	−2.34270	+	1.70207i	−0.140759	+	0.102268i	−0.655936	−	0.754816i	$-0.727726\pi$
$277$	−2.34270	+	1.70207i	−0.140759	+	0.102268i	0.515177	+	0.857084i	$0.327726\pi$
$278$	−0.519086	+	1.59758i	−0.0311327	+	0.0958166i
$279$	−5.70007	+	17.5430i	−0.341254	+	1.05027i
$280$	−18.1443	−	7.39921i	−1.08433	−	0.442187i
$281$	−3.16488	−	9.74050i	−0.188801	−	0.581070i	0.811192	−	0.584780i	$-0.198819\pi$
$281$	−3.16488	−	9.74050i	−0.188801	−	0.581070i	−0.999993	+	0.00371008i	$0.998819\pi$
$282$	8.14183			0.484839
$283$	2.15784	+	6.64115i	0.128270	+	0.394776i	0.994483	−	0.104900i	$-0.0334524\pi$
$283$	2.15784	+	6.64115i	0.128270	+	0.394776i	−0.866212	+	0.499676i	$0.833452\pi$
$284$	−11.0283	−	8.01251i	−0.654408	−	0.475455i
$285$	−0.298638	+	0.353571i	−0.0176898	+	0.0209438i
$286$	−0.245234	+	0.178173i	−0.0145010	+	0.0105356i
$287$	22.3943	+	16.2704i	1.32190	+	0.960413i
$288$	8.21539	+	5.96883i	0.484096	+	0.351716i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−1.99383	−	0.813083i	−0.117082	−	0.0477459i
$291$	−16.0697	−	11.6753i	−0.942024	−	0.684420i
$292$	−3.00736	−	9.25571i	−0.175993	−	0.541650i
$293$	−0.508765			−0.0297223			−0.0148612	−	0.999890i	$-0.504731\pi$
$293$	−0.508765			−0.0297223			−0.0148612	+	0.999890i	$0.504731\pi$
$294$	−0.589330	−	1.81377i	−0.0343704	−	0.105781i
$295$	11.8817	−	2.92159i	0.691777	−	0.170101i
$296$	−6.83529	+	21.0368i	−0.397293	+	1.22274i
$297$	1.74987	−	5.38556i	0.101538	−	0.312502i
$298$	−13.2354	+	9.61609i	−0.766707	+	0.557045i
$299$	−1.69603			−0.0980842
$300$	−2.59215	+	5.22847i	−0.149658	+	0.301866i
$301$	20.1630			1.16218
$302$	−9.36624	+	6.80497i	−0.538967	+	0.391582i
$303$	−4.86996	+	14.9882i	−0.279772	+	0.861049i
$304$	0.0330744	−	0.101793i	0.00189695	−	0.00583821i
$305$	0.431226	−	5.89250i	0.0246919	−	0.337404i
$306$	0.552559	+	1.70060i	0.0315877	+	0.0972168i
$307$	2.58902			0.147763			0.0738817	−	0.997267i	$-0.476461\pi$
$307$	2.58902			0.147763			0.0738817	+	0.997267i	$0.476461\pi$
$308$	1.12934	+	3.47575i	0.0643500	+	0.198049i
$309$	−2.26206	−	1.64348i	−0.128684	−	0.0934945i
$310$	19.9106	−	4.89584i	1.13085	−	0.278065i
$311$	−9.84996	+	7.15642i	−0.558540	+	0.405803i	−0.830924	−	0.556385i	$-0.812188\pi$
$311$	−9.84996	+	7.15642i	−0.558540	+	0.405803i	0.272384	+	0.962189i	$0.412188\pi$
$312$	−0.727953	−	0.528889i	−0.0412122	−	0.0299424i
$313$	12.1701	+	8.84213i	0.687897	+	0.499787i	0.875968	−	0.482369i	$-0.160223\pi$
$313$	12.1701	+	8.84213i	0.687897	+	0.499787i	−0.188071	+	0.982155i	$0.560223\pi$
$314$	−2.48702	+	1.80693i	−0.140351	+	0.101971i
$315$	12.3036	−	3.02533i	0.693227	−	0.170458i
$316$	−2.60029	−	1.88922i	−0.146278	−	0.106277i
$317$	4.56111	+	14.0376i	0.256177	+	0.788433i	0.993595	+	0.112996i	$0.0360448\pi$
$317$	4.56111	+	14.0376i	0.256177	+	0.788433i	−0.737418	+	0.675437i	$0.763955\pi$
$318$	−12.9549			−0.726473
$319$	0.347481	+	1.06944i	0.0194552	+	0.0598769i
$320$	1.00116	−	13.6804i	0.0559664	−	0.764755i
$321$	5.98412	−	18.4172i	0.334001	−	1.02795i
$322$	5.05502	−	15.5577i	0.281705	−	0.866999i
$323$	−0.159408	+	0.115817i	−0.00886972	+	0.00644423i
$324$	−0.318678			−0.0177043
$325$	−0.648590	+	1.30823i	−0.0359773	+	0.0725676i
$326$	−7.03420			−0.389588
$327$	4.05127	−	2.94342i	0.224036	−	0.162772i
$328$	−8.39810	+	25.8467i	−0.463707	+	1.42714i
$329$	7.58985	−	23.3592i	0.418442	−	1.28783i
$330$	−2.36751	+	0.582148i	−0.130327	+	0.0320462i
$331$	3.21481	+	9.89416i	0.176702	+	0.543832i	0.999707	−	0.0242015i	$-0.00770432\pi$
$331$	3.21481	+	9.89416i	0.176702	+	0.543832i	−0.823005	+	0.568034i	$0.807704\pi$
$332$	−0.657081			−0.0360620
$333$	−4.41968	−	13.6024i	−0.242197	−	0.745405i
$334$	−9.56990	−	6.95294i	−0.523642	−	0.380448i
$335$	−4.07244	−	1.66074i	−0.222501	−	0.0907357i
$336$	1.37913	−	1.00199i	0.0752375	−	0.0546632i
$337$	9.06632	+	6.58707i	0.493874	+	0.358821i	0.806672	−	0.590999i	$-0.201266\pi$
$337$	9.06632	+	6.58707i	0.493874	+	0.358821i	−0.312798	+	0.949820i	$0.601266\pi$
$338$	9.85066	+	7.15692i	0.535805	+	0.389285i
$339$	−4.81445	+	3.49790i	−0.261485	+	0.189980i
$340$	−1.60318	+	1.89808i	−0.0869446	+	0.102938i
$341$	−8.66253	−	6.29369i	−0.469102	−	0.340823i
$342$	0.108876	+	0.335085i	0.00588733	+	0.0181193i
$343$	15.1600			0.818562
$344$	6.11725	+	18.8270i	0.329820	+	1.01508i
$345$	−12.6312	−	5.15100i	−0.680043	−	0.277320i
$346$	−4.89503	+	15.0653i	−0.263158	+	0.809918i
$347$	4.33171	−	13.3316i	0.232539	−	0.715680i	−0.764900	−	0.644149i	$-0.777212\pi$
$347$	4.33171	−	13.3316i	0.232539	−	0.715680i	0.997438	−	0.0715309i	$-0.0227885\pi$
$348$	−0.964432	+	0.700701i	−0.0516990	+	0.0375615i
$349$	4.62104			0.247359			0.123679	−	0.992322i	$-0.460531\pi$
$349$	4.62104			0.247359			0.123679	+	0.992322i	$0.460531\pi$
$350$	−10.0673	−	9.84871i	−0.538120	−	0.526435i
$351$	1.50210			0.0801764
$352$	−4.76889	+	3.46480i	−0.254183	+	0.184674i
$353$	−8.79972	+	27.0827i	−0.468362	+	1.44147i	0.386343	+	0.922355i	$0.373738\pi$
$353$	−8.79972	+	27.0827i	−0.468362	+	1.44147i	−0.854705	+	0.519114i	$0.826262\pi$
$354$	−1.67461	+	5.15392i	−0.0890045	+	0.273928i
$355$	−14.4620	−	23.3116i	−0.767561	−	1.23725i
$356$	2.55027	+	7.84892i	0.135164	+	0.415992i
$357$	−3.13826			−0.166095
$358$	−1.27307	−	3.91809i	−0.0672836	−	0.207078i
$359$	21.2494	+	15.4386i	1.12150	+	0.814816i	0.984435	−	0.175746i	$-0.0562339\pi$
$359$	21.2494	+	15.4386i	1.12150	+	0.814816i	0.137062	+	0.990562i	$0.456234\pi$
$360$	6.55764	+	10.5704i	0.345618	+	0.557111i
$361$	15.3399	−	11.1451i	0.807364	−	0.586584i
$362$	−1.17169	−	0.851283i	−0.0615827	−	0.0447424i
$363$	−8.31798	−	6.04336i	−0.436581	−	0.317194i
$364$	−0.784287	+	0.569818i	−0.0411078	+	0.0298666i
$365$	1.42947	−	19.5330i	0.0748219	−	1.02241i
$366$	2.11701	+	1.53810i	0.110658	+	0.0803978i
$367$	5.19225	+	15.9801i	0.271033	+	0.834154i	0.990242	+	0.139360i	$0.0445046\pi$
$367$	5.19225	+	15.9801i	0.271033	+	0.834154i	−0.719209	+	0.694794i	$0.755495\pi$
$368$	3.15467			0.164448
$369$	−5.43019	−	16.7124i	−0.282684	−	0.870013i
$370$	−10.2584	+	12.1454i	−0.533311	+	0.631411i
$371$	−12.0766	+	37.1679i	−0.626985	+	1.92966i
$372$	3.50780	−	10.7959i	0.181871	−	0.559741i
$373$	15.8009	−	11.4800i	0.818138	−	0.594412i	−0.0980405	−	0.995182i	$-0.531257\pi$
$373$	15.8009	−	11.4800i	0.818138	−	0.594412i	0.916179	+	0.400770i	$0.131257\pi$
$374$	−1.03797			−0.0536722
$375$	−8.80359	+	7.77324i	−0.454616	+	0.401408i
$376$	24.1140			1.24358
$377$	−0.241313	+	0.175324i	−0.0124283	+	0.00902967i
$378$	−4.47701	+	13.7788i	−0.230273	+	0.708707i
$379$	−8.95418	+	27.5581i	−0.459945	+	1.41557i	0.405285	+	0.914191i	$0.367172\pi$
$379$	−8.95418	+	27.5581i	−0.459945	+	1.41557i	−0.865230	+	0.501375i	$0.832828\pi$
$380$	−0.315890	+	0.373996i	−0.0162048	+	0.0191856i
$381$	−4.34163	−	13.3622i	−0.222428	−	0.684564i
$382$	15.7736			0.807047
$383$	7.96971	+	24.5283i	0.407233	+	1.25334i	0.919016	+	0.394220i	$0.128985\pi$
$383$	7.96971	+	24.5283i	0.407233	+	1.25334i	−0.511783	+	0.859115i	$0.671015\pi$
$384$	−4.18528	−	3.04078i	−0.213579	−	0.155174i
$385$	−0.536801	+	7.33513i	−0.0273579	+	0.373833i
$386$	11.1334	−	8.08889i	0.566675	−	0.411714i
$387$	−10.3554	−	7.52362i	−0.526393	−	0.382447i
$388$	−16.9980	−	12.3498i	−0.862944	−	0.626965i
$389$	−3.14553	+	2.28536i	−0.159485	+	0.115873i	−0.664665	−	0.747141i	$-0.731426\pi$
$389$	−3.14553	+	2.28536i	−0.159485	+	0.115873i	0.505181	+	0.863014i	$0.331426\pi$
$390$	−0.340930	−	0.549555i	−0.0172637	−	0.0278278i
$391$	−4.69845	−	3.41362i	−0.237611	−	0.172634i
$392$	−1.74544	−	5.37192i	−0.0881581	−	0.271323i
$393$	17.6163			0.888626
$394$	−0.366405	−	1.12768i	−0.0184592	−	0.0568116i
$395$	−3.40990	−	5.49651i	−0.171571	−	0.276560i
$396$	0.716929	−	2.20648i	0.0360271	−	0.110880i
$397$	−4.70748	+	14.4881i	−0.236262	+	0.727139i	0.760690	+	0.649116i	$0.224861\pi$
$397$	−4.70748	+	14.4881i	−0.236262	+	0.727139i	−0.996952	+	0.0780234i	$0.975139\pi$
$398$	4.60964	−	3.34910i	0.231060	−	0.167875i
$399$	−0.618362			−0.0309568
$400$	1.20639	−	2.43334i	0.0603197	−	0.121667i
$401$	20.8713			1.04226			0.521130	−	0.853477i	$-0.325511\pi$
$401$	20.8713			1.04226			0.521130	+	0.853477i	$0.325511\pi$
$402$	1.57588	−	1.14495i	0.0785980	−	0.0571048i
$403$	0.877697	−	2.70127i	0.0437212	−	0.134560i
$404$	−5.15128	+	15.8540i	−0.256286	+	0.788766i
$405$	−0.593845	−	0.242169i	−0.0295084	−	0.0120335i
$406$	−0.889021	−	2.73613i	−0.0441214	−	0.135792i
$407$	8.30228			0.411529
$408$	−0.952117	−	2.93031i	−0.0471368	−	0.145072i
$409$	27.2884	+	19.8262i	1.34933	+	0.980343i	0.999045	+	0.0436984i	$0.0139140\pi$
$409$	27.2884	+	19.8262i	1.34933	+	0.980343i	0.350281	+	0.936645i	$0.386086\pi$
$410$	−12.6039	+	14.9224i	−0.622464	+	0.736963i
$411$	13.3682	−	9.71257i	0.659405	−	0.479086i
$412$	−2.39273	−	1.73842i	−0.117882	−	0.0856459i
$413$	13.2257	+	9.60902i	0.650793	+	0.472829i
$414$	−8.40138	+	6.10396i	−0.412905	+	0.299993i
$415$	−1.22445	−	0.499328i	−0.0601057	−	0.0245110i
$416$	−1.26501	−	0.919081i	−0.0620220	−	0.0450616i
$417$	0.578343	+	1.77996i	0.0283216	+	0.0871648i
$418$	−0.204521			−0.0100035
$419$	5.37823	+	16.5525i	0.262744	+	0.808642i	0.992205	+	0.124620i	$0.0397710\pi$
$419$	5.37823	+	16.5525i	0.262744	+	0.808642i	−0.729461	+	0.684023i	$0.760229\pi$
$420$	−7.57157	+	1.86178i	−0.369455	+	0.0908454i
$421$	5.24682	−	16.1481i	0.255714	−	0.787008i	−0.737974	−	0.674830i	$-0.764217\pi$
$421$	5.24682	−	16.1481i	0.255714	−	0.787008i	0.993688	−	0.112179i	$-0.0357829\pi$
$422$	−0.784531	+	2.41454i	−0.0381904	+	0.117538i
$423$	−12.6142	+	9.16478i	−0.613325	+	0.445607i
$424$	−38.3690			−1.86336
$425$	−4.42985	+	2.31871i	−0.214879	+	0.112474i
$426$	12.1502			0.588679
$427$	6.38635	−	4.63995i	0.309057	−	0.224543i
$428$	6.32981	−	19.4811i	0.305963	−	0.941657i
$429$	−0.104364	+	0.321200i	−0.00503875	+	0.0155077i
$430$	−1.03846	+	14.1900i	−0.0500789	+	0.684304i
$431$	−4.85539	−	14.9433i	−0.233876	−	0.719796i	−0.997269	−	0.0738611i	$-0.976468\pi$
$431$	−4.85539	−	14.9433i	−0.233876	−	0.719796i	0.763393	−	0.645935i	$-0.223532\pi$
$432$	−2.79395			−0.134424
$433$	−3.06895	−	9.44525i	−0.147484	−	0.453910i	0.849838	−	0.527044i	$-0.176700\pi$
$433$	−3.06895	−	9.44525i	−0.147484	−	0.453910i	−0.997322	+	0.0731344i	$0.976700\pi$
$434$	22.1629	+	16.1023i	1.06385	+	0.772933i
$435$	−2.32966	+	0.572841i	−0.111699	+	0.0274656i
$436$	4.28530	−	3.11345i	0.205229	−	0.149107i
$437$	−0.925780	−	0.672619i	−0.0442861	−	0.0321757i
$438$	7.01769	+	5.09865i	0.335318	+	0.243623i
$439$	−0.520103	+	0.377877i	−0.0248232	+	0.0180351i	−0.600128	−	0.799904i	$-0.704884\pi$
$439$	−0.520103	+	0.377877i	−0.0248232	+	0.0180351i	0.575304	+	0.817939i	$0.304884\pi$
$440$	−7.01195	+	1.72417i	−0.334281	+	0.0821967i
$441$	2.95471	+	2.14672i	0.140700	+	0.102225i
$442$	−0.0850830	−	0.261859i	−0.00404699	−	0.0124553i
$443$	−9.12289			−0.433442			−0.216721	−	0.976234i	$-0.569536\pi$
$443$	−9.12289			−0.433442			−0.216721	+	0.976234i	$0.569536\pi$
$444$	2.71985	+	8.37085i	0.129079	+	0.397263i
$445$	−1.21220	+	16.5642i	−0.0574639	+	0.785218i
$446$	−0.883266	+	2.71841i	−0.0418239	+	0.128721i
$447$	−5.63259	+	17.3353i	−0.266412	+	0.819933i
$448$	14.8269	−	10.7724i	0.700506	−	0.508947i
$449$	−11.1964			−0.528391			−0.264195	−	0.964469i	$-0.585106\pi$
$449$	−11.1964			−0.528391			−0.264195	+	0.964469i	$0.585106\pi$
$450$	1.49545	+	8.81463i	0.0704962	+	0.415526i
$451$	10.2005			0.480323
$452$	−5.09257	+	3.69997i	−0.239534	+	0.174032i
$453$	−3.98599	+	12.2676i	−0.187278	+	0.576383i
$454$	−5.05087	+	15.5450i	−0.237049	+	0.729562i
$455$	−1.89451	+	0.465841i	−0.0888158	+	0.0218390i
$456$	−0.187605	−	0.577388i	−0.00878539	−	0.0270387i
$457$	−25.2963			−1.18331			−0.591655	−	0.806192i	$-0.701525\pi$
$457$	−25.2963			−1.18331			−0.591655	+	0.806192i	$0.701525\pi$
$458$	−4.61544	−	14.2049i	−0.215665	−	0.663749i
$459$	4.16121	+	3.02330i	0.194229	+	0.141116i
$460$	−13.3609	−	5.44855i	−0.622955	−	0.254040i
$461$	−9.09821	+	6.61024i	−0.423746	+	0.307869i	−0.779143	−	0.626846i	$-0.784346\pi$
$461$	−9.09821	+	6.61024i	−0.423746	+	0.307869i	0.355397	+	0.934715i	$0.384346\pi$
$462$	−2.63531	−	1.91467i	−0.122606	−	0.0890784i
$463$	18.0948	+	13.1466i	0.840936	+	0.610976i	0.922632	−	0.385681i	$-0.126034\pi$
$463$	18.0948	+	13.1466i	0.840936	+	0.610976i	−0.0816958	+	0.996657i	$0.526034\pi$
$464$	0.448849	−	0.326108i	0.0208373	−	0.0151392i
$465$	14.7407	−	17.4521i	0.683582	−	0.809323i
$466$	−10.5626	−	7.67420i	−0.489305	−	0.355501i
$467$	1.07567	+	3.31056i	0.0497759	+	0.153195i	0.972855	−	0.231416i	$-0.0743358\pi$
$467$	1.07567	+	3.31056i	0.0497759	+	0.153195i	−0.923079	+	0.384610i	$0.874336\pi$
$468$	0.615417			0.0284477
$469$	−1.81584	−	5.58859i	−0.0838478	−	0.258057i
$470$	16.0485	+	6.54454i	0.740260	+	0.301877i
$471$	−1.05840	+	3.25743i	−0.0487686	+	0.150094i
$472$	−4.95976	+	15.2646i	−0.228292	+	0.702609i
$473$	6.01112	−	4.36733i	0.276391	−	0.200810i
$474$	2.86482			0.131586
$475$	−0.872856	+	0.456878i	−0.0400494	+	0.0209630i
$476$	−3.31955			−0.152151
$477$	20.0711	−	14.5825i	0.918994	−	0.667688i
$478$	5.47360	−	16.8460i	0.250357	−	0.770519i
$479$	2.97186	−	9.14643i	0.135788	−	0.417911i	−0.859924	−	0.510422i	$-0.829489\pi$
$479$	2.97186	−	9.14643i	0.135788	−	0.417911i	0.995712	+	0.0925108i	$0.0294893\pi$
$480$	−6.62982	−	10.6868i	−0.302609	−	0.487783i
$481$	0.680543	+	2.09450i	0.0310301	+	0.0955008i
$482$	23.8548			1.08656
$483$	−5.63208	−	17.3338i	−0.256268	−	0.788713i
$484$	−8.79848	−	6.39247i	−0.399931	−	0.290567i
$485$	−22.2904	−	35.9305i	−1.01215	−	1.63152i
$486$	11.9995	−	8.71812i	0.544307	−	0.395462i
$487$	−6.71041	−	4.87540i	−0.304078	−	0.220925i	0.425274	−	0.905065i	$-0.360178\pi$
$487$	−6.71041	−	4.87540i	−0.304078	−	0.220925i	−0.729351	+	0.684140i	$0.760178\pi$
$488$	6.27005	+	4.55546i	0.283832	+	0.206216i
$489$	−6.34042	+	4.60659i	−0.286724	+	0.208317i
$490$	0.296304	−	4.04886i	0.0133856	−	0.182909i
$491$	14.9225	+	10.8418i	0.673443	+	0.489285i	0.871176	−	0.490971i	$-0.163358\pi$
$491$	14.9225	+	10.8418i	0.673443	+	0.489285i	−0.197733	+	0.980256i	$0.563358\pi$
$492$	3.34172	+	10.2847i	0.150656	+	0.463672i
$493$	−1.02138			−0.0460005
$494$	−0.0167647	−	0.0515965i	−0.000754281	−	0.00232144i
$495$	3.01272	−	3.56689i	0.135412	−	0.160320i
$496$	−1.63254	+	5.02444i	−0.0733032	+	0.225604i
$497$	11.3265	−	34.8593i	0.508061	−	1.56365i
$498$	0.473816	−	0.344247i	0.0212322	−	0.0154261i
$499$	−29.9613			−1.34125			−0.670625	−	0.741796i	$-0.733974\pi$
$499$	−29.9613			−1.34125			−0.670625	+	0.741796i	$0.733974\pi$
$500$	−9.31215	+	8.22228i	−0.416452	+	0.367711i
$501$	−13.1794			−0.588812
$502$	16.2045	−	11.7732i	0.723240	−	0.525465i
$503$	−11.8704	+	36.5333i	−0.529274	+	1.62894i	0.226432	+	0.974027i	$0.427294\pi$
$503$	−11.8704	+	36.5333i	−0.529274	+	1.62894i	−0.755706	+	0.654911i	$0.772706\pi$
$504$	−5.13588	+	15.8066i	−0.228770	+	0.704083i
$505$	−21.6470	+	25.6288i	−0.963277	+	1.14047i
$506$	−1.86279	−	5.73308i	−0.0828112	−	0.254867i
$507$	13.5661			0.602490
$508$	−4.59243	−	14.1340i	−0.203756	−	0.627097i
$509$	−7.44262	−	5.40738i	−0.329888	−	0.239678i	0.410495	−	0.911863i	$-0.365356\pi$
$509$	−7.44262	−	5.40738i	−0.329888	−	0.239678i	−0.740383	+	0.672185i	$0.765356\pi$
$510$	0.161630	−	2.20860i	0.00715710	−	0.0977984i
$511$	21.1701	−	15.3810i	0.936510	−	0.680415i
$512$	4.93094	+	3.58254i	0.217919	+	0.158327i
$513$	0.819924	+	0.595709i	0.0362005	+	0.0263012i
$514$	−4.43984	+	3.22573i	−0.195833	+	0.142281i
$515$	−3.13772	−	5.05777i	−0.138264	−	0.222872i
$516$	6.37266	+	4.63001i	0.280541	+	0.203825i
$517$	−2.79689	−	8.60793i	−0.123007	−	0.378576i
$518$	−21.2412			−0.933285
$519$	5.45382	+	16.7851i	0.239396	+	0.736786i
$520$	−1.00975	−	1.62764i	−0.0442803	−	0.0713767i
$521$	−4.06407	+	12.5079i	−0.178050	+	0.547982i	−0.999760	−	0.0219248i	$-0.993021\pi$
$521$	−4.06407	+	12.5079i	−0.178050	+	0.547982i	0.821710	+	0.569906i	$0.193021\pi$
$522$	−0.564371	+	1.73695i	−0.0247018	+	0.0760244i
$523$	31.0434	−	22.5544i	1.35743	−	0.986234i	0.358831	−	0.933402i	$-0.383175\pi$
$523$	31.0434	−	22.5544i	1.35743	−	0.986234i	0.998603	−	0.0528318i	$-0.0168247\pi$
$524$	18.6340			0.814028
$525$	−15.5241	−	2.28442i	−0.677529	−	0.0997001i
$526$	2.45975			0.107250
$527$	7.86833	−	5.71667i	0.342750	−	0.249022i
$528$	0.194120	−	0.597440i	0.00844798	−	0.0260002i
$529$	3.31521	−	10.2032i	0.144139	−	0.443616i
$530$	−25.5355	−	10.4133i	−1.10919	−	0.452326i
$531$	−3.20697	−	9.87004i	−0.139171	−	0.428323i
$532$	−0.654083			−0.0283581
$533$	0.836141	+	2.57338i	0.0362173	+	0.111465i
$534$	−5.95106	−	4.32370i	−0.257528	−	0.187105i
$535$	26.5995	−	31.4923i	1.14999	−	1.36153i
$536$	4.66736	−	3.39104i	0.201599	−	0.146471i
$537$	−3.71340	−	2.69794i	−0.160245	−	0.116425i
$538$	0.466066	+	0.338617i	0.0200935	+	0.0145988i
$539$	−1.71516	+	1.24613i	−0.0738771	+	0.0536748i
$540$	11.8332	+	4.82555i	0.509219	+	0.207659i
$541$	−2.77792	−	2.01827i	−0.119432	−	0.0867724i	0.526466	−	0.850196i	$-0.323517\pi$
$541$	−2.77792	−	2.01827i	−0.119432	−	0.0867724i	−0.645898	+	0.763424i	$0.723517\pi$
$542$	1.78628	+	5.49759i	0.0767271	+	0.236142i
$543$	−1.61362			−0.0692470
$544$	−1.65455	−	5.09218i	−0.0709382	−	0.218325i
$545$	10.3515	−	2.54533i	0.443409	−	0.109030i
$546$	0.267013	−	0.821782i	0.0114271	−	0.0351690i
$547$	−0.131849	+	0.405791i	−0.00563747	+	0.0173504i	−0.953836	−	0.300329i	$-0.902904\pi$
$547$	−0.131849	+	0.405791i	−0.00563747	+	0.0173504i	0.948198	+	0.317679i	$0.102904\pi$
$548$	14.1404	−	10.2736i	0.604050	−	0.438868i
$549$	−5.01126			−0.213876
$550$	−5.13456	−	0.755563i	−0.218938	−	0.0322173i
$551$	−0.201252			−0.00857361
$552$	14.4765	−	10.5178i	0.616159	−	0.447666i
$553$	2.67060	−	8.21927i	0.113566	−	0.349519i
$554$	0.843654	−	2.59650i	0.0358434	−	0.110315i
$555$	−1.29281	+	17.6656i	−0.0548767	+	0.749865i
$556$	0.611752	+	1.88278i	0.0259440	+	0.0798476i
$557$	−29.6009			−1.25423			−0.627115	−	0.778927i	$-0.715764\pi$
$557$	−29.6009			−1.25423			−0.627115	+	0.778927i	$0.715764\pi$
$558$	−5.37407	−	16.5397i	−0.227502	−	0.700180i
$559$	1.59452	+	1.15849i	0.0674411	+	0.0489988i
$560$	3.52383	−	0.866476i	0.148909	−	0.0366153i
$561$	−0.935597	+	0.679751i	−0.0395009	+	0.0286991i
$562$	7.81188	+	5.67566i	0.329524	+	0.239413i
$563$	5.35336	+	3.88944i	0.225617	+	0.163920i	0.694852	−	0.719153i	$-0.255470\pi$
$563$	5.35336	+	3.88944i	0.225617	+	0.163920i	−0.469234	+	0.883074i	$0.655470\pi$
$564$	7.76275	−	5.63997i	0.326871	−	0.237486i
$565$	−12.3015	+	3.02482i	−0.517528	+	0.127255i
$566$	−5.32620	−	3.86971i	−0.223877	−	0.162656i
$567$	−0.264787	−	0.814929i	−0.0111200	−	0.0342238i
$568$	35.9857			1.50993
$569$	6.86753	+	21.1361i	0.287902	+	0.886071i	0.985514	+	0.169595i	$0.0542461\pi$
$569$	6.86753	+	21.1361i	0.287902	+	0.886071i	−0.697612	+	0.716476i	$0.745754\pi$
$570$	0.0318475	−	0.435181i	0.00133395	−	0.0182277i
$571$	13.6249	−	41.9330i	0.570183	−	1.75484i	−0.0818437	−	0.996645i	$-0.526081\pi$
$571$	13.6249	−	41.9330i	0.570183	−	1.75484i	0.652026	−	0.758196i	$-0.273919\pi$
$572$	−0.110393	+	0.339754i	−0.00461576	+	0.0142058i
$573$	14.2179	−	10.3299i	0.593960	−	0.431537i
$574$	−26.0978			−1.08930
$575$	−20.7571	−	20.3064i	−0.865631	−	0.846834i
$576$	−11.6344			−0.484768
$577$	−5.37974	+	3.90861i	−0.223962	+	0.162718i	−0.694108	−	0.719871i	$-0.744201\pi$
$577$	−5.37974	+	3.90861i	−0.223962	+	0.162718i	0.470147	+	0.882588i	$0.344201\pi$
$578$	0.291343	−	0.896663i	0.0121183	−	0.0372963i
$579$	4.73804	−	14.5822i	0.196906	−	0.606015i
$580$	−2.46424	+	0.605933i	−0.102322	+	0.0251600i
$581$	−0.545963	−	1.68030i	−0.0226504	−	0.0697106i
$582$	18.7272			0.776269
$583$	4.45027	+	13.6965i	0.184311	+	0.567251i
$584$	20.7846	+	15.1009i	0.860072	+	0.624879i
$585$	1.14681	+	0.467667i	0.0474147	+	0.0193356i
$586$	0.388059	−	0.281941i	0.0160306	−	0.0116469i
$587$	14.8192	+	10.7668i	0.611653	+	0.444392i	0.849996	−	0.526789i	$-0.176604\pi$
$587$	14.8192	+	10.7668i	0.611653	+	0.444392i	−0.238343	+	0.971181i	$0.576604\pi$
$588$	−1.81832	−	1.32108i	−0.0749861	−	0.0544806i
$589$	1.55037	−	1.12641i	0.0638819	−	0.0464129i
$590$	−7.44365	+	8.81287i	−0.306450	+	0.362820i
$591$	−1.06877	−	0.776504i	−0.0439632	−	0.0319411i
$592$	−1.26583	−	3.89581i	−0.0520252	−	0.160117i
$593$	−12.2313			−0.502279			−0.251140	−	0.967951i	$-0.580805\pi$
$593$	−12.2313			−0.502279			−0.251140	+	0.967951i	$0.580805\pi$
$594$	1.64979	+	5.07755i	0.0676919	+	0.208334i
$595$	−6.18587	−	2.52259i	−0.253596	−	0.103416i
$596$	−5.95796	+	18.3367i	−0.244048	+	0.751102i
$597$	1.96172	−	6.03756i	0.0802879	−	0.247101i
$598$	1.29365	−	0.939888i	0.0529011	−	0.0384349i
$599$	−5.63970			−0.230432			−0.115216	−	0.993340i	$-0.536756\pi$
$599$	−5.63970			−0.230432			−0.115216	+	0.993340i	$0.536756\pi$
$600$	−2.57682	−	15.1885i	−0.105198	−	0.620069i
$601$	17.9321			0.731465			0.365733	−	0.930720i	$-0.380818\pi$
$601$	17.9321			0.731465			0.365733	+	0.930720i	$0.380818\pi$
$602$	−15.3793	+	11.1737i	−0.626813	+	0.455407i
$603$	−1.15274	+	3.54776i	−0.0469431	+	0.144476i
$604$	−4.21625	+	12.9763i	−0.171557	+	0.527997i
$605$	−11.5379	−	18.5983i	−0.469082	−	0.756127i
$606$	−4.59143	−	14.1310i	−0.186514	−	0.574031i
$607$	−29.7932			−1.20927			−0.604634	−	0.796503i	$-0.706681\pi$
$607$	−29.7932			−1.20927			−0.604634	+	0.796503i	$0.706681\pi$
$608$	−0.326012	−	1.00336i	−0.0132215	−	0.0406916i
$609$	−2.59318	−	1.88406i	−0.105081	−	0.0763459i
$610$	2.93652	+	4.73346i	0.118896	+	0.191652i
$611$	1.94234	−	1.41119i	0.0785787	−	0.0570908i
$612$	1.70486	+	1.23866i	0.0689150	+	0.0500697i
$613$	11.2019	+	8.13864i	0.452440	+	0.328717i	0.790558	−	0.612387i	$-0.209790\pi$
$613$	11.2019	+	8.13864i	0.452440	+	0.328717i	−0.338119	+	0.941104i	$0.609790\pi$
$614$	−1.97477	+	1.43475i	−0.0796953	+	0.0579020i
$615$	−1.58840	+	21.7047i	−0.0640503	+	0.875218i
$616$	−7.80512	−	5.67075i	−0.314477	−	0.228481i
$617$	−0.685798	−	2.11067i	−0.0276092	−	0.0849724i	0.936302	−	0.351195i	$-0.114224\pi$
$617$	−0.685798	−	2.11067i	−0.0276092	−	0.0849724i	−0.963912	+	0.266222i	$0.914224\pi$
$618$	2.63615			0.106041
$619$	9.41170	+	28.9662i	0.378288	+	1.16425i	0.941233	+	0.337757i	$0.109668\pi$
$619$	9.41170	+	28.9662i	0.378288	+	1.16425i	−0.562945	+	0.826494i	$0.690332\pi$
$620$	15.5922	−	18.4603i	0.626197	−	0.741383i
$621$	−9.23085	+	28.4096i	−0.370421	+	1.14004i
$622$	3.54717	−	10.9171i	0.142229	−	0.437735i
$623$	−17.9524	+	13.0432i	−0.719249	+	0.522565i
$624$	0.166634			0.00667069
$625$	−23.6011	+	8.24545i	−0.944045	+	0.329818i
$626$	−14.1828			−0.566858
$627$	−0.184350	+	0.133938i	−0.00736221	+	0.00534896i
$628$	−1.11954	+	3.44560i	−0.0446746	+	0.137494i
$629$	−2.33033	+	7.17202i	−0.0929164	+	0.285967i
$630$	−7.70797	+	9.12581i	−0.307093	+	0.363581i
$631$	2.89503	+	8.90998i	0.115249	+	0.354701i	0.991999	−	0.126246i	$-0.0402930\pi$
$631$	2.89503	+	8.90998i	0.115249	+	0.354701i	−0.876750	+	0.480947i	$0.840293\pi$
$632$	8.48486			0.337510
$633$	0.874090	+	2.69017i	0.0347420	+	0.106925i
$634$	−11.2582	−	8.17955i	−0.447120	−	0.324852i
$635$	2.18289	−	29.8282i	0.0866253	−	1.18369i
$636$	−12.3517	+	8.97403i	−0.489777	+	0.355844i
$637$	−0.454967	−	0.330553i	−0.0180264	−	0.0130970i
$638$	−0.857687	−	0.623146i	−0.0339562	−	0.0246706i
$639$	−18.8244	+	13.6768i	−0.744683	+	0.541044i
$640$	−5.80542	−	9.35792i	−0.229479	−	0.369904i
$641$	−30.3011	−	22.0150i	−1.19682	−	0.869542i	−0.202853	−	0.979209i	$-0.565021\pi$
$641$	−30.3011	−	22.0150i	−1.19682	−	0.869542i	−0.993968	+	0.109668i	$0.965021\pi$
$642$	5.64188	+	17.3639i	0.222667	+	0.685299i
$643$	−33.8632			−1.33543			−0.667717	−	0.744415i	$-0.732728\pi$
$643$	−33.8632			−1.33543			−0.667717	+	0.744415i	$0.732728\pi$
$644$	−5.95743	−	18.3351i	−0.234755	−	0.722503i
$645$	8.35679	+	13.4706i	0.329048	+	0.530402i
$646$	0.0574062	−	0.176678i	0.00225862	−	0.00695131i
$647$	−2.80429	+	8.63073i	−0.110248	+	0.339309i	−0.990926	−	0.134406i	$-0.957087\pi$
$647$	−2.80429	+	8.63073i	−0.110248	+	0.339309i	0.880678	+	0.473715i	$0.157087\pi$
$648$	0.680596	−	0.494482i	0.0267363	−	0.0194251i
$649$	6.02423			0.236472
$650$	−0.230270	−	1.35728i	−0.00903192	−	0.0532368i
$651$	30.5221			1.19625
$652$	−6.70669	+	4.87269i	−0.262654	+	0.190829i
$653$	8.31105	−	25.5788i	0.325237	−	1.00098i	−0.646097	−	0.763255i	$-0.723600\pi$
$653$	8.31105	−	25.5788i	0.325237	−	1.00098i	0.971334	−	0.237720i	$-0.0764001\pi$
$654$	−1.45895	+	4.49017i	−0.0570493	+	0.175580i
$655$	34.7237	+	14.1603i	1.35677	+	0.553288i
$656$	−1.55524	−	4.78655i	−0.0607221	−	0.186883i
$657$	−16.6118			−0.648090
$658$	7.15577	+	22.0232i	0.278961	+	0.858553i
$659$	−38.0659	−	27.6565i	−1.48284	−	1.07734i	−0.976628	−	0.214935i	$-0.931046\pi$
$659$	−38.0659	−	27.6565i	−1.48284	−	1.07734i	−0.506210	−	0.862410i	$-0.668954\pi$
$660$	−1.85401	+	2.19505i	−0.0721674	+	0.0854423i
$661$	25.1546	−	18.2759i	0.978401	−	0.710850i	0.0210501	−	0.999778i	$-0.493299\pi$
$661$	25.1546	−	18.2759i	0.978401	−	0.710850i	0.957351	+	0.288929i	$0.0932990\pi$
$662$	−7.93511	−	5.76520i	−0.308407	−	0.224071i
$663$	−0.248179	−	0.180312i	−0.00963846	−	0.00700275i
$664$	1.40332	−	1.01957i	0.0544594	−	0.0395671i
$665$	−1.21886	−	0.497050i	−0.0472654	−	0.0192748i
$666$	10.9091	+	7.92593i	0.422719	+	0.307123i
$667$	−1.83301	−	5.64143i	−0.0709745	−	0.218437i
$668$	−13.9407			−0.539383
$669$	0.984096	+	3.02874i	0.0380474	+	0.117098i
$670$	4.02657	−	0.990096i	0.155560	−	0.0382508i
$671$	0.898916	−	2.76658i	0.0347023	−	0.106803i
$672$	5.19241	−	15.9806i	0.200302	−	0.616465i
$673$	−35.6286	+	25.8857i	−1.37338	+	0.997821i	−0.375918	+	0.926653i	$0.622673\pi$
$673$	−35.6286	+	25.8857i	−1.37338	+	0.997821i	−0.997464	+	0.0711681i	$0.977327\pi$
$674$	−10.5657			−0.406974
$675$	18.3837	+	17.9845i	0.707588	+	0.692223i
$676$	14.3497			0.551913
$677$	18.7237	−	13.6036i	0.719611	−	0.522828i	−0.166649	−	0.986016i	$-0.553295\pi$
$677$	18.7237	−	13.6036i	0.719611	−	0.522828i	0.886260	+	0.463188i	$0.153295\pi$
$678$	1.73378	−	5.33603i	0.0665855	−	0.204929i
$679$	17.4576	−	53.7290i	0.669962	−	2.06193i
$680$	0.478706	−	6.54130i	0.0183576	−	0.250847i
$681$	5.62746	+	17.3195i	0.215645	+	0.663686i
$682$	10.0951			0.386561
$683$	14.1788	+	43.6378i	0.542535	+	1.66975i	0.726779	+	0.686872i	$0.241017\pi$
$683$	14.1788	+	43.6378i	0.542535	+	1.66975i	−0.184243	+	0.982881i	$0.558983\pi$
$684$	0.335925	+	0.244064i	0.0128444	+	0.00933202i
$685$	34.1573	−	8.39897i	1.30509	−	0.320908i
$686$	−11.5632	+	8.40118i	−0.441486	+	0.320758i
$687$	−13.4628	−	9.78127i	−0.513636	−	0.373179i
$688$	−2.96585	−	2.15482i	−0.113072	−	0.0821516i
$689$	−3.09056	+	2.24542i	−0.117741	+	0.0855437i
$690$	12.4890	−	3.07092i	0.475446	−	0.116908i
$691$	−38.9330	−	28.2864i	−1.48108	−	1.07607i	−0.977207	−	0.212289i	$-0.931908\pi$
$691$	−38.9330	−	28.2864i	−1.48108	−	1.07607i	−0.503873	−	0.863778i	$-0.668092\pi$
$692$	5.76887	+	17.7548i	0.219300	+	0.674935i
$693$	6.23815			0.236968
$694$	4.08397	+	12.5692i	0.155025	+	0.477119i
$695$	−0.290780	+	3.97337i	−0.0110299	+	0.150719i
$696$	0.972470	−	2.99296i	0.0368614	−	0.113448i
$697$	−2.86314	+	8.81183i	−0.108449	+	0.333772i
$698$	−3.52468	+	2.56083i	−0.133411	+	0.0969290i
$699$	−14.5466			−0.550202
$700$	−16.4209	−	2.41638i	−0.620653	−	0.0913305i
$701$	−48.7471			−1.84115			−0.920577	−	0.390562i	$-0.872281\pi$
$701$	−48.7471			−1.84115			−0.920577	+	0.390562i	$0.872281\pi$
$702$	−1.14573	+	0.832419i	−0.0432426	+	0.0314176i
$703$	−0.459167	+	1.41317i	−0.0173178	+	0.0532988i
$704$	2.08697	−	6.42304i	0.0786558	−	0.242078i
$705$	18.7515	−	4.61083i	0.706223	−	0.173654i
$706$	−8.29644	−	25.5338i	−0.312241	−	0.960978i
$707$	−44.8223			−1.68572
$708$	1.97356	+	6.07398i	0.0741708	+	0.228274i
$709$	−30.4383	−	22.1147i	−1.14313	−	0.830535i	−0.155581	−	0.987823i	$-0.549725\pi$
$709$	−30.4383	−	22.1147i	−1.14313	−	0.830535i	−0.987553	+	0.157288i	$0.949725\pi$
$710$	23.9494	+	9.76652i	0.898804	+	0.366531i
$711$	−4.43850	+	3.22476i	−0.166457	+	0.120938i
$712$	−17.6255	−	12.8057i	−0.660544	−	0.479913i
$713$	45.6961	+	33.2002i	1.71133	+	1.24336i
$714$	2.39370	−	1.73913i	0.0895821	−	0.0650852i
$715$	−0.463899	+	0.549231i	−0.0173488	+	0.0205401i
$716$	−3.92791	−	2.85380i	−0.146793	−	0.106651i
$717$	−6.09845	−	18.7691i	−0.227751	−	0.700944i
$718$	−24.7634			−0.924163
$719$	−10.4296	−	32.0991i	−0.388959	−	1.19709i	−0.933567	−	0.358403i	$-0.883321\pi$
$719$	−10.4296	−	32.0991i	−0.388959	−	1.19709i	0.544607	−	0.838691i	$-0.316679\pi$
$720$	−2.13309	−	0.869872i	−0.0794956	−	0.0324182i
$721$	2.45743	−	7.56319i	0.0915194	−	0.281668i
$722$	−5.52421	+	17.0018i	−0.205590	+	0.632741i
$723$	21.5020	−	15.6221i	0.799668	−	0.580993i
$724$	−1.70683			−0.0634340
$725$	−5.05248	−	0.743484i	−0.187644	−	0.0276123i
$726$	9.69355			0.359762
$727$	19.2817	−	14.0090i	0.715118	−	0.519563i	−0.169703	−	0.985495i	$-0.554281\pi$
$727$	19.2817	−	14.0090i	0.715118	−	0.519563i	0.884821	+	0.465932i	$0.154281\pi$
$728$	0.790824	−	2.43391i	0.0293099	−	0.0902065i
$729$	4.84072	−	14.8982i	0.179286	−	0.551786i
$730$	9.73427	+	15.6909i	0.360281	+	0.580748i
$731$	2.08554	+	6.41862i	0.0771363	+	0.237401i
$732$	3.08391			0.113985
$733$	−11.3579	−	34.9560i	−0.419514	−	1.29113i	−0.908151	−	0.418643i	$-0.862506\pi$
$733$	−11.3579	−	34.9560i	−0.419514	−	1.29113i	0.488637	−	0.872487i	$-0.337494\pi$
$734$	−12.8160	−	9.31140i	−0.473049	−	0.343690i
$735$	−2.38445	−	3.84357i	−0.0879518	−	0.141772i
$736$	25.1566	−	18.2773i	0.927284	−	0.673711i
$737$	−1.75184	−	1.27279i	−0.0645299	−	0.0468837i
$738$	13.4033	+	9.73810i	0.493384	+	0.358464i
$739$	11.8437	−	8.60496i	0.435678	−	0.316539i	−0.348237	−	0.937406i	$-0.613220\pi$
$739$	11.8437	−	8.60496i	0.435678	−	0.316539i	0.783915	+	0.620868i	$0.213220\pi$
$740$	−1.36749	+	18.6861i	−0.0502700	+	0.686916i
$741$	−0.0489010	−	0.0355286i	−0.00179642	−	0.00130518i
$742$	−11.3859	−	35.0422i	−0.417989	−	1.28644i
$743$	17.2716			0.633633			0.316816	−	0.948487i	$-0.397386\pi$
$743$	17.2716			0.633633			0.316816	+	0.948487i	$0.397386\pi$
$744$	9.26008	+	28.4996i	0.339491	+	1.04485i
$745$	−25.0369	+	29.6423i	−0.917280	+	1.08601i
$746$	−5.69022	+	17.5127i	−0.208334	+	0.641185i
$747$	−0.346590	+	1.06669i	−0.0126810	+	0.0390283i
$748$	−0.989643	+	0.719018i	−0.0361849	+	0.0262899i
$749$	55.0770			2.01247
$750$	2.40723	−	10.8077i	0.0878996	−	0.394641i
$751$	44.8896			1.63804			0.819022	−	0.573762i	$-0.194517\pi$
$751$	44.8896			1.63804			0.819022	+	0.573762i	$0.194517\pi$
$752$	−3.61280	+	2.62486i	−0.131745	+	0.0957187i
$753$	6.89613	−	21.2241i	0.251309	−	0.773449i
$754$	0.0869019	−	0.267456i	0.00316478	−	0.00974019i
$755$	−17.7177	+	20.9768i	−0.644814	+	0.763424i
$756$	5.27624	+	16.2386i	0.191895	+	0.590592i
$757$	−11.6458			−0.423272			−0.211636	−	0.977349i	$-0.567879\pi$
$757$	−11.6458			−0.423272			−0.211636	+	0.977349i	$0.567879\pi$
$758$	−8.44206	−	25.9820i	−0.306630	−	0.943709i
$759$	−5.43357	−	3.94772i	−0.197226	−	0.143293i
$760$	0.0943241	−	1.28889i	0.00342149	−	0.0467531i
$761$	−3.79878	+	2.75997i	−0.137706	+	0.100049i	−0.654505	−	0.756057i	$-0.727123\pi$
$761$	−3.79878	+	2.75997i	−0.137706	+	0.100049i	0.516800	+	0.856106i	$0.327123\pi$
$762$	10.7164	+	7.78595i	0.388216	+	0.282055i
$763$	11.5224	+	8.37152i	0.417139	+	0.303069i
$764$	15.0392	−	10.9266i	0.544099	−	0.395311i
$765$	2.23567	+	3.60375i	0.0808310	+	0.130294i
$766$	−19.6717	−	14.2923i	−0.710766	−	0.516402i
$767$	0.493810	+	1.51979i	0.0178304	+	0.0548765i
$768$	17.7650			0.641039
$769$	9.08054	+	27.9470i	0.327453	+	1.00780i	0.970321	+	0.241819i	$0.0777441\pi$
$769$	9.08054	+	27.9470i	0.327453	+	1.00780i	−0.642869	+	0.765976i	$0.722256\pi$
$770$	−3.65545	−	5.89233i	−0.131733	−	0.212345i
$771$	−1.88946	+

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.762747 + 0.554168i) q^{2} +(-0.324602 + 0.999022i) q^{3} +(-0.343353 + 1.05673i) q^{4} +(-1.44286 + 1.70826i) q^{5} +(-0.306037 - 0.941886i) q^{6} -2.98759 q^{7} +(-0.906403 - 2.78962i) q^{8} +(1.53437 + 1.11479i) q^{9} +(0.153870 - 2.10256i) q^{10} +(-0.890676 + 0.647114i) q^{11} +(-0.944246 - 0.686035i) q^{12} +(-0.236263 - 0.171655i) q^{13} +(2.27877 - 1.65563i) q^{14} +(-1.23824 - 1.99595i) q^{15} +(0.439455 + 0.319283i) q^{16} +(-0.309017 - 0.951057i) q^{17} -1.78812 q^{18} +(-0.0608886 - 0.187396i) q^{19} +(-1.30977 - 2.11125i) q^{20} +(0.969777 - 2.98467i) q^{21} +(0.320751 - 0.987169i) q^{22} +(4.69845 - 3.41362i) q^{23} +3.08111 q^{24} +(-0.836327 - 4.92956i) q^{25} +0.275335 q^{26} +(-4.16121 + 3.02330i) q^{27} +(1.02580 - 3.15708i) q^{28} +(0.315623 - 0.971387i) q^{29} +(2.05056 + 0.836214i) q^{30} +(3.00543 + 9.24977i) q^{31} +5.35423 q^{32} +(-0.357366 - 1.09986i) q^{33} +(0.762747 + 0.554168i) q^{34} +(4.31066 - 5.10359i) q^{35} +(-1.70486 + 1.23866i) q^{36} +(-6.10089 - 4.43255i) q^{37} +(0.150291 + 0.109193i) q^{38} +(0.248179 - 0.180312i) q^{39} +(6.07322 + 2.47665i) q^{40} +(-7.49579 - 5.44601i) q^{41} +(0.914313 + 2.81397i) q^{42} -6.74894 q^{43} +(-0.378010 - 1.16340i) q^{44} +(-4.11823 + 1.01263i) q^{45} +(-1.69201 + 5.20746i) q^{46} +(-2.54046 + 7.81874i) q^{47} +(-0.461618 + 0.335385i) q^{48} +1.92568 q^{49} +(3.36971 + 3.29654i) q^{50} +1.05043 q^{51} +(0.262515 - 0.190728i) q^{52} +(4.04225 - 12.4408i) q^{53} +(1.49854 - 4.61203i) q^{54} +(0.179677 - 2.45520i) q^{55} +(2.70796 + 8.33424i) q^{56} +0.206977 q^{57} +(0.297572 + 0.915831i) q^{58} +(-4.42688 - 3.21631i) q^{59} +(2.53434 - 0.623171i) q^{60} +(-2.13763 + 1.55308i) q^{61} +(-7.41831 - 5.38972i) q^{62} +(-4.58407 - 3.33052i) q^{63} +(-4.96284 + 3.60571i) q^{64} +(0.634125 - 0.155926i) q^{65} +(0.882088 + 0.640874i) q^{66} +(0.607795 + 1.87060i) q^{67} +1.11111 q^{68} +(1.88516 + 5.80192i) q^{69} +(-0.459699 + 6.28158i) q^{70} +(-3.79117 + 11.6680i) q^{71} +(1.71907 - 5.29076i) q^{72} +(-7.08602 + 5.14830i) q^{73} +7.10982 q^{74} +(5.19621 + 0.764635i) q^{75} +0.218933 q^{76} +(2.66097 - 1.93331i) q^{77} +(-0.0893741 + 0.275065i) q^{78} +(-0.893899 + 2.75114i) q^{79} +(-1.17949 + 0.290025i) q^{80} +(0.0886289 + 0.272772i) q^{81} +8.73539 q^{82} +(0.182744 + 0.562427i) q^{83} +(2.82102 + 2.04959i) q^{84} +(2.07052 + 0.844356i) q^{85} +(5.14773 - 3.74005i) q^{86} +(0.867986 + 0.630629i) q^{87} +(2.61251 + 1.89810i) q^{88} +(6.00901 - 4.36580i) q^{89} +(2.58000 - 3.05457i) q^{90} +(0.705856 + 0.512834i) q^{91} +(1.99406 + 6.13708i) q^{92} -10.2163 q^{93} +(-2.39517 - 7.37156i) q^{94} +(0.407975 + 0.166372i) q^{95} +(-1.73800 + 5.34900i) q^{96} +(-5.84338 + 17.9841i) q^{97} +(-1.46881 + 1.06715i) q^{98} -2.08802 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) \) 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Introduction

L-functions

Modular forms

Varieties

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