LMFDB - Embedded newform 425.2.k.c.86.17

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			86.17
Character	$\chi$	$=$	425.86
Dual form			425.2.k.c.341.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.64574 - 1.19570i) q^{2} +(-0.929019 + 2.85923i) q^{3} +(0.660733 - 2.03353i) q^{4} +(-2.22620 - 0.209856i) q^{5} +(1.88986 + 5.81638i) q^{6} -4.33298 q^{7} +(-0.0868601 - 0.267328i) q^{8} +(-4.88505 - 3.54920i) q^{9} +(-3.91468 + 2.31650i) q^{10} +(0.0744152 - 0.0540658i) q^{11} +(5.20048 + 3.77837i) q^{12} +(-1.26366 - 0.918105i) q^{13} +(-7.13098 + 5.18096i) q^{14} +(2.66821 - 6.17025i) q^{15} +(2.99705 + 2.17748i) q^{16} +(-0.309017 - 0.951057i) q^{17} -12.2833 q^{18} +(1.60661 + 4.94462i) q^{19} +(-1.89767 + 4.38837i) q^{20} +(4.02542 - 12.3890i) q^{21} +(0.0578217 - 0.177957i) q^{22} +(-5.47509 + 3.97789i) q^{23} +0.845046 q^{24} +(4.91192 + 0.934364i) q^{25} -3.17745 q^{26} +(7.38966 - 5.36890i) q^{27} +(-2.86294 + 8.81123i) q^{28} +(0.0930244 - 0.286300i) q^{29} +(-2.98659 - 13.3450i) q^{30} +(0.384831 + 1.18439i) q^{31} +8.09816 q^{32} +(0.0854533 + 0.262998i) q^{33} +(-1.64574 - 1.19570i) q^{34} +(9.64608 + 0.909304i) q^{35} +(-10.4451 + 7.58881i) q^{36} +(-2.03935 - 1.48168i) q^{37} +(8.55636 + 6.21656i) q^{38} +(3.79904 - 2.76016i) q^{39} +(0.137267 + 0.613353i) q^{40} +(6.14949 + 4.46787i) q^{41} +(-8.18872 - 25.2023i) q^{42} -9.32601 q^{43} +(-0.0607757 - 0.187048i) q^{44} +(10.1303 + 8.92638i) q^{45} +(-4.25423 + 13.0932i) q^{46} +(-4.16904 + 12.8310i) q^{47} +(-9.01023 + 6.54632i) q^{48} +11.7747 q^{49} +(9.20098 - 4.33547i) q^{50} +3.00637 q^{51} +(-2.70193 + 1.96307i) q^{52} +(2.84999 - 8.77137i) q^{53} +(5.74187 - 17.6717i) q^{54} +(-0.177009 + 0.104745i) q^{55} +(0.376363 + 1.15833i) q^{56} -15.6304 q^{57} +(-0.189235 - 0.582405i) q^{58} +(5.17314 + 3.75850i) q^{59} +(-10.7844 - 9.50276i) q^{60} +(-7.65519 + 5.56182i) q^{61} +(2.04951 + 1.48905i) q^{62} +(21.1668 + 15.3786i) q^{63} +(7.33340 - 5.32803i) q^{64} +(2.62049 + 2.30907i) q^{65} +(0.455102 + 0.330651i) q^{66} +(-1.98116 - 6.09737i) q^{67} -2.13818 q^{68} +(-6.28722 - 19.3501i) q^{69} +(16.9622 - 10.0374i) q^{70} +(2.91831 - 8.98163i) q^{71} +(-0.524483 + 1.61419i) q^{72} +(6.71108 - 4.87588i) q^{73} -5.12789 q^{74} +(-7.23483 + 13.1763i) q^{75} +11.1166 q^{76} +(-0.322440 + 0.234266i) q^{77} +(2.95191 - 9.08504i) q^{78} +(1.61334 - 4.96536i) q^{79} +(-6.21507 - 5.47646i) q^{80} +(2.88800 + 8.88835i) q^{81} +15.4627 q^{82} +(0.00764730 + 0.0235360i) q^{83} +(-22.5336 - 16.3716i) q^{84} +(0.488348 + 2.18209i) q^{85} +(-15.3482 + 11.1511i) q^{86} +(0.732174 + 0.531956i) q^{87} +(-0.0209170 - 0.0151971i) q^{88} +(-8.37401 + 6.08407i) q^{89} +(27.3451 + 2.57773i) q^{90} +(5.47543 + 3.97813i) q^{91} +(4.47157 + 13.7621i) q^{92} -3.74395 q^{93} +(8.48087 + 26.1014i) q^{94} +(-2.53896 - 11.3449i) q^{95} +(-7.52335 + 23.1545i) q^{96} +(0.377116 - 1.16064i) q^{97} +(19.3782 - 14.0791i) q^{98} -0.555412 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 $

$2$	1.64574	−	1.19570i	1.16372	−	0.845489i	0.173473	−	0.984839i	$-0.444501\pi$
$2$	1.64574	−	1.19570i	1.16372	−	0.845489i	0.990243	+	0.139349i	$0.0445010\pi$
$3$	−0.929019	+	2.85923i	−0.536369	+	1.65078i	0.204302	+	0.978908i	$0.434508\pi$
$3$	−0.929019	+	2.85923i	−0.536369	+	1.65078i	−0.740671	+	0.671867i	$0.765492\pi$
$4$	0.660733	−	2.03353i	0.330366	−	1.01676i
$5$	−2.22620	−	0.209856i	−0.995586	−	0.0938506i
$5$	−2.22620	−	0.209856i	−0.995586	−	0.0938506i
$6$	1.88986	+	5.81638i	0.771531	+	2.37453i
$7$	−4.33298			−1.63771			−0.818857	−	0.573998i	$-0.805392\pi$
$7$	−4.33298			−1.63771			−0.818857	+	0.573998i	$0.805392\pi$
$8$	−0.0868601	−	0.267328i	−0.0307097	−	0.0945147i
$9$	−4.88505	−	3.54920i	−1.62835	−	1.18307i
$10$	−3.91468	+	2.31650i	−1.23793	+	0.732542i
$11$	0.0744152	−	0.0540658i	0.0224370	−	0.0163015i	−0.576510	−	0.817090i	$-0.695586\pi$
$11$	0.0744152	−	0.0540658i	0.0224370	−	0.0163015i	0.598947	+	0.800788i	$0.295586\pi$
$12$	5.20048	+	3.77837i	1.50125	+	1.09072i
$13$	−1.26366	−	0.918105i	−0.350477	−	0.254636i	0.398592	−	0.917128i	$-0.369499\pi$
$13$	−1.26366	−	0.918105i	−0.350477	−	0.254636i	−0.749069	+	0.662492i	$0.769499\pi$
$14$	−7.13098	+	5.18096i	−1.90583	+	1.38467i
$15$	2.66821	−	6.17025i	0.688928	−	1.59315i
$16$	2.99705	+	2.17748i	0.749262	+	0.544371i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	−12.2833			−2.89521
$19$	1.60661	+	4.94462i	0.368580	+	1.13437i	0.947708	+	0.319137i	$0.103393\pi$
$19$	1.60661	+	4.94462i	0.368580	+	1.13437i	−0.579128	+	0.815237i	$0.696607\pi$
$20$	−1.89767	+	4.38837i	−0.424332	+	0.981270i
$21$	4.02542	−	12.3890i	0.878419	−	2.70350i
$22$	0.0578217	−	0.177957i	0.0123276	−	0.0379405i
$23$	−5.47509	+	3.97789i	−1.14164	+	0.829447i	−0.987346	−	0.158579i	$-0.949309\pi$
$23$	−5.47509	+	3.97789i	−1.14164	+	0.829447i	−0.154289	+	0.988026i	$0.549309\pi$
$24$	0.845046			0.172494
$25$	4.91192	+	0.934364i	0.982384	+	0.186873i
$26$	−3.17745			−0.623148
$27$	7.38966	−	5.36890i	1.42214	−	1.03325i
$28$	−2.86294	+	8.81123i	−0.541045	+	1.66517i
$29$	0.0930244	−	0.286300i	0.0172742	−	0.0531645i	−0.942048	−	0.335479i	$-0.891102\pi$
$29$	0.0930244	−	0.286300i	0.0172742	−	0.0531645i	0.959322	+	0.282314i	$0.0911020\pi$
$30$	−2.98659	−	13.3450i	−0.545275	−	2.43646i
$31$	0.384831	+	1.18439i	0.0691176	+	0.212722i	0.979649	−	0.200717i	$-0.0643273\pi$
$31$	0.384831	+	1.18439i	0.0691176	+	0.212722i	−0.910532	+	0.413440i	$0.864327\pi$
$32$	8.09816			1.43157
$33$	0.0854533	+	0.262998i	0.0148755	+	0.0457821i
$34$	−1.64574	−	1.19570i	−0.282243	−	0.205061i
$35$	9.64608	+	0.909304i	1.63048	+	0.153700i
$36$	−10.4451	+	7.58881i	−1.74085	+	1.26480i
$37$	−2.03935	−	1.48168i	−0.335267	−	0.243586i	0.407395	−	0.913252i	$-0.366437\pi$
$37$	−2.03935	−	1.48168i	−0.335267	−	0.243586i	−0.742662	+	0.669666i	$0.766437\pi$
$38$	8.55636	+	6.21656i	1.38802	+	1.00846i
$39$	3.79904	−	2.76016i	0.608333	−	0.441980i
$40$	0.137267	+	0.613353i	0.0217039	+	0.0969796i
$41$	6.14949	+	4.46787i	0.960389	+	0.697763i	0.953241	−	0.302211i	$-0.0977247\pi$
$41$	6.14949	+	4.46787i	0.960389	+	0.697763i	0.00714799	+	0.999974i	$0.497725\pi$
$42$	−8.18872	−	25.2023i	−1.26355	−	3.88880i
$43$	−9.32601			−1.42220			−0.711102	−	0.703089i	$-0.751804\pi$
$43$	−9.32601			−1.42220			−0.711102	+	0.703089i	$0.751804\pi$
$44$	−0.0607757	−	0.187048i	−0.00916228	−	0.0281986i
$45$	10.1303	+	8.92638i	1.51013	+	1.33067i
$46$	−4.25423	+	13.0932i	−0.627251	+	1.93048i
$47$	−4.16904	+	12.8310i	−0.608117	+	1.87159i	−0.134364	+	0.990932i	$0.542899\pi$
$47$	−4.16904	+	12.8310i	−0.608117	+	1.87159i	−0.473752	+	0.880658i	$0.657101\pi$
$48$	−9.01023	+	6.54632i	−1.30051	+	0.944879i
$49$	11.7747			1.68210
$50$	9.20098	−	4.33547i	1.30122	−	0.613128i
$51$	3.00637			0.420976
$52$	−2.70193	+	1.96307i	−0.374691	+	0.272229i
$53$	2.84999	−	8.77137i	0.391476	−	1.20484i	−0.540196	−	0.841539i	$-0.681650\pi$
$53$	2.84999	−	8.77137i	0.391476	−	1.20484i	0.931672	−	0.363301i	$-0.118350\pi$
$54$	5.74187	−	17.6717i	0.781370	−	2.40481i
$55$	−0.177009	+	0.104745i	−0.0238679	+	0.0141238i
$56$	0.376363	+	1.15833i	0.0502936	+	0.154788i
$57$	−15.6304			−2.07029
$58$	−0.189235	−	0.582405i	−0.0248478	−	0.0764736i
$59$	5.17314	+	3.75850i	0.673485	+	0.489316i	0.871190	−	0.490946i	$-0.163349\pi$
$59$	5.17314	+	3.75850i	0.673485	+	0.489316i	−0.197705	+	0.980262i	$0.563349\pi$
$60$	−10.7844	−	9.50276i	−1.39226	−	1.22680i
$61$	−7.65519	+	5.56182i	−0.980147	+	0.712118i	−0.957741	−	0.287630i	$-0.907133\pi$
$61$	−7.65519	+	5.56182i	−0.980147	+	0.712118i	−0.0224055	+	0.999749i	$0.507133\pi$
$62$	2.04951	+	1.48905i	0.260288	+	0.189110i
$63$	21.1668	+	15.3786i	2.66677	+	1.93752i
$64$	7.33340	−	5.32803i	0.916676	−	0.666004i
$65$	2.62049	+	2.30907i	0.325032	+	0.286405i
$66$	0.455102	+	0.330651i	0.0560191	+	0.0407003i
$67$	−1.98116	−	6.09737i	−0.242037	−	0.744912i	−0.996110	−	0.0881218i	$-0.971914\pi$
$67$	−1.98116	−	6.09737i	−0.242037	−	0.744912i	0.754073	−	0.656791i	$-0.228086\pi$
$68$	−2.13818			−0.259292
$69$	−6.28722	−	19.3501i	−0.756892	−	2.32947i
$70$	16.9622	−	10.0374i	2.02737	−	1.19969i
$71$	2.91831	−	8.98163i	0.346340	−	1.06592i	−0.614523	−	0.788899i	$-0.710652\pi$
$71$	2.91831	−	8.98163i	0.346340	−	1.06592i	0.960863	−	0.277025i	$-0.0893484\pi$
$72$	−0.524483	+	1.61419i	−0.0618109	+	0.190235i
$73$	6.71108	−	4.87588i	0.785472	−	0.570679i	−0.121144	−	0.992635i	$-0.538656\pi$
$73$	6.71108	−	4.87588i	0.785472	−	0.570679i	0.906616	+	0.421956i	$0.138656\pi$
$74$	−5.12789			−0.596105
$75$	−7.23483	+	13.1763i	−0.835406	+	1.52146i
$76$	11.1166			1.27516
$77$	−0.322440	+	0.234266i	−0.0367454	+	0.0266971i
$78$	2.95191	−	9.08504i	0.334238	−	1.02868i
$79$	1.61334	−	4.96536i	0.181515	−	0.558646i	−0.818356	−	0.574712i	$-0.805114\pi$
$79$	1.61334	−	4.96536i	0.181515	−	0.558646i	0.999871	+	0.0160656i	$0.00511406\pi$
$80$	−6.21507	−	5.47646i	−0.694865	−	0.612287i
$81$	2.88800	+	8.88835i	0.320889	+	0.987594i
$82$	15.4627			1.70757
$83$	0.00764730	+	0.0235360i	0.000839400	+	0.00258341i	0.951475	−	0.307725i	$-0.0995677\pi$
$83$	0.00764730	+	0.0235360i	0.000839400	+	0.00258341i	−0.950636	+	0.310308i	$0.899568\pi$
$84$	−22.5336	−	16.3716i	−2.45862	−	1.78629i
$85$	0.488348	+	2.18209i	0.0529688	+	0.236681i
$86$	−15.3482	+	11.1511i	−1.65504	+	1.20246i
$87$	0.732174	+	0.531956i	0.0784973	+	0.0570316i
$88$	−0.0209170	−	0.0151971i	−0.00222976	−	0.00162002i
$89$	−8.37401	+	6.08407i	−0.887643	+	0.644910i	−0.935262	−	0.353955i	$-0.884837\pi$
$89$	−8.37401	+	6.08407i	−0.887643	+	0.644910i	0.0476193	+	0.998866i	$0.484837\pi$
$90$	27.3451	+	2.57773i	2.88243	+	0.271717i
$91$	5.47543	+	3.97813i	0.573981	+	0.417022i
$92$	4.47157	+	13.7621i	0.466193	+	1.43479i
$93$	−3.74395			−0.388229
$94$	8.48087	+	26.1014i	0.874735	+	2.69216i
$95$	−2.53896	−	11.3449i	−0.260492	−	1.16396i
$96$	−7.52335	+	23.1545i	−0.767849	+	2.36320i
$97$	0.377116	−	1.16064i	0.0382903	−	0.117845i	−0.930084	−	0.367346i	$-0.880266\pi$
$97$	0.377116	−	1.16064i	0.0382903	−	0.117845i	0.968375	+	0.249501i	$0.0802665\pi$
$98$	19.3782	−	14.0791i	1.95749	−	1.42220i
$99$	−0.555412			−0.0558210
$100$	5.14552	−	9.37116i	0.514552	−	0.937116i
$101$	−14.2114			−1.41408			−0.707041	−	0.707172i	$-0.749971\pi$
$101$	−14.2114			−1.41408			−0.707041	+	0.707172i	$0.749971\pi$
$102$	4.94771	−	3.59472i	0.489897	−	0.355931i
$103$	−1.28231	+	3.94653i	−0.126349	+	0.388863i	−0.994145	−	0.108059i	$-0.965537\pi$
$103$	−1.28231	+	3.94653i	−0.126349	+	0.388863i	0.867795	+	0.496922i	$0.165537\pi$
$104$	−0.135673	+	0.417559i	−0.0133038	+	0.0409450i
$105$	−11.5613	+	26.7356i	−1.12827	+	2.60912i
$106$	−5.79759	−	17.8432i	−0.563112	−	1.73308i
$107$	3.92810			0.379744			0.189872	−	0.981809i	$-0.439193\pi$
$107$	3.92810			0.379744			0.189872	+	0.981809i	$0.439193\pi$
$108$	−6.03521	−	18.5745i	−0.580738	−	1.78733i
$109$	−1.39217	−	1.01147i	−0.133346	−	0.0968815i	0.519113	−	0.854706i	$-0.326262\pi$
$109$	−1.39217	−	1.01147i	−0.133346	−	0.0968815i	−0.652459	+	0.757824i	$0.726262\pi$
$110$	−0.166068	+	0.384033i	−0.0158340	+	0.0366161i
$111$	6.13104	−	4.45446i	0.581933	−	0.422799i
$112$	−12.9862	−	9.43499i	−1.22708	−	0.891523i
$113$	8.05325	+	5.85103i	0.757586	+	0.550418i	0.898169	−	0.439651i	$-0.144898\pi$
$113$	8.05325	+	5.85103i	0.757586	+	0.550418i	−0.140583	+	0.990069i	$0.544898\pi$
$114$	−25.7236	+	18.6893i	−2.40923	+	1.75041i
$115$	13.0234	−	7.70658i	1.21444	−	0.718643i
$116$	−0.520734	−	0.378335i	−0.0483489	−	0.0351275i
$117$	2.91452	+	8.96998i	0.269448	+	0.829275i
$118$	13.0077			1.19746
$119$	1.33897	+	4.12091i	0.122743	+	0.377763i
$120$	−1.88124	−	0.177338i	−0.171733	−	0.0161887i
$121$	−3.39657	+	10.4536i	−0.308779	+	0.950325i
$122$	−5.94820	+	18.3067i	−0.538524	+	1.65741i
$123$	−18.4876	+	13.4321i	−1.66697	+	1.21113i
$124$	2.66275			0.239122
$125$	−10.7388	−	3.11088i	−0.960510	−	0.278245i
$126$	53.2234			4.74152
$127$	−6.64409	+	4.82721i	−0.589568	+	0.428346i	−0.842161	−	0.539227i	$-0.818717\pi$
$127$	−6.64409	+	4.82721i	−0.589568	+	0.428346i	0.252593	+	0.967573i	$0.418717\pi$
$128$	0.693222	−	2.13352i	0.0612728	−	0.188578i
$129$	8.66405	−	26.6652i	0.762827	−	2.34774i
$130$	7.07362	+	0.666807i	0.620398	+	0.0584829i
$131$	−2.59139	−	7.97548i	−0.226411	−	0.696821i	−0.998145	−	0.0608759i	$-0.980611\pi$
$131$	−2.59139	−	7.97548i	−0.226411	−	0.696821i	0.771735	−	0.635945i	$-0.219389\pi$
$132$	0.591275			0.0514639
$133$	−6.96139	−	21.4250i	−0.603629	−	1.85778i
$134$	−10.5511	−	7.66583i	−0.911478	−	0.662227i
$135$	−17.5775	+	10.4015i	−1.51283	+	0.895216i
$136$	−0.227403	+	0.165218i	−0.0194996	+	0.0141673i
$137$	−10.0376	−	7.29275i	−0.857570	−	0.623061i	0.0696526	−	0.997571i	$-0.477811\pi$
$137$	−10.0376	−	7.29275i	−0.857570	−	0.623061i	−0.927223	+	0.374510i	$0.877811\pi$
$138$	−33.4841	−	24.3276i	−2.85035	−	2.07090i
$139$	13.9143	−	10.1093i	1.18019	−	0.857461i	0.188001	−	0.982169i	$-0.439799\pi$
$139$	13.9143	−	10.1093i	1.18019	−	0.857461i	0.992194	+	0.124707i	$0.0397992\pi$
$140$	8.22257	−	19.0147i	0.694934	−	1.60704i
$141$	−32.8136	−	23.8404i	−2.76340	−	2.00773i
$142$	−5.93657	−	18.2709i	−0.498186	−	1.53326i
$143$	−0.143674			−0.0120146
$144$	−6.91242	−	21.2742i	−0.576035	−	1.77285i
$145$	−0.267173	+	0.617838i	−0.0221875	+	0.0513087i
$146$	5.21461	−	16.0489i	0.431564	−	1.32822i
$147$	−10.9390	+	33.6666i	−0.902230	+	2.77678i
$148$	−4.36049	+	3.16808i	−0.358430	+	0.260415i
$149$	−9.79102			−0.802112			−0.401056	−	0.916054i	$-0.631357\pi$
$149$	−9.79102			−0.802112			−0.401056	+	0.916054i	$0.631357\pi$
$150$	3.84821	+	30.3354i	0.314205	+	2.47688i
$151$	−11.2928			−0.918992			−0.459496	−	0.888180i	$-0.651970\pi$
$151$	−11.2928			−0.918992			−0.459496	+	0.888180i	$0.651970\pi$
$152$	1.18229	−	0.858980i	0.0958960	−	0.0696725i
$153$	−1.86592	+	5.74272i	−0.150851	+	0.464272i
$154$	−0.250540	+	0.771084i	−0.0201891	+	0.0621357i
$155$	−0.608158	−	2.71744i	−0.0488485	−	0.218270i
$156$	−3.10271	−	9.54917i	−0.248416	−	0.764546i
$157$	12.7315			1.01609			0.508044	−	0.861331i	$-0.330369\pi$
$157$	12.7315			1.01609			0.508044	+	0.861331i	$0.330369\pi$
$158$	−3.28194	−	10.1008i	−0.261097	−	0.803575i
$159$	22.4316	+	16.2975i	1.77894	+	1.29248i
$160$	−18.0281	−	1.69945i	−1.42525	−	0.134353i
$161$	23.7235	−	17.2361i	1.86967	−	1.35840i
$162$	15.3807	+	11.1747i	1.20842	+	0.877971i
$163$	6.33832	+	4.60506i	0.496455	+	0.360696i	0.807661	−	0.589647i	$-0.200733\pi$
$163$	6.33832	+	4.60506i	0.496455	+	0.360696i	−0.311206	+	0.950342i	$0.600733\pi$
$164$	13.1487	−	9.55309i	1.02674	−	0.745971i
$165$	−0.135044	−	0.603419i	−0.0105132	−	0.0469761i
$166$	0.0407275	+	0.0295903i	0.00316107	+	0.00229665i
$167$	7.32183	+	22.5343i	0.566580	+	1.74375i	0.663210	+	0.748433i	$0.269194\pi$
$167$	7.32183	+	22.5343i	0.566580	+	1.74375i	−0.0966301	+	0.995320i	$0.530806\pi$
$168$	−3.66157			−0.282496
$169$	−3.26329	−	10.0434i	−0.251023	−	0.772568i
$170$	3.41283	+	3.00724i	0.261752	+	0.230645i
$171$	9.70109	−	29.8569i	0.741861	−	2.28321i
$172$	−6.16200	+	18.9647i	−0.469848	+	1.44604i
$173$	−15.6873	+	11.3975i	−1.19269	+	0.866537i	−0.993546	−	0.113434i	$-0.963815\pi$
$173$	−15.6873	+	11.3975i	−1.19269	+	0.866537i	−0.199140	+	0.979971i	$0.563815\pi$
$174$	1.84103			0.139568
$175$	−21.2833	−	4.04858i	−1.60886	−	0.306044i
$176$	0.340753			0.0256852
$177$	−15.5524	+	11.2994i	−1.16899	+	0.849319i
$178$	−6.50673	+	20.0256i	−0.487700	+	1.50099i
$179$	−6.97450	+	21.4653i	−0.521298	+	1.60439i	0.250223	+	0.968188i	$0.419496\pi$
$179$	−6.97450	+	21.4653i	−0.521298	+	1.60439i	−0.771521	+	0.636203i	$0.780504\pi$
$180$	24.8454	−	14.7022i	1.85187	−	1.09584i
$181$	5.26809	+	16.2135i	0.391574	+	1.20514i	0.931598	+	0.363491i	$0.118415\pi$
$181$	5.26809	+	16.2135i	0.391574	+	1.20514i	−0.540023	+	0.841650i	$0.681585\pi$
$182$	13.7678			1.02054
$183$	−8.79069	−	27.0550i	−0.649827	−	1.99996i
$184$	1.53897	+	1.11812i	0.113454	+	0.0824292i
$185$	4.22906	+	3.72647i	0.310927	+	0.273976i
$186$	−6.16158	+	4.47665i	−0.451789	+	0.328244i
$187$	−0.0744152	−	0.0540658i	−0.00544178	−	0.00395368i
$188$	23.3375	+	16.9557i	1.70206	+	1.23662i
$189$	−32.0192	+	23.2633i	−2.32906	+	1.69216i
$190$	−17.7436	−	15.6349i	−1.28725	−	1.13427i
$191$	15.2065	+	11.0482i	1.10031	+	0.799419i	0.981110	−	0.193451i	$-0.0619681\pi$
$191$	15.2065	+	11.0482i	1.10031	+	0.799419i	0.119197	+	0.992871i	$0.461968\pi$
$192$	8.42117	+	25.9177i	0.607746	+	1.87045i
$193$	24.3411			1.75211			0.876055	−	0.482211i	$-0.160166\pi$
$193$	24.3411			1.75211			0.876055	+	0.482211i	$0.160166\pi$
$194$	−0.767148	−	2.36104i	−0.0550780	−	0.169513i
$195$	−9.03665	+	5.34742i	−0.647128	+	0.382936i
$196$	7.77995	−	23.9442i	0.555711	−	1.71030i
$197$	−4.97681	+	15.3170i	−0.354583	+	1.09129i	0.601668	+	0.798746i	$0.294503\pi$
$197$	−4.97681	+	15.3170i	−0.354583	+	1.09129i	−0.956251	+	0.292548i	$0.905497\pi$
$198$	−0.914066	+	0.664108i	−0.0649599	+	0.0471961i
$199$	13.0210			0.923032			0.461516	−	0.887132i	$-0.347306\pi$
$199$	13.0210			0.923032			0.461516	+	0.887132i	$0.347306\pi$
$200$	−0.176868	−	1.39425i	−0.0125065	−	0.0985885i
$201$	19.2743			1.35950
$202$	−23.3882	+	16.9926i	−1.64559	+	1.19559i
$203$	−0.403073	+	1.24053i	−0.0282902	+	0.0870682i
$204$	1.98641	−	6.11353i	0.139076	−	0.428033i
$205$	−12.7524	−	11.2369i	−0.890665	−	0.784817i
$206$	2.60853	+	8.02824i	0.181745	+	0.559354i
$207$	40.8644			2.84027
$208$	−1.78810	−	5.50321i	−0.123982	−	0.381579i
$209$	0.386891	+	0.281093i	0.0267618	+	0.0194436i
$210$	12.9409	+	57.8238i	0.893004	+	3.99022i
$211$	6.51974	−	4.73687i	0.448838	−	0.326100i	−0.340299	−	0.940317i	$-0.610528\pi$
$211$	6.51974	−	4.73687i	0.448838	−	0.326100i	0.789137	+	0.614218i	$0.210528\pi$
$212$	−15.9537	−	11.5911i	−1.09571	−	0.796077i
$213$	22.9694	+	16.6882i	1.57383	+	1.14346i
$214$	6.46465	−	4.69684i	0.441914	−	0.321069i
$215$	20.7616	+	1.95712i	1.41593	+	0.133475i
$216$	−2.07712	−	1.50912i	−0.141330	−	0.102682i
$217$	−1.66746	−	5.13193i	−0.113195	−	0.348378i
$218$	−3.50058			−0.237089
$219$	7.70654	+	23.7183i	0.520760	+	1.60273i
$220$	0.0960455	+	0.429161i	0.00647538	+	0.0289340i
$221$	−0.482676	+	1.48552i	−0.0324683	+	0.0999272i
$222$	4.76391	−	14.6618i	0.319733	−	0.984036i
$223$	6.41470	−	4.66055i	0.429560	−	0.312094i	−0.351913	−	0.936033i	$-0.614469\pi$
$223$	6.41470	−	4.66055i	0.429560	−	0.312094i	0.781473	+	0.623939i	$0.214469\pi$
$224$	−35.0892			−2.34450
$225$	−20.6787	−	21.9978i	−1.37858	−	1.46652i
$226$	20.2497			1.34699
$227$	−18.8413	+	13.6890i	−1.25054	+	0.908571i	−0.998253	−	0.0590815i	$-0.981183\pi$
$227$	−18.8413	+	13.6890i	−1.25054	+	0.908571i	−0.252287	+	0.967652i	$0.581183\pi$
$228$	−10.3275	+	31.7848i	−0.683955	+	2.10500i
$229$	3.45877	−	10.6450i	0.228562	−	0.703441i	−0.769349	−	0.638829i	$-0.779419\pi$
$229$	3.45877	−	10.6450i	0.228562	−	0.703441i	0.997910	−	0.0646120i	$-0.0205810\pi$
$230$	12.2184	−	28.2552i	0.805660	−	1.86309i
$231$	−0.370267	−	1.13957i	−0.0243618	−	0.0749779i
$232$	−0.0846160			−0.00555531
$233$	1.34607	+	4.14277i	0.0881838	+	0.271402i	0.985417	−	0.170154i	$-0.0544266\pi$
$233$	1.34607	+	4.14277i	0.0881838	+	0.271402i	−0.897234	+	0.441556i	$0.854427\pi$
$234$	15.5220	+	11.2774i	1.01470	+	0.737225i
$235$	11.9738	−	27.6894i	0.781082	−	1.80626i
$236$	11.0611	−	8.03634i	0.720015	−	0.523121i
$237$	12.6983	+	9.22583i	0.824841	+	0.599282i
$238$	7.13098	+	5.18096i	0.462233	+	0.335832i
$239$	12.9515	−	9.40983i	0.837764	−	0.608671i	−0.0839809	−	0.996467i	$-0.526763\pi$
$239$	12.9515	−	9.40983i	0.837764	−	0.608671i	0.921745	+	0.387796i	$0.126763\pi$
$240$	21.4324	−	12.6825i	1.38345	−	0.818655i
$241$	−2.25100	−	1.63545i	−0.145000	−	0.105349i	0.512920	−	0.858436i	$-0.328564\pi$
$241$	−2.25100	−	1.63545i	−0.145000	−	0.105349i	−0.657920	+	0.753088i	$0.728564\pi$
$242$	6.90948	+	21.2652i	0.444158	+	1.36698i
$243$	−0.694453			−0.0445492
$244$	6.25208	+	19.2419i	0.400248	+	1.23184i
$245$	−26.2129	−	2.47100i	−1.67468	−	0.157867i
$246$	−14.3652	+	44.2114i	−0.915890	+	2.81882i
$247$	2.50947	−	7.72337i	0.159674	−	0.491426i
$248$	0.283193	−	0.205752i	0.0179828	−	0.0130653i
$249$	−0.0743992			−0.00471486
$250$	−21.3930	+	7.72074i	−1.35301	+	0.488302i
$251$	−14.8473			−0.937156			−0.468578	−	0.883422i	$-0.655233\pi$
$251$	−14.8473			−0.937156			−0.468578	+	0.883422i	$0.655233\pi$
$252$	45.2584	−	32.8822i	2.85101	−	2.07138i
$253$	−0.192362	+	0.592031i	−0.0120937	+	0.0372206i
$254$	−5.16255	+	15.8887i	−0.323928	+	0.996946i
$255$	−6.69277	−	0.630906i	−0.419118	−	0.0395089i
$256$	4.19203	+	12.9018i	0.262002	+	0.806360i
$257$	6.73046			0.419835			0.209917	−	0.977719i	$-0.432681\pi$
$257$	6.73046			0.419835			0.209917	+	0.977719i	$0.432681\pi$
$258$	−17.6248	−	54.2437i	−1.09727	−	3.37706i
$259$	8.83647	+	6.42007i	0.549072	+	0.398924i
$260$	6.42700	−	3.80317i	0.398586	−	0.235862i
$261$	−1.47056	+	1.06843i	−0.0910256	+	0.0661339i
$262$	−13.8011	−	10.0271i	−0.852632	−	0.619474i
$263$	16.5176	+	12.0007i	1.01852	+	0.739996i	0.965978	−	0.258623i	$-0.0832686\pi$
$263$	16.5176	+	12.0007i	1.01852	+	0.739996i	0.0525390	+	0.998619i	$0.483269\pi$
$264$	0.0628842	−	0.0456881i	0.00387026	−	0.00281191i
$265$	−8.18537	+	18.9287i	−0.502823	+	1.16278i
$266$	−37.0745	−	26.9362i	−2.27319	−	1.65157i
$267$	−9.61613	−	29.5954i	−0.588498	−	1.81121i
$268$	−13.7082			−0.837360
$269$	−0.438931	−	1.35089i	−0.0267621	−	0.0823653i	0.936783	−	0.349910i	$-0.113788\pi$
$269$	−0.438931	−	1.35089i	−0.0267621	−	0.0823653i	−0.963546	+	0.267545i	$0.913788\pi$
$270$	−16.4911	+	38.1357i	−1.00361	+	2.32086i
$271$	5.21034	−	16.0358i	0.316506	−	0.974104i	−0.658625	−	0.752472i	$-0.728861\pi$
$271$	5.21034	−	16.0358i	0.316506	−	0.974104i	0.975130	−	0.221633i	$-0.0711386\pi$
$272$	1.14477	−	3.52324i	0.0694119	−	0.213628i
$273$	−16.4612	+	11.9597i	−0.996275	+	0.723836i
$274$	−25.2393			−1.52476
$275$	0.416039	−	0.196036i	0.0250881	−	0.0118214i
$276$	−43.5030			−2.61857
$277$	−1.23197	+	0.895080i	−0.0740220	+	0.0537801i	−0.624181	−	0.781280i	$-0.714567\pi$
$277$	−1.23197	+	0.895080i	−0.0740220	+	0.0537801i	0.550159	+	0.835060i	$0.314567\pi$
$278$	10.8116	−	33.2747i	0.648437	−	1.99568i
$279$	2.32371	−	7.15163i	0.139117	−	0.428157i
$280$	−0.594777	−	2.65765i	−0.0355447	−	0.158825i
$281$	3.82528	+	11.7730i	0.228197	+	0.702319i	0.997951	+	0.0639781i	$0.0203788\pi$
$281$	3.82528	+	11.7730i	0.228197	+	0.702319i	−0.769754	+	0.638340i	$0.779621\pi$
$282$	−82.5088			−4.91333
$283$	2.28009	+	7.01741i	0.135538	+	0.417142i	0.995673	−	0.0929237i	$-0.0296213\pi$
$283$	2.28009	+	7.01741i	0.135538	+	0.417142i	−0.860136	+	0.510065i	$0.829621\pi$
$284$	−16.3362	−	11.8689i	−0.969373	−	0.704291i
$285$	34.7963	+	3.28013i	2.06115	+	0.194298i
$286$	−0.236450	+	0.171791i	−0.0139816	+	0.0101582i
$287$	−26.6456	−	19.3592i	−1.57284	−	1.14274i
$288$	−39.5599	−	28.7420i	−2.33109	−	1.69364i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	0.299053	+	1.33626i	0.0175610	+	0.0784680i
$291$	2.96820	+	2.15652i	0.173999	+	0.126417i
$292$	−5.48101	−	16.8688i	−0.320752	−	0.987173i
$293$	5.13328			0.299890			0.149945	−	0.988694i	$-0.452090\pi$
$293$	5.13328			0.299890			0.149945	+	0.988694i	$0.452090\pi$
$294$	22.2526	+	68.4864i	1.29780	+	3.99421i
$295$	−10.7277	−	9.45279i	−0.624590	−	0.550363i
$296$	−0.218955	+	0.673874i	−0.0127265	+	0.0391681i
$297$	0.259629	−	0.799055i	0.0150652	−	0.0463659i
$298$	−16.1135	+	11.7071i	−0.933430	+	0.678177i
$299$	10.5708			0.611324
$300$	22.0140	+	23.4182i	1.27098	+	1.35205i
$301$	40.4095			2.32916
$302$	−18.5850	+	13.5028i	−1.06945	+	0.776998i
$303$	13.2026	−	40.6335i	0.758471	−	2.33433i
$304$	−5.95176	+	18.3176i	−0.341357	+	1.05059i
$305$	18.2092	−	10.7752i	1.04265	−	0.616988i
$306$	3.79576	+	11.6821i	0.216989	+	0.667823i
$307$	−8.48549			−0.484293			−0.242146	−	0.970240i	$-0.577851\pi$
$307$	−8.48549			−0.484293			−0.242146	+	0.970240i	$0.577851\pi$
$308$	0.263340	+	0.810477i	0.0150052	+	0.0461812i
$309$	−10.0927	−	7.33281i	−0.574156	−	0.417149i
$310$	−4.25012	−	3.74503i	−0.241391	−	0.212704i
$311$	−24.6160	+	17.8846i	−1.39585	+	1.01414i	−0.400651	+	0.916231i	$0.631216\pi$
$311$	−24.6160	+	17.8846i	−1.39585	+	1.01414i	−0.995195	+	0.0979105i	$0.968784\pi$
$312$	−1.06785	−	0.775840i	−0.0604553	−	0.0439233i
$313$	−6.88374	−	5.00133i	−0.389092	−	0.282692i	0.375991	−	0.926623i	$-0.377302\pi$
$313$	−6.88374	−	5.00133i	−0.389092	−	0.282692i	−0.765083	+	0.643931i	$0.777302\pi$
$314$	20.9528	−	15.2231i	1.18244	−	0.859091i
$315$	−43.8943	−	38.6778i	−2.47316	−	2.17925i
$316$	−9.03120	−	6.56155i	−0.508045	−	0.369116i
$317$	−2.97777	−	9.16464i	−0.167248	−	0.514737i	0.831947	−	0.554856i	$-0.187226\pi$
$317$	−2.97777	−	9.16464i	−0.167248	−	0.514737i	−0.999195	+	0.0401184i	$0.987226\pi$
$318$	56.4037			3.16296
$319$	−0.00855659	−	0.0263345i	−0.000479077	−	0.00147445i
$320$	−17.4437	+	10.3223i	−0.975134	+	0.577034i
$321$	−3.64928	+	11.2313i	−0.203683	+	0.626872i
$322$	18.4335	−	56.7324i	1.02726	−	3.16158i
$323$	4.20615	−	3.05594i	0.234036	−	0.170037i
$324$	19.9829			1.11016
$325$	−5.34917	−	5.69038i	−0.296718	−	0.315645i
$326$	15.9375			0.882698
$327$	4.18538	−	3.04086i	0.231452	−	0.168160i
$328$	0.660240	−	2.03201i	0.0364556	−	0.112199i
$329$	18.0644	−	55.5964i	0.995920	−	3.06513i
$330$	−0.943758	−	0.831600i	−0.0519521	−	0.0457781i
$331$	1.30469	+	4.01543i	0.0717124	+	0.220708i	0.980489	−	0.196576i	$-0.0629821\pi$
$331$	1.30469	+	4.01543i	0.0717124	+	0.220708i	−0.908776	+	0.417284i	$0.862982\pi$
$332$	0.0529138			0.00290402
$333$	4.70358	+	14.4761i	0.257754	+	0.793286i
$334$	38.9941	+	28.3309i	2.13366	+	1.55020i
$335$	3.13087	+	13.9897i	0.171058	+	0.764340i
$336$	39.0412	−	28.3651i	2.12987	−	1.54744i
$337$	−0.0969916	−	0.0704685i	−0.00528347	−	0.00383866i	0.585140	−	0.810932i	$-0.301039\pi$
$337$	−0.0969916	−	0.0704685i	−0.00528347	−	0.00383866i	−0.590424	+	0.807093i	$0.701039\pi$
$338$	−17.3794	−	12.6269i	−0.945317	−	0.686813i
$339$	−24.2110	+	17.5903i	−1.31496	+	0.955376i
$340$	4.76000	+	0.448710i	0.258148	+	0.0243347i
$341$	0.0926721	+	0.0673302i	0.00501848	+	0.00364614i
$342$	−19.7345	−	60.7364i	−1.06712	−	3.28425i
$343$	−20.6888			−1.11709
$344$	0.810058	+	2.49310i	0.0436754	+	0.134419i
$345$	9.93586	+	44.3965i	0.534929	+	2.39023i
$346$	−12.1893	+	37.5148i	−0.655300	+	2.01681i
$347$	4.27666	−	13.1622i	0.229583	−	0.706585i	−0.768211	−	0.640197i	$-0.778853\pi$
$347$	4.27666	−	13.1622i	0.229583	−	0.706585i	0.997794	−	0.0663876i	$-0.0211474\pi$
$348$	1.56552	−	1.13742i	0.0839205	−	0.0609718i
$349$	10.0766			0.539388			0.269694	−	0.962946i	$-0.413077\pi$
$349$	10.0766			0.539388			0.269694	+	0.962946i	$0.413077\pi$
$350$	−39.8677	+	18.7855i	−2.13102	+	1.00413i
$351$	−14.2672			−0.761529
$352$	0.602627	−	0.437834i	0.0321201	−	0.0233366i
$353$	−6.47601	+	19.9311i	−0.344683	+	1.06083i	0.617070	+	0.786908i	$0.288320\pi$
$353$	−6.47601	+	19.9311i	−0.344683	+	1.06083i	−0.961753	+	0.273918i	$0.911680\pi$
$354$	−12.0844	+	37.1920i	−0.642279	+	1.97673i
$355$	−8.38159	+	19.3825i	−0.444849	+	1.02871i
$356$	6.83914	+	21.0487i	0.362474	+	1.11558i
$357$	−13.0265			−0.689438
$358$	14.1879	+	43.6658i	0.749853	+	2.30781i
$359$	−13.9534	−	10.1377i	−0.736433	−	0.535050i	0.155159	−	0.987889i	$-0.450411\pi$
$359$	−13.9534	−	10.1377i	−0.736433	−	0.535050i	−0.891592	+	0.452840i	$0.850411\pi$
$360$	1.50635	−	3.48345i	0.0793918	−	0.183594i
$361$	−6.49678	+	4.72019i	−0.341936	+	0.248431i
$362$	28.0565	+	20.3842i	1.47462	+	1.07137i
$363$	−26.7337	−	19.4231i	−1.40315	−	1.01945i
$364$	11.7074	−	8.50595i	0.613636	−	0.445833i
$365$	−15.9634	+	9.44632i	−0.835564	+	0.494443i
$366$	−46.8169	−	34.0145i	−2.44716	−	1.77797i
$367$	−1.77812	−	5.47250i	−0.0928173	−	0.285662i	0.893861	−	0.448343i	$-0.147986\pi$
$367$	−1.77812	−	5.47250i	−0.0928173	−	0.285662i	−0.986679	+	0.162681i	$0.947986\pi$
$368$	−25.0709			−1.30691
$369$	−14.1832	−	43.6515i	−0.738350	−	2.27241i
$370$	11.4157	+	1.07612i	0.593474	+	0.0559449i
$371$	−12.3490	+	38.0062i	−0.641126	+	1.97318i
$372$	−2.47375	+	7.61342i	−0.128258	+	0.394737i
$373$	2.16697	−	1.57440i	0.112202	−	0.0815192i	−0.530270	−	0.847829i	$-0.677909\pi$
$373$	2.16697	−	1.57440i	0.112202	−	0.0815192i	0.642471	+	0.766310i	$0.277909\pi$
$374$	−0.187115			−0.00967548
$375$	18.8713	−	27.8147i	0.974509	−	1.43634i
$376$	3.79220			0.195568
$377$	−0.380405	+	0.276380i	−0.0195918	+	0.0142343i
$378$	−24.8794	+	76.5710i	−1.27966	+	3.93839i
$379$	9.80453	−	30.1752i	0.503625	−	1.55000i	−0.299446	−	0.954113i	$-0.596802\pi$
$379$	9.80453	−	30.1752i	0.503625	−	1.55000i	0.803070	−	0.595884i	$-0.203198\pi$
$380$	−24.7477	−	2.33288i	−1.26953	−	0.119674i
$381$	−7.62961	−	23.4815i	−0.390877	−	1.20300i
$382$	38.2364			1.95635
$383$	−5.07572	−	15.6215i	−0.259357	−	0.798219i	−0.992940	−	0.118619i	$-0.962153\pi$
$383$	−5.07572	−	15.6215i	−0.259357	−	0.798219i	0.733583	−	0.679600i	$-0.237847\pi$
$384$	5.45620	+	3.96416i	0.278435	+	0.202295i
$385$	0.766977	−	0.453857i	0.0390888	−	0.0231307i
$386$	40.0592	−	29.1047i	2.03896	−	1.48139i
$387$	45.5581	+	33.0999i	2.31585	+	1.68256i
$388$	−2.11103	−	1.53375i	−0.107171	−	0.0778644i
$389$	−18.7351	+	13.6119i	−0.949908	+	0.690149i	−0.950785	−	0.309851i	$-0.899721\pi$
$389$	−18.7351	+	13.6119i	−0.949908	+	0.690149i	0.000877159		1.00000i	$0.499721\pi$
$390$	−8.47809	+	19.6056i	−0.429305	+	0.992769i
$391$	5.47509	+	3.97789i	0.276887	+	0.201170i
$392$	−1.02275	−	3.14771i	−0.0516569	−	0.158984i
$393$	25.2111			1.27173
$394$	10.1241	+	31.1587i	0.510043	+	1.56975i
$395$	−4.63363	+	10.7153i	−0.233143	+	0.539145i
$396$	−0.366979	+	1.12945i	−0.0184414	+	0.0567568i
$397$	5.51208	−	16.9644i	0.276643	−	0.851420i	−0.712137	−	0.702041i	$-0.752272\pi$
$397$	5.51208	−	16.9644i	0.276643	−	0.851420i	0.988780	−	0.149379i	$-0.0477276\pi$
$398$	21.4292	−	15.5692i	1.07415	−	0.780414i
$399$	67.7261			3.39054
$400$	12.6867	+	13.4960i	0.634335	+	0.674798i
$401$	−23.6775			−1.18240			−0.591200	−	0.806525i	$-0.701346\pi$
$401$	−23.6775			−1.18240			−0.591200	+	0.806525i	$0.701346\pi$
$402$	31.7205	−	23.0463i	1.58208	−	1.14945i
$403$	0.601095	−	1.84998i	0.0299427	−	0.0921541i
$404$	−9.38991	+	28.8992i	−0.467165	+	1.43779i
$405$	−4.56398	−	20.3933i	−0.226786	−	1.01335i
$406$	0.819952	+	2.52355i	0.0406935	+	0.125242i
$407$	−0.231867			−0.0114932
$408$	−0.261133	−	0.803686i	−0.0129280	−	0.0397884i
$409$	−17.4290	−	12.6629i	−0.861810	−	0.626141i	0.0665671	−	0.997782i	$-0.478795\pi$
$409$	−17.4290	−	12.6629i	−0.861810	−	0.626141i	−0.928377	+	0.371641i	$0.878795\pi$
$410$	−34.4231	−	3.24495i	−1.70004	−	0.160257i
$411$	30.1767	−	21.9247i	1.48851	−	1.08146i
$412$	7.17812	+	5.21521i	0.353640	+	0.256935i
$413$	−22.4151	−	16.2855i	−1.10298	−	0.801359i
$414$	67.2523	−	48.8617i	3.30527	−	2.40142i
$415$	−0.0120852	−	0.0540006i	−0.000593241	−	0.00265078i
$416$	−10.2333	−	7.43496i	−0.501731	−	0.364529i
$417$	15.9782	+	49.1759i	0.782456	+	2.40815i
$418$	0.972826			0.0475825
$419$	4.48199	+	13.7942i	0.218960	+	0.673889i	0.998849	+	0.0479708i	$0.0152754\pi$
$419$	4.48199	+	13.7942i	0.218960	+	0.673889i	−0.779889	+	0.625918i	$0.784725\pi$
$420$	46.7286	+	41.1753i	2.28012	+	2.00915i
$421$	−5.29582	+	16.2989i	−0.258103	+	0.794358i	0.735100	+	0.677959i	$0.237135\pi$
$421$	−5.29582	+	16.2989i	−0.258103	+	0.794358i	−0.993202	+	0.116399i	$0.962865\pi$
$422$	5.06594	−	15.5914i	0.246606	−	0.758975i
$423$	65.9056	−	47.8832i	3.20444	−	2.32816i
$424$	−2.59238			−0.125897
$425$	−0.629234	−	4.96025i	−0.0305223	−	0.240607i
$426$	57.7558			2.79828
$427$	33.1698	−	24.0993i	1.60520	−	1.16625i
$428$	2.59543	−	7.98790i	0.125455	−	0.386110i
$429$	0.133476	−	0.410796i	0.00644427	−	0.0198334i
$430$	36.5083	−	21.6037i	1.76059	−	1.04182i
$431$	6.54865	+	20.1547i	0.315437	+	0.970816i	0.975574	+	0.219671i	$0.0704984\pi$
$431$	6.54865	+	20.1547i	0.315437	+	0.970816i	−0.660137	+	0.751146i	$0.729502\pi$
$432$	33.8378			1.62802
$433$	0.627957	+	1.93265i	0.0301777	+	0.0928773i	0.965011	−	0.262210i	$-0.0844512\pi$
$433$	0.627957	+	1.93265i	0.0301777	+	0.0928773i	−0.934833	+	0.355087i	$0.884451\pi$
$434$	−8.88048	−	6.45205i	−0.426277	−	0.309708i
$435$	−1.51833	−	1.33789i	−0.0727984	−	0.0641469i
$436$	−2.97671	+	2.16271i	−0.142559	+	0.103575i
$437$	−28.4655	−	20.6814i	−1.36169	−	0.989324i
$438$	41.0430	+	29.8195i	1.96111	+	1.42483i
$439$	−0.693910	+	0.504155i	−0.0331185	+	0.0240620i	−0.604221	−	0.796817i	$-0.706516\pi$
$439$	−0.693910	+	0.504155i	−0.0331185	+	0.0240620i	0.571103	+	0.820879i	$0.306516\pi$
$440$	0.0433762	+	0.0382213i	0.00206788	+	0.00182213i
$441$	−57.5202	−	41.7909i	−2.73906	−	1.99004i
$442$	0.981885	+	3.02193i	0.0467035	+	0.143739i
$443$	16.4642			0.782236			0.391118	−	0.920341i	$-0.372088\pi$
$443$	16.4642			0.782236			0.391118	+	0.920341i	$0.372088\pi$
$444$	−5.00729	−	15.4108i	−0.237635	−	0.731366i
$445$	19.9190	−	11.7870i	0.944251	−	0.558758i
$446$	4.98431	−	15.3401i	0.236014	−	0.726377i
$447$	9.09605	−	27.9947i	0.430228	−	1.32411i
$448$	−31.7755	+	23.0863i	−1.50125	+	1.09072i
$449$	−12.6554			−0.597244			−0.298622	−	0.954372i	$-0.596527\pi$
$449$	−12.6554			−0.597244			−0.298622	+	0.954372i	$0.596527\pi$
$450$	−60.3347	−	11.4771i	−2.84421	−	0.541036i
$451$	0.699174			0.0329228
$452$	17.2193	−	12.5105i	0.809926	−	0.588446i
$453$	10.4912	−	32.2886i	0.492919	−	1.51705i
$454$	−14.6400	+	45.0572i	−0.687087	+	2.11464i
$455$	−11.3546	−	10.0052i	−0.532310	−	0.469049i
$456$	1.35765	+	4.17843i	0.0635780	+	0.195673i
$457$	30.1799			1.41176			0.705878	−	0.708334i	$-0.250553\pi$
$457$	30.1799			1.41176			0.705878	+	0.708334i	$0.250553\pi$
$458$	−7.03600	−	21.6546i	−0.328771	−	1.01185i
$459$	−7.38966	−	5.36890i	−0.344920	−	0.250599i
$460$	−7.06654	−	31.5755i	−0.329479	−	1.47221i
$461$	3.79337	−	2.75605i	0.176675	−	0.128362i	−0.495933	−	0.868361i	$-0.665174\pi$
$461$	3.79337	−	2.75605i	0.176675	−	0.128362i	0.672608	+	0.739999i	$0.265174\pi$
$462$	−1.97195	−	1.43270i	−0.0917433	−	0.0666554i
$463$	11.1203	+	8.07936i	0.516804	+	0.375480i	0.815398	−	0.578900i	$-0.196518\pi$
$463$	11.1203	+	8.07936i	0.516804	+	0.375480i	−0.298595	+	0.954380i	$0.596518\pi$
$464$	0.902211	−	0.655495i	0.0418841	−	0.0304306i
$465$	8.33477	+	0.785691i	0.386516	+	0.0364356i
$466$	7.16880	+	5.20844i	0.332088	+	0.241276i
$467$	−1.19833	−	3.68807i	−0.0554519	−	0.170663i	0.919495	−	0.393102i	$-0.128598\pi$
$467$	−1.19833	−	3.68807i	−0.0554519	−	0.170663i	−0.974947	+	0.222439i	$0.928598\pi$
$468$	20.1664			0.932193
$469$	8.58431	+	26.4198i	0.396387	+	1.21995i
$470$	−13.4025	−	59.8867i	−0.618213	−	2.76237i
$471$	−11.8278	+	36.4023i	−0.544998	+	1.67733i
$472$	0.555414	−	1.70939i	0.0255650	−	0.0786809i
$473$	−0.693997	+	0.504219i	−0.0319100	+	0.0231840i
$474$	31.9294			1.46657
$475$	3.27144	+	25.7887i	0.150104	+	1.18327i
$476$	9.26468			0.424646
$477$	−45.0537	+	32.7334i	−2.06287	+	1.49876i
$478$	10.0635	−	30.9723i	0.460295	−	1.41664i
$479$	5.78721	−	17.8112i	0.264424	−	0.813814i	−0.727401	−	0.686212i	$-0.759272\pi$
$479$	5.78721	−	17.8112i	0.264424	−	0.813814i	0.991825	−	0.127602i	$-0.0407280\pi$
$480$	21.6076	−	49.9677i	0.986247	−	2.28070i
$481$	1.21672	+	3.74468i	0.0554776	+	0.170743i
$482$	−5.66009			−0.257810
$483$	27.2424	+	83.8435i	1.23957	+	3.81501i
$484$	19.0134	+	13.8140i	0.864245	+	0.627911i
$485$	−1.08310	+	2.50468i	−0.0491812	+	0.113732i
$486$	−1.14289	+	0.830360i	−0.0518426	+	0.0376659i
$487$	−16.0867	−	11.6877i	−0.728959	−	0.529620i	0.160275	−	0.987072i	$-0.448762\pi$
$487$	−16.0867	−	11.6877i	−0.728959	−	0.529620i	−0.889234	+	0.457453i	$0.848762\pi$
$488$	2.15176	+	1.56335i	0.0974056	+	0.0707693i
$489$	−19.0553	+	13.8445i	−0.861711	+	0.626070i
$490$	−46.0943	+	27.2762i	−2.08233	+	1.23221i
$491$	0.126149	+	0.0916527i	0.00569303	+	0.00413623i	0.590628	−	0.806944i	$-0.298880\pi$
$491$	0.126149	+	0.0916527i	0.00569303	+	0.00413623i	−0.584935	+	0.811080i	$0.698880\pi$
$492$	15.0991	+	46.4701i	0.680718	+	2.09503i
$493$	−0.301033			−0.0135579
$494$	−5.10490	−	15.7113i	−0.229680	−	0.706883i
$495$	1.23646	+	0.116557i	0.0555747	+	0.00523884i
$496$	−1.42563	+	4.38763i	−0.0640125	+	0.197010i
$497$	−12.6450	+	38.9172i	−0.567205	+	1.74568i
$498$	−0.122442	+	0.0889593i	−0.00548675	+	0.00398636i
$499$	−23.6226			−1.05749			−0.528746	−	0.848780i	$-0.677337\pi$
$499$	−23.6226			−1.05749			−0.528746	+	0.848780i	$0.677337\pi$
$500$	−13.4215	+	19.7822i	−0.600230	+	0.884688i
$501$	−71.2327			−3.18244
$502$	−24.4349	+	17.7530i	−1.09058	+	0.792355i
$503$	−1.38202	+	4.25343i	−0.0616213	+	0.189651i	−0.977128	−	0.212652i	$-0.931790\pi$
$503$	−1.38202	+	4.25343i	−0.0616213	+	0.189651i	0.915507	+	0.402303i	$0.131790\pi$
$504$	2.27258	−	6.99427i	0.101229	−	0.311550i
$505$	31.6373	+	2.98234i	1.40784	+	0.132713i
$506$	0.391313	+	1.20434i	0.0173960	+	0.0535394i
$507$	31.7480			1.40998
$508$	5.42630	+	16.7004i	0.240753	+	0.740962i
$509$	−9.68212	−	7.03447i	−0.429152	−	0.311798i	0.352157	−	0.935941i	$-0.385448\pi$
$509$	−9.68212	−	7.03447i	−0.429152	−	0.311798i	−0.781310	+	0.624143i	$0.785448\pi$
$510$	−11.7690	+	6.96426i	−0.521139	+	0.308383i
$511$	−29.0790	+	21.1271i	−1.28638	+	0.934609i
$512$	25.9554	+	18.8577i	1.14708	+	0.833402i
$513$	38.4194	+	27.9134i	1.69626	+	1.23240i
$514$	11.0766	−	8.04763i	0.488569	−	0.354966i
$515$	3.68287	−	8.51666i	0.162287	−	0.375289i
$516$	−48.4998	−	35.2371i	−2.13508	−	1.55123i
$517$	0.383477	+	1.18022i	0.0168653	+	0.0519061i
$518$	22.2191			0.976249
$519$	−18.0142	−	55.4422i	−0.790738	−	2.43364i
$520$	0.389663	−	0.901097i	0.0170878	−	0.0395157i
$521$	2.82456	−	8.69311i	0.123746	−	0.380852i	−0.869924	−	0.493185i	$-0.835832\pi$
$521$	2.82456	−	8.69311i	0.123746	−	0.380852i	0.993671	+	0.112333i	$0.0358324\pi$
$522$	−1.14265	+	3.51671i	−0.0500124	+	0.153922i
$523$	−21.0110	+	15.2654i	−0.918746	+	0.667508i	−0.943212	−	0.332193i	$-0.892212\pi$
$523$	−21.0110	+	15.2654i	−0.918746	+	0.667508i	0.0244655	+	0.999701i	$0.492212\pi$
$524$	−17.9306			−0.783300
$525$	31.3484	−	57.0925i	1.36816	−	2.49172i
$526$	41.5330			1.81092
$527$	1.00750	−	0.731992i	0.0438874	−	0.0318861i
$528$	−0.316566	+	0.974291i	−0.0137768	+	0.0424006i
$529$	7.04565	−	21.6843i	0.306333	−	0.942795i
$530$	9.16210	+	40.9391i	0.397976	+	1.77828i
$531$	−11.9314	−	36.7210i	−0.517777	−	1.59355i
$532$	−48.1678			−2.08834
$533$	−3.66891	−	11.2918i	−0.158918	−	0.489100i
$534$	−51.2130	−	37.2084i	−2.21620	−	1.61017i
$535$	−8.74473	−	0.824337i	−0.378068	−	0.0356392i
$536$	−1.45791	+	1.05924i	−0.0629723	+	0.0457520i
$537$	−54.8947	−	39.8833i	−2.36888	−	1.72109i
$538$	−2.33763	−	1.69839i	−0.100782	−	0.0732227i
$539$	0.876219	−	0.636610i	0.0377414	−	0.0274208i
$540$	9.53761	+	42.6170i	0.410433	+	1.83394i
$541$	34.1030	+	24.7773i	1.46620	+	1.06526i	0.981692	+	0.190473i	$0.0610023\pi$
$541$	34.1030	+	24.7773i	1.46620	+	1.06526i	0.484511	+	0.874785i	$0.338998\pi$
$542$	−10.5991	−	32.6208i	−0.455272	−	1.40118i
$543$	−51.2523			−2.19945
$544$	−2.50247	−	7.70181i	−0.107293	−	0.330212i
$545$	2.88699	+	2.54389i	0.123665	+	0.108968i
$546$	−12.7906	+	39.3653i	−0.547386	+	1.68468i
$547$	2.14685	−	6.60732i	0.0917927	−	0.282509i	−0.894612	−	0.446844i	$-0.852548\pi$
$547$	2.14685	−	6.60732i	0.0917927	−	0.282509i	0.986405	+	0.164335i	$0.0525479\pi$
$548$	−21.4622	+	15.5932i	−0.916818	+	0.666107i
$549$	57.1360			2.43851
$550$	0.450292	−	0.820084i	0.0192005	−	0.0349685i
$551$	1.56510			0.0666754
$552$	−4.62670	+	3.36150i	−0.196925	+	0.143075i
$553$	−6.99059	+	21.5148i	−0.297270	+	0.914903i
$554$	−0.957260	+	2.94614i	−0.0406701	+	0.125170i
$555$	−14.5837	+	8.62988i	−0.619044	+	0.366318i
$556$	−11.3639	−	34.9746i	−0.481939	−	1.48325i
$557$	7.06218			0.299234			0.149617	−	0.988744i	$-0.452196\pi$
$557$	7.06218			0.299234			0.149617	+	0.988744i	$0.452196\pi$
$558$	−4.72700	−	14.5482i	−0.200110	−	0.615875i
$559$	11.7849	+	8.56226i	0.498450	+	0.362145i
$560$	26.9298	+	23.7294i	1.13799	+	1.00275i
$561$	0.223720	−	0.162542i	0.00944545	−	0.00686252i
$562$	20.3724	+	14.8014i	0.859360	+	0.624361i
$563$	23.1128	+	16.7925i	0.974090	+	0.707718i	0.956380	−	0.292125i	$-0.0943624\pi$
$563$	23.1128	+	16.7925i	0.974090	+	0.707718i	0.0177102	+	0.999843i	$0.494362\pi$
$564$	−70.1612	+	50.9751i	−2.95432	+	2.14644i
$565$	−16.7003	−	14.7156i	−0.702585	−	0.619089i
$566$	12.1432	+	8.82254i	0.510416	+	0.370839i
$567$	−12.5136	−	38.5130i	−0.525524	−	1.61740i
$568$	−2.65452			−0.111381
$569$	3.35519	+	10.3262i	0.140657	+	0.432898i	0.996427	−	0.0844587i	$-0.0269161\pi$
$569$	3.35519	+	10.3262i	0.140657	+	0.432898i	−0.855770	+	0.517357i	$0.826916\pi$
$570$	61.1878	−	36.2078i	2.56288	−	1.51658i
$571$	−2.37221	+	7.30092i	−0.0992740	+	0.305534i	−0.988344	−	0.152237i	$-0.951352\pi$
$571$	−2.37221	+	7.30092i	−0.0992740	+	0.305534i	0.889070	+	0.457771i	$0.151352\pi$
$572$	−0.0949300	+	0.292165i	−0.00396922	+	0.0122160i
$573$	−45.7165	+	33.2150i	−1.90983	+	1.38757i
$574$	−66.9997			−2.79651
$575$	−30.6100	+	14.4233i	−1.27653	+	0.601495i
$576$	−54.7343			−2.28060
$577$	16.7544	−	12.1728i	0.697495	−	0.506760i	−0.181621	−	0.983369i	$-0.558134\pi$
$577$	16.7544	−	12.1728i	0.697495	−	0.506760i	0.879115	+	0.476609i	$0.158134\pi$
$578$	−0.628618	+	1.93469i	−0.0261471	+	0.0804724i
$579$	−22.6133	+	69.5967i	−0.939778	+	2.89234i
$580$	1.07986	+	0.951528i	0.0448388	+	0.0395101i
$581$	−0.0331356	−	0.101981i	−0.00137470	−	0.00423088i
$582$	7.46344			0.309370
$583$	−0.262149	−	0.806810i	−0.0108571	−	0.0334147i
$584$	−1.88638	−	1.37054i	−0.0780591	−	0.0567133i
$585$	−4.60590	−	20.5806i	−0.190430	−	0.850902i
$586$	8.44807	−	6.13788i	0.348986	−	0.253554i
$587$	−16.7516	−	12.1707i	−0.691411	−	0.502340i	0.185712	−	0.982604i	$-0.440541\pi$
$587$	−16.7516	−	12.1707i	−0.691411	−	0.502340i	−0.877124	+	0.480264i	$0.840541\pi$
$588$	61.2343	+	44.4893i	2.52526	+	1.83471i
$589$	−5.23808	+	3.80569i	−0.215831	+	0.156811i
$590$	−28.9577	−	2.72975i	−1.19217	−	0.112382i
$591$	−39.1713	−	28.4596i	−1.61129	−	1.17067i
$592$	−2.88571	−	8.88130i	−0.118602	−	0.365019i
$593$	27.0435			1.11054			0.555272	−	0.831668i	$-0.312614\pi$
$593$	27.0435			1.11054			0.555272	+	0.831668i	$0.312614\pi$
$594$	−0.528150	−	1.62548i	−0.0216703	−	0.0666942i
$595$	−2.11600	−	9.45496i	−0.0867477	−	0.387615i
$596$	−6.46925	+	19.9103i	−0.264991	+	0.815558i
$597$	−12.0967	+	37.2299i	−0.495086	+	1.52372i
$598$	17.3968	−	12.6395i	0.711408	−	0.516868i
$599$	10.2086			0.417113			0.208557	−	0.978010i	$-0.433123\pi$
$599$	10.2086			0.417113			0.208557	+	0.978010i	$0.433123\pi$
$600$	4.15080	+	0.789580i	0.169456	+	0.0322345i
$601$	2.19589			0.0895724			0.0447862	−	0.998997i	$-0.485739\pi$
$601$	2.19589			0.0895724			0.0447862	+	0.998997i	$0.485739\pi$
$602$	66.5036	−	48.3177i	2.71048	−	1.96928i
$603$	−11.9627	+	36.8175i	−0.487160	+	1.49932i
$604$	−7.46150	+	22.9641i	−0.303604	+	0.934397i
$605$	9.75519	−	22.5589i	0.396605	−	0.917151i
$606$	−26.8574	−	82.6587i	−1.09101	−	3.35778i
$607$	−31.8580			−1.29307			−0.646537	−	0.762882i	$-0.723784\pi$
$607$	−31.8580			−1.29307			−0.646537	+	0.762882i	$0.723784\pi$
$608$	13.0106	+	40.0424i	0.527648	+	1.62393i
$609$	−3.17250	−	2.30495i	−0.128556	−	0.0934015i
$610$	17.0836	−	39.5060i	0.691696	−	1.59955i
$611$	17.0484	−	12.3864i	0.689706	−	0.501101i
$612$	10.4451	+	7.58881i	0.422218	+	0.306759i
$613$	27.0610	+	19.6610i	1.09298	+	0.794099i	0.979901	−	0.199486i	$-0.0639273\pi$
$613$	27.0610	+	19.6610i	1.09298	+	0.794099i	0.113083	+	0.993586i	$0.463927\pi$
$614$	−13.9649	+	10.1461i	−0.563579	+	0.409464i
$615$	43.9760	−	26.0227i	1.77328	−	1.04934i
$616$	0.0906330	+	0.0658487i	0.00365171	+	0.00265312i
$617$	−3.74481	−	11.5253i	−0.150760	−	0.463993i	0.846946	−	0.531678i	$-0.178438\pi$
$617$	−3.74481	−	11.5253i	−0.150760	−	0.463993i	−0.997707	+	0.0676857i	$0.978438\pi$
$618$	−25.3779			−1.02085
$619$	−9.72565	−	29.9325i	−0.390907	−	1.20309i	−0.932104	−	0.362192i	$-0.882029\pi$
$619$	−9.72565	−	29.9325i	−0.390907	−	1.20309i	0.541197	−	0.840896i	$-0.317971\pi$
$620$	−5.92782	−	0.558796i	−0.238067	−	0.0224418i
$621$	−19.1022	+	58.7904i	−0.766544	+	2.35918i
$622$	−19.1270	+	58.8669i	−0.766923	+	2.36035i
$623$	36.2844	−	26.3622i	1.45370	−	1.05618i
$624$	17.3961			0.696401
$625$	23.2539	+	9.17904i	0.930157	+	0.367162i
$626$	−17.3090			−0.691805
$627$	−1.16314	+	0.845068i	−0.0464512	+	0.0337488i
$628$	8.41214	−	25.8899i	0.335681	−	1.03312i
$629$	−0.778963	+	2.39740i	−0.0310593	+	0.0955906i
$630$	−118.486	−	11.1693i	−4.72059	−	0.444995i
$631$	−13.7642	−	42.3618i	−0.547943	−	1.68640i	−0.713887	−	0.700261i	$-0.753067\pi$
$631$	−13.7642	−	42.3618i	−0.547943	−	1.68640i	0.165943	−	0.986135i	$-0.446933\pi$
$632$	−1.46751			−0.0583746
$633$	7.48682	+	23.0421i	0.297575	+	0.915840i
$634$	−15.8588	−	11.5221i	−0.629834	−	0.457602i
$635$	15.8041	−	9.35203i	0.627166	−	0.371124i
$636$	47.9628	−	34.8470i	1.90185	−	1.38177i
$637$	−14.8793	−	10.8104i	−0.589539	−	0.428325i
$638$	−0.0455702	−	0.0331087i	−0.00180414	−	0.00131078i
$639$	−46.1337	+	33.5181i	−1.82502	+	1.32595i
$640$	−1.99098	+	4.60416i	−0.0787005	+	0.181995i
$641$	31.5113	+	22.8943i	1.24462	+	0.904271i	0.997897	−	0.0648147i	$-0.0206456\pi$
$641$	31.5113	+	22.8943i	1.24462	+	0.904271i	0.246725	+	0.969086i	$0.420646\pi$
$642$	7.42355	+	22.8473i	0.292984	+	0.901713i
$643$	−47.5876			−1.87667			−0.938336	−	0.345724i	$-0.887633\pi$
$643$	−47.5876			−1.87667			−0.938336	+	0.345724i	$0.887633\pi$
$644$	−19.3752	−	59.6308i	−0.763490	−	2.34978i
$645$	−24.8837	+	57.5438i	−0.979797	+	2.26579i
$646$	3.26824	−	10.0586i	0.128587	−	0.395750i
$647$	11.6163	−	35.7514i	0.456685	−	1.40553i	−0.412461	−	0.910975i	$-0.635331\pi$
$647$	11.6163	−	35.7514i	0.456685	−	1.40553i	0.869146	−	0.494556i	$-0.164669\pi$
$648$	2.12525	−	1.54408i	0.0834877	−	0.0606574i
$649$	0.588167			0.0230876
$650$	−15.6074	−	2.96889i	−0.612171	−	0.116449i
$651$	16.2225			0.635808
$652$	13.5524	−	9.84642i	0.530754	−	0.385616i
$653$	9.06228	−	27.8908i	0.354634	−	1.09145i	−0.601587	−	0.798807i	$-0.705465\pi$
$653$	9.06228	−	27.8908i	0.354634	−	1.09145i	0.956221	−	0.292645i	$-0.0945353\pi$
$654$	3.25210	−	10.0089i	0.127167	−	0.391381i
$655$	4.09524	+	18.2988i	0.160014	+	0.714994i
$656$	8.70162	+	26.7808i	0.339741	+	1.04562i
$657$	−50.0894			−1.95418
$658$	−36.7474	−	113.097i	−1.43256	−	4.40898i
$659$	7.87589	+	5.72217i	0.306801	+	0.222904i	0.730523	−	0.682888i	$-0.239276\pi$
$659$	7.87589	+	5.72217i	0.306801	+	0.222904i	−0.423721	+	0.905793i	$0.639276\pi$
$660$	−1.31630	−	0.124083i	−0.0512368	−	0.00482992i
$661$	2.14295	−	1.55695i	0.0833512	−	0.0605582i	−0.545329	−	0.838222i	$-0.683595\pi$
$661$	2.14295	−	1.55695i	0.0833512	−	0.0605582i	0.628680	+	0.777664i	$0.283595\pi$
$662$	6.94845	+	5.04834i	0.270059	+	0.196209i
$663$	−3.79904	−	2.76016i	−0.147542	−	0.107196i
$664$	0.00562757	−	0.00408867i	0.000218392	−	0.000158671i
$665$	11.0013	+	49.1571i	0.426611	+	1.90623i
$666$	25.0500	+	18.1999i	0.970668	+	0.705232i
$667$	0.629551	+	1.93756i	0.0243763	+	0.0750225i
$668$	50.6618			1.96016
$669$	7.36619	+	22.6708i	0.284794	+	0.876504i
$670$	21.8802	+	19.2799i	0.845304	+	0.744847i
$671$	−0.268958	+	0.827768i	−0.0103830	+	0.0319556i
$672$	32.5985	−	100.328i	1.25752	−	3.87024i
$673$	17.5017	−	12.7157i	0.674640	−	0.490155i	−0.196935	−	0.980417i	$-0.563099\pi$
$673$	17.5017	−	12.7157i	0.674640	−	0.490155i	0.871575	+	0.490262i	$0.163099\pi$
$674$	−0.243883			−0.00939401
$675$	41.3139	−	19.4670i	1.59017	−	0.749284i
$676$	−22.5797			−0.868448
$677$	−7.38197	+	5.36332i	−0.283712	+	0.206129i	−0.720535	−	0.693419i	$-0.756104\pi$
$677$	−7.38197	+	5.36332i	−0.283712	+	0.206129i	0.436823	+	0.899548i	$0.356104\pi$
$678$	−18.8123	+	57.8984i	−0.722483	+	2.22357i
$679$	−1.63404	+	5.02905i	−0.0627086	+	0.192997i
$680$	0.540915	−	0.320085i	0.0207432	−	0.0122747i
$681$	−21.6360	−	66.5889i	−0.829095	−	2.55169i
$682$	0.233021			0.00892285
$683$	1.83918	+	5.66040i	0.0703741	+	0.216589i	0.980058	−	0.198712i	$-0.0636760\pi$
$683$	1.83918	+	5.66040i	0.0703741	+	0.216589i	−0.909684	+	0.415302i	$0.863676\pi$
$684$	−54.3049	−	39.4549i	−2.07640	−	1.50859i
$685$	20.8153	+	18.3416i	0.795310	+	0.700795i
$686$	−34.0485	+	24.7377i	−1.29998	+	0.944489i
$687$	27.2232	+	19.7788i	1.03863	+	0.754609i
$688$	−27.9505	−	20.3072i	−1.06560	−	0.774206i
$689$	−11.6545	+	8.46746i	−0.444000	+	0.322585i
$690$	69.4369	+	61.1849i	2.64342	+	2.32927i
$691$	15.7783	+	11.4636i	0.600235	+	0.436096i	0.845962	−	0.533243i	$-0.179027\pi$
$691$	15.7783	+	11.4636i	0.600235	+	0.436096i	−0.245727	+	0.969339i	$0.579027\pi$
$692$	12.8120	+	39.4313i	0.487040	+	1.49895i
$693$	2.40659			0.0914189
$694$	−8.69981	−	26.7753i	−0.330240	−	1.01637i
$695$	−33.0975	+	19.5854i	−1.25546	+	0.742915i
$696$	0.0786098	−	0.241936i	0.00297970	−	0.00917057i
$697$	2.34890	−	7.22916i	0.0889708	−	0.273824i
$698$	16.5835	−	12.0486i	0.627694	−	0.456047i
$699$	−13.0956			−0.495323
$700$	−22.2954	+	40.6050i	−0.842689	+	1.53473i
$701$	26.5124			1.00136			0.500680	−	0.865633i	$-0.333083\pi$
$701$	26.5124			1.00136			0.500680	+	0.865633i	$0.333083\pi$
$702$	−23.4802	+	17.0594i	−0.886204	+	0.643865i
$703$	4.04989	−	12.4643i	0.152745	−	0.470099i
$704$	0.257653	−	0.792973i	0.00971064	−	0.0298863i
$705$	68.0464	+	59.9597i	2.56278	+	2.25821i
$706$	13.1738	+	40.5449i	0.495804	+	1.52593i
$707$	61.5776			2.31586
$708$	12.7018	+	39.0920i	0.477362	+	1.46917i
$709$	7.88616	+	5.72963i	0.296171	+	0.215181i	0.725940	−	0.687758i	$-0.241405\pi$
$709$	7.88616	+	5.72963i	0.296171	+	0.215181i	−0.429769	+	0.902939i	$0.641405\pi$
$710$	9.38173	+	41.9205i	0.352090	+	1.57325i
$711$	−25.5043	+	18.5300i	−0.956486	+	0.694928i
$712$	2.35381	+	1.71014i	0.0882127	+	0.0640903i
$713$	−6.81834	−	4.95382i	−0.255349	−	0.185522i
$714$	−21.4383	+	15.5759i	−0.802310	+	0.582912i
$715$	0.319846	+	0.0301509i	0.0119616	+	0.00112758i
$716$	39.0420	+	28.3657i	1.45907	+	1.06007i
$717$	14.8726	+	45.7733i	0.555429	+	1.70943i
$718$	−35.0854			−1.30938
$719$	5.11944	+	15.7560i	0.190923	+	0.587600i	1.00000		0.000102179i	$-3.25245e-5\pi$
$719$	5.11944	+	15.7560i	0.190923	+	0.587600i	−0.809077	+	0.587703i	$0.800033\pi$
$720$	10.9239	+	48.8113i	0.407109	+	1.81909i
$721$	5.55621	−	17.1003i	0.206924	−	0.636847i
$722$	−5.04810	+	15.5364i	−0.187871	+	0.578207i
$723$	6.76735	−	4.91677i	0.251680	−	0.182857i
$724$	36.4514			1.35471
$725$	0.724437	−	1.31936i	0.0269049	−	0.0489999i
$726$	−67.2211			−2.49481
$727$	17.7589	−	12.9026i	0.658640	−	0.478530i	−0.207563	−	0.978222i	$-0.566553\pi$
$727$	17.7589	−	12.9026i	0.658640	−	0.478530i	0.866203	+	0.499692i	$0.166553\pi$
$728$	0.587869	−	1.80928i	0.0217879	−	0.0670562i
$729$	−8.01883	+	24.6794i	−0.296994	+	0.914053i
$730$	−14.9767	+	34.6337i	−0.554313	+	1.28185i
$731$	2.88190	+	8.86957i	0.106591	+	0.328053i
$732$	−60.8253			−2.24817
$733$	−9.34903	−	28.7734i	−0.345314	−	1.06277i	−0.961415	−	0.275101i	$-0.911289\pi$
$733$	−9.34903	−	28.7734i	−0.345314	−	1.06277i	0.616101	−	0.787667i	$-0.288711\pi$
$734$	−9.46982	−	6.88022i	−0.349537	−	0.253954i
$735$	31.4174	−	72.6530i	1.15885	−	2.67985i
$736$	−44.3382	+	32.2136i	−1.63433	+	1.18741i
$737$	−0.477087	−	0.346624i	−0.0175737	−	0.0127681i
$738$	−75.5362	−	54.8803i	−2.78053	−	2.02017i
$739$	16.5459	−	12.0213i	0.608652	−	0.442212i	−0.240287	−	0.970702i	$-0.577242\pi$
$739$	16.5459	−	12.0213i	0.608652	−	0.442212i	0.848939	+	0.528490i	$0.177242\pi$
$740$	10.3722	−	6.13770i	0.381288	−	0.225626i
$741$	19.7515	+	14.3503i	0.725590	+	0.527172i
$742$	25.1209	+	77.3141i	0.922216	+	2.83829i
$743$	34.5073			1.26595			0.632975	−	0.774172i	$-0.281834\pi$
$743$	34.5073			1.26595			0.632975	+	0.774172i	$0.281834\pi$
$744$	0.325199	+	1.00086i	0.0119224	+	0.0366933i
$745$	21.7968	+	2.05471i	0.798571	+	0.0752787i
$746$	1.68377	−	5.18211i	0.0616472	−	0.189730i
$747$	0.0461763	−	0.142116i	0.00168950	−	0.00519976i
$748$	−0.159113	+	0.115602i	−0.00581774	+	0.00422684i
$749$	−17.0204			−0.621912
$750$	−2.20080	−	68.3403i	−0.0803618	−	2.49543i
$751$	−13.6245			−0.497164			−0.248582	−	0.968611i	$-0.579965\pi$
$751$	−13.6245			−0.497164			−0.248582	+	0.968611i	$0.579965\pi$
$752$	−40.4340	+	29.3770i	−1.47448	+	1.07127i
$753$	13.7935	−	42.4519i	0.502662	−	1.54703i
$754$	−0.295580	+	0.909701i	−0.0107644	+	0.0331294i
$755$	25.1399	+	2.36986i	0.914936	+	0.0862480i
$756$	26.1505	+	80.4828i	0.951083	+	2.92713i
$757$	−44.4393			−1.61517			−0.807587	−	0.589748i	$-0.799227\pi$
$757$	−44.4393			−1.61517			−0.807587	+	0.589748i	$0.799227\pi$
$758$	−19.9449	−	61.3840i	−0.724430	−	2.22957i
$759$	−1.51404	−	1.10002i	−0.0549562	−	0.0399280i
$760$	−2.81226	+	1.66415i	−0.102012	+	0.0603651i
$761$	−37.9170	+	27.5483i	−1.37449	+	0.998624i	−0.377117	+	0.926166i	$0.623085\pi$
$761$	−37.9170	+	27.5483i	−1.37449	+	0.998624i	−0.997371	+	0.0724589i	$0.976915\pi$
$762$	−40.6333	−	29.5218i	−1.47199	−	1.06946i
$763$	6.03226	+	4.38269i	0.218382	+	0.158664i
$764$	32.5143	−	23.6230i	1.17632	−	0.854650i
$765$	5.35906	−	12.3929i	0.193757	−	0.448065i
$766$	−27.0319	−	19.6399i	−0.976704	−	0.709617i
$767$	−3.08640	−	9.49896i	−0.111443	−	0.342988i
$768$	−40.7835			−1.47165
$769$	8.72499	+	26.8528i	0.314631	+	0.968335i	0.975906	+	0.218192i	$0.0700158\pi$
$769$	8.72499	+	26.8528i	0.314631	+	0.968335i	−0.661275	+	0.750144i	$0.729984\pi$
$770$	0.719570	−	1.66401i	0.0259315	−	0.0599667i
$771$	−6.25273	+	19.2439i	−0.225187	+	0.693053i
$772$	16.0830	&minus

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+(1.64574 - 1.19570i) q^{2} +(-0.929019 + 2.85923i) q^{3} +(0.660733 - 2.03353i) q^{4} +(-2.22620 - 0.209856i) q^{5} +(1.88986 + 5.81638i) q^{6} -4.33298 q^{7} +(-0.0868601 - 0.267328i) q^{8} +(-4.88505 - 3.54920i) q^{9} +(-3.91468 + 2.31650i) q^{10} +(0.0744152 - 0.0540658i) q^{11} +(5.20048 + 3.77837i) q^{12} +(-1.26366 - 0.918105i) q^{13} +(-7.13098 + 5.18096i) q^{14} +(2.66821 - 6.17025i) q^{15} +(2.99705 + 2.17748i) q^{16} +(-0.309017 - 0.951057i) q^{17} -12.2833 q^{18} +(1.60661 + 4.94462i) q^{19} +(-1.89767 + 4.38837i) q^{20} +(4.02542 - 12.3890i) q^{21} +(0.0578217 - 0.177957i) q^{22} +(-5.47509 + 3.97789i) q^{23} +0.845046 q^{24} +(4.91192 + 0.934364i) q^{25} -3.17745 q^{26} +(7.38966 - 5.36890i) q^{27} +(-2.86294 + 8.81123i) q^{28} +(0.0930244 - 0.286300i) q^{29} +(-2.98659 - 13.3450i) q^{30} +(0.384831 + 1.18439i) q^{31} +8.09816 q^{32} +(0.0854533 + 0.262998i) q^{33} +(-1.64574 - 1.19570i) q^{34} +(9.64608 + 0.909304i) q^{35} +(-10.4451 + 7.58881i) q^{36} +(-2.03935 - 1.48168i) q^{37} +(8.55636 + 6.21656i) q^{38} +(3.79904 - 2.76016i) q^{39} +(0.137267 + 0.613353i) q^{40} +(6.14949 + 4.46787i) q^{41} +(-8.18872 - 25.2023i) q^{42} -9.32601 q^{43} +(-0.0607757 - 0.187048i) q^{44} +(10.1303 + 8.92638i) q^{45} +(-4.25423 + 13.0932i) q^{46} +(-4.16904 + 12.8310i) q^{47} +(-9.01023 + 6.54632i) q^{48} +11.7747 q^{49} +(9.20098 - 4.33547i) q^{50} +3.00637 q^{51} +(-2.70193 + 1.96307i) q^{52} +(2.84999 - 8.77137i) q^{53} +(5.74187 - 17.6717i) q^{54} +(-0.177009 + 0.104745i) q^{55} +(0.376363 + 1.15833i) q^{56} -15.6304 q^{57} +(-0.189235 - 0.582405i) q^{58} +(5.17314 + 3.75850i) q^{59} +(-10.7844 - 9.50276i) q^{60} +(-7.65519 + 5.56182i) q^{61} +(2.04951 + 1.48905i) q^{62} +(21.1668 + 15.3786i) q^{63} +(7.33340 - 5.32803i) q^{64} +(2.62049 + 2.30907i) q^{65} +(0.455102 + 0.330651i) q^{66} +(-1.98116 - 6.09737i) q^{67} -2.13818 q^{68} +(-6.28722 - 19.3501i) q^{69} +(16.9622 - 10.0374i) q^{70} +(2.91831 - 8.98163i) q^{71} +(-0.524483 + 1.61419i) q^{72} +(6.71108 - 4.87588i) q^{73} -5.12789 q^{74} +(-7.23483 + 13.1763i) q^{75} +11.1166 q^{76} +(-0.322440 + 0.234266i) q^{77} +(2.95191 - 9.08504i) q^{78} +(1.61334 - 4.96536i) q^{79} +(-6.21507 - 5.47646i) q^{80} +(2.88800 + 8.88835i) q^{81} +15.4627 q^{82} +(0.00764730 + 0.0235360i) q^{83} +(-22.5336 - 16.3716i) q^{84} +(0.488348 + 2.18209i) q^{85} +(-15.3482 + 11.1511i) q^{86} +(0.732174 + 0.531956i) q^{87} +(-0.0209170 - 0.0151971i) q^{88} +(-8.37401 + 6.08407i) q^{89} +(27.3451 + 2.57773i) q^{90} +(5.47543 + 3.97813i) q^{91} +(4.47157 + 13.7621i) q^{92} -3.74395 q^{93} +(8.48087 + 26.1014i) q^{94} +(-2.53896 - 11.3449i) q^{95} +(-7.52335 + 23.1545i) q^{96} +(0.377116 - 1.16064i) q^{97} +(19.3782 - 14.0791i) q^{98} -0.555412 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

Fields

Representations

Groups

Database

Properties

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