LMFDB - Embedded newform 425.2.k.c.86.12

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			86.12
Character	$\chi$	$=$	425.86
Dual form			425.2.k.c.341.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.419644 - 0.304889i) q^{2} +(1.00213 - 3.08423i) q^{3} +(-0.534891 + 1.64622i) q^{4} +(-2.22841 + 0.184895i) q^{5} +(-0.519812 - 1.59982i) q^{6} -3.33055 q^{7} +(0.598031 + 1.84055i) q^{8} +(-6.08119 - 4.41824i) q^{9} +(-0.878766 + 0.757007i) q^{10} +(-1.76134 + 1.27969i) q^{11} +(4.54131 + 3.29946i) q^{12} +(-1.56415 - 1.13642i) q^{13} +(-1.39764 + 1.01545i) q^{14} +(-1.66290 + 7.05823i) q^{15} +(-1.98860 - 1.44480i) q^{16} +(-0.309017 - 0.951057i) q^{17} -3.89901 q^{18} +(-1.07633 - 3.31259i) q^{19} +(0.887578 - 3.76736i) q^{20} +(-3.33764 + 10.2722i) q^{21} +(-0.348972 + 1.07403i) q^{22} +(5.68035 - 4.12702i) q^{23} +6.27599 q^{24} +(4.93163 - 0.824042i) q^{25} -1.00286 q^{26} +(-11.8502 + 8.60969i) q^{27} +(1.78148 - 5.48283i) q^{28} +(1.66022 - 5.10964i) q^{29} +(1.45415 + 3.46894i) q^{30} +(-1.33303 - 4.10266i) q^{31} -5.14555 q^{32} +(2.18177 + 6.71480i) q^{33} +(-0.419644 - 0.304889i) q^{34} +(7.42183 - 0.615800i) q^{35} +(10.5262 - 7.64772i) q^{36} +(9.39182 + 6.82356i) q^{37} +(-1.46165 - 1.06195i) q^{38} +(-5.07246 + 3.68536i) q^{39} +(-1.67297 - 3.99093i) q^{40} +(-4.45403 - 3.23604i) q^{41} +(1.73126 + 5.32827i) q^{42} -2.06109 q^{43} +(-1.16453 - 3.58405i) q^{44} +(14.3683 + 8.72128i) q^{45} +(1.12544 - 3.46375i) q^{46} +(-3.37178 + 10.3773i) q^{47} +(-6.44894 + 4.68543i) q^{48} +4.09255 q^{49} +(1.81828 - 1.84940i) q^{50} -3.24296 q^{51} +(2.70745 - 1.96707i) q^{52} +(-1.78616 + 5.49725i) q^{53} +(-2.34787 + 7.22600i) q^{54} +(3.68838 - 3.17733i) q^{55} +(-1.99177 - 6.13004i) q^{56} -11.2954 q^{57} +(-0.861170 - 2.65041i) q^{58} +(-6.16333 - 4.47792i) q^{59} +(-10.7300 - 6.51288i) q^{60} +(1.59635 - 1.15982i) q^{61} +(-1.81025 - 1.31523i) q^{62} +(20.2537 + 14.7152i) q^{63} +(1.81790 - 1.32079i) q^{64} +(3.69568 + 2.24320i) q^{65} +(2.96283 + 2.15262i) q^{66} +(-1.02466 - 3.15358i) q^{67} +1.73094 q^{68} +(-7.03624 - 21.6553i) q^{69} +(2.92677 - 2.52125i) q^{70} +(-0.893924 + 2.75121i) q^{71} +(4.49526 - 13.8350i) q^{72} +(-2.90730 + 2.11227i) q^{73} +6.02164 q^{74} +(2.40059 - 16.0361i) q^{75} +6.02899 q^{76} +(5.86623 - 4.26206i) q^{77} +(-1.00500 + 3.09307i) q^{78} +(2.75626 - 8.48288i) q^{79} +(4.69855 + 2.85193i) q^{80} +(7.71043 + 23.7303i) q^{81} -2.85574 q^{82} +(-3.66235 - 11.2715i) q^{83} +(-15.1251 - 10.9890i) q^{84} +(0.864462 + 2.06221i) q^{85} +(-0.864925 + 0.628405i) q^{86} +(-14.0956 - 10.2410i) q^{87} +(-3.40867 - 2.47654i) q^{88} +(-14.0323 + 10.1950i) q^{89} +(8.68859 - 0.720905i) q^{90} +(5.20946 + 3.78490i) q^{91} +(3.75563 + 11.5586i) q^{92} -13.9894 q^{93} +(1.74897 + 5.38278i) q^{94} +(3.01098 + 7.18281i) q^{95} +(-5.15650 + 15.8701i) q^{96} +(4.57668 - 14.0856i) q^{97} +(1.71741 - 1.24777i) q^{98} +16.3650 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 $

$2$	0.419644	−	0.304889i	0.296733	−	0.215589i	−0.429450	−	0.903091i	$-0.641293\pi$
$2$	0.419644	−	0.304889i	0.296733	−	0.215589i	0.726183	+	0.687502i	$0.241293\pi$
$3$	1.00213	−	3.08423i	0.578579	−	1.78068i	−0.0450753	−	0.998984i	$-0.514353\pi$
$3$	1.00213	−	3.08423i	0.578579	−	1.78068i	0.623654	−	0.781700i	$-0.285647\pi$
$4$	−0.534891	+	1.64622i	−0.267445	+	0.823112i
$5$	−2.22841	+	0.184895i	−0.996576	+	0.0826874i
$5$	−2.22841	+	0.184895i	−0.996576	+	0.0826874i
$6$	−0.519812	−	1.59982i	−0.212212	−	0.653123i
$7$	−3.33055			−1.25883			−0.629414	−	0.777070i	$-0.716705\pi$
$7$	−3.33055			−1.25883			−0.629414	+	0.777070i	$0.716705\pi$
$8$	0.598031	+	1.84055i	0.211436	+	0.650733i
$9$	−6.08119	−	4.41824i	−2.02706	−	1.47275i
$10$	−0.878766	+	0.757007i	−0.277890	+	0.239387i
$11$	−1.76134	+	1.27969i	−0.531064	+	0.385841i	−0.820756	−	0.571279i	$-0.806447\pi$
$11$	−1.76134	+	1.27969i	−0.531064	+	0.385841i	0.289692	+	0.957120i	$0.406447\pi$
$12$	4.54131	+	3.29946i	1.31096	+	0.952471i
$13$	−1.56415	−	1.13642i	−0.433816	−	0.315186i	0.349357	−	0.936990i	$-0.386400\pi$
$13$	−1.56415	−	1.13642i	−0.433816	−	0.315186i	−0.783173	+	0.621804i	$0.786400\pi$
$14$	−1.39764	+	1.01545i	−0.373536	+	0.271390i
$15$	−1.66290	+	7.05823i	−0.429358	+	1.82243i
$16$	−1.98860	−	1.44480i	−0.497150	−	0.361201i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	−3.89901			−0.919004
$19$	−1.07633	−	3.31259i	−0.246926	−	0.759961i	−0.995314	−	0.0966992i	$-0.969172\pi$
$19$	−1.07633	−	3.31259i	−0.246926	−	0.759961i	0.748387	−	0.663262i	$-0.230828\pi$
$20$	0.887578	−	3.76736i	0.198468	−	0.842408i
$21$	−3.33764	+	10.2722i	−0.728332	+	2.24158i
$22$	−0.348972	+	1.07403i	−0.0744011	+	0.228983i
$23$	5.68035	−	4.12702i	1.18443	−	0.860542i	0.191770	−	0.981440i	$-0.438577\pi$
$23$	5.68035	−	4.12702i	1.18443	−	0.860542i	0.992665	+	0.120898i	$0.0385772\pi$
$24$	6.27599			1.28108
$25$	4.93163	−	0.824042i	0.986326	−	0.164808i
$26$	−1.00286			−0.196678
$27$	−11.8502	+	8.60969i	−2.28058	+	1.65693i
$28$	1.78148	−	5.48283i	0.336668	−	1.03616i
$29$	1.66022	−	5.10964i	0.308296	−	0.948836i	−0.670131	−	0.742243i	$-0.733762\pi$
$29$	1.66022	−	5.10964i	0.308296	−	0.948836i	0.978427	−	0.206594i	$-0.0662378\pi$
$30$	1.45415	+	3.46894i	0.265491	+	0.633339i
$31$	−1.33303	−	4.10266i	−0.239420	−	0.736859i	−0.996504	−	0.0835420i	$-0.973377\pi$
$31$	−1.33303	−	4.10266i	−0.239420	−	0.736859i	0.757084	−	0.653317i	$-0.226623\pi$
$32$	−5.14555			−0.909613
$33$	2.18177	+	6.71480i	0.379798	+	1.16890i
$34$	−0.419644	−	0.304889i	−0.0719683	−	0.0522880i
$35$	7.42183	−	0.615800i	1.25452	−	0.104089i
$36$	10.5262	−	7.64772i	1.75436	−	1.27462i
$37$	9.39182	+	6.82356i	1.54401	+	1.12179i	0.947760	+	0.318983i	$0.103341\pi$
$37$	9.39182	+	6.82356i	1.54401	+	1.12179i	0.596245	+	0.802802i	$0.296659\pi$
$38$	−1.46165	−	1.06195i	−0.237110	−	0.172271i
$39$	−5.07246	+	3.68536i	−0.812243	+	0.590129i
$40$	−1.67297	−	3.99093i	−0.264519	−	0.631021i
$41$	−4.45403	−	3.23604i	−0.695602	−	0.505385i	0.182895	−	0.983132i	$-0.441453\pi$
$41$	−4.45403	−	3.23604i	−0.695602	−	0.505385i	−0.878497	+	0.477748i	$0.841453\pi$
$42$	1.73126	+	5.32827i	0.267139	+	0.822170i
$43$	−2.06109			−0.314314			−0.157157	−	0.987574i	$-0.550233\pi$
$43$	−2.06109			−0.314314			−0.157157	+	0.987574i	$0.550233\pi$
$44$	−1.16453	−	3.58405i	−0.175559	−	0.540316i
$45$	14.3683	+	8.72128i	2.14190	+	1.30009i
$46$	1.12544	−	3.46375i	0.165937	−	0.510702i
$47$	−3.37178	+	10.3773i	−0.491825	+	1.51368i	0.330022	+	0.943973i	$0.392944\pi$
$47$	−3.37178	+	10.3773i	−0.491825	+	1.51368i	−0.821847	+	0.569709i	$0.807056\pi$
$48$	−6.44894	+	4.68543i	−0.930825	+	0.676284i
$49$	4.09255			0.584650
$50$	1.81828	−	1.84940i	0.257144	−	0.261545i
$51$	−3.24296			−0.454105
$52$	2.70745	−	1.96707i	0.375455	−	0.272784i
$53$	−1.78616	+	5.49725i	−0.245349	+	0.755105i	0.750230	+	0.661176i	$0.229943\pi$
$53$	−1.78616	+	5.49725i	−0.245349	+	0.755105i	−0.995579	+	0.0939286i	$0.970057\pi$
$54$	−2.34787	+	7.22600i	−0.319504	+	0.983334i
$55$	3.68838	−	3.17733i	0.497341	−	0.428432i
$56$	−1.99177	−	6.13004i	−0.266162	−	0.819161i
$57$	−11.2954			−1.49612
$58$	−0.861170	−	2.65041i	−0.113077	−	0.348016i
$59$	−6.16333	−	4.47792i	−0.802398	−	0.582976i	0.109219	−	0.994018i	$-0.465165\pi$
$59$	−6.16333	−	4.47792i	−0.802398	−	0.582976i	−0.911617	+	0.411042i	$0.865165\pi$
$60$	−10.7300	−	6.51288i	−1.38523	−	0.840809i
$61$	1.59635	−	1.15982i	0.204392	−	0.148499i	−0.480881	−	0.876786i	$-0.659683\pi$
$61$	1.59635	−	1.15982i	0.204392	−	0.148499i	0.685273	+	0.728287i	$0.259683\pi$
$62$	−1.81025	−	1.31523i	−0.229903	−	0.167034i
$63$	20.2537	+	14.7152i	2.55173	+	1.85394i
$64$	1.81790	−	1.32079i	0.227238	−	0.165098i
$65$	3.69568	+	2.24320i	0.458392	+	0.278235i
$66$	2.96283	+	2.15262i	0.364700	+	0.264970i
$67$	−1.02466	−	3.15358i	−0.125182	−	0.385271i	0.868752	−	0.495247i	$-0.164923\pi$
$67$	−1.02466	−	3.15358i	−0.125182	−	0.385271i	−0.993934	+	0.109976i	$0.964923\pi$
$68$	1.73094			0.209908
$69$	−7.03624	−	21.6553i	−0.847064	−	2.60700i
$70$	2.92677	−	2.52125i	0.349816	−	0.301347i
$71$	−0.893924	+	2.75121i	−0.106089	+	0.326509i	−0.989985	−	0.141176i	$-0.954912\pi$
$71$	−0.893924	+	2.75121i	−0.106089	+	0.326509i	0.883895	+	0.467685i	$0.154912\pi$
$72$	4.49526	−	13.8350i	0.529771	−	1.63047i
$73$	−2.90730	+	2.11227i	−0.340273	+	0.247223i	−0.744777	−	0.667313i	$-0.767444\pi$
$73$	−2.90730	+	2.11227i	−0.340273	+	0.247223i	0.404504	+	0.914536i	$0.367444\pi$
$74$	6.02164			0.700002
$75$	2.40059	−	16.0361i	0.277196	−	1.85169i
$76$	6.02899			0.691572
$77$	5.86623	−	4.26206i	0.668519	−	0.485707i
$78$	−1.00500	+	3.09307i	−0.113794	+	0.350221i
$79$	2.75626	−	8.48288i	0.310103	−	0.954399i	−0.667620	−	0.744502i	$-0.732687\pi$
$79$	2.75626	−	8.48288i	0.310103	−	0.954399i	0.977723	−	0.209897i	$-0.0673129\pi$
$80$	4.69855	+	2.85193i	0.525314	+	0.318856i
$81$	7.71043	+	23.7303i	0.856714	+	2.63669i
$82$	−2.85574			−0.315363
$83$	−3.66235	−	11.2715i	−0.401995	−	1.23721i	−0.923379	−	0.383890i	$-0.874584\pi$
$83$	−3.66235	−	11.2715i	−0.401995	−	1.23721i	0.521384	−	0.853322i	$-0.325416\pi$
$84$	−15.1251	−	10.9890i	−1.65028	−	1.19900i
$85$	0.864462	+	2.06221i	0.0937641	+	0.223678i
$86$	−0.864925	+	0.628405i	−0.0932672	+	0.0677626i
$87$	−14.0956	−	10.2410i	−1.51120	−	1.09795i
$88$	−3.40867	−	2.47654i	−0.363365	−	0.264000i
$89$	−14.0323	+	10.1950i	−1.48742	+	1.08067i	−0.512348	+	0.858778i	$0.671224\pi$
$89$	−14.0323	+	10.1950i	−1.48742	+	1.08067i	−0.975071	+	0.221895i	$0.928776\pi$
$90$	8.68859	−	0.720905i	0.915857	−	0.0759901i
$91$	5.20946	+	3.78490i	0.546100	+	0.396765i
$92$	3.75563	+	11.5586i	0.391551	+	1.20507i
$93$	−13.9894			−1.45064
$94$	1.74897	+	5.38278i	0.180393	+	0.555191i
$95$	3.01098	+	7.18281i	0.308920	+	0.736941i
$96$	−5.15650	+	15.8701i	−0.526283	+	1.61973i
$97$	4.57668	−	14.0856i	0.464691	−	1.43017i	−0.394680	−	0.918819i	$-0.629144\pi$
$97$	4.57668	−	14.0856i	0.464691	−	1.43017i	0.859371	−	0.511353i	$-0.170856\pi$
$98$	1.71741	−	1.24777i	0.173485	−	0.126044i
$99$	16.3650			1.64475
$100$	−1.28132	+	8.55934i	−0.128132	+	0.855934i
$101$	−18.1738			−1.80837			−0.904183	−	0.427146i	$-0.859519\pi$
$101$	−18.1738			−1.80837			−0.904183	+	0.427146i	$0.859519\pi$
$102$	−1.36089	+	0.988741i	−0.134748	+	0.0979000i
$103$	0.388769	−	1.19651i	0.0383065	−	0.117895i	−0.930075	−	0.367371i	$-0.880258\pi$
$103$	0.388769	−	1.19651i	0.0383065	−	0.117895i	0.968381	+	0.249475i	$0.0802581\pi$
$104$	1.15623	−	3.55850i	0.113377	−	0.348940i
$105$	5.53835	−	23.5078i	0.540488	−	2.29412i
$106$	0.926498	+	2.85147i	0.0899894	+	0.276959i
$107$	6.88044			0.665157			0.332579	−	0.943076i	$-0.392081\pi$
$107$	6.88044			0.665157			0.332579	+	0.943076i	$0.392081\pi$
$108$	−7.83490	−	24.1133i	−0.753914	−	2.32031i
$109$	9.58883	+	6.96670i	0.918444	+	0.667288i	0.943136	−	0.332407i	$-0.107861\pi$
$109$	9.58883	+	6.96670i	0.918444	+	0.667288i	−0.0246925	+	0.999695i	$0.507861\pi$
$110$	0.579072	−	2.45789i	0.0552123	−	0.234351i
$111$	30.4573	−	22.1285i	2.89088	−	2.10034i
$112$	6.62313	+	4.81198i	0.625827	+	0.454690i
$113$	−1.83987	−	1.33674i	−0.173080	−	0.125750i	0.497873	−	0.867250i	$-0.334115\pi$
$113$	−1.83987	−	1.33674i	−0.173080	−	0.125750i	−0.670953	+	0.741500i	$0.734115\pi$
$114$	−4.74006	+	3.44385i	−0.443947	+	0.322546i
$115$	−11.8951	+	10.2470i	−1.10922	+	0.955533i
$116$	7.52357	+	5.46619i	0.698546	+	0.507523i
$117$	4.49090	+	13.8216i	0.415183	+	1.27780i
$118$	−3.95167			−0.363781
$119$	1.02920	+	3.16754i	0.0943462	+	0.290368i
$120$	−13.9855	+	1.16040i	−1.27669	+	0.105929i
$121$	−1.93447	+	5.95369i	−0.175861	+	0.541244i
$122$	0.316283	−	0.973418i	0.0286349	−	0.0881292i
$123$	−14.4442	+	10.4943i	−1.30239	+	0.946242i
$124$	7.46692			0.670550
$125$	−10.8373	+	2.74814i	−0.969320	+	0.245801i
$126$	12.9858			1.15687
$127$	11.2612	−	8.18177i	0.999274	−	0.726015i	0.0373412	−	0.999303i	$-0.488111\pi$
$127$	11.2612	−	8.18177i	0.999274	−	0.726015i	0.961932	+	0.273288i	$0.0881112\pi$
$128$	3.54030	−	10.8959i	0.312921	−	0.963073i
$129$	−2.06548	+	6.35690i	−0.181855	+	0.559694i
$130$	2.23480	−	0.185424i	0.196004	−	0.0162628i
$131$	−3.13978	−	9.66326i	−0.274324	−	0.844283i	−0.989397	−	0.145233i	$-0.953607\pi$
$131$	−3.13978	−	9.66326i	−0.274324	−	0.844283i	0.715073	−	0.699049i	$-0.246393\pi$
$132$	−12.2211			−1.06371
$133$	3.58476	+	11.0328i	0.310838	+	0.956661i
$134$	−1.39148	−	1.01097i	−0.120206	−	0.0873346i
$135$	24.8153	−	21.3770i	2.13576	−	1.83984i
$136$	1.56567	−	1.13752i	0.134255	−	0.0975418i
$137$	9.19193	+	6.67833i	0.785320	+	0.570568i	0.906571	−	0.422054i	$-0.138691\pi$
$137$	9.19193	+	6.67833i	0.785320	+	0.570568i	−0.121251	+	0.992622i	$0.538691\pi$
$138$	−9.55519	−	6.94225i	−0.813391	−	0.590963i
$139$	3.86585	−	2.80870i	0.327897	−	0.238231i	−0.411641	−	0.911346i	$-0.635044\pi$
$139$	3.86585	−	2.80870i	0.327897	−	0.238231i	0.739538	+	0.673115i	$0.235044\pi$
$140$	−2.95612	+	12.5474i	−0.249838	+	1.06045i
$141$	28.6270	+	20.7987i	2.41083	+	1.75157i
$142$	0.463685	+	1.42708i	0.0389116	+	0.119758i
$143$	4.20925			0.351996
$144$	5.70957	+	17.5722i	0.475797	+	1.46435i
$145$	−2.75491	+	11.6933i	−0.228783	+	0.971079i
$146$	−0.576019	+	1.77280i	−0.0476717	+	0.146718i
$147$	4.10126	−	12.6224i	0.338266	−	1.04108i
$148$	−16.2567	+	11.8112i	−1.33629	+	0.970873i
$149$	−7.22500			−0.591895			−0.295947	−	0.955204i	$-0.595635\pi$
$149$	−7.22500			−0.591895			−0.295947	+	0.955204i	$0.595635\pi$
$150$	−3.88184	−	7.46135i	−0.316951	−	0.609217i
$151$	3.07160			0.249963			0.124981	−	0.992159i	$-0.460113\pi$
$151$	3.07160			0.249963			0.124981	+	0.992159i	$0.460113\pi$
$152$	5.45332	−	3.96207i	0.442323	−	0.321366i
$153$	−2.32281	+	7.14887i	−0.187788	+	0.577952i
$154$	1.16227	−	3.57710i	0.0936583	−	0.288251i
$155$	3.72911	+	8.89594i	0.299529	+	0.714539i
$156$	−3.35371	−	10.3217i	−0.268512	−	0.826394i
$157$	9.38119			0.748700			0.374350	−	0.927287i	$-0.377866\pi$
$157$	9.38119			0.748700			0.374350	+	0.927287i	$0.377866\pi$
$158$	−1.42969	−	4.40014i	−0.113740	−	0.350056i
$159$	15.1648	+	11.0179i	1.20265	+	0.873776i
$160$	11.4664	−	0.951384i	0.906498	−	0.0752135i
$161$	−18.9187	+	13.7452i	−1.49100	+	1.08328i
$162$	10.4707	+	7.60742i	0.822657	+	0.597696i
$163$	−4.23368	−	3.07595i	−0.331608	−	0.240927i	0.409505	−	0.912308i	$-0.365701\pi$
$163$	−4.23368	−	3.07595i	−0.331608	−	0.240927i	−0.741112	+	0.671381i	$0.765701\pi$
$164$	7.70966	−	5.60140i	0.602023	−	0.437396i
$165$	−6.10341	−	14.5599i	−0.475150	−	1.13349i
$166$	−4.97345	−	3.61342i	−0.386014	−	0.280456i
$167$	−0.195942	−	0.603047i	−0.0151624	−	0.0466651i	0.943189	−	0.332257i	$-0.107810\pi$
$167$	−0.195942	−	0.603047i	−0.0151624	−	0.0466651i	−0.958351	+	0.285591i	$0.907810\pi$
$168$	−20.9025			−1.61266
$169$	−2.86212	−	8.80869i	−0.220163	−	0.677591i
$170$	0.991510	+	0.601828i	0.0760454	+	0.0461581i
$171$	−8.09050	+	24.9000i	−0.618696	+	1.90415i
$172$	1.10246	−	3.39302i	0.0840618	−	0.258716i
$173$	6.50507	−	4.72621i	0.494571	−	0.359327i	−0.312368	−	0.949961i	$-0.601122\pi$
$173$	6.50507	−	4.72621i	0.494571	−	0.359327i	0.806939	+	0.590634i	$0.201122\pi$
$174$	−9.03749			−0.685130
$175$	−16.4250	+	2.74451i	−1.24162	+	0.207466i
$176$	5.35150			0.403384
$177$	−19.9874	+	14.5217i	−1.50235	+	1.09152i
$178$	−2.78020	+	8.55657i	−0.208385	+	0.641342i
$179$	−0.118260	+	0.363966i	−0.00883915	+	0.0272041i	−0.955379	−	0.295383i	$-0.904553\pi$
$179$	−0.118260	+	0.363966i	−0.00883915	+	0.0272041i	0.946540	+	0.322587i	$0.104553\pi$
$180$	−22.0426	+	18.9885i	−1.64296	+	1.41532i
$181$	2.21743	+	6.82455i	0.164820	+	0.507265i	0.999023	−	0.0441933i	$-0.0140717\pi$
$181$	2.21743	+	6.82455i	0.164820	+	0.507265i	−0.834203	+	0.551458i	$0.814072\pi$
$182$	3.34009			0.247584
$183$	−1.97740	−	6.08580i	−0.146173	−	0.449875i
$184$	10.9930	+	7.98689i	0.810415	+	0.588801i
$185$	−22.1905	−	13.4692i	−1.63148	−	0.990274i
$186$	−5.87058	+	4.26522i	−0.430452	+	0.312741i
$187$	1.76134	+	1.27969i	0.128802	+	0.0935801i
$188$	−15.2798	−	11.1014i	−1.11439	−	0.809654i
$189$	39.4677	−	28.6750i	2.87085	−	2.08580i
$190$	3.45350	+	2.09621i	0.250543	+	0.152075i
$191$	−7.79164	−	5.66096i	−0.563783	−	0.409612i	0.269059	−	0.963124i	$-0.413287\pi$
$191$	−7.79164	−	5.66096i	−0.563783	−	0.409612i	−0.832842	+	0.553511i	$0.813287\pi$
$192$	−2.25184	−	6.93044i	−0.162512	−	0.500162i
$193$	−12.7999			−0.921359			−0.460680	−	0.887566i	$-0.652394\pi$
$193$	−12.7999			−0.921359			−0.460680	+	0.887566i	$0.652394\pi$
$194$	−2.37396	−	7.30629i	−0.170440	−	0.524561i
$195$	10.6221	−	9.15035i	0.760665	−	0.655271i
$196$	−2.18907	+	6.73726i	−0.156362	+	0.481233i
$197$	2.23898	−	6.89086i	0.159520	−	0.490953i	−0.839070	−	0.544023i	$-0.816900\pi$
$197$	2.23898	−	6.89086i	0.159520	−	0.490953i	0.998591	+	0.0530694i	$0.0169005\pi$
$198$	6.86748	−	4.98951i	0.488050	−	0.354589i
$199$	−4.72920			−0.335244			−0.167622	−	0.985851i	$-0.553609\pi$
$199$	−4.72920			−0.335244			−0.167622	+	0.985851i	$0.553609\pi$
$200$	4.46596	+	8.58411i	0.315791	+	0.606988i
$201$	−10.7532			−0.758473
$202$	−7.62654	+	5.54100i	−0.536601	+	0.389864i
$203$	−5.52945	+	17.0179i	−0.388091	+	1.19442i
$204$	1.73463	−	5.33863i	0.121448	−	0.373779i
$205$	10.5237	+	6.38770i	0.735009	+	0.446136i
$206$	−0.201657	−	0.620638i	−0.0140501	−	0.0432419i
$207$	−52.7775			−3.66829
$208$	1.46856	+	4.51976i	0.101826	+	0.313389i
$209$	6.13487	+	4.45724i	0.424358	+	0.308314i
$210$	−4.84312	−	11.5535i	−0.334207	−	0.797265i
$211$	22.0799	−	16.0420i	1.52004	−	1.10437i	0.558573	−	0.829455i	$-0.311349\pi$
$211$	22.0799	−	16.0420i	1.52004	−	1.10437i	0.961468	−	0.274919i	$-0.0886509\pi$
$212$	−8.09430	−	5.88085i	−0.555919	−	0.403899i
$213$	7.58956	+	5.51414i	0.520028	+	0.377823i
$214$	2.88733	−	2.09777i	0.197374	−	0.143401i
$215$	4.59296	−	0.381085i	0.313238	−	0.0259898i
$216$	−22.9334	−	16.6621i	−1.56042	−	1.13371i
$217$	4.43974	+	13.6641i	0.301389	+	0.927580i
$218$	6.14796			0.416392
$219$	3.60126	+	11.0835i	0.243351	+	0.748957i
$220$	3.25772	+	7.77143i	0.219636	+	0.523950i
$221$	−0.597451	+	1.83876i	−0.0401889	+	0.123689i
$222$	6.03446	−	18.5722i	0.405006	−	1.24648i
$223$	−3.49417	+	2.53867i	−0.233987	+	0.170002i	−0.698600	−	0.715512i	$-0.746193\pi$
$223$	−3.49417	+	2.53867i	−0.233987	+	0.170002i	0.464613	+	0.885514i	$0.346193\pi$
$224$	17.1375			1.14505
$225$	−33.6310	−	16.7780i	−2.24207	−	1.11853i
$226$	−1.17965			−0.0784689
$227$	7.91007	−	5.74700i	0.525010	−	0.381442i	−0.293478	−	0.955966i	$-0.594813\pi$
$227$	7.91007	−	5.74700i	0.525010	−	0.381442i	0.818488	+	0.574524i	$0.194813\pi$
$228$	6.04182	−	18.5948i	0.400129	−	1.23147i
$229$	−3.14122	+	9.66768i	−0.207578	+	0.638859i	0.792020	+	0.610495i	$0.209030\pi$
$229$	−3.14122	+	9.66768i	−0.207578	+	0.638859i	−0.999598	+	0.0283633i	$0.990970\pi$
$230$	−1.86752	+	7.92675i	−0.123140	+	0.522674i
$231$	−7.26649	−	22.3640i	−0.478100	−	1.47144i
$232$	10.3974			0.682624
$233$	−3.90541	−	12.0196i	−0.255852	−	0.787431i	−0.993661	−	0.112421i	$-0.964139\pi$
$233$	−3.90541	−	12.0196i	−0.255852	−	0.787431i	0.737809	−	0.675010i	$-0.235861\pi$
$234$	6.09861	+	4.43090i	0.398679	+	0.289657i
$235$	5.59501	−	23.7483i	0.364978	−	1.54917i
$236$	10.6684	−	7.75103i	0.694452	−	0.504549i
$237$	−23.4011	−	17.0019i	−1.52006	−	1.10439i
$238$	1.39764	+	1.01545i	0.0905957	+	0.0658217i
$239$	−0.657366	+	0.477604i	−0.0425214	+	0.0308936i	−0.608843	−	0.793291i	$-0.708366\pi$
$239$	−0.657366	+	0.477604i	−0.0425214	+	0.0308936i	0.566322	+	0.824184i	$0.308366\pi$
$240$	13.5046	−	11.6334i	0.871717	−	0.750935i
$241$	−14.2039	−	10.3197i	−0.914951	−	0.664751i	0.0273114	−	0.999627i	$-0.491305\pi$
$241$	−14.2039	−	10.3197i	−0.914951	−	0.664751i	−0.942262	+	0.334876i	$0.891305\pi$
$242$	1.00343	+	3.08822i	0.0645026	+	0.198519i
$243$	36.9735			2.37185
$244$	1.05544	+	3.24832i	0.0675679	+	0.207953i
$245$	−9.11988	+	0.756691i	−0.582648	+	0.0483432i
$246$	−2.86181	+	8.80776i	−0.182463	+	0.561562i
$247$	−2.08096	+	6.40454i	−0.132408	+	0.407511i
$248$	6.75396	−	4.90704i	0.428877	−	0.311597i
$249$	−38.4342			−2.43567
$250$	−3.70994	+	4.45742i	−0.234637	+	0.281912i
$251$	−1.69648			−0.107081			−0.0535404	−	0.998566i	$-0.517051\pi$
$251$	−1.69648			−0.107081			−0.0535404	+	0.998566i	$0.517051\pi$
$252$	−35.0580	+	25.4711i	−2.20845	+	1.60453i
$253$	−4.72373	+	14.5382i	−0.296979	+	0.914006i
$254$	2.23118	−	6.86685i	0.139996	−	0.430865i
$255$	7.22664	−	0.599605i	0.452550	−	0.0375487i
$256$	−0.447627	−	1.37765i	−0.0279767	−	0.0861033i
$257$	−15.2497			−0.951252			−0.475626	−	0.879648i	$-0.657778\pi$
$257$	−15.2497			−0.951252			−0.475626	+	0.879648i	$0.657778\pi$
$258$	1.07138	+	3.29737i	0.0667013	+	0.205286i
$259$	−31.2799	−	22.7262i	−1.94364	−	1.41214i
$260$	−5.66960	+	4.88404i	−0.351614	+	0.302895i
$261$	−32.6718	+	23.7374i	−2.02233	+	1.46931i
$262$	−4.26381	−	3.09784i	−0.263419	−	0.191385i
$263$	6.58181	+	4.78197i	0.405852	+	0.294869i	0.771920	−	0.635719i	$-0.219296\pi$
$263$	6.58181	+	4.78197i	0.405852	+	0.294869i	−0.366068	+	0.930588i	$0.619296\pi$
$264$	−11.0542	+	8.03132i	−0.680337	+	0.494293i
$265$	2.96390	−	12.5804i	0.182071	−	0.772806i
$266$	4.86808	+	3.53687i	0.298481	+	0.216859i
$267$	17.3818	+	53.4956i	1.06375	+	3.27388i
$268$	5.73958			0.350600
$269$	2.09188	+	6.43816i	0.127544	+	0.392541i	0.994356	−	0.106094i	$-0.0338345\pi$
$269$	2.09188	+	6.43816i	0.127544	+	0.392541i	−0.866812	+	0.498636i	$0.833835\pi$
$270$	3.89597	−	16.5366i	0.237101	−	1.00639i
$271$	1.27455	−	3.92266i	0.0774233	−	0.238284i	−0.904853	−	0.425725i	$-0.860019\pi$
$271$	1.27455	−	3.92266i	0.0774233	−	0.238284i	0.982276	+	0.187440i	$0.0600192\pi$
$272$	−0.759578	+	2.33774i	−0.0460562	+	0.141746i
$273$	16.8941	−	12.2743i	1.02248	−	0.742872i
$274$	5.89348			0.356038
$275$	−7.63176	+	7.76237i	−0.460212	+	0.468088i
$276$	39.4131			2.37239
$277$	3.36998	−	2.44843i	0.202482	−	0.147112i	−0.481923	−	0.876213i	$-0.660062\pi$
$277$	3.36998	−	2.44843i	0.202482	−	0.147112i	0.684406	+	0.729101i	$0.260062\pi$
$278$	0.765936	−	2.35731i	0.0459378	−	0.141382i
$279$	−10.0201	+	30.8387i	−0.599888	+	1.84627i
$280$	5.57190	+	13.2920i	0.332984	+	0.794348i
$281$	3.23140	+	9.94524i	0.192769	+	0.593283i	0.999995	+	0.00304075i	$0.000967904\pi$
$281$	3.23140	+	9.94524i	0.192769	+	0.593283i	−0.807226	+	0.590243i	$0.799032\pi$
$282$	18.3544			1.09299
$283$	9.89813	+	30.4633i	0.588383	+	1.81086i	0.585239	+	0.810861i	$0.301001\pi$
$283$	9.89813	+	30.4633i	0.588383	+	1.81086i	0.00314338	+	0.999995i	$0.498999\pi$
$284$	−4.05096	−	2.94320i	−0.240380	−	0.174647i
$285$	25.1709	−	2.08846i	1.49099	−	0.123710i
$286$	1.76639	−	1.28335i	0.104449	−	0.0758864i
$287$	14.8344	+	10.7778i	0.875644	+	0.636193i
$288$	31.2910	+	22.7343i	1.84384	+	1.33963i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	2.40909	+	5.74698i	0.141467	+	0.337474i
$291$	−38.8567	−	28.2311i	−2.27782	−	1.65494i
$292$	−1.92219	−	5.91589i	−0.112488	−	0.346201i
$293$	31.0771			1.81555			0.907773	−	0.419462i	$-0.137781\pi$
$293$	31.0771			1.81555			0.907773	+	0.419462i	$0.137781\pi$
$294$	−2.12736	−	6.54733i	−0.124070	−	0.381848i
$295$	14.5624	+	8.83908i	0.847855	+	0.514631i
$296$	−6.94250	+	21.3668i	−0.403525	+	1.24192i
$297$	9.85455	−	30.3292i	0.571819	−	1.75988i
$298$	−3.03192	+	2.20282i	−0.175635	+	0.127606i
$299$	−13.5749			−0.785058
$300$	25.1149	+	12.5295i	1.45001	+	0.723388i
$301$	6.86457			0.395667
$302$	1.28898	−	0.936495i	0.0741722	−	0.0538892i
$303$	−18.2125	+	56.0524i	−1.04628	+	3.22013i
$304$	−2.64566	+	8.14250i	−0.151739	+	0.467005i
$305$	−3.34288	+	2.87970i	−0.191413	+	0.164891i
$306$	1.20486	+	3.70817i	0.0688772	+	0.211982i
$307$	16.7802			0.957698			0.478849	−	0.877897i	$-0.341054\pi$
$307$	16.7802			0.957698			0.478849	+	0.877897i	$0.341054\pi$
$308$	3.87852	+	11.9369i	0.220999	+	0.680166i
$309$	−3.30071	−	2.39811i	−0.187771	−	0.136424i
$310$	4.27717	+	2.59616i	0.242927	+	0.147452i
$311$	−7.95441	+	5.77922i	−0.451053	+	0.327709i	−0.790011	−	0.613092i	$-0.789925\pi$
$311$	−7.95441	+	5.77922i	−0.451053	+	0.327709i	0.338958	+	0.940801i	$0.389925\pi$
$312$	−9.81657	−	7.13215i	−0.555754	−	0.403779i
$313$	−17.4161	−	12.6536i	−0.984418	−	0.715222i	−0.0257265	−	0.999669i	$-0.508190\pi$
$313$	−17.4161	−	12.6536i	−0.984418	−	0.715222i	−0.958692	+	0.284447i	$0.908190\pi$
$314$	3.93676	−	2.86022i	0.222164	−	0.161412i
$315$	−47.8543	−	29.0466i	−2.69629	−	1.63659i
$316$	12.4904	+	9.07483i	0.702642	+	0.510499i
$317$	−4.34502	−	13.3726i	−0.244041	−	0.751080i	−0.995793	−	0.0916344i	$-0.970791\pi$
$317$	−4.34502	−	13.3726i	−0.244041	−	0.751080i	0.751752	−	0.659446i	$-0.229209\pi$
$318$	9.72306			0.545242
$319$	3.61453	+	11.1244i	0.202375	+	0.622846i
$320$	−3.80683	+	3.27937i	−0.212808	+	0.183323i
$321$	6.89509	−	21.2209i	0.384846	−	1.18443i
$322$	−3.74834	+	11.5362i	−0.208887	+	0.642887i
$323$	−2.81786	+	2.04730i	−0.156790	+	0.113915i
$324$	−43.1895			−2.39942
$325$	−8.65024	−	4.31547i	−0.479829	−	0.239379i
$326$	−2.71446			−0.150340
$327$	31.0962	−	22.5927i	1.71962	−	1.24938i
$328$	3.29245	−	10.1331i	0.181795	−	0.559508i
$329$	11.2299	−	34.5620i	0.619124	−	1.90547i
$330$	−7.00042	−	4.24912i	−0.385360	−	0.233906i
$331$	3.45234	+	10.6252i	0.189758	+	0.584014i	0.999998	−	0.00208388i	$-0.000663319\pi$
$331$	3.45234	+	10.6252i	0.189758	+	0.584014i	−0.810240	+	0.586098i	$0.800663\pi$
$332$	20.5144			1.12588
$333$	−26.9653	−	82.9907i	−1.47769	−	4.54786i
$334$	−0.266088	−	0.193324i	−0.0145597	−	0.0105782i
$335$	2.86644	+	6.83801i	0.156610	+	0.373601i
$336$	21.4785	−	15.6051i	1.17175	−	0.851325i
$337$	7.88936	+	5.73195i	0.429761	+	0.312239i	0.781553	−	0.623839i	$-0.214428\pi$
$337$	7.88936	+	5.73195i	0.429761	+	0.312239i	−0.351793	+	0.936078i	$0.614428\pi$
$338$	−3.88674	−	2.82388i	−0.211411	−	0.153599i
$339$	−5.96661	+	4.33499i	−0.324062	+	0.235445i
$340$	−3.85725	+	0.320042i	−0.209189	+	0.0173567i
$341$	7.59806	+	5.52031i	0.411458	+	0.298942i
$342$	4.19660	+	12.9158i	0.226926	+	0.698408i
$343$	9.68340			0.522854
$344$	−1.23260	−	3.79355i	−0.0664572	−	0.204534i
$345$	19.6836	+	46.9560i	1.05973	+	2.52803i
$346$	1.28884	−	3.96665i	0.0692885	−	0.213248i
$347$	−9.78152	+	30.1044i	−0.525099	+	1.61609i	0.239020	+	0.971015i	$0.423174\pi$
$347$	−9.78152	+	30.1044i	−0.525099	+	1.61609i	−0.764119	+	0.645075i	$0.776826\pi$
$348$	24.3986	−	17.7266i	1.30790	−	0.950247i
$349$	6.86158			0.367292			0.183646	−	0.982992i	$-0.441210\pi$
$349$	6.86158			0.367292			0.183646	+	0.982992i	$0.441210\pi$
$350$	−6.05588	+	6.15952i	−0.323701	+	0.329240i
$351$	28.3197			1.51159
$352$	9.06306	−	6.58470i	0.483063	−	0.350965i
$353$	0.436508	−	1.34343i	0.0232330	−	0.0715038i	−0.938768	−	0.344550i	$-0.888031\pi$
$353$	0.436508	−	1.34343i	0.0232330	−	0.0715038i	0.962001	+	0.273047i	$0.0880314\pi$
$354$	−3.96008	+	12.1879i	−0.210476	+	0.647779i
$355$	1.48334	−	6.29612i	0.0787278	−	0.334163i
$356$	−9.27759	−	28.5535i	−0.491712	−	1.51333i
$357$	10.8008			0.571640
$358$	0.0613423	+	0.188792i	0.00324204	+	0.00997797i
$359$	3.43756	+	2.49753i	0.181427	+	0.131815i	0.674792	−	0.738008i	$-0.264233\pi$
$359$	3.43756	+	2.49753i	0.181427	+	0.131815i	−0.493365	+	0.869822i	$0.664233\pi$
$360$	−7.45927	+	31.6612i	−0.393138	+	1.66869i
$361$	5.55653	−	4.03705i	0.292449	−	0.212476i
$362$	3.01126	+	2.18781i	0.158268	+	0.114989i
$363$	16.4240	+	11.9327i	0.862035	+	0.626305i
$364$	−9.01728	+	6.55144i	−0.472634	+	0.343389i
$365$	6.08810	−	5.24456i	0.318666	−	0.274513i
$366$	−2.68529	−	1.95098i	−0.140363	−	0.101979i
$367$	−11.2138	−	34.5126i	−0.585357	−	1.80154i	−0.597830	−	0.801623i	$-0.703970\pi$
$367$	−11.2138	−	34.5126i	−0.585357	−	1.80154i	0.0124728	−	0.999922i	$-0.496030\pi$
$368$	−17.2587			−0.899670
$369$	12.7882	+	39.3580i	0.665726	+	2.04889i
$370$	−13.4187	+	1.11337i	−0.697605	+	0.0578813i
$371$	5.94891	−	18.3088i	0.308852	−	0.950548i
$372$	7.48282	−	23.0297i	0.387966	−	1.19404i
$373$	7.79219	−	5.66136i	0.403464	−	0.293134i	−0.367486	−	0.930029i	$-0.619781\pi$
$373$	7.79219	−	5.66136i	0.403464	−	0.293134i	0.770951	+	0.636895i	$0.219781\pi$
$374$	1.12930			0.0583946
$375$	−2.38450	+	36.1789i	−0.123135	+	1.86827i
$376$	−21.1163			−1.08899
$377$	−8.40352	+	6.10551i	−0.432803	+	0.314450i
$378$	7.81969	−	24.0665i	0.402201	−	1.23785i
$379$	−0.0318826	+	0.0981245i	−0.00163770	+	0.00504032i	−0.951872	−	0.306496i	$-0.900843\pi$
$379$	−0.0318826	+	0.0981245i	−0.00163770	+	0.00504032i	0.950234	+	0.311536i	$0.100843\pi$
$380$	−13.4351	+	1.11473i	−0.689204	+	0.0571843i
$381$	−13.9493	−	42.9315i	−0.714644	−	2.19945i
$382$	−4.99567			−0.255601
$383$	−9.52964	−	29.3292i	−0.486942	−	1.49865i	−0.829149	−	0.559028i	$-0.811174\pi$
$383$	−9.52964	−	29.3292i	−0.486942	−	1.49865i	0.342207	−	0.939625i	$-0.388826\pi$
$384$	−30.0578	−	21.8382i	−1.53388	−	1.11443i
$385$	−12.2843	+	10.5823i	−0.626068	+	0.539322i
$386$	−5.37141	+	3.90256i	−0.273398	+	0.198635i
$387$	12.5339	+	9.10642i	0.637134	+	0.462905i
$388$	20.7400	+	15.0685i	1.05291	+	0.764985i
$389$	3.42063	−	2.48524i	0.173433	−	0.126006i	−0.497682	−	0.867359i	$-0.665815\pi$
$389$	3.42063	−	2.48524i	0.173433	−	0.126006i	0.671115	+	0.741353i	$0.265815\pi$
$390$	1.66766	−	7.07845i	0.0844452	−	0.358431i
$391$	−5.68035	−	4.12702i	−0.287268	−	0.208712i
$392$	2.44747	+	7.53255i	0.123616	+	0.380451i
$393$	−32.9502			−1.66212
$394$	−1.16137	−	3.57434i	−0.0585092	−	0.180073i
$395$	−4.57363	+	19.4130i	−0.230124	+	0.976772i
$396$	−8.75350	+	26.9405i	−0.439880	+	1.35381i
$397$	−9.41280	+	28.9696i	−0.472415	+	1.45394i	0.376998	+	0.926214i	$0.376956\pi$
$397$	−9.41280	+	28.9696i	−0.472415	+	1.45394i	−0.849413	+	0.527729i	$0.823044\pi$
$398$	−1.98458	+	1.44188i	−0.0994779	+	0.0722749i
$399$	37.6200			1.88336
$400$	−10.9976	−	5.48654i	−0.549881	−	0.274327i
$401$	−22.1623			−1.10673			−0.553366	−	0.832938i	$-0.686657\pi$
$401$	−22.1623			−1.10673			−0.553366	+	0.832938i	$0.686657\pi$
$402$	−4.51252	+	3.27854i	−0.225064	+	0.163519i
$403$	−2.57728	+	7.93204i	−0.128383	+	0.395123i
$404$	9.72102	−	29.9182i	0.483639	−	1.48849i
$405$	−21.5696	−	51.4551i	−1.07180	−	2.55683i
$406$	2.86817	+	8.82732i	0.142345	+	0.438092i
$407$	−25.2742			−1.25280
$408$	−1.93939	−	5.96882i	−0.0960140	−	0.295501i
$409$	21.9455	+	15.9444i	1.08514	+	0.788397i	0.978571	−	0.205908i	$-0.0660149\pi$
$409$	21.9455	+	15.9444i	1.08514	+	0.788397i	0.106565	+	0.994306i	$0.466015\pi$
$410$	6.36375	−	0.528010i	0.314283	−	0.0260766i
$411$	29.8090	−	21.6575i	1.47037	−	1.06829i
$412$	1.76177	+	1.28000i	0.0867962	+	0.0630611i
$413$	20.5273	+	14.9139i	1.01008	+	0.733867i
$414$	−22.1477	+	16.0913i	−1.08850	+	0.790842i
$415$	10.2453	+	24.4405i	0.502920	+	1.19974i
$416$	8.04838	+	5.84749i	0.394604	+	0.286697i
$417$	−4.78862	−	14.7379i	−0.234500	−	0.721716i
$418$	3.93342			0.192390
$419$	−11.4886	−	35.3584i	−0.561257	−	1.72737i	−0.678818	−	0.734306i	$-0.737508\pi$
$419$	−11.4886	−	35.3584i	−0.561257	−	1.72737i	0.117561	−	0.993066i	$-0.462492\pi$
$420$	35.7366	+	21.6915i	1.74377	+	1.05843i
$421$	4.06602	−	12.5139i	0.198165	−	0.609891i	−0.801760	−	0.597647i	$-0.796103\pi$
$421$	4.06602	−	12.5139i	0.198165	−	0.609891i	0.999925	−	0.0122439i	$-0.00389745\pi$
$422$	4.37466	−	13.4638i	0.212955	−	0.655408i
$423$	66.3538	−	48.2089i	3.22623	−	2.34400i
$424$	−11.1861			−0.543247
$425$	−2.30767	−	4.43561i	−0.111938	−	0.215159i
$426$	4.86611			0.235764
$427$	−5.31672	+	3.86282i	−0.257294	+	0.186935i
$428$	−3.68028	+	11.3267i	−0.177893	+	0.547499i
$429$	4.21821	−	12.9823i	0.203657	−	0.626793i
$430$	1.81122	−	1.56026i	0.0873447	−	0.0752426i
$431$	−3.50816	−	10.7970i	−0.168982	−	0.520074i	0.830325	−	0.557279i	$-0.188155\pi$
$431$	−3.50816	−	10.7970i	−0.168982	−	0.520074i	−0.999308	+	0.0372050i	$0.988155\pi$
$432$	36.0046			1.73227
$433$	−1.39164	−	4.28304i	−0.0668781	−	0.205830i	0.912033	−	0.410117i	$-0.134512\pi$
$433$	−1.39164	−	4.28304i	−0.0668781	−	0.205830i	−0.978911	+	0.204288i	$0.934512\pi$
$434$	6.02914	+	4.38043i	0.289408	+	0.210267i
$435$	33.3042	+	20.2150i	1.59682	+	0.969236i
$436$	−16.5977	+	12.0589i	−0.794886	+	0.577519i
$437$	−19.7850	−	14.3747i	−0.946447	−	0.687634i
$438$	4.89050	+	3.55315i	0.233677	+	0.169776i
$439$	29.6257	−	21.5243i	1.41396	−	1.02730i	0.421226	−	0.906956i	$-0.361600\pi$
$439$	29.6257	−	21.5243i	1.41396	−	1.02730i	0.992732	−	0.120345i	$-0.0384001\pi$
$440$	8.05381	+	4.88851i	0.383950	+	0.233050i
$441$	−24.8876	−	18.0819i	−1.18512	−	0.861042i
$442$	0.309902	+	0.953781i	0.0147406	+	0.0453667i
$443$	−7.69770			−0.365729			−0.182864	−	0.983138i	$-0.558537\pi$
$443$	−7.69770			−0.365729			−0.182864	+	0.983138i	$0.558537\pi$
$444$	20.1372	+	61.9758i	0.955667	+	2.94124i
$445$	29.3847	−	25.3132i	1.39297	−	1.19996i
$446$	−0.692297	+	2.13067i	−0.0327812	+	0.100890i
$447$	−7.24037	+	22.2836i	−0.342458	+	1.05398i
$448$	−6.05462	+	4.39894i	−0.286054	+	0.207830i
$449$	−10.5597			−0.498341			−0.249171	−	0.968460i	$-0.580158\pi$
$449$	−10.5597			−0.498341			−0.249171	+	0.968460i	$0.580158\pi$
$450$	−19.2284	+	3.21295i	−0.906438	+	0.151460i
$451$	11.9862			0.564407
$452$	3.18470	−	2.31382i	0.149796	−	0.108833i
$453$	3.07813	−	9.47352i	0.144623	−	0.445105i
$454$	1.56721	−	4.82339i	0.0735530	−	0.226373i
$455$	−12.3086	−	7.47110i	−0.577037	−	0.350251i
$456$	−6.75502	−	20.7898i	−0.316333	−	0.973572i
$457$	8.23652			0.385288			0.192644	−	0.981269i	$-0.438294\pi$
$457$	8.23652			0.385288			0.192644	+	0.981269i	$0.438294\pi$
$458$	1.62938	+	5.01470i	0.0761357	+	0.234322i
$459$	11.8502	+	8.60969i	0.553121	+	0.401866i
$460$	−10.5062	−	25.0630i	−0.489854	−	1.16857i
$461$	−15.1512	+	11.0080i	−0.705661	+	0.512692i	−0.881771	−	0.471678i	$-0.843648\pi$
$461$	−15.1512	+	11.0080i	−0.705661	+	0.512692i	0.176110	+	0.984370i	$0.443648\pi$
$462$	−9.86786	−	7.16942i	−0.459094	−	0.333552i
$463$	−30.1871	−	21.9322i	−1.40291	−	1.01928i	−0.994305	−	0.106567i	$-0.966014\pi$
$463$	−30.1871	−	21.9322i	−1.40291	−	1.01928i	−0.408609	−	0.912710i	$-0.633986\pi$
$464$	−10.6839	+	7.76233i	−0.495989	+	0.360357i
$465$	31.1742	−	2.58657i	1.44567	−	0.119949i
$466$	−5.30352	−	3.85323i	−0.245681	−	0.178498i
$467$	7.86012	+	24.1909i	0.363723	+	1.11942i	0.950777	+	0.309876i	$0.100288\pi$
$467$	7.86012	+	24.1909i	0.363723	+	1.11942i	−0.587054	+	0.809548i	$0.699712\pi$
$468$	−25.1555			−1.16281
$469$	3.41268	+	10.5031i	0.157583	+	0.484990i
$470$	−4.89267	−	11.6717i	−0.225682	−	0.538374i
$471$	9.40116	−	28.9338i	0.433183	−	1.33320i
$472$	4.55598	−	14.0219i	0.209706	−	0.645408i
$473$	3.63029	−	2.63756i	0.166921	−	0.121275i
$474$	−15.0038			−0.689147
$475$	−8.03776	−	15.4495i	−0.368798	−	0.708874i
$476$	−5.76499			−0.264238
$477$	35.1502	−	25.5381i	1.60942	−	1.16931i
$478$	−0.130243	+	0.400847i	−0.00595718	+	0.0183343i
$479$	−1.30910	+	4.02900i	−0.0598144	+	0.184090i	−0.976499	−	0.215521i	$-0.930855\pi$
$479$	−1.30910	+	4.02900i	−0.0598144	+	0.184090i	0.916685	+	0.399611i	$0.130855\pi$
$480$	8.55651	−	36.3184i	0.390549	−	1.65770i
$481$	−6.93576	−	21.3461i	−0.316243	−	0.973297i
$482$	−9.10692			−0.414809
$483$	23.4346	+	72.1241i	1.06631	+	3.28176i
$484$	−8.76637	−	6.36914i	−0.398471	−	0.289506i
$485$	−7.59437	+	32.2346i	−0.344842	+	1.46370i
$486$	15.5157	−	11.2728i	0.703806	−	0.511345i
$487$	0.407187	+	0.295839i	0.0184514	+	0.0134057i	0.596973	−	0.802262i	$-0.296370\pi$
$487$	0.407187	+	0.295839i	0.0184514	+	0.0134057i	−0.578521	+	0.815667i	$0.696370\pi$
$488$	3.08937	+	2.24456i	0.139849	+	0.101606i
$489$	−13.7296	+	9.97517i	−0.620876	+	0.451093i
$490$	−3.59639	+	3.09809i	−0.162469	+	0.139958i
$491$	−8.59767	−	6.24657i	−0.388008	−	0.281904i	0.376631	−	0.926363i	$-0.377082\pi$
$491$	−8.59767	−	6.24657i	−0.388008	−	0.281904i	−0.764639	+	0.644459i	$0.777082\pi$
$492$	−9.54995	−	29.3917i	−0.430545	−	1.32508i
$493$	−5.37259			−0.241969
$494$	1.07941	+	3.32208i	0.0485650	+	0.149468i
$495$	−36.4680	+	3.02580i	−1.63911	+	0.136000i
$496$	−3.27666	+	10.0845i	−0.147126	+	0.452808i
$497$	2.97726	−	9.16305i	0.133548	−	0.411019i
$498$	−16.1287	+	11.7182i	−0.722743	+	0.525104i
$499$	23.1081			1.03446			0.517230	−	0.855846i	$-0.326963\pi$
$499$	23.1081			1.03446			0.517230	+	0.855846i	$0.326963\pi$
$500$	1.27274	−	19.3106i	0.0569186	−	0.863597i
$501$	−2.05630			−0.0918685
$502$	−0.711917	+	0.517238i	−0.0317744	+	0.0230855i
$503$	1.85784	−	5.71785i	0.0828371	−	0.254946i	−0.901056	−	0.433702i	$-0.857207\pi$
$503$	1.85784	−	5.71785i	0.0828371	−	0.254946i	0.983894	+	0.178756i	$0.0572071\pi$
$504$	−14.9717	+	46.0781i	−0.666892	+	2.05248i
$505$	40.4988	−	3.36025i	1.80217	−	0.149529i
$506$	2.45024	+	7.54106i	0.108926	+	0.335241i
$507$	−30.0363			−1.33396
$508$	7.44549	+	22.9149i	0.330340	+	1.01668i
$509$	26.0232	+	18.9070i	1.15346	+	0.838036i	0.988937	−	0.148338i	$-0.0473922\pi$
$509$	26.0232	+	18.9070i	1.15346	+	0.838036i	0.164521	+	0.986374i	$0.447392\pi$
$510$	2.84980	−	2.45494i	0.126191	−	0.108707i
$511$	9.68289	−	7.03503i	0.428346	−	0.311211i
$512$	17.9294	+	13.0265i	0.792374	+	0.575694i
$513$	41.2751	+	29.9881i	1.82234	+	1.32401i
$514$	−6.39945	+	4.64947i	−0.282268	+	0.205080i
$515$	−0.645109	+	2.73819i	−0.0284269	+	0.120659i
$516$	−9.36007	−	6.80049i	−0.412054	−	0.299375i
$517$	−7.34083	−	22.5928i	−0.322849	−	0.993628i
$518$	−20.0554			−0.881182
$519$	−8.05782	−	24.7994i	−0.353699	−	1.08857i
$520$	−1.91860	+	8.14359i	−0.0841363	+	0.357120i
$521$	−2.50727	+	7.71658i	−0.109845	+	0.338069i	−0.990837	−	0.135062i	$-0.956877\pi$
$521$	−2.50727	+	7.71658i	−0.109845	+	0.338069i	0.880992	+	0.473132i	$0.156877\pi$
$522$	−6.47322	+	19.9225i	−0.283325	+	0.871985i
$523$	33.1919	−	24.1153i	1.45138	−	1.05449i	0.465874	−	0.884851i	$-0.345740\pi$
$523$	33.1919	−	24.1153i	1.45138	−	1.05449i	0.985506	−	0.169638i	$-0.0542599\pi$
$524$	17.5873			0.768306
$525$	−7.99527	+	53.4090i	−0.348942	+	2.33096i
$526$	4.21998			0.184000
$527$	−3.48993	+	2.53558i	−0.152024	+	0.110452i
$528$	5.36289	−	16.5053i	0.233390	−	0.718300i
$529$	8.12673	−	25.0115i	0.353336	−	1.08746i
$530$	−2.59184	−	6.18293i	−0.112582	−	0.268569i
$531$	17.6958	+	54.4622i	0.767934	+	2.36346i
$532$	−20.0798			−0.870571
$533$	3.28925	+	10.1233i	0.142473	+	0.438488i
$534$	23.6044	+	17.1496i	1.02146	+	0.742134i
$535$	−15.3324	+	1.27216i	−0.662880	+	0.0550001i
$536$	5.19154	−	3.77188i	0.224240	−	0.162920i
$537$	1.00405	+	0.729482i	0.0433278	+	0.0314795i
$538$	2.84077	+	2.06394i	0.122474	+	0.0889827i
$539$	−7.20838	+	5.23719i	−0.310487	+	0.225582i
$540$	21.9178	+	52.2858i	0.943192	+	2.25002i
$541$	−20.6382	−	14.9945i	−0.887305	−	0.644665i	0.0478687	−	0.998854i	$-0.484757\pi$
$541$	−20.6382	−	14.9945i	−0.887305	−	0.644665i	−0.935174	+	0.354189i	$0.884757\pi$
$542$	−0.661118	−	2.03471i	−0.0283975	−	0.0873984i
$543$	23.2707			0.998639
$544$	1.59006	+	4.89370i	0.0681733	+	0.209816i
$545$	−22.6560	−	13.7517i	−0.970475	−	0.589060i
$546$	3.34720	−	10.3016i	0.143247	−	0.440869i
$547$	−5.20972	+	16.0339i	−0.222751	+	0.685558i	0.775761	+	0.631027i	$0.217366\pi$
$547$	−5.20972	+	16.0339i	−0.222751	+	0.685558i	−0.998512	+	0.0545312i	$0.982634\pi$
$548$	−15.9107	+	11.5598i	−0.679671	+	0.493810i
$549$	−14.8321			−0.633017
$550$	−0.835958	+	5.58427i	−0.0356454	+	0.238114i
$551$	−18.7131			−0.797205
$552$	35.6498	−	25.9011i	1.51736	−	1.10243i
$553$	−9.17984	+	28.2527i	−0.390367	+	1.20142i
$554$	0.667690	−	2.05494i	0.0283674	−	0.0873059i
$555$	−63.7798	+	54.9428i	−2.70730	+	2.33219i
$556$	2.55595	+	7.86640i	0.108396	+	0.333610i
$557$	42.7813			1.81270			0.906351	−	0.422525i	$-0.138856\pi$
$557$	42.7813			1.81270			0.906351	+	0.422525i	$0.138856\pi$
$558$	5.19751	+	15.9963i	0.220028	+	0.677177i
$559$	3.22385	+	2.34227i	0.136354	+	0.0990673i
$560$	−15.6488	−	9.49850i	−0.661281	−	0.401385i
$561$	5.71195	−	4.14997i	0.241159	−	0.175212i
$562$	4.38823	+	3.18824i	0.185106	+	0.134488i
$563$	7.54687	+	5.48312i	0.318063	+	0.231086i	0.735348	−	0.677689i	$-0.237019\pi$
$563$	7.54687	+	5.48312i	0.318063	+	0.231086i	−0.417286	+	0.908775i	$0.637019\pi$
$564$	−49.5517	+	36.0014i	−2.08650	+	1.51593i
$565$	4.34714	+	2.63863i	0.182885	+	0.111008i
$566$	13.4416	+	9.76590i	0.564993	+	0.410491i
$567$	−25.6799	−	79.0347i	−1.07846	−	3.31915i
$568$	−5.59834			−0.234901
$569$	−5.77873	−	17.7851i	−0.242257	−	0.745590i	−0.996076	−	0.0885076i	$-0.971790\pi$
$569$	−5.77873	−	17.7851i	−0.242257	−	0.745590i	0.753819	−	0.657083i	$-0.228210\pi$
$570$	9.92604	−	8.55073i	0.415756	−	0.358151i
$571$	0.427907	−	1.31696i	0.0179073	−	0.0551131i	−0.941704	−	0.336444i	$-0.890776\pi$
$571$	0.427907	−	1.31696i	0.0179073	−	0.0551131i	0.959611	+	0.281331i	$0.0907758\pi$
$572$	−2.25149	+	6.92938i	−0.0941395	+	0.289732i
$573$	−25.2679	+	18.3582i	−1.05558	+	0.766926i
$574$	9.51117			0.396988
$575$	24.6125	−	25.0338i	1.02641	−	1.04398i
$576$	−16.8906			−0.703774
$577$	−17.5492	+	12.7502i	−0.730581	+	0.530798i	−0.889747	−	0.456454i	$-0.849119\pi$
$577$	−17.5492	+	12.7502i	−0.730581	+	0.530798i	0.159166	+	0.987252i	$0.449119\pi$
$578$	−0.160290	+	0.493321i	−0.00666717	+	0.0205194i
$579$	−12.8272	+	39.4780i	−0.533079	+	1.64065i
$580$	−17.7763	−	10.7899i	−0.738120	−	0.448024i
$581$	12.1976	+	37.5404i	0.506042	+	1.55744i
$582$	−24.9133			−1.03269
$583$	−3.88872	−	11.9683i	−0.161054	−	0.495675i
$584$	−5.62640	−	4.08782i	−0.232822	−	0.169155i
$585$	−12.5631	−	29.9698i	−0.519420	−	1.23910i
$586$	13.0413	−	9.47507i	0.538732	−	0.391412i
$587$	3.03243	+	2.20319i	0.125162	+	0.0909353i	0.648605	−	0.761125i	$-0.275353\pi$
$587$	3.03243	+	2.20319i	0.125162	+	0.0909353i	−0.523443	+	0.852061i	$0.675353\pi$
$588$	18.5855	+	13.5032i	0.766455	+	0.556862i
$589$	−12.1557	+	8.83161i	−0.500865	+	0.363900i
$590$	8.80595	−	0.730643i	0.362535	−	0.0300801i
$591$	−19.0093	−	13.8111i	−0.781938	−	0.568111i
$592$	−8.81788	−	27.1386i	−0.362413	−	1.11539i
$593$	−17.4374			−0.716070			−0.358035	−	0.933708i	$-0.616553\pi$
$593$	−17.4374			−0.716070			−0.358035	+	0.933708i	$0.616553\pi$
$594$	−5.11163	−	15.7320i	−0.209733	−	0.645491i
$595$	−2.87913	−	6.86829i	−0.118033	−	0.281572i
$596$	3.86458	−	11.8940i	0.158299	−	0.487196i
$597$	−4.73926	+	14.5860i	−0.193965	+	0.596963i
$598$	−5.69662	+	4.13884i	−0.232952	+	0.169250i
$599$	31.4883			1.28658			0.643288	−	0.765624i	$-0.277570\pi$
$599$	31.4883			1.28658			0.643288	+	0.765624i	$0.277570\pi$
$600$	30.9509	−	5.17168i	1.26356	−	0.211133i
$601$	−10.9766			−0.447745			−0.223872	−	0.974618i	$-0.571870\pi$
$601$	−10.9766			−0.447745			−0.223872	+	0.974618i	$0.571870\pi$
$602$	2.88067	−	2.09293i	0.117407	−	0.0853015i
$603$	−7.70213	+	23.7047i	−0.313655	+	0.965330i
$604$	−1.64297	+	5.05653i	−0.0668514	+	0.205747i
$605$	3.20999	−	13.6249i	0.130505	−	0.553932i
$606$	9.44698	+	29.0748i	0.383758	+	1.18108i
$607$	−20.6642			−0.838735			−0.419368	−	0.907817i	$-0.637748\pi$
$607$	−20.6642			−0.838735			−0.419368	+	0.907817i	$0.637748\pi$
$608$	5.53829	+	17.0451i	0.224607	+	0.691270i
$609$	46.9460	+	34.1082i	1.90235	+	1.38214i
$610$	−0.524828	+	2.22766i	−0.0212497	+	0.0901951i
$611$	17.0669	−	12.3998i	0.690453	−	0.501643i
$612$	−10.5262	−	7.64772i	−0.425496	−	0.309141i
$613$	−38.3567	−	27.8677i	−1.54921	−	1.12557i	−0.944211	−	0.329342i	$-0.893173\pi$
$613$	−38.3567	−	27.8677i	−1.54921	−	1.12557i	−0.605000	−	0.796225i	$-0.706827\pi$
$614$	7.04171	−	5.11610i	0.284180	−	0.206469i
$615$	30.2473	−	26.0563i	1.21969	−	1.05069i
$616$	11.3527	+	8.24824i	0.457415	+	0.332331i
$617$	−8.02960	−	24.7126i	−0.323260	−	0.994891i	−0.972220	−	0.234068i	$-0.924796\pi$
$617$	−8.02960	−	24.7126i	−0.323260	−	0.994891i	0.648961	−	0.760822i	$-0.275204\pi$
$618$	−2.11628			−0.0851292
$619$	−5.28989	−	16.2806i	−0.212618	−	0.654372i	−0.999314	−	0.0370312i	$-0.988210\pi$
$619$	−5.28989	−	16.2806i	−0.212618	−	0.654372i	0.786696	−	0.617341i	$-0.211790\pi$
$620$	−16.6394	+	1.38059i	−0.668253	+	0.0554460i
$621$	−31.7811	+	97.8121i	−1.27533	+	3.92506i
$622$	−1.57600	+	4.85042i	−0.0631917	+	0.194484i
$623$	46.7352	−	33.9551i	1.87241	−	1.36038i
$624$	15.4117			0.616962
$625$	23.6419	−	8.12774i	0.945676	−	0.325110i
$626$	−11.1665			−0.446303
$627$	19.8951	−	14.4546i	0.794534	−	0.577263i
$628$	−5.01791	+	15.4435i	−0.200236	+	0.616264i
$629$	3.58736	−	11.0407i	0.143037	−	0.440223i
$630$	−28.9378	+	2.40101i	−1.15291	+	0.0956585i
$631$	−5.53357	−	17.0306i	−0.220288	−	0.677976i	−0.998736	−	0.0502670i	$-0.983993\pi$
$631$	−5.53357	−	17.0306i	−0.220288	−	0.677976i	0.778448	−	0.627709i	$-0.216007\pi$
$632$	17.2615			0.686626
$633$	−27.3503	−	84.1756i	−1.08708	−	3.34568i
$634$	−5.90052	−	4.28698i	−0.234340	−	0.170258i
$635$	−23.5819	+	20.3145i	−0.935819	+	0.806156i
$636$	−26.2495	+	19.0713i	−1.04086	+	0.756228i
$637$	−6.40135	−	4.65085i	−0.253631	−	0.184273i
$638$	4.90851	+	3.56624i	0.194330	+	0.141189i
$639$	17.5917	−	12.7811i	0.695915	−	0.505612i
$640$	−5.87465	+	24.9352i	−0.232216	+	0.985650i
$641$	−11.3857	−	8.27217i	−0.449707	−	0.326731i	0.339773	−	0.940507i	$-0.389650\pi$
$641$	−11.3857	−	8.27217i	−0.449707	−	0.326731i	−0.789480	+	0.613776i	$0.789650\pi$
$642$	−3.57654	−	11.0074i	−0.141155	−	0.434429i
$643$	0.908361			0.0358223			0.0179111	−	0.999840i	$-0.494298\pi$
$643$	0.908361			0.0358223			0.0179111	+	0.999840i	$0.494298\pi$
$644$	−12.5083	−	38.4966i	−0.492896	−	1.51698i
$645$	3.42738	−	14.5477i	0.134953	−	0.572814i
$646$	−0.558299	+	1.71827i	−0.0219660	+	0.0676044i
$647$	−13.2660	+	40.8286i	−0.521541	+	1.60514i	0.249515	+	0.968371i	$0.419729\pi$
$647$	−13.2660	+	40.8286i	−0.521541	+	1.60514i	−0.771056	+	0.636767i	$0.780271\pi$
$648$	−39.0657	+	28.3829i	−1.53464	+	1.11498i
$649$	16.5861			0.651060
$650$	−4.94576	+	0.826403i	−0.193989	+	0.0324142i
$651$	46.5925			1.82610
$652$	7.32826	−	5.32429i	0.286997	−	0.208515i
$653$	−10.4062	+	32.0270i	−0.407226	+	1.25331i	0.511796	+	0.859107i	$0.328980\pi$
$653$	−10.4062	+	32.0270i	−0.407226	+	1.25331i	−0.919022	+	0.394206i	$0.871020\pi$
$654$	6.16105	−	18.9618i	0.240916	−	0.741463i
$655$	8.78341	+	20.9532i	0.343196	+	0.818708i
$656$	4.18184	+	12.8704i	0.163273	+	0.502504i
$657$	27.0124			1.05385
$658$	−5.82503	−	17.9276i	−0.227083	−	0.698891i
$659$	−9.38176	−	6.81625i	−0.365461	−	0.265523i	0.389865	−	0.920872i	$-0.372522\pi$
$659$	−9.38176	−	6.81625i	−0.365461	−	0.265523i	−0.755326	+	0.655349i	$0.772522\pi$
$660$	27.2336	−	2.25961i	1.06007	−	0.0879552i
$661$	−23.3935	+	16.9964i	−0.909902	+	0.661083i	−0.940990	−	0.338434i	$-0.890103\pi$
$661$	−23.3935	+	16.9964i	−0.909902	+	0.661083i	0.0310880	+	0.999517i	$0.490103\pi$
$662$	4.68826	+	3.40622i	0.182214	+	0.132386i
$663$	5.07246	+	3.68536i	0.196998	+	0.143127i
$664$	18.5556	−	13.4815i	0.720099	−	0.523182i
$665$	−10.0282	−	23.9227i	−0.388877	−	0.927683i
$666$	−36.6188	−	26.6051i	−1.41895	−	1.03093i
$667$	−11.6569	−	35.8763i	−0.451358	−	1.38914i
$668$	1.09756			0.0424658
$669$	4.32823	+	13.3209i	0.167339	+	0.515017i
$670$	3.28772	+	1.99558i	0.127016	+	0.0770961i
$671$	−1.32751	+	4.08566i	−0.0512480	+	0.157725i
$672$	17.1740	−	52.8560i	0.662500	−	2.03897i
$673$	8.14488	−	5.91760i	0.313962	−	0.228107i	−0.419633	−	0.907694i	$-0.637841\pi$
$673$	8.14488	−	5.91760i	0.313962	−	0.228107i	0.733595	+	0.679587i	$0.237841\pi$
$674$	5.05833			0.194839
$675$	−51.3461	+	52.2248i	−1.97631	+	2.01014i
$676$	16.0320			0.616615
$677$	23.4463	−	17.0347i	0.901114	−	0.654698i	−0.0376376	−	0.999291i	$-0.511983\pi$
$677$	23.4463	−	17.0347i	0.901114	−	0.654698i	0.938752	+	0.344594i	$0.111983\pi$
$678$	−1.18216	+	3.63830i	−0.0454005	+	0.139728i
$679$	−15.2428	+	46.9126i	−0.584966	+	1.80034i
$680$	−3.27862	+	2.82435i	−0.125730	+	0.108309i
$681$	−9.79820	−	30.1558i	−0.375468	−	1.15557i
$682$	4.87156			0.186542
$683$	0.178039	+	0.547948i	0.00681247	+	0.0209666i	0.954405	−	0.298515i	$-0.0964913\pi$
$683$	0.178039	+	0.547948i	0.00681247	+	0.0209666i	−0.947592	+	0.319482i	$0.896491\pi$
$684$	−36.6634	−	26.6375i	−1.40186	−	1.01851i
$685$	−21.7182	−	13.1825i	−0.829809	−	0.503678i
$686$	4.06358	−	2.95236i	0.155148	−	0.112722i
$687$	26.6695	+	19.3765i	1.01750	+	0.739261i
$688$	4.09869	+	2.97787i	0.156261	+	0.113530i
$689$	9.04100	−	6.56867i	0.344434	−	0.250246i
$690$	22.5765	+	13.7035i	0.859471	+	0.521682i
$691$	−24.5556	−	17.8407i	−0.934140	−	0.678692i	0.0128630	−	0.999917i	$-0.495905\pi$
$691$	−24.5556	−	17.8407i	−0.934140	−	0.678692i	−0.947003	+	0.321225i	$0.895905\pi$
$692$	4.30090	+	13.2368i	0.163496	+	0.503188i
$693$	−54.5045			−2.07045
$694$	5.07375	+	15.6154i	0.192597	+	0.592752i
$695$	−8.09538	+	6.97372i	−0.307075	+	0.264528i
$696$	10.4195	−	32.0681i	0.394952	−	1.21554i
$697$	−1.70129	+	5.23602i	−0.0644408	+	0.198328i
$698$	2.87942	−	2.09202i	0.108988	−	0.0791841i
$699$	−40.9850			−1.55020
$700$	4.26751	−	28.5073i	0.161297	−	1.07747i
$701$	−1.16659			−0.0440615			−0.0220308	−	0.999757i	$-0.507013\pi$
$701$	−1.16659			−0.0440615			−0.0220308	+	0.999757i	$0.507013\pi$
$702$	11.8842	−	8.63435i	0.448539	−	0.325883i
$703$	12.4950	−	38.4557i	0.471258	−	1.45038i
$704$	−1.51176	+	4.65270i	−0.0569764	+	0.175355i
$705$	−67.6383	−	41.0552i	−2.54741	−	1.54623i
$706$	−0.226420	−	0.696850i	−0.00852144	−	0.0262263i
$707$	60.5289			2.27642
$708$	−13.2149	−	40.6713i	−0.496646	−	1.52852i
$709$	−24.0086	−	17.4432i	−0.901661	−	0.655095i	0.0372312	−	0.999307i	$-0.488146\pi$
$709$	−24.0086	−	17.4432i	−0.901661	−	0.655095i	−0.938892	+	0.344212i	$0.888146\pi$
$710$	−1.29714	−	3.09438i	−0.0486808	−	0.116130i
$711$	−54.2408	+	39.4082i	−2.03419	+	1.47792i
$712$	−27.1562	−	19.7302i	−1.01772	−	0.739419i
$713$	−24.5038	−	17.8031i	−0.917676	−	0.666731i
$714$	4.53250	−	3.29305i	0.169624	−	0.123239i
$715$	−9.37995	+	0.778269i	−0.350790	+	0.0291056i
$716$	−0.535914	−	0.389364i	−0.0200280	−	0.0145512i
$717$	0.814278	+	2.50609i	0.0304098	+	0.0935917i
$718$	2.20402			0.0822532
$719$	3.98593	+	12.2674i	0.148650	+	0.457497i	0.997462	−	0.0711968i	$-0.0226818\pi$
$719$	3.98593	+	12.2674i	0.148650	+	0.457497i	−0.848812	+	0.528694i	$0.822682\pi$
$720$	−15.9723	−	38.1025i	−0.595251	−	1.42000i
$721$	−1.29481	+	3.98503i	−0.0482214	+	0.148410i
$722$	1.10091	−	3.38825i	0.0409715	−	0.126097i
$723$	−46.0625	+	33.4663i	−1.71308	+	1.24463i
$724$	−12.4208			−0.461616
$725$	3.97704	−	26.5669i	0.147704	−	0.986671i
$726$	10.5304			0.390819
$727$	19.9482	−	14.4932i	0.739838	−	0.537524i	−0.152822	−	0.988254i	$-0.548836\pi$
$727$	19.9482	−	14.4932i	0.739838	−	0.537524i	0.892661	+	0.450730i	$0.148836\pi$
$728$	−3.85087	+	11.8518i	−0.142723	+	0.439256i
$729$	13.9209	−	42.8442i	0.515589	−	1.58682i
$730$	0.955825	−	4.05704i	0.0353767	−	0.150158i
$731$	0.636913	+	1.96022i	0.0235571	+	0.0725012i
$732$	11.0763			0.409391
$733$	14.6384	+	45.0525i	0.540683	+	1.66405i	0.731038	+	0.682337i	$0.239036\pi$
$733$	14.6384	+	45.0525i	0.540683	+	1.66405i	−0.190355	+	0.981715i	$0.560964\pi$
$734$	−15.2283	−	11.0640i	−0.562088	−	0.408381i
$735$	−6.80549	+	28.8862i	−0.251024	+	1.06548i
$736$	−29.2285	+	21.2358i	−1.07738	+	0.782760i
$737$	5.84037	+	4.24328i	0.215133	+	0.156303i
$738$	17.3663	+	12.6173i	0.639261	+	0.464451i
$739$	−38.9558	+	28.3030i	−1.43301	+	1.04114i	−0.443565	+	0.896242i	$0.646286\pi$
$739$	−38.9558	+	28.3030i	−1.43301	+	1.04114i	−0.989446	+	0.144901i	$0.953714\pi$
$740$	34.0428	−	29.3259i	1.25144	−	1.07804i
$741$	17.6677	+	12.8363i	0.649039	+	0.471555i
$742$	−3.08574	−	9.49695i	−0.113281	−	0.348644i
$743$	38.0146			1.39462			0.697310	−	0.716770i	$-0.254380\pi$
$743$	38.0146			1.39462			0.697310	+	0.716770i	$0.254380\pi$
$744$	−8.36612	−	25.7483i	−0.306717	−	0.943977i
$745$	16.1003	−	1.33586i	0.589868	−	0.0489422i
$746$	1.54386	−	4.75151i	0.0565247	−	0.173965i
$747$	−27.5290	+	84.7255i	−1.00723	+	3.09994i
$748$	−3.04878	+	2.21507i	−0.111474	+	0.0809909i
$749$	−22.9156			−0.837319
$750$	10.0299	+	15.9092i	0.366240	+	0.580923i
$751$	−26.4232			−0.964196			−0.482098	−	0.876117i	$-0.660125\pi$
$751$	−26.4232			−0.964196			−0.482098	+	0.876117i	$0.660125\pi$
$752$	21.6982	−	15.7647i	0.791254	−	0.574880i
$753$	−1.70009	+	5.23234i	−0.0619548	+	0.190677i
$754$	−1.66498	+	5.12428i	−0.0606349	+	0.186615i
$755$	−6.84478	+	0.567921i	−0.249107	+	0.0206688i
$756$	26.0945	+	80.3107i	0.949048	+	2.92087i
$757$	35.0296			1.27317			0.636586	−	0.771205i	$-0.280346\pi$
$757$	35.0296			1.27317			0.636586	+	0.771205i	$0.280346\pi$
$758$	0.0165378	+	0.0508980i	0.000600678	+	0.00184870i
$759$	40.1053	+	29.1382i	1.45573	+	1.05765i
$760$	−11.4197	+	9.83740i	−0.414235	+	0.356840i
$761$	30.8755	−	22.4324i	1.11924	−	0.813172i	0.135143	−	0.990826i	$-0.456851\pi$
$761$	30.8755	−	22.4324i	1.11924	−	0.813172i	0.984093	+	0.177654i	$0.0568507\pi$
$762$	−18.9431	−	13.7629i	−0.686235	−	0.498579i
$763$	−31.9361	−	23.2029i	−1.15616	−	0.840002i
$764$	13.4869	−	9.79879i	0.487938	−	0.354508i
$765$	3.85438	−	16.3601i	0.139356	−	0.591500i
$766$	−12.9412	−	9.40233i	−0.467585	−	0.339720i
$767$	4.55156	+	14.0082i	0.164347	+	0.505809i
$768$	−4.69758			−0.169509
$769$	−0.628149	−	1.93324i	−0.0226516	−	0.0697146i	0.939092	−	0.343667i	$-0.111669\pi$
$769$	−0.628149	−	1.93324i	−0.0226516	−	0.0697146i	−0.961743	+	0.273952i	$0.911669\pi$
$770$	−1.92863	+	8.18614i	−0.0695029	+	0.295008i
$771$	−15.2822	+	47.0338i	−0.550375	+	1.69388i
$772$	6.84656	−	21.0716i

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+(0.419644 - 0.304889i) q^{2} +(1.00213 - 3.08423i) q^{3} +(-0.534891 + 1.64622i) q^{4} +(-2.22841 + 0.184895i) q^{5} +(-0.519812 - 1.59982i) q^{6} -3.33055 q^{7} +(0.598031 + 1.84055i) q^{8} +(-6.08119 - 4.41824i) q^{9} +(-0.878766 + 0.757007i) q^{10} +(-1.76134 + 1.27969i) q^{11} +(4.54131 + 3.29946i) q^{12} +(-1.56415 - 1.13642i) q^{13} +(-1.39764 + 1.01545i) q^{14} +(-1.66290 + 7.05823i) q^{15} +(-1.98860 - 1.44480i) q^{16} +(-0.309017 - 0.951057i) q^{17} -3.89901 q^{18} +(-1.07633 - 3.31259i) q^{19} +(0.887578 - 3.76736i) q^{20} +(-3.33764 + 10.2722i) q^{21} +(-0.348972 + 1.07403i) q^{22} +(5.68035 - 4.12702i) q^{23} +6.27599 q^{24} +(4.93163 - 0.824042i) q^{25} -1.00286 q^{26} +(-11.8502 + 8.60969i) q^{27} +(1.78148 - 5.48283i) q^{28} +(1.66022 - 5.10964i) q^{29} +(1.45415 + 3.46894i) q^{30} +(-1.33303 - 4.10266i) q^{31} -5.14555 q^{32} +(2.18177 + 6.71480i) q^{33} +(-0.419644 - 0.304889i) q^{34} +(7.42183 - 0.615800i) q^{35} +(10.5262 - 7.64772i) q^{36} +(9.39182 + 6.82356i) q^{37} +(-1.46165 - 1.06195i) q^{38} +(-5.07246 + 3.68536i) q^{39} +(-1.67297 - 3.99093i) q^{40} +(-4.45403 - 3.23604i) q^{41} +(1.73126 + 5.32827i) q^{42} -2.06109 q^{43} +(-1.16453 - 3.58405i) q^{44} +(14.3683 + 8.72128i) q^{45} +(1.12544 - 3.46375i) q^{46} +(-3.37178 + 10.3773i) q^{47} +(-6.44894 + 4.68543i) q^{48} +4.09255 q^{49} +(1.81828 - 1.84940i) q^{50} -3.24296 q^{51} +(2.70745 - 1.96707i) q^{52} +(-1.78616 + 5.49725i) q^{53} +(-2.34787 + 7.22600i) q^{54} +(3.68838 - 3.17733i) q^{55} +(-1.99177 - 6.13004i) q^{56} -11.2954 q^{57} +(-0.861170 - 2.65041i) q^{58} +(-6.16333 - 4.47792i) q^{59} +(-10.7300 - 6.51288i) q^{60} +(1.59635 - 1.15982i) q^{61} +(-1.81025 - 1.31523i) q^{62} +(20.2537 + 14.7152i) q^{63} +(1.81790 - 1.32079i) q^{64} +(3.69568 + 2.24320i) q^{65} +(2.96283 + 2.15262i) q^{66} +(-1.02466 - 3.15358i) q^{67} +1.73094 q^{68} +(-7.03624 - 21.6553i) q^{69} +(2.92677 - 2.52125i) q^{70} +(-0.893924 + 2.75121i) q^{71} +(4.49526 - 13.8350i) q^{72} +(-2.90730 + 2.11227i) q^{73} +6.02164 q^{74} +(2.40059 - 16.0361i) q^{75} +6.02899 q^{76} +(5.86623 - 4.26206i) q^{77} +(-1.00500 + 3.09307i) q^{78} +(2.75626 - 8.48288i) q^{79} +(4.69855 + 2.85193i) q^{80} +(7.71043 + 23.7303i) q^{81} -2.85574 q^{82} +(-3.66235 - 11.2715i) q^{83} +(-15.1251 - 10.9890i) q^{84} +(0.864462 + 2.06221i) q^{85} +(-0.864925 + 0.628405i) q^{86} +(-14.0956 - 10.2410i) q^{87} +(-3.40867 - 2.47654i) q^{88} +(-14.0323 + 10.1950i) q^{89} +(8.68859 - 0.720905i) q^{90} +(5.20946 + 3.78490i) q^{91} +(3.75563 + 11.5586i) q^{92} -13.9894 q^{93} +(1.74897 + 5.38278i) q^{94} +(3.01098 + 7.18281i) q^{95} +(-5.15650 + 15.8701i) q^{96} +(4.57668 - 14.0856i) q^{97} +(1.71741 - 1.24777i) q^{98} +16.3650 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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