LMFDB - Embedded newform 425.2.r.a.69.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(69,425)]

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([9, 0]))

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

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

chi := DirichletCharacter("425.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, 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:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.1
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.60604 + 0.846752i) q^{2} +(-1.86275 - 2.56385i) q^{3} +(4.45640 - 3.23776i) q^{4} +(0.0540158 + 2.23542i) q^{5} +(7.02533 + 5.10420i) q^{6} -2.47810i q^{7} +(-5.65071 + 7.77753i) q^{8} +(-2.17645 + 6.69843i) q^{9} +(-2.03361 - 5.77983i) q^{10} +(-1.18679 - 3.65255i) q^{11} +(-16.6023 - 5.39440i) q^{12} +(-1.34575 - 0.437262i) q^{13} +(2.09834 + 6.45802i) q^{14} +(5.63065 - 4.30250i) q^{15} +(4.73592 - 14.5757i) q^{16} +(0.587785 - 0.809017i) q^{17} -19.2993i q^{18} +(-0.679976 - 0.494032i) q^{19} +(7.47846 + 9.78701i) q^{20} +(-6.35348 + 4.61608i) q^{21} +(6.18561 + 8.51377i) q^{22} +(-1.51412 + 0.491967i) q^{23} +30.4663 q^{24} +(-4.99416 + 0.241496i) q^{25} +3.87733 q^{26} +(12.1860 - 3.95947i) q^{27} +(-8.02351 - 11.0434i) q^{28} +(-4.61529 + 3.35321i) q^{29} +(-11.0305 + 15.9802i) q^{30} +(-3.88614 - 2.82345i) q^{31} +22.7677i q^{32} +(-7.15392 + 9.84652i) q^{33} +(-0.846752 + 2.60604i) q^{34} +(5.53959 - 0.133857i) q^{35} +(11.9888 + 36.8977i) q^{36} +(4.34079 + 1.41041i) q^{37} +(2.19036 + 0.711693i) q^{38} +(1.38572 + 4.26482i) q^{39} +(-17.6912 - 12.2116i) q^{40} +(-0.386186 + 1.18856i) q^{41} +(12.6487 - 17.4095i) q^{42} +8.80279i q^{43} +(-17.1149 - 12.4347i) q^{44} +(-15.0913 - 4.50345i) q^{45} +(3.52927 - 2.56417i) q^{46} +(2.80817 + 3.86511i) q^{47} +(-46.1916 + 15.0086i) q^{48} +0.859006 q^{49} +(12.8105 - 4.85817i) q^{50} -3.16909 q^{51} +(-7.41296 + 2.40862i) q^{52} +(-1.10303 - 1.51819i) q^{53} +(-28.4044 + 20.6370i) q^{54} +(8.10087 - 2.85026i) q^{55} +(19.2735 + 14.0030i) q^{56} +2.66361i q^{57} +(9.18828 - 12.6466i) q^{58} +(-1.27514 + 3.92447i) q^{59} +(11.1619 - 37.4044i) q^{60} +(3.05333 + 9.39720i) q^{61} +(12.5182 + 4.06740i) q^{62} +(16.5994 + 5.39347i) q^{63} +(-9.80678 - 30.1822i) q^{64} +(0.904770 - 3.03194i) q^{65} +(10.3058 - 31.7180i) q^{66} +(-9.16910 + 12.6202i) q^{67} -5.50841i q^{68} +(4.08175 + 2.96556i) q^{69} +(-14.3230 + 5.03950i) q^{70} +(0.0639051 - 0.0464298i) q^{71} +(-39.7988 - 54.7783i) q^{72} +(3.40877 - 1.10758i) q^{73} -12.5065 q^{74} +(9.92202 + 12.3544i) q^{75} -4.62980 q^{76} +(-9.05140 + 2.94098i) q^{77} +(-7.22249 - 9.94090i) q^{78} +(0.953265 - 0.692588i) q^{79} +(32.8385 + 9.79943i) q^{80} +(-15.7568 - 11.4480i) q^{81} -3.42443i q^{82} +(-5.68451 + 7.82406i) q^{83} +(-13.3679 + 41.1421i) q^{84} +(1.84024 + 1.27024i) q^{85} +(-7.45378 - 22.9404i) q^{86} +(17.1942 + 5.58674i) q^{87} +(35.1140 + 11.4092i) q^{88} +(1.37884 + 4.24364i) q^{89} +(43.1419 - 1.04247i) q^{90} +(-1.08358 + 3.33492i) q^{91} +(-5.15465 + 7.09476i) q^{92} +15.2228i q^{93} +(-10.5910 - 7.69480i) q^{94} +(1.06764 - 1.54671i) q^{95} +(58.3730 - 42.4105i) q^{96} +(0.481530 + 0.662769i) q^{97} +(-2.23860 + 0.727365i) q^{98} +27.0494 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	−2.60604	+	0.846752i	−1.84275	+	0.598744i	−0.844771	+	0.535128i	$0.820263\pi$
$2$	−2.60604	+	0.846752i	−1.84275	+	0.598744i	−0.997974	+	0.0636161i	$0.979737\pi$
$3$	−1.86275	−	2.56385i	−1.07546	−	1.48024i	−0.864426	−	0.502760i	$-0.832318\pi$
$3$	−1.86275	−	2.56385i	−1.07546	−	1.48024i	−0.211031	−	0.977479i	$-0.567682\pi$
$4$	4.45640	−	3.23776i	2.22820	−	1.61888i
$5$	0.0540158	+	2.23542i	0.0241566	+	0.999708i
$5$	0.0540158	+	2.23542i	0.0241566	+	0.999708i
$6$	7.02533	+	5.10420i	2.86808	+	2.08378i
$7$		−	2.47810i		−	0.936635i	−0.883560	−	0.468317i	$-0.844860\pi$
$7$		−	2.47810i		−	0.936635i	0.883560	−	0.468317i	$-0.155140\pi$
$8$	−5.65071	+	7.77753i	−1.99783	+	2.74977i
$9$	−2.17645	+	6.69843i	−0.725484	+	2.23281i
$10$	−2.03361	−	5.77983i	−0.643084	−	1.82774i
$11$	−1.18679	−	3.65255i	−0.357830	−	1.10129i	−0.954351	−	0.298689i	$-0.903451\pi$
$11$	−1.18679	−	3.65255i	−0.357830	−	1.10129i	0.596521	−	0.802597i	$-0.296549\pi$
$12$	−16.6023	−	5.39440i	−4.79266	−	1.55723i
$13$	−1.34575	−	0.437262i	−0.373245	−	0.121275i	0.116387	−	0.993204i	$-0.462869\pi$
$13$	−1.34575	−	0.437262i	−0.373245	−	0.121275i	−0.489632	+	0.871929i	$0.662869\pi$
$14$	2.09834	+	6.45802i	0.560805	+	1.72598i
$15$	5.63065	−	4.30250i	1.45383	−	1.11090i
$16$	4.73592	−	14.5757i	1.18398	−	3.64392i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$18$		−	19.2993i		−	4.54888i
$19$	−0.679976	−	0.494032i	−0.155997	−	0.113339i	0.507048	−	0.861918i	$-0.330737\pi$
$19$	−0.679976	−	0.494032i	−0.155997	−	0.113339i	−0.663046	+	0.748579i	$0.730737\pi$
$20$	7.47846	+	9.78701i	1.67223	+	2.18844i
$21$	−6.35348	+	4.61608i	−1.38644	+	1.00731i
$22$	6.18561	+	8.51377i	1.31878	+	1.81514i
$23$	−1.51412	+	0.491967i	−0.315716	+	0.102582i	−0.462588	−	0.886573i	$-0.653079\pi$
$23$	−1.51412	+	0.491967i	−0.315716	+	0.102582i	0.146873	+	0.989155i	$0.453079\pi$
$24$	30.4663			6.21890
$25$	−4.99416	+	0.241496i	−0.998833	+	0.0482991i
$26$	3.87733			0.760408
$27$	12.1860	−	3.95947i	2.34519	−	0.762000i
$28$	−8.02351	−	11.0434i	−1.51630	−	2.08701i
$29$	−4.61529	+	3.35321i	−0.857038	+	0.622675i	−0.927078	−	0.374870i	$-0.877687\pi$
$29$	−4.61529	+	3.35321i	−0.857038	+	0.622675i	0.0700394	+	0.997544i	$0.477687\pi$
$30$	−11.0305	+	15.9802i	−2.01389	+	2.91758i
$31$	−3.88614	−	2.82345i	−0.697972	−	0.507106i	0.181299	−	0.983428i	$-0.441970\pi$
$31$	−3.88614	−	2.82345i	−0.697972	−	0.507106i	−0.879271	+	0.476322i	$0.841970\pi$
$32$			22.7677i			4.02480i
$33$	−7.15392	+	9.84652i	−1.24534	+	1.71406i
$34$	−0.846752	+	2.60604i	−0.145217	+	0.446931i
$35$	5.53959	−	0.133857i	0.936362	−	0.0226259i
$36$	11.9888	+	36.8977i	1.99813	+	6.14962i
$37$	4.34079	+	1.41041i	0.713621	+	0.231870i	0.643255	−	0.765652i	$-0.277583\pi$
$37$	4.34079	+	1.41041i	0.713621	+	0.231870i	0.0703659	+	0.997521i	$0.477583\pi$
$38$	2.19036	+	0.711693i	0.355324	+	0.115452i
$39$	1.38572	+	4.26482i	0.221893	+	0.682917i
$40$	−17.6912	−	12.2116i	−2.79723	−	1.93082i
$41$	−0.386186	+	1.18856i	−0.0603122	+	0.185622i	−0.976673	−	0.214731i	$-0.931112\pi$
$41$	−0.386186	+	1.18856i	−0.0603122	+	0.185622i	0.916361	+	0.400353i	$0.131112\pi$
$42$	12.6487	−	17.4095i	1.95174	−	2.68634i
$43$			8.80279i			1.34241i	0.741271	+	0.671206i	$0.234224\pi$
$43$			8.80279i			1.34241i	−0.741271	+	0.671206i	$0.765776\pi$
$44$	−17.1149	−	12.4347i	−2.58017	−	1.87460i
$45$	−15.0913	−	4.50345i	−2.24968	−	0.671335i
$46$	3.52927	−	2.56417i	0.520363	−	0.378066i
$47$	2.80817	+	3.86511i	0.409614	+	0.563785i	0.963124	−	0.269057i	$-0.0867121\pi$
$47$	2.80817	+	3.86511i	0.409614	+	0.563785i	−0.553511	+	0.832842i	$0.686712\pi$
$48$	−46.1916	+	15.0086i	−6.66719	+	2.16630i
$49$	0.859006			0.122715
$50$	12.8105	−	4.85817i	1.81168	−	0.687048i
$51$	−3.16909			−0.443762
$52$	−7.41296	+	2.40862i	−1.02799	+	0.334015i
$53$	−1.10303	−	1.51819i	−0.151513	−	0.208540i	0.726513	−	0.687153i	$-0.241140\pi$
$53$	−1.10303	−	1.51819i	−0.151513	−	0.208540i	−0.878026	+	0.478613i	$0.841140\pi$
$54$	−28.4044	+	20.6370i	−3.86535	+	2.80834i
$55$	8.10087	−	2.85026i	1.09232	−	0.384328i
$56$	19.2735	+	14.0030i	2.57553	+	1.87124i
$57$			2.66361i			0.352804i
$58$	9.18828	−	12.6466i	1.20648	−	1.66058i
$59$	−1.27514	+	3.92447i	−0.166009	+	0.510923i	−0.999109	−	0.0421992i	$-0.986564\pi$
$59$	−1.27514	+	3.92447i	−0.166009	+	0.510923i	0.833100	+	0.553122i	$0.186564\pi$
$60$	11.1619	−	37.4044i	1.44100	−	4.82888i
$61$	3.05333	+	9.39720i	0.390939	+	1.20319i	0.932079	+	0.362255i	$0.117993\pi$
$61$	3.05333	+	9.39720i	0.390939	+	1.20319i	−0.541140	+	0.840933i	$0.682007\pi$
$62$	12.5182	+	4.06740i	1.58981	+	0.516561i
$63$	16.5994	+	5.39347i	2.09133	+	0.679514i
$64$	−9.80678	−	30.1822i	−1.22585	−	3.77277i
$65$	0.904770	−	3.03194i	0.112223	−	0.376065i
$66$	10.3058	−	31.7180i	1.26856	−	3.90421i
$67$	−9.16910	+	12.6202i	−1.12018	+	1.54180i	−0.314691	+	0.949194i	$0.601901\pi$
$67$	−9.16910	+	12.6202i	−1.12018	+	1.54180i	−0.805492	+	0.592606i	$0.798099\pi$
$68$		−	5.50841i		−	0.667993i
$69$	4.08175	+	2.96556i	0.491385	+	0.357012i
$70$	−14.3230	+	5.03950i	−1.71193	+	0.602335i
$71$	0.0639051	−	0.0464298i	0.00758414	−	0.00551020i	−0.583987	−	0.811763i	$-0.698508\pi$
$71$	0.0639051	−	0.0464298i	0.00758414	−	0.00551020i	0.591571	+	0.806253i	$0.298508\pi$
$72$	−39.7988	−	54.7783i	−4.69033	−	6.45569i
$73$	3.40877	−	1.10758i	0.398966	−	0.129632i	−0.102660	−	0.994717i	$-0.532735\pi$
$73$	3.40877	−	1.10758i	0.398966	−	0.129632i	0.501626	+	0.865085i	$0.332735\pi$
$74$	−12.5065			−1.45385
$75$	9.92202	+	12.3544i	1.14570	+	1.42657i
$76$	−4.62980			−0.531075
$77$	−9.05140	+	2.94098i	−1.03150	+	0.335156i
$78$	−7.22249	−	9.94090i	−0.817785	−	1.12559i
$79$	0.953265	−	0.692588i	0.107251	−	0.0779222i	−0.532867	−	0.846199i	$-0.678885\pi$
$79$	0.953265	−	0.692588i	0.107251	−	0.0779222i	0.640118	+	0.768277i	$0.278885\pi$
$80$	32.8385	+	9.79943i	3.67145	+	1.09561i
$81$	−15.7568	−	11.4480i	−1.75075	−	1.27200i
$82$		−	3.42443i		−	0.378165i
$83$	−5.68451	+	7.82406i	−0.623956	+	0.858802i	−0.997633	−	0.0687565i	$-0.978097\pi$
$83$	−5.68451	+	7.82406i	−0.623956	+	0.858802i	0.373677	+	0.927559i	$0.378097\pi$
$84$	−13.3679	+	41.1421i	−1.45856	+	4.48897i
$85$	1.84024	+	1.27024i	0.199602	+	0.137777i
$86$	−7.45378	−	22.9404i	−0.803762	−	2.47372i
$87$	17.1942	+	5.58674i	1.84341	+	0.598962i
$88$	35.1140	+	11.4092i	3.74317	+	1.21623i
$89$	1.37884	+	4.24364i	0.146157	+	0.449825i	0.997158	−	0.0753389i	$-0.0240039\pi$
$89$	1.37884	+	4.24364i	0.146157	+	0.449825i	−0.851001	+	0.525164i	$0.824004\pi$
$90$	43.1419	−	1.04247i	4.54755	−	0.109886i
$91$	−1.08358	+	3.33492i	−0.113590	+	0.349594i
$92$	−5.15465	+	7.09476i	−0.537409	+	0.739680i
$93$			15.2228i			1.57854i
$94$	−10.5910	−	7.69480i	−1.09238	−	0.793658i
$95$	1.06764	−	1.54671i	0.109537	−	0.158690i
$96$	58.3730	−	42.4105i	5.95767	−	4.32850i
$97$	0.481530	+	0.662769i	0.0488920	+	0.0672940i	0.832763	−	0.553630i	$-0.186758\pi$
$97$	0.481530	+	0.662769i	0.0488920	+	0.0672940i	−0.783871	+	0.620924i	$0.786758\pi$
$98$	−2.23860	+	0.727365i	−0.226133	+	0.0734750i
$99$	27.0494			2.71856
$100$	−21.4741	+	17.2461i	−2.14741	+	1.72461i
$101$	2.20014			0.218923			0.109461	−	0.993991i	$-0.465087\pi$
$101$	2.20014			0.218923			0.109461	+	0.993991i	$0.465087\pi$
$102$	8.25877	−	2.68344i	0.817740	−	0.265700i
$103$	−7.23075	−	9.95227i	−0.712467	−	0.980627i	−0.999741	−	0.0227782i	$-0.992749\pi$
$103$	−7.23075	−	9.95227i	−0.712467	−	0.980627i	0.287274	−	0.957849i	$-0.407251\pi$
$104$	11.0053	−	7.99580i	1.07916	−	0.784053i
$105$	−10.6620	−	13.9533i	−1.04051	−	1.36171i
$106$	4.16008	+	3.02247i	0.404062	+	0.293569i
$107$		−	19.0805i		−	1.84458i	−0.386500	−	0.922289i	$-0.626316\pi$
$107$		−	19.0805i		−	1.84458i	0.386500	−	0.922289i	$-0.373684\pi$
$108$	41.4858	−	57.1003i	3.99197	−	5.49448i
$109$	−2.42501	+	7.46341i	−0.232274	+	0.714865i	0.765198	+	0.643795i	$0.222641\pi$
$109$	−2.42501	+	7.46341i	−0.232274	+	0.714865i	−0.997471	+	0.0710696i	$0.977359\pi$
$110$	−18.6977	+	14.2873i	−1.78275	+	1.36224i
$111$	−4.46971	−	13.7564i	−0.424246	−	1.30570i
$112$	−36.1200	−	11.7361i	−3.41302	−	1.10896i
$113$	9.75399	+	3.16926i	0.917578	+	0.298139i	0.729473	−	0.684010i	$-0.239765\pi$
$113$	9.75399	+	3.16926i	0.917578	+	0.298139i	0.188105	+	0.982149i	$0.439765\pi$
$114$	−2.25542	−	6.94147i	−0.211239	−	0.650128i
$115$	−1.18154	−	3.35811i	−0.110179	−	0.313146i
$116$	−9.71069	+	29.8864i	−0.901615	+	2.77489i
$117$	5.85793	−	8.06276i	0.541566	−	0.745402i
$118$		−	11.3070i		−	1.04090i
$119$	−2.00483	−	1.45659i	−0.183782	−	0.133526i
$120$	1.64566	+	68.1048i	0.150228	+	6.21709i
$121$	−3.03349	+	2.20396i	−0.275772	+	0.200360i
$122$	−15.9142	−	21.9040i	−1.44080	−	1.98310i
$123$	3.76665	−	1.22386i	0.339628	−	0.110352i
$124$	−26.4598			−2.37616
$125$	−0.809607	−	11.1510i	−0.0724135	−	0.997375i
$126$	−47.8256			−4.26064
$127$	−1.74295	+	0.566319i	−0.154662	+	0.0502527i	−0.385325	−	0.922781i	$-0.625911\pi$
$127$	−1.74295	+	0.566319i	−0.154662	+	0.0502527i	0.230663	+	0.973034i	$0.425911\pi$
$128$	24.3486	+	33.5129i	2.15213	+	2.96215i
$129$	22.5690	−	16.3974i	1.98709	−	1.44371i
$130$	0.209437	+	8.66745i	0.0183689	+	0.760186i
$131$	−7.81052	−	5.67468i	−0.682409	−	0.495799i	0.191747	−	0.981444i	$-0.438585\pi$
$131$	−7.81052	−	5.67468i	−0.682409	−	0.495799i	−0.874156	+	0.485645i	$0.838585\pi$
$132$			67.0427i			5.83532i
$133$	−1.22426	+	1.68505i	−0.106157	+	0.146112i
$134$	13.2088	−	40.6526i	1.14107	−	3.51185i
$135$	9.50929	+	27.0269i	0.818429	+	2.32610i
$136$	2.97075	+	9.14304i	0.254740	+	0.784009i
$137$	0.659453	+	0.214269i	0.0563408	+	0.0183062i	0.337052	−	0.941486i	$-0.390570\pi$
$137$	0.659453	+	0.214269i	0.0563408	+	0.0183062i	−0.280711	+	0.959792i	$0.590570\pi$
$138$	−13.1483	−	4.27214i	−1.11926	−	0.363668i
$139$	0.478914	+	1.47394i	0.0406209	+	0.125018i	0.969311	−	0.245840i	$-0.0790637\pi$
$139$	0.478914	+	1.47394i	0.0406209	+	0.125018i	−0.928690	+	0.370858i	$0.879064\pi$
$140$	24.2532	−	18.5324i	2.04977	−	1.56627i
$141$	4.67866	−	14.3994i	0.394015	−	1.21265i
$142$	−0.127224	+	0.175109i	−0.0106764	+	0.0146949i
$143$			5.43437i			0.454445i
$144$	87.3266	+	63.4465i	7.27721	+	5.28721i
$145$	−7.74511	−	10.1360i	−0.643196	−	0.841746i
$146$	−7.94553	+	5.77276i	−0.657577	+	0.477757i
$147$	−1.60011	−	2.20236i	−0.131975	−	0.181648i
$148$	23.9108	−	7.76911i	1.96546	−	0.638617i
$149$	−13.8952			−1.13834			−0.569172	−	0.822219i	$-0.692736\pi$
$149$	−13.8952			−1.13834			−0.569172	+	0.822219i	$0.692736\pi$
$150$	−36.3183	−	23.7946i	−2.96538	−	1.94282i
$151$	−16.5125			−1.34377			−0.671883	−	0.740657i	$-0.734514\pi$
$151$	−16.5125			−1.34377			−0.671883	+	0.740657i	$0.734514\pi$
$152$	7.68470	−	2.49691i	0.623311	−	0.202526i
$153$	4.13986	+	5.69802i	0.334688	+	0.460658i
$154$	21.0980	−	15.3286i	1.70012	−	1.23521i
$155$	6.10167	−	8.83965i	0.490098	−	0.710018i
$156$	19.9838	+	14.5191i	1.59998	+	1.16246i
$157$			5.39586i			0.430636i	0.976544	+	0.215318i	$0.0690788\pi$
$157$			5.39586i			0.430636i	−0.976544	+	0.215318i	$0.930921\pi$
$158$	−1.89779	+	2.61209i	−0.150980	+	0.207806i
$159$	−1.83775	+	5.65602i	−0.145743	+	0.448552i
$160$	−50.8953	+	1.22982i	−4.02363	+	0.0972256i
$161$	1.21915	+	3.75214i	0.0960821	+	0.295710i
$162$	50.7564	+	16.4917i	3.98780	+	1.29571i
$163$	17.3324	+	5.63164i	1.35758	+	0.441104i	0.895234	−	0.445597i	$-0.147008\pi$
$163$	17.3324	+	5.63164i	1.35758	+	0.441104i	0.462344	+	0.886701i	$0.347008\pi$
$164$	2.12727	+	6.54707i	0.166112	+	0.511240i
$165$	−22.3975	−	15.4601i	−1.74364	−	1.20357i
$166$	8.18900	−	25.2032i	0.635590	−	1.95614i
$167$	−11.1382	+	15.3305i	−0.861903	+	1.18631i	0.119210	+	0.992869i	$0.461964\pi$
$167$	−11.1382	+	15.3305i	−0.861903	+	1.18631i	−0.981112	+	0.193438i	$0.938036\pi$
$168$		−	75.4985i		−	5.82484i
$169$	−8.89737	−	6.46432i	−0.684413	−	0.497255i
$170$	−5.87131	−	1.75208i	−0.450309	−	0.134378i
$171$	4.78917	−	3.47954i	0.366237	−	0.266087i
$172$	28.5013	+	39.2287i	2.17321	+	2.99116i
$173$	−20.2330	+	6.57409i	−1.53828	+	0.499819i	−0.950902	−	0.309491i	$-0.899841\pi$
$173$	−20.2330	+	6.57409i	−1.53828	+	0.499819i	−0.587382	+	0.809310i	$0.699841\pi$
$174$	−49.5394			−3.75557
$175$	0.598451	+	12.3761i	0.0452387	+	0.935542i
$176$	−58.8589			−4.43666
$177$	12.4370	−	4.04103i	0.934823	−	0.303742i
$178$	−7.18663	−	9.89155i	−0.538661	−	0.741403i
$179$	−20.3493	+	14.7846i	−1.52098	+	1.10505i	−0.559976	+	0.828509i	$0.689190\pi$
$179$	−20.3493	+	14.7846i	−1.52098	+	1.10505i	−0.961001	+	0.276546i	$0.910810\pi$
$180$	−81.8341	+	28.7930i	−6.09955	+	2.14610i
$181$	1.19329	+	0.866976i	0.0886966	+	0.0644418i	0.631250	−	0.775580i	$-0.282542\pi$
$181$	1.19329	+	0.866976i	0.0886966	+	0.0644418i	−0.542553	+	0.840021i	$0.682542\pi$
$182$		−	9.60843i		−	0.712224i
$183$	18.4054	−	25.3329i	1.36057	−	1.87266i
$184$	4.72956	−	14.5561i	0.348668	−	1.07309i
$185$	−2.91838	+	9.77965i	−0.214563	+	0.719014i
$186$	−12.8900	−	39.6713i	−0.945139	−	2.90884i
$187$	−3.65255	−	1.18679i	−0.267101	−	0.0867864i
$188$	25.0286	+	8.13230i	1.82540	+	0.593109i
$189$	−9.81197	−	30.1981i	−0.713715	−	2.19659i
$190$	−1.47261	+	4.93482i	−0.106835	+	0.358009i
$191$	2.44097	−	7.51255i	0.176623	−	0.543589i	−0.823081	−	0.567924i	$-0.807747\pi$
$191$	2.44097	−	7.51255i	0.176623	−	0.543589i	0.999704	+	0.0243349i	$0.00774681\pi$
$192$	−59.1150	+	81.3648i	−4.26626	+	5.87200i
$193$			10.5039i			0.756089i	0.925787	+	0.378044i	$0.123403\pi$
$193$			10.5039i			0.756089i	−0.925787	+	0.378044i	$0.876597\pi$
$194$	−1.81609	−	1.31946i	−0.130387	−	0.0947320i
$195$	−9.45879	+	3.32803i	−0.677358	+	0.238325i
$196$	3.82807	−	2.78126i	0.273434	−	0.198661i
$197$	−11.5772	−	15.9346i	−0.824840	−	1.13529i	−0.988862	−	0.148838i	$-0.952447\pi$
$197$	−11.5772	−	15.9346i	−0.824840	−	1.13529i	0.164022	−	0.986457i	$-0.447553\pi$
$198$	−70.4916	+	22.9041i	−5.00962	+	1.62772i
$199$	0.116942			0.00828980			0.00414490	−	0.999991i	$-0.498681\pi$
$199$	0.116942			0.00828980			0.00414490	+	0.999991i	$0.498681\pi$
$200$	26.3423	−	40.2069i	1.86268	−	2.84306i
$201$	49.4359			3.48694
$202$	−5.73365	+	1.86298i	−0.403419	+	0.131079i
$203$	8.30959	+	11.4372i	0.583219	+	0.802732i
$204$	−14.1227	+	10.2608i	−0.988789	+	0.718397i
$205$	−2.67778	−	0.799086i	−0.187025	−	0.0558106i
$206$	27.2707	+	19.8133i	1.90004	+	1.38046i
$207$		−	11.2130i		−	0.779355i
$208$	−12.7468	+	17.5444i	−0.883829	+	1.21649i
$209$	−0.997490	+	3.06996i	−0.0689978	+	0.212354i
$210$	39.6007	+	27.3348i	2.73271	+	1.88628i
$211$	−4.94085	−	15.2064i	−0.340142	−	1.04685i	−0.964133	−	0.265418i	$-0.914490\pi$
$211$	−4.94085	−	15.2064i	−0.340142	−	1.04685i	0.623991	−	0.781431i	$-0.285510\pi$
$212$	−9.83111	−	3.19432i	−0.675203	−	0.219387i
$213$	−0.238078	−	0.0773562i	−0.0163128	−	0.00530036i
$214$	16.1564	+	49.7244i	1.10443	+	3.39909i
$215$	−19.6779	+	0.475490i	−1.34202	+	0.0324281i
$216$	−38.0646	+	117.151i	−2.58997	+	7.97110i
$217$	−6.99679	+	9.63026i	−0.474973	+	0.653745i
$218$		−	21.5033i		−	1.45639i
$219$	−9.18933	−	6.67644i	−0.620957	−	0.451152i
$220$	26.8722	−	38.9306i	1.81173	−	2.62470i
$221$	−1.14477	+	0.831721i	−0.0770053	+	0.0559476i
$222$	23.2965	+	32.0648i	1.56356	+	2.15205i
$223$	9.26693	−	3.01101i	0.620559	−	0.201632i	0.0181708	−	0.999835i	$-0.494216\pi$
$223$	9.26693	−	3.01101i	0.620559	−	0.201632i	0.602389	+	0.798203i	$0.294216\pi$
$224$	56.4208			3.76977
$225$	9.25192	−	33.9787i	0.616794	−	2.26524i
$226$	−28.1028			−1.86937
$227$	−21.8178	+	7.08905i	−1.44810	+	0.470517i	−0.924413	−	0.381393i	$-0.875444\pi$
$227$	−21.8178	+	7.08905i	−1.44810	+	0.470517i	−0.523689	+	0.851910i	$0.675444\pi$
$228$	8.62414	+	11.8701i	0.571148	+	0.786117i
$229$	−4.23077	+	3.07383i	−0.279577	+	0.203125i	−0.718733	−	0.695286i	$-0.755278\pi$
$229$	−4.23077	+	3.07383i	−0.279577	+	0.203125i	0.439156	+	0.898411i	$0.355278\pi$
$230$	5.92262	+	7.75089i	0.390526	+	0.511079i
$231$	24.4007	+	17.7281i	1.60545	+	1.16643i
$232$		−	54.8436i		−	3.60066i
$233$	9.55296	−	13.1485i	0.625836	−	0.861389i	−0.371926	−	0.928262i	$-0.621302\pi$
$233$	9.55296	−	13.1485i	0.625836	−	0.861389i	0.997761	+	0.0668737i	$0.0213025\pi$
$234$	−8.43883	+	25.9720i	−0.551664	+	1.69785i
$235$	−8.48845	+	6.48620i	−0.553725	+	0.423113i
$236$	7.02398	+	21.6176i	0.457222	+	1.40719i
$237$	−3.55138	−	1.15391i	−0.230687	−	0.0749547i
$238$	6.45802	+	2.09834i	0.418612	+	0.136015i
$239$	6.84485	+	21.0663i	0.442757	+	1.36267i	0.884925	+	0.465733i	$0.154209\pi$
$239$	6.84485	+	21.0663i	0.442757	+	1.36267i	−0.442168	+	0.896932i	$0.645791\pi$
$240$	−36.0455	−	102.447i	−2.32672	−	6.61291i
$241$	2.32151	−	7.14486i	0.149541	−	0.460241i	−0.848026	−	0.529955i	$-0.822209\pi$
$241$	2.32151	−	7.14486i	0.149541	−	0.460241i	0.997567	+	0.0697142i	$0.0222087\pi$
$242$	6.03918	−	8.31222i	0.388213	−	0.534330i
$243$			23.2834i			1.49363i
$244$	44.0328	+	31.9917i	2.81891	+	2.04806i
$245$	0.0463999	+	1.92023i	0.00296438	+	0.122679i
$246$	−8.77973	+	6.37885i	−0.559775	+	0.406700i
$247$	0.699059	+	0.962172i	0.0444801	+	0.0612216i
$248$	43.9189	−	14.2701i	2.78885	−	0.906154i
$249$	30.6485			1.94227
$250$	11.5520	+	28.3743i	0.730612	+	1.79455i
$251$	29.8092			1.88154			0.940770	−	0.339045i	$-0.110104\pi$
$251$	29.8092			1.88154			0.940770	+	0.339045i	$0.110104\pi$
$252$	91.4363	−	29.7095i	5.75995	−	1.87152i
$253$	3.59387	+	4.94654i	0.225945	+	0.310986i
$254$	4.06266	−	2.95169i	0.254914	−	0.185206i
$255$	−0.171181	−	7.08424i	−0.0107198	−	0.443632i
$256$	−40.4814	−	29.4115i	−2.53009	−	1.83822i
$257$		−	28.6148i		−	1.78494i	−0.451104	−	0.892471i	$-0.648970\pi$
$257$		−	28.6148i		−	1.78494i	0.451104	−	0.892471i	$-0.351030\pi$
$258$	−44.9312	+	61.8425i	−2.79729	+	3.85014i
$259$	3.49514	−	10.7569i	0.217177	−	0.668403i
$260$	−5.78468	−	16.4409i	−0.358750	−	1.01962i
$261$	−12.4163	−	38.2133i	−0.768547	−	2.36534i
$262$	25.1595	+	8.17483i	1.55436	+	0.505043i
$263$	−21.7747	−	7.07504i	−1.34269	−	0.436265i	−0.452461	−	0.891784i	$-0.649454\pi$
$263$	−21.7747	−	7.07504i	−1.34269	−	0.436265i	−0.890226	+	0.455519i	$0.849454\pi$
$264$	−36.1569	−	111.280i	−2.22531	−	6.84879i
$265$	3.33421	−	2.54774i	0.204819	−	0.156507i
$266$	1.76365	−	5.42795i	0.108136	−	0.332809i
$267$	8.31163	−	11.4400i	0.508664	−	0.700115i
$268$			85.9279i			5.24888i
$269$	−0.733959	−	0.533253i	−0.0447503	−	0.0325130i	0.565185	−	0.824964i	$-0.308805\pi$
$269$	−0.733959	−	0.533253i	−0.0447503	−	0.0325130i	−0.609936	+	0.792451i	$0.708805\pi$
$270$	−47.6666	−	62.3810i	−2.90090	−	3.79638i
$271$	7.74372	−	5.62614i	0.470398	−	0.341764i	−0.327199	−	0.944956i	$-0.606105\pi$
$271$	7.74372	−	5.62614i	0.470398	−	0.341764i	0.797596	+	0.603192i	$0.206105\pi$
$272$	−9.00826	−	12.3988i	−0.546206	−	0.751788i
$273$	10.5687	−	3.43396i	0.639644	−	0.207833i
$274$	−1.89999			−0.114783
$275$	6.80908	+	17.9548i	0.410603	+	1.08272i
$276$	27.7917			1.67286
$277$	15.3600	−	4.99075i	0.922890	−	0.299865i	0.191238	−	0.981544i	$-0.438750\pi$
$277$	15.3600	−	4.99075i	0.922890	−	0.299865i	0.731652	+	0.681679i	$0.238750\pi$
$278$	−2.49613	−	3.43563i	−0.149708	−	0.206055i
$279$	27.3707	−	19.8860i	1.63864	−	1.19054i
$280$	−30.2615	+	43.8407i	−1.80847	+	2.61999i
$281$	17.9763	+	13.0605i	1.07237	+	0.779126i	0.976338	−	0.216252i	$-0.0693833\pi$
$281$	17.9763	+	13.0605i	1.07237	+	0.779126i	0.0960369	+	0.995378i	$0.469383\pi$
$282$			41.4871i			2.47052i
$283$	2.02206	−	2.78313i	0.120199	−	0.165440i	−0.744677	−	0.667425i	$-0.767397\pi$
$283$	2.02206	−	2.78313i	0.120199	−	0.165440i	0.864877	+	0.501985i	$0.167397\pi$
$284$	0.134458	−	0.413819i	0.00797861	−	0.0245556i
$285$	−5.95428	+	0.143877i	−0.352701	+	0.00852255i
$286$	−4.60157	−	14.1622i	−0.272096	−	0.837426i
$287$	2.94537	+	0.957009i	0.173860	+	0.0564905i
$288$	−152.508	−	49.5529i	−8.98662	−	2.91993i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	28.7667	+	19.8565i	1.68924	+	1.16601i
$291$	0.802273	−	2.46914i	0.0470301	−	0.144744i
$292$	11.6048	−	15.9726i	0.679117	−	0.934725i
$293$			18.7036i			1.09267i	0.837566	+	0.546337i	$0.183978\pi$
$293$			18.7036i			1.09267i	−0.837566	+	0.546337i	$0.816022\pi$
$294$	6.03480	+	4.38454i	0.351956	+	0.255711i
$295$	−8.84170	−	2.63848i	−0.514784	−	0.153618i
$296$	−35.4980	+	25.7908i	−2.06328	+	1.49906i
$297$	−28.9243	−	39.8109i	−1.67836	−	2.31006i
$298$	36.2115	−	11.7658i	2.09768	−	0.681576i
$299$	2.25275			0.130280
$300$	84.2172	+	22.9312i	4.86228	+	1.32393i
$301$	21.8142			1.25735
$302$	43.0321	−	13.9820i	2.47622	−	0.804573i
$303$	−4.09831	−	5.64084i	−0.235442	−	0.324058i
$304$	−10.4212	+	7.57141i	−0.597694	+	0.434250i
$305$	−20.8417	+	7.33307i	−1.19339	+	0.419890i
$306$	−15.6134	−	11.3438i	−0.892560	−	0.648483i
$307$			3.12777i			0.178511i	0.996009	+	0.0892557i	$0.0284488\pi$
$307$			3.12777i			0.178511i	−0.996009	+	0.0892557i	$0.971551\pi$
$308$	−30.8145	+	42.4125i	−1.75582	+	2.41667i
$309$	−12.0471	+	37.0771i	−0.685335	+	2.10924i
$310$	−8.41616	+	28.2030i	−0.478006	+	1.60183i
$311$	7.43170	+	22.8724i	0.421413	+	1.29698i	0.906387	+	0.422447i	$0.138829\pi$
$311$	7.43170	+	22.8724i	0.421413	+	1.29698i	−0.484975	+	0.874528i	$0.661171\pi$
$312$	−41.0001	−	13.3217i	−2.32117	−	0.754195i
$313$	26.5400	+	8.62336i	1.50013	+	0.487421i	0.940055	−	0.341023i	$-0.110773\pi$
$313$	26.5400	+	8.62336i	1.50013	+	0.487421i	0.560072	+	0.828444i	$0.310773\pi$
$314$	−4.56895	−	14.0618i	−0.257841	−	0.793553i
$315$	−11.1600	+	37.3979i	−0.628796	+	2.10713i
$316$	2.00569	−	6.17289i	0.112829	−	0.347252i
$317$	−6.81150	+	9.37522i	−0.382572	+	0.526565i	−0.956264	−	0.292506i	$-0.905511\pi$
$317$	−6.81150	+	9.37522i	−0.382572	+	0.526565i	0.573692	+	0.819071i	$0.305511\pi$
$318$		−	16.2959i		−	0.913829i
$319$	17.7251	+	12.8781i	0.992417	+	0.721033i
$320$	66.9400	−	23.5525i	3.74206	−	1.31663i
$321$	−48.9195	+	35.5421i	−2.73042	+	1.98376i
$322$	−6.35427	−	8.74591i	−0.354110	−	0.487390i
$323$	−0.799360	+	0.259728i	−0.0444776	+	0.0144516i
$324$	−107.284			−5.96024
$325$	6.82651	+	1.85876i	0.378667	+	0.103106i
$326$	−49.9374			−2.76578
$327$	23.6522	−	7.68508i	1.30797	−	0.424986i
$328$	−7.06183	−	9.71978i	−0.389925	−	0.536685i
$329$	9.57815	−	6.95893i	0.528060	−	0.383658i
$330$	71.4595	+	21.3245i	3.93372	+	1.17387i
$331$	−13.0038	−	9.44782i	−0.714754	−	0.519299i	0.169950	−	0.985453i	$-0.445639\pi$
$331$	−13.0038	−	9.44782i	−0.714754	−	0.519299i	−0.884704	+	0.466154i	$0.845639\pi$
$332$			53.2722i			2.92369i
$333$	−18.8950	+	26.0068i	−1.03544	+	1.42516i
$334$	16.0455	−	49.3831i	0.877973	−	2.70212i
$335$	−28.7066	−	19.8151i	−1.56841	−	1.08261i
$336$	37.1928	+	114.468i	2.02903	+	6.24472i
$337$	−30.7130	−	9.97926i	−1.67304	−	0.543605i	−0.689502	−	0.724283i	$-0.742171\pi$
$337$	−30.7130	−	9.97926i	−1.67304	−	0.543605i	−0.983542	+	0.180678i	$0.942171\pi$
$338$	28.6605	+	9.31237i	1.55893	+	0.506526i
$339$	−10.0437	−	30.9113i	−0.545498	−	1.67887i
$340$	12.3136	−	0.297541i	0.667798	−	0.0161364i
$341$	−5.70077	+	17.5452i	−0.308714	+	0.950124i
$342$	−9.53445	+	13.1230i	−0.515564	+	0.709613i
$343$		−	19.4754i		−	1.05157i
$344$	−68.4640	−	49.7420i	−3.69133	−	2.68191i
$345$	−6.40879	+	9.28459i	−0.345038	+	0.499866i
$346$	47.1612	−	34.2646i	2.53540	−	1.84208i
$347$	−14.3502	−	19.7514i	−0.770360	−	1.06031i	−0.996281	−	0.0861635i	$-0.972539\pi$
$347$	−14.3502	−	19.7514i	−0.770360	−	1.06031i	0.225921	−	0.974146i	$-0.427461\pi$
$348$	94.7129	−	30.7741i	5.07714	−	1.64966i
$349$	−28.3868			−1.51951			−0.759755	−	0.650210i	$-0.774681\pi$
$349$	−28.3868			−1.51951			−0.759755	+	0.650210i	$0.774681\pi$
$350$	−12.0390	−	31.7457i	−0.643514	−	1.69688i
$351$	−18.1307			−0.967743
$352$	83.1603	−	27.0204i	4.43246	−	1.44019i
$353$	−16.2796	−	22.4069i	−0.866475	−	1.19260i	−0.979987	−	0.199064i	$-0.936210\pi$
$353$	−16.2796	−	22.4069i	−0.866475	−	1.19260i	0.113512	−	0.993537i	$-0.463790\pi$
$354$	−28.9895	+	21.0621i	−1.54078	+	1.11944i
$355$	0.107242	+	0.140347i	0.00569180	+	0.00744882i
$356$	19.8846	+	14.4470i	1.05388	+	0.765689i
$357$			7.85334i			0.415643i
$358$	40.5120	−	55.7601i	2.14113	−	2.94701i
$359$	2.12089	−	6.52742i	0.111936	−	0.344504i	−0.879359	−	0.476158i	$-0.842029\pi$
$359$	2.12089	−	6.52742i	0.111936	−	0.344504i	0.991296	+	0.131654i	$0.0420289\pi$
$360$	120.303	−	91.9257i	6.34050	−	4.84491i
$361$	−5.65302	−	17.3982i	−0.297527	−	0.915695i
$362$	−3.84387	−	1.24895i	−0.202029	−	0.0656433i
$363$	11.3013	+	3.67200i	0.593162	+	0.192730i
$364$	5.96880	+	18.3701i	0.312850	+	0.962854i
$365$	2.66002	+	7.56019i	0.139232	+	0.395718i
$366$	−26.5145	+	81.6032i	−1.38593	+	4.26547i
$367$	−3.71820	+	5.11767i	−0.194089	+	0.267140i	−0.894959	−	0.446149i	$-0.852795\pi$
$367$	−3.71820	+	5.11767i	−0.194089	+	0.267140i	0.700870	+	0.713289i	$0.252795\pi$
$368$			24.3992i			1.27190i
$369$	−7.12096	−	5.17368i	−0.370703	−	0.269331i
$370$	−0.675550	−	27.9573i	−0.0351202	−	1.45343i
$371$	−3.76224	+	2.73343i	−0.195326	+	0.141913i
$372$	49.2880	+	67.8391i	2.55546	+	3.51729i
$373$	0.744846	−	0.242015i	0.0385667	−	0.0125311i	−0.289670	−	0.957127i	$-0.593546\pi$
$373$	0.744846	−	0.242015i	0.0385667	−	0.0125311i	0.328237	+	0.944595i	$0.393546\pi$
$374$	10.5236			0.544162
$375$	−27.0814	+	22.8472i	−1.39848	+	1.17982i
$376$	−45.9292			−2.36862
$377$	7.67727	−	2.49450i	0.395400	−	0.128473i
$378$	51.1407	+	70.3891i	2.63039	+	3.62042i
$379$	−5.37860	+	3.90778i	−0.276280	+	0.200729i	−0.717293	−	0.696771i	$-0.754619\pi$
$379$	−5.37860	+	3.90778i	−0.276280	+	0.200729i	0.441013	+	0.897501i	$0.354619\pi$
$380$	−0.250083	−	10.3495i	−0.0128290	−	0.530920i
$381$	4.69863	+	3.41375i	0.240718	+	0.174892i
$382$			21.6449i			1.10745i
$383$	3.16017	−	4.34960i	0.161477	−	0.222254i	−0.720610	−	0.693341i	$-0.756138\pi$
$383$	3.16017	−	4.34960i	0.161477	−	0.222254i	0.882087	+	0.471087i	$0.156138\pi$
$384$	40.5669	−	124.852i	2.07017	−	6.37133i
$385$	−7.06323	−	20.0748i	−0.359975	−	1.02311i
$386$	−8.89422	−	27.3736i	−0.452704	−	1.39328i
$387$	−58.9649	−	19.1588i	−2.99735	−	0.973899i
$388$	4.29178	+	1.39448i	0.217882	+	0.0707942i
$389$	−8.58681	−	26.4275i	−0.435369	−	1.33993i	−0.892709	−	0.450635i	$-0.851198\pi$
$389$	−8.58681	−	26.4275i	−0.435369	−	1.33993i	0.457340	−	0.889292i	$-0.348802\pi$
$390$	21.8319	−	16.6822i	1.10550	−	0.844737i
$391$	−0.491967	+	1.51412i	−0.0248799	+	0.0765723i
$392$	−4.85399	+	6.68095i	−0.245164	+	0.337439i
$393$			30.5955i			1.54334i
$394$	43.6632	+	31.7232i	2.19972	+	1.59819i
$395$	1.59971	+	2.09353i	0.0804903	+	0.105337i
$396$	120.543	−	87.5794i	6.05750	−	4.40103i
$397$	11.7692	+	16.1989i	0.590677	+	0.812997i	0.994815	−	0.101701i	$-0.0324285\pi$
$397$	11.7692	+	16.1989i	0.590677	+	0.812997i	−0.404138	+	0.914698i	$0.632428\pi$
$398$	−0.304755	+	0.0990209i	−0.0152760	+	0.00496347i
$399$	6.60070			0.330449
$400$	−20.1320	+	73.9370i	−1.00660	+	3.69685i
$401$	6.32067			0.315639			0.157820	−	0.987468i	$-0.449554\pi$
$401$	6.32067			0.315639			0.157820	+	0.987468i	$0.449554\pi$
$402$	−128.832	+	41.8600i	−6.42555	+	2.08779i
$403$	3.99520	+	5.49893i	0.199015	+	0.273921i
$404$	9.80472	−	7.12354i	0.487803	−	0.354410i
$405$	24.7399	−	35.8414i	1.22933	−	1.78097i
$406$	−31.3395	−	22.7695i	−1.55535	−	1.13003i
$407$		−	17.5288i		−	0.868871i
$408$	17.9076	−	24.6477i	0.886559	−	1.22024i
$409$	−1.32399	+	4.07484i	−0.0654673	+	0.201488i	−0.978439	−	0.206535i	$-0.933781\pi$
$409$	−1.32399	+	4.07484i	−0.0654673	+	0.201488i	0.912972	+	0.408022i	$0.133781\pi$
$410$	7.65503	−	0.184974i	0.378055	−	0.00913519i
$411$	−0.679039	−	2.08987i	−0.0334945	−	0.103085i
$412$	−64.4462	−	20.9398i	−3.17504	−	1.03163i
$413$	9.72524	+	3.15992i	0.478548	+	0.155490i
$414$	9.49460	+	29.2214i	0.466634	+	1.43615i
$415$	−17.7971	−	12.2846i	−0.873624	−	0.603029i
$416$	9.95546	−	30.6397i	0.488106	−	1.50224i
$417$	2.88688	−	3.97345i	0.141371	−	0.194581i
$418$		−	8.84505i		−	0.432626i
$419$	10.3879	+	7.54727i	0.507484	+	0.368708i	0.811868	−	0.583841i	$-0.198451\pi$
$419$	10.3879	+	7.54727i	0.507484	+	0.368708i	−0.304385	+	0.952549i	$0.598451\pi$
$420$	−92.6918	−	27.6605i	−4.52290	−	1.34969i
$421$	−4.51778	+	3.28236i	−0.220183	+	0.159972i	−0.692409	−	0.721505i	$-0.743451\pi$
$421$	−4.51778	+	3.28236i	−0.220183	+	0.159972i	0.472226	+	0.881477i	$0.343451\pi$
$422$	25.7520	+	35.4447i	1.25359	+	1.72542i
$423$	−32.0020	+	10.3981i	−1.55599	+	0.505573i
$424$	18.0407			0.876135
$425$	−2.74012	+	4.18231i	−0.132915	+	0.202872i
$426$	0.685941			0.0332339
$427$	23.2872	−	7.56648i	1.12695	−	0.366167i
$428$	−61.7780	−	85.0302i	−2.98615	−	4.11009i
$429$	13.9329	−	10.1229i	0.672687	−	0.488736i
$430$	50.8787	−	17.9014i	2.45359	−	0.863284i
$431$	−5.25849	−	3.82052i	−0.253293	−	0.184028i	0.453892	−	0.891057i	$-0.350035\pi$
$431$	−5.25849	−	3.82052i	−0.253293	−	0.184028i	−0.707185	+	0.707029i	$0.750035\pi$
$432$		−	196.371i		−	9.44788i
$433$	−1.59296	+	2.19253i	−0.0765530	+	0.105366i	−0.845576	−	0.533855i	$-0.820743\pi$
$433$	−1.59296	+	2.19253i	−0.0765530	+	0.105366i	0.769023	+	0.639221i	$0.220743\pi$
$434$	10.0794	−	31.0213i	0.483829	−	1.48907i
$435$	−11.5599	+	38.7380i	−0.554256	+	1.85735i
$436$	13.3579	+	41.1115i	0.639729	+	1.96888i
$437$	1.27261	+	0.413497i	0.0608773	+	0.0197802i
$438$	29.6010	+	9.61795i	1.41439	+	0.459563i
$439$	9.87065	+	30.3787i	0.471100	+	1.44990i	0.851146	+	0.524930i	$0.175908\pi$
$439$	9.87065	+	30.3787i	0.471100	+	1.44990i	−0.380045	+	0.924968i	$0.624092\pi$
$440$	−23.6077	+	79.1108i	−1.12545	+	3.77146i
$441$	−1.86958	+	5.75399i	−0.0890278	+	0.274000i
$442$	2.27904	−	3.13683i	0.108403	−	0.149204i
$443$		−	16.1662i		−	0.768081i	−0.923316	−	0.384040i	$-0.874532\pi$
$443$		−	16.1662i		−	0.768081i	0.923316	−	0.384040i	$-0.125468\pi$
$444$	−64.4586	−	46.8319i	−3.05907	−	2.22255i
$445$	−9.41183	+	3.31151i	−0.446164	+	0.156981i
$446$	−21.6004	+	15.6936i	−1.02281	+	0.743113i
$447$	25.8833	+	35.6253i	1.22424	+	1.68502i
$448$	−74.7945	+	24.3022i	−3.53371	+	1.14817i
$449$	−22.3508			−1.05480			−0.527400	−	0.849617i	$-0.676833\pi$
$449$	−22.3508			−1.05480			−0.527400	+	0.849617i	$0.676833\pi$
$450$	4.66069	+	96.3837i	0.219707	+	4.54357i
$451$	4.79960			0.226004
$452$	53.7290	−	17.4576i	2.52720	−	0.821137i
$453$	30.7586	+	42.3355i	1.44516	+	1.98910i
$454$	50.8554	−	36.9486i	2.38676	−	1.73408i
$455$	−7.51345	−	2.24211i	−0.352236	−	0.105112i
$456$	−20.7163	−	15.0513i	−0.970131	−	0.704842i
$457$			8.17010i			0.382181i	0.981572	+	0.191091i	$0.0612024\pi$
$457$			8.17010i			0.382181i	−0.981572	+	0.191091i	$0.938798\pi$
$458$	8.42276	−	11.5929i	0.393570	−	0.541702i
$459$	3.95947	−	12.1860i	0.184812	−	0.568793i
$460$	−16.1382	−	11.1395i	−0.752446	−	0.519384i
$461$	−5.82299	−	17.9213i	−0.271204	−	0.834679i	−0.990199	−	0.139664i	$-0.955398\pi$
$461$	−5.82299	−	17.9213i	−0.271204	−	0.834679i	0.718995	−	0.695015i	$-0.244602\pi$
$462$	−78.6004	−	25.5388i	−3.65682	−	1.18817i
$463$	−5.28583	−	1.71747i	−0.245653	−	0.0798176i	0.183602	−	0.983001i	$-0.441224\pi$
$463$	−5.28583	−	1.71747i	−0.245653	−	0.0798176i	−0.429256	+	0.903183i	$0.641224\pi$
$464$	27.0175	+	83.1515i	1.25426	+	3.86021i
$465$	−34.0294	+	0.822275i	−1.57808	+	0.0381321i
$466$	−13.7618	+	42.3545i	−0.637504	+	1.96204i
$467$	13.2372	−	18.2194i	0.612544	−	0.843095i	−0.384240	−	0.923233i	$-0.625536\pi$
$467$	13.2372	−	18.2194i	0.612544	−	0.843095i	0.996784	+	0.0801387i	$0.0255363\pi$
$468$		−	54.8974i		−	2.53764i
$469$	31.2741	+	22.7220i	1.44410	+	1.04920i
$470$	16.6290	−	24.0909i	0.767038	−	1.11123i
$471$	13.8342	−	10.0511i	0.637445	−	0.463131i
$472$	−23.3173	−	32.0935i	−1.07326	−	1.47722i
$473$	32.1526	−	10.4470i	1.47838	−	0.480355i
$474$	10.2321			0.469976
$475$	3.51522	+	2.30306i	0.161289	+	0.105672i
$476$	−13.6504			−0.625665
$477$	12.5702	−	4.08431i	0.575551	−	0.187008i
$478$	−35.6759	−	49.1036i	−1.63178	−	2.24595i
$479$	5.17807	−	3.76209i	0.236592	−	0.171894i	−0.463172	−	0.886269i	$-0.653289\pi$
$479$	5.17807	−	3.76209i	0.236592	−	0.171894i	0.699764	+	0.714374i	$0.253289\pi$
$480$	97.9581	+	128.197i	4.47116	+	5.85137i
$481$	−5.22491	−	3.79612i	−0.238236	−	0.173088i
$482$			20.5855i			0.937644i
$483$	7.34898	−	10.1150i	0.334390	−	0.460248i
$484$	−6.38255	+	19.6435i	−0.290116	+	0.892885i
$485$	−1.45555	+	1.11222i	−0.0660933	+	0.0505033i
$486$	−19.7153	−	60.6774i	−0.894303	−	2.75238i
$487$	−9.89023	−	3.21353i	−0.448169	−	0.145619i	0.0762323	−	0.997090i	$-0.475711\pi$
$487$	−9.89023	−	3.21353i	−0.448169	−	0.145619i	−0.524402	+	0.851471i	$0.675711\pi$
$488$	−90.3405	−	29.3534i	−4.08952	−	1.32877i
$489$	−17.8472	−	54.9280i	−0.807077	−	2.48393i
$490$	−1.74688	−	4.96491i	−0.0789161	−	0.224292i
$491$	−4.98142	+	15.3312i	−0.224808	+	0.691889i	0.773503	+	0.633793i	$0.218503\pi$
$491$	−4.98142	+	15.3312i	−0.224808	+	0.691889i	−0.998311	+	0.0580957i	$0.981497\pi$
$492$	12.8231	−	17.6495i	0.578112	−	0.795703i
$493$			5.70481i			0.256932i
$494$	−2.63649	−	1.91553i	−0.118621	−	0.0861836i
$495$	1.46109	+	60.4665i	0.0656713	+	2.71777i
$496$	−59.5581	+	43.2715i	−2.67424	+	1.94295i
$497$	−0.115058	−	0.158363i	−0.00516105	−	0.00710357i
$498$	−79.8711	+	25.9517i	−3.57911	+	1.16292i
$499$	6.24494			0.279562			0.139781	−	0.990182i	$-0.455360\pi$
$499$	6.24494			0.279562			0.139781	+	0.990182i	$0.455360\pi$
$500$	−39.7122	−	47.0719i	−1.77598	−	2.10512i
$501$	60.0527			2.68296
$502$	−77.6839	+	25.2410i	−3.46720	+	1.12656i
$503$	−6.41935	−	8.83548i	−0.286225	−	0.393955i	0.641558	−	0.767074i	$-0.278288\pi$
$503$	−6.41935	−	8.83548i	−0.286225	−	0.393955i	−0.927783	+	0.373119i	$0.878288\pi$
$504$	−135.746	+	98.6255i	−6.04662	+	4.39313i
$505$	0.118843	+	4.91824i	0.00528843	+	0.218859i
$506$	−13.5543	−	9.84774i	−0.602560	−	0.437786i
$507$			34.8529i			1.54787i
$508$	−5.93367	+	8.16700i	−0.263264	+	0.362352i
$509$	−2.47506	+	7.61745i	−0.109705	+	0.337638i	−0.990806	−	0.135291i	$-0.956803\pi$
$509$	−2.47506	+	7.61745i	−0.109705	+	0.337638i	0.881101	+	0.472929i	$0.156803\pi$
$510$	6.44470	+	18.3168i	0.285376	+	0.811083i
$511$	−2.74469	−	8.44728i	−0.121418	−	0.373686i
$512$	51.6066	+	16.7680i	2.28071	+	0.741048i
$513$	−10.2423	−	3.32792i	−0.452208	−	0.146931i
$514$	24.2297	+	74.5712i	1.06872	+	3.28919i
$515$	21.8569	−	16.7013i	0.963130	−	0.735948i
$516$	47.4858	−	146.146i	2.09045	−	6.43373i
$517$	10.7848	−	14.8441i	0.474316	−	0.652841i
$518$			30.9924i			1.36173i
$519$	54.5439	+	39.6284i	2.39421	+	1.73950i
$520$	18.4684	+	24.1695i	0.809893	+	1.05990i
$521$	21.3164	−	15.4873i	0.933888	−	0.678510i	−0.0130535	−	0.999915i	$-0.504155\pi$
$521$	21.3164	−	15.4873i	0.933888	−	0.678510i	0.946942	+	0.321405i	$0.104155\pi$
$522$	64.7144	+	89.0717i	2.83247	+	3.89856i
$523$	−38.5360	+	12.5211i	−1.68506	+	0.547509i	−0.985883	−	0.167438i	$-0.946451\pi$
$523$	−38.5360	+	12.5211i	−1.68506	+	0.547509i	−0.699178	+	0.714948i	$0.746451\pi$
$524$	−53.1801			−2.32318
$525$	30.6156	−	24.5878i	1.33617	−	1.07310i
$526$	62.7365			2.73544
$527$	−4.56843	+	1.48437i	−0.199004	+	0.0646604i
$528$	109.639	+	150.905i	4.77143	+	6.56731i
$529$	−16.5569	+	12.0293i	−0.719864	+	0.523012i
$530$	−6.53177	+	9.46276i	−0.283722	+	0.411036i
$531$	−23.5125	−	17.0828i	−1.02036	−	0.741332i
$532$			11.4731i			0.497423i
$533$	1.03942	−	1.43064i	0.0450224	−	0.0619680i
$534$	−11.9736	+	36.8509i	−0.518147	+	1.59469i
$535$	42.6528	−	1.03065i	1.84404	−	0.0445588i
$536$	−46.3420	−	142.626i	−2.00167	−	6.16050i
$537$	75.8111	+	24.6325i	3.27149	+	1.06297i
$538$	2.36426	+	0.768193i	0.101930	+	0.0331192i
$539$	−1.01946	−	3.13756i	−0.0439111	−	0.135144i
$540$	129.884	+	89.6536i	5.58931	+	3.85808i
$541$	6.58982	−	20.2814i	0.283319	−	0.871965i	−0.703579	−	0.710617i	$-0.748416\pi$
$541$	6.58982	−	20.2814i	0.283319	−	0.871965i	0.986898	−	0.161348i	$-0.0515842\pi$
$542$	−15.4165	+	21.2189i	−0.662194	+	0.911432i
$543$		−	4.67437i		−	0.200597i
$544$	18.4195	+	13.3825i	0.789729	+	0.573771i
$545$	−16.8148	−	5.01776i	−0.720267	−	0.214937i
$546$	−24.6346	+	17.8981i	−1.05426	+	0.765966i
$547$	−16.0596	−	22.1041i	−0.686658	−	0.945104i	0.313332	−	0.949644i	$-0.398555\pi$
$547$	−16.0596	−	22.1041i	−0.686658	−	0.945104i	−0.999990	+	0.00454018i	$0.998555\pi$
$548$	3.63254	−	1.18028i	0.155174	−	0.0504192i
$549$	−69.5919			−2.97011
$550$	−32.9480	−	41.0254i	−1.40491	−	1.74933i
$551$	4.79488			0.204269
$552$	−46.1296	+	14.9884i	−1.96340	+	0.637949i
$553$	−1.71630	−	2.36229i	−0.0729846	−	0.100455i
$554$	−35.8026	+	26.0121i	−1.52111	+	1.10515i
$555$	30.5098	−	10.7347i	1.29507	−	0.455664i
$556$	6.90651	+	5.01787i	0.292901	+	0.212805i
$557$			45.7182i			1.93714i	0.248737	+	0.968571i	$0.419984\pi$
$557$			45.7182i			1.93714i	−0.248737	+	0.968571i	$0.580016\pi$
$558$	−54.4905	+	74.9997i	−2.30676	+	3.17499i
$559$	3.84912	−	11.8464i	0.162801	−	0.501049i
$560$	24.2840	−	81.3771i	1.02619	−	3.43881i
$561$	3.76104	+	11.5753i	0.158791	+	0.488709i
$562$	−57.9058	−	18.8147i	−2.44261	−	0.793652i
$563$	35.5765	+	11.5595i	1.49937	+	0.487175i	0.939834	−	0.341631i	$-0.110979\pi$
$563$	35.5765	+	11.5595i	1.49937	+	0.487175i	0.559537	+	0.828806i	$0.310979\pi$
$564$	−25.7720	−	79.3181i	−1.08520	−	3.33989i
$565$	−6.55775	+	21.9754i	−0.275887	+	0.924513i
$566$	−2.91295	+	8.96513i	−0.122440	+	0.376832i
$567$	−28.3693	+	39.0470i	−1.19140	+	1.63982i
$568$			0.759385i			0.0318631i
$569$	−35.6752	−	25.9195i	−1.49558	−	1.08660i	−0.972100	−	0.234567i	$-0.924633\pi$
$569$	−35.6752	−	25.9195i	−1.49558	−	1.08660i	−0.523482	−	0.852037i	$-0.675367\pi$
$570$	15.3952	−	5.41675i	0.644835	−	0.226883i
$571$	−9.93415	+	7.21758i	−0.415731	+	0.302046i	−0.775918	−	0.630834i	$-0.782713\pi$
$571$	−9.93415	+	7.21758i	−0.415731	+	0.302046i	0.360187	+	0.932880i	$0.382713\pi$
$572$	17.5952	+	24.2177i	0.735692	+	1.01259i
$573$	−23.8080	+	7.73568i	−0.994592	+	0.323162i
$574$	−8.48609			−0.354203
$575$	7.44295	−	2.82262i	0.310393	−	0.117711i
$576$	223.517			9.31321
$577$	28.8910	−	9.38727i	1.20275	−	0.390797i	0.361978	−	0.932187i	$-0.382102\pi$
$577$	28.8910	−	9.38727i	1.20275	−	0.390797i	0.840772	+	0.541390i	$0.182102\pi$
$578$	1.61062	+	2.21683i	0.0669929	+	0.0922078i
$579$	26.9305	−	19.5661i	1.11919	−	0.813141i
$580$	−67.3331	−	20.0931i	−2.79586	−	0.834320i
$581$	19.3888	+	14.0868i	0.804384	+	0.584419i
$582$			7.11400i			0.294885i
$583$	−4.23622	+	5.83066i	−0.175446	+	0.241481i
$584$	−10.6478	+	32.7704i	−0.440607	+	1.35605i
$585$	18.3400	+	12.6594i	0.758267	+	0.523402i
$586$	−15.8373	−	48.7421i	−0.654232	−	2.01352i
$587$	27.7717	+	9.02358i	1.14626	+	0.372443i	0.819734	−	0.572744i	$-0.194121\pi$
$587$	27.7717	+	9.02358i	1.14626	+	0.372443i	0.326528	+	0.945188i	$0.394121\pi$
$588$	−14.2614	−	4.63382i	−0.588132	−	0.191096i
$589$	1.24761	+	3.83975i	0.0514069	+	0.158214i
$590$	25.2759	−	0.610759i	1.04059	−	0.0251446i
$591$	−19.2886	+	59.3643i	−0.793428	+	2.44192i
$592$	41.1153	−	56.5903i	1.68983	−	2.32585i
$593$		−	13.5989i		−	0.558441i	−0.960227	−	0.279220i	$-0.909924\pi$
$593$		−	13.5989i		−	0.558441i	0.960227	−	0.279220i	$-0.0900760\pi$
$594$	109.088	+	79.2569i	4.47593	+	3.25195i
$595$	3.14780	−	4.56030i	0.129047	−	0.186954i
$596$	−61.9227	+	44.9895i	−2.53645	+	1.84284i
$597$	−0.217833	−	0.299822i	−0.00891532	−	0.0122709i
$598$	−5.87075	+	1.90752i	−0.240073	+	0.0780043i
$599$	13.6938			0.559514			0.279757	−	0.960071i	$-0.409746\pi$
$599$	13.6938			0.559514			0.279757	+	0.960071i	$0.409746\pi$
$600$	−152.154	+	7.35747i	−6.21164	+	0.300367i
$601$	−6.53887			−0.266726			−0.133363	−	0.991067i	$-0.542578\pi$
$601$	−6.53887			−0.266726			−0.133363	+	0.991067i	$0.542578\pi$
$602$	−56.8486	+	18.4712i	−2.31698	+	0.752831i
$603$	−64.5793	−	88.8858i	−2.62987	−	3.61971i
$604$	−73.5862	+	53.4635i	−2.99418	+	2.17540i
$605$	−5.09063	−	6.66207i	−0.206964	−	0.270852i
$606$	15.4567	+	11.2300i	0.627887	+	0.456187i
$607$			16.9355i			0.687391i	0.939081	+	0.343695i	$0.111679\pi$
$607$			16.9355i			0.687391i	−0.939081	+	0.343695i	$0.888321\pi$
$608$	11.2480	−	15.4815i	0.456166	−	0.627858i
$609$	13.8445	−	42.6091i	0.561009	−	1.72661i
$610$	48.1049	−	36.7580i	1.94771	−	1.48829i
$611$	−2.08904	−	6.42939i	−0.0845134	−	0.260105i
$612$	36.8977	+	11.9888i	1.49150	+	0.484618i
$613$	−25.7784	−	8.37590i	−1.04118	−	0.338300i	−0.261978	−	0.965074i	$-0.584375\pi$
$613$	−25.7784	−	8.37590i	−1.04118	−	0.338300i	−0.779201	+	0.626774i	$0.784375\pi$
$614$	−2.64845	−	8.15108i	−0.106883	−	0.328951i
$615$	2.93929	+	8.35393i	0.118524	+	0.336863i
$616$	28.2733	−	87.0162i	1.13916	−	3.50598i
$617$	2.97110	−	4.08937i	0.119612	−	0.164632i	−0.745012	−	0.667051i	$-0.767556\pi$
$617$	2.97110	−	4.08937i	0.119612	−	0.164632i	0.864624	+	0.502419i	$0.167556\pi$
$618$		−	106.825i		−	4.29714i
$619$	−23.3926	−	16.9957i	−0.940229	−	0.683117i	0.00824659	−	0.999966i	$-0.497375\pi$
$619$	−23.3926	−	16.9957i	−0.940229	−	0.683117i	−0.948476	+	0.316849i	$0.897375\pi$
$620$	−1.42925	−	59.1487i	−0.0574001	−	2.37547i
$621$	−16.5031	+	11.9902i	−0.662247	+	0.481151i
$622$	−38.7345	−	53.3135i	−1.55311	−	2.13768i
$623$	10.5162	−	3.41692i	0.421322	−	0.136896i
$624$	68.7252			2.75121
$625$	24.8834	−	2.41214i	0.995334	−	0.0964855i
$626$	−76.4659			−3.05619
$627$	9.72898	−	3.16114i	0.388538	−	0.126244i
$628$	17.4705	+	24.0461i	0.697149	+	0.959543i
$629$	3.69250	−	2.68276i	0.147229	−	0.106968i
$630$	−2.58334	−	106.910i	−0.102923	−	4.25940i
$631$	25.9979	+	18.8886i	1.03496	+	0.751942i	0.969295	−	0.245900i	$-0.0790835\pi$
$631$	25.9979	+	18.8886i	1.03496	+	0.751942i	0.0656638	+	0.997842i	$0.479084\pi$
$632$			11.3277i			0.450590i
$633$	−29.7833	+	40.9932i	−1.18378	+	1.62933i
$634$	9.81251	−	30.1998i	0.389705	−	1.19939i
$635$	−1.36010	−	3.86563i	−0.0539741	−	0.153403i
$636$	10.1231	+	31.1557i	0.401407	+	1.23540i
$637$	−1.15601	−	0.375610i	−0.0458028	−	0.0148822i
$638$	−57.0968	−	18.5519i	−2.26049	−	0.734476i
$639$	0.171920	+	0.529116i	0.00680106	+	0.0209315i
$640$	−73.6001	+	56.2394i	−2.90930	+	2.22306i
$641$	9.12035	−	28.0696i	0.360232	−	1.10868i	−0.592681	−	0.805437i	$-0.701931\pi$
$641$	9.12035	−	28.0696i	0.360232	−	1.10868i	0.952913	−	0.303243i	$-0.0980695\pi$
$642$	97.3905	−	134.047i	3.84370	−	5.29040i
$643$			8.87613i			0.350040i	0.984565	+	0.175020i	$0.0559991\pi$
$643$			8.87613i			0.350040i	−0.984565	+	0.175020i	$0.944001\pi$
$644$	17.5815	+	12.7737i	0.692810	+	0.503356i
$645$	37.8740	+	49.5654i	1.49129	+	1.95164i
$646$	1.86324	−	1.35372i	0.0733080	−	0.0532614i
$647$	−23.5813	−	32.4569i	−0.927076	−	1.27601i	−0.960989	−	0.276586i	$-0.910797\pi$
$647$	−23.5813	−	32.4569i	−0.927076	−	1.27601i	0.0339132	−	0.999425i	$-0.489203\pi$
$648$	178.074	−	57.8598i	6.99541	−	2.27295i
$649$	15.8477			0.622075
$650$	−19.3640	+	0.936359i	−0.759520	+	0.0367270i
$651$	37.7238			1.47851
$652$	95.4739	−	31.0214i	3.73905	−	1.21489i
$653$	−2.29281	−	3.15578i	−0.0897246	−	0.123495i	0.761795	−	0.647818i	$-0.224318\pi$
$653$	−2.29281	−	3.15578i	−0.0897246	−	0.123495i	−0.851519	+	0.524323i	$0.824318\pi$
$654$	−55.1312	+	40.0552i	−2.15580	+	1.56628i
$655$	12.2634	−	17.7663i	0.479170	−	0.694186i
$656$	15.4951	+	11.2578i	0.604982	+	0.439545i
$657$			25.2440i			0.984862i
$658$	−19.0685	+	26.2455i	−0.743368	+	1.02316i
$659$	−5.20876	+	16.0309i	−0.202905	+	0.624476i	0.796888	+	0.604127i	$0.206478\pi$
$659$	−5.20876	+	16.0309i	−0.202905	+	0.624476i	−0.999793	+	0.0203494i	$0.993522\pi$
$660$	−149.868	+	3.62137i	−5.83361	+	0.140961i
$661$	−0.682638	−	2.10094i	−0.0265515	−	0.0817172i	0.936903	−	0.349590i	$-0.113679\pi$
$661$	−0.682638	−	2.10094i	−0.0265515	−	0.0817172i	−0.963454	+	0.267873i	$0.913679\pi$
$662$	41.8883	+	13.6103i	1.62804	+	0.528981i
$663$	4.26482	+	1.38572i	0.165632	+	0.0538170i
$664$	−28.7304	−	88.4230i	−1.11495	−	3.43148i
$665$	−3.83292	−	2.64571i	−0.148634	−	0.102596i
$666$	27.2198	−	83.7740i	1.05475	−	3.24618i
$667$	5.33844	−	7.34773i	0.206705	−	0.284505i
$668$			104.382i			4.03865i
$669$	−24.9817	−	18.1503i	−0.965848	−	0.701730i
$670$	91.5889	+	27.3313i	3.53839	+	1.05590i
$671$	30.7001	−	22.3049i	1.18516	−	0.861072i
$672$	−105.098	−	144.654i	−4.05423	−	5.58016i
$673$	18.5948	−	6.04181i	0.716775	−	0.232894i	0.0721509	−	0.997394i	$-0.477014\pi$
$673$	18.5948	−	6.04181i	0.716775	−	0.232894i	0.644625	+	0.764499i	$0.277014\pi$
$674$	88.4892			3.40848
$675$	−59.9026	+	22.7171i	−2.30565	+	0.874381i
$676$	−60.5801			−2.33000
$677$	−23.5589	+	7.65475i	−0.905442	+	0.294196i	−0.724481	−	0.689294i	$-0.757921\pi$
$677$	−23.5589	+	7.65475i	−0.905442	+	0.294196i	−0.180961	+	0.983490i	$0.557921\pi$
$678$	52.3484	+	72.0514i	2.01043	+	2.76712i
$679$	1.64241	−	1.19328i	0.0630299	−	0.0457939i
$680$	−20.2780	+	7.13474i	−0.777627	+	0.273605i
$681$	58.8164	+	42.7326i	2.25385	+	1.63752i
$682$		−	50.5505i		−	1.93568i
$683$	5.40777	−	7.44315i	0.206923	−	0.284804i	−0.692924	−	0.721010i	$-0.743678\pi$
$683$	5.40777	−	7.44315i	0.206923	−	0.284804i	0.899847	+	0.436206i	$0.143678\pi$
$684$	10.0765	−	31.0124i	0.385286	−	1.18579i
$685$	−0.443360	+	1.48572i	−0.0169399	+	0.0567666i
$686$	16.4909	+	50.7536i	0.629624	+	1.93778i
$687$	15.7617	+	5.12128i	0.601346	+	0.195389i
$688$	128.306	+	41.6893i	4.89164	+	1.58939i
$689$	0.820562	+	2.52543i	0.0312609	+	0.0962112i
$690$	8.83978	−	29.6226i	0.336525	−	1.12771i
$691$	−10.3577	+	31.8776i	−0.394024	+	1.21268i	0.535694	+	0.844412i	$0.320050\pi$
$691$	−10.3577	+	31.8776i	−0.394024	+	1.21268i	−0.929719	+	0.368270i	$0.879950\pi$
$692$	−68.8808	+	94.8063i	−2.61846	+	3.60400i
$693$		−	67.0311i		−	2.54630i
$694$	54.1217	+	39.3217i	2.05443	+	1.49263i
$695$	−3.26901	+	1.15019i	−0.124001	+	0.0436291i
$696$	−140.611	+	102.160i	−5.32983	+	3.87235i
$697$	0.734570	+	1.01105i	0.0278238	+	0.0382962i
$698$	73.9770	−	24.0366i	2.80007	−	0.909798i
$699$	−51.5056			−1.94812
$700$	42.7377	+	53.2150i	1.61533	+	2.01134i
$701$	−9.01827			−0.340616			−0.170308	−	0.985391i	$-0.554476\pi$
$701$	−9.01827			−0.340616			−0.170308	+	0.985391i	$0.554476\pi$
$702$	47.2491	−	15.3522i	1.78330	−	0.579430i
$703$	−2.25485	−	3.10353i	−0.0850432	−	0.117052i
$704$	−98.6034	+	71.6396i	−3.71626	+	2.70002i
$705$	32.4415	+	9.68096i	1.22182	+	0.364606i
$706$	61.3983	+	44.6085i	2.31075	+	1.67886i
$707$		−	5.45218i		−	0.205051i
$708$	42.3404	−	58.2765i	1.59125	−	2.19017i
$709$	−16.0056	+	49.2602i	−0.601104	+	1.85001i	−0.0794690	+	0.996837i	$0.525322\pi$
$709$	−16.0056	+	49.2602i	−0.601104	+	1.85001i	−0.521635	+	0.853169i	$0.674678\pi$
$710$	−0.398314	−	0.274941i	−0.0149485	−	0.0103183i
$711$	2.56451	+	7.89276i	0.0961768	+	0.296002i
$712$	−40.7965	−	13.2556i	−1.52891	−	0.496775i
$713$	7.27313	+	2.36318i	0.272381	+	0.0885019i
$714$	−6.64983	−	20.4661i	−0.248864	−	0.765924i
$715$	−12.1481	+	0.293542i	−0.454312	+	0.0109779i
$716$	−42.8154	+	131.772i	−1.60009	+	4.92456i
$717$	41.2606	−	56.7903i	1.54091	−	2.12087i
$718$			18.8066i			0.701855i
$719$	28.1678	+	20.4651i	1.05048	+	0.763218i	0.972304	−	0.233721i	$-0.0750903\pi$
$719$	28.1678	+	20.4651i	1.05048	+	0.763218i	0.0781763	+	0.996940i	$0.475090\pi$
$720$	−137.112	+	198.638i	−5.10987	+	7.40281i
$721$	−24.6628	+	17.9185i	−0.918489	+	0.667321i
$722$	29.4640	+	40.5537i	1.09653	+	1.50925i
$723$	−22.6427	+	7.35707i	−0.842092	+	0.273612i
$724$	8.12484			0.301957
$725$	22.2397	−	17.8610i	0.825963	−	0.663342i
$726$	−32.5608			−1.20844
$727$	−36.3618	+	11.8147i	−1.34858	+	0.438182i	−0.892216	−	0.451609i	$-0.850850\pi$
$727$	−36.3618	+	11.8147i	−1.34858	+	0.438182i	−0.456369	+	0.889791i	$0.650850\pi$
$728$	−19.8144	−	27.2722i	−0.734371	−	1.01078i
$729$	12.4248	−	9.02714i	0.460177	−	0.334339i
$730$	−13.3337	−	17.4497i	−0.493503	−	0.645844i
$731$	7.12161	+	5.17415i	0.263402	+	0.191373i
$732$		−	172.486i		−	6.37525i
$733$	5.35969	−	7.37698i	0.197965	−	0.272475i	−0.698481	−	0.715629i	$-0.746140\pi$
$733$	5.35969	−	7.37698i	0.197965	−	0.272475i	0.896446	+	0.443153i	$0.146140\pi$
$734$	5.35637	−	16.4852i	0.197707	−	0.608480i
$735$	4.83676	−	3.69587i	0.178407	−	0.136324i
$736$	−11.2010	−	34.4731i	−0.412873	−	1.27069i
$737$	56.9776	+	18.5132i	2.09880	+	0.681941i
$738$	22.9383	+	7.45311i	0.844371	+	0.274353i
$739$	1.86324	+	5.73445i	0.0685403	+	0.210945i	0.979460	−	0.201638i	$-0.0646265\pi$
$739$	1.86324	+	5.73445i	0.0685403	+	0.210945i	−0.910920	+	0.412583i	$0.864627\pi$
$740$	18.6587	+	53.0310i	0.685909	+	1.94946i
$741$	1.16470	−	3.58456i	0.0427862	−	0.131682i
$742$	7.49000	−	10.3091i	0.274967	−	0.378459i
$743$		−	35.3818i		−	1.29803i	−0.760775	−	0.649015i	$-0.775181\pi$
$743$		−	35.3818i		−	1.29803i	0.760775	−	0.649015i	$-0.224819\pi$
$744$	−118.396	−	86.0199i	−4.34062	−	3.15364i
$745$	−0.750563	−	31.0617i	−0.0274985	−	1.13801i
$746$	−1.73617	+	1.26140i	−0.0635656	+	0.0461831i
$747$	−40.0369	−	55.1060i	−1.46487	−	2.01622i
$748$	−20.1198	+	6.53731i	−0.735651	+	0.239028i
$749$	−47.2834			−1.72770
$750$	51.2291	−	82.4717i	1.87062	−	3.01144i
$751$	18.3236			0.668638			0.334319	−	0.942460i	$-0.391494\pi$
$751$	18.3236			0.668638			0.334319	+	0.942460i	$0.391494\pi$
$752$	69.6359	−	22.6261i	2.53936	−	0.825088i
$753$	−55.5270	−	76.4263i	−2.02352	−	2.78513i
$754$	−17.8950	+	13.0015i	−0.651698	+	0.473487i
$755$	−0.891936	−	36.9123i	−0.0324609	−	1.34337i
$756$	−141.500	−	102.806i	−5.14632	−	3.73902i
$757$		−	4.06503i		−	0.147746i	−0.997268	−	0.0738729i	$-0.976464\pi$
$757$		−	4.06503i		−	0.147746i	0.997268	−	0.0738729i	$-0.0235359\pi$
$758$	10.7079	−	14.7381i	0.388928	−	0.535314i
$759$	5.98772	−	18.4283i	0.217340	−	0.668905i
$760$	5.99672	+	17.0436i	0.217524	+	0.618237i
$761$	11.1104	+	34.1944i	0.402753	+	1.23955i	0.922757	+	0.385382i	$0.125930\pi$
$761$	11.1104	+	34.1944i	0.402753	+	1.23955i	−0.520004	+	0.854164i	$0.674070\pi$
$762$	−15.1354	−	4.91779i	−0.548297	−	0.178153i
$763$	18.4951	+	6.00942i	0.669567	+	0.217556i
$764$	−13.4459	−	41.3822i	−0.486455	−	1.49716i
$765$	−12.5138	+	9.56208i	−0.452439	+	0.345718i
$766$	−4.55248	+	14.0111i	−0.164488	+	0.506242i
$767$	3.43204	−	4.72380i	0.123924	−	0.170567i
$768$			158.574i			5.72206i
$769$	−9.63581	−	7.00082i	−0.347476	−	0.252456i	0.400333	−	0.916370i	$-0.368894\pi$
$769$	−9.63581	−	7.00082i	−0.347476	−	0.252456i	−0.747809	+	0.663913i	$0.768894\pi$
$770$	35.4054	+	46.3348i	1.27592	+	1.66979i
$771$	−73.3641	+	53.3021i	−2.64214	+	1.91963i
$772$	34.0092	+	46.8096i

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.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.60604 + 0.846752i) q^{2} +(-1.86275 - 2.56385i) q^{3} +(4.45640 - 3.23776i) q^{4} +(0.0540158 + 2.23542i) q^{5} +(7.02533 + 5.10420i) q^{6} -2.47810i q^{7} +(-5.65071 + 7.77753i) q^{8} +(-2.17645 + 6.69843i) q^{9} +(-2.03361 - 5.77983i) q^{10} +(-1.18679 - 3.65255i) q^{11} +(-16.6023 - 5.39440i) q^{12} +(-1.34575 - 0.437262i) q^{13} +(2.09834 + 6.45802i) q^{14} +(5.63065 - 4.30250i) q^{15} +(4.73592 - 14.5757i) q^{16} +(0.587785 - 0.809017i) q^{17} -19.2993i q^{18} +(-0.679976 - 0.494032i) q^{19} +(7.47846 + 9.78701i) q^{20} +(-6.35348 + 4.61608i) q^{21} +(6.18561 + 8.51377i) q^{22} +(-1.51412 + 0.491967i) q^{23} +30.4663 q^{24} +(-4.99416 + 0.241496i) q^{25} +3.87733 q^{26} +(12.1860 - 3.95947i) q^{27} +(-8.02351 - 11.0434i) q^{28} +(-4.61529 + 3.35321i) q^{29} +(-11.0305 + 15.9802i) q^{30} +(-3.88614 - 2.82345i) q^{31} +22.7677i q^{32} +(-7.15392 + 9.84652i) q^{33} +(-0.846752 + 2.60604i) q^{34} +(5.53959 - 0.133857i) q^{35} +(11.9888 + 36.8977i) q^{36} +(4.34079 + 1.41041i) q^{37} +(2.19036 + 0.711693i) q^{38} +(1.38572 + 4.26482i) q^{39} +(-17.6912 - 12.2116i) q^{40} +(-0.386186 + 1.18856i) q^{41} +(12.6487 - 17.4095i) q^{42} +8.80279i q^{43} +(-17.1149 - 12.4347i) q^{44} +(-15.0913 - 4.50345i) q^{45} +(3.52927 - 2.56417i) q^{46} +(2.80817 + 3.86511i) q^{47} +(-46.1916 + 15.0086i) q^{48} +0.859006 q^{49} +(12.8105 - 4.85817i) q^{50} -3.16909 q^{51} +(-7.41296 + 2.40862i) q^{52} +(-1.10303 - 1.51819i) q^{53} +(-28.4044 + 20.6370i) q^{54} +(8.10087 - 2.85026i) q^{55} +(19.2735 + 14.0030i) q^{56} +2.66361i q^{57} +(9.18828 - 12.6466i) q^{58} +(-1.27514 + 3.92447i) q^{59} +(11.1619 - 37.4044i) q^{60} +(3.05333 + 9.39720i) q^{61} +(12.5182 + 4.06740i) q^{62} +(16.5994 + 5.39347i) q^{63} +(-9.80678 - 30.1822i) q^{64} +(0.904770 - 3.03194i) q^{65} +(10.3058 - 31.7180i) q^{66} +(-9.16910 + 12.6202i) q^{67} -5.50841i q^{68} +(4.08175 + 2.96556i) q^{69} +(-14.3230 + 5.03950i) q^{70} +(0.0639051 - 0.0464298i) q^{71} +(-39.7988 - 54.7783i) q^{72} +(3.40877 - 1.10758i) q^{73} -12.5065 q^{74} +(9.92202 + 12.3544i) q^{75} -4.62980 q^{76} +(-9.05140 + 2.94098i) q^{77} +(-7.22249 - 9.94090i) q^{78} +(0.953265 - 0.692588i) q^{79} +(32.8385 + 9.79943i) q^{80} +(-15.7568 - 11.4480i) q^{81} -3.42443i q^{82} +(-5.68451 + 7.82406i) q^{83} +(-13.3679 + 41.1421i) q^{84} +(1.84024 + 1.27024i) q^{85} +(-7.45378 - 22.9404i) q^{86} +(17.1942 + 5.58674i) q^{87} +(35.1140 + 11.4092i) q^{88} +(1.37884 + 4.24364i) q^{89} +(43.1419 - 1.04247i) q^{90} +(-1.08358 + 3.33492i) q^{91} +(-5.15465 + 7.09476i) q^{92} +15.2228i q^{93} +(-10.5910 - 7.69480i) q^{94} +(1.06764 - 1.54671i) q^{95} +(58.3730 - 42.4105i) q^{96} +(0.481530 + 0.662769i) q^{97} +(-2.23860 + 0.727365i) q^{98} +27.0494 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

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