LMFDB - Embedded newform 425.2.r.a.69.17

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			69.17
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.419745 + 0.136383i) q^{2} +(1.18389 + 1.62948i) q^{3} +(-1.46045 + 1.06108i) q^{4} +(-0.544497 - 2.16876i) q^{5} +(-0.719166 - 0.522504i) q^{6} -3.59659i q^{7} +(0.987136 - 1.35868i) q^{8} +(-0.326569 + 1.00508i) q^{9} +(0.524333 + 0.836067i) q^{10} +(-1.50976 - 4.64657i) q^{11} +(-3.45801 - 1.12358i) q^{12} +(5.02344 + 1.63221i) q^{13} +(0.490515 + 1.50965i) q^{14} +(2.88933 - 3.45482i) q^{15} +(0.886639 - 2.72879i) q^{16} +(-0.587785 + 0.809017i) q^{17} -0.466415i q^{18} +(-2.39152 - 1.73754i) q^{19} +(3.09643 + 2.58961i) q^{20} +(5.86057 - 4.25795i) q^{21} +(1.26743 + 1.74447i) q^{22} +(-5.79450 + 1.88275i) q^{23} +3.38260 q^{24} +(-4.40705 + 2.36177i) q^{25} -2.33117 q^{26} +(3.72234 - 1.20946i) q^{27} +(3.81626 + 5.25263i) q^{28} +(2.97252 - 2.15967i) q^{29} +(-0.741603 + 1.84420i) q^{30} +(4.70717 + 3.41996i) q^{31} +4.62515i q^{32} +(5.78411 - 7.96114i) q^{33} +(0.136383 - 0.419745i) q^{34} +(-7.80014 + 1.95833i) q^{35} +(-0.589527 - 1.81438i) q^{36} +(3.66498 + 1.19082i) q^{37} +(1.24080 + 0.403161i) q^{38} +(3.28752 + 10.1180i) q^{39} +(-3.48414 - 1.40107i) q^{40} +(-1.71798 + 5.28739i) q^{41} +(-1.87923 + 2.58654i) q^{42} -12.3629i q^{43} +(7.13530 + 5.18410i) q^{44} +(2.35759 + 0.160989i) q^{45} +(2.17544 - 1.58055i) q^{46} +(-0.643200 - 0.885289i) q^{47} +(5.49620 - 1.78582i) q^{48} -5.93543 q^{49} +(1.52773 - 1.59239i) q^{50} -2.01415 q^{51} +(-9.06838 + 2.94650i) q^{52} +(-7.65338 - 10.5340i) q^{53} +(-1.39748 + 1.01533i) q^{54} +(-9.25523 + 5.80435i) q^{55} +(-4.88660 - 3.55032i) q^{56} -5.95399i q^{57} +(-0.953160 + 1.31191i) q^{58} +(-1.53669 + 4.72944i) q^{59} +(-0.553891 + 8.11139i) q^{60} +(2.19852 + 6.76636i) q^{61} +(-2.44224 - 0.793532i) q^{62} +(3.61484 + 1.17453i) q^{63} +(1.14248 + 3.51620i) q^{64} +(0.804635 - 11.7834i) q^{65} +(-1.34208 + 4.13051i) q^{66} +(5.88778 - 8.10383i) q^{67} -1.80521i q^{68} +(-9.92794 - 7.21307i) q^{69} +(3.00699 - 1.88581i) q^{70} +(13.0997 - 9.51752i) q^{71} +(1.04321 + 1.43585i) q^{72} +(-4.59685 + 1.49361i) q^{73} -1.70077 q^{74} +(-9.06590 - 4.38513i) q^{75} +5.33636 q^{76} +(-16.7118 + 5.42999i) q^{77} +(-2.75985 - 3.79860i) q^{78} +(-1.22713 + 0.891561i) q^{79} +(-6.40087 - 0.437087i) q^{80} +(8.94253 + 6.49713i) q^{81} -2.45366i q^{82} +(3.33657 - 4.59240i) q^{83} +(-4.04104 + 12.4370i) q^{84} +(2.07461 + 0.834258i) q^{85} +(1.68609 + 5.18925i) q^{86} +(7.03827 + 2.28687i) q^{87} +(-7.80352 - 2.53552i) q^{88} +(0.475510 + 1.46347i) q^{89} +(-1.01154 + 0.253961i) q^{90} +(5.87040 - 18.0672i) q^{91} +(6.46483 - 8.89808i) q^{92} +11.7191i q^{93} +(0.390719 + 0.283874i) q^{94} +(-2.46614 + 6.13272i) q^{95} +(-7.53660 + 5.47566i) q^{96} +(4.79226 + 6.59598i) q^{97} +(2.49137 - 0.809495i) q^{98} +5.16320 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 $

$2$	−0.419745	+	0.136383i	−0.296805	+	0.0964377i	−0.453634	−	0.891188i	$-0.649873\pi$
$2$	−0.419745	+	0.136383i	−0.296805	+	0.0964377i	0.156829	+	0.987626i	$0.449873\pi$
$3$	1.18389	+	1.62948i	0.683518	+	0.940782i	0.999969	−	0.00782710i	$-0.00249147\pi$
$3$	1.18389	+	1.62948i	0.683518	+	0.940782i	−0.316452	+	0.948609i	$0.602491\pi$
$4$	−1.46045	+	1.06108i	−0.730224	+	0.530539i
$5$	−0.544497	−	2.16876i	−0.243506	−	0.969899i
$5$	−0.544497	−	2.16876i	−0.243506	−	0.969899i
$6$	−0.719166	−	0.522504i	−0.293598	−	0.213312i
$7$		−	3.59659i		−	1.35938i	−0.733499	−	0.679691i	$-0.762114\pi$
$7$		−	3.59659i		−	1.35938i	0.733499	−	0.679691i	$-0.237886\pi$
$8$	0.987136	−	1.35868i	0.349005	−	0.480365i
$9$	−0.326569	+	1.00508i	−0.108856	+	0.335025i
$10$	0.524333	+	0.836067i	0.165809	+	0.264387i
$11$	−1.50976	−	4.64657i	−0.455210	−	1.40099i	−0.870888	−	0.491481i	$-0.836456\pi$
$11$	−1.50976	−	4.64657i	−0.455210	−	1.40099i	0.415678	−	0.909512i	$-0.363544\pi$
$12$	−3.45801	−	1.12358i	−0.998243	−	0.324349i
$13$	5.02344	+	1.63221i	1.39325	+	0.452695i	0.907002	−	0.421126i	$-0.138365\pi$
$13$	5.02344	+	1.63221i	1.39325	+	0.452695i	0.486249	+	0.873820i	$0.338365\pi$
$14$	0.490515	+	1.50965i	0.131096	+	0.403471i
$15$	2.88933	−	3.45482i	0.746022	−	0.892030i
$16$	0.886639	−	2.72879i	0.221660	−	0.682198i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$18$		−	0.466415i		−	0.109935i
$19$	−2.39152	−	1.73754i	−0.548653	−	0.398619i	0.278636	−	0.960397i	$-0.410118\pi$
$19$	−2.39152	−	1.73754i	−0.548653	−	0.398619i	−0.827288	+	0.561777i	$0.810118\pi$
$20$	3.09643	+	2.58961i	0.692384	+	0.579054i
$21$	5.86057	−	4.25795i	1.27888	−	0.929162i
$22$	1.26743	+	1.74447i	0.270217	+	0.371922i
$23$	−5.79450	+	1.88275i	−1.20824	+	0.392580i	−0.842785	−	0.538250i	$-0.819086\pi$
$23$	−5.79450	+	1.88275i	−1.20824	+	0.392580i	−0.365452	+	0.930830i	$0.619086\pi$
$24$	3.38260			0.690470
$25$	−4.40705	+	2.36177i	−0.881409	+	0.472353i
$26$	−2.33117			−0.457180
$27$	3.72234	−	1.20946i	0.716364	−	0.232761i
$28$	3.81626	+	5.25263i	0.721205	+	0.992654i
$29$	2.97252	−	2.15967i	0.551984	−	0.401040i	−0.276532	−	0.961005i	$-0.589185\pi$
$29$	2.97252	−	2.15967i	0.551984	−	0.401040i	0.828516	+	0.559965i	$0.189185\pi$
$30$	−0.741603	+	1.84420i	−0.135398	+	0.336703i
$31$	4.70717	+	3.41996i	0.845433	+	0.614243i	0.923883	−	0.382675i	$-0.124997\pi$
$31$	4.70717	+	3.41996i	0.845433	+	0.614243i	−0.0784499	+	0.996918i	$0.524997\pi$
$32$			4.62515i			0.817619i
$33$	5.78411	−	7.96114i	1.00688	−	1.38586i
$34$	0.136383	−	0.419745i	0.0233896	−	0.0719857i
$35$	−7.80014	+	1.95833i	−1.31846	+	0.331018i
$36$	−0.589527	−	1.81438i	−0.0982545	−	0.302396i
$37$	3.66498	+	1.19082i	0.602519	+	0.195770i	0.594364	−	0.804196i	$-0.297404\pi$
$37$	3.66498	+	1.19082i	0.602519	+	0.195770i	0.00815538	+	0.999967i	$0.497404\pi$
$38$	1.24080	+	0.403161i	0.201285	+	0.0654013i
$39$	3.28752	+	10.1180i	0.526425	+	1.62017i
$40$	−3.48414	−	1.40107i	−0.550890	−	0.221528i
$41$	−1.71798	+	5.28739i	−0.268303	+	0.825751i	0.722611	+	0.691255i	$0.242942\pi$
$41$	−1.71798	+	5.28739i	−0.268303	+	0.825751i	−0.990914	+	0.134497i	$0.957058\pi$
$42$	−1.87923	+	2.58654i	−0.289972	+	0.399112i
$43$		−	12.3629i		−	1.88532i	−0.333756	−	0.942660i	$-0.608316\pi$
$43$		−	12.3629i		−	1.88532i	0.333756	−	0.942660i	$-0.391684\pi$
$44$	7.13530	+	5.18410i	1.07569	+	0.781532i
$45$	2.35759	+	0.160989i	0.351448	+	0.0239989i
$46$	2.17544	−	1.58055i	0.320751	−	0.233039i
$47$	−0.643200	−	0.885289i	−0.0938204	−	0.129133i	0.759526	−	0.650477i	$-0.225431\pi$
$47$	−0.643200	−	0.885289i	−0.0938204	−	0.129133i	−0.853347	+	0.521344i	$0.825431\pi$
$48$	5.49620	−	1.78582i	0.793308	−	0.257761i
$49$	−5.93543			−0.847919
$50$	1.52773	−	1.59239i	0.216054	−	0.225198i
$51$	−2.01415			−0.282037
$52$	−9.06838	+	2.94650i	−1.25756	+	0.408605i
$53$	−7.65338	−	10.5340i	−1.05127	−	1.44695i	−0.887701	−	0.460421i	$-0.847698\pi$
$53$	−7.65338	−	10.5340i	−1.05127	−	1.44695i	−0.163572	−	0.986531i	$-0.552302\pi$
$54$	−1.39748	+	1.01533i	−0.190173	+	0.138169i
$55$	−9.25523	+	5.80435i	−1.24798	+	0.782659i
$56$	−4.88660	−	3.55032i	−0.652999	−	0.474432i
$57$		−	5.95399i		−	0.788626i
$58$	−0.953160	+	1.31191i	−0.125156	+	0.172263i
$59$	−1.53669	+	4.72944i	−0.200060	+	0.615720i	0.799821	+	0.600239i	$0.204928\pi$
$59$	−1.53669	+	4.72944i	−0.200060	+	0.615720i	−0.999880	+	0.0154811i	$0.995072\pi$
$60$	−0.553891	+	8.11139i	−0.0715070	+	1.04718i
$61$	2.19852	+	6.76636i	0.281492	+	0.866343i	0.987428	+	0.158068i	$0.0505265\pi$
$61$	2.19852	+	6.76636i	0.281492	+	0.866343i	−0.705936	+	0.708275i	$0.749473\pi$
$62$	−2.44224	−	0.793532i	−0.310165	−	0.100779i
$63$	3.61484	+	1.17453i	0.455428	+	0.147977i
$64$	1.14248	+	3.51620i	0.142810	+	0.439525i
$65$	0.804635	−	11.7834i	0.0998027	−	1.46155i
$66$	−1.34208	+	4.13051i	−0.165199	+	0.508430i
$67$	5.88778	−	8.10383i	0.719307	−	0.990041i	−0.280240	−	0.959930i	$-0.590414\pi$
$67$	5.88778	−	8.10383i	0.719307	−	0.990041i	0.999547	−	0.0301106i	$-0.00958596\pi$
$68$		−	1.80521i		−	0.218914i
$69$	−9.92794	−	7.21307i	−1.19518	−	0.868352i
$70$	3.00699	−	1.88581i	0.359404	−	0.225397i
$71$	13.0997	−	9.51752i	1.55465	−	1.12952i	0.614427	−	0.788973i	$-0.289387\pi$
$71$	13.0997	−	9.51752i	1.55465	−	1.12952i	0.940227	−	0.340549i	$-0.110613\pi$
$72$	1.04321	+	1.43585i	0.122943	+	0.169216i
$73$	−4.59685	+	1.49361i	−0.538021	+	0.174814i	−0.565408	−	0.824811i	$-0.691281\pi$
$73$	−4.59685	+	1.49361i	−0.538021	+	0.174814i	0.0273870	+	0.999625i	$0.491281\pi$
$74$	−1.70077			−0.197710
$75$	−9.06590	−	4.38513i	−1.04684	−	0.506352i
$76$	5.33636			0.612123
$77$	−16.7118	+	5.42999i	−1.90448	+	0.618804i
$78$	−2.75985	−	3.79860i	−0.312491	−	0.430107i
$79$	−1.22713	+	0.891561i	−0.138063	+	0.100308i	−0.654673	−	0.755912i	$-0.727194\pi$
$79$	−1.22713	+	0.891561i	−0.138063	+	0.100308i	0.516610	+	0.856221i	$0.327194\pi$
$80$	−6.40087	−	0.437087i	−0.715639	−	0.0488679i
$81$	8.94253	+	6.49713i	0.993614	+	0.721903i
$82$		−	2.45366i		−	0.270961i
$83$	3.33657	−	4.59240i	0.366236	−	0.504081i	−0.585637	−	0.810574i	$-0.699155\pi$
$83$	3.33657	−	4.59240i	0.366236	−	0.504081i	0.951873	+	0.306492i	$0.0991554\pi$
$84$	−4.04104	+	12.4370i	−0.440914	+	1.35699i
$85$	2.07461	+	0.834258i	0.225023	+	0.0904880i
$86$	1.68609	+	5.18925i	0.181816	+	0.559572i
$87$	7.03827	+	2.28687i	0.754582	+	0.245179i
$88$	−7.80352	−	2.53552i	−0.831858	−	0.270287i
$89$	0.475510	+	1.46347i	0.0504040	+	0.155127i	0.973090	−	0.230424i	$-0.0740113\pi$
$89$	0.475510	+	1.46347i	0.0504040	+	0.155127i	−0.922686	+	0.385551i	$0.874011\pi$
$90$	−1.01154	+	0.253961i	−0.106626	+	0.0267699i
$91$	5.87040	−	18.0672i	0.615385	−	1.89396i
$92$	6.46483	−	8.89808i	0.674005	−	0.927689i
$93$			11.7191i			1.21521i
$94$	0.390719	+	0.283874i	0.0402996	+	0.0292794i
$95$	−2.46614	+	6.13272i	−0.253020	+	0.629204i
$96$	−7.53660	+	5.47566i	−0.769201	+	0.558857i
$97$	4.79226	+	6.59598i	0.486580	+	0.669720i	0.979753	−	0.200211i	$-0.0641629\pi$
$97$	4.79226	+	6.59598i	0.486580	+	0.669720i	−0.493173	+	0.869931i	$0.664163\pi$
$98$	2.49137	−	0.809495i	0.251666	−	0.0817714i
$99$	5.16320			0.518921
$100$	3.93024	−	8.12546i	0.393024	−	0.812546i
$101$	−9.66741			−0.961943			−0.480971	−	0.876736i	$-0.659716\pi$
$101$	−9.66741			−0.961943			−0.480971	+	0.876736i	$0.659716\pi$
$102$	0.845430	−	0.274697i	0.0837100	−	0.0271990i
$103$	5.96378	+	8.20844i	0.587629	+	0.808802i	0.994506	−	0.104681i	$-0.0333823\pi$
$103$	5.96378	+	8.20844i	0.587629	+	0.808802i	−0.406877	+	0.913483i	$0.633382\pi$
$104$	7.17647	−	5.21401i	0.703711	−	0.511276i
$105$	−12.4255	−	10.3917i	−1.21261	−	1.01413i
$106$	4.64913	+	3.37779i	0.451563	+	0.328080i
$107$			8.48729i			0.820498i	0.911974	+	0.410249i	$0.134558\pi$
$107$			8.48729i			0.820498i	−0.911974	+	0.410249i	$0.865442\pi$
$108$	−4.15295	+	5.71604i	−0.399618	+	0.550027i
$109$	−5.66122	+	17.4234i	−0.542247	+	1.66886i	0.185202	+	0.982701i	$0.440706\pi$
$109$	−5.66122	+	17.4234i	−0.542247	+	1.66886i	−0.727448	+	0.686163i	$0.759294\pi$
$110$	3.09322	−	3.69861i	0.294927	−	0.352649i
$111$	2.39850	+	7.38182i	0.227655	+	0.700651i
$112$	−9.81434	−	3.18887i	−0.927368	−	0.301320i
$113$	−4.20909	−	1.36762i	−0.395958	−	0.128655i	0.104268	−	0.994549i	$-0.466750\pi$
$113$	−4.20909	−	1.36762i	−0.395958	−	0.128655i	−0.500227	+	0.865895i	$0.666750\pi$
$114$	0.812027	+	2.49916i	0.0760533	+	0.234068i
$115$	7.23832	+	11.5417i	0.674977	+	1.07627i
$116$	−2.04965	+	6.30816i	−0.190305	+	0.585698i
$117$	−3.28100	+	4.51591i	−0.303329	+	0.417496i
$118$		−	2.19474i		−	0.202042i
$119$	2.90970	+	2.11402i	0.266732	+	0.193792i
$120$	−1.84181	−	7.33604i	−0.168134	−	0.669686i
$121$	−10.4120	+	7.56477i	−0.946547	+	0.687706i
$122$	−1.84564	−	2.54030i	−0.167096	−	0.229988i
$123$	−10.6496	+	3.46026i	−0.960241	+	0.312001i
$124$	−10.5034			−0.943236
$125$	7.52173	+	8.27185i	0.672764	+	0.739857i
$126$	−1.67750			−0.149444
$127$	−11.8492	+	3.85005i	−1.05145	+	0.341637i	−0.783237	−	0.621723i	$-0.786433\pi$
$127$	−11.8492	+	3.85005i	−1.05145	+	0.341637i	−0.268213	+	0.963360i	$0.586433\pi$
$128$	−6.39630	−	8.80375i	−0.565358	−	0.778149i
$129$	20.1451	−	14.6362i	1.77367	−	1.28865i
$130$	1.26932	+	5.05575i	0.111326	+	0.443419i
$131$	15.0573	+	10.9397i	1.31556	+	0.955809i	0.999976	+	0.00691095i	$0.00219984\pi$
$131$	15.0573	+	10.9397i	1.31556	+	0.955809i	0.315582	+	0.948898i	$0.397800\pi$
$132$			17.7642i			1.54618i
$133$	−6.24922	+	8.60131i	−0.541876	+	0.745829i
$134$	−1.36614	+	4.20454i	−0.118016	+	0.363217i
$135$	−4.64983	−	7.41431i	−0.400194	−	0.638122i
$136$	0.518968	+	1.59722i	0.0445012	+	0.136961i
$137$	−3.10372	−	1.00846i	−0.265169	−	0.0861585i	0.173415	−	0.984849i	$-0.444520\pi$
$137$	−3.10372	−	1.00846i	−0.265169	−	0.0861585i	−0.438584	+	0.898690i	$0.644520\pi$
$138$	5.15095	+	1.67365i	0.438478	+	0.142470i
$139$	1.40327	+	4.31882i	0.119024	+	0.366318i	0.992765	−	0.120073i	$-0.0383130\pi$
$139$	1.40327	+	4.31882i	0.119024	+	0.366318i	−0.873741	+	0.486391i	$0.838313\pi$
$140$	9.31375	−	11.1366i	0.787156	−	0.941214i
$141$	0.681085	−	2.09617i	0.0573577	−	0.176529i
$142$	−4.20052	+	5.78153i	−0.352500	+	0.485175i
$143$		−	25.8060i		−	2.15801i
$144$	2.45310	+	1.78228i	0.204425	+	0.148523i
$145$	−6.30233	−	5.27076i	−0.523380	−	0.437713i
$146$	1.72580	−	1.25387i	0.142829	−	0.103771i
$147$	−7.02689	−	9.67168i	−0.579568	−	0.797707i
$148$	−6.61607	+	2.14969i	−0.543838	+	0.176704i
$149$	−2.01275			−0.164891			−0.0824454	−	0.996596i	$-0.526273\pi$
$149$	−2.01275			−0.164891			−0.0824454	+	0.996596i	$0.526273\pi$
$150$	4.40343	+	0.604199i	0.359539	+	0.0493326i
$151$	11.6149			0.945206			0.472603	−	0.881275i	$-0.343314\pi$
$151$	11.6149			0.945206			0.472603	+	0.881275i	$0.343314\pi$
$152$	−4.72152	+	1.53411i	−0.382965	+	0.124433i
$153$	−0.621171	−	0.854969i	−0.0502187	−	0.0691201i
$154$	6.27413	−	4.55842i	0.505584	−	0.367328i
$155$	4.85404	−	12.0709i	0.389886	−	0.969557i
$156$	−15.5372	−	11.2884i	−1.24397	−	0.903798i
$157$			8.88147i			0.708818i	0.935090	+	0.354409i	$0.115318\pi$
$157$			8.88147i			0.708818i	−0.935090	+	0.354409i	$0.884682\pi$
$158$	0.393487	−	0.541588i	0.0313041	−	0.0430865i
$159$	8.10417	−	24.9421i	0.642703	−	1.97804i
$160$	10.0309	−	2.51838i	0.793009	−	0.199096i
$161$	6.77147	+	20.8404i	0.533666	+	1.64246i
$162$	−4.63968	−	1.50752i	−0.364528	−	0.118442i
$163$	21.1700	+	6.87856i	1.65817	+	0.538771i	0.980486	−	0.196587i	$-0.0629857\pi$
$163$	21.1700	+	6.87856i	1.65817	+	0.538771i	0.677680	+	0.735357i	$0.262986\pi$
$164$	−3.10131	−	9.54486i	−0.242172	−	0.745329i
$165$	−20.4152	−	8.20953i	−1.58932	−	0.639111i
$166$	−0.774183	+	2.38269i	−0.0600883	+	0.184933i
$167$	−0.933445	+	1.28478i	−0.0722322	+	0.0994191i	−0.843604	−	0.536965i	$-0.819571\pi$
$167$	−0.933445	+	1.28478i	−0.0722322	+	0.0994191i	0.771372	+	0.636384i	$0.219571\pi$
$168$		−	12.1658i		−	0.938612i
$169$	12.0536	+	8.75745i	0.927200	+	0.673650i
$170$	−0.984587	−	0.0672331i	−0.0755144	−	0.00515655i
$171$	2.52736	−	1.83623i	0.193272	−	0.140420i
$172$	13.1180	+	18.0553i	1.00024	+	1.37671i
$173$	−9.98482	+	3.24426i	−0.759132	+	0.246657i	−0.662906	−	0.748703i	$-0.730677\pi$
$173$	−9.98482	+	3.24426i	−0.759132	+	0.246657i	−0.0962259	+	0.995360i	$0.530677\pi$
$174$	−3.26617			−0.247608
$175$	8.49430	+	15.8503i	0.642109	+	1.19817i
$176$	−14.0181			−1.05666
$177$	−9.52580	+	3.09512i	−0.716003	+	0.232643i
$178$	−0.399186	−	0.549433i	−0.0299203	−	0.0411817i
$179$	1.07548	−	0.781385i	0.0803855	−	0.0584035i	−0.546867	−	0.837220i	$-0.684180\pi$
$179$	1.07548	−	0.781385i	0.0803855	−	0.0584035i	0.627252	+	0.778816i	$0.284180\pi$
$180$	−3.61395	+	2.26647i	−0.269368	+	0.168932i
$181$	6.36938	+	4.62762i	0.473432	+	0.343968i	0.798777	−	0.601627i	$-0.205481\pi$
$181$	6.36938	+	4.62762i	0.473432	+	0.343968i	−0.325345	+	0.945595i	$0.605481\pi$
$182$			8.38426i			0.621483i
$183$	−8.42285	+	11.5931i	−0.622635	+	0.856984i
$184$	−3.16192	+	9.73139i	−0.233100	+	0.717407i
$185$	0.587042	−	8.59686i	0.0431602	−	0.632054i
$186$	−1.59829	−	4.91904i	−0.117192	−	0.360681i
$187$	4.64657	+	1.50976i	0.339791	+	0.110405i
$188$	1.87872	+	0.610434i	0.137020	+	0.0445204i
$189$	−4.34993	−	13.3877i	−0.316411	−	0.973812i
$190$	0.198747	−	2.91052i	0.0144186	−	0.211151i
$191$	6.60549	−	20.3296i	0.477956	−	1.47100i	−0.363973	−	0.931410i	$-0.618580\pi$
$191$	6.60549	−	20.3296i	0.477956	−	1.47100i	0.841929	−	0.539588i	$-0.181420\pi$
$192$	−4.37701	+	6.02444i	−0.315884	+	0.434776i
$193$		−	11.3070i		−	0.813897i	−0.913451	−	0.406948i	$-0.866593\pi$
$193$		−	11.3070i		−	0.813897i	0.913451	−	0.406948i	$-0.133407\pi$
$194$	−2.91111	−	2.11504i	−0.209005	−	0.151851i
$195$	20.1534	−	12.6391i	1.44321	−	0.905101i
$196$	8.66840	−	6.29796i	0.619171	−	0.449854i
$197$	−7.01589	−	9.65655i	−0.499862	−	0.688001i	0.482307	−	0.876002i	$-0.339799\pi$
$197$	−7.01589	−	9.65655i	−0.499862	−	0.688001i	−0.982169	+	0.188002i	$0.939799\pi$
$198$	−2.16723	+	0.704175i	−0.154018	+	0.0500435i
$199$	0.834392			0.0591485			0.0295742	−	0.999563i	$-0.490585\pi$
$199$	0.834392			0.0591485			0.0295742	+	0.999563i	$0.490585\pi$
$200$	−1.14148	+	8.31914i	−0.0807146	+	0.588252i
$201$	20.1755			1.42307
$202$	4.05785	−	1.31847i	0.285509	−	0.0927676i
$203$	−7.76742	−	10.6909i	−0.545166	−	0.750357i
$204$	2.94156	−	2.13717i	0.205951	−	0.149632i
$205$	12.4025	+	0.846913i	0.866229	+	0.0591510i
$206$	−3.62276	−	2.63209i	−0.252410	−	0.183387i
$207$		−	6.43877i		−	0.447525i
$208$	8.90795	−	12.2607i	0.617655	−	0.850129i
$209$	−4.46298	+	13.7356i	−0.308711	+	0.950114i
$210$	6.63283	+	2.66724i	0.457708	+	0.184057i
$211$	−0.139316	−	0.428770i	−0.00959089	−	0.0295177i	0.946147	−	0.323739i	$-0.104940\pi$
$211$	−0.139316	−	0.428770i	−0.00959089	−	0.0295177i	−0.955737	+	0.294221i	$0.904940\pi$
$212$	22.3547	+	7.26349i	1.53533	+	0.498859i
$213$	31.0173	+	10.0781i	2.12527	+	0.690541i
$214$	−1.15753	−	3.56250i	−0.0791269	−	0.243528i
$215$	−26.8121	+	6.73154i	−1.82857	+	0.459087i
$216$	2.03119	−	6.25135i	0.138205	−	0.425351i
$217$	12.3002	−	16.9298i	0.834991	−	1.14927i
$218$		−	8.08550i		−	0.547619i
$219$	−7.87597	−	5.72223i	−0.532209	−	0.386672i
$220$	7.35792	−	18.2975i	0.496071	−	1.23362i
$221$	−4.27319	+	3.10466i	−0.287446	+	0.208842i
$222$	−2.01352	−	2.77137i	−0.135138	−	0.186002i
$223$	−26.3581	+	8.56428i	−1.76507	+	0.573507i	−0.997706	−	0.0677026i	$-0.978433\pi$
$223$	−26.3581	+	8.56428i	−1.76507	+	0.573507i	−0.767366	+	0.641209i	$0.778433\pi$
$224$	16.6348			1.11146
$225$	−0.934551	−	5.20070i	−0.0623034	−	0.346713i
$226$	1.95327			0.129929
$227$	15.1494	−	4.92232i	1.00550	−	0.326706i	0.240438	−	0.970665i	$-0.422709\pi$
$227$	15.1494	−	4.92232i	1.00550	−	0.326706i	0.765060	+	0.643958i	$0.222709\pi$
$228$	6.31765	+	8.69550i	0.418397	+	0.575874i
$229$	2.78044	−	2.02011i	0.183737	−	0.133493i	−0.492115	−	0.870530i	$-0.663776\pi$
$229$	2.78044	−	2.02011i	0.183737	−	0.133493i	0.675852	+	0.737038i	$0.263776\pi$
$230$	−4.61235	−	3.85740i	−0.304130	−	0.254350i
$231$	−28.6329	−	20.8030i	−1.88391	−	1.36874i
$232$		−	6.17058i		−	0.405119i
$233$	14.0602	−	19.3522i	0.921115	−	1.26781i	−0.0421114	−	0.999113i	$-0.513408\pi$
$233$	14.0602	−	19.3522i	0.921115	−	1.26781i	0.963226	−	0.268693i	$-0.0865915\pi$
$234$	0.761289	−	2.34301i	0.0497670	−	0.153167i
$235$	−1.56976	+	1.87698i	−0.102400	+	0.122441i
$236$	−2.77405	−	8.53764i	−0.180575	−	0.555753i
$237$	−2.90556	−	0.944075i	−0.188737	−	0.0613242i
$238$	−1.50965	−	0.490515i	−0.0978561	−	0.0317954i
$239$	0.164722	+	0.506964i	0.0106550	+	0.0327927i	0.956243	−	0.292575i	$-0.0945120\pi$
$239$	0.164722	+	0.506964i	0.0106550	+	0.0327927i	−0.945588	+	0.325367i	$0.894512\pi$
$240$	−6.86569	−	10.9476i	−0.443178	−	0.706662i
$241$	−4.46523	+	13.7426i	−0.287631	+	0.885236i	0.697967	+	0.716130i	$0.254088\pi$
$241$	−4.46523	+	13.7426i	−0.287631	+	0.885236i	−0.985598	+	0.169106i	$0.945912\pi$
$242$	3.33868	−	4.59530i	0.214619	−	0.295397i
$243$			10.5219i			0.674978i
$244$	−10.3905	−	7.54911i	−0.665181	−	0.483282i
$245$	3.23183	+	12.8725i	0.206474	+	0.822396i
$246$	3.99819	−	2.90486i	0.254915	−	0.185207i
$247$	−9.17762	−	12.6319i	−0.583958	−	0.803749i
$248$	9.29324	−	3.01956i	0.590122	−	0.191742i
$249$	11.4334			0.724560
$250$	−4.28536	−	2.44623i	−0.271030	−	0.154713i
$251$	0.222991			0.0140751			0.00703753	−	0.999975i	$-0.497760\pi$
$251$	0.222991			0.0140751			0.00703753	+	0.999975i	$0.497760\pi$
$252$	−6.52557	+	2.12028i	−0.411072	+	0.133565i
$253$	17.4966	+	24.0820i	1.10000	+	1.51403i
$254$	4.44858	−	3.23208i	0.279129	−	0.202799i
$255$	1.09670	+	4.36821i	0.0686779	+	0.273548i
$256$	−2.09661	−	1.52328i	−0.131038	−	0.0952050i
$257$		−	9.94770i		−	0.620521i	−0.950652	−	0.310260i	$-0.899584\pi$
$257$		−	9.94770i		−	0.620521i	0.950652	−	0.310260i	$-0.100416\pi$
$258$	−6.45965	+	8.89095i	−0.402160	+	0.553526i
$259$	4.28290	−	13.1814i	0.266127	−	0.819053i
$260$	11.3279	+	18.0628i	0.702530	+	1.12021i
$261$	1.19989	+	3.69289i	0.0742716	+	0.228584i
$262$	−7.81221	−	2.53834i	−0.482640	−	0.156819i
$263$	−12.6602	−	4.11355i	−0.780663	−	0.253653i	−0.108540	−	0.994092i	$-0.534617\pi$
$263$	−12.6602	−	4.11355i	−0.780663	−	0.253653i	−0.672123	+	0.740439i	$0.734617\pi$
$264$	−5.10691	−	15.7175i	−0.314309	−	0.967343i
$265$	−18.6784	+	22.3341i	−1.14741	+	1.37197i
$266$	1.45000	−	4.46265i	0.0889054	−	0.273623i
$267$	−1.82175	+	2.50742i	−0.111489	+	0.153451i
$268$			18.0826i			1.10457i
$269$	4.76060	+	3.45878i	0.290259	+	0.210885i	0.723380	−	0.690451i	$-0.242588\pi$
$269$	4.76060	+	3.45878i	0.290259	+	0.210885i	−0.433121	+	0.901336i	$0.642588\pi$
$270$	2.96293	+	2.47796i	0.180318	+	0.150804i
$271$	−4.48552	+	3.25892i	−0.272476	+	0.197965i	−0.715629	−	0.698481i	$-0.753860\pi$
$271$	−4.48552	+	3.25892i	−0.272476	+	0.197965i	0.443153	+	0.896446i	$0.353860\pi$
$272$	1.68649	+	2.32125i	0.102258	+	0.140746i
$273$	36.3901	−	11.8239i	2.20243	−	0.715613i
$274$	1.44031			0.0870123
$275$	17.6277	+	16.9119i	1.06299	+	1.01983i
$276$	22.1529			1.33345
$277$	3.24291	−	1.05368i	0.194847	−	0.0633097i	−0.209968	−	0.977708i	$-0.567336\pi$
$277$	3.24291	−	1.05368i	0.194847	−	0.0633097i	0.404815	+	0.914399i	$0.367336\pi$
$278$	−1.17803	−	1.62142i	−0.0706537	−	0.0972465i
$279$	−4.97454	+	3.61421i	−0.297818	+	0.216377i
$280$	−5.03906	+	12.5310i	−0.301141	+	0.748871i
$281$	15.4662	+	11.2368i	0.922634	+	0.670333i	0.944178	−	0.329435i	$-0.106858\pi$
$281$	15.4662	+	11.2368i	0.922634	+	0.670333i	−0.0215441	+	0.999768i	$0.506858\pi$
$282$			0.972744i			0.0579261i
$283$	−3.56399	+	4.90542i	−0.211857	+	0.291597i	−0.901700	−	0.432363i	$-0.857680\pi$
$283$	−3.56399	+	4.90542i	−0.211857	+	0.291597i	0.689842	+	0.723960i	$0.257680\pi$
$284$	−9.03267	+	27.7997i	−0.535990	+	1.64961i
$285$	−12.9128	+	3.24193i	−0.764888	+	0.192035i
$286$	3.51951	+	10.8319i	0.208113	+	0.640506i
$287$	19.0165	+	6.17885i	1.12251	+	0.364726i
$288$	−4.64863	−	1.51043i	−0.273923	−	0.0890031i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	3.36422	+	1.35284i	0.197554	+	0.0794418i
$291$	−5.07453	+	15.6178i	−0.297474	+	0.915531i
$292$	5.12863	−	7.05896i	0.300131	−	0.413094i
$293$			2.76818i			0.161719i	0.996726	+	0.0808593i	$0.0257664\pi$
$293$			2.76818i			0.161719i	−0.996726	+	0.0808593i	$0.974234\pi$
$294$	4.26856	+	3.10129i	0.248947	+	0.180871i
$295$	11.0937	+	0.757543i	0.645903	+	0.0441058i
$296$	5.23578	−	3.80402i	0.304324	−	0.221104i
$297$	−11.2397	−	15.4701i	−0.652192	−	0.897666i
$298$	0.844842	−	0.274506i	0.0489404	−	0.0159017i
$299$	−32.1814			−1.86110
$300$	17.8933	−	3.21537i	1.03307	−	0.185639i
$301$	−44.4641			−2.56287
$302$	−4.87529	+	1.58408i	−0.280542	+	0.0911535i
$303$	−11.4451	−	15.7529i	−0.657505	−	0.904978i
$304$	−6.86181	+	4.98540i	−0.393552	+	0.285932i
$305$	13.4775	−	8.45233i	0.771721	−	0.483979i
$306$	0.377337	+	0.274152i	0.0215709	+	0.0156722i
$307$			8.88354i			0.507011i	0.967334	+	0.253505i	$0.0815835\pi$
$307$			8.88354i			0.507011i	−0.967334	+	0.253505i	$0.918416\pi$
$308$	18.6451	−	25.6627i	1.06240	−	1.46227i
$309$	−6.31505	+	19.4357i	−0.359251	+	1.10566i
$310$	−0.391188	+	5.72871i	−0.0222180	+	0.325369i
$311$	2.72922	+	8.39966i	0.154760	+	0.476301i	0.998136	−	0.0610213i	$-0.0194358\pi$
$311$	2.72922	+	8.39966i	0.154760	+	0.476301i	−0.843377	+	0.537323i	$0.819436\pi$
$312$	16.9923	+	5.52112i	0.961998	+	0.312572i
$313$	3.01830	+	0.980705i	0.170604	+	0.0554327i	0.393074	−	0.919507i	$-0.371412\pi$
$313$	3.01830	+	0.980705i	0.170604	+	0.0554327i	−0.222469	+	0.974940i	$0.571412\pi$
$314$	−1.21129	−	3.72795i	−0.0683568	−	0.210381i
$315$	0.579012	−	8.47926i	0.0326236	−	0.477752i
$316$	0.846142	−	2.60416i	0.0475992	−	0.146495i
$317$	−1.74179	+	2.39736i	−0.0978285	+	0.134649i	−0.855125	−	0.518422i	$-0.826520\pi$
$317$	−1.74179	+	2.39736i	−0.0978285	+	0.134649i	0.757297	+	0.653071i	$0.226520\pi$
$318$			11.5746i			0.649071i
$319$	−14.5228	−	10.5515i	−0.813123	−	0.590768i
$320$	7.00372	−	4.39233i	0.391520	−	0.245539i
$321$	−13.8299	+	10.0480i	−0.771909	+	0.560825i
$322$	−5.68458	−	7.82416i	−0.316789	−	0.436023i
$323$	2.81140	−	0.913480i	0.156431	−	0.0508274i
$324$	−19.9541			−1.10856
$325$	−25.9934	+	4.67095i	−1.44186	+	0.259098i
$326$	−9.82415			−0.544109
$327$	−35.0934	+	11.4025i	−1.94067	+	0.630562i
$328$	5.48797	+	7.55355i	0.303023	+	0.417075i
$329$	−3.18402	+	2.31332i	−0.175541	+	0.127538i
$330$	9.68884	+	0.661608i	0.533353	+	0.0364203i
$331$	−4.59799	−	3.34064i	−0.252729	−	0.183618i	0.454207	−	0.890896i	$-0.349923\pi$
$331$	−4.59799	−	3.34064i	−0.252729	−	0.183618i	−0.706935	+	0.707278i	$0.749923\pi$
$332$			10.2473i			0.562395i
$333$	−2.39374	+	3.29470i	−0.131176	+	0.180548i
$334$	0.216587	−	0.666586i	0.0118511	−	0.0364740i
$335$	−20.7811	−	8.35667i	−1.13540	−	0.456574i
$336$	−6.42287	−	19.7676i	−0.350396	−	1.07841i
$337$	6.03209	+	1.95995i	0.328589	+	0.106765i	0.468666	−	0.883376i	$-0.344735\pi$
$337$	6.03209	+	1.95995i	0.328589	+	0.106765i	−0.140077	+	0.990141i	$0.544735\pi$
$338$	−6.25381	−	2.03199i	−0.340162	−	0.110525i
$339$	−2.75459	−	8.47775i	−0.149609	−	0.460448i
$340$	−3.91508	+	0.982933i	−0.212325	+	0.0533070i
$341$	8.78437	−	27.0355i	0.475700	−	1.46406i
$342$	−0.810415	+	1.11544i	−0.0438222	+	0.0603161i
$343$		−	3.82880i		−	0.206736i
$344$	−16.7971	−	12.2038i	−0.905641	−	0.657987i
$345$	−10.2377	+	25.4588i	−0.551179	+	1.37066i
$346$	3.74862	−	2.72353i	0.201527	−	0.146418i
$347$	12.7316	+	17.5236i	0.683470	+	0.940716i	0.999969	−	0.00787674i	$-0.00250727\pi$
$347$	12.7316	+	17.5236i	0.683470	+	0.940716i	−0.316499	+	0.948593i	$0.602507\pi$
$348$	−12.7056	+	4.12829i	−0.681091	+	0.221300i
$349$	14.3598			0.768662			0.384331	−	0.923195i	$-0.374432\pi$
$349$	14.3598			0.768662			0.384331	+	0.923195i	$0.374432\pi$
$350$	−5.72716	−	5.49461i	−0.306130	−	0.293700i
$351$	20.6730			1.10344
$352$	21.4911	−	6.98288i	1.14548	−	0.372189i
$353$	3.14214	+	4.32479i	0.167239	+	0.230185i	0.884408	−	0.466714i	$-0.154562\pi$
$353$	3.14214	+	4.32479i	0.167239	+	0.230185i	−0.717169	+	0.696899i	$0.754562\pi$
$354$	3.57628	−	2.59832i	0.190077	−	0.138099i
$355$	−27.7740	−	23.2280i	−1.47409	−	1.23281i
$356$	−2.24731	−	1.63277i	−0.119107	−	0.0865365i
$357$			7.24406i			0.383397i
$358$	−0.344861	+	0.474661i	−0.0182265	+	0.0250866i
$359$	2.79041	−	8.58800i	0.147272	−	0.453257i	−0.850024	−	0.526744i	$-0.823413\pi$
$359$	2.79041	−	8.58800i	0.147272	−	0.453257i	0.997296	+	0.0734868i	$0.0234127\pi$
$360$	2.54599	−	3.04428i	0.134186	−	0.160448i
$361$	−3.17100	−	9.75934i	−0.166895	−	0.513649i
$362$	−3.30465	−	1.07374i	−0.173688	−	0.0564348i
$363$	−24.6533	−	8.01035i	−1.29396	−	0.420434i
$364$	10.5973	+	32.6152i	0.555451	+	1.70950i
$365$	5.74225	+	9.15621i	0.300563	+	0.479258i
$366$	1.95435	−	6.01487i	0.102155	−	0.314402i
$367$	19.8127	−	27.2698i	1.03421	−	1.42347i	0.132476	−	0.991186i	$-0.457707\pi$
$367$	19.8127	−	27.2698i	1.03421	−	1.42347i	0.901737	−	0.432286i	$-0.142293\pi$
$368$			17.4813i			0.911277i
$369$	−4.75319	−	3.45340i	−0.247441	−	0.179777i
$370$	0.926062	+	3.68856i	0.0481437	+	0.191759i
$371$	−37.8863	+	27.5260i	−1.96696	+	1.42908i
$372$	−12.4349	−	17.1151i	−0.644718	−	0.887379i
$373$	6.66836	−	2.16668i	0.345274	−	0.112186i	−0.131246	−	0.991350i	$-0.541898\pi$
$373$	6.66836	−	2.16668i	0.345274	−	0.112186i	0.476521	+	0.879163i	$0.341898\pi$
$374$	−2.15628			−0.111499
$375$	−4.57395	+	22.0495i	−0.236198	+	1.13863i
$376$	−1.83775			−0.0947746
$377$	18.4573	−	5.99715i	0.950601	−	0.308869i
$378$	3.65172	+	5.02617i	0.187824	+	0.258518i
$379$	22.9834	−	16.6984i	1.18058	−	0.857740i	0.188341	−	0.982104i	$-0.439689\pi$
$379$	22.9834	−	16.6984i	1.18058	−	0.857740i	0.992237	+	0.124364i	$0.0396889\pi$
$380$	−2.90563	−	11.5733i	−0.149056	−	0.593697i
$381$	−20.3018	−	14.7501i	−1.04009	−	0.755670i
$382$			9.43413i			0.482692i
$383$	−9.74162	+	13.4082i	−0.497774	+	0.685126i	−0.981798	−	0.189928i	$-0.939175\pi$
$383$	−9.74162	+	13.4082i	−0.497774	+	0.685126i	0.484024	+	0.875054i	$0.339175\pi$
$384$	6.77305	−	20.8453i	0.345636	−	1.06376i
$385$	20.8759	+	33.2872i	1.06393	+	1.69647i
$386$	1.54209	+	4.74606i	0.0784903	+	0.241568i
$387$	12.4256	+	4.03733i	0.631630	+	0.205229i
$388$	−13.9977	−	4.54812i	−0.710625	−	0.230896i
$389$	6.26802	+	19.2910i	0.317801	+	0.978091i	0.974586	+	0.224013i	$0.0719159\pi$
$389$	6.26802	+	19.2910i	0.317801	+	0.978091i	−0.656785	+	0.754078i	$0.728084\pi$
$390$	−6.73553	+	8.05377i	−0.341067	+	0.407819i
$391$	1.88275	−	5.79450i	0.0952147	−	0.293041i
$392$	−5.85908	+	8.06434i	−0.295928	+	0.407311i
$393$			37.4869i			1.89097i
$394$	4.26188	+	3.09644i	0.214711	+	0.155996i
$395$	2.60175	+	2.17589i	0.130908	+	0.109481i
$396$	−7.54058	+	5.47855i	−0.378928	+	0.275308i
$397$	1.68640	+	2.32113i	0.0846381	+	0.116494i	0.849237	−	0.528013i	$-0.177063\pi$
$397$	1.68640	+	2.32113i	0.0846381	+	0.116494i	−0.764598	+	0.644507i	$0.777063\pi$
$398$	−0.350232	+	0.113797i	−0.0175556	+	0.00570414i
$399$	−21.4141			−1.07204
$400$	2.53732	+	14.1200i	0.126866	+	0.705998i
$401$	4.10594			0.205041			0.102521	−	0.994731i	$-0.467309\pi$
$401$	4.10594			0.205041			0.102521	+	0.994731i	$0.467309\pi$
$402$	−8.46857	+	2.75161i	−0.422374	+	0.137238i
$403$	18.0641	+	24.8631i	0.899836	+	1.23852i
$404$	14.1187	−	10.2579i	0.702434	−	0.510348i
$405$	9.22153	−	22.9319i	0.458222	−	1.13949i
$406$	4.71841	+	3.42812i	0.234171	+	0.170135i
$407$		−	18.8274i		−	0.933241i
$408$	−1.98824	+	2.73658i	−0.0984326	+	0.135481i
$409$	4.41436	−	13.5860i	0.218276	−	0.671785i	−0.780629	−	0.624995i	$-0.785101\pi$
$409$	4.41436	−	13.5860i	0.218276	−	0.671785i	0.998905	−	0.0467896i	$-0.0148990\pi$
$410$	−5.32140	+	1.33601i	−0.262805	+	0.0659808i
$411$	−2.03119	−	6.25136i	−0.100191	−	0.308357i
$412$	−17.4196	−	5.65997i	−0.858201	−	0.278847i
$413$	17.0098	+	5.52683i	0.836999	+	0.271957i
$414$	0.878141	+	2.70264i	0.0431583	+	0.132828i
$415$	−11.7766	−	4.73568i	−0.578089	−	0.232465i
$416$	−7.54924	+	23.2342i	−0.370132	+	1.13915i
$417$	−5.37613	+	7.39961i	−0.263270	+	0.362360i
$418$		−	6.37414i		−	0.311770i
$419$	−2.96168	−	2.15178i	−0.144687	−	0.105121i	0.513087	−	0.858337i	$-0.328502\pi$
$419$	−2.96168	−	2.15178i	−0.144687	−	0.105121i	−0.657774	+	0.753215i	$0.728502\pi$
$420$	29.1733	+	1.99212i	1.42351	+	0.0972054i
$421$	−13.5130	+	9.81773i	−0.658581	+	0.478487i	−0.866183	−	0.499726i	$-0.833434\pi$
$421$	−13.5130	+	9.81773i	−0.658581	+	0.478487i	0.207602	+	0.978213i	$0.433434\pi$
$422$	0.116954	+	0.160974i	0.00569324	+	0.00783607i
$423$	1.09983	−	0.357357i	0.0534757	−	0.0173753i
$424$	−21.8672			−1.06196
$425$	0.679687	−	4.95359i	0.0329697	−	0.240284i
$426$	−14.3938			−0.697384
$427$	24.3358	−	7.90718i	1.17769	−	0.382655i
$428$	−9.00568	−	12.3953i	−0.435306	−	0.599147i
$429$	42.0504	−	30.5514i	2.03021	−	1.47504i
$430$	10.3362	−	6.48226i	0.498455	−	0.312602i
$431$	−10.1244	−	7.35582i	−0.487676	−	0.354318i	0.316614	−	0.948555i	$-0.397454\pi$
$431$	−10.1244	−	7.35582i	−0.487676	−	0.354318i	−0.804290	+	0.594237i	$0.797454\pi$
$432$		−	11.2298i		−	0.540296i
$433$	1.12480	−	1.54815i	0.0540542	−	0.0743992i	−0.781134	−	0.624363i	$-0.785359\pi$
$433$	1.12480	−	1.54815i	0.0540542	−	0.0743992i	0.835188	+	0.549964i	$0.185359\pi$
$434$	−2.85401	+	8.78373i	−0.136997	+	0.421632i
$435$	1.12736	−	16.5095i	0.0540529	−	0.791571i
$436$	−10.2197	−	31.4530i	−0.489435	−	1.50633i
$437$	17.1290	+	5.56556i	0.819393	+	0.266237i
$438$	4.08632	+	1.32772i	0.195252	+	0.0634411i
$439$	12.5659	+	38.6737i	0.599736	+	1.84580i	0.529579	+	0.848261i	$0.322350\pi$
$439$	12.5659	+	38.6737i	0.599736	+	1.84580i	0.0701570	+	0.997536i	$0.477650\pi$
$440$	−1.24994	+	18.3046i	−0.0595884	+	0.872635i
$441$	1.93833	−	5.96557i	0.0923014	−	0.284075i
$442$	1.37023	−	1.88596i	0.0651751	−	0.0897058i
$443$			7.27647i			0.345716i	0.984947	+	0.172858i	$0.0553001\pi$
$443$			7.27647i			0.345716i	−0.984947	+	0.172858i	$0.944700\pi$
$444$	−11.3356	−	8.23577i	−0.537962	−	0.390852i
$445$	2.91500	−	1.82812i	0.138184	−	0.0866613i
$446$	9.89568	−	7.18963i	0.468574	−	0.340439i
$447$	−2.38287	−	3.27974i	−0.112706	−	0.155126i
$448$	12.6463	−	4.10904i	0.597482	−	0.194134i
$449$	32.7248			1.54438			0.772188	−	0.635394i	$-0.219162\pi$
$449$	32.7248			1.54438			0.772188	+	0.635394i	$0.219162\pi$
$450$	1.10156	+	2.05551i	0.0519282	+	0.0968977i
$451$	27.1619			1.27901
$452$	7.59831	−	2.46884i	0.357395	−	0.116125i
$453$	13.7507	+	18.9262i	0.646065	+	0.889233i
$454$	−5.68755	+	4.13224i	−0.266930	+	0.193936i
$455$	−42.3799	−	2.89394i	−1.98680	−	0.135670i
$456$	−8.08955	−	5.87740i	−0.378828	−	0.275235i
$457$		−	21.6233i		−	1.01150i	−0.862681	−	0.505749i	$-0.831216\pi$
$457$		−	21.6233i		−	1.01150i	0.862681	−	0.505749i	$-0.168784\pi$
$458$	−0.891568	+	1.22714i	−0.0416602	+	0.0573404i
$459$	−1.20946	+	3.72234i	−0.0564528	+	0.173744i
$460$	−22.8179	−	9.17569i	−1.06389	−	0.427819i
$461$	−4.05742	−	12.4874i	−0.188973	−	0.581598i	0.811021	−	0.585016i	$-0.198912\pi$
$461$	−4.05742	−	12.4874i	−0.188973	−	0.581598i	−0.999994	+	0.00341815i	$0.998912\pi$
$462$	14.8557	+	4.82692i	0.691151	+	0.224569i
$463$	−22.9049	−	7.44224i	−1.06448	−	0.345870i	−0.276144	−	0.961116i	$-0.589057\pi$
$463$	−22.9049	−	7.44224i	−1.06448	−	0.345870i	−0.788335	+	0.615246i	$0.789057\pi$
$464$	−3.25773	−	10.0262i	−0.151236	−	0.465457i
$465$	25.4159	−	6.38102i	1.17864	−	0.295912i
$466$	−3.26238	+	10.0406i	−0.151127	+	0.465121i
$467$	−14.8192	+	20.3968i	−0.685749	+	0.943853i	−0.999985	−	0.00549200i	$-0.998252\pi$
$467$	−14.8192	+	20.3968i	−0.685749	+	0.943853i	0.314236	+	0.949345i	$0.398252\pi$
$468$		−	10.0766i		−	0.465793i
$469$	−29.1461	−	21.1759i	−1.34584	−	0.977812i
$470$	0.402909	−	1.00194i	0.0185848	−	0.0462163i
$471$	−14.4722	+	10.5147i	−0.666843	+	0.484490i
$472$	4.90886	+	6.75646i	0.225948	+	0.310991i
$473$	−57.4449	+	18.6650i	−2.64132	+	0.858216i
$474$	1.34835			0.0619319
$475$	14.6432	+	2.00921i	0.671877	+	0.0921889i
$476$	−6.49261			−0.297588
$477$	13.0868	−	4.25216i	0.599204	−	0.194693i
$478$	−0.138283	−	0.190330i	−0.00632491	−	0.00870550i
$479$	−26.1041	+	18.9658i	−1.19273	+	0.866568i	−0.993550	−	0.113396i	$-0.963827\pi$
$479$	−26.1041	+	18.9658i	−1.19273	+	0.866568i	−0.199178	+	0.979963i	$0.563827\pi$
$480$	15.9791	+	13.3636i	0.729341	+	0.609962i
$481$	16.4671	+	11.9641i	0.750836	+	0.545514i
$482$		−	6.37736i		−	0.290481i
$483$	−25.9424	+	35.7067i	−1.18042	+	1.62471i
$484$	7.17940	−	22.0959i	0.326336	−	1.00436i
$485$	11.6957	−	13.9847i	0.531076	−	0.635015i
$486$	−1.43501	−	4.41650i	−0.0650933	−	0.200337i
$487$	2.48307	+	0.806799i	0.112519	+	0.0365595i	0.364735	−	0.931111i	$-0.381160\pi$
$487$	2.48307	+	0.806799i	0.112519	+	0.0365595i	−0.252217	+	0.967671i	$0.581160\pi$
$488$	11.3635	+	3.69224i	0.514403	+	0.167140i
$489$	13.8545	+	42.6396i	0.626520	+	1.92823i
$490$	−3.11215	−	4.96242i	−0.140592	−	0.224179i
$491$	6.90128	−	21.2400i	0.311450	−	0.958546i	−0.665740	−	0.746183i	$-0.731884\pi$
$491$	6.90128	−	21.2400i	0.311450	−	0.958546i	0.977191	−	0.212363i	$-0.0681158\pi$
$492$	11.8816	−	16.3536i	0.535663	−	0.737276i
$493$			3.67424i			0.165480i
$494$	5.57505	+	4.05051i	0.250833	+	0.182241i
$495$	−2.81134	−	11.1977i	−0.126361	−	0.503301i
$496$	13.5059	−	9.81263i	0.606434	−	0.440600i
$497$	−34.2306	−	47.1144i	−1.53545	−	2.11337i
$498$	−4.79910	+	1.55932i	−0.215053	+	0.0698749i
$499$	17.0356			0.762618			0.381309	−	0.924448i	$-0.375473\pi$
$499$	17.0356			0.762618			0.381309	+	0.924448i	$0.375473\pi$
$500$	−19.7622	−	4.09947i	−0.883792	−	0.183334i
$501$	−3.19862			−0.142904
$502$	−0.0935993	+	0.0304123i	−0.00417754	+	0.00135737i
$503$	−0.262703	−	0.361580i	−0.0117134	−	0.0161221i	0.803120	−	0.595817i	$-0.203172\pi$
$503$	−0.262703	−	0.361580i	−0.0117134	−	0.0161221i	−0.814834	+	0.579695i	$0.803172\pi$
$504$	5.16416	−	3.75198i	0.230030	−	0.167126i
$505$	5.26387	+	20.9663i	0.234239	+	0.932988i
$506$	−10.6285	−	7.72207i	−0.472495	−	0.343288i
$507$			30.0089i			1.33274i
$508$	13.2200	−	18.1958i	0.586543	−	0.807307i
$509$	−12.7303	+	39.1797i	−0.564259	+	1.73661i	0.105884	+	0.994378i	$0.466233\pi$
$509$	−12.7303	+	39.1797i	−0.564259	+	1.73661i	−0.670143	+	0.742232i	$0.733767\pi$
$510$	−1.05609	−	1.68396i	−0.0467643	−	0.0745672i
$511$	5.37189	+	16.5330i	0.237639	+	0.731376i
$512$	21.7866	+	7.07891i	0.962843	+	0.312847i
$513$	−11.0035	−	3.57527i	−0.485818	−	0.157852i
$514$	1.35670	+	4.17550i	0.0598416	+	0.184173i
$515$	14.5549	−	17.4035i	0.641365	−	0.766889i
$516$	−13.8906	+	42.7510i	−0.611501	+	1.88201i
$517$	−3.14248	+	4.32525i	−0.138206	+	0.190224i
$518$			6.11695i			0.268764i
$519$	−17.1074	−	12.4292i	−0.750930	−	0.545583i
$520$	−15.2155	−	12.7250i	−0.667244	−	0.558030i
$521$	3.47021	−	2.52126i	0.152033	−	0.110458i	−0.509168	−	0.860667i	$-0.670047\pi$
$521$	3.47021	−	2.52126i	0.152033	−	0.110458i	0.661201	+	0.750209i	$0.270047\pi$
$522$	−1.00730	−	1.38643i	−0.0440883	−	0.0606824i
$523$	17.0204	−	5.53027i	0.744251	−	0.241822i	0.0877456	−	0.996143i	$-0.472034\pi$
$523$	17.0204	−	5.53027i	0.744251	−	0.241822i	0.656506	+	0.754321i	$0.272034\pi$
$524$	−33.5983			−1.46775
$525$	−15.7715	+	32.6063i	−0.688325	+	1.42306i
$526$	5.87509			0.256166
$527$	−5.53361	+	1.79798i	−0.241048	+	0.0783212i
$528$	−16.5959	−	22.8423i	−0.722243	−	0.994083i
$529$	11.4241	−	8.30012i	0.496702	−	0.360875i
$530$	4.79418	−	11.9220i	0.208246	−	0.517861i
$531$	−4.25161	−	3.08898i	−0.184504	−	0.134050i
$532$		−	19.1927i		−	0.832108i
$533$	−17.2603	+	23.7568i	−0.747627	+	1.02902i
$534$	0.422699	−	1.30093i	0.0182920	−	0.0562969i
$535$	18.4069	−	4.62131i	0.795800	−	0.199796i
$536$	−5.19845	−	15.9992i	−0.224539	−	0.691059i
$537$	2.54650	+	0.827409i	0.109890	+	0.0357054i
$538$	−2.46996	−	0.802538i	−0.106487	−	0.0345999i
$539$	8.96109	+	27.5794i	0.385981	+	1.18793i
$540$	14.6580	+	5.89438i	0.630780	+	0.253654i
$541$	−10.7943	+	33.2213i	−0.464082	+	1.42830i	0.396052	+	0.918228i	$0.370380\pi$
$541$	−10.7943	+	33.2213i	−0.464082	+	1.42830i	−0.860133	+	0.510069i	$0.829620\pi$
$542$	1.43831	−	1.97967i	0.0617808	−	0.0850339i
$543$			15.8574i			0.680505i
$544$	−3.74183	−	2.71860i	−0.160430	−	0.116559i
$545$	40.8698	+	2.79082i	1.75067	+	0.119546i
$546$	−13.6620	+	9.92602i	−0.584680	+	0.424795i
$547$	−22.4394	−	30.8852i	−0.959441	−	1.32056i	−0.947204	−	0.320632i	$-0.896105\pi$
$547$	−22.4394	−	30.8852i	−0.959441	−	1.32056i	−0.0122367	−	0.999925i	$-0.503895\pi$
$548$	5.60288	−	1.82049i	0.239343	−	0.0777673i
$549$	−7.51868			−0.320889
$550$	−9.70565	−	4.69457i	−0.413850	−	0.200177i
$551$	−10.8614			−0.462710
$552$	−19.6005	+	6.36858i	−0.834251	+	0.271065i
$553$	3.20658	+	4.41347i	0.136357	+	0.187680i
$554$	−1.21749	+	0.884557i	−0.0517261	+	0.0375812i
$555$	14.7034	−	9.22115i	0.624126	−	0.391416i
$556$	−6.63201	−	4.81844i	−0.281260	−	0.204347i
$557$			11.9696i			0.507167i	0.967314	+	0.253583i	$0.0816092\pi$
$557$			11.9696i			0.507167i	−0.967314	+	0.253583i	$0.918391\pi$
$558$	1.59512	−	2.19549i	0.0675268	−	0.0929427i
$559$	20.1788	−	62.1041i	0.853474	−	2.62672i
$560$	−1.57202	+	23.0213i	−0.0664301	+	0.972827i
$561$	3.04088	+	9.35888i	0.128386	+	0.395132i
$562$	−8.02437	−	2.60728i	−0.338488	−	0.109981i
$563$	−23.8153	−	7.73807i	−1.00370	−	0.326121i	−0.239355	−	0.970932i	$-0.576936\pi$
$563$	−23.8153	−	7.73807i	−1.00370	−	0.326121i	−0.764342	+	0.644811i	$0.776936\pi$
$564$	1.22950	+	3.78403i	0.0517715	+	0.159336i
$565$	−0.674196	+	9.87318i	−0.0283636	+	0.415368i
$566$	0.826952	−	2.54510i	0.0347594	−	0.106978i
$567$	23.3675	−	32.1626i	0.981342	−	1.35070i
$568$		−	27.1934i		−	1.14101i
$569$	−3.50203	−	2.54437i	−0.146813	−	0.106666i	0.511954	−	0.859013i	$-0.328922\pi$
$569$	−3.50203	−	2.54437i	−0.146813	−	0.106666i	−0.658767	+	0.752347i	$0.728922\pi$
$570$	4.97794	−	3.12188i	0.208503	−	0.130761i
$571$	14.0997	−	10.2441i	0.590056	−	0.428700i	−0.252280	−	0.967654i	$-0.581180\pi$
$571$	14.0997	−	10.2441i	0.590056	−	0.428700i	0.842335	+	0.538954i	$0.181180\pi$
$572$	27.3822	+	37.6883i	1.14491	+	1.57583i
$573$	40.9469	−	13.3044i	1.71058	−	0.555801i
$574$	−8.82480			−0.368340
$575$	21.0900	−	21.9826i	0.879515	−	0.916739i
$576$	−3.90715			−0.162798
$577$	27.4693	−	8.92532i	1.14356	−	0.371566i	0.324848	−	0.945766i	$-0.394687\pi$
$577$	27.4693	−	8.92532i	1.14356	−	0.371566i	0.818715	+	0.574200i	$0.194687\pi$
$578$	0.259417	+	0.357057i	0.0107903	+	0.0148516i
$579$	18.4246	−	13.3862i	0.765699	−	0.556313i
$580$	14.7969	+	1.01042i	0.614409	+	0.0419553i
$581$	−16.5170	−	12.0003i	−0.685239	−	0.497855i
$582$		−	7.24757i		−	0.300422i
$583$	−37.3920	+	51.4657i	−1.54862	+	2.13149i
$584$	−2.50839	+	7.72003i	−0.103798	+	0.319457i
$585$	11.5804	+	4.65680i	0.478791	+	0.192535i
$586$	−0.377534	−	1.16193i	−0.0155958	−	0.0479988i
$587$	15.3939	+	5.00180i	0.635376	+	0.206446i	0.608955	−	0.793205i	$-0.291589\pi$
$587$	15.3939	+	5.00180i	0.635376	+	0.206446i	0.0264211	+	0.999651i	$0.491589\pi$
$588$	20.5248	+	6.66892i	0.846429	+	0.275021i
$589$	−5.31498	−	16.3578i	−0.219000	−	0.674012i
$590$	−4.75986	+	1.19503i	−0.195960	+	0.0491985i
$591$	7.42914	−	22.8645i	0.305594	−	0.940522i
$592$	6.49902	−	8.94514i	0.267108	−	0.367643i
$593$			11.2104i			0.460355i	0.973149	+	0.230177i	$0.0739306\pi$
$593$			11.2104i			0.460355i	−0.973149	+	0.230177i	$0.926069\pi$
$594$	6.82767	+	4.96059i	0.280143	+	0.203535i
$595$	3.00048	−	7.46152i	0.123008	−	0.305892i
$596$	2.93952	−	2.13568i	0.120407	−	0.0874810i
$597$	0.987827	+	1.35963i	0.0404291	+	0.0556458i
$598$	13.5080	−	4.38901i	0.552382	−	0.179480i
$599$	−29.3466			−1.19907			−0.599534	−	0.800349i	$-0.704647\pi$
$599$	−29.3466			−1.19907			−0.599534	+	0.800349i	$0.704647\pi$
$600$	−14.9073	+	7.98891i	−0.608586	+	0.326146i
$601$	−13.3470			−0.544434			−0.272217	−	0.962236i	$-0.587757\pi$
$601$	−13.3470			−0.544434			−0.272217	+	0.962236i	$0.587757\pi$
$602$	18.6636	−	6.06417i	0.760672	−	0.247157i
$603$	6.22220	+	8.56413i	0.253388	+	0.348758i
$604$	−16.9629	+	12.3243i	−0.690212	+	0.501469i
$605$	22.0755	+	18.4622i	0.897496	+	0.750594i
$606$	6.95247	+	5.05126i	0.282425	+	0.205194i
$607$		−	26.1774i		−	1.06251i	−0.847213	−	0.531254i	$-0.821721\pi$
$607$		−	26.1774i		−	1.06251i	0.847213	−	0.531254i	$-0.178279\pi$
$608$	8.03640	−	11.0612i	0.325919	−	0.448589i
$609$	8.22494	−	25.3138i	0.333291	−	1.02576i
$610$	−4.50437	+	5.38594i	−0.182376	+	0.218070i
$611$	−1.78610	−	5.49704i	−0.0722577	−	0.222386i
$612$	1.81438	+	0.589527i	0.0733419	+	0.0238302i
$613$	−29.0323	−	9.43315i	−1.17260	−	0.381001i	−0.342988	−	0.939340i	$-0.611439\pi$
$613$	−29.0323	−	9.43315i	−1.17260	−	0.381001i	−0.829613	+	0.558338i	$0.811439\pi$
$614$	−1.21157	−	3.72882i	−0.0488949	−	0.150483i
$615$	13.3032	+	21.2123i	0.536435	+	0.855363i
$616$	−9.11921	+	28.0660i	−0.367423	+	1.13081i
$617$	5.15202	−	7.09115i	0.207413	−	0.285479i	−0.692619	−	0.721304i	$-0.743543\pi$
$617$	5.15202	−	7.09115i	0.207413	−	0.285479i	0.900032	+	0.435825i	$0.143543\pi$
$618$		−	9.01933i		−	0.362811i
$619$	−2.24672	−	1.63233i	−0.0903031	−	0.0656091i	0.541718	−	0.840561i	$-0.317774\pi$
$619$	−2.24672	−	1.63233i	−0.0903031	−	0.0656091i	−0.632021	+	0.774952i	$0.717774\pi$
$620$	5.71909	+	22.7794i	0.229684	+	0.914844i
$621$	−19.2920	+	14.0164i	−0.774161	+	0.562461i
$622$	−2.29115	−	3.15350i	−0.0918668	−	0.126444i
$623$	5.26349	−	1.71021i	0.210877	−	0.0685182i
$624$	30.5247			1.22196
$625$	13.8441	−	20.8168i	0.553764	−	0.832673i
$626$	−1.40067			−0.0559820
$627$	−27.6656	+	8.98911i	−1.10486	+	0.358990i
$628$	−9.42393	−	12.9709i	−0.376056	−	0.517596i
$629$	−3.11762	+	2.26508i	−0.124308	+	0.0903147i
$630$	0.913394	+	3.63810i	0.0363905	+	0.144945i
$631$	29.5252	+	21.4513i	1.17538	+	0.853963i	0.991643	−	0.129012i	$-0.0411806\pi$
$631$	29.5252	+	21.4513i	1.17538	+	0.853963i	0.183737	+	0.982976i	$0.441181\pi$
$632$			2.54736i			0.101329i
$633$	0.533738	−	0.734627i	0.0212142	−	0.0291988i
$634$	0.404146	−	1.24383i	0.0160507	−	0.0493989i
$635$	14.8017	+	23.6018i	0.587388	+	0.936610i
$636$	14.6298	+	45.0258i	0.580108	+	1.78539i
$637$	−29.8163	−	9.68790i	−1.18136	−	0.383849i
$638$	7.53493	+	2.44825i	0.298311	+	0.0969271i
$639$	5.28787	+	16.2744i	0.209185	+	0.643804i
$640$	−15.6105	+	18.6657i	−0.617058	+	0.737825i
$641$	−9.32263	+	28.6921i	−0.368222	+	1.13327i	0.579717	+	0.814818i	$0.303163\pi$
$641$	−9.32263	+	28.6921i	−0.368222	+	1.13327i	−0.947939	+	0.318452i	$0.896837\pi$
$642$	4.43465	−	6.10377i	0.175022	−	0.240897i
$643$		−	28.4527i		−	1.12207i	−0.827793	−	0.561033i	$-0.810404\pi$
$643$		−	28.4527i		−	1.12207i	0.827793	−	0.561033i	$-0.189596\pi$
$644$	−32.0027	−	23.2513i	−1.26108	−	0.916230i
$645$	−42.7114	−	35.7204i	−1.68176	−	1.40649i
$646$	−1.05549	+	0.766858i	−0.0415277	+	0.0301716i
$647$	16.2959	+	22.4294i	0.640658	+	0.881790i	0.998651	−	0.0519344i	$-0.0165387\pi$
$647$	16.2959	+	22.4294i	0.640658	+	0.881790i	−0.357992	+	0.933724i	$0.616539\pi$
$648$	17.6550	−	5.73645i	0.693554	−	0.225349i
$649$	24.2957			0.953689
$650$	10.2736	−	5.50569i	0.402963	−	0.215951i
$651$	42.1488			1.65194
$652$	−38.2165	+	12.4173i	−1.49667	+	0.486298i
$653$	1.37176	+	1.88806i	0.0536809	+	0.0738855i	0.835014	−	0.550229i	$-0.185460\pi$
$653$	1.37176	+	1.88806i	0.0536809	+	0.0738855i	−0.781333	+	0.624115i	$0.785460\pi$
$654$	13.1752	−	9.57233i	0.515190	−	0.374308i
$655$	15.5270	−	38.6122i	0.606692	−	1.50870i
$656$	12.9050	+	9.37600i	0.503854	+	0.366071i
$657$		−	5.10796i		−	0.199280i
$658$	1.02098	−	1.40525i	0.0398018	−	0.0547825i
$659$	1.12983	−	3.47727i	0.0440121	−	0.135455i	−0.926636	−	0.375960i	$-0.877313\pi$
$659$	1.12983	−	3.47727i	0.0440121	−	0.135455i	0.970648	+	0.240505i	$0.0773130\pi$
$660$	38.5263	−	9.67257i	1.49964	−	0.376504i
$661$	2.92607	+	9.00552i	0.113811	+	0.350274i	0.991697	−	0.128595i	$-0.0410468\pi$
$661$	2.92607	+	9.00552i	0.113811	+	0.350274i	−0.877886	+	0.478869i	$0.841047\pi$
$662$	2.38559	+	0.775126i	0.0927187	+	0.0301261i
$663$	−10.1180	−	3.28752i	−0.392949	−	0.127677i
$664$	−2.94593	−	9.06665i	−0.114324	−	0.351854i
$665$	22.0569	+	8.86967i	0.855329	+	0.343951i
$666$	0.555418	−	1.70940i	0.0215220	−	0.0662379i
$667$	−13.1582	+	18.1107i	−0.509487	+	0.701249i
$668$		−	2.86681i		−	0.110920i
$669$	−45.1604	−	32.8110i	−1.74600	−	1.26854i
$670$	9.86250	+	0.673467i	0.381022	+	0.0260183i
$671$	28.1211	−	20.4312i	1.08560	−	0.788736i
$672$	19.6937	+	27.1060i	0.759701	+	1.04564i
$673$	4.52736	−	1.47103i	0.174517	−	0.0567040i	−0.220455	−	0.975397i	$-0.570754\pi$
$673$	4.52736	−	1.47103i	0.174517	−	0.0567040i	0.394972	+	0.918693i	$0.370754\pi$
$674$	−2.79925			−0.107823
$675$	−13.5480	+	14.1214i	−0.521464	+	0.543535i
$676$	−26.8960			−1.03446
$677$	26.2944	−	8.54358i	1.01058	−	0.328357i	0.243493	−	0.969903i	$-0.421707\pi$
$677$	26.2944	−	8.54358i	1.01058	−	0.328357i	0.767085	+	0.641546i	$0.221707\pi$
$678$	2.31245	+	3.18281i	0.0888091	+	0.122235i
$679$	23.7230	−	17.2358i	0.910405	−	0.661448i
$680$	3.18141	−	1.99520i	0.122002	−	0.0765124i
$681$	25.9560	+	18.8581i	0.994635	+	0.722645i
$682$			12.5461i			0.480414i
$683$	4.55586	−	6.27060i	0.174325	−	0.239938i	−0.712910	−	0.701256i	$-0.752623\pi$
$683$	4.55586	−	6.27060i	0.174325	−	0.239938i	0.887235	+	0.461318i	$0.152623\pi$
$684$	−1.74269	+	5.36345i	−0.0666334	+	0.205077i
$685$	−0.497142	+	7.28033i	−0.0189948	+	0.278167i
$686$	0.522185	+	1.60712i	0.0199371	+	0.0613602i
$687$	6.58346	+	2.13910i	0.251175	+	0.0816116i
$688$	−33.7357	−	10.9614i	−1.28616	−	0.417899i
$689$	−21.2526	−	65.4087i	−0.809659	−	2.49187i
$690$	0.825059	−	12.0825i	0.0314095	−	0.459972i
$691$	2.10111	−	6.46654i	0.0799298	−	0.245999i	−0.903104	−	0.429421i	$-0.858718\pi$
$691$	2.10111	−	6.46654i	0.0799298	−	0.245999i	0.983034	+	0.183422i	$0.0587176\pi$
$692$	11.1399	−	15.3328i	0.423475	−	0.582864i
$693$		−	18.5699i		−	0.705411i
$694$	−7.73398	−	5.61906i	−0.293578	−	0.213297i
$695$	8.60242	−	5.39495i	0.326308	−	0.204642i
$696$	10.0549	−	7.30528i	0.381128	−	0.276906i
$697$	−3.26779	−	4.49772i	−0.123776	−	0.170363i
$698$	−6.02746	+	1.95844i	−0.228143	+	0.0741280i
$699$	48.1798			1.82233
$700$	−29.2239	−	14.1355i	−1.10456	−	0.534270i
$701$	15.4370			0.583047			0.291523	−	0.956564i	$-0.405838\pi$
$701$	15.4370			0.583047			0.291523	+	0.956564i	$0.405838\pi$
$702$	−8.67741	+	2.81946i	−0.327508	+	0.106414i
$703$	−6.69577	−	9.21594i	−0.252536	−	0.347586i
$704$	14.6134	−	10.6172i	0.550762	−	0.400152i
$705$	−4.91693	−	0.335756i	−0.185182	−	0.0126453i
$706$	−1.90873	−	1.38677i	−0.0718359	−	0.0521918i
$707$			34.7697i			1.30765i
$708$	10.6278	−	14.6279i	0.399416	−	0.549749i
$709$	−4.43052	+	13.6357i	−0.166392	+	0.512101i	−0.999136	−	0.0415565i	$-0.986768\pi$
$709$	−4.43052	+	13.6357i	−0.166392	+	0.512101i	0.832744	+	0.553658i	$0.186768\pi$
$710$	14.8259	+	5.96191i	0.556407	+	0.223746i
$711$	−0.495344	−	1.52451i	−0.0185769	−	0.0571737i
$712$	2.45777	+	0.798579i	0.0921090	+	0.0299280i
$713$	−33.7147	−	10.9546i	−1.26262	−	0.410251i
$714$	−0.987971	−	3.04066i	−0.0369739	−	0.113794i
$715$	−55.9670	+	14.0513i	−2.09305	+	0.525488i
$716$	−0.741579	+	2.28234i	−0.0277141	+	0.0852952i
$717$	−0.631075	+	0.868600i	−0.0235679	+	0.0324385i
$718$			3.98534i			0.148731i
$719$	−17.6825	−	12.8471i	−0.659447	−	0.479117i	0.207029	−	0.978335i	$-0.433621\pi$
$719$	−17.6825	−	12.8471i	−0.659447	−	0.479117i	−0.866476	+	0.499218i	$0.833621\pi$
$720$	2.52963	−	6.29062i	0.0942739	−	0.234438i
$721$	29.5224	−	21.4493i	1.09947	−	0.798812i
$722$	2.66202	+	3.66396i	0.0990703	+	0.136359i
$723$	−27.6796	+	8.99364i	−1.02941	+	0.334477i
$724$	−14.2124			−0.528200
$725$	−7.99943	+	16.5382i	−0.297091	+	0.614212i
$726$	11.4406			0.424600
$727$	−36.8496	+	11.9732i	−1.36667	+	0.444060i	−0.898266	−	0.439452i	$-0.855173\pi$
$727$	−36.8496	+	11.9732i	−1.36667	+	0.444060i	−0.468409	+	0.883512i	$0.655173\pi$
$728$	−18.7526	−	25.8108i	−0.695019	−	0.956612i
$729$	9.68240	−	7.03468i	0.358608	−	0.260544i
$730$	−3.65904	−	3.06013i	−0.135427	−	0.113260i
$731$	10.0018	+	7.26671i	0.369929	+	0.268769i
$732$		−	25.8684i		−	0.956122i
$733$	30.2231	−	41.5986i	1.11632	−	1.53648i	0.304551	−	0.952496i	$-0.401493\pi$
$733$	30.2231	−	41.5986i	1.11632	−	1.53648i	0.811766	−	0.583983i	$-0.198507\pi$
$734$	−4.59712	+	14.1485i	−0.169683	+	0.522230i
$735$	−17.1494	+	20.5058i	−0.632567	+	0.756369i
$736$	−8.70800	−	26.8005i	−0.320981	−	0.987878i
$737$	−46.5441	−	15.1231i	−1.71448	−	0.557067i
$738$	2.46612	+	0.801289i	0.0907790	+	0.0294959i
$739$	−13.4316	−	41.3382i	−0.494089	−	1.52065i	−0.818372	−	0.574690i	$-0.805123\pi$
$739$	−13.4316	−	41.3382i	−0.494089	−	1.52065i	0.324282	−	0.945960i	$-0.394877\pi$
$740$	8.26460	+	13.1782i	0.303813	+	0.484439i
$741$	9.71819	−	29.9095i	0.357007	−	1.09875i
$742$	12.1485	−	16.7210i	0.445986	−	0.613847i
$743$		−	8.98940i		−	0.329789i	−0.986311	−	0.164895i	$-0.947272\pi$
$743$		−	8.98940i		−	0.329789i	0.986311	−	0.164895i	$-0.0527284\pi$
$744$	15.9225	+	11.5684i	0.583746	+	0.424116i
$745$	1.09594	+	4.36517i	0.0401520	+	0.159928i
$746$	−2.50351	+	1.81891i	−0.0916601	+	0.0665949i
$747$	3.52609	+	4.85325i	0.129013	+	0.177571i
$748$	−8.38804	+	2.72544i	−0.306697	+	0.0996520i
$749$	30.5253			1.11537
$750$	−1.08729	−	9.87897i	−0.0397023	−	0.360729i
$751$	11.6656			0.425683			0.212842	−	0.977087i	$-0.431728\pi$
$751$	11.6656			0.425683			0.212842	+	0.977087i	$0.431728\pi$
$752$	−2.98606	+	0.970229i	−0.108890	+	0.0353806i
$753$	0.263996	+	0.363359i	0.00962055	+	0.0132416i
$754$	−6.92947	+	5.03455i	−0.252356	+	0.183348i
$755$	−6.32427	−	25.1899i	−0.230164	−	0.916755i
$756$	20.5582	+	14.9364i	0.747696	+	0.543233i
$757$			32.5586i			1.18336i	0.806172	+	0.591681i	$0.201536\pi$
$757$			32.5586i			1.18336i	−0.806172	+	0.591681i	$0.798464\pi$
$758$	−7.36978	+	10.1436i	−0.267683	+	0.368434i
$759$	−18.5272	+	57.0209i	−0.672495	+	2.06973i
$760$	5.89798	+	9.40452i	0.213942	+	0.341138i
$761$	−6.47834	−	19.9383i	−0.234840	−	0.722762i	−0.997143	−	0.0755417i	$-0.975931\pi$
$761$	−6.47834	−	19.9383i	−0.234840	−	0.722762i	0.762303	−	0.647220i	$-0.224069\pi$
$762$	10.5332	+	3.42246i	0.381579	+	0.123983i
$763$	62.6649	+	20.3611i	2.26862	+	0.737120i
$764$	11.9243	+	36.6993i	0.431407	+	1.32773i
$765$	−1.51600	+	1.81270i	−0.0548110	+	0.0655383i
$766$	2.26034	−	6.95662i	0.0816695	−	0.251353i
$767$	−15.4389	+	21.2498i	−0.557467	+	0.767287i
$768$		−	5.21979i		−	0.188353i
$769$	−5.00398	−	3.63561i	−0.180448	−	0.131103i	0.493894	−	0.869522i	$-0.335573\pi$
$769$	−5.00398	−	3.63561i	−0.180448	−	0.131103i	−0.674343	+	0.738419i	$0.735573\pi$
$770$	−13.3024	−	11.1250i	−0.479384	−	0.400919i
$771$	16.2096	−	11.7770i	0.583774	−	0.424137i

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+(-0.419745 + 0.136383i) q^{2} +(1.18389 + 1.62948i) q^{3} +(-1.46045 + 1.06108i) q^{4} +(-0.544497 - 2.16876i) q^{5} +(-0.719166 - 0.522504i) q^{6} -3.59659i q^{7} +(0.987136 - 1.35868i) q^{8} +(-0.326569 + 1.00508i) q^{9} +(0.524333 + 0.836067i) q^{10} +(-1.50976 - 4.64657i) q^{11} +(-3.45801 - 1.12358i) q^{12} +(5.02344 + 1.63221i) q^{13} +(0.490515 + 1.50965i) q^{14} +(2.88933 - 3.45482i) q^{15} +(0.886639 - 2.72879i) q^{16} +(-0.587785 + 0.809017i) q^{17} -0.466415i q^{18} +(-2.39152 - 1.73754i) q^{19} +(3.09643 + 2.58961i) q^{20} +(5.86057 - 4.25795i) q^{21} +(1.26743 + 1.74447i) q^{22} +(-5.79450 + 1.88275i) q^{23} +3.38260 q^{24} +(-4.40705 + 2.36177i) q^{25} -2.33117 q^{26} +(3.72234 - 1.20946i) q^{27} +(3.81626 + 5.25263i) q^{28} +(2.97252 - 2.15967i) q^{29} +(-0.741603 + 1.84420i) q^{30} +(4.70717 + 3.41996i) q^{31} +4.62515i q^{32} +(5.78411 - 7.96114i) q^{33} +(0.136383 - 0.419745i) q^{34} +(-7.80014 + 1.95833i) q^{35} +(-0.589527 - 1.81438i) q^{36} +(3.66498 + 1.19082i) q^{37} +(1.24080 + 0.403161i) q^{38} +(3.28752 + 10.1180i) q^{39} +(-3.48414 - 1.40107i) q^{40} +(-1.71798 + 5.28739i) q^{41} +(-1.87923 + 2.58654i) q^{42} -12.3629i q^{43} +(7.13530 + 5.18410i) q^{44} +(2.35759 + 0.160989i) q^{45} +(2.17544 - 1.58055i) q^{46} +(-0.643200 - 0.885289i) q^{47} +(5.49620 - 1.78582i) q^{48} -5.93543 q^{49} +(1.52773 - 1.59239i) q^{50} -2.01415 q^{51} +(-9.06838 + 2.94650i) q^{52} +(-7.65338 - 10.5340i) q^{53} +(-1.39748 + 1.01533i) q^{54} +(-9.25523 + 5.80435i) q^{55} +(-4.88660 - 3.55032i) q^{56} -5.95399i q^{57} +(-0.953160 + 1.31191i) q^{58} +(-1.53669 + 4.72944i) q^{59} +(-0.553891 + 8.11139i) q^{60} +(2.19852 + 6.76636i) q^{61} +(-2.44224 - 0.793532i) q^{62} +(3.61484 + 1.17453i) q^{63} +(1.14248 + 3.51620i) q^{64} +(0.804635 - 11.7834i) q^{65} +(-1.34208 + 4.13051i) q^{66} +(5.88778 - 8.10383i) q^{67} -1.80521i q^{68} +(-9.92794 - 7.21307i) q^{69} +(3.00699 - 1.88581i) q^{70} +(13.0997 - 9.51752i) q^{71} +(1.04321 + 1.43585i) q^{72} +(-4.59685 + 1.49361i) q^{73} -1.70077 q^{74} +(-9.06590 - 4.38513i) q^{75} +5.33636 q^{76} +(-16.7118 + 5.42999i) q^{77} +(-2.75985 - 3.79860i) q^{78} +(-1.22713 + 0.891561i) q^{79} +(-6.40087 - 0.437087i) q^{80} +(8.94253 + 6.49713i) q^{81} -2.45366i q^{82} +(3.33657 - 4.59240i) q^{83} +(-4.04104 + 12.4370i) q^{84} +(2.07461 + 0.834258i) q^{85} +(1.68609 + 5.18925i) q^{86} +(7.03827 + 2.28687i) q^{87} +(-7.80352 - 2.53552i) q^{88} +(0.475510 + 1.46347i) q^{89} +(-1.01154 + 0.253961i) q^{90} +(5.87040 - 18.0672i) q^{91} +(6.46483 - 8.89808i) q^{92} +11.7191i q^{93} +(0.390719 + 0.283874i) q^{94} +(-2.46614 + 6.13272i) q^{95} +(-7.53660 + 5.47566i) q^{96} +(4.79226 + 6.59598i) q^{97} +(2.49137 - 0.809495i) q^{98} +5.16320 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

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Database

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