LMFDB - Embedded newform 444.2.c.c.371.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [444,2,Mod(371,444)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(444, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("444.371");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 444 = 2^{2} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	444.c (of order $2$, degree $1$, 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:	$3.54535784974$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + 3x^{16} - 7x^{14} + 12x^{12} - 40x^{10} + 48x^{8} - 112x^{6} + 192x^{4} - 256x^{2} + 1024 $ x^20 - x^18 + 3x^16 - 7x^14 + 12x^12 - 40x^10 + 48x^8 - 112x^6 + 192x^4 - 256x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			371.2
Root			$-1.40476 + 0.163239i$ of defining polynomial
Character	$\chi$	$=$	444.371
Dual form			444.2.c.c.371.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40476 + 0.163239i) q^{2} +(-1.72087 + 0.196528i) q^{3} +(1.94671 - 0.458624i) q^{4} -3.43563i q^{5} +(2.38532 - 0.556987i) q^{6} -4.57374i q^{7} +(-2.65979 + 0.962036i) q^{8} +(2.92275 - 0.676395i) q^{9} +O(q^{10})$	\(q+(-1.40476 + 0.163239i) q^{2} +(-1.72087 + 0.196528i) q^{3} +(1.94671 - 0.458624i) q^{4} -3.43563i q^{5} +(2.38532 - 0.556987i) q^{6} -4.57374i q^{7} +(-2.65979 + 0.962036i) q^{8} +(2.92275 - 0.676395i) q^{9} +(0.560830 + 4.82624i) q^{10} +3.04006 q^{11} +(-3.25989 + 1.17181i) q^{12} -6.03699 q^{13} +(0.746614 + 6.42501i) q^{14} +(0.675197 + 5.91226i) q^{15} +(3.57933 - 1.78561i) q^{16} +0.831815i q^{17} +(-3.99536 + 1.42728i) q^{18} +2.65036i q^{19} +(-1.57567 - 6.68817i) q^{20} +(0.898867 + 7.87079i) q^{21} +(-4.27055 + 0.496257i) q^{22} +1.78503 q^{23} +(4.38807 - 2.17826i) q^{24} -6.80358 q^{25} +(8.48053 - 0.985475i) q^{26} +(-4.89673 + 1.73839i) q^{27} +(-2.09763 - 8.90373i) q^{28} -7.42526i q^{29} +(-1.91360 - 8.19510i) q^{30} +1.01613i q^{31} +(-4.73662 + 3.09265i) q^{32} +(-5.23153 + 0.597456i) q^{33} +(-0.135785 - 1.16850i) q^{34} -15.7137 q^{35} +(5.37953 - 2.65719i) q^{36} +1.00000 q^{37} +(-0.432643 - 3.72312i) q^{38} +(10.3889 - 1.18644i) q^{39} +(3.30520 + 9.13807i) q^{40} +5.34242i q^{41} +(-2.54752 - 10.9098i) q^{42} -8.74524i q^{43} +(5.91810 - 1.39424i) q^{44} +(-2.32385 - 10.0415i) q^{45} +(-2.50754 + 0.291387i) q^{46} +1.38195 q^{47} +(-5.80862 + 3.77624i) q^{48} -13.9191 q^{49} +(9.55740 - 1.11061i) q^{50} +(-0.163475 - 1.43144i) q^{51} +(-11.7523 + 2.76871i) q^{52} +6.20716i q^{53} +(6.59497 - 3.24136i) q^{54} -10.4445i q^{55} +(4.40010 + 12.1652i) q^{56} +(-0.520869 - 4.56091i) q^{57} +(1.21209 + 10.4307i) q^{58} -8.65144 q^{59} +(4.02592 + 11.1998i) q^{60} -6.78253 q^{61} +(-0.165873 - 1.42743i) q^{62} +(-3.09366 - 13.3679i) q^{63} +(6.14897 - 5.11763i) q^{64} +20.7409i q^{65} +(7.25152 - 1.69327i) q^{66} +10.8942i q^{67} +(0.381491 + 1.61930i) q^{68} +(-3.07179 + 0.350807i) q^{69} +(22.0740 - 2.56509i) q^{70} +1.12810 q^{71} +(-7.12320 + 4.61087i) q^{72} +5.61209 q^{73} +(-1.40476 + 0.163239i) q^{74} +(11.7080 - 1.33709i) q^{75} +(1.21552 + 5.15947i) q^{76} -13.9044i q^{77} +(-14.4002 + 3.36253i) q^{78} -4.16150i q^{79} +(-6.13471 - 12.2973i) q^{80} +(8.08498 - 3.95387i) q^{81} +(-0.872093 - 7.50482i) q^{82} -1.49323 q^{83} +(5.35957 + 14.9099i) q^{84} +2.85781 q^{85} +(1.42757 + 12.2850i) q^{86} +(1.45927 + 12.7779i) q^{87} +(-8.08592 + 2.92465i) q^{88} -15.3343i q^{89} +(4.90362 + 13.7266i) q^{90} +27.6116i q^{91} +(3.47492 - 0.818657i) q^{92} +(-0.199699 - 1.74863i) q^{93} +(-1.94132 + 0.225589i) q^{94} +9.10566 q^{95} +(7.54329 - 6.25290i) q^{96} +16.7540 q^{97} +(19.5530 - 2.27214i) q^{98} +(8.88534 - 2.05628i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{4} - q^{6} - 6 q^{9}+O(q^{10}) $ 20 * q + 2 * q^4 - q^6 - 6 * q^9	$ 20 q + 2 q^{4} - q^{6} - 6 q^{9} + 6 q^{10} + 9 q^{12} + 32 q^{13} - 10 q^{16} - 5 q^{18} + 48 q^{21} + 16 q^{22} + 37 q^{24} - 48 q^{25} - 10 q^{28} - 44 q^{30} - 60 q^{33} + 30 q^{34} + 25 q^{36} + 20 q^{37} - 38 q^{40} - 18 q^{42} + 18 q^{45} - 8 q^{46} - 15 q^{48} - 96 q^{49} - 84 q^{52} + 59 q^{54} - 20 q^{57} + 14 q^{58} + 20 q^{60} - 36 q^{61} + 26 q^{64} - 52 q^{66} - 22 q^{69} + 136 q^{70} - 19 q^{72} + 48 q^{73} + 22 q^{76} - 99 q^{78} + 58 q^{81} + 2 q^{82} + 40 q^{84} + 48 q^{85} - 100 q^{88} + 11 q^{90} + 16 q^{93} - 20 q^{94} + 45 q^{96} + 48 q^{97}+O(q^{100}) $ 20 * q + 2 * q^4 - q^6 - 6 * q^9 + 6 * q^10 + 9 * q^12 + 32 * q^13 - 10 * q^16 - 5 * q^18 + 48 * q^21 + 16 * q^22 + 37 * q^24 - 48 * q^25 - 10 * q^28 - 44 * q^30 - 60 * q^33 + 30 * q^34 + 25 * q^36 + 20 * q^37 - 38 * q^40 - 18 * q^42 + 18 * q^45 - 8 * q^46 - 15 * q^48 - 96 * q^49 - 84 * q^52 + 59 * q^54 - 20 * q^57 + 14 * q^58 + 20 * q^60 - 36 * q^61 + 26 * q^64 - 52 * q^66 - 22 * q^69 + 136 * q^70 - 19 * q^72 + 48 * q^73 + 22 * q^76 - 99 * q^78 + 58 * q^81 + 2 * q^82 + 40 * q^84 + 48 * q^85 - 100 * q^88 + 11 * q^90 + 16 * q^93 - 20 * q^94 + 45 * q^96 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/444\mathbb{Z}\right)^\times$.

$n$	$149$	$223$	$409$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.40476	+	0.163239i	−0.993316	+	0.115428i
$2$	−1.40476	+	0.163239i	−0.993316	+	0.115428i
$3$	−1.72087	+	0.196528i	−0.993542	+	0.113465i
$3$	−1.72087	+	0.196528i	−0.993542	+	0.113465i
$4$	1.94671	−	0.458624i	0.973353	−	0.229312i
$5$		−	3.43563i		−	1.53646i	−0.640173	−	0.768231i	$-0.721137\pi$
$5$		−	3.43563i		−	1.53646i	0.640173	−	0.768231i	$-0.278863\pi$
$6$	2.38532	−	0.556987i	0.973804	−	0.227389i
$7$		−	4.57374i		−	1.72871i	−0.502881	−	0.864356i	$-0.667727\pi$
$7$		−	4.57374i		−	1.72871i	0.502881	−	0.864356i	$-0.332273\pi$
$8$	−2.65979	+	0.962036i	−0.940378	+	0.340131i
$9$	2.92275	−	0.676395i	0.974251	−	0.225465i
$10$	0.560830	+	4.82624i	0.177350	+	1.52619i
$11$	3.04006			0.916612			0.458306	−	0.888795i	$-0.348456\pi$
$11$	3.04006			0.916612			0.458306	+	0.888795i	$0.348456\pi$
$12$	−3.25989	+	1.17181i	−0.941048	+	0.338273i
$13$	−6.03699			−1.67436			−0.837180	−	0.546927i	$-0.815798\pi$
$13$	−6.03699			−1.67436			−0.837180	+	0.546927i	$0.815798\pi$
$14$	0.746614	+	6.42501i	0.199541	+	1.71716i
$15$	0.675197	+	5.91226i	0.174335	+	1.52654i
$16$	3.57933	−	1.78561i	0.894832	−	0.446403i
$17$			0.831815i			0.201745i	0.994899	+	0.100872i	$0.0321634\pi$
$17$			0.831815i			0.201745i	−0.994899	+	0.100872i	$0.967837\pi$
$18$	−3.99536	+	1.42728i	−0.941714	+	0.336414i
$19$			2.65036i			0.608034i	0.952667	+	0.304017i	$0.0983280\pi$
$19$			2.65036i			0.608034i	−0.952667	+	0.304017i	$0.901672\pi$
$20$	−1.57567	−	6.68817i	−0.352329	−	1.49552i
$21$	0.898867	+	7.87079i	0.196149	+	1.71755i
$22$	−4.27055	+	0.496257i	−0.910485	+	0.105802i
$23$	1.78503			0.372204			0.186102	−	0.982530i	$-0.440415\pi$
$23$	1.78503			0.372204			0.186102	+	0.982530i	$0.440415\pi$
$24$	4.38807	−	2.17826i	0.895712	−	0.444635i
$25$	−6.80358			−1.36072
$26$	8.48053	−	0.985475i	1.66317	−	0.193267i
$27$	−4.89673	+	1.73839i	−0.942377	+	0.334553i
$28$	−2.09763	−	8.90373i	−0.396415	−	1.68265i
$29$		−	7.42526i		−	1.37884i	−0.724364	−	0.689418i	$-0.757866\pi$
$29$		−	7.42526i		−	1.37884i	0.724364	−	0.689418i	$-0.242134\pi$
$30$	−1.91360	−	8.19510i	−0.349375	−	1.49621i
$31$			1.01613i			0.182503i	0.995828	+	0.0912515i	$0.0290867\pi$
$31$			1.01613i			0.182503i	−0.995828	+	0.0912515i	$0.970913\pi$
$32$	−4.73662	+	3.09265i	−0.837323	+	0.546708i
$33$	−5.23153	+	0.597456i	−0.910692	+	0.104004i
$34$	−0.135785	−	1.16850i	−0.0232869	−	0.200396i
$35$	−15.7137			−2.65610
$36$	5.37953	−	2.65719i	0.896588	−	0.442865i
$37$	1.00000			0.164399
$37$	1.00000			0.164399
$38$	−0.432643	−	3.72312i	−0.0701839	−	0.603970i
$39$	10.3889	−	1.18644i	1.66355	−	0.189982i
$40$	3.30520	+	9.13807i	0.522599	+	1.44486i
$41$			5.34242i			0.834346i	0.908827	+	0.417173i	$0.136979\pi$
$41$			5.34242i			0.834346i	−0.908827	+	0.417173i	$0.863021\pi$
$42$	−2.54752	−	10.9098i	−0.393090	−	1.68343i
$43$		−	8.74524i		−	1.33364i	−0.745220	−	0.666818i	$-0.767656\pi$
$43$		−	8.74524i		−	1.33364i	0.745220	−	0.666818i	$-0.232344\pi$
$44$	5.91810	−	1.39424i	0.892187	−	0.210190i
$45$	−2.32385	−	10.0415i	−0.346419	−	1.49690i
$46$	−2.50754	+	0.291387i	−0.369716	+	0.0429626i
$47$	1.38195			0.201579			0.100789	−	0.994908i	$-0.467863\pi$
$47$	1.38195			0.201579			0.100789	+	0.994908i	$0.467863\pi$
$48$	−5.80862	+	3.77624i	−0.838402	+	0.545053i
$49$	−13.9191			−1.98844
$50$	9.55740	−	1.11061i	1.35162	−	0.157064i
$51$	−0.163475	−	1.43144i	−0.0228910	−	0.200442i
$52$	−11.7523	+	2.76871i	−1.62974	+	0.383951i
$53$			6.20716i			0.852619i	0.904577	+	0.426310i	$0.140187\pi$
$53$			6.20716i			0.852619i	−0.904577	+	0.426310i	$0.859813\pi$
$54$	6.59497	−	3.24136i	0.897461	−	0.441093i
$55$		−	10.4445i		−	1.40834i
$56$	4.40010	+	12.1652i	0.587989	+	1.62564i
$57$	−0.520869	−	4.56091i	−0.0689908	−	0.604107i
$58$	1.21209	+	10.4307i	0.159156	+	1.36962i
$59$	−8.65144			−1.12632			−0.563161	−	0.826347i	$-0.690415\pi$
$59$	−8.65144			−1.12632			−0.563161	+	0.826347i	$0.690415\pi$
$60$	4.02592	+	11.1998i	0.519744	+	1.44588i
$61$	−6.78253			−0.868414			−0.434207	−	0.900813i	$-0.642971\pi$
$61$	−6.78253			−0.868414			−0.434207	+	0.900813i	$0.642971\pi$
$62$	−0.165873	−	1.42743i	−0.0210659	−	0.181283i
$63$	−3.09366	−	13.3679i	−0.389764	−	1.68420i
$64$	6.14897	−	5.11763i	0.768622	−	0.639704i
$65$			20.7409i			2.57259i
$66$	7.25152	−	1.69327i	0.892600	−	0.208428i
$67$			10.8942i			1.33094i	0.746425	+	0.665470i	$0.231769\pi$
$67$			10.8942i			1.33094i	−0.746425	+	0.665470i	$0.768231\pi$
$68$	0.381491	+	1.61930i	0.0462625	+	0.196369i
$69$	−3.07179	+	0.350807i	−0.369800	+	0.0422322i
$70$	22.0740	−	2.56509i	2.63835	−	0.306587i
$71$	1.12810			0.133881			0.0669407	−	0.997757i	$-0.478676\pi$
$71$	1.12810			0.133881			0.0669407	+	0.997757i	$0.478676\pi$
$72$	−7.12320	+	4.61087i	−0.839477	+	0.543396i
$73$	5.61209			0.656846			0.328423	−	0.944531i	$-0.393483\pi$
$73$	5.61209			0.656846			0.328423	+	0.944531i	$0.393483\pi$
$74$	−1.40476	+	0.163239i	−0.163300	+	0.0189762i
$75$	11.7080	−	1.33709i	1.35193	−	0.154394i
$76$	1.21552	+	5.15947i	0.139430	+	0.591832i
$77$		−	13.9044i		−	1.58456i
$78$	−14.4002	+	3.36253i	−1.63050	+	0.380731i
$79$		−	4.16150i		−	0.468205i	−0.972212	−	0.234103i	$-0.924785\pi$
$79$		−	4.16150i		−	0.468205i	0.972212	−	0.234103i	$-0.0752152\pi$
$80$	−6.13471	−	12.2973i	−0.685882	−	1.37488i
$81$	8.08498	−	3.95387i	0.898331	−	0.439319i
$82$	−0.872093	−	7.50482i	−0.0963065	−	0.828769i
$83$	−1.49323			−0.163903			−0.0819516	−	0.996636i	$-0.526115\pi$
$83$	−1.49323			−0.163903			−0.0819516	+	0.996636i	$0.526115\pi$
$84$	5.35957	+	14.9099i	0.584777	+	1.62680i
$85$	2.85781			0.309973
$86$	1.42757	+	12.2850i	0.153938	+	1.32472i
$87$	1.45927	+	12.7779i	0.156450	+	1.36993i
$88$	−8.08592	+	2.92465i	−0.861961	+	0.311768i
$89$		−	15.3343i		−	1.62543i	−0.582658	−	0.812717i	$-0.697987\pi$
$89$		−	15.3343i		−	1.62543i	0.582658	−	0.812717i	$-0.302013\pi$
$90$	4.90362	+	13.7266i	0.516887	+	1.44691i
$91$			27.6116i			2.89449i
$92$	3.47492	−	0.818657i	0.362286	−	0.0853509i
$93$	−0.199699	−	1.74863i	−0.0207078	−	0.181324i
$94$	−1.94132	+	0.225589i	−0.200231	+	0.0232678i
$95$	9.10566			0.934221
$96$	7.54329	−	6.25290i	0.769884	−	0.638184i
$97$	16.7540			1.70111			0.850555	−	0.525886i	$-0.176266\pi$
$97$	16.7540			1.70111			0.850555	+	0.525886i	$0.176266\pi$
$98$	19.5530	−	2.27214i	1.97515	−	0.229521i
$99$	8.88534	−	2.05628i	0.893010	−	0.206664i
$100$	−13.2446	+	3.12029i	−1.32446	+	0.312029i
$101$			1.82422i			0.181517i	0.995873	+	0.0907583i	$0.0289291\pi$
$101$			1.82422i			0.181517i	−0.995873	+	0.0907583i	$0.971071\pi$
$102$	0.463310	+	1.98415i	0.0458746	+	0.196460i
$103$			1.54896i			0.152623i	0.997084	+	0.0763117i	$0.0243144\pi$
$103$			1.54896i			0.152623i	−0.997084	+	0.0763117i	$0.975686\pi$
$104$	16.0571	−	5.80781i	1.57453	−	0.569502i
$105$	27.0412	−	3.08818i	2.63895	−	0.301375i
$106$	−1.01325	−	8.71958i	−0.0984158	−	0.846920i
$107$	5.56789			0.538268			0.269134	−	0.963103i	$-0.413262\pi$
$107$	5.56789			0.538268			0.269134	+	0.963103i	$0.413262\pi$
$108$	−8.73524	+	5.62989i	−0.840548	+	0.541736i
$109$	−5.53681			−0.530330			−0.265165	−	0.964203i	$-0.585427\pi$
$109$	−5.53681			−0.530330			−0.265165	+	0.964203i	$0.585427\pi$
$110$	1.70496	+	14.6721i	0.162561	+	1.39893i
$111$	−1.72087	+	0.196528i	−0.163337	+	0.0186536i
$112$	−8.16693	−	16.3709i	−0.771703	−	1.54691i
$113$			3.38698i			0.318620i	0.987229	+	0.159310i	$0.0509269\pi$
$113$			3.38698i			0.318620i	−0.987229	+	0.159310i	$0.949073\pi$
$114$	1.47622	+	6.32196i	0.138260	+	0.592106i
$115$		−	6.13270i		−	0.571877i
$116$	−3.40541	−	14.4548i	−0.316184	−	1.34209i
$117$	−17.6446	+	4.08340i	−1.63125	+	0.377510i
$118$	12.1532	−	1.41225i	1.11879	−	0.130009i
$119$	3.80451			0.348758
$120$	−7.48370	−	15.0758i	−0.683165	−	1.37623i
$121$	−1.75805			−0.159823
$122$	9.52783	−	1.10718i	0.862609	−	0.100239i
$123$	−1.04993	−	9.19358i	−0.0946693	−	0.828957i
$124$	0.466024	+	1.97811i	0.0418502	+	0.177640i
$125$			6.19644i			0.554227i
$126$	6.52802	+	18.2737i	0.581562	+	1.62795i
$127$		−	16.8124i		−	1.49186i	−0.666023	−	0.745931i	$-0.732005\pi$
$127$		−	16.8124i		−	1.49186i	0.666023	−	0.745931i	$-0.267995\pi$
$128$	−7.80244	+	8.19280i	−0.689644	+	0.724148i
$129$	1.71868	+	15.0494i	0.151322	+	1.32502i
$130$	−3.38573	−	29.1360i	−0.296948	−	2.55540i
$131$	−11.1768			−0.976524			−0.488262	−	0.872697i	$-0.662369\pi$
$131$	−11.1768			−0.976524			−0.488262	+	0.872697i	$0.662369\pi$
$132$	−9.91024	+	3.56238i	−0.862576	+	0.310065i
$133$	12.1221			1.05112
$134$	−1.77836	−	15.3038i	−0.153627	−	1.32204i
$135$	5.97246	+	16.8234i	0.514028	+	1.44793i
$136$	−0.800236	−	2.21245i	−0.0686197	−	0.189716i
$137$			11.9411i			1.02020i	0.860116	+	0.510099i	$0.170391\pi$
$137$			11.9411i			1.02020i	−0.860116	+	0.510099i	$0.829609\pi$
$138$	4.25787	−	0.994237i	0.362454	−	0.0846351i
$139$			15.6097i			1.32399i	0.749507	+	0.661997i	$0.230291\pi$
$139$			15.6097i			1.32399i	−0.749507	+	0.661997i	$0.769709\pi$
$140$	−30.5899	+	7.20668i	−2.58532	+	0.609076i
$141$	−2.37816	+	0.271592i	−0.200277	+	0.0228722i
$142$	−1.58472	+	0.184151i	−0.132987	+	0.0154536i
$143$	−18.3528			−1.53474
$144$	9.25371	−	7.63995i	0.771143	−	0.636662i
$145$	−25.5105			−2.11853
$146$	−7.88365	+	0.916114i	−0.652455	+	0.0758182i
$147$	23.9529	−	2.73549i	1.97560	−	0.225619i
$148$	1.94671	−	0.458624i	0.160018	−	0.0376987i
$149$		−	13.9682i		−	1.14432i	−0.820143	−	0.572159i	$-0.806106\pi$
$149$		−	13.9682i		−	1.14432i	0.820143	−	0.572159i	$-0.193894\pi$
$150$	−16.2287	+	3.78951i	−1.32507	+	0.309412i
$151$		−	9.39057i		−	0.764194i	−0.924122	−	0.382097i	$-0.875202\pi$
$151$		−	9.39057i		−	0.764194i	0.924122	−	0.382097i	$-0.124798\pi$
$152$	−2.54974	−	7.04940i	−0.206811	−	0.571782i
$153$	0.562636	+	2.43119i	0.0454864	+	0.196550i
$154$	2.26975	+	19.5324i	0.182902	+	1.57397i
$155$	3.49107			0.280409
$156$	19.6799	−	7.07422i	1.57565	−	0.566391i
$157$	−4.42113			−0.352845			−0.176422	−	0.984315i	$-0.556452\pi$
$157$	−4.42113			−0.352845			−0.176422	+	0.984315i	$0.556452\pi$
$158$	0.679320	+	5.84591i	0.0540438	+	0.465076i
$159$	−1.21988	−	10.6817i	−0.0967427	−	0.847113i
$160$	10.6252	+	16.2733i	0.839996	+	1.28652i
$161$		−	8.16425i		−	0.643433i
$162$	−10.7120	+	6.87403i	−0.841617	+	0.540075i
$163$		−	6.40323i		−	0.501540i	−0.968047	−	0.250770i	$-0.919316\pi$
$163$		−	6.40323i		−	0.501540i	0.968047	−	0.250770i	$-0.0806838\pi$
$164$	2.45016	+	10.4001i	0.191326	+	0.812113i
$165$	2.05264	+	17.9736i	0.159798	+	1.39924i
$166$	2.09763	−	0.243754i	0.162808	−	0.0189189i
$167$	2.58583			0.200098			0.100049	−	0.994983i	$-0.468100\pi$
$167$	2.58583			0.200098			0.100049	+	0.994983i	$0.468100\pi$
$168$	−9.96278	−	20.0699i	−0.768646	−	1.54843i
$169$	23.4453			1.80348
$170$	−4.01454	+	0.466507i	−0.307901	+	0.0357795i
$171$	1.79269	+	7.74635i	0.137090	+	0.592378i
$172$	−4.01078	−	17.0244i	−0.305819	−	1.29810i
$173$		−	13.0535i		−	0.992443i	−0.868196	−	0.496221i	$-0.834720\pi$
$173$		−	13.0535i		−	0.992443i	0.868196	−	0.496221i	$-0.165280\pi$
$174$	−4.13578	−	17.7116i	−0.313532	−	1.34272i
$175$			31.1178i			2.35229i
$176$	10.8814	−	5.42837i	0.820213	−	0.409179i
$177$	14.8880	−	1.70025i	1.11905	−	0.127798i
$178$	2.50316	+	21.5410i	0.187620	+	1.61457i
$179$	−5.62589			−0.420499			−0.210249	−	0.977648i	$-0.567428\pi$
$179$	−5.62589			−0.420499			−0.210249	+	0.977648i	$0.567428\pi$
$180$	−9.12913	−	18.4821i	−0.680445	−	1.37757i
$181$	4.12305			0.306464			0.153232	−	0.988190i	$-0.451032\pi$
$181$	4.12305			0.306464			0.153232	+	0.988190i	$0.451032\pi$
$182$	−4.50731	−	38.7878i	−0.334104	−	2.87514i
$183$	11.6718	−	1.33296i	0.862806	−	0.0985349i
$184$	−4.74780	+	1.71726i	−0.350012	+	0.126598i
$185$		−	3.43563i		−	0.252593i
$186$	0.565974	+	2.42381i	0.0414992	+	0.177722i
$187$			2.52876i			0.184922i
$188$	2.69026	−	0.633798i	0.196207	−	0.0462245i
$189$	7.95093	+	22.3964i	0.578345	+	1.62910i
$190$	−12.7913	+	1.48640i	−0.927977	+	0.107835i
$191$	16.9329			1.22522			0.612611	−	0.790385i	$-0.290119\pi$
$191$	16.9329			1.22522			0.612611	+	0.790385i	$0.290119\pi$
$192$	−9.57580	+	10.0152i	−0.691074	+	0.722784i
$193$	1.58456			0.114059			0.0570295	−	0.998372i	$-0.481837\pi$
$193$	1.58456			0.114059			0.0570295	+	0.998372i	$0.481837\pi$
$194$	−23.5354	+	2.73491i	−1.68974	+	0.196355i
$195$	−4.07616	−	35.6923i	−0.291900	−	2.55598i
$196$	−27.0964	+	6.38364i	−1.93546	+	0.455974i
$197$			4.74066i			0.337758i	0.985637	+	0.168879i	$0.0540147\pi$
$197$			4.74066i			0.337758i	−0.985637	+	0.168879i	$0.945985\pi$
$198$	−12.1461	+	4.33902i	−0.863186	+	0.308361i
$199$			17.8927i			1.26838i	0.773177	+	0.634191i	$0.218667\pi$
$199$			17.8927i			1.26838i	−0.773177	+	0.634191i	$0.781333\pi$
$200$	18.0961	−	6.54529i	1.27959	−	0.462822i
$201$	−2.14101	−	18.7475i	−0.151016	−	1.32234i
$202$	−0.297784	−	2.56259i	−0.0209520	−	0.180303i
$203$	−33.9612			−2.38361
$204$	−0.974731	−	2.71162i	−0.0682448	−	0.189851i
$205$	18.3546			1.28194
$206$	−0.252851	−	2.17592i	−0.0176170	−	0.151603i
$207$	5.21719	−	1.20738i	0.362620	−	0.0839190i
$208$	−21.6084	+	10.7797i	−1.49827	+	0.747440i
$209$			8.05724i			0.557331i
$210$	−37.4822	+	8.75233i	−2.58652	+	0.603968i
$211$		−	26.4214i		−	1.81892i	−0.415790	−	0.909461i	$-0.636495\pi$
$211$		−	26.4214i		−	1.81892i	0.415790	−	0.909461i	$-0.363505\pi$
$212$	2.84676	+	12.0835i	0.195516	+	0.829899i
$213$	−1.94132	+	0.221704i	−0.133017	+	0.0151909i
$214$	−7.82156	+	0.908899i	−0.534671	+	0.0621310i
$215$	−30.0454			−2.04908
$216$	11.3519	−	9.33458i	0.772399	−	0.635138i
$217$	4.64753			0.315495
$218$	7.77790	−	0.903825i	0.526786	−	0.0612148i
$219$	−9.65766	+	1.10293i	−0.652604	+	0.0745292i
$220$	−4.79011	−	20.3324i	−0.322949	−	1.37081i
$221$		−	5.02166i		−	0.337793i
$222$	2.38532	−	0.556987i	0.160092	−	0.0373825i
$223$		−	10.0758i		−	0.674729i	−0.941374	−	0.337364i	$-0.890465\pi$
$223$		−	10.0758i		−	0.674729i	0.941374	−	0.337364i	$-0.109535\pi$
$224$	14.1450	+	21.6641i	0.945100	+	1.44749i
$225$	−19.8852	+	4.60191i	−1.32568	+	0.306794i
$226$	−0.552888	−	4.75789i	−0.0367775	−	0.316490i
$227$	−6.80841			−0.451890			−0.225945	−	0.974140i	$-0.572547\pi$
$227$	−6.80841			−0.451890			−0.225945	+	0.974140i	$0.572547\pi$
$228$	−3.10572	−	8.63987i	−0.205682	−	0.572189i
$229$	4.50034			0.297391			0.148695	−	0.988883i	$-0.452493\pi$
$229$	4.50034			0.297391			0.148695	+	0.988883i	$0.452493\pi$
$230$	1.00110	+	8.61498i	0.0660104	+	0.568055i
$231$	2.73261	+	23.9277i	0.179792	+	1.57432i
$232$	7.14337	+	19.7496i	0.468985	+	1.29663i
$233$		−	21.3239i		−	1.39697i	−0.715623	−	0.698487i	$-0.753857\pi$
$233$		−	21.3239i		−	1.39697i	0.715623	−	0.698487i	$-0.246143\pi$
$234$	24.1199	−	8.61649i	1.57677	−	0.563278i
$235$		−	4.74789i		−	0.309718i
$236$	−16.8418	+	3.96776i	−1.09631	+	0.258279i
$237$	0.817850	+	7.16138i	0.0531251	+	0.465181i
$238$	−5.34442	+	0.621045i	−0.346427	+	0.0402564i
$239$	−6.64354			−0.429735			−0.214867	−	0.976643i	$-0.568932\pi$
$239$	−6.64354			−0.429735			−0.214867	+	0.976643i	$0.568932\pi$
$240$	12.9738	+	19.9563i	0.837453	+	1.28817i
$241$	11.4761			0.739240			0.369620	−	0.929183i	$-0.379488\pi$
$241$	11.4761			0.739240			0.369620	+	0.929183i	$0.379488\pi$
$242$	2.46964	−	0.286983i	0.158755	−	0.0184480i
$243$	−13.1361	+	8.39301i	−0.842682	+	0.538412i
$244$	−13.2036	+	3.11063i	−0.845273	+	0.199138i
$245$			47.8209i			3.05517i
$246$	2.97566	+	12.7434i	0.189721	+	0.812489i
$247$		−	16.0002i		−	1.01807i
$248$	−0.977558	−	2.70270i	−0.0620750	−	0.171622i
$249$	2.56964	−	0.293461i	0.162845	−	0.0185973i
$250$	−1.01150	−	8.70452i	−0.0639731	−	0.550522i
$251$	10.3944			0.656091			0.328046	−	0.944662i	$-0.393610\pi$
$251$	10.3944			0.656091			0.328046	+	0.944662i	$0.393610\pi$
$252$	−12.1533	−	24.6046i	−0.765585	−	1.54994i
$253$	5.42658			0.341166
$254$	2.74445	+	23.6175i	0.172202	+	1.48189i
$255$	−4.91791	+	0.561639i	−0.307971	+	0.0351712i
$256$	9.62317	−	12.7826i	0.601448	−	0.798912i
$257$		−	22.6348i		−	1.41192i	−0.708253	−	0.705959i	$-0.750516\pi$
$257$		−	22.6348i		−	1.41192i	0.708253	−	0.705959i	$-0.249484\pi$
$258$	−4.87099	−	20.8602i	−0.303254	−	1.29870i
$259$		−	4.57374i		−	0.284198i
$260$	9.51228	+	40.3764i	0.589927	+	2.50404i
$261$	−5.02241	−	21.7022i	−0.310880	−	1.34333i
$262$	15.7008	−	1.82450i	0.969996	−	0.112718i
$263$	23.6333			1.45729			0.728646	−	0.684891i	$-0.240150\pi$
$263$	23.6333			1.45729			0.728646	+	0.684891i	$0.240150\pi$
$264$	13.3400	−	6.62203i	0.821020	−	0.407558i
$265$	21.3255			1.31002
$266$	−17.0286	+	1.97880i	−1.04409	+	0.121328i
$267$	3.01362	+	26.3883i	0.184430	+	1.61494i
$268$	4.99635	+	21.2078i	0.305201	+	1.29547i
$269$		−	11.8741i		−	0.723977i	−0.932183	−	0.361989i	$-0.882098\pi$
$269$		−	11.8741i		−	0.723977i	0.932183	−	0.361989i	$-0.117902\pi$
$270$	−11.1361	−	22.6579i	−0.677723	−	1.37892i
$271$		−	3.71293i		−	0.225544i	−0.993621	−	0.112772i	$-0.964027\pi$
$271$		−	3.71293i		−	0.225544i	0.993621	−	0.112772i	$-0.0359730\pi$
$272$	1.48530	+	2.97734i	0.0900595	+	0.180528i
$273$	−5.42645	−	47.5159i	−0.328424	−	2.87579i
$274$	−1.94926	−	16.7744i	−0.117759	−	1.01338i
$275$	−20.6833			−1.24725
$276$	−5.81899	+	2.09172i	−0.350262	+	0.125907i
$277$	13.3909			0.804582			0.402291	−	0.915512i	$-0.368214\pi$
$277$	13.3909			0.804582			0.402291	+	0.915512i	$0.368214\pi$
$278$	−2.54811	−	21.9278i	−0.152825	−	1.31514i
$279$	0.687309	+	2.96991i	0.0411481	+	0.177804i
$280$	41.7951	−	15.1171i	2.49774	−	0.903422i
$281$		−	5.62558i		−	0.335594i	−0.985822	−	0.167797i	$-0.946335\pi$
$281$		−	5.62558i		−	0.335594i	0.985822	−	0.167797i	$-0.0536653\pi$
$282$	3.29641	−	0.769731i	0.196298	−	0.0458368i
$283$		−	17.1874i		−	1.02169i	−0.859674	−	0.510844i	$-0.829333\pi$
$283$		−	17.1874i		−	1.02169i	0.859674	−	0.510844i	$-0.170667\pi$
$284$	2.19609	−	0.517376i	0.130314	−	0.0307006i
$285$	−15.6696	+	1.78951i	−0.928188	+	0.106002i
$286$	25.7813	−	2.99590i	1.52448	−	0.177151i
$287$	24.4348			1.44234
$288$	−11.7521	+	12.2429i	−0.692500	+	0.721418i
$289$	16.3081			0.959299
$290$	35.8361	−	4.16431i	2.10437	−	0.244537i
$291$	−28.8314	+	3.29262i	−1.69012	+	0.193017i
$292$	10.9251	−	2.57384i	0.639343	−	0.150623i
$293$			18.9792i			1.10878i	0.832258	+	0.554388i	$0.187048\pi$
$293$			18.9792i			1.10878i	−0.832258	+	0.554388i	$0.812952\pi$
$294$	−33.2016	+	7.75276i	−1.93635	+	0.452150i
$295$			29.7232i			1.73055i
$296$	−2.65979	+	0.962036i	−0.154597	+	0.0559172i
$297$	−14.8864	+	5.28480i	−0.863794	+	0.306655i
$298$	2.28016	+	19.6220i	0.132086	+	1.13667i
$299$	−10.7762			−0.623204
$300$	22.1789	−	7.97252i	1.28050	−	0.460294i
$301$	−39.9985			−2.30547
$302$	1.53291	+	13.1915i	0.0882091	+	0.759086i
$303$	−0.358510	−	3.13923i	−0.0205958	−	0.180344i
$304$	4.73252	+	9.48650i	0.271428	+	0.544088i
$305$			23.3023i			1.33429i
$306$	−1.18723	−	3.32340i	−0.0678697	−	0.189986i
$307$			3.20042i			0.182658i	0.995821	+	0.0913289i	$0.0291115\pi$
$307$			3.20042i			0.182658i	−0.995821	+	0.0913289i	$0.970889\pi$
$308$	−6.37691	−	27.0678i	−0.363358	−	1.54233i
$309$	−0.304413	−	2.66555i	−0.0173175	−	0.151638i
$310$	−4.90411	+	0.569879i	−0.278535	+	0.0323670i
$311$	7.43191			0.421425			0.210712	−	0.977548i	$-0.432422\pi$
$311$	7.43191			0.421425			0.210712	+	0.977548i	$0.432422\pi$
$312$	−26.4908	+	13.1501i	−1.49974	+	0.744479i
$313$	−29.6264			−1.67458			−0.837291	−	0.546757i	$-0.815862\pi$
$313$	−29.6264			−1.67458			−0.837291	+	0.546757i	$0.815862\pi$
$314$	6.21063	−	0.721702i	0.350486	−	0.0407280i
$315$	−45.9273	+	10.6287i	−2.58771	+	0.598858i
$316$	−1.90856	−	8.10121i	−0.107365	−	0.455729i
$317$		−	18.7522i		−	1.05323i	−0.850104	−	0.526616i	$-0.823461\pi$
$317$		−	18.7522i		−	1.05323i	0.850104	−	0.526616i	$-0.176539\pi$
$318$	3.45731	+	14.8061i	0.193876	+	0.830284i
$319$		−	22.5732i		−	1.26386i
$320$	−17.5823	−	21.1256i	−0.982881	−	1.18096i
$321$	−9.58159	+	1.09424i	−0.534792	+	0.0610748i
$322$	1.33273	+	11.4688i	0.0742700	+	0.639132i
$323$	−2.20461			−0.122668
$324$	13.9257	−	11.4050i	0.773652	−	0.633611i
$325$	41.0732			2.27833
$326$	1.04526	+	8.99501i	0.0578916	+	0.498188i
$327$	9.52811	−	1.08814i	0.526906	−	0.0601741i
$328$	−5.13960	−	14.2097i	−0.283787	−	0.784600i
$329$		−	6.32070i		−	0.348472i
$330$	−5.81747	−	24.9136i	−0.320241	−	1.37145i
$331$		−	0.859429i		−	0.0472385i	−0.999721	−	0.0236192i	$-0.992481\pi$
$331$		−	0.859429i		−	0.0472385i	0.999721	−	0.0236192i	$-0.00751893\pi$
$332$	−2.90688	+	0.684831i	−0.159536	+	0.0375850i
$333$	2.92275	−	0.676395i	0.160166	−	0.0370662i
$334$	−3.63248	+	0.422109i	−0.198760	+	0.0230968i
$335$	37.4285			2.04494
$336$	17.2715	+	26.5671i	0.942239	+	1.44935i
$337$	−2.17995			−0.118750			−0.0593748	−	0.998236i	$-0.518911\pi$
$337$	−2.17995			−0.118750			−0.0593748	+	0.998236i	$0.518911\pi$
$338$	−32.9350	+	3.82719i	−1.79143	+	0.208172i
$339$	−0.665635	−	5.82853i	−0.0361523	−	0.316562i
$340$	5.56332	−	1.31066i	0.301713	−	0.0710806i
$341$			3.08911i			0.167284i
$342$	−3.78281	−	10.5891i	−0.204551	−	0.572594i
$343$			31.6462i			1.70873i
$344$	8.41324	+	23.2605i	0.453611	+	1.25412i
$345$	1.20525	+	10.5535i	0.0648882	+	0.568184i
$346$	2.13085	+	18.3371i	0.114555	+	0.985809i
$347$	14.1835			0.761410			0.380705	−	0.924696i	$-0.375681\pi$
$347$	14.1835			0.761410			0.380705	+	0.924696i	$0.375681\pi$
$348$	8.70101	+	24.2055i	0.466423	+	1.29755i
$349$	6.13571			0.328437			0.164218	−	0.986424i	$-0.447490\pi$
$349$	6.13571			0.328437			0.164218	+	0.986424i	$0.447490\pi$
$350$	−5.07965	−	43.7131i	−0.271519	−	2.33656i
$351$	29.5616	−	10.4946i	1.57788	−	0.560162i
$352$	−14.3996	+	9.40182i	−0.767500	+	0.501119i
$353$		−	1.08746i		−	0.0578799i	−0.999581	−	0.0289400i	$-0.990787\pi$
$353$		−	1.08746i		−	0.0578799i	0.999581	−	0.0289400i	$-0.00921316\pi$
$354$	−20.6365	+	4.81874i	−1.09682	+	0.256113i
$355$		−	3.87575i		−	0.205704i
$356$	−7.03269	−	29.8514i	−0.372732	−	1.58212i
$357$	−6.54704	+	0.747691i	−0.346506	+	0.0395720i
$358$	7.90303	−	0.918366i	0.417688	−	0.0485372i
$359$	−30.9197			−1.63188			−0.815940	−	0.578137i	$-0.803780\pi$
$359$	−30.9197			−1.63188			−0.815940	+	0.578137i	$0.803780\pi$
$360$	15.8412	+	24.4727i	0.834907	+	1.28982i
$361$	11.9756			0.630295
$362$	−5.79191	+	0.673045i	−0.304416	+	0.0353744i
$363$	3.02537	−	0.345506i	0.158791	−	0.0181344i
$364$	12.6634	+	53.7518i	0.663741	+	2.81736i
$365$		−	19.2811i		−	1.00922i
$366$	−16.1785	+	3.77778i	−0.845665	+	0.197468i
$367$			10.5017i			0.548185i	0.961703	+	0.274092i	$0.0883774\pi$
$367$			10.5017i			0.548185i	−0.961703	+	0.274092i	$0.911623\pi$
$368$	6.38920	−	3.18737i	0.333060	−	0.166153i
$369$	3.61359	+	15.6146i	0.188116	+	0.812862i
$370$	0.560830	+	4.82624i	0.0291562	+	0.250904i
$371$	28.3899			1.47393
$372$	−1.19072	−	3.31248i	−0.0617359	−	0.171744i
$373$	21.1614			1.09570			0.547848	−	0.836578i	$-0.315447\pi$
$373$	21.1614			1.09570			0.547848	+	0.836578i	$0.315447\pi$
$374$	−0.412794	−	3.55231i	−0.0213451	−	0.183686i
$375$	−1.21777	−	10.6632i	−0.0628855	−	0.550647i
$376$	−3.67571	+	1.32949i	−0.189560	+	0.0685633i
$377$			44.8263i			2.30867i
$378$	−14.8251	−	30.1637i	−0.762522	−	1.55145i
$379$		−	30.7845i		−	1.58129i	−0.612274	−	0.790646i	$-0.709745\pi$
$379$		−	30.7845i		−	1.58129i	0.612274	−	0.790646i	$-0.290255\pi$
$380$	17.7260	−	4.17608i	0.909327	−	0.214228i
$381$	3.30411	+	28.9319i	0.169275	+	1.48223i
$382$	−23.7867	+	2.76412i	−1.21703	+	0.141424i
$383$	−8.36975			−0.427674			−0.213837	−	0.976869i	$-0.568596\pi$
$383$	−8.36975			−0.427674			−0.213837	+	0.976869i	$0.568596\pi$
$384$	11.8168	−	15.6321i	0.603025	−	0.797722i
$385$	−47.7705			−2.43461
$386$	−2.22592	+	0.258662i	−0.113297	+	0.0131655i
$387$	−5.91524	−	25.5602i	−0.300689	−	1.29930i
$388$	32.6151	−	7.68379i	1.65578	−	0.390085i
$389$		−	16.2928i		−	0.826078i	−0.910713	−	0.413039i	$-0.864467\pi$
$389$		−	16.2928i		−	0.826078i	0.910713	−	0.413039i	$-0.135533\pi$
$390$	11.5524	+	49.4737i	0.584979	+	2.50520i
$391$			1.48481i			0.0750902i
$392$	37.0219	−	13.3907i	1.86989	−	0.676332i
$393$	19.2338	−	2.19656i	0.970217	−	0.110802i
$394$	−0.773862	−	6.65949i	−0.0389866	−	0.335500i
$395$	−14.2974			−0.719380
$396$	16.3541	−	8.07801i	0.821823	−	0.405935i
$397$	3.93170			0.197326			0.0986631	−	0.995121i	$-0.468543\pi$
$397$	3.93170			0.197326			0.0986631	+	0.995121i	$0.468543\pi$
$398$	−2.92080	−	25.1350i	−0.146406	−	1.25990i
$399$	−20.8604	+	2.38232i	−1.04433	+	0.119265i
$400$	−24.3522	+	12.1486i	−1.21761	+	0.607428i
$401$			32.0403i			1.60002i	0.599988	+	0.800009i	$0.295172\pi$
$401$			32.0403i			1.60002i	−0.599988	+	0.800009i	$0.704828\pi$
$402$	6.06794	+	25.9862i	0.302641	+	1.29607i
$403$		−	6.13440i		−	0.305576i
$404$	0.836631	+	3.55122i	0.0416240	+	0.176680i
$405$	−13.5841	−	27.7770i	−0.674998	−	1.38025i
$406$	47.7074	−	5.54381i	2.36768	−	0.275134i
$407$	3.04006			0.150690
$408$	1.81191	+	3.65007i	0.0897028	+	0.180705i
$409$	2.70365			0.133687			0.0668435	−	0.997763i	$-0.478707\pi$
$409$	2.70365			0.133687			0.0668435	+	0.997763i	$0.478707\pi$
$410$	−25.7838	+	2.99619i	−1.27337	+	0.147971i
$411$	−2.34676	−	20.5490i	−0.115757	−	1.01361i
$412$	0.710390	+	3.01537i	0.0349984	+	0.148556i
$413$			39.5694i			1.94708i
$414$	−7.13182	+	2.54774i	−0.350510	+	0.125214i
$415$			5.13019i			0.251831i
$416$	28.5949	−	18.6703i	1.40198	−	0.915386i
$417$	−3.06773	−	26.8621i	−0.150227	−	1.31544i
$418$	−1.31526	−	11.3185i	−0.0643314	−	0.553606i
$419$	34.2786			1.67462			0.837310	−	0.546728i	$-0.184127\pi$
$419$	34.2786			1.67462			0.837310	+	0.546728i	$0.184127\pi$
$420$	51.2249	−	18.4135i	2.49952	−	0.898487i
$421$	−23.4564			−1.14320			−0.571598	−	0.820533i	$-0.693676\pi$
$421$	−23.4564			−1.14320			−0.571598	+	0.820533i	$0.693676\pi$
$422$	4.31300	+	37.1157i	0.209954	+	1.80676i
$423$	4.03911	−	0.934748i	0.196388	−	0.0454490i
$424$	−5.97151	−	16.5097i	−0.290002	−	0.801784i
$425$		−	5.65932i		−	0.274517i
$426$	2.69089	−	0.628340i	0.130374	−	0.0304432i
$427$			31.0215i			1.50124i
$428$	10.8390	−	2.55357i	0.523925	−	0.123431i
$429$	31.5827	−	3.60684i	1.52483	−	0.174140i
$430$	42.2067	−	4.90460i	2.03539	−	0.236521i
$431$	19.5528			0.941824			0.470912	−	0.882180i	$-0.343925\pi$
$431$	19.5528			0.941824			0.470912	+	0.882180i	$0.343925\pi$
$432$	−14.4229	+	14.9659i	−0.693923	+	0.720049i
$433$	−35.8422			−1.72246			−0.861232	−	0.508212i	$-0.830307\pi$
$433$	−35.8422			−1.72246			−0.861232	+	0.508212i	$0.830307\pi$
$434$	−6.52867	+	0.758660i	−0.313386	+	0.0364169i
$435$	43.9001	−	5.01352i	2.10485	−	0.240380i
$436$	−10.7785	+	2.53932i	−0.516199	+	0.121611i
$437$			4.73096i			0.226313i
$438$	13.3867	−	3.12586i	0.639639	−	0.149360i
$439$			10.8215i			0.516484i	0.966080	+	0.258242i	$0.0831432\pi$
$439$			10.8215i			0.516484i	−0.966080	+	0.258242i	$0.916857\pi$
$440$	10.0480	+	27.7802i	0.479020	+	1.32437i
$441$	−40.6821	+	9.41482i	−1.93724	+	0.448325i
$442$	0.819732	+	7.05423i	0.0389907	+	0.335536i
$443$	−12.9997			−0.617633			−0.308817	−	0.951122i	$-0.599933\pi$
$443$	−12.9997			−0.617633			−0.308817	+	0.951122i	$0.599933\pi$
$444$	−3.25989	+	1.17181i	−0.154707	+	0.0556117i
$445$	−52.6831			−2.49742
$446$	1.64477	+	14.1542i	0.0778823	+	0.670219i
$447$	2.74513	+	24.0374i	0.129840	+	1.13693i
$448$	−23.4067	−	28.1238i	−1.10586	−	1.32872i
$449$			21.3123i			1.00579i	0.864348	+	0.502894i	$0.167731\pi$
$449$			21.3123i			1.00579i	−0.864348	+	0.502894i	$0.832269\pi$
$450$	27.1827	−	9.71063i	1.28141	−	0.457763i
$451$			16.2413i			0.764771i
$452$	1.55335	+	6.59345i	0.0730634	+	0.310130i
$453$	1.84551	+	16.1599i	0.0867095	+	0.759259i
$454$	9.56419	−	1.11140i	0.448870	−	0.0521606i
$455$	94.8635			4.44727
$456$	5.77316	+	11.6300i	0.270353	+	0.544623i
$457$	−28.9238			−1.35300			−0.676499	−	0.736444i	$-0.736504\pi$
$457$	−28.9238			−1.35300			−0.676499	+	0.736444i	$0.736504\pi$
$458$	−6.32190	+	0.734632i	−0.295403	+	0.0343271i
$459$	−1.44602	−	4.07318i	−0.0674943	−	0.190120i
$460$	−2.81261	−	11.9386i	−0.131138	−	0.556638i
$461$		−	17.6140i		−	0.820368i	−0.912003	−	0.410184i	$-0.865465\pi$
$461$		−	17.6140i		−	0.820368i	0.912003	−	0.410184i	$-0.134535\pi$
$462$	−7.74459	−	33.1666i	−0.360311	−	1.54305i
$463$			1.30975i			0.0608692i	0.999537	+	0.0304346i	$0.00968913\pi$
$463$			1.30975i			0.0608692i	−0.999537	+	0.0304346i	$0.990311\pi$
$464$	−13.2586	−	26.5774i	−0.615517	−	1.23383i
$465$	−6.00765	+	0.686091i	−0.278598	+	0.0318167i
$466$	3.48090	+	29.9550i	0.161249	+	1.38764i
$467$	29.9653			1.38663			0.693315	−	0.720635i	$-0.256150\pi$
$467$	29.9653			1.38663			0.693315	+	0.720635i	$0.256150\pi$
$468$	−32.4762	+	16.0414i	−1.50121	+	0.741516i
$469$	49.8273			2.30081
$470$	0.775042	+	6.66965i	0.0357500	+	0.307648i
$471$	7.60817	−	0.868875i	0.350566	−	0.0400356i
$472$	23.0110	−	8.32300i	1.05917	−	0.383097i
$473$		−	26.5860i		−	1.22243i
$474$	−2.31790	−	9.92652i	−0.106465	−	0.455940i
$475$		−	18.0319i		−	0.827362i
$476$	7.40625	−	1.74484i	0.339465	−	0.0799746i
$477$	4.19850	+	18.1420i	0.192236	+	0.830665i
$478$	9.33258	−	1.08449i	0.426862	−	0.0496033i
$479$	−23.2387			−1.06180			−0.530901	−	0.847434i	$-0.678146\pi$
$479$	−23.2387			−1.06180			−0.530901	+	0.847434i	$0.678146\pi$
$480$	−21.4827	−	25.9160i	−0.980546	−	1.18290i
$481$	−6.03699			−0.275263
$482$	−16.1212	+	1.87335i	−0.734299	+	0.0853287i
$483$	1.60450	+	14.0496i	0.0730074	+	0.639278i
$484$	−3.42241	+	0.806286i	−0.155564	+	0.0366494i
$485$		−	57.5606i		−	2.61369i
$486$	17.0830	−	13.9345i	0.774902	−	0.632082i
$487$			13.2487i			0.600356i	0.953883	+	0.300178i	$0.0970462\pi$
$487$			13.2487i			0.600356i	−0.953883	+	0.300178i	$0.902954\pi$
$488$	18.0401	−	6.52504i	0.816637	−	0.295375i
$489$	1.25841	+	11.0191i	0.0569074	+	0.498301i
$490$	−7.80626	−	67.1770i	−0.352651	−	3.03475i
$491$	11.0745			0.499784			0.249892	−	0.968274i	$-0.419605\pi$
$491$	11.0745			0.499784			0.249892	+	0.968274i	$0.419605\pi$
$492$	−6.26031	−	17.4157i	−0.282237	−	0.785159i
$493$	6.17644			0.278173
$494$	2.61186	+	22.4765i	0.117513	+	1.01126i
$495$	−7.06463	−	30.5268i	−0.317531	−	1.37208i
$496$	1.81442	+	3.63708i	0.0814700	+	0.163310i
$497$		−	5.15966i		−	0.231442i
$498$	−3.56183	+	0.831709i	−0.159609	+	0.0372698i
$499$			35.1563i			1.57381i	0.617072	+	0.786907i	$0.288319\pi$
$499$			35.1563i			1.57381i	−0.617072	+	0.786907i	$0.711681\pi$
$500$	2.84184	+	12.0627i	0.127091	+	0.539458i
$501$	−4.44987	+	0.508188i	−0.198805	+	0.0227042i
$502$	−14.6017	+	1.69678i	−0.651706	+	0.0757311i
$503$	−33.9179			−1.51232			−0.756162	−	0.654384i	$-0.772928\pi$
$503$	−33.9179			−1.51232			−0.756162	+	0.654384i	$0.772928\pi$
$504$	21.0889	+	32.5797i	0.939374	+	1.45121i
$505$	6.26735			0.278893
$506$	−7.62305	+	0.885832i	−0.338886	+	0.0393800i
$507$	−40.3462	+	4.60765i	−1.79184	+	0.204633i
$508$	−7.71059	−	32.7289i	−0.342102	−	1.45211i
$509$			2.18241i			0.0967335i	0.998830	+	0.0483668i	$0.0154016\pi$
$509$			2.18241i			0.0967335i	−0.998830	+	0.0483668i	$0.984598\pi$
$510$	6.81680	−	1.59176i	0.301853	−	0.0704845i
$511$		−	25.6683i		−	1.13550i
$512$	−11.4316	+	19.5274i	−0.505212	+	0.862996i
$513$	−4.60735	−	12.9781i	−0.203419	−	0.572997i
$514$	3.69488	+	31.7964i	0.162974	+	1.40248i
$515$	5.32166			0.234500
$516$	10.2478	+	28.5085i	0.451133	+	1.25502i
$517$	4.20122			0.184770
$518$	0.746614	+	6.42501i	0.0328043	+	0.282299i
$519$	2.56538	+	22.4634i	0.112608	+	0.986034i
$520$	−19.9535	−	55.1665i	−0.875019	−	2.41921i
$521$		−	11.3535i		−	0.497406i	−0.968580	−	0.248703i	$-0.919996\pi$
$521$		−	11.3535i		−	0.497406i	0.968580	−	0.248703i	$-0.0800044\pi$
$522$	10.5979	+	29.6666i	0.463859	+	1.29847i
$523$		−	30.3431i		−	1.32681i	−0.748259	−	0.663406i	$-0.769110\pi$
$523$		−	30.3431i		−	1.32681i	0.748259	−	0.663406i	$-0.230890\pi$
$524$	−21.7580	+	5.12596i	−0.950502	+	0.223929i
$525$	−6.11551	−	53.5496i	−0.266903	−	2.33709i
$526$	−33.1991	+	3.85788i	−1.44755	+	0.168212i
$527$	−0.845235			−0.0368190
$528$	−17.6585	+	11.4800i	−0.768489	+	0.499602i
$529$	−19.8137			−0.861464
$530$	−29.9573	+	3.48116i	−1.30126	+	0.151212i
$531$	−25.2860	+	5.85179i	−1.09732	+	0.253946i
$532$	23.5981	−	5.55947i	1.02311	−	0.241034i
$533$		−	32.2521i		−	1.39700i
$534$	−8.54102	−	36.5773i	−0.369606	−	1.58285i
$535$		−	19.1292i		−	0.827029i
$536$	−10.4806	−	28.9763i	−0.452694	−	1.25159i
$537$	9.68140	−	1.10564i	0.417783	−	0.0477120i
$538$	1.93832	+	16.6803i	0.0835669	+	0.719138i
$539$	−42.3149			−1.82263
$540$	19.3422	+	30.0111i	0.832358	+	1.29147i
$541$	−38.1148			−1.63868			−0.819341	−	0.573307i	$-0.805660\pi$
$541$	−38.1148			−1.63868			−0.819341	+	0.573307i	$0.805660\pi$
$542$	0.606096	+	5.21578i	0.0260340	+	0.224037i
$543$	−7.09522	+	0.810295i	−0.304485	+	0.0347731i
$544$	−2.57251	−	3.93999i	−0.110295	−	0.168926i
$545$			19.0225i			0.814833i
$546$	15.3793	+	65.8627i	0.658175	+	2.81866i
$547$			4.92379i			0.210526i	0.994444	+	0.105263i	$0.0335685\pi$
$547$			4.92379i			0.210526i	−0.994444	+	0.105263i	$0.966432\pi$
$548$	5.47648	+	23.2458i	0.233944	+	0.993013i
$549$	−19.8237	+	4.58767i	−0.846053	+	0.195797i
$550$	29.0551	−	3.37632i	1.23891	−	0.143967i
$551$	19.6796			0.838379
$552$	7.83283	−	3.88825i	0.333387	−	0.165495i
$553$	−19.0336			−0.809392
$554$	−18.8110	+	2.18592i	−0.799204	+	0.0928709i
$555$	0.675197	+	5.91226i	0.0286605	+	0.250962i
$556$	7.15897	+	30.3874i	0.303608	+	1.28871i
$557$		−	2.31879i		−	0.0982501i	−0.998793	−	0.0491250i	$-0.984357\pi$
$557$		−	2.31879i		−	0.0982501i	0.998793	−	0.0491250i	$-0.0156433\pi$
$558$	−1.45031	−	4.05982i	−0.0613965	−	0.171866i
$559$			52.7950i			2.23299i
$560$	−56.2445	+	28.0586i	−2.37676	+	1.18569i
$561$	−0.496972	−	4.35166i	−0.0209822	−	0.183727i
$562$	0.918315	+	7.90259i	0.0387368	+	0.333351i
$563$	24.6545			1.03906			0.519532	−	0.854451i	$-0.326106\pi$
$563$	24.6545			1.03906			0.519532	+	0.854451i	$0.326106\pi$
$564$	−4.50502	+	1.61939i	−0.189695	+	0.0681887i
$565$	11.6364			0.489547
$566$	2.80567	+	24.1442i	0.117931	+	1.01486i
$567$	−18.0840	−	36.9786i	−0.759456	−	1.55296i
$568$	−3.00052	+	1.08528i	−0.125899	+	0.0455372i
$569$			20.6863i			0.867215i	0.901102	+	0.433608i	$0.142760\pi$
$569$			20.6863i			0.867215i	−0.901102	+	0.433608i	$0.857240\pi$
$570$	21.7199	−	5.07174i	0.909748	−	0.212432i
$571$		−	3.32202i		−	0.139022i	−0.997581	−	0.0695110i	$-0.977856\pi$
$571$		−	3.32202i		−	0.139022i	0.997581	−	0.0695110i	$-0.0221439\pi$
$572$	−35.7275	+	8.41704i	−1.49384	+	0.351934i
$573$	−29.1392	+	3.32778i	−1.21731	+	0.139020i
$574$	−34.3251	+	3.98873i	−1.43270	+	0.166486i
$575$	−12.1446			−0.506464
$576$	14.5104	−	19.1167i	0.604600	−	0.796530i
$577$	16.7550			0.697521			0.348761	−	0.937212i	$-0.386603\pi$
$577$	16.7550			0.697521			0.348761	+	0.937212i	$0.386603\pi$
$578$	−22.9090	+	2.66212i	−0.952887	+	0.110730i
$579$	−2.72681	+	0.311409i	−0.113322	+	0.0129417i
$580$	−49.6614	+	11.6997i	−2.06208	+	0.485805i
$581$			6.82964i			0.283341i
$582$	39.9637	−	9.33176i	1.65655	−	0.386814i
$583$			18.8701i			0.781521i
$584$	−14.9270	+	5.39904i	−0.617683	+	0.223414i
$585$	14.0291	+	60.6205i	0.580030	+	2.50635i
$586$	−3.09815	−	26.6612i	−0.127983	−	1.10137i
$587$	−12.3968			−0.511671			−0.255835	−	0.966720i	$-0.582351\pi$
$587$	−12.3968			−0.511671			−0.255835	+	0.966720i	$0.582351\pi$
$588$	45.3747	−	16.3106i	1.87122	−	0.672637i
$589$	−2.69312			−0.110968
$590$	−4.85199	−	41.7539i	−0.199753	−	1.71898i
$591$	−0.931671	−	8.15803i	−0.0383238	−	0.335577i
$592$	3.57933	−	1.78561i	0.147109	−	0.0733883i
$593$		−	28.5969i		−	1.17433i	−0.809467	−	0.587166i	$-0.800244\pi$
$593$		−	28.5969i		−	1.17433i	0.809467	−	0.587166i	$-0.199756\pi$
$594$	20.0491	−	9.85391i	0.822624	−	0.404311i
$595$		−	13.0709i		−	0.535854i
$596$	−6.40615	−	27.1919i	−0.262406	−	1.11383i
$597$	−3.51642	−	30.7910i	−0.143917	−	1.26019i
$598$	15.1380	−	1.75910i	0.619038	−	0.0719349i
$599$	19.8833			0.812411			0.406205	−	0.913782i	$-0.366852\pi$
$599$	19.8833			0.812411			0.406205	+	0.913782i	$0.366852\pi$
$600$	−29.8546	+	14.8199i	−1.21881	+	0.605022i
$601$	0.333153			0.0135896			0.00679480	−	0.999977i	$-0.497837\pi$
$601$	0.333153			0.0135896			0.00679480	+	0.999977i	$0.497837\pi$
$602$	56.1883	−	6.52932i	2.29006	−	0.266115i
$603$	7.36879	+	31.8411i	0.300081	+	1.29667i
$604$	−4.30674	−	18.2807i	−0.175239	−	0.743830i
$605$			6.04003i			0.245562i
$606$	1.01607	+	4.35135i	0.0412749	+	0.176762i
$607$		−	22.8588i		−	0.927808i	−0.885885	−	0.463904i	$-0.846448\pi$
$607$		−	22.8588i		−	0.927808i	0.885885	−	0.463904i	$-0.153552\pi$
$608$	−8.19662	−	12.5537i	−0.332417	−	0.509121i
$609$	58.4427	−	6.67432i	2.36822	−	0.270457i
$610$	−3.80385	−	32.7341i	−0.154013	−	1.32537i
$611$	−8.34285			−0.337516
$612$	2.21029	+	4.47477i	0.0893456	+	0.180882i
$613$	−40.1069			−1.61990			−0.809952	−	0.586497i	$-0.800507\pi$
$613$	−40.1069			−1.61990			−0.809952	+	0.586497i	$0.800507\pi$
$614$	−0.522435	−	4.49583i	−0.0210837	−	0.181437i
$615$	−31.5858	+	3.60719i	−1.27366	+	0.145456i
$616$	13.3766	+	36.9829i	0.538957	+	1.49008i
$617$			10.1413i			0.408272i	0.978943	+	0.204136i	$0.0654384\pi$
$617$			10.1413i			0.408272i	−0.978943	+	0.204136i	$0.934562\pi$
$618$	0.862750	+	3.69477i	0.0347049	+	0.148625i
$619$		−	38.6528i		−	1.55359i	−0.629756	−	0.776793i	$-0.716845\pi$
$619$		−	38.6528i		−	1.55359i	0.629756	−	0.776793i	$-0.283155\pi$
$620$	6.79608	−	1.60109i	0.272937	−	0.0643012i
$621$	−8.74080	+	3.10307i	−0.350756	+	0.124522i
$622$	−10.4401	+	1.21318i	−0.418608	+	0.0486441i
$623$	−70.1352			−2.80991
$624$	35.0666	−	22.7971i	1.40379	−	0.912615i
$625$	−12.7292			−0.509168
$626$	41.6180	−	4.83619i	1.66339	−	0.193293i
$627$	−1.58347	−	13.8654i	−0.0632378	−	0.553732i
$628$	−8.60664	+	2.02764i	−0.343442	+	0.0809115i
$629$			0.831815i			0.0331666i
$630$	62.7818	−	22.4279i	2.50129	−	0.893548i
$631$		−	37.9437i		−	1.51051i	−0.655429	−	0.755257i	$-0.727512\pi$
$631$		−	37.9437i		−	1.51051i	0.655429	−	0.755257i	$-0.272488\pi$
$632$	4.00351	+	11.0687i	0.159251	+	0.440290i
$633$	5.19253	+	45.4676i	0.206385	+	1.80717i
$634$	3.06110	+	26.3424i	0.121572	+	1.04619i
$635$	−57.7614			−2.29219
$636$	−7.27363	−	20.2346i	−0.288418	−	0.802356i
$637$	84.0295			3.32937
$638$	3.68484	+	31.7100i	0.145884	+	1.25541i
$639$	3.29717	−	0.763045i	0.130434	−	0.0301856i
$640$	28.1475	+	26.8063i	1.11263	+	1.05961i
$641$		−	31.9013i		−	1.26002i	−0.776585	−	0.630012i	$-0.783050\pi$
$641$		−	31.9013i		−	1.26002i	0.776585	−	0.630012i	$-0.216950\pi$
$642$	13.2812	−	3.10124i	0.524168	−	0.122396i
$643$		−	10.6433i		−	0.419731i	−0.977730	−	0.209865i	$-0.932697\pi$
$643$		−	10.6433i		−	0.419731i	0.977730	−	0.209865i	$-0.0673026\pi$
$644$	−3.74432	−	15.8934i	−0.147547	−	0.626288i
$645$	51.7042	−	5.90476i	2.03585	−	0.232500i
$646$	3.09695	−	0.359879i	0.121848	−	0.0141592i
$647$	29.6815			1.16690			0.583449	−	0.812150i	$-0.301703\pi$
$647$	29.6815			1.16690			0.583449	+	0.812150i	$0.301703\pi$
$648$	−17.7006	+	18.2945i	−0.695344	+	0.718677i
$649$	−26.3009			−1.03240
$650$	−57.6980	+	6.70476i	−2.26310	+	0.262982i
$651$	−7.99778	+	0.913369i	−0.313458	+	0.0357978i
$652$	−2.93668	−	12.4652i	−0.115009	−	0.488175i
$653$			42.6832i			1.67032i	0.550006	+	0.835160i	$0.314625\pi$
$653$			42.6832i			1.67032i	−0.550006	+	0.835160i	$0.685375\pi$
$654$	−13.2071	+	3.08393i	−0.516438	+	0.120591i
$655$			38.3995i			1.50039i
$656$	9.53949	+	19.1223i	0.372455	+	0.746599i
$657$	16.4028	−	3.79599i	0.639933	−	0.148096i
$658$	1.03179	+	8.87908i	0.0402232	+	0.346142i
$659$	41.4193			1.61347			0.806733	−	0.590916i	$-0.201233\pi$
$659$	41.4193			1.61347			0.806733	+	0.590916i	$0.201233\pi$
$660$	12.2390	+	34.0480i	0.476403	+	1.32531i
$661$	−32.1076			−1.24884			−0.624421	−	0.781088i	$-0.714665\pi$
$661$	−32.1076			−1.24884			−0.624421	+	0.781088i	$0.714665\pi$
$662$	0.140293	+	1.20729i	0.00545262	+	0.0469227i
$663$	0.986896	+	8.64160i	0.0383279	+	0.335612i
$664$	3.97167	−	1.43654i	0.154131	−	0.0557486i
$665$		−	41.6469i		−	1.61500i
$666$	−3.99536	+	1.42728i	−0.154817	+	0.0553061i
$667$		−	13.2543i		−	0.513208i
$668$	5.03386	−	1.18593i	0.194766	−	0.0458848i
$669$	1.98018	+	17.3392i	0.0765583	+	0.670371i
$670$	−52.5781	+	6.10981i	−2.03127	+	0.236042i
$671$	−20.6193			−0.795998
$672$	−28.5992	−	34.5010i	−1.10324	−	1.33091i
$673$	7.66957			0.295640			0.147820	−	0.989014i	$-0.452774\pi$
$673$	7.66957			0.295640			0.147820	+	0.989014i	$0.452774\pi$
$674$	3.06231	−	0.355854i	0.117956	−	0.0137070i
$675$	33.3153	−	11.8273i	1.28231	−	0.455231i
$676$	45.6411	−	10.7526i	1.75543	−	0.413561i
$677$			24.7997i			0.953128i	0.879140	+	0.476564i	$0.158118\pi$
$677$			24.7997i			0.953128i	−0.879140	+	0.476564i	$0.841882\pi$
$678$	1.88650	+	8.07903i	0.0724507	+	0.310273i
$679$		−	76.6284i		−	2.94073i
$680$	−7.60118	+	2.74932i	−0.291492	+	0.105432i
$681$	11.7164	−	1.33804i	0.448972	−	0.0512739i
$682$	−0.504263	−	4.33945i	−0.0193092	−	0.166166i
$683$	−29.1415			−1.11507			−0.557534	−	0.830154i	$-0.688252\pi$
$683$	−29.1415			−1.11507			−0.557534	+	0.830154i	$0.688252\pi$
$684$	7.04250	+	14.2577i	0.269277	+	0.545156i
$685$	41.0253			1.56750
$686$	−5.16590	−	44.4553i	−0.197235	−	1.69731i
$687$	−7.74448	+	0.884442i	−0.295470	+	0.0337436i
$688$	−15.6156	−	31.3021i	−0.595340	−	1.19338i
$689$		−	37.4726i		−	1.42759i
$690$	−3.41584	−	14.6285i	−0.130039	−	0.556896i
$691$			35.3033i			1.34300i	0.741004	+	0.671501i	$0.234350\pi$
$691$			35.3033i			1.34300i	−0.741004	+	0.671501i	$0.765650\pi$
$692$	−5.98667	−	25.4114i	−0.227579	−	0.965997i
$693$	−9.40489	−	40.6392i	−0.357262	−	1.54376i
$694$	−19.9244	+	2.31530i	−0.756321	+	0.0878878i
$695$	53.6291			2.03427
$696$	−16.1741	−	32.5826i	−0.613079	−	1.23504i
$697$	−4.44390			−0.168325
$698$	−8.61920	+	1.00159i	−0.326242	+	0.0379107i
$699$	4.19073	+	36.6955i	0.158508	+	1.38795i
$700$	14.2714	+	60.5772i	0.539408	+	2.28960i
$701$			29.3000i			1.10665i	0.832967	+	0.553323i	$0.186641\pi$
$701$			29.3000i			1.10665i	−0.832967	+	0.553323i	$0.813359\pi$
$702$	−39.8138	+	19.5681i	−1.50267	+	0.738549i
$703$			2.65036i			0.0999602i
$704$	18.6932	−	15.5579i	0.704527	−	0.586360i
$705$	0.933092	+	8.17048i	0.0351423	+	0.307718i
$706$	0.177517	+	1.52763i	0.00668094	+	0.0574930i
$707$	8.34350			0.313790
$708$	28.2027	−	10.1379i	1.05992	−	0.381004i
$709$	15.3272			0.575627			0.287813	−	0.957687i	$-0.407072\pi$
$709$	15.3272			0.575627			0.287813	+	0.957687i	$0.407072\pi$
$710$	0.632675	+	5.44451i	0.0237439	+	0.204329i
$711$	−2.81482	−	12.1630i	−0.105564	−	0.456149i
$712$	14.7522	+	40.7861i	0.552861	+	1.52852i
$713$			1.81383i			0.0679284i
$714$	9.07497	−	2.11906i	0.339622	−	0.0793039i
$715$			63.0535i			2.35807i
$716$	−10.9520	+	2.58017i	−0.409294	+	0.0964255i
$717$	11.4326	−	1.30564i	0.426959	−	0.0487600i
$718$	43.4348	−	5.04731i	1.62097	−	0.188364i
$719$	−31.6812			−1.18151			−0.590756	−	0.806851i	$-0.701170\pi$
$719$	−31.6812			−1.18151			−0.590756	+	0.806851i	$0.701170\pi$
$720$	−26.2481	−	31.7924i	−0.978208	−	1.18483i
$721$	7.08454			0.263842
$722$	−16.8229	+	1.95489i	−0.626082	+	0.0727534i
$723$	−19.7488	+	2.25537i	−0.734466	+	0.0838781i
$724$	8.02637	−	1.89093i	0.298298	−	0.0702760i
$725$			50.5184i			1.87620i
$726$	−4.19352	+	0.979213i	−0.155636	+	0.0363420i
$727$		−	11.1736i		−	0.414407i	−0.978298	−	0.207203i	$-0.933564\pi$
$727$		−	11.1736i		−	0.414407i	0.978298	−	0.207203i	$-0.0664362\pi$
$728$	−26.5634	−	73.4412i	−0.984505	−	2.72191i
$729$	20.9560	−	17.0248i	0.776149	−	0.630550i
$730$	3.14743	+	27.0853i	0.116492	+	1.00247i
$731$	7.27442			0.269054
$732$	22.1103	−	7.94785i	0.817219	−	0.293761i
$733$	21.4104			0.790812			0.395406	−	0.918506i	$-0.370604\pi$
$733$	21.4104			0.790812			0.395406	+	0.918506i	$0.370604\pi$
$734$	−1.71429	−	14.7524i	−0.0632757	−	0.544521i
$735$	−9.39814	−	82.2934i	−0.346656	−	3.03544i
$736$	−8.45499	+	5.52046i	−0.311655	+	0.203487i
$737$			33.1190i			1.21995i
$738$	−7.62514	−	21.3449i	−0.280685	−	0.785715i
$739$			31.3270i			1.15238i	0.817315	+	0.576192i	$0.195462\pi$
$739$			31.3270i			1.15238i	−0.817315	+	0.576192i	$0.804538\pi$
$740$	−1.57567	−	6.68817i	−0.0579226	−	0.245862i
$741$	3.14448	+	27.5342i	0.115515	+	1.01149i
$742$	−39.8811	+	4.63435i	−1.46408	+	0.170133i
$743$	−27.8183			−1.02055			−0.510276	−	0.860010i	$-0.670457\pi$
$743$	−27.8183			−1.02055			−0.510276	+	0.860010i	$0.670457\pi$
$744$	2.21340	+	4.45887i	0.0811472	+	0.163470i
$745$	−47.9896			−1.75820
$746$	−29.7267	+	3.45438i	−1.08837	+	0.126474i
$747$	−4.36434	+	1.01001i	−0.159683	+	0.0369544i
$748$	1.15975	+	4.92276i	0.0424048	+	0.179994i
$749$		−	25.4661i		−	0.930511i
$750$	3.45134	+	14.7805i	0.126025	+	0.539708i
$751$			5.20136i			0.189800i	0.995487	+	0.0949002i	$0.0302532\pi$
$751$			5.20136i			0.189800i	−0.995487	+	0.0949002i	$0.969747\pi$
$752$	4.94647	−	2.46764i	0.180379	−	0.0899855i
$753$	−17.8874	+	2.04280i	−0.651854	+	0.0744436i
$754$	−7.31741	−	62.9702i	−0.266484	−	2.29324i
$755$	−32.2626			−1.17415
$756$	25.7497	+	39.9527i	0.936506	+	1.45307i
$757$	31.0853			1.12981			0.564907	−	0.825155i	$-0.308912\pi$
$757$	31.0853			1.12981			0.564907	+	0.825155i	$0.308912\pi$
$758$	5.02523	+	43.2448i	0.182525	+	1.57072i
$759$	−9.33842	+	1.06647i	−0.338963	+	0.0387106i
$760$	−24.2192	+	8.75998i	−0.878521	+	0.317758i
$761$			7.91869i			0.287052i	0.989647	+	0.143526i	$0.0458441\pi$
$761$			7.91869i			0.287052i	−0.989647	+	0.143526i	$0.954156\pi$
$762$	−9.36432	−	40.1031i	−0.339233	−	1.45278i
$763$			25.3239i			0.916788i
$764$	32.9634	−	7.76584i	1.19257	−	0.280958i
$765$	8.35268	−	1.93301i	0.301992	−	0.0698881i
$766$	11.7575	−	1.36627i	0.424816	−	0.0493654i
$767$	52.2287			1.88587
$768$	−14.0480	+	23.8883i	−0.506915	+	0.861996i
$769$	23.1548			0.834983			0.417491	−	0.908681i	$-0.362909\pi$
$769$	23.1548			0.834983			0.417491	+	0.908681i	$0.362909\pi$
$770$	67.1062	−	7.79803i	2.41834	−	0.281021i
$771$	4.44836	+	38.9514i	0.160204	+	1.40280i
$772$	3.08467	−	0.726716i	0.111020	−	0.0261551i
$773$			30.1412i			1.08410i	0.840345	+	0.542052i	$0.182352\pi$
$773$			30.1412i			1.08410i	−0.840345	+	0.542052i	$0.817648\pi$
$774$	12.4819	+	34.9403i	0.448653	+	1.25590i
$775$		−	6.91335i		−	0.248335i
$776$	−44.5621	+	16.1179i	−1.59969	+	0.578601i
$777$	0.898867	+	7.87079i	0.0322467	+	0.282363i
$778$	2.65963	+	22.8875i	0.0953523	+	0.820557i
$779$	−14.1593			−0.507310
$780$	−24.3044	−	67.6130i	−0.870239	−	2.42093i
$781$	3.42950			0.122717
$782$	−0.242380	−	2.08581i	−0.00866748	−	0.0745883i
$783$	12.9080	+	36.3595i	0.461294	+	1.29938i
$784$	−49.8210	+	24.8541i	−1.77932	+	0.887648i
$785$			15.1894i			0.542132i
$786$	−26.6603	+	6.22535i	−0.950943	+	0.222051i
$787$			15.5581i			0.554587i	0.960785	+	0.277293i	$0.0894374\pi$
$787$			15.5581i			0.554587i	−0.960785	+	0.277293i	$0.910563\pi$
$788$	2.17418	+	9.22867i	0.0774520	+	0.328758i
$789$	−40.6697	+	4.64460i	−1.44788	+	0.165352i
$790$	20.0844	−	2.33390i	0.714571	−	0.0830363i
$791$	15.4912			0.550802
$792$	−21.6549	+	14.0173i	−0.769474	+	0.498083i
$793$	40.9461			1.45404
$794$	−5.52310	+	0.641808i	−0.196007	+	0.0227769i
$795$	−36.6984	+	4.19106i	−1.30156	+	0.148642i
$796$	8.20604	+	34.8319i	0.290855	+	1.23458i
$797$			28.9309i			1.02479i	0.858751	+	0.512393i	$0.171241\pi$
$797$			28.9309i			1.02479i	−0.858751	+	0.512393i	$0.828759\pi$
$798$	28.9150	−	6.75183i	1.02358	−	0.239012i
$799$			1.14953i			0.0406675i
$800$	32.2260	−	21.0411i	1.13936	−	0.743914i
$801$	−10.3721	−	44.8184i	−0.366479	−	1.58358i
$802$	−5.23024	−	45.0090i	−0.184686	−	1.58932i
$803$	17.0611			0.602073
$804$	−12.7660	−	35.5139i	−0.450221	−	1.25248i
$805$	−28.0494			−0.988611
$806$	1.00137	+	8.61736i	0.0352719	+	0.303534i
$807$	2.33359	+	20.4337i	0.0821463	+	0.719302i
$808$	−1.75496	−	4.85204i	−0.0617394	−	0.170694i
$809$		−	22.2920i		−	0.783744i	−0.920020	−	0.391872i	$-0.871828\pi$
$809$		−	22.2920i		−	0.783744i	0.920020	−	0.391872i	$-0.128172\pi$
$810$	23.6167	+	36.8026i	0.829805	+	1.29311i
$811$		−	36.7906i		−	1.29189i	−0.763383	−	0.645946i	$-0.776463\pi$
$811$		−	36.7906i		−	1.29189i	0.763383	−	0.645946i	$-0.223537\pi$
$812$	−66.1125	+	15.5754i	−2.32009	+	0.546591i
$813$	0.729693	+	6.38945i	0.0255915	+	0.224088i
$814$	−4.27055	+	0.496257i	−0.149683	+	0.0173938i
$815$	−21.9992			−0.770597
$816$	−3.14113	−	4.83169i	−0.109962	−	0.169143i
$817$	23.1780			0.810896
$818$	−3.79798	+	0.441342i	−0.132793	+	0.0154312i
$819$	18.6764	+	80.7020i	0.652606	+	2.81996i
$820$	35.7310	−	8.41786i	1.24778	−	0.293965i
$821$			3.11175i			0.108601i	0.998525	+	0.0543004i	$0.0172929\pi$
$821$			3.11175i			0.108601i	−0.998525	+	0.0543004i	$0.982707\pi$
$822$	6.65105	+	28.4834i	0.231982	+	0.993473i
$823$			24.2777i			0.846268i	0.906067	+	0.423134i	$0.139070\pi$
$823$			24.2777i			0.846268i	−0.906067	+	0.423134i	$0.860930\pi$
$824$	−1.49015	−	4.11991i	−0.0519120	−	0.143524i
$825$	35.5931	−	4.06484i	1.23919	−	0.141519i
$826$	−6.45929	−	55.5856i	−0.224747	−	1.93407i
$827$	44.3087			1.54077			0.770383	−	0.637581i	$-0.220065\pi$
$827$	44.3087			1.54077			0.770383	+	0.637581i	$0.220065\pi$
$828$	9.60261	−	4.74315i	0.333714	−	0.164836i
$829$	6.10240			0.211945			0.105972	−	0.994369i	$-0.466204\pi$
$829$	6.10240			0.211945			0.105972	+	0.994369i	$0.466204\pi$
$830$	−0.837448	−	7.20668i	−0.0290682	−	0.250148i
$831$	−23.0439	+	2.63168i	−0.799386	+	0.0912921i
$832$	−37.1213	+	30.8951i	−1.28695	+	1.07110i
$833$		−	11.5781i		−	0.401158i
$834$	8.69438	+	37.2341i	0.301062	+	1.28931i
$835$		−	8.88397i		−	0.307443i
$836$	3.69525	+	15.6851i	0.127803	+	0.542480i
$837$	−1.76643	−	4.97574i	−0.0610569	−	0.171987i
$838$	−48.1533	+	5.59562i	−1.66343	+	0.193297i
$839$	−6.87782			−0.237449			−0.118724	−	0.992927i	$-0.537880\pi$
$839$	−6.87782			−0.237449			−0.118724	+	0.992927i	$0.537880\pi$
$840$	−68.9529	+	34.2285i	−2.37910	+	1.18099i
$841$	−26.1345			−0.901190
$842$	32.9507	−	3.82901i	1.13556	−	0.131956i
$843$	1.10558	+	9.68086i	0.0380783	+	0.333427i
$844$	−12.1175	−	51.4346i	−0.417101	−	1.77045i
$845$		−	80.5495i		−	2.77099i
$846$	−5.52140	+	1.97244i	−0.189830	+	0.0678139i
$847$			8.04088i			0.276288i
$848$	11.0836	+	22.2175i	0.380612	+	0.762951i
$849$	3.37781	+	29.5773i	0.115926	+	1.01509i
$850$	0.923823	+	7.94999i	0.0316869	+	0.272682i
$851$	1.78503			0.0611899
$852$	−3.67749	+	1.32193i	−0.125989	+	0.0452885i
$853$	46.2949			1.58511			0.792553	−	0.609803i	$-0.208751\pi$
$853$	46.2949			1.58511			0.792553	+	0.609803i	$0.208751\pi$
$854$	−5.06393	−	43.5778i	−0.173284	−	1.49120i
$855$	26.6136	−	6.15903i	0.910166	−	0.210634i
$856$	−14.8094	+	5.35651i	−0.506176	+	0.183082i
$857$		−	56.6637i		−	1.93560i	−0.251729	−	0.967798i	$-0.580999\pi$
$857$		−	56.6637i		−	1.93560i	0.251729	−	0.967798i	$-0.419001\pi$
$858$	−43.7774	+	10.2223i	−1.49453	+	0.348983i
$859$		−	39.9897i		−	1.36443i	−0.731152	−	0.682215i	$-0.761017\pi$
$859$		−	39.9897i		−	1.36443i	0.731152	−	0.682215i	$-0.238983\pi$
$860$	−58.4896	+	13.7796i	−1.99448	+	0.469879i
$861$	−42.0491	+	4.80212i	−1.43303	+	0.163656i
$862$	−27.4670	+	3.19178i	−0.935528	+	0.108712i
$863$	−39.6921			−1.35113			−0.675567	−	0.737299i	$-0.736101\pi$
$863$	−39.6921			−1.35113			−0.675567	+	0.737299i	$0.736101\pi$
$864$	17.8177	−	23.3779i	0.606172	−	0.795334i
$865$	−44.8472			−1.52485
$866$	50.3497	−	5.85085i	1.71095	−	0.198820i
$867$	−28.0640	+	3.20499i	−0.953104	+	0.108847i
$868$	9.04738	−	2.13147i	0.307088	−	0.0723469i
$869$		−	12.6512i		−	0.429162i
$870$	−60.8507	+	14.2090i	−2.06303	+	0.481731i
$871$		−	65.7683i		−	2.22847i
$872$	14.7268	−	5.32662i	0.498711	−	0.180382i
$873$	48.9678	−	11.3323i	1.65731	−	0.383541i
$874$	−0.772279	−	6.64587i	−0.0261227	−	0.224800i
$875$	28.3409			0.958098
$876$	−18.2948	+	6.57632i	−0.618124	+	0.222193i
$877$	16.7158			0.564454			0.282227	−	0.959348i	$-0.408927\pi$
$877$	16.7158			0.564454			0.282227	+	0.959348i	$0.408927\pi$
$878$	−1.76650	−	15.2017i	−0.0596165	−	0.513032i
$879$	−3.72994	−	32.6606i	−0.125808	−	1.10162i
$880$	−18.6499	−	37.3844i	−0.628687	−	1.26023i
$881$		−	36.0686i		−	1.21518i	−0.794250	−	0.607591i	$-0.792136\pi$
$881$		−	36.0686i		−	1.21518i	0.794250	−	0.607591i	$-0.207864\pi$
$882$	55.6118	−	19.8665i	1.87255	−	0.668939i
$883$			25.8261i			0.869117i	0.900644	+	0.434558i	$0.143096\pi$
$883$			25.8261i			0.869117i	−0.900644	+	0.434558i	$0.856904\pi$
$884$	−2.30306	−	9.77570i	−0.0774602	−	0.328792i
$885$	−5.84143	−	51.1496i	−0.196357	−	1.71937i
$886$	18.2614	−	2.12206i	0.613505	−	0.0712919i
$887$	34.8534			1.17026			0.585132	−	0.810938i	$-0.301043\pi$
$887$	34.8534			1.17026			0.585132	+	0.810938i	$0.301043\pi$
$888$	4.38807	−	2.17826i	0.147254	−	0.0730975i
$889$	−76.8957			−2.57900
$890$	74.0072	−	8.59995i	2.48073	−	0.288271i
$891$	24.5788	−	12.0200i	0.823421	−	0.402685i
$892$	−4.62103	−	19.6147i	−0.154723	−	0.656749i
$893$			3.66268i			0.122567i
$894$	−7.78010	−	33.3186i	−0.260205	−	1.11434i
$895$			19.3285i			0.646080i
$896$	37.4717	+	35.6863i	1.25184	+	1.19220i
$897$	18.5444	−	2.11782i	0.619179	−	0.0707120i
$898$	−3.47900	−	29.9386i	−0.116096	−	0.999066i
$899$	7.54506			0.251642
$900$	−36.6001	+	18.0784i	−1.22000	+	0.602613i
$901$	−5.16321			−0.172011
$902$	−2.65121	−	22.8151i	−0.0882757	−	0.759659i
$903$	68.8320	−	7.86081i	2.29058	−	0.261591i
$904$	−3.25839	−	9.00865i	−0.108373	−	0.299623i
$905$		−	14.1653i		−	0.470871i
$906$	−5.23043	−	22.3995i	−0.173769	−	0.744175i
$907$		−	36.5836i		−	1.21474i	−0.794419	−	0.607370i	$-0.792225\pi$
$907$		−	36.5836i		−	1.21474i	0.794419	−	0.607370i	$-0.207775\pi$
$908$	−13.2540	+	3.12250i	−0.439849	+	0.103624i
$909$	1.23389	+	5.33174i	0.0409257	+	0.176843i
$910$	−133.261	+	15.4855i	−4.41754	+	0.513338i
$911$	50.0972			1.65980			0.829898	−	0.557916i	$-0.188399\pi$
$911$	50.0972			1.65980			0.829898	+	0.557916i	$0.188399\pi$
$912$	−10.0084	−	15.3949i	−0.331411	−	0.509777i
$913$	−4.53950			−0.150236
$914$	40.6310	−	4.72150i	1.34395	−	0.156173i
$915$	−4.57955	−	40.1001i	−0.151395	−	1.32567i
$916$	8.76084	−	2.06397i	0.289466	−	0.0681954i
$917$			51.1199i			1.68813i
$918$	2.69621	+	5.48579i	0.0889882	+	0.181058i
$919$		−	16.1671i		−	0.533304i	−0.963793	−	0.266652i	$-0.914083\pi$
$919$		−	16.1671i		−	0.533304i	0.963793	−	0.266652i	$-0.0859174\pi$
$920$	5.89988	+	16.3117i	0.194513	+	0.537781i
$921$	−0.628972	−	5.50750i	−0.0207253	−	0.181478i
$922$	2.87530	+	24.7435i	0.0946931	+	0.814884i
$923$	−6.81036			−0.224166
$924$	16.2934	+	45.3269i	0.536013	+	1.49114i
$925$	−6.80358			−0.223700
$926$	−0.213803	−	1.83988i	−0.00702599	−	0.0604624i
$927$	1.04771	+	4.52723i	0.0344113	+	0.148694i
$928$	22.9637	+	35.1706i	0.753821	+	1.15453i
$929$			39.2112i			1.28648i	0.765665	+	0.643239i	$0.222410\pi$
$929$			39.2112i			1.28648i	−0.765665	+	0.643239i	$0.777590\pi$
$930$	8.32732	−	1.94448i	0.273063	−	0.0637620i
$931$		−	36.8906i		−	1.20904i
$932$	−9.77965	−	41.5113i	−0.320343	−	1.35975i
$933$	−12.7893	+	1.46058i	−0.418703	+	0.0478171i
$934$	−42.0941	+	4.89152i	−1.37736	+	0.160055i
$935$	8.68791			0.284125
$936$	43.0027	−	27.8358i	1.40559	−	0.909841i
$937$	38.7211			1.26496			0.632482	−	0.774575i	$-0.282036\pi$
$937$	38.7211			1.26496			0.632482	+	0.774575i	$0.282036\pi$
$938$	−69.9954	+	8.13377i	−2.28543	+	0.265577i
$939$	50.9830	−	5.82241i	1.66377	−	0.190007i
$940$	−2.17750	−	9.24275i	−0.0710222	−	0.301465i
$941$			57.8148i			1.88471i	0.334614	+	0.942355i	$0.391394\pi$
$941$			57.8148i			1.88471i	−0.334614	+	0.942355i	$0.608606\pi$
$942$	−10.5458	+	2.46251i	−0.343601	+	0.0802330i
$943$			9.53636i			0.310547i
$944$	−30.9663	+	15.4481i	−1.00787	+	0.502794i
$945$	76.9458	−	27.3165i	2.50305	−	0.888606i
$946$	4.33988	+	37.3470i	0.141102	+	1.21426i
$947$	26.1922			0.851133			0.425567	−	0.904927i	$-0.360075\pi$
$947$	26.1922			0.851133			0.425567	+	0.904927i	$0.360075\pi$
$948$	4.87650	+	13.5660i	0.158381	+	0.440604i
$949$	−33.8802			−1.09980
$950$	2.94352	+	25.3305i	0.0955004	+	0.821831i
$951$	3.68534	+	32.2701i	0.119505	+	1.04643i
$952$	−10.1192	+	3.66007i	−0.327965	+	0.118624i
$953$			31.0349i			1.00532i	0.864484	+	0.502660i	$0.167645\pi$
$953$			31.0349i			1.00532i	−0.864484	+	0.502660i	$0.832355\pi$
$954$	−8.85937	−	24.7998i	−0.286833	−	0.802924i
$955$		−	58.1753i		−	1.88251i
$956$	−12.9330	+	3.04689i	−0.418284	+	0.0985434i
$957$	4.43626	+	38.8455i	0.143404	+	1.25570i
$958$	32.6448	−	3.79346i	1.05470	−	0.122561i
$959$	54.6156			1.76363
$960$	34.4085	+	32.8989i	1.11053	+	1.06181i
$961$	29.9675			0.966693
$962$	8.48053	−	0.985475i	0.273423	−	0.0317730i
$963$	16.2736	−	3.76610i	0.524409	−	0.121361i
$964$	22.3406	−	5.26322i	0.719542	−	0.169517i
$965$		−	5.44396i		−	0.175247i
$966$	−4.54738	−	19.4744i	−0.146310	−	0.626578i
$967$			1.06012i			0.0340912i	0.999855	+	0.0170456i	$0.00542605\pi$
$967$			1.06012i			0.0340912i	−0.999855	+	0.0170456i	$0.994574\pi$
$968$	4.67605	−	1.69131i	0.150294	−	0.0543608i
$969$	3.79383	−	0.433267i	0.121875	−	0.0139185i
$970$	9.39615	+	80.8589i	0.301692	+	2.59622i
$971$	4.30320			0.138096			0.0690481	−	0.997613i	$-0.478004\pi$
$971$	4.30320			0.138096			0.0690481	+	0.997613i	$0.478004\pi$
$972$	−21.7229	+	22.3633i	−0.696763	+	0.717302i
$973$	71.3945			2.28880
$974$	−2.16271	−	18.6113i	−0.0692977	−	0.596344i
$975$	−70.6814	+	8.07202i	−2.26362	+	0.258511i
$976$	−24.2769	+	12.1110i	−0.777085	+	0.387663i
$977$			21.8853i			0.700172i	0.936718	+	0.350086i	$0.113848\pi$
$977$			21.8853i			0.700172i	−0.936718	+	0.350086i	$0.886152\pi$
$978$	−3.56652	−	15.2738i	−0.114045	−	0.488402i
$979$		−	46.6172i		−	1.48989i
$980$	21.9318	+	93.0933i	0.700587	+	2.97376i
$981$	−16.1827	+	3.74508i	−0.516675	+	0.119571i
$982$	−15.5570	+	1.80779i	−0.496444	+	0.0576889i
$983$	−1.53179			−0.0488565			−0.0244282	−	0.999702i	$-0.507777\pi$
$983$	−1.53179			−0.0488565			−0.0244282	+	0.999702i	$0.507777\pi$
$984$	11.6372	+	23.4429i	0.370979	+	0.747333i
$985$	16.2872			0.518952
$986$	−8.67643	+	1.00824i	−0.276314	+	0.0321088i
$987$	1.24219	+	10.8771i	0.0395395	+	0.346221i
$988$	−7.33808	−	31.1477i	−0.233455	−	0.990940i
$989$		−	15.6105i		−	0.496385i
$990$	14.9073	+	41.7296i	0.473784	+	1.32625i
$991$			34.6230i			1.09983i	0.835219	+	0.549917i	$0.185341\pi$
$991$			34.6230i			1.09983i	−0.835219	+	0.549917i	$0.814659\pi$
$992$	−3.14254	−	4.81304i	−0.0997759	−	0.152814i
$993$	0.168902	+	1.47896i	0.00535993	+	0.0469334i
$994$	0.842259	+	7.24809i	0.0267148	+	0.229895i
$995$	61.4728			1.94882
$996$	4.86775	−	1.74978i	0.154241	−	0.0554440i
$997$	42.2477			1.33800			0.669000	−	0.743263i	$-0.266723\pi$
$997$	42.2477			1.33800			0.669000	+	0.743263i	$0.266723\pi$
$998$	−5.73890	−	49.3862i	−0.181662	−	1.56329i
$999$	−4.89673	+	1.73839i	−0.154926	+	0.0550001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	444.2.c.c.371.2	yes	20
3.2	odd	2	inner	444.2.c.c.371.19	yes	20
4.3	odd	2	inner	444.2.c.c.371.20	yes	20
12.11	even	2	inner	444.2.c.c.371.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
444.2.c.c.371.1	✓	20	12.11	even	2	inner
444.2.c.c.371.2	yes	20	1.1	even	1	trivial
444.2.c.c.371.19	yes	20	3.2	odd	2	inner
444.2.c.c.371.20	yes	20	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	444.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40476 + 0.163239i) q^{2} +(-1.72087 + 0.196528i) q^{3} +(1.94671 - 0.458624i) q^{4} -3.43563i q^{5} +(2.38532 - 0.556987i) q^{6} -4.57374i q^{7} +(-2.65979 + 0.962036i) q^{8} +(2.92275 - 0.676395i) q^{9} +O(q^{10})\)	\(q+(-1.40476 + 0.163239i) q^{2} +(-1.72087 + 0.196528i) q^{3} +(1.94671 - 0.458624i) q^{4} -3.43563i q^{5} +(2.38532 - 0.556987i) q^{6} -4.57374i q^{7} +(-2.65979 + 0.962036i) q^{8} +(2.92275 - 0.676395i) q^{9} +(0.560830 + 4.82624i) q^{10} +3.04006 q^{11} +(-3.25989 + 1.17181i) q^{12} -6.03699 q^{13} +(0.746614 + 6.42501i) q^{14} +(0.675197 + 5.91226i) q^{15} +(3.57933 - 1.78561i) q^{16} +0.831815i q^{17} +(-3.99536 + 1.42728i) q^{18} +2.65036i q^{19} +(-1.57567 - 6.68817i) q^{20} +(0.898867 + 7.87079i) q^{21} +(-4.27055 + 0.496257i) q^{22} +1.78503 q^{23} +(4.38807 - 2.17826i) q^{24} -6.80358 q^{25} +(8.48053 - 0.985475i) q^{26} +(-4.89673 + 1.73839i) q^{27} +(-2.09763 - 8.90373i) q^{28} -7.42526i q^{29} +(-1.91360 - 8.19510i) q^{30} +1.01613i q^{31} +(-4.73662 + 3.09265i) q^{32} +(-5.23153 + 0.597456i) q^{33} +(-0.135785 - 1.16850i) q^{34} -15.7137 q^{35} +(5.37953 - 2.65719i) q^{36} +1.00000 q^{37} +(-0.432643 - 3.72312i) q^{38} +(10.3889 - 1.18644i) q^{39} +(3.30520 + 9.13807i) q^{40} +5.34242i q^{41} +(-2.54752 - 10.9098i) q^{42} -8.74524i q^{43} +(5.91810 - 1.39424i) q^{44} +(-2.32385 - 10.0415i) q^{45} +(-2.50754 + 0.291387i) q^{46} +1.38195 q^{47} +(-5.80862 + 3.77624i) q^{48} -13.9191 q^{49} +(9.55740 - 1.11061i) q^{50} +(-0.163475 - 1.43144i) q^{51} +(-11.7523 + 2.76871i) q^{52} +6.20716i q^{53} +(6.59497 - 3.24136i) q^{54} -10.4445i q^{55} +(4.40010 + 12.1652i) q^{56} +(-0.520869 - 4.56091i) q^{57} +(1.21209 + 10.4307i) q^{58} -8.65144 q^{59} +(4.02592 + 11.1998i) q^{60} -6.78253 q^{61} +(-0.165873 - 1.42743i) q^{62} +(-3.09366 - 13.3679i) q^{63} +(6.14897 - 5.11763i) q^{64} +20.7409i q^{65} +(7.25152 - 1.69327i) q^{66} +10.8942i q^{67} +(0.381491 + 1.61930i) q^{68} +(-3.07179 + 0.350807i) q^{69} +(22.0740 - 2.56509i) q^{70} +1.12810 q^{71} +(-7.12320 + 4.61087i) q^{72} +5.61209 q^{73} +(-1.40476 + 0.163239i) q^{74} +(11.7080 - 1.33709i) q^{75} +(1.21552 + 5.15947i) q^{76} -13.9044i q^{77} +(-14.4002 + 3.36253i) q^{78} -4.16150i q^{79} +(-6.13471 - 12.2973i) q^{80} +(8.08498 - 3.95387i) q^{81} +(-0.872093 - 7.50482i) q^{82} -1.49323 q^{83} +(5.35957 + 14.9099i) q^{84} +2.85781 q^{85} +(1.42757 + 12.2850i) q^{86} +(1.45927 + 12.7779i) q^{87} +(-8.08592 + 2.92465i) q^{88} -15.3343i q^{89} +(4.90362 + 13.7266i) q^{90} +27.6116i q^{91} +(3.47492 - 0.818657i) q^{92} +(-0.199699 - 1.74863i) q^{93} +(-1.94132 + 0.225589i) q^{94} +9.10566 q^{95} +(7.54329 - 6.25290i) q^{96} +16.7540 q^{97} +(19.5530 - 2.27214i) q^{98} +(8.88534 - 2.05628i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4} - q^{6} - 6 q^{9}+O(q^{10}) \) 20 * q + 2 * q^4 - q^6 - 6 * q^9	\( 20 q + 2 q^{4} - q^{6} - 6 q^{9} + 6 q^{10} + 9 q^{12} + 32 q^{13} - 10 q^{16} - 5 q^{18} + 48 q^{21} + 16 q^{22} + 37 q^{24} - 48 q^{25} - 10 q^{28} - 44 q^{30} - 60 q^{33} + 30 q^{34} + 25 q^{36} + 20 q^{37} - 38 q^{40} - 18 q^{42} + 18 q^{45} - 8 q^{46} - 15 q^{48} - 96 q^{49} - 84 q^{52} + 59 q^{54} - 20 q^{57} + 14 q^{58} + 20 q^{60} - 36 q^{61} + 26 q^{64} - 52 q^{66} - 22 q^{69} + 136 q^{70} - 19 q^{72} + 48 q^{73} + 22 q^{76} - 99 q^{78} + 58 q^{81} + 2 q^{82} + 40 q^{84} + 48 q^{85} - 100 q^{88} + 11 q^{90} + 16 q^{93} - 20 q^{94} + 45 q^{96} + 48 q^{97}+O(q^{100}) \) 20 * q + 2 * q^4 - q^6 - 6 * q^9 + 6 * q^10 + 9 * q^12 + 32 * q^13 - 10 * q^16 - 5 * q^18 + 48 * q^21 + 16 * q^22 + 37 * q^24 - 48 * q^25 - 10 * q^28 - 44 * q^30 - 60 * q^33 + 30 * q^34 + 25 * q^36 + 20 * q^37 - 38 * q^40 - 18 * q^42 + 18 * q^45 - 8 * q^46 - 15 * q^48 - 96 * q^49 - 84 * q^52 + 59 * q^54 - 20 * q^57 + 14 * q^58 + 20 * q^60 - 36 * q^61 + 26 * q^64 - 52 * q^66 - 22 * q^69 + 136 * q^70 - 19 * q^72 + 48 * q^73 + 22 * q^76 - 99 * q^78 + 58 * q^81 + 2 * q^82 + 40 * q^84 + 48 * q^85 - 100 * q^88 + 11 * q^90 + 16 * q^93 - 20 * q^94 + 45 * q^96 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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