LMFDB - Embedded newform 403.2.r.a.218.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(218,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

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

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

chi := DirichletCharacter("403.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.r (of order $6$, degree $2$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			218.8
Character	$\chi$	$=$	403.218
Dual form			403.2.r.a.342.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56202 + 0.901835i) q^{2} +(0.553992 + 0.959542i) q^{3} +(0.626612 - 1.08532i) q^{4} +0.771735i q^{5} +(-1.73070 - 0.999218i) q^{6} +(3.80672 + 2.19781i) q^{7} -1.34694i q^{8} +(0.886187 - 1.53492i) q^{9} +O(q^{10})$	\(q+(-1.56202 + 0.901835i) q^{2} +(0.553992 + 0.959542i) q^{3} +(0.626612 - 1.08532i) q^{4} +0.771735i q^{5} +(-1.73070 - 0.999218i) q^{6} +(3.80672 + 2.19781i) q^{7} -1.34694i q^{8} +(0.886187 - 1.53492i) q^{9} +(-0.695977 - 1.20547i) q^{10} +(4.70330 - 2.71545i) q^{11} +1.38855 q^{12} +(3.40753 - 1.17844i) q^{13} -7.92826 q^{14} +(-0.740511 + 0.427534i) q^{15} +(2.46794 + 4.27460i) q^{16} +(-0.585633 + 1.01435i) q^{17} +3.19678i q^{18} +(-5.24197 - 3.02646i) q^{19} +(0.837582 + 0.483578i) q^{20} +4.87028i q^{21} +(-4.89778 + 8.48320i) q^{22} +(-0.575237 - 0.996341i) q^{23} +(1.29244 - 0.746191i) q^{24} +4.40443 q^{25} +(-4.25989 + 4.91378i) q^{26} +5.28771 q^{27} +(4.77068 - 2.75435i) q^{28} +(-2.41217 - 4.17801i) q^{29} +(0.771131 - 1.33564i) q^{30} +1.00000i q^{31} +(-5.37700 - 3.10441i) q^{32} +(5.21118 + 3.00868i) q^{33} -2.11258i q^{34} +(-1.69613 + 2.93778i) q^{35} +(-1.11059 - 1.92360i) q^{36} +(-5.52259 + 3.18847i) q^{37} +10.9175 q^{38} +(3.01851 + 2.61682i) q^{39} +1.03948 q^{40} +(-10.1628 + 5.86751i) q^{41} +(-4.39219 - 7.60749i) q^{42} +(-2.82424 + 4.89172i) q^{43} -6.80614i q^{44} +(1.18455 + 0.683901i) q^{45} +(1.79707 + 1.03754i) q^{46} -4.06481i q^{47} +(-2.73443 + 4.73618i) q^{48} +(6.16077 + 10.6708i) q^{49} +(-6.87982 + 3.97206i) q^{50} -1.29774 q^{51} +(0.856214 - 4.43670i) q^{52} +1.26335 q^{53} +(-8.25953 + 4.76864i) q^{54} +(2.09561 + 3.62970i) q^{55} +(2.96031 - 5.12742i) q^{56} -6.70652i q^{57} +(7.53574 + 4.35076i) q^{58} +(-7.47234 - 4.31416i) q^{59} +1.07159i q^{60} +(-0.487781 + 0.844861i) q^{61} +(-0.901835 - 1.56202i) q^{62} +(6.74694 - 3.89535i) q^{63} +1.32691 q^{64} +(0.909442 + 2.62971i) q^{65} -10.8533 q^{66} +(-7.34983 + 4.24343i) q^{67} +(0.733929 + 1.27120i) q^{68} +(0.637353 - 1.10393i) q^{69} -6.11851i q^{70} +(-3.32559 - 1.92003i) q^{71} +(-2.06744 - 1.19364i) q^{72} +4.37422i q^{73} +(5.75095 - 9.96093i) q^{74} +(2.44001 + 4.22623i) q^{75} +(-6.56937 + 3.79283i) q^{76} +23.8722 q^{77} +(-7.07492 - 1.36535i) q^{78} +8.38024 q^{79} +(-3.29885 + 1.90459i) q^{80} +(0.270787 + 0.469016i) q^{81} +(10.5830 - 18.3304i) q^{82} -12.8430i q^{83} +(5.28583 + 3.05178i) q^{84} +(-0.782805 - 0.451953i) q^{85} -10.1880i q^{86} +(2.67265 - 4.62916i) q^{87} +(-3.65754 - 6.33505i) q^{88} +(-9.37105 + 5.41038i) q^{89} -2.46706 q^{90} +(15.5615 + 3.00313i) q^{91} -1.44180 q^{92} +(-0.959542 + 0.553992i) q^{93} +(3.66579 + 6.34934i) q^{94} +(2.33562 - 4.04541i) q^{95} -6.87927i q^{96} +(0.0599268 + 0.0345988i) q^{97} +(-19.2465 - 11.1120i) q^{98} -9.62559i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) $ 68 * q + 32 * q^4 - 34 * q^9	$ 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) $ 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.56202	+	0.901835i	−1.10452	+	0.637694i	−0.937404	−	0.348244i	$-0.886778\pi$
$2$	−1.56202	+	0.901835i	−1.10452	+	0.637694i	−0.167114	+	0.985938i	$0.553445\pi$
$3$	0.553992	+	0.959542i	0.319847	+	0.553992i	0.980456	−	0.196739i	$-0.0630351\pi$
$3$	0.553992	+	0.959542i	0.319847	+	0.553992i	−0.660609	+	0.750730i	$0.729702\pi$
$4$	0.626612	−	1.08532i	0.313306	−	0.542662i
$5$			0.771735i			0.345130i	0.984998	+	0.172565i	$0.0552055\pi$
$5$			0.771735i			0.345130i	−0.984998	+	0.172565i	$0.944794\pi$
$6$	−1.73070	−	0.999218i	−0.706554	−	0.407929i
$7$	3.80672	+	2.19781i	1.43881	+	0.830695i	0.997767	−	0.0667923i	$-0.0212765\pi$
$7$	3.80672	+	2.19781i	1.43881	+	0.830695i	0.441040	+	0.897488i	$0.354610\pi$
$8$		−	1.34694i		−	0.476214i
$9$	0.886187	−	1.53492i	0.295396	−	0.511640i
$10$	−0.695977	−	1.20547i	−0.220087	−	0.381202i
$11$	4.70330	−	2.71545i	1.41810	−	0.818740i	0.421967	−	0.906611i	$-0.361340\pi$
$11$	4.70330	−	2.71545i	1.41810	−	0.818740i	0.996132	+	0.0878717i	$0.0280066\pi$
$12$	1.38855			0.400840
$13$	3.40753	−	1.17844i	0.945080	−	0.326840i
$13$	3.40753	−	1.17844i	0.945080	−	0.326840i
$14$	−7.92826			−2.11892
$15$	−0.740511	+	0.427534i	−0.191199	+	0.110389i
$16$	2.46794	+	4.27460i	0.616985	+	1.06865i
$17$	−0.585633	+	1.01435i	−0.142037	+	0.246015i	−0.928263	−	0.371923i	$-0.878698\pi$
$17$	−0.585633	+	1.01435i	−0.142037	+	0.246015i	0.786227	+	0.617938i	$0.212032\pi$
$18$			3.19678i			0.753487i
$19$	−5.24197	−	3.02646i	−1.20259	−	0.694316i	−0.241461	−	0.970411i	$-0.577626\pi$
$19$	−5.24197	−	3.02646i	−1.20259	−	0.694316i	−0.961131	+	0.276094i	$0.910960\pi$
$20$	0.837582	+	0.483578i	0.187289	+	0.108131i
$21$			4.87028i			1.06278i
$22$	−4.89778	+	8.48320i	−1.04421	+	1.80862i
$23$	−0.575237	−	0.996341i	−0.119945	−	0.207751i	0.799800	−	0.600266i	$-0.204939\pi$
$23$	−0.575237	−	0.996341i	−0.119945	−	0.207751i	−0.919746	+	0.392515i	$0.871605\pi$
$24$	1.29244	−	0.746191i	0.263819	−	0.152316i
$25$	4.40443			0.880885
$26$	−4.25989	+	4.91378i	−0.835433	+	0.963672i
$27$	5.28771			1.01762
$28$	4.77068	−	2.75435i	0.901574	−	0.520524i
$29$	−2.41217	−	4.17801i	−0.447929	−	0.775836i	0.550322	−	0.834953i	$-0.314505\pi$
$29$	−2.41217	−	4.17801i	−0.447929	−	0.775836i	−0.998251	+	0.0591165i	$0.981172\pi$
$30$	0.771131	−	1.33564i	0.140789	−	0.243853i
$31$			1.00000i			0.179605i
$31$			1.00000i			0.179605i
$32$	−5.37700	−	3.10441i	−0.950528	−	0.548787i
$33$	5.21118	+	3.00868i	0.907150	+	0.523743i
$34$		−	2.11258i		−	0.362304i
$35$	−1.69613	+	2.93778i	−0.286698	+	0.496576i
$36$	−1.11059	−	1.92360i	−0.185098	−	0.320600i
$37$	−5.52259	+	3.18847i	−0.907909	+	0.524181i	−0.879758	−	0.475422i	$-0.842295\pi$
$37$	−5.52259	+	3.18847i	−0.907909	+	0.524181i	−0.0281510	+	0.999604i	$0.508962\pi$
$38$	10.9175			1.77104
$39$	3.01851	+	2.61682i	0.483348	+	0.419027i
$40$	1.03948			0.164356
$41$	−10.1628	+	5.86751i	−1.58717	+	0.916350i	−0.593394	+	0.804912i	$0.702212\pi$
$41$	−10.1628	+	5.86751i	−1.58717	+	0.916350i	−0.993771	+	0.111438i	$0.964454\pi$
$42$	−4.39219	−	7.60749i	−0.677729	−	1.17386i
$43$	−2.82424	+	4.89172i	−0.430692	+	0.745981i	−0.996933	−	0.0782590i	$-0.975064\pi$
$43$	−2.82424	+	4.89172i	−0.430692	+	0.745981i	0.566241	+	0.824240i	$0.308397\pi$
$44$		−	6.80614i		−	1.02606i
$45$	1.18455	+	0.683901i	0.176582	+	0.101950i
$46$	1.79707	+	1.03754i	0.264963	+	0.152977i
$47$		−	4.06481i		−	0.592914i	−0.955046	−	0.296457i	$-0.904195\pi$
$47$		−	4.06481i		−	0.592914i	0.955046	−	0.296457i	$-0.0958052\pi$
$48$	−2.73443	+	4.73618i	−0.394682	+	0.683609i
$49$	6.16077	+	10.6708i	0.880109	+	1.52439i
$50$	−6.87982	+	3.97206i	−0.972953	+	0.561735i
$51$	−1.29774			−0.181720
$52$	0.856214	−	4.43670i	0.118735	−	0.615260i
$53$	1.26335			0.173535			0.0867674	−	0.996229i	$-0.472346\pi$
$53$	1.26335			0.173535			0.0867674	+	0.996229i	$0.472346\pi$
$54$	−8.25953	+	4.76864i	−1.12398	+	0.648930i
$55$	2.09561	+	3.62970i	0.282572	+	0.489429i
$56$	2.96031	−	5.12742i	0.395589	−	0.685180i
$57$		−	6.70652i		−	0.888301i
$58$	7.53574	+	4.35076i	0.989491	+	0.571283i
$59$	−7.47234	−	4.31416i	−0.972816	−	0.561656i	−0.0727223	−	0.997352i	$-0.523169\pi$
$59$	−7.47234	−	4.31416i	−0.972816	−	0.561656i	−0.900094	+	0.435697i	$0.856502\pi$
$60$			1.07159i			0.138342i
$61$	−0.487781	+	0.844861i	−0.0624540	+	0.108173i	−0.895562	−	0.444937i	$-0.853226\pi$
$61$	−0.487781	+	0.844861i	−0.0624540	+	0.108173i	0.833108	+	0.553111i	$0.186559\pi$
$62$	−0.901835	−	1.56202i	−0.114533	−	0.198377i
$63$	6.74694	−	3.89535i	0.850034	−	0.490767i
$64$	1.32691			0.165863
$65$	0.909442	+	2.62971i	0.112802	+	0.326176i
$66$	−10.8533			−1.33595
$67$	−7.34983	+	4.24343i	−0.897925	+	0.518417i	−0.876526	−	0.481354i	$-0.840145\pi$
$67$	−7.34983	+	4.24343i	−0.897925	+	0.518417i	−0.0213986	+	0.999771i	$0.506812\pi$
$68$	0.733929	+	1.27120i	0.0890020	+	0.154156i
$69$	0.637353	−	1.10393i	0.0767283	−	0.132897i
$70$		−	6.11851i		−	0.731302i
$71$	−3.32559	−	1.92003i	−0.394675	−	0.227866i	0.289509	−	0.957175i	$-0.406508\pi$
$71$	−3.32559	−	1.92003i	−0.394675	−	0.227866i	−0.684184	+	0.729309i	$0.739841\pi$
$72$	−2.06744	−	1.19364i	−0.243650	−	0.140671i
$73$			4.37422i			0.511964i	0.966682	+	0.255982i	$0.0823988\pi$
$73$			4.37422i			0.511964i	−0.966682	+	0.255982i	$0.917601\pi$
$74$	5.75095	−	9.96093i	0.668534	−	1.15793i
$75$	2.44001	+	4.22623i	0.281749	+	0.488003i
$76$	−6.56937	+	3.79283i	−0.753558	+	0.435067i
$77$	23.8722			2.72049
$78$	−7.07492	−	1.36535i	−0.801077	−	0.154595i
$79$	8.38024			0.942851			0.471425	−	0.881906i	$-0.343740\pi$
$79$	8.38024			0.942851			0.471425	+	0.881906i	$0.343740\pi$
$80$	−3.29885	+	1.90459i	−0.368823	+	0.212940i
$81$	0.270787	+	0.469016i	0.0300874	+	0.0521129i
$82$	10.5830	−	18.3304i	1.16870	−	2.02425i
$83$		−	12.8430i		−	1.40971i	−0.709353	−	0.704853i	$-0.751013\pi$
$83$		−	12.8430i		−	1.40971i	0.709353	−	0.704853i	$-0.248987\pi$
$84$	5.28583	+	3.05178i	0.576732	+	0.332976i
$85$	−0.782805	−	0.451953i	−0.0849072	−	0.0490212i
$86$		−	10.1880i		−	1.09860i
$87$	2.67265	−	4.62916i	0.286538	−	0.496298i
$88$	−3.65754	−	6.33505i	−0.389895	−	0.675318i
$89$	−9.37105	+	5.41038i	−0.993329	+	0.573499i	−0.906268	−	0.422704i	$-0.861081\pi$
$89$	−9.37105	+	5.41038i	−0.993329	+	0.573499i	−0.0870612	+	0.996203i	$0.527748\pi$
$90$	−2.46706			−0.260051
$91$	15.5615	+	3.00313i	1.63129	+	0.314814i
$92$	−1.44180			−0.150318
$93$	−0.959542	+	0.553992i	−0.0994998	+	0.0574463i
$94$	3.66579	+	6.34934i	0.378097	+	0.654884i
$95$	2.33562	−	4.04541i	0.239630	−	0.415051i
$96$		−	6.87927i		−	0.702112i
$97$	0.0599268	+	0.0345988i	0.00608465	+	0.00351297i	0.503039	−	0.864264i	$-0.332215\pi$
$97$	0.0599268	+	0.0345988i	0.00608465	+	0.00351297i	−0.496955	+	0.867777i	$0.665548\pi$
$98$	−19.2465	−	11.1120i	−1.94419	−	1.12248i
$99$		−	9.62559i		−	0.967408i
$100$	2.75987	−	4.78023i	0.275987	−	0.478023i
$101$	0.771499	+	1.33627i	0.0767670	+	0.132964i	0.901853	−	0.432042i	$-0.142207\pi$
$101$	0.771499	+	1.33627i	0.0767670	+	0.132964i	−0.825086	+	0.565007i	$0.808874\pi$
$102$	2.02710	−	1.17035i	0.200713	−	0.115882i
$103$	−4.80271			−0.473225			−0.236612	−	0.971604i	$-0.576037\pi$
$103$	−4.80271			−0.473225			−0.236612	+	0.971604i	$0.576037\pi$
$104$	−1.58728	−	4.58973i	−0.155646	−	0.450060i
$105$	−3.75856			−0.366798
$106$	−1.97339	+	1.13934i	−0.191672	+	0.110662i
$107$	6.18532	+	10.7133i	0.597957	+	1.03569i	0.993122	+	0.117082i	$0.0373541\pi$
$107$	6.18532	+	10.7133i	0.597957	+	1.03569i	−0.395165	+	0.918610i	$0.629313\pi$
$108$	3.31334	−	5.73888i	0.318827	−	0.552224i
$109$		−	6.83808i		−	0.654970i	−0.944856	−	0.327485i	$-0.893799\pi$
$109$		−	6.83808i		−	0.654970i	0.944856	−	0.327485i	$-0.106201\pi$
$110$	−6.54678	−	3.77978i	−0.624211	−	0.360388i
$111$	−6.11894	−	3.53277i	−0.580784	−	0.335316i
$112$			21.6963i			2.05011i
$113$	3.48893	−	6.04301i	0.328211	−	0.568478i	−0.653946	−	0.756541i	$-0.726888\pi$
$113$	3.48893	−	6.04301i	0.328211	−	0.568478i	0.982157	+	0.188063i	$0.0602209\pi$
$114$	6.04818	+	10.4757i	0.566464	+	0.981144i
$115$	0.768910	−	0.443931i	0.0717013	−	0.0413967i
$116$	−6.04599			−0.561356
$117$	1.21090	−	6.27461i	0.111948	−	0.580088i
$118$	15.5626			1.43266
$119$	−4.45868	+	2.57422i	−0.408727	+	0.235979i
$120$	0.575862	+	0.997422i	0.0525687	+	0.0910517i
$121$	9.24736	−	16.0169i	0.840669	−	1.45608i
$122$		−	1.75959i		−	0.159306i
$123$	−11.2602	−	6.50110i	−1.01530	−	0.586184i
$124$	1.08532	+	0.626612i	0.0974650	+	0.0562714i
$125$			7.25772i			0.649150i
$126$	−7.02592	+	12.1692i	−0.625918	+	1.08412i
$127$	−7.37671	−	12.7768i	−0.654577	−	1.13376i	−0.982000	−	0.188883i	$-0.939513\pi$
$127$	−7.37671	−	12.7768i	−0.654577	−	1.13376i	0.327423	−	0.944878i	$-0.393820\pi$
$128$	8.68133	−	5.01217i	0.767329	−	0.443017i
$129$	−6.25842			−0.551023
$130$	−3.79214	−	3.28750i	−0.332592	−	0.288333i
$131$	−17.3028			−1.51175			−0.755875	−	0.654716i	$-0.772788\pi$
$131$	−17.3028			−1.51175			−0.755875	+	0.654716i	$0.772788\pi$
$132$	6.53078	−	3.77055i	0.568431	−	0.328184i
$133$	−13.3032	−	23.0418i	−1.15353	−	1.99797i
$134$	7.65374	−	13.2567i	0.661183	−	1.14520i
$135$			4.08071i			0.351211i
$136$	1.36626	+	0.788810i	0.117156	+	0.0676399i
$137$	1.33498	+	0.770749i	0.114055	+	0.0658495i	0.555942	−	0.831221i	$-0.312358\pi$
$137$	1.33498	+	0.770749i	0.114055	+	0.0658495i	−0.441887	+	0.897070i	$0.645691\pi$
$138$			2.29915i			0.195717i
$139$	−8.46083	+	14.6546i	−0.717638	+	1.24299i	0.244295	+	0.969701i	$0.421444\pi$
$139$	−8.46083	+	14.6546i	−0.717638	+	1.24299i	−0.961933	+	0.273285i	$0.911890\pi$
$140$	2.12563	+	3.68170i	0.179648	+	0.311160i
$141$	3.90036	−	2.25187i	0.328469	−	0.189642i
$142$	6.92621			0.581235
$143$	12.8267	−	14.7955i	1.07262	−	1.23727i
$144$	8.74822			0.729018
$145$	3.22431	−	1.86156i	0.267764	−	0.154594i
$146$	−3.94483	−	6.83264i	−0.326476	−	0.565474i
$147$	−6.82602	+	11.8230i	−0.563001	+	0.975146i
$148$			7.99174i			0.656917i
$149$	7.99695	+	4.61704i	0.655136	+	0.378243i	0.790421	−	0.612564i	$-0.209862\pi$
$149$	7.99695	+	4.61704i	0.655136	+	0.378243i	−0.135285	+	0.990807i	$0.543195\pi$
$150$	−7.62272	−	4.40098i	−0.622393	−	0.359339i
$151$			21.7043i			1.76627i	0.469119	+	0.883135i	$0.344571\pi$
$151$			21.7043i			1.76627i	−0.469119	+	0.883135i	$0.655429\pi$
$152$	−4.07644	+	7.06061i	−0.330643	+	0.572691i
$153$	1.03796	+	1.79780i	0.0839141	+	0.145343i
$154$	−37.2890	+	21.5288i	−3.00483	+	1.73484i
$155$	−0.771735			−0.0619872
$156$	4.73154	−	1.63632i	0.378826	−	0.131011i
$157$	22.7044			1.81201			0.906003	−	0.423272i	$-0.139119\pi$
$157$	22.7044			1.81201			0.906003	+	0.423272i	$0.139119\pi$
$158$	−13.0901	+	7.55759i	−1.04140	+	0.601250i
$159$	0.699887	+	1.21224i	0.0555046	+	0.0961368i
$160$	2.39578	−	4.14961i	0.189403	−	0.328056i
$161$		−	5.05706i		−	0.398552i
$162$	−0.845950	−	0.488410i	−0.0664641	−	0.0383731i
$163$	−3.16124	−	1.82514i	−0.247608	−	0.142956i	0.371061	−	0.928609i	$-0.378994\pi$
$163$	−3.16124	−	1.82514i	−0.247608	−	0.142956i	−0.618668	+	0.785652i	$0.712328\pi$
$164$			14.7066i			1.14839i
$165$	−2.32190	+	4.02165i	−0.180760	+	0.313085i
$166$	11.5823	+	20.0611i	0.898961	+	1.55705i
$167$	−18.0767	+	10.4366i	−1.39882	+	0.807607i	−0.994269	−	0.106910i	$-0.965904\pi$
$167$	−18.0767	+	10.4366i	−1.39882	+	0.807607i	−0.404548	+	0.914517i	$0.632571\pi$
$168$	6.55996			0.506112
$169$	10.2226	−	8.03114i	0.786351	−	0.617780i
$170$	1.63035			0.125042
$171$	−9.29073	+	5.36401i	−0.710480	+	0.410196i
$172$	3.53940	+	6.13043i	0.269877	+	0.467441i
$173$	−4.05899	+	7.03037i	−0.308599	+	0.534509i	−0.978056	−	0.208341i	$-0.933193\pi$
$173$	−4.05899	+	7.03037i	−0.308599	+	0.534509i	0.669457	+	0.742851i	$0.266527\pi$
$174$			9.64114i			0.730893i
$175$	16.7664	+	9.68011i	1.26742	+	0.731747i
$176$	23.2149	+	13.4031i	1.74989	+	1.01030i
$177$		−	9.56003i		−	0.718576i
$178$	9.75853	−	16.9023i	0.731433	−	1.26688i
$179$	11.5613	+	20.0247i	0.864132	+	1.49672i	0.867907	+	0.496727i	$0.165465\pi$
$179$	11.5613	+	20.0247i	0.864132	+	1.49672i	−0.00377519	+	0.999993i	$0.501202\pi$
$180$	1.48451	−	0.857081i	0.110649	−	0.0638831i
$181$	−8.27560			−0.615120			−0.307560	−	0.951529i	$-0.599513\pi$
$181$	−8.27560			−0.615120			−0.307560	+	0.951529i	$0.599513\pi$
$182$	−27.0158	+	9.34297i	−2.00254	+	0.692547i
$183$	−1.08091			−0.0799029
$184$	−1.34201	+	0.774808i	−0.0989341	+	0.0571196i
$185$	−2.46065	−	4.26198i	−0.180911	−	0.313347i
$186$	0.999218	−	1.73070i	0.0732662	−	0.126901i
$187$			6.36103i			0.465165i
$188$	−4.41164	−	2.54706i	−0.321752	−	0.185764i
$189$	20.1289	+	11.6214i	1.46416	+	0.845332i
$190$			8.42537i			0.611241i
$191$	−5.99143	+	10.3775i	−0.433524	+	0.750886i	−0.997174	−	0.0751277i	$-0.976064\pi$
$191$	−5.99143	+	10.3775i	−0.433524	+	0.750886i	0.563649	+	0.826014i	$0.309397\pi$
$192$	0.735094	+	1.27322i	0.0530509	+	0.0918868i
$193$	5.88123	−	3.39553i	0.423340	−	0.244416i	−0.273165	−	0.961967i	$-0.588071\pi$
$193$	5.88123	−	3.39553i	0.423340	−	0.244416i	0.696505	+	0.717552i	$0.254737\pi$
$194$	−0.124810			−0.00896080
$195$	−2.01949	+	2.32949i	−0.144619	+	0.166818i
$196$	15.4416			1.10297
$197$	2.21397	−	1.27824i	0.157739	−	0.0910707i	−0.419053	−	0.907962i	$-0.637638\pi$
$197$	2.21397	−	1.27824i	0.157739	−	0.0910707i	0.576792	+	0.816891i	$0.304304\pi$
$198$	8.68069	+	15.0354i	0.616910	+	1.06852i
$199$	−2.52695	+	4.37681i	−0.179131	+	0.310264i	−0.941583	−	0.336781i	$-0.890662\pi$
$199$	−2.52695	+	4.37681i	−0.179131	+	0.310264i	0.762452	+	0.647044i	$0.223995\pi$
$200$		−	5.93248i		−	0.419490i
$201$	−8.14349	−	4.70165i	−0.574398	−	0.331629i
$202$	−2.41020	−	1.39153i	−0.169581	−	0.0979076i
$203$		−	21.2060i		−	1.48837i
$204$	−0.813181	+	1.40847i	−0.0569341	+	0.0986127i
$205$	−4.52816	−	7.84300i	−0.316260	−	0.547779i
$206$	7.50194	−	4.33125i	0.522685	−	0.301772i
$207$	−2.03907			−0.141725
$208$	13.4469	+	11.6575i	0.932377	+	0.808303i
$209$	−32.8728			−2.27386
$210$	5.87097	−	3.38960i	0.405135	−	0.233905i
$211$	−5.75706	−	9.97152i	−0.396332	−	0.686468i	0.596938	−	0.802287i	$-0.296384\pi$
$211$	−5.75706	−	9.97152i	−0.396332	−	0.686468i	−0.993270	+	0.115820i	$0.963050\pi$
$212$	0.791632	−	1.37115i	0.0543695	−	0.0941708i
$213$		−	4.25473i		−	0.291529i
$214$	−19.3232	−	11.1563i	−1.32091	−	0.762627i
$215$	−3.77511	−	2.17956i	−0.257461	−	0.148645i
$216$		−	7.12221i		−	0.484605i
$217$	−2.19781	+	3.80672i	−0.149197	+	0.258417i
$218$	6.16682	+	10.6812i	0.417670	+	0.723425i
$219$	−4.19725	+	2.42328i	−0.283624	+	0.163750i
$220$	5.25253			0.354126
$221$	−0.800219	+	4.14655i	−0.0538285	+	0.278927i
$222$	12.7439			0.855315
$223$	−5.01462	+	2.89519i	−0.335804	+	0.193877i	−0.658415	−	0.752655i	$-0.728773\pi$
$223$	−5.01462	+	2.89519i	−0.335804	+	0.193877i	0.322611	+	0.946532i	$0.395439\pi$
$224$	−13.6458	−	23.6353i	−0.911750	−	1.57920i
$225$	3.90314	−	6.76044i	0.260210	−	0.450696i
$226$			12.5858i			0.837192i
$227$	9.72159	+	5.61276i	0.645245	+	0.372532i	0.786632	−	0.617422i	$-0.211823\pi$
$227$	9.72159	+	5.61276i	0.645245	+	0.372532i	−0.141387	+	0.989954i	$0.545156\pi$
$228$	−7.27875	−	4.20239i	−0.482047	−	0.278310i
$229$		−	26.0722i		−	1.72290i	−0.507842	−	0.861450i	$-0.669556\pi$
$229$		−	26.0722i		−	1.72290i	0.507842	−	0.861450i	$-0.330444\pi$
$230$	−0.800704	+	1.38686i	−0.0527969	+	0.0914469i
$231$	13.2250	+	22.9064i	0.870142	+	1.50713i
$232$	−5.62751	+	3.24904i	−0.369464	+	0.213310i
$233$	3.14064			0.205750			0.102875	−	0.994694i	$-0.467196\pi$
$233$	3.14064			0.205750			0.102875	+	0.994694i	$0.467196\pi$
$234$	3.76720	+	10.8931i	0.246270	+	0.712106i
$235$	3.13696			0.204633
$236$	−9.36452	+	5.40661i	−0.609578	+	0.351940i
$237$	4.64258	+	8.04119i	0.301568	+	0.522331i
$238$	4.64305	−	8.04199i	0.300964	−	0.521285i
$239$			10.9723i			0.709737i	0.934916	+	0.354868i	$0.115474\pi$
$239$			10.9723i			0.709737i	−0.934916	+	0.354868i	$0.884526\pi$
$240$	−3.65507	−	2.11026i	−0.235934	−	0.136217i
$241$	−5.75097	−	3.32032i	−0.370453	−	0.213881i	0.303204	−	0.952926i	$-0.401944\pi$
$241$	−5.75097	−	3.32032i	−0.370453	−	0.213881i	−0.673656	+	0.739045i	$0.735277\pi$
$242$			33.3584i			2.14436i
$243$	7.63154	−	13.2182i	0.489563	−	0.847949i
$244$	0.611299	+	1.05880i	0.0391344	+	0.0677828i
$245$	−8.23499	+	4.75448i	−0.526114	+	0.303752i
$246$	23.4517			1.49522
$247$	−21.4287	−	4.13540i	−1.36347	−	0.263129i
$248$	1.34694			0.0855305
$249$	12.3234	−	7.11493i	0.780966	−	0.450891i
$250$	−6.54527	−	11.3367i	−0.413959	−	0.716998i
$251$	−6.09671	+	10.5598i	−0.384821	+	0.666529i	−0.991744	−	0.128231i	$-0.959070\pi$
$251$	−6.09671	+	10.5598i	−0.384821	+	0.666529i	0.606923	+	0.794760i	$0.292403\pi$
$252$		−	9.76348i		−	0.615042i
$253$	−5.41103	−	3.12406i	−0.340189	−	0.196408i
$254$	23.0452	+	13.3051i	1.44598	+	0.834839i
$255$		−	1.00151i		−	0.0627171i
$256$	−10.3672	+	17.9565i	−0.647950	+	1.12228i
$257$	9.43664	+	16.3447i	0.588641	+	1.01956i	0.994411	+	0.105581i	$0.0336703\pi$
$257$	9.43664	+	16.3447i	0.588641	+	1.01956i	−0.405769	+	0.913976i	$0.632996\pi$
$258$	9.77580	−	5.64406i	0.608614	−	0.351384i
$259$	−28.0306			−1.74174
$260$	3.42396	+	0.660770i	0.212345	+	0.0409792i
$261$	−8.55054			−0.529265
$262$	27.0273	−	15.6042i	1.66976	−	0.964034i
$263$	3.64200	+	6.30813i	0.224576	+	0.388976i	0.956192	−	0.292740i	$-0.0945671\pi$
$263$	3.64200	+	6.30813i	0.224576	+	0.388976i	−0.731616	+	0.681716i	$0.761234\pi$
$264$	4.05249	−	7.01913i	0.249414	−	0.431997i
$265$			0.974973i			0.0598921i
$266$	41.5597	+	23.9945i	2.54819	+	1.47120i
$267$	−10.3830	−	5.99461i	−0.635427	−	0.366864i
$268$			10.6359i			0.649693i
$269$	9.02400	−	15.6300i	0.550203	−	0.952980i	−0.448056	−	0.894005i	$-0.647884\pi$
$269$	9.02400	−	15.6300i	0.550203	−	0.952980i	0.998259	−	0.0589746i	$-0.0187831\pi$
$270$	−3.68012	−	6.37416i	−0.223965	−	0.387919i
$271$	0.762776	−	0.440389i	0.0463353	−	0.0267517i	−0.476653	−	0.879091i	$-0.658150\pi$
$271$	0.762776	−	0.440389i	0.0463353	−	0.0267517i	0.522989	+	0.852340i	$0.324817\pi$
$272$	−5.78122			−0.350538
$273$	5.73933	+	16.5956i	0.347360	+	1.00441i
$274$	−2.78035			−0.167967
$275$	20.7153	−	11.9600i	1.24918	−	0.721216i
$276$	−0.798747	−	1.38347i	−0.0480789	−	0.0832751i
$277$	10.6773	−	18.4936i	0.641534	−	1.11117i	−0.343556	−	0.939132i	$-0.611631\pi$
$277$	10.6773	−	18.4936i	0.641534	−	1.11117i	0.985090	−	0.172038i	$-0.0550352\pi$
$278$		−	30.5211i		−	1.83053i
$279$	1.53492	+	0.886187i	0.0918933	+	0.0530546i
$280$	3.95700	+	2.28458i	0.236476	+	0.136530i
$281$			16.9935i			1.01374i	0.862021	+	0.506872i	$0.169198\pi$
$281$			16.9935i			1.01374i	−0.862021	+	0.506872i	$0.830802\pi$
$282$	−4.06163	+	7.03496i	−0.241867	+	0.418926i
$283$	−10.0096	−	17.3371i	−0.595006	−	1.03058i	−0.993546	−	0.113430i	$-0.963816\pi$
$283$	−10.0096	−	17.3371i	−0.595006	−	1.03058i	0.398540	−	0.917151i	$-0.369517\pi$
$284$	−4.16772	+	2.40623i	−0.247308	+	0.142784i
$285$	5.17566			0.306579
$286$	−6.69241	+	34.6785i	−0.395730	+	2.05058i
$287$	−51.5827			−3.04483
$288$	−9.53004	+	5.50217i	−0.561563	+	0.324219i
$289$	7.81407	+	13.5344i	0.459651	+	0.796139i
$290$	−3.35763	+	5.81559i	−0.197167	+	0.341503i
$291$			0.0766697i			0.00449446i
$292$	4.74745	+	2.74094i	0.277824	+	0.160402i
$293$	−23.1301	−	13.3542i	−1.35127	−	0.780158i	−0.362845	−	0.931849i	$-0.618195\pi$
$293$	−23.1301	−	13.3542i	−1.35127	−	0.780158i	−0.988428	+	0.151692i	$0.951528\pi$
$294$		−	24.6238i		−	1.43609i
$295$	3.32938	−	5.76666i	0.193844	−	0.335748i
$296$	4.29467	+	7.43858i	0.249622	+	0.432359i
$297$	24.8697	−	14.3585i	1.44309	−	0.833166i
$298$	−16.6552			−0.964812
$299$	−3.13427	−	2.71718i	−0.181259	−	0.157139i
$300$	6.11577			0.353094
$301$	−21.5022	+	12.4143i	−1.23937	+	0.715548i
$302$	−19.5737	−	33.9026i	−1.12634	−	1.95088i
$303$	−0.854808	+	1.48057i	−0.0491074	+	0.0850565i
$304$		−	29.8764i		−	1.71353i
$305$	−0.652009	−	0.376437i	−0.0373339	−	0.0215547i
$306$	−3.24264	−	1.87214i	−0.185369	−	0.107023i
$307$		−	26.9507i		−	1.53816i	−0.639152	−	0.769080i	$-0.720715\pi$
$307$		−	26.9507i		−	1.53816i	0.639152	−	0.769080i	$-0.279285\pi$
$308$	14.9586	−	25.9091i	0.852347	−	1.47631i
$309$	−2.66066	−	4.60840i	−0.151360	−	0.262162i
$310$	1.20547	−	0.695977i	0.0684660	−	0.0395288i
$311$	17.1492			0.972443			0.486222	−	0.873836i	$-0.338375\pi$
$311$	17.1492			0.972443			0.486222	+	0.873836i	$0.338375\pi$
$312$	3.52470	−	4.06574i	0.199547	−	0.230177i
$313$	−18.2964			−1.03417			−0.517087	−	0.855933i	$-0.672984\pi$
$313$	−18.2964			−1.03417			−0.517087	+	0.855933i	$0.672984\pi$
$314$	−35.4648	+	20.4756i	−2.00139	+	1.15550i
$315$	3.00617	+	5.20684i	0.169379	+	0.293372i
$316$	5.25116	−	9.09528i	0.295401	−	0.511649i
$317$		−	20.2800i		−	1.13904i	−0.821978	−	0.569519i	$-0.807130\pi$
$317$		−	20.2800i		−	1.13904i	0.821978	−	0.569519i	$-0.192870\pi$
$318$	−2.18648	−	1.26236i	−0.122612	−	0.0707899i
$319$	−22.6903	−	13.1003i	−1.27042	−	0.733475i
$320$			1.02402i			0.0572444i
$321$	−6.85323	+	11.8701i	−0.382510	+	0.662527i
$322$	4.56063	+	7.89924i	0.254154	+	0.440208i
$323$	6.13974	−	3.54478i	0.341624	−	0.197237i
$324$	0.678713			0.0377063
$325$	15.0082	−	5.19035i	0.832507	−	0.287909i
$326$	6.58391			0.364649
$327$	6.56143	−	3.78824i	0.362848	−	0.209490i
$328$	7.90316	+	13.6887i	0.436379	+	0.755830i
$329$	8.93370	−	15.4736i	0.492531	−	0.853089i
$330$		−	8.37588i		−	0.461077i
$331$	25.8655	+	14.9335i	1.42170	+	0.820817i	0.996444	−	0.0842572i	$-0.0268517\pi$
$331$	25.8655	+	14.9335i	1.42170	+	0.820817i	0.425253	+	0.905074i	$0.360185\pi$
$332$	−13.9389	−	8.04760i	−0.764994	−	0.441670i
$333$			11.3023i			0.619363i
$334$	18.8242	−	32.6044i	1.03001	−	1.78403i
$335$	−3.27480	−	5.67212i	−0.178921	−	0.309901i
$336$	−20.8185	+	12.0196i	−1.13574	+	0.655720i
$337$	25.6842			1.39911			0.699555	−	0.714579i	$-0.253382\pi$
$337$	25.6842			1.39911			0.699555	+	0.714579i	$0.253382\pi$
$338$	−8.72513	+	21.7639i	−0.474584	+	1.18380i
$339$	7.73136			0.419910
$340$	−0.981031	+	0.566398i	−0.0532039	+	0.0307173i
$341$	2.71545	+	4.70330i	0.147050	+	0.254698i
$342$	9.67490	−	16.7574i	0.523159	−	0.906137i
$343$			23.3915i			1.26302i
$344$	6.58884	+	3.80407i	0.355247	+	0.205102i
$345$	0.851940	+	0.491868i	0.0458669	+	0.0264813i
$346$		−	14.6421i		−	0.787167i
$347$	−2.17506	+	3.76732i	−0.116763	+	0.202240i	−0.918483	−	0.395460i	$-0.870585\pi$
$347$	−2.17506	+	3.76732i	−0.116763	+	0.202240i	0.801720	+	0.597700i	$0.203919\pi$
$348$	−3.34943	−	5.80138i	−0.179548	−	0.310986i
$349$	4.31619	−	2.49195i	0.231040	−	0.133391i	−0.380012	−	0.924982i	$-0.624080\pi$
$349$	4.31619	−	2.49195i	0.231040	−	0.133391i	0.611052	+	0.791591i	$0.290747\pi$
$350$	−34.9194			−1.86652
$351$	18.0180	−	6.23124i	0.961732	−	0.332599i
$352$	−33.7195			−1.79726
$353$	−8.34116	+	4.81577i	−0.443955	+	0.256318i	−0.705274	−	0.708935i	$-0.749176\pi$
$353$	−8.34116	+	4.81577i	−0.443955	+	0.256318i	0.261319	+	0.965253i	$0.415843\pi$
$354$	8.62157	+	14.9330i	0.458231	+	0.793680i
$355$	1.48176	−	2.56648i	0.0786434	−	0.136214i
$356$			13.5608i			0.718723i
$357$	−4.94015	−	2.85219i	−0.261460	−	0.150954i
$358$	−36.1180	−	20.8528i	−1.90890	−	1.10210i
$359$		−	36.8886i		−	1.94691i	−0.228887	−	0.973453i	$-0.573509\pi$
$359$		−	36.8886i		−	1.94691i	0.228887	−	0.973453i	$-0.426491\pi$
$360$	0.921171	−	1.59551i	0.0485500	−	0.0840910i
$361$	8.81886	+	15.2747i	0.464151	+	0.803932i
$362$	12.9267	−	7.46322i	0.679411	−	0.392258i
$363$	20.4918			1.07554
$364$	13.0104	−	15.0075i	0.681931	−	0.786607i
$365$	−3.37574			−0.176694
$366$	1.68840	−	0.974799i	0.0882541	−	0.0509536i
$367$	1.56657	+	2.71338i	0.0817743	+	0.141637i	0.904012	−	0.427507i	$-0.140608\pi$
$367$	1.56657	+	2.71338i	0.0817743	+	0.141637i	−0.822238	+	0.569144i	$0.807275\pi$
$368$	2.83930	−	4.91781i	0.148009	−	0.256359i
$369$			20.7988i			1.08274i
$370$	7.68720	+	4.43820i	0.399638	+	0.230731i
$371$	4.80923	+	2.77661i	0.249683	+	0.144155i
$372$			1.38855i			0.0719930i
$373$	8.77281	−	15.1950i	0.454239	−	0.786765i	−0.544405	−	0.838822i	$-0.683245\pi$
$373$	8.77281	−	15.1950i	0.454239	−	0.786765i	0.998644	+	0.0520574i	$0.0165779\pi$
$374$	−5.73660	−	9.93608i	−0.296632	−	0.513782i
$375$	−6.96408	+	4.02072i	−0.359624	+	0.207629i
$376$	−5.47505			−0.282354
$377$	−13.1431	−	11.3941i	−0.676903	−	0.586826i
$378$	−41.9223			−2.15625
$379$	−24.6650	+	14.2403i	−1.26695	+	0.731476i	−0.974410	−	0.224776i	$-0.927835\pi$
$379$	−24.6650	+	14.2403i	−1.26695	+	0.731476i	−0.292544	+	0.956252i	$0.594502\pi$
$380$	−2.92706	−	5.06981i	−0.150155	−	0.260076i
$381$	8.17327	−	14.1565i	0.418729	−	0.725260i
$382$		−	21.6131i		−	1.10582i
$383$	−9.24097	−	5.33528i	−0.472191	−	0.272620i	0.244965	−	0.969532i	$-0.421223\pi$
$383$	−9.24097	−	5.33528i	−0.472191	−	0.272620i	−0.717157	+	0.696912i	$0.754557\pi$
$384$	9.61877	+	5.55340i	0.490856	+	0.283396i
$385$			18.4230i			0.938924i
$386$	−6.12441	+	10.6078i	−0.311724	+	0.539923i
$387$	5.00560	+	8.66996i	0.254449	+	0.440719i
$388$	0.0751018	−	0.0433600i	0.00381271	−	0.00220127i
$389$	−14.5072			−0.735545			−0.367773	−	0.929916i	$-0.619880\pi$
$389$	−14.5072			−0.735545			−0.367773	+	0.929916i	$0.619880\pi$
$390$	1.05369	−	5.45996i	0.0533555	−	0.276476i
$391$	1.34751			0.0681466
$392$	14.3728	−	8.29816i	0.725938	−	0.419120i
$393$	−9.58559	−	16.6027i	−0.483529	−	0.837497i
$394$	−2.30552	+	3.99328i	−0.116150	+	0.201178i
$395$			6.46732i			0.325406i
$396$	−10.4469	−	6.03151i	−0.524976	−	0.303095i
$397$	26.6092	+	15.3628i	1.33548	+	0.771037i	0.986133	−	0.165958i	$-0.0530717\pi$
$397$	26.6092	+	15.3628i	1.33548	+	0.771037i	0.349342	+	0.936995i	$0.386405\pi$
$398$		−	9.11557i		−	0.456922i
$399$	14.7397	−	25.5299i	0.737907	−	1.27809i
$400$	10.8699	+	18.8271i	0.543493	+	0.941357i
$401$	26.8763	−	15.5171i	1.34214	−	0.774885i	0.355020	−	0.934859i	$-0.384474\pi$
$401$	26.8763	−	15.5171i	1.34214	−	0.774885i	0.987121	+	0.159973i	$0.0511409\pi$
$402$	16.9604			0.845910
$403$	1.17844	+	3.40753i	0.0587022	+	0.169741i
$404$	1.93372			0.0962063
$405$	−0.361956	+	0.208975i	−0.0179857	+	0.0103841i
$406$	19.1243	+	33.1243i	0.949124	+	1.64393i
$407$	−17.3163	+	29.9927i	−0.858336	+	1.48668i
$408$			1.74798i			0.0865377i
$409$	1.56955	+	0.906182i	0.0776094	+	0.0448078i	0.538303	−	0.842752i	$-0.319066\pi$
$409$	1.56955	+	0.906182i	0.0776094	+	0.0448078i	−0.460693	+	0.887559i	$0.652399\pi$
$410$	14.1462	+	8.16730i	0.698630	+	0.403354i
$411$			1.70795i			0.0842471i
$412$	−3.00943	+	5.21249i	−0.148264	+	0.256801i
$413$	−18.9634	−	32.8456i	−0.933129	−	1.61623i
$414$	3.18508	−	1.83891i	0.156538	−	0.0903773i
$415$	9.91142			0.486532
$416$	−21.9806	−	4.24192i	−1.07769	−	0.207977i
$417$	−18.7489			−0.918139
$418$	51.3481	−	29.6458i	2.51152	−	1.45002i
$419$	9.29506	+	16.0995i	0.454094	+	0.786513i	0.998636	−	0.0522205i	$-0.0166299\pi$
$419$	9.29506	+	16.0995i	0.454094	+	0.786513i	−0.544542	+	0.838734i	$0.683297\pi$
$420$	−2.35516	+	4.07926i	−0.114920	+	0.199048i
$421$		−	5.36839i		−	0.261639i	−0.991406	−	0.130820i	$-0.958239\pi$
$421$		−	5.36839i		−	0.261639i	0.991406	−	0.130820i	$-0.0417609\pi$
$422$	17.9853	+	10.3838i	0.875512	+	0.505477i
$423$	−6.23917	−	3.60218i	−0.303359	−	0.175144i
$424$		−	1.70166i		−	0.0826397i
$425$	−2.57938	+	4.46761i	−0.125118	+	0.216711i
$426$	3.83706	+	6.64599i	0.185906	+	0.321999i
$427$	−3.71370	+	2.14410i	−0.179718	+	0.103760i
$428$	15.5032			0.749375
$429$	21.3028	+	4.11111i	1.02851	+	0.198486i
$430$	7.86242			0.379160
$431$	−19.4215	+	11.2130i	−0.935500	+	0.540111i	−0.888547	−	0.458786i	$-0.848285\pi$
$431$	−19.4215	+	11.2130i	−0.935500	+	0.540111i	−0.0469534	+	0.998897i	$0.514951\pi$
$432$	13.0497	+	22.6028i	0.627856	+	1.08748i
$433$	−6.64763	+	11.5140i	−0.319465	+	0.553329i	−0.980376	−	0.197134i	$-0.936836\pi$
$433$	−6.64763	+	11.5140i	−0.319465	+	0.553329i	0.660912	+	0.750464i	$0.270170\pi$
$434$		−	7.92826i		−	0.380569i
$435$	3.57248	+	2.06257i	0.171287	+	0.0988928i
$436$	−7.42154	−	4.28483i	−0.355427	−	0.205206i
$437$			6.96372i			0.333120i
$438$	4.37080	−	7.57045i	0.208845	−	0.361730i
$439$	−15.8070	−	27.3785i	−0.754426	−	1.30670i	−0.945659	−	0.325160i	$-0.894582\pi$
$439$	−15.8070	−	27.3785i	−0.754426	−	1.30670i	0.191233	−	0.981545i	$-0.438751\pi$
$440$	4.88897	−	2.82265i	0.233073	−	0.134565i
$441$	21.8384			1.03992
$442$	−2.48954	−	7.19867i	−0.118415	−	0.342406i
$443$	26.6865			1.26791			0.633957	−	0.773368i	$-0.281430\pi$
$443$	26.6865			1.26791			0.633957	+	0.773368i	$0.281430\pi$
$444$	−7.66841	+	4.42736i	−0.363926	+	0.210113i
$445$	−4.17537	−	7.23196i	−0.197932	−	0.342828i
$446$	5.22198	−	9.04473i	0.247268	−	0.428280i
$447$			10.2312i			0.483920i
$448$	5.05116	+	2.91629i	0.238645	+	0.137782i
$449$	17.1490	+	9.90098i	0.809311	+	0.467256i	0.846717	−	0.532044i	$-0.178576\pi$
$449$	17.1490	+	9.90098i	0.809311	+	0.467256i	−0.0374054	+	0.999300i	$0.511909\pi$
$450$			14.0800i			0.663736i
$451$	−31.8659	+	55.1933i	−1.50050	+	2.59895i
$452$	−4.37242	−	7.57325i	−0.205661	−	0.356215i
$453$	−20.8262	+	12.0240i	−0.978499	+	0.564936i
$454$	−20.2471			−0.950246
$455$	−2.31762	+	12.0094i	−0.108652	+	0.563008i
$456$	−9.03326			−0.423021
$457$	−19.2636	+	11.1219i	−0.901114	+	0.520258i	−0.877561	−	0.479464i	$-0.840831\pi$
$457$	−19.2636	+	11.1219i	−0.901114	+	0.520258i	−0.0235524	+	0.999723i	$0.507498\pi$
$458$	23.5128	+	40.7254i	1.09868	+	1.90297i
$459$	−3.09665	+	5.36356i	−0.144539	+	0.250350i
$460$		−	1.11269i		−	0.0518794i
$461$	4.55219	+	2.62821i	0.212017	+	0.122408i	0.602248	−	0.798309i	$-0.294272\pi$
$461$	4.55219	+	2.62821i	0.212017	+	0.122408i	−0.390232	+	0.920717i	$0.627605\pi$
$462$	−41.3156	−	23.8536i	−1.92217	−	1.10977i
$463$			1.95426i			0.0908223i	0.998968	+	0.0454112i	$0.0144598\pi$
$463$			1.95426i			0.0908223i	−0.998968	+	0.0454112i	$0.985540\pi$
$464$	11.9062	−	20.6221i	0.552731	−	0.957358i
$465$	−0.427534	−	0.740511i	−0.0198264	−	0.0343404i
$466$	−4.90575	+	2.83234i	−0.227255	+	0.131206i
$467$	32.8358			1.51946			0.759730	−	0.650239i	$-0.225331\pi$
$467$	32.8358			1.51946			0.759730	+	0.650239i	$0.225331\pi$
$468$	−6.05122	−	5.24597i	−0.279718	−	0.242495i
$469$	−37.3051			−1.72259
$470$	−4.90000	+	2.82902i	−0.226020	+	0.130493i
$471$	12.5780	+	21.7858i	0.579565	+	1.00384i
$472$	−5.81090	+	10.0648i	−0.267468	+	0.463268i
$473$			30.6763i			1.41050i
$474$	−14.5037	−	8.37369i	−0.666175	−	0.384616i
$475$	−23.0879	−	13.3298i	−1.05934	−	0.611613i
$476$			6.45216i			0.295734i
$477$	1.11957	−	1.93915i	0.0512614	−	0.0887874i
$478$	−9.89517	−	17.1389i	−0.452595	−	0.783917i
$479$	−12.1735	+	7.02839i	−0.556222	+	0.321135i	−0.751628	−	0.659587i	$-0.770731\pi$
$479$	−12.1735	+	7.02839i	−0.556222	+	0.321135i	0.195405	+	0.980723i	$0.437398\pi$
$480$	5.30897			0.242320
$481$	−15.0610	+	17.3729i	−0.686723	+	0.792134i
$482$	11.9775			0.545562
$483$	4.85246	−	2.80157i	0.220794	−	0.127476i
$484$	−11.5890	−	20.0728i	−0.526773	−	0.912398i
$485$	−0.0267011	+	0.0462476i	−0.00121243	+	0.00210000i
$486$			27.5295i			1.24877i
$487$	−6.63768	−	3.83227i	−0.300782	−	0.173657i	0.342012	−	0.939696i	$-0.388892\pi$
$487$	−6.63768	−	3.83227i	−0.300782	−	0.173657i	−0.642794	+	0.766039i	$0.722225\pi$
$488$	1.13797	+	0.657010i	0.0515137	+	0.0297414i
$489$		−	4.04446i		−	0.182897i
$490$	8.57550	−	14.8532i	0.387402	−	0.671000i
$491$	−16.9491	−	29.3567i	−0.764901	−	1.32485i	−0.940299	−	0.340350i	$-0.889455\pi$
$491$	−16.9491	−	29.3567i	−0.764901	−	1.32485i	0.175398	−	0.984498i	$-0.443879\pi$
$492$	−14.1116	+	8.14733i	−0.636200	+	0.367310i
$493$	5.65059			0.254490
$494$	37.2016	−	12.8655i	1.67378	−	0.578848i
$495$	7.42840			0.333882
$496$	−4.27460	+	2.46794i	−0.191935	+	0.110814i
$497$	−8.43975	−	14.6181i	−0.378574	−	0.655710i
$498$	−12.8330	+	22.2274i	−0.575060	+	0.996033i
$499$		−	31.4186i		−	1.40649i	−0.710947	−	0.703245i	$-0.751734\pi$
$499$		−	31.4186i		−	1.40649i	0.710947	−	0.703245i	$-0.248266\pi$
$500$	7.87698	+	4.54778i	0.352269	+	0.203383i
$501$	−20.0287	−	11.5636i	−0.894815	−	0.516622i
$502$		−	21.9929i		−	0.981591i
$503$	8.42508	−	14.5927i	0.375656	−	0.650654i	−0.614769	−	0.788707i	$-0.710751\pi$
$503$	8.42508	−	14.5927i	0.375656	−	0.650654i	0.990425	+	0.138052i	$0.0440842\pi$
$504$	−5.24678	−	9.08769i	−0.233710	−	0.404798i
$505$	−1.03125	+	0.595392i	−0.0458900	+	0.0264946i
$506$	11.2695			0.500992
$507$	13.3694	+	5.35979i	0.593757	+	0.238037i
$508$	−18.4893			−0.820332
$509$	20.5415	−	11.8596i	0.910484	−	0.525668i	0.0298971	−	0.999553i	$-0.490482\pi$
$509$	20.5415	−	11.8596i	0.910484	−	0.525668i	0.880587	+	0.473885i	$0.157149\pi$
$510$	0.903199	+	1.56439i	0.0399943	+	0.0692722i
$511$	−9.61373	+	16.6515i	−0.425286	+	0.736617i
$512$		−	17.3493i		−	0.766740i
$513$	−27.7180	−	16.0030i	−1.22378	−	0.706550i
$514$	−29.4805	−	17.0206i	−1.30033	−	0.750746i
$515$		−	3.70641i		−	0.163324i
$516$	−3.92160	+	6.79241i	−0.172639	+	0.299019i
$517$	−11.0378	−	19.1180i	−0.485442	−	0.840811i
$518$	43.7845	−	25.2790i	1.92378	−	1.11070i
$519$	−8.99458			−0.394818
$520$	3.54205	−	1.22496i	0.155329	−	0.0537181i
$521$	8.07286			0.353678			0.176839	−	0.984240i	$-0.443413\pi$
$521$	8.07286			0.353678			0.176839	+	0.984240i	$0.443413\pi$
$522$	13.3561	−	7.71117i	0.584583	−	0.337509i
$523$	−16.4687	−	28.5247i	−0.720128	−	1.24730i	−0.960948	−	0.276728i	$-0.910750\pi$
$523$	−16.4687	−	28.5247i	−0.720128	−	1.24730i	0.240820	−	0.970570i	$-0.422584\pi$
$524$	−10.8421	+	18.7791i	−0.473641	+	0.820370i
$525$			21.4508i			0.936189i
$526$	−11.3778	−	6.56897i	−0.496095	−	0.286421i
$527$	−1.01435	−	0.585633i	−0.0441856	−	0.0255106i
$528$			29.7009i			1.29257i
$529$	10.8382	−	18.7723i	0.471226	−	0.816188i
$530$	−0.879264	−	1.52293i	−0.0381928	−	0.0661519i
$531$	−13.2438	+	7.64630i	−0.574731	+	0.331821i
$532$	−33.3437			−1.44563
$533$	−27.7156	+	31.9700i	−1.20050	+	1.38477i
$534$	21.6246			0.935787
$535$	−8.26781	+	4.77342i	−0.357449	+	0.206373i
$536$	5.71563	+	9.89976i	0.246878	+	0.427604i
$537$	−12.8097	+	22.1871i	−0.552780	+	0.957443i
$538$			32.5526i			1.40344i
$539$	57.9519	+	33.4585i	2.49616	+	1.44116i
$540$	4.42889	+	2.55702i	0.190589	+	0.110037i
$541$		−	22.2562i		−	0.956871i	−0.878123	−	0.478435i	$-0.841204\pi$
$541$		−	22.2562i		−	0.956871i	0.878123	−	0.478435i	$-0.158796\pi$
$542$	−0.794316	+	1.37580i	−0.0341188	+	0.0590955i
$543$	−4.58461	−	7.94078i	−0.196744	−	0.340771i
$544$	6.29789	−	3.63609i	0.270020	−	0.155896i
$545$	5.27718			0.226050
$546$	−23.9315	−	20.7469i	−1.02417	−	0.887884i
$547$	−0.321415			−0.0137427			−0.00687136	−	0.999976i	$-0.502187\pi$
$547$	−0.321415			−0.0137427			−0.00687136	+	0.999976i	$0.502187\pi$
$548$	1.67302	−	0.965921i	0.0714680	−	0.0412621i
$549$	0.864530	+	1.49741i	0.0368972	+	0.0639079i
$550$	−21.5719	+	37.3636i	−0.919829	+	1.59319i
$551$			29.2013i			1.24402i
$552$	−1.48692	−	0.858475i	−0.0632876	−	0.0365391i
$553$	31.9013	+	18.4182i	1.35658	+	0.783222i
$554$			38.5165i			1.63641i
$555$	2.72636	−	4.72220i	0.115728	−	0.200446i
$556$	10.6033	+	18.3655i	0.449681	+	0.778870i
$557$	28.4115	−	16.4034i	1.20383	−	0.695034i	0.242428	−	0.970169i	$-0.422056\pi$
$557$	28.4115	−	16.4034i	1.20383	−	0.695034i	0.961405	+	0.275136i	$0.0887228\pi$
$558$	−3.19678			−0.135330
$559$	−3.85909	+	19.9969i	−0.163222	+	0.845779i
$560$	−16.7438			−0.707553
$561$	−6.10367	+	3.52396i	−0.257697	+	0.148782i
$562$	−15.3253	−	26.5442i	−0.646458	−	1.11970i
$563$	6.55543	−	11.3543i	0.276278	−	0.478528i	−0.694178	−	0.719803i	$-0.744232\pi$
$563$	6.55543	−	11.3543i	0.276278	−	0.478528i	0.970457	+	0.241275i	$0.0775655\pi$
$564$		−	5.64420i		−	0.237664i
$565$	4.66360	+	2.69253i	0.196199	+	0.113276i
$566$	31.2703	+	18.0539i	1.31439	+	0.758863i
$567$			2.38055i			0.0999738i
$568$	−2.58616	+	4.47936i	−0.108513	+	0.187950i
$569$	−3.96039	−	6.85959i	−0.166028	−	0.287569i	0.770992	−	0.636845i	$-0.219761\pi$
$569$	−3.96039	−	6.85959i	−0.166028	−	0.287569i	−0.937020	+	0.349276i	$0.886428\pi$
$570$	−8.08450	+	4.66759i	−0.338622	+	0.195504i
$571$	−25.1527			−1.05261			−0.526304	−	0.850297i	$-0.676422\pi$
$571$	−25.1527			−1.05261			−0.526304	+	0.850297i	$0.676422\pi$
$572$	−8.02062	−	23.1922i	−0.335359	−	0.969713i
$573$	−13.2768			−0.554646
$574$	80.5734	−	46.5191i	3.36307	−	1.94167i
$575$	−2.53359	−	4.38831i	−0.105658	−	0.183005i
$576$	1.17589	−	2.03669i	0.0489952	−	0.0848623i
$577$		−	8.99328i		−	0.374395i	−0.982322	−	0.187198i	$-0.940060\pi$
$577$		−	8.99328i		−	0.374395i	0.982322	−	0.187198i	$-0.0599404\pi$
$578$	−24.4115	−	14.0940i	−1.01539	−	0.586233i
$579$	6.51630	+	3.76219i	0.270808	+	0.156351i
$580$		−	4.66590i		−	0.193741i
$581$	28.2266	−	48.8899i	1.17104	−	2.02829i
$582$	−0.0691434	−	0.119760i	−0.00286609	−	0.00496421i
$583$	5.94193	−	3.43057i	0.246089	−	0.142080i
$584$	5.89180			0.243804
$585$	4.84233	+	0.934494i	0.200206	+	0.0386366i
$586$	48.1730			1.99001
$587$	−4.64202	+	2.68007i	−0.191597	+	0.110618i	−0.592730	−	0.805401i	$-0.701950\pi$
$587$	−4.64202	+	2.68007i	−0.191597	+	0.110618i	0.401133	+	0.916020i	$0.368616\pi$
$588$	8.55454	+	14.8169i	0.352783	+	0.611039i
$589$	3.02646	−	5.24197i	0.124703	−	0.215992i
$590$			12.0102i			0.494453i
$591$	2.45304	+	1.41627i	0.100905	+	0.0582574i
$592$	−27.2588	−	15.7379i	−1.12033	−	0.646824i
$593$			15.8227i			0.649759i	0.945755	+	0.324879i	$0.105324\pi$
$593$			15.8227i			0.649759i	−0.945755	+	0.324879i	$0.894676\pi$
$594$	−25.8980	+	44.8567i	−1.06261	+	1.84049i
$595$	−1.98662	−	3.44092i	−0.0814433	−	0.141064i
$596$	10.0220	−	5.78619i	0.410516	−	0.237012i
$597$	−5.59964			−0.229178
$598$	7.34625	+	1.41771i	0.300410	+	0.0579745i
$599$	22.5066			0.919593			0.459797	−	0.888024i	$-0.347922\pi$
$599$	22.5066			0.919593			0.459797	+	0.888024i	$0.347922\pi$
$600$	5.69246	−	3.28654i	0.232394	−	0.134173i
$601$	4.61763	+	7.99798i	0.188357	+	0.326244i	0.944703	−	0.327928i	$-0.106350\pi$
$601$	4.61763	+	7.99798i	0.188357	+	0.326244i	−0.756345	+	0.654172i	$0.773017\pi$
$602$	22.3913	−	38.7829i	0.912601	−	1.58067i
$603$			15.0419i			0.612553i
$604$	23.5562	+	13.6002i	0.958488	+	0.553383i
$605$	12.3608	+	7.13651i	0.502538	+	0.290140i
$606$		−	3.08358i		−	0.125262i
$607$	−4.11052	+	7.11962i	−0.166841	+	0.288977i	−0.937307	−	0.348504i	$-0.886690\pi$
$607$	−4.11052	+	7.11962i	−0.166841	+	0.288977i	0.770467	+	0.637480i	$0.220023\pi$
$608$	18.7907	+	32.5465i	0.762064	+	1.31993i
$609$	20.3481	−	11.7480i	0.824545	−	0.476051i
$610$	1.35794			0.0549813
$611$	−4.79013	−	13.8510i	−0.193788	−	0.560351i
$612$	2.60159			0.105163
$613$	5.74587	−	3.31738i	0.232074	−	0.133988i	−0.379455	−	0.925210i	$-0.623888\pi$
$613$	5.74587	−	3.31738i	0.232074	−	0.133988i	0.611528	+	0.791223i	$0.290555\pi$
$614$	24.3051	+	42.0977i	0.980875	+	1.69893i
$615$	5.01712	−	8.68991i	0.202310	−	0.350411i
$616$		−	32.1544i		−	1.29554i
$617$	21.0292	+	12.1412i	0.846605	+	0.488788i	0.859504	−	0.511129i	$-0.170773\pi$
$617$	21.0292	+	12.1412i	0.846605	+	0.488788i	−0.0128986	+	0.999917i	$0.504106\pi$
$618$	8.31202	+	4.79895i	0.334359	+	0.193042i
$619$			6.89786i			0.277248i	0.990345	+	0.138624i	$0.0442680\pi$
$619$			6.89786i			0.277248i	−0.990345	+	0.138624i	$0.955732\pi$
$620$	−0.483578	+	0.837582i	−0.0194210	+	0.0336381i
$621$	−3.04169	−	5.26836i	−0.122059	−	0.211412i
$622$	−26.7875	+	15.4658i	−1.07408	+	0.620121i
$623$	−47.5640			−1.90561
$624$	−3.73638	+	19.3611i	−0.149575	+	0.775062i
$625$	16.4211			0.656844
$626$	28.5794	−	16.5003i	1.14226	−	0.659486i
$627$	−18.2112	−	31.5428i	−0.727287	−	1.25970i
$628$	14.2268	−	24.6416i	0.567712	−	0.983307i
$629$		−	7.46909i		−	0.297812i
$630$	−9.39143	−	5.42214i	−0.374163	−	0.216023i
$631$	−6.94561	−	4.01005i	−0.276500	−	0.159638i	0.355338	−	0.934738i	$-0.384366\pi$
$631$	−6.94561	−	4.01005i	−0.276500	−	0.159638i	−0.631838	+	0.775100i	$0.717699\pi$
$632$		−	11.2877i		−	0.448999i
$633$	6.37872	−	11.0483i	0.253532	−	0.439129i
$634$	18.2892	+	31.6778i	0.726357	+	1.25809i
$635$	9.86033	−	5.69286i	0.391295	−	0.225914i
$636$	1.75423			0.0695597
$637$	33.5679	+	29.1009i	1.33001	+	1.15302i
$638$	47.2571			1.87093
$639$	−5.89420	+	3.40302i	−0.233171	+	0.134621i
$640$	3.86806	+	6.69968i	0.152899	+	0.264828i
$641$	−15.5726	+	26.9726i	−0.615082	+	1.06535i	0.375288	+	0.926908i	$0.377544\pi$
$641$	−15.5726	+	26.9726i	−0.615082	+	1.06535i	−0.990370	+	0.138445i	$0.955790\pi$
$642$		−	24.7219i		−	0.975697i
$643$	23.0748	+	13.3222i	0.909981	+	0.525378i	0.880425	−	0.474185i	$-0.157257\pi$
$643$	23.0748	+	13.3222i	0.909981	+	0.525378i	0.0295560	+	0.999563i	$0.490591\pi$
$644$	−5.48855	−	3.16881i	−0.216279	−	0.124869i
$645$		−	4.82984i		−	0.190175i
$646$	−6.39362	+	11.0741i	−0.251553	+	0.435703i
$647$	−0.622426	−	1.07807i	−0.0244701	−	0.0423835i	0.853531	−	0.521042i	$-0.174457\pi$
$647$	−0.622426	−	1.07807i	−0.0244701	−	0.0423835i	−0.878001	+	0.478659i	$0.841123\pi$
$648$	0.631735	−	0.364732i	0.0248169	−	0.0143280i
$649$	−46.8596			−1.83940
$650$	−18.7624	+	21.6424i	−0.735921	+	0.848884i
$651$	−4.87028			−0.190881
$652$	−3.96175	+	2.28732i	−0.155154	+	0.0895782i
$653$	−9.17302	−	15.8881i	−0.358968	−	0.621751i	0.628821	−	0.777550i	$-0.283538\pi$
$653$	−9.17302	−	15.8881i	−0.358968	−	0.621751i	−0.987789	+	0.155800i	$0.950205\pi$
$654$	−6.83273	+	11.8346i	−0.267181	+	0.462771i
$655$		−	13.3531i		−	0.521751i
$656$	−50.1624	−	28.9613i	−1.95851	−	1.13075i
$657$	6.71409	+	3.87638i	0.261941	+	0.151232i
$658$			32.2269i			1.25634i
$659$	−8.18629	+	14.1791i	−0.318893	+	0.552338i	−0.980257	−	0.197726i	$-0.936644\pi$
$659$	−8.18629	+	14.1791i	−0.318893	+	0.552338i	0.661365	+	0.750065i	$0.269978\pi$
$660$	2.90986	+	5.04003i	0.113266	+	0.196183i
$661$	17.9932	−	10.3884i	0.699853	−	0.404060i	−0.107440	−	0.994212i	$-0.534265\pi$
$661$	17.9932	−	10.3884i	0.699853	−	0.404060i	0.807293	+	0.590151i	$0.200932\pi$
$662$	−53.8701			−2.09372
$663$	−4.42210	+	1.52931i	−0.171740	+	0.0593935i
$664$	−17.2988			−0.671322
$665$	17.7821	−	10.2665i	0.689561	−	0.398118i
$666$	−10.1928	−	17.6545i	−0.394964	−	0.684098i
$667$	−2.77514	+	4.80669i	−0.107454	+	0.186116i
$668$			26.1588i			1.01211i
$669$	−5.55612	−	3.20783i	−0.214812	−	0.124022i
$670$	10.2306	+	5.90666i	0.395244	+	0.228194i
$671$			5.29818i			0.204534i
$672$	15.1193	−	26.1875i	0.583241	−	1.01020i
$673$	6.65698	+	11.5302i	0.256608	+	0.444458i	0.965331	−	0.261029i	$-0.0840618\pi$
$673$	6.65698	+	11.5302i	0.256608	+	0.444458i	−0.708723	+	0.705487i	$0.750728\pi$
$674$	−40.1194	+	23.1629i	−1.54534	+	0.892203i
$675$	23.2893			0.896406
$676$	−2.31081	−	16.1272i	−0.0888771	−	0.620277i
$677$	9.58632			0.368432			0.184216	−	0.982886i	$-0.441025\pi$
$677$	9.58632			0.368432			0.184216	+	0.982886i	$0.441025\pi$
$678$	−12.0766	+	6.97241i	−0.463798	+	0.267774i
$679$	0.152083	+	0.263416i	0.00583642	+	0.0101090i
$680$	−0.608752	+	1.05439i	−0.0233446	+	0.0404340i
$681$			12.4377i			0.476614i
$682$	−8.48320	−	4.89778i	−0.324839	−	0.187546i
$683$	20.2327	+	11.6813i	0.774181	+	0.446974i	0.834364	−	0.551214i	$-0.185835\pi$
$683$	20.2327	+	11.6813i	0.774181	+	0.446974i	−0.0601829	+	0.998187i	$0.519168\pi$
$684$			13.4446i			0.514068i
$685$	−0.594813	+	1.03025i	−0.0227266	+	0.0393637i
$686$	−21.0952	−	36.5380i	−0.805420	−	1.39503i
$687$	25.0174	−	14.4438i	0.954473	−	0.551065i
$688$	−27.8802			−1.06292
$689$	4.30492	−	1.48878i	0.164004	−	0.0567181i
$690$	−1.77433			−0.0675477
$691$	4.75944	−	2.74786i	0.181057	−	0.104534i	−0.406732	−	0.913548i	$-0.633332\pi$
$691$	4.75944	−	2.74786i	0.181057	−	0.104534i	0.587789	+	0.809014i	$0.299998\pi$
$692$	5.08682	+	8.81064i	0.193372	+	0.334930i
$693$	21.1552	−	36.6420i	0.803621	−	1.39191i
$694$		−	7.84618i		−	0.297837i
$695$	−11.3095	−	6.52952i	−0.428992	−	0.247679i
$696$	−6.23518	−	3.59988i	−0.236344	−	0.136453i
$697$		−	13.7448i		−	0.520622i
$698$	−4.49466	+	7.78498i	−0.170125	+	0.294666i
$699$	1.73989	+	3.01357i	0.0658086	+	0.113984i
$700$	21.0121	−	12.1313i	0.794183	−	0.458522i
$701$	−43.4482			−1.64101			−0.820507	−	0.571636i	$-0.806309\pi$
$701$	−43.4482			−1.64101			−0.820507	+	0.571636i	$0.806309\pi$
$702$	−22.5251	+	25.9826i	−0.850154	+	0.980652i
$703$	38.5990			1.45579
$704$	6.24084	−	3.60315i	0.235210	−	0.135799i
$705$	1.73785	+	3.01004i	0.0654511	+	0.113365i
$706$	8.68606	−	15.0447i	0.326904	−	0.566215i
$707$			6.78244i			0.255080i
$708$	−10.3757	−	5.99043i	−0.389944	−	0.225134i
$709$	−2.58897	−	1.49474i	−0.0972307	−	0.0561361i	0.450596	−	0.892728i	$-0.351211\pi$
$709$	−2.58897	−	1.49474i	−0.0972307	−	0.0561361i	−0.547827	+	0.836592i	$0.684545\pi$
$710$			5.34520i			0.200602i
$711$	7.42646	−	12.8630i	0.278514	−	0.482400i
$712$	7.28743	+	12.6222i	0.273108	+	0.473037i
$713$	0.996341	−	0.575237i	0.0373132	−	0.0215428i
$714$	10.2888			0.385050
$715$	11.4182	+	9.89878i	0.427018	+	0.370193i
$716$	28.9778			1.08295
$717$	−10.5283	+	6.07854i	−0.393188	+	0.227007i
$718$	33.2674	+	57.6209i	1.24153	+	2.15039i
$719$	−4.33930	+	7.51590i	−0.161829	+	0.280296i	−0.935525	−	0.353262i	$-0.885073\pi$
$719$	−4.33930	+	7.51590i	−0.161829	+	0.280296i	0.773696	+	0.633557i	$0.218406\pi$
$720$			6.75130i			0.251606i
$721$	−18.2826	−	10.5555i	−0.680879	−	0.393106i
$722$	−27.5505	−	15.9063i	−1.02532	−	0.591972i
$723$		−	7.35773i		−	0.273637i
$724$	−5.18559	+	8.98170i	−0.192721	+	0.333802i
$725$	−10.6242	−	18.4017i	−0.394574	−	0.683422i
$726$	−32.0087	+	18.4803i	−1.18796	+	0.685867i
$727$	3.15935			0.117174			0.0585869	−	0.998282i	$-0.481341\pi$
$727$	3.15935			0.117174			0.0585869	+	0.998282i	$0.481341\pi$
$728$	4.04503	−	20.9604i	0.149919	−	0.776844i
$729$	18.5359			0.686517
$730$	5.27299	−	3.04436i	0.195162	−	0.112677i
$731$	−3.30793	−	5.72951i	−0.122348	−	0.211913i
$732$	−0.677309	+	1.17313i	−0.0250341	+	0.0433603i
$733$		−	28.0004i		−	1.03422i	−0.855920	−	0.517109i	$-0.827008\pi$
$733$		−	28.0004i		−	1.03422i	0.855920	−	0.517109i	$-0.172992\pi$
$734$	−4.89404	−	2.82557i	−0.180642	−	0.104294i
$735$	−9.12423	−	5.26788i	−0.336552	−	0.194309i
$736$			7.14309i			0.263298i
$737$	−23.0457	+	39.9162i	−0.848897	+	1.47033i
$738$	−18.7571	−	32.4883i	−0.690458	−	1.19591i
$739$	−42.3817	+	24.4691i	−1.55903	+	0.900109i	−0.561685	+	0.827351i	$0.689847\pi$
$739$	−42.3817	+	24.4691i	−1.55903	+	0.900109i	−0.997350	+	0.0727582i	$0.976820\pi$
$740$	−6.16750			−0.226722
$741$	−7.90323	−	22.8527i	−0.290332	−	0.839515i
$742$	−10.0162			−0.367706
$743$	−13.1491	+	7.59161i	−0.482392	+	0.278509i	−0.721413	−	0.692505i	$-0.756507\pi$
$743$	−13.1491	+	7.59161i	−0.482392	+	0.278509i	0.239021	+	0.971014i	$0.423174\pi$
$744$	0.746191	+	1.29244i	0.0273567	+	0.0473832i
$745$	−3.56313	+	6.17152i	−0.130543	+	0.226107i
$746$			31.6465i			1.15866i
$747$	−19.7130	−	11.3813i	−0.721262	−	0.416421i
$748$	6.90378	+	3.98590i	0.252427	+	0.145739i
$749$			54.3767i			1.98688i
$750$	7.25204	−	12.5609i	0.264807	−	0.458660i
$751$	7.95992	+	13.7870i	0.290462	+	0.503094i	0.973919	−	0.226896i	$-0.0728578\pi$
$751$	7.95992	+	13.7870i	0.290462	+	0.503094i	−0.683457	+	0.729990i	$0.739525\pi$
$752$	17.3754	−	10.0317i	0.633617	−	0.365819i
$753$	−13.5101			−0.492335
$754$	30.8054	+	5.94496i	1.12187	+	0.216503i
$755$	−16.7499			−0.609593
$756$	25.2260	−	14.5642i	0.917460	−	0.529696i
$757$	11.2728	+	19.5250i	0.409715	+	0.709648i	0.994858	−	0.101283i	$-0.0322947\pi$
$757$	11.2728	+	19.5250i	0.409715	+	0.709648i	−0.585142	+	0.810931i	$0.698961\pi$
$758$	25.6848	−	44.4874i	0.932915	−	1.61586i
$759$		−	6.92281i		−	0.251282i
$760$	−5.44891	−	3.14593i	−0.197653	−	0.114115i
$761$	−17.0671	−	9.85369i	−0.618682	−	0.357196i	0.157674	−	0.987491i	$-0.449601\pi$
$761$	−17.0671	−	9.85369i	−0.618682	−	0.357196i	−0.776356	+	0.630295i	$0.782934\pi$
$762$			29.4838i			1.06808i
$763$	15.0288	−	26.0307i	0.544080	−	0.942374i
$764$	7.50860	+	13.0053i	0.271652	+	0.470515i
$765$	−1.38742	+	0.801029i	−0.0501624	+	0.0289613i
$766$	19.2462			0.695392
$767$	−30.5462	−	5.89494i	−1.10296	−	0.212854i
$768$	−22.9734			−0.828980
$769$	−4.23795	+	2.44678i	−0.152824	+	0.0882332i	−0.574462	−	0.818531i	$-0.694789\pi$
$769$	−4.23795	+	2.44678i	−0.152824	+	0.0882332i	0.421638	+	0.906764i	$0.361455\pi$
$770$	−16.6145	−	28.7772i	−0.598746	−	1.03706i
$771$	−10.4556	+	18.1097i	−0.376551	+	0.652205i
$772$		−	8.51072i		−	0.306308i
$773$	34.4908	+	19.9133i	1.24055	+	0.716231i	0.969206	−	0.246252i	$-0.0791992\pi$
$773$	34.4908	+	19.9133i	1.24055	+	0.716231i	0.271342	+	0.962483i	$0.412533\pi$
$774$	−15.6377	−	9.02846i	−0.562087	−	0.324521i
$775$			4.40443i			0.158212i
$776$	0.0466023	−	0.0807176i	0.00167293	−	0.00289759i
$777$	−15.5287	−	26.8966i	−0.557091	−	0.964909i
$778$	22.6606	−	13.0831i	0.812423	−	0.469052i
$779$	71.0310			2.54495
$780$	1.26281	+	3.65149i	0.0452157	+	0.130744i
$781$	−20.8550			−0.746252
$782$	−2.10484	+	1.21523i	−0.0752691	+	0.0434566i
$783$	−12.7549	−	22.0921i	−0.455822	−	0.789506i
$784$	−30.4088	+	52.6696i	−1.08603	+	1.88106i
$785$			17.5217i			0.625378i
$786$	29.9458	+	17.2892i	1.06813	+	0.616687i
$787$	22.7376	+	13.1276i	0.810510	+	0.467948i	0.847133	−	0.531381i	$-0.178327\pi$
$787$	22.7376	+	13.1276i	0.810510	+	0.467948i	−0.0366233	+	0.999329i	$0.511660\pi$
$788$		−	3.20384i		−	0.114132i
$789$	−4.03528	+	6.98931i	−0.143660	+	0.248826i
$790$	−5.83246	−	10.1021i	−0.207509	−	0.359417i
$791$	26.5628	−	15.3360i	0.944465	−	0.545287i
$792$	−12.9651			−0.460693
$793$	−0.666512	+	3.45371i	−0.0236685	+	0.122645i
$794$	−55.4188			−1.96674
$795$	−0.935527	+	0.540127i	−0.0331797	+	0.0191563i
$796$	3.16684	+	5.48512i	0.112246	+	0.194415i
$797$	−8.19833	+	14.1999i	−0.290400	+	0.502987i	−0.973904	−	0.226959i	$-0.927122\pi$
$797$	−8.19833	+	14.1999i	−0.290400	+	0.502987i	0.683505	+	0.729946i	$0.260455\pi$
$798$			53.1710i			1.88223i
$799$	4.12313	+	2.38049i	0.145866	+	0.0842156i
$800$	−23.6826	−	13.6731i	−0.837306	−	0.483419i
$801$			19.1784i			0.677636i
$802$	−27.9877	+	48.4761i	−0.988279	+	1.71175i
$803$	11.8780	+	20.5733i	0.419165	+	0.726016i
$804$	−10.2056	+	5.89222i	−0.359925	+	0.207803i
$805$	3.90271			0.137552
$806$	−4.91378	−	4.25989i	−0.173081	−	0.150048i
$807$	19.9969			0.703924
$808$	1.79988	−	1.03916i	0.0633195	−	0.0365575i
$809$	7.07958	+	12.2622i	0.248905	+	0.431116i	0.963222	−	0.268706i	$-0.0865961\pi$
$809$	7.07958	+	12.2622i	0.248905	+	0.431116i	−0.714317	+	0.699822i	$0.753263\pi$
$810$	0.376923	−	0.652849i	0.0132437	−	0.0229388i
$811$		−	20.7922i		−	0.730114i	−0.930985	−	0.365057i	$-0.881049\pi$
$811$		−	20.7922i		−	0.730114i	0.930985	−	0.365057i	$-0.118951\pi$
$812$	−23.0154	−	13.2880i	−0.807682	−	0.466316i
$813$	0.845143	+	0.487944i	0.0296405	+	0.0171129i
$814$		−	62.4657i		−	2.18942i
$815$	1.40853	−	2.43964i	0.0493385	−	0.0854569i
$816$	−3.20275	−	5.54732i	−0.112119	−	0.194195i
$817$	29.6092	−	17.0949i	1.03589	−	0.598073i
$818$	−3.26891			−0.114295
$819$	18.4000	−	21.2244i	0.642947	−	0.741639i
$820$	−11.3496			−0.396345
$821$	−23.2386	+	13.4168i	−0.811034	+	0.468251i	−0.847315	−	0.531091i	$-0.821782\pi$
$821$	−23.2386	+	13.4168i	−0.811034	+	0.468251i	0.0362805	+	0.999342i	$0.488449\pi$
$822$	−1.54029	−	2.66786i	−0.0537238	−	0.0930524i
$823$	0.596052	−	1.03239i	0.0207771	−	0.0359870i	−0.855450	−	0.517886i	$-0.826719\pi$
$823$	0.596052	−	1.03239i	0.0207771	−	0.0359870i	0.876227	+	0.481899i	$0.160053\pi$
$824$			6.46894i			0.225356i
$825$	22.9522	+	13.2515i	0.799095	+	0.461358i
$826$	59.2426	+	34.2038i	2.06132	+	1.19010i
$827$			8.94631i			0.311094i	0.987829	+	0.155547i	$0.0497140\pi$
$827$			8.94631i			0.311094i	−0.987829	+	0.155547i	$0.950286\pi$
$828$	−1.27771	+	2.21305i	−0.0444034	+	0.0769089i
$829$	−23.8676	−	41.3398i	−0.828955	−	1.43579i	−0.898859	−	0.438238i	$-0.855603\pi$
$829$	−23.8676	−	41.3398i	−0.828955	−	1.43579i	0.0699039	−	0.997554i	$-0.477731\pi$
$830$	−15.4819	+	8.93846i	−0.537383	+	0.310258i
$831$	23.6605			0.820772
$832$	4.52147	−	1.56368i	0.156754	−	0.0542107i
$833$	−14.4318			−0.500032
$834$	29.2863	−	16.9084i	1.01410	−	0.585491i
$835$	−8.05427	−	13.9504i	−0.278730	−	0.482774i
$836$	−20.5985	+	35.6776i	−0.712413	+	1.23394i
$837$			5.28771i			0.182770i
$838$	−29.0382	−	16.7652i	−1.00311	−	0.579145i
$839$	−42.6237	−	24.6088i	−1.47153	−	0.849591i	−0.472046	−	0.881574i	$-0.656484\pi$
$839$	−42.6237	−	24.6088i	−1.47153	−	0.849591i	−0.999488	+	0.0319829i	$0.989818\pi$
$840$			5.06255i			0.174674i
$841$	2.86285	−	4.95860i	0.0987189	−	0.170986i
$842$	4.84140	+	8.38556i	0.166846	+	0.288985i
$843$	−16.3059	+	9.41423i	−0.561606	+	0.324243i
$844$	−14.4298			−0.496693
$845$	6.19791	+	7.88911i	0.213214	+	0.271393i
$846$	12.9943			0.446753
$847$	70.4043	−	40.6479i	2.41912	−	1.39668i
$848$	3.11788	+	5.40032i	0.107068	+	0.185448i
$849$	11.0904	−	19.2092i	0.380622	−	0.659257i
$850$		−	9.30468i		−	0.319148i
$851$	6.35360	+	3.66826i	0.217799	+	0.125746i
$852$	−4.61776	−	2.66607i	−0.158202	−	0.0913379i
$853$			46.8047i			1.60256i	0.598288	+	0.801281i	$0.295848\pi$
$853$			46.8047i			1.60256i	−0.598288	+	0.801281i	$0.704152\pi$
$854$	3.86725	−	6.69828i	0.132335	−	0.229210i
$855$	−4.13959	−	7.16998i	−0.141571	−	0.245208i
$856$	14.4301	−	8.33123i	0.493211	−	0.284756i
$857$	26.2083			0.895257			0.447629	−	0.894220i	$-0.352269\pi$
$857$	26.2083			0.895257			0.447629	+	0.894220i	$0.352269\pi$
$858$	−36.9830	+	12.7900i	−1.26258	+	0.436642i
$859$	39.6143			1.35162			0.675812	−	0.737074i	$-0.263793\pi$
$859$	39.6143			1.35162			0.675812	+	0.737074i	$0.263793\pi$
$860$	−4.73106	+	2.73148i	−0.161328	+	0.0931427i
$861$	−28.5764	−	49.4958i	−0.973881	−	1.68681i
$862$	20.2246	−	35.0300i	0.688851	−	1.19313i
$863$			57.2856i			1.95003i	0.222149	+	0.975013i	$0.428693\pi$
$863$			57.2856i			1.95003i	−0.222149	+	0.975013i	$0.571307\pi$
$864$	−28.4320	−	16.4152i	−0.967276	−	0.558457i
$865$	−5.42558	−	3.13246i	−0.184475	−	0.106507i
$866$		−	23.9803i		−	0.814883i
$867$	−8.65786	+	14.9958i	−0.294036	+	0.509286i
$868$	2.75435	+	4.77068i	0.0934888	+	0.161927i
$869$	39.4148	−	22.7561i	1.33706	−	0.771949i
$870$	−7.44040			−0.252253
$871$	−20.0442	+	23.1210i	−0.679171	+	0.783424i
$872$	−9.21046			−0.311906
$873$	0.106213	−	0.0613219i	0.00359476	−	0.00207543i
$874$	−6.28013	−	10.8775i	−0.212428	−	0.367937i
$875$	−15.9511	+	27.6281i	−0.539246	+	0.934002i
$876$			6.07384i			0.205216i
$877$	42.2980	+	24.4207i	1.42830	+	0.824630i	0.996987	−	0.0775716i	$-0.0247166\pi$
$877$	42.2980	+	24.4207i	1.42830	+	0.824630i	0.431314	+	0.902202i	$0.358050\pi$
$878$	49.3818	+	28.5106i	1.66655	+	0.962185i
$879$		−	29.5923i		−	0.998125i
$880$	−10.3437	+	17.9158i	−0.348685	+	0.603940i
$881$	−15.5523	−	26.9374i	−0.523971	−	0.907544i	−0.999611	−	0.0279039i	$-0.991117\pi$
$881$	−15.5523	−	26.9374i	−0.523971	−	0.907544i	0.475640	−	0.879640i	$-0.342217\pi$
$882$	−34.1120	+	19.6946i	−1.14861	+	0.663151i
$883$	−32.2081			−1.08389			−0.541945	−	0.840414i	$-0.682312\pi$
$883$	−32.2081			−1.08389			−0.541945	+	0.840414i	$0.682312\pi$
$884$	3.99892	+	3.46677i	0.134498	+	0.116600i
$885$	7.37780			0.248002
$886$	−41.6849	+	24.0668i	−1.40043	+	0.808540i
$887$	9.87609	+	17.1059i	0.331607	+	0.574360i	0.982827	−	0.184529i	$-0.0590760\pi$
$887$	9.87609	+	17.1059i	0.331607	+	0.574360i	−0.651220	+	0.758889i	$0.725743\pi$
$888$	−4.75842	+	8.24182i	−0.159682	+	0.276577i
$889$		−	64.8505i		−	2.17502i
$890$	13.0441	+	7.53100i	0.437238	+	0.252440i
$891$	2.54718	+	1.47062i	0.0853338	+	0.0492675i
$892$			7.25666i			0.242971i
$893$	−12.3020	+	21.3076i	−0.411670	+	0.713033i
$894$	−9.22686	−	15.9814i	−0.308592	−	0.534498i
$895$	−15.4538	+	8.92225i	−0.516563	+	0.298238i
$896$	44.0633			1.47205
$897$	0.870891	−	4.51276i	0.0290782	−	0.150677i
$898$	−35.7162			−1.19186
$899$	4.17801	−	2.41217i	0.139344	−	0.0804505i
$900$	−4.89151	−	8.47235i	−0.163050	−	0.282412i
$901$	−0.739860	+	1.28148i	−0.0246483	+	0.0426921i
$902$		−	114.951i		−	3.82745i
$903$	−23.8241	−	13.7548i	−0.792815	−	0.457732i
$904$	−8.13955	−	4.69937i	−0.270717	−	0.156299i
$905$		−	6.38656i		−	0.212297i
$906$	21.6873	−	37.5635i	0.720513	−	1.24796i
$907$	22.4903	+	38.9544i	0.746778	+	1.29346i	0.949359	+	0.314193i	$0.101734\pi$
$907$	22.4903	+	38.9544i	0.746778	+	1.29346i	−0.202581	+	0.979266i	$0.564933\pi$
$908$	12.1833	−	7.03405i	0.404318	−	0.233433i
$909$	2.73477			0.0907065
$910$	−7.21029	−	20.8490i	−0.239019	−	0.691139i
$911$	−24.7942			−0.821469			−0.410735	−	0.911755i	$-0.634728\pi$
$911$	−24.7942			−0.821469			−0.410735	+	0.911755i	$0.634728\pi$
$912$	28.6677	−	16.5513i	0.949281	−	0.548068i
$913$	−34.8746	−	60.4047i	−1.15418	−	1.99910i
$914$	20.0601	−	34.7452i	0.663531	−	1.14927i
$915$		−	0.834173i		−	0.0275769i
$916$	−28.2968	−	16.3372i	−0.934953	−	0.539795i
$917$	−65.8669	−	38.0283i	−2.17512	−	1.25580i
$918$		−	11.1707i		−	0.368688i
$919$	25.8933	−	44.8484i	0.854140	−	1.47941i	−0.0233014	−	0.999728i	$-0.507418\pi$
$919$	25.8933	−	44.8484i	0.854140	−	1.47941i	0.877441	−	0.479685i	$-0.159249\pi$
$920$	−0.597946	−	1.03567i	−0.0197137	−	0.0341451i
$921$	25.8604	−	14.9305i	0.852128	−	0.491976i
$922$	−9.48084			−0.312235
$923$	−13.5947	−	2.62357i	−0.447476	−	0.0863557i
$924$	33.1478			1.09048
$925$	−24.3239	+	14.0434i	−0.799763	+	0.461744i
$926$	−1.76242	−	3.05261i	−0.0579168	−	0.100315i
$927$	−4.25609	+	7.37177i	−0.139788	+	0.242121i
$928$			29.9535i			0.983271i
$929$	24.5508	+	14.1744i	0.805487	+	0.465048i	0.845386	−	0.534156i	$-0.179370\pi$
$929$	24.5508	+	14.1744i	0.805487	+	0.465048i	−0.0398993	+	0.999204i	$0.512704\pi$
$930$	1.33564	+	0.771131i	0.0437973	+	0.0252864i
$931$		−	74.5811i		−	2.44430i
$932$	1.96796	−	3.40861i	0.0644628	−	0.111653i
$933$	9.50052	+	16.4554i	0.311033	+	0.538725i
$934$	−51.2903	+	29.6125i	−1.67827	+	0.968949i
$935$	−4.90903			−0.160542
$936$	−8.45150	−	1.63101i	−0.276246	−	0.0533111i
$937$	2.21095			0.0722287			0.0361143	−	0.999348i	$-0.488502\pi$
$937$	2.21095			0.0722287			0.0361143	+	0.999348i	$0.488502\pi$
$938$	58.2714	−	33.6430i	1.90263	−	1.09848i
$939$	−10.1361	−	17.5562i	−0.330778	−	0.572924i
$940$	1.96566	−	3.40462i	0.0641126	−	0.111046i
$941$		−	22.2919i		−	0.726694i	−0.931654	−	0.363347i	$-0.881634\pi$
$941$		−	22.2919i		−	0.726694i	0.931654	−	0.363347i	$-0.118366\pi$
$942$	−39.2943	−	22.6866i	−1.28028	−	0.739169i
$943$	11.6921	+	6.75042i	0.380746	+	0.219824i
$944$		−	42.5883i		−	1.38613i
$945$	−8.96863	+	15.5341i	−0.291750	+	0.505325i
$946$	−27.6650	−	47.9172i	−0.899466	−	1.55792i
$947$	−12.3416	+	7.12545i	−0.401050	+	0.231546i	−0.686937	−	0.726717i	$-0.741045\pi$
$947$	−12.3416	+	7.12545i	−0.401050	+	0.231546i	0.285887	+	0.958263i	$0.407712\pi$
$948$	11.6364			0.377933
$949$	5.15476	+	14.9053i	0.167330	+	0.483847i
$950$	48.0851			1.56009
$951$	19.4595	−	11.2349i	0.631017	−	0.364318i
$952$	3.46731	+	6.00556i	0.112376	+	0.194641i
$953$	19.8078	−	34.3082i	0.641639	−	1.11135i	−0.343428	−	0.939179i	$-0.611588\pi$
$953$	19.8078	−	34.3082i	0.641639	−	1.11135i	0.985067	−	0.172173i	$-0.0550787\pi$
$954$			4.03865i			0.130756i
$955$	−8.00864	−	4.62379i	−0.259154	−	0.149622i
$956$	11.9085	+	6.87536i	0.385147	+	0.222365i
$957$		−	29.0298i		−	0.938399i
$958$	12.6769	−	21.9570i	0.409572	−	0.709399i
$959$	3.38792	+	5.86805i	0.109402	+	0.189489i
$960$	−0.982589	+	0.567298i	−0.0317129	+	0.0183095i
$961$	−1.00000			−0.0322581
$962$	7.85819	−	40.7194i	0.253358	−	1.31284i
$963$	21.9254			0.706536
$964$	−7.20726	+	4.16111i	−0.232130	+	0.134020i
$965$	2.62045	+	4.53875i	0.0843552	+	0.146107i
$966$	−5.05310	+	8.75223i	−0.162581	+	0.281598i
$967$			35.4974i			1.14152i	0.821117	+	0.570760i	$0.193351\pi$
$967$			35.4974i			1.14152i	−0.821117	+	0.570760i	$0.806649\pi$
$968$	−21.5737	−	12.4556i	−0.693406	−	0.400338i
$969$	6.80273	+	3.92756i	0.218535	+	0.126171i
$970$		−	0.0963198i		−	0.00309264i
$971$	2.96522	−	5.13591i	0.0951584	−	0.164819i	−0.814516	−	0.580141i	$-0.802998\pi$
$971$	2.96522	−	5.13591i	0.0951584	−	0.164819i	0.909675	+	0.415321i	$0.136331\pi$
$972$	−9.56403	−	16.5654i	−0.306766	−	0.531335i
$973$	−64.4161	+	37.1907i	−2.06509	+	1.19228i
$974$	13.8243			0.442959
$975$	13.2948	+	11.5256i	0.425774	+	0.369115i
$976$	−4.81525			−0.154133
$977$	−9.00755	+	5.20051i	−0.288177	+	0.166379i	−0.637119	−	0.770765i	$-0.719874\pi$
$977$	−9.00755	+	5.20051i	−0.288177	+	0.166379i	0.348942	+	0.937144i	$0.386541\pi$
$978$	3.64743	+	6.31754i	0.116632	+	0.202013i
$979$	−29.3832	+	50.8932i	−0.939092	+	1.62656i
$980$			11.9169i			0.380670i
$981$	−10.4959	−	6.05982i	−0.335109	−	0.193475i
$982$	52.9497	+	30.5705i	1.68969	+	0.975545i
$983$			21.6354i			0.690062i	0.938591	+	0.345031i	$0.112132\pi$
$983$			21.6354i			0.690062i	−0.938591	+	0.345031i	$0.887868\pi$
$984$	−8.75657	+	15.1668i	−0.279149	+	0.483500i
$985$	0.986460	+	1.70860i	0.0314312	+	0.0544405i
$986$	−8.82635	+	5.09590i	−0.281088	+	0.162286i
$987$	19.7968			0.630139
$988$	−17.9157	+	20.6658i	−0.569975	+	0.657466i
$989$	6.49843			0.206638
$990$	−11.6033	+	6.69919i	−0.368778	+	0.212914i
$991$	−13.2496	−	22.9489i	−0.420886	−	0.728996i	0.575141	−	0.818055i	$-0.304947\pi$
$991$	−13.2496	−	22.9489i	−0.420886	−	0.728996i	−0.996026	+	0.0890590i	$0.971614\pi$
$992$	3.10441	−	5.37700i	0.0985651	−	0.170720i
$993$			33.0920i			1.05014i
$994$	26.3662	+	15.2225i	0.836284	+	0.482829i
$995$	−3.37773	−	1.95014i	−0.107081	−	0.0618235i
$996$		−	17.8332i		−	0.565067i
$997$	−7.64585	+	13.2430i	−0.242147	+	0.419410i	−0.961325	−	0.275415i	$-0.911185\pi$
$997$	−7.64585	+	13.2430i	−0.242147	+	0.419410i	0.719179	+	0.694825i	$0.244518\pi$
$998$	28.3344	+	49.0766i	0.896910	+	1.55349i
$999$	−29.2019	+	16.8597i	−0.923906	+	0.533417i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.r.a.218.8	✓	68
13.2	odd	12		5239.2.a.q.1.10		34
13.4	even	6	inner	403.2.r.a.342.8	yes	68
13.11	odd	12		5239.2.a.r.1.25		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.r.a.218.8	✓	68	1.1	even	1	trivial
403.2.r.a.342.8	yes	68	13.4	even	6	inner
5239.2.a.q.1.10		34	13.2	odd	12
5239.2.a.r.1.25		34	13.11	odd	12

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.56202 + 0.901835i) q^{2} +(0.553992 + 0.959542i) q^{3} +(0.626612 - 1.08532i) q^{4} +0.771735i q^{5} +(-1.73070 - 0.999218i) q^{6} +(3.80672 + 2.19781i) q^{7} -1.34694i q^{8} +(0.886187 - 1.53492i) q^{9} +O(q^{10})\)	\(q+(-1.56202 + 0.901835i) q^{2} +(0.553992 + 0.959542i) q^{3} +(0.626612 - 1.08532i) q^{4} +0.771735i q^{5} +(-1.73070 - 0.999218i) q^{6} +(3.80672 + 2.19781i) q^{7} -1.34694i q^{8} +(0.886187 - 1.53492i) q^{9} +(-0.695977 - 1.20547i) q^{10} +(4.70330 - 2.71545i) q^{11} +1.38855 q^{12} +(3.40753 - 1.17844i) q^{13} -7.92826 q^{14} +(-0.740511 + 0.427534i) q^{15} +(2.46794 + 4.27460i) q^{16} +(-0.585633 + 1.01435i) q^{17} +3.19678i q^{18} +(-5.24197 - 3.02646i) q^{19} +(0.837582 + 0.483578i) q^{20} +4.87028i q^{21} +(-4.89778 + 8.48320i) q^{22} +(-0.575237 - 0.996341i) q^{23} +(1.29244 - 0.746191i) q^{24} +4.40443 q^{25} +(-4.25989 + 4.91378i) q^{26} +5.28771 q^{27} +(4.77068 - 2.75435i) q^{28} +(-2.41217 - 4.17801i) q^{29} +(0.771131 - 1.33564i) q^{30} +1.00000i q^{31} +(-5.37700 - 3.10441i) q^{32} +(5.21118 + 3.00868i) q^{33} -2.11258i q^{34} +(-1.69613 + 2.93778i) q^{35} +(-1.11059 - 1.92360i) q^{36} +(-5.52259 + 3.18847i) q^{37} +10.9175 q^{38} +(3.01851 + 2.61682i) q^{39} +1.03948 q^{40} +(-10.1628 + 5.86751i) q^{41} +(-4.39219 - 7.60749i) q^{42} +(-2.82424 + 4.89172i) q^{43} -6.80614i q^{44} +(1.18455 + 0.683901i) q^{45} +(1.79707 + 1.03754i) q^{46} -4.06481i q^{47} +(-2.73443 + 4.73618i) q^{48} +(6.16077 + 10.6708i) q^{49} +(-6.87982 + 3.97206i) q^{50} -1.29774 q^{51} +(0.856214 - 4.43670i) q^{52} +1.26335 q^{53} +(-8.25953 + 4.76864i) q^{54} +(2.09561 + 3.62970i) q^{55} +(2.96031 - 5.12742i) q^{56} -6.70652i q^{57} +(7.53574 + 4.35076i) q^{58} +(-7.47234 - 4.31416i) q^{59} +1.07159i q^{60} +(-0.487781 + 0.844861i) q^{61} +(-0.901835 - 1.56202i) q^{62} +(6.74694 - 3.89535i) q^{63} +1.32691 q^{64} +(0.909442 + 2.62971i) q^{65} -10.8533 q^{66} +(-7.34983 + 4.24343i) q^{67} +(0.733929 + 1.27120i) q^{68} +(0.637353 - 1.10393i) q^{69} -6.11851i q^{70} +(-3.32559 - 1.92003i) q^{71} +(-2.06744 - 1.19364i) q^{72} +4.37422i q^{73} +(5.75095 - 9.96093i) q^{74} +(2.44001 + 4.22623i) q^{75} +(-6.56937 + 3.79283i) q^{76} +23.8722 q^{77} +(-7.07492 - 1.36535i) q^{78} +8.38024 q^{79} +(-3.29885 + 1.90459i) q^{80} +(0.270787 + 0.469016i) q^{81} +(10.5830 - 18.3304i) q^{82} -12.8430i q^{83} +(5.28583 + 3.05178i) q^{84} +(-0.782805 - 0.451953i) q^{85} -10.1880i q^{86} +(2.67265 - 4.62916i) q^{87} +(-3.65754 - 6.33505i) q^{88} +(-9.37105 + 5.41038i) q^{89} -2.46706 q^{90} +(15.5615 + 3.00313i) q^{91} -1.44180 q^{92} +(-0.959542 + 0.553992i) q^{93} +(3.66579 + 6.34934i) q^{94} +(2.33562 - 4.04541i) q^{95} -6.87927i q^{96} +(0.0599268 + 0.0345988i) q^{97} +(-19.2465 - 11.1120i) q^{98} -9.62559i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) \) 68 * q + 32 * q^4 - 34 * q^9	\( 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) \) 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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