LMFDB - Embedded newform 403.2.l.c.25.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(25,403)]

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([3, 2]))

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

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

chi := DirichletCharacter("403.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.l (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			25.16
Character	$\chi$	$=$	403.25
Dual form			403.2.l.c.129.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.177509i q^{2} +(0.311192 + 0.539000i) q^{3} +1.96849 q^{4} +(1.82613 + 1.05431i) q^{5} +(0.0956771 - 0.0552392i) q^{6} +(1.99646 - 1.15265i) q^{7} -0.704441i q^{8} +(1.30632 - 2.26261i) q^{9} +O(q^{10})$	\(q-0.177509i q^{2} +(0.311192 + 0.539000i) q^{3} +1.96849 q^{4} +(1.82613 + 1.05431i) q^{5} +(0.0956771 - 0.0552392i) q^{6} +(1.99646 - 1.15265i) q^{7} -0.704441i q^{8} +(1.30632 - 2.26261i) q^{9} +(0.187150 - 0.324153i) q^{10} +(-3.83942 - 2.21669i) q^{11} +(0.612578 + 1.06102i) q^{12} +(-2.60672 - 2.49098i) q^{13} +(-0.204606 - 0.354388i) q^{14} +1.31238i q^{15} +3.81194 q^{16} +(3.63636 + 6.29835i) q^{17} +(-0.401633 - 0.231883i) q^{18} +(-5.84727 + 3.37592i) q^{19} +(3.59471 + 2.07541i) q^{20} +(1.24256 + 0.717393i) q^{21} +(-0.393482 + 0.681531i) q^{22} -9.13913 q^{23} +(0.379694 - 0.219216i) q^{24} +(-0.276843 - 0.479507i) q^{25} +(-0.442171 + 0.462715i) q^{26} +3.49321 q^{27} +(3.93001 - 2.26899i) q^{28} -0.638044 q^{29} +0.232958 q^{30} +(4.14520 + 3.71717i) q^{31} -2.08553i q^{32} -2.75927i q^{33} +(1.11801 - 0.645485i) q^{34} +4.86104 q^{35} +(2.57148 - 4.45393i) q^{36} +(2.94161 - 1.69834i) q^{37} +(0.599255 + 1.03794i) q^{38} +(0.531451 - 2.18020i) q^{39} +(0.742703 - 1.28640i) q^{40} +(1.49289 + 0.861918i) q^{41} +(0.127344 - 0.220565i) q^{42} +(-1.66436 - 2.88275i) q^{43} +(-7.55787 - 4.36354i) q^{44} +(4.77101 - 2.75454i) q^{45} +1.62227i q^{46} +9.94211i q^{47} +(1.18624 + 2.05463i) q^{48} +(-0.842774 + 1.45973i) q^{49} +(-0.0851166 + 0.0491421i) q^{50} +(-2.26321 + 3.91999i) q^{51} +(-5.13131 - 4.90348i) q^{52} +(-5.41936 + 9.38660i) q^{53} -0.620076i q^{54} +(-4.67418 - 8.09592i) q^{55} +(-0.811978 - 1.40639i) q^{56} +(-3.63924 - 2.10112i) q^{57} +0.113258i q^{58} +(-1.57839 + 0.911283i) q^{59} +2.58340i q^{60} +1.62489 q^{61} +(0.659830 - 0.735808i) q^{62} -6.02294i q^{63} +7.25367 q^{64} +(-2.13392 - 7.29715i) q^{65} -0.489793 q^{66} +(-1.49673 - 0.864137i) q^{67} +(7.15813 + 12.3983i) q^{68} +(-2.84402 - 4.92599i) q^{69} -0.862877i q^{70} +(6.34620 + 3.66398i) q^{71} +(-1.59388 - 0.920225i) q^{72} +(1.36850 + 0.790105i) q^{73} +(-0.301470 - 0.522161i) q^{74} +(0.172303 - 0.298437i) q^{75} +(-11.5103 + 6.64547i) q^{76} -10.2203 q^{77} +(-0.387004 - 0.0943371i) q^{78} +(-2.85115 - 4.93834i) q^{79} +(6.96108 + 4.01898i) q^{80} +(-2.83190 - 4.90499i) q^{81} +(0.152998 - 0.265000i) q^{82} +(2.14235 + 1.23688i) q^{83} +(2.44597 + 1.41218i) q^{84} +15.3354i q^{85} +(-0.511714 + 0.295438i) q^{86} +(-0.198554 - 0.343906i) q^{87} +(-1.56153 + 2.70465i) q^{88} -12.4713i q^{89} +(-0.488955 - 0.846895i) q^{90} +(-8.07545 - 1.96849i) q^{91} -17.9903 q^{92} +(-0.713603 + 3.39101i) q^{93} +1.76481 q^{94} -14.2371 q^{95} +(1.12410 - 0.649001i) q^{96} +7.23658i q^{97} +(0.259114 + 0.149600i) q^{98} +(-10.0310 + 5.79142i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		−	0.177509i		−	0.125518i	−0.998029	−	0.0627588i	$-0.980010\pi$
$2$		−	0.177509i		−	0.125518i	0.998029	−	0.0627588i	$-0.0199899\pi$
$3$	0.311192	+	0.539000i	0.179667	+	0.311192i	0.941766	−	0.336268i	$-0.109165\pi$
$3$	0.311192	+	0.539000i	0.179667	+	0.311192i	−0.762100	+	0.647460i	$0.775831\pi$
$4$	1.96849			0.984245
$5$	1.82613	+	1.05431i	0.816668	+	0.471504i	0.849266	−	0.527965i	$-0.177045\pi$
$5$	1.82613	+	1.05431i	0.816668	+	0.471504i	−0.0325980	+	0.999469i	$0.510378\pi$
$6$	0.0956771	−	0.0552392i	0.0390600	−	0.0225513i
$7$	1.99646	−	1.15265i	0.754590	−	0.435663i	−0.0727602	−	0.997349i	$-0.523181\pi$
$7$	1.99646	−	1.15265i	0.754590	−	0.435663i	0.827350	+	0.561687i	$0.189847\pi$
$8$		−	0.704441i		−	0.249058i
$9$	1.30632	−	2.26261i	0.435440	−	0.754204i
$10$	0.187150	−	0.324153i	0.0591820	−	0.102506i
$11$	−3.83942	−	2.21669i	−1.15763	−	0.668358i	−0.206895	−	0.978363i	$-0.566336\pi$
$11$	−3.83942	−	2.21669i	−1.15763	−	0.668358i	−0.950735	+	0.310005i	$0.899669\pi$
$12$	0.612578	+	1.06102i	0.176836	+	0.306289i
$13$	−2.60672	−	2.49098i	−0.722974	−	0.690875i
$13$	−2.60672	−	2.49098i	−0.722974	−	0.690875i
$14$	−0.204606	−	0.354388i	−0.0546833	−	0.0947143i
$15$			1.31238i			0.338854i
$16$	3.81194			0.952984
$17$	3.63636	+	6.29835i	0.881946	+	1.52758i	0.849175	+	0.528112i	$0.177100\pi$
$17$	3.63636	+	6.29835i	0.881946	+	1.52758i	0.0327713	+	0.999463i	$0.489567\pi$
$18$	−0.401633	−	0.231883i	−0.0946658	−	0.0546553i
$19$	−5.84727	+	3.37592i	−1.34146	+	0.774490i	−0.987021	−	0.160591i	$-0.948660\pi$
$19$	−5.84727	+	3.37592i	−1.34146	+	0.774490i	−0.354434	+	0.935081i	$0.615327\pi$
$20$	3.59471	+	2.07541i	0.803802	+	0.464075i
$21$	1.24256	+	0.717393i	0.271149	+	0.156548i
$22$	−0.393482	+	0.681531i	−0.0838907	+	0.145303i
$23$	−9.13913			−1.90564			−0.952820	−	0.303536i	$-0.901833\pi$
$23$	−9.13913			−1.90564			−0.952820	+	0.303536i	$0.901833\pi$
$24$	0.379694	−	0.219216i	0.0775047	−	0.0447473i
$25$	−0.276843	−	0.479507i	−0.0553687	−	0.0959014i
$26$	−0.442171	+	0.462715i	−0.0867169	+	0.0907460i
$27$	3.49321			0.672269
$28$	3.93001	−	2.26899i	0.742701	−	0.428799i
$29$	−0.638044			−0.118482			−0.0592409	−	0.998244i	$-0.518868\pi$
$29$	−0.638044			−0.118482			−0.0592409	+	0.998244i	$0.518868\pi$
$30$	0.232958			0.0425321
$31$	4.14520	+	3.71717i	0.744499	+	0.667623i
$31$	4.14520	+	3.71717i	0.744499	+	0.667623i
$32$		−	2.08553i		−	0.368674i
$33$		−	2.75927i		−	0.480326i
$34$	1.11801	−	0.645485i	0.191738	−	0.110700i
$35$	4.86104			0.821666
$36$	2.57148	−	4.45393i	0.428580	−	0.742322i
$37$	2.94161	−	1.69834i	0.483597	−	0.279205i	−0.238317	−	0.971187i	$-0.576596\pi$
$37$	2.94161	−	1.69834i	0.483597	−	0.279205i	0.721914	+	0.691982i	$0.243262\pi$
$38$	0.599255	+	1.03794i	0.0972121	+	0.168376i
$39$	0.531451	−	2.18020i	0.0851002	−	0.349111i
$40$	0.742703	−	1.28640i	0.117432	−	0.203397i
$41$	1.49289	+	0.861918i	0.233150	+	0.134609i	0.612024	−	0.790839i	$-0.290355\pi$
$41$	1.49289	+	0.861918i	0.233150	+	0.134609i	−0.378875	+	0.925448i	$0.623689\pi$
$42$	0.127344	−	0.220565i	0.0196495	−	0.0340340i
$43$	−1.66436	−	2.88275i	−0.253812	−	0.439616i	0.710760	−	0.703435i	$-0.248351\pi$
$43$	−1.66436	−	2.88275i	−0.253812	−	0.439616i	−0.964572	+	0.263819i	$0.915018\pi$
$44$	−7.55787	−	4.36354i	−1.13939	−	0.657828i
$45$	4.77101	−	2.75454i	0.711220	−	0.410623i
$46$			1.62227i			0.239191i
$47$			9.94211i			1.45021i	0.688641	+	0.725103i	$0.258208\pi$
$47$			9.94211i			1.45021i	−0.688641	+	0.725103i	$0.741792\pi$
$48$	1.18624	+	2.05463i	0.171219	+	0.296561i
$49$	−0.842774	+	1.45973i	−0.120396	+	0.208532i
$50$	−0.0851166	+	0.0491421i	−0.0120373	+	0.00694974i
$51$	−2.26321	+	3.91999i	−0.316912	+	0.548909i
$52$	−5.13131	−	4.90348i	−0.711584	−	0.679990i
$53$	−5.41936	+	9.38660i	−0.744406	+	1.28935i	0.206066	+	0.978538i	$0.433934\pi$
$53$	−5.41936	+	9.38660i	−0.744406	+	1.28935i	−0.950472	+	0.310811i	$0.899399\pi$
$54$		−	0.620076i		−	0.0843816i
$55$	−4.67418	−	8.09592i	−0.630266	−	1.09165i
$56$	−0.811978	−	1.40639i	−0.108505	−	0.187936i
$57$	−3.63924	−	2.10112i	−0.482030	−	0.278300i
$58$			0.113258i			0.0148716i
$59$	−1.57839	+	0.911283i	−0.205489	+	0.118639i	−0.599213	−	0.800590i	$-0.704520\pi$
$59$	−1.57839	+	0.911283i	−0.205489	+	0.118639i	0.393724	+	0.919229i	$0.371186\pi$
$60$			2.58340i			0.333515i
$61$	1.62489			0.208045			0.104023	−	0.994575i	$-0.466829\pi$
$61$	1.62489			0.208045			0.104023	+	0.994575i	$0.466829\pi$
$62$	0.659830	−	0.735808i	0.0837984	−	0.0934477i
$63$		−	6.02294i		−	0.758819i
$64$	7.25367			0.906709
$65$	−2.13392	−	7.29715i	−0.264680	−	0.905101i
$66$	−0.489793			−0.0602894
$67$	−1.49673	−	0.864137i	−0.182855	−	0.105571i	0.405779	−	0.913971i	$-0.367000\pi$
$67$	−1.49673	−	0.864137i	−0.182855	−	0.105571i	−0.588633	+	0.808400i	$0.700334\pi$
$68$	7.15813	+	12.3983i	0.868051	+	1.50351i
$69$	−2.84402	−	4.92599i	−0.342380	−	0.593019i
$70$		−	0.862877i		−	0.103134i
$71$	6.34620	+	3.66398i	0.753155	+	0.434834i	0.826833	−	0.562448i	$-0.190140\pi$
$71$	6.34620	+	3.66398i	0.753155	+	0.434834i	−0.0736778	+	0.997282i	$0.523474\pi$
$72$	−1.59388	−	0.920225i	−0.187840	−	0.108450i
$73$	1.36850	+	0.790105i	0.160171	+	0.0924748i	0.577943	−	0.816077i	$-0.303856\pi$
$73$	1.36850	+	0.790105i	0.160171	+	0.0924748i	−0.417772	+	0.908552i	$0.637189\pi$
$74$	−0.301470	−	0.522161i	−0.0350451	−	0.0607000i
$75$	0.172303	−	0.298437i	0.0198958	−	0.0344606i
$76$	−11.5103	+	6.64547i	−1.32032	+	0.762288i
$77$	−10.2203			−1.16471
$78$	−0.387004	−	0.0943371i	−0.0438195	−	0.0106816i
$79$	−2.85115	−	4.93834i	−0.320780	−	0.555607i	0.659869	−	0.751380i	$-0.270612\pi$
$79$	−2.85115	−	4.93834i	−0.320780	−	0.555607i	−0.980649	+	0.195774i	$0.937278\pi$
$80$	6.96108	+	4.01898i	0.778272	+	0.449336i
$81$	−2.83190	−	4.90499i	−0.314655	−	0.544999i
$82$	0.152998	−	0.265000i	0.0168958	−	0.0292644i
$83$	2.14235	+	1.23688i	0.235153	+	0.135766i	0.612947	−	0.790124i	$-0.289984\pi$
$83$	2.14235	+	1.23688i	0.235153	+	0.135766i	−0.377794	+	0.925890i	$0.623317\pi$
$84$	2.44597	+	1.41218i	0.266877	+	0.154082i
$85$			15.3354i			1.66336i
$86$	−0.511714	+	0.295438i	−0.0551795	+	0.0318579i
$87$	−0.198554	−	0.343906i	−0.0212872	−	0.0368706i
$88$	−1.56153	+	2.70465i	−0.166460	+	0.288317i
$89$		−	12.4713i		−	1.32195i	−0.750407	−	0.660976i	$-0.770143\pi$
$89$		−	12.4713i		−	1.32195i	0.750407	−	0.660976i	$-0.229857\pi$
$90$	−0.488955	−	0.846895i	−0.0515404	−	0.0892706i
$91$	−8.07545	−	1.96849i	−0.846537	−	0.206354i
$92$	−17.9903			−1.87562
$93$	−0.713603	+	3.39101i	−0.0739972	+	0.351632i
$94$	1.76481			0.182026
$95$	−14.2371			−1.46070
$96$	1.12410	−	0.649001i	0.114728	−	0.0662384i
$97$			7.23658i			0.734763i	0.930070	+	0.367382i	$0.119746\pi$
$97$			7.23658i			0.734763i	−0.930070	+	0.367382i	$0.880254\pi$
$98$	0.259114	+	0.149600i	0.0261745	+	0.0151118i
$99$	−10.0310	+	5.79142i	−1.00816	+	0.582059i
$100$	−0.544964	−	0.943905i	−0.0544964	−	0.0943905i
$101$	−7.19412			−0.715842			−0.357921	−	0.933752i	$-0.616514\pi$
$101$	−7.19412			−0.715842			−0.357921	+	0.933752i	$0.616514\pi$
$102$	0.695832	+	0.401739i	0.0688977	+	0.0397781i
$103$	6.73489	−	11.6652i	0.663608	−	1.14940i	−0.316053	−	0.948742i	$-0.602358\pi$
$103$	6.73489	−	11.6652i	0.663608	−	1.14940i	0.979661	−	0.200661i	$-0.0643090\pi$
$104$	−1.75475	+	1.83628i	−0.172068	+	0.180062i
$105$	1.51272	+	2.62010i	0.147626	+	0.255696i
$106$	1.66620	+	0.961983i	0.161836	+	0.0934360i
$107$	0.326395	+	0.565332i	0.0315538	+	0.0546527i	0.881371	−	0.472425i	$-0.156621\pi$
$107$	0.326395	+	0.565332i	0.0315538	+	0.0546527i	−0.849817	+	0.527077i	$0.823288\pi$
$108$	6.87636			0.661678
$109$		−	11.6385i		−	1.11476i	−0.830256	−	0.557382i	$-0.811806\pi$
$109$		−	11.6385i		−	1.11476i	0.830256	−	0.557382i	$-0.188194\pi$
$110$	−1.43710	+	0.829707i	−0.137022	+	0.0791095i
$111$	1.83081	+	1.05702i	0.173773	+	0.100328i
$112$	7.61037	−	4.39385i	0.719112	−	0.415180i
$113$	1.39270	−	2.41222i	0.131014	−	0.226923i	−0.793054	−	0.609152i	$-0.791510\pi$
$113$	1.39270	−	2.41222i	0.131014	−	0.226923i	0.924068	+	0.382229i	$0.124843\pi$
$114$	−0.372967	+	0.645997i	−0.0349315	+	0.0605032i
$115$	−16.6892	−	9.63551i	−1.55628	−	0.898516i
$116$	−1.25598			−0.116615
$117$	−9.04134	+	2.64397i	−0.835872	+	0.244436i
$118$	0.161761	+	0.280178i	0.0148913	+	0.0257924i
$119$	14.5197	+	8.38293i	1.33101	+	0.768462i
$120$	0.924491			0.0843941
$121$	4.32745	+	7.49537i	0.393405	+	0.681397i
$122$		−	0.288431i		−	0.0261133i
$123$			1.07289i			0.0967390i
$124$	8.15978	+	7.31721i	0.732770	+	0.657105i
$125$		−	11.7107i		−	1.04743i
$126$	−1.06912			−0.0952452
$127$	3.12070	+	5.40522i	0.276918	+	0.479635i	0.970617	−	0.240629i	$-0.0773538\pi$
$127$	3.12070	+	5.40522i	0.276918	+	0.479635i	−0.693700	+	0.720264i	$0.744020\pi$
$128$		−	5.45866i		−	0.482482i
$129$	1.03587	−	1.79418i	0.0912032	−	0.157969i
$130$	−1.29531	+	0.378789i	−0.113606	+	0.0332220i
$131$	−4.85712	−	8.41278i	−0.424369	−	0.735028i	0.571993	−	0.820259i	$-0.306171\pi$
$131$	−4.85712	−	8.41278i	−0.424369	−	0.735028i	−0.996361	+	0.0852308i	$0.972837\pi$
$132$		−	5.43159i		−	0.472759i
$133$	−7.78255	+	13.4798i	−0.674832	+	1.16884i
$134$	−0.153392	+	0.265682i	−0.0132510	+	0.0229515i
$135$	6.37905	+	3.68294i	0.549021	+	0.316977i
$136$	4.43682	−	2.56160i	0.380454	−	0.219655i
$137$	11.8923	+	6.86605i	1.01603	+	0.586606i	0.912952	−	0.408067i	$-0.133797\pi$
$137$	11.8923	+	6.86605i	1.01603	+	0.586606i	0.103080	+	0.994673i	$0.467130\pi$
$138$	−0.874406	+	0.504838i	−0.0744343	+	0.0429747i
$139$	−16.0370			−1.36024			−0.680119	−	0.733102i	$-0.738072\pi$
$139$	−16.0370			−1.36024			−0.680119	+	0.733102i	$0.738072\pi$
$140$	9.56891			0.808721
$141$	−5.35879	+	3.09390i	−0.451292	+	0.260554i
$142$	0.650388	−	1.12650i	0.0545793	−	0.0945342i
$143$	4.48656	+	15.3422i	0.375185	+	1.28298i
$144$	4.97961	−	8.62493i	0.414967	−	0.718744i
$145$	−1.16515	−	0.672699i	−0.0967604	−	0.0558646i
$146$	0.140251	−	0.242921i	0.0116072	−	0.0201043i
$147$	−1.04906			−0.0865248
$148$	5.79053	−	3.34316i	0.475978	−	0.274806i
$149$	4.51836	−	2.60868i	0.370159	−	0.213711i	−0.303369	−	0.952873i	$-0.598112\pi$
$149$	4.51836	−	2.60868i	0.370159	−	0.213711i	0.673528	+	0.739162i	$0.264778\pi$
$150$	−0.0529752	−	0.0305852i	−0.00432541	−	0.00249727i
$151$		−	15.8717i		−	1.29162i	−0.763496	−	0.645812i	$-0.776519\pi$
$151$		−	15.8717i		−	1.29162i	0.763496	−	0.645812i	$-0.223481\pi$
$152$	2.37814	+	4.11906i	0.192893	+	0.334100i
$153$	19.0010			1.53614
$154$			1.81420i			0.146192i
$155$	3.65059	+	11.1584i	0.293222	+	0.896261i
$156$	1.04616	−	4.29170i	0.0837595	−	0.343611i
$157$	12.7405			1.01680			0.508400	−	0.861121i	$-0.330237\pi$
$157$	12.7405			1.01680			0.508400	+	0.861121i	$0.330237\pi$
$158$	−0.876598	+	0.506104i	−0.0697384	+	0.0402635i
$159$	−6.74584			−0.534980
$160$	2.19881	−	3.80845i	0.173831	−	0.301084i
$161$	−18.2459	+	10.5343i	−1.43798	+	0.830216i
$162$	−0.870679	+	0.502687i	−0.0684070	+	0.0394948i
$163$		−	4.66669i		−	0.365523i	−0.983157	−	0.182762i	$-0.941496\pi$
$163$		−	4.66669i		−	0.365523i	0.983157	−	0.182762i	$-0.0585036\pi$
$164$	2.93873	+	1.69668i	0.229476	+	0.132488i
$165$	2.90913	−	5.03877i	0.226476	−	0.392267i
$166$	0.219558	−	0.380285i	0.0170410	−	0.0295158i
$167$	−13.0048	+	7.50835i	−1.00634	+	0.581014i	−0.910119	−	0.414346i	$-0.864010\pi$
$167$	−13.0048	+	7.50835i	−1.00634	+	0.581014i	−0.0962255	+	0.995360i	$0.530677\pi$
$168$	0.505362	−	0.875312i	0.0389895	−	0.0675318i
$169$	0.589988	+	12.9866i	0.0453837	+	0.998970i
$170$	2.72217			0.208781
$171$			17.6401i			1.34897i
$172$	−3.27628	−	5.67468i	−0.249814	−	0.432690i
$173$	7.62580	−	13.2083i	0.579779	−	1.00421i	−0.415726	−	0.909490i	$-0.636472\pi$
$173$	7.62580	−	13.2083i	0.579779	−	1.00421i	0.995504	−	0.0947160i	$-0.0301943\pi$
$174$	−0.0610463	+	0.0352451i	−0.00462791	+	0.00267192i
$175$	−1.10541	−	0.638210i	−0.0835613	−	0.0482441i
$176$	−14.6356	−	8.44989i	−1.10320	−	0.636935i
$177$	−0.982363	−	0.567167i	−0.0738389	−	0.0426309i
$178$	−2.21376			−0.165928
$179$	−1.05313	−	1.82407i	−0.0787145	−	0.136338i	0.823981	−	0.566617i	$-0.191748\pi$
$179$	−1.05313	−	1.82407i	−0.0787145	−	0.136338i	−0.902696	+	0.430280i	$0.858415\pi$
$180$	9.39168	−	5.42229i	0.700015	−	0.404154i
$181$	10.4591	−	18.1157i	0.777417	−	1.34653i	−0.156008	−	0.987756i	$-0.549863\pi$
$181$	10.4591	−	18.1157i	0.777417	−	1.34653i	0.933426	−	0.358771i	$-0.116804\pi$
$182$	−0.349425	+	1.43346i	−0.0259011	+	0.106255i
$183$	0.505651	+	0.875813i	0.0373788	+	0.0647420i
$184$			6.43798i			0.474614i
$185$	7.16233			0.526585
$186$	0.601934	+	0.126671i	0.0441359	+	0.00928794i
$187$		−	32.2427i		−	2.35782i
$188$			19.5709i			1.42736i
$189$	6.97405	−	4.02647i	0.507287	−	0.292883i
$190$			2.52721i			0.183343i
$191$	−3.86611	+	6.69631i	−0.279742	+	0.484528i	−0.971321	−	0.237774i	$-0.923582\pi$
$191$	−3.86611	+	6.69631i	−0.279742	+	0.484528i	0.691578	+	0.722301i	$0.256916\pi$
$192$	2.25728	+	3.90973i	0.162905	+	0.282160i
$193$	12.0335	−	6.94756i	0.866192	−	0.500096i	0.000111226	−	1.00000i	$-0.499965\pi$
$193$	12.0335	−	6.94756i	0.866192	−	0.500096i	0.866081	+	0.499904i	$0.166631\pi$
$194$	1.28456			0.0922257
$195$	3.26911	−	3.42100i	0.234106	−	0.244983i
$196$	−1.65899	+	2.87346i	−0.118499	+	0.205247i
$197$	10.5063	+	6.06582i	0.748543	+	0.432171i	0.825167	−	0.564889i	$-0.191081\pi$
$197$	10.5063	+	6.06582i	0.748543	+	0.432171i	−0.0766242	+	0.997060i	$0.524414\pi$
$198$	1.02803	+	1.78059i	0.0730587	+	0.126541i
$199$	3.32950	−	5.76686i	0.236022	−	0.408802i	−0.723547	−	0.690275i	$-0.757490\pi$
$199$	3.32950	−	5.76686i	0.236022	−	0.408802i	0.959569	+	0.281473i	$0.0908230\pi$
$200$	−0.337785	+	0.195020i	−0.0238850	+	0.0137900i
$201$		−	1.07565i		−	0.0758704i
$202$			1.27702i			0.0898507i
$203$	−1.27383	+	0.735445i	−0.0894052	+	0.0516181i
$204$	−4.45510	+	7.71647i	−0.311920	+	0.540261i
$205$	1.81746	+	3.14794i	0.126937	+	0.219862i
$206$	−2.07067	−	1.19550i	−0.144270	−	0.0832945i
$207$	−11.9386	+	20.6783i	−0.829791	+	1.43724i
$208$	−9.93666	−	9.49548i	−0.688983	−	0.658393i
$209$	29.9335			2.07055
$210$	0.465090	−	0.268520i	0.0320943	−	0.0185296i
$211$	−4.33279	−	7.50462i	−0.298282	−	0.516639i	0.677461	−	0.735558i	$-0.263080\pi$
$211$	−4.33279	−	7.50462i	−0.298282	−	0.516639i	−0.975743	+	0.218919i	$0.929747\pi$
$212$	−10.6680	+	18.4774i	−0.732678	+	1.26904i
$213$			4.56080i			0.312501i
$214$	0.100351	−	0.0579379i	0.00685988	−	0.00396055i
$215$		−	7.01903i		−	0.478694i
$216$		−	2.46076i		−	0.167434i
$217$	12.5603	+	2.64319i	0.852650	+	0.179431i
$218$	−2.06593			−0.139922
$219$			0.983497i			0.0664586i
$220$	−9.20108	−	15.9367i	−0.620337	−	1.07445i
$221$	6.21014	−	25.4762i	0.417739	−	1.71371i
$222$	0.187630	−	0.324984i	0.0125929	−	0.0218115i
$223$	15.2966	−	8.83148i	1.02433	−	0.591400i	0.108978	−	0.994044i	$-0.465242\pi$
$223$	15.2966	−	8.83148i	1.02433	−	0.591400i	0.915356	+	0.402644i	$0.131909\pi$
$224$	−2.40390	−	4.16368i	−0.160617	−	0.278198i
$225$	−1.44658			−0.0964389
$226$	−0.428190	−	0.247216i	−0.0284828	−	0.0164445i
$227$	18.7353	+	10.8168i	1.24351	+	0.717939i	0.969807	−	0.243875i	$-0.0784188\pi$
$227$	18.7353	+	10.8168i	1.24351	+	0.717939i	0.273701	+	0.961815i	$0.411752\pi$
$228$	−7.16382	−	4.13603i	−0.474435	−	0.273915i
$229$	−13.2127	+	7.62836i	−0.873121	+	0.504096i	−0.868384	−	0.495892i	$-0.834841\pi$
$229$	−13.2127	+	7.62836i	−0.873121	+	0.504096i	−0.00473670	+	0.999989i	$0.501508\pi$
$230$	−1.71039	+	2.96248i	−0.112780	+	0.195340i
$231$	−3.18048	−	5.50875i	−0.209260	−	0.362449i
$232$			0.449465i			0.0295088i
$233$	−11.1940			−0.733341			−0.366670	−	0.930351i	$-0.619502\pi$
$233$	−11.1940			−0.733341			−0.366670	+	0.930351i	$0.619502\pi$
$234$	0.469328	+	1.60492i	0.0306810	+	0.104917i
$235$	−10.4821	+	18.1555i	−0.683777	+	1.18434i
$236$	−3.10704	+	1.79385i	−0.202251	+	0.116770i
$237$	1.77451	−	3.07354i	0.115267	−	0.199648i
$238$	1.48804	−	2.57736i	0.0964554	−	0.167066i
$239$	−13.4528	−	7.76696i	−0.870187	−	0.502403i	−0.00277683	−	0.999996i	$-0.500884\pi$
$239$	−13.4528	−	7.76696i	−0.870187	−	0.502403i	−0.867410	+	0.497593i	$0.834217\pi$
$240$			5.00269i			0.322922i
$241$	2.34241	−	1.35239i	0.150888	−	0.0871151i	−0.422655	−	0.906291i	$-0.638902\pi$
$241$	2.34241	−	1.35239i	0.150888	−	0.0871151i	0.573543	+	0.819175i	$0.305569\pi$
$242$	1.33049	−	0.768160i	0.0855273	−	0.0493792i
$243$	7.00235	−	12.1284i	0.449201	−	0.778039i
$244$	3.19857			0.204768
$245$	−3.07802	+	1.77710i	−0.196648	+	0.113535i
$246$	0.190447			0.0121424
$247$	23.6516	+	5.76537i	1.50491	+	0.366842i
$248$	2.61853	−	2.92005i	0.166277	−	0.185423i
$249$			1.53963i			0.0975702i
$250$	−2.07874			−0.131471
$251$	−5.56233	−	9.63424i	−0.351091	−	0.608108i	0.635350	−	0.772225i	$-0.280856\pi$
$251$	−5.56233	−	9.63424i	−0.351091	−	0.608108i	−0.986441	+	0.164117i	$0.947523\pi$
$252$		−	11.8561i		−	0.746864i
$253$	35.0890	+	20.2586i	2.20603	+	1.27365i
$254$	0.959472	−	0.553952i	0.0602027	−	0.0347580i
$255$	−8.26580	+	4.77226i	−0.517625	+	0.298851i
$256$	13.5384			0.846149
$257$	−4.82248	+	8.35277i	−0.300818	+	0.521032i	−0.976321	−	0.216325i	$-0.930593\pi$
$257$	−4.82248	+	8.35277i	−0.300818	+	0.521032i	0.675504	+	0.737357i	$0.263926\pi$
$258$	−0.318482	−	0.183876i	−0.0198278	−	0.0114476i
$259$	3.91519	−	6.78132i	0.243278	−	0.421370i
$260$	−4.20060	−	14.3644i	−0.260510	−	0.890841i
$261$	−0.833490	+	1.44365i	−0.0515917	+	0.0893595i
$262$	−1.49334	+	0.862181i	−0.0922589	+	0.0532657i
$263$	19.2206			1.18519			0.592597	−	0.805499i	$-0.298103\pi$
$263$	19.2206			1.18519			0.592597	+	0.805499i	$0.298103\pi$
$264$	−1.94374			−0.119629
$265$	−19.7929	+	11.4274i	−1.21587	+	0.701980i
$266$	2.39277	+	1.38147i	0.146710	+	0.0847033i
$267$	6.72201	−	3.88095i	0.411380	−	0.237511i
$268$	−2.94630	−	1.70105i	−0.179974	−	0.103908i
$269$	−2.47431	+	4.28562i	−0.150861	+	0.261299i	−0.931544	−	0.363628i	$-0.881538\pi$
$269$	−2.47431	+	4.28562i	−0.150861	+	0.261299i	0.780683	+	0.624927i	$0.214871\pi$
$270$	0.653754	−	1.13234i	0.0397862	−	0.0689118i
$271$		−	4.03105i		−	0.244869i	−0.992477	−	0.122434i	$-0.960930\pi$
$271$		−	4.03105i		−	0.244869i	0.992477	−	0.122434i	$-0.0390701\pi$
$272$	13.8616	+	24.0089i	0.840481	+	1.45576i
$273$	−1.45200	−	4.96525i	−0.0878788	−	0.300510i
$274$	1.21878	−	2.11099i	0.0736294	−	0.127530i
$275$			2.45471i			0.148024i
$276$	−5.59843	−	9.69676i	−0.336986	−	0.583677i
$277$	11.7173			0.704027			0.352013	−	0.935995i	$-0.385497\pi$
$277$	11.7173			0.704027			0.352013	+	0.935995i	$0.385497\pi$
$278$			2.84670i			0.170734i
$279$	13.8255	−	4.52316i	0.827709	−	0.270795i
$280$		−	3.42432i		−	0.204642i
$281$		−	19.6933i		−	1.17480i	−0.809296	−	0.587401i	$-0.800151\pi$
$281$		−	19.6933i		−	1.17480i	0.809296	−	0.587401i	$-0.199849\pi$
$282$	0.549194	+	0.951232i	0.0327040	+	0.0566451i
$283$	−15.8694			−0.943336			−0.471668	−	0.881776i	$-0.656348\pi$
$283$	−15.8694			−0.943336			−0.471668	+	0.881776i	$0.656348\pi$
$284$	12.4924	+	7.21251i	0.741289	+	0.427983i
$285$	−4.43048	−	7.67381i	−0.262439	−	0.454557i
$286$	2.72338	−	0.796403i	0.161037	−	0.0470923i
$287$	3.97398			0.234576
$288$	−4.71875	−	2.72437i	−0.278055	−	0.160535i
$289$	−17.9462	+	31.0837i	−1.05566	+	1.82845i
$290$	−0.119410	+	0.206824i	−0.00701199	+	0.0121451i
$291$	−3.90052	+	2.25196i	−0.228652	+	0.132012i
$292$	2.69388	+	1.55531i	0.157648	+	0.0910179i
$293$	−18.6240	+	10.7526i	−1.08803	+	0.628172i	−0.933050	−	0.359746i	$-0.882863\pi$
$293$	−18.6240	+	10.7526i	−1.08803	+	0.628172i	−0.154976	+	0.987918i	$0.549530\pi$
$294$			0.186217i			0.0108604i
$295$	−3.84311			−0.223755
$296$	−1.19638	−	2.07219i	−0.0695381	−	0.120444i
$297$	−13.4119	−	7.74338i	−0.778239	−	0.449316i
$298$	−0.463063	−	0.802048i	−0.0268245	−	0.0464614i
$299$	23.8232	+	22.7654i	1.37773	+	1.31656i
$300$	0.339176	−	0.587471i	0.0195824	−	0.0339176i
$301$	−6.64564	−	3.83686i	−0.383048	−	0.221153i
$302$	−2.81737			−0.162122
$303$	−2.23875	−	3.87763i	−0.128613	−	0.222764i
$304$	−22.2894	+	12.8688i	−1.27839	+	0.738076i
$305$	2.96724	+	1.71314i	0.169904	+	0.0980941i
$306$		−	3.37284i		−	0.192812i
$307$	−13.3403	+	7.70204i	−0.761373	+	0.439579i	−0.829788	−	0.558078i	$-0.811539\pi$
$307$	−13.3403	+	7.70204i	−0.761373	+	0.439579i	0.0684155	+	0.997657i	$0.478206\pi$
$308$	−20.1186			−1.14636
$309$	8.38336			0.476913
$310$	1.98070	−	0.648011i	0.112496	−	0.0368045i
$311$	−6.08294			−0.344932			−0.172466	−	0.985016i	$-0.555173\pi$
$311$	−6.08294			−0.344932			−0.172466	+	0.985016i	$0.555173\pi$
$312$	−1.53582	−	0.374376i	−0.0869487	−	0.0211949i
$313$	13.0147	+	22.5421i	0.735633	+	1.27415i	0.954445	+	0.298387i	$0.0964485\pi$
$313$	13.0147	+	22.5421i	0.735633	+	1.27415i	−0.218812	+	0.975767i	$0.570218\pi$
$314$		−	2.26154i		−	0.127626i
$315$	6.35007	−	10.9986i	0.357786	−	0.619704i
$316$	−5.61247	−	9.72108i	−0.315726	−	0.546853i
$317$	1.29542	−	0.747913i	0.0727582	−	0.0420070i	−0.463180	−	0.886264i	$-0.653291\pi$
$317$	1.29542	−	0.747913i	0.0727582	−	0.0420070i	0.535938	+	0.844257i	$0.319958\pi$
$318$			1.19744i			0.0671493i
$319$	2.44972	+	1.41435i	0.137158	+	0.0791883i
$320$	13.2461	+	7.64765i	0.740481	+	0.427517i
$321$	−0.203143	+	0.351853i	−0.0113383	+	0.0196385i
$322$	1.86992	+	3.23880i	0.104207	+	0.180491i
$323$	−42.5255	−	24.5521i	−2.36618	−	1.36612i
$324$	−5.57457	−	9.65543i	−0.309698	−	0.536413i
$325$	−0.472791	+	1.93955i	−0.0262257	+	0.107587i
$326$	−0.828377			−0.0458796
$327$	6.27314	−	3.62180i	0.346905	−	0.200286i
$328$	0.607171	−	1.05165i	0.0335254	−	0.0580677i
$329$	11.4598	+	19.8490i	0.631800	+	1.09431i
$330$	−0.894424	−	0.516396i	−0.0492364	−	0.0284267i
$331$	27.2646	+	15.7412i	1.49860	+	0.865215i	0.999999	−	0.00161815i	$-0.000515075\pi$
$331$	27.2646	+	15.7412i	1.49860	+	0.865215i	0.498598	+	0.866833i	$0.333848\pi$
$332$	4.21719	+	2.43480i	0.231448	+	0.133627i
$333$		−	8.87429i		−	0.486308i
$334$	1.33280	+	2.30847i	0.0729274	+	0.126314i
$335$	−1.82214	−	3.15604i	−0.0995543	−	0.172433i
$336$	4.73657	+	2.73466i	0.258401	+	0.149188i
$337$	6.70046			0.364998			0.182499	−	0.983206i	$-0.441581\pi$
$337$	6.70046			0.364998			0.182499	+	0.983206i	$0.441581\pi$
$338$	2.30523	−	0.104728i	0.125388	−	0.00569645i
$339$	1.73358			0.0941552
$340$			30.1877i			1.63716i
$341$	−7.67535	−	23.4604i	−0.415643	−	1.27045i
$342$	3.13128			0.169320
$343$			20.0229i			1.08113i
$344$	−2.03073	+	1.17244i	−0.109490	+	0.0632139i
$345$		−	11.9940i		−	0.645733i
$346$	−2.34458	−	1.35364i	−0.126045	−	0.0727724i
$347$	−10.5100	−	18.2038i	−0.564206	−	0.977233i	−0.997123	−	0.0757993i	$-0.975849\pi$
$347$	−10.5100	−	18.2038i	−0.564206	−	0.977233i	0.432917	−	0.901434i	$-0.357484\pi$
$348$	−0.390852	−	0.676976i	−0.0209519	−	0.0362897i
$349$		−	21.2859i		−	1.13941i	−0.821850	−	0.569704i	$-0.807058\pi$
$349$		−	21.2859i		−	1.13941i	0.821850	−	0.569704i	$-0.192942\pi$
$350$	−0.113288	+	0.196220i	−0.00605549	+	0.0104884i
$351$	−9.10583	−	8.70154i	−0.486033	−	0.464454i
$352$	−4.62299	+	8.00725i	−0.246406	+	0.426788i
$353$	2.90376	−	1.67649i	0.154551	−	0.0892303i	−0.420730	−	0.907186i	$-0.638226\pi$
$353$	2.90376	−	1.67649i	0.154551	−	0.0892303i	0.575281	+	0.817956i	$0.304893\pi$
$354$	−0.100677	+	0.174378i	−0.00535093	+	0.00926808i
$355$	7.72597	+	13.3818i	0.410052	+	0.710230i
$356$		−	24.5496i		−	1.30112i
$357$			10.4348i			0.552268i
$358$	−0.323789	+	0.186939i	−0.0171128	+	0.00988006i
$359$	−15.9483	−	9.20775i	−0.841718	−	0.485966i	0.0161297	−	0.999870i	$-0.494866\pi$
$359$	−15.9483	−	9.20775i	−0.841718	−	0.485966i	−0.857848	+	0.513904i	$0.828199\pi$
$360$	−1.94041	−	3.36089i	−0.102269	−	0.177135i
$361$	13.2937	−	23.0254i	0.699668	−	1.21186i
$362$	−3.21569	−	1.85658i	−0.169013	−	0.0975796i
$363$	−2.69333	+	4.66499i	−0.141363	+	0.244849i
$364$	−15.8965	−	3.87496i	−0.833200	−	0.203103i
$365$	1.66604	+	2.88566i	0.0872044	+	0.151043i
$366$	0.155464	−	0.0897574i	0.00812625	−	0.00469169i
$367$	−13.5138	+	23.4067i	−0.705417	+	1.22182i	0.261124	+	0.965305i	$0.415907\pi$
$367$	−13.5138	+	23.4067i	−0.705417	+	1.22182i	−0.966541	+	0.256513i	$0.917426\pi$
$368$	−34.8378			−1.81604
$369$	3.90037	−	2.25188i	0.203045	−	0.117228i
$370$		−	1.27137i		−	0.0660956i
$371$			24.9866i			1.29724i
$372$	−1.40472	+	6.67518i	−0.0728314	+	0.346092i
$373$	−24.1486			−1.25037			−0.625183	−	0.780478i	$-0.714976\pi$
$373$	−24.1486			−1.25037			−0.625183	+	0.780478i	$0.714976\pi$
$374$	−5.72336			−0.295948
$375$	6.31204	−	3.64426i	0.325953	−	0.188189i
$376$	7.00363			0.361185
$377$	1.66320	+	1.58936i	0.0856594	+	0.0818562i
$378$	−0.714733	−	1.23795i	−0.0367619	−	0.0636735i
$379$	18.4380	−	10.6452i	0.947095	−	0.546806i	0.0549180	−	0.998491i	$-0.482510\pi$
$379$	18.4380	−	10.6452i	0.947095	−	0.546806i	0.892177	+	0.451685i	$0.149177\pi$
$380$	−28.0257			−1.43769
$381$	−1.94227	+	3.36412i	−0.0995057	+	0.172349i
$382$	1.18865	+	0.686269i	0.0608167	+	0.0351126i
$383$	8.11184	+	4.68337i	0.414496	+	0.239309i	0.692720	−	0.721207i	$-0.256412\pi$
$383$	8.11184	+	4.68337i	0.414496	+	0.239309i	−0.278224	+	0.960516i	$0.589746\pi$
$384$	2.94222	−	1.69869i	0.150144	−	0.0866859i
$385$	−18.6636	−	10.7754i	−0.951185	−	0.549167i
$386$	−1.23325	−	2.13606i	−0.0627709	−	0.108722i
$387$	−8.69674			−0.442080
$388$			14.2451i			0.723187i
$389$	12.7629	+	22.1060i	0.647106	+	1.12082i	0.983811	+	0.179211i	$0.0573543\pi$
$389$	12.7629	+	22.1060i	0.647106	+	1.12082i	−0.336705	+	0.941610i	$0.609312\pi$
$390$	−0.607256	−	0.580295i	−0.0307496	−	0.0293844i
$391$	−33.2331	−	57.5615i	−1.68067	−	2.91101i
$392$	1.02829	+	0.593685i	0.0519366	+	0.0299856i
$393$	3.02299	−	5.23597i	0.152490	−	0.264120i
$394$	1.07673	−	1.86496i	0.0542451	−	0.0939553i
$395$		−	12.0240i		−	0.604995i
$396$	−19.7460	+	11.4004i	−0.992273	+	0.572889i
$397$	−9.57746	+	5.52955i	−0.480679	+	0.277520i	−0.720699	−	0.693248i	$-0.756179\pi$
$397$	−9.57746	+	5.52955i	−0.480679	+	0.277520i	0.240020	+	0.970768i	$0.422846\pi$
$398$	−1.02367	−	0.591014i	−0.0513118	−	0.0296249i
$399$	−9.68745			−0.484979
$400$	−1.05531	−	1.82785i	−0.0527655	−	0.0913925i
$401$			27.5214i			1.37435i	0.726490	+	0.687177i	$0.241150\pi$
$401$			27.5214i			1.37435i	−0.726490	+	0.687177i	$0.758850\pi$
$402$	−0.190937			−0.00952307
$403$	−1.54596	−	20.0152i	−0.0770097	−	0.997030i
$404$	−14.1616			−0.704564
$405$		−	11.9428i		−	0.593445i
$406$	0.130548	+	0.226116i	0.00647898	+	0.0112219i
$407$	−15.0588			−0.746436
$408$	2.76140	+	1.59430i	0.136710	+	0.0789295i
$409$	−6.83852	+	3.94822i	−0.338143	+	0.195227i	−0.659451	−	0.751748i	$-0.729211\pi$
$409$	−6.83852	+	3.94822i	−0.338143	+	0.195227i	0.321307	+	0.946975i	$0.395878\pi$
$410$	0.558787	−	0.322616i	0.0275965	−	0.0159329i
$411$			8.54663i			0.421574i
$412$	13.2576	−	22.9628i	0.653153	−	1.13129i
$413$	−2.10079	+	3.63867i	−0.103373	+	0.179047i
$414$	3.67058	+	2.11921i	0.180399	+	0.104153i
$415$	2.60813	+	4.51741i	0.128028	+	0.221751i
$416$	−5.19504	+	5.43641i	−0.254708	+	0.266542i
$417$	−4.99057	−	8.64392i	−0.244389	−	0.423295i
$418$		−	5.31346i		−	0.259890i
$419$	26.9102			1.31465			0.657324	−	0.753608i	$-0.271688\pi$
$419$	26.9102			1.31465			0.657324	+	0.753608i	$0.271688\pi$
$420$	2.97777	+	5.15764i	0.145300	+	0.251667i
$421$	23.0878	+	13.3298i	1.12523	+	0.649653i	0.942731	−	0.333553i	$-0.108248\pi$
$421$	23.0878	+	13.3298i	1.12523	+	0.649653i	0.182500	+	0.983206i	$0.441581\pi$
$422$	−1.33213	+	0.769108i	−0.0648473	+	0.0374396i
$423$	22.4951	+	12.9876i	1.09375	+	0.631477i
$424$	6.61231	+	3.81762i	0.321122	+	0.185400i
$425$	2.01340	−	3.48732i	0.0976644	−	0.169160i
$426$	0.809581			0.0392243
$427$	3.24401	−	1.87293i	0.156989	−	0.0906375i
$428$	0.642505	+	1.11285i	0.0310566	+	0.0537917i
$429$	−6.87329	+	7.19263i	−0.331846	+	0.347264i
$430$	−1.24594			−0.0600845
$431$	−25.2229	+	14.5624i	−1.21494	+	0.701448i	−0.963832	−	0.266510i	$-0.914129\pi$
$431$	−25.2229	+	14.5624i	−1.21494	+	0.701448i	−0.251111	+	0.967958i	$0.580796\pi$
$432$	13.3159			0.640662
$433$	22.0114			1.05780			0.528899	−	0.848685i	$-0.322605\pi$
$433$	22.0114			1.05780			0.528899	+	0.848685i	$0.322605\pi$
$434$	0.469188	−	2.22957i	0.0225218	−	0.107023i
$435$		−	0.837354i		−	0.0401480i
$436$		−	22.9102i		−	1.09720i
$437$	53.4389	−	30.8530i	2.55633	−	1.47590i
$438$	0.174579			0.00834172
$439$	−16.3497	+	28.3185i	−0.780329	+	1.35157i	0.151422	+	0.988469i	$0.451615\pi$
$439$	−16.3497	+	28.3185i	−0.780329	+	1.35157i	−0.931750	+	0.363100i	$0.881718\pi$
$440$	−5.70310	+	3.29269i	−0.271885	+	0.156973i
$441$	2.20186	+	3.81374i	0.104851	+	0.181607i
$442$	−4.52224	−	1.10235i	−0.215101	−	0.0524336i
$443$	1.55276	−	2.68946i	0.0737739	−	0.127780i	−0.826779	−	0.562528i	$-0.809829\pi$
$443$	1.55276	−	2.68946i	0.0737739	−	0.127780i	0.900552	+	0.434747i	$0.143162\pi$
$444$	3.60393	+	2.08073i	0.171035	+	0.0987470i
$445$	13.1486	−	22.7741i	0.623305	−	1.07960i
$446$	−1.56766	−	2.71527i	−0.0742311	−	0.128572i
$447$	2.81215	+	1.62360i	0.133010	+	0.0767935i
$448$	14.4816	−	8.36098i	0.684193	−	0.395019i
$449$		−	27.4104i		−	1.29358i	−0.762670	−	0.646788i	$-0.776112\pi$
$449$		−	27.4104i		−	1.29358i	0.762670	−	0.646788i	$-0.223888\pi$
$450$			0.256781i			0.0121048i
$451$	−3.82121	−	6.61854i	−0.179934	−	0.311655i
$452$	2.74151	−	4.74843i	0.128950	−	0.223348i
$453$	8.55487	−	4.93916i	0.401943	−	0.232062i
$454$	1.92008	−	3.32568i	0.0901140	−	0.156082i
$455$	−12.6714	−	12.1088i	−0.594043	−	0.567668i
$456$	−1.48011	+	2.56363i	−0.0693127	+	0.120053i
$457$			28.3739i			1.32728i	0.748054	+	0.663638i	$0.230989\pi$
$457$			28.3739i			1.32728i	−0.748054	+	0.663638i	$0.769011\pi$
$458$	1.35410	+	2.34537i	0.0632730	+	0.109592i
$459$	12.7026	+	22.0015i	0.592905	+	1.02694i
$460$	−32.8525	−	18.9674i	−1.53176	−	0.884360i
$461$		−	8.45607i		−	0.393838i	−0.980420	−	0.196919i	$-0.936906\pi$
$461$		−	8.45607i		−	0.393838i	0.980420	−	0.196919i	$-0.0630937\pi$
$462$	−0.977851	+	0.564563i	−0.0454938	+	0.0262658i
$463$			11.7725i			0.547113i	0.961856	+	0.273557i	$0.0882001\pi$
$463$			11.7725i			0.547113i	−0.961856	+	0.273557i	$0.911800\pi$
$464$	−2.43219			−0.112911
$465$	−4.87832	+	5.44005i	−0.226227	+	0.252276i
$466$			1.98702i			0.0920472i
$467$	−10.9044			−0.504596			−0.252298	−	0.967650i	$-0.581186\pi$
$467$	−10.9044			−0.504596			−0.252298	+	0.967650i	$0.581186\pi$
$468$	−17.7978	+	5.20464i	−0.822703	+	0.240585i
$469$	−3.98421			−0.183974
$470$	3.22277	+	1.86066i	0.148655	+	0.0858260i
$471$	3.96473	+	6.86711i	0.182685	+	0.316420i
$472$	0.641945	+	1.11188i	0.0295479	+	0.0511785i
$473$			14.7575i			0.678550i
$474$	−0.545580	−	0.314991i	−0.0250593	−	0.0144680i
$475$	3.23756	+	1.86920i	0.148549	+	0.0857650i
$476$	28.5818	+	16.5017i	1.31004	+	0.756355i
$477$	14.1588	+	24.5238i	0.648288	+	1.12287i
$478$	−1.37870	+	2.38798i	−0.0630604	+	0.109224i
$479$	−27.5740	+	15.9199i	−1.25989	+	0.727398i	−0.973053	−	0.230582i	$-0.925937\pi$
$479$	−27.5740	+	15.9199i	−1.25989	+	0.727398i	−0.286837	+	0.957979i	$0.592604\pi$
$480$	2.73700			0.124927
$481$	−11.8985	−	2.90041i	−0.542524	−	0.132247i
$482$	−0.240061	−	0.415798i	−0.0109345	−	0.0189391i
$483$	−11.3559	−	6.55635i	−0.516713	−	0.298324i
$484$	8.51855	+	14.7546i	0.387207	+	0.670662i
$485$	−7.62963	+	13.2149i	−0.346444	+	0.600058i
$486$	−2.15290	−	1.24298i	−0.0976575	−	0.0563826i
$487$	−31.0021	−	17.8991i	−1.40484	−	0.811083i	−0.409954	−	0.912106i	$-0.634455\pi$
$487$	−31.0021	−	17.8991i	−1.40484	−	0.811083i	−0.994884	+	0.101023i	$0.967788\pi$
$488$		−	1.14464i		−	0.0518153i
$489$	2.51534	−	1.45223i	0.113748	−	0.0656723i
$490$	0.315450	+	0.546375i	0.0142506	+	0.0246827i
$491$	8.97171	−	15.5395i	0.404888	−	0.701286i	−0.589421	−	0.807826i	$-0.700644\pi$
$491$	8.97171	−	15.5395i	0.404888	−	0.701286i	0.994308	+	0.106540i	$0.0339773\pi$
$492$			2.11197i			0.0952149i
$493$	−2.32016	−	4.01863i	−0.104495	−	0.180990i
$494$	1.02340	−	4.19836i	0.0460451	−	0.188893i
$495$	−24.4239			−1.09777
$496$	15.8012	+	14.1696i	0.709496	+	0.636234i
$497$	16.8932			0.757764
$498$	0.273298			0.0122468
$499$	0.917631	−	0.529795i	0.0410788	−	0.0237169i	−0.479320	−	0.877640i	$-0.659117\pi$
$499$	0.917631	−	0.529795i	0.0410788	−	0.0237169i	0.520399	+	0.853923i	$0.325783\pi$
$500$		−	23.0523i		−	1.03093i
$501$	−8.09400	−	4.67307i	−0.361613	−	0.208777i
$502$	−1.71016	+	0.987362i	−0.0763282	+	0.0440681i
$503$	8.39005	+	14.5320i	0.374094	+	0.647949i	0.990191	−	0.139721i	$-0.0446205\pi$
$503$	8.39005	+	14.5320i	0.374094	+	0.647949i	−0.616097	+	0.787670i	$0.711287\pi$
$504$	−4.24281			−0.188990
$505$	−13.1374	−	7.58487i	−0.584605	−	0.337522i
$506$	3.59608	−	6.22860i	0.159865	−	0.276895i
$507$	−6.81618	+	4.35933i	−0.302717	+	0.193605i
$508$	6.14307	+	10.6401i	0.272555	+	0.472079i
$509$	−12.0337	−	6.94766i	−0.533384	−	0.307950i	0.209009	−	0.977914i	$-0.432976\pi$
$509$	−12.0337	−	6.94766i	−0.533384	−	0.307950i	−0.742394	+	0.669964i	$0.766309\pi$
$510$	0.847118	+	1.46725i	0.0375110	+	0.0649710i
$511$	3.64287			0.161151
$512$		−	13.3205i		−	0.588688i
$513$	−20.4258	+	11.7928i	−0.901819	+	0.520666i
$514$	1.48269	+	0.856031i	0.0653986	+	0.0377579i
$515$	24.5975	−	14.2014i	1.08390	−	0.625787i
$516$	2.03910	−	3.53182i	0.0897663	−	0.155480i
$517$	22.0386	−	38.1720i	0.969256	−	1.67880i
$518$	−1.20374	−	0.694981i	−0.0528894	−	0.0305357i
$519$	9.49234			0.416667
$520$	−5.14042	+	1.50322i	−0.225422	+	0.0659206i
$521$	10.1180	+	17.5249i	0.443278	+	0.767779i	0.997930	−	0.0643026i	$-0.0204823\pi$
$521$	10.1180	+	17.5249i	0.443278	+	0.767779i	−0.554653	+	0.832082i	$0.687149\pi$
$522$	0.256260	+	0.147952i	0.0112162	+	0.00647567i
$523$	14.1021			0.616643			0.308321	−	0.951282i	$-0.400233\pi$
$523$	14.1021			0.616643			0.308321	+	0.951282i	$0.400233\pi$
$524$	−9.56120	−	16.5605i	−0.417683	−	0.723448i
$525$		−	0.794423i		−	0.0346714i
$526$		−	3.41183i		−	0.148763i
$527$	−8.33863	+	39.6249i	−0.363237	+	1.72609i
$528$		−	10.5181i		−	0.457744i
$529$	60.5237			2.63146
$530$	2.02846	+	3.51340i	0.0881108	+	0.152612i
$531$			4.76171i			0.206640i
$532$	−15.3199	+	26.5348i	−0.664201	+	1.15043i
$533$	−1.74451	−	5.96554i	−0.0755632	−	0.258396i
$534$	−0.688903	−	1.19321i	−0.0298117	−	0.0516354i
$535$			1.37649i			0.0595109i
$536$	−0.608734	+	1.05436i	−0.0262933	+	0.0455413i
$537$	0.655450	−	1.13527i	0.0282847	−	0.0489906i
$538$	0.760735	+	0.439211i	0.0327976	+	0.0189357i
$539$	6.47153	−	3.73634i	0.278749	−	0.160936i
$540$	12.5571	+	7.24984i	0.540371	+	0.311983i
$541$	−33.7679	+	19.4959i	−1.45180	+	0.838194i	−0.998583	−	0.0532085i	$-0.983055\pi$
$541$	−33.7679	+	19.4959i	−1.45180	+	0.838194i	−0.453212	+	0.891403i	$0.649722\pi$
$542$	−0.715546			−0.0307353
$543$	13.0191			0.558704
$544$	13.1354	−	7.58375i	0.563177	−	0.325150i
$545$	12.2706	−	21.2533i	0.525615	−	0.910392i
$546$	−0.881374	+	0.257742i	−0.0377193	+	0.0110303i
$547$	−16.2249	+	28.1024i	−0.693727	+	1.20157i	0.276881	+	0.960904i	$0.410699\pi$
$547$	−16.2249	+	28.1024i	−0.693727	+	1.20157i	−0.970608	+	0.240667i	$0.922634\pi$
$548$	23.4100	+	13.5158i	1.00002	+	0.577364i
$549$	2.12262	−	3.67648i	0.0905912	−	0.156909i
$550$	0.435732			0.0185797
$551$	3.73082	−	2.15399i	0.158938	−	0.0917630i
$552$	−3.47007	+	2.00345i	−0.147696	+	0.0852723i
$553$	−11.3844	−	6.57279i	−0.484114	−	0.279503i
$554$		−	2.07993i		−	0.0883677i
$555$	2.22886	+	3.86049i	0.0946097	+	0.163869i
$556$	−31.5686			−1.33881
$557$		−	7.40371i		−	0.313705i	−0.987622	−	0.156853i	$-0.949865\pi$
$557$		−	7.40371i		−	0.313705i	0.987622	−	0.156853i	$-0.0501347\pi$
$558$	−0.802900	−	2.45414i	−0.0339895	−	0.103892i
$559$	−2.84238	+	11.6604i	−0.120220	+	0.493184i
$560$	18.5300			0.783035
$561$	17.3788	−	10.0337i	0.733735	−	0.423622i
$562$	−3.49572			−0.147458
$563$	17.7861	−	30.8064i	0.749595	−	1.29834i	−0.198422	−	0.980117i	$-0.563582\pi$
$563$	17.7861	−	30.8064i	0.749595	−	1.29834i	0.948017	−	0.318220i	$-0.103085\pi$
$564$	−10.5487	+	6.09032i	−0.444182	+	0.256449i
$565$	5.08648	−	2.93668i	0.213990	−	0.123547i
$566$			2.81695i			0.118405i
$567$	−11.3075	−	6.52840i	−0.474872	−	0.274167i
$568$	2.58106	−	4.47052i	0.108299	−	0.187579i
$569$	2.69060	−	4.66026i	0.112796	−	0.195368i	−0.804101	−	0.594493i	$-0.797353\pi$
$569$	2.69060	−	4.66026i	0.112796	−	0.195368i	0.916896	+	0.399125i	$0.130686\pi$
$570$	−1.36217	+	0.786448i	−0.0570549	+	0.0329407i
$571$	−13.9447	+	24.1530i	−0.583569	+	1.01077i	0.411483	+	0.911417i	$0.365011\pi$
$571$	−13.9447	+	24.1530i	−0.583569	+	1.01077i	−0.995052	+	0.0993539i	$0.968322\pi$
$572$	8.83175	+	30.2011i	0.369274	+	1.26277i
$573$	−4.81241			−0.201041
$574$		−	0.705415i		−	0.0294435i
$575$	2.53011	+	4.38228i	0.105513	+	0.182754i
$576$	9.47561	−	16.4122i	0.394817	−	0.683844i
$577$	37.5618	−	21.6863i	1.56372	−	0.902812i	0.566841	−	0.823827i	$-0.308165\pi$
$577$	37.5618	−	21.6863i	1.56372	−	0.902812i	0.996876	−	0.0789849i	$-0.0251679\pi$
$578$	5.51762	+	3.18560i	0.229503	+	0.132504i
$579$	7.48947	+	4.32405i	0.311252	+	0.179701i
$580$	−2.29359	−	1.32420i	−0.0952360	−	0.0549845i
$581$	5.70280			0.236592
$582$	0.399743	+	0.692375i	0.0165699	+	0.0286999i
$583$	41.6144	−	24.0261i	1.72349	−	0.995059i
$584$	0.556583	−	0.964030i	0.0230316	−	0.0398918i
$585$	−19.2982	−	4.70418i	−0.797883	−	0.194494i
$586$	1.90868	+	3.30592i	0.0788467	+	0.136566i
$587$		−	27.9682i		−	1.15437i	−0.816614	−	0.577185i	$-0.804151\pi$
$587$		−	27.9682i		−	1.15437i	0.816614	−	0.577185i	$-0.195849\pi$
$588$	−2.06506			−0.0851616
$589$	−36.7870	−	7.74142i	−1.51578	−	0.318980i
$590$			0.682186i			0.0280851i
$591$			7.55053i			0.310587i
$592$	11.2132	−	6.47396i	0.460861	−	0.266078i
$593$			13.4247i			0.551288i	0.961260	+	0.275644i	$0.0888911\pi$
$593$			13.4247i			0.551288i	−0.961260	+	0.275644i	$0.911109\pi$
$594$	−1.37452	+	2.38073i	−0.0563971	+	0.0976827i
$595$	17.6765	+	30.6166i	0.724665	+	1.25516i
$596$	8.89436	−	5.13516i	0.364327	−	0.210344i
$597$	4.14445			0.169621
$598$	4.04106	−	4.22882i	0.165251	−	0.172929i
$599$	8.84805	−	15.3253i	0.361522	−	0.626174i	−0.626690	−	0.779269i	$-0.715591\pi$
$599$	8.84805	−	15.3253i	0.361522	−	0.626174i	0.988211	+	0.153095i	$0.0489241\pi$
$600$	−0.210232	−	0.121377i	−0.00858267	−	0.00495520i
$601$	−7.09939	−	12.2965i	−0.289590	−	0.501585i	0.684122	−	0.729368i	$-0.260186\pi$
$601$	−7.09939	−	12.2965i	−0.289590	−	0.501585i	−0.973712	+	0.227783i	$0.926852\pi$
$602$	−0.681076	+	1.17966i	−0.0277586	+	0.0480793i
$603$	−3.91041	+	2.25768i	−0.159244	+	0.0919397i
$604$		−	31.2434i		−	1.27128i
$605$			18.2500i			0.741967i
$606$	−0.688313	+	0.397398i	−0.0279608	+	0.0161432i
$607$	−13.3328	+	23.0932i	−0.541163	+	0.937322i	0.457674	+	0.889120i	$0.348683\pi$
$607$	−13.3328	+	23.0932i	−0.541163	+	0.937322i	−0.998838	+	0.0482025i	$0.984651\pi$
$608$	7.04060	+	12.1947i	0.285534	+	0.494560i
$609$	−0.792810	−	0.457729i	−0.0321263	−	0.0185481i
$610$	0.304097	−	0.526712i	0.0123125	−	0.0213259i
$611$	24.7656	−	25.9163i	1.00191	−	1.04846i
$612$	37.4032			1.51194
$613$	−39.8799	+	23.0247i	−1.61073	+	0.929957i	−0.621533	+	0.783388i	$0.713490\pi$
$613$	−39.8799	+	23.0247i	−1.61073	+	0.929957i	−0.989200	+	0.146570i	$0.953177\pi$
$614$	1.36718	+	2.36802i	0.0551749	+	0.0955657i
$615$	−1.13116	+	1.95923i	−0.0456128	+	0.0790036i
$616$			7.19962i			0.290081i
$617$	−1.59801	+	0.922614i	−0.0643336	+	0.0371430i	−0.531822	−	0.846856i	$-0.678492\pi$
$617$	−1.59801	+	0.922614i	−0.0643336	+	0.0371430i	0.467488	+	0.883999i	$0.345159\pi$
$618$		−	1.48812i		−	0.0598609i
$619$		−	1.59885i		−	0.0642632i	−0.999484	−	0.0321316i	$-0.989770\pi$
$619$		−	1.59885i		−	0.0642632i	0.999484	−	0.0321316i	$-0.0102296\pi$
$620$	7.18614	+	21.9651i	0.288603	+	0.882140i
$621$	−31.9249			−1.28110
$622$			1.07977i			0.0432950i
$623$	−14.3751	−	24.8983i	−0.575925	−	0.997531i
$624$	2.02586	−	8.31077i	0.0810992	−	0.332697i
$625$	10.9625	−	18.9876i	0.438500	−	0.759504i
$626$	4.00141	−	2.31022i	0.159929	−	0.0923349i
$627$	9.31507	+	16.1342i	0.372008	+	0.644337i
$628$	25.0795			1.00078
$629$	21.3935	+	12.3515i	0.853013	+	0.492487i
$630$	−1.95236	−	1.12719i	−0.0777837	−	0.0449084i
$631$	38.7293	+	22.3604i	1.54179	+	0.890153i	0.998726	+	0.0504628i	$0.0160696\pi$
$631$	38.7293	+	22.3604i	1.54179	+	0.890153i	0.543065	+	0.839691i	$0.317264\pi$
$632$	−3.47877	+	2.00847i	−0.138378	+	0.0798926i
$633$	2.69666	−	4.67075i	0.107183	−	0.185646i
$634$	−0.132761	−	0.229949i	−0.00527262	−	0.00913244i
$635$			13.1608i			0.522271i
$636$	−13.2791			−0.526551
$637$	5.83303	−	1.70576i	0.231113	−	0.0675848i
$638$	0.251059	−	0.434847i	0.00993952	−	0.0172158i
$639$	16.5803	−	9.57265i	0.655907	−	0.378688i
$640$	5.75514	−	9.96820i	0.227492	−	0.394028i
$641$	12.9174	−	22.3735i	0.510205	−	0.883701i	−0.489725	−	0.871877i	$-0.662903\pi$
$641$	12.9174	−	22.3735i	0.510205	−	0.883701i	0.999930	−	0.0118242i	$-0.00376385\pi$
$642$	0.0624570	+	0.0360596i	0.00246498	+	0.00142316i
$643$		−	15.6490i		−	0.617137i	−0.951202	−	0.308568i	$-0.900150\pi$
$643$		−	15.6490i		−	0.617137i	0.951202	−	0.308568i	$-0.0998499\pi$
$644$	−35.9168	+	20.7366i	−1.41532	+	0.817136i
$645$	3.78326	−	2.18426i	0.148966	−	0.0860053i
$646$	−4.35821	+	7.54864i	−0.171472	+	0.296997i
$647$	2.83716			0.111540			0.0557702	−	0.998444i	$-0.482239\pi$
$647$	2.83716			0.111540			0.0557702	+	0.998444i	$0.482239\pi$
$648$	−3.45528	+	1.99491i	−0.135736	+	0.0783674i
$649$	8.08013			0.317173
$650$	0.344288	+	0.0839245i	0.0135041	+	0.00329179i
$651$	2.48399	+	7.59255i	0.0973552	+	0.297575i
$652$		−	9.18633i		−	0.359765i
$653$	−19.0412			−0.745141			−0.372570	−	0.928004i	$-0.621524\pi$
$653$	−19.0412			−0.745141			−0.372570	+	0.928004i	$0.621524\pi$
$654$	−0.642900	−	1.11354i	−0.0251394	−	0.0435427i
$655$		−	20.4837i		−	0.800365i
$656$	5.69079	+	3.28558i	0.222188	+	0.128280i
$657$	3.57540	−	2.06426i	0.139490	−	0.0805344i
$658$	3.52337	−	2.03422i	0.137355	−	0.0793020i
$659$	3.11251			0.121246			0.0606231	−	0.998161i	$-0.480691\pi$
$659$	3.11251			0.121246			0.0606231	+	0.998161i	$0.480691\pi$
$660$	5.72660	−	9.91876i	0.222908	−	0.386087i
$661$	−29.8334	−	17.2243i	−1.16038	−	0.669948i	−0.208988	−	0.977918i	$-0.567017\pi$
$661$	−29.8334	−	17.2243i	−1.16038	−	0.669948i	−0.951396	+	0.307970i	$0.900350\pi$
$662$	2.79420	−	4.83970i	0.108600	−	0.188100i
$663$	15.6642	−	4.58071i	0.608347	−	0.177900i
$664$	0.871313	−	1.50916i	0.0338135	−	0.0585667i
$665$	−28.4238	+	16.4105i	−1.10223	+	0.636372i
$666$	−1.57526			−0.0610402
$667$	5.83117			0.225784
$668$	−25.5999	+	14.7801i	−0.990490	+	0.571860i
$669$	9.52034	+	5.49657i	0.368077	+	0.212510i
$670$	−0.560225	+	0.323446i	−0.0216434	+	0.0124958i
$671$	−6.23862	−	3.60187i	−0.240839	−	0.139049i
$672$	1.49615	−	2.59141i	0.0577152	−	0.0999656i
$673$	−3.27940	+	5.68009i	−0.126412	+	0.218951i	−0.922284	−	0.386513i	$-0.873679\pi$
$673$	−3.27940	+	5.68009i	−0.126412	+	0.218951i	0.795872	+	0.605465i	$0.207013\pi$
$674$		−	1.18939i		−	0.0458136i
$675$	−0.967073	−	1.67502i	−0.0372227	−	0.0644716i
$676$	1.16139	+	25.5640i	0.0446687	+	0.983231i
$677$	4.80721	−	8.32633i	0.184756	−	0.320007i	−0.758738	−	0.651396i	$-0.774184\pi$
$677$	4.80721	−	8.32633i	0.184756	−	0.320007i	0.943494	+	0.331389i	$0.107517\pi$
$678$		−	0.307726i		−	0.0118181i
$679$	8.34128	+	14.4475i	0.320109	+	0.554445i
$680$	10.8029			0.414273
$681$			13.4645i			0.515959i
$682$	−4.16443	+	1.36244i	−0.159464	+	0.0521705i
$683$		−	25.7995i		−	0.987189i	−0.869692	−	0.493595i	$-0.835683\pi$
$683$		−	25.7995i		−	0.987189i	0.869692	−	0.493595i	$-0.164317\pi$
$684$			34.7244i			1.32772i
$685$	14.4779	+	25.0765i	0.553174	+	0.958125i
$686$	3.55423			0.135701
$687$	−8.22337	−	4.74777i	−0.313741	−	0.181139i
$688$	−6.34443	−	10.9889i	−0.241879	−	0.418947i
$689$	37.5086	−	10.9687i	1.42897	−	0.417875i
$690$	−2.12903			−0.0810509
$691$	−30.4991	−	17.6087i	−1.16024	−	0.669865i	−0.208878	−	0.977942i	$-0.566981\pi$
$691$	−30.4991	−	17.6087i	−1.16024	−	0.669865i	−0.951361	+	0.308077i	$0.900315\pi$
$692$	15.0113	−	26.0004i	0.570644	−	0.988385i
$693$	−13.3510	+	23.1246i	−0.507163	+	0.878432i
$694$	−3.23134	+	1.86561i	−0.122660	+	0.0708177i
$695$	−29.2855	−	16.9080i	−1.11086	−	0.641357i
$696$	−0.242262	+	0.139870i	−0.00918290	+	0.00530175i
$697$			12.5370i			0.474871i
$698$	−3.77843			−0.143016
$699$	−3.48347	−	6.03354i	−0.131757	−	0.228210i
$700$	−2.17599	−	1.25631i	−0.0822448	−	0.0474841i
$701$	−3.59467	−	6.22616i	−0.135769	−	0.235159i	0.790122	−	0.612950i	$-0.210017\pi$
$701$	−3.59467	−	6.22616i	−0.135769	−	0.235159i	−0.925891	+	0.377791i	$0.876684\pi$
$702$	−1.54460	+	1.61636i	−0.0582971	+	0.0610057i
$703$	−11.4669	+	19.8613i	−0.432483	+	0.749082i
$704$	−27.8499	−	16.0792i	−1.04963	−	0.606006i
$705$	−13.0478			−0.491408
$706$	−0.297591	−	0.515442i	−0.0112000	−	0.0193989i
$707$	−14.3628	+	8.29234i	−0.540167	+	0.311866i
$708$	−1.93377	−	1.11646i	−0.0726756	−	0.0419593i
$709$			24.8610i			0.933673i	0.884344	+	0.466837i	$0.154606\pi$
$709$			24.8610i			0.933673i	−0.884344	+	0.466837i	$0.845394\pi$
$710$	2.37538	−	1.37143i	0.0891464	−	0.0514687i
$711$	−14.8981			−0.558721
$712$	−8.78527			−0.329242
$713$	−37.8835	−	33.9717i	−1.41875	−	1.27225i
$714$	1.85227			0.0693193
$715$	−7.98253	+	32.7471i	−0.298530	+	1.22467i
$716$	−2.07307	−	3.59067i	−0.0774744	−	0.134190i
$717$		−	9.66805i		−	0.361060i
$718$	−1.63445	+	2.83096i	−0.0609973	+	0.105650i
$719$	11.0930	+	19.2136i	0.413699	+	0.716547i	0.995291	−	0.0969334i	$-0.0309034\pi$
$719$	11.0930	+	19.2136i	0.413699	+	0.716547i	−0.581592	+	0.813480i	$0.697570\pi$
$720$	18.1868	−	10.5001i	0.677781	−	0.391317i
$721$		−	31.0520i		−	1.15644i
$722$	−4.08720	−	2.35975i	−0.152110	−	0.0878207i
$723$	1.45788	+	0.841705i	0.0542190	+	0.0313034i
$724$	20.5886	−	35.6605i	0.765170	−	1.32531i
$725$	0.176638	+	0.305947i	0.00656019	+	0.0113626i
$726$	0.828076	+	0.478090i	0.0307328	+	0.0177436i
$727$	2.10380	+	3.64389i	0.0780256	+	0.135144i	0.902398	−	0.430904i	$-0.141805\pi$
$727$	2.10380	+	3.64389i	0.0780256	+	0.135144i	−0.824372	+	0.566048i	$0.808472\pi$
$728$	−1.38669	+	5.68868i	−0.0513941	+	0.210837i
$729$	−8.27511			−0.306485
$730$	0.512230	−	0.295736i	0.0189585	−	0.0109457i
$731$	12.1044	−	20.9654i	0.447698	−	0.775435i
$732$	0.995369	+	1.72403i	0.0367899	+	0.0637220i
$733$	22.8876	+	13.2141i	0.845371	+	0.488075i	0.859086	−	0.511831i	$-0.171032\pi$
$733$	22.8876	+	13.2141i	0.845371	+	0.488075i	−0.0137152	+	0.999906i	$0.504366\pi$
$734$	4.15488	+	2.39882i	0.153360	+	0.0885422i
$735$	−1.91571	−	1.10604i	−0.0706620	−	0.0407967i
$736$			19.0600i			0.702560i
$737$	3.83105	+	6.63557i	0.141119	+	0.244425i
$738$	−0.399728	−	0.692350i	−0.0147142	−	0.0254857i
$739$	40.5324	+	23.4014i	1.49101	+	0.860834i	0.999947	−	0.0102910i	$-0.00327578\pi$
$739$	40.5324	+	23.4014i	1.49101	+	0.860834i	0.491061	+	0.871125i	$0.336609\pi$
$740$	14.0990			0.518289
$741$	4.25264	+	14.5423i	0.156225	+	0.534226i
$742$	4.43534			0.162826
$743$		−	5.29404i		−	0.194220i	−0.995274	−	0.0971098i	$-0.969040\pi$
$743$		−	5.29404i		−	0.194220i	0.995274	−	0.0971098i	$-0.0309598\pi$
$744$	2.38877	+	0.502691i	0.0875765	+	0.0184296i
$745$	11.0015			0.403062
$746$			4.28658i			0.156943i
$747$	5.59718	−	3.23153i	0.204790	−	0.118236i
$748$		−	63.4695i		−	2.32068i
$749$	1.30327	+	0.752441i	0.0476203	+	0.0274936i
$750$	−0.646888	−	1.12044i	−0.0236210	−	0.0409128i
$751$	−8.85694	−	15.3407i	−0.323194	−	0.559789i	0.657951	−	0.753061i	$-0.271423\pi$
$751$	−8.85694	−	15.3407i	−0.323194	−	0.559789i	−0.981145	+	0.193272i	$0.938090\pi$
$752$			37.8987i			1.38202i
$753$	3.46190	−	5.99619i	0.126159	−	0.218513i
$754$	0.282125	−	0.295233i	0.0102744	−	0.0107518i
$755$	16.7338	−	28.9838i	0.609006	−	1.05483i
$756$	13.7284	−	7.92607i	0.499295	−	0.288268i
$757$	−24.8102	+	42.9725i	−0.901740	+	1.56186i	−0.0765066	+	0.997069i	$0.524377\pi$
$757$	−24.8102	+	42.9725i	−0.901740	+	1.56186i	−0.825234	+	0.564791i	$0.808957\pi$
$758$	−1.88961	−	3.27290i	−0.0686337	−	0.118877i
$759$			25.2173i			0.915329i
$760$			10.0292i			0.363798i
$761$	0.0239750	−	0.0138420i	0.000869093	−	0.000501771i	−0.499565	−	0.866276i	$-0.666507\pi$
$761$	0.0239750	−	0.0138420i	0.000869093	−	0.000501771i	0.500434	+	0.865774i	$0.333174\pi$
$762$	0.597160	+	0.344770i	0.0216328	+	0.0124897i
$763$	−13.4151	−	23.2357i	−0.485661	−	0.841189i
$764$	−7.61041	+	13.1816i	−0.275335	+	0.476894i
$765$	34.6982	+	20.0330i	1.25451	+	0.724294i
$766$	0.831339	−	1.43992i	0.0300375	−	0.0520265i
$767$	6.38441	+	1.55628i	0.230528	+	0.0561941i
$768$	4.21303	+	7.29719i	0.152025	+	0.263315i
$769$	27.3868	−	15.8117i	0.987592	−	0.570186i	0.0830380	−	0.996546i	$-0.473538\pi$
$769$	27.3868	−	15.8117i	0.987592	−	0.570186i	0.904554	+	0.426360i	$0.140204\pi$
$770$	−1.91273	+	3.31295i	−0.0689301	+	0.119390i
$771$	−6.00286			−0.216188
$772$	23.6879	−	13.6762i	0.852546	−	0.492217i
$773$		−	42.8156i		−	1.53997i	−0.638062	−	0.769985i	$-0.720264\pi$
$773$		−	42.8156i		−	1.53997i	0.638062	−	0.769985i	$-0.279736\pi$
$774$			1.54375i			0.0554888i
$775$	0.634838	−	3.01672i	0.0228040	−	0.108364i
$776$	5.09775			0.182998
$777$	4.87350			0.174836
$778$	3.92401	−	2.26553i	0.140683	−	0.0812232i
$779$	−11.6391			−0.417013
$780$	6.43521	−	6.73420i	0.230417	−	0.241123i
$781$	−16.2438	−	28.1351i	−0.581250	−	1.00675i
$782$	−10.2177	+	5.89917i	−0.365383	+	0.210954i
$783$	−2.22883			−0.0796517
$784$	−3.21260	+	5.56439i	−0.114736	+	0.198728i
$785$	23.2657	+	13.4325i	0.830389	+	0.479425i
$786$	−0.929431	−	0.536607i	−0.0331517	−	0.0191401i
$787$	−6.27627	+	3.62361i	−0.223725	+	0.129168i	−0.607674	−	0.794187i	$-0.707897\pi$
$787$	−6.27627	+	3.62361i	−0.223725	+	0.129168i	0.383949	+	0.923354i	$0.374564\pi$
$788$	20.6816	+	11.9405i	0.736750	+	0.425363i
$789$	5.98130	+	10.3599i	0.212940	+	0.368823i
$790$	−2.13437			−0.0759375
$791$		−	6.42119i		−	0.228311i
$792$	4.07971	+	7.06627i	0.144966	+	0.251089i
$793$	−4.23562	−	4.04756i	−0.150411	−	0.143733i
$794$	0.981543	+	1.70008i	0.0348337	+	0.0603337i
$795$	−12.3187	−	7.11223i	−0.436901	−	0.252245i
$796$	6.55408	−	11.3520i	0.232303	−	0.402361i
$797$	−6.64601	+	11.5112i	−0.235414	+	0.407748i	−0.959393	−	0.282073i	$-0.908978\pi$
$797$	−6.64601	+	11.5112i	−0.235414	+	0.407748i	0.723979	+	0.689822i	$0.242311\pi$
$798$			1.71961i			0.0608734i
$799$	−62.6189	+	36.1530i	−2.21530	+	1.27900i
$800$	−1.00003	+	0.577367i	−0.0353563	+	0.0204130i
$801$	−28.2176	−	16.2915i	−0.997021	−	0.575630i
$802$	4.88529			0.172506
$803$	−3.50284	−	6.06710i	−0.123613	−	0.214103i
$804$		−	2.11740i		−	0.0746751i
$805$	−44.4257			−1.56580
$806$	−3.55288	+	0.274421i	−0.125145	+	0.00966607i
$807$	−3.07993			−0.108419
$808$			5.06784i			0.178286i
$809$	−10.1624	−	17.6018i	−0.357291	−	0.618845i	0.630217	−	0.776419i	$-0.282966\pi$
$809$	−10.1624	−	17.6018i	−0.357291	−	0.618845i	−0.987507	+	0.157574i	$0.949633\pi$
$810$	−2.11996			−0.0744877
$811$	−2.74325	−	1.58382i	−0.0963285	−	0.0556153i	0.451062	−	0.892493i	$-0.351045\pi$
$811$	−2.74325	−	1.58382i	−0.0963285	−	0.0556153i	−0.547390	+	0.836877i	$0.684379\pi$
$812$	−2.50752	+	1.44772i	−0.0879967	+	0.0508049i
$813$	2.17274	−	1.25443i	0.0762012	−	0.0439948i
$814$			2.67306i			0.0936908i
$815$	4.92015	−	8.52196i	0.172346	−	0.298511i
$816$	−8.62721	+	14.9428i	−0.302013	+	0.523101i
$817$	19.4639	+	11.2375i	0.680956	+	0.393150i
$818$	0.700844	+	1.21390i	0.0245044	+	0.0424429i
$819$	−15.0031	+	15.7001i	−0.524249	+	0.548607i
$820$	3.57766	+	6.19669i	0.124937	+	0.216398i
$821$		−	31.2486i		−	1.09058i	−0.838246	−	0.545292i	$-0.816419\pi$
$821$		−	31.2486i		−	1.09058i	0.838246	−	0.545292i	$-0.183581\pi$
$822$	1.51710			0.0529150
$823$	−2.79849	−	4.84712i	−0.0975491	−	0.168960i	0.813121	−	0.582095i	$-0.197767\pi$
$823$	−2.79849	−	4.84712i	−0.0975491	−	0.168960i	−0.910670	+	0.413135i	$0.864434\pi$
$824$	−8.21742	−	4.74433i	−0.286268	−	0.165277i
$825$	−1.32309	+	0.763885i	−0.0460640	+	0.0265951i
$826$	0.645896	+	0.372908i	0.0224736	+	0.0129751i
$827$	21.7407	+	12.5520i	0.756000	+	0.436477i	0.827858	−	0.560938i	$-0.189559\pi$
$827$	21.7407	+	12.5520i	0.756000	+	0.436477i	−0.0718578	+	0.997415i	$0.522893\pi$
$828$	−23.5011	+	40.7050i	−0.816718	+	1.41460i
$829$	−29.2446			−1.01571			−0.507854	−	0.861443i	$-0.669561\pi$
$829$	−29.2446			−1.01571			−0.507854	+	0.861443i	$0.669561\pi$
$830$	0.801880	−	0.462965i	0.0278337	−	0.0160698i
$831$	3.64634	+	6.31565i	0.126490	+	0.219087i
$832$	−18.9083	−	18.0688i	−0.655527	−	0.626423i
$833$	−12.2585			−0.424732
$834$	−1.53437	+	0.885870i	−0.0531309	+	0.0306752i
$835$	−31.6646			−1.09580
$836$	58.9239			2.03792
$837$	14.4801	+	12.9849i	0.500504	+	0.448823i
$838$		−	4.77679i		−	0.165011i
$839$		−	6.06616i		−	0.209427i	−0.994502	−	0.104714i	$-0.966607\pi$
$839$		−	6.06616i		−	0.209427i	0.994502	−	0.104714i	$-0.0333926\pi$
$840$	1.84571	−	1.06562i	0.0636829	−	0.0367674i
$841$	−28.5929			−0.985962
$842$	2.36615	−	4.09829i	0.0815428	−	0.141236i
$843$	10.6147	−	6.12838i	0.365588	−	0.211073i
$844$	−8.52906	−	14.7728i	−0.293582	−	0.508500i
$845$	−12.6146	+	24.3372i	−0.433954	+	0.837225i
$846$	2.30541	−	3.99308i	0.0792615	−	0.137285i
$847$	17.2791	+	9.97612i	0.593718	+	0.342783i
$848$	−20.6582	+	35.7811i	−0.709407	+	1.22873i
$849$	−4.93842	−	8.55359i	−0.169486	−	0.293558i
$850$	−0.619029	−	0.357396i	−0.0212325	−	0.0122586i
$851$	−26.8837	+	15.5213i	−0.921562	+	0.532064i
$852$			8.97789i			0.307577i
$853$			55.1198i			1.88727i	0.330992	+	0.943633i	$0.392617\pi$
$853$			55.1198i			1.88727i	−0.330992	+	0.943633i	$0.607383\pi$
$854$	−0.332462	−	0.575840i	−0.0113766	−	0.0197049i
$855$	−18.5982	+	32.2131i	−0.636046	+	1.10166i
$856$	0.398243	−	0.229926i	0.0136117	−	0.00785871i
$857$	3.28373	−	5.68758i	0.112170	−	0.194284i	−0.804475	−	0.593987i	$-0.797553\pi$
$857$	3.28373	−	5.68758i	0.112170	−	0.194284i	0.916645	+	0.399702i	$0.130887\pi$
$858$	1.27675	+	1.22007i	0.0435877	+	0.0416524i
$859$	−9.41315	+	16.3041i	−0.321173	+	0.556287i	−0.980730	−	0.195367i	$-0.937410\pi$
$859$	−9.41315	+	16.3041i	−0.321173	+	0.556287i	0.659558	+	0.751654i	$0.270744\pi$
$860$		−	13.8169i		−	0.471152i
$861$	1.23667	+	2.14197i	0.0421455	+	0.0729982i
$862$	2.58496	+	4.47728i	0.0880440	+	0.152497i
$863$	−13.2602	−	7.65576i	−0.451381	−	0.260605i	0.257032	−	0.966403i	$-0.417255\pi$
$863$	−13.2602	−	7.65576i	−0.451381	−	0.260605i	−0.708413	+	0.705798i	$0.750589\pi$
$864$		−	7.28522i		−	0.247848i
$865$	27.8513	−	16.0800i	0.946973	−	0.546735i
$866$		−	3.90721i		−	0.132772i
$867$	−22.3388			−0.758665
$868$	24.7249	+	5.20309i	0.839217	+	0.176604i
$869$			25.2805i			0.857582i
$870$	−0.148638			−0.00503928
$871$	1.74900	+	5.98089i	0.0592627	+	0.202655i
$872$	−8.19862			−0.277640
$873$	16.3736	+	9.45328i	0.554161	+	0.319945i
$874$	−5.47667	−	9.48587i	−0.185251	−	0.320864i
$875$	−13.4983	−	23.3798i	−0.456328	−	0.790382i
$876$			1.93600i			0.0654115i
$877$	−30.3042	−	17.4962i	−1.02330	−	0.590803i	−0.108243	−	0.994124i	$-0.534522\pi$
$877$	−30.3042	−	17.4962i	−1.02330	−	0.590803i	−0.915059	+	0.403321i	$0.867856\pi$
$878$	5.02678	+	2.90221i	0.169646	+	0.0979450i
$879$	−11.5913	−	6.69223i	−0.390964	−	0.225723i
$880$	−17.8177	−	30.8611i	−0.600634	−	1.04033i
$881$	21.5525	−	37.3300i	0.726121	−	1.25768i	−0.232390	−	0.972623i	$-0.574654\pi$
$881$	21.5525	−	37.3300i	0.726121	−	1.25768i	0.958511	−	0.285056i	$-0.0920122\pi$
$882$	0.676972	−	0.390850i	0.0227948	−	0.0131606i
$883$	4.62824			0.155753			0.0778763	−	0.996963i	$-0.475186\pi$
$883$	4.62824			0.155753			0.0778763	+	0.996963i	$0.475186\pi$
$884$	12.2246	−	50.1496i	0.411158	−	1.68671i
$885$	−1.19594	−	2.07144i	−0.0402012	−	0.0696306i
$886$	−0.477402	−	0.275628i	−0.0160386	−	0.00925992i
$887$	−2.04007	−	3.53350i	−0.0684988	−	0.118643i	0.829742	−	0.558147i	$-0.188488\pi$
$887$	−2.04007	−	3.53350i	−0.0684988	−	0.118643i	−0.898241	+	0.439504i	$0.855154\pi$
$888$	0.744607	−	1.28970i	0.0249874	−	0.0432794i
$889$	12.4607	+	7.19419i	0.417918	+	0.241285i
$890$	−4.04260	−	2.33400i	−0.135508	−	0.0782357i
$891$			25.1098i			0.841210i
$892$	30.1112	−	17.3847i	1.00820	−	0.582082i
$893$	−33.5638	−	58.1342i	−1.12317	−	1.94539i
$894$	0.288203	−	0.499182i	0.00963894	−	0.0166951i
$895$		−	4.44131i		−	0.148457i
$896$	−6.29195	−	10.8980i	−0.210199	−	0.364076i
$897$	−4.85699	+	19.9251i	−0.162170	+	0.665279i
$898$	−4.86558			−0.162366
$899$	−2.64482	−	2.37172i	−0.0882097	−	0.0791013i
$900$	−2.84759			−0.0949196
$901$	−78.8268			−2.62610
$902$	−1.17485	+	0.678299i	−0.0391182	+	0.0225849i
$903$		−	4.77600i		−	0.158935i
$904$	−1.69927	−	0.981073i	−0.0565168	−	0.0326300i
$905$	38.1992	−	22.0543i	1.26978	−	0.733110i
$906$	−0.876743	−	1.51856i	−0.0291278	−	0.0504509i
$907$	15.1134			0.501832			0.250916	−	0.968009i	$-0.419268\pi$
$907$	15.1134			0.501832			0.250916	+	0.968009i	$0.419268\pi$
$908$	36.8803	+	21.2929i	1.22392	+	0.706629i
$909$	−9.39782	+	16.2775i	−0.311706	+	0.539891i
$910$	−2.14941	+	2.24928i	−0.0712524	+	0.0745629i
$911$	−6.99016	−	12.1073i	−0.231594	−	0.401133i	0.726683	−	0.686973i	$-0.241061\pi$
$911$	−6.99016	−	12.1073i	−0.231594	−	0.401133i	−0.958277	+	0.285840i	$0.907727\pi$
$912$	−13.8726	−	8.00933i	−0.459367	−	0.265215i
$913$	−5.48358	−	9.49785i	−0.181480	−	0.314333i
$914$	5.03662			0.166596
$915$			2.13246i			0.0704969i
$916$	−26.0091	+	15.0164i	−0.859365	+	0.496155i
$917$	−19.3941	−	11.1972i	−0.640448	−	0.369763i
$918$	3.90546	−	2.25482i	0.128899	−	0.0744200i
$919$	−11.7075	+	20.2780i	−0.386194	+	0.668908i	−0.991934	−	0.126755i	$-0.959544\pi$
$919$	−11.7075	+	20.2780i	−0.386194	+	0.668908i	0.605740	+	0.795663i	$0.292877\pi$
$920$	−6.78765	+	11.7566i	−0.223782	+	0.387602i
$921$	−8.30280	−	4.79362i	−0.273587	−	0.157955i
$922$	−1.50103			−0.0494336
$923$	−7.41585	−	25.3592i	−0.244096	−	0.834710i
$924$	−6.26075	−	10.8439i	−0.205963	−	0.356739i
$925$	−1.62873	−	0.940348i	−0.0535523	−	0.0309184i
$926$	2.08972			0.0686724
$927$	−17.5958	−	30.4769i	−0.577923	−	1.00099i
$928$			1.33066i			0.0436812i
$929$			42.8885i			1.40713i	0.710633	+	0.703563i	$0.248409\pi$
$929$			42.8885i			1.40713i	−0.710633	+	0.703563i	$0.751591\pi$
$930$	0.965657	+	0.865944i	0.0316651	+	0.0283954i
$931$		−	11.3806i		−	0.372983i
$932$	−22.0352			−0.721787
$933$	−1.89296	−	3.27870i	−0.0619727	−	0.107340i
$934$			1.93563i			0.0633356i
$935$	33.9940	−	58.8793i	1.11172	−	1.92556i
$936$	1.86253	+	6.36910i	0.0608785	+	0.208180i
$937$	14.5016	+	25.1175i	0.473746	+	0.820552i	0.999548	−	0.0300551i	$-0.00956827\pi$
$937$	14.5016	+	25.1175i	0.473746	+	0.820552i	−0.525803	+	0.850607i	$0.676235\pi$
$938$			0.707231i			0.0230919i
$939$	−8.10012	+	14.0298i	−0.264337	+	0.457846i
$940$	−20.6339	+	35.7390i	−0.673004	+	1.16568i
$941$	−0.916612	−	0.529206i	−0.0298807	−	0.0172516i	0.484985	−	0.874522i	$-0.338825\pi$
$941$	−0.916612	−	0.529206i	−0.0298807	−	0.0172516i	−0.514866	+	0.857271i	$0.672158\pi$
$942$	1.21897	−	0.703774i	0.0397163	−	0.0229302i
$943$	−13.6437	−	7.87718i	−0.444299	−	0.256516i
$944$	−6.01672	+	3.47375i	−0.195827	+	0.113061i
$945$	16.9807			0.552381
$946$	2.61958			0.0851700
$947$	−21.0371	+	12.1458i	−0.683615	+	0.394685i	−0.801216	−	0.598376i	$-0.795813\pi$
$947$	−21.0371	+	12.1458i	−0.683615	+	0.394685i	0.117601	+	0.993061i	$0.462480\pi$
$948$	3.49311	−	6.05024i	0.113451	−	0.196503i
$949$	−1.59916	−	5.46850i	−0.0519110	−	0.177515i
$950$	0.331800	−	0.574694i	0.0107650	−	0.0186455i
$951$	0.806250	+	0.465489i	0.0261445	+	0.0150945i
$952$	5.90528	−	10.2282i	0.191391	−	0.331499i
$953$	−9.61869			−0.311580			−0.155790	−	0.987790i	$-0.549792\pi$
$953$	−9.61869			−0.311580			−0.155790	+	0.987790i	$0.549792\pi$
$954$	4.35319	−	2.51331i	0.140940	−	0.0813715i
$955$	−14.1200	+	8.15220i	−0.456913	+	0.263799i
$956$	−26.4817	−	15.2892i	−0.856478	−	0.494488i
$957$			1.76053i			0.0569100i
$958$	2.82592	+	4.89463i	0.0913012	+	0.158138i
$959$	31.6567			1.02225
$960$			9.51954i			0.307242i
$961$	3.36531	+	30.8168i	0.108558	+	0.994090i
$962$	−0.514847	+	2.11208i	−0.0165993	+	0.0680963i
$963$	1.70550			0.0549591
$964$	4.61101	−	2.66217i	0.148511	−	0.0857426i
$965$	29.2996			0.943189
$966$	−1.16381	+	2.01578i	−0.0374449	+	0.0648565i
$967$	−15.9291	+	9.19668i	−0.512246	+	0.295745i	−0.733756	−	0.679413i	$-0.762235\pi$
$967$	−15.9291	+	9.19668i	−0.512246	+	0.295745i	0.221510	+	0.975158i	$0.428901\pi$
$968$	5.28005	−	3.04844i	0.169707	−	0.0979805i
$969$		−	30.5617i		−	0.981782i
$970$	2.34576	+	1.35432i	0.0753178	+	0.0434848i
$971$	−3.80276	+	6.58658i	−0.122036	+	0.211373i	−0.920571	−	0.390576i	$-0.872276\pi$
$971$	−3.80276	+	6.58658i	−0.122036	+	0.211373i	0.798534	+	0.601950i	$0.205609\pi$
$972$	13.7841	−	23.8747i	0.442124	−	0.765781i
$973$	−32.0171	+	18.4851i	−1.02642	+	0.592605i
$974$	−3.17724	+	5.50313i	−0.101805	+	0.176332i
$975$	−1.19255	+	0.348739i	−0.0381921	+	0.0111686i
$976$	6.19396			0.198264
$977$			33.8731i			1.08370i	0.840477	+	0.541848i	$0.182275\pi$
$977$			33.8731i			1.08370i	−0.840477	+	0.541848i	$0.817725\pi$
$978$	−0.257784	−	0.446495i	−0.00824303	−	0.0142773i
$979$	−27.6450	+	47.8825i	−0.883537	+	1.53033i
$980$	−6.05906	+	3.49820i	−0.193549	+	0.111746i
$981$	−26.3334	−	15.2036i	−0.840759	−	0.485413i
$982$	−2.75839	−	1.59256i	−0.0880237	−	0.0508205i
$983$	−32.6680	−	18.8609i	−1.04195	−	0.601568i	−0.121562	−	0.992584i	$-0.538790\pi$
$983$	−32.6680	−	18.8609i	−1.04195	−	0.601568i	−0.920384	+	0.391016i	$0.872124\pi$
$984$	0.755786			0.0240936
$985$	12.7906	+	22.1539i	0.407541	+	0.705881i
$986$	−0.713342	+	0.411848i	−0.0227174	+	0.0131159i
$987$	−7.13240	+	12.3537i	−0.227027	+	0.393222i
$988$	46.5579	+	11.3491i	1.48120	+	0.361062i
$989$	15.2108	+	26.3459i	0.483675	+	0.837750i
$990$			4.33545i			0.137790i
$991$	29.3464			0.932219			0.466110	−	0.884727i	$-0.345655\pi$
$991$	29.3464			0.932219			0.466110	+	0.884727i	$0.345655\pi$
$992$	7.75228	−	8.64495i	0.246135	−	0.274477i
$993$			19.5941i			0.621801i
$994$		−	2.99869i		−	0.0951127i
$995$	12.1602	−	7.02067i	0.385503	−	0.222570i
$996$			3.03075i			0.0960331i
$997$	−8.64560	+	14.9746i	−0.273809	+	0.474251i	−0.969834	−	0.243767i	$-0.921617\pi$
$997$	−8.64560	+	14.9746i	−0.273809	+	0.474251i	0.696025	+	0.718018i	$0.254950\pi$
$998$	−0.0940431	−	0.162887i	−0.00297688	−	0.00515611i
$999$	10.2757	−	5.93266i	0.325108	−	0.187701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.l.c.25.16	✓	68
13.12	even	2	inner	403.2.l.c.25.19	yes	68
31.5	even	3	inner	403.2.l.c.129.16	yes	68
403.129	even	6	inner	403.2.l.c.129.19	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.16	✓	68	1.1	even	1	trivial
403.2.l.c.25.19	yes	68	13.12	even	2	inner
403.2.l.c.129.16	yes	68	31.5	even	3	inner
403.2.l.c.129.19	yes	68	403.129	even	6	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.177509i q^{2} +(0.311192 + 0.539000i) q^{3} +1.96849 q^{4} +(1.82613 + 1.05431i) q^{5} +(0.0956771 - 0.0552392i) q^{6} +(1.99646 - 1.15265i) q^{7} -0.704441i q^{8} +(1.30632 - 2.26261i) q^{9} +O(q^{10})\)	\(q-0.177509i q^{2} +(0.311192 + 0.539000i) q^{3} +1.96849 q^{4} +(1.82613 + 1.05431i) q^{5} +(0.0956771 - 0.0552392i) q^{6} +(1.99646 - 1.15265i) q^{7} -0.704441i q^{8} +(1.30632 - 2.26261i) q^{9} +(0.187150 - 0.324153i) q^{10} +(-3.83942 - 2.21669i) q^{11} +(0.612578 + 1.06102i) q^{12} +(-2.60672 - 2.49098i) q^{13} +(-0.204606 - 0.354388i) q^{14} +1.31238i q^{15} +3.81194 q^{16} +(3.63636 + 6.29835i) q^{17} +(-0.401633 - 0.231883i) q^{18} +(-5.84727 + 3.37592i) q^{19} +(3.59471 + 2.07541i) q^{20} +(1.24256 + 0.717393i) q^{21} +(-0.393482 + 0.681531i) q^{22} -9.13913 q^{23} +(0.379694 - 0.219216i) q^{24} +(-0.276843 - 0.479507i) q^{25} +(-0.442171 + 0.462715i) q^{26} +3.49321 q^{27} +(3.93001 - 2.26899i) q^{28} -0.638044 q^{29} +0.232958 q^{30} +(4.14520 + 3.71717i) q^{31} -2.08553i q^{32} -2.75927i q^{33} +(1.11801 - 0.645485i) q^{34} +4.86104 q^{35} +(2.57148 - 4.45393i) q^{36} +(2.94161 - 1.69834i) q^{37} +(0.599255 + 1.03794i) q^{38} +(0.531451 - 2.18020i) q^{39} +(0.742703 - 1.28640i) q^{40} +(1.49289 + 0.861918i) q^{41} +(0.127344 - 0.220565i) q^{42} +(-1.66436 - 2.88275i) q^{43} +(-7.55787 - 4.36354i) q^{44} +(4.77101 - 2.75454i) q^{45} +1.62227i q^{46} +9.94211i q^{47} +(1.18624 + 2.05463i) q^{48} +(-0.842774 + 1.45973i) q^{49} +(-0.0851166 + 0.0491421i) q^{50} +(-2.26321 + 3.91999i) q^{51} +(-5.13131 - 4.90348i) q^{52} +(-5.41936 + 9.38660i) q^{53} -0.620076i q^{54} +(-4.67418 - 8.09592i) q^{55} +(-0.811978 - 1.40639i) q^{56} +(-3.63924 - 2.10112i) q^{57} +0.113258i q^{58} +(-1.57839 + 0.911283i) q^{59} +2.58340i q^{60} +1.62489 q^{61} +(0.659830 - 0.735808i) q^{62} -6.02294i q^{63} +7.25367 q^{64} +(-2.13392 - 7.29715i) q^{65} -0.489793 q^{66} +(-1.49673 - 0.864137i) q^{67} +(7.15813 + 12.3983i) q^{68} +(-2.84402 - 4.92599i) q^{69} -0.862877i q^{70} +(6.34620 + 3.66398i) q^{71} +(-1.59388 - 0.920225i) q^{72} +(1.36850 + 0.790105i) q^{73} +(-0.301470 - 0.522161i) q^{74} +(0.172303 - 0.298437i) q^{75} +(-11.5103 + 6.64547i) q^{76} -10.2203 q^{77} +(-0.387004 - 0.0943371i) q^{78} +(-2.85115 - 4.93834i) q^{79} +(6.96108 + 4.01898i) q^{80} +(-2.83190 - 4.90499i) q^{81} +(0.152998 - 0.265000i) q^{82} +(2.14235 + 1.23688i) q^{83} +(2.44597 + 1.41218i) q^{84} +15.3354i q^{85} +(-0.511714 + 0.295438i) q^{86} +(-0.198554 - 0.343906i) q^{87} +(-1.56153 + 2.70465i) q^{88} -12.4713i q^{89} +(-0.488955 - 0.846895i) q^{90} +(-8.07545 - 1.96849i) q^{91} -17.9903 q^{92} +(-0.713603 + 3.39101i) q^{93} +1.76481 q^{94} -14.2371 q^{95} +(1.12410 - 0.649001i) q^{96} +7.23658i q^{97} +(0.259114 + 0.149600i) q^{98} +(-10.0310 + 5.79142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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