LMFDB - Embedded newform 403.2.l.c.129.16

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			129.16
Character	$\chi$	$=$	403.129
Dual form			403.2.l.c.25.19

$q$-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} +(3.46062 - 1.01199i) 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} +(-0.179638 - 0.614289i) 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} +(6.81219 - 1.99210i) 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} +(-5.25256 + 5.49661i) 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 $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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	−0.762100	−	0.647460i	$-0.775831\pi$
$3$	0.311192	−	0.539000i	0.179667	−	0.311192i	0.941766	+	0.336268i	$0.109165\pi$
$4$	1.96849			0.984245
$5$	−1.82613	+	1.05431i	−0.816668	+	0.471504i	−0.849266	−	0.527965i	$-0.822955\pi$
$5$	−1.82613	+	1.05431i	−0.816668	+	0.471504i	0.0325980	+	0.999469i	$0.489622\pi$
$6$	−0.0956771	−	0.0552392i	−0.0390600	−	0.0225513i
$7$	−1.99646	−	1.15265i	−0.754590	−	0.435663i	0.0727602	−	0.997349i	$-0.476819\pi$
$7$	−1.99646	−	1.15265i	−0.754590	−	0.435663i	−0.827350	+	0.561687i	$0.810153\pi$
$8$		−	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	$-0.433664\pi$
$11$	3.83942	−	2.21669i	1.15763	−	0.668358i	0.950735	+	0.310005i	$0.100331\pi$
$12$	0.612578	−	1.06102i	0.176836	−	0.306289i
$13$	3.46062	−	1.01199i	0.959802	−	0.280677i
$13$	3.46062	−	1.01199i	0.959802	−	0.280677i
$14$	−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	0.0327713	−	0.999463i	$-0.489567\pi$
$17$	3.63636	−	6.29835i	0.881946	−	1.52758i	0.849175	−	0.528112i	$-0.177100\pi$
$18$	0.401633	−	0.231883i	0.0946658	−	0.0546553i
$19$	5.84727	+	3.37592i	1.34146	+	0.774490i	0.987021	−	0.160591i	$-0.0513401\pi$
$19$	5.84727	+	3.37592i	1.34146	+	0.774490i	0.354434	+	0.935081i	$0.384673\pi$
$20$	−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
$26$	−0.179638	−	0.614289i	−0.0352298	−	0.120472i
$27$	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	$-0.423404\pi$
$37$	−2.94161	−	1.69834i	−0.483597	−	0.279205i	−0.721914	+	0.691982i	$0.756738\pi$
$38$	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	$-0.709645\pi$
$41$	−1.49289	+	0.861918i	−0.233150	+	0.134609i	0.378875	+	0.925448i	$0.376311\pi$
$42$	0.127344	+	0.220565i	0.0196495	+	0.0340340i
$43$	−1.66436	+	2.88275i	−0.253812	+	0.439616i	−0.964572	−	0.263819i	$-0.915018\pi$
$43$	−1.66436	+	2.88275i	−0.253812	+	0.439616i	0.710760	+	0.703435i	$0.248351\pi$
$44$	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
$52$	6.81219	−	1.99210i	0.944681	−	0.276255i
$53$	−5.41936	−	9.38660i	−0.744406	−	1.28935i	−0.950472	−	0.310811i	$-0.899399\pi$
$53$	−5.41936	−	9.38660i	−0.744406	−	1.28935i	0.206066	−	0.978538i	$-0.433934\pi$
$54$		−	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	$-0.295480\pi$
$59$	1.57839	+	0.911283i	0.205489	+	0.118639i	−0.393724	+	0.919229i	$0.628814\pi$
$60$			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
$65$	−5.25256	+	5.49661i	−0.651500	+	0.681770i
$66$	−0.489793			−0.0602894
$67$	1.49673	−	0.864137i	0.182855	−	0.105571i	−0.405779	−	0.913971i	$-0.633000\pi$
$67$	1.49673	−	0.864137i	0.182855	−	0.105571i	0.588633	+	0.808400i	$0.299666\pi$
$68$	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	$-0.809860\pi$
$71$	−6.34620	+	3.66398i	−0.753155	+	0.434834i	0.0736778	+	0.997282i	$0.476526\pi$
$72$	1.59388	−	0.920225i	0.187840	−	0.108450i
$73$	−1.36850	+	0.790105i	−0.160171	+	0.0924748i	−0.577943	−	0.816077i	$-0.696144\pi$
$73$	−1.36850	+	0.790105i	−0.160171	+	0.0924748i	0.417772	+	0.908552i	$0.362811\pi$
$74$	−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	−0.980649	−	0.195774i	$-0.937278\pi$
$79$	−2.85115	+	4.93834i	−0.320780	+	0.555607i	0.659869	+	0.751380i	$0.270612\pi$
$80$	−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	$-0.710016\pi$
$83$	−2.14235	+	1.23688i	−0.235153	+	0.135766i	0.377794	+	0.925890i	$0.376683\pi$
$84$	−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	0.979661	+	0.200661i	$0.0643090\pi$
$103$	6.73489	+	11.6652i	0.663608	+	1.14940i	−0.316053	+	0.948742i	$0.602358\pi$
$104$	−0.712890	−	2.43780i	−0.0699047	−	0.239046i
$105$	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	−0.849817	−	0.527077i	$-0.823288\pi$
$107$	0.326395	−	0.565332i	0.0315538	−	0.0546527i	0.881371	+	0.472425i	$0.156621\pi$
$108$	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	0.924068	−	0.382229i	$-0.124843\pi$
$113$	1.39270	+	2.41222i	0.131014	+	0.226923i	−0.793054	+	0.609152i	$0.791510\pi$
$114$	−0.372967	−	0.645997i	−0.0349315	−	0.0605032i
$115$	16.6892	−	9.63551i	1.55628	−	0.898516i
$116$	−1.25598			−0.116615
$117$	6.81042	+	6.50804i	0.629624	+	0.601669i
$118$	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	−0.693700	−	0.720264i	$-0.744020\pi$
$127$	3.12070	−	5.40522i	0.276918	−	0.479635i	0.970617	+	0.240629i	$0.0773538\pi$
$128$		−	5.45866i		−	0.482482i
$129$	1.03587	+	1.79418i	0.0912032	+	0.157969i
$130$	0.975695	+	0.932375i	0.0855741	+	0.0817747i
$131$	−4.85712	+	8.41278i	−0.424369	+	0.735028i	−0.996361	−	0.0852308i	$-0.972837\pi$
$131$	−4.85712	+	8.41278i	−0.424369	+	0.735028i	0.571993	+	0.820259i	$0.306171\pi$
$132$		−	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	$-0.866203\pi$
$137$	−11.8923	+	6.86605i	−1.01603	+	0.586606i	−0.103080	+	0.994673i	$0.532870\pi$
$138$	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
$143$	11.0435	−	11.5566i	0.923504	−	0.966411i
$144$	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	$-0.401888\pi$
$149$	−4.51836	−	2.60868i	−0.370159	−	0.213711i	−0.673528	+	0.739162i	$0.735222\pi$
$150$	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	$-0.135990\pi$
$167$	13.0048	+	7.50835i	1.00634	+	0.581014i	0.0962255	+	0.995360i	$0.469323\pi$
$168$	0.505362	+	0.875312i	0.0389895	+	0.0675318i
$169$	10.9517	−	7.00425i	0.842441	−	0.538788i
$170$	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	0.995504	+	0.0947160i	$0.0301943\pi$
$173$	7.62580	+	13.2083i	0.579779	+	1.00421i	−0.415726	+	0.909490i	$0.636472\pi$
$174$	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	−0.902696	−	0.430280i	$-0.858415\pi$
$179$	−1.05313	+	1.82407i	−0.0787145	+	0.136338i	0.823981	+	0.566617i	$0.191748\pi$
$180$	−9.39168	−	5.42229i	−0.700015	−	0.404154i
$181$	10.4591	+	18.1157i	0.777417	+	1.34653i	0.933426	+	0.358771i	$0.116804\pi$
$181$	10.4591	+	18.1157i	0.777417	+	1.34653i	−0.156008	+	0.987756i	$0.549863\pi$
$182$	−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	0.691578	−	0.722301i	$-0.256916\pi$
$191$	−3.86611	−	6.69631i	−0.279742	−	0.484528i	−0.971321	+	0.237774i	$0.923582\pi$
$192$	2.25728	−	3.90973i	0.162905	−	0.282160i
$193$	−12.0335	−	6.94756i	−0.866192	−	0.500096i	−0.000111226	−	1.00000i	$-0.500035\pi$
$193$	−12.0335	−	6.94756i	−0.866192	−	0.500096i	−0.866081	+	0.499904i	$0.833369\pi$
$194$	1.28456			0.0922257
$195$	1.32812	+	4.54163i	0.0951084	+	0.325233i
$196$	−1.65899	−	2.87346i	−0.118499	−	0.205247i
$197$	−10.5063	+	6.06582i	−0.748543	+	0.432171i	−0.825167	−	0.564889i	$-0.808919\pi$
$197$	−10.5063	+	6.06582i	−0.748543	+	0.432171i	0.0766242	+	0.997060i	$0.475586\pi$
$198$	1.02803	−	1.78059i	0.0730587	−	0.126541i
$199$	3.32950	+	5.76686i	0.236022	+	0.408802i	0.959569	−	0.281473i	$-0.0908230\pi$
$199$	3.32950	+	5.76686i	0.236022	+	0.408802i	−0.723547	+	0.690275i	$0.757490\pi$
$200$	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
$208$	13.1917	−	3.85766i	0.914677	−	0.267480i
$209$	29.9335			2.07055
$210$	−0.465090	−	0.268520i	−0.0320943	−	0.0185296i
$211$	−4.33279	+	7.50462i	−0.298282	+	0.516639i	−0.975743	−	0.218919i	$-0.929747\pi$
$211$	−4.33279	+	7.50462i	−0.298282	+	0.516639i	0.677461	+	0.735558i	$0.263080\pi$
$212$	−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	$-0.534758\pi$
$223$	−15.2966	−	8.83148i	−1.02433	−	0.591400i	−0.915356	+	0.402644i	$0.868091\pi$
$224$	−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	$-0.921581\pi$
$227$	−18.7353	+	10.8168i	−1.24351	+	0.717939i	−0.273701	+	0.961815i	$0.588248\pi$
$228$	7.16382	−	4.13603i	0.474435	−	0.273915i
$229$	13.2127	+	7.62836i	0.873121	+	0.504096i	0.868384	−	0.495892i	$-0.165159\pi$
$229$	13.2127	+	7.62836i	0.873121	+	0.504096i	0.00473670	+	0.999989i	$0.498492\pi$
$230$	−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	$0.619502\pi$
$234$	1.15523	−	1.20891i	0.0755200	−	0.0790288i
$235$	−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	$-0.499116\pi$
$239$	13.4528	−	7.76696i	0.870187	−	0.502403i	0.867410	+	0.497593i	$0.165783\pi$
$240$			5.00269i			0.322922i
$241$	−2.34241	−	1.35239i	−0.150888	−	0.0871151i	0.422655	−	0.906291i	$-0.361098\pi$
$241$	−2.34241	−	1.35239i	−0.150888	−	0.0871151i	−0.573543	+	0.819175i	$0.694431\pi$
$242$	−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	−0.986441	−	0.164117i	$-0.947523\pi$
$251$	−5.56233	+	9.63424i	−0.351091	+	0.608108i	0.635350	+	0.772225i	$0.280856\pi$
$252$		−	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	0.675504	−	0.737357i	$-0.263926\pi$
$257$	−4.82248	−	8.35277i	−0.300818	−	0.521032i	−0.976321	+	0.216325i	$0.930593\pi$
$258$	0.318482	−	0.183876i	0.0198278	−	0.0114476i
$259$	3.91519	+	6.78132i	0.243278	+	0.421370i
$260$	−10.3396	+	10.8200i	−0.641236	+	0.671029i
$261$	−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	0.780683	−	0.624927i	$-0.214871\pi$
$269$	−2.47431	−	4.28562i	−0.150861	−	0.261299i	−0.931544	+	0.363628i	$0.881538\pi$
$270$	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
$273$	−3.57403	+	3.74009i	−0.216310	+	0.226360i
$274$	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
$286$	−2.05140	−	1.96032i	−0.121302	−	0.115916i
$287$	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	$-0.117137\pi$
$293$	18.6240	+	10.7526i	1.08803	+	0.628172i	0.154976	+	0.987918i	$0.450470\pi$
$294$			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
$299$	−31.6270	+	9.24874i	−1.82904	+	0.534869i
$300$	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	$-0.188461\pi$
$307$	13.3403	+	7.70204i	0.761373	+	0.439579i	−0.0684155	+	0.997657i	$0.521794\pi$
$308$	−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	−0.218812	−	0.975767i	$-0.570218\pi$
$313$	13.0147	−	22.5421i	0.735633	−	1.27415i	0.954445	−	0.298387i	$-0.0964485\pi$
$314$		−	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	$-0.346709\pi$
$317$	−1.29542	−	0.747913i	−0.0727582	−	0.0420070i	−0.535938	+	0.844257i	$0.680042\pi$
$318$			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	$-0.999485\pi$
$331$	−27.2646	+	15.7412i	−1.49860	+	0.865215i	−0.498598	+	0.866833i	$0.666152\pi$
$332$	−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	$0.441581\pi$
$338$	−1.24331	−	1.94403i	−0.0676274	−	0.105741i
$339$	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	0.432917	+	0.901434i	$0.357484\pi$
$347$	−10.5100	+	18.2038i	−0.564206	+	0.977233i	−0.997123	+	0.0757993i	$0.975849\pi$
$348$	−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
$351$	12.0887	−	3.53511i	0.645246	−	0.188690i
$352$	−4.62299	−	8.00725i	−0.246406	−	0.426788i
$353$	−2.90376	−	1.67649i	−0.154551	−	0.0892303i	0.420730	−	0.907186i	$-0.361774\pi$
$353$	−2.90376	−	1.67649i	−0.154551	−	0.0892303i	−0.575281	+	0.817956i	$0.695107\pi$
$354$	−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	$-0.505134\pi$
$359$	15.9483	−	9.20775i	0.841718	−	0.485966i	0.857848	+	0.513904i	$0.171801\pi$
$360$	−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	−0.966541	−	0.256513i	$-0.917426\pi$
$367$	−13.5138	−	23.4067i	−0.705417	−	1.22182i	0.261124	−	0.965305i	$-0.415907\pi$
$368$	−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
$377$	−2.20803	+	0.645697i	−0.113719	+	0.0332551i
$378$	−0.714733	+	1.23795i	−0.0367619	+	0.0636735i
$379$	−18.4380	−	10.6452i	−0.947095	−	0.546806i	−0.0549180	−	0.998491i	$-0.517490\pi$
$379$	−18.4380	−	10.6452i	−0.947095	−	0.546806i	−0.892177	+	0.451685i	$0.850823\pi$
$380$	−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	$-0.743588\pi$
$383$	−8.11184	+	4.68337i	−0.414496	+	0.239309i	0.278224	+	0.960516i	$0.410254\pi$
$384$	−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	−0.336705	−	0.941610i	$-0.609312\pi$
$389$	12.7629	−	22.1060i	0.647106	−	1.12082i	0.983811	−	0.179211i	$-0.0573543\pi$
$390$	0.806178	−	0.235752i	0.0408224	−	0.0119378i
$391$	−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	$-0.243821\pi$
$397$	9.57746	+	5.52955i	0.480679	+	0.277520i	−0.240020	+	0.970768i	$0.577154\pi$
$398$	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
$403$	−10.5832	+	17.0586i	−0.527186	+	0.849750i
$404$	−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	$-0.270789\pi$
$409$	6.83852	+	3.94822i	0.338143	+	0.195227i	−0.321307	+	0.946975i	$0.604122\pi$
$410$	−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
$416$	−2.11055	−	7.21724i	−0.103478	−	0.353854i
$417$	−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	$-0.891752\pi$
$421$	−23.0878	+	13.3298i	−1.12523	+	0.649653i	−0.182500	+	0.983206i	$0.558419\pi$
$422$	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
$429$	−2.79236	−	9.54876i	−0.134816	−	0.461018i
$430$	−1.24594			−0.0600845
$431$	25.2229	+	14.5624i	1.21494	+	0.701448i	0.963832	−	0.266510i	$-0.0858707\pi$
$431$	25.2229	+	14.5624i	1.21494	+	0.701448i	0.251111	+	0.967958i	$0.419204\pi$
$432$	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	−0.931750	−	0.363100i	$-0.881718\pi$
$439$	−16.3497	−	28.3185i	−0.780329	−	1.35157i	0.151422	−	0.988469i	$-0.451615\pi$
$440$	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	0.900552	−	0.434747i	$-0.143162\pi$
$443$	1.55276	+	2.68946i	0.0737739	+	0.127780i	−0.826779	+	0.562528i	$0.809829\pi$
$444$	−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
$455$	16.8222	−	4.91934i	0.788637	−	0.230622i
$456$	−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	$0.581186\pi$
$468$	13.4062	+	12.8110i	0.619704	+	0.592190i
$469$	−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	$-0.0740629\pi$
$479$	27.5740	+	15.9199i	1.25989	+	0.727398i	0.286837	+	0.957979i	$0.407396\pi$
$480$	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	$-0.365545\pi$
$487$	31.0021	−	17.8991i	1.40484	−	0.811083i	0.994884	+	0.101023i	$0.0322116\pi$
$488$		−	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	0.994308	−	0.106540i	$-0.0339773\pi$
$491$	8.97171	+	15.5395i	0.404888	+	0.701286i	−0.589421	+	0.807826i	$0.700644\pi$
$492$			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	$-0.340883\pi$
$499$	−0.917631	−	0.529795i	−0.0410788	−	0.0237169i	−0.520399	+	0.853923i	$0.674217\pi$
$500$		−	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	−0.616097	−	0.787670i	$-0.711287\pi$
$503$	8.39005	−	14.5320i	0.374094	−	0.647949i	0.990191	+	0.139721i	$0.0446205\pi$
$504$	−4.24281			−0.188990
$505$	13.1374	−	7.58487i	0.584605	−	0.337522i
$506$	3.59608	+	6.22860i	0.159865	+	0.276895i
$507$	−0.367199	−	8.08265i	−0.0163079	−	0.358963i
$508$	6.14307	−	10.6401i	0.272555	−	0.472079i
$509$	12.0337	−	6.94766i	0.533384	−	0.307950i	−0.209009	−	0.977914i	$-0.567024\pi$
$509$	12.0337	−	6.94766i	0.533384	−	0.307950i	0.742394	+	0.669964i	$0.233691\pi$
$510$	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
$520$	3.87204	+	3.70012i	0.169800	+	0.162261i
$521$	10.1180	−	17.5249i	0.443278	−	0.767779i	−0.554653	−	0.832082i	$-0.687149\pi$
$521$	10.1180	−	17.5249i	0.443278	−	0.767779i	0.997930	+	0.0643026i	$0.0204823\pi$
$522$	−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
$533$	−4.29405	+	4.49356i	−0.185996	+	0.194638i
$534$	−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	$-0.0169448\pi$
$541$	33.7679	+	19.4959i	1.45180	+	0.838194i	0.453212	+	0.891403i	$0.350278\pi$
$542$	−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
$546$	0.663898	+	0.634422i	0.0284122	+	0.0271507i
$547$	−16.2249	−	28.1024i	−0.693727	−	1.20157i	−0.970608	−	0.240667i	$-0.922634\pi$
$547$	−16.2249	−	28.1024i	−0.693727	−	1.20157i	0.276881	−	0.960904i	$-0.410699\pi$
$548$	−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	0.948017	+	0.318220i	$0.103085\pi$
$563$	17.7861	+	30.8064i	0.749595	+	1.29834i	−0.198422	+	0.980117i	$0.563582\pi$
$564$	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	0.916896	−	0.399125i	$-0.130686\pi$
$569$	2.69060	+	4.66026i	0.112796	+	0.195368i	−0.804101	+	0.594493i	$0.797353\pi$
$570$	1.36217	+	0.786448i	0.0570549	+	0.0329407i
$571$	−13.9447	−	24.1530i	−0.583569	−	1.01077i	−0.995052	−	0.0993539i	$-0.968322\pi$
$571$	−13.9447	−	24.1530i	−0.583569	−	1.01077i	0.411483	−	0.911417i	$-0.365011\pi$
$572$	21.7390	−	22.7491i	0.908954	−	0.951186i
$573$	−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	−0.996876	−	0.0789849i	$-0.974832\pi$
$577$	−37.5618	−	21.6863i	−1.56372	−	0.902812i	−0.566841	−	0.823827i	$-0.691835\pi$
$578$	−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
$598$	1.64173	+	5.61407i	0.0671354	+	0.229576i
$599$	8.84805	+	15.3253i	0.361522	+	0.626174i	0.988211	−	0.153095i	$-0.0489241\pi$
$599$	8.84805	+	15.3253i	0.361522	+	0.626174i	−0.626690	+	0.779269i	$0.715591\pi$
$600$	0.210232	−	0.121377i	0.00858267	−	0.00495520i
$601$	−7.09939	+	12.2965i	−0.289590	+	0.501585i	−0.973712	−	0.227783i	$-0.926852\pi$
$601$	−7.09939	+	12.2965i	−0.289590	+	0.501585i	0.684122	+	0.729368i	$0.260186\pi$
$602$	−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	−0.998838	−	0.0482025i	$-0.984651\pi$
$607$	−13.3328	−	23.0932i	−0.541163	−	0.937322i	0.457674	−	0.889120i	$-0.348683\pi$
$608$	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
$611$	10.0614	+	34.4058i	0.407039	+	1.39191i
$612$	37.4032			1.51194
$613$	39.8799	+	23.0247i	1.61073	+	0.929957i	0.989200	+	0.146570i	$0.0468232\pi$
$613$	39.8799	+	23.0247i	1.61073	+	0.929957i	0.621533	+	0.783388i	$0.286510\pi$
$614$	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	$-0.321508\pi$
$617$	1.59801	+	0.922614i	0.0643336	+	0.0371430i	−0.467488	+	0.883999i	$0.654841\pi$
$618$		−	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	−0.543065	+	0.839691i	$0.682736\pi$
$631$	−38.7293	+	22.3604i	−1.54179	+	0.890153i	−0.998726	+	0.0504628i	$0.983930\pi$
$632$	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
$637$	−4.39375	−	4.19867i	−0.174087	−	0.166358i
$638$	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	0.999930	+	0.0118242i	$0.00376385\pi$
$641$	12.9174	+	22.3735i	0.510205	+	0.883701i	−0.489725	+	0.871877i	$0.662903\pi$
$642$	−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	$-0.432983\pi$
$661$	29.8334	−	17.2243i	1.16038	−	0.669948i	0.951396	+	0.307970i	$0.0996496\pi$
$662$	2.79420	+	4.83970i	0.108600	+	0.188100i
$663$	−11.7991	−	11.2752i	−0.458239	−	0.437894i
$664$	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	0.795872	−	0.605465i	$-0.207013\pi$
$673$	−3.27940	−	5.68009i	−0.126412	−	0.218951i	−0.922284	+	0.386513i	$0.873679\pi$
$674$		−	1.18939i		−	0.0458136i
$675$	−0.967073	+	1.67502i	−0.0372227	+	0.0644716i
$676$	21.5584	−	13.7878i	0.829169	−	0.530300i
$677$	4.80721	+	8.32633i	0.184756	+	0.320007i	0.943494	−	0.331389i	$-0.107517\pi$
$677$	4.80721	+	8.32633i	0.184756	+	0.320007i	−0.758738	+	0.651396i	$0.774184\pi$
$678$		−	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
$689$	−28.2535	−	26.9991i	−1.07637	−	1.02858i
$690$	−2.12903			−0.0810509
$691$	30.4991	−	17.6087i	1.16024	−	0.669865i	0.208878	−	0.977942i	$-0.433019\pi$
$691$	30.4991	−	17.6087i	1.16024	−	0.669865i	0.951361	+	0.308077i	$0.0996855\pi$
$692$	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	−0.925891	−	0.377791i	$-0.876684\pi$
$701$	−3.59467	+	6.22616i	−0.135769	+	0.235159i	0.790122	+	0.612950i	$0.210017\pi$
$702$	−0.627513	−	2.14584i	−0.0236839	−	0.0809897i
$703$	−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	−0.581592	−	0.813480i	$-0.697570\pi$
$719$	11.0930	−	19.2136i	0.413699	−	0.716547i	0.995291	+	0.0969334i	$0.0309034\pi$
$720$	−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	−0.824372	−	0.566048i	$-0.808472\pi$
$727$	2.10380	−	3.64389i	0.0780256	−	0.135144i	0.902398	+	0.430904i	$0.141805\pi$
$728$	−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	$-0.828968\pi$
$733$	−22.8876	+	13.2141i	−0.845371	+	0.488075i	0.0137152	+	0.999906i	$0.495634\pi$
$734$	−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	$-0.996724\pi$
$739$	−40.5324	+	23.4014i	−1.49101	+	0.860834i	−0.491061	+	0.871125i	$0.663391\pi$
$740$	14.0990			0.518289
$741$	10.4677	−	10.9541i	0.384541	−	0.402407i
$742$	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	−0.981145	−	0.193272i	$-0.938090\pi$
$751$	−8.85694	+	15.3407i	−0.323194	+	0.559789i	0.657951	+	0.753061i	$0.271423\pi$
$752$			37.8987i			1.38202i
$753$	3.46190	+	5.99619i	0.126159	+	0.218513i
$754$	0.114617	+	0.391944i	0.00417410	+	0.0142738i
$755$	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	−0.825234	−	0.564791i	$-0.808957\pi$
$757$	−24.8102	−	42.9725i	−0.901740	−	1.56186i	−0.0765066	−	0.997069i	$-0.524377\pi$
$758$	−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	$-0.333493\pi$
$761$	−0.0239750	−	0.0138420i	−0.000869093	−	0.000501771i	−0.500434	+	0.865774i	$0.666826\pi$
$762$	−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	$-0.526462\pi$
$769$	−27.3868	−	15.8117i	−0.987592	−	0.570186i	−0.904554	+	0.426360i	$0.859796\pi$
$770$	−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
$780$	2.61438	+	8.94015i	0.0936100	+	0.320109i
$781$	−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	$-0.292103\pi$
$787$	6.27627	+	3.62361i	0.223725	+	0.129168i	−0.383949	+	0.923354i	$0.625436\pi$
$788$	−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
$793$	5.62311	−	1.64437i	0.199682	−	0.0583934i
$794$	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	0.723979	−	0.689822i	$-0.242311\pi$
$797$	−6.64601	−	11.5112i	−0.235414	−	0.407748i	−0.959393	+	0.282073i	$0.908978\pi$
$798$			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
$806$	3.02805	+	1.87861i	0.106659	+	0.0661711i
$807$	−3.07993			−0.108419
$808$			5.06784i			0.178286i
$809$	−10.1624	+	17.6018i	−0.357291	+	0.618845i	−0.987507	−	0.157574i	$-0.949633\pi$
$809$	−10.1624	+	17.6018i	−0.357291	+	0.618845i	0.630217	+	0.776419i	$0.282966\pi$
$810$	−2.11996			−0.0744877
$811$	2.74325	−	1.58382i	0.0963285	−	0.0556153i	−0.451062	−	0.892493i	$-0.648955\pi$
$811$	2.74325	−	1.58382i	0.0963285	−	0.0556153i	0.547390	+	0.836877i	$0.315621\pi$
$812$	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
$819$	−6.09518	−	20.8431i	−0.212983	−	0.728317i
$820$	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	−0.910670	−	0.413135i	$-0.864434\pi$
$823$	−2.79849	+	4.84712i	−0.0975491	+	0.168960i	0.813121	+	0.582095i	$0.197767\pi$
$824$	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	$-0.810441\pi$
$827$	−21.7407	+	12.5520i	−0.756000	+	0.436477i	0.0718578	+	0.997415i	$0.477107\pi$
$828$	−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
$832$	25.1022	−	7.34067i	0.870262	−	0.254492i
$833$	−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	0.916645	−	0.399702i	$-0.130887\pi$
$857$	3.28373	+	5.68758i	0.112170	+	0.194284i	−0.804475	+	0.593987i	$0.797553\pi$
$858$	−1.69499	+	0.495668i	−0.0578659	+	0.0169218i
$859$	−9.41315	−	16.3041i	−0.321173	−	0.556287i	0.659558	−	0.751654i	$-0.270744\pi$
$859$	−9.41315	−	16.3041i	−0.321173	−	0.556287i	−0.980730	+	0.195367i	$0.937410\pi$
$860$		−	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	$-0.582745\pi$
$863$	13.2602	−	7.65576i	0.451381	−	0.260605i	0.708413	+	0.705798i	$0.249411\pi$
$864$		−	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
$871$	4.30510	−	4.50513i	0.145873	−	0.152650i
$872$	−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	$-0.465478\pi$
$877$	30.3042	−	17.4962i	1.02330	−	0.590803i	0.915059	+	0.403321i	$0.132144\pi$
$878$	−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	0.958511	+	0.285056i	$0.0920122\pi$
$881$	21.5525	+	37.3300i	0.726121	+	1.25768i	−0.232390	+	0.972623i	$0.574654\pi$
$882$	−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	−0.898241	−	0.439504i	$-0.855154\pi$
$887$	−2.04007	+	3.53350i	−0.0684988	+	0.118643i	0.829742	+	0.558147i	$0.188488\pi$
$888$	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
$910$	−0.873226	−	2.98609i	−0.0289472	−	0.0989878i
$911$	−6.99016	+	12.1073i	−0.231594	+	0.401133i	−0.958277	−	0.285840i	$-0.907727\pi$
$911$	−6.99016	+	12.1073i	−0.231594	+	0.401133i	0.726683	+	0.686973i	$0.241061\pi$
$912$	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	0.605740	−	0.795663i	$-0.292877\pi$
$919$	−11.7075	−	20.2780i	−0.386194	−	0.668908i	−0.991934	+	0.126755i	$0.959544\pi$
$920$	−6.78765	−	11.7566i	−0.223782	−	0.387602i
$921$	8.30280	−	4.79362i	0.273587	−	0.157955i
$922$	−1.50103			−0.0494336
$923$	−18.2538	+	19.1019i	−0.600832	+	0.628748i
$924$	−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
$936$	4.58454	−	4.79754i	0.149850	−	0.156813i
$937$	14.5016	−	25.1175i	0.473746	−	0.820552i	−0.525803	−	0.850607i	$-0.676235\pi$
$937$	14.5016	−	25.1175i	0.473746	−	0.820552i	0.999548	+	0.0300551i	$0.00956827\pi$
$938$			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	$-0.661175\pi$
$941$	0.916612	−	0.529206i	0.0298807	−	0.0172516i	0.514866	+	0.857271i	$0.327842\pi$
$942$	−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	$-0.204187\pi$
$947$	21.0371	+	12.1458i	0.683615	+	0.394685i	−0.117601	+	0.993061i	$0.537520\pi$
$948$	3.49311	+	6.05024i	0.113451	+	0.196503i
$949$	−3.93628	+	4.11917i	−0.127777	+	0.133714i
$950$	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	$-0.237765\pi$
$967$	15.9291	+	9.19668i	0.512246	+	0.295745i	−0.221510	+	0.975158i	$0.571099\pi$
$968$	−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	0.798534	−	0.601950i	$-0.205609\pi$
$971$	−3.80276	−	6.58658i	−0.122036	−	0.211373i	−0.920571	+	0.390576i	$0.872276\pi$
$972$	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
$975$	0.898291	+	0.858407i	0.0287683	+	0.0274910i
$976$	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	$-0.461210\pi$
$983$	32.6680	−	18.8609i	1.04195	−	0.601568i	0.920384	+	0.391016i	$0.127876\pi$
$984$	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	0.696025	−	0.718018i	$-0.254950\pi$
$997$	−8.64560	−	14.9746i	−0.273809	−	0.474251i	−0.969834	+	0.243767i	$0.921617\pi$
$998$	−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.129.16	yes	68
13.12	even	2	inner	403.2.l.c.129.19	yes	68
31.25	even	3	inner	403.2.l.c.25.16	✓	68
403.25	even	6	inner	403.2.l.c.25.19	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.16	✓	68	31.25	even	3	inner
403.2.l.c.25.19	yes	68	403.25	even	6	inner
403.2.l.c.129.16	yes	68	1.1	even	1	trivial
403.2.l.c.129.19	yes	68	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
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} +(3.46062 - 1.01199i) 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} +(-0.179638 - 0.614289i) 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} +(6.81219 - 1.99210i) 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} +(-5.25256 + 5.49661i) 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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