LMFDB - Embedded newform 403.2.l.c.129.28

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			129.28
Character	$\chi$	$=$	403.129
Dual form			403.2.l.c.25.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00957i q^{2} +(-1.67472 + 2.90070i) q^{3} -2.03837 q^{4} +(-0.151987 + 0.0877499i) q^{5} +(-5.82915 - 3.36546i) q^{6} +(-2.39273 - 1.38144i) q^{7} -0.0771108i q^{8} +(-4.10936 - 7.11762i) q^{9} +O(q^{10})$	\(q+2.00957i q^{2} +(-1.67472 + 2.90070i) q^{3} -2.03837 q^{4} +(-0.151987 + 0.0877499i) q^{5} +(-5.82915 - 3.36546i) q^{6} +(-2.39273 - 1.38144i) q^{7} -0.0771108i q^{8} +(-4.10936 - 7.11762i) q^{9} +(-0.176340 - 0.305429i) q^{10} +(3.13903 - 1.81232i) q^{11} +(3.41370 - 5.91270i) q^{12} +(2.94803 + 2.07584i) q^{13} +(2.77611 - 4.80836i) q^{14} -0.587826i q^{15} -3.92178 q^{16} +(-2.82097 + 4.88607i) q^{17} +(14.3034 - 8.25805i) q^{18} +(-4.40913 - 2.54561i) q^{19} +(0.309807 - 0.178867i) q^{20} +(8.01430 - 4.62706i) q^{21} +(3.64199 + 6.30811i) q^{22} -4.59797 q^{23} +(0.223675 + 0.129139i) q^{24} +(-2.48460 + 4.30345i) q^{25} +(-4.17155 + 5.92427i) q^{26} +17.4798 q^{27} +(4.87728 + 2.81590i) q^{28} -0.682120 q^{29} +1.18128 q^{30} +(-2.55488 + 4.94698i) q^{31} -8.03532i q^{32} +12.1405i q^{33} +(-9.81890 - 5.66894i) q^{34} +0.484886 q^{35} +(8.37641 + 14.5084i) q^{36} +(-0.536456 - 0.309723i) q^{37} +(5.11559 - 8.86046i) q^{38} +(-10.9585 + 5.07489i) q^{39} +(0.00676647 + 0.0117199i) q^{40} +(9.51308 - 5.49238i) q^{41} +(9.29840 + 16.1053i) q^{42} +(-1.15378 + 1.99841i) q^{43} +(-6.39851 + 3.69418i) q^{44} +(1.24914 + 0.721192i) q^{45} -9.23993i q^{46} -6.66939i q^{47} +(6.56788 - 11.3759i) q^{48} +(0.316775 + 0.548670i) q^{49} +(-8.64809 - 4.99298i) q^{50} +(-9.44867 - 16.3656i) q^{51} +(-6.00918 - 4.23134i) q^{52} +(0.973922 + 1.68688i) q^{53} +35.1269i q^{54} +(-0.318062 + 0.550900i) q^{55} +(-0.106524 + 0.184506i) q^{56} +(14.7681 - 8.52637i) q^{57} -1.37077i q^{58} +(3.24194 + 1.87174i) q^{59} +1.19821i q^{60} +6.97955 q^{61} +(-9.94130 - 5.13421i) q^{62} +22.7074i q^{63} +8.30397 q^{64} +(-0.630218 - 0.0568125i) q^{65} -24.3972 q^{66} +(-10.5204 + 6.07396i) q^{67} +(5.75019 - 9.95962i) q^{68} +(7.70030 - 13.3373i) q^{69} +0.974413i q^{70} +(-13.0677 + 7.54466i) q^{71} +(-0.548846 + 0.316876i) q^{72} +(0.229978 - 0.132778i) q^{73} +(0.622410 - 1.07805i) q^{74} +(-8.32201 - 14.4141i) q^{75} +(8.98745 + 5.18891i) q^{76} -10.0145 q^{77} +(-10.1983 - 22.0219i) q^{78} +(-0.904237 + 1.56618i) q^{79} +(0.596061 - 0.344136i) q^{80} +(-16.9456 + 29.3507i) q^{81} +(11.0373 + 19.1172i) q^{82} +(-9.00049 + 5.19644i) q^{83} +(-16.3361 + 9.43167i) q^{84} -0.990161i q^{85} +(-4.01594 - 2.31860i) q^{86} +(1.14236 - 1.97862i) q^{87} +(-0.139750 - 0.242053i) q^{88} -1.17340i q^{89} +(-1.44929 + 2.51024i) q^{90} +(-4.18618 - 9.03947i) q^{91} +9.37236 q^{92} +(-10.0710 - 15.6957i) q^{93} +13.4026 q^{94} +0.893510 q^{95} +(23.3080 + 13.4569i) q^{96} +7.88737i q^{97} +(-1.10259 + 0.636581i) q^{98} +(-25.7988 - 14.8950i) 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 $

$2$			2.00957i			1.42098i	0.703707	+	0.710490i	$0.251527\pi$
$2$			2.00957i			1.42098i	−0.703707	+	0.710490i	$0.748473\pi$
$3$	−1.67472	+	2.90070i	−0.966899	+	1.67472i	−0.262475	+	0.964939i	$0.584539\pi$
$3$	−1.67472	+	2.90070i	−0.966899	+	1.67472i	−0.704424	+	0.709779i	$0.748795\pi$
$4$	−2.03837			−1.01919
$5$	−0.151987	+	0.0877499i	−0.0679708	+	0.0392430i	−0.533600	−	0.845737i	$-0.679161\pi$
$5$	−0.151987	+	0.0877499i	−0.0679708	+	0.0392430i	0.465629	+	0.884980i	$0.345828\pi$
$6$	−5.82915	−	3.36546i	−2.37974	−	1.37394i
$7$	−2.39273	−	1.38144i	−0.904367	−	0.522137i	−0.0257528	−	0.999668i	$-0.508198\pi$
$7$	−2.39273	−	1.38144i	−0.904367	−	0.522137i	−0.878615	+	0.477532i	$0.841532\pi$
$8$		−	0.0771108i		−	0.0272628i
$9$	−4.10936	−	7.11762i	−1.36979	−	2.37254i
$10$	−0.176340	−	0.305429i	−0.0557635	−	0.0965852i
$11$	3.13903	−	1.81232i	0.946454	−	0.546435i	0.0544763	−	0.998515i	$-0.482651\pi$
$11$	3.13903	−	1.81232i	0.946454	−	0.546435i	0.891978	+	0.452080i	$0.149318\pi$
$12$	3.41370	−	5.91270i	0.985450	−	1.70685i
$13$	2.94803	+	2.07584i	0.817636	+	0.575735i
$13$	2.94803	+	2.07584i	0.817636	+	0.575735i
$14$	2.77611	−	4.80836i	0.741946	−	1.28509i
$15$		−	0.587826i		−	0.151776i
$16$	−3.92178			−0.980446
$17$	−2.82097	+	4.88607i	−0.684186	+	1.18505i	0.289505	+	0.957176i	$0.406509\pi$
$17$	−2.82097	+	4.88607i	−0.684186	+	1.18505i	−0.973692	+	0.227869i	$0.926824\pi$
$18$	14.3034	−	8.25805i	3.37134	−	1.94644i
$19$	−4.40913	−	2.54561i	−1.01152	−	0.584004i	−0.0998869	−	0.994999i	$-0.531848\pi$
$19$	−4.40913	−	2.54561i	−1.01152	−	0.584004i	−0.911638	+	0.410995i	$0.865181\pi$
$20$	0.309807	−	0.178867i	0.0692749	−	0.0399959i
$21$	8.01430	−	4.62706i	1.74886	−	1.00971i
$22$	3.64199	+	6.30811i	0.776474	+	1.34489i
$23$	−4.59797			−0.958742			−0.479371	−	0.877612i	$-0.659135\pi$
$23$	−4.59797			−0.958742			−0.479371	+	0.877612i	$0.659135\pi$
$24$	0.223675	+	0.129139i	0.0456575	+	0.0263604i
$25$	−2.48460	+	4.30345i	−0.496920	+	0.860691i
$26$	−4.17155	+	5.92427i	−0.818109	+	1.16185i
$27$	17.4798			3.36399
$28$	4.87728	+	2.81590i	0.921718	+	0.532154i
$29$	−0.682120			−0.126667			−0.0633333	−	0.997992i	$-0.520173\pi$
$29$	−0.682120			−0.126667			−0.0633333	+	0.997992i	$0.520173\pi$
$30$	1.18128			0.215671
$31$	−2.55488	+	4.94698i	−0.458870	+	0.888503i
$31$	−2.55488	+	4.94698i	−0.458870	+	0.888503i
$32$		−	8.03532i		−	1.42046i
$33$			12.1405i			2.11339i
$34$	−9.81890	−	5.66894i	−1.68393	−	0.972216i
$35$	0.484886			0.0819608
$36$	8.37641	+	14.5084i	1.39607	+	2.41806i
$37$	−0.536456	−	0.309723i	−0.0881928	−	0.0509181i	0.455255	−	0.890361i	$-0.349548\pi$
$37$	−0.536456	−	0.309723i	−0.0881928	−	0.0509181i	−0.543448	+	0.839443i	$0.682881\pi$
$38$	5.11559	−	8.86046i	0.829858	−	1.43736i
$39$	−10.9585	+	5.07489i	−1.75477	+	0.812632i
$40$	0.00676647	+	0.0117199i	0.00106987	+	0.00185307i
$41$	9.51308	−	5.49238i	1.48569	−	0.857765i	0.485826	−	0.874056i	$-0.338519\pi$
$41$	9.51308	−	5.49238i	1.48569	−	0.857765i	0.999867	+	0.0162903i	$0.00518561\pi$
$42$	9.29840	+	16.1053i	1.43477	+	2.48510i
$43$	−1.15378	+	1.99841i	−0.175950	+	0.304754i	−0.940490	−	0.339822i	$-0.889633\pi$
$43$	−1.15378	+	1.99841i	−0.175950	+	0.304754i	0.764540	+	0.644577i	$0.222966\pi$
$44$	−6.39851	+	3.69418i	−0.964612	+	0.556919i
$45$	1.24914	+	0.721192i	0.186211	+	0.107509i
$46$		−	9.23993i		−	1.36235i
$47$		−	6.66939i		−	0.972830i	−0.873728	−	0.486415i	$-0.838304\pi$
$47$		−	6.66939i		−	0.972830i	0.873728	−	0.486415i	$-0.161696\pi$
$48$	6.56788	−	11.3759i	0.947992	−	1.64197i
$49$	0.316775	+	0.548670i	0.0452536	+	0.0783815i
$50$	−8.64809	−	4.99298i	−1.22302	−	0.706114i
$51$	−9.44867	−	16.3656i	−1.32308	−	2.29164i
$52$	−6.00918	−	4.23134i	−0.833323	−	0.586781i
$53$	0.973922	+	1.68688i	0.133778	+	0.231711i	0.925130	−	0.379650i	$-0.123956\pi$
$53$	0.973922	+	1.68688i	0.133778	+	0.231711i	−0.791352	+	0.611361i	$0.790622\pi$
$54$			35.1269i			4.78016i
$55$	−0.318062	+	0.550900i	−0.0428875	+	0.0742833i
$56$	−0.106524	+	0.184506i	−0.0142349	+	0.0246556i
$57$	14.7681	−	8.52637i	1.95608	−	1.12935i
$58$		−	1.37077i		−	0.179991i
$59$	3.24194	+	1.87174i	0.422065	+	0.243679i	0.695960	−	0.718080i	$-0.254979\pi$
$59$	3.24194	+	1.87174i	0.422065	+	0.243679i	−0.273896	+	0.961759i	$0.588312\pi$
$60$			1.19821i			0.154688i
$61$	6.97955			0.893640			0.446820	−	0.894624i	$-0.352556\pi$
$61$	6.97955			0.893640			0.446820	+	0.894624i	$0.352556\pi$
$62$	−9.94130	−	5.13421i	−1.26255	−	0.652046i
$63$			22.7074i			2.86087i
$64$	8.30397			1.03800
$65$	−0.630218	−	0.0568125i	−0.0781689	−	0.00704673i
$66$	−24.3972			−3.00309
$67$	−10.5204	+	6.07396i	−1.28527	+	0.742052i	−0.977807	−	0.209507i	$-0.932814\pi$
$67$	−10.5204	+	6.07396i	−1.28527	+	0.742052i	−0.307465	+	0.951559i	$0.599481\pi$
$68$	5.75019	−	9.95962i	0.697313	−	1.20778i
$69$	7.70030	−	13.3373i	0.927007	−	1.60562i
$70$			0.974413i			0.116465i
$71$	−13.0677	+	7.54466i	−1.55086	+	0.895387i	−0.552783	+	0.833325i	$0.686434\pi$
$71$	−13.0677	+	7.54466i	−1.55086	+	0.895387i	−0.998072	+	0.0620621i	$0.980232\pi$
$72$	−0.548846	+	0.316876i	−0.0646821	+	0.0373442i
$73$	0.229978	−	0.132778i	0.0269169	−	0.0155405i	−0.486481	−	0.873691i	$-0.661720\pi$
$73$	0.229978	−	0.132778i	0.0269169	−	0.0155405i	0.513398	+	0.858151i	$0.328386\pi$
$74$	0.622410	−	1.07805i	0.0723537	−	0.125320i
$75$	−8.32201	−	14.4141i	−0.960943	−	1.66440i
$76$	8.98745	+	5.18891i	1.03093	+	0.595209i
$77$	−10.0145			−1.14126
$78$	−10.1983	−	22.0219i	−1.15473	−	2.49349i
$79$	−0.904237	+	1.56618i	−0.101735	+	0.176209i	−0.912399	−	0.409301i	$-0.865773\pi$
$79$	−0.904237	+	1.56618i	−0.101735	+	0.176209i	0.810665	+	0.585511i	$0.199106\pi$
$80$	0.596061	−	0.344136i	0.0666417	−	0.0384756i
$81$	−16.9456	+	29.3507i	−1.88285	+	3.26119i
$82$	11.0373	+	19.1172i	1.21887	+	2.11114i
$83$	−9.00049	+	5.19644i	−0.987932	+	0.570383i	−0.904656	−	0.426143i	$-0.859872\pi$
$83$	−9.00049	+	5.19644i	−0.987932	+	0.570383i	−0.0832769	+	0.996526i	$0.526539\pi$
$84$	−16.3361	+	9.43167i	−1.78242	+	1.02908i
$85$		−	0.990161i		−	0.107398i
$86$	−4.01594	−	2.31860i	−0.433050	−	0.250021i
$87$	1.14236	−	1.97862i	0.122474	−	0.212131i
$88$	−0.139750	−	0.242053i	−0.0148974	−	0.0258030i
$89$		−	1.17340i		−	0.124380i	−0.998064	−	0.0621900i	$-0.980192\pi$
$89$		−	1.17340i		−	0.124380i	0.998064	−	0.0621900i	$-0.0198085\pi$
$90$	−1.44929	+	2.51024i	−0.152768	+	0.264602i
$91$	−4.18618	−	9.03947i	−0.438831	−	0.947594i
$92$	9.37236			0.977136
$93$	−10.0710	−	15.6957i	−1.04431	−	1.62757i
$94$	13.4026			1.38237
$95$	0.893510			0.0916722
$96$	23.3080	+	13.4569i	2.37887	+	1.37344i
$97$			7.88737i			0.800841i	0.916331	+	0.400421i	$0.131136\pi$
$97$			7.88737i			0.800841i	−0.916331	+	0.400421i	$0.868864\pi$
$98$	−1.10259	+	0.636581i	−0.111379	+	0.0643044i
$99$	−25.7988	−	14.8950i	−2.59288	−	1.49700i
$100$	5.06454	−	8.77204i	0.506454	−	0.877204i
$101$	−1.24008			−0.123392			−0.0616962	−	0.998095i	$-0.519651\pi$
$101$	−1.24008			−0.123392			−0.0616962	+	0.998095i	$0.519651\pi$
$102$	32.8878	−	18.9878i	3.25637	−	1.88007i
$103$	5.36932	+	9.29993i	0.529055	+	0.916350i	0.999426	+	0.0338810i	$0.0107867\pi$
$103$	5.36932	+	9.29993i	0.529055	+	0.916350i	−0.470371	+	0.882469i	$0.655880\pi$
$104$	0.160070	−	0.227325i	0.0156962	−	0.0222911i
$105$	−0.812048	+	1.40651i	−0.0792478	+	0.137261i
$106$	−3.38991	+	1.95716i	−0.329257	+	0.190097i
$107$	4.81071	−	8.33240i	0.465069	−	0.805523i	−0.534136	−	0.845399i	$-0.679363\pi$
$107$	4.81071	−	8.33240i	0.465069	−	0.805523i	0.999205	+	0.0398756i	$0.0126962\pi$
$108$	−35.6303			−3.42853
$109$			5.68742i			0.544756i	0.962190	+	0.272378i	$0.0878101\pi$
$109$			5.68742i			0.544756i	−0.962190	+	0.272378i	$0.912190\pi$
$110$	−1.10707	−	0.639168i	−0.105555	−	0.0609423i
$111$	1.79683	−	1.03740i	0.170547	−	0.0984654i
$112$	9.38377	+	5.41772i	0.886683	+	0.511927i
$113$	−2.89659	−	5.01704i	−0.272488	−	0.471964i	0.697010	−	0.717061i	$-0.254513\pi$
$113$	−2.89659	−	5.01704i	−0.272488	−	0.471964i	−0.969498	+	0.245098i	$0.921180\pi$
$114$	17.1343	+	29.6776i	1.60478	+	2.77956i
$115$	0.698832	−	0.403471i	0.0651665	−	0.0376239i
$116$	1.39041			0.129097
$117$	2.66055	−	29.5134i	0.245968	−	2.72851i
$118$	−3.76138	+	6.51491i	−0.346264	+	0.599746i
$119$	13.4997	−	7.79403i	1.23751	−	0.714478i
$120$	−0.0453277			−0.00413784
$121$	1.06902	−	1.85159i	0.0971832	−	0.168326i
$122$			14.0259i			1.26984i
$123$			36.7927i			3.31749i
$124$	5.20780	−	10.0838i	0.467674	−	0.905550i
$125$		−	1.74959i		−	0.156488i
$126$	−45.6321			−4.06523
$127$	−0.805677	+	1.39547i	−0.0714923	+	0.123828i	−0.899556	−	0.436806i	$-0.856109\pi$
$127$	−0.805677	+	1.39547i	−0.0714923	+	0.123828i	0.828063	+	0.560635i	$0.189443\pi$
$128$			0.616773i			0.0545156i
$129$	−3.86451	−	6.69354i	−0.340252	−	0.589333i
$130$	0.114169	−	1.26647i	0.0100133	−	0.111077i
$131$	−6.35334	+	11.0043i	−0.555094	+	0.961451i	0.442802	+	0.896619i	$0.353984\pi$
$131$	−6.35334	+	11.0043i	−0.555094	+	0.961451i	−0.997896	+	0.0648314i	$0.979349\pi$
$132$		−	24.7469i		−	2.15394i
$133$	7.03325	+	12.1819i	0.609860	+	1.05631i
$134$	−12.2060	−	21.1415i	−1.05444	−	1.82635i
$135$	−2.65671	+	1.53385i	−0.228653	+	0.132013i
$136$	0.376769	+	0.217528i	0.0323077	+	0.0186528i
$137$	−6.37020	+	3.67784i	−0.544243	+	0.314219i	−0.746797	−	0.665052i	$-0.768409\pi$
$137$	−6.37020	+	3.67784i	−0.544243	+	0.314219i	0.202554	+	0.979271i	$0.435076\pi$
$138$	26.8022	+	15.4743i	2.28156	+	1.31726i
$139$	−10.6126			−0.900150			−0.450075	−	0.892991i	$-0.648603\pi$
$139$	−10.6126			−0.900150			−0.450075	+	0.892991i	$0.648603\pi$
$140$	−0.988379			−0.0835332
$141$	19.3459	+	11.1693i	1.62922	+	0.940629i
$142$	−15.1615	−	26.2605i	−1.27233	−	2.20374i
$143$	13.0161	+	1.17336i	1.08846	+	0.0981216i
$144$	16.1160	+	27.9138i	1.34300	+	2.32615i
$145$	0.103674	−	0.0598560i	0.00860963	−	0.00497077i
$146$	0.266827	+	0.462158i	0.0220828	+	0.0382485i
$147$	−2.12203			−0.175022
$148$	1.09350	+	0.631331i	0.0898849	+	0.0518951i
$149$	1.15596	+	0.667396i	0.0947002	+	0.0546752i	0.546602	−	0.837392i	$-0.315921\pi$
$149$	1.15596	+	0.667396i	0.0947002	+	0.0546752i	−0.451902	+	0.892068i	$0.649254\pi$
$150$	28.9662	−	16.7237i	2.36508	−	1.36548i
$151$		−	12.6532i		−	1.02970i	−0.857279	−	0.514852i	$-0.827847\pi$
$151$		−	12.6532i		−	1.02970i	0.857279	−	0.514852i	$-0.172153\pi$
$152$	−0.196294	+	0.339992i	−0.0159216	+	0.0275770i
$153$	46.3696			3.74876
$154$		−	20.1248i		−	1.62170i
$155$	−0.0457873	−	0.976068i	−0.00367773	−	0.0783997i
$156$	22.3375	−	10.3445i	1.78843	−	0.828223i
$157$	8.65077			0.690407			0.345203	−	0.938528i	$-0.387810\pi$
$157$	8.65077			0.690407			0.345203	+	0.938528i	$0.387810\pi$
$158$	−3.14736	−	1.81713i	−0.250390	−	0.144563i
$159$	−6.52418			−0.517401
$160$	0.705099	+	1.22127i	0.0557430	+	0.0965496i
$161$	11.0017	+	6.35183i	0.867055	+	0.500594i
$162$	−58.9823	−	34.0534i	−4.63408	−	2.67549i
$163$			8.95031i			0.701042i	0.936555	+	0.350521i	$0.113996\pi$
$163$			8.95031i			0.701042i	−0.936555	+	0.350521i	$0.886004\pi$
$164$	−19.3912	+	11.1955i	−1.51420	+	0.874222i
$165$	−1.06533	−	1.84520i	−0.0829357	−	0.143649i
$166$	−10.4426	−	18.0871i	−0.810503	−	1.40383i
$167$	−12.4085	−	7.16406i	−0.960200	−	0.554372i	−0.0639654	−	0.997952i	$-0.520375\pi$
$167$	−12.4085	−	7.16406i	−0.960200	−	0.554372i	−0.896235	+	0.443580i	$0.853708\pi$
$168$	−0.356796	−	0.617990i	−0.0275274	−	0.0476789i
$169$	4.38175	+	12.2393i	0.337058	+	0.941484i
$170$	1.98980			0.152610
$171$			41.8434i			3.19984i
$172$	2.35183	−	4.07350i	0.179326	−	0.310601i
$173$	−0.425547	−	0.737069i	−0.0323537	−	0.0560383i	0.849395	−	0.527757i	$-0.176967\pi$
$173$	−0.425547	−	0.737069i	−0.0323537	−	0.0560383i	−0.881749	+	0.471719i	$0.843634\pi$
$174$	3.97618	+	2.29565i	0.301434	+	0.174033i
$175$	11.8900	−	6.86467i	0.898796	−	0.518920i
$176$	−12.3106	+	7.10753i	−0.927947	+	0.535750i
$177$	−10.8587	+	6.26926i	−0.816188	+	0.471226i
$178$	2.35803			0.176742
$179$	7.01751	−	12.1547i	0.524513	−	0.908484i	−0.475079	−	0.879943i	$-0.657581\pi$
$179$	7.01751	−	12.1547i	0.524513	−	0.908484i	0.999593	−	0.0285409i	$-0.00908608\pi$
$180$	−2.54622	−	1.47006i	−0.189784	−	0.109572i
$181$	8.95892	+	15.5173i	0.665912	+	1.15339i	0.979037	+	0.203681i	$0.0652905\pi$
$181$	8.95892	+	15.5173i	0.665912	+	1.15339i	−0.313126	+	0.949712i	$0.601376\pi$
$182$	18.1655	−	8.41242i	1.34651	−	0.623570i
$183$	−11.6888	+	20.2456i	−0.864059	+	1.49659i
$184$			0.354553i			0.0261380i
$185$	0.108713			0.00799271
$186$	31.5417	−	20.2383i	2.31275	−	1.48395i
$187$			20.4500i			1.49545i
$188$			13.5947i			0.991495i
$189$	−41.8244	−	24.1473i	−3.04228	−	1.75646i
$190$			1.79557i			0.130264i
$191$	7.80076	+	13.5113i	0.564443	+	0.977644i	0.997101	+	0.0760863i	$0.0242424\pi$
$191$	7.80076	+	13.5113i	0.564443	+	0.977644i	−0.432658	+	0.901558i	$0.642424\pi$
$192$	−13.9068	+	24.0873i	−1.00364	+	1.73835i
$193$	6.05340	+	3.49493i	0.435733	+	0.251571i	0.701786	−	0.712388i	$-0.252386\pi$
$193$	6.05340	+	3.49493i	0.435733	+	0.251571i	−0.266053	+	0.963958i	$0.585720\pi$
$194$	−15.8502			−1.13798
$195$	1.22023	−	1.73293i	0.0873827	−	0.124097i
$196$	−0.645705	−	1.11839i	−0.0461218	−	0.0798853i
$197$	−4.32766	+	2.49857i	−0.308333	+	0.178016i	−0.646180	−	0.763185i	$-0.723635\pi$
$197$	−4.32766	+	2.49857i	−0.308333	+	0.178016i	0.337847	+	0.941201i	$0.390301\pi$
$198$	29.9325	−	51.8446i	2.12721	−	3.68443i
$199$	2.18218	+	3.77964i	0.154690	+	0.267932i	0.932946	−	0.360016i	$-0.117229\pi$
$199$	2.18218	+	3.77964i	0.154690	+	0.267932i	−0.778256	+	0.627947i	$0.783895\pi$
$200$	0.331843	+	0.191590i	0.0234648	+	0.0135474i
$201$		−	40.6887i		−	2.86996i
$202$		−	2.49202i		−	0.175338i
$203$	1.63213	+	0.942311i	0.114553	+	0.0661373i
$204$	19.2599	+	33.3591i	1.34846	+	2.33561i
$205$	−0.963911	+	1.66954i	−0.0673225	+	0.116606i
$206$	−18.6889	+	10.7900i	−1.30212	+	0.751777i
$207$	18.8947	+	32.7266i	1.31327	+	2.27466i
$208$	−11.5615	−	8.14101i	−0.801648	−	0.564477i
$209$	−18.4539			−1.27648
$210$	−2.82648	−	1.63187i	−0.195045	−	0.112610i
$211$	−12.3773	+	21.4380i	−0.852085	+	1.47586i	0.0272376	+	0.999629i	$0.491329\pi$
$211$	−12.3773	+	21.4380i	−0.852085	+	1.47586i	−0.879323	+	0.476226i	$0.842004\pi$
$212$	−1.98522	−	3.43849i	−0.136345	−	0.236157i
$213$		−	50.5408i		−	3.46300i
$214$	16.7445	+	9.66746i	1.14463	+	0.660854i
$215$		−	0.404977i		−	0.0276192i
$216$		−	1.34788i		−	0.0917117i
$217$	12.9471	−	8.30736i	0.878907	−	0.563940i
$218$	−11.4293			−0.774088
$219$			0.889464i			0.0601044i
$220$	0.648329	−	1.12294i	0.0437103	−	0.0757085i
$221$	−18.4590	+	8.54837i	−1.24169	+	0.575026i
$222$	2.08472	+	3.61085i	0.139917	+	0.242344i
$223$	9.72410	+	5.61421i	0.651174	+	0.375955i	0.788906	−	0.614514i	$-0.210648\pi$
$223$	9.72410	+	5.61421i	0.651174	+	0.375955i	−0.137732	+	0.990470i	$0.543981\pi$
$224$	−11.1003	+	19.2264i	−0.741673	+	1.28462i
$225$	40.8405			2.72270
$226$	10.0821	−	5.82090i	0.670651	−	0.387201i
$227$	10.2055	−	5.89213i	0.677361	−	0.391074i	−0.121499	−	0.992592i	$-0.538770\pi$
$227$	10.2055	−	5.89213i	0.677361	−	0.391074i	0.798860	+	0.601517i	$0.205437\pi$
$228$	−30.1029	+	17.3799i	−1.99361	+	1.15101i
$229$	12.8461	+	7.41669i	0.848893	+	0.490109i	0.860277	−	0.509827i	$-0.170290\pi$
$229$	12.8461	+	7.41669i	0.848893	+	0.490109i	−0.0113842	+	0.999935i	$0.503624\pi$
$230$	0.810803	+	1.40435i	0.0534628	+	0.0926003i
$231$	16.7714	−	29.0490i	1.10348	−	1.91128i
$232$			0.0525989i			0.00345329i
$233$	8.67614			0.568393			0.284196	−	0.958766i	$-0.408273\pi$
$233$	8.67614			0.568393			0.284196	+	0.958766i	$0.408273\pi$
$234$	59.3091	+	5.34657i	3.87716	+	0.349516i
$235$	0.585238	+	1.01366i	0.0381767	+	0.0661240i
$236$	−6.60828	−	3.81529i	−0.430163	−	0.248354i
$237$	−3.02868	−	5.24583i	−0.196734	−	0.340753i
$238$	15.6627	+	27.1285i	1.01526	+	1.75848i
$239$	−3.79249	+	2.18960i	−0.245316	+	0.141633i	−0.617618	−	0.786479i	$-0.711902\pi$
$239$	−3.79249	+	2.18960i	−0.245316	+	0.141633i	0.372302	+	0.928112i	$0.378569\pi$
$240$			2.30532i			0.148808i
$241$	4.81474	+	2.77979i	0.310145	+	0.179062i	0.646991	−	0.762497i	$-0.276027\pi$
$241$	4.81474	+	2.77979i	0.310145	+	0.179062i	−0.336847	+	0.941560i	$0.609360\pi$
$242$	3.72090	+	2.14826i	0.239188	+	0.138095i
$243$	−30.5386	−	52.8944i	−1.95905	−	3.39318i
$244$	−14.2269			−0.910785
$245$	−0.0962915	−	0.0555939i	−0.00615184	−	0.00355177i
$246$	−73.9376			−4.71409
$247$	−7.71396	−	16.6572i	−0.490827	−	1.05987i
$248$	0.381466	+	0.197009i	0.0242231	+	0.0125101i
$249$		−	34.8103i		−	2.20601i
$250$	3.51593			0.222367
$251$	14.2723	−	24.7203i	0.900859	−	1.56033i	0.0744781	−	0.997223i	$-0.476271\pi$
$251$	14.2723	−	24.7203i	0.900859	−	1.56033i	0.826381	−	0.563111i	$-0.190396\pi$
$252$		−	46.2862i		−	2.91575i
$253$	−14.4332	+	8.33299i	−0.907405	+	0.523891i
$254$	−2.80430	−	1.61906i	−0.175957	−	0.101589i
$255$	2.87216	+	1.65824i	0.179861	+	0.103843i
$256$	15.3685			0.960531
$257$	4.58260	+	7.93730i	0.285855	+	0.495115i	0.972816	−	0.231579i	$-0.0743892\pi$
$257$	4.58260	+	7.93730i	0.285855	+	0.495115i	−0.686961	+	0.726694i	$0.741056\pi$
$258$	13.4511	−	7.76601i	0.837431	−	0.483491i
$259$	0.855730	+	1.48217i	0.0531725	+	0.0920974i
$260$	1.28462	+	0.115805i	0.0796687	+	0.00718193i
$261$	2.80308	+	4.85508i	0.173506	+	0.300522i
$262$	−22.1139	−	12.7675i	−1.36620	−	0.788777i
$263$	29.5497			1.82212			0.911058	−	0.412279i	$-0.135267\pi$
$263$	29.5497			1.82212			0.911058	+	0.412279i	$0.135267\pi$
$264$	0.936165			0.0576170
$265$	−0.296048	−	0.170923i	−0.0181861	−	0.0104997i
$266$	−24.4805	+	14.1338i	−1.50099	+	0.866599i
$267$	3.40367	+	1.96511i	0.208301	+	0.120263i
$268$	21.4445	−	12.3810i	1.30993	−	0.756289i
$269$	0.697510	+	1.20812i	0.0425279	+	0.0736605i	0.886506	−	0.462717i	$-0.153126\pi$
$269$	0.697510	+	1.20812i	0.0425279	+	0.0736605i	−0.843978	+	0.536378i	$0.819792\pi$
$270$	−3.08238	−	5.33884i	−0.187588	−	0.324911i
$271$		−	14.7038i		−	0.893190i	−0.894736	−	0.446595i	$-0.852637\pi$
$271$		−	14.7038i		−	0.893190i	0.894736	−	0.446595i	$-0.147363\pi$
$272$	11.0632	−	19.1621i	0.670808	−	1.16187i
$273$	33.2314	+	2.99573i	2.01126	+	0.181310i
$274$	−7.39088	−	12.8014i	−0.446499	−	0.773359i
$275$			18.0116i			1.08614i
$276$	−15.6961	+	27.1864i	−0.944792	+	1.63643i
$277$	−10.0833			−0.605845			−0.302922	−	0.953015i	$-0.597962\pi$
$277$	−10.0833			−0.605845			−0.302922	+	0.953015i	$0.597962\pi$
$278$		−	21.3268i		−	1.27910i
$279$	45.7097	−	2.14424i	2.73657	−	0.128372i
$280$		−	0.0373900i		−	0.00223448i
$281$			13.6807i			0.816124i	0.912954	+	0.408062i	$0.133795\pi$
$281$			13.6807i			0.816124i	−0.912954	+	0.408062i	$0.866205\pi$
$282$	−22.4456	+	38.8769i	−1.33661	+	2.31508i
$283$	−13.2904			−0.790034			−0.395017	−	0.918674i	$-0.629261\pi$
$283$	−13.2904			−0.790034			−0.395017	+	0.918674i	$0.629261\pi$
$284$	26.6369	−	15.3788i	1.58061	−	0.912566i
$285$	−1.49638	+	2.59180i	−0.0886377	+	0.153525i
$286$	−2.35796	+	26.1567i	−0.139429	+	1.54668i
$287$	−30.3496			−1.79148
$288$	−57.1924	+	33.0200i	−3.37009	+	1.94572i
$289$	−7.41578	−	12.8445i	−0.436222	−	0.755559i
$290$	0.120285	+	0.208339i	0.00706337	+	0.0122341i
$291$	−22.8789	−	13.2091i	−1.34118	−	0.774333i
$292$	−0.468782	+	0.270651i	−0.0274334	+	0.0158387i
$293$	−25.5298	−	14.7396i	−1.49147	−	0.861099i	−0.491514	−	0.870870i	$-0.663556\pi$
$293$	−25.5298	−	14.7396i	−1.49147	−	0.861099i	−0.999952	+	0.00977093i	$0.996890\pi$
$294$		−	4.26438i		−	0.248704i
$295$	−0.656979			−0.0382508
$296$	−0.0238830	+	0.0413666i	−0.00138817	+	0.00240438i
$297$	54.8696	−	31.6790i	3.18386	−	1.83820i
$298$	−1.34118	+	2.32299i	−0.0776924	+	0.134567i
$299$	−13.5549	−	9.54466i	−0.783902	−	0.551982i
$300$	16.9633	+	29.3814i	0.979379	+	1.69633i
$301$	5.52137	−	3.18777i	0.318247	−	0.183740i
$302$	25.4275			1.46319
$303$	2.07678	−	3.59709i	0.119308	−	0.206647i
$304$	17.2917	+	9.98335i	0.991745	+	0.572584i
$305$	−1.06080	+	0.612455i	−0.0607414	+	0.0350691i
$306$			93.1830i			5.32691i
$307$	−25.1578	−	14.5249i	−1.43583	−	0.828979i	−0.438277	−	0.898840i	$-0.644411\pi$
$307$	−25.1578	−	14.5249i	−1.43583	−	0.828979i	−0.997557	+	0.0698609i	$0.977744\pi$
$308$	20.4132			1.16315
$309$	−35.9684			−2.04617
$310$	1.96148	−	0.0920128i	0.111404	−	0.00522598i
$311$	9.96731			0.565194			0.282597	−	0.959239i	$-0.408804\pi$
$311$	9.96731			0.565194			0.282597	+	0.959239i	$0.408804\pi$
$312$	0.391329	+	0.845020i	0.0221546	+	0.0478398i
$313$	−2.64792	+	4.58632i	−0.149669	+	0.259234i	−0.931105	−	0.364751i	$-0.881154\pi$
$313$	−2.64792	+	4.58632i	−0.149669	+	0.259234i	0.781436	+	0.623985i	$0.214487\pi$
$314$			17.3843i			0.981054i
$315$	−1.99257	−	3.45124i	−0.112269	−	0.194455i
$316$	1.84317	−	3.19246i	0.103686	−	0.179590i
$317$	4.00241	+	2.31080i	0.224798	+	0.129787i	0.608170	−	0.793807i	$-0.291904\pi$
$317$	4.00241	+	2.31080i	0.224798	+	0.129787i	−0.383372	+	0.923594i	$0.625237\pi$
$318$		−	13.1108i		−	0.735217i
$319$	−2.14120	+	1.23622i	−0.119884	+	0.0692151i
$320$	−1.26210	+	0.728673i	−0.0705535	+	0.0407341i
$321$	16.1132	+	27.9088i	0.899350	+	1.55772i
$322$	−12.7645	+	22.1087i	−0.711335	+	1.23207i
$323$	24.8761	−	14.3622i	1.38414	−	0.799135i
$324$	34.5415	−	59.8276i	1.91897	−	3.32376i
$325$	−16.2580	+	7.52907i	−0.901830	+	0.417637i
$326$	−17.9863			−0.996168
$327$	−16.4975	−	9.52483i	−0.912313	−	0.526724i
$328$	−0.423522	−	0.733561i	−0.0233851	−	0.0405042i
$329$	−9.21339	+	15.9581i	−0.507950	+	0.879796i
$330$	3.70807	−	2.14085i	0.204122	−	0.117850i
$331$	8.06543	−	4.65658i	0.443316	−	0.255949i	−0.261687	−	0.965153i	$-0.584279\pi$
$331$	8.06543	−	4.65658i	0.443316	−	0.255949i	0.705003	+	0.709204i	$0.250946\pi$
$332$	18.3464	−	10.5923i	1.00689	−	0.581326i
$333$			5.09106i			0.278988i
$334$	14.3967	−	24.9358i	0.787751	−	1.36443i
$335$	1.06598	−	1.84633i	0.0582407	−	0.100876i
$336$	−31.4304	+	18.1463i	−1.71467	+	0.989963i
$337$	−18.6775			−1.01743			−0.508713	−	0.860936i	$-0.669879\pi$
$337$	−18.6775			−1.01743			−0.508713	+	0.860936i	$0.669879\pi$
$338$	−24.5957	+	8.80543i	−1.33783	+	0.478952i
$339$	19.4039			1.05388
$340$			2.01832i			0.109459i
$341$	0.945657	+	20.1590i	0.0512102	+	1.09167i
$342$	−84.0872			−4.54692
$343$			17.5898i			0.949759i
$344$	0.154099	+	0.0889690i	0.00830845	+	0.00479689i
$345$			2.70280i			0.145514i
$346$	1.48119	−	0.855167i	0.0796294	−	0.0459740i
$347$	−12.4857	+	21.6258i	−0.670266	+	1.16093i	0.307563	+	0.951528i	$0.400487\pi$
$347$	−12.4857	+	21.6258i	−0.670266	+	1.16093i	−0.977829	+	0.209407i	$0.932847\pi$
$348$	−2.32855	+	4.03317i	−0.124824	+	0.216201i
$349$			7.95522i			0.425833i	0.977070	+	0.212917i	$0.0682962\pi$
$349$			7.95522i			0.425833i	−0.977070	+	0.212917i	$0.931704\pi$
$350$	13.7950	+	23.8937i	0.737376	+	1.27717i
$351$	51.5309	+	36.2853i	2.75052	+	1.93677i
$352$	−14.5626	−	25.2231i	−0.776188	−	1.34440i
$353$	7.55882	+	4.36408i	0.402315	+	0.232277i	0.687482	−	0.726201i	$-0.258716\pi$
$353$	7.55882	+	4.36408i	0.402315	+	0.232277i	−0.285167	+	0.958478i	$0.592049\pi$
$354$	−12.5985	−	21.8213i	−0.669604	−	1.15979i
$355$	1.32409	−	2.29339i	0.0702753	−	0.121720i
$356$			2.39182i			0.126766i
$357$			52.2112i			2.76331i
$358$	24.4257	+	14.1022i	1.29094	+	0.745323i
$359$	21.5232	−	12.4264i	1.13595	−	0.655842i	0.190527	−	0.981682i	$-0.438980\pi$
$359$	21.5232	−	12.4264i	1.13595	−	0.655842i	0.945425	+	0.325840i	$0.105647\pi$
$360$	0.0556118	−	0.0963224i	0.00293100	−	0.00507664i
$361$	3.46030	+	5.99342i	0.182121	+	0.315443i
$362$	−31.1831	+	18.0036i	−1.63895	+	0.946247i
$363$	3.58060	+	6.20178i	0.187933	+	0.325509i
$364$	8.53299	+	18.4258i	0.447250	+	0.965775i
$365$	−0.0233025	+	0.0403612i	−0.00121971	+	0.00211260i
$366$	−40.6849	−	23.4894i	−2.12663	−	1.22781i
$367$	−9.11621	−	15.7897i	−0.475862	−	0.824218i	0.523755	−	0.851869i	$-0.324531\pi$
$367$	−9.11621	−	15.7897i	−0.475862	−	0.824218i	−0.999618	+	0.0276511i	$0.991197\pi$
$368$	18.0322			0.939995
$369$	−78.1854	−	45.1403i	−4.07017	−	2.34991i
$370$			0.218466i			0.0113575i
$371$		−	5.38167i		−	0.279403i
$372$	20.5284	+	31.9937i	1.06435	+	1.65880i
$373$	27.0952			1.40293			0.701467	−	0.712702i	$-0.252529\pi$
$373$	27.0952			1.40293			0.701467	+	0.712702i	$0.252529\pi$
$374$	−41.0958			−2.12501
$375$	5.07504	+	2.93008i	0.262074	+	0.151308i
$376$	−0.514282			−0.0265221
$377$	−2.01091	−	1.41597i	−0.103567	−	0.0729264i
$378$	48.5258	−	84.0491i	2.49590	−	4.32302i
$379$	−8.95362	−	5.16938i	−0.459917	−	0.265533i	0.252093	−	0.967703i	$-0.418881\pi$
$379$	−8.95362	−	5.16938i	−0.459917	−	0.265533i	−0.712009	+	0.702170i	$0.752215\pi$
$380$	−1.82131			−0.0934310
$381$	−2.69856	−	4.67405i	−0.138252	−	0.239459i
$382$	−27.1519	+	15.6762i	−1.38921	+	0.802063i
$383$	15.9500	−	9.20873i	0.815006	−	0.470544i	−0.0336851	−	0.999432i	$-0.510724\pi$
$383$	15.9500	−	9.20873i	0.815006	−	0.470544i	0.848691	+	0.528888i	$0.177391\pi$
$384$	−1.78907	−	1.03292i	−0.0912982	−	0.0527110i
$385$	1.52207	−	0.878770i	0.0775721	−	0.0447863i
$386$	−7.02331	+	12.1647i	−0.357477	+	0.619169i
$387$	18.9652			0.964056
$388$		−	16.0774i		−	0.816206i
$389$	−14.7190	+	25.4940i	−0.746281	+	1.29260i	0.203313	+	0.979114i	$0.434829\pi$
$389$	−14.7190	+	25.4940i	−0.746281	+	1.29260i	−0.949594	+	0.313482i	$0.898504\pi$
$390$	3.48244	+	2.45214i	0.176340	+	0.124169i
$391$	12.9707	−	22.4660i	0.655958	−	1.13615i
$392$	0.0423084	−	0.0244268i	0.00213690	−	0.00123374i
$393$	−21.2801	−	36.8582i	−1.07344	−	1.85925i
$394$	−5.02106	−	8.69673i	−0.252957	−	0.438135i
$395$		−	0.317387i		−	0.0159695i
$396$	52.5876	+	30.3615i	2.64263	+	1.52572i
$397$	0.739740	+	0.427089i	0.0371265	+	0.0214350i	0.518448	−	0.855109i	$-0.326510\pi$
$397$	0.739740	+	0.427089i	0.0371265	+	0.0214350i	−0.481322	+	0.876544i	$0.659843\pi$
$398$	−7.59546	+	4.38524i	−0.380726	+	0.219812i
$399$	−47.1148			−2.35869
$400$	9.74406	−	16.8772i	0.487203	−	0.843861i
$401$			1.86349i			0.0930583i	0.998917	+	0.0465291i	$0.0148160\pi$
$401$			1.86349i			0.0930583i	−0.998917	+	0.0465291i	$0.985184\pi$
$402$	81.7668			4.07816
$403$	−17.8010	+	9.28030i	−0.886732	+	0.462285i
$404$	2.52774			0.125760
$405$		−	5.94791i		−	0.295554i
$406$	−1.89364	+	3.27988i	−0.0939798	+	0.162778i
$407$	−2.24527			−0.111294
$408$	−1.26196	+	0.728595i	−0.0624765	+	0.0360708i
$409$	23.2785	+	13.4398i	1.15105	+	0.664556i	0.949142	−	0.314849i	$-0.101954\pi$
$409$	23.2785	+	13.4398i	1.15105	+	0.664556i	0.201904	+	0.979405i	$0.435287\pi$
$410$	−3.35506	−	1.93705i	−0.165695	−	0.0956640i
$411$		−	24.6374i		−	1.21527i
$412$	−10.9447	−	18.9567i	−0.539205	−	0.933931i
$413$	−5.17140	−	8.95712i	−0.254468	−	0.440751i
$414$	−65.7664	+	37.9702i	−3.23224	+	1.86614i
$415$	0.911974	−	1.57959i	0.0447670	−	0.0775388i
$416$	16.6801	−	23.6884i	0.817808	−	1.16142i
$417$	17.7731	−	30.7840i	0.870354	−	1.50750i
$418$		−	37.0844i		−	1.81386i
$419$	13.5545			0.662183			0.331091	−	0.943599i	$-0.392583\pi$
$419$	13.5545			0.662183			0.331091	+	0.943599i	$0.392583\pi$
$420$	1.65526	−	2.86699i	0.0807682	−	0.139895i
$421$	0.734228	−	0.423907i	0.0357841	−	0.0206600i	−0.482001	−	0.876171i	$-0.660090\pi$
$421$	0.734228	−	0.423907i	0.0357841	−	0.0206600i	0.517785	+	0.855511i	$0.326757\pi$
$422$	−43.0812	−	24.8730i	−2.09716	−	1.21080i
$423$	−47.4702	+	27.4069i	−2.30808	+	1.33257i
$424$	0.130077	−	0.0751000i	0.00631709	−	0.00364718i
$425$	−14.0180	−	24.2799i	−0.679972	−	1.17775i
$426$	101.565			4.92085
$427$	−16.7002	−	9.64186i	−0.808179	−	0.466602i
$428$	−9.80602	+	16.9845i	−0.473992	+	0.820978i
$429$	−25.2018	+	35.7906i	−1.21675	+	1.72799i
$430$	0.813829			0.0392463
$431$	18.8413	+	10.8780i	0.907555	+	0.523977i	0.879644	−	0.475633i	$-0.157781\pi$
$431$	18.8413	+	10.8780i	0.907555	+	0.523977i	0.0279113	+	0.999610i	$0.491114\pi$
$432$	−68.5519			−3.29821
$433$	−15.0918			−0.725265			−0.362632	−	0.931932i	$-0.618122\pi$
$433$	−15.0918			−0.725265			−0.362632	+	0.931932i	$0.618122\pi$
$434$	16.6942	+	26.0181i	0.801348	+	1.24891i
$435$			0.400968i			0.0192249i
$436$		−	11.5931i		−	0.555208i
$437$	20.2730	+	11.7046i	0.969791	+	0.559909i
$438$	−1.78744			−0.0854072
$439$	3.91685	+	6.78419i	0.186941	+	0.323792i	0.944229	−	0.329290i	$-0.106809\pi$
$439$	3.91685	+	6.78419i	0.186941	+	0.323792i	−0.757288	+	0.653081i	$0.773476\pi$
$440$	0.0424803	+	0.0245260i	0.00202517	+	0.00116923i
$441$	2.60349	−	4.50937i	0.123975	−	0.214732i
$442$	−17.1786	−	37.0947i	−0.817101	−	1.76441i
$443$	−3.68420	−	6.38123i	−0.175042	−	0.303181i	0.765134	−	0.643871i	$-0.222673\pi$
$443$	−3.68420	−	6.38123i	−0.175042	−	0.303181i	−0.940176	+	0.340690i	$0.889339\pi$
$444$	−3.66260	+	2.11460i	−0.173819	+	0.100355i
$445$	0.102966	+	0.178342i	0.00488104	+	0.00845421i
$446$	−11.2821	+	19.5413i	−0.534225	+	0.925305i
$447$	−3.87183	+	2.23540i	−0.183131	+	0.105731i
$448$	−19.8692	−	11.4715i	−0.938730	−	0.541976i
$449$		−	36.5703i		−	1.72586i	−0.505326	−	0.862929i	$-0.668628\pi$
$449$		−	36.5703i		−	1.72586i	0.505326	−	0.862929i	$-0.331372\pi$
$450$			82.0718i			3.86890i
$451$	19.9079	−	34.4815i	0.937427	−	1.62367i
$452$	5.90433	+	10.2266i	0.277716	+	0.481019i
$453$	36.7031	+	21.1906i	1.72446	+	0.995619i
$454$	11.8407	+	20.5086i	0.555709	+	0.962517i
$455$	1.42946	+	1.00655i	0.0670141	+	0.0471877i
$456$	−0.657476	−	1.13878i	−0.0307891	−	0.0533283i
$457$		−	19.4014i		−	0.907559i	−0.891114	−	0.453779i	$-0.850075\pi$
$457$		−	19.4014i		−	0.907559i	0.891114	−	0.453779i	$-0.149925\pi$
$458$	−14.9044	+	25.8151i	−0.696435	+	1.20626i
$459$	−49.3100	+	85.4074i	−2.30159	+	3.98648i
$460$	−1.42448	+	0.822424i	−0.0664167	+	0.0383457i
$461$			39.5944i			1.84410i	0.387075	+	0.922048i	$0.373485\pi$
$461$			39.5944i			1.84410i	−0.387075	+	0.922048i	$0.626515\pi$
$462$	58.3759	+	33.7034i	2.71589	+	1.56802i
$463$			38.8032i			1.80334i	0.432425	+	0.901670i	$0.357658\pi$
$463$			38.8032i			1.80334i	−0.432425	+	0.901670i	$0.642342\pi$
$464$	2.67513			0.124190
$465$	2.90796	+	1.50182i	0.134853	+	0.0696454i
$466$			17.4353i			0.807675i
$467$	26.2277			1.21367			0.606837	−	0.794827i	$-0.292438\pi$
$467$	26.2277			1.21367			0.606837	+	0.794827i	$0.292438\pi$
$468$	−5.42320	+	60.1592i	−0.250687	+	2.78086i
$469$	33.5633			1.54981
$470$	−2.03703	+	1.17608i	−0.0939610	+	0.0542484i
$471$	−14.4876	+	25.0933i	−0.667553	+	1.15624i
$472$	0.144331	−	0.249989i	0.00664338	−	0.0115067i
$473$			8.36408i			0.384581i
$474$	10.5419	−	6.08635i	0.484204	−	0.279555i
$475$	21.9099	−	12.6497i	1.00529	−	0.580406i
$476$	−27.5173	+	15.8871i	−1.26125	+	0.728186i
$477$	8.00440	−	13.8640i	0.366496	−	0.634790i
$478$	−4.40015	−	7.62128i	−0.201258	−	0.348589i
$479$	22.4688	+	12.9724i	1.02663	+	0.592722i	0.916016	−	0.401142i	$-0.131386\pi$
$479$	22.4688	+	12.9724i	1.02663	+	0.592722i	0.110609	+	0.993864i	$0.464720\pi$
$480$	−4.72337			−0.215591
$481$	−0.938551	−	2.02667i	−0.0427943	−	0.0924082i
$482$	−5.58618	+	9.67556i	−0.254444	+	0.440709i
$483$	−36.8495	+	21.2751i	−1.67671	+	0.968049i
$484$	−2.17905	+	3.77423i	−0.0990478	+	0.171556i
$485$	−0.692116	−	1.19878i	−0.0314274	−	0.0544338i
$486$	106.295	−	61.3695i	4.82164	−	2.78378i
$487$	−4.91773	+	2.83925i	−0.222843	+	0.128659i	−0.607266	−	0.794498i	$-0.707734\pi$
$487$	−4.91773	+	2.83925i	−0.222843	+	0.128659i	0.384423	+	0.923157i	$0.374401\pi$
$488$		−	0.538199i		−	0.0243631i
$489$	−25.9621	−	14.9892i	−1.17405	−	0.677837i
$490$	0.111720	−	0.193505i	0.00504699	−	0.00874164i
$491$	8.89948	+	15.4143i	0.401628	+	0.695640i	0.993923	−	0.110082i	$-0.0351112\pi$
$491$	8.89948	+	15.4143i	0.401628	+	0.695640i	−0.592295	+	0.805721i	$0.701778\pi$
$492$		−	74.9973i		−	3.38114i
$493$	1.92424	−	3.33289i	0.0866635	−	0.150106i
$494$	33.4738	−	15.5017i	1.50606	−	0.697456i
$495$	5.22813			0.234987
$496$	10.0197	−	19.4010i	0.449897	−	0.871130i
$497$	41.6901			1.87006
$498$	69.9537			3.13470
$499$	−34.4310	−	19.8787i	−1.54134	−	0.889895i	−0.998754	−	0.0498957i	$-0.984111\pi$
$499$	−34.4310	−	19.8787i	−1.54134	−	0.889895i	−0.542588	−	0.839999i	$-0.682556\pi$
$500$			3.56632i			0.159491i
$501$	41.5615	−	23.9956i	1.85683	−	1.07204i
$502$	49.6773	+	28.6812i	2.21720	+	1.28010i
$503$	−4.45418	+	7.71487i	−0.198602	+	0.343989i	−0.948075	−	0.318046i	$-0.896973\pi$
$503$	−4.45418	+	7.71487i	−0.198602	+	0.343989i	0.749473	+	0.662035i	$0.230307\pi$
$504$	1.75099			0.0779952
$505$	0.188476	−	0.108817i	0.00838708	−	0.00484228i
$506$	−16.7457	−	29.0045i	−0.744438	−	1.28941i
$507$	−42.8407	−	7.78724i	−1.90262	−	0.345843i
$508$	1.64227	−	2.84449i	0.0728639	−	0.126204i
$509$	19.4463	−	11.2273i	0.861941	−	0.497642i	−0.00272062	−	0.999996i	$-0.500866\pi$
$509$	19.4463	−	11.2273i	0.861941	−	0.497642i	0.864662	+	0.502354i	$0.167533\pi$
$510$	−3.33235	+	5.77180i	−0.147559	+	0.255580i
$511$	−0.733702			−0.0324571
$512$			32.1176i			1.41941i
$513$	−77.0707	−	44.4968i	−3.40275	−	1.96458i
$514$	−15.9506	+	9.20905i	−0.703549	+	0.406194i
$515$	−1.63214	−	0.942315i	−0.0719205	−	0.0415233i
$516$	7.87732	+	13.6439i	0.346780	+	0.600640i
$517$	−12.0871	−	20.9354i	−0.531589	−	0.920739i
$518$	−2.97852	+	1.71965i	−0.130869	+	0.0755570i
$519$	2.85069			0.125131
$520$	−0.00438086	+	0.0485967i	−0.000192114	+	0.00213110i
$521$	4.01271	−	6.95021i	0.175800	−	0.304494i	−0.764638	−	0.644460i	$-0.777082\pi$
$521$	4.01271	−	6.95021i	0.175800	−	0.304494i	0.940438	+	0.339966i	$0.110416\pi$
$522$	−9.75661	+	5.63298i	−0.427035	+	0.246549i
$523$	4.57571			0.200082			0.100041	−	0.994983i	$-0.468103\pi$
$523$	4.57571			0.200082			0.100041	+	0.994983i	$0.468103\pi$
$524$	12.9505	−	22.4309i	0.565744	−	0.979897i
$525$			45.9856i			2.00697i
$526$			59.3823i			2.58919i
$527$	−16.9640	−	26.4386i	−0.738964	−	1.15168i
$528$		−	47.6125i		−	2.07207i
$529$	−1.85871			−0.0808136
$530$	0.343482	−	0.594928i	0.0149199	−	0.0258420i
$531$		−	30.7666i		−	1.33516i
$532$	−14.3364	−	24.8313i	−0.621561	−	1.07657i
$533$	39.4461	+	3.55597i	1.70860	+	0.154026i
$534$	−3.94903	+	6.83992i	−0.170891	+	0.295992i
$535$			1.68856i			0.0730027i
$536$	0.468368	+	0.811238i	0.0202304	+	0.0350401i
$537$	23.5047	+	40.7113i	1.01430	+	1.75682i
$538$	−2.42781	+	1.40169i	−0.104670	+	0.0604313i
$539$	1.98873	+	1.14820i	0.0856608	+	0.0494563i
$540$	5.41535	−	3.12656i	0.233040	−	0.134546i
$541$	−30.5752	−	17.6526i	−1.31453	−	0.758944i	−0.331686	−	0.943390i	$-0.607618\pi$
$541$	−30.5752	−	17.6526i	−1.31453	−	0.758944i	−0.982843	+	0.184446i	$0.940951\pi$
$542$	29.5482			1.26921
$543$	−60.0147			−2.57548
$544$	39.2611	+	22.6674i	1.68331	+	0.971858i
$545$	−0.499071	−	0.864416i	−0.0213778	−	0.0370275i
$546$	−6.02013	+	66.7809i	−0.257638	+	2.85796i
$547$	−15.3255	−	26.5446i	−0.655273	−	1.13497i	−0.981825	−	0.189786i	$-0.939220\pi$
$547$	−15.3255	−	26.5446i	−0.655273	−	1.13497i	0.326553	−	0.945179i	$-0.394113\pi$
$548$	12.9848	−	7.49680i	0.554685	−	0.320248i
$549$	−28.6815	−	49.6778i	−1.22410	−	2.12020i
$550$	−36.1955			−1.54338
$551$	3.00756	+	1.73642i	0.128126	+	0.0739738i
$552$	−1.02845	−	0.593776i	−0.0437738	−	0.0252728i
$553$	4.32719	−	2.49830i	0.184011	−	0.106239i
$554$		−	20.2630i		−	0.860894i
$555$	−0.182063	+	0.315343i	−0.00772815	+	0.0133855i
$556$	21.6325			0.917420
$557$		−	25.9114i		−	1.09790i	−0.835855	−	0.548951i	$-0.815028\pi$
$557$		−	25.9114i		−	1.09790i	0.835855	−	0.548951i	$-0.184972\pi$
$558$	4.30900	+	91.8568i	0.182414	+	3.88861i
$559$	−7.54976	+	3.49629i	−0.319321	+	0.147877i
$560$	−1.90162			−0.0803581
$561$	−59.3194	−	34.2480i	−2.50447	−	1.44595i
$562$	−27.4924			−1.15970
$563$	15.3056	+	26.5100i	0.645053	+	1.11726i	0.984289	+	0.176563i	$0.0564980\pi$
$563$	15.3056	+	26.5100i	0.645053	+	1.11726i	−0.339236	+	0.940701i	$0.610169\pi$
$564$	−39.4341	−	22.7673i	−1.66047	−	0.958675i
$565$	0.880490	+	0.508351i	0.0370425	+	0.0213865i
$566$		−	26.7081i		−	1.12262i
$567$	81.0927	−	46.8189i	3.40557	−	1.96621i
$568$	0.581776	+	1.00766i	0.0244108	+	0.0422807i
$569$	−10.2814	−	17.8080i	−0.431020	−	0.746548i	0.565941	−	0.824445i	$-0.308513\pi$
$569$	−10.2814	−	17.8080i	−0.431020	−	0.746548i	−0.996961	+	0.0778970i	$0.975179\pi$
$570$	−5.20841	−	3.00707i	−0.218156	−	0.125952i
$571$	1.58774	+	2.75004i	0.0664447	+	0.115086i	0.897334	−	0.441352i	$-0.145501\pi$
$571$	1.58774	+	2.75004i	0.0664447	+	0.115086i	−0.830889	+	0.556438i	$0.812168\pi$
$572$	−26.5316	−	2.39175i	−1.10934	−	0.100004i
$573$	−52.2563			−2.18304
$574$		−	60.9897i		−	2.54566i
$575$	11.4241	−	19.7871i	0.476418	−	0.825180i
$576$	−34.1240	−	59.1046i	−1.42183	−	2.46269i
$577$	−19.9466	−	11.5162i	−0.830390	−	0.479426i	0.0235963	−	0.999722i	$-0.492488\pi$
$577$	−19.9466	−	11.5162i	−0.830390	−	0.479426i	−0.853986	+	0.520296i	$0.825822\pi$
$578$	25.8119	−	14.9025i	1.07363	−	0.619863i
$579$	−20.2755	+	11.7061i	−0.842621	+	0.486487i
$580$	−0.211325	+	0.122009i	−0.00877481	+	0.00506614i
$581$	28.7143			1.19127
$582$	26.5447	−	45.9767i	1.10031	−	1.90580i
$583$	6.11435	+	3.53012i	0.253230	+	0.146203i
$584$	−0.0102386	−	0.0177338i	−0.000423678	−	0.000733831i
$585$	2.18542	+	4.71912i	0.0903562	+	0.195112i
$586$	29.6203	−	51.3039i	1.22360	−	2.11935i
$587$			5.72572i			0.236326i	0.992994	+	0.118163i	$0.0377005\pi$
$587$			5.72572i			0.236326i	−0.992994	+	0.118163i	$0.962300\pi$
$588$	4.32550			0.178380
$589$	23.8579	−	15.3081i	0.983048	−	0.630761i
$590$		−	1.32024i		−	0.0543536i
$591$		−	16.7376i		−	0.688494i
$592$	2.10386	+	1.21467i	0.0864683	+	0.0499225i
$593$		−	3.64539i		−	0.149698i	−0.997195	−	0.0748490i	$-0.976153\pi$
$593$		−	3.64539i		−	0.149698i	0.997195	−	0.0748490i	$-0.0238475\pi$
$594$	63.6611	+	110.264i	2.61205	+	4.52420i
$595$	−1.36785	+	2.36919i	−0.0560764	+	0.0971272i
$596$	−2.35628	−	1.36040i	−0.0965171	−	0.0557242i
$597$	−14.6181			−0.598280
$598$	19.1807	−	27.2396i	0.784355	−	1.11391i
$599$	−4.48160	−	7.76236i	−0.183113	−	0.317161i	0.759826	−	0.650127i	$-0.225284\pi$
$599$	−4.48160	−	7.76236i	−0.183113	−	0.317161i	−0.942939	+	0.332965i	$0.891951\pi$
$600$	−1.11149	+	0.641717i	−0.0453763	+	0.0261980i
$601$	−6.12644	+	10.6113i	−0.249903	+	0.432844i	−0.963499	−	0.267713i	$-0.913732\pi$
$601$	−6.12644	+	10.6113i	−0.249903	+	0.432844i	0.713596	+	0.700558i	$0.247065\pi$
$602$	6.40604	+	11.0956i	0.261091	+	0.452222i
$603$	86.4643	+	49.9202i	3.52110	+	2.03291i
$604$			25.7919i			1.04946i
$605$			0.375224i			0.0152550i
$606$	7.22861	+	4.17344i	0.293642	+	0.169534i
$607$	23.8290	+	41.2730i	0.967187	+	1.67522i	0.703620	+	0.710576i	$0.251566\pi$
$607$	23.8290	+	41.2730i	0.967187	+	1.67522i	0.263567	+	0.964641i	$0.415101\pi$
$608$	−20.4548	+	35.4288i	−0.829553	+	1.43683i
$609$	−5.46672	+	3.15621i	−0.221523	+	0.127896i
$610$	−1.23077	−	2.13176i	−0.0498325	−	0.0863124i
$611$	13.8446	−	19.6615i	0.560093	−	0.795421i
$612$	−94.5185			−3.82068
$613$	13.4143	+	7.74477i	0.541800	+	0.312808i	0.745808	−	0.666161i	$-0.232064\pi$
$613$	13.4143	+	7.74477i	0.541800	+	0.312808i	−0.204008	+	0.978969i	$0.565397\pi$
$614$	29.1888	−	50.5564i	1.17796	−	2.04029i
$615$	−3.22856	−	5.59203i	−0.130188	−	0.225492i
$616$			0.772225i			0.0311138i
$617$	−18.7924	−	10.8498i	−0.756552	−	0.436795i	0.0715046	−	0.997440i	$-0.477220\pi$
$617$	−18.7924	−	10.8498i	−0.756552	−	0.436795i	−0.828056	+	0.560645i	$0.810553\pi$
$618$		−	72.2810i		−	2.90757i
$619$			21.7005i			0.872217i	0.899894	+	0.436109i	$0.143644\pi$
$619$			21.7005i			0.872217i	−0.899894	+	0.436109i	$0.856356\pi$
$620$	0.0933316	+	1.98959i	0.00374829	+	0.0799039i
$621$	−80.3714			−3.22520
$622$			20.0300i			0.803130i
$623$	−1.62098	+	2.80763i	−0.0649434	+	0.112485i
$624$	42.9769	−	19.9026i	1.72045	−	0.796742i
$625$	−12.2695	−	21.2514i	−0.490779	−	0.850054i
$626$	−9.21654	−	5.32117i	−0.368367	−	0.212677i
$627$	30.9051	−	53.5291i	1.23423	−	2.13775i
$628$	−17.6335			−0.703653
$629$	3.02666	−	1.74744i	0.120681	−	0.0696750i
$630$	6.93551	−	4.00422i	0.276317	−	0.159532i
$631$	−11.9398	+	6.89344i	−0.475316	+	0.274424i	−0.718462	−	0.695566i	$-0.755154\pi$
$631$	−11.9398	+	6.89344i	−0.475316	+	0.274424i	0.243147	+	0.969990i	$0.421820\pi$
$632$	0.120770	+	0.0697265i	0.00480396	+	0.00277357i
$633$	−41.4568	−	71.8053i	−1.64776	−	2.85401i
$634$	−4.64370	+	8.04313i	−0.184425	+	0.319434i
$635$		−	0.282792i		−	0.0112223i
$636$	13.2987			0.527328
$637$	−0.205092	+	2.27507i	−0.00812603	+	0.0901416i
$638$	−2.48427	−	4.30289i	−0.0983533	−	0.170353i
$639$	107.400	+	62.0075i	4.24869	+	2.45298i
$640$	−0.0541218	−	0.0937417i	−0.00213935	−	0.00370547i
$641$	−7.41249	−	12.8388i	−0.292776	−	0.507103i	0.681689	−	0.731642i	$-0.261246\pi$
$641$	−7.41249	−	12.8388i	−0.292776	−	0.507103i	−0.974465	+	0.224539i	$0.927912\pi$
$642$	−56.0848	+	32.3806i	−2.21349	+	1.27796i
$643$		−	26.6855i		−	1.05237i	−0.850369	−	0.526187i	$-0.823621\pi$
$643$		−	26.6855i		−	1.05237i	0.850369	−	0.526187i	$-0.176379\pi$
$644$	−22.4255	−	12.9474i	−0.883690	−	0.510199i
$645$	1.17471	+	0.678222i	0.0462543	+	0.0267050i
$646$	28.8619	+	49.9902i	1.13556	+	1.96684i
$647$	9.95334			0.391306			0.195653	−	0.980673i	$-0.437317\pi$
$647$	9.95334			0.391306			0.195653	+	0.980673i	$0.437317\pi$
$648$	2.26326	+	1.30669i	0.0889091	+	0.0513317i
$649$	13.5687			0.532620
$650$	−15.1302	−	32.6715i	−0.593455	−	1.28148i
$651$	2.41437	+	51.4681i	0.0946266	+	2.01720i
$652$		−	18.2441i		−	0.714493i
$653$	1.09420			0.0428194			0.0214097	−	0.999771i	$-0.493185\pi$
$653$	1.09420			0.0428194			0.0214097	+	0.999771i	$0.493185\pi$
$654$	19.1408	−	33.1529i	0.748465	−	1.29638i
$655$		−	2.23002i		−	0.0871341i
$656$	−37.3082	+	21.5399i	−1.45664	+	0.840993i
$657$	−1.89013	−	1.09127i	−0.0737410	−	0.0425744i
$658$	−32.0688	−	18.5149i	−1.25017	−	0.721788i
$659$	26.8176			1.04467			0.522333	−	0.852742i	$-0.325062\pi$
$659$	26.8176			1.04467			0.522333	+	0.852742i	$0.325062\pi$
$660$	2.17154	+	3.76121i	0.0845269	+	0.146405i
$661$	−32.5521	+	18.7940i	−1.26613	+	0.731001i	−0.974254	−	0.225455i	$-0.927613\pi$
$661$	−32.5521	+	18.7940i	−1.26613	+	0.731001i	−0.291877	+	0.956456i	$0.594280\pi$
$662$	9.35772	+	16.2080i	0.363698	+	0.629943i
$663$	6.11742	−	67.8601i	0.237581	−	2.63547i
$664$	0.400702	+	0.694036i	0.0155502	+	0.0269338i
$665$	−2.13793	−	1.23433i	−0.0829053	−	0.0478654i
$666$	−10.2308			−0.396437
$667$	3.13637			0.121441
$668$	25.2932	+	14.6030i	0.978622	+	0.565008i
$669$	−32.5702	+	18.8044i	−1.25924	+	0.727022i
$670$	3.71033	+	2.14216i	0.143343	+	0.0827588i
$671$	21.9090	−	12.6492i	0.845789	−	0.488316i
$672$	−37.1799	−	64.3975i	−1.43425	−	2.48419i
$673$	5.53634	+	9.58922i	0.213410	+	0.369637i	0.952780	−	0.303663i	$-0.0982096\pi$
$673$	5.53634	+	9.58922i	0.213410	+	0.369637i	−0.739369	+	0.673300i	$0.764876\pi$
$674$		−	37.5337i		−	1.44574i
$675$	−43.4303	+	75.2234i	−1.67163	+	2.89535i
$676$	−8.93164	−	24.9482i	−0.343524	−	0.959547i
$677$	15.5170	+	26.8762i	0.596365	+	1.03293i	0.993353	+	0.115111i	$0.0367222\pi$
$677$	15.5170	+	26.8762i	0.596365	+	1.03293i	−0.396988	+	0.917824i	$0.629944\pi$
$678$			38.9935i			1.49754i
$679$	10.8960	−	18.8724i	0.418149	−	0.724255i
$680$	−0.0763521			−0.00292797
$681$			39.4706i			1.51252i
$682$	−40.5109	+	1.90036i	−1.55124	+	0.0727687i
$683$		−	46.1431i		−	1.76562i	−0.469735	−	0.882808i	$-0.655650\pi$
$683$		−	46.1431i		−	1.76562i	0.469735	−	0.882808i	$-0.344350\pi$
$684$		−	85.2924i		−	3.26124i
$685$	0.645460	−	1.11797i	0.0246618	−	0.0427154i
$686$	−35.3479			−1.34959
$687$	−43.0271	+	24.8417i	−1.64159	+	0.947771i
$688$	4.52488	−	7.83732i	0.172509	−	0.298795i
$689$	−0.630553	+	6.99469i	−0.0240222	+	0.266476i
$690$	−5.43147			−0.206772
$691$	−39.5781	+	22.8504i	−1.50562	+	0.869271i	−0.505643	+	0.862743i	$0.668745\pi$
$691$	−39.5781	+	22.8504i	−1.50562	+	0.869271i	−0.999979	+	0.00652832i	$0.997922\pi$
$692$	0.867423	+	1.50242i	0.0329745	+	0.0571135i
$693$	41.1531	+	71.2793i	1.56328	+	2.70768i
$694$	−43.4586	−	25.0908i	−1.64967	−	0.952435i
$695$	1.61298	−	0.931256i	0.0611839	−	0.0353246i
$696$	−0.152573	−	0.0880883i	−0.00578328	−	0.00333898i
$697$			61.9754i			2.34749i
$698$	−15.9866			−0.605100
$699$	−14.5301	+	25.1669i	−0.549579	+	0.951898i
$700$	−24.2362	+	13.9928i	−0.916041	+	0.528876i
$701$	21.9190	−	37.9648i	0.827868	−	1.43391i	−0.0718396	−	0.997416i	$-0.522887\pi$
$701$	21.9190	−	37.9648i	0.827868	−	1.43391i	0.899708	−	0.436493i	$-0.143780\pi$
$702$	−72.9178	+	103.555i	−2.75211	+	3.90843i
$703$	1.57687	+	2.73122i	0.0594728	+	0.103010i
$704$	26.0664	−	15.0495i	0.982416	−	0.567198i
$705$	−3.92044			−0.147652
$706$	−8.76993	+	15.1900i	−0.330061	+	0.571682i
$707$	2.96717	+	1.71310i	0.111592	+	0.0644277i
$708$	22.1340	−	12.7791i	0.831847	−	0.480267i
$709$			1.08083i			0.0405915i	0.999794	+	0.0202957i	$0.00646077\pi$
$709$			1.08083i			0.0405915i	−0.999794	+	0.0202957i	$0.993539\pi$
$710$	4.60872	+	2.66085i	0.172962	+	0.0998598i
$711$	14.8633			0.557419
$712$	−0.0904817			−0.00339095
$713$	11.7473	−	22.7460i	0.439938	−	0.851846i
$714$	−104.922			−3.92661
$715$	−2.08124	+	0.963821i	−0.0778339	+	0.0360449i
$716$	−14.3043	+	24.7758i	−0.534577	+	0.925914i
$717$		−	14.6678i		−	0.547780i
$718$	24.9718	+	43.2524i	0.931939	+	1.61416i
$719$	6.17161	−	10.6895i	0.230162	−	0.398653i	−0.727693	−	0.685903i	$-0.759408\pi$
$719$	6.17161	−	10.6895i	0.230162	−	0.398653i	0.957856	+	0.287250i	$0.0927410\pi$
$720$	−4.89886	−	2.82836i	−0.182570	−	0.105407i
$721$		−	29.6697i		−	1.10496i
$722$	−12.0442	+	6.95372i	−0.448239	+	0.258791i
$723$	−16.1267	+	9.31073i	−0.599757	+	0.346270i
$724$	−18.2616	−	31.6300i	−0.678688	−	1.17552i
$725$	1.69480	−	2.93547i	0.0629431	−	0.109021i
$726$	−12.4629	+	7.19547i	−0.462542	+	0.267049i
$727$	24.0812	−	41.7098i	0.893121	−	1.54693i	0.0570083	−	0.998374i	$-0.481844\pi$
$727$	24.0812	−	41.7098i	0.893121	−	1.54693i	0.836113	−	0.548557i	$-0.184823\pi$
$728$	−0.697041	+	0.322800i	−0.0258341	+	0.0119638i
$729$	102.901			3.81113
$730$	−0.0811086	−	0.0468281i	−0.00300196	−	0.00173319i
$731$	−6.50957	−	11.2749i	−0.240765	−	0.417017i
$732$	23.8261	−	41.2680i	0.880637	−	1.52531i
$733$	24.4689	−	14.1271i	0.903780	−	0.521798i	0.0253556	−	0.999678i	$-0.491928\pi$
$733$	24.4689	−	14.1271i	0.903780	−	0.521798i	0.878425	+	0.477881i	$0.158595\pi$
$734$	31.7306	−	18.3197i	1.17120	−	0.676191i
$735$	0.322522	−	0.186208i	0.0118964	−	0.00686840i
$736$			36.9461i			1.36185i
$737$	−22.0159	+	38.1327i	−0.810967	+	1.40464i
$738$	90.7127	−	157.119i	3.33918	−	5.78363i
$739$	−3.94587	+	2.27815i	−0.145151	+	0.0838030i	−0.570817	−	0.821078i	$-0.693373\pi$
$739$	−3.94587	+	2.27815i	−0.145151	+	0.0838030i	0.425666	+	0.904881i	$0.360040\pi$
$740$	−0.221597			−0.00814606
$741$	61.2362	+	5.52029i	2.24957	+	0.202793i
$742$	10.8149			0.397026
$743$			26.2348i			0.962460i	0.876594	+	0.481230i	$0.159810\pi$
$743$			26.2348i			0.962460i	−0.876594	+	0.481230i	$0.840190\pi$
$744$	−1.21031	+	0.776581i	−0.0443722	+	0.0284709i
$745$	−0.234256			−0.00858247
$746$			54.4496i			1.99354i
$747$	73.9726	+	42.7081i	2.70651	+	1.56261i
$748$		−	41.6848i		−	1.52415i
$749$	−23.0215	+	13.2915i	−0.841187	+	0.485659i
$750$	−5.88819	+	10.1986i	−0.215006	+	0.372402i
$751$	−9.99131	+	17.3054i	−0.364588	+	0.631485i	−0.988710	−	0.149842i	$-0.952123\pi$
$751$	−9.99131	+	17.3054i	−0.364588	+	0.631485i	0.624122	+	0.781327i	$0.285457\pi$
$752$			26.1559i			0.953807i
$753$	47.8041	+	82.7992i	1.74208	+	3.01737i
$754$	2.84550	−	4.04107i	0.103627	−	0.147167i
$755$	1.11032	+	1.92313i	0.0404086	+	0.0699898i
$756$	85.2537	+	49.2213i	3.10065	+	1.79016i
$757$	4.87944	+	8.45144i	0.177346	+	0.307173i	0.940971	−	0.338488i	$-0.109915\pi$
$757$	4.87944	+	8.45144i	0.177346	+	0.307173i	−0.763624	+	0.645661i	$0.776582\pi$
$758$	10.3882	−	17.9929i	0.377317	−	0.653533i
$759$		−	55.8216i		−	2.02620i
$760$		−	0.0688993i		−	0.00249924i
$761$	−6.54994	−	3.78161i	−0.237435	−	0.137083i	0.376562	−	0.926391i	$-0.377106\pi$
$761$	−6.54994	−	3.78161i	−0.237435	−	0.137083i	−0.613997	+	0.789308i	$0.710439\pi$
$762$	9.39283	−	5.42295i	0.340266	−	0.196453i
$763$	7.85685	−	13.6085i	0.284437	−	0.492660i
$764$	−15.9009	−	27.5411i	−0.575273	−	0.996401i
$765$	−7.04759	+	4.06893i	−0.254806	+	0.147112i
$766$	18.5056	+	32.0526i	0.668634	+	1.15811i
$767$	5.67191	+	12.2477i	0.204801	+	0.442239i
$768$	−25.7379	+	44.5794i	−0.928737	+	1.60862i
$769$	−11.6617	−	6.73288i	−0.420531	−	0.242794i	0.274773	−	0.961509i	$-0.411397\pi$
$769$	−11.6617	−	6.73288i	−0.420531	−	0.242794i	−0.695305	+	0.718715i	$0.744731\pi$
$770$	1.76595	+	3.05871i	0.0636404	+	0.110228i
$771$	−30.6983			−1.10557
$772$	−12.3391	−	7.12397i	−0.444093	−	0.256397i
$773$			17.9046i			0.643985i	0.946742	+	0.321992i	$0.104353\pi$
$773$			17.9046i			0.643985i	−0.946742	+	0.321992i	$0.895647\pi$
$774$			38.1119i			1.36990i
$775$	−14.9412	−	23.2861i	−0.536705	−	0.836460i
$776$	0.608202			0.0218332
$777$	−5.73243			−0.205650
$778$	−51.2319	−	29.5788i	−1.83675	−	1.06045i
$779$	−55.9259			−2.00375
$780$	−2.48729	+	3.53235i	−0.0890593	+	0.126478i
$781$	−27.3467	+	47.3659i	−0.978542	+	1.69488i
$782$	45.1469	+	26.0656i	1.61445	+	0.932104i
$783$	−11.9233			−0.426105
$784$	−1.24232	−	2.15177i	−0.0443687	−	0.0768488i
$785$	−1.31481	+	0.759104i	−0.0469275	+	0.0270936i
$786$	74.0692	−	42.7639i	2.64196	−	1.52534i
$787$	36.6222	+	21.1438i	1.30544	+	0.753696i	0.981331	−	0.192324i	$-0.0616025\pi$
$787$	36.6222	+	21.1438i	1.30544	+	0.753696i	0.324108	+	0.946020i	$0.394936\pi$
$788$	8.82137	−	5.09302i	0.314248	−	0.181431i
$789$	−49.4875	+	85.7148i	−1.76180	+	3.05153i
$790$	0.637811			0.0226923
$791$			16.0059i			0.569105i
$792$	−1.14856	+	1.98937i	−0.0408124	+	0.0706892i
$793$	20.5759	+	14.4885i	0.730672	+	0.514500i
$794$	−0.858265	+	1.48656i	−0.0304587	+	0.0527560i
$795$	0.991593	−	0.572496i	0.0351682	−	0.0203043i
$796$	−4.44809	−	7.70432i	−0.157658	−	0.273072i
$797$	−21.0980	−	36.5428i	−0.747329	−	1.29441i	−0.949099	−	0.314978i	$-0.898003\pi$
$797$	−21.0980	−	36.5428i	−0.747329	−	1.29441i	0.201770	−	0.979433i	$-0.435331\pi$
$798$		−	94.6805i		−	3.35165i
$799$	32.5871	+	18.8142i	1.15285	+	0.665597i
$800$	34.5796	+	19.9646i	1.22257	+	0.705854i
$801$	−8.35181	+	4.82192i	−0.295097	+	0.170374i
$802$	−3.74481			−0.132234
$803$	0.481273	−	0.833590i	0.0169838	−	0.0294167i
$804$			82.9387i			2.92502i
$805$	−2.22949			−0.0785792
$806$	−18.6494	−	35.7724i	−0.656898	−	1.26003i
$807$	−4.67253			−0.164481
$808$			0.0956235i			0.00336402i
$809$	16.4695	−	28.5260i	0.579037	−	1.00292i	−0.416553	−	0.909112i	$-0.636762\pi$
$809$	16.4695	−	28.5260i	0.579037	−	1.00292i	0.995590	−	0.0938107i	$-0.0299048\pi$
$810$	11.9527			0.419976
$811$	5.97591	−	3.45019i	0.209843	−	0.121153i	−0.391396	−	0.920223i	$-0.628008\pi$
$811$	5.97591	−	3.45019i	0.209843	−	0.121153i	0.601238	+	0.799070i	$0.294674\pi$
$812$	−3.32689	−	1.92078i	−0.116751	−	0.0674062i
$813$	42.6511	+	24.6246i	1.49584	+	0.863624i
$814$		−	4.51203i		−	0.158146i
$815$	−0.785389	−	1.36033i	−0.0275110	−	0.0476504i
$816$	37.0556	+	64.1823i	1.29721	+	2.24683i
$817$	10.1743	−	5.87416i	0.355955	−	0.205511i
$818$	−27.0083	+	46.7797i	−0.944322	+	1.63561i
$819$	−47.1370	+	66.9421i	−1.64710	+	2.33915i
$820$	1.96481	−	3.40315i	0.0686141	−	0.118843i
$821$			13.2388i			0.462036i	0.972949	+	0.231018i	$0.0742057\pi$
$821$			13.2388i			0.462036i	−0.972949	+	0.231018i	$0.925794\pi$
$822$	49.5105			1.72688
$823$	−25.4944	+	44.1576i	−0.888678	+	1.53924i	−0.0472398	+	0.998884i	$0.515042\pi$
$823$	−25.4944	+	44.1576i	−0.888678	+	1.53924i	−0.841439	+	0.540353i	$0.818291\pi$
$824$	0.717126	−	0.414033i	0.0249823	−	0.0144235i
$825$	−52.2461	−	30.1643i	−1.81898	−	1.05019i
$826$	18.0000	−	10.3923i	0.626299	−	0.361594i
$827$	−23.1427	+	13.3614i	−0.804750	+	0.464622i	−0.845129	−	0.534562i	$-0.820477\pi$
$827$	−23.1427	+	13.3614i	−0.804750	+	0.464622i	0.0403797	+	0.999184i	$0.487143\pi$
$828$	−38.5144	−	66.7090i	−1.33847	−	2.31830i
$829$	36.3267			1.26168			0.630839	−	0.775914i	$-0.282711\pi$
$829$	36.3267			1.26168			0.630839	+	0.775914i	$0.282711\pi$
$830$	3.17429	+	1.83268i	0.110181	+	0.0636131i
$831$	16.8866	−	29.2485i	0.585791	−	1.01462i
$832$	24.4804	+	17.2377i	0.848704	+	0.597611i
$833$	−3.57445			−0.123847
$834$	61.8626	+	35.7164i	2.14213	+	1.23676i
$835$	2.51458			0.0870207
$836$	37.6159			1.30097
$837$	−44.6588	+	86.4721i	−1.54363	+	2.98891i
$838$			27.2388i			0.940949i
$839$		−	31.8093i		−	1.09818i	−0.835764	−	0.549089i	$-0.814975\pi$
$839$		−	31.8093i		−	1.09818i	0.835764	−	0.549089i	$-0.185025\pi$
$840$	0.108457	+	0.0626177i	0.00374212	+	0.00216052i
$841$	−28.5347			−0.983956
$842$	0.851871	+	1.47548i	0.0293574	+	0.0508485i
$843$	−39.6837	−	22.9114i	−1.36678	−	0.789110i
$844$	25.2294	−	43.6987i	0.868433	−	1.50417i
$845$	−1.73997	−	1.47572i	−0.0598567	−	0.0507663i
$846$	−55.0761	−	95.3947i	−1.89356	−	3.27974i
$847$	−5.11573	+	2.95357i	−0.175779	+	0.101486i
$848$	−3.81951	−	6.61559i	−0.131163	−	0.227180i
$849$	22.2577	−	38.5515i	0.763884	−	1.32309i
$850$	48.7921	−	28.1701i	1.67355	−	0.966227i
$851$	2.46661	+	1.42410i	0.0845542	+	0.0488174i
$852$			103.021i			3.52944i
$853$		−	23.8173i		−	0.815488i	−0.913096	−	0.407744i	$-0.866316\pi$
$853$		−	23.8173i		−	0.815488i	0.913096	−	0.407744i	$-0.133684\pi$
$854$	19.3760	−	33.5602i	0.663033	−	1.14841i
$855$	−3.67175	−	6.35967i	−0.125571	−	0.217496i
$856$	−0.642518	−	0.370958i	−0.0219608	−	0.0126791i
$857$	18.5886	+	32.1963i	0.634973	+	1.09981i	0.986521	+	0.163636i	$0.0523222\pi$
$857$	18.5886	+	32.1963i	0.634973	+	1.09981i	−0.351548	+	0.936170i	$0.614344\pi$
$858$	−71.9237	−	50.6448i	−2.45543	−	1.72898i
$859$	−9.16551	−	15.8751i	−0.312723	−	0.541652i	0.666228	−	0.745748i	$-0.267908\pi$
$859$	−9.16551	−	15.8751i	−0.312723	−	0.541652i	−0.978951	+	0.204096i	$0.934575\pi$
$860$			0.825493i			0.0281491i
$861$	50.8271	−	88.0351i	1.73218	−	3.00023i
$862$	−21.8602	+	37.8630i	−0.744561	+	1.28962i
$863$	−4.05799	+	2.34288i	−0.138135	+	0.0797525i	−0.567475	−	0.823391i	$-0.692080\pi$
$863$	−4.05799	+	2.34288i	−0.138135	+	0.0797525i	0.429340	+	0.903143i	$0.358746\pi$
$864$		−	140.456i		−	4.77840i
$865$	0.129356	+	0.0746834i	0.00439822	+	0.00253931i
$866$		−	30.3280i		−	1.03059i
$867$	49.6773			1.68713
$868$	−26.3910	+	16.9335i	−0.895770	+	0.574760i
$869$			6.55507i			0.222365i
$870$	−0.805773			−0.0273183
$871$	−43.6231	−	3.93251i	−1.47811	−	0.133248i
$872$	0.438562			0.0148516
$873$	56.1393	−	32.4121i	1.90003	−	1.09698i
$874$	−23.5213	+	40.7401i	−0.795620	+	1.37805i
$875$	−2.41696	+	4.18631i	−0.0817083	+	0.141523i
$876$		−	1.81306i		−	0.0612576i
$877$	−20.4585	+	11.8117i	−0.690833	+	0.398853i	−0.803924	−	0.594732i	$-0.797258\pi$
$877$	−20.4585	+	11.8117i	−0.690833	+	0.398853i	0.113091	+	0.993585i	$0.463925\pi$
$878$	−13.6333	+	7.87119i	−0.460102	+	0.265640i
$879$	85.5104	−	49.3695i	2.88419	−	1.66519i
$880$	1.24737	−	2.16051i	0.0420489	−	0.0728308i
$881$	5.27213	+	9.13160i	0.177623	+	0.307651i	0.941066	−	0.338224i	$-0.109826\pi$
$881$	5.27213	+	9.13160i	0.177623	+	0.307651i	−0.763443	+	0.645875i	$0.776493\pi$
$882$	9.06189	+	5.23189i	0.305130	+	0.176167i
$883$	46.3184			1.55874			0.779370	−	0.626564i	$-0.215539\pi$
$883$	46.3184			1.55874			0.779370	+	0.626564i	$0.215539\pi$
$884$	37.6264	−	17.4248i	1.26551	−	0.586058i
$885$	1.10025	−	1.90570i	0.0369846	−	0.0640593i
$886$	12.8235	−	7.40367i	0.430815	−	0.248731i
$887$	−10.2462	+	17.7470i	−0.344035	+	0.595887i	−0.985178	−	0.171535i	$-0.945127\pi$
$887$	−10.2462	+	17.7470i	−0.344035	+	0.595887i	0.641143	+	0.767422i	$0.278461\pi$
$888$	−0.0799946	−	0.138555i	−0.00268444	−	0.00464959i
$889$	3.85554	−	2.22599i	0.129311	−	0.0746575i
$890$	−0.358390	+	0.206917i	−0.0120133	+	0.00693586i
$891$			122.844i			4.11542i
$892$	−19.8213	−	11.4438i	−0.663667	−	0.383168i
$893$	−16.9777	+	29.4062i	−0.568137	+	0.984042i
$894$	−4.49219	−	7.78071i	−0.150241	−	0.260226i
$895$			2.46314i			0.0823338i
$896$	0.852038	−	1.47577i	0.0284646	−	0.0493021i
$897$	50.3869	−	23.3342i	1.68237	−	0.779105i
$898$	73.4905			2.45241
$899$	1.74274	−	3.37443i	0.0581235	−	0.112544i
$900$	−83.2481			−2.77494
$901$	−10.9896			−0.366118
$902$	69.2930	+	40.0063i	2.30720	+	1.33207i
$903$			21.3544i			0.710631i
$904$	−0.386869	+	0.223359i	−0.0128671	+	0.00742880i
$905$	−2.72329	−	1.57229i	−0.0905251	−	0.0522647i
$906$	−42.5839	+	73.7575i	−1.41476	+	2.45043i
$907$	26.7668			0.888778			0.444389	−	0.895834i	$-0.353421\pi$
$907$	26.7668			0.888778			0.444389	+	0.895834i	$0.353421\pi$
$908$	−20.8025	+	12.0104i	−0.690357	+	0.398578i
$909$	5.09593	+	8.82641i	0.169021	+	0.292753i
$910$	−2.02273	+	2.87260i	−0.0670528	+	0.0952257i
$911$	−3.78741	+	6.55998i	−0.125482	+	0.217342i	−0.921921	−	0.387377i	$-0.873381\pi$
$911$	−3.78741	+	6.55998i	−0.125482	+	0.217342i	0.796439	+	0.604719i	$0.206715\pi$
$912$	−57.9173	+	33.4386i	−1.91783	+	1.10726i
$913$	−18.8352	+	32.6236i	−0.623355	+	1.07968i
$914$	38.9885			1.28962
$915$		−	4.10276i		−	0.135633i
$916$	−26.1851	−	15.1180i	−0.865180	−	0.499512i
$917$	30.4037	−	17.5536i	1.00402	−	0.579670i
$918$	−171.632	−	99.0919i	−5.66471	−	3.27052i
$919$	8.89492	+	15.4065i	0.293416	+	0.508212i	0.974615	−	0.223886i	$-0.0718745\pi$
$919$	8.89492	+	15.4065i	0.293416	+	0.508212i	−0.681199	+	0.732098i	$0.738541\pi$
$920$	−0.0311120	−	0.0538876i	−0.00102573	−	0.00177662i
$921$	84.2646	−	48.6502i	2.77661	−	1.60308i
$922$	−79.5678			−2.62043
$923$	−54.1856	−	4.88469i	−1.78354	−	0.160782i
$924$	−34.1864	+	59.2126i	−1.12465	+	1.94795i
$925$	2.66576	−	1.53908i	0.0876495	−	0.0506045i
$926$	−77.9778			−2.56251
$927$	44.1290	−	76.4336i	1.44939	−	2.51041i
$928$			5.48106i			0.179924i
$929$		−	50.2854i		−	1.64981i	−0.565270	−	0.824906i	$-0.691228\pi$
$929$		−	50.2854i		−	1.64981i	0.565270	−	0.824906i	$-0.308772\pi$
$930$	−3.01802	+	5.84375i	−0.0989648	+	0.191624i
$931$		−	3.22555i		−	0.105713i
$932$	−17.6852			−0.579298
$933$	−16.6924	+	28.9122i	−0.546486	+	0.946541i
$934$			52.7064i			1.72461i
$935$	−1.79449	−	3.10815i	−0.0586861	−	0.101647i
$936$	−2.27580	−	0.205157i	−0.0743868	−	0.00670578i
$937$	−17.4497	+	30.2238i	−0.570058	+	0.987370i	0.426501	+	0.904487i	$0.359746\pi$
$937$	−17.4497	+	30.2238i	−0.570058	+	0.987370i	−0.996559	+	0.0828826i	$0.973587\pi$
$938$			67.4479i			2.20225i
$939$	−8.86902	−	15.3616i	−0.289430	−	0.501307i
$940$	−1.19293	−	2.06622i	−0.0389092	−	0.0673927i
$941$	26.4024	−	15.2434i	0.860694	−	0.496922i	−0.00355056	−	0.999994i	$-0.501130\pi$
$941$	26.4024	−	15.2434i	0.860694	−	0.496922i	0.864245	+	0.503072i	$0.167797\pi$
$942$	−50.4267	−	29.1139i	−1.64299	−	0.948581i
$943$	−43.7408	+	25.2538i	−1.42440	+	0.822376i
$944$	−12.7142	−	7.34054i	−0.413812	−	0.238914i
$945$	8.47571			0.275715
$946$	−16.8082			−0.546482
$947$	−14.1923	−	8.19392i	−0.461187	−	0.266267i	0.251356	−	0.967895i	$-0.419123\pi$
$947$	−14.1923	−	8.19392i	−0.461187	−	0.266267i	−0.712543	+	0.701628i	$0.752457\pi$
$948$	6.17358	+	10.6930i	0.200509	+	0.347291i
$949$	0.953610	+	0.0859655i	0.0309555	+	0.00279056i
$950$	25.4204	+	44.0294i	0.824746	+	1.42850i
$951$	−13.4058	+	7.73986i	−0.434714	+	0.250982i
$952$	−0.601004	−	1.04097i	−0.0194787	−	0.0337380i
$953$	−34.3992			−1.11430			−0.557150	−	0.830412i	$-0.688105\pi$
$953$	−34.3992			−1.11430			−0.557150	+	0.830412i	$0.688105\pi$
$954$	27.8607	+	16.0854i	0.902024	+	0.520784i
$955$	−2.37123	−	1.36903i	−0.0767313	−	0.0443008i
$956$	7.73051	−	4.46321i	0.250023	−	0.144351i
$957$		−	8.28129i		−	0.267696i
$958$	−26.0689	+	45.1526i	−0.842247	+	1.45881i
$959$	20.3229			0.656261
$960$		−	4.88129i		−	0.157543i
$961$	−17.9452	−	25.2779i	−0.578876	−	0.815415i
$962$	4.07274	−	1.88608i	0.131310	−	0.0608098i
$963$	−79.0758			−2.54818
$964$	−9.81423	−	5.66625i	−0.316095	−	0.182498i
$965$	−1.22672			−0.0394895
$966$	−42.7537	−	74.0516i	−1.37558	−	2.38257i
$967$	10.8699	+	6.27575i	0.349553	+	0.201815i	0.664488	−	0.747299i	$-0.268649\pi$
$967$	10.8699	+	6.27575i	0.349553	+	0.201815i	−0.314935	+	0.949113i	$0.601983\pi$
$968$	−0.142778	−	0.0824327i	−0.00458905	−	0.00264949i
$969$			96.2107i			3.09073i
$970$	2.40903	−	1.39086i	0.0773494	−	0.0446577i
$971$	−9.33075	−	16.1613i	−0.299438	−	0.518642i	0.676570	−	0.736379i	$-0.263466\pi$
$971$	−9.33075	−	16.1613i	−0.299438	−	0.518642i	−0.976007	+	0.217737i	$0.930132\pi$
$972$	62.2491	+	107.819i	1.99664	+	3.45828i
$973$	25.3931	+	14.6607i	0.814066	+	0.470001i
$974$	−5.70567	−	9.88252i	−0.182822	−	0.316656i
$975$	5.38798	−	59.7685i	0.172553	−	1.91412i
$976$	−27.3723			−0.876166
$977$		−	2.80114i		−	0.0896165i	−0.998996	−	0.0448082i	$-0.985732\pi$
$977$		−	2.80114i		−	0.0896165i	0.998996	−	0.0448082i	$-0.0142677\pi$
$978$	30.1219	−	52.1727i	0.963194	−	1.66830i
$979$	−2.12657	−	3.68334i	−0.0679656	−	0.117720i
$980$	0.196278	+	0.113321i	0.00626987	+	0.00361991i
$981$	40.4809	−	23.3717i	1.29246	−	0.746200i
$982$	−30.9762	+	17.8841i	−0.988491	+	0.570705i
$983$	−23.3578	+	13.4856i	−0.744999	+	0.430125i	−0.823884	−	0.566759i	$-0.808197\pi$
$983$	−23.3578	+	13.4856i	−0.744999	+	0.430125i	0.0788853	+	0.996884i	$0.474864\pi$
$984$	2.83712			0.0904441
$985$	0.438499	−	0.759503i	0.0139717	−	0.0241998i
$986$	6.69767	+	3.86690i	0.213297	+	0.123147i
$987$	−30.8596	−	53.4505i	−0.982273	−	1.70135i
$988$	15.7239	+	33.9536i	0.500244	+	1.08021i
$989$	5.30504	−	9.18861i	0.168691	−	0.292181i
$990$			10.5063i			0.333912i
$991$	16.0943			0.511252			0.255626	−	0.966776i	$-0.417718\pi$
$991$	16.0943			0.511252			0.255626	+	0.966776i	$0.417718\pi$
$992$	39.7506	+	20.5293i	1.26208	+	0.651806i
$993$			31.1938i			0.989906i
$994$			83.7792i			2.65732i
$995$	−0.663327	−	0.382972i	−0.0210289	−	0.0121410i
$996$			70.9563i			2.24834i
$997$	−25.6312	−	44.3945i	−0.811747	−	1.40599i	−0.911640	−	0.410989i	$-0.865183\pi$
$997$	−25.6312	−	44.3945i	−0.811747	−	1.40599i	0.0998927	−	0.994998i	$-0.468150\pi$
$998$	39.9477	−	69.1915i	1.26452	−	2.19022i
$999$	−9.37713	−	5.41389i	−0.296679	−	0.171288i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.l.c.129.28	yes	68
13.12	even	2	inner	403.2.l.c.129.7	yes	68
31.25	even	3	inner	403.2.l.c.25.28	yes	68
403.25	even	6	inner	403.2.l.c.25.7	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.7	✓	68	403.25	even	6	inner
403.2.l.c.25.28	yes	68	31.25	even	3	inner
403.2.l.c.129.7	yes	68	13.12	even	2	inner
403.2.l.c.129.28	yes	68	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+2.00957i q^{2} +(-1.67472 + 2.90070i) q^{3} -2.03837 q^{4} +(-0.151987 + 0.0877499i) q^{5} +(-5.82915 - 3.36546i) q^{6} +(-2.39273 - 1.38144i) q^{7} -0.0771108i q^{8} +(-4.10936 - 7.11762i) q^{9} +O(q^{10})\)	\(q+2.00957i q^{2} +(-1.67472 + 2.90070i) q^{3} -2.03837 q^{4} +(-0.151987 + 0.0877499i) q^{5} +(-5.82915 - 3.36546i) q^{6} +(-2.39273 - 1.38144i) q^{7} -0.0771108i q^{8} +(-4.10936 - 7.11762i) q^{9} +(-0.176340 - 0.305429i) q^{10} +(3.13903 - 1.81232i) q^{11} +(3.41370 - 5.91270i) q^{12} +(2.94803 + 2.07584i) q^{13} +(2.77611 - 4.80836i) q^{14} -0.587826i q^{15} -3.92178 q^{16} +(-2.82097 + 4.88607i) q^{17} +(14.3034 - 8.25805i) q^{18} +(-4.40913 - 2.54561i) q^{19} +(0.309807 - 0.178867i) q^{20} +(8.01430 - 4.62706i) q^{21} +(3.64199 + 6.30811i) q^{22} -4.59797 q^{23} +(0.223675 + 0.129139i) q^{24} +(-2.48460 + 4.30345i) q^{25} +(-4.17155 + 5.92427i) q^{26} +17.4798 q^{27} +(4.87728 + 2.81590i) q^{28} -0.682120 q^{29} +1.18128 q^{30} +(-2.55488 + 4.94698i) q^{31} -8.03532i q^{32} +12.1405i q^{33} +(-9.81890 - 5.66894i) q^{34} +0.484886 q^{35} +(8.37641 + 14.5084i) q^{36} +(-0.536456 - 0.309723i) q^{37} +(5.11559 - 8.86046i) q^{38} +(-10.9585 + 5.07489i) q^{39} +(0.00676647 + 0.0117199i) q^{40} +(9.51308 - 5.49238i) q^{41} +(9.29840 + 16.1053i) q^{42} +(-1.15378 + 1.99841i) q^{43} +(-6.39851 + 3.69418i) q^{44} +(1.24914 + 0.721192i) q^{45} -9.23993i q^{46} -6.66939i q^{47} +(6.56788 - 11.3759i) q^{48} +(0.316775 + 0.548670i) q^{49} +(-8.64809 - 4.99298i) q^{50} +(-9.44867 - 16.3656i) q^{51} +(-6.00918 - 4.23134i) q^{52} +(0.973922 + 1.68688i) q^{53} +35.1269i q^{54} +(-0.318062 + 0.550900i) q^{55} +(-0.106524 + 0.184506i) q^{56} +(14.7681 - 8.52637i) q^{57} -1.37077i q^{58} +(3.24194 + 1.87174i) q^{59} +1.19821i q^{60} +6.97955 q^{61} +(-9.94130 - 5.13421i) q^{62} +22.7074i q^{63} +8.30397 q^{64} +(-0.630218 - 0.0568125i) q^{65} -24.3972 q^{66} +(-10.5204 + 6.07396i) q^{67} +(5.75019 - 9.95962i) q^{68} +(7.70030 - 13.3373i) q^{69} +0.974413i q^{70} +(-13.0677 + 7.54466i) q^{71} +(-0.548846 + 0.316876i) q^{72} +(0.229978 - 0.132778i) q^{73} +(0.622410 - 1.07805i) q^{74} +(-8.32201 - 14.4141i) q^{75} +(8.98745 + 5.18891i) q^{76} -10.0145 q^{77} +(-10.1983 - 22.0219i) q^{78} +(-0.904237 + 1.56618i) q^{79} +(0.596061 - 0.344136i) q^{80} +(-16.9456 + 29.3507i) q^{81} +(11.0373 + 19.1172i) q^{82} +(-9.00049 + 5.19644i) q^{83} +(-16.3361 + 9.43167i) q^{84} -0.990161i q^{85} +(-4.01594 - 2.31860i) q^{86} +(1.14236 - 1.97862i) q^{87} +(-0.139750 - 0.242053i) q^{88} -1.17340i q^{89} +(-1.44929 + 2.51024i) q^{90} +(-4.18618 - 9.03947i) q^{91} +9.37236 q^{92} +(-10.0710 - 15.6957i) q^{93} +13.4026 q^{94} +0.893510 q^{95} +(23.3080 + 13.4569i) q^{96} +7.88737i q^{97} +(-1.10259 + 0.636581i) q^{98} +(-25.7988 - 14.8950i) 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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