LMFDB - Embedded newform 363.3.h.h.269.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(245,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 8]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("363.245");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (of order $10$, degree $4$, not 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:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			269.2
Root			$0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	363.269
Dual form			363.3.h.h.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(0.303706 + 2.98459i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-6.29412 - 2.04508i) q^{5} +(1.21113 + 2.74466i) q^{6} +(7.16312 - 5.20431i) q^{7} +(-4.11450 + 5.66312i) q^{8} +(-8.81553 + 1.81288i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(0.303706 + 2.98459i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-6.29412 - 2.04508i) q^{5} +(1.21113 + 2.74466i) q^{6} +(7.16312 - 5.20431i) q^{7} +(-4.11450 + 5.66312i) q^{8} +(-8.81553 + 1.81288i) q^{9} -6.61803 q^{10} +(-6.00000 - 6.70820i) q^{12} +(-4.09017 - 12.5882i) q^{13} +(5.20431 - 7.16312i) q^{14} +(4.19217 - 19.4065i) q^{15} +(1.54508 - 4.75528i) q^{16} +(5.70634 + 1.85410i) q^{17} +(-7.82385 + 4.44829i) q^{18} +(-7.38197 - 5.36331i) q^{19} +(18.8824 - 6.13525i) q^{20} +(17.7082 + 19.7984i) q^{21} -17.5279i q^{23} +(-18.1517 - 10.5602i) q^{24} +(15.2082 + 11.0494i) q^{25} +(-7.77997 - 10.7082i) q^{26} +(-8.08802 - 25.7601i) q^{27} +(-8.20820 + 25.2623i) q^{28} +(-15.5147 - 21.3541i) q^{29} +(-2.00994 - 19.7521i) q^{30} +(-1.91641 - 5.89810i) q^{31} -33.0000i q^{32} +6.00000 q^{34} +(-55.7288 + 18.1074i) q^{35} +(18.1990 - 19.9448i) q^{36} +(15.8541 - 11.5187i) q^{37} +(-8.67802 - 2.81966i) q^{38} +(36.3285 - 16.0306i) q^{39} +(37.4787 - 27.2299i) q^{40} +(3.28969 - 4.52786i) q^{41} +(22.9595 + 13.3572i) q^{42} -26.2918 q^{43} +(59.1935 + 6.61803i) q^{45} +(-5.41641 - 16.6700i) q^{46} +(-10.4086 + 14.3262i) q^{47} +(14.6618 + 3.16723i) q^{48} +(9.08359 - 27.9564i) q^{49} +(17.8783 + 5.80902i) q^{50} +(-3.80068 + 17.5942i) q^{51} +(32.1246 + 23.3399i) q^{52} +(-21.1805 + 6.88197i) q^{53} +(-15.6525 - 22.0000i) q^{54} +61.9787i q^{56} +(13.7653 - 23.6610i) q^{57} +(-21.3541 - 15.5147i) q^{58} +(-12.8783 - 17.7254i) q^{59} +(24.0459 + 54.4928i) q^{60} +(-28.8541 + 88.8038i) q^{61} +(-3.64522 - 5.01722i) q^{62} +(-53.7119 + 58.8646i) q^{63} +(-4.01722 - 12.3637i) q^{64} +87.5967i q^{65} -76.7902 q^{67} +(-17.1190 + 5.56231i) q^{68} +(52.3134 - 5.32332i) q^{69} +(-47.4058 + 34.4423i) q^{70} +(-62.5982 - 20.3394i) q^{71} +(26.0049 - 57.3824i) q^{72} +(-12.1525 + 8.82929i) q^{73} +(11.5187 - 15.8541i) q^{74} +(-28.3591 + 48.7460i) q^{75} +27.3738 q^{76} +(29.5967 - 26.4721i) q^{78} +(36.4828 + 112.282i) q^{79} +(-19.4499 + 26.7705i) q^{80} +(74.4270 - 31.9629i) q^{81} +(1.72949 - 5.32282i) q^{82} +(-105.744 - 34.3582i) q^{83} +(-77.8903 - 16.8258i) q^{84} +(-32.1246 - 23.3399i) q^{85} +(-25.0050 + 8.12461i) q^{86} +(59.0213 - 52.7902i) q^{87} -97.6656i q^{89} +(58.3414 - 11.9977i) q^{90} +(-94.8115 - 68.8846i) q^{91} +(30.9079 + 42.5410i) q^{92} +(17.0214 - 7.51098i) q^{93} +(-5.47214 + 16.8415i) q^{94} +(35.4946 + 48.8541i) q^{95} +(98.4914 - 10.0223i) q^{96} +(-37.4483 - 115.254i) q^{97} -29.3951i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 6 q^{4} - 10 q^{6} + 26 q^{7} + 2 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 6 * q^4 - 10 * q^6 + 26 * q^7 + 2 * q^9	$ 8 q + 4 q^{3} - 6 q^{4} - 10 q^{6} + 26 q^{7} + 2 q^{9} - 44 q^{10} - 48 q^{12} + 12 q^{13} + 60 q^{15} - 10 q^{16} - 40 q^{18} - 68 q^{19} + 88 q^{21} - 70 q^{24} + 68 q^{25} - 44 q^{27} - 12 q^{28} - 32 q^{30} + 92 q^{31} + 48 q^{34} + 6 q^{36} + 100 q^{37} - 24 q^{39} + 112 q^{40} + 40 q^{42} - 264 q^{43} + 80 q^{45} + 64 q^{46} + 20 q^{48} + 180 q^{49} - 60 q^{51} + 96 q^{52} - 224 q^{57} - 144 q^{58} - 150 q^{60} - 204 q^{61} - 26 q^{63} + 26 q^{64} - 24 q^{67} + 200 q^{69} - 178 q^{70} + 280 q^{72} + 28 q^{73} + 84 q^{75} - 264 q^{76} + 40 q^{78} + 350 q^{79} + 158 q^{81} + 148 q^{82} - 156 q^{84} - 96 q^{85} + 660 q^{87} - 6 q^{90} - 356 q^{91} - 184 q^{93} - 8 q^{94} + 330 q^{96} - 474 q^{97}+O(q^{100}) $ 8 * q + 4 * q^3 - 6 * q^4 - 10 * q^6 + 26 * q^7 + 2 * q^9 - 44 * q^10 - 48 * q^12 + 12 * q^13 + 60 * q^15 - 10 * q^16 - 40 * q^18 - 68 * q^19 + 88 * q^21 - 70 * q^24 + 68 * q^25 - 44 * q^27 - 12 * q^28 - 32 * q^30 + 92 * q^31 + 48 * q^34 + 6 * q^36 + 100 * q^37 - 24 * q^39 + 112 * q^40 + 40 * q^42 - 264 * q^43 + 80 * q^45 + 64 * q^46 + 20 * q^48 + 180 * q^49 - 60 * q^51 + 96 * q^52 - 224 * q^57 - 144 * q^58 - 150 * q^60 - 204 * q^61 - 26 * q^63 + 26 * q^64 - 24 * q^67 + 200 * q^69 - 178 * q^70 + 280 * q^72 + 28 * q^73 + 84 * q^75 - 264 * q^76 + 40 * q^78 + 350 * q^79 + 158 * q^81 + 148 * q^82 - 156 * q^84 - 96 * q^85 + 660 * q^87 - 6 * q^90 - 356 * q^91 - 184 * q^93 - 8 * q^94 + 330 * q^96 - 474 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.951057	−	0.309017i	0.475528	−	0.154508i	−0.0614403	−	0.998111i	$-0.519569\pi$
$2$	0.951057	−	0.309017i	0.475528	−	0.154508i	0.536969	+	0.843602i	$0.319569\pi$
$3$	0.303706	+	2.98459i	0.101235	+	0.994862i
$3$	0.303706	+	2.98459i	0.101235	+	0.994862i
$4$	−2.42705	+	1.76336i	−0.606763	+	0.440839i
$5$	−6.29412	−	2.04508i	−1.25882	−	0.409017i	−0.397749	−	0.917494i	$-0.630209\pi$
$5$	−6.29412	−	2.04508i	−1.25882	−	0.409017i	−0.861076	+	0.508477i	$0.830209\pi$
$6$	1.21113	+	2.74466i	0.201855	+	0.457444i
$7$	7.16312	−	5.20431i	1.02330	−	0.743473i	0.0563454	−	0.998411i	$-0.482055\pi$
$7$	7.16312	−	5.20431i	1.02330	−	0.743473i	0.966957	+	0.254938i	$0.0820552\pi$
$8$	−4.11450	+	5.66312i	−0.514312	+	0.707890i
$9$	−8.81553	+	1.81288i	−0.979503	+	0.201431i
$10$	−6.61803			−0.661803
$11$		0			0
$11$		0			0
$12$	−6.00000	−	6.70820i	−0.500000	−	0.559017i
$13$	−4.09017	−	12.5882i	−0.314628	−	0.968327i	−0.975907	−	0.218186i	$-0.929986\pi$
$13$	−4.09017	−	12.5882i	−0.314628	−	0.968327i	0.661279	−	0.750140i	$-0.270014\pi$
$14$	5.20431	−	7.16312i	0.371736	−	0.511651i
$15$	4.19217	−	19.4065i	0.279478	−	1.29376i
$16$	1.54508	−	4.75528i	0.0965678	−	0.297205i
$17$	5.70634	+	1.85410i	0.335667	+	0.109065i	0.472001	−	0.881598i	$-0.343532\pi$
$17$	5.70634	+	1.85410i	0.335667	+	0.109065i	−0.136334	+	0.990663i	$0.543532\pi$
$18$	−7.82385	+	4.44829i	−0.434659	+	0.247127i
$19$	−7.38197	−	5.36331i	−0.388525	−	0.282280i	0.376326	−	0.926487i	$-0.377187\pi$
$19$	−7.38197	−	5.36331i	−0.388525	−	0.282280i	−0.764851	+	0.644208i	$0.777187\pi$
$20$	18.8824	−	6.13525i	0.944119	−	0.306763i
$21$	17.7082	+	19.7984i	0.843248	+	0.942780i
$22$		0			0
$23$		−	17.5279i		−	0.762081i	−0.924558	−	0.381041i	$-0.875566\pi$
$23$		−	17.5279i		−	0.762081i	0.924558	−	0.381041i	$-0.124434\pi$
$24$	−18.1517	−	10.5602i	−0.756320	−	0.440006i
$25$	15.2082	+	11.0494i	0.608328	+	0.441976i
$26$	−7.77997	−	10.7082i	−0.299229	−	0.411854i
$27$	−8.08802	−	25.7601i	−0.299556	−	0.954079i
$28$	−8.20820	+	25.2623i	−0.293150	+	0.902223i
$29$	−15.5147	−	21.3541i	−0.534988	−	0.736348i	0.452892	−	0.891565i	$-0.350392\pi$
$29$	−15.5147	−	21.3541i	−0.534988	−	0.736348i	−0.987880	+	0.155217i	$0.950392\pi$
$30$	−2.00994	−	19.7521i	−0.0669979	−	0.658403i
$31$	−1.91641	−	5.89810i	−0.0618196	−	0.190261i	0.915377	−	0.402598i	$-0.131893\pi$
$31$	−1.91641	−	5.89810i	−0.0618196	−	0.190261i	−0.977197	+	0.212337i	$0.931893\pi$
$32$		−	33.0000i		−	1.03125i
$33$		0			0
$34$	6.00000			0.176471
$35$	−55.7288	+	18.1074i	−1.59225	+	0.517354i
$36$	18.1990	−	19.9448i	0.505527	−	0.554024i
$37$	15.8541	−	11.5187i	0.428489	−	0.311316i	−0.352555	−	0.935791i	$-0.614687\pi$
$37$	15.8541	−	11.5187i	0.428489	−	0.311316i	0.781045	+	0.624475i	$0.214687\pi$
$38$	−8.67802	−	2.81966i	−0.228369	−	0.0742016i
$39$	36.3285	−	16.0306i	0.931501	−	0.411041i
$40$	37.4787	−	27.2299i	0.936968	−	0.680747i
$41$	3.28969	−	4.52786i	0.0802362	−	0.110436i	−0.767012	−	0.641632i	$-0.778257\pi$
$41$	3.28969	−	4.52786i	0.0802362	−	0.110436i	0.847249	+	0.531197i	$0.178257\pi$
$42$	22.9595	+	13.3572i	0.546656	+	0.318029i
$43$	−26.2918			−0.611437			−0.305719	−	0.952122i	$-0.598897\pi$
$43$	−26.2918			−0.611437			−0.305719	+	0.952122i	$0.598897\pi$
$44$		0			0
$45$	59.1935	+	6.61803i	1.31541	+	0.147067i
$46$	−5.41641	−	16.6700i	−0.117748	−	0.362391i
$47$	−10.4086	+	14.3262i	−0.221460	+	0.304814i	−0.905262	−	0.424854i	$-0.860325\pi$
$47$	−10.4086	+	14.3262i	−0.221460	+	0.304814i	0.683802	+	0.729668i	$0.260325\pi$
$48$	14.6618	+	3.16723i	0.305454	+	0.0659840i
$49$	9.08359	−	27.9564i	0.185379	−	0.570539i
$50$	17.8783	+	5.80902i	0.357566	+	0.116180i
$51$	−3.80068	+	17.5942i	−0.0745231	+	0.344984i
$52$	32.1246	+	23.3399i	0.617781	+	0.448844i
$53$	−21.1805	+	6.88197i	−0.399632	+	0.129848i	−0.501936	−	0.864905i	$-0.667379\pi$
$53$	−21.1805	+	6.88197i	−0.399632	+	0.129848i	0.102304	+	0.994753i	$0.467379\pi$
$54$	−15.6525	−	22.0000i	−0.289861	−	0.407407i
$55$		0			0
$56$			61.9787i			1.10676i
$57$	13.7653	−	23.6610i	0.241497	−	0.415105i
$58$	−21.3541	−	15.5147i	−0.368174	−	0.267494i
$59$	−12.8783	−	17.7254i	−0.218276	−	0.300431i	0.685811	−	0.727780i	$-0.259448\pi$
$59$	−12.8783	−	17.7254i	−0.218276	−	0.300431i	−0.904087	+	0.427349i	$0.859448\pi$
$60$	24.0459	+	54.4928i	0.400765	+	0.908213i
$61$	−28.8541	+	88.8038i	−0.473018	+	1.45580i	0.375594	+	0.926784i	$0.377439\pi$
$61$	−28.8541	+	88.8038i	−0.473018	+	1.45580i	−0.848612	+	0.529016i	$0.822561\pi$
$62$	−3.64522	−	5.01722i	−0.0587939	−	0.0809229i
$63$	−53.7119	+	58.8646i	−0.852570	+	0.934358i
$64$	−4.01722	−	12.3637i	−0.0627691	−	0.193183i
$65$			87.5967i			1.34764i
$66$		0			0
$67$	−76.7902			−1.14612			−0.573062	−	0.819512i	$-0.694244\pi$
$67$	−76.7902			−1.14612			−0.573062	+	0.819512i	$0.694244\pi$
$68$	−17.1190	+	5.56231i	−0.251750	+	0.0817986i
$69$	52.3134	−	5.32332i	0.758166	−	0.0771496i
$70$	−47.4058	+	34.4423i	−0.677225	+	0.492033i
$71$	−62.5982	−	20.3394i	−0.881665	−	0.286470i	−0.167017	−	0.985954i	$-0.553413\pi$
$71$	−62.5982	−	20.3394i	−0.881665	−	0.286470i	−0.714648	+	0.699484i	$0.753413\pi$
$72$	26.0049	−	57.3824i	0.361179	−	0.796978i
$73$	−12.1525	+	8.82929i	−0.166472	+	0.120949i	−0.667902	−	0.744249i	$-0.732808\pi$
$73$	−12.1525	+	8.82929i	−0.166472	+	0.120949i	0.501430	+	0.865198i	$0.332808\pi$
$74$	11.5187	−	15.8541i	0.155658	−	0.214245i
$75$	−28.3591	+	48.7460i	−0.378121	+	0.649947i
$76$	27.3738			0.360182
$77$		0			0
$78$	29.5967	−	26.4721i	0.379445	−	0.339386i
$79$	36.4828	+	112.282i	0.461807	+	1.42130i	0.862954	+	0.505283i	$0.168612\pi$
$79$	36.4828	+	112.282i	0.461807	+	1.42130i	−0.401146	+	0.916014i	$0.631388\pi$
$80$	−19.4499	+	26.7705i	−0.243124	+	0.334631i
$81$	74.4270	−	31.9629i	0.918851	−	0.394604i
$82$	1.72949	−	5.32282i	0.0210913	−	0.0649125i
$83$	−105.744	−	34.3582i	−1.27402	−	0.413954i	−0.407549	−	0.913183i	$-0.633616\pi$
$83$	−105.744	−	34.3582i	−1.27402	−	0.413954i	−0.866470	+	0.499229i	$0.833616\pi$
$84$	−77.8903	−	16.8258i	−0.927265	−	0.200307i
$85$	−32.1246	−	23.3399i	−0.377937	−	0.274587i
$86$	−25.0050	+	8.12461i	−0.290756	+	0.0944722i
$87$	59.0213	−	52.7902i	0.678406	−	0.606784i
$88$		0			0
$89$		−	97.6656i		−	1.09737i	−0.836030	−	0.548683i	$-0.815129\pi$
$89$		−	97.6656i		−	1.09737i	0.836030	−	0.548683i	$-0.184871\pi$
$90$	58.3414	−	11.9977i	0.648238	−	0.133307i
$91$	−94.8115	−	68.8846i	−1.04188	−	0.756974i
$92$	30.9079	+	42.5410i	0.335955	+	0.462402i
$93$	17.0214	−	7.51098i	0.183025	−	0.0807632i
$94$	−5.47214	+	16.8415i	−0.0582142	+	0.179165i
$95$	35.4946	+	48.8541i	0.373627	+	0.514254i
$96$	98.4914	−	10.0223i	1.02595	−	0.104399i
$97$	−37.4483	−	115.254i	−0.386065	−	1.18819i	−0.935705	−	0.352785i	$-0.885235\pi$
$97$	−37.4483	−	115.254i	−0.386065	−	1.18819i	0.549639	−	0.835402i	$-0.314765\pi$
$98$		−	29.3951i		−	0.299950i
$99$		0			0
$100$	−56.3951			−0.563951
$101$	176.505	−	57.3500i	1.74758	−	0.567822i	0.751780	−	0.659414i	$-0.229195\pi$
$101$	176.505	−	57.3500i	1.74758	−	0.567822i	0.995797	+	0.0915916i	$0.0291954\pi$
$102$	1.82224	+	17.9075i	0.0178651	+	0.175564i
$103$	−139.627	+	101.445i	−1.35560	+	0.984903i	−0.356892	+	0.934146i	$0.616164\pi$
$103$	−139.627	+	101.445i	−1.35560	+	0.984903i	−0.998711	+	0.0507577i	$0.983836\pi$
$104$	88.1177	+	28.6312i	0.847286	+	0.275300i
$105$	−70.9683	−	160.828i	−0.675888	−	1.53170i
$106$	−18.0172	+	13.0903i	−0.169974	+	0.123493i
$107$	−38.6658	+	53.2188i	−0.361362	+	0.497372i	−0.950528	−	0.310640i	$-0.899457\pi$
$107$	−38.6658	+	53.2188i	−0.361362	+	0.497372i	0.589165	+	0.808012i	$0.299457\pi$
$108$	65.0543	+	48.2591i	0.602355	+	0.446843i
$109$	−107.331			−0.984690			−0.492345	−	0.870400i	$-0.663860\pi$
$109$	−107.331			−0.984690			−0.492345	+	0.870400i	$0.663860\pi$
$110$		0			0
$111$	39.1935	+	43.8197i	0.353095	+	0.394772i
$112$	−13.6803	−	42.1038i	−0.122146	−	0.375926i
$113$	−18.6126	+	25.6180i	−0.164713	+	0.226708i	−0.883393	−	0.468633i	$-0.844747\pi$
$113$	−18.6126	+	25.6180i	−0.164713	+	0.226708i	0.718680	+	0.695341i	$0.244747\pi$
$114$	5.77995	−	26.7567i	0.0507013	−	0.234708i
$115$	−35.8460	+	110.323i	−0.311704	+	0.959327i
$116$	75.3098	+	24.4696i	0.649222	+	0.210945i
$117$	58.8779	+	103.557i	0.503230	+	0.885103i
$118$	−17.7254	−	12.8783i	−0.150215	−	0.109138i
$119$	50.5245	−	16.4164i	0.424576	−	0.137953i
$120$	92.6525	+	103.589i	0.772104	+	0.863238i
$121$		0			0
$122$			93.3738i			0.765359i
$123$	14.5129	+	8.44321i	0.117991	+	0.0686440i
$124$	15.0517	+	10.9357i	0.121384	+	0.0881909i
$125$	24.1242	+	33.2041i	0.192994	+	0.265633i
$126$	−32.8929	+	72.5814i	−0.261055	+	0.576043i
$127$	31.3394	−	96.4527i	0.246767	−	0.759470i	−0.748574	−	0.663051i	$-0.769261\pi$
$127$	31.3394	−	96.4527i	0.246767	−	0.759470i	0.995341	−	0.0964190i	$-0.0307389\pi$
$128$	69.9464	+	96.2730i	0.546457	+	0.752133i
$129$	−7.98498	−	78.4702i	−0.0618991	−	0.608296i
$130$	27.0689	+	83.3095i	0.208222	+	0.640842i
$131$		−	130.992i		−	0.999938i	−0.866043	−	0.499969i	$-0.833345\pi$
$131$		−	130.992i		−	0.999938i	0.866043	−	0.499969i	$-0.166655\pi$
$132$		0			0
$133$	−80.7902			−0.607445
$134$	−73.0319	+	23.7295i	−0.545014	+	0.177086i
$135$	−1.77467	+	178.678i	−0.0131457	+	1.32354i
$136$	−33.9787	+	24.6870i	−0.249843	+	0.181522i
$137$	198.531	+	64.5066i	1.44913	+	0.470851i	0.924731	−	0.380622i	$-0.124290\pi$
$137$	198.531	+	64.5066i	1.44913	+	0.470851i	0.524399	+	0.851472i	$0.324290\pi$
$138$	48.1080	−	21.2285i	0.348609	−	0.153830i
$139$	66.0000	−	47.9518i	0.474820	−	0.344977i	−0.324497	−	0.945887i	$-0.605195\pi$
$139$	66.0000	−	47.9518i	0.474820	−	0.344977i	0.799317	+	0.600910i	$0.205195\pi$
$140$	103.327	−	142.217i	0.738049	−	1.01584i
$141$	−45.9191	−	26.7145i	−0.325667	−	0.189464i
$142$	−65.8197			−0.463519
$143$		0			0
$144$	−5.00000	+	44.7214i	−0.0347222	+	0.310565i
$145$	53.9803	+	166.134i	0.372278	+	1.14575i
$146$	−8.82929	+	12.1525i	−0.0604746	+	0.0832361i
$147$	86.1971	+	18.6202i	0.586375	+	0.126668i
$148$	−18.1672	+	55.9128i	−0.122751	+	0.377789i
$149$	6.64966	+	2.16061i	0.0446286	+	0.0145007i	0.331246	−	0.943544i	$-0.392531\pi$
$149$	6.64966	+	2.16061i	0.0446286	+	0.0145007i	−0.286618	+	0.958045i	$0.592531\pi$
$150$	−11.9078	+	55.1236i	−0.0793851	+	0.367491i
$151$	44.8607	+	32.5932i	0.297091	+	0.215849i	0.726337	−	0.687338i	$-0.241221\pi$
$151$	44.8607	+	32.5932i	0.297091	+	0.215849i	−0.429247	+	0.903187i	$0.641221\pi$
$152$	60.7462	−	19.7376i	0.399646	−	0.129853i
$153$	−53.6656	−	6.00000i	−0.350756	−	0.0392157i
$154$		0			0
$155$			41.0426i			0.264791i
$156$	−59.9035	+	102.967i	−0.383997	+	0.660046i
$157$	−33.9787	−	24.6870i	−0.216425	−	0.157242i	0.474291	−	0.880368i	$-0.342704\pi$
$157$	−33.9787	−	24.6870i	−0.216425	−	0.157242i	−0.690716	+	0.723126i	$0.742704\pi$
$158$	69.3944	+	95.5132i	0.439205	+	0.604514i
$159$	−26.9725	−	61.1250i	−0.169638	−	0.384434i
$160$	−67.4878	+	207.706i	−0.421799	+	1.29816i
$161$	−91.2204	−	125.554i	−0.566587	−	0.779840i
$162$	60.9072	−	53.3977i	0.375970	−	0.329616i
$163$	−49.0689	−	151.018i	−0.301036	−	0.926494i	−0.981127	−	0.193366i	$-0.938060\pi$
$163$	−49.0689	−	151.018i	−0.301036	−	0.926494i	0.680091	−	0.733128i	$-0.261940\pi$
$164$			16.7902i			0.102380i
$165$		0			0
$166$	−111.185			−0.669791
$167$	271.220	−	88.1246i	1.62407	−	0.527692i	0.651173	−	0.758930i	$-0.274277\pi$
$167$	271.220	−	88.1246i	1.62407	−	0.527692i	0.972897	+	0.231237i	$0.0742774\pi$
$168$	−184.981	+	18.8233i	−1.10108	+	0.112044i
$169$	−5.01064	+	3.64045i	−0.0296488	+	0.0215411i
$170$	−37.7647	−	12.2705i	−0.222146	−	0.0721795i
$171$	74.7989	+	33.8978i	0.437421	+	0.198233i
$172$	63.8115	−	46.3618i	0.370997	−	0.269545i
$173$	−35.1486	+	48.3779i	−0.203171	+	0.279641i	−0.898429	−	0.439120i	$-0.855290\pi$
$173$	−35.1486	+	48.3779i	−0.203171	+	0.279641i	0.695257	+	0.718761i	$0.255290\pi$
$174$	39.8195	−	68.4451i	0.228848	−	0.393363i
$175$	166.443			0.951101
$176$		0			0
$177$	48.9919	−	43.8197i	0.276790	−	0.247569i
$178$	−30.1803	−	92.8855i	−0.169552	−	0.521829i
$179$	155.080	−	213.449i	0.866369	−	1.19245i	−0.113644	−	0.993521i	$-0.536252\pi$
$179$	155.080	−	213.449i	0.866369	−	1.19245i	0.980013	−	0.198933i	$-0.0637475\pi$
$180$	−155.336	+	88.3169i	−0.862975	+	0.490649i
$181$	69.8278	−	214.908i	0.385789	−	1.18734i	−0.550117	−	0.835087i	$-0.685417\pi$
$181$	69.8278	−	214.908i	0.385789	−	1.18734i	0.935906	−	0.352249i	$-0.114583\pi$
$182$	−111.458	−	36.2148i	−0.612405	−	0.198982i
$183$	−273.806	−	59.1473i	−1.49621	−	0.323209i
$184$	99.2624	+	72.1183i	0.539469	+	0.391947i
$185$	−123.344	+	40.0770i	−0.666726	+	0.216633i
$186$	13.8673	−	12.4033i	0.0745551	−	0.0666842i
$187$		0			0
$188$		−	53.1246i		−	0.282578i
$189$	−191.999	−	142.430i	−1.01587	−	0.753599i
$190$	48.8541	+	35.4946i	0.257127	+	0.186814i
$191$	−35.3172	−	48.6099i	−0.184907	−	0.254502i	0.706493	−	0.707720i	$-0.250276\pi$
$191$	−35.3172	−	48.6099i	−0.184907	−	0.254502i	−0.891400	+	0.453218i	$0.850276\pi$
$192$	35.6806	−	15.7447i	0.185836	−	0.0820036i
$193$	11.0279	−	33.9403i	0.0571392	−	0.175856i	−0.918414	−	0.395622i	$-0.870529\pi$
$193$	11.0279	−	33.9403i	0.0571392	−	0.175856i	0.975553	+	0.219765i	$0.0705292\pi$
$194$	−71.2310	−	98.0410i	−0.367170	−	0.505366i
$195$	−261.440	+	26.6037i	−1.34072	+	0.136429i
$196$	27.2508	+	83.8693i	0.139035	+	0.427904i
$197$			145.605i			0.739111i	0.929209	+	0.369556i	$0.120490\pi$
$197$			145.605i			0.739111i	−0.929209	+	0.369556i	$0.879510\pi$
$198$		0			0
$199$	241.185			1.21199			0.605993	−	0.795470i	$-0.292776\pi$
$199$	241.185			1.21199			0.605993	+	0.795470i	$0.292776\pi$
$200$	−125.148	+	40.6631i	−0.625741	+	0.203316i
$201$	−23.3217	−	229.187i	−0.116028	−	1.14023i
$202$	150.144	−	109.086i	0.743289	−	0.540031i
$203$	−222.267	−	72.2188i	−1.09491	−	0.355758i
$204$	−21.8003	−	49.4039i	−0.106864	−	0.242176i
$205$	−29.9656	+	21.7713i	−0.146173	+	0.106201i
$206$	−101.445	+	139.627i	−0.492452	+	0.677802i
$207$	31.7758	+	154.517i	0.153506	+	0.746461i
$208$	−66.1803			−0.318175
$209$		0			0
$210$	−117.193	−	131.026i	−0.558064	−	0.623935i
$211$	13.2067	+	40.6459i	0.0625908	+	0.192635i	0.977462	−	0.211111i	$-0.0677081\pi$
$211$	13.2067	+	40.6459i	0.0625908	+	0.192635i	−0.914871	+	0.403745i	$0.867708\pi$
$212$	39.2708	−	54.0517i	0.185240	−	0.254961i
$213$	41.6932	−	193.007i	0.195743	−	0.906136i
$214$	−20.3278	+	62.5625i	−0.0949897	+	0.292348i
$215$	165.484	+	53.7690i	0.769692	+	0.250088i
$216$	179.161	+	60.1866i	0.829448	+	0.278641i
$217$	−44.4230	−	32.2752i	−0.204714	−	0.148734i
$218$	−102.078	+	33.1672i	−0.468248	+	0.152143i
$219$	−30.0426	−	33.5886i	−0.137181	−	0.153373i
$220$		0			0
$221$		−	79.4164i		−	0.359350i
$222$	50.8162	+	29.5635i	0.228902	+	0.133169i
$223$	134.290	+	97.5676i	0.602198	+	0.437523i	0.846659	−	0.532137i	$-0.178611\pi$
$223$	134.290	+	97.5676i	0.602198	+	0.437523i	−0.244460	+	0.969659i	$0.578611\pi$
$224$	−171.742	−	236.383i	−0.766706	−	1.05528i
$225$	−154.100	−	69.8357i	−0.684887	−	0.310381i
$226$	−9.78522	+	30.1158i	−0.0432974	+	0.133256i
$227$	200.771	+	276.338i	0.884455	+	1.21735i	0.975167	+	0.221470i	$0.0710856\pi$
$227$	200.771	+	276.338i	0.884455	+	1.21735i	−0.0907125	+	0.995877i	$0.528914\pi$
$228$	8.31360	+	81.6996i	0.0364632	+	0.358332i
$229$	76.2574	+	234.696i	0.333002	+	1.02487i	0.967698	+	0.252112i	$0.0811251\pi$
$229$	76.2574	+	234.696i	0.333002	+	1.02487i	−0.634697	+	0.772761i	$0.718875\pi$
$230$			116.000i			0.504348i
$231$		0			0
$232$	184.766			0.796405
$233$	−378.873	+	123.103i	−1.62606	+	0.528340i	−0.973362	−	0.229274i	$-0.926365\pi$
$233$	−378.873	+	123.103i	−1.62606	+	0.528340i	−0.652703	+	0.757614i	$0.726365\pi$
$234$	87.9971	+	80.2943i	0.376056	+	0.343138i
$235$	94.8115	−	68.8846i	0.403453	−	0.293126i
$236$	62.5125	+	20.3115i	0.264883	+	0.0860658i
$237$	−324.037	+	142.987i	−1.36724	+	0.603320i
$238$	42.9787	−	31.2259i	0.180583	−	0.131201i
$239$	−94.7567	+	130.421i	−0.396472	+	0.545696i	−0.959854	−	0.280500i	$-0.909500\pi$
$239$	−94.7567	+	130.421i	−0.396472	+	0.545696i	0.563382	+	0.826196i	$0.309500\pi$
$240$	−85.8060	−	49.9196i	−0.357525	−	0.207998i
$241$	−159.644			−0.662425			−0.331212	−	0.943556i	$-0.607458\pi$
$241$	−159.644			−0.662425			−0.331212	+	0.943556i	$0.607458\pi$
$242$		0			0
$243$	118.000	+	212.426i	0.485597	+	0.874183i
$244$	−86.5623	−	266.411i	−0.354764	−	1.09185i
$245$	−114.347	+	157.384i	−0.466720	+	0.642386i
$246$	16.4117	+	3.54524i	0.0667142	+	0.0144115i
$247$	−37.3212	+	114.863i	−0.151098	+	0.465032i
$248$	41.2867	+	13.4149i	0.166479	+	0.0540922i
$249$	70.4300	−	326.036i	0.282851	−	1.30938i
$250$	33.2041	+	24.1242i	0.132817	+	0.0964969i
$251$	−46.4601	+	15.0958i	−0.185100	+	0.0601426i	−0.400100	−	0.916471i	$-0.631025\pi$
$251$	−46.4601	+	15.0958i	−0.185100	+	0.0601426i	0.215000	+	0.976614i	$0.431025\pi$
$252$	26.5623	−	237.580i	0.105406	−	0.942780i
$253$		0			0
$254$		−	101.416i		−	0.399277i
$255$	59.9035	−	102.967i	0.234916	−	0.403793i
$256$	138.342	+	100.511i	0.540398	+	0.392622i
$257$	−94.4196	−	129.957i	−0.367391	−	0.505671i	0.584798	−	0.811179i	$-0.301174\pi$
$257$	−94.4196	−	129.957i	−0.367391	−	0.505671i	−0.952190	+	0.305508i	$0.901174\pi$
$258$	−31.8428	−	72.1621i	−0.123422	−	0.279698i
$259$	53.6180	−	165.019i	0.207019	−	0.637140i
$260$	−154.464	−	212.602i	−0.594093	−	0.817699i
$261$	175.482	+	160.121i	0.672346	+	0.613492i
$262$	−40.4787	−	124.581i	−0.154499	−	0.475499i
$263$		−	140.420i		−	0.533914i	−0.963708	−	0.266957i	$-0.913982\pi$
$263$		−	140.420i		−	0.533914i	0.963708	−	0.266957i	$-0.0860183\pi$
$264$		0			0
$265$	147.387			0.556177
$266$	−76.8361	+	24.9656i	−0.288857	+	0.0938555i
$267$	291.492	−	29.6617i	1.09173	−	0.111092i
$268$	186.374	−	135.409i	0.695425	−	0.505256i
$269$	−393.494	−	127.854i	−1.46280	−	0.475294i	−0.533879	−	0.845561i	$-0.679266\pi$
$269$	−393.494	−	127.854i	−1.46280	−	0.475294i	−0.928925	+	0.370267i	$0.879266\pi$
$270$	53.5268	+	170.481i	0.198247	+	0.631413i
$271$	−46.7426	+	33.9605i	−0.172482	+	0.125316i	−0.670677	−	0.741749i	$-0.733996\pi$
$271$	−46.7426	+	33.9605i	−0.172482	+	0.125316i	0.498195	+	0.867065i	$0.333996\pi$
$272$	17.6336	−	24.2705i	0.0648293	−	0.0892298i
$273$	176.797	−	303.894i	0.647609	−	1.11316i
$274$	208.748			0.761853
$275$		0			0
$276$	−117.580	+	105.167i	−0.426016	+	0.381041i
$277$	−101.708	−	313.026i	−0.367178	−	1.13006i	−0.948606	−	0.316459i	$-0.897506\pi$
$277$	−101.708	−	313.026i	−0.367178	−	1.13006i	0.581429	−	0.813597i	$-0.302494\pi$
$278$	47.9518	−	66.0000i	0.172489	−	0.237410i
$279$	27.5867	+	48.5206i	0.0988769	+	0.173909i
$280$	126.752	−	390.102i	0.452685	−	1.39322i
$281$	375.820	+	122.111i	1.33744	+	0.434560i	0.888449	−	0.458976i	$-0.151784\pi$
$281$	375.820	+	122.111i	1.33744	+	0.434560i	0.448991	+	0.893536i	$0.351784\pi$
$282$	−51.9269	−	11.2172i	−0.184138	−	0.0397773i
$283$	−232.254	−	168.743i	−0.820686	−	0.596264i	0.0962226	−	0.995360i	$-0.469324\pi$
$283$	−232.254	−	168.743i	−0.820686	−	0.596264i	−0.916909	+	0.399096i	$0.869324\pi$
$284$	187.795	−	61.0182i	0.661249	−	0.214853i
$285$	−135.029	+	120.774i	−0.473787	+	0.423768i
$286$		0			0
$287$		−	49.5542i		−	0.172663i
$288$	59.8249	+	290.912i	0.207725	+	1.01011i
$289$	−204.681	−	148.710i	−0.708240	−	0.514566i
$290$	102.677	+	141.322i	0.354057	+	0.487318i
$291$	332.613	−	146.771i	1.14300	−	0.504369i
$292$	13.9255	−	42.8583i	0.0476901	−	0.146775i
$293$	−42.1829	−	58.0598i	−0.143969	−	0.198156i	0.730943	−	0.682439i	$-0.239081\pi$
$293$	−42.1829	−	58.0598i	−0.143969	−	0.198156i	−0.874912	+	0.484283i	$0.839081\pi$
$294$	87.7323	−	8.92748i	0.298409	−	0.0303656i
$295$	44.8075	+	137.903i	0.151890	+	0.467468i
$296$			137.177i			0.463437i
$297$		0			0
$298$	6.99187			0.0234626
$299$	−220.645	+	71.6919i	−0.737944	+	0.239772i
$300$	−17.1275	−	168.316i	−0.0570918	−	0.561054i
$301$	−188.331	+	136.831i	−0.625685	+	0.454587i
$302$	52.7369	+	17.1353i	0.174625	+	0.0567393i
$303$	224.772	+	509.378i	0.741822	+	1.68111i
$304$	−36.9098	+	26.8166i	−0.121414	+	0.0882124i
$305$	363.223	−	499.933i	1.19089	−	1.63912i
$306$	−52.8932	+	10.8773i	−0.172853	+	0.0355466i
$307$	116.961			0.380979			0.190489	−	0.981689i	$-0.438992\pi$
$307$	116.961			0.380979			0.190489	+	0.981689i	$0.438992\pi$
$308$		0			0
$309$	−345.177	−	385.920i	−1.11708	−	1.24893i
$310$	12.6829	+	39.0338i	0.0409124	+	0.125916i
$311$	−107.648	+	148.164i	−0.346133	+	0.476412i	−0.946220	−	0.323523i	$-0.895133\pi$
$311$	−107.648	+	148.164i	−0.346133	+	0.476412i	0.600087	+	0.799935i	$0.295133\pi$
$312$	−58.6904	+	271.691i	−0.188110	+	0.870803i
$313$	−23.1089	+	71.1220i	−0.0738305	+	0.227227i	−0.981161	−	0.193191i	$-0.938116\pi$
$313$	−23.1089	+	71.1220i	−0.0738305	+	0.227227i	0.907331	+	0.420418i	$0.138116\pi$
$314$	−39.9444	−	12.9787i	−0.127211	−	0.0413335i
$315$	458.452	−	260.656i	1.45540	−	0.827478i
$316$	−286.539	−	208.183i	−0.906770	−	0.658807i
$317$	−16.8069	+	5.46090i	−0.0530187	+	0.0172268i	−0.335406	−	0.942074i	$-0.608874\pi$
$317$	−16.8069	+	5.46090i	−0.0530187	+	0.0172268i	0.282388	+	0.959300i	$0.408874\pi$
$318$	−44.5410	−	49.7984i	−0.140066	−	0.156599i
$319$		0			0
$320$			86.0344i			0.268858i
$321$	−170.579	−	99.2384i	−0.531400	−	0.309154i
$322$	−125.554	−	91.2204i	−0.389920	−	0.283293i
$323$	−32.1799	−	44.2918i	−0.0996281	−	0.137126i
$324$	−124.276	+	208.817i	−0.383568	+	0.644496i
$325$	76.8885	−	236.639i	0.236580	−	0.728119i
$326$	−93.3346	−	128.464i	−0.286302	−	0.394061i
$327$	−32.5972	−	320.340i	−0.0996855	−	0.979632i
$328$	12.1064	+	37.2598i	0.0369099	+	0.113597i
$329$			156.790i			0.476566i
$330$		0			0
$331$	−395.580			−1.19511			−0.597554	−	0.801829i	$-0.703860\pi$
$331$	−395.580			−1.19511			−0.597554	+	0.801829i	$0.703860\pi$
$332$	317.231	−	103.075i	0.955514	−	0.310465i
$333$	−118.880	+	130.285i	−0.356998	+	0.391245i
$334$	230.713	−	167.623i	0.690758	−	0.501865i
$335$	483.327	+	157.043i	1.44277	+	0.468784i
$336$	121.508	−	53.6173i	0.361630	−	0.159575i
$337$	−404.753	+	294.070i	−1.20105	+	0.872611i	−0.994387	−	0.105802i	$-0.966259\pi$
$337$	−404.753	+	294.070i	−1.20105	+	0.872611i	−0.206659	+	0.978413i	$0.566259\pi$
$338$	−3.64045	+	5.01064i	−0.0107705	+	0.0148244i
$339$	−82.1120	−	47.7706i	−0.242218	−	0.140916i
$340$	119.125			0.350367
$341$		0			0
$342$	81.6130	+	9.12461i	0.238635	+	0.0266802i
$343$	53.6403	+	165.088i	0.156386	+	0.481306i
$344$	108.178	−	148.894i	0.314470	−	0.432830i
$345$	−340.154	−	73.4798i	−0.985954	−	0.212985i
$346$	−18.4787	+	56.8716i	−0.0534067	+	0.164369i
$347$	−586.779	−	190.656i	−1.69100	−	0.549441i	−0.704010	−	0.710190i	$-0.748609\pi$
$347$	−586.779	−	190.656i	−1.69100	−	0.549441i	−0.986995	+	0.160750i	$0.948609\pi$
$348$	−50.1597	+	232.200i	−0.144137	+	0.667242i
$349$	250.957	+	182.331i	0.719076	+	0.522439i	0.886089	−	0.463516i	$-0.153412\pi$
$349$	250.957	+	182.331i	0.719076	+	0.522439i	−0.167013	+	0.985955i	$0.553412\pi$
$350$	158.296	−	51.4336i	0.452276	−	0.146953i
$351$	−291.193	+	207.177i	−0.829611	+	0.590249i
$352$		0			0
$353$			308.577i			0.874157i	0.899423	+	0.437078i	$0.143987\pi$
$353$			308.577i			0.874157i	−0.899423	+	0.437078i	$0.856013\pi$
$354$	33.0530	−	56.8143i	0.0933701	−	0.160492i
$355$	352.405	+	256.037i	0.992691	+	0.721232i
$356$	172.219	+	237.039i	0.483762	+	0.665841i
$357$	64.3408	+	145.809i	0.180226	+	0.408429i
$358$	81.5304	−	250.925i	0.227738	−	0.700907i
$359$	80.4033	+	110.666i	0.223965	+	0.308261i	0.906181	−	0.422889i	$-0.138984\pi$
$359$	80.4033	+	110.666i	0.223965	+	0.308261i	−0.682217	+	0.731150i	$0.738984\pi$
$360$	−281.030	+	307.990i	−0.780639	+	0.855528i
$361$	−85.8268	−	264.148i	−0.237747	−	0.731711i
$362$		−	225.967i		−	0.624220i
$363$		0			0
$364$	351.580			0.965880
$365$	94.5458	−	30.7198i	0.259030	−	0.0841639i
$366$	−278.682	+	28.3582i	−0.761427	+	0.0774815i
$367$	101.956	−	74.0753i	0.277809	−	0.201840i	−0.440152	−	0.897923i	$-0.645076\pi$
$367$	101.956	−	74.0753i	0.277809	−	0.201840i	0.717961	+	0.696083i	$0.245076\pi$
$368$	−83.3499	−	27.0820i	−0.226494	−	0.0735925i
$369$	−20.7919	+	45.8793i	−0.0563465	+	0.124334i
$370$	−104.923	+	76.2310i	−0.283576	+	0.206030i
$371$	−115.903	+	159.526i	−0.312406	+	0.429990i
$372$	−28.0672	+	48.2442i	−0.0754494	+	0.129689i
$373$	347.528			0.931710			0.465855	−	0.884861i	$-0.345747\pi$
$373$	347.528			0.931710			0.465855	+	0.884861i	$0.345747\pi$
$374$		0			0
$375$	−91.7740	+	82.0851i	−0.244731	+	0.218894i
$376$	−38.3050	−	117.891i	−0.101875	−	0.313539i
$377$	−205.353	+	282.644i	−0.544703	+	0.749720i
$378$	−226.615	−	76.1283i	−0.599512	−	0.201398i
$379$	−146.584	+	451.138i	−0.386764	+	1.19034i	0.548428	+	0.836198i	$0.315226\pi$
$379$	−146.584	+	451.138i	−0.386764	+	1.19034i	−0.935192	+	0.354140i	$0.884774\pi$
$380$	−172.294	−	55.9818i	−0.453406	−	0.147321i
$381$	297.390	+	64.2419i	0.780550	+	0.168614i
$382$	−48.6099	−	35.3172i	−0.127251	−	0.0924533i
$383$	278.142	−	90.3738i	0.726219	−	0.235963i	0.0775019	−	0.996992i	$-0.475306\pi$
$383$	278.142	−	90.3738i	0.726219	−	0.235963i	0.648718	+	0.761029i	$0.275306\pi$
$384$	−266.092	+	238.000i	−0.692948	+	0.619792i
$385$		0			0
$386$		−	35.6869i		−	0.0924532i
$387$	231.776	−	47.6638i	0.598904	−	0.123162i
$388$	294.123	+	213.693i	0.758049	+	0.550755i
$389$	−46.1712	−	63.5492i	−0.118692	−	0.163365i	0.745537	−	0.666464i	$-0.232193\pi$
$389$	−46.1712	−	63.5492i	−0.118692	−	0.163365i	−0.864229	+	0.503099i	$0.832193\pi$
$390$	−240.423	+	106.091i	−0.616470	+	0.272028i
$391$	32.4984	−	100.020i	0.0831162	−	0.255805i
$392$	120.946	+	166.468i	0.308536	+	0.424663i
$393$	390.957	−	39.7830i	0.994801	−	0.101229i
$394$	44.9944	+	138.478i	0.114199	+	0.351468i
$395$		−	781.330i		−	1.97805i
$396$		0			0
$397$	166.741			0.420004			0.210002	−	0.977701i	$-0.432653\pi$
$397$	166.741			0.420004			0.210002	+	0.977701i	$0.432653\pi$
$398$	229.381	−	74.5304i	0.576334	−	0.187262i
$399$	−24.5365	−	241.126i	−0.0614950	−	0.604325i
$400$	76.0410	−	55.2470i	0.190103	−	0.138118i
$401$	−187.280	−	60.8510i	−0.467033	−	0.151748i	0.0660410	−	0.997817i	$-0.478963\pi$
$401$	−187.280	−	60.8510i	−0.467033	−	0.151748i	−0.533074	+	0.846069i	$0.678963\pi$
$402$	−93.0030	−	210.763i	−0.231351	−	0.524287i
$403$	−66.4083	+	48.2484i	−0.164785	+	0.119723i
$404$	−327.259	+	450.433i	−0.810046	+	1.11493i
$405$	−533.819	+	48.9690i	−1.31807	+	0.120911i
$406$	−233.705			−0.575628
$407$		0			0
$408$	−84.0000	−	93.9149i	−0.205882	−	0.230183i
$409$	222.747	+	685.545i	0.544614	+	1.67615i	0.721906	+	0.691991i	$0.243266\pi$
$409$	222.747	+	685.545i	0.544614	+	1.67615i	−0.177292	+	0.984158i	$0.556734\pi$
$410$	−21.7713	+	29.9656i	−0.0531006	+	0.0730867i
$411$	−132.230	+	612.124i	−0.321729	+	1.48935i
$412$	159.998	−	492.425i	0.388346	−	1.19521i
$413$	−184.497	−	59.9468i	−0.446725	−	0.145150i
$414$	77.9691	+	137.135i	0.188331	+	0.331245i
$415$	595.298	+	432.509i	1.43445	+	1.04219i
$416$	−415.412	+	134.976i	−0.998587	+	0.324461i
$417$	163.161	+	182.420i	0.391273	+	0.437457i
$418$		0			0
$419$		−	267.408i		−	0.638206i	−0.947720	−	0.319103i	$-0.896618\pi$
$419$		−	267.408i		−	0.638206i	0.947720	−	0.319103i	$-0.103382\pi$
$420$	455.841	+	265.196i	1.08534	+	0.631419i
$421$	−554.959	−	403.202i	−1.31819	−	0.957723i	−0.999953	−	0.00971339i	$-0.996908\pi$
$421$	−554.959	−	403.202i	−1.31819	−	0.957723i	−0.318240	−	0.948010i	$-0.603092\pi$
$422$	25.1205	+	34.5755i	0.0595274	+	0.0819324i
$423$	65.7858	−	145.163i	0.155522	−	0.343175i
$424$	48.1738	−	148.264i	0.113617	−	0.349678i
$425$	66.2964	+	91.2492i	0.155992	+	0.214704i
$426$	−19.9898	−	196.445i	−0.0469245	−	0.461137i
$427$	255.477	+	786.278i	0.598307	+	1.84140i
$428$		−	197.346i		−	0.461090i
$429$		0			0
$430$	174.000			0.404651
$431$	525.351	−	170.697i	1.21891	−	0.396049i	0.372227	−	0.928142i	$-0.378594\pi$
$431$	525.351	−	170.697i	1.21891	−	0.396049i	0.846686	+	0.532093i	$0.178594\pi$
$432$	−134.993	−	1.34078i	−0.312485	−	0.00310366i
$433$	230.263	−	167.296i	0.531786	−	0.386365i	−0.289239	−	0.957257i	$-0.593402\pi$
$433$	230.263	−	167.296i	0.531786	−	0.386365i	0.821025	+	0.570892i	$0.193402\pi$
$434$	−52.2224	−	16.9681i	−0.120328	−	0.0390969i
$435$	−479.448	+	211.565i	−1.10218	+	0.486356i
$436$	260.498	−	189.263i	0.597474	−	0.434090i
$437$	−94.0074	+	129.390i	−0.215120	+	0.296087i
$438$	−38.9516	−	22.6610i	−0.0889307	−	0.0517375i
$439$	532.058			1.21198			0.605988	−	0.795474i	$-0.292778\pi$
$439$	532.058			1.21198			0.605988	+	0.795474i	$0.292778\pi$
$440$		0			0
$441$	−29.3951	+	262.918i	−0.0666556	+	0.596186i
$442$	−24.5410	−	75.5295i	−0.0555227	−	0.170881i
$443$	70.7087	−	97.3222i	0.159613	−	0.219689i	−0.721719	−	0.692187i	$-0.756648\pi$
$443$	70.7087	−	97.3222i	0.159613	−	0.219689i	0.881332	+	0.472498i	$0.156648\pi$
$444$	−172.394	−	37.2405i	−0.388275	−	0.0838749i
$445$	−199.735	+	614.720i	−0.448842	+	1.38139i
$446$	157.868	+	51.2943i	0.353963	+	0.115010i
$447$	−4.42898	+	20.5027i	−0.00990822	+	0.0458673i
$448$	−93.1205	−	67.6560i	−0.207858	−	0.151018i
$449$	−65.3078	+	21.2198i	−0.145452	+	0.0472601i	−0.380838	−	0.924642i	$-0.624364\pi$
$449$	−65.3078	+	21.2198i	−0.145452	+	0.0472601i	0.235386	+	0.971902i	$0.424364\pi$
$450$	−168.138	−	18.7984i	−0.373639	−	0.0417742i
$451$		0			0
$452$		−	94.9969i		−	0.210170i
$453$	−83.6528	+	143.789i	−0.184664	+	0.317416i
$454$	276.338	+	200.771i	0.608674	+	0.442227i
$455$	455.881	+	627.466i	1.00194	+	1.37905i
$456$	77.3576	+	175.308i	0.169644	+	0.384447i
$457$	214.924	−	661.467i	0.470292	−	1.44741i	−0.381911	−	0.924199i	$-0.624734\pi$
$457$	214.924	−	661.467i	0.470292	−	1.44741i	0.852203	−	0.523212i	$-0.175266\pi$
$458$	145.050	+	199.644i	0.316703	+	0.435905i
$459$	1.60894	−	161.992i	0.00350531	−	0.352924i
$460$	−107.538	−	330.968i	−0.233778	−	0.719495i
$461$			824.322i			1.78812i	0.447950	+	0.894059i	$0.352154\pi$
$461$			824.322i			1.78812i	−0.447950	+	0.894059i	$0.647846\pi$
$462$		0			0
$463$	−158.137			−0.341548			−0.170774	−	0.985310i	$-0.554627\pi$
$463$	−158.137			−0.341548			−0.170774	+	0.985310i	$0.554627\pi$
$464$	−125.516	+	40.7827i	−0.270509	+	0.0878938i
$465$	−122.495	+	12.4649i	−0.263430	+	0.0268062i
$466$	−322.289	+	234.156i	−0.691607	+	0.502482i
$467$	725.951	+	235.876i	1.55450	+	0.505087i	0.955331	−	0.295537i	$-0.0954984\pi$
$467$	725.951	+	235.876i	1.55450	+	0.505087i	0.599167	+	0.800624i	$0.295498\pi$
$468$	−325.508	−	147.516i	−0.695529	−	0.315204i
$469$	−550.058	+	399.640i	−1.17283	+	0.852111i
$470$	68.8846	−	94.8115i	0.146563	−	0.201727i
$471$	63.3609	−	108.910i	0.134524	−	0.231231i
$472$	153.369			0.324934
$473$		0			0
$474$	−263.992	+	236.122i	−0.556945	+	0.498147i
$475$	−53.0050	−	163.133i	−0.111590	−	0.343437i
$476$	−93.6776	+	128.936i	−0.196802	+	0.270874i
$477$	174.241	−	99.0658i	0.365286	−	0.207685i
$478$	−49.8166	+	153.320i	−0.104219	+	0.320752i
$479$	71.1607	+	23.1215i	0.148561	+	0.0482704i	0.382353	−	0.924016i	$-0.375114\pi$
$479$	71.1607	+	23.1215i	0.148561	+	0.0482704i	−0.233793	+	0.972286i	$0.575114\pi$
$480$	−640.414	−	138.342i	−1.33419	−	0.288212i
$481$	−209.846	−	152.462i	−0.436270	−	0.316969i
$482$	−151.831	+	49.3328i	−0.315002	+	0.102350i
$483$	347.023	−	310.387i	0.718475	−	0.642623i
$484$		0			0
$485$			802.009i			1.65363i
$486$	177.868	+	165.566i	0.365984	+	0.340670i
$487$	−245.112	−	178.085i	−0.503311	−	0.365677i	0.306969	−	0.951719i	$-0.400685\pi$
$487$	−245.112	−	178.085i	−0.503311	−	0.365677i	−0.810280	+	0.586043i	$0.800685\pi$
$488$	−384.186	−	528.787i	−0.787267	−	1.08358i
$489$	435.825	−	192.316i	0.891258	−	0.393284i
$490$	−60.1155	+	185.017i	−0.122685	+	0.377585i
$491$	−469.508	−	646.222i	−0.956227	−	1.31613i	−0.948705	−	0.316162i	$-0.897606\pi$
$491$	−469.508	−	646.222i	−0.956227	−	1.31613i	−0.00752206	−	0.999972i	$-0.502394\pi$
$492$	−50.1120	+	5.09930i	−0.101854	+	0.0103644i
$493$	−48.9392	−	150.620i	−0.0992682	−	0.305516i
$494$			120.774i			0.244482i
$495$		0			0
$496$	−31.0081			−0.0625164
$497$	−554.251	+	180.087i	−1.11519	+	0.362348i
$498$	−33.7677	−	331.842i	−0.0678066	−	0.666350i
$499$	−473.066	+	343.702i	−0.948028	+	0.688782i	−0.950340	−	0.311215i	$-0.899264\pi$
$499$	−473.066	+	343.702i	−0.948028	+	0.688782i	0.00231194	+	0.999997i	$0.499264\pi$
$500$	−117.101	−	38.0486i	−0.234203	−	0.0760971i
$501$	345.387	+	782.715i	0.689395	+	1.56231i
$502$	−39.5213	+	28.7139i	−0.0787277	+	0.0571990i
$503$	325.595	−	448.143i	0.647306	−	0.890940i	−0.351673	−	0.936123i	$-0.614387\pi$
$503$	325.595	−	448.143i	0.647306	−	0.890940i	0.998979	+	0.0451830i	$0.0143871\pi$
$504$	−112.360	−	546.375i	−0.222936	−	1.08408i
$505$	−1228.23			−2.43214
$506$		0			0
$507$	−12.3870	−	13.8491i	−0.0244319	−	0.0273157i
$508$	94.0182	+	289.358i	0.185075	+	0.569603i
$509$	−50.4847	+	69.4863i	−0.0991841	+	0.136515i	−0.855724	−	0.517432i	$-0.826888\pi$
$509$	−50.4847	+	69.4863i	−0.0991841	+	0.136515i	0.756540	+	0.653947i	$0.226888\pi$
$510$	25.1530	−	116.439i	0.0493197	−	0.228311i
$511$	−41.0993	+	126.491i	−0.0804291	+	0.247535i
$512$	−290.072	−	94.2502i	−0.566547	−	0.184082i
$513$	−78.4541	+	233.539i	−0.152932	+	0.455242i
$514$	−129.957	−	94.4196i	−0.252835	−	0.183696i
$515$	1086.29	−	352.958i	2.10931	−	0.685356i
$516$	157.751	+	176.371i	0.305719	+	0.341804i
$517$		0			0
$518$		−	173.512i		−	0.334964i
$519$	−155.063	−	90.2114i	−0.298772	−	0.173818i
$520$	−496.071	−	360.417i	−0.953982	−	0.693109i
$521$	431.206	+	593.503i	0.827650	+	1.13916i	0.988356	+	0.152160i	$0.0486229\pi$
$521$	431.206	+	593.503i	0.827650	+	1.13916i	−0.160706	+	0.987002i	$0.551377\pi$
$522$	216.374	+	98.0576i	0.414509	+	0.187850i
$523$	−93.0151	+	286.271i	−0.177849	+	0.547363i	−0.999752	−	0.0222642i	$-0.992912\pi$
$523$	−93.0151	+	286.271i	−0.177849	+	0.547363i	0.821903	+	0.569627i	$0.192912\pi$
$524$	230.985	+	317.924i	0.440812	+	0.606725i
$525$	50.5497	+	496.763i	0.0962851	+	0.946215i
$526$	−43.3920	−	133.547i	−0.0824943	−	0.253891i
$527$		−	37.2098i		−	0.0706067i
$528$		0			0
$529$	221.774			0.419232
$530$	140.173	−	45.5451i	0.264478	−	0.0859341i
$531$	145.663	+	132.912i	0.274318	+	0.250305i
$532$	196.082	−	142.462i	0.368575	−	0.267786i
$533$	−70.4533	−	22.8916i	−0.132182	−	0.0429487i
$534$	268.059	−	118.286i	0.501983	−	0.221509i
$535$	352.204	−	255.891i	0.658325	−	0.478301i
$536$	315.953	−	434.872i	0.589465	−	0.811329i
$537$	684.157	+	398.024i	1.27404	+	0.741199i
$538$	−413.745			−0.769042
$539$		0			0
$540$	−310.766	−	436.790i	−0.575492	−	0.808871i
$541$	−117.991	−	363.138i	−0.218097	−	0.671235i	−0.998919	−	0.0464809i	$-0.985199\pi$
$541$	−117.991	−	363.138i	−0.218097	−	0.671235i	0.780822	−	0.624754i	$-0.214801\pi$
$542$	−33.9605	+	46.7426i	−0.0626578	+	0.0862410i
$543$	662.618	+	143.138i	1.22029	+	0.263606i
$544$	61.1854	−	188.309i	0.112473	−	0.346157i
$545$	675.556	+	219.502i	1.23955	+	0.402755i
$546$	74.2358	−	343.654i	0.135963	−	0.629402i
$547$	150.498	+	109.344i	0.275134	+	0.199897i	0.716792	−	0.697287i	$-0.245610\pi$
$547$	150.498	+	109.344i	0.275134	+	0.199897i	−0.441658	+	0.897183i	$0.645610\pi$
$548$	−595.592	+	193.520i	−1.08685	+	0.353138i
$549$	93.3738	−	835.161i	0.170080	−	1.52124i
$550$		0			0
$551$			240.845i			0.437106i
$552$	−185.097	+	318.160i	−0.335320	+	0.576377i
$553$	845.683	+	614.425i	1.52926	+	1.11108i
$554$	−193.461	−	266.276i	−0.349207	−	0.480642i
$555$	−157.074	−	355.960i	−0.283016	−	0.641370i
$556$	−75.6293	+	232.763i	−0.136024	+	0.418638i
$557$	256.630	+	353.221i	0.460736	+	0.634149i	0.974661	−	0.223686i	$-0.0718091\pi$
$557$	256.630	+	353.221i	0.460736	+	0.634149i	−0.513925	+	0.857835i	$0.671809\pi$
$558$	41.2302	+	37.6211i	0.0738892	+	0.0674213i
$559$	107.538	+	330.968i	0.192376	+	0.592071i
$560$			292.984i			0.523185i
$561$		0			0
$562$	395.161			0.703133
$563$	−235.525	+	76.5267i	−0.418339	+	0.135927i	−0.510620	−	0.859806i	$-0.670584\pi$
$563$	−235.525	+	76.5267i	−0.418339	+	0.135927i	0.0922811	+	0.995733i	$0.470584\pi$
$564$	158.555	−	16.1343i	0.281126	−	0.0286069i
$565$	169.541	−	123.179i	0.300073	−	0.218016i
$566$	−273.031	−	88.7132i	−0.482387	−	0.156737i
$567$	366.784	−	616.295i	0.646886	−	1.08694i
$568$	372.745	−	270.815i	0.656240	−	0.476787i
$569$	163.177	−	224.594i	0.286778	−	0.394716i	−0.641186	−	0.767385i	$-0.721557\pi$
$569$	163.177	−	224.594i	0.286778	−	0.394716i	0.927964	+	0.372669i	$0.121557\pi$
$570$	−91.0994	+	156.589i	−0.159823	+	0.274718i
$571$	1010.88			1.77037			0.885187	−	0.465236i	$-0.154031\pi$
$571$	1010.88			1.77037			0.885187	+	0.465236i	$0.154031\pi$
$572$		0			0
$573$	134.354	−	120.170i	0.234476	−	0.209721i
$574$	−15.3131	−	47.1288i	−0.0266778	−	0.0821060i
$575$	193.673	−	266.567i	0.336822	−	0.463595i
$576$	57.8278	+	101.710i	0.100396	+	0.176580i
$577$	80.4017	−	247.451i	0.139344	−	0.428858i	−0.856896	−	0.515489i	$-0.827610\pi$
$577$	80.4017	−	247.451i	0.139344	−	0.428858i	0.996240	+	0.0866313i	$0.0276102\pi$
$578$	−240.617	−	78.1813i	−0.416293	−	0.135262i
$579$	104.647	+	22.6058i	0.180737	+	0.0390428i
$580$	−423.967	−	308.030i	−0.730977	−	0.531086i
$581$	−936.264	+	304.211i	−1.61147	+	0.523598i
$582$	270.979	−	242.371i	0.465599	−	0.416445i
$583$		0			0
$584$		−	105.149i		−	0.180050i
$585$	−158.802	−	772.211i	−0.271456	−	1.32002i
$586$	−58.0598	−	42.1829i	−0.0990781	−	0.0719845i
$587$	−592.051	−	814.889i	−1.00861	−	1.38823i	−0.919893	−	0.392169i	$-0.871725\pi$
$587$	−592.051	−	814.889i	−1.00861	−	1.38823i	−0.0887124	−	0.996057i	$-0.528275\pi$
$588$	−242.039	+	106.804i	−0.411631	+	0.181639i
$589$	−17.4865	+	53.8178i	−0.0296884	+	0.0913716i
$590$	85.2289	+	117.307i	0.144456	+	0.198826i
$591$	−434.570	+	44.2211i	−0.735314	+	0.0748242i
$592$	−30.2786	−	93.1881i	−0.0511464	−	0.157412i
$593$			13.9837i			0.0235813i	0.999930	+	0.0117907i	$0.00375317\pi$
$593$			13.9837i			0.0235813i	−0.999930	+	0.0117907i	$0.996247\pi$
$594$		0			0
$595$	−351.580			−0.590892
$596$	−19.9490	+	6.48182i	−0.0334715	+	0.0108755i
$597$	73.2495	+	719.839i	0.122696	+	1.20576i
$598$	−187.692	+	136.366i	−0.313866	+	0.228037i
$599$	−164.882	−	53.5735i	−0.275263	−	0.0894383i	0.168133	−	0.985764i	$-0.446226\pi$
$599$	−164.882	−	53.5735i	−0.275263	−	0.0894383i	−0.443396	+	0.896326i	$0.646226\pi$
$600$	−159.371	−	361.166i	−0.265618	−	0.601944i
$601$	635.183	−	461.488i	1.05688	−	0.767866i	0.0833691	−	0.996519i	$-0.473432\pi$
$601$	635.183	−	461.488i	1.05688	−	0.767866i	0.973508	+	0.228652i	$0.0734319\pi$
$602$	−136.831	+	188.331i	−0.227293	+	0.312843i
$603$	676.946	−	139.211i	1.12263	−	0.230864i
$604$	−166.353			−0.275418
$605$		0			0
$606$	371.177	+	414.989i	0.612504	+	0.684800i
$607$	4.12343	+	12.6906i	0.00679312	+	0.0209071i	0.954396	−	0.298545i	$-0.0965012\pi$
$607$	4.12343	+	12.6906i	0.00679312	+	0.0209071i	−0.947603	+	0.319452i	$0.896501\pi$
$608$	−176.989	+	243.605i	−0.291101	+	0.400666i
$609$	148.040	−	685.308i	0.243086	−	1.12530i
$610$	190.957	−	587.707i	0.313045	−	0.963453i
$611$	222.915	+	72.4296i	0.364837	+	0.118543i
$612$	140.829	−	80.0693i	0.230113	−	0.130832i
$613$	504.890	+	366.824i	0.823639	+	0.598408i	0.917752	−	0.397153i	$-0.130002\pi$
$613$	504.890	+	366.824i	0.823639	+	0.598408i	−0.0941138	+	0.995561i	$0.530002\pi$
$614$	111.236	−	36.1428i	0.181166	−	0.0588645i
$615$	−74.0789	−	82.8228i	−0.120454	−	0.134671i
$616$		0			0
$617$		−	1103.25i		−	1.78808i	−0.447986	−	0.894041i	$-0.647859\pi$
$617$		−	1103.25i		−	1.78808i	0.447986	−	0.894041i	$-0.352141\pi$
$618$	−447.539	−	260.366i	−0.724173	−	0.421304i
$619$	148.220	+	107.688i	0.239450	+	0.173971i	0.701038	−	0.713124i	$-0.252720\pi$
$619$	148.220	+	107.688i	0.239450	+	0.173971i	−0.461588	+	0.887094i	$0.652720\pi$
$620$	−72.3727	−	99.6124i	−0.116730	−	0.160665i
$621$	−451.520	+	141.766i	−0.727085	+	0.228286i
$622$	−56.5936	+	174.177i	−0.0909866	+	0.280028i
$623$	−508.282	−	699.591i	−0.815862	−	1.12294i
$624$	−20.0994	−	197.521i	−0.0322105	−	0.316540i
$625$	−229.161	−	705.285i	−0.366658	−	1.12846i
$626$			74.7821i			0.119460i
$627$		0			0
$628$	126.000			0.200637
$629$	111.826	−	36.3344i	0.177783	−	0.0577653i
$630$	355.467	−	389.568i	0.564233	−	0.618362i
$631$	−225.579	+	163.893i	−0.357494	+	0.259735i	−0.752006	−	0.659156i	$-0.770914\pi$
$631$	−225.579	+	163.893i	−0.357494	+	0.259735i	0.394512	+	0.918891i	$0.370914\pi$
$632$	−785.977	−	255.379i	−1.24363	−	0.404081i
$633$	−117.300	+	51.7608i	−0.185309	+	0.0817706i
$634$	−14.2968	+	10.3872i	−0.0225502	+	0.0163837i
$635$	−394.508	+	542.994i	−0.621273	+	0.855108i
$636$	173.249	+	100.791i	0.272404	+	0.158477i
$637$	−389.076			−0.610794
$638$		0			0
$639$	588.709	+	65.8197i	0.921297	+	0.103004i
$640$	−243.365	−	749.001i	−0.380258	−	1.17031i
$641$	403.414	−	555.251i	0.629350	−	0.866226i	−0.368641	−	0.929572i	$-0.620177\pi$
$641$	403.414	−	555.251i	0.629350	−	0.866226i	0.997992	+	0.0633453i	$0.0201769\pi$
$642$	−192.897	−	41.6694i	−0.300463	−	0.0649057i
$643$	−41.7670	+	128.546i	−0.0649565	+	0.199916i	−0.978267	−	0.207348i	$-0.933517\pi$
$643$	−41.7670	+	128.546i	−0.0649565	+	0.199916i	0.913311	+	0.407263i	$0.133517\pi$
$644$	442.793	+	143.872i	0.687567	+	0.223404i
$645$	−110.220	+	510.231i	−0.170883	+	0.791056i
$646$	−44.2918	−	32.1799i	−0.0685632	−	0.0498140i
$647$	87.3625	−	28.3858i	0.135027	−	0.0438730i	−0.240724	−	0.970594i	$-0.577385\pi$
$647$	87.3625	−	28.3858i	0.135027	−	0.0438730i	0.375751	+	0.926721i	$0.377385\pi$
$648$	−125.220	+	553.000i	−0.193240	+	0.853395i
$649$		0			0
$650$		−	248.817i		−	0.382795i
$651$	82.8366	−	142.386i	0.127245	−	0.218720i
$652$	385.392	+	280.004i	0.591092	+	0.429454i
$653$	−463.947	−	638.568i	−0.710485	−	0.977898i	−0.999787	−	0.0206605i	$-0.993423\pi$
$653$	−463.947	−	638.568i	−0.710485	−	0.977898i	0.289302	−	0.957238i	$-0.406577\pi$
$654$	−129.992	−	294.588i	−0.198765	−	0.450440i
$655$	−267.890	+	824.479i	−0.408992	+	1.25875i
$656$	−16.4484	−	22.6393i	−0.0250738	−	0.0345112i
$657$	91.1241	−	99.8658i	0.138697	−	0.152003i
$658$	48.4508	+	149.116i	0.0736335	+	0.226621i
$659$		−	4.76585i		−	0.00723194i	−0.999993	−	0.00361597i	$-0.998849\pi$
$659$		−	4.76585i		−	0.00723194i	0.999993	−	0.00361597i	$-0.00115100\pi$
$660$		0			0
$661$	−1267.85			−1.91808			−0.959042	−	0.283264i	$-0.908583\pi$
$661$	−1267.85			−1.91808			−0.959042	+	0.283264i	$0.908583\pi$
$662$	−376.219	+	122.241i	−0.568307	+	0.184654i
$663$	237.025	−	24.1193i	0.357504	−	0.0363790i
$664$	629.656	−	457.472i	0.948277	−	0.688964i
$665$	508.504	+	165.223i	0.764667	+	0.248456i
$666$	−72.8017	+	160.644i	−0.109312	+	0.241207i
$667$	−374.292	+	271.939i	−0.561157	+	0.407705i
$668$	−502.869	+	692.140i	−0.752798	+	1.03614i
$669$	−250.414	+	430.433i	−0.374311	+	0.643397i
$670$	508.200			0.758508
$671$		0			0
$672$	653.346	−	584.371i	0.972242	−	0.869599i
$673$	−56.6882	−	174.468i	−0.0842322	−	0.259240i	0.900066	−	0.435753i	$-0.143518\pi$
$673$	−56.6882	−	174.468i	−0.0842322	−	0.259240i	−0.984298	+	0.176514i	$0.943518\pi$
$674$	−294.070	+	404.753i	−0.436306	+	0.600523i
$675$	161.630	−	481.133i	0.239452	−	0.712790i
$676$	5.74169	−	17.6711i	0.00849362	−	0.0261407i
$677$	−144.690	−	47.0128i	−0.213723	−	0.0694428i	0.200199	−	0.979755i	$-0.435841\pi$
$677$	−144.690	−	47.0128i	−0.213723	−	0.0694428i	−0.413922	+	0.910313i	$0.635841\pi$
$678$	−92.8551	−	20.0585i	−0.136954	−	0.0295848i
$679$	−868.065	−	630.686i	−1.27845	−	0.928846i
$680$	264.353	−	85.8936i	0.388755	−	0.126314i
$681$	−763.779	+	683.145i	−1.12156	+	1.00315i
$682$		0			0
$683$		−	778.746i		−	1.14019i	−0.821580	−	0.570093i	$-0.806907\pi$
$683$		−	778.746i		−	1.14019i	0.821580	−	0.570093i	$-0.193093\pi$
$684$	−241.315	+	49.6254i	−0.352799	+	0.0725517i
$685$	−1117.66	−	812.025i	−1.63162	−	1.18544i
$686$	102.030	+	140.432i	0.148732	+	0.204711i
$687$	−677.311	+	298.875i	−0.985897	+	0.435044i
$688$	−40.6231	+	125.025i	−0.0590451	+	0.181722i
$689$	173.264	+	238.477i	0.251471	+	0.346121i
$690$	−346.212	+	35.2299i	−0.501757	+	0.0510579i
$691$	−139.925	−	430.645i	−0.202496	−	0.623219i	−0.999807	−	0.0196502i	$-0.993745\pi$
$691$	−139.925	−	430.645i	−0.202496	−	0.623219i	0.797311	−	0.603569i	$-0.206255\pi$
$692$		−	179.395i		−	0.259242i
$693$		0			0
$694$	−616.976			−0.889014
$695$	−513.478	+	166.839i	−0.738817	+	0.240056i
$696$	56.1145	+	551.450i	0.0806243	+	0.792313i
$697$	27.1672	−	19.7381i	0.0389773	−	0.0283187i
$698$	295.018	+	95.8572i	0.422662	+	0.137331i
$699$	−482.479	−	1093.39i	−0.690241	−	1.56422i
$700$	−403.965	+	293.498i	−0.577093	+	0.419282i
$701$	31.2472	−	43.0081i	0.0445752	−	0.0613525i	−0.786148	−	0.618039i	$-0.787927\pi$
$701$	31.2472	−	43.0081i	0.0445752	−	0.0613525i	0.830723	+	0.556686i	$0.187927\pi$
$702$	−212.920	+	287.021i	−0.303305	+	0.408862i
$703$	−178.813			−0.254357
$704$		0			0
$705$	234.387	+	262.053i	0.332464	+	0.371706i
$706$	95.3557	+	293.475i	0.135065	+	0.415686i
$707$	965.861	−	1329.39i	1.36614	−	1.88033i
$708$	−41.6361	+	192.743i	−0.0588081	+	0.272235i
$709$	333.942	−	1027.77i	0.471005	−	1.44960i	−0.380266	−	0.924877i	$-0.624168\pi$
$709$	333.942	−	1027.77i	0.471005	−	1.44960i	0.851271	−	0.524726i	$-0.175832\pi$
$710$	414.277	+	134.607i	0.583489	+	0.189587i
$711$	−525.169	−	923.690i	−0.738634	−	1.29914i
$712$	553.092	+	401.845i	0.776815	+	0.564389i
$713$	−103.381	+	33.5905i	−0.144994	+	0.0471116i
$714$	106.249	+	118.790i	0.148808	+	0.166373i
$715$		0			0
$716$			791.514i			1.10547i
$717$	−418.032	−	243.200i	−0.583030	−	0.339191i
$718$	110.666	+	80.4033i	0.154130	+	0.111982i
$719$	533.914	+	734.869i	0.742578	+	1.02207i	0.998466	+	0.0553647i	$0.0176322\pi$
$719$	533.914	+	734.869i	0.742578	+	1.02207i	−0.255888	+	0.966706i	$0.582368\pi$
$720$	122.930	−	271.256i	0.170736	−	0.376745i
$721$	−472.214	+	1453.33i	−0.654943	+	2.01571i
$722$	−163.252	−	224.698i	−0.226111	−	0.311215i
$723$	−48.4850	−	476.473i	−0.0670608	−	0.659021i
$724$	209.483	+	644.724i	0.289342	+	0.890502i
$725$		−	496.185i		−	0.684394i
$726$		0			0
$727$	−64.4195			−0.0886101			−0.0443050	−	0.999018i	$-0.514107\pi$
$727$	−64.4195			−0.0886101			−0.0443050	+	0.999018i	$0.514107\pi$
$728$	780.203	−	253.503i	1.07171	−	0.348219i
$729$	−598.168	+	416.697i	−0.820532	+	0.571600i
$730$	80.4255	−	58.4325i	0.110172	−	0.0800446i
$731$	−150.030	−	48.7477i	−0.205239	−	0.0666863i
$732$	768.839	−	339.264i	1.05033	−	0.463475i
$733$	857.620	−	623.097i	1.17001	−	0.850065i	0.179003	−	0.983849i	$-0.442713\pi$
$733$	857.620	−	623.097i	1.17001	−	0.850065i	0.991011	+	0.133784i	$0.0427128\pi$
$734$	74.0753	−	101.956i	0.100920	−	0.138904i
$735$	−504.455	−	293.479i	−0.686334	−	0.399291i
$736$	−578.420			−0.785896
$737$		0			0
$738$	−5.59675	+	50.0588i	−0.00758367	+	0.0678304i
$739$	49.4164	+	152.088i	0.0668693	+	0.205803i	0.978908	−	0.204302i	$-0.0654923\pi$
$739$	49.4164	+	152.088i	0.0668693	+	0.205803i	−0.912039	+	0.410104i	$0.865492\pi$
$740$	228.693	−	314.769i	0.309045	−	0.425363i
$741$	−354.153	−	76.5039i	−0.477939	−	0.103244i
$742$	−60.9336	+	187.534i	−0.0821208	+	0.252742i
$743$	60.0542	+	19.5128i	0.0808266	+	0.0262622i	0.349151	−	0.937066i	$-0.386470\pi$
$743$	60.0542	+	19.5128i	0.0808266	+	0.0262622i	−0.268325	+	0.963329i	$0.586470\pi$
$744$	−27.4988	+	127.298i	−0.0369607	+	0.171099i
$745$	−37.4352	−	27.1983i	−0.0502486	−	0.0365077i
$746$	330.519	−	107.392i	0.443054	−	0.143957i
$747$	994.472	+	111.185i	1.33129	+	0.148843i
$748$		0			0
$749$			582.442i			0.777626i
$750$	−61.9165	+	106.427i	−0.0825554	+	0.141903i
$751$	−132.939	−	96.5860i	−0.177016	−	0.128610i	0.495749	−	0.868466i	$-0.334894\pi$
$751$	−132.939	−	96.5860i	−0.177016	−	0.128610i	−0.672765	+	0.739856i	$0.734894\pi$
$752$	52.0431	+	71.6312i	0.0692063	+	0.0952542i
$753$	−59.1649	−	134.079i	−0.0785723	−	0.178060i
$754$	−107.961	+	332.268i	−0.143184	+	0.440674i
$755$	−215.703	−	296.890i	−0.285699	−	0.393231i
$756$	717.147	+	7.12286i	0.948607	+	0.00942177i
$757$	−280.054	−	861.917i	−0.369952	−	1.13860i	−0.946821	−	0.321759i	$-0.895726\pi$
$757$	−280.054	−	861.917i	−0.369952	−	1.13860i	0.576869	−	0.816836i	$-0.304274\pi$
$758$			474.354i			0.625797i
$759$		0			0
$760$	−422.709			−0.556196
$761$	218.038	−	70.8448i	0.286515	−	0.0930943i	−0.162234	−	0.986752i	$-0.551870\pi$
$761$	218.038	−	70.8448i	0.286515	−	0.0930943i	0.448749	+	0.893658i	$0.351870\pi$
$762$	302.686	−	30.8008i	0.397226	−	0.0404210i
$763$	−768.827	+	558.585i	−1.00764	+	0.732091i
$764$	171.433	+	55.7020i	0.224389	+	0.0729084i
$765$	325.508	+	147.516i	0.425500	+	0.192831i
$766$	236.602	−	171.901i	0.308880	−	0.224414i
$767$	−170.458	+	234.615i	−0.222240	+	0.305886i
$768$	−257.969	+	443.419i	−0.335898	+	0.577369i
$769$	541.254			0.703842			0.351921	−	0.936030i	$-0.385529\pi$
$769$	541.254			0.703842			0.351921	+	0.936030i	$0.385529\pi$
$770$		0			0
$771$	359.193	−	321.272i	0.465880	−	0.416696i
$772$	33.0836	+	101.821i	0.0428544	+	0.131892i
$773$	−440.204	+	605.889i	−0.569475	+	0.783815i	−0.992492	−	0.122307i	$-0.960971\pi$
$773$	−440.204	+	605.889i	−0.569475	+	0.783815i	0.423018	+	0.906122i	$0.360971\pi$
$774$	205.703	−	116.954i	0.265766	−	0.151103i
$775$	36.0254	−	110.875i	0.0464843	−	0.143064i
$776$	806.779	+	262.138i	1.03966	+	0.337807i
$777$	508.799	+	109.910i	0.654825	+	0.141455i
$778$	−63.5492	−	46.1712i	−0.0816827	−	0.0593460i
$779$	−48.5687	+	15.7809i	−0.0623475	+	0.0202579i
$780$	587.617	−	525.580i	0.753355	−	0.673821i
$781$		0			0
$782$		−	105.167i		−	0.134485i
$783$	−424.601	+	572.372i	−0.542275	+	0.730999i
$784$	−118.906	−	86.3901i	−0.151666	−	0.110191i
$785$	163.379	+	224.872i	0.208126	+	0.286462i
$786$	359.528	−	158.648i	0.457415	−	0.201842i
$787$	76.0971	−	234.203i	0.0966926	−	0.297589i	−0.890998	−	0.454006i	$-0.849994\pi$
$787$	76.0971	−	234.203i	0.0966926	−	0.297589i	0.987691	+	0.156417i	$0.0499944\pi$
$788$	−256.753	−	353.390i	−0.325829	−	0.448465i
$789$	419.094	−	42.6463i	0.531172	−	0.0540510i
$790$	−241.444	−	743.089i	−0.305626	−	0.940619i
$791$			280.371i			0.354451i
$792$		0			0
$793$	1235.90			1.55852
$794$	158.581	−	51.5259i	0.199724	−	0.0648941i
$795$	44.7623	+	439.889i	0.0563048	+	0.553320i
$796$	−585.369	+	425.296i	−0.735388	+	0.534291i
$797$	−955.181	−	310.357i	−1.19847	−	0.389407i	−0.359273	−	0.933233i	$-0.616975\pi$
$797$	−955.181	−	310.357i	−1.19847	−	0.389407i	−0.839198	+	0.543826i	$0.816975\pi$
$798$	−97.8475	−	221.742i	−0.122616	−	0.277872i
$799$	−85.9574	+	62.4517i	−0.107581	+	0.0781624i
$800$	364.630	−	501.871i	0.455788	−	0.627338i
$801$	177.056	+	860.974i	0.221043	+	1.07487i
$802$	−196.918			−0.245534
$803$		0			0
$804$	460.741	+	515.125i	0.573062	+	0.640702i
$805$	317.384	+	976.807i	0.394266	+	1.21343i
$806$	−48.2484	+	66.4083i	−0.0598616	+	0.0823924i
$807$	262.085	−	1213.25i	0.324765	−	1.50341i
$808$	−401.450	+	1235.54i	−0.496844	+	1.52913i
$809$	−1261.42	−	409.861i	−1.55924	−	0.506627i	−0.602633	−	0.798018i	$-0.705882\pi$
$809$	−1261.42	−	409.861i	−1.55924	−	0.506627i	−0.956604	+	0.291392i	$0.905882\pi$
$810$	−492.560	+	211.532i	−0.608099	+	0.261150i
$811$	940.338	+	683.196i	1.15948	+	0.842411i	0.989712	−	0.143073i	$-0.0456983\pi$
$811$	940.338	+	683.196i	1.15948	+	0.842411i	0.169768	+	0.985484i	$0.445698\pi$
$812$	666.800	−	216.657i	0.821183	−	0.266818i
$813$	−115.554	−	129.193i	−0.142133	−	0.158910i
$814$		0			0
$815$			1050.88i			1.28942i
$816$	77.7929	+	45.2578i	0.0953344	+	0.0554630i
$817$	194.085	+	141.011i	0.237558	+	0.172596i
$818$	423.690	+	583.159i	0.517959	+	0.712909i
$819$	960.693	+	435.372i	1.17301	+	0.531590i
$820$	34.3375	−	105.680i	0.0418750	−	0.128878i
$821$	557.320	+	767.085i	0.678830	+	0.934330i	0.999919	−	0.0127192i	$-0.00404874\pi$
$821$	557.320	+	767.085i	0.678830	+	0.934330i	−0.321089	+	0.947049i	$0.604049\pi$
$822$	63.3980	+	623.026i	0.0771265	+	0.757939i
$823$	456.674	+	1405.50i	0.554890	+	1.70778i	0.696234	+	0.717815i	$0.254858\pi$
$823$	456.674	+	1405.50i	0.554890	+	1.70778i	−0.141344	+	0.989961i	$0.545142\pi$
$824$		−	1208.12i		−	1.46617i
$825$		0			0
$826$	−193.992			−0.234857
$827$	−152.775	+	49.6397i	−0.184734	+	0.0600238i	−0.399923	−	0.916549i	$-0.630963\pi$
$827$	−152.775	+	49.6397i	−0.184734	+	0.0600238i	0.215189	+	0.976572i	$0.430963\pi$
$828$	−349.591	−	318.989i	−0.422211	−	0.385253i
$829$	−176.026	+	127.891i	−0.212336	+	0.154271i	−0.688870	−	0.724885i	$-0.741893\pi$
$829$	−176.026	+	127.891i	−0.212336	+	0.154271i	0.476534	+	0.879156i	$0.341893\pi$
$830$	699.815	+	227.384i	0.843150	+	0.273956i
$831$	903.363	−	398.625i	1.08708	−	0.479693i
$832$	−139.207	+	101.140i	−0.167316	+	0.121562i
$833$	103.668	−	142.687i	0.124452	−	0.171293i
$834$	211.546	+	123.072i	0.253652	+	0.147568i
$835$	−1887.31			−2.26025
$836$		0			0
$837$	−136.436	+	97.0708i	−0.163006	+	0.115975i
$838$	−82.6337	−	254.320i	−0.0986082	−	0.303485i
$839$	−322.053	+	443.267i	−0.383853	+	0.528328i	−0.956600	−	0.291404i	$-0.905878\pi$
$839$	−322.053	+	443.267i	−0.383853	+	0.528328i	0.572747	+	0.819732i	$0.305878\pi$
$840$	1202.79	+	259.825i	1.43189	+	0.309316i
$841$	44.5904	−	137.235i	0.0530207	−	0.163181i
$842$	−652.394	−	211.976i	−0.774815	−	0.251753i
$843$	−250.313	+	1158.75i	−0.296932	+	1.37456i
$844$	−103.726	−	75.3616i	−0.122899	−	0.0892910i
$845$	38.9826	−	12.6662i	0.0461333	−	0.0149896i
$846$	17.7082	−	158.387i	0.0209317	−	0.187219i
$847$		0			0
$848$			111.353i			0.131312i
$849$	433.090	−	744.431i	0.510118	−	0.876833i
$850$	91.2492	+	66.2964i	0.107352	+	0.0779958i
$851$	−201.898	−	277.889i	−0.237248	−	0.326544i
$852$	239.149	+	541.958i	0.280691	+	0.636101i
$853$	226.029	−	695.647i	0.264982	−	0.815530i	−0.726716	−	0.686938i	$-0.758954\pi$
$853$	226.029	−	695.647i	0.264982	−	0.815530i	0.991698	−	0.128592i	$-0.0410457\pi$
$854$	485.946	+	668.848i	0.569024	+	0.783194i
$855$	−401.470	−	366.327i	−0.469555	−	0.428453i
$856$	−142.295	−	437.938i	−0.166232	−	0.511609i
$857$		−	333.112i		−	0.388696i	−0.980933	−	0.194348i	$-0.937741\pi$
$857$		−	333.112i		−	0.388696i	0.980933	−	0.194348i	$-0.0622590\pi$
$858$		0			0
$859$	146.468			0.170510			0.0852551	−	0.996359i	$-0.472829\pi$
$859$	146.468			0.170510			0.0852551	+	0.996359i	$0.472829\pi$
$860$	−496.452	+	161.307i	−0.577269	+	0.187566i
$861$	147.899	−	15.0499i	0.171776	−	0.0174796i
$862$	446.890	−	324.685i	0.518434	−	0.376665i
$863$	605.334	+	196.685i	0.701430	+	0.227908i	0.637954	−	0.770075i	$-0.279781\pi$
$863$	605.334	+	196.685i	0.701430	+	0.227908i	0.0634766	+	0.997983i	$0.479781\pi$
$864$	−850.084	+	266.905i	−0.983894	+	0.308917i
$865$	320.167	−	232.615i	0.370135	−	0.268919i
$866$	167.296	−	230.263i	0.193183	−	0.265893i
$867$	381.674	−	656.053i	0.440224	−	0.756694i
$868$	164.729			0.189781
$869$		0			0
$870$	−390.605	+	349.368i	−0.448971	+	0.401572i
$871$	314.085	+	966.655i	0.360603	+	1.10982i
$872$	441.614	−	607.830i	0.506438	−	0.697052i
$873$	539.068	+	948.137i	0.617489	+	1.08607i
$874$	−49.4226	+	152.107i	−0.0565476	+	0.174036i
$875$	345.609	+	112.295i	0.394982	+	0.128337i
$876$	132.144	+	28.5455i	0.150849	+	0.0325862i
$877$	−1026.53	−	745.817i	−1.17050	−	0.850418i	−0.179431	−	0.983770i	$-0.557426\pi$
$877$	−1026.53	−	745.817i	−1.17050	−	0.850418i	−0.991069	+	0.133352i	$0.957426\pi$
$878$	506.017	−	164.415i	0.576329	−	0.187261i
$879$	160.473	−	143.532i	0.182564	−	0.163290i
$880$		0			0
$881$			425.862i			0.483385i	0.970353	+	0.241693i	$0.0777025\pi$
$881$			425.862i			0.483385i	−0.970353	+	0.241693i	$0.922297\pi$
$882$	53.2897	+	259.133i	0.0604192	+	0.293802i
$883$	−562.423	−	408.624i	−0.636946	−	0.462768i	0.221854	−	0.975080i	$-0.428789\pi$
$883$	−562.423	−	408.624i	−0.636946	−	0.462768i	−0.858800	+	0.512312i	$0.828789\pi$
$884$	140.039	+	192.748i	0.158416	+	0.218040i
$885$	−397.976	+	175.614i	−0.449690	+	0.198434i
$886$	37.1738	−	114.409i	0.0419568	−	0.129130i
$887$	250.832	+	345.241i	0.282787	+	0.389223i	0.926655	−	0.375914i	$-0.122671\pi$
$887$	250.832	+	345.241i	0.282787	+	0.389223i	−0.643867	+	0.765137i	$0.722671\pi$
$888$	−409.417	+	41.6616i	−0.461056	+	0.0469162i
$889$	−277.482	−	854.002i	−0.312128	−	0.960633i
$890$			646.354i			0.726241i
$891$		0			0
$892$	−497.976			−0.558269
$893$	153.672	−	49.9311i	0.172085	−	0.0559139i
$894$	2.12347	+	20.8678i	0.00237525	+	0.0233421i
$895$	−1412.61	+	1026.32i	−1.57834	+	1.14673i
$896$	1002.07	+	325.592i	1.11838	+	0.363384i
$897$	−280.982	−	636.761i	−0.313247	−	0.709879i
$898$	−55.5542	+	40.3625i	−0.0618643	+	0.0449471i
$899$	−96.2161	+	132.430i	−0.107026	+	0.147308i
$900$	497.153	−	102.237i	0.552392	−	0.113597i
$901$	−133.623			−0.148305
$902$		0			0
$903$	−465.580	−	520.535i	−0.515593	−	0.576451i
$904$	−68.4965	−	210.811i	−0.0757705	−	0.233198i
$905$	−879.010	+	1209.85i	−0.971281	+	1.33685i
$906$	−35.1251	+	162.602i	−0.0387695	+	0.179472i
$907$	−212.589	+	654.280i	−0.234387	+	0.721368i	0.762816	+	0.646616i	$0.223816\pi$
$907$	−212.589	+	654.280i	−0.234387	+	0.721368i	−0.997202	+	0.0747516i	$0.976184\pi$
$908$	−974.564	−	316.655i	−1.07331	−	0.348739i
$909$	−1452.02	+	825.553i	−1.59738	+	0.908199i
$910$	627.466	+	455.881i	0.689523	+	0.500968i
$911$	−1626.87	+	528.602i	−1.78581	+	0.580243i	−0.999303	−	0.0373428i	$-0.988111\pi$
$911$	−1626.87	+	528.602i	−1.78581	+	0.580243i	−0.786503	+	0.617586i	$0.788111\pi$
$912$	−91.2461	−	102.016i	−0.100051	−	0.111860i
$913$		0			0
$914$		−	695.507i		−	0.760949i
$915$	1602.41	+	932.237i	1.75126	+	1.01884i
$916$	−598.933	−	435.150i	−0.653857	−	0.475055i
$917$	−681.722	−	938.310i	−0.743427	−	1.02324i
$918$	−48.5281	−	154.561i	−0.0528628	−	0.168367i
$919$	119.301	−	367.169i	0.129816	−	0.399531i	−0.864932	−	0.501889i	$-0.832639\pi$
$919$	119.301	−	367.169i	0.129816	−	0.399531i	0.994748	+	0.102358i	$0.0326386\pi$
$920$	−477.282	−	656.922i	−0.518784	−	0.714045i
$921$	35.5216	+	349.079i	0.0385686	+	0.379022i
$922$	254.729	+	783.977i	0.276279	+	0.850300i
$923$			871.193i			0.943872i
$924$		0			0
$925$	368.387			0.398256
$926$	−150.397	+	48.8669i	−0.162416	+	0.0527720i
$927$	1046.98	−	1147.42i	1.12943	−	1.23778i
$928$	−704.685	+	511.984i	−0.759359	+	0.551707i
$929$	71.0024	+	23.0701i	0.0764288	+	0.0248332i	0.346982	−	0.937872i	$-0.387207\pi$
$929$	71.0024	+	23.0701i	0.0764288	+	0.0248332i	−0.270553	+	0.962705i	$0.587207\pi$
$930$	−112.648	+	49.7079i	−0.121127	+	0.0534493i
$931$	−216.994	+	157.655i	−0.233076	+	0.169340i
$932$	702.469	−	966.866i	0.753722	−	1.03741i
$933$	−474.902	−	276.285i	−0.509005	−	0.296125i
$934$	763.310			0.817248
$935$		0			0
$936$	−828.709	−	92.6525i	−0.885373	−	0.0989877i
$937$	−175.615	−	540.488i	−0.187423	−	0.576828i	0.812559	−	0.582879i	$-0.198074\pi$
$937$	−175.615	−	540.488i	−0.187423	−	0.576828i	−0.999982	+	0.00605080i	$0.998074\pi$
$938$	−399.640	+	550.058i	−0.426056	+	0.586415i
$939$	−219.288	−	47.3705i	−0.233534	−	0.0504478i
$940$	−108.644	+	334.373i	−0.115579	+	0.355716i
$941$	−189.720	−	61.6436i	−0.201615	−	0.0655086i	0.206469	−	0.978453i	$-0.433803\pi$
$941$	−189.720	−	61.6436i	−0.201615	−	0.0655086i	−0.408084	+	0.912945i	$0.633803\pi$
$942$	26.6048	−	123.159i	0.0282428	−	0.130742i
$943$	−79.3638	−	57.6612i	−0.0841610	−	0.0611465i
$944$	−104.187	+	33.8525i	−0.110368	+	0.0358608i
$945$	917.184	+	1289.13i	0.970565	+	1.36416i
$946$		0			0
$947$		−	984.860i		−	1.03998i	−0.854173	−	0.519990i	$-0.825936\pi$
$947$		−	984.860i		−	1.03998i	0.854173	−	0.519990i	$-0.174064\pi$
$948$	534.317	−	918.429i	0.563625	−	0.968807i
$949$	160.851	+	116.865i	0.169495	+	0.123146i
$950$	−100.822	−	138.769i	−0.106128	−	0.146073i
$951$	−21.4029	−	48.5032i	−0.0225057	−	0.0510023i
$952$	−114.915	+	353.672i	−0.120709	+	0.371504i
$953$	−448.110	−	616.771i	−0.470210	−	0.647189i	0.506377	−	0.862312i	$-0.330985\pi$
$953$	−448.110	−	616.771i	−0.470210	−	0.647189i	−0.976587	+	0.215124i	$0.930985\pi$
$954$	135.100	−	148.061i	0.141614	−	0.155200i
$955$	122.879	+	378.183i	0.128669	+	0.396004i
$956$		−	483.629i		−	0.505888i
$957$		0			0
$958$	74.8228			0.0781031
$959$	1757.81	−	571.148i	1.83296	−	0.595566i
$960$	−256.777	+	26.1292i	−0.267476	+	0.0272179i
$961$	746.350	−	542.255i	0.776639	−	0.564262i
$962$	−246.689	−	80.1540i	−0.256433	−	0.0833202i
$963$	244.380	−	539.248i	0.253769	−	0.559967i
$964$	387.465	−	281.510i	0.401935	−	0.292023i
$965$	−138.821	+	191.071i	−0.143856	+	0.198001i
$966$	234.124	−	402.432i	0.242364	−	0.416596i
$967$	1466.73			1.51679			0.758394	−	0.651797i	$-0.225985\pi$
$967$	1466.73			1.51679			0.758394	+	0.651797i	$0.225985\pi$
$968$		0			0
$969$	122.420	−	109.495i	0.126336	−	0.112998i
$970$	247.834	+	762.756i	0.255499	+	0.786346i
$971$	−671.579	+	924.349i	−0.691637	+	0.951956i	0.308363	+	0.951269i	$0.400219\pi$
$971$	−671.579	+	924.349i	−0.691637	+	0.951956i	−1.00000		0.000687448i	$0.999781\pi$
$972$	−660.975	−	307.494i	−0.680016	−	0.316352i
$973$	223.210	−	686.969i	0.229404	−	0.706032i
$974$	−288.147	−	93.6246i	−0.295839	−	0.0961238i
$975$	729.620	+	157.612i	0.748328	+	0.161653i
$976$	377.705	+	274.419i	0.386993	+	0.281167i
$977$	−36.8048	+	11.9586i	−0.0376713	+	0.0122401i	−0.327792	−	0.944750i	$-0.606305\pi$
$977$	−36.8048	+	11.9586i	−0.0376713	+	0.0122401i	0.290121	+	0.956990i	$0.406305\pi$
$978$	355.066	−	317.580i	0.363053	−	0.324724i
$979$		0			0
$980$		−	583.614i		−	0.595524i
$981$	946.181	−	194.578i	0.964507	−	0.198347i
$982$	−646.222	−	469.508i	−0.658067	−	0.478114i
$983$	712.747	+	981.012i	0.725073	+	0.997978i	0.999340	+	0.0363240i	$0.0115648\pi$
$983$	712.747	+	981.012i	0.725073	+	0.997978i	−0.274267	+	0.961654i	$0.588435\pi$
$984$	−107.528	+	47.4487i	−0.109277	+	0.0482202i
$985$	297.774	−	916.455i	0.302309	−	0.930411i
$986$	−93.0880	−	128.125i	−0.0944097	−	0.129944i
$987$	−467.954	+	47.6182i	−0.474118	+	0.0482454i
$988$	−111.964	−	344.589i	−0.113324	−	0.348774i
$989$			460.839i			0.465965i
$990$		0			0
$991$	−1413.89			−1.42673			−0.713367	−	0.700790i	$-0.752831\pi$
$991$	−1413.89			−1.42673			−0.713367	+	0.700790i	$0.752831\pi$
$992$	−194.637	+	63.2415i	−0.196207	+	0.0637515i
$993$	−120.140	−	1180.64i	−0.120987	−	1.18897i
$994$	−471.474	+	342.546i	−0.474320	+	0.344614i
$995$	−1518.05	−	493.245i	−1.52568	−	0.495723i
$996$	403.980	+	915.498i	0.405602	+	0.919175i
$997$	−762.909	+	554.286i	−0.765204	+	0.555953i	−0.900502	−	0.434852i	$-0.856801\pi$
$997$	−762.909	+	554.286i	−0.765204	+	0.555953i	0.135298	+	0.990805i	$0.456801\pi$
$998$	−343.702	+	473.066i	−0.344391	+	0.474014i
$999$	−424.951	−	315.240i	−0.425376	−	0.315556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.h.269.2		8
3.2	odd	2	inner	363.3.h.h.269.1		8
11.2	odd	10		363.3.h.i.251.2		8
11.3	even	5		363.3.b.f.122.1		4
11.4	even	5		33.3.h.a.14.2	yes	8
11.5	even	5		33.3.h.a.26.1	yes	8
11.6	odd	10		363.3.h.g.323.2		8
11.7	odd	10		363.3.h.g.245.1		8
11.8	odd	10		363.3.b.g.122.3		4
11.9	even	5	inner	363.3.h.h.251.1		8
11.10	odd	2		363.3.h.i.269.1		8
33.2	even	10		363.3.h.i.251.1		8
33.5	odd	10		33.3.h.a.26.2	yes	8
33.8	even	10		363.3.b.g.122.2		4
33.14	odd	10		363.3.b.f.122.4		4
33.17	even	10		363.3.h.g.323.1		8
33.20	odd	10	inner	363.3.h.h.251.2		8
33.26	odd	10		33.3.h.a.14.1	✓	8
33.29	even	10		363.3.h.g.245.2		8
33.32	even	2		363.3.h.i.269.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.a.14.1	✓	8	33.26	odd	10
33.3.h.a.14.2	yes	8	11.4	even	5
33.3.h.a.26.1	yes	8	11.5	even	5
33.3.h.a.26.2	yes	8	33.5	odd	10
363.3.b.f.122.1		4	11.3	even	5
363.3.b.f.122.4		4	33.14	odd	10
363.3.b.g.122.2		4	33.8	even	10
363.3.b.g.122.3		4	11.8	odd	10
363.3.h.g.245.1		8	11.7	odd	10
363.3.h.g.245.2		8	33.29	even	10
363.3.h.g.323.1		8	33.17	even	10
363.3.h.g.323.2		8	11.6	odd	10
363.3.h.h.251.1		8	11.9	even	5	inner
363.3.h.h.251.2		8	33.20	odd	10	inner
363.3.h.h.269.1		8	3.2	odd	2	inner
363.3.h.h.269.2		8	1.1	even	1	trivial
363.3.h.i.251.1		8	33.2	even	10
363.3.h.i.251.2		8	11.2	odd	10
363.3.h.i.269.1		8	11.10	odd	2
363.3.h.i.269.2		8	33.32	even	2

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.303706 + 2.98459i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-6.29412 - 2.04508i) q^{5} +(1.21113 + 2.74466i) q^{6} +(7.16312 - 5.20431i) q^{7} +(-4.11450 + 5.66312i) q^{8} +(-8.81553 + 1.81288i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.303706 + 2.98459i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(-6.29412 - 2.04508i) q^{5} +(1.21113 + 2.74466i) q^{6} +(7.16312 - 5.20431i) q^{7} +(-4.11450 + 5.66312i) q^{8} +(-8.81553 + 1.81288i) q^{9} -6.61803 q^{10} +(-6.00000 - 6.70820i) q^{12} +(-4.09017 - 12.5882i) q^{13} +(5.20431 - 7.16312i) q^{14} +(4.19217 - 19.4065i) q^{15} +(1.54508 - 4.75528i) q^{16} +(5.70634 + 1.85410i) q^{17} +(-7.82385 + 4.44829i) q^{18} +(-7.38197 - 5.36331i) q^{19} +(18.8824 - 6.13525i) q^{20} +(17.7082 + 19.7984i) q^{21} -17.5279i q^{23} +(-18.1517 - 10.5602i) q^{24} +(15.2082 + 11.0494i) q^{25} +(-7.77997 - 10.7082i) q^{26} +(-8.08802 - 25.7601i) q^{27} +(-8.20820 + 25.2623i) q^{28} +(-15.5147 - 21.3541i) q^{29} +(-2.00994 - 19.7521i) q^{30} +(-1.91641 - 5.89810i) q^{31} -33.0000i q^{32} +6.00000 q^{34} +(-55.7288 + 18.1074i) q^{35} +(18.1990 - 19.9448i) q^{36} +(15.8541 - 11.5187i) q^{37} +(-8.67802 - 2.81966i) q^{38} +(36.3285 - 16.0306i) q^{39} +(37.4787 - 27.2299i) q^{40} +(3.28969 - 4.52786i) q^{41} +(22.9595 + 13.3572i) q^{42} -26.2918 q^{43} +(59.1935 + 6.61803i) q^{45} +(-5.41641 - 16.6700i) q^{46} +(-10.4086 + 14.3262i) q^{47} +(14.6618 + 3.16723i) q^{48} +(9.08359 - 27.9564i) q^{49} +(17.8783 + 5.80902i) q^{50} +(-3.80068 + 17.5942i) q^{51} +(32.1246 + 23.3399i) q^{52} +(-21.1805 + 6.88197i) q^{53} +(-15.6525 - 22.0000i) q^{54} +61.9787i q^{56} +(13.7653 - 23.6610i) q^{57} +(-21.3541 - 15.5147i) q^{58} +(-12.8783 - 17.7254i) q^{59} +(24.0459 + 54.4928i) q^{60} +(-28.8541 + 88.8038i) q^{61} +(-3.64522 - 5.01722i) q^{62} +(-53.7119 + 58.8646i) q^{63} +(-4.01722 - 12.3637i) q^{64} +87.5967i q^{65} -76.7902 q^{67} +(-17.1190 + 5.56231i) q^{68} +(52.3134 - 5.32332i) q^{69} +(-47.4058 + 34.4423i) q^{70} +(-62.5982 - 20.3394i) q^{71} +(26.0049 - 57.3824i) q^{72} +(-12.1525 + 8.82929i) q^{73} +(11.5187 - 15.8541i) q^{74} +(-28.3591 + 48.7460i) q^{75} +27.3738 q^{76} +(29.5967 - 26.4721i) q^{78} +(36.4828 + 112.282i) q^{79} +(-19.4499 + 26.7705i) q^{80} +(74.4270 - 31.9629i) q^{81} +(1.72949 - 5.32282i) q^{82} +(-105.744 - 34.3582i) q^{83} +(-77.8903 - 16.8258i) q^{84} +(-32.1246 - 23.3399i) q^{85} +(-25.0050 + 8.12461i) q^{86} +(59.0213 - 52.7902i) q^{87} -97.6656i q^{89} +(58.3414 - 11.9977i) q^{90} +(-94.8115 - 68.8846i) q^{91} +(30.9079 + 42.5410i) q^{92} +(17.0214 - 7.51098i) q^{93} +(-5.47214 + 16.8415i) q^{94} +(35.4946 + 48.8541i) q^{95} +(98.4914 - 10.0223i) q^{96} +(-37.4483 - 115.254i) q^{97} -29.3951i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 6 q^{4} - 10 q^{6} + 26 q^{7} + 2 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 6 * q^4 - 10 * q^6 + 26 * q^7 + 2 * q^9	\( 8 q + 4 q^{3} - 6 q^{4} - 10 q^{6} + 26 q^{7} + 2 q^{9} - 44 q^{10} - 48 q^{12} + 12 q^{13} + 60 q^{15} - 10 q^{16} - 40 q^{18} - 68 q^{19} + 88 q^{21} - 70 q^{24} + 68 q^{25} - 44 q^{27} - 12 q^{28} - 32 q^{30} + 92 q^{31} + 48 q^{34} + 6 q^{36} + 100 q^{37} - 24 q^{39} + 112 q^{40} + 40 q^{42} - 264 q^{43} + 80 q^{45} + 64 q^{46} + 20 q^{48} + 180 q^{49} - 60 q^{51} + 96 q^{52} - 224 q^{57} - 144 q^{58} - 150 q^{60} - 204 q^{61} - 26 q^{63} + 26 q^{64} - 24 q^{67} + 200 q^{69} - 178 q^{70} + 280 q^{72} + 28 q^{73} + 84 q^{75} - 264 q^{76} + 40 q^{78} + 350 q^{79} + 158 q^{81} + 148 q^{82} - 156 q^{84} - 96 q^{85} + 660 q^{87} - 6 q^{90} - 356 q^{91} - 184 q^{93} - 8 q^{94} + 330 q^{96} - 474 q^{97}+O(q^{100}) \) 8 * q + 4 * q^3 - 6 * q^4 - 10 * q^6 + 26 * q^7 + 2 * q^9 - 44 * q^10 - 48 * q^12 + 12 * q^13 + 60 * q^15 - 10 * q^16 - 40 * q^18 - 68 * q^19 + 88 * q^21 - 70 * q^24 + 68 * q^25 - 44 * q^27 - 12 * q^28 - 32 * q^30 + 92 * q^31 + 48 * q^34 + 6 * q^36 + 100 * q^37 - 24 * q^39 + 112 * q^40 + 40 * q^42 - 264 * q^43 + 80 * q^45 + 64 * q^46 + 20 * q^48 + 180 * q^49 - 60 * q^51 + 96 * q^52 - 224 * q^57 - 144 * q^58 - 150 * q^60 - 204 * q^61 - 26 * q^63 + 26 * q^64 - 24 * q^67 + 200 * q^69 - 178 * q^70 + 280 * q^72 + 28 * q^73 + 84 * q^75 - 264 * q^76 + 40 * q^78 + 350 * q^79 + 158 * q^81 + 148 * q^82 - 156 * q^84 - 96 * q^85 + 660 * q^87 - 6 * q^90 - 356 * q^91 - 184 * q^93 - 8 * q^94 + 330 * q^96 - 474 * q^97

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