LMFDB - Embedded newform 368.3.k.b.45.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,3,Mod(45,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("368.45");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	368.k (of order $4$, 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:	$10.0272737285$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$88$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			45.19
Character	$\chi$	$=$	368.45
Dual form			368.3.k.b.229.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.52002 + 1.29982i) q^{2} +(0.968686 + 0.968686i) q^{3} +(0.620917 - 3.95151i) q^{4} +(-3.86184 - 3.86184i) q^{5} +(-2.73154 - 0.213300i) q^{6} -4.96433 q^{7} +(4.19246 + 6.81346i) q^{8} -7.12330i q^{9} +(10.8898 + 0.850361i) q^{10} +(-2.50654 - 2.50654i) q^{11} +(4.42925 - 3.22630i) q^{12} +(10.5972 + 10.5972i) q^{13} +(7.54588 - 6.45275i) q^{14} -7.48182i q^{15} +(-15.2289 - 4.90713i) q^{16} +22.9106i q^{17} +(9.25903 + 10.8275i) q^{18} +(-17.7764 + 17.7764i) q^{19} +(-17.6580 + 12.8622i) q^{20} +(-4.80888 - 4.80888i) q^{21} +(7.06805 + 0.551929i) q^{22} +(11.0659 + 20.1630i) q^{23} +(-2.53892 + 10.6613i) q^{24} +4.82766i q^{25} +(-29.8823 - 2.33345i) q^{26} +(15.6184 - 15.6184i) q^{27} +(-3.08244 + 19.6166i) q^{28} +(27.0630 + 27.0630i) q^{29} +(9.72505 + 11.3725i) q^{30} -3.45374 q^{31} +(29.5267 - 12.3360i) q^{32} -4.85610i q^{33} +(-29.7797 - 34.8245i) q^{34} +(19.1715 + 19.1715i) q^{35} +(-28.1478 - 4.42298i) q^{36} +(46.6306 + 46.6306i) q^{37} +(3.91429 - 50.1267i) q^{38} +20.5306i q^{39} +(10.1219 - 42.5032i) q^{40} +42.8441i q^{41} +(13.5603 + 1.05889i) q^{42} +(-47.6976 - 47.6976i) q^{43} +(-11.4610 + 8.34827i) q^{44} +(-27.5090 + 27.5090i) q^{45} +(-43.0287 - 16.2644i) q^{46} +5.74565 q^{47} +(-9.99858 - 19.5055i) q^{48} -24.3554 q^{49} +(-6.27511 - 7.33814i) q^{50} +(-22.1931 + 22.1931i) q^{51} +(48.4548 - 35.2948i) q^{52} +(-25.0753 - 25.0753i) q^{53} +(-3.43911 + 44.0415i) q^{54} +19.3597i q^{55} +(-20.8128 - 33.8243i) q^{56} -34.4395 q^{57} +(-76.3135 - 5.95916i) q^{58} +(-66.0777 + 66.0777i) q^{59} +(-29.5645 - 4.64560i) q^{60} +(8.06717 - 8.06717i) q^{61} +(5.24975 - 4.48925i) q^{62} +35.3624i q^{63} +(-28.8465 + 57.1304i) q^{64} -81.8491i q^{65} +(6.31207 + 7.38136i) q^{66} +(66.7527 - 66.7527i) q^{67} +(90.5314 + 14.2256i) q^{68} +(-8.81219 + 30.2510i) q^{69} +(-54.0605 - 4.22147i) q^{70} +109.541i q^{71} +(48.5343 - 29.8642i) q^{72} -59.8301i q^{73} +(-131.491 - 10.2679i) q^{74} +(-4.67649 + 4.67649i) q^{75} +(59.2061 + 81.2815i) q^{76} +(12.4433 + 12.4433i) q^{77} +(-26.6862 - 31.2070i) q^{78} +9.87381i q^{79} +(39.8612 + 77.7623i) q^{80} -33.8510 q^{81} +(-55.6897 - 65.1238i) q^{82} +(-80.3371 + 80.3371i) q^{83} +(-21.9883 + 16.0164i) q^{84} +(88.4770 - 88.4770i) q^{85} +(134.500 + 10.5028i) q^{86} +52.4312i q^{87} +(6.56963 - 27.5868i) q^{88} -26.4900 q^{89} +(6.05738 - 77.5712i) q^{90} +(-52.6078 - 52.6078i) q^{91} +(86.5453 - 31.2076i) q^{92} +(-3.34559 - 3.34559i) q^{93} +(-8.73350 + 7.46833i) q^{94} +137.300 q^{95} +(40.5517 + 16.6524i) q^{96} +152.701i q^{97} +(37.0207 - 31.6578i) q^{98} +(-17.8548 + 17.8548i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 4 q^{2} - 4 q^{3} - 16 q^{4} - 64 q^{6} - 4 q^{8} - 28 q^{12} - 4 q^{13} - 80 q^{16} + 72 q^{18} + 68 q^{24} + 96 q^{26} + 212 q^{27} + 28 q^{29} - 8 q^{31} + 136 q^{32} - 104 q^{35} - 264 q^{36}+ \cdots - 240 q^{98}+O(q^{100}) $ 176 * q - 4 * q^2 - 4 * q^3 - 16 * q^4 - 64 * q^6 - 4 * q^8 - 28 * q^12 - 4 * q^13 - 80 * q^16 + 72 * q^18 + 68 * q^24 + 96 * q^26 + 212 * q^27 + 28 * q^29 - 8 * q^31 + 136 * q^32 - 104 * q^35 - 264 * q^36 - 32 * q^46 - 8 * q^47 - 520 * q^48 + 1728 * q^49 + 88 * q^50 - 56 * q^52 - 148 * q^54 + 540 * q^58 + 296 * q^59 - 812 * q^62 - 352 * q^64 - 80 * q^69 + 124 * q^70 + 712 * q^72 + 132 * q^75 + 24 * q^77 - 320 * q^78 - 440 * q^81 - 844 * q^82 + 416 * q^85 - 492 * q^92 - 1084 * q^93 - 596 * q^94 - 8 * q^95 + 664 * q^96 - 240 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.52002	+	1.29982i	−0.760010	+	0.649912i
$2$	−1.52002	+	1.29982i	−0.760010	+	0.649912i
$3$	0.968686	+	0.968686i	0.322895	+	0.322895i	0.849877	−	0.526981i	$-0.176676\pi$
$3$	0.968686	+	0.968686i	0.322895	+	0.322895i	−0.526981	+	0.849877i	$0.676676\pi$
$4$	0.620917	−	3.95151i	0.155229	−	0.987878i
$5$	−3.86184	−	3.86184i	−0.772369	−	0.772369i	0.206152	−	0.978520i	$-0.433906\pi$
$5$	−3.86184	−	3.86184i	−0.772369	−	0.772369i	−0.978520	+	0.206152i	$0.933906\pi$
$6$	−2.73154	−	0.213300i	−0.455257	−	0.0355501i
$7$	−4.96433			−0.709190			−0.354595	−	0.935020i	$-0.615381\pi$
$7$	−4.96433			−0.709190			−0.354595	+	0.935020i	$0.615381\pi$
$8$	4.19246	+	6.81346i	0.524058	+	0.851683i
$9$		−	7.12330i		−	0.791477i
$10$	10.8898	+	0.850361i	1.08898	+	0.0850361i
$11$	−2.50654	−	2.50654i	−0.227867	−	0.227867i	0.583934	−	0.811801i	$-0.301513\pi$
$11$	−2.50654	−	2.50654i	−0.227867	−	0.227867i	−0.811801	+	0.583934i	$0.801513\pi$
$12$	4.42925	−	3.22630i	0.369104	−	0.268858i
$13$	10.5972	+	10.5972i	0.815166	+	0.815166i	0.985403	−	0.170237i	$-0.0544534\pi$
$13$	10.5972	+	10.5972i	0.815166	+	0.815166i	−0.170237	+	0.985403i	$0.554453\pi$
$14$	7.54588	−	6.45275i	0.538991	−	0.460911i
$15$		−	7.48182i		−	0.498788i
$16$	−15.2289	−	4.90713i	−0.951808	−	0.306695i
$17$			22.9106i			1.34768i	0.738877	+	0.673840i	$0.235356\pi$
$17$			22.9106i			1.34768i	−0.738877	+	0.673840i	$0.764644\pi$
$18$	9.25903	+	10.8275i	0.514390	+	0.601530i
$19$	−17.7764	+	17.7764i	−0.935601	+	0.935601i	−0.998048	−	0.0624470i	$-0.980110\pi$
$19$	−17.7764	+	17.7764i	−0.935601	+	0.935601i	0.0624470	+	0.998048i	$0.480110\pi$
$20$	−17.6580	+	12.8622i	−0.882901	+	0.643112i
$21$	−4.80888	−	4.80888i	−0.228994	−	0.228994i
$22$	7.06805	+	0.551929i	0.321275	+	0.0250877i
$23$	11.0659	+	20.1630i	0.481127	+	0.876651i
$23$	11.0659	+	20.1630i	0.481127	+	0.876651i
$24$	−2.53892	+	10.6613i	−0.105788	+	0.444220i
$25$			4.82766i			0.193106i
$26$	−29.8823	−	2.33345i	−1.14932	−	0.0897480i
$27$	15.6184	−	15.6184i	0.578460	−	0.578460i
$28$	−3.08244	+	19.6166i	−0.110087	+	0.700593i
$29$	27.0630	+	27.0630i	0.933208	+	0.933208i	0.997905	−	0.0646970i	$-0.0206081\pi$
$29$	27.0630	+	27.0630i	0.933208	+	0.933208i	−0.0646970	+	0.997905i	$0.520608\pi$
$30$	9.72505	+	11.3725i	0.324168	+	0.379084i
$31$	−3.45374			−0.111411			−0.0557055	−	0.998447i	$-0.517741\pi$
$31$	−3.45374			−0.111411			−0.0557055	+	0.998447i	$0.517741\pi$
$32$	29.5267	−	12.3360i	0.922708	−	0.385500i
$33$		−	4.85610i		−	0.147154i
$34$	−29.7797	−	34.8245i	−0.875874	−	1.02425i
$35$	19.1715	+	19.1715i	0.547756	+	0.547756i
$36$	−28.1478	−	4.42298i	−0.781883	−	0.122861i
$37$	46.6306	+	46.6306i	1.26029	+	1.26029i	0.950954	+	0.309332i	$0.100106\pi$
$37$	46.6306	+	46.6306i	1.26029	+	1.26029i	0.309332	+	0.950954i	$0.399894\pi$
$38$	3.91429	−	50.1267i	0.103008	−	1.31912i
$39$			20.5306i			0.526426i
$40$	10.1219	−	42.5032i	0.253047	−	1.06258i
$41$			42.8441i			1.04498i	0.852646	+	0.522489i	$0.174996\pi$
$41$			42.8441i			1.04498i	−0.852646	+	0.522489i	$0.825004\pi$
$42$	13.5603	+	1.05889i	0.322864	+	0.0252118i
$43$	−47.6976	−	47.6976i	−1.10925	−	1.10925i	−0.993250	−	0.115997i	$-0.962994\pi$
$43$	−47.6976	−	47.6976i	−1.10925	−	1.10925i	−0.115997	−	0.993250i	$-0.537006\pi$
$44$	−11.4610	+	8.34827i	−0.260477	+	0.189733i
$45$	−27.5090	+	27.5090i	−0.611312	+	0.611312i
$46$	−43.0287	−	16.2644i	−0.935407	−	0.353573i
$47$	5.74565			0.122248			0.0611240	−	0.998130i	$-0.480532\pi$
$47$	5.74565			0.122248			0.0611240	+	0.998130i	$0.480532\pi$
$48$	−9.99858	−	19.5055i	−0.208304	−	0.406365i
$49$	−24.3554			−0.497050
$50$	−6.27511	−	7.33814i	−0.125502	−	0.146763i
$51$	−22.1931	+	22.1931i	−0.435160	+	0.435160i
$52$	48.4548	−	35.2948i	0.931822	−	0.678747i
$53$	−25.0753	−	25.0753i	−0.473119	−	0.473119i	0.429803	−	0.902923i	$-0.358583\pi$
$53$	−25.0753	−	25.0753i	−0.473119	−	0.473119i	−0.902923	+	0.429803i	$0.858583\pi$
$54$	−3.43911	+	44.0415i	−0.0636872	+	0.815583i
$55$			19.3597i			0.351995i
$56$	−20.8128	−	33.8243i	−0.371657	−	0.604005i
$57$	−34.4395			−0.604202
$58$	−76.3135	−	5.95916i	−1.31575	−	0.102744i
$59$	−66.0777	+	66.0777i	−1.11996	+	1.11996i	−0.128214	+	0.991746i	$0.540925\pi$
$59$	−66.0777	+	66.0777i	−1.11996	+	1.11996i	−0.991746	+	0.128214i	$0.959075\pi$
$60$	−29.5645	−	4.64560i	−0.492742	−	0.0774266i
$61$	8.06717	−	8.06717i	0.132249	−	0.132249i	−0.637884	−	0.770133i	$-0.720190\pi$
$61$	8.06717	−	8.06717i	0.132249	−	0.132249i	0.770133	+	0.637884i	$0.220190\pi$
$62$	5.24975	−	4.48925i	0.0846734	−	0.0724073i
$63$			35.3624i			0.561308i
$64$	−28.8465	+	57.1304i	−0.450726	+	0.892662i
$65$		−	81.8491i		−	1.25922i
$66$	6.31207	+	7.38136i	0.0956374	+	0.111839i
$67$	66.7527	−	66.7527i	0.996309	−	0.996309i	−0.00368470	−	0.999993i	$-0.501173\pi$
$67$	66.7527	−	66.7527i	0.996309	−	0.996309i	0.999993	+	0.00368470i	$0.00117288\pi$
$68$	90.5314	+	14.2256i	1.33134	+	0.209200i
$69$	−8.81219	+	30.2510i	−0.127713	+	0.438420i
$70$	−54.0605	−	4.22147i	−0.772293	−	0.0603068i
$71$			109.541i			1.54282i	0.636335	+	0.771412i	$0.280449\pi$
$71$			109.541i			1.54282i	−0.636335	+	0.771412i	$0.719551\pi$
$72$	48.5343	−	29.8642i	0.674087	−	0.414780i
$73$		−	59.8301i		−	0.819590i	−0.912178	−	0.409795i	$-0.865600\pi$
$73$		−	59.8301i		−	0.819590i	0.912178	−	0.409795i	$-0.134400\pi$
$74$	−131.491	−	10.2679i	−1.77690	−	0.138755i
$75$	−4.67649	+	4.67649i	−0.0623532	+	0.0623532i
$76$	59.2061	+	81.2815i	0.779028	+	1.06949i
$77$	12.4433	+	12.4433i	0.161601	+	0.161601i
$78$	−26.6862	−	31.2070i	−0.342131	−	0.400089i
$79$			9.87381i			0.124985i	0.998045	+	0.0624925i	$0.0199049\pi$
$79$			9.87381i			0.124985i	−0.998045	+	0.0624925i	$0.980095\pi$
$80$	39.8612	+	77.7623i	0.498264	+	0.972028i
$81$	−33.8510			−0.417914
$82$	−55.6897	−	65.1238i	−0.679143	−	0.794193i
$83$	−80.3371	+	80.3371i	−0.967917	+	0.967917i	−0.999501	−	0.0315844i	$-0.989945\pi$
$83$	−80.3371	+	80.3371i	−0.967917	+	0.967917i	0.0315844	+	0.999501i	$0.489945\pi$
$84$	−21.9883	+	16.0164i	−0.261765	+	0.190672i
$85$	88.4770	−	88.4770i	1.04091	−	1.04091i
$86$	134.500	+	10.5028i	1.56395	+	0.122126i
$87$			52.4312i			0.602657i
$88$	6.56963	−	27.5868i	0.0746549	−	0.313486i
$89$	−26.4900			−0.297641			−0.148820	−	0.988864i	$-0.547548\pi$
$89$	−26.4900			−0.297641			−0.148820	+	0.988864i	$0.547548\pi$
$90$	6.05738	−	77.5712i	0.0673042	−	0.861902i
$91$	−52.6078	−	52.6078i	−0.578107	−	0.578107i
$92$	86.5453	−	31.2076i	0.940710	−	0.339213i
$93$	−3.34559	−	3.34559i	−0.0359741	−	0.0359741i
$94$	−8.73350	+	7.46833i	−0.0929096	+	0.0794504i
$95$	137.300			1.44526
$96$	40.5517	+	16.6524i	0.422414	+	0.173462i
$97$			152.701i			1.57424i	0.616802	+	0.787119i	$0.288428\pi$
$97$			152.701i			1.57424i	−0.616802	+	0.787119i	$0.711572\pi$
$98$	37.0207	−	31.6578i	0.377763	−	0.323038i
$99$	−17.8548	+	17.8548i	−0.180352	+	0.180352i
$100$	19.0766	+	2.99758i	0.190766	+	0.0299758i
$101$	112.234	−	112.234i	1.11123	−	1.11123i	0.118241	−	0.992985i	$-0.462275\pi$
$101$	112.234	−	112.234i	1.11123	−	1.11123i	0.992985	−	0.118241i	$-0.0377254\pi$
$102$	4.88684	−	62.5812i	0.0479102	−	0.613541i
$103$	−61.8814			−0.600791			−0.300395	−	0.953815i	$-0.597119\pi$
$103$	−61.8814			−0.600791			−0.300395	+	0.953815i	$0.597119\pi$
$104$	−27.7751	+	116.631i	−0.267068	+	1.12146i
$105$			37.1422i			0.353736i
$106$	70.7085	+	5.52148i	0.667061	+	0.0520894i
$107$	69.6664	+	69.6664i	0.651087	+	0.651087i	0.953255	−	0.302167i	$-0.0977102\pi$
$107$	69.6664	+	69.6664i	0.651087	+	0.651087i	−0.302167	+	0.953255i	$0.597710\pi$
$108$	−52.0186	−	71.4141i	−0.481654	−	0.661242i
$109$	141.403	−	141.403i	1.29728	−	1.29728i	0.367095	−	0.930184i	$-0.380352\pi$
$109$	141.403	−	141.403i	1.29728	−	1.29728i	0.930184	−	0.367095i	$-0.119648\pi$
$110$	−25.1642	−	29.4272i	−0.228766	−	0.267520i
$111$			90.3408i			0.813881i
$112$	75.6014	+	24.3606i	0.675012	+	0.217505i
$113$			89.8043i			0.794728i	0.917661	+	0.397364i	$0.130075\pi$
$113$			89.8043i			0.794728i	−0.917661	+	0.397364i	$0.869925\pi$
$114$	52.3488	−	44.7653i	0.459200	−	0.392678i
$115$	35.1314	−	120.601i	0.305490	−	1.04870i
$116$	123.744	−	90.1360i	1.06676	−	0.777035i
$117$	75.4867	−	75.4867i	0.645185	−	0.645185i
$118$	14.5500	−	186.329i	0.123305	−	1.57906i
$119$		−	113.736i		−	0.955762i
$120$	50.9771	−	31.3673i	0.424809	−	0.261394i
$121$		−	108.435i		−	0.896153i
$122$	−1.77636	+	22.7482i	−0.0145603	+	0.186460i
$123$	−41.5025	+	41.5025i	−0.337418	+	0.337418i
$124$	−2.14449	+	13.6475i	−0.0172943	+	0.110060i
$125$	−77.9024	+	77.9024i	−0.623219	+	0.623219i
$126$	−45.9649	−	53.7515i	−0.364800	−	0.426599i
$127$	−80.4144			−0.633184			−0.316592	−	0.948562i	$-0.602539\pi$
$127$	−80.4144			−0.633184			−0.316592	+	0.948562i	$0.602539\pi$
$128$	−30.4122	−	124.335i	−0.237595	−	0.971364i
$129$		−	92.4080i		−	0.716341i
$130$	106.389	+	124.412i	0.818380	+	0.957017i
$131$	−48.3690	−	48.3690i	−0.369229	−	0.369229i	0.497967	−	0.867196i	$-0.334080\pi$
$131$	−48.3690	−	48.3690i	−0.369229	−	0.369229i	−0.867196	+	0.497967i	$0.834080\pi$
$132$	−19.1889	−	3.01524i	−0.145371	−	0.0228427i
$133$	88.2480	−	88.2480i	0.663519	−	0.663519i
$134$	−14.6987	+	188.232i	−0.109691	+	1.40472i
$135$	−120.632			−0.893568
$136$	−156.100	+	96.0518i	−1.14780	+	0.706263i
$137$	82.5459			0.602525			0.301263	−	0.953541i	$-0.402592\pi$
$137$	82.5459			0.602525			0.301263	+	0.953541i	$0.402592\pi$
$138$	−25.9262	−	57.4364i	−0.187871	−	0.416206i
$139$	−48.0812	+	48.0812i	−0.345908	+	0.345908i	−0.858583	−	0.512675i	$-0.828655\pi$
$139$	−48.0812	+	48.0812i	−0.345908	+	0.345908i	0.512675	+	0.858583i	$0.328655\pi$
$140$	87.6602	−	63.8524i	0.626144	−	0.456089i
$141$	5.56573	+	5.56573i	0.0394733	+	0.0394733i
$142$	−142.383	−	166.504i	−1.00270	−	1.17256i
$143$		−	53.1244i		−	0.371499i
$144$	−34.9549	+	108.480i	−0.242742	+	0.753334i
$145$		−	209.026i		−	1.44156i
$146$	77.7685	+	90.9429i	0.532661	+	0.622896i
$147$	−23.5928	−	23.5928i	−0.160495	−	0.160495i
$148$	213.215	−	155.308i	1.44064	−	1.04938i
$149$	135.993	+	135.993i	0.912702	+	0.912702i	0.996484	−	0.0837822i	$-0.0267000\pi$
$149$	135.993	+	135.993i	0.912702	+	0.912702i	−0.0837822	+	0.996484i	$0.526700\pi$
$150$	1.02974	−	13.1870i	0.00686495	−	0.0879130i
$151$			99.7596i			0.660660i	0.943866	+	0.330330i	$0.107160\pi$
$151$			99.7596i			0.660660i	−0.943866	+	0.330330i	$0.892840\pi$
$152$	−195.646	−	46.5919i	−1.28714	−	0.306526i
$153$	163.199			1.06666
$154$	−35.0881	−	2.73996i	−0.227845	−	0.0177919i
$155$	13.3378	+	13.3378i	0.0860503	+	0.0860503i
$156$	81.1271	+	12.7478i	0.520045	+	0.0817168i
$157$	−56.4880	+	56.4880i	−0.359796	+	0.359796i	−0.863738	−	0.503941i	$-0.831883\pi$
$157$	−56.4880	+	56.4880i	−0.359796	+	0.359796i	0.503941	+	0.863738i	$0.331883\pi$
$158$	−12.8342	−	15.0084i	−0.0812292	−	0.0949898i
$159$		−	48.5802i		−	0.305536i
$160$	−161.667	−	66.3877i	−1.01042	−	0.414923i
$161$	−54.9349	−	100.096i	−0.341210	−	0.621712i
$162$	51.4542	−	44.0003i	0.317618	−	0.271607i
$163$	89.3238	+	89.3238i	0.547999	+	0.547999i	0.925862	−	0.377863i	$-0.123341\pi$
$163$	89.3238	+	89.3238i	0.547999	+	0.547999i	−0.377863	+	0.925862i	$0.623341\pi$
$164$	169.299	+	26.6026i	1.03231	+	0.162211i
$165$	−18.7535	+	18.7535i	−0.113658	+	0.113658i
$166$	17.6899	−	226.538i	0.106566	−	1.36469i
$167$			109.877i			0.657949i	0.944339	+	0.328974i	$0.106703\pi$
$167$			109.877i			0.657949i	−0.944339	+	0.328974i	$0.893297\pi$
$168$	12.6040	−	52.9261i	0.0750241	−	0.315036i
$169$			55.5994i			0.328991i
$170$	−19.4823	+	249.491i	−0.114602	+	1.46760i
$171$	126.627	+	126.627i	0.740507	+	0.740507i
$172$	−218.094	+	158.861i	−1.26799	+	0.923613i
$173$	−147.003	−	147.003i	−0.849728	−	0.849728i	0.140371	−	0.990099i	$-0.455171\pi$
$173$	−147.003	−	147.003i	−0.849728	−	0.849728i	−0.990099	+	0.140371i	$0.955171\pi$
$174$	−68.1512	−	79.6964i	−0.391674	−	0.458025i
$175$		−	23.9661i		−	0.136949i
$176$	25.8720	+	50.4718i	0.147000	+	0.286772i
$177$	−128.017			−0.723260
$178$	40.2654	−	34.4324i	0.226210	−	0.193440i
$179$	130.969	+	130.969i	0.731672	+	0.731672i	0.970951	−	0.239279i	$-0.0769109\pi$
$179$	130.969	+	130.969i	0.731672	+	0.731672i	−0.239279	+	0.970951i	$0.576911\pi$
$180$	91.6215	+	125.783i	0.509009	+	0.698796i
$181$	80.3980	+	80.3980i	0.444188	+	0.444188i	0.893417	−	0.449229i	$-0.148301\pi$
$181$	80.3980	+	80.3980i	0.444188	+	0.444188i	−0.449229	+	0.893417i	$0.648301\pi$
$182$	148.346	+	11.5840i	0.815086	+	0.0636484i
$183$	15.6291			0.0854050
$184$	−90.9861	+	159.930i	−0.494490	+	0.869183i
$185$		−	360.160i		−	1.94681i
$186$	9.43403	+	0.736684i	0.0507206	+	0.00396067i
$187$	57.4263	−	57.4263i	0.307092	−	0.307092i
$188$	3.56758	−	22.7040i	0.0189765	−	0.120766i
$189$	−77.5349	+	77.5349i	−0.410238	+	0.410238i
$190$	−208.698	+	178.465i	−1.09841	+	0.939290i
$191$			99.0898i			0.518795i	0.965771	+	0.259397i	$0.0835239\pi$
$191$			99.0898i			0.518795i	−0.965771	+	0.259397i	$0.916476\pi$
$192$	−83.2846	+	27.3982i	−0.433774	+	0.142699i
$193$	−169.000			−0.875645			−0.437823	−	0.899061i	$-0.644250\pi$
$193$	−169.000			−0.875645			−0.437823	+	0.899061i	$0.644250\pi$
$194$	−198.484	−	232.108i	−1.02312	−	1.19644i
$195$	79.2861	−	79.2861i	0.406595	−	0.406595i
$196$	−15.1227	+	96.2408i	−0.0771567	+	0.491025i
$197$	61.9870	−	61.9870i	0.314655	−	0.314655i	−0.532055	−	0.846710i	$-0.678580\pi$
$197$	61.9870	−	61.9870i	0.314655	−	0.314655i	0.846710	+	0.532055i	$0.178580\pi$
$198$	3.93156	−	50.3478i	0.0198563	−	0.254282i
$199$	−341.847			−1.71782			−0.858912	−	0.512123i	$-0.828859\pi$
$199$	−341.847			−1.71782			−0.858912	+	0.512123i	$0.828859\pi$
$200$	−32.8931	+	20.2398i	−0.164465	+	0.101199i
$201$	129.325			0.643407
$202$	−24.7134	+	316.482i	−0.122344	+	1.56674i
$203$	−134.350	−	134.350i	−0.661822	−	0.661822i
$204$	73.9164	+	101.477i	0.362335	+	0.497435i
$205$	165.457	−	165.457i	0.807108	−	0.807108i
$206$	94.0610	−	80.4350i	0.456607	−	0.390461i
$207$	143.627	−	78.8258i	0.693849	−	0.380801i
$208$	−109.382	−	213.385i	−0.525873	−	1.02589i
$209$	89.1146			0.426386
$210$	−48.2784	−	56.4569i	−0.229897	−	0.268843i
$211$	−163.693	−	163.693i	−0.775797	−	0.775797i	0.203316	−	0.979113i	$-0.434828\pi$
$211$	−163.693	−	163.693i	−0.775797	−	0.775797i	−0.979113	+	0.203316i	$0.934828\pi$
$212$	−114.655	+	83.5158i	−0.540826	+	0.393942i
$213$	−106.110	+	106.110i	−0.498171	+	0.498171i
$214$	−196.448	−	15.3402i	−0.917982	−	0.0716833i
$215$			368.401i			1.71349i
$216$	171.895	+	40.9358i	0.795810	+	0.189518i
$217$	17.1455			0.0790115
$218$	−31.1364	+	398.735i	−0.142828	+	1.82906i
$219$	57.9565	−	57.9565i	0.264642	−	0.264642i
$220$	76.5002	+	12.0208i	0.347728	+	0.0546399i
$221$	−242.787	+	242.787i	−1.09858	+	1.09858i
$222$	−117.427	−	137.320i	−0.528951	−	0.618557i
$223$	−178.675			−0.801232			−0.400616	−	0.916246i	$-0.631204\pi$
$223$	−178.675			−0.801232			−0.400616	+	0.916246i	$0.631204\pi$
$224$	−146.580	+	61.2399i	−0.654375	+	0.273392i
$225$	34.3889			0.152839
$226$	−116.730	−	136.504i	−0.516503	−	0.604001i
$227$	280.890	−	280.890i	1.23740	−	1.23740i	0.276342	−	0.961059i	$-0.410878\pi$
$227$	280.890	−	280.890i	1.23740	−	1.23740i	0.961059	−	0.276342i	$-0.0891223\pi$
$228$	−21.3841	+	136.088i	−0.0937900	+	0.596879i
$229$	124.050	+	124.050i	0.541703	+	0.541703i	0.924028	−	0.382325i	$-0.124876\pi$
$229$	124.050	+	124.050i	0.541703	+	0.541703i	−0.382325	+	0.924028i	$0.624876\pi$
$230$	103.360	+	228.981i	0.449390	+	0.995568i
$231$			24.1073i			0.104360i
$232$	−70.9321	+	297.854i	−0.305742	+	1.28385i
$233$			389.389i			1.67120i	0.549339	+	0.835600i	$0.314880\pi$
$233$			389.389i			1.67120i	−0.549339	+	0.835600i	$0.685120\pi$
$234$	−16.6218	+	212.861i	−0.0710335	+	0.909660i
$235$	−22.1888	−	22.1888i	−0.0944205	−	0.0944205i
$236$	220.078	+	302.136i	0.932534	+	1.28024i
$237$	−9.56462	+	9.56462i	−0.0403571	+	0.0403571i
$238$	147.836	+	172.880i	0.621161	+	0.726388i
$239$	98.6362			0.412704			0.206352	−	0.978478i	$-0.433841\pi$
$239$	98.6362			0.412704			0.206352	+	0.978478i	$0.433841\pi$
$240$	−36.7143	+	113.940i	−0.152976	+	0.474751i
$241$		−	212.141i		−	0.880252i	−0.897936	−	0.440126i	$-0.854934\pi$
$241$		−	212.141i		−	0.880252i	0.897936	−	0.440126i	$-0.145066\pi$
$242$	140.946	+	164.823i	0.582420	+	0.681085i
$243$	−173.357	−	173.357i	−0.713402	−	0.713402i
$244$	−26.8685	−	36.8866i	−0.110117	−	0.151175i
$245$	94.0569	+	94.0569i	0.383906	+	0.383906i
$246$	9.13866	−	117.030i	0.0371490	−	0.475733i
$247$	−376.759			−1.52534
$248$	−14.4797	−	23.5319i	−0.0583858	−	0.0948868i
$249$	−155.643			−0.625071
$250$	17.1538	−	219.673i	0.0686151	−	0.878690i
$251$	−131.351	−	131.351i	−0.523311	−	0.523311i	0.395259	−	0.918570i	$-0.370655\pi$
$251$	−131.351	−	131.351i	−0.523311	−	0.523311i	−0.918570	+	0.395259i	$0.870655\pi$
$252$	139.735	+	21.9571i	0.554504	+	0.0871314i
$253$	22.8021	−	78.2764i	0.0901270	−	0.309393i
$254$	122.231	−	104.524i	0.481226	−	0.411514i
$255$	171.413			0.672207
$256$	207.840	+	149.461i	0.811876	+	0.583830i
$257$	−276.833			−1.07717			−0.538586	−	0.842571i	$-0.681041\pi$
$257$	−276.833			−1.07717			−0.538586	+	0.842571i	$0.681041\pi$
$258$	120.114	+	140.462i	0.465558	+	0.544426i
$259$	−231.490	−	231.490i	−0.893782	−	0.893782i
$260$	−323.428	−	50.8215i	−1.24395	−	0.195467i
$261$	192.778	−	192.778i	0.738613	−	0.738613i
$262$	136.393	+	10.6506i	0.520584	+	0.0406513i
$263$	−136.946			−0.520708			−0.260354	−	0.965513i	$-0.583839\pi$
$263$	−136.946			−0.520708			−0.260354	+	0.965513i	$0.583839\pi$
$264$	33.0868	−	20.3590i	0.125329	−	0.0771175i
$265$			193.674i			0.730845i
$266$	−19.4318	+	248.846i	−0.0730520	+	0.935510i
$267$	−25.6605	−	25.6605i	−0.0961068	−	0.0961068i
$268$	−222.326	−	305.222i	−0.829575	−	1.13889i
$269$	−269.558	−	269.558i	−1.00207	−	1.00207i	−0.999998	−	0.00207680i	$-0.999339\pi$
$269$	−269.558	−	269.558i	−1.00207	−	1.00207i	−0.00207680	−	0.999998i	$-0.500661\pi$
$270$	183.362	−	156.800i	0.679120	−	0.580740i
$271$	−231.194			−0.853113			−0.426557	−	0.904461i	$-0.640274\pi$
$271$	−231.194			−0.853113			−0.426557	+	0.904461i	$0.640274\pi$
$272$	112.425	−	348.903i	0.413328	−	1.28273i
$273$		−	101.921i		−	0.373336i
$274$	−125.471	+	107.295i	−0.457925	+	0.391588i
$275$	12.1007	−	12.1007i	0.0440026	−	0.0440026i
$276$	114.066	+	53.6048i	0.413281	+	0.194220i
$277$	147.801	−	147.801i	0.533576	−	0.533576i	−0.388058	−	0.921635i	$-0.626854\pi$
$277$	147.801	−	147.801i	0.533576	−	0.533576i	0.921635	+	0.388058i	$0.126854\pi$
$278$	10.5873	−	135.582i	0.0380838	−	0.487703i
$279$			24.6020i			0.0881792i
$280$	−50.2483	+	211.000i	−0.179458	+	0.753570i
$281$	−247.505			−0.880802			−0.440401	−	0.897801i	$-0.645164\pi$
$281$	−247.505			−0.880802			−0.440401	+	0.897801i	$0.645164\pi$
$282$	−15.6945	−	1.22555i	−0.0556542	−	0.00434592i
$283$	315.317	+	315.317i	1.11419	+	1.11419i	0.992577	+	0.121617i	$0.0388079\pi$
$283$	315.317	+	315.317i	1.11419	+	1.11419i	0.121617	+	0.992577i	$0.461192\pi$
$284$	432.851	+	68.0156i	1.52412	+	0.239492i
$285$	133.000	+	133.000i	0.466667	+	0.466667i
$286$	69.0523	+	80.7501i	0.241442	+	0.282343i
$287$		−	212.692i		−	0.741088i
$288$	−87.8729	−	210.327i	−0.305114	−	0.730302i
$289$	−235.894			−0.816243
$290$	271.697	+	317.724i	0.936888	+	1.09560i
$291$	−147.919	+	147.919i	−0.508314	+	0.508314i
$292$	−236.419	−	37.1495i	−0.809655	−	0.127224i
$293$	−100.387	−	100.387i	−0.342619	−	0.342619i	0.514732	−	0.857351i	$-0.327891\pi$
$293$	−100.387	−	100.387i	−0.342619	−	0.342619i	−0.857351	+	0.514732i	$0.827891\pi$
$294$	66.5279	+	5.19503i	0.226285	+	0.0176702i
$295$	510.363			1.73005
$296$	−122.219	+	513.213i	−0.412901	+	1.73383i
$297$	−78.2963			−0.263624
$298$	−383.478	−	29.9450i	−1.28684	−	0.100487i
$299$	−96.4029	+	330.937i	−0.322418	+	1.10681i
$300$	15.5755	+	21.3829i	0.0519183	+	0.0712764i
$301$	236.787	+	236.787i	0.786666	+	0.786666i
$302$	−129.670	−	151.637i	−0.429371	−	0.502108i
$303$	217.439			0.717619
$304$	357.947	−	183.485i	1.17746	−	0.603568i
$305$	−62.3083			−0.204290
$306$	−248.065	+	212.130i	−0.810671	+	0.693234i
$307$	−208.170	−	208.170i	−0.678079	−	0.678079i	0.281487	−	0.959565i	$-0.409173\pi$
$307$	−208.170	−	208.170i	−0.678079	−	0.678079i	−0.959565	+	0.281487i	$0.909173\pi$
$308$	56.8961	−	41.4436i	0.184728	−	0.134557i
$309$	−59.9437	−	59.9437i	−0.193992	−	0.193992i
$310$	−37.6105	−	2.93693i	−0.121324	−	0.00947396i
$311$			139.841i			0.449649i	0.974399	+	0.224825i	$0.0721809\pi$
$311$			139.841i			0.449649i	−0.974399	+	0.224825i	$0.927819\pi$
$312$	−139.885	+	86.0739i	−0.448348	+	0.275878i
$313$	−279.768			−0.893828			−0.446914	−	0.894577i	$-0.647477\pi$
$313$	−279.768			−0.893828			−0.446914	+	0.894577i	$0.647477\pi$
$314$	12.4384	−	159.287i	0.0396128	−	0.507285i
$315$	136.564	−	136.564i	0.433536	−	0.433536i
$316$	39.0165	+	6.13082i	0.123470	+	0.0194013i
$317$	56.4863	+	56.4863i	0.178190	+	0.178190i	0.790566	−	0.612376i	$-0.209786\pi$
$317$	56.4863	+	56.4863i	0.178190	+	0.178190i	−0.612376	+	0.790566i	$0.709786\pi$
$318$	63.1457	+	73.8429i	0.198571	+	0.232210i
$319$		−	135.669i		−	0.425295i
$320$	332.029	−	109.228i	1.03759	−	0.341337i
$321$			134.970i			0.420466i
$322$	213.609	+	80.7417i	0.663381	+	0.250751i
$323$	−407.268	−	407.268i	−1.26089	−	1.26089i
$324$	−21.0187	+	133.763i	−0.0648724	+	0.412848i
$325$	−51.1595	+	51.1595i	−0.157414	+	0.157414i
$326$	−251.879	−	19.6687i	−0.772635	−	0.0603335i
$327$	273.951			0.837770
$328$	−291.916	+	179.622i	−0.889989	+	0.547629i
$329$	−28.5233			−0.0866970
$330$	4.12944	−	52.8819i	0.0125134	−	0.160248i
$331$	146.057	−	146.057i	0.441259	−	0.441259i	−0.451176	−	0.892435i	$-0.648995\pi$
$331$	146.057	−	146.057i	0.441259	−	0.441259i	0.892435	+	0.451176i	$0.148995\pi$
$332$	267.570	+	367.336i	0.805935	+	1.10643i
$333$	332.164	−	332.164i	0.997488	−	0.997488i
$334$	−142.821	−	167.016i	−0.427609	−	0.500047i
$335$	−515.577			−1.53903
$336$	49.6362	+	96.8318i	0.147727	+	0.288190i
$337$		−	58.9622i		−	0.174962i	−0.996166	−	0.0874810i	$-0.972118\pi$
$337$		−	58.9622i		−	0.174962i	0.996166	−	0.0874810i	$-0.0278817\pi$
$338$	−72.2694	−	84.5122i	−0.213815	−	0.250036i
$339$	−86.9921	+	86.9921i	−0.256614	+	0.256614i
$340$	−294.681	−	404.555i	−0.866710	−	1.18987i
$341$	8.65694	+	8.65694i	0.0253869	+	0.0253869i
$342$	−357.067	−	27.8827i	−1.04406	−	0.0815283i
$343$	364.161			1.06169
$344$	125.015	−	524.956i	0.363416	−	1.52604i
$345$	150.856	−	82.7933i	0.437263	−	0.239980i
$346$	414.525	+	32.3694i	1.19805	+	0.0935533i
$347$	291.060	−	291.060i	0.838790	−	0.838790i	−0.149909	−	0.988700i	$-0.547898\pi$
$347$	291.060	−	291.060i	0.838790	−	0.838790i	0.988700	+	0.149909i	$0.0478982\pi$
$348$	207.182	+	32.5554i	0.595352	+	0.0935500i
$349$	145.858	+	145.858i	0.417931	+	0.417931i	0.884490	−	0.466559i	$-0.154507\pi$
$349$	145.858	+	145.858i	0.417931	+	0.417931i	−0.466559	+	0.884490i	$0.654507\pi$
$350$	31.1517	+	36.4289i	0.0890049	+	0.104083i
$351$	331.021			0.943081
$352$	−104.930	−	43.0891i	−0.298098	−	0.122412i
$353$	116.102			0.328900			0.164450	−	0.986385i	$-0.447415\pi$
$353$	116.102			0.328900			0.164450	+	0.986385i	$0.447415\pi$
$354$	194.588	−	166.400i	0.549685	−	0.470055i
$355$	423.028	−	423.028i	1.19163	−	1.19163i
$356$	−16.4481	+	104.676i	−0.0462026	+	0.294033i
$357$	110.174	−	110.174i	0.308611	−	0.308611i
$358$	−369.313	−	28.8389i	−1.03160	−	0.0805556i
$359$	282.619			0.787241			0.393620	−	0.919273i	$-0.371222\pi$
$359$	282.619			0.787241			0.393620	+	0.919273i	$0.371222\pi$
$360$	−302.763	−	72.1011i	−0.841007	−	0.200281i
$361$		−	271.003i		−	0.750700i
$362$	−226.710	−	17.7033i	−0.626270	−	0.0489041i
$363$	105.039	−	105.039i	0.289364	−	0.289364i
$364$	−240.545	+	175.215i	−0.660839	+	0.481361i
$365$	−231.054	+	231.054i	−0.633026	+	0.633026i
$366$	−23.7566	+	20.3151i	−0.0649086	+	0.0555057i
$367$			707.871i			1.92880i	0.264439	+	0.964402i	$0.414813\pi$
$367$			707.871i			1.92880i	−0.264439	+	0.964402i	$0.585187\pi$
$368$	−69.5797	−	361.362i	−0.189075	−	0.981963i
$369$	305.191			0.827076
$370$	468.145	+	547.450i	1.26526	+	1.47960i
$371$	124.482	+	124.482i	0.335531	+	0.335531i
$372$	−15.2975	+	11.1428i	−0.0411222	+	0.0299538i
$373$	297.466	+	297.466i	0.797497	+	0.797497i	0.982700	−	0.185204i	$-0.0592945\pi$
$373$	297.466	+	297.466i	0.797497	+	0.797497i	−0.185204	+	0.982700i	$0.559294\pi$
$374$	−12.6450	+	161.933i	−0.0338102	+	0.432976i
$375$	−150.926			−0.402469
$376$	24.0884	+	39.1478i	0.0640650	+	0.104116i
$377$			573.582i			1.52144i
$378$	17.0729	−	218.636i	0.0451663	−	0.578403i
$379$	−133.617	−	133.617i	−0.352551	−	0.352551i	0.508507	−	0.861058i	$-0.330198\pi$
$379$	−133.617	−	133.617i	−0.352551	−	0.352551i	−0.861058	+	0.508507i	$0.830198\pi$
$380$	85.2517	−	542.541i	0.224346	−	1.42774i
$381$	−77.8963	−	77.8963i	−0.204452	−	0.204452i
$382$	−128.799	−	150.618i	−0.337171	−	0.394289i
$383$			75.1085i			0.196106i	0.995181	+	0.0980529i	$0.0312614\pi$
$383$			75.1085i			0.196106i	−0.995181	+	0.0980529i	$0.968739\pi$
$384$	90.9813	−	149.901i	0.236931	−	0.390367i
$385$		−	96.1080i		−	0.249631i
$386$	256.883	−	219.670i	0.665499	−	0.569092i
$387$	−339.764	+	339.764i	−0.877943	+	0.877943i
$388$	603.400	+	94.8147i	1.55515	+	0.244368i
$389$	−456.914	−	456.914i	−1.17459	−	1.17459i	−0.981104	−	0.193483i	$-0.938021\pi$
$389$	−456.914	−	456.914i	−1.17459	−	1.17459i	−0.193483	−	0.981104i	$-0.561979\pi$
$390$	−17.4585	+	223.574i	−0.0447653	+	0.573267i
$391$	−461.945	+	253.527i	−1.18145	+	0.648405i
$392$	−102.109	−	165.945i	−0.260483	−	0.423329i
$393$		−	93.7087i		−	0.238444i
$394$	−13.6493	+	174.794i	−0.0346429	+	0.443639i
$395$	38.1311	−	38.1311i	0.0965345	−	0.0965345i
$396$	59.4672	+	81.6399i	0.150170	+	0.206161i
$397$	−98.4535	−	98.4535i	−0.247994	−	0.247994i	0.572153	−	0.820147i	$-0.306108\pi$
$397$	−98.4535	−	98.4535i	−0.247994	−	0.247994i	−0.820147	+	0.572153i	$0.806108\pi$
$398$	519.614	−	444.341i	1.30556	−	1.11643i
$399$	170.969			0.428494
$400$	23.6899	−	73.5201i	0.0592249	−	0.183800i
$401$			262.459i			0.654510i	0.944936	+	0.327255i	$0.106124\pi$
$401$			262.459i			0.654510i	−0.944936	+	0.327255i	$0.893876\pi$
$402$	−196.576	+	168.099i	−0.488995	+	0.418158i
$403$	−36.5998	−	36.5998i	−0.0908184	−	0.0908184i
$404$	−373.805	−	513.181i	−0.925261	−	1.27025i
$405$	130.727	+	130.727i	0.322783	+	0.322783i
$406$	378.845	+	29.5833i	0.933117	+	0.0728652i
$407$		−	233.763i		−	0.574356i
$408$	−244.256	−	58.1681i	−0.598667	−	0.142569i
$409$			394.126i			0.963632i	0.876272	+	0.481816i	$0.160023\pi$
$409$			394.126i			0.963632i	−0.876272	+	0.481816i	$0.839977\pi$
$410$	−36.4329	+	466.563i	−0.0888608	+	1.13796i
$411$	79.9611	+	79.9611i	0.194553	+	0.194553i
$412$	−38.4233	+	244.525i	−0.0932603	+	0.593508i
$413$	328.031	−	328.031i	0.794265	−	0.794265i
$414$	−115.856	+	306.506i	−0.279845	+	0.740353i
$415$	620.498			1.49518
$416$	443.625	+	182.172i	1.06641	+	0.437914i
$417$	−93.1513			−0.223384
$418$	−135.456	+	115.833i	−0.324057	+	0.277113i
$419$	−269.657	+	269.657i	−0.643573	+	0.643573i	−0.951432	−	0.307859i	$-0.900387\pi$
$419$	−269.657	+	269.657i	−0.643573	+	0.643573i	0.307859	+	0.951432i	$0.400387\pi$
$420$	146.768	+	23.0623i	0.349448	+	0.0549102i
$421$	121.759	+	121.759i	0.289214	+	0.289214i	0.836769	−	0.547555i	$-0.184441\pi$
$421$	121.759	+	121.759i	0.289214	+	0.289214i	−0.547555	+	0.836769i	$0.684441\pi$
$422$	461.589	+	36.0445i	1.09381	+	0.0854136i
$423$		−	40.9280i		−	0.0967565i
$424$	65.7223	−	275.977i	0.155005	−	0.650889i
$425$	−110.604			−0.260246
$426$	23.3651	−	299.215i	0.0548476	−	0.702382i
$427$	−40.0481	+	40.0481i	−0.0937895	+	0.0937895i
$428$	318.545	−	232.031i	0.744263	−	0.542127i
$429$	51.4608	−	51.4608i	0.119955	−	0.119955i
$430$	−478.857	−	559.977i	−1.11362	−	1.30227i
$431$			283.847i			0.658579i	0.944229	+	0.329289i	$0.106809\pi$
$431$			283.847i			0.658579i	−0.944229	+	0.329289i	$0.893191\pi$
$432$	−314.493	+	161.210i	−0.727993	+	0.373171i
$433$		−	498.566i		−	1.15142i	−0.817653	−	0.575711i	$-0.804725\pi$
$433$		−	498.566i		−	1.15142i	0.817653	−	0.575711i	$-0.195275\pi$
$434$	−26.0615	+	22.2861i	−0.0600495	+	0.0513505i
$435$	202.481	−	202.481i	0.465473	−	0.465473i
$436$	−470.957	−	646.557i	−1.08018	−	1.48293i
$437$	−555.138	−	161.713i	−1.27034	−	0.370053i
$438$	−12.7618	+	163.428i	−0.0291365	+	0.373124i
$439$		−	302.918i		−	0.690019i	−0.938599	−	0.345009i	$-0.887876\pi$
$439$		−	302.918i		−	0.690019i	0.938599	−	0.345009i	$-0.112124\pi$
$440$	−131.907	+	81.1649i	−0.299788	+	0.184466i
$441$			173.491i			0.393404i
$442$	53.4606	−	684.621i	0.120952	−	1.54892i
$443$	408.336	−	408.336i	0.921751	−	0.921751i	−0.0754026	−	0.997153i	$-0.524024\pi$
$443$	408.336	−	408.336i	0.921751	−	0.921751i	0.997153	+	0.0754026i	$0.0240242\pi$
$444$	356.983	+	56.0942i	0.804016	+	0.126338i
$445$	102.300	+	102.300i	0.229888	+	0.229888i
$446$	271.589	−	232.246i	0.608944	−	0.520730i
$447$			263.468i			0.589414i
$448$	143.203	−	283.614i	0.319651	−	0.633067i
$449$	−305.430			−0.680245			−0.340123	−	0.940381i	$-0.610469\pi$
$449$	−305.430			−0.680245			−0.340123	+	0.940381i	$0.610469\pi$
$450$	−52.2717	+	44.6994i	−0.116159	+	0.0993321i
$451$	107.390	−	107.390i	0.238116	−	0.238116i
$452$	354.863	+	55.7610i	0.785095	+	0.123365i
$453$	−96.6357	+	96.6357i	−0.213324	+	0.213324i
$454$	−61.8508	+	792.066i	−0.136235	+	1.74464i
$455$			406.326i			0.893024i
$456$	−144.387	−	234.652i	−0.316637	−	0.514589i
$457$	−119.262			−0.260967			−0.130483	−	0.991451i	$-0.541653\pi$
$457$	−119.262			−0.260967			−0.130483	+	0.991451i	$0.541653\pi$
$458$	−349.802	−	27.3153i	−0.763759	−	0.0596404i
$459$	357.827	+	357.827i	0.779579	+	0.779579i
$460$	−454.743	−	213.705i	−0.988572	−	0.464577i
$461$	542.761	+	542.761i	1.17736	+	1.17736i	0.980415	+	0.196941i	$0.0631007\pi$
$461$	542.761	+	542.761i	1.17736	+	1.17736i	0.196941	+	0.980415i	$0.436899\pi$
$462$	−31.3352	−	36.6435i	−0.0678251	−	0.0793150i
$463$	−506.187			−1.09328			−0.546638	−	0.837369i	$-0.684093\pi$
$463$	−506.187			−1.09328			−0.546638	+	0.837369i	$0.684093\pi$
$464$	−279.339	−	544.943i	−0.602024	−	1.17445i
$465$			25.8403i			0.0555705i
$466$	−506.138	−	591.880i	−1.08613	−	1.27013i
$467$	390.153	−	390.153i	0.835445	−	0.835445i	−0.152810	−	0.988256i	$-0.548832\pi$
$467$	390.153	−	390.153i	0.835445	−	0.835445i	0.988256	+	0.152810i	$0.0488324\pi$
$468$	−251.416	−	345.158i	−0.537213	−	0.737516i
$469$	−331.382	+	331.382i	−0.706572	+	0.706572i
$470$	62.5690	+	4.88588i	0.133125	+	0.0103955i
$471$	−109.438			−0.232353
$472$	−727.246	−	173.189i	−1.54078	−	0.366927i
$473$			239.112i			0.505522i
$474$	2.10609	−	26.9707i	0.00444323	−	0.0569003i
$475$	−85.8185	−	85.8185i	−0.180671	−	0.180671i
$476$	−449.428	−	70.6204i	−0.944176	−	0.148362i
$477$	−178.619	+	178.619i	−0.374463	+	0.374463i
$478$	−149.929	+	128.210i	−0.313659	+	0.268221i
$479$		−	448.578i		−	0.936490i	−0.883599	−	0.468245i	$-0.844887\pi$
$479$		−	448.578i		−	0.936490i	0.883599	−	0.468245i	$-0.155113\pi$
$480$	−92.2957	−	220.913i	−0.192283	−	0.460236i
$481$			988.303i			2.05468i
$482$	275.746	+	322.458i	0.572086	+	0.669000i
$483$	43.7466	−	150.176i	0.0905727	−	0.310923i
$484$	−428.481	−	67.3289i	−0.885290	−	0.139109i
$485$	589.707	−	589.707i	1.21589	−	1.21589i
$486$	488.839	+	38.1724i	1.00584	+	0.0785440i
$487$		−	126.573i		−	0.259903i	−0.991520	−	0.129951i	$-0.958518\pi$
$487$		−	126.573i		−	0.259903i	0.991520	−	0.129951i	$-0.0414821\pi$
$488$	88.7867	+	21.1440i	0.181940	+	0.0433279i
$489$			173.053i			0.353893i
$490$	−265.226	−	20.7109i	−0.541277	−	0.0422672i
$491$	−25.7043	+	25.7043i	−0.0523509	+	0.0523509i	−0.732798	−	0.680447i	$-0.761786\pi$
$491$	−25.7043	+	25.7043i	−0.0523509	+	0.0523509i	0.680447	+	0.732798i	$0.261786\pi$
$492$	138.228	+	189.767i	0.280951	+	0.385705i
$493$	−620.030	+	620.030i	−1.25767	+	1.25767i
$494$	572.681	−	489.720i	1.15927	−	0.991337i
$495$	137.905			0.278596
$496$	52.5967	+	16.9479i	0.106042	+	0.0341692i
$497$		−	543.795i		−	1.09416i
$498$	236.580	−	202.308i	0.475060	−	0.406241i
$499$	−196.030	−	196.030i	−0.392845	−	0.392845i	0.482855	−	0.875700i	$-0.339600\pi$
$499$	−196.030	−	196.030i	−0.392845	−	0.392845i	−0.875700	+	0.482855i	$0.839600\pi$
$500$	259.461	+	356.203i	0.518923	+	0.712407i
$501$	−106.437	+	106.437i	−0.212449	+	0.212449i
$502$	370.389	+	28.9229i	0.737827	+	0.0576154i
$503$	492.988			0.980096			0.490048	−	0.871695i	$-0.336979\pi$
$503$	492.988			0.980096			0.490048	+	0.871695i	$0.336979\pi$
$504$	−240.940	+	148.256i	−0.478056	+	0.294158i
$505$	−866.858			−1.71655
$506$	67.0859	+	148.620i	0.132581	+	0.293716i
$507$	−53.8584	+	53.8584i	−0.106230	+	0.106230i
$508$	−49.9307	+	317.758i	−0.0982887	+	0.625509i
$509$	−42.3253	−	42.3253i	−0.0831539	−	0.0831539i	0.664306	−	0.747460i	$-0.268727\pi$
$509$	−42.3253	−	42.3253i	−0.0831539	−	0.0831539i	−0.747460	+	0.664306i	$0.768727\pi$
$510$	−260.551	+	222.807i	−0.510884	+	0.436876i
$511$			297.016i			0.581245i
$512$	−510.193	+	42.9727i	−0.996472	+	0.0839311i
$513$			555.279i			1.08242i
$514$	420.792	−	359.834i	0.818661	−	0.700067i
$515$	238.976	+	238.976i	0.464032	+	0.464032i
$516$	−365.151	−	57.3777i	−0.707658	−	0.111197i
$517$	−14.4017	−	14.4017i	−0.0278563	−	0.0278563i
$518$	652.764	+	50.9730i	1.26016	+	0.0984035i
$519$		−	284.799i		−	0.548746i
$520$	557.676	−	343.149i	1.07245	−	0.659903i
$521$	273.112			0.524208			0.262104	−	0.965040i	$-0.415584\pi$
$521$	273.112			0.524208			0.262104	+	0.965040i	$0.415584\pi$
$522$	−42.4489	+	543.604i	−0.0813197	+	1.04139i
$523$	−598.146	−	598.146i	−1.14368	−	1.14368i	−0.987771	−	0.155911i	$-0.950169\pi$
$523$	−598.146	−	598.146i	−1.14368	−	1.14368i	−0.155911	−	0.987771i	$-0.549831\pi$
$524$	−221.164	+	161.098i	−0.422068	+	0.307438i
$525$	23.2156	−	23.2156i	0.0442202	−	0.0442202i
$526$	208.161	−	178.006i	0.395743	−	0.338414i
$527$		−	79.1272i		−	0.150146i
$528$	−23.8295	+	73.9532i	−0.0451316	+	0.140063i
$529$	−284.091	+	446.244i	−0.537034	+	0.843561i
$530$	−251.742	−	294.388i	−0.474985	−	0.555449i
$531$	470.691	+	470.691i	0.886424	+	0.886424i
$532$	−293.919	−	403.508i	−0.552479	−	0.758474i
$533$	−454.025	+	454.025i	−0.851830	+	0.851830i
$534$	72.3586	+	5.65034i	0.135503	+	0.0105812i
$535$		−	538.081i		−	1.00576i
$536$	734.675	+	174.958i	1.37066	+	0.326415i
$537$			253.736i			0.472507i
$538$	760.111	+	59.3555i	1.41285	+	0.110326i
$539$	61.0479	+	61.0479i	0.113261	+	0.113261i
$540$	−74.9023	+	476.678i	−0.138708	+	0.882737i
$541$	236.983	+	236.983i	0.438046	+	0.438046i	0.891354	−	0.453308i	$-0.149756\pi$
$541$	236.983	+	236.983i	0.438046	+	0.438046i	−0.453308	+	0.891354i	$0.649756\pi$
$542$	351.419	−	300.511i	0.648374	−	0.554448i
$543$			155.761i			0.286852i
$544$	282.624	+	676.473i	0.519530	+	1.24352i
$545$	−1092.15			−2.00395
$546$	132.479	+	154.922i	0.242636	+	0.283739i
$547$	52.8163	+	52.8163i	0.0965563	+	0.0965563i	0.753735	−	0.657179i	$-0.228250\pi$
$547$	52.8163	+	52.8163i	0.0965563	+	0.0965563i	−0.657179	+	0.753735i	$0.728250\pi$
$548$	51.2542	−	326.181i	0.0935296	−	0.595222i
$549$	−57.4649	−	57.4649i	−0.104672	−	0.104672i
$550$	−2.66453	+	34.1221i	−0.00484460	+	0.0620402i
$551$	−962.168			−1.74622
$552$	−243.059	+	66.7847i	−0.440324	+	0.120987i
$553$		−	49.0169i		−	0.0886381i
$554$	−32.5451	+	416.775i	−0.0587456	+	0.752301i
$555$	348.882	−	348.882i	0.628616	−	0.628616i
$556$	160.139	+	219.848i	0.288020	+	0.395410i
$557$	251.390	−	251.390i	0.451328	−	0.451328i	−0.444467	−	0.895795i	$-0.646607\pi$
$557$	251.390	−	251.390i	0.451328	−	0.451328i	0.895795	+	0.444467i	$0.146607\pi$
$558$	−31.9783	−	37.3955i	−0.0573087	−	0.0670171i
$559$		−	1010.92i		−	1.80844i
$560$	−197.884	−	386.037i	−0.353364	−	0.689353i
$561$	111.256			0.198317
$562$	376.213	−	321.713i	0.669418	−	0.572444i
$563$	−33.8785	+	33.8785i	−0.0601750	+	0.0601750i	−0.736554	−	0.676379i	$-0.763548\pi$
$563$	−33.8785	+	33.8785i	−0.0601750	+	0.0601750i	0.676379	+	0.736554i	$0.263548\pi$
$564$	25.4489	−	18.5372i	0.0451222	−	0.0328674i
$565$	346.810	−	346.810i	0.613823	−	0.613823i
$566$	−889.144	−	69.4314i	−1.57093	−	0.122670i
$567$	168.048			0.296380
$568$	−746.350	+	459.245i	−1.31400	+	0.808530i
$569$	737.778			1.29662			0.648311	−	0.761376i	$-0.275476\pi$
$569$	737.778			1.29662			0.648311	+	0.761376i	$0.275476\pi$
$570$	−375.039	−	29.2861i	−0.657964	−	0.0513790i
$571$	−6.63781	−	6.63781i	−0.0116249	−	0.0116249i	0.701270	−	0.712895i	$-0.252617\pi$
$571$	−6.63781	−	6.63781i	−0.0116249	−	0.0116249i	−0.712895	+	0.701270i	$0.752617\pi$
$572$	−209.922	−	32.9858i	−0.366996	−	0.0576676i
$573$	−95.9868	+	95.9868i	−0.167516	+	0.167516i
$574$	276.462	+	323.296i	0.481642	+	0.563234i
$575$	−97.3400	+	53.4225i	−0.169287	+	0.0929087i
$576$	406.957	+	205.482i	0.706522	+	0.356740i
$577$	1032.74			1.78985			0.894924	−	0.446218i	$-0.147229\pi$
$577$	1032.74			1.78985			0.894924	+	0.446218i	$0.147229\pi$
$578$	358.564	−	306.621i	0.620353	−	0.530486i
$579$	−163.707	−	163.707i	−0.282742	−	0.282742i
$580$	−825.971	−	129.788i	−1.42409	−	0.223773i
$581$	398.820	−	398.820i	0.686437	−	0.686437i
$582$	32.5712	−	417.109i	0.0559643	−	0.716682i
$583$			125.705i			0.215617i
$584$	407.650	−	250.835i	0.698031	−	0.429513i
$585$	−583.035			−0.996642
$586$	283.076	+	22.1048i	0.483065	+	0.0377216i
$587$	−78.3187	+	78.3187i	−0.133422	+	0.133422i	−0.770664	−	0.637242i	$-0.780075\pi$
$587$	−78.3187	+	78.3187i	−0.133422	+	0.133422i	0.637242	+	0.770664i	$0.280075\pi$
$588$	−107.876	+	78.5780i	−0.183463	+	0.133636i
$589$	61.3951	−	61.3951i	0.104236	−	0.104236i
$590$	−775.762	+	663.382i	−1.31485	+	1.12438i
$591$	120.092			0.203201
$592$	−481.311	−	938.956i	−0.813026	−	1.58607i
$593$	−476.153			−0.802957			−0.401478	−	0.915868i	$-0.631504\pi$
$593$	−476.153			−0.802957			−0.401478	+	0.915868i	$0.631504\pi$
$594$	119.012	−	101.771i	0.200357	−	0.171332i
$595$	−439.229	+	439.229i	−0.738200	+	0.738200i
$596$	621.817	−	452.936i	1.04332	−	0.759960i
$597$	−331.142	−	331.142i	−0.554677	−	0.554677i
$598$	−283.626	−	628.338i	−0.474291	−	1.05073i
$599$			391.546i			0.653666i	0.945082	+	0.326833i	$0.105982\pi$
$599$			391.546i			0.653666i	−0.945082	+	0.326833i	$0.894018\pi$
$600$	−51.4691	−	12.2571i	−0.0857818	−	0.0204284i
$601$			433.682i			0.721600i	0.932643	+	0.360800i	$0.117496\pi$
$601$			433.682i			0.721600i	−0.932643	+	0.360800i	$0.882504\pi$
$602$	−667.701	−	52.1394i	−1.10914	−	0.0866103i
$603$	−475.499	−	475.499i	−0.788556	−	0.788556i
$604$	394.202	+	61.9425i	0.652652	+	0.102554i
$605$	−418.757	+	418.757i	−0.692160	+	0.692160i
$606$	−330.511	+	282.632i	−0.545397	+	0.466389i
$607$	742.545			1.22330			0.611652	−	0.791127i	$-0.290505\pi$
$607$	742.545			1.22330			0.611652	+	0.791127i	$0.290505\pi$
$608$	−305.589	+	744.168i	−0.502613	+	1.22396i
$609$		−	260.286i		−	0.427398i
$610$	94.7098	−	80.9898i	0.155262	−	0.132770i
$611$	60.8876	+	60.8876i	0.0996523	+	0.0996523i
$612$	101.333	−	644.882i	0.165577	−	1.05373i
$613$	93.7355	+	93.7355i	0.152913	+	0.152913i	0.779418	−	0.626505i	$-0.215515\pi$
$613$	93.7355	+	93.7355i	0.152913	+	0.152913i	−0.626505	+	0.779418i	$0.715515\pi$
$614$	587.007	+	45.8382i	0.956038	+	0.0746550i
$615$	320.552			0.521223
$616$	−32.6138	+	136.950i	−0.0529445	+	0.222321i
$617$	942.229			1.52711			0.763557	−	0.645741i	$-0.223451\pi$
$617$	942.229			1.52711			0.763557	+	0.645741i	$0.223451\pi$
$618$	169.032	+	13.1993i	0.273514	+	0.0213582i
$619$	631.547	+	631.547i	1.02027	+	1.02027i	0.999790	+	0.0204802i	$0.00651951\pi$
$619$	631.547	+	631.547i	1.02027	+	1.02027i	0.0204802	+	0.999790i	$0.493480\pi$
$620$	60.9862	−	44.4228i	0.0983648	−	0.0716497i
$621$	487.746	+	142.082i	0.785420	+	0.228795i
$622$	−181.769	−	212.561i	−0.292232	−	0.341738i
$623$	131.505			0.211084
$624$	100.746	−	312.659i	0.161453	−	0.501057i
$625$	722.385			1.15582
$626$	425.253	−	363.649i	0.679318	−	0.580909i
$627$	86.3241	+	86.3241i	0.137678	+	0.137678i
$628$	188.139	+	258.288i	0.299584	+	0.411286i
$629$	−1068.33	+	1068.33i	−1.69846	+	1.69846i
$630$	−30.0708	+	385.089i	−0.0477314	+	0.611252i
$631$	−24.5704			−0.0389388			−0.0194694	−	0.999810i	$-0.506198\pi$
$631$	−24.5704			−0.0389388			−0.0194694	+	0.999810i	$0.506198\pi$
$632$	−67.2748	+	41.3956i	−0.106448	+	0.0654994i
$633$		−	317.134i		−	0.501002i
$634$	−159.282	−	12.4380i	−0.251234	−	0.0196184i
$635$	310.548	+	310.548i	0.489051	+	0.489051i
$636$	−191.965	−	30.1643i	−0.301832	−	0.0474281i
$637$	−258.098	−	258.098i	−0.405178	−	0.405178i
$638$	176.346	+	206.220i	0.276404	+	0.323228i
$639$	780.290			1.22111
$640$	−362.714	+	597.608i	−0.566740	+	0.933762i
$641$		−	1087.77i		−	1.69700i	−0.529198	−	0.848498i	$-0.677507\pi$
$641$		−	1087.77i		−	1.69700i	0.529198	−	0.848498i	$-0.322493\pi$
$642$	−175.437	−	205.156i	−0.273266	−	0.319558i
$643$	152.471	−	152.471i	0.237125	−	0.237125i	−0.578534	−	0.815658i	$-0.696375\pi$
$643$	152.471	−	152.471i	0.237125	−	0.237125i	0.815658	+	0.578534i	$0.196375\pi$
$644$	−429.639	+	154.925i	−0.667142	+	0.240566i
$645$	−356.865	+	356.865i	−0.553279	+	0.553279i
$646$	1148.43	+	89.6787i	1.77776	+	0.138822i
$647$			39.7499i			0.0614372i	0.999528	+	0.0307186i	$0.00977957\pi$
$647$			39.7499i			0.0614372i	−0.999528	+	0.0307186i	$0.990220\pi$
$648$	−141.919	−	230.642i	−0.219011	−	0.355930i
$649$	331.253			0.510405
$650$	11.2651	−	144.262i	0.0173309	−	0.221941i
$651$	16.6086	+	16.6086i	0.0255125	+	0.0255125i
$652$	408.427	−	297.502i	0.626422	−	0.456291i
$653$	395.876	+	395.876i	0.606242	+	0.606242i	0.941962	−	0.335720i	$-0.108980\pi$
$653$	395.876	+	395.876i	0.606242	+	0.606242i	−0.335720	+	0.941962i	$0.608980\pi$
$654$	−416.411	+	356.088i	−0.636713	+	0.544477i
$655$			373.587i			0.570361i
$656$	210.241	−	652.469i	0.320490	−	0.994618i
$657$	−426.187			−0.648687
$658$	43.3560	−	37.0753i	0.0658906	−	0.0563454i
$659$	−405.743	+	405.743i	−0.615695	+	0.615695i	−0.944424	−	0.328729i	$-0.893380\pi$
$659$	−405.743	+	405.743i	−0.615695	+	0.615695i	0.328729	+	0.944424i	$0.393380\pi$
$660$	62.4603	+	85.7490i	0.0946368	+	0.129923i
$661$	505.963	+	505.963i	0.765450	+	0.765450i	0.977302	−	0.211852i	$-0.0679494\pi$
$661$	505.963	+	505.963i	0.765450	+	0.765450i	−0.211852	+	0.977302i	$0.567949\pi$
$662$	−32.1611	+	411.857i	−0.0485817	+	0.622140i
$663$	−470.368			−0.709455
$664$	−884.184	−	210.563i	−1.33160	−	0.317113i
$665$	−681.600			−1.02496
$666$	−73.1410	+	936.649i	−0.109821	+	1.40638i
$667$	−246.194	+	845.148i	−0.369106	+	1.26709i
$668$	434.182	+	68.2248i	0.649973	+	0.102133i
$669$	−173.080	−	173.080i	−0.258714	−	0.258714i
$670$	783.686	−	670.159i	1.16968	−	1.00024i
$671$	−40.4414			−0.0602703
$672$	−201.312	−	82.6678i	−0.299572	−	0.123018i
$673$	826.926			1.22872			0.614358	−	0.789027i	$-0.289415\pi$
$673$	826.926			1.22872			0.614358	+	0.789027i	$0.289415\pi$
$674$	76.6404	+	89.6236i	0.113710	+	0.132973i
$675$	75.4004	+	75.4004i	0.111704	+	0.111704i
$676$	219.702	+	34.5226i	0.325003	+	0.0510690i
$677$	359.452	+	359.452i	0.530948	+	0.530948i	0.920854	−	0.389906i	$-0.127493\pi$
$677$	359.452	+	359.452i	0.530948	+	0.530948i	−0.389906	+	0.920854i	$0.627493\pi$
$678$	19.1553	−	245.304i	0.0282526	−	0.361805i
$679$		−	758.058i		−	1.11643i
$680$	973.772	+	231.898i	1.43202	+	0.341026i
$681$	544.189			0.799102
$682$	−24.4112	−	1.90622i	−0.0357935	−	0.00279504i
$683$	−728.526	+	728.526i	−1.06666	+	1.06666i	−0.0690415	+	0.997614i	$0.521994\pi$
$683$	−728.526	+	728.526i	−1.06666	+	1.06666i	−0.997614	+	0.0690415i	$0.978006\pi$
$684$	578.992	−	421.743i	0.846480	−	0.616583i
$685$	−318.779	−	318.779i	−0.465371	−	0.465371i
$686$	−553.531	+	473.344i	−0.806897	+	0.690006i
$687$			240.331i			0.349827i
$688$	492.325	+	960.441i	0.715589	+	1.39599i
$689$		−	531.454i		−	0.771341i
$690$	−121.687	+	321.933i	−0.176358	+	0.466570i
$691$	658.838	+	658.838i	0.953456	+	0.953456i	0.998964	−	0.0455076i	$-0.0144905\pi$
$691$	658.838	+	658.838i	0.953456	+	0.953456i	−0.0455076	+	0.998964i	$0.514491\pi$
$692$	−672.161	+	489.608i	−0.971331	+	0.707525i
$693$	88.6372	−	88.6372i	0.127904	−	0.127904i
$694$	−64.0902	+	820.744i	−0.0923490	+	1.18263i
$695$	371.364			0.534337
$696$	−357.238	+	219.816i	−0.513272	+	0.315827i
$697$	−981.582			−1.40830
$698$	−411.296	−	32.1173i	−0.589250	−	0.0460133i
$699$	−377.196	+	377.196i	−0.539622	+	0.539622i
$700$	−94.7024	−	14.8810i	−0.135289	−	0.0212585i
$701$	−377.367	+	377.367i	−0.538327	+	0.538327i	−0.923037	−	0.384711i	$-0.874301\pi$
$701$	−377.367	+	377.367i	−0.538327	+	0.538327i	0.384711	+	0.923037i	$0.374301\pi$
$702$	−503.159	+	430.269i	−0.716751	+	0.612919i
$703$	−1657.85			−2.35825
$704$	215.504	−	70.8947i	0.306114	−	0.100703i
$705$		−	42.9880i		−	0.0609758i
$706$	−176.477	+	150.912i	−0.249967	+	0.213756i
$707$	−557.165	+	557.165i	−0.788070	+	0.788070i
$708$	−79.4880	+	505.861i	−0.112271	+	0.714493i
$709$	−8.38287	−	8.38287i	−0.0118235	−	0.0118235i	0.701170	−	0.712994i	$-0.252661\pi$
$709$	−8.38287	−	8.38287i	−0.0118235	−	0.0118235i	−0.712994	+	0.701170i	$0.752661\pi$
$710$	−93.1491	+	1192.87i	−0.131196	+	1.68010i
$711$	70.3341			0.0989228
$712$	−111.059	−	180.489i	−0.155981	−	0.253495i
$713$	−38.2188	−	69.6377i	−0.0536028	−	0.0976685i
$714$	−24.2599	+	310.674i	−0.0339774	+	0.435117i
$715$	−205.158	+	205.158i	−0.286934	+	0.286934i
$716$	598.848	−	436.206i	0.836380	−	0.609226i
$717$	95.5475	+	95.5475i	0.133260	+	0.133260i
$718$	−429.587	+	367.355i	−0.598310	+	0.511637i
$719$	−493.164			−0.685902			−0.342951	−	0.939353i	$-0.611426\pi$
$719$	−493.164			−0.685902			−0.342951	+	0.939353i	$0.611426\pi$
$720$	553.924	−	283.943i	0.769338	−	0.394365i
$721$	307.200			0.426075
$722$	352.256	+	411.929i	0.487889	+	0.570539i
$723$	205.498	−	205.498i	0.284229	−	0.284229i
$724$	367.614	−	267.773i	0.507754	−	0.369852i
$725$	−130.651	+	130.651i	−0.180208	+	0.180208i
$726$	−23.1291	+	296.193i	−0.0318583	+	0.407980i
$727$	1075.26			1.47904			0.739521	−	0.673133i	$-0.235052\pi$
$727$	1075.26			1.47904			0.739521	+	0.673133i	$0.235052\pi$
$728$	137.885	−	578.997i	0.189402	−	0.795326i
$729$		−	31.1973i		−	0.0427946i
$730$	50.8772	−	651.537i	0.0696948	−	0.892516i
$731$	1092.78	−	1092.78i	1.49491	−	1.49491i
$732$	9.70439	−	61.7587i	0.0132574	−	0.0843697i
$733$	−228.200	+	228.200i	−0.311323	+	0.311323i	−0.845422	−	0.534099i	$-0.820651\pi$
$733$	−228.200	+	228.200i	−0.311323	+	0.311323i	0.534099	+	0.845422i	$0.320651\pi$
$734$	−920.108	−	1075.98i	−1.25355	−	1.46591i
$735$			182.223i			0.247923i
$736$	575.470	+	458.836i	0.781888	+	0.623419i
$737$	−334.636			−0.454052
$738$	−463.896	+	396.694i	−0.628586	+	0.537526i
$739$	227.365	+	227.365i	0.307666	+	0.307666i	0.844003	−	0.536338i	$-0.180193\pi$
$739$	227.365	+	227.365i	0.307666	+	0.307666i	−0.536338	+	0.844003i	$0.680193\pi$
$740$	−1423.18	−	223.630i	−1.92321	−	0.302202i
$741$	−364.961	−	364.961i	−0.492525	−	0.492525i
$742$	−351.020	−	27.4104i	−0.473073	−	0.0369413i
$743$	−214.590			−0.288816			−0.144408	−	0.989518i	$-0.546128\pi$
$743$	−214.590			−0.288816			−0.144408	+	0.989518i	$0.546128\pi$
$744$	8.76877	−	36.8213i	0.0117860	−	0.0494910i
$745$		−	1050.36i		−	1.40988i
$746$	−838.808	−	65.5008i	−1.12441	−	0.0878027i
$747$	572.265	+	572.265i	0.766084	+	0.766084i
$748$	−191.264	−	262.578i	−0.255700	−	0.351040i
$749$	−345.847	−	345.847i	−0.461745	−	0.461745i
$750$	229.410	−	196.177i	0.305880	−	0.261569i
$751$		−	584.412i		−	0.778178i	−0.921200	−	0.389089i	$-0.872790\pi$
$751$		−	584.412i		−	0.778178i	0.921200	−	0.389089i	$-0.127210\pi$
$752$	−87.5001	−	28.1946i	−0.116357	−	0.0374929i
$753$		−	254.476i		−	0.337949i
$754$	−745.556	−	871.856i	−0.988801	−	1.15631i
$755$	385.256	−	385.256i	0.510273	−	0.510273i
$756$	258.238	+	354.523i	0.341584	+	0.468946i
$757$	−523.764	−	523.764i	−0.691895	−	0.691895i	0.270754	−	0.962649i	$-0.412727\pi$
$757$	−523.764	−	523.764i	−0.691895	−	0.691895i	−0.962649	+	0.270754i	$0.912727\pi$
$758$	376.778	+	29.4219i	0.497069	+	0.0388151i
$759$	97.9134	−	53.7372i	0.129003	−	0.0708000i
$760$	575.623	+	935.485i	0.757399	+	1.23090i
$761$			513.357i			0.674583i	0.941400	+	0.337291i	$0.109511\pi$
$761$			513.357i			0.674583i	−0.941400	+	0.337291i	$0.890489\pi$
$762$	219.655	+	17.1524i	0.288261	+	0.0225097i
$763$	−701.973	+	701.973i	−0.920017	+	0.920017i
$764$	391.555	+	61.5266i	0.512506	+	0.0805321i
$765$	−630.248	−	630.248i	−0.823854	−	0.823854i
$766$	−97.6278	−	114.166i	−0.127451	−	0.149042i
$767$	−1400.47			−1.82591
$768$	56.5516	+	346.112i	0.0736348	+	0.450667i
$769$		−	510.984i		−	0.664479i	−0.943195	−	0.332240i	$-0.892196\pi$
$769$		−	510.984i		−	0.664479i	0.943195	−	0.332240i	$-0.107804\pi$
$770$	124.923	+	146.086i	0.162238	+	0.189722i
$771$	−268.164	−	268.164i	−0.347814	−	0.347814i
$772$	−104.935	+	667.804i	−0.135926	+	0.865031i
$773$	−389.388	−	389.388i	−0.503735	−	0.503735i	0.408861	−	0.912597i	$-0.365926\pi$
$773$	−389.388	−	389.388i	−0.503735	−	0.503735i	−0.912597	+	0.408861i	$0.865926\pi$
$774$	74.8146	−	958.081i	0.0966597	−	1.23783i
$775$		−	16.6735i		−	0.0215142i
$776$	−1040.42	+	640.194i	−1.34075	+	0.824992i
$777$		−	448.481i		−	0.577196i
$778$	1288.43	+	100.611i	1.65608	+	0.129320i
$779$	−761.615	−	761.615i	−0.977682	−	0.977682i
$780$	−264.070	−	362.530i	−0.338551	−	0.464782i
$781$	274.568	−	274.568i	0.351559	−	0.351559i
$782$	372.626	−	985.813i	0.476504	−	1.26063i
$783$	845.363			1.07965
$784$	370.907	+	119.515i	0.473096	+	0.152443i
$785$	436.296			0.555791
$786$	121.805	+	142.439i	0.154968	+	0.181220i
$787$	163.512	−	163.512i	0.207767	−	0.207767i	−0.595551	−	0.803318i	$-0.703066\pi$
$787$	163.512	−	163.512i	0.207767	−	0.207767i	0.803318	+	0.595551i	$0.203066\pi$
$788$	−206.454	−	283.432i	−0.261997	−	0.359685i
$789$	−132.658	−	132.658i	−0.168134	−	0.168134i
$790$	−8.39631	+	107.524i	−0.0106282	+	0.136106i
$791$		−	445.818i		−	0.563613i
$792$	−196.509	−	46.7974i	−0.248117	−	0.0590876i
$793$	170.978			0.215609
$794$	277.623	+	21.6790i	0.349652	+	0.0273036i
$795$	−187.609	+	187.609i	−0.235986	+	0.235986i
$796$	−212.259	+	1350.81i	−0.266657	+	1.69700i
$797$	369.221	−	369.221i	0.463264	−	0.463264i	−0.436460	−	0.899724i	$-0.643768\pi$
$797$	369.221	−	369.221i	0.463264	−	0.463264i	0.899724	+	0.436460i	$0.143768\pi$
$798$	−259.877	+	222.230i	−0.325660	+	0.278484i
$799$			131.636i			0.164751i
$800$	59.5539	+	142.545i	0.0744424	+	0.178181i
$801$			188.696i			0.235576i
$802$	−341.150	−	398.942i	−0.425374	−	0.497434i
$803$	−149.966	+	149.966i	−0.186758	+	0.186758i
$804$	80.3000	−	511.028i	0.0998756	−	0.635608i
$805$	−174.404	+	598.703i	−0.216651	+	0.743731i
$806$	103.206	+	8.05912i	0.128047	+	0.00999891i
$807$		−	522.234i		−	0.647130i
$808$	1235.24	+	294.164i	1.52876	+	0.364065i
$809$		−	1152.53i		−	1.42463i	−0.701860	−	0.712315i	$-0.747647\pi$
$809$		−	1152.53i		−	1.42463i	0.701860	−	0.712315i	$-0.252353\pi$
$810$	−368.630	−	28.7856i	−0.455099	−	0.0355378i
$811$	26.1148	−	26.1148i	0.0322007	−	0.0322007i	−0.690823	−	0.723024i	$-0.742752\pi$
$811$	26.1148	−	26.1148i	0.0322007	−	0.0322007i	0.723024	+	0.690823i	$0.242752\pi$
$812$	−614.305	+	447.465i	−0.756534	+	0.551065i
$813$	−223.954	−	223.954i	−0.275466	−	0.275466i
$814$	303.850	+	355.324i	0.373281	+	0.436516i
$815$		−	689.909i		−	0.846514i
$816$	446.882	−	229.073i	0.547650	−	0.280727i
$817$	1695.79			2.07563
$818$	−512.294	−	599.078i	−0.626276	−	0.732370i
$819$	−374.741	+	374.741i	−0.457559	+	0.457559i
$820$	−551.071	−	756.541i	−0.672038	−	0.922611i
$821$	−835.893	+	835.893i	−1.01814	+	1.01814i	−0.0183073	+	0.999832i	$0.505828\pi$
$821$	−835.893	+	835.893i	−1.01814	+	1.01814i	−0.999832	+	0.0183073i	$0.994172\pi$
$822$	−225.478	−	17.6071i	−0.274304	−	0.0214198i
$823$		−	1023.01i		−	1.24303i	−0.783403	−	0.621515i	$-0.786518\pi$
$823$		−	1023.01i		−	1.24303i	0.783403	−	0.621515i	$-0.213482\pi$
$824$	−259.436	−	421.627i	−0.314849	−	0.511683i
$825$	23.4436			0.0284165
$826$	−72.2311	+	924.997i	−0.0874469	+	1.11985i
$827$	−199.641	−	199.641i	−0.241403	−	0.241403i	0.576027	−	0.817431i	$-0.304602\pi$
$827$	−199.641	−	199.641i	−0.241403	−	0.241403i	−0.817431	+	0.576027i	$0.804602\pi$
$828$	−222.301	−	616.488i	−0.268479	−	0.744550i
$829$	680.945	+	680.945i	0.821405	+	0.821405i	0.986310	−	0.164904i	$-0.0527316\pi$
$829$	680.945	+	680.945i	0.821405	+	0.821405i	−0.164904	+	0.986310i	$0.552732\pi$
$830$	−943.170	+	806.538i	−1.13635	+	0.971733i
$831$	286.345			0.344579
$832$	−911.110	+	299.729i	−1.09508	+	0.360251i
$833$		−	557.997i		−	0.669864i
$834$	141.592	−	121.080i	0.169774	−	0.145180i
$835$	424.329	−	424.329i	0.508179	−	0.508179i
$836$	55.3328	−	352.138i	0.0661876	−	0.421217i
$837$	−53.9419	+	53.9419i	−0.0644467	+	0.0644467i
$838$	59.3773	−	760.390i	0.0708560	−	0.907387i
$839$	−1233.69			−1.47043			−0.735216	−	0.677833i	$-0.762919\pi$
$839$	−1233.69			−1.47043			−0.735216	+	0.677833i	$0.762919\pi$
$840$	−253.067	+	155.718i	−0.301270	+	0.185378i
$841$			623.815i			0.741754i
$842$	−343.342	−	26.8108i	−0.407769	−	0.0318419i
$843$	−239.755	−	239.755i	−0.284407	−	0.284407i
$844$	−748.476	+	545.196i	−0.886820	+	0.645967i
$845$	214.716	−	214.716i	0.254102	−	0.254102i
$846$	53.1992	+	62.2113i	0.0628832	+	0.0735358i
$847$			538.305i			0.635543i
$848$	258.822	+	504.918i	0.305215	+	0.595422i
$849$			610.886i			0.719536i
$850$	168.121	−	143.766i	0.197789	−	0.169137i
$851$	−424.201	+	1456.22i	−0.498474	+	1.71119i
$852$	353.411	+	485.182i	0.414802	+	0.569463i
$853$	852.790	−	852.790i	0.999754	−	0.999754i	−0.000246301	−	1.00000i	$-0.500078\pi$
$853$	852.790	−	852.790i	0.999754	−	0.999754i	1.00000		0.000246301i	$7.84002e-5\pi$
$854$	8.81842	−	112.929i	0.0103260	−	0.132236i
$855$		−	978.025i		−	1.14389i
$856$	−182.595	+	766.743i	−0.213312	+	0.895727i
$857$		−	963.509i		−	1.12428i	−0.827042	−	0.562141i	$-0.809978\pi$
$857$		−	963.509i		−	1.12428i	0.827042	−	0.562141i	$-0.190022\pi$
$858$	−11.3315	+	145.111i	−0.0132068	+	0.169128i
$859$	−143.123	+	143.123i	−0.166616	+	0.166616i	−0.785490	−	0.618874i	$-0.787589\pi$
$859$	−143.123	+	143.123i	−0.166616	+	0.166616i	0.618874	+	0.785490i	$0.287589\pi$
$860$	1455.74	+	228.747i	1.69272	+	0.265985i
$861$	206.032	−	206.032i	0.239294	−	0.239294i
$862$	−368.952	−	431.454i	−0.428018	−	0.500526i
$863$	−353.986			−0.410181			−0.205090	−	0.978743i	$-0.565749\pi$
$863$	−353.986			−0.410181			−0.205090	+	0.978743i	$0.565749\pi$
$864$	268.491	−	653.828i	0.310753	−	0.756745i
$865$			1135.40i			1.31261i
$866$	648.047	+	757.829i	0.748323	+	0.875092i
$867$	−228.508	−	228.508i	−0.263561	−	0.263561i
$868$	10.6459	−	67.7507i	0.0122649	−	0.0780538i
$869$	24.7491	−	24.7491i	0.0284800	−	0.0284800i
$870$	−44.5854	+	570.964i	−0.0512476	+	0.656281i
$871$	1414.78			1.62431
$872$	1556.27	+	370.618i	1.78472	+	0.425020i
$873$	1087.73			1.24597
$874$	1054.02	−	475.774i	1.20597	−	0.544364i
$875$	386.733	−	386.733i	0.441981	−	0.441981i
$876$	−193.030	−	265.002i	−0.220354	−	0.302514i
$877$	−791.110	−	791.110i	−0.902064	−	0.902064i	0.0935505	−	0.995615i	$-0.470178\pi$
$877$	−791.110	−	791.110i	−0.902064	−	0.902064i	−0.995615	+	0.0935505i	$0.970178\pi$
$878$	393.740	+	460.442i	0.448451	+	0.524421i
$879$		−	194.487i		−	0.221260i
$880$	95.0006	−	294.828i	0.107955	−	0.335032i
$881$			495.654i			0.562604i	0.959619	+	0.281302i	$0.0907663\pi$
$881$			495.654i			0.562604i	−0.959619	+	0.281302i	$0.909234\pi$
$882$	−225.508	−	263.710i	−0.255678	−	0.298990i
$883$	510.320	+	510.320i	0.577939	+	0.577939i	0.934335	−	0.356396i	$-0.115995\pi$
$883$	510.320	+	510.320i	0.577939	+	0.577939i	−0.356396	+	0.934335i	$0.615995\pi$
$884$	808.625	+	1110.13i	0.914734	+	1.25580i
$885$	494.382	+	494.382i	0.558623	+	0.558623i
$886$	−89.9137	+	1151.44i	−0.101483	+	1.29960i
$887$		−	160.804i		−	0.181290i	−0.995883	−	0.0906448i	$-0.971107\pi$
$887$		−	160.804i		−	0.181290i	0.995883	−	0.0906448i	$-0.0288928\pi$
$888$	−615.533	+	378.751i	−0.693168	+	0.426521i
$889$	399.203			0.449048
$890$	−288.471	−	22.5261i	−0.324125	−	0.0253102i
$891$	84.8489	+	84.8489i	0.0952288	+	0.0952288i
$892$	−110.942	+	706.036i	−0.124375	+	0.791520i
$893$	−102.137	+	102.137i	−0.114375	+	0.114375i
$894$	−342.462	−	400.477i	−0.383067	−	0.447961i
$895$		−	1011.57i		−	1.13024i
$896$	150.976	+	617.238i	0.168500	+	0.688882i
$897$	−413.958	+	227.190i	−0.461492	+	0.253278i
$898$	464.260	−	397.005i	0.516993	−	0.442100i
$899$	−93.4687	−	93.4687i	−0.103970	−	0.103970i
$900$	21.3526	−	135.888i	0.0237252	−	0.150987i
$901$	574.490	−	574.490i	0.637614	−	0.637614i
$902$	−23.6469	+	302.824i	−0.0262161	+	0.335725i
$903$			458.744i			0.508022i
$904$	−611.878	+	376.501i	−0.676856	+	0.416484i
$905$		−	620.969i		−	0.686153i
$906$	21.2788	−	272.498i	0.0234865	−	0.300770i
$907$	−557.020	−	557.020i	−0.614135	−	0.614135i	0.329886	−	0.944021i	$-0.392990\pi$
$907$	−557.020	−	557.020i	−0.614135	−	0.614135i	−0.944021	+	0.329886i	$0.892990\pi$
$908$	−935.532	−	1284.35i	−1.03032	−	1.41448i
$909$	−799.474	−	799.474i	−0.879510	−	0.879510i
$910$	−528.152	−	617.623i	−0.580387	−	0.678707i
$911$		−	1089.62i		−	1.19607i	−0.801471	−	0.598034i	$-0.795949\pi$
$911$		−	1089.62i		−	1.19607i	0.801471	−	0.598034i	$-0.204051\pi$
$912$	524.477	+	168.999i	0.575085	+	0.185306i
$913$	402.736			0.441113
$914$	181.280	−	155.019i	0.198337	−	0.169605i
$915$	−60.3572	−	60.3572i	−0.0659641	−	0.0659641i
$916$	567.211	−	413.161i	0.619225	−	0.451049i
$917$	240.120	+	240.120i	0.261853	+	0.261853i
$918$	−1009.01	−	78.7919i	−1.09914	−	0.0858300i
$919$	506.594			0.551245			0.275622	−	0.961266i	$-0.411116\pi$
$919$	506.594			0.551245			0.275622	+	0.961266i	$0.411116\pi$
$920$	968.998	−	266.249i	1.05326	−	0.289401i
$921$		−	403.303i		−	0.437897i
$922$	−1530.50	−	119.514i	−1.65998	−	0.129624i
$923$	−1160.82	+	1160.82i	−1.25766	+	1.25766i
$924$	95.2602	+	14.9686i	0.103095	+	0.0161998i
$925$	−225.117	+	225.117i	−0.243369	+	0.243369i
$926$	769.413	−	657.953i	0.830900	−	0.710533i
$927$			440.800i			0.475512i
$928$	1132.93	+	465.232i	1.22083	+	0.501327i
$929$	−478.159			−0.514703			−0.257351	−	0.966318i	$-0.582850\pi$
$929$	−478.159			−0.514703			−0.257351	+	0.966318i	$0.582850\pi$
$930$	−33.5878	−	39.2777i	−0.0361159	−	0.0422341i
$931$	432.953	−	432.953i	0.465040	−	0.465040i
$932$	1538.68	+	241.779i	1.65094	+	0.259419i
$933$	−135.462	+	135.462i	−0.145190	+	0.145190i
$934$	−85.9100	+	1100.17i	−0.0919807	+	1.17791i
$935$	−443.542			−0.474377
$936$	830.801	+	197.850i	0.887607	+	0.211378i
$937$	539.497			0.575771			0.287885	−	0.957665i	$-0.407048\pi$
$937$	539.497			0.575771			0.287885	+	0.957665i	$0.407048\pi$
$938$	72.9690	−	934.446i	0.0777921	−	0.996211i
$939$	−271.007	−	271.007i	−0.288613	−	0.288613i
$940$	−101.457	+	73.9020i	−0.107933	+	0.0786191i
$941$	145.998	−	145.998i	0.155151	−	0.155151i	−0.625263	−	0.780414i	$-0.715008\pi$
$941$	145.998	−	145.998i	0.155151	−	0.155151i	0.780414	+	0.625263i	$0.215008\pi$
$942$	166.348	−	142.251i	0.176591	−	0.151009i
$943$	−863.864	+	474.109i	−0.916081	+	0.502767i
$944$	1330.54	−	682.040i	1.40947	−	0.722500i
$945$	598.855			0.633709
$946$	−310.803	−	363.455i	−0.328545	−	0.384202i
$947$	−999.395	−	999.395i	−1.05533	−	1.05533i	−0.998377	−	0.0569505i	$-0.981862\pi$
$947$	−999.395	−	999.395i	−1.05533	−	1.05533i	−0.0569505	−	0.998377i	$-0.518138\pi$
$948$	31.8559	+	43.7336i	0.0336033	+	0.0461325i
$949$	634.029	−	634.029i	0.668102	−	0.668102i
$950$	241.995	+	18.8969i	0.254731	+	0.0198915i
$951$			109.435i			0.115074i
$952$	774.933	−	476.833i	0.814005	−	0.500875i
$953$	641.807			0.673460			0.336730	−	0.941601i	$-0.390679\pi$
$953$	641.807			0.673460			0.336730	+	0.941601i	$0.390679\pi$
$954$	39.3311	−	503.677i	0.0412276	−	0.527964i
$955$	382.669	−	382.669i	0.400701	−	0.400701i
$956$	61.2450	−	389.762i	0.0640638	−	0.407701i
$957$	131.421	−	131.421i	0.137326	−	0.137326i
$958$	583.073	+	681.848i	0.608636	+	0.711741i
$959$	−409.785			−0.427305
$960$	427.440	+	215.824i	0.445249	+	0.224817i
$961$	−949.072			−0.987588
$962$	−1284.62	−	1502.24i	−1.33536	−	1.56158i
$963$	496.254	−	496.254i	0.515321	−	0.515321i
$964$	−838.277	−	131.722i	−0.869582	−	0.136641i
$965$	652.650	+	652.650i	0.676321	+	0.676321i
$966$	128.706	+	285.133i	0.133236	+	0.295169i
$967$		−	90.2380i		−	0.0933174i	−0.998911	−	0.0466587i	$-0.985143\pi$
$967$		−	90.2380i		−	0.0933174i	0.998911	−	0.0466587i	$-0.0148573\pi$
$968$	738.814	−	454.608i	0.763238	−	0.469636i
$969$		−	789.030i		−	0.814272i
$970$	−129.851	+	1662.88i	−0.133867	+	1.71431i
$971$	869.444	+	869.444i	0.895411	+	0.895411i	0.995026	−	0.0996148i	$-0.0317611\pi$
$971$	869.444	+	869.444i	0.895411	+	0.895411i	−0.0996148	+	0.995026i	$0.531761\pi$
$972$	−792.661	+	577.381i	−0.815495	+	0.594013i
$973$	238.691	−	238.691i	0.245315	−	0.245315i
$974$	164.522	+	192.393i	0.168914	+	0.197529i
$975$	−99.1149			−0.101656
$976$	−162.441	+	83.2677i	−0.166435	+	0.0853153i
$977$			1505.30i			1.54074i	0.637596	+	0.770371i	$0.279929\pi$
$977$			1505.30i			1.54074i	−0.637596	+	0.770371i	$0.720071\pi$
$978$	−224.939	−	263.045i	−0.229999	−	0.268962i
$979$	66.3983	+	66.3983i	0.0678226	+	0.0678226i
$980$	430.069	−	313.265i	0.438845	−	0.319659i
$981$	−1007.26	−	1007.26i	−1.02677	−	1.02677i
$982$	5.65997	−	72.4820i	0.00576372	−	0.0738106i
$983$	305.706			0.310992			0.155496	−	0.987836i	$-0.450302\pi$
$983$	305.706			0.310992			0.155496	+	0.987836i	$0.450302\pi$
$984$	−456.773	−	108.778i	−0.464200	−	0.110546i
$985$	−478.768			−0.486059
$986$	136.528	−	1748.39i	0.138466	−	1.77321i
$987$	−27.6301	−	27.6301i	−0.0279941	−	0.0279941i
$988$	−233.936	+	1488.77i	−0.236778	+	1.50685i
$989$	433.908	−	1489.54i	0.438734	−	1.50611i
$990$	−209.618	+	179.252i	−0.211736	+	0.181063i
$991$	406.920			0.410615			0.205308	−	0.978697i	$-0.434181\pi$
$991$	406.920			0.410615			0.205308	+	0.978697i	$0.434181\pi$
$992$	−101.977	+	42.6053i	−0.102800	+	0.0429489i
$993$	282.966			0.284961
$994$	706.838	+	826.580i	0.711105	+	0.831569i
$995$	1320.16	+	1320.16i	1.32679	+	1.32679i
$996$	−96.6413	+	615.025i	−0.0970294	+	0.617495i
$997$	−79.2605	+	79.2605i	−0.0794990	+	0.0794990i	−0.745738	−	0.666239i	$-0.767903\pi$
$997$	−79.2605	+	79.2605i	−0.0794990	+	0.0794990i	0.666239	+	0.745738i	$0.267903\pi$
$998$	552.773	+	43.1649i	0.553881	+	0.0432514i
$999$	1456.59			1.45805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.3.k.b.45.19	✓	176
16.5	even	4	inner	368.3.k.b.229.20	yes	176
23.22	odd	2	inner	368.3.k.b.45.20	yes	176
368.229	odd	4	inner	368.3.k.b.229.19	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
368.3.k.b.45.19	✓	176	1.1	even	1	trivial
368.3.k.b.45.20	yes	176	23.22	odd	2	inner
368.3.k.b.229.19	yes	176	368.229	odd	4	inner
368.3.k.b.229.20	yes	176	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	368.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.52002 + 1.29982i) q^{2} +(0.968686 + 0.968686i) q^{3} +(0.620917 - 3.95151i) q^{4} +(-3.86184 - 3.86184i) q^{5} +(-2.73154 - 0.213300i) q^{6} -4.96433 q^{7} +(4.19246 + 6.81346i) q^{8} -7.12330i q^{9} +(10.8898 + 0.850361i) q^{10} +(-2.50654 - 2.50654i) q^{11} +(4.42925 - 3.22630i) q^{12} +(10.5972 + 10.5972i) q^{13} +(7.54588 - 6.45275i) q^{14} -7.48182i q^{15} +(-15.2289 - 4.90713i) q^{16} +22.9106i q^{17} +(9.25903 + 10.8275i) q^{18} +(-17.7764 + 17.7764i) q^{19} +(-17.6580 + 12.8622i) q^{20} +(-4.80888 - 4.80888i) q^{21} +(7.06805 + 0.551929i) q^{22} +(11.0659 + 20.1630i) q^{23} +(-2.53892 + 10.6613i) q^{24} +4.82766i q^{25} +(-29.8823 - 2.33345i) q^{26} +(15.6184 - 15.6184i) q^{27} +(-3.08244 + 19.6166i) q^{28} +(27.0630 + 27.0630i) q^{29} +(9.72505 + 11.3725i) q^{30} -3.45374 q^{31} +(29.5267 - 12.3360i) q^{32} -4.85610i q^{33} +(-29.7797 - 34.8245i) q^{34} +(19.1715 + 19.1715i) q^{35} +(-28.1478 - 4.42298i) q^{36} +(46.6306 + 46.6306i) q^{37} +(3.91429 - 50.1267i) q^{38} +20.5306i q^{39} +(10.1219 - 42.5032i) q^{40} +42.8441i q^{41} +(13.5603 + 1.05889i) q^{42} +(-47.6976 - 47.6976i) q^{43} +(-11.4610 + 8.34827i) q^{44} +(-27.5090 + 27.5090i) q^{45} +(-43.0287 - 16.2644i) q^{46} +5.74565 q^{47} +(-9.99858 - 19.5055i) q^{48} -24.3554 q^{49} +(-6.27511 - 7.33814i) q^{50} +(-22.1931 + 22.1931i) q^{51} +(48.4548 - 35.2948i) q^{52} +(-25.0753 - 25.0753i) q^{53} +(-3.43911 + 44.0415i) q^{54} +19.3597i q^{55} +(-20.8128 - 33.8243i) q^{56} -34.4395 q^{57} +(-76.3135 - 5.95916i) q^{58} +(-66.0777 + 66.0777i) q^{59} +(-29.5645 - 4.64560i) q^{60} +(8.06717 - 8.06717i) q^{61} +(5.24975 - 4.48925i) q^{62} +35.3624i q^{63} +(-28.8465 + 57.1304i) q^{64} -81.8491i q^{65} +(6.31207 + 7.38136i) q^{66} +(66.7527 - 66.7527i) q^{67} +(90.5314 + 14.2256i) q^{68} +(-8.81219 + 30.2510i) q^{69} +(-54.0605 - 4.22147i) q^{70} +109.541i q^{71} +(48.5343 - 29.8642i) q^{72} -59.8301i q^{73} +(-131.491 - 10.2679i) q^{74} +(-4.67649 + 4.67649i) q^{75} +(59.2061 + 81.2815i) q^{76} +(12.4433 + 12.4433i) q^{77} +(-26.6862 - 31.2070i) q^{78} +9.87381i q^{79} +(39.8612 + 77.7623i) q^{80} -33.8510 q^{81} +(-55.6897 - 65.1238i) q^{82} +(-80.3371 + 80.3371i) q^{83} +(-21.9883 + 16.0164i) q^{84} +(88.4770 - 88.4770i) q^{85} +(134.500 + 10.5028i) q^{86} +52.4312i q^{87} +(6.56963 - 27.5868i) q^{88} -26.4900 q^{89} +(6.05738 - 77.5712i) q^{90} +(-52.6078 - 52.6078i) q^{91} +(86.5453 - 31.2076i) q^{92} +(-3.34559 - 3.34559i) q^{93} +(-8.73350 + 7.46833i) q^{94} +137.300 q^{95} +(40.5517 + 16.6524i) q^{96} +152.701i q^{97} +(37.0207 - 31.6578i) q^{98} +(-17.8548 + 17.8548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 4 q^{2} - 4 q^{3} - 16 q^{4} - 64 q^{6} - 4 q^{8} - 28 q^{12} - 4 q^{13} - 80 q^{16} + 72 q^{18} + 68 q^{24} + 96 q^{26} + 212 q^{27} + 28 q^{29} - 8 q^{31} + 136 q^{32} - 104 q^{35} - 264 q^{36}+ \cdots - 240 q^{98}+O(q^{100}) \) 176 * q - 4 * q^2 - 4 * q^3 - 16 * q^4 - 64 * q^6 - 4 * q^8 - 28 * q^12 - 4 * q^13 - 80 * q^16 + 72 * q^18 + 68 * q^24 + 96 * q^26 + 212 * q^27 + 28 * q^29 - 8 * q^31 + 136 * q^32 - 104 * q^35 - 264 * q^36 - 32 * q^46 - 8 * q^47 - 520 * q^48 + 1728 * q^49 + 88 * q^50 - 56 * q^52 - 148 * q^54 + 540 * q^58 + 296 * q^59 - 812 * q^62 - 352 * q^64 - 80 * q^69 + 124 * q^70 + 712 * q^72 + 132 * q^75 + 24 * q^77 - 320 * q^78 - 440 * q^81 - 844 * q^82 + 416 * q^85 - 492 * q^92 - 1084 * q^93 - 596 * q^94 - 8 * q^95 + 664 * q^96 - 240 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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