LMFDB - Embedded newform 360.3.u.b.253.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,3,Mod(37,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 0, 1]))

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

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

chi := DirichletCharacter("360.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	360.u (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:	$9.80928951697$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} - 3x^{16} + 11x^{14} + x^{12} - 40x^{10} + 4x^{8} + 176x^{6} - 192x^{4} - 256x^{2} + 1024 $ x^20 - x^18 - 3x^16 + 11x^14 + x^12 - 40x^10 + 4x^8 + 176x^6 - 192x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.1
Root			$-1.27574 - 0.610320i$ of defining polynomial
Character	$\chi$	$=$	360.253
Dual form			360.3.u.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.88606 - 0.665418i) q^{2} +(3.11444 + 2.51004i) q^{4} +(-2.34539 + 4.41578i) q^{5} +(1.47907 - 1.47907i) q^{7} +(-4.20379 - 6.80648i) q^{8} +(7.36189 - 6.76776i) q^{10} +11.3076i q^{11} +(-3.17204 + 3.17204i) q^{13} +(-3.77383 + 1.80542i) q^{14} +(3.39943 + 15.6347i) q^{16} +(9.94834 - 9.94834i) q^{17} -11.2705 q^{19} +(-18.3883 + 7.86567i) q^{20} +(7.52426 - 21.3267i) q^{22} +(-1.67851 - 1.67851i) q^{23} +(-13.9983 - 20.7135i) q^{25} +(8.09340 - 3.87192i) q^{26} +(8.31902 - 0.893952i) q^{28} -41.1865 q^{29} -29.2537 q^{31} +(3.99209 - 31.7500i) q^{32} +(-25.3830 + 12.1433i) q^{34} +(3.06227 + 10.0003i) q^{35} +(-8.60159 - 8.60159i) q^{37} +(21.2568 + 7.49961i) q^{38} +(39.9155 - 2.59916i) q^{40} +19.6639 q^{41} +(-25.1228 + 25.1228i) q^{43} +(-28.3824 + 35.2167i) q^{44} +(2.04886 + 4.28268i) q^{46} +(-41.7392 + 41.7392i) q^{47} +44.6247i q^{49} +(12.6185 + 48.3815i) q^{50} +(-17.8411 + 1.91718i) q^{52} +(-2.16209 + 2.16209i) q^{53} +(-49.9317 - 26.5206i) q^{55} +(-16.2850 - 3.84958i) q^{56} +(77.6802 + 27.4063i) q^{58} -38.9669 q^{59} +87.5112i q^{61} +(55.1742 + 19.4660i) q^{62} +(-28.6564 + 57.2260i) q^{64} +(-6.56738 - 21.4467i) q^{65} +(-31.1362 - 31.1362i) q^{67} +(55.9542 - 6.01278i) q^{68} +(0.878753 - 20.8988i) q^{70} -134.120 q^{71} +(-26.1299 - 26.1299i) q^{73} +(10.4994 + 21.9468i) q^{74} +(-35.1013 - 28.2894i) q^{76} +(16.7247 + 16.7247i) q^{77} -23.1510i q^{79} +(-77.0125 - 21.6583i) q^{80} +(-37.0873 - 13.0847i) q^{82} +(68.3496 - 68.3496i) q^{83} +(20.5970 + 67.2625i) q^{85} +(64.1002 - 30.6659i) q^{86} +(76.9647 - 47.5346i) q^{88} -75.2561i q^{89} +9.38338i q^{91} +(-1.01449 - 9.44074i) q^{92} +(106.497 - 50.9485i) q^{94} +(26.4337 - 49.7681i) q^{95} +(57.5730 - 57.5730i) q^{97} +(29.6941 - 84.1648i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 4 q^{7} - 4 q^{8} + 6 q^{10} - 56 q^{16} + 12 q^{17} + 24 q^{20} + 92 q^{22} + 4 q^{23} - 28 q^{25} - 100 q^{26} + 68 q^{28} - 136 q^{31} - 128 q^{32} + 188 q^{38} + 156 q^{40} + 8 q^{41}+ \cdots - 546 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 - 4 * q^7 - 4 * q^8 + 6 * q^10 - 56 * q^16 + 12 * q^17 + 24 * q^20 + 92 * q^22 + 4 * q^23 - 28 * q^25 - 100 * q^26 + 68 * q^28 - 136 * q^31 - 128 * q^32 + 188 * q^38 + 156 * q^40 + 8 * q^41 - 240 * q^46 - 188 * q^47 + 274 * q^50 - 332 * q^52 + 96 * q^55 + 360 * q^56 + 268 * q^58 - 336 * q^62 + 60 * q^65 - 396 * q^68 + 300 * q^70 - 248 * q^71 - 124 * q^73 + 424 * q^76 - 496 * q^80 - 676 * q^82 + 672 * q^86 - 304 * q^88 + 628 * q^92 + 488 * q^95 + 100 * q^97 - 546 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	−1.88606	−	0.665418i	−0.943029	−	0.332709i
$2$	−1.88606	−	0.665418i	−0.943029	−	0.332709i
$3$		0			0
$3$		0			0
$4$	3.11444	+	2.51004i	0.778609	+	0.627509i
$5$	−2.34539	+	4.41578i	−0.469078	+	0.883157i
$5$	−2.34539	+	4.41578i	−0.469078	+	0.883157i
$6$		0			0
$7$	1.47907	−	1.47907i	0.211296	−	0.211296i	−0.593522	−	0.804818i	$-0.702263\pi$
$7$	1.47907	−	1.47907i	0.211296	−	0.211296i	0.804818	+	0.593522i	$0.202263\pi$
$8$	−4.20379	−	6.80648i	−0.525473	−	0.850810i
$9$		0			0
$10$	7.36189	−	6.76776i	0.736189	−	0.676776i
$11$			11.3076i			1.02796i	0.857802	+	0.513980i	$0.171829\pi$
$11$			11.3076i			1.02796i	−0.857802	+	0.513980i	$0.828171\pi$
$12$		0			0
$13$	−3.17204	+	3.17204i	−0.244003	+	0.244003i	−0.818504	−	0.574501i	$-0.805196\pi$
$13$	−3.17204	+	3.17204i	−0.244003	+	0.244003i	0.574501	+	0.818504i	$0.305196\pi$
$14$	−3.77383	+	1.80542i	−0.269559	+	0.128958i
$15$		0			0
$16$	3.39943	+	15.6347i	0.212464	+	0.977169i
$17$	9.94834	−	9.94834i	0.585197	−	0.585197i	−0.351130	−	0.936327i	$-0.614203\pi$
$17$	9.94834	−	9.94834i	0.585197	−	0.585197i	0.936327	+	0.351130i	$0.114203\pi$
$18$		0			0
$19$	−11.2705			−0.593185			−0.296592	−	0.955004i	$-0.595850\pi$
$19$	−11.2705			−0.593185			−0.296592	+	0.955004i	$0.595850\pi$
$20$	−18.3883	+	7.86567i	−0.919417	+	0.393283i
$21$		0			0
$22$	7.52426	−	21.3267i	0.342012	−	0.969396i
$23$	−1.67851	−	1.67851i	−0.0729787	−	0.0729787i	0.669675	−	0.742654i	$-0.266433\pi$
$23$	−1.67851	−	1.67851i	−0.0729787	−	0.0729787i	−0.742654	+	0.669675i	$0.766433\pi$
$24$		0			0
$25$	−13.9983	−	20.7135i	−0.559932	−	0.828539i
$26$	8.09340	−	3.87192i	0.311284	−	0.148920i
$27$		0			0
$28$	8.31902	−	0.893952i	0.297108	−	0.0319269i
$29$	−41.1865			−1.42022			−0.710112	−	0.704088i	$-0.751356\pi$
$29$	−41.1865			−1.42022			−0.710112	+	0.704088i	$0.751356\pi$
$30$		0			0
$31$	−29.2537			−0.943668			−0.471834	−	0.881687i	$-0.656408\pi$
$31$	−29.2537			−0.943668			−0.471834	+	0.881687i	$0.656408\pi$
$32$	3.99209	−	31.7500i	0.124753	−	0.992188i
$33$		0			0
$34$	−25.3830	+	12.1433i	−0.746558	+	0.357157i
$35$	3.06227	+	10.0003i	0.0874934	+	0.285722i
$36$		0			0
$37$	−8.60159	−	8.60159i	−0.232475	−	0.232475i	0.581250	−	0.813725i	$-0.302564\pi$
$37$	−8.60159	−	8.60159i	−0.232475	−	0.232475i	−0.813725	+	0.581250i	$0.802564\pi$
$38$	21.2568	+	7.49961i	0.559391	+	0.197358i
$39$		0			0
$40$	39.9155	−	2.59916i	0.997887	−	0.0649791i
$41$	19.6639			0.479607			0.239804	−	0.970821i	$-0.422917\pi$
$41$	19.6639			0.479607			0.239804	+	0.970821i	$0.422917\pi$
$42$		0			0
$43$	−25.1228	+	25.1228i	−0.584251	+	0.584251i	−0.936069	−	0.351818i	$-0.885564\pi$
$43$	−25.1228	+	25.1228i	−0.584251	+	0.584251i	0.351818	+	0.936069i	$0.385564\pi$
$44$	−28.3824	+	35.2167i	−0.645054	+	0.800379i
$45$		0			0
$46$	2.04886	+	4.28268i	0.0445404	+	0.0931018i
$47$	−41.7392	+	41.7392i	−0.888068	+	0.888068i	−0.994337	−	0.106269i	$-0.966109\pi$
$47$	−41.7392	+	41.7392i	−0.888068	+	0.888068i	0.106269	+	0.994337i	$0.466109\pi$
$48$		0			0
$49$			44.6247i			0.910708i
$50$	12.6185	+	48.3815i	0.252370	+	0.967631i
$51$		0			0
$52$	−17.8411	+	1.91718i	−0.343098	+	0.0368689i
$53$	−2.16209	+	2.16209i	−0.0407941	+	0.0407941i	−0.727210	−	0.686415i	$-0.759183\pi$
$53$	−2.16209	+	2.16209i	−0.0407941	+	0.0407941i	0.686415	+	0.727210i	$0.259183\pi$
$54$		0			0
$55$	−49.9317	−	26.5206i	−0.907850	−	0.482193i
$56$	−16.2850	−	3.84958i	−0.290804	−	0.0687425i
$57$		0			0
$58$	77.6802	+	27.4063i	1.33931	+	0.472522i
$59$	−38.9669			−0.660456			−0.330228	−	0.943901i	$-0.607126\pi$
$59$	−38.9669			−0.660456			−0.330228	+	0.943901i	$0.607126\pi$
$60$		0			0
$61$			87.5112i			1.43461i	0.696759	+	0.717305i	$0.254625\pi$
$61$			87.5112i			1.43461i	−0.696759	+	0.717305i	$0.745375\pi$
$62$	55.1742	+	19.4660i	0.889907	+	0.313967i
$63$		0			0
$64$	−28.6564	+	57.2260i	−0.447756	+	0.894156i
$65$	−6.56738	−	21.4467i	−0.101037	−	0.329950i
$66$		0			0
$67$	−31.1362	−	31.1362i	−0.464719	−	0.464719i	0.435479	−	0.900199i	$-0.356579\pi$
$67$	−31.1362	−	31.1362i	−0.464719	−	0.464719i	−0.900199	+	0.435479i	$0.856579\pi$
$68$	55.9542	−	6.01278i	0.822856	−	0.0884232i
$69$		0			0
$70$	0.878753	−	20.8988i	0.0125536	−	0.298554i
$71$	−134.120			−1.88902			−0.944510	−	0.328483i	$-0.893463\pi$
$71$	−134.120			−1.88902			−0.944510	+	0.328483i	$0.893463\pi$
$72$		0			0
$73$	−26.1299	−	26.1299i	−0.357943	−	0.357943i	0.505111	−	0.863054i	$-0.331452\pi$
$73$	−26.1299	−	26.1299i	−0.357943	−	0.357943i	−0.863054	+	0.505111i	$0.831452\pi$
$74$	10.4994	+	21.9468i	0.141884	+	0.296578i
$75$		0			0
$76$	−35.1013	−	28.2894i	−0.461859	−	0.372229i
$77$	16.7247	+	16.7247i	0.217204	+	0.217204i
$78$		0			0
$79$		−	23.1510i		−	0.293050i	−0.989207	−	0.146525i	$-0.953191\pi$
$79$		−	23.1510i		−	0.293050i	0.989207	−	0.146525i	$-0.0468090\pi$
$80$	−77.0125	−	21.6583i	−0.962656	−	0.270729i
$81$		0			0
$82$	−37.0873	−	13.0847i	−0.452284	−	0.159570i
$83$	68.3496	−	68.3496i	0.823489	−	0.823489i	−0.163118	−	0.986607i	$-0.552155\pi$
$83$	68.3496	−	68.3496i	0.823489	−	0.823489i	0.986607	+	0.163118i	$0.0521550\pi$
$84$		0			0
$85$	20.5970	+	67.2625i	0.242318	+	0.791323i
$86$	64.1002	−	30.6659i	0.745352	−	0.356580i
$87$		0			0
$88$	76.9647	−	47.5346i	0.874599	−	0.540165i
$89$		−	75.2561i		−	0.845574i	−0.906229	−	0.422787i	$-0.861052\pi$
$89$		−	75.2561i		−	0.845574i	0.906229	−	0.422787i	$-0.138948\pi$
$90$		0			0
$91$			9.38338i			0.103114i
$92$	−1.01449	−	9.44074i	−0.0110271	−	0.102617i
$93$		0			0
$94$	106.497	−	50.9485i	1.13294	−	0.542006i
$95$	26.4337	−	49.7681i	0.278250	−	0.523875i
$96$		0			0
$97$	57.5730	−	57.5730i	0.593536	−	0.593536i	−0.345049	−	0.938585i	$-0.612138\pi$
$97$	57.5730	−	57.5730i	0.593536	−	0.593536i	0.938585	+	0.345049i	$0.112138\pi$
$98$	29.6941	−	84.1648i	0.303001	−	0.858824i
$99$		0			0
$100$	8.39476	−	99.6470i	0.0839476	−	0.996470i
$101$			112.245i			1.11133i	0.831405	+	0.555666i	$0.187537\pi$
$101$			112.245i			1.11133i	−0.831405	+	0.555666i	$0.812463\pi$
$102$		0			0
$103$	25.4523	+	25.4523i	0.247109	+	0.247109i	0.819783	−	0.572674i	$-0.194094\pi$
$103$	25.4523	+	25.4523i	0.247109	+	0.247109i	−0.572674	+	0.819783i	$0.694094\pi$
$104$	34.9250	+	8.25586i	0.335818	+	0.0793833i
$105$		0			0
$106$	5.51652	−	2.63913i	0.0520426	−	0.0248975i
$107$	−66.0387	−	66.0387i	−0.617184	−	0.617184i	0.327624	−	0.944808i	$-0.393752\pi$
$107$	−66.0387	−	66.0387i	−0.617184	−	0.617184i	−0.944808	+	0.327624i	$0.893752\pi$
$108$		0			0
$109$	91.2619			0.837266			0.418633	−	0.908156i	$-0.362509\pi$
$109$	91.2619			0.837266			0.418633	+	0.908156i	$0.362509\pi$
$110$	76.5269	+	83.2450i	0.695699	+	0.756772i
$111$		0			0
$112$	28.1529	+	18.0969i	0.251365	+	0.161579i
$113$	127.312	+	127.312i	1.12666	+	1.12666i	0.990717	+	0.135940i	$0.0434056\pi$
$113$	127.312	+	127.312i	1.12666	+	1.12666i	0.135940	+	0.990717i	$0.456594\pi$
$114$		0			0
$115$	11.3487	−	3.47518i	0.0986844	−	0.0302190i
$116$	−128.273	−	103.380i	−1.10580	−	0.891204i
$117$		0			0
$118$	73.4938	+	25.9293i	0.622829	+	0.219740i
$119$		−	29.4287i		−	0.247300i
$120$		0			0
$121$	−6.86087			−0.0567014
$122$	58.2316	−	165.051i	0.477308	−	1.35288i
$123$		0			0
$124$	−91.1088	−	73.4279i	−0.734749	−	0.592160i
$125$	124.298	−	13.2323i	0.994381	−	0.105858i
$126$		0			0
$127$	−14.5303	+	14.5303i	−0.114412	+	0.114412i	−0.761995	−	0.647583i	$-0.775780\pi$
$127$	−14.5303	+	14.5303i	−0.114412	+	0.114412i	0.647583	+	0.761995i	$0.275780\pi$
$128$	92.1268	−	88.8631i	0.719741	−	0.694243i
$129$		0			0
$130$	−1.88459	+	44.8199i	−0.0144968	+	0.344768i
$131$			51.9051i			0.396222i	0.980180	+	0.198111i	$0.0634807\pi$
$131$			51.9051i			0.396222i	−0.980180	+	0.198111i	$0.936519\pi$
$132$		0			0
$133$	−16.6699	+	16.6699i	−0.125338	+	0.125338i
$134$	38.0061	+	79.4433i	0.283628	+	0.592860i
$135$		0			0
$136$	−109.534	−	25.8925i	−0.805396	−	0.190386i
$137$	98.7636	−	98.7636i	0.720902	−	0.720902i	−0.247887	−	0.968789i	$-0.579736\pi$
$137$	98.7636	−	98.7636i	0.720902	−	0.720902i	0.968789	+	0.247887i	$0.0797362\pi$
$138$		0			0
$139$	48.6381			0.349914			0.174957	−	0.984576i	$-0.444021\pi$
$139$	48.6381			0.349914			0.174957	+	0.984576i	$0.444021\pi$
$140$	−15.5638	+	38.8316i	−0.111170	+	0.277369i
$141$		0			0
$142$	252.959	+	89.2462i	1.78140	+	0.628494i
$143$	−35.8681	−	35.8681i	−0.250826	−	0.250826i
$144$		0			0
$145$	96.5984	−	181.871i	0.666196	−	1.25428i
$146$	31.8952	+	66.6697i	0.218460	+	0.456642i
$147$		0			0
$148$	−5.19880	−	48.3794i	−0.0351270	−	0.326888i
$149$	222.425			1.49278			0.746391	−	0.665508i	$-0.231785\pi$
$149$	222.425			1.49278			0.746391	+	0.665508i	$0.231785\pi$
$150$		0			0
$151$	−199.700			−1.32252			−0.661259	−	0.750157i	$-0.729978\pi$
$151$	−199.700			−1.32252			−0.661259	+	0.750157i	$0.729978\pi$
$152$	47.3788	+	76.7125i	0.311703	+	0.504688i
$153$		0			0
$154$	−20.4149	−	42.6728i	−0.132564	−	0.277096i
$155$	68.6113	−	129.178i	0.442654	−	0.833407i
$156$		0			0
$157$	−191.183	−	191.183i	−1.21773	−	1.21773i	−0.968426	−	0.249302i	$-0.919799\pi$
$157$	−191.183	−	191.183i	−1.21773	−	1.21773i	−0.249302	−	0.968426i	$-0.580201\pi$
$158$	−15.4051	+	43.6641i	−0.0975006	+	0.276355i
$159$		0			0
$160$	130.838	+	92.0944i	0.817739	+	0.575590i
$161$	−4.96529			−0.0308403
$162$		0			0
$163$	100.849	−	100.849i	0.618705	−	0.618705i	−0.326494	−	0.945199i	$-0.605867\pi$
$163$	100.849	−	100.849i	0.618705	−	0.618705i	0.945199	+	0.326494i	$0.105867\pi$
$164$	61.2420	+	49.3571i	0.373427	+	0.300958i
$165$		0			0
$166$	−174.392	+	83.4303i	−1.05056	+	0.502592i
$167$	−208.556	+	208.556i	−1.24884	+	1.24884i	−0.292609	+	0.956232i	$0.594523\pi$
$167$	−208.556	+	208.556i	−1.24884	+	1.24884i	−0.956232	+	0.292609i	$0.905477\pi$
$168$		0			0
$169$			148.876i			0.880925i
$170$	5.91054	−	140.567i	0.0347679	−	0.826862i
$171$		0			0
$172$	−141.302	+	15.1842i	−0.821526	+	0.0882803i
$173$	−122.257	+	122.257i	−0.706689	+	0.706689i	−0.965838	−	0.259148i	$-0.916558\pi$
$173$	−122.257	+	122.257i	−0.706689	+	0.706689i	0.259148	+	0.965838i	$0.416558\pi$
$174$		0			0
$175$	−51.3413	−	9.93224i	−0.293379	−	0.0567556i
$176$	−176.790	+	38.4393i	−1.00449	+	0.218405i
$177$		0			0
$178$	−50.0768	+	141.937i	−0.281330	+	0.797402i
$179$	−63.7773			−0.356298			−0.178149	−	0.984004i	$-0.557011\pi$
$179$	−63.7773			−0.356298			−0.178149	+	0.984004i	$0.557011\pi$
$180$		0			0
$181$		−	192.099i		−	1.06132i	−0.847585	−	0.530660i	$-0.821944\pi$
$181$		−	192.099i		−	1.06132i	0.847585	−	0.530660i	$-0.178056\pi$
$182$	6.24387	−	17.6976i	0.0343070	−	0.0972396i
$183$		0			0
$184$	−4.36865	+	18.4809i	−0.0237427	+	0.100439i
$185$	58.1568	−	17.8087i	0.314361	−	0.0962631i
$186$		0			0
$187$	112.491	+	112.491i	0.601559	+	0.601559i
$188$	−234.761	+	25.2272i	−1.24873	+	0.134187i
$189$		0			0
$190$	−82.9722	+	76.2761i	−0.436696	+	0.401453i
$191$	170.796			0.894218			0.447109	−	0.894480i	$-0.352454\pi$
$191$	170.796			0.894218			0.447109	+	0.894480i	$0.352454\pi$
$192$		0			0
$193$	111.295	+	111.295i	0.576656	+	0.576656i	0.933980	−	0.357325i	$-0.116311\pi$
$193$	111.295	+	111.295i	0.576656	+	0.576656i	−0.357325	+	0.933980i	$0.616311\pi$
$194$	−146.896	+	70.2760i	−0.757197	+	0.362247i
$195$		0			0
$196$	−112.010	+	138.981i	−0.571477	+	0.709085i
$197$	−96.8892	−	96.8892i	−0.491823	−	0.491823i	0.417057	−	0.908880i	$-0.363062\pi$
$197$	−96.8892	−	96.8892i	−0.491823	−	0.491823i	−0.908880	+	0.417057i	$0.863062\pi$
$198$		0			0
$199$			139.805i			0.702540i	0.936274	+	0.351270i	$0.114250\pi$
$199$			139.805i			0.702540i	−0.936274	+	0.351270i	$0.885750\pi$
$200$	−82.1400	+	182.354i	−0.410700	+	0.911771i
$201$		0			0
$202$	74.6896	−	211.700i	0.369751	−	1.04802i
$203$	−60.9179	+	60.9179i	−0.300088	+	0.300088i
$204$		0			0
$205$	−46.1195	+	86.8315i	−0.224973	+	0.423569i
$206$	−31.0681	−	64.9409i	−0.150816	−	0.315247i
$207$		0			0
$208$	−60.3771	−	38.8108i	−0.290274	−	0.186590i
$209$		−	127.442i		−	0.609770i
$210$		0			0
$211$			9.55891i			0.0453029i	0.999743	+	0.0226514i	$0.00721080\pi$
$211$			9.55891i			0.0453029i	−0.999743	+	0.0226514i	$0.992789\pi$
$212$	−12.1606	+	1.30677i	−0.0573614	+	0.00616399i
$213$		0			0
$214$	80.6095	+	168.496i	0.376680	+	0.787365i
$215$	−52.0141	−	169.860i	−0.241926	−	0.790044i
$216$		0			0
$217$	−43.2684	+	43.2684i	−0.199394	+	0.199394i
$218$	−172.125	−	60.7274i	−0.789566	−	0.278566i
$219$		0			0
$220$	−88.9415	−	207.927i	−0.404279	−	0.945124i
$221$			63.1131i			0.285580i
$222$		0			0
$223$	276.355	+	276.355i	1.23926	+	1.23926i	0.960304	+	0.278957i	$0.0899888\pi$
$223$	276.355	+	276.355i	1.23926	+	1.23926i	0.278957	+	0.960304i	$0.410011\pi$
$224$	−41.0560	−	52.8652i	−0.183286	−	0.236006i
$225$		0			0
$226$	−155.403	−	324.834i	−0.687622	−	1.43732i
$227$	−160.929	−	160.929i	−0.708938	−	0.708938i	0.257374	−	0.966312i	$-0.417143\pi$
$227$	−160.929	−	160.929i	−0.708938	−	0.708938i	−0.966312	+	0.257374i	$0.917143\pi$
$228$		0			0
$229$	40.2472			0.175752			0.0878760	−	0.996131i	$-0.471992\pi$
$229$	40.2472			0.175752			0.0878760	+	0.996131i	$0.471992\pi$
$230$	−23.7168	−	0.997243i	−0.103116	−	0.00433584i
$231$		0			0
$232$	173.139	+	280.335i	0.746290	+	1.20834i
$233$	241.061	+	241.061i	1.03460	+	1.03460i	0.999380	+	0.0352176i	$0.0112124\pi$
$233$	241.061	+	241.061i	1.03460	+	1.03460i	0.0352176	+	0.999380i	$0.488788\pi$
$234$		0			0
$235$	−86.4166	−	282.206i	−0.367730	−	1.20088i
$236$	−121.360	−	97.8083i	−0.514237	−	0.414442i
$237$		0			0
$238$	−19.5824	+	55.5042i	−0.0822789	+	0.233211i
$239$			249.002i			1.04185i	0.853603	+	0.520925i	$0.174413\pi$
$239$			249.002i			1.04185i	−0.853603	+	0.520925i	$0.825587\pi$
$240$		0			0
$241$	324.753			1.34752			0.673762	−	0.738948i	$-0.264677\pi$
$241$	324.753			1.34752			0.673762	+	0.738948i	$0.264677\pi$
$242$	12.9400	+	4.56535i	0.0534711	+	0.0188651i
$243$		0			0
$244$	−219.656	+	272.548i	−0.900231	+	1.11700i
$245$	−197.053	−	104.662i	−0.804298	−	0.427193i
$246$		0			0
$247$	35.7505	−	35.7505i	0.144739	−	0.144739i
$248$	122.976	+	199.115i	0.495872	+	0.802882i
$249$		0			0
$250$	−243.238	−	57.7530i	−0.972951	−	0.231012i
$251$			166.729i			0.664260i	0.943234	+	0.332130i	$0.107767\pi$
$251$			166.729i			0.664260i	−0.943234	+	0.332130i	$0.892233\pi$
$252$		0			0
$253$	18.9799	−	18.9799i	0.0750192	−	0.0750192i
$254$	37.0738	−	17.7363i	0.145960	−	0.0698280i
$255$		0			0
$256$	−232.888	+	106.298i	−0.909718	+	0.415227i
$257$	−184.509	+	184.509i	−0.717933	+	0.717933i	−0.968182	−	0.250248i	$-0.919488\pi$
$257$	−184.509	+	184.509i	−0.717933	+	0.717933i	0.250248	+	0.968182i	$0.419488\pi$
$258$		0			0
$259$	−25.4448			−0.0982424
$260$	33.3784	−	83.2789i	0.128378	−	0.320303i
$261$		0			0
$262$	34.5386	−	97.8962i	0.131827	−	0.373649i
$263$	−3.85637	−	3.85637i	−0.0146630	−	0.0146630i	0.699737	−	0.714400i	$-0.253300\pi$
$263$	−3.85637	−	3.85637i	−0.0146630	−	0.0146630i	−0.714400	+	0.699737i	$0.753300\pi$
$264$		0			0
$265$	−4.47638	−	14.6183i	−0.0168920	−	0.0551632i
$266$	42.5329	−	20.3480i	0.159898	−	0.0764962i
$267$		0			0
$268$	−18.8187	−	175.125i	−0.0702190	−	0.653450i
$269$	163.125			0.606413			0.303206	−	0.952925i	$-0.401943\pi$
$269$	163.125			0.606413			0.303206	+	0.952925i	$0.401943\pi$
$270$		0			0
$271$	100.647			0.371391			0.185696	−	0.982607i	$-0.440546\pi$
$271$	100.647			0.371391			0.185696	+	0.982607i	$0.440546\pi$
$272$	189.358	+	121.721i	0.696169	+	0.447502i
$273$		0			0
$274$	−251.993	+	120.555i	−0.919682	+	0.439981i
$275$	234.219	−	158.287i	0.851704	−	0.575587i
$276$		0			0
$277$	172.773	+	172.773i	0.623729	+	0.623729i	0.946483	−	0.322754i	$-0.104609\pi$
$277$	172.773	+	172.773i	0.623729	+	0.623729i	−0.322754	+	0.946483i	$0.604609\pi$
$278$	−91.7343	−	32.3647i	−0.329980	−	0.116420i
$279$		0			0
$280$	55.1936	−	62.8823i	0.197120	−	0.224580i
$281$	300.384			1.06898			0.534491	−	0.845174i	$-0.320503\pi$
$281$	300.384			1.06898			0.534491	+	0.845174i	$0.320503\pi$
$282$		0			0
$283$	−151.310	+	151.310i	−0.534663	+	0.534663i	−0.921957	−	0.387293i	$-0.873410\pi$
$283$	−151.310	+	151.310i	−0.534663	+	0.534663i	0.387293	+	0.921957i	$0.373410\pi$
$284$	−417.709	−	336.647i	−1.47081	−	1.18538i
$285$		0			0
$286$	43.7820	+	91.5165i	0.153084	+	0.319988i
$287$	29.0844	−	29.0844i	0.101339	−	0.101339i
$288$		0			0
$289$			91.0610i			0.315090i
$290$	−303.211	+	278.741i	−1.04555	+	0.961175i
$291$		0			0
$292$	−15.7929	−	146.967i	−0.0540852	−	0.503311i
$293$	−154.132	+	154.132i	−0.526048	+	0.526048i	−0.919391	−	0.393344i	$-0.871318\pi$
$293$	−154.132	+	154.132i	−0.526048	+	0.526048i	0.393344	+	0.919391i	$0.371318\pi$
$294$		0			0
$295$	91.3925	−	172.069i	0.309805	−	0.583286i
$296$	−22.3873	+	94.7058i	−0.0756328	+	0.319952i
$297$		0			0
$298$	−419.506	−	148.005i	−1.40774	−	0.496662i
$299$	10.6486			0.0356141
$300$		0			0
$301$			74.3170i			0.246900i
$302$	376.647	+	132.884i	1.24717	+	0.440014i
$303$		0			0
$304$	−38.3133	−	176.211i	−0.126031	−	0.579642i
$305$	−386.431	−	205.248i	−1.26699	−	0.672944i
$306$		0			0
$307$	−97.0784	−	97.0784i	−0.316216	−	0.316216i	0.531096	−	0.847312i	$-0.321781\pi$
$307$	−97.0784	−	97.0784i	−0.316216	−	0.316216i	−0.847312	+	0.531096i	$0.821781\pi$
$308$	10.1084	+	94.0678i	0.0328195	+	0.305415i
$309$		0			0
$310$	−215.362	+	197.982i	−0.694718	+	0.638652i
$311$	74.0447			0.238086			0.119043	−	0.992889i	$-0.462017\pi$
$311$	74.0447			0.238086			0.119043	+	0.992889i	$0.462017\pi$
$312$		0			0
$313$	−125.892	−	125.892i	−0.402212	−	0.402212i	0.476800	−	0.879012i	$-0.341797\pi$
$313$	−125.892	−	125.892i	−0.402212	−	0.402212i	−0.879012	+	0.476800i	$0.841797\pi$
$314$	233.366	+	487.800i	0.743204	+	1.55350i
$315$		0			0
$316$	58.1098	−	72.1023i	0.183892	−	0.228172i
$317$	−257.161	−	257.161i	−0.811233	−	0.811233i	0.173585	−	0.984819i	$-0.444465\pi$
$317$	−257.161	−	257.161i	−0.811233	−	0.811233i	−0.984819	+	0.173585i	$0.944465\pi$
$318$		0			0
$319$		−	465.719i		−	1.45993i
$320$	−185.487	−	260.758i	−0.579648	−	0.814867i
$321$		0			0
$322$	9.36482	+	3.30399i	0.0290833	+	0.0102608i
$323$	−112.123	+	112.123i	−0.347130	+	0.347130i
$324$		0			0
$325$	110.107	+	21.3008i	0.338791	+	0.0655409i
$326$	−257.314	+	123.100i	−0.789306	+	0.377608i
$327$		0			0
$328$	−82.6628	−	133.842i	−0.252021	−	0.408055i
$329$			123.471i			0.375291i
$330$		0			0
$331$			403.967i			1.22045i	0.792230	+	0.610223i	$0.208920\pi$
$331$			403.967i			1.22045i	−0.792230	+	0.610223i	$0.791080\pi$
$332$	384.430	−	41.3105i	1.15792	−	0.124429i
$333$		0			0
$334$	532.127	−	254.572i	1.59319	−	0.762193i
$335$	210.517	−	64.4642i	0.628409	−	0.192430i
$336$		0			0
$337$	−101.745	+	101.745i	−0.301915	+	0.301915i	−0.841763	−	0.539848i	$-0.818482\pi$
$337$	−101.745	+	101.745i	−0.301915	+	0.301915i	0.539848	+	0.841763i	$0.318482\pi$
$338$	99.0650	−	280.789i	0.293092	−	0.830738i
$339$		0			0
$340$	−104.683	+	261.184i	−0.307892	+	0.768188i
$341$		−	330.788i		−	0.970053i
$342$		0			0
$343$	138.478	+	138.478i	0.403726	+	0.403726i
$344$	276.609	+	65.3870i	0.804095	+	0.190078i
$345$		0			0
$346$	311.937	−	149.232i	0.901551	−	0.431307i
$347$	196.538	+	196.538i	0.566391	+	0.566391i	0.931116	−	0.364724i	$-0.118837\pi$
$347$	196.538	+	196.538i	0.566391	+	0.566391i	−0.364724	+	0.931116i	$0.618837\pi$
$348$		0			0
$349$	454.536			1.30240			0.651198	−	0.758908i	$-0.274267\pi$
$349$	454.536			1.30240			0.651198	+	0.758908i	$0.274267\pi$
$350$	90.2236	+	52.8962i	0.257782	+	0.151132i
$351$		0			0
$352$	359.015	+	45.1408i	1.01993	+	0.128241i
$353$	−204.788	−	204.788i	−0.580135	−	0.580135i	0.354805	−	0.934940i	$-0.384547\pi$
$353$	−204.788	−	204.788i	−0.580135	−	0.580135i	−0.934940	+	0.354805i	$0.884547\pi$
$354$		0			0
$355$	314.565	−	592.247i	0.886097	−	1.66830i
$356$	188.896	−	234.380i	0.530606	−	0.658372i
$357$		0			0
$358$	120.288	+	42.4386i	0.336000	+	0.118544i
$359$		−	27.2061i		−	0.0757831i	−0.999282	−	0.0378916i	$-0.987936\pi$
$359$		−	27.2061i		−	0.0757831i	0.999282	−	0.0378916i	$-0.0120641\pi$
$360$		0			0
$361$	−233.976			−0.648132
$362$	−127.826	+	362.310i	−0.353111	+	1.00086i
$363$		0			0
$364$	−23.5526	+	29.2239i	−0.0647050	+	0.0802855i
$365$	176.669	−	54.0991i	0.484023	−	0.148217i
$366$		0			0
$367$	50.4416	−	50.4416i	0.137443	−	0.137443i	−0.635038	−	0.772481i	$-0.719016\pi$
$367$	50.4416	−	50.4416i	0.137443	−	0.137443i	0.772481	+	0.635038i	$0.219016\pi$
$368$	20.5370	−	31.9490i	0.0558072	−	0.0868179i
$369$		0			0
$370$	−121.537	−	5.11040i	−0.328479	−	0.0138119i
$371$			6.39578i			0.0172393i
$372$		0			0
$373$	−105.787	+	105.787i	−0.283612	+	0.283612i	−0.834548	−	0.550936i	$-0.814271\pi$
$373$	−105.787	+	105.787i	−0.283612	+	0.283612i	0.550936	+	0.834548i	$0.314271\pi$
$374$	−137.312	−	287.019i	−0.367143	−	0.767432i
$375$		0			0
$376$	459.560	+	108.634i	1.22223	+	0.288921i
$377$	130.645	−	130.645i	0.346540	−	0.346540i
$378$		0			0
$379$	−595.709			−1.57179			−0.785896	−	0.618359i	$-0.787798\pi$
$379$	−595.709			−1.57179			−0.785896	+	0.618359i	$0.787798\pi$
$380$	207.246	−	88.6501i	0.545384	−	0.233290i
$381$		0			0
$382$	−322.131	−	113.651i	−0.843274	−	0.297514i
$383$	59.2677	+	59.2677i	0.154746	+	0.154746i	0.780234	−	0.625488i	$-0.215100\pi$
$383$	59.2677	+	59.2677i	0.154746	+	0.154746i	−0.625488	+	0.780234i	$0.715100\pi$
$384$		0			0
$385$	−113.079	+	34.6268i	−0.293711	+	0.0899397i
$386$	−135.851	−	283.966i	−0.351945	−	0.735662i
$387$		0			0
$388$	323.818	−	34.7971i	0.834582	−	0.0896833i
$389$	254.508			0.654263			0.327131	−	0.944979i	$-0.393918\pi$
$389$	254.508			0.654263			0.327131	+	0.944979i	$0.393918\pi$
$390$		0			0
$391$	−33.3968			−0.0854138
$392$	303.737	−	187.593i	0.774839	−	0.478553i
$393$		0			0
$394$	118.267	+	247.211i	0.300170	+	0.627438i
$395$	102.230	+	54.2981i	0.258810	+	0.137464i
$396$		0			0
$397$	−372.832	−	372.832i	−0.939122	−	0.939122i	0.0591281	−	0.998250i	$-0.481168\pi$
$397$	−372.832	−	372.832i	−0.939122	−	0.939122i	−0.998250	+	0.0591281i	$0.981168\pi$
$398$	93.0291	−	263.681i	0.233741	−	0.662516i
$399$		0			0
$400$	276.263	−	289.273i	0.690657	−	0.723183i
$401$	−471.865			−1.17672			−0.588360	−	0.808599i	$-0.700226\pi$
$401$	−471.865			−1.17672			−0.588360	+	0.808599i	$0.700226\pi$
$402$		0			0
$403$	92.7940	−	92.7940i	0.230258	−	0.230258i
$404$	−281.738	+	349.579i	−0.697372	+	0.865294i
$405$		0			0
$406$	155.431	−	74.3589i	0.382834	−	0.183150i
$407$	97.2629	−	97.2629i	0.238975	−	0.238975i
$408$		0			0
$409$			182.192i			0.445457i	0.974880	+	0.222729i	$0.0714964\pi$
$409$			182.192i			0.445457i	−0.974880	+	0.222729i	$0.928504\pi$
$410$	144.763	−	133.081i	0.353082	−	0.324587i
$411$		0			0
$412$	15.3833	+	143.156i	0.0373382	+	0.347465i
$413$	−57.6349	+	57.6349i	−0.139552	+	0.139552i
$414$		0			0
$415$	141.511	+	462.123i	0.340989	+	1.11355i
$416$	88.0493	+	113.375i	0.211657	+	0.272537i
$417$		0			0
$418$	−84.8022	+	240.363i	−0.202876	+	0.575031i
$419$	452.553			1.08008			0.540039	−	0.841640i	$-0.318410\pi$
$419$	452.553			1.08008			0.540039	+	0.841640i	$0.318410\pi$
$420$		0			0
$421$		−	65.0180i		−	0.154437i	−0.997014	−	0.0772186i	$-0.975396\pi$
$421$		−	65.0180i		−	0.154437i	0.997014	−	0.0772186i	$-0.0246039\pi$
$422$	6.36068	−	18.0287i	0.0150727	−	0.0427220i
$423$		0			0
$424$	23.8052	+	5.62726i	0.0561443	+	0.0132718i
$425$	−345.325	−	66.8048i	−0.812528	−	0.157188i
$426$		0			0
$427$	129.436	+	129.436i	0.303128	+	0.303128i
$428$	−39.9137	−	371.433i	−0.0932564	−	0.867833i
$429$		0			0
$430$	−14.9260	+	354.976i	−0.0347117	+	0.825526i
$431$	433.432			1.00564			0.502821	−	0.864391i	$-0.332296\pi$
$431$	433.432			1.00564			0.502821	+	0.864391i	$0.332296\pi$
$432$		0			0
$433$	−280.632	−	280.632i	−0.648112	−	0.648112i	0.304425	−	0.952536i	$-0.401536\pi$
$433$	−280.632	−	280.632i	−0.648112	−	0.648112i	−0.952536	+	0.304425i	$0.901536\pi$
$434$	110.398	−	52.8152i	0.254374	−	0.121694i
$435$		0			0
$436$	284.230	+	229.071i	0.651903	+	0.525392i
$437$	18.9177	+	18.9177i	0.0432899	+	0.0432899i
$438$		0			0
$439$		−	557.674i		−	1.27033i	−0.772377	−	0.635164i	$-0.780932\pi$
$439$		−	557.674i		−	1.27033i	0.772377	−	0.635164i	$-0.219068\pi$
$440$	29.3902	+	451.346i	0.0667959	+	1.02579i
$441$		0			0
$442$	41.9966	−	119.035i	0.0950150	−	0.269310i
$443$	−128.300	+	128.300i	−0.289616	+	0.289616i	−0.836928	−	0.547313i	$-0.815651\pi$
$443$	−128.300	+	128.300i	−0.289616	+	0.289616i	0.547313	+	0.836928i	$0.315651\pi$
$444$		0			0
$445$	332.315	+	176.505i	0.746775	+	0.396640i
$446$	−337.330	−	705.114i	−0.756346	−	1.58097i
$447$		0			0
$448$	42.2566	+	127.026i	0.0943227	+	0.283541i
$449$			512.154i			1.14065i	0.821417	+	0.570327i	$0.193184\pi$
$449$			512.154i			1.14065i	−0.821417	+	0.570327i	$0.806816\pi$
$450$		0			0
$451$			222.351i			0.493017i
$452$	76.9475	+	716.065i	0.170238	+	1.58421i
$453$		0			0
$454$	196.436	+	410.606i	0.432679	+	0.904419i
$455$	−41.4350	−	22.0077i	−0.0910659	−	0.0483685i
$456$		0			0
$457$	−388.529	+	388.529i	−0.850173	+	0.850173i	−0.990154	−	0.139981i	$-0.955296\pi$
$457$	−388.529	+	388.529i	−0.850173	+	0.850173i	0.139981	+	0.990154i	$0.455296\pi$
$458$	−75.9086	−	26.7812i	−0.165739	−	0.0584743i
$459$		0			0
$460$	44.0676	+	17.6624i	0.0957992	+	0.0383966i
$461$		−	36.0020i		−	0.0780954i	−0.999237	−	0.0390477i	$-0.987568\pi$
$461$		−	36.0020i		−	0.0780954i	0.999237	−	0.0390477i	$-0.0124324\pi$
$462$		0			0
$463$	−338.658	−	338.658i	−0.731442	−	0.731442i	0.239463	−	0.970905i	$-0.423029\pi$
$463$	−338.658	−	338.658i	−0.731442	−	0.731442i	−0.970905	+	0.239463i	$0.923029\pi$
$464$	−140.011	−	643.939i	−0.301747	−	1.38780i
$465$		0			0
$466$	−294.249	−	615.062i	−0.631436	−	1.31988i
$467$	43.6060	+	43.6060i	0.0933748	+	0.0933748i	0.752251	−	0.658876i	$-0.228968\pi$
$467$	43.6060	+	43.6060i	0.0933748	+	0.0933748i	−0.658876	+	0.752251i	$0.728968\pi$
$468$		0			0
$469$	−92.1055			−0.196387
$470$	−24.7982	+	589.760i	−0.0527622	+	1.25481i
$471$		0			0
$472$	163.808	+	265.227i	0.347052	+	0.561922i
$473$	−284.077	−	284.077i	−0.600586	−	0.600586i
$474$		0			0
$475$	157.768	+	233.451i	0.332143	+	0.491476i
$476$	73.8671	−	91.6538i	0.155183	−	0.192550i
$477$		0			0
$478$	165.691	−	469.632i	0.346633	−	0.982495i
$479$		−	870.273i		−	1.81685i	−0.418043	−	0.908427i	$-0.637284\pi$
$479$		−	870.273i		−	1.81685i	0.418043	−	0.908427i	$-0.362716\pi$
$480$		0			0
$481$	54.5692			0.113449
$482$	−612.504	−	216.097i	−1.27075	−	0.448334i
$483$		0			0
$484$	−21.3677	−	17.2210i	−0.0441482	−	0.0355806i
$485$	119.199	+	389.261i	0.245771	+	0.802600i
$486$		0			0
$487$	−611.867	+	611.867i	−1.25640	+	1.25640i	−0.303603	+	0.952799i	$0.598190\pi$
$487$	−611.867	+	611.867i	−1.25640	+	1.25640i	−0.952799	+	0.303603i	$0.901810\pi$
$488$	595.644	−	367.879i	1.22058	−	0.753849i
$489$		0			0
$490$	302.009	+	328.522i	0.616345	+	0.670453i
$491$			719.282i			1.46493i	0.680803	+	0.732467i	$0.261631\pi$
$491$			719.282i			1.46493i	−0.680803	+	0.732467i	$0.738369\pi$
$492$		0			0
$493$	−409.738	+	409.738i	−0.831111	+	0.831111i
$494$	−91.2167	+	43.6386i	−0.184649	+	0.0883372i
$495$		0			0
$496$	−99.4459	−	457.373i	−0.200496	−	0.922123i
$497$	−198.374	+	198.374i	−0.399143	+	0.399143i
$498$		0			0
$499$	186.103			0.372952			0.186476	−	0.982459i	$-0.440293\pi$
$499$	186.103			0.372952			0.186476	+	0.982459i	$0.440293\pi$
$500$	420.331	+	270.780i	0.840661	+	0.541561i
$501$		0			0
$502$	110.945	−	314.461i	0.221006	−	0.626417i
$503$	302.420	+	302.420i	0.601232	+	0.601232i	0.940639	−	0.339408i	$-0.110227\pi$
$503$	302.420	+	302.420i	0.601232	+	0.601232i	−0.339408	+	0.940639i	$0.610227\pi$
$504$		0			0
$505$	−495.648	−	263.257i	−0.981481	−	0.521302i
$506$	−48.4267	+	23.1676i	−0.0957049	+	0.0457857i
$507$		0			0
$508$	−81.7255	+	8.78213i	−0.160877	+	0.0172877i
$509$	107.882			0.211949			0.105975	−	0.994369i	$-0.466204\pi$
$509$	107.882			0.211949			0.105975	+	0.994369i	$0.466204\pi$
$510$		0			0
$511$	−77.2960			−0.151264
$512$	509.973	−	45.5168i	0.996041	−	0.0888999i
$513$		0			0
$514$	470.770	−	225.219i	0.915895	−	0.438169i
$515$	−172.087	+	52.6962i	−0.334150	+	0.102323i
$516$		0			0
$517$	−471.968	−	471.968i	−0.912898	−	0.912898i
$518$	47.9903	+	16.9314i	0.0926455	+	0.0326861i
$519$		0			0
$520$	−118.369	+	134.858i	−0.227633	+	0.259343i
$521$	374.569			0.718942			0.359471	−	0.933156i	$-0.382957\pi$
$521$	374.569			0.718942			0.359471	+	0.933156i	$0.382957\pi$
$522$		0			0
$523$	−161.196	+	161.196i	−0.308213	+	0.308213i	−0.844216	−	0.536003i	$-0.819934\pi$
$523$	−161.196	+	161.196i	−0.308213	+	0.308213i	0.536003	+	0.844216i	$0.319934\pi$
$524$	−130.284	+	161.655i	−0.248633	+	0.308502i
$525$		0			0
$526$	4.70725	+	9.83945i	0.00894914	+	0.0187062i
$527$	−291.026	+	291.026i	−0.552231	+	0.552231i
$528$		0			0
$529$		−	523.365i		−	0.989348i
$530$	−1.28455	+	30.5496i	−0.00242367	+	0.0576407i
$531$		0			0
$532$	−93.7596	+	10.0753i	−0.176240	+	0.0189385i
$533$	−62.3747	+	62.3747i	−0.117026	+	0.117026i
$534$		0			0
$535$	446.499	−	136.726i	0.834577	−	0.255563i
$536$	−81.0380	+	342.818i	−0.151190	+	0.639585i
$537$		0			0
$538$	−307.663	−	108.546i	−0.571865	−	0.201759i
$539$	−504.596			−0.936171
$540$		0			0
$541$		−	319.556i		−	0.590676i	−0.955393	−	0.295338i	$-0.904568\pi$
$541$		−	319.556i		−	0.590676i	0.955393	−	0.295338i	$-0.0954323\pi$
$542$	−189.826	−	66.9724i	−0.350233	−	0.123565i
$543$		0			0
$544$	−276.145	−	355.575i	−0.507620	−	0.653630i
$545$	−214.045	+	402.993i	−0.392743	+	0.739437i
$546$		0			0
$547$	631.421	+	631.421i	1.15433	+	1.15433i	0.985674	+	0.168659i	$0.0539438\pi$
$547$	631.421	+	631.421i	1.15433	+	1.15433i	0.168659	+	0.985674i	$0.446056\pi$
$548$	555.493	−	59.6927i	1.01367	−	0.108928i
$549$		0			0
$550$	−547.077	+	142.684i	−0.994686	+	0.259426i
$551$	464.193			0.842456
$552$		0			0
$553$	−34.2420	−	34.2420i	−0.0619205	−	0.0619205i
$554$	−210.894	−	440.826i	−0.380675	−	0.795716i
$555$		0			0
$556$	151.480	+	122.083i	0.272447	+	0.219575i
$557$	−405.826	−	405.826i	−0.728592	−	0.728592i	0.241747	−	0.970339i	$-0.422280\pi$
$557$	−405.826	−	405.826i	−0.728592	−	0.728592i	−0.970339	+	0.241747i	$0.922280\pi$
$558$		0			0
$559$		−	159.381i		−	0.285118i
$560$	−145.941	+	81.8729i	−0.260610	+	0.146202i
$561$		0			0
$562$	−566.542	−	199.881i	−1.00808	−	0.355660i
$563$	241.881	−	241.881i	0.429628	−	0.429628i	−0.458873	−	0.888502i	$-0.651747\pi$
$563$	241.881	−	241.881i	0.429628	−	0.429628i	0.888502	+	0.458873i	$0.151747\pi$
$564$		0			0
$565$	−860.780	+	263.587i	−1.52351	+	0.466525i
$566$	386.063	−	184.695i	0.682091	−	0.326316i
$567$		0			0
$568$	563.813	+	912.888i	0.992629	+	1.60720i
$569$		−	416.031i		−	0.731162i	−0.930780	−	0.365581i	$-0.880870\pi$
$569$		−	416.031i		−	0.731162i	0.930780	−	0.365581i	$-0.119130\pi$
$570$		0			0
$571$			907.558i			1.58942i	0.606991	+	0.794709i	$0.292377\pi$
$571$			907.558i			1.58942i	−0.606991	+	0.794709i	$0.707623\pi$
$572$	−21.6786	−	201.739i	−0.0378997	−	0.352690i
$573$		0			0
$574$	−74.2081	+	35.5016i	−0.129282	+	0.0618494i
$575$	−11.2715	+	58.2641i	−0.0196026	+	0.101329i
$576$		0			0
$577$	467.070	−	467.070i	0.809480	−	0.809480i	−0.175075	−	0.984555i	$-0.556017\pi$
$577$	467.070	−	467.070i	0.809480	−	0.809480i	0.984555	+	0.175075i	$0.0560167\pi$
$578$	60.5936	−	171.746i	0.104833	−	0.297139i
$579$		0			0
$580$	757.352	−	323.959i	1.30578	−	0.558551i
$581$		−	202.188i		−	0.348000i
$582$		0			0
$583$	−24.4479	−	24.4479i	−0.0419347	−	0.0419347i
$584$	−68.0080	+	287.697i	−0.116452	+	0.492631i
$585$		0			0
$586$	393.264	−	188.140i	0.671100	−	0.321058i
$587$	−247.149	−	247.149i	−0.421038	−	0.421038i	0.464523	−	0.885561i	$-0.346226\pi$
$587$	−247.149	−	247.149i	−0.421038	−	0.421038i	−0.885561	+	0.464523i	$0.846226\pi$
$588$		0			0
$589$	329.704			0.559769
$590$	−286.870	+	263.719i	−0.486220	+	0.446981i
$591$		0			0
$592$	105.243	−	163.724i	0.177775	−	0.276560i
$593$	−315.219	−	315.219i	−0.531567	−	0.531567i	0.389472	−	0.921038i	$-0.372658\pi$
$593$	−315.219	−	315.219i	−0.531567	−	0.531567i	−0.921038	+	0.389472i	$0.872658\pi$
$594$		0			0
$595$	129.951	+	69.0217i	0.218405	+	0.116003i
$596$	692.727	+	558.294i	1.16229	+	0.936734i
$597$		0			0
$598$	−20.0839	−	7.08579i	−0.0335851	−	0.0118491i
$599$		−	423.660i		−	0.707278i	−0.935382	−	0.353639i	$-0.884944\pi$
$599$		−	423.660i		−	0.707278i	0.935382	−	0.353639i	$-0.115056\pi$
$600$		0			0
$601$	293.629			0.488568			0.244284	−	0.969704i	$-0.421447\pi$
$601$	293.629			0.488568			0.244284	+	0.969704i	$0.421447\pi$
$602$	49.4519	−	140.166i	0.0821460	−	0.232834i
$603$		0			0
$604$	−621.954	−	501.255i	−1.02973	−	0.829893i
$605$	16.0914	−	30.2961i	0.0265974	−	0.0500762i
$606$		0			0
$607$	−143.784	+	143.784i	−0.236876	+	0.236876i	−0.815555	−	0.578679i	$-0.803568\pi$
$607$	−143.784	+	143.784i	−0.236876	+	0.236876i	0.578679	+	0.815555i	$0.303568\pi$
$608$	−44.9929	+	357.839i	−0.0740015	+	0.588551i
$609$		0			0
$610$	592.255	+	644.248i	0.970910	+	1.05614i
$611$		−	264.797i		−	0.433383i
$612$		0			0
$613$	304.429	−	304.429i	0.496622	−	0.496622i	−0.413763	−	0.910385i	$-0.635786\pi$
$613$	304.429	−	304.429i	0.496622	−	0.496622i	0.910385	+	0.413763i	$0.135786\pi$
$614$	118.498	+	247.693i	0.192993	+	0.403409i
$615$		0			0
$616$	43.5293	−	184.144i	0.0706645	−	0.298935i
$617$	−815.279	+	815.279i	−1.32136	+	1.32136i	−0.408683	+	0.912676i	$0.634012\pi$
$617$	−815.279	+	815.279i	−1.32136	+	1.32136i	−0.912676	+	0.408683i	$0.865988\pi$
$618$		0			0
$619$	−1062.25			−1.71607			−0.858036	−	0.513589i	$-0.828316\pi$
$619$	−1062.25			−1.71607			−0.858036	+	0.513589i	$0.828316\pi$
$620$	537.927	−	230.100i	0.867625	−	0.371129i
$621$		0			0
$622$	−139.653	−	49.2707i	−0.224522	−	0.0792133i
$623$	−111.309	−	111.309i	−0.178667	−	0.178667i
$624$		0			0
$625$	−233.095	+	579.906i	−0.372953	+	0.927850i
$626$	153.669	+	321.212i	0.245478	+	0.513118i
$627$		0			0
$628$	−115.551	−	1075.31i	−0.183999	−	1.71227i
$629$	−171.143			−0.272088
$630$		0			0
$631$	842.984			1.33595			0.667975	−	0.744184i	$-0.267161\pi$
$631$	842.984			1.33595			0.667975	+	0.744184i	$0.267161\pi$
$632$	−157.577	+	97.3218i	−0.249330	+	0.153990i
$633$		0			0
$634$	313.901	+	656.140i	0.495112	+	1.03492i
$635$	−30.0835	−	98.2421i	−0.0473756	−	0.154712i
$636$		0			0
$637$	−141.551	−	141.551i	−0.222216	−	0.222216i
$638$	−309.898	+	878.373i	−0.485734	+	1.37676i
$639$		0			0
$640$	176.327	+	615.231i	0.275511	+	0.961298i
$641$	169.581			0.264557			0.132278	−	0.991213i	$-0.457771\pi$
$641$	169.581			0.264557			0.132278	+	0.991213i	$0.457771\pi$
$642$		0			0
$643$	493.738	−	493.738i	0.767867	−	0.767867i	−0.209864	−	0.977731i	$-0.567302\pi$
$643$	493.738	−	493.738i	0.767867	−	0.767867i	0.977731	+	0.209864i	$0.0673021\pi$
$644$	−15.4641	−	12.4630i	−0.0240125	−	0.0193526i
$645$		0			0
$646$	286.079	−	136.862i	0.442847	−	0.211860i
$647$	509.311	−	509.311i	0.787189	−	0.787189i	−0.193844	−	0.981032i	$-0.562095\pi$
$647$	509.311	−	509.311i	0.787189	−	0.787189i	0.981032	+	0.193844i	$0.0620954\pi$
$648$		0			0
$649$		−	440.620i		−	0.678922i
$650$	−193.495	−	113.442i	−0.297684	−	0.174526i
$651$		0			0
$652$	567.222	−	60.9530i	0.869972	−	0.0934863i
$653$	239.798	−	239.798i	0.367226	−	0.367226i	−0.499239	−	0.866464i	$-0.666387\pi$
$653$	239.798	−	239.798i	0.367226	−	0.367226i	0.866464	+	0.499239i	$0.166387\pi$
$654$		0			0
$655$	−229.202	−	121.738i	−0.349927	−	0.185859i
$656$	66.8461	+	307.439i	0.101899	+	0.468657i
$657$		0			0
$658$	82.1597	−	232.873i	0.124863	−	0.353911i
$659$	−900.540			−1.36653			−0.683263	−	0.730173i	$-0.739440\pi$
$659$	−900.540			−1.36653			−0.683263	+	0.730173i	$0.739440\pi$
$660$		0			0
$661$			59.7896i			0.0904533i	0.998977	+	0.0452267i	$0.0144010\pi$
$661$			59.7896i			0.0904533i	−0.998977	+	0.0452267i	$0.985599\pi$
$662$	268.807	−	761.906i	0.406053	−	1.15092i
$663$		0			0
$664$	−752.547	−	177.893i	−1.13335	−	0.267911i
$665$	−34.5133	−	112.708i	−0.0518997	−	0.169486i
$666$		0			0
$667$	69.1320	+	69.1320i	0.103646	+	0.103646i
$668$	−1173.02	+	126.051i	−1.75602	+	0.188700i
$669$		0			0
$670$	−439.943	−	18.4987i	−0.656632	−	0.0276101i
$671$	−989.538			−1.47472
$672$		0			0
$673$	190.854	+	190.854i	0.283587	+	0.283587i	0.834538	−	0.550951i	$-0.185735\pi$
$673$	190.854	+	190.854i	0.283587	+	0.283587i	−0.550951	+	0.834538i	$0.685735\pi$
$674$	259.601	−	124.194i	0.385164	−	0.184265i
$675$		0			0
$676$	−373.685	+	463.666i	−0.552788	+	0.685896i
$677$	−503.850	−	503.850i	−0.744240	−	0.744240i	0.229151	−	0.973391i	$-0.426405\pi$
$677$	−503.850	−	503.850i	−0.744240	−	0.744240i	−0.973391	+	0.229151i	$0.926405\pi$
$678$		0			0
$679$		−	170.310i		−	0.250824i
$680$	371.235	−	422.950i	0.545934	−	0.621985i
$681$		0			0
$682$	−220.112	+	623.886i	−0.322745	+	0.914788i
$683$	−141.973	+	141.973i	−0.207866	+	0.207866i	−0.803360	−	0.595494i	$-0.796956\pi$
$683$	−141.973	+	141.973i	−0.207866	+	0.207866i	0.595494	+	0.803360i	$0.296956\pi$
$684$		0			0
$685$	204.480	+	667.758i	0.298510	+	0.974829i
$686$	−169.032	−	353.323i	−0.246402	−	0.515048i
$687$		0			0
$688$	−478.190	−	307.384i	−0.695044	−	0.446779i
$689$		−	13.7165i		−	0.0199078i
$690$		0			0
$691$		−	1271.56i		−	1.84017i	−0.391717	−	0.920086i	$-0.628119\pi$
$691$		−	1271.56i		−	1.84017i	0.391717	−	0.920086i	$-0.371881\pi$
$692$	−687.633	+	73.8922i	−0.993689	+	0.106781i
$693$		0			0
$694$	−239.902	−	501.462i	−0.345680	−	0.722568i
$695$	−114.075	+	214.775i	−0.164137	+	0.309029i
$696$		0			0
$697$	195.623	−	195.623i	0.280665	−	0.280665i
$698$	−857.282	−	302.457i	−1.22820	−	0.433319i
$699$		0			0
$700$	−134.969	−	159.802i	−0.192813	−	0.228288i
$701$			799.199i			1.14008i	0.821615	+	0.570042i	$0.193073\pi$
$701$			799.199i			1.14008i	−0.821615	+	0.570042i	$0.806927\pi$
$702$		0			0
$703$	96.9443	+	96.9443i	0.137901	+	0.137901i
$704$	−647.086	−	324.034i	−0.919156	−	0.460275i
$705$		0			0
$706$	249.972	+	522.511i	0.354068	+	0.740101i
$707$	166.018	+	166.018i	0.234821	+	0.234821i
$708$		0			0
$709$	479.020			0.675628			0.337814	−	0.941213i	$-0.390313\pi$
$709$	479.020			0.675628			0.337814	+	0.941213i	$0.390313\pi$
$710$	−987.379	+	907.695i	−1.39067	+	1.27844i
$711$		0			0
$712$	−512.229	+	316.361i	−0.719423	+	0.444327i
$713$	49.1027	+	49.1027i	0.0688677	+	0.0688677i
$714$		0			0
$715$	242.510	−	74.2610i	0.339175	−	0.103862i
$716$	−198.631	−	160.083i	−0.277417	−	0.223580i
$717$		0			0
$718$	−18.1035	+	51.3124i	−0.0252137	+	0.0714657i
$719$			800.764i			1.11372i	0.830607	+	0.556859i	$0.187994\pi$
$719$			800.764i			1.11372i	−0.830607	+	0.556859i	$0.812006\pi$
$720$		0			0
$721$	75.2916			0.104427
$722$	441.292	+	155.692i	0.611207	+	0.215639i
$723$		0			0
$724$	482.175	−	598.280i	0.665988	−	0.826353i
$725$	576.541	+	853.116i	0.795229	+	1.17671i
$726$		0			0
$727$	144.435	−	144.435i	0.198673	−	0.198673i	−0.600758	−	0.799431i	$-0.705134\pi$
$727$	144.435	−	144.435i	0.198673	−	0.198673i	0.799431	+	0.600758i	$0.205134\pi$
$728$	63.8678	−	39.4457i	0.0877305	−	0.0541837i
$729$		0			0
$730$	−369.206	−	15.5244i	−0.505761	−	0.0212662i
$731$			499.860i			0.683803i
$732$		0			0
$733$	−748.614	+	748.614i	−1.02130	+	1.02130i	−0.0215340	+	0.999768i	$0.506855\pi$
$733$	−748.614	+	748.614i	−1.02130	+	1.02130i	−0.999768	+	0.0215340i	$0.993145\pi$
$734$	−128.701	+	61.5711i	−0.175341	+	0.0838843i
$735$		0			0
$736$	−59.9935	+	46.5920i	−0.0815129	+	0.0633043i
$737$	352.074	−	352.074i	0.477713	−	0.477713i
$738$		0			0
$739$	−731.874			−0.990358			−0.495179	−	0.868791i	$-0.664897\pi$
$739$	−731.874			−0.990358			−0.495179	+	0.868791i	$0.664897\pi$
$740$	225.826	+	90.5118i	0.305170	+	0.122313i
$741$		0			0
$742$	4.25587	−	12.0628i	0.00573567	−	0.0162572i
$743$	676.219	+	676.219i	0.910119	+	0.910119i	0.996281	−	0.0861618i	$-0.0274602\pi$
$743$	676.219	+	676.219i	0.910119	+	0.910119i	−0.0861618	+	0.996281i	$0.527460\pi$
$744$		0			0
$745$	−521.672	+	982.179i	−0.700231	+	1.31836i
$746$	269.914	−	129.128i	0.361814	−	0.173094i
$747$		0			0
$748$	67.9898	+	632.705i	0.0908955	+	0.845863i
$749$	−195.352			−0.260817
$750$		0			0
$751$	−59.2858			−0.0789424			−0.0394712	−	0.999221i	$-0.512567\pi$
$751$	−59.2858			−0.0789424			−0.0394712	+	0.999221i	$0.512567\pi$
$752$	−794.469	−	510.690i	−1.05648	−	0.679109i
$753$		0			0
$754$	−333.339	+	159.471i	−0.442094	+	0.211500i
$755$	468.375	−	881.834i	0.620364	−	1.16799i
$756$		0			0
$757$	597.444	+	597.444i	0.789225	+	0.789225i	0.981367	−	0.192142i	$-0.0615434\pi$
$757$	597.444	+	597.444i	0.789225	+	0.789225i	−0.192142	+	0.981367i	$0.561543\pi$
$758$	1123.54	+	396.396i	1.48225	+	0.522949i
$759$		0			0
$760$	−449.868	+	29.2939i	−0.591931	+	0.0385446i
$761$	−32.0333			−0.0420937			−0.0210469	−	0.999778i	$-0.506700\pi$
$761$	−32.0333			−0.0420937			−0.0210469	+	0.999778i	$0.506700\pi$
$762$		0			0
$763$	134.983	−	134.983i	0.176911	−	0.176911i
$764$	531.932	+	428.703i	0.696246	+	0.561130i
$765$		0			0
$766$	−72.3445	−	151.220i	−0.0944445	−	0.197415i
$767$	123.605	−	123.605i	0.161153	−	0.161153i
$768$		0			0
$769$			1416.08i			1.84145i	0.390208	+	0.920727i	$0.372403\pi$
$769$			1416.08i			1.84145i	−0.390208	+	0.920727i	$0.627597\pi$
$770$	236.314	+	9.93655i	0.306902	+	0.0129046i
$771$		0			0
$772$	67.2664	+	625.973i	0.0871327	+	0.810846i
$773$	−77.7861	+	77.7861i	−0.100629	+	0.100629i	−0.755629	−	0.655000i	$-0.772669\pi$
$773$	−77.7861	+	77.7861i	−0.100629	+	0.100629i	0.655000	+	0.755629i	$0.272669\pi$
$774$		0			0
$775$	409.502	+	605.946i	0.528390	+	0.781865i
$776$	−633.894	−	149.845i	−0.816874	−	0.193099i
$777$		0			0
$778$	−480.017	−	169.354i	−0.616989	−	0.217679i
$779$	−221.622			−0.284496
$780$		0			0
$781$		−	1516.57i		−	1.94184i
$782$	62.9883	+	22.2228i	0.0805477	+	0.0284180i
$783$		0			0
$784$	−697.693	+	151.698i	−0.889915	+	0.193493i
$785$	1292.62	−	395.825i	1.64665	−	0.504235i
$786$		0			0
$787$	−494.548	−	494.548i	−0.628396	−	0.628396i	0.319268	−	0.947664i	$-0.396563\pi$
$787$	−494.548	−	494.548i	−0.628396	−	0.628396i	−0.947664	+	0.319268i	$0.896563\pi$
$788$	−58.5598	−	544.951i	−0.0743145	−	0.691562i
$789$		0			0
$790$	−156.680	−	170.435i	−0.198330	−	0.215740i
$791$	376.609			0.476117
$792$		0			0
$793$	−277.589	−	277.589i	−0.350050	−	0.350050i
$794$	455.093	+	951.271i	0.573165	+	1.19807i
$795$		0			0
$796$	−350.917	+	435.415i	−0.440850	+	0.547004i
$797$	562.627	+	562.627i	0.705931	+	0.705931i	0.965677	−	0.259746i	$-0.0836388\pi$
$797$	562.627	+	562.627i	0.705931	+	0.705931i	−0.259746	+	0.965677i	$0.583639\pi$
$798$		0			0
$799$			830.472i			1.03939i
$800$	−713.535	+	361.756i	−0.891919	+	0.452195i
$801$		0			0
$802$	889.965	+	313.988i	1.10968	+	0.391506i
$803$	295.465	−	295.465i	0.367951	−	0.367951i
$804$		0			0
$805$	11.6455	−	21.9256i	0.0144665	−	0.0272368i
$806$	−236.762	+	113.268i	−0.293749	+	0.140531i
$807$		0			0
$808$	763.991	−	471.852i	0.945533	−	0.583976i
$809$			440.667i			0.544706i	0.962197	+	0.272353i	$0.0878018\pi$
$809$			440.667i			0.544706i	−0.962197	+	0.272353i	$0.912198\pi$
$810$		0			0
$811$			911.348i			1.12373i	0.827228	+	0.561867i	$0.189917\pi$
$811$			911.348i			1.12373i	−0.827228	+	0.561867i	$0.810083\pi$
$812$	−342.631	+	36.8188i	−0.421960	+	0.0453433i
$813$		0			0
$814$	−248.164	+	118.723i	−0.304870	+	0.145851i
$815$	208.797	+	681.857i	0.256193	+	0.836634i
$816$		0			0
$817$	283.147	−	283.147i	0.346569	−	0.346569i
$818$	121.234	−	343.625i	0.148208	−	0.420079i
$819$		0			0
$820$	−361.587	+	154.670i	−0.440959	+	0.188622i
$821$		−	893.060i		−	1.08777i	−0.839159	−	0.543885i	$-0.816953\pi$
$821$		−	893.060i		−	1.08777i	0.839159	−	0.543885i	$-0.183047\pi$
$822$		0			0
$823$	−852.293	−	852.293i	−1.03559	−	1.03559i	−0.999343	−	0.0362500i	$-0.988459\pi$
$823$	−852.293	−	852.293i	−1.03559	−	1.03559i	−0.0362500	−	0.999343i	$-0.511541\pi$
$824$	66.2445	−	280.236i	0.0803938	−	0.340093i
$825$		0			0
$826$	147.054	−	70.3515i	0.178032	−	0.0851713i
$827$	608.192	+	608.192i	0.735419	+	0.735419i	0.971688	−	0.236269i	$-0.0759245\pi$
$827$	608.192	+	608.192i	0.735419	+	0.735419i	−0.236269	+	0.971688i	$0.575925\pi$
$828$		0			0
$829$	1550.55			1.87039			0.935195	−	0.354133i	$-0.115224\pi$
$829$	1550.55			1.87039			0.935195	+	0.354133i	$0.115224\pi$
$830$	40.6081	−	965.756i	0.0489254	−	1.16356i
$831$		0			0
$832$	−90.6240	−	272.422i	−0.108923	−	0.327431i
$833$	443.942	+	443.942i	0.532943	+	0.532943i
$834$		0			0
$835$	−431.794	−	1410.09i	−0.517119	−	1.68873i
$836$	319.884	−	396.910i	0.382636	−	0.474773i
$837$		0			0
$838$	−853.541	−	301.137i	−1.01855	−	0.359352i
$839$		−	736.198i		−	0.877471i	−0.898616	−	0.438736i	$-0.855426\pi$
$839$		−	736.198i		−	0.877471i	0.898616	−	0.438736i	$-0.144574\pi$
$840$		0			0
$841$	855.330			1.01704
$842$	−43.2642	+	122.628i	−0.0513827	+	0.145639i
$843$		0			0
$844$	−23.9932	+	29.7706i	−0.0284280	+	0.0352732i
$845$	−657.406	−	349.173i	−0.777995	−	0.413222i
$846$		0			0
$847$	−10.1477	+	10.1477i	−0.0119808	+	0.0119808i
$848$	−41.1535	−	26.4537i	−0.0485300	−	0.0311954i
$849$		0			0
$850$	606.849	+	355.783i	0.713940	+	0.418568i
$851$			28.8757i			0.0339315i
$852$		0			0
$853$	369.135	−	369.135i	0.432749	−	0.432749i	−0.456813	−	0.889563i	$-0.651009\pi$
$853$	369.135	−	369.135i	0.432749	−	0.432749i	0.889563	+	0.456813i	$0.151009\pi$
$854$	−157.994	−	330.252i	−0.185005	−	0.386712i
$855$		0			0
$856$	−171.878	+	727.103i	−0.200793	+	0.849420i
$857$	715.466	−	715.466i	0.834849	−	0.834849i	−0.153326	−	0.988176i	$-0.548999\pi$
$857$	715.466	−	715.466i	0.834849	−	0.834849i	0.988176	+	0.153326i	$0.0489986\pi$
$858$		0			0
$859$	−151.972			−0.176918			−0.0884588	−	0.996080i	$-0.528194\pi$
$859$	−151.972			−0.176918			−0.0884588	+	0.996080i	$0.528194\pi$
$860$	264.359	−	659.574i	0.307394	−	0.766947i
$861$		0			0
$862$	−817.477	−	288.413i	−0.948350	−	0.334586i
$863$	−744.617	−	744.617i	−0.862824	−	0.862824i	0.128841	−	0.991665i	$-0.458874\pi$
$863$	−744.617	−	744.617i	−0.862824	−	0.862824i	−0.991665	+	0.128841i	$0.958874\pi$
$864$		0			0
$865$	−253.121	−	826.602i	−0.292625	−	0.955610i
$866$	342.551	+	716.027i	0.395556	+	0.826821i
$867$		0			0
$868$	−243.362	+	26.1514i	−0.280371	+	0.0301284i
$869$	261.781			0.301244
$870$		0			0
$871$	197.531			0.226786
$872$	−383.646	−	621.173i	−0.439961	−	0.712354i
$873$		0			0
$874$	−23.0917	−	48.2680i	−0.0264207	−	0.0552266i
$875$	164.274	−	203.417i	0.187742	−	0.232477i
$876$		0			0
$877$	−603.681	−	603.681i	−0.688348	−	0.688348i	0.273519	−	0.961867i	$-0.411812\pi$
$877$	−603.681	−	603.681i	−0.688348	−	0.688348i	−0.961867	+	0.273519i	$0.911812\pi$
$878$	−371.087	+	1051.81i	−0.422650	+	1.19796i
$879$		0			0
$880$	244.903	−	870.823i	0.278298	−	0.989571i
$881$	639.526			0.725910			0.362955	−	0.931807i	$-0.381768\pi$
$881$	639.526			0.725910			0.362955	+	0.931807i	$0.381768\pi$
$882$		0			0
$883$	1033.88	−	1033.88i	1.17087	−	1.17087i	0.188870	−	0.982002i	$-0.439518\pi$
$883$	1033.88	−	1033.88i	1.17087	−	1.17087i	0.982002	−	0.188870i	$-0.0604825\pi$
$884$	−158.416	+	196.562i	−0.179204	+	0.222355i
$885$		0			0
$886$	327.354	−	156.608i	0.369474	−	0.176758i
$887$	−801.770	+	801.770i	−0.903912	+	0.903912i	−0.995772	−	0.0918602i	$-0.970719\pi$
$887$	−801.770	+	801.770i	−0.903912	+	0.903912i	0.0918602	+	0.995772i	$0.470719\pi$
$888$		0			0
$889$			42.9829i			0.0483497i
$890$	−509.316	−	554.027i	−0.572265	−	0.622502i
$891$		0			0
$892$	167.029	+	1554.35i	0.187252	+	1.74255i
$893$	470.422	−	470.422i	0.526788	−	0.526788i
$894$		0			0
$895$	149.583	−	281.627i	0.167132	−	0.314667i
$896$	4.82729	−	267.698i	0.00538760	−	0.298770i
$897$		0			0
$898$	340.797	−	965.953i	0.379506	−	1.07567i
$899$	1204.86			1.34022
$900$		0			0
$901$			43.0184i			0.0477452i
$902$	147.956	−	419.367i	0.164031	−	0.464930i
$903$		0			0
$904$	331.355	−	1401.74i	0.366543	−	1.55060i
$905$	848.267	+	450.547i	0.937312	+	0.497842i
$906$		0			0
$907$	488.802	+	488.802i	0.538922	+	0.538922i	0.923212	−	0.384291i	$-0.125554\pi$
$907$	488.802	+	488.802i	0.538922	+	0.538922i	−0.384291	+	0.923212i	$0.625554\pi$
$908$	−97.2654	−	905.140i	−0.107120	−	0.996851i
$909$		0			0
$910$	63.5045	+	69.0794i	0.0697851	+	0.0759114i
$911$	−999.285			−1.09691			−0.548455	−	0.836180i	$-0.684784\pi$
$911$	−999.285			−1.09691			−0.548455	+	0.836180i	$0.684784\pi$
$912$		0			0
$913$	772.867	+	772.867i	0.846514	+	0.846514i
$914$	991.323	−	474.254i	1.08460	−	0.518878i
$915$		0			0
$916$	125.347	+	101.022i	0.136842	+	0.110286i
$917$	76.7716	+	76.7716i	0.0837204	+	0.0837204i
$918$		0			0
$919$			1337.55i			1.45544i	0.685875	+	0.727719i	$0.259419\pi$
$919$			1337.55i			1.45544i	−0.685875	+	0.727719i	$0.740581\pi$
$920$	−71.3613	−	62.6358i	−0.0775666	−	0.0680824i
$921$		0			0
$922$	−23.9564	+	67.9018i	−0.0259831	+	0.0736463i
$923$	425.436	−	425.436i	0.460927	−	0.460927i
$924$		0			0
$925$	−57.7611	+	298.576i	−0.0624444	+	0.322785i
$926$	413.379	+	864.078i	0.446414	+	0.933129i
$927$		0			0
$928$	−164.420	+	1307.67i	−0.177177	+	1.40913i
$929$			135.066i			0.145388i	0.997354	+	0.0726942i	$0.0231597\pi$
$929$			135.066i			0.145388i	−0.997354	+	0.0726942i	$0.976840\pi$
$930$		0			0
$931$		−	502.943i		−	0.540218i
$932$	145.697	+	1355.84i	0.156328	+	1.45477i
$933$		0			0
$934$	−53.2273	−	111.260i	−0.0569885	−	0.119122i
$935$	−760.574	+	232.902i	−0.813448	+	0.249093i
$936$		0			0
$937$	1002.83	−	1002.83i	1.07026	−	1.07026i	0.0729231	−	0.997338i	$-0.476767\pi$
$937$	1002.83	−	1002.83i	1.07026	−	1.07026i	0.997338	−	0.0729231i	$-0.0232328\pi$
$938$	173.716	+	61.2887i	0.185199	+	0.0653397i
$939$		0			0
$940$	439.208	−	1095.82i	0.467243	−	1.16577i
$941$		−	133.203i		−	0.141554i	−0.997492	−	0.0707772i	$-0.977452\pi$
$941$		−	133.203i		−	0.141554i	0.997492	−	0.0707772i	$-0.0225479\pi$
$942$		0			0
$943$	−33.0061	−	33.0061i	−0.0350011	−	0.0350011i
$944$	−132.465	−	609.235i	−0.140323	−	0.645377i
$945$		0			0
$946$	346.756	+	724.817i	0.366550	+	0.766191i
$947$	671.287	+	671.287i	0.708857	+	0.708857i	0.966295	−	0.257438i	$-0.0828784\pi$
$947$	671.287	+	671.287i	0.708857	+	0.708857i	−0.257438	+	0.966295i	$0.582878\pi$
$948$		0			0
$949$	165.770			0.174679
$950$	−142.217	−	545.285i	−0.149702	−	0.573984i
$951$		0			0
$952$	−200.306	+	123.712i	−0.210405	+	0.129949i
$953$	−834.636	−	834.636i	−0.875798	−	0.875798i	0.117299	−	0.993097i	$-0.462577\pi$
$953$	−834.636	−	834.636i	−0.875798	−	0.875798i	−0.993097	+	0.117299i	$0.962577\pi$
$954$		0			0
$955$	−400.582	+	754.196i	−0.419458	+	0.789734i
$956$	−625.004	+	775.501i	−0.653770	+	0.811193i
$957$		0			0
$958$	−579.096	+	1641.39i	−0.604484	+	1.71335i
$959$		−	292.157i		−	0.304648i
$960$		0			0
$961$	−105.221			−0.109491
$962$	−102.921	−	36.3114i	−0.106986	−	0.0377457i
$963$		0			0
$964$	1011.42	+	815.143i	1.04919	+	0.845584i
$965$	−752.482	+	230.424i	−0.779774	+	0.238781i
$966$		0			0
$967$	249.412	−	249.412i	0.257923	−	0.257923i	−0.566286	−	0.824209i	$-0.691620\pi$
$967$	249.412	−	249.412i	0.257923	−	0.257923i	0.824209	+	0.566286i	$0.191620\pi$
$968$	28.8416	+	46.6983i	0.0297951	+	0.0482421i
$969$		0			0
$970$	34.2055	−	813.487i	0.0352634	−	0.838646i
$971$		−	1425.94i		−	1.46852i	−0.678867	−	0.734262i	$-0.737529\pi$
$971$		−	1425.94i		−	1.46852i	0.678867	−	0.734262i	$-0.262471\pi$
$972$		0			0
$973$	71.9394	−	71.9394i	0.0739357	−	0.0739357i
$974$	1561.17	−	746.870i	1.60284	−	0.766807i
$975$		0			0
$976$	−1368.21	+	297.488i	−1.40186	+	0.304804i
$977$	651.241	−	651.241i	0.666572	−	0.666572i	−0.290349	−	0.956921i	$-0.593771\pi$
$977$	651.241	−	651.241i	0.666572	−	0.666572i	0.956921	+	0.290349i	$0.0937714\pi$
$978$		0			0
$979$	850.963			0.869217
$980$	−351.003	−	820.574i	−0.358166	−	0.837320i
$981$		0			0
$982$	478.624	−	1356.61i	0.487397	−	1.38148i
$983$	301.766	+	301.766i	0.306985	+	0.306985i	0.843739	−	0.536754i	$-0.180350\pi$
$983$	301.766	+	301.766i	0.306985	+	0.306985i	−0.536754	+	0.843739i	$0.680350\pi$
$984$		0			0
$985$	655.085	−	200.599i	0.665061	−	0.203654i
$986$	1045.44	−	500.142i	1.06028	−	0.507244i
$987$		0			0
$988$	201.078	−	21.6076i	0.203520	−	0.0218701i
$989$	84.3377			0.0852758
$990$		0			0
$991$	−672.650			−0.678759			−0.339380	−	0.940650i	$-0.610217\pi$
$991$	−672.650			−0.678759			−0.339380	+	0.940650i	$0.610217\pi$
$992$	−116.784	+	928.806i	−0.117725	+	0.936296i
$993$		0			0
$994$	506.147	−	242.143i	0.509202	−	0.243605i
$995$	−617.350	−	327.898i	−0.620453	−	0.329546i
$996$		0			0
$997$	65.6794	+	65.6794i	0.0658771	+	0.0658771i	0.739278	−	0.673401i	$-0.235167\pi$
$997$	65.6794	+	65.6794i	0.0658771	+	0.0658771i	−0.673401	+	0.739278i	$0.735167\pi$
$998$	−351.002	−	123.837i	−0.351705	−	0.124085i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.3.u.b.253.1		20
3.2	odd	2		40.3.i.a.13.10	yes	20
5.2	odd	4	inner	360.3.u.b.37.6		20
8.5	even	2	inner	360.3.u.b.253.6		20
12.11	even	2		160.3.m.a.113.10		20
15.2	even	4		40.3.i.a.37.5	yes	20
15.8	even	4		200.3.i.b.157.6		20
15.14	odd	2		200.3.i.b.93.1		20
24.5	odd	2		40.3.i.a.13.5	✓	20
24.11	even	2		160.3.m.a.113.1		20
40.37	odd	4	inner	360.3.u.b.37.1		20
60.23	odd	4		800.3.m.b.657.10		20
60.47	odd	4		160.3.m.a.17.1		20
60.59	even	2		800.3.m.b.593.1		20
120.29	odd	2		200.3.i.b.93.6		20
120.53	even	4		200.3.i.b.157.1		20
120.59	even	2		800.3.m.b.593.10		20
120.77	even	4		40.3.i.a.37.10	yes	20
120.83	odd	4		800.3.m.b.657.1		20
120.107	odd	4		160.3.m.a.17.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.i.a.13.5	✓	20	24.5	odd	2
40.3.i.a.13.10	yes	20	3.2	odd	2
40.3.i.a.37.5	yes	20	15.2	even	4
40.3.i.a.37.10	yes	20	120.77	even	4
160.3.m.a.17.1		20	60.47	odd	4
160.3.m.a.17.10		20	120.107	odd	4
160.3.m.a.113.1		20	24.11	even	2
160.3.m.a.113.10		20	12.11	even	2
200.3.i.b.93.1		20	15.14	odd	2
200.3.i.b.93.6		20	120.29	odd	2
200.3.i.b.157.1		20	120.53	even	4
200.3.i.b.157.6		20	15.8	even	4
360.3.u.b.37.1		20	40.37	odd	4	inner
360.3.u.b.37.6		20	5.2	odd	4	inner
360.3.u.b.253.1		20	1.1	even	1	trivial
360.3.u.b.253.6		20	8.5	even	2	inner
800.3.m.b.593.1		20	60.59	even	2
800.3.m.b.593.10		20	120.59	even	2
800.3.m.b.657.1		20	120.83	odd	4
800.3.m.b.657.10		20	60.23	odd	4

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	360.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.88606 - 0.665418i) q^{2} +(3.11444 + 2.51004i) q^{4} +(-2.34539 + 4.41578i) q^{5} +(1.47907 - 1.47907i) q^{7} +(-4.20379 - 6.80648i) q^{8} +(7.36189 - 6.76776i) q^{10} +11.3076i q^{11} +(-3.17204 + 3.17204i) q^{13} +(-3.77383 + 1.80542i) q^{14} +(3.39943 + 15.6347i) q^{16} +(9.94834 - 9.94834i) q^{17} -11.2705 q^{19} +(-18.3883 + 7.86567i) q^{20} +(7.52426 - 21.3267i) q^{22} +(-1.67851 - 1.67851i) q^{23} +(-13.9983 - 20.7135i) q^{25} +(8.09340 - 3.87192i) q^{26} +(8.31902 - 0.893952i) q^{28} -41.1865 q^{29} -29.2537 q^{31} +(3.99209 - 31.7500i) q^{32} +(-25.3830 + 12.1433i) q^{34} +(3.06227 + 10.0003i) q^{35} +(-8.60159 - 8.60159i) q^{37} +(21.2568 + 7.49961i) q^{38} +(39.9155 - 2.59916i) q^{40} +19.6639 q^{41} +(-25.1228 + 25.1228i) q^{43} +(-28.3824 + 35.2167i) q^{44} +(2.04886 + 4.28268i) q^{46} +(-41.7392 + 41.7392i) q^{47} +44.6247i q^{49} +(12.6185 + 48.3815i) q^{50} +(-17.8411 + 1.91718i) q^{52} +(-2.16209 + 2.16209i) q^{53} +(-49.9317 - 26.5206i) q^{55} +(-16.2850 - 3.84958i) q^{56} +(77.6802 + 27.4063i) q^{58} -38.9669 q^{59} +87.5112i q^{61} +(55.1742 + 19.4660i) q^{62} +(-28.6564 + 57.2260i) q^{64} +(-6.56738 - 21.4467i) q^{65} +(-31.1362 - 31.1362i) q^{67} +(55.9542 - 6.01278i) q^{68} +(0.878753 - 20.8988i) q^{70} -134.120 q^{71} +(-26.1299 - 26.1299i) q^{73} +(10.4994 + 21.9468i) q^{74} +(-35.1013 - 28.2894i) q^{76} +(16.7247 + 16.7247i) q^{77} -23.1510i q^{79} +(-77.0125 - 21.6583i) q^{80} +(-37.0873 - 13.0847i) q^{82} +(68.3496 - 68.3496i) q^{83} +(20.5970 + 67.2625i) q^{85} +(64.1002 - 30.6659i) q^{86} +(76.9647 - 47.5346i) q^{88} -75.2561i q^{89} +9.38338i q^{91} +(-1.01449 - 9.44074i) q^{92} +(106.497 - 50.9485i) q^{94} +(26.4337 - 49.7681i) q^{95} +(57.5730 - 57.5730i) q^{97} +(29.6941 - 84.1648i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 4 q^{7} - 4 q^{8} + 6 q^{10} - 56 q^{16} + 12 q^{17} + 24 q^{20} + 92 q^{22} + 4 q^{23} - 28 q^{25} - 100 q^{26} + 68 q^{28} - 136 q^{31} - 128 q^{32} + 188 q^{38} + 156 q^{40} + 8 q^{41}+ \cdots - 546 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 4 * q^7 - 4 * q^8 + 6 * q^10 - 56 * q^16 + 12 * q^17 + 24 * q^20 + 92 * q^22 + 4 * q^23 - 28 * q^25 - 100 * q^26 + 68 * q^28 - 136 * q^31 - 128 * q^32 + 188 * q^38 + 156 * q^40 + 8 * q^41 - 240 * q^46 - 188 * q^47 + 274 * q^50 - 332 * q^52 + 96 * q^55 + 360 * q^56 + 268 * q^58 - 336 * q^62 + 60 * q^65 - 396 * q^68 + 300 * q^70 - 248 * q^71 - 124 * q^73 + 424 * q^76 - 496 * q^80 - 676 * q^82 + 672 * q^86 - 304 * q^88 + 628 * q^92 + 488 * q^95 + 100 * q^97 - 546 * q^98

Introduction

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