LMFDB - Embedded newform 504.3.g.a.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,3,Mod(379,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("504.379");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.g (of order $2$, degree $1$, 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:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 6x^{2} + 16 $ x^4 + 6*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.1
Root			$0.707107 + 1.87083i$ of defining polynomial
Character	$\chi$	$=$	504.379
Dual form			504.3.g.a.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.87083i) q^{2} +(-3.00000 + 2.64575i) q^{4} +1.54985i q^{5} -2.64575i q^{7} +(7.07107 + 3.74166i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.87083i) q^{2} +(-3.00000 + 2.64575i) q^{4} +1.54985i q^{5} -2.64575i q^{7} +(7.07107 + 3.74166i) q^{8} +(2.89949 - 1.09591i) q^{10} +4.48528 q^{11} +1.54985i q^{13} +(-4.94975 + 1.87083i) q^{14} +(2.00000 - 15.8745i) q^{16} -23.6569 q^{17} -24.8701 q^{19} +(-4.10051 - 4.64954i) q^{20} +(-3.17157 - 8.39119i) q^{22} +35.2248i q^{23} +22.5980 q^{25} +(2.89949 - 1.09591i) q^{26} +(7.00000 + 7.93725i) q^{28} -22.4499i q^{29} +46.7156i q^{31} +(-31.1127 + 7.48331i) q^{32} +(16.7279 + 44.2579i) q^{34} +4.10051 q^{35} +58.5826i q^{37} +(17.5858 + 46.5276i) q^{38} +(-5.79899 + 10.9591i) q^{40} +26.9706 q^{41} -17.1716 q^{43} +(-13.4558 + 11.8669i) q^{44} +(65.8995 - 24.9077i) q^{46} -36.1326i q^{47} -7.00000 q^{49} +(-15.9792 - 42.2769i) q^{50} +(-4.10051 - 4.64954i) q^{52} +97.8149i q^{53} +6.95149i q^{55} +(9.89949 - 18.7083i) q^{56} +(-42.0000 + 15.8745i) q^{58} -61.5563 q^{59} +37.6825i q^{61} +(87.3970 - 33.0329i) q^{62} +(36.0000 + 52.9150i) q^{64} -2.40202 q^{65} -33.3726 q^{67} +(70.9706 - 62.5902i) q^{68} +(-2.89949 - 7.67134i) q^{70} +102.199i q^{71} +69.3137 q^{73} +(109.598 - 41.4241i) q^{74} +(74.6102 - 65.8000i) q^{76} -11.8669i q^{77} -38.7005i q^{79} +(24.6030 + 3.09969i) q^{80} +(-19.0711 - 50.4573i) q^{82} -3.61522 q^{83} -36.6645i q^{85} +(12.1421 + 32.1251i) q^{86} +(31.7157 + 16.7824i) q^{88} -44.0589 q^{89} +4.10051 q^{91} +(-93.1960 - 105.674i) q^{92} +(-67.5980 + 25.5496i) q^{94} -38.5447i q^{95} +96.1076 q^{97} +(4.94975 + 13.0958i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{4}+O(q^{10}) $ 4 * q - 12 * q^4	$ 4 q - 12 q^{4} - 28 q^{10} - 16 q^{11} + 8 q^{16} - 72 q^{17} + 8 q^{19} - 56 q^{20} - 24 q^{22} - 68 q^{25} - 28 q^{26} + 28 q^{28} + 16 q^{34} + 56 q^{35} + 76 q^{38} + 56 q^{40} + 40 q^{41} - 80 q^{43} + 48 q^{44} + 224 q^{46} - 28 q^{49} - 112 q^{50} - 56 q^{52} - 168 q^{58} - 184 q^{59} + 112 q^{62} + 144 q^{64} - 168 q^{65} - 224 q^{67} + 216 q^{68} + 28 q^{70} + 232 q^{73} + 280 q^{74} - 24 q^{76} + 336 q^{80} - 48 q^{82} - 88 q^{83} - 8 q^{86} + 240 q^{88} - 312 q^{89} + 56 q^{91} - 56 q^{92} - 112 q^{94} - 136 q^{97}+O(q^{100}) $ 4 * q - 12 * q^4 - 28 * q^10 - 16 * q^11 + 8 * q^16 - 72 * q^17 + 8 * q^19 - 56 * q^20 - 24 * q^22 - 68 * q^25 - 28 * q^26 + 28 * q^28 + 16 * q^34 + 56 * q^35 + 76 * q^38 + 56 * q^40 + 40 * q^41 - 80 * q^43 + 48 * q^44 + 224 * q^46 - 28 * q^49 - 112 * q^50 - 56 * q^52 - 168 * q^58 - 184 * q^59 + 112 * q^62 + 144 * q^64 - 168 * q^65 - 224 * q^67 + 216 * q^68 + 28 * q^70 + 232 * q^73 + 280 * q^74 - 24 * q^76 + 336 * q^80 - 48 * q^82 - 88 * q^83 - 8 * q^86 + 240 * q^88 - 312 * q^89 + 56 * q^91 - 56 * q^92 - 112 * q^94 - 136 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	−0.707107	−	1.87083i	−0.353553	−	0.935414i
$2$	−0.707107	−	1.87083i	−0.353553	−	0.935414i
$3$		0			0
$3$		0			0
$4$	−3.00000	+	2.64575i	−0.750000	+	0.661438i
$5$			1.54985i			0.309969i	0.987917	+	0.154985i	$0.0495328\pi$
$5$			1.54985i			0.309969i	−0.987917	+	0.154985i	$0.950467\pi$
$6$		0			0
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	7.07107	+	3.74166i	0.883883	+	0.467707i
$9$		0			0
$10$	2.89949	−	1.09591i	0.289949	−	0.109591i
$11$	4.48528			0.407753			0.203876	−	0.978997i	$-0.434646\pi$
$11$	4.48528			0.407753			0.203876	+	0.978997i	$0.434646\pi$
$12$		0			0
$13$			1.54985i			0.119219i	0.998222	+	0.0596094i	$0.0189855\pi$
$13$			1.54985i			0.119219i	−0.998222	+	0.0596094i	$0.981014\pi$
$14$	−4.94975	+	1.87083i	−0.353553	+	0.133631i
$15$		0			0
$16$	2.00000	−	15.8745i	0.125000	−	0.992157i
$17$	−23.6569			−1.39158			−0.695790	−	0.718245i	$-0.744945\pi$
$17$	−23.6569			−1.39158			−0.695790	+	0.718245i	$0.744945\pi$
$18$		0			0
$19$	−24.8701			−1.30895			−0.654475	−	0.756083i	$-0.727110\pi$
$19$	−24.8701			−1.30895			−0.654475	+	0.756083i	$0.727110\pi$
$20$	−4.10051	−	4.64954i	−0.205025	−	0.232477i
$21$		0			0
$22$	−3.17157	−	8.39119i	−0.144162	−	0.381418i
$23$			35.2248i			1.53151i	0.643132	+	0.765756i	$0.277635\pi$
$23$			35.2248i			1.53151i	−0.643132	+	0.765756i	$0.722365\pi$
$24$		0			0
$25$	22.5980			0.903919
$26$	2.89949	−	1.09591i	0.111519	−	0.0421502i
$27$		0			0
$28$	7.00000	+	7.93725i	0.250000	+	0.283473i
$29$		−	22.4499i		−	0.774136i	−0.922051	−	0.387068i	$-0.873488\pi$
$29$		−	22.4499i		−	0.774136i	0.922051	−	0.387068i	$-0.126512\pi$
$30$		0			0
$31$			46.7156i			1.50696i	0.657473	+	0.753478i	$0.271625\pi$
$31$			46.7156i			1.50696i	−0.657473	+	0.753478i	$0.728375\pi$
$32$	−31.1127	+	7.48331i	−0.972272	+	0.233854i
$33$		0			0
$34$	16.7279	+	44.2579i	0.491998	+	1.30170i
$35$	4.10051			0.117157
$36$		0			0
$37$			58.5826i			1.58331i	0.610966	+	0.791657i	$0.290781\pi$
$37$			58.5826i			1.58331i	−0.610966	+	0.791657i	$0.709219\pi$
$38$	17.5858	+	46.5276i	0.462784	+	1.22441i
$39$		0			0
$40$	−5.79899	+	10.9591i	−0.144975	+	0.273977i
$41$	26.9706			0.657819			0.328909	−	0.944362i	$-0.393319\pi$
$41$	26.9706			0.657819			0.328909	+	0.944362i	$0.393319\pi$
$42$		0			0
$43$	−17.1716			−0.399339			−0.199669	−	0.979863i	$-0.563987\pi$
$43$	−17.1716			−0.399339			−0.199669	+	0.979863i	$0.563987\pi$
$44$	−13.4558	+	11.8669i	−0.305815	+	0.269703i
$45$		0			0
$46$	65.8995	−	24.9077i	1.43260	−	0.541471i
$47$		−	36.1326i		−	0.768780i	−0.923171	−	0.384390i	$-0.874412\pi$
$47$		−	36.1326i		−	0.768780i	0.923171	−	0.384390i	$-0.125588\pi$
$48$		0			0
$49$	−7.00000			−0.142857
$50$	−15.9792	−	42.2769i	−0.319584	−	0.845539i
$51$		0			0
$52$	−4.10051	−	4.64954i	−0.0788559	−	0.0894141i
$53$			97.8149i			1.84556i	0.385322	+	0.922782i	$0.374090\pi$
$53$			97.8149i			1.84556i	−0.385322	+	0.922782i	$0.625910\pi$
$54$		0			0
$55$			6.95149i			0.126391i
$56$	9.89949	−	18.7083i	0.176777	−	0.334077i
$57$		0			0
$58$	−42.0000	+	15.8745i	−0.724138	+	0.273698i
$59$	−61.5563			−1.04333			−0.521664	−	0.853151i	$-0.674689\pi$
$59$	−61.5563			−1.04333			−0.521664	+	0.853151i	$0.674689\pi$
$60$		0			0
$61$			37.6825i			0.617746i	0.951103	+	0.308873i	$0.0999518\pi$
$61$			37.6825i			0.617746i	−0.951103	+	0.308873i	$0.900048\pi$
$62$	87.3970	−	33.0329i	1.40963	−	0.532790i
$63$		0			0
$64$	36.0000	+	52.9150i	0.562500	+	0.826797i
$65$	−2.40202			−0.0369542
$66$		0			0
$67$	−33.3726			−0.498098			−0.249049	−	0.968491i	$-0.580118\pi$
$67$	−33.3726			−0.498098			−0.249049	+	0.968491i	$0.580118\pi$
$68$	70.9706	−	62.5902i	1.04368	−	0.920443i
$69$		0			0
$70$	−2.89949	−	7.67134i	−0.0414214	−	0.109591i
$71$			102.199i			1.43942i	0.694277	+	0.719708i	$0.255724\pi$
$71$			102.199i			1.43942i	−0.694277	+	0.719708i	$0.744276\pi$
$72$		0			0
$73$	69.3137			0.949503			0.474751	−	0.880120i	$-0.342538\pi$
$73$	69.3137			0.949503			0.474751	+	0.880120i	$0.342538\pi$
$74$	109.598	−	41.4241i	1.48105	−	0.559786i
$75$		0			0
$76$	74.6102	−	65.8000i	0.981713	−	0.865789i
$77$		−	11.8669i		−	0.154116i
$78$		0			0
$79$		−	38.7005i		−	0.489880i	−0.969538	−	0.244940i	$-0.921232\pi$
$79$		−	38.7005i		−	0.489880i	0.969538	−	0.244940i	$-0.0787682\pi$
$80$	24.6030	+	3.09969i	0.307538	+	0.0387461i
$81$		0			0
$82$	−19.0711	−	50.4573i	−0.232574	−	0.615333i
$83$	−3.61522			−0.0435569			−0.0217785	−	0.999763i	$-0.506933\pi$
$83$	−3.61522			−0.0435569			−0.0217785	+	0.999763i	$0.506933\pi$
$84$		0			0
$85$		−	36.6645i		−	0.431347i
$86$	12.1421	+	32.1251i	0.141188	+	0.373547i
$87$		0			0
$88$	31.7157	+	16.7824i	0.360406	+	0.190709i
$89$	−44.0589			−0.495044			−0.247522	−	0.968882i	$-0.579616\pi$
$89$	−44.0589			−0.495044			−0.247522	+	0.968882i	$0.579616\pi$
$90$		0			0
$91$	4.10051			0.0450605
$92$	−93.1960	−	105.674i	−1.01300	−	1.14863i
$93$		0			0
$94$	−67.5980	+	25.5496i	−0.719127	+	0.271805i
$95$		−	38.5447i		−	0.405734i
$96$		0			0
$97$	96.1076			0.990800			0.495400	−	0.868665i	$-0.335021\pi$
$97$	96.1076			0.990800			0.495400	+	0.868665i	$0.335021\pi$
$98$	4.94975	+	13.0958i	0.0505076	+	0.133631i
$99$		0			0
$100$	−67.7939	+	59.7886i	−0.677939	+	0.597886i
$101$			19.6162i			0.194219i	0.995274	+	0.0971097i	$0.0309598\pi$
$101$			19.6162i			0.194219i	−0.995274	+	0.0971097i	$0.969040\pi$
$102$		0			0
$103$		−	43.0841i		−	0.418293i	−0.977884	−	0.209146i	$-0.932932\pi$
$103$		−	43.0841i		−	0.418293i	0.977884	−	0.209146i	$-0.0670685\pi$
$104$	−5.79899	+	10.9591i	−0.0557595	+	0.105376i
$105$		0			0
$106$	182.995	−	69.1656i	1.72637	−	0.652506i
$107$	−15.5980			−0.145776			−0.0728878	−	0.997340i	$-0.523221\pi$
$107$	−15.5980			−0.145776			−0.0728878	+	0.997340i	$0.523221\pi$
$108$		0			0
$109$		−	3.85180i		−	0.0353376i	−0.999844	−	0.0176688i	$-0.994376\pi$
$109$		−	3.85180i		−	0.0353376i	0.999844	−	0.0176688i	$-0.00562445\pi$
$110$	13.0051	−	4.91545i	0.118228	−	0.0446859i
$111$		0			0
$112$	−42.0000	−	5.29150i	−0.375000	−	0.0472456i
$113$	13.7746			0.121899			0.0609496	−	0.998141i	$-0.480587\pi$
$113$	13.7746			0.121899			0.0609496	+	0.998141i	$0.480587\pi$
$114$		0			0
$115$	−54.5929			−0.474721
$116$	59.3970	+	67.3498i	0.512043	+	0.580602i
$117$		0			0
$118$	43.5269	+	115.161i	0.368872	+	0.975944i
$119$			62.5902i			0.525968i
$120$		0			0
$121$	−100.882			−0.833738
$122$	70.4975	−	26.6455i	0.577848	−	0.218406i
$123$		0			0
$124$	−123.598	−	140.147i	−0.996758	−	1.13022i
$125$			73.7695i			0.590156i
$126$		0			0
$127$		−	125.025i		−	0.984445i	−0.870469	−	0.492223i	$-0.836185\pi$
$127$		−	125.025i		−	0.984445i	0.870469	−	0.492223i	$-0.163815\pi$
$128$	73.5391	−	104.766i	0.574524	−	0.818488i
$129$		0			0
$130$	1.69848	+	4.49377i	0.0130653	+	0.0345674i
$131$	−100.350			−0.766033			−0.383016	−	0.923742i	$-0.625115\pi$
$131$	−100.350			−0.766033			−0.383016	+	0.923742i	$0.625115\pi$
$132$		0			0
$133$			65.8000i			0.494737i
$134$	23.5980	+	62.4344i	0.176104	+	0.465928i
$135$		0			0
$136$	−167.279	−	88.5158i	−1.22999	−	0.650852i
$137$	−57.3137			−0.418348			−0.209174	−	0.977878i	$-0.567078\pi$
$137$	−57.3137			−0.418348			−0.209174	+	0.977878i	$0.567078\pi$
$138$		0			0
$139$	−183.664			−1.32132			−0.660662	−	0.750684i	$-0.729724\pi$
$139$	−183.664			−1.32132			−0.660662	+	0.750684i	$0.729724\pi$
$140$	−12.3015	+	10.8489i	−0.0878680	+	0.0774923i
$141$		0			0
$142$	191.196	−	72.2653i	1.34645	−	0.508910i
$143$			6.95149i			0.0486118i
$144$		0			0
$145$	34.7939			0.239958
$146$	−49.0122	−	129.674i	−0.335700	−	0.888179i
$147$		0			0
$148$	−154.995	−	175.748i	−1.04726	−	1.18748i
$149$			192.310i			1.29067i	0.763900	+	0.645335i	$0.223282\pi$
$149$			192.310i			1.29067i	−0.763900	+	0.645335i	$0.776718\pi$
$150$		0			0
$151$			114.753i			0.759954i	0.924996	+	0.379977i	$0.124068\pi$
$151$			114.753i			0.759954i	−0.924996	+	0.379977i	$0.875932\pi$
$152$	−175.858	−	93.0552i	−1.15696	−	0.612205i
$153$		0			0
$154$	−22.2010	+	8.39119i	−0.144162	+	0.0544883i
$155$	−72.4020			−0.467110
$156$		0			0
$157$			212.146i			1.35125i	0.737245	+	0.675625i	$0.236126\pi$
$157$			212.146i			1.35125i	−0.737245	+	0.675625i	$0.763874\pi$
$158$	−72.4020	+	27.3654i	−0.458241	+	0.173199i
$159$		0			0
$160$	−11.5980	−	48.2199i	−0.0724874	−	0.301374i
$161$	93.1960			0.578857
$162$		0			0
$163$	−240.534			−1.47567			−0.737835	−	0.674982i	$-0.764152\pi$
$163$	−240.534			−1.47567			−0.737835	+	0.674982i	$0.764152\pi$
$164$	−80.9117	+	71.3574i	−0.493364	+	0.435106i
$165$		0			0
$166$	2.55635	+	6.76346i	0.0153997	+	0.0407438i
$167$		−	212.101i		−	1.27006i	−0.772486	−	0.635032i	$-0.780987\pi$
$167$		−	212.101i		−	1.27006i	0.772486	−	0.635032i	$-0.219013\pi$
$168$		0			0
$169$	166.598			0.985787
$170$	−68.5929	+	25.9257i	−0.403488	+	0.152504i
$171$		0			0
$172$	51.5147	−	45.4317i	0.299504	−	0.264138i
$173$		−	182.213i		−	1.05325i	−0.850096	−	0.526627i	$-0.823456\pi$
$173$		−	182.213i		−	1.05325i	0.850096	−	0.526627i	$-0.176544\pi$
$174$		0			0
$175$		−	59.7886i		−	0.341649i
$176$	8.97056	−	71.2016i	0.0509691	−	0.404555i
$177$		0			0
$178$	31.1543	+	82.4266i	0.175024	+	0.463071i
$179$	−57.2061			−0.319587			−0.159793	−	0.987150i	$-0.551083\pi$
$179$	−57.2061			−0.319587			−0.159793	+	0.987150i	$0.551083\pi$
$180$		0			0
$181$		−	326.212i		−	1.80228i	−0.433533	−	0.901138i	$-0.642733\pi$
$181$		−	326.212i		−	1.80228i	0.433533	−	0.901138i	$-0.357267\pi$
$182$	−2.89949	−	7.67134i	−0.0159313	−	0.0421502i
$183$		0			0
$184$	−131.799	+	249.077i	−0.716299	+	1.35368i
$185$	−90.7939			−0.490778
$186$		0			0
$187$	−106.108			−0.567421
$188$	95.5980	+	108.398i	0.508500	+	0.576585i
$189$		0			0
$190$	−72.1106	+	27.2552i	−0.379530	+	0.143449i
$191$			97.0628i			0.508182i	0.967180	+	0.254091i	$0.0817763\pi$
$191$			97.0628i			0.508182i	−0.967180	+	0.254091i	$0.918224\pi$
$192$		0			0
$193$	157.304			0.815045			0.407522	−	0.913195i	$-0.366393\pi$
$193$	157.304			0.815045			0.407522	+	0.913195i	$0.366393\pi$
$194$	−67.9584	−	179.801i	−0.350301	−	0.926809i
$195$		0			0
$196$	21.0000	−	18.5203i	0.107143	−	0.0944911i
$197$		−	124.117i		−	0.630034i	−0.949086	−	0.315017i	$-0.897990\pi$
$197$		−	124.117i		−	0.630034i	0.949086	−	0.315017i	$-0.102010\pi$
$198$		0			0
$199$		−	180.975i		−	0.909421i	−0.890639	−	0.454710i	$-0.849743\pi$
$199$		−	180.975i		−	0.909421i	0.890639	−	0.454710i	$-0.150257\pi$
$200$	159.792	+	84.5539i	0.798959	+	0.422769i
$201$		0			0
$202$	36.6985	−	13.8707i	0.181676	−	0.0686669i
$203$	−59.3970			−0.292596
$204$		0			0
$205$			41.8002i			0.203903i
$206$	−80.6030	+	30.4651i	−0.391277	+	0.147889i
$207$		0			0
$208$	24.6030	+	3.09969i	0.118284	+	0.0149024i
$209$	−111.549			−0.533728
$210$		0			0
$211$	164.049			0.777482			0.388741	−	0.921347i	$-0.372910\pi$
$211$	164.049			0.777482			0.388741	+	0.921347i	$0.372910\pi$
$212$	−258.794	−	293.445i	−1.22073	−	1.38417i
$213$		0			0
$214$	11.0294	+	29.1811i	0.0515394	+	0.136361i
$215$		−	26.6133i		−	0.123783i
$216$		0			0
$217$	123.598			0.569576
$218$	−7.20606	+	2.72363i	−0.0330553	+	0.0124937i
$219$		0			0
$220$	−18.3919	−	20.8545i	−0.0835996	−	0.0947931i
$221$		−	36.6645i		−	0.165903i
$222$		0			0
$223$		−	10.5830i		−	0.0474574i	−0.999718	−	0.0237287i	$-0.992446\pi$
$223$		−	10.5830i		−	0.0474574i	0.999718	−	0.0237287i	$-0.00755379\pi$
$224$	19.7990	+	82.3165i	0.0883883	+	0.367484i
$225$		0			0
$226$	−9.74012	−	25.7699i	−0.0430979	−	0.114026i
$227$	−105.806			−0.466106			−0.233053	−	0.972464i	$-0.574872\pi$
$227$	−105.806			−0.466106			−0.233053	+	0.972464i	$0.574872\pi$
$228$		0			0
$229$		−	74.8788i		−	0.326982i	−0.986545	−	0.163491i	$-0.947725\pi$
$229$		−	74.8788i		−	0.326982i	0.986545	−	0.163491i	$-0.0522754\pi$
$230$	38.6030	+	102.134i	0.167839	+	0.444061i
$231$		0			0
$232$	84.0000	−	158.745i	0.362069	−	0.684246i
$233$	419.137			1.79887			0.899436	−	0.437053i	$-0.143978\pi$
$233$	419.137			1.79887			0.899436	+	0.437053i	$0.143978\pi$
$234$		0			0
$235$	56.0000			0.238298
$236$	184.669	−	162.863i	0.782496	−	0.690097i
$237$		0			0
$238$	117.095	−	44.2579i	0.491998	−	0.185958i
$239$		−	148.318i		−	0.620577i	−0.950642	−	0.310288i	$-0.899574\pi$
$239$		−	148.318i		−	0.620577i	0.950642	−	0.310288i	$-0.100426\pi$
$240$		0			0
$241$	−459.872			−1.90818			−0.954092	−	0.299515i	$-0.903175\pi$
$241$	−459.872			−1.90818			−0.954092	+	0.299515i	$0.903175\pi$
$242$	71.3345	+	188.733i	0.294771	+	0.779890i
$243$		0			0
$244$	−99.6985	−	113.047i	−0.408600	−	0.463309i
$245$		−	10.8489i		−	0.0442813i
$246$		0			0
$247$		−	38.5447i		−	0.156052i
$248$	−174.794	+	330.329i	−0.704814	+	1.33197i
$249$		0			0
$250$	138.010	−	52.1629i	0.552040	−	0.208652i
$251$	−124.919			−0.497685			−0.248842	−	0.968544i	$-0.580050\pi$
$251$	−124.919			−0.497685			−0.248842	+	0.968544i	$0.580050\pi$
$252$		0			0
$253$			157.993i			0.624478i
$254$	−233.899	+	88.4057i	−0.920864	+	0.348054i
$255$		0			0
$256$	−248.000	−	63.4980i	−0.968750	−	0.248039i
$257$	427.352			1.66285			0.831425	−	0.555637i	$-0.187526\pi$
$257$	427.352			1.66285			0.831425	+	0.555637i	$0.187526\pi$
$258$		0			0
$259$	154.995			0.598436
$260$	7.20606	−	6.35515i	0.0277156	−	0.0244429i
$261$		0			0
$262$	70.9584	+	187.738i	0.270833	+	0.716558i
$263$		−	257.624i		−	0.979558i	−0.871847	−	0.489779i	$-0.837078\pi$
$263$		−	257.624i		−	0.979558i	0.871847	−	0.489779i	$-0.162922\pi$
$264$		0			0
$265$	−151.598			−0.572068
$266$	123.101	−	46.5276i	0.462784	−	0.174916i
$267$		0			0
$268$	100.118	−	88.2956i	0.373574	−	0.329461i
$269$			215.246i			0.800171i	0.916478	+	0.400085i	$0.131020\pi$
$269$			215.246i			0.800171i	−0.916478	+	0.400085i	$0.868980\pi$
$270$		0			0
$271$			378.549i			1.39686i	0.715678	+	0.698431i	$0.246118\pi$
$271$			378.549i			1.39686i	−0.715678	+	0.698431i	$0.753882\pi$
$272$	−47.3137	+	375.541i	−0.173947	+	1.38067i
$273$		0			0
$274$	40.5269	+	107.224i	0.147908	+	0.391329i
$275$	101.358			0.368576
$276$		0			0
$277$		−	166.449i		−	0.600898i	−0.953798	−	0.300449i	$-0.902864\pi$
$277$		−	166.449i		−	0.600898i	0.953798	−	0.300449i	$-0.0971365\pi$
$278$	129.870	+	343.604i	0.467158	+	1.23599i
$279$		0			0
$280$	28.9949	+	15.3427i	0.103553	+	0.0547953i
$281$	421.765			1.50094			0.750471	−	0.660904i	$-0.229827\pi$
$281$	421.765			1.50094			0.750471	+	0.660904i	$0.229827\pi$
$282$		0			0
$283$	−345.439			−1.22063			−0.610316	−	0.792158i	$-0.708957\pi$
$283$	−345.439			−1.22063			−0.610316	+	0.792158i	$0.708957\pi$
$284$	−270.392	−	306.596i	−0.952084	−	1.07956i
$285$		0			0
$286$	13.0051	−	4.91545i	0.0454722	−	0.0171869i
$287$		−	71.3574i		−	0.248632i
$288$		0			0
$289$	270.647			0.936494
$290$	−24.6030	−	65.0935i	−0.0848380	−	0.224460i
$291$		0			0
$292$	−207.941	+	183.387i	−0.712127	+	0.628037i
$293$		−	511.038i		−	1.74416i	−0.489365	−	0.872079i	$-0.662771\pi$
$293$		−	511.038i		−	1.74416i	0.489365	−	0.872079i	$-0.337229\pi$
$294$		0			0
$295$		−	95.4028i		−	0.323399i
$296$	−219.196	+	414.241i	−0.740527	+	1.39946i
$297$		0			0
$298$	359.779	−	135.984i	1.20731	−	0.456321i
$299$	−54.5929			−0.182585
$300$		0			0
$301$			45.4317i			0.150936i
$302$	214.683	−	81.1427i	0.710872	−	0.268684i
$303$		0			0
$304$	−49.7401	+	394.800i	−0.163619	+	1.29868i
$305$	−58.4020			−0.191482
$306$		0			0
$307$	223.331			0.727462			0.363731	−	0.931504i	$-0.381503\pi$
$307$	223.331			0.727462			0.363731	+	0.931504i	$0.381503\pi$
$308$	31.3970	+	35.6008i	0.101938	+	0.115587i
$309$		0			0
$310$	51.1960	+	135.452i	0.165148	+	0.436941i
$311$			12.3988i			0.0398674i	0.999801	+	0.0199337i	$0.00634551\pi$
$311$			12.3988i			0.0398674i	−0.999801	+	0.0199337i	$0.993654\pi$
$312$		0			0
$313$	410.049			1.31006			0.655030	−	0.755603i	$-0.272656\pi$
$313$	410.049			1.31006			0.655030	+	0.755603i	$0.272656\pi$
$314$	396.889	−	150.010i	1.26398	−	0.477739i
$315$		0			0
$316$	102.392	+	116.102i	0.324025	+	0.367410i
$317$			130.316i			0.411092i	0.978647	+	0.205546i	$0.0658970\pi$
$317$			130.316i			0.411092i	−0.978647	+	0.205546i	$0.934103\pi$
$318$		0			0
$319$		−	100.694i		−	0.315656i
$320$	−82.0101	+	55.7944i	−0.256282	+	0.174358i
$321$		0			0
$322$	−65.8995	−	174.354i	−0.204657	−	0.541471i
$323$	588.347			1.82151
$324$		0			0
$325$			35.0234i			0.107764i
$326$	170.083	+	449.998i	0.521728	+	1.38036i
$327$		0			0
$328$	190.711	+	100.915i	0.581435	+	0.307666i
$329$	−95.5980			−0.290571
$330$		0			0
$331$	214.260			0.647311			0.323655	−	0.946175i	$-0.395088\pi$
$331$	214.260			0.647311			0.323655	+	0.946175i	$0.395088\pi$
$332$	10.8457	−	9.56498i	0.0326677	−	0.0288102i
$333$		0			0
$334$	−396.804	+	149.978i	−1.18804	+	0.449035i
$335$		−	51.7223i		−	0.154395i
$336$		0			0
$337$	164.049			0.486792			0.243396	−	0.969927i	$-0.421739\pi$
$337$	164.049			0.486792			0.243396	+	0.969927i	$0.421739\pi$
$338$	−117.803	−	311.676i	−0.348528	−	0.922119i
$339$		0			0
$340$	97.0051	+	109.993i	0.285309	+	0.323510i
$341$			209.533i			0.614466i
$342$		0			0
$343$			18.5203i			0.0539949i
$344$	−121.421	−	64.2501i	−0.352969	−	0.186774i
$345$		0			0
$346$	−340.889	+	128.844i	−0.985229	+	0.372382i
$347$	109.691			0.316113			0.158057	−	0.987430i	$-0.449477\pi$
$347$	109.691			0.316113			0.158057	+	0.987430i	$0.449477\pi$
$348$		0			0
$349$			463.479i			1.32802i	0.747723	+	0.664010i	$0.231147\pi$
$349$			463.479i			1.32802i	−0.747723	+	0.664010i	$0.768853\pi$
$350$	−111.854	+	42.2769i	−0.319584	+	0.120791i
$351$		0			0
$352$	−139.549	+	33.5648i	−0.396447	+	0.0953545i
$353$	−78.0975			−0.221240			−0.110620	−	0.993863i	$-0.535284\pi$
$353$	−78.0975			−0.221240			−0.110620	+	0.993863i	$0.535284\pi$
$354$		0			0
$355$	−158.392			−0.446174
$356$	132.177	−	116.569i	0.371283	−	0.327441i
$357$		0			0
$358$	40.4508	+	107.023i	0.112991	+	0.298946i
$359$			365.114i			1.01703i	0.861053	+	0.508515i	$0.169805\pi$
$359$			365.114i			1.01703i	−0.861053	+	0.508515i	$0.830195\pi$
$360$		0			0
$361$	257.520			0.713351
$362$	−610.286	+	230.667i	−1.68587	+	0.637200i
$363$		0			0
$364$	−12.3015	+	10.8489i	−0.0337954	+	0.0298047i
$365$			107.426i			0.294316i
$366$		0			0
$367$			220.739i			0.601468i	0.953708	+	0.300734i	$0.0972317\pi$
$367$			220.739i			0.601468i	−0.953708	+	0.300734i	$0.902768\pi$
$368$	559.176	+	70.4495i	1.51950	+	0.191439i
$369$		0			0
$370$	64.2010	+	169.860i	0.173516	+	0.459081i
$371$	258.794			0.697558
$372$		0			0
$373$			251.553i			0.674406i	0.941432	+	0.337203i	$0.109481\pi$
$373$			251.553i			0.674406i	−0.941432	+	0.337203i	$0.890519\pi$
$374$	75.0294	+	198.509i	0.200613	+	0.530773i
$375$		0			0
$376$	135.196	−	255.496i	0.359564	−	0.679512i
$377$	34.7939			0.0922916
$378$		0			0
$379$	286.024			0.754682			0.377341	−	0.926074i	$-0.376839\pi$
$379$	286.024			0.754682			0.377341	+	0.926074i	$0.376839\pi$
$380$	101.980	+	115.634i	0.268368	+	0.304301i
$381$		0			0
$382$	181.588	−	68.6338i	0.475361	−	0.179670i
$383$			106.894i			0.279096i	0.990215	+	0.139548i	$0.0445649\pi$
$383$			106.894i			0.279096i	−0.990215	+	0.139548i	$0.955435\pi$
$384$		0			0
$385$	18.3919			0.0477712
$386$	−111.230	−	294.288i	−0.288162	−	0.762404i
$387$		0			0
$388$	−288.323	+	254.277i	−0.743100	+	0.655353i
$389$		−	77.1807i		−	0.198408i	−0.995067	−	0.0992040i	$-0.968370\pi$
$389$		−	77.1807i		−	0.198408i	0.995067	−	0.0992040i	$-0.0316296\pi$
$390$		0			0
$391$		−	833.307i		−	2.13122i
$392$	−49.4975	−	26.1916i	−0.126269	−	0.0668153i
$393$		0			0
$394$	−232.201	+	87.7637i	−0.589343	+	0.222751i
$395$	59.9798			0.151848
$396$		0			0
$397$		−	657.514i		−	1.65621i	−0.560576	−	0.828103i	$-0.689420\pi$
$397$		−	657.514i		−	1.65621i	0.560576	−	0.828103i	$-0.310580\pi$
$398$	−338.573	+	127.968i	−0.850685	+	0.321529i
$399$		0			0
$400$	45.1960	−	358.732i	0.112990	−	0.896830i
$401$	−318.794			−0.794997			−0.397499	−	0.917603i	$-0.630122\pi$
$401$	−318.794			−0.794997			−0.397499	+	0.917603i	$0.630122\pi$
$402$		0			0
$403$	−72.4020			−0.179658
$404$	−51.8995	−	58.8485i	−0.128464	−	0.145665i
$405$		0			0
$406$	42.0000	+	111.122i	0.103448	+	0.273698i
$407$			262.759i			0.645600i
$408$		0			0
$409$	145.265			0.355171			0.177585	−	0.984105i	$-0.443171\pi$
$409$	145.265			0.355171			0.177585	+	0.984105i	$0.443171\pi$
$410$	78.2010	−	29.5572i	0.190734	−	0.0720907i
$411$		0			0
$412$	113.990	+	129.252i	0.276675	+	0.313719i
$413$			162.863i			0.394341i
$414$		0			0
$415$		−	5.60304i		−	0.0135013i
$416$	−11.5980	−	48.2199i	−0.0278798	−	0.115913i
$417$		0			0
$418$	78.8772	+	208.689i	0.188701	+	0.499257i
$419$	−707.012			−1.68738			−0.843690	−	0.536831i	$-0.819621\pi$
$419$	−707.012			−1.68738			−0.843690	+	0.536831i	$0.819621\pi$
$420$		0			0
$421$		−	121.989i		−	0.289761i	−0.989449	−	0.144880i	$-0.953720\pi$
$421$		−	121.989i		−	0.289761i	0.989449	−	0.144880i	$-0.0462798\pi$
$422$	−116.000	−	306.907i	−0.274882	−	0.727268i
$423$		0			0
$424$	−365.990	+	691.656i	−0.863184	+	1.63126i
$425$	−534.597			−1.25788
$426$		0			0
$427$	99.6985			0.233486
$428$	46.7939	−	41.2684i	0.109332	−	0.0964214i
$429$		0			0
$430$	−49.7889	+	18.8184i	−0.115788	+	0.0437638i
$431$		−	588.861i		−	1.36627i	−0.730294	−	0.683133i	$-0.760617\pi$
$431$		−	588.861i		−	1.36627i	0.730294	−	0.683133i	$-0.239383\pi$
$432$		0			0
$433$	137.696			0.318004			0.159002	−	0.987278i	$-0.449172\pi$
$433$	137.696			0.318004			0.159002	+	0.987278i	$0.449172\pi$
$434$	−87.3970	−	231.231i	−0.201376	−	0.532790i
$435$		0			0
$436$	10.1909	+	11.5554i	0.0233736	+	0.0265032i
$437$		−	876.042i		−	2.00467i
$438$		0			0
$439$			440.543i			1.00352i	0.865008	+	0.501758i	$0.167313\pi$
$439$			440.543i			1.00352i	−0.865008	+	0.501758i	$0.832687\pi$
$440$	−26.0101	+	49.1545i	−0.0591139	+	0.111715i
$441$		0			0
$442$	−68.5929	+	25.9257i	−0.155188	+	0.0586554i
$443$	487.058			1.09945			0.549727	−	0.835344i	$-0.314732\pi$
$443$	487.058			1.09945			0.549727	+	0.835344i	$0.314732\pi$
$444$		0			0
$445$		−	68.2844i		−	0.153448i
$446$	−19.7990	+	7.48331i	−0.0443924	+	0.0167787i
$447$		0			0
$448$	140.000	−	95.2470i	0.312500	−	0.212605i
$449$	−264.039			−0.588059			−0.294030	−	0.955796i	$-0.594996\pi$
$449$	−264.039			−0.588059			−0.294030	+	0.955796i	$0.594996\pi$
$450$		0			0
$451$	120.971			0.268227
$452$	−41.3238	+	36.4442i	−0.0914244	+	0.0806287i
$453$		0			0
$454$	74.8162	+	197.945i	0.164793	+	0.436003i
$455$			6.35515i			0.0139674i
$456$		0			0
$457$	−514.323			−1.12543			−0.562717	−	0.826650i	$-0.690244\pi$
$457$	−514.323			−1.12543			−0.562717	+	0.826650i	$0.690244\pi$
$458$	−140.085	+	52.9473i	−0.305863	+	0.115605i
$459$		0			0
$460$	163.779	−	144.439i	0.356041	−	0.313999i
$461$		−	202.224i		−	0.438664i	−0.975650	−	0.219332i	$-0.929612\pi$
$461$		−	202.224i		−	0.438664i	0.975650	−	0.219332i	$-0.0703878\pi$
$462$		0			0
$463$			722.653i			1.56081i	0.625277	+	0.780403i	$0.284986\pi$
$463$			722.653i			1.56081i	−0.625277	+	0.780403i	$0.715014\pi$
$464$	−356.382	−	44.8999i	−0.768064	−	0.0967670i
$465$		0			0
$466$	−296.375	−	784.134i	−0.635997	−	1.68269i
$467$	347.282			0.743645			0.371822	−	0.928304i	$-0.378733\pi$
$467$	347.282			0.743645			0.371822	+	0.928304i	$0.378733\pi$
$468$		0			0
$469$			88.2956i			0.188263i
$470$	−39.5980	−	104.766i	−0.0842510	−	0.222907i
$471$		0			0
$472$	−435.269	−	230.323i	−0.922180	−	0.487972i
$473$	−77.0193			−0.162832
$474$		0			0
$475$	−562.013			−1.18319
$476$	−165.598	−	187.770i	−0.347895	−	0.394476i
$477$		0			0
$478$	−277.477	+	104.877i	−0.580496	+	0.219407i
$479$			29.1811i			0.0609210i	0.999536	+	0.0304605i	$0.00969737\pi$
$479$			29.1811i			0.0609210i	−0.999536	+	0.0304605i	$0.990303\pi$
$480$		0			0
$481$	−90.7939			−0.188761
$482$	325.179	+	860.342i	0.674645	+	1.78494i
$483$		0			0
$484$	302.647	−	266.909i	0.625303	−	0.551466i
$485$			148.952i			0.307117i
$486$		0			0
$487$		−	701.643i		−	1.44074i	−0.693588	−	0.720372i	$-0.743971\pi$
$487$		−	701.643i		−	1.44074i	0.693588	−	0.720372i	$-0.256029\pi$
$488$	−140.995	+	266.455i	−0.288924	+	0.546015i
$489$		0			0
$490$	−20.2965	+	7.67134i	−0.0414214	+	0.0156558i
$491$	59.9512			0.122100			0.0610501	−	0.998135i	$-0.480555\pi$
$491$	59.9512			0.122100			0.0610501	+	0.998135i	$0.480555\pi$
$492$		0			0
$493$			531.095i			1.07727i
$494$	−72.1106	+	27.2552i	−0.145973	+	0.0551726i
$495$		0			0
$496$	741.588	+	93.4313i	1.49514	+	0.188370i
$497$	270.392			0.544048
$498$		0			0
$499$	−84.2843			−0.168906			−0.0844532	−	0.996427i	$-0.526914\pi$
$499$	−84.2843			−0.168906			−0.0844532	+	0.996427i	$0.526914\pi$
$500$	−195.176	−	221.309i	−0.390352	−	0.442617i
$501$		0			0
$502$	88.3310	+	233.702i	0.175958	+	0.465541i
$503$			409.987i			0.815083i	0.913187	+	0.407542i	$0.133614\pi$
$503$			409.987i			0.815083i	−0.913187	+	0.407542i	$0.866386\pi$
$504$		0			0
$505$	−30.4020			−0.0602020
$506$	295.578	−	111.718i	0.584146	−	0.220786i
$507$		0			0
$508$	330.784	+	375.074i	0.651149	+	0.738334i
$509$			477.033i			0.937196i	0.883411	+	0.468598i	$0.155241\pi$
$509$			477.033i			0.937196i	−0.883411	+	0.468598i	$0.844759\pi$
$510$		0			0
$511$		−	183.387i		−	0.358878i
$512$	56.5685	+	508.865i	0.110485	+	0.993878i
$513$		0			0
$514$	−302.184	−	799.503i	−0.587906	−	1.55545i
$515$	66.7737			0.129658
$516$		0			0
$517$		−	162.065i		−	0.313472i
$518$	−109.598	−	289.969i	−0.211579	−	0.559786i
$519$		0			0
$520$	−16.9848	−	8.98754i	−0.0326632	−	0.0172837i
$521$	−210.873			−0.404747			−0.202373	−	0.979308i	$-0.564865\pi$
$521$	−210.873			−0.404747			−0.202373	+	0.979308i	$0.564865\pi$
$522$		0			0
$523$	511.566			0.978139			0.489069	−	0.872245i	$-0.337337\pi$
$523$	511.566			0.978139			0.489069	+	0.872245i	$0.337337\pi$
$524$	301.051	−	265.502i	0.574525	−	0.506683i
$525$		0			0
$526$	−481.970	+	182.167i	−0.916292	+	0.346326i
$527$		−	1105.15i		−	2.09705i
$528$		0			0
$529$	−711.784			−1.34553
$530$	107.196	+	283.614i	0.202257	+	0.535120i
$531$		0			0
$532$	−174.090	−	197.400i	−0.327238	−	0.371053i
$533$			41.8002i			0.0784244i
$534$		0			0
$535$		−	24.1745i		−	0.0451859i
$536$	−235.980	−	124.869i	−0.440261	−	0.232964i
$537$		0			0
$538$	402.688	−	152.202i	0.748491	−	0.282903i
$539$	−31.3970			−0.0582504
$540$		0			0
$541$		−	342.417i		−	0.632933i	−0.948604	−	0.316466i	$-0.897504\pi$
$541$		−	342.417i		−	0.632933i	0.948604	−	0.316466i	$-0.102496\pi$
$542$	708.201	−	267.675i	1.30664	−	0.493865i
$543$		0			0
$544$	736.029	−	177.032i	1.35299	−	0.325426i
$545$	5.96970			0.0109536
$546$		0			0
$547$	−441.976			−0.807999			−0.404000	−	0.914759i	$-0.632380\pi$
$547$	−441.976			−0.807999			−0.404000	+	0.914759i	$0.632380\pi$
$548$	171.941	−	151.638i	0.313761	−	0.276711i
$549$		0			0
$550$	−71.6711	−	189.624i	−0.130311	−	0.344771i
$551$			558.331i			1.01331i
$552$		0			0
$553$	−102.392			−0.185157
$554$	−311.397	+	117.697i	−0.562088	+	0.212449i
$555$		0			0
$556$	550.992	−	485.929i	0.990993	−	0.873973i
$557$			365.710i			0.656571i	0.944579	+	0.328285i	$0.106471\pi$
$557$			365.710i			0.656571i	−0.944579	+	0.328285i	$0.893529\pi$
$558$		0			0
$559$		−	26.6133i		−	0.0476087i
$560$	8.20101	−	65.0935i	0.0146447	−	0.116238i
$561$		0			0
$562$	−298.233	−	789.049i	−0.530663	−	1.40400i
$563$	−806.389			−1.43231			−0.716154	−	0.697943i	$-0.754099\pi$
$563$	−806.389			−1.43231			−0.716154	+	0.697943i	$0.754099\pi$
$564$		0			0
$565$			21.3485i			0.0377850i
$566$	244.262	+	646.256i	0.431558	+	1.14180i
$567$		0			0
$568$	−382.392	+	722.653i	−0.673225	+	1.27228i
$569$	−222.891			−0.391725			−0.195862	−	0.980631i	$-0.562751\pi$
$569$	−222.891			−0.391725			−0.195862	+	0.980631i	$0.562751\pi$
$570$		0			0
$571$	573.082			1.00365			0.501823	−	0.864970i	$-0.332663\pi$
$571$	573.082			1.00365			0.501823	+	0.864970i	$0.332663\pi$
$572$	−18.3919	−	20.8545i	−0.0321537	−	0.0364589i
$573$		0			0
$574$	−133.497	+	50.4573i	−0.232574	+	0.0879047i
$575$			796.008i			1.38436i
$576$		0			0
$577$	−723.901			−1.25459			−0.627297	−	0.778780i	$-0.715839\pi$
$577$	−723.901			−1.25459			−0.627297	+	0.778780i	$0.715839\pi$
$578$	−191.376	−	506.334i	−0.331101	−	0.876010i
$579$		0			0
$580$	−104.382	+	92.0561i	−0.179969	+	0.158717i
$581$			9.56498i			0.0164630i
$582$		0			0
$583$			438.727i			0.752534i
$584$	490.122	+	259.348i	0.839250	+	0.444089i
$585$		0			0
$586$	−956.065	+	361.359i	−1.63151	+	0.616653i
$587$	−21.1198			−0.0359793			−0.0179896	−	0.999838i	$-0.505727\pi$
$587$	−21.1198			−0.0359793			−0.0179896	+	0.999838i	$0.505727\pi$
$588$		0			0
$589$		−	1161.82i		−	1.97253i
$590$	−178.482	+	67.4600i	−0.302512	+	0.114339i
$591$		0			0
$592$	929.970	+	117.165i	1.57089	+	0.197914i
$593$	128.745			0.217108			0.108554	−	0.994091i	$-0.465378\pi$
$593$	128.745			0.217108			0.108554	+	0.994091i	$0.465378\pi$
$594$		0			0
$595$	−97.0051			−0.163034
$596$	−508.804	−	576.930i	−0.853698	−	0.968003i
$597$		0			0
$598$	38.6030	+	102.134i	0.0645536	+	0.170793i
$599$		−	324.130i		−	0.541119i	−0.962703	−	0.270559i	$-0.912791\pi$
$599$		−	324.130i		−	0.541119i	0.962703	−	0.270559i	$-0.0872086\pi$
$600$		0			0
$601$	−721.862			−1.20110			−0.600551	−	0.799587i	$-0.705052\pi$
$601$	−721.862			−1.20110			−0.600551	+	0.799587i	$0.705052\pi$
$602$	84.9949	−	32.1251i	0.141188	−	0.0533639i
$603$		0			0
$604$	−303.608	−	344.259i	−0.502662	−	0.569966i
$605$		−	156.352i		−	0.258433i
$606$		0			0
$607$			705.999i			1.16310i	0.813512	+	0.581548i	$0.197553\pi$
$607$			705.999i			1.16310i	−0.813512	+	0.581548i	$0.802447\pi$
$608$	773.775	−	186.110i	1.27266	−	0.306103i
$609$		0			0
$610$	41.2965	+	109.260i	0.0676991	+	0.179115i
$611$	56.0000			0.0916530
$612$		0			0
$613$			21.8269i			0.0356066i	0.999842	+	0.0178033i	$0.00566727\pi$
$613$			21.8269i			0.0356066i	−0.999842	+	0.0178033i	$0.994333\pi$
$614$	−157.919	−	417.814i	−0.257197	−	0.680479i
$615$		0			0
$616$	44.4020	−	83.9119i	0.0720812	−	0.136221i
$617$	699.578			1.13384			0.566919	−	0.823774i	$-0.308135\pi$
$617$	699.578			1.13384			0.566919	+	0.823774i	$0.308135\pi$
$618$		0			0
$619$	96.1981			0.155409			0.0777044	−	0.996976i	$-0.475241\pi$
$619$	96.1981			0.155409			0.0777044	+	0.996976i	$0.475241\pi$
$620$	217.206	−	191.558i	0.350332	−	0.308964i
$621$		0			0
$622$	23.1960	−	8.76725i	0.0372925	−	0.0140953i
$623$			116.569i			0.187109i
$624$		0			0
$625$	450.618			0.720989
$626$	−289.948	−	767.131i	−0.463176	−	1.22545i
$627$		0			0
$628$	−561.286	−	636.439i	−0.893768	−	1.01344i
$629$		−	1385.88i		−	2.20331i
$630$		0			0
$631$			269.399i			0.426940i	0.976950	+	0.213470i	$0.0684766\pi$
$631$			269.399i			0.426940i	−0.976950	+	0.213470i	$0.931523\pi$
$632$	144.804	−	273.654i	0.229120	−	0.432997i
$633$		0			0
$634$	243.799	−	92.1474i	0.384541	−	0.145343i
$635$	193.769			0.305148
$636$		0			0
$637$		−	10.8489i		−	0.0170313i
$638$	−188.382	+	71.2016i	−0.295269	+	0.111601i
$639$		0			0
$640$	162.372	+	113.974i	0.253706	+	0.178085i
$641$	−635.813			−0.991908			−0.495954	−	0.868349i	$-0.665182\pi$
$641$	−635.813			−0.991908			−0.495954	+	0.868349i	$0.665182\pi$
$642$		0			0
$643$	1281.70			1.99332			0.996658	−	0.0816828i	$-0.0260295\pi$
$643$	1281.70			1.99332			0.996658	+	0.0816828i	$0.0260295\pi$
$644$	−279.588	+	246.573i	−0.434143	+	0.382878i
$645$		0			0
$646$	−416.024	−	1100.70i	−0.644001	−	1.70387i
$647$			260.761i			0.403031i	0.979485	+	0.201516i	$0.0645867\pi$
$647$			260.761i			0.403031i	−0.979485	+	0.201516i	$0.935413\pi$
$648$		0			0
$649$	−276.098			−0.425420
$650$	65.5227	−	24.7653i	0.100804	−	0.0381004i
$651$		0			0
$652$	721.602	−	636.393i	1.10675	−	0.976063i
$653$			1090.58i			1.67011i	0.550167	+	0.835055i	$0.314564\pi$
$653$			1090.58i			1.67011i	−0.550167	+	0.835055i	$0.685436\pi$
$654$		0			0
$655$		−	155.527i		−	0.237446i
$656$	53.9411	−	428.144i	0.0822273	−	0.652659i
$657$		0			0
$658$	67.5980	+	178.847i	0.102732	+	0.271805i
$659$	362.780			0.550500			0.275250	−	0.961373i	$-0.411239\pi$
$659$	362.780			0.550500			0.275250	+	0.961373i	$0.411239\pi$
$660$		0			0
$661$			117.834i			0.178266i	0.996020	+	0.0891330i	$0.0284096\pi$
$661$			117.834i			0.178266i	−0.996020	+	0.0891330i	$0.971590\pi$
$662$	−151.505	−	400.844i	−0.228859	−	0.605504i
$663$		0			0
$664$	−25.5635	−	13.5269i	−0.0384992	−	0.0203719i
$665$	−101.980			−0.153353
$666$		0			0
$667$	790.794			1.18560
$668$	561.166	+	636.302i	0.840068	+	0.952548i
$669$		0			0
$670$	−96.7636	+	36.5732i	−0.144423	+	0.0545869i
$671$			169.017i			0.251888i
$672$		0			0
$673$	−6.56854			−0.00976009			−0.00488005	−	0.999988i	$-0.501553\pi$
$673$	−6.56854			−0.00976009			−0.00488005	+	0.999988i	$0.501553\pi$
$674$	−116.000	−	306.907i	−0.172107	−	0.455352i
$675$		0			0
$676$	−499.794	+	440.777i	−0.739340	+	0.652037i
$677$		−	125.796i		−	0.185813i	−0.995675	−	0.0929066i	$-0.970384\pi$
$677$		−	125.796i		−	0.185813i	0.995675	−	0.0929066i	$-0.0296158\pi$
$678$		0			0
$679$		−	254.277i		−	0.374487i
$680$	137.186	−	259.257i	0.201744	−	0.381260i
$681$		0			0
$682$	392.000	−	148.162i	0.574780	−	0.217246i
$683$	553.775			0.810797			0.405399	−	0.914140i	$-0.367133\pi$
$683$	553.775			0.810797			0.405399	+	0.914140i	$0.367133\pi$
$684$		0			0
$685$		−	88.8274i		−	0.129675i
$686$	34.6482	−	13.0958i	0.0505076	−	0.0190901i
$687$		0			0
$688$	−34.3431	+	272.590i	−0.0499174	+	0.396207i
$689$	−151.598			−0.220026
$690$		0			0
$691$	−1046.83			−1.51494			−0.757471	−	0.652868i	$-0.773565\pi$
$691$	−1046.83			−1.51494			−0.757471	+	0.652868i	$0.773565\pi$
$692$	482.090	+	546.639i	0.696662	+	0.789941i
$693$		0			0
$694$	−77.5635	−	205.214i	−0.111763	−	0.295697i
$695$		−	284.651i		−	0.409569i
$696$		0			0
$697$	−638.039			−0.915407
$698$	867.090	−	327.729i	1.24225	−	0.469526i
$699$		0			0
$700$	158.186	+	179.366i	0.225980	+	0.256237i
$701$			625.993i			0.893000i	0.894784	+	0.446500i	$0.147330\pi$
$701$			625.993i			0.893000i	−0.894784	+	0.446500i	$0.852670\pi$
$702$		0			0
$703$		−	1456.95i		−	2.07248i
$704$	161.470	+	237.339i	0.229361	+	0.337129i
$705$		0			0
$706$	55.2233	+	146.107i	0.0782200	+	0.206951i
$707$	51.8995			0.0734081
$708$		0			0
$709$			593.492i			0.837083i	0.908198	+	0.418541i	$0.137459\pi$
$709$			593.492i			0.837083i	−0.908198	+	0.418541i	$0.862541\pi$
$710$	112.000	+	296.324i	0.157746	+	0.417358i
$711$		0			0
$712$	−311.543	−	164.853i	−0.437561	−	0.231535i
$713$	−1645.55			−2.30792
$714$		0			0
$715$	−10.7737			−0.0150682
$716$	171.618	−	151.353i	0.239690	−	0.211387i
$717$		0			0
$718$	683.065	−	258.174i	0.951344	−	0.359574i
$719$			611.505i			0.850493i	0.905078	+	0.425247i	$0.139813\pi$
$719$			611.505i			0.850493i	−0.905078	+	0.425247i	$0.860187\pi$
$720$		0			0
$721$	−113.990			−0.158100
$722$	−182.094	−	481.775i	−0.252208	−	0.667279i
$723$		0			0
$724$	863.075	+	978.635i	1.19209	+	1.35171i
$725$		−	507.323i		−	0.699756i
$726$		0			0
$727$			944.144i			1.29868i	0.760496	+	0.649342i	$0.224956\pi$
$727$			944.144i			1.29868i	−0.760496	+	0.649342i	$0.775044\pi$
$728$	28.9949	+	15.3427i	0.0398282	+	0.0210751i
$729$		0			0
$730$	200.975	−	75.9613i	0.275308	−	0.104057i
$731$	406.225			0.555712
$732$		0			0
$733$		−	218.254i		−	0.297755i	−0.988856	−	0.148878i	$-0.952434\pi$
$733$		−	218.254i		−	0.297755i	0.988856	−	0.148878i	$-0.0475660\pi$
$734$	412.965	−	156.086i	0.562622	−	0.212651i
$735$		0			0
$736$	−263.598	−	1095.94i	−0.358149	−	1.48905i
$737$	−149.685			−0.203101
$738$		0			0
$739$	−7.29942			−0.00987743			−0.00493872	−	0.999988i	$-0.501572\pi$
$739$	−7.29942			−0.00987743			−0.00493872	+	0.999988i	$0.501572\pi$
$740$	272.382	−	240.218i	0.368084	−	0.324619i
$741$		0			0
$742$	−182.995	−	484.159i	−0.246624	−	0.652506i
$743$			106.867i			0.143832i	0.997411	+	0.0719159i	$0.0229113\pi$
$743$			106.867i			0.143832i	−0.997411	+	0.0719159i	$0.977089\pi$
$744$		0			0
$745$	−298.051			−0.400068
$746$	470.613	−	177.875i	0.630849	−	0.238438i
$747$		0			0
$748$	318.323	−	280.734i	0.425565	−	0.375313i
$749$			41.2684i			0.0550980i
$750$		0			0
$751$			127.463i			0.169725i	0.996393	+	0.0848624i	$0.0270451\pi$
$751$			127.463i			0.169725i	−0.996393	+	0.0848624i	$0.972955\pi$
$752$	−573.588	−	72.2653i	−0.762750	−	0.0960974i
$753$		0			0
$754$	−24.6030	−	65.0935i	−0.0326300	−	0.0863309i
$755$	−177.849			−0.235562
$756$		0			0
$757$			704.275i			0.930350i	0.885219	+	0.465175i	$0.154009\pi$
$757$			704.275i			0.930350i	−0.885219	+	0.465175i	$0.845991\pi$
$758$	−202.250	−	535.103i	−0.266820	−	0.705940i
$759$		0			0
$760$	144.221	−	272.552i	0.189765	−	0.358622i
$761$	1002.93			1.31791			0.658955	−	0.752182i	$-0.270999\pi$
$761$	1002.93			1.31791			0.658955	+	0.752182i	$0.270999\pi$
$762$		0			0
$763$	−10.1909			−0.0133564
$764$	−256.804	−	291.188i	−0.336131	−	0.381137i
$765$		0			0
$766$	199.980	−	75.5853i	0.261070	−	0.0986753i
$767$		−	95.4028i		−	0.124384i
$768$		0			0
$769$	−646.950			−0.841288			−0.420644	−	0.907226i	$-0.638196\pi$
$769$	−646.950			−0.841288			−0.420644	+	0.907226i	$0.638196\pi$
$770$	−13.0051	−	34.4081i	−0.0168897	−	0.0446859i
$771$		0			0
$772$	−471.911	+	416.186i	−0.611283	+	0.539101i
$773$			564.265i			0.729968i	0.931014	+	0.364984i	$0.118925\pi$
$773$			564.265i			0.729968i	−0.931014	+	0.364984i	$0.881075\pi$
$774$		0			0
$775$			1055.68i			1.36217i
$776$	679.584	+	359.602i	0.875752	+	0.463404i
$777$		0			0
$778$	−144.392	+	54.5750i	−0.185594	+	0.0701478i
$779$	−670.759			−0.861052
$780$		0			0
$781$			458.389i			0.586926i
$782$	−1558.97	+	589.237i	−1.99357	+	0.753500i
$783$		0			0
$784$	−14.0000	+	111.122i	−0.0178571	+	0.141737i
$785$	−328.794			−0.418846
$786$		0			0
$787$	923.345			1.17325			0.586623	−	0.809860i	$-0.300457\pi$
$787$	923.345			1.17325			0.586623	+	0.809860i	$0.300457\pi$
$788$	328.382	+	372.350i	0.416728	+	0.472525i
$789$		0			0
$790$	−42.4121	−	112.212i	−0.0536862	−	0.142040i
$791$		−	36.4442i		−	0.0460735i
$792$		0			0
$793$	−58.4020			−0.0736469
$794$	−1230.10	+	464.932i	−1.54924	+	0.585557i
$795$		0			0
$796$	478.814	+	542.924i	0.601525	+	0.682066i
$797$			207.983i			0.260957i	0.991451	+	0.130479i	$0.0416514\pi$
$797$			207.983i			0.260957i	−0.991451	+	0.130479i	$0.958349\pi$
$798$		0			0
$799$			854.785i			1.06982i
$800$	−703.084	+	169.108i	−0.878855	+	0.211385i
$801$		0			0
$802$	225.421	+	596.409i	0.281074	+	0.743652i
$803$	310.891			0.387162
$804$		0			0
$805$			144.439i			0.179428i
$806$	51.1960	+	135.452i	0.0635186	+	0.168054i
$807$		0			0
$808$	−73.3970	+	138.707i	−0.0908378	+	0.171667i
$809$	−340.540			−0.420939			−0.210470	−	0.977600i	$-0.567499\pi$
$809$	−340.540			−0.420939			−0.210470	+	0.977600i	$0.567499\pi$
$810$		0			0
$811$	−907.380			−1.11884			−0.559420	−	0.828884i	$-0.688976\pi$
$811$	−907.380			−1.11884			−0.559420	+	0.828884i	$0.688976\pi$
$812$	178.191	−	157.150i	0.219447	−	0.193534i
$813$		0			0
$814$	491.578	−	185.799i	0.603904	−	0.228254i
$815$		−	372.791i		−	0.457412i
$816$		0			0
$817$	427.058			0.522715
$818$	−102.718	−	271.766i	−0.125572	−	0.332232i
$819$		0			0
$820$	−110.593	−	125.401i	−0.134869	−	0.152928i
$821$		−	633.423i		−	0.771526i	−0.922598	−	0.385763i	$-0.873938\pi$
$821$		−	633.423i		−	0.771526i	0.922598	−	0.385763i	$-0.126062\pi$
$822$		0			0
$823$		−	143.649i		−	0.174544i	−0.996185	−	0.0872718i	$-0.972185\pi$
$823$		−	143.649i		−	0.174544i	0.996185	−	0.0872718i	$-0.0278149\pi$
$824$	161.206	−	304.651i	0.195638	−	0.369722i
$825$		0			0
$826$	304.688	−	115.161i	0.368872	−	0.139421i
$827$	−1545.57			−1.86888			−0.934442	−	0.356114i	$-0.884101\pi$
$827$	−1545.57			−1.86888			−0.934442	+	0.356114i	$0.884101\pi$
$828$		0			0
$829$		−	743.956i		−	0.897413i	−0.893679	−	0.448707i	$-0.851885\pi$
$829$		−	743.956i		−	0.897413i	0.893679	−	0.448707i	$-0.148115\pi$
$830$	−10.4823	+	3.96195i	−0.0126293	+	0.00477343i
$831$		0			0
$832$	−82.0101	+	55.7944i	−0.0985698	+	0.0670606i
$833$	165.598			0.198797
$834$		0			0
$835$	328.723			0.393681
$836$	334.648	−	295.131i	0.400296	−	0.353028i
$837$		0			0
$838$	499.933	+	1322.70i	0.596579	+	1.57840i
$839$		−	96.3107i		−	0.114792i	−0.998351	−	0.0573961i	$-0.981720\pi$
$839$		−	96.3107i		−	0.114792i	0.998351	−	0.0573961i	$-0.0182798\pi$
$840$		0			0
$841$	337.000			0.400713
$842$	−228.221	+	86.2595i	−0.271047	+	0.102446i
$843$		0			0
$844$	−492.146	+	434.032i	−0.583112	+	0.514256i
$845$			258.201i			0.305563i
$846$		0			0
$847$			266.909i			0.315123i
$848$	1552.76	+	195.630i	1.83109	+	0.230696i
$849$		0			0
$850$	378.017	+	1000.14i	0.444726	+	1.17663i
$851$	−2063.56			−2.42486
$852$		0			0
$853$		−	904.866i		−	1.06080i	−0.847746	−	0.530402i	$-0.822041\pi$
$853$		−	904.866i		−	1.06080i	0.847746	−	0.530402i	$-0.177959\pi$
$854$	−70.4975	−	186.519i	−0.0825497	−	0.218406i
$855$		0			0
$856$	−110.294	−	58.3623i	−0.128849	−	0.0681803i
$857$	−160.932			−0.187785			−0.0938926	−	0.995582i	$-0.529931\pi$
$857$	−160.932			−0.187785			−0.0938926	+	0.995582i	$0.529931\pi$
$858$		0			0
$859$	231.693			0.269724			0.134862	−	0.990864i	$-0.456941\pi$
$859$	231.693			0.269724			0.134862	+	0.990864i	$0.456941\pi$
$860$	70.4121	+	79.8398i	0.0818746	+	0.0928370i
$861$		0			0
$862$	−1101.66	+	416.388i	−1.27803	+	0.483048i
$863$			1337.35i			1.54965i	0.632176	+	0.774825i	$0.282162\pi$
$863$			1337.35i			1.54965i	−0.632176	+	0.774825i	$0.717838\pi$
$864$		0			0
$865$	282.402			0.326476
$866$	−97.3654	−	257.605i	−0.112431	−	0.297465i
$867$		0			0
$868$	−370.794	+	327.010i	−0.427182	+	0.376739i
$869$		−	173.583i		−	0.199750i
$870$		0			0
$871$		−	51.7223i		−	0.0593827i
$872$	14.4121	−	27.2363i	0.0165277	−	0.0312343i
$873$		0			0
$874$	−1638.92	+	619.455i	−1.87520	+	0.708759i
$875$	195.176			0.223058
$876$		0			0
$877$			1436.14i			1.63755i	0.574111	+	0.818777i	$0.305348\pi$
$877$			1436.14i			1.63755i	−0.574111	+	0.818777i	$0.694652\pi$
$878$	824.181	−	311.511i	0.938703	−	0.354796i
$879$		0			0
$880$	110.352	+	13.9030i	0.125399	+	0.0157988i
$881$	186.706			0.211926			0.105963	−	0.994370i	$-0.466208\pi$
$881$	186.706			0.211926			0.105963	+	0.994370i	$0.466208\pi$
$882$		0			0
$883$	1277.99			1.44733			0.723664	−	0.690153i	$-0.242457\pi$
$883$	1277.99			1.44733			0.723664	+	0.690153i	$0.242457\pi$
$884$	97.0051	+	109.993i	0.109734	+	0.124427i
$885$		0			0
$886$	−344.402	−	911.202i	−0.388716	−	1.02844i
$887$			980.717i			1.10566i	0.833295	+	0.552828i	$0.186451\pi$
$887$			980.717i			1.10566i	−0.833295	+	0.552828i	$0.813549\pi$
$888$		0			0
$889$	−330.784			−0.372085
$890$	−127.748	+	48.2844i	−0.143538	+	0.0542521i
$891$		0			0
$892$	28.0000	+	31.7490i	0.0313901	+	0.0355931i
$893$			898.621i			1.00629i
$894$		0			0
$895$		−	88.6605i		−	0.0990621i
$896$	−277.186	−	194.566i	−0.309359	−	0.217150i
$897$		0			0
$898$	186.704	+	493.971i	0.207910	+	0.550079i
$899$	1048.76			1.16659
$900$		0			0
$901$		−	2313.99i		−	2.56825i
$902$	−85.5391	−	226.315i	−0.0948327	−	0.250904i
$903$		0			0
$904$	97.4012	+	51.5398i	0.107745	+	0.0570131i
$905$	505.578			0.558649
$906$		0			0
$907$	−658.372			−0.725878			−0.362939	−	0.931813i	$-0.618227\pi$
$907$	−658.372			−0.725878			−0.362939	+	0.931813i	$0.618227\pi$
$908$	317.418	−	279.937i	0.349580	−	0.308300i
$909$		0			0
$910$	11.8894	−	4.49377i	0.0130653	−	0.00493821i
$911$			276.507i			0.303520i	0.988417	+	0.151760i	$0.0484941\pi$
$911$			276.507i			0.303520i	−0.988417	+	0.151760i	$0.951506\pi$
$912$		0			0
$913$	−16.2153			−0.0177605
$914$	363.681	+	962.210i	0.397901	+	1.05275i
$915$		0			0
$916$	198.111	+	224.636i	0.216278	+	0.245236i
$917$			265.502i			0.289533i
$918$		0			0
$919$		−	1339.73i		−	1.45782i	−0.684611	−	0.728908i	$-0.740028\pi$
$919$		−	1339.73i		−	1.45782i	0.684611	−	0.728908i	$-0.259972\pi$
$920$	−386.030	−	204.268i	−0.419598	−	0.222030i
$921$		0			0
$922$	−378.327	+	142.994i	−0.410333	+	0.155091i
$923$	−158.392			−0.171606
$924$		0			0
$925$			1323.85i			1.43119i
$926$	1351.96	−	510.993i	1.46000	−	0.551828i
$927$		0			0
$928$	168.000	+	698.478i	0.181034	+	0.752671i
$929$	−35.4012			−0.0381067			−0.0190534	−	0.999818i	$-0.506065\pi$
$929$	−35.4012			−0.0381067			−0.0190534	+	0.999818i	$0.506065\pi$
$930$		0			0
$931$	174.090			0.186993
$932$	−1257.41	+	1108.93i	−1.34915	+	1.18984i
$933$		0			0
$934$	−245.566	−	649.705i	−0.262918	−	0.695616i
$935$		−	164.450i		−	0.175883i
$936$		0			0
$937$	610.235			0.651265			0.325633	−	0.945496i	$-0.394423\pi$
$937$	610.235			0.651265			0.325633	+	0.945496i	$0.394423\pi$
$938$	165.186	−	62.4344i	0.176104	−	0.0665612i
$939$		0			0
$940$	−168.000	+	148.162i	−0.178723	+	0.157619i
$941$			1852.90i			1.96907i	0.175175	+	0.984537i	$0.443951\pi$
$941$			1852.90i			1.96907i	−0.175175	+	0.984537i	$0.556049\pi$
$942$		0			0
$943$			950.032i			1.00746i
$944$	−123.113	+	977.177i	−0.130416	+	1.03514i
$945$		0			0
$946$	54.4609	+	144.090i	0.0575697	+	0.152315i
$947$	1832.90			1.93548			0.967738	−	0.251959i	$-0.0810748\pi$
$947$	1832.90			1.93548			0.967738	+	0.251959i	$0.0810748\pi$
$948$		0			0
$949$			107.426i			0.113199i
$950$	397.403	+	1051.43i	0.418319	+	1.10677i
$951$		0			0
$952$	−234.191	+	442.579i	−0.245999	+	0.464894i
$953$	−349.687			−0.366933			−0.183467	−	0.983026i	$-0.558732\pi$
$953$	−349.687			−0.366933			−0.183467	+	0.983026i	$0.558732\pi$
$954$		0			0
$955$	−150.432			−0.157521
$956$	392.412	+	444.954i	0.410473	+	0.465433i
$957$		0			0
$958$	54.5929	−	20.6342i	0.0569864	−	0.0215388i
$959$			151.638i			0.158121i
$960$		0			0
$961$	−1221.35			−1.27092
$962$	64.2010	+	169.860i	0.0667370	+	0.176570i
$963$		0			0
$964$	1379.62	−	1216.71i	1.43114	−	1.26214i
$965$			243.796i			0.252639i
$966$		0			0
$967$		−	632.128i		−	0.653700i	−0.945076	−	0.326850i	$-0.894013\pi$
$967$		−	632.128i		−	0.653700i	0.945076	−	0.326850i	$-0.105987\pi$
$968$	−713.345	−	377.467i	−0.736927	−	0.389945i
$969$		0			0
$970$	278.664	−	105.325i	0.287282	−	0.108582i
$971$	−656.497			−0.676104			−0.338052	−	0.941128i	$-0.609768\pi$
$971$	−656.497			−0.676104			−0.338052	+	0.941128i	$0.609768\pi$
$972$		0			0
$973$			485.929i			0.499413i
$974$	−1312.65	+	496.136i	−1.34769	+	0.509380i
$975$		0			0
$976$	598.191	+	75.3650i	0.612901	+	0.0772182i
$977$	−169.314			−0.173300			−0.0866498	−	0.996239i	$-0.527616\pi$
$977$	−169.314			−0.173300			−0.0866498	+	0.996239i	$0.527616\pi$
$978$		0			0
$979$	−197.616			−0.201855
$980$	28.7035	+	32.5467i	0.0292893	+	0.0332110i
$981$		0			0
$982$	−42.3919	−	112.158i	−0.0431690	−	0.114214i
$983$		−	698.607i		−	0.710689i	−0.934735	−	0.355345i	$-0.884364\pi$
$983$		−	698.607i		−	0.710689i	0.934735	−	0.355345i	$-0.115636\pi$
$984$		0			0
$985$	192.362			0.195291
$986$	993.588	−	375.541i	1.00770	−	0.380873i
$987$		0			0
$988$	101.980	+	115.634i	0.103218	+	0.117039i
$989$		−	604.865i		−	0.611592i
$990$		0			0
$991$			429.702i			0.433605i	0.976216	+	0.216802i	$0.0695627\pi$
$991$			429.702i			0.433605i	−0.976216	+	0.216802i	$0.930437\pi$
$992$	−349.588	−	1453.45i	−0.352407	−	1.46517i
$993$		0			0
$994$	−191.196	−	505.857i	−0.192350	−	0.508910i
$995$	280.483			0.281892
$996$		0			0
$997$		−	52.3910i		−	0.0525487i	−0.999655	−	0.0262743i	$-0.991636\pi$
$997$		−	52.3910i		−	0.0525487i	0.999655	−	0.0262743i	$-0.00836434\pi$
$998$	59.5980	+	157.681i	0.0597174	+	0.157997i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.g.a.379.1		4
3.2	odd	2		56.3.g.a.43.4	yes	4
4.3	odd	2		2016.3.g.a.1135.3		4
8.3	odd	2	inner	504.3.g.a.379.2		4
8.5	even	2		2016.3.g.a.1135.2		4
12.11	even	2		224.3.g.a.15.1		4
21.2	odd	6		392.3.k.i.67.3		8
21.5	even	6		392.3.k.j.67.3		8
21.11	odd	6		392.3.k.i.275.1		8
21.17	even	6		392.3.k.j.275.1		8
21.20	even	2		392.3.g.h.99.4		4
24.5	odd	2		224.3.g.a.15.2		4
24.11	even	2		56.3.g.a.43.3	✓	4
48.5	odd	4		1792.3.d.g.1023.2		8
48.11	even	4		1792.3.d.g.1023.8		8
48.29	odd	4		1792.3.d.g.1023.7		8
48.35	even	4		1792.3.d.g.1023.1		8
84.83	odd	2		1568.3.g.h.687.4		4
168.11	even	6		392.3.k.i.275.3		8
168.59	odd	6		392.3.k.j.275.3		8
168.83	odd	2		392.3.g.h.99.3		4
168.107	even	6		392.3.k.i.67.1		8
168.125	even	2		1568.3.g.h.687.3		4
168.131	odd	6		392.3.k.j.67.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.a.43.3	✓	4	24.11	even	2
56.3.g.a.43.4	yes	4	3.2	odd	2
224.3.g.a.15.1		4	12.11	even	2
224.3.g.a.15.2		4	24.5	odd	2
392.3.g.h.99.3		4	168.83	odd	2
392.3.g.h.99.4		4	21.20	even	2
392.3.k.i.67.1		8	168.107	even	6
392.3.k.i.67.3		8	21.2	odd	6
392.3.k.i.275.1		8	21.11	odd	6
392.3.k.i.275.3		8	168.11	even	6
392.3.k.j.67.1		8	168.131	odd	6
392.3.k.j.67.3		8	21.5	even	6
392.3.k.j.275.1		8	21.17	even	6
392.3.k.j.275.3		8	168.59	odd	6
504.3.g.a.379.1		4	1.1	even	1	trivial
504.3.g.a.379.2		4	8.3	odd	2	inner
1568.3.g.h.687.3		4	168.125	even	2
1568.3.g.h.687.4		4	84.83	odd	2
1792.3.d.g.1023.1		8	48.35	even	4
1792.3.d.g.1023.2		8	48.5	odd	4
1792.3.d.g.1023.7		8	48.29	odd	4
1792.3.d.g.1023.8		8	48.11	even	4
2016.3.g.a.1135.2		4	8.5	even	2
2016.3.g.a.1135.3		4	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.87083i) q^{2} +(-3.00000 + 2.64575i) q^{4} +1.54985i q^{5} -2.64575i q^{7} +(7.07107 + 3.74166i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.87083i) q^{2} +(-3.00000 + 2.64575i) q^{4} +1.54985i q^{5} -2.64575i q^{7} +(7.07107 + 3.74166i) q^{8} +(2.89949 - 1.09591i) q^{10} +4.48528 q^{11} +1.54985i q^{13} +(-4.94975 + 1.87083i) q^{14} +(2.00000 - 15.8745i) q^{16} -23.6569 q^{17} -24.8701 q^{19} +(-4.10051 - 4.64954i) q^{20} +(-3.17157 - 8.39119i) q^{22} +35.2248i q^{23} +22.5980 q^{25} +(2.89949 - 1.09591i) q^{26} +(7.00000 + 7.93725i) q^{28} -22.4499i q^{29} +46.7156i q^{31} +(-31.1127 + 7.48331i) q^{32} +(16.7279 + 44.2579i) q^{34} +4.10051 q^{35} +58.5826i q^{37} +(17.5858 + 46.5276i) q^{38} +(-5.79899 + 10.9591i) q^{40} +26.9706 q^{41} -17.1716 q^{43} +(-13.4558 + 11.8669i) q^{44} +(65.8995 - 24.9077i) q^{46} -36.1326i q^{47} -7.00000 q^{49} +(-15.9792 - 42.2769i) q^{50} +(-4.10051 - 4.64954i) q^{52} +97.8149i q^{53} +6.95149i q^{55} +(9.89949 - 18.7083i) q^{56} +(-42.0000 + 15.8745i) q^{58} -61.5563 q^{59} +37.6825i q^{61} +(87.3970 - 33.0329i) q^{62} +(36.0000 + 52.9150i) q^{64} -2.40202 q^{65} -33.3726 q^{67} +(70.9706 - 62.5902i) q^{68} +(-2.89949 - 7.67134i) q^{70} +102.199i q^{71} +69.3137 q^{73} +(109.598 - 41.4241i) q^{74} +(74.6102 - 65.8000i) q^{76} -11.8669i q^{77} -38.7005i q^{79} +(24.6030 + 3.09969i) q^{80} +(-19.0711 - 50.4573i) q^{82} -3.61522 q^{83} -36.6645i q^{85} +(12.1421 + 32.1251i) q^{86} +(31.7157 + 16.7824i) q^{88} -44.0589 q^{89} +4.10051 q^{91} +(-93.1960 - 105.674i) q^{92} +(-67.5980 + 25.5496i) q^{94} -38.5447i q^{95} +96.1076 q^{97} +(4.94975 + 13.0958i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{4}+O(q^{10}) \) 4 * q - 12 * q^4	\( 4 q - 12 q^{4} - 28 q^{10} - 16 q^{11} + 8 q^{16} - 72 q^{17} + 8 q^{19} - 56 q^{20} - 24 q^{22} - 68 q^{25} - 28 q^{26} + 28 q^{28} + 16 q^{34} + 56 q^{35} + 76 q^{38} + 56 q^{40} + 40 q^{41} - 80 q^{43} + 48 q^{44} + 224 q^{46} - 28 q^{49} - 112 q^{50} - 56 q^{52} - 168 q^{58} - 184 q^{59} + 112 q^{62} + 144 q^{64} - 168 q^{65} - 224 q^{67} + 216 q^{68} + 28 q^{70} + 232 q^{73} + 280 q^{74} - 24 q^{76} + 336 q^{80} - 48 q^{82} - 88 q^{83} - 8 q^{86} + 240 q^{88} - 312 q^{89} + 56 q^{91} - 56 q^{92} - 112 q^{94} - 136 q^{97}+O(q^{100}) \) 4 * q - 12 * q^4 - 28 * q^10 - 16 * q^11 + 8 * q^16 - 72 * q^17 + 8 * q^19 - 56 * q^20 - 24 * q^22 - 68 * q^25 - 28 * q^26 + 28 * q^28 + 16 * q^34 + 56 * q^35 + 76 * q^38 + 56 * q^40 + 40 * q^41 - 80 * q^43 + 48 * q^44 + 224 * q^46 - 28 * q^49 - 112 * q^50 - 56 * q^52 - 168 * q^58 - 184 * q^59 + 112 * q^62 + 144 * q^64 - 168 * q^65 - 224 * q^67 + 216 * q^68 + 28 * q^70 + 232 * q^73 + 280 * q^74 - 24 * q^76 + 336 * q^80 - 48 * q^82 - 88 * q^83 - 8 * q^86 + 240 * q^88 - 312 * q^89 + 56 * q^91 - 56 * q^92 - 112 * q^94 - 136 * q^97

Introduction

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