LMFDB - Embedded newform 630.3.v.b.451.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,3,Mod(271,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("630.271");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	630.v (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.1662566547$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.2
Root			$-1.01575 + 1.40294i$ of defining polynomial
Character	$\chi$	$=$	630.451
Dual form			630.3.v.b.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-6.51658 + 2.55620i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-6.51658 + 2.55620i) q^{7} +2.82843 q^{8} +(-2.73861 - 1.58114i) q^{10} +(6.16205 - 10.6730i) q^{11} +7.26007i q^{13} +(7.73861 + 6.17364i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-8.04643 - 4.64561i) q^{17} +(5.26235 - 3.03822i) q^{19} +4.47214i q^{20} -17.4289 q^{22} +(-1.12514 - 1.94880i) q^{23} +(2.50000 - 4.33013i) q^{25} +(8.89173 - 5.13364i) q^{26} +(2.08911 - 13.8433i) q^{28} -42.2122 q^{29} +(-1.05527 - 0.609262i) q^{31} +(-2.82843 + 4.89898i) q^{32} +13.1398i q^{34} +(-9.76139 + 12.2358i) q^{35} +(-17.5296 - 30.3622i) q^{37} +(-7.44209 - 4.29669i) q^{38} +(5.47723 - 3.16228i) q^{40} -57.8811i q^{41} -34.0190 q^{43} +(12.3241 + 21.3460i) q^{44} +(-1.59119 + 2.75603i) q^{46} +(-49.4411 + 28.5448i) q^{47} +(35.9317 - 33.3154i) q^{49} -7.07107 q^{50} +(-12.5748 - 7.26007i) q^{52} +(7.27009 - 12.5922i) q^{53} -27.5575i q^{55} +(-18.4317 + 7.23003i) q^{56} +(29.8485 + 51.6992i) q^{58} +(-50.1067 - 28.9291i) q^{59} +(-5.07658 + 2.93096i) q^{61} +1.72325i q^{62} +8.00000 q^{64} +(8.11700 + 14.0591i) q^{65} +(-24.7355 + 42.8431i) q^{67} +(16.0929 - 9.29122i) q^{68} +(21.8881 + 3.30318i) q^{70} -101.986 q^{71} +(71.2783 + 41.1525i) q^{73} +(-24.7906 + 42.9387i) q^{74} +12.1529i q^{76} +(-12.8732 + 85.3029i) q^{77} +(-55.8530 - 96.7403i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(-70.8895 + 40.9281i) q^{82} -91.6237i q^{83} -20.7758 q^{85} +(24.0551 + 41.6646i) q^{86} +(17.4289 - 30.1878i) q^{88} +(-110.673 + 63.8973i) q^{89} +(-18.5582 - 47.3108i) q^{91} +4.50057 q^{92} +(69.9203 + 40.3685i) q^{94} +(6.79367 - 11.7670i) q^{95} +61.4455i q^{97} +(-66.2104 - 20.4496i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4}+O(q^{10}) $ 8 * q - 8 * q^4	$ 8 q - 8 q^{4} + 4 q^{11} + 40 q^{14} - 16 q^{16} - 84 q^{17} + 108 q^{19} - 48 q^{22} - 12 q^{23} + 20 q^{25} + 96 q^{26} - 72 q^{29} - 132 q^{31} - 100 q^{35} - 96 q^{37} + 168 q^{38} - 112 q^{43} + 8 q^{44} + 8 q^{46} + 24 q^{47} + 156 q^{49} + 48 q^{52} - 32 q^{53} - 16 q^{56} + 104 q^{58} - 132 q^{59} + 96 q^{61} + 64 q^{64} - 20 q^{65} - 120 q^{67} + 168 q^{68} - 8 q^{71} + 24 q^{73} + 16 q^{74} + 216 q^{77} + 12 q^{79} + 24 q^{82} + 120 q^{85} + 40 q^{86} + 48 q^{88} - 492 q^{89} - 308 q^{91} + 48 q^{92} + 480 q^{94} + 40 q^{95}+O(q^{100}) $ 8 * q - 8 * q^4 + 4 * q^11 + 40 * q^14 - 16 * q^16 - 84 * q^17 + 108 * q^19 - 48 * q^22 - 12 * q^23 + 20 * q^25 + 96 * q^26 - 72 * q^29 - 132 * q^31 - 100 * q^35 - 96 * q^37 + 168 * q^38 - 112 * q^43 + 8 * q^44 + 8 * q^46 + 24 * q^47 + 156 * q^49 + 48 * q^52 - 32 * q^53 - 16 * q^56 + 104 * q^58 - 132 * q^59 + 96 * q^61 + 64 * q^64 - 20 * q^65 - 120 * q^67 + 168 * q^68 - 8 * q^71 + 24 * q^73 + 16 * q^74 + 216 * q^77 + 12 * q^79 + 24 * q^82 + 120 * q^85 + 40 * q^86 + 48 * q^88 - 492 * q^89 - 308 * q^91 + 48 * q^92 + 480 * q^94 + 40 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$6$		0			0
$7$	−6.51658	+	2.55620i	−0.930940	+	0.365172i
$7$	−6.51658	+	2.55620i	−0.930940	+	0.365172i
$8$	2.82843			0.353553
$9$		0			0
$10$	−2.73861	−	1.58114i	−0.273861	−	0.158114i
$11$	6.16205	−	10.6730i	0.560187	−	0.970272i	−0.437293	−	0.899319i	$-0.644063\pi$
$11$	6.16205	−	10.6730i	0.560187	−	0.970272i	0.997480	−	0.0709528i	$-0.0226040\pi$
$12$		0			0
$13$			7.26007i			0.558467i	0.960223	+	0.279233i	$0.0900803\pi$
$13$			7.26007i			0.558467i	−0.960223	+	0.279233i	$0.909920\pi$
$14$	7.73861	+	6.17364i	0.552758	+	0.440975i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−8.04643	−	4.64561i	−0.473319	−	0.273271i	0.244309	−	0.969697i	$-0.421439\pi$
$17$	−8.04643	−	4.64561i	−0.473319	−	0.273271i	−0.717628	+	0.696426i	$0.754772\pi$
$18$		0			0
$19$	5.26235	−	3.03822i	0.276966	−	0.159906i	−0.355083	−	0.934835i	$-0.615547\pi$
$19$	5.26235	−	3.03822i	0.276966	−	0.159906i	0.632049	+	0.774928i	$0.282214\pi$
$20$			4.47214i			0.223607i
$21$		0			0
$22$	−17.4289			−0.792224
$23$	−1.12514	−	1.94880i	−0.0489192	−	0.0847306i	0.840529	−	0.541767i	$-0.182244\pi$
$23$	−1.12514	−	1.94880i	−0.0489192	−	0.0847306i	−0.889448	+	0.457036i	$0.848911\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	8.89173	−	5.13364i	0.341990	−	0.197448i
$27$		0			0
$28$	2.08911	−	13.8433i	0.0746112	−	0.494402i
$29$	−42.2122			−1.45559			−0.727797	−	0.685793i	$-0.759456\pi$
$29$	−42.2122			−1.45559			−0.727797	+	0.685793i	$0.759456\pi$
$30$		0			0
$31$	−1.05527	−	0.609262i	−0.0340411	−	0.0196536i	0.482883	−	0.875685i	$-0.339590\pi$
$31$	−1.05527	−	0.609262i	−0.0340411	−	0.0196536i	−0.516924	+	0.856031i	$0.672923\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$		0			0
$34$			13.1398i			0.386464i
$35$	−9.76139	+	12.2358i	−0.278897	+	0.349595i
$36$		0			0
$37$	−17.5296	−	30.3622i	−0.473774	−	0.820600i	0.525775	−	0.850623i	$-0.323775\pi$
$37$	−17.5296	−	30.3622i	−0.473774	−	0.820600i	−0.999549	+	0.0300231i	$0.990442\pi$
$38$	−7.44209	−	4.29669i	−0.195845	−	0.113071i
$39$		0			0
$40$	5.47723	−	3.16228i	0.136931	−	0.0790569i
$41$		−	57.8811i		−	1.41173i	−0.708345	−	0.705867i	$-0.750558\pi$
$41$		−	57.8811i		−	1.41173i	0.708345	−	0.705867i	$-0.249442\pi$
$42$		0			0
$43$	−34.0190			−0.791140			−0.395570	−	0.918436i	$-0.629453\pi$
$43$	−34.0190			−0.791140			−0.395570	+	0.918436i	$0.629453\pi$
$44$	12.3241	+	21.3460i	0.280093	+	0.485136i
$45$		0			0
$46$	−1.59119	+	2.75603i	−0.0345911	+	0.0599136i
$47$	−49.4411	+	28.5448i	−1.05194	+	0.607337i	−0.923191	−	0.384340i	$-0.874429\pi$
$47$	−49.4411	+	28.5448i	−1.05194	+	0.607337i	−0.128747	+	0.991677i	$0.541096\pi$
$48$		0			0
$49$	35.9317	−	33.3154i	0.733300	−	0.679906i
$50$	−7.07107			−0.141421
$51$		0			0
$52$	−12.5748	−	7.26007i	−0.241823	−	0.139617i
$53$	7.27009	−	12.5922i	0.137172	−	0.237588i	−0.789253	−	0.614068i	$-0.789532\pi$
$53$	7.27009	−	12.5922i	0.137172	−	0.237588i	0.926425	+	0.376480i	$0.122866\pi$
$54$		0			0
$55$		−	27.5575i		−	0.501046i
$56$	−18.4317	+	7.23003i	−0.329137	+	0.129108i
$57$		0			0
$58$	29.8485	+	51.6992i	0.514630	+	0.891365i
$59$	−50.1067	−	28.9291i	−0.849266	−	0.490324i	0.0111375	−	0.999938i	$-0.496455\pi$
$59$	−50.1067	−	28.9291i	−0.849266	−	0.490324i	−0.860403	+	0.509614i	$0.829788\pi$
$60$		0			0
$61$	−5.07658	+	2.93096i	−0.0832226	+	0.0480486i	−0.541034	−	0.841001i	$-0.681967\pi$
$61$	−5.07658	+	2.93096i	−0.0832226	+	0.0480486i	0.457811	+	0.889049i	$0.348634\pi$
$62$			1.72325i			0.0277944i
$63$		0			0
$64$	8.00000			0.125000
$65$	8.11700	+	14.0591i	0.124877	+	0.216293i
$66$		0			0
$67$	−24.7355	+	42.8431i	−0.369186	+	0.639449i	−0.989439	−	0.144953i	$-0.953697\pi$
$67$	−24.7355	+	42.8431i	−0.369186	+	0.639449i	0.620252	+	0.784402i	$0.287030\pi$
$68$	16.0929	−	9.29122i	0.236660	−	0.136636i
$69$		0			0
$70$	21.8881	+	3.30318i	0.312687	+	0.0471882i
$71$	−101.986			−1.43643			−0.718214	−	0.695822i	$-0.755040\pi$
$71$	−101.986			−1.43643			−0.718214	+	0.695822i	$0.755040\pi$
$72$		0			0
$73$	71.2783	+	41.1525i	0.976415	+	0.563733i	0.901186	−	0.433433i	$-0.142698\pi$
$73$	71.2783	+	41.1525i	0.976415	+	0.563733i	0.0752290	+	0.997166i	$0.476031\pi$
$74$	−24.7906	+	42.9387i	−0.335009	+	0.580252i
$75$		0			0
$76$			12.1529i			0.159906i
$77$	−12.8732	+	85.3029i	−0.167185	+	1.10783i
$78$		0			0
$79$	−55.8530	−	96.7403i	−0.707001	−	1.22456i	−0.965965	−	0.258674i	$-0.916714\pi$
$79$	−55.8530	−	96.7403i	−0.707001	−	1.22456i	0.258964	−	0.965887i	$-0.416619\pi$
$80$	−7.74597	−	4.47214i	−0.0968246	−	0.0559017i
$81$		0			0
$82$	−70.8895	+	40.9281i	−0.864507	+	0.499123i
$83$		−	91.6237i		−	1.10390i	−0.833877	−	0.551950i	$-0.813884\pi$
$83$		−	91.6237i		−	1.10390i	0.833877	−	0.551950i	$-0.186116\pi$
$84$		0			0
$85$	−20.7758			−0.244421
$86$	24.0551	+	41.6646i	0.279710	+	0.484472i
$87$		0			0
$88$	17.4289	−	30.1878i	0.198056	−	0.343043i
$89$	−110.673	+	63.8973i	−1.24352	+	0.717947i	−0.969809	−	0.243864i	$-0.921585\pi$
$89$	−110.673	+	63.8973i	−1.24352	+	0.717947i	−0.273712	+	0.961812i	$0.588252\pi$
$90$		0			0
$91$	−18.5582	−	47.3108i	−0.203936	−	0.519899i
$92$	4.50057			0.0489192
$93$		0			0
$94$	69.9203	+	40.3685i	0.743833	+	0.429452i
$95$	6.79367	−	11.7670i	0.0715123	−	0.123863i
$96$		0			0
$97$			61.4455i			0.633459i	0.948516	+	0.316729i	$0.102585\pi$
$97$			61.4455i			0.633459i	−0.948516	+	0.316729i	$0.897415\pi$
$98$	−66.2104	−	20.4496i	−0.675616	−	0.208669i
$99$		0			0
$100$	5.00000	+	8.66025i	0.0500000	+	0.0866025i
$101$	−53.8141	−	31.0696i	−0.532813	−	0.307620i	0.209348	−	0.977841i	$-0.432866\pi$
$101$	−53.8141	−	31.0696i	−0.532813	−	0.307620i	−0.742161	+	0.670221i	$0.766199\pi$
$102$		0			0
$103$	−154.102	+	88.9709i	−1.49614	+	0.863795i	−0.999990	−	0.00444312i	$-0.998586\pi$
$103$	−154.102	+	88.9709i	−1.49614	+	0.863795i	−0.496147	+	0.868238i	$0.665252\pi$
$104$			20.5346i			0.197448i
$105$		0			0
$106$	−20.5629			−0.193990
$107$	42.4855	+	73.5871i	0.397061	+	0.687730i	0.993362	−	0.115031i	$-0.0366968\pi$
$107$	42.4855	+	73.5871i	0.397061	+	0.687730i	−0.596301	+	0.802761i	$0.703363\pi$
$108$		0			0
$109$	86.4291	−	149.700i	0.792928	−	1.37339i	−0.131219	−	0.991353i	$-0.541889\pi$
$109$	86.4291	−	149.700i	0.792928	−	1.37339i	0.924147	−	0.382037i	$-0.124777\pi$
$110$	−33.7510	+	19.4861i	−0.306827	+	0.177147i
$111$		0			0
$112$	21.8881	+	17.4617i	0.195429	+	0.155908i
$113$	82.0616			0.726209			0.363105	−	0.931748i	$-0.381717\pi$
$113$	82.0616			0.726209			0.363105	+	0.931748i	$0.381717\pi$
$114$		0			0
$115$	−4.35766	−	2.51590i	−0.0378927	−	0.0218774i
$116$	42.2122	−	73.1137i	0.363898	−	0.630290i
$117$		0			0
$118$			81.8238i			0.693422i
$119$	64.3103	+	9.70520i	0.540423	+	0.0815563i
$120$		0			0
$121$	−15.4418	−	26.7460i	−0.127618	−	0.221042i
$122$	7.17937	+	4.14501i	0.0588473	+	0.0339755i
$123$		0			0
$124$	2.11055	−	1.21852i	0.0170205	−	0.00982681i
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	−193.480			−1.52346			−0.761732	−	0.647892i	$-0.775651\pi$
$127$	−193.480			−1.52346			−0.761732	+	0.647892i	$0.775651\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	11.4792	−	19.8825i	0.0883013	−	0.152942i
$131$	156.850	−	90.5572i	1.19733	−	0.691276i	0.237368	−	0.971420i	$-0.423715\pi$
$131$	156.850	−	90.5572i	1.19733	−	0.691276i	0.959958	+	0.280143i	$0.0903820\pi$
$132$		0			0
$133$	−26.5263	+	33.2504i	−0.199446	+	0.250003i
$134$	69.9625			0.522108
$135$		0			0
$136$	−22.7587	−	13.1398i	−0.167344	−	0.0966159i
$137$	0.631666	−	1.09408i	0.00461070	−	0.00798597i	−0.863711	−	0.503988i	$-0.831866\pi$
$137$	0.631666	−	1.09408i	0.00461070	−	0.00798597i	0.868322	+	0.496002i	$0.165199\pi$
$138$		0			0
$139$			12.1327i			0.0872857i	0.999047	+	0.0436428i	$0.0138964\pi$
$139$			12.1327i			0.0872857i	−0.999047	+	0.0436428i	$0.986104\pi$
$140$	−11.4317	−	29.1430i	−0.0816548	−	0.208165i
$141$		0			0
$142$	72.1153	+	124.907i	0.507854	+	0.879629i
$143$	77.4866	+	44.7369i	0.541865	+	0.312846i
$144$		0			0
$145$	−81.7436	+	47.1947i	−0.563749	+	0.325481i
$146$		−	116.397i		−	0.797239i
$147$		0			0
$148$	70.1185			0.473774
$149$	144.863	+	250.910i	0.972233	+	1.68396i	0.688780	+	0.724971i	$0.258147\pi$
$149$	144.863	+	250.910i	0.972233	+	1.68396i	0.283453	+	0.958986i	$0.408520\pi$
$150$		0			0
$151$	−58.6516	+	101.588i	−0.388421	+	0.672765i	−0.992237	−	0.124358i	$-0.960313\pi$
$151$	−58.6516	+	101.588i	−0.388421	+	0.672765i	0.603816	+	0.797124i	$0.293646\pi$
$152$	14.8842	−	8.59339i	0.0979223	−	0.0565354i
$153$		0			0
$154$	113.577	−	44.5518i	0.737513	−	0.289298i
$155$	−2.72470			−0.0175787
$156$		0			0
$157$	159.121	+	91.8687i	1.01351	+	0.585151i	0.912218	−	0.409705i	$-0.134368\pi$
$157$	159.121	+	91.8687i	1.01351	+	0.585151i	0.101294	+	0.994857i	$0.467702\pi$
$158$	−78.9881	+	136.811i	−0.499925	+	0.865895i
$159$		0			0
$160$			12.6491i			0.0790569i
$161$	12.3136	+	9.82345i	0.0764821	+	0.0610152i
$162$		0			0
$163$	−60.7854	−	105.283i	−0.372917	−	0.645911i	0.617096	−	0.786888i	$-0.288309\pi$
$163$	−60.7854	−	105.283i	−0.372917	−	0.645911i	−0.990013	+	0.140977i	$0.954976\pi$
$164$	100.253	+	57.8811i	0.611298	+	0.352933i
$165$		0			0
$166$	−112.216	+	64.7878i	−0.675998	+	0.390288i
$167$		−	94.6539i		−	0.566790i	−0.959003	−	0.283395i	$-0.908539\pi$
$167$		−	94.6539i		−	0.566790i	0.959003	−	0.283395i	$-0.0914608\pi$
$168$		0			0
$169$	116.291			0.688115
$170$	14.6907	+	25.4450i	0.0864159	+	0.149677i
$171$		0			0
$172$	34.0190	−	58.9227i	0.197785	−	0.342574i
$173$	225.766	−	130.346i	1.30501	−	0.753445i	0.323747	−	0.946144i	$-0.395057\pi$
$173$	225.766	−	130.346i	1.30501	−	0.753445i	0.981258	+	0.192699i	$0.0617240\pi$
$174$		0			0
$175$	−5.22278	+	34.6081i	−0.0298445	+	0.197761i
$176$	−49.2964			−0.280093
$177$		0			0
$178$	156.516	+	90.3645i	0.879302	+	0.507666i
$179$	153.264	−	265.462i	0.856225	−	1.48303i	−0.0192782	−	0.999814i	$-0.506137\pi$
$179$	153.264	−	265.462i	0.856225	−	1.48303i	0.875504	−	0.483212i	$-0.160530\pi$
$180$		0			0
$181$		−	314.885i		−	1.73970i	−0.493318	−	0.869849i	$-0.664216\pi$
$181$		−	314.885i		−	1.73970i	0.493318	−	0.869849i	$-0.335784\pi$
$182$	−44.8211	+	56.1828i	−0.246270	+	0.308697i
$183$		0			0
$184$	−3.18238	−	5.51205i	−0.0172956	−	0.0299568i
$185$	−67.8920	−	39.1974i	−0.366984	−	0.211878i
$186$		0			0
$187$	−99.1651	+	57.2530i	−0.530295	+	0.306166i
$188$		−	114.179i		−	0.607337i
$189$		0			0
$190$	−19.2154			−0.101134
$191$	−45.3946	−	78.6257i	−0.237668	−	0.411653i	0.722377	−	0.691500i	$-0.243050\pi$
$191$	−45.3946	−	78.6257i	−0.237668	−	0.411653i	−0.960045	+	0.279847i	$0.909716\pi$
$192$		0			0
$193$	114.828	−	198.887i	0.594961	−	1.03050i	−0.398591	−	0.917129i	$-0.630501\pi$
$193$	114.828	−	198.887i	0.594961	−	1.03050i	0.993552	−	0.113374i	$-0.0361659\pi$
$194$	75.2551	−	43.4485i	0.387913	−	0.223962i
$195$		0			0
$196$	21.7723	+	95.5509i	0.111083	+	0.487504i
$197$	−227.989			−1.15730			−0.578652	−	0.815574i	$-0.696421\pi$
$197$	−227.989			−1.15730			−0.578652	+	0.815574i	$0.696421\pi$
$198$		0			0
$199$	9.56623	+	5.52307i	0.0480715	+	0.0277541i	0.523843	−	0.851815i	$-0.324498\pi$
$199$	9.56623	+	5.52307i	0.0480715	+	0.0277541i	−0.475772	+	0.879569i	$0.657831\pi$
$200$	7.07107	−	12.2474i	0.0353553	−	0.0612372i
$201$		0			0
$202$			87.8781i			0.435040i
$203$	275.079	−	107.903i	1.35507	−	0.531541i
$204$		0			0
$205$	−64.7130	−	112.086i	−0.315673	−	0.546762i
$206$	217.933	+	125.824i	1.05793	+	0.610796i
$207$		0			0
$208$	25.1496	−	14.5201i	0.120912	−	0.0698083i
$209$		−	74.8867i		−	0.358310i
$210$		0			0
$211$	151.187			0.716526			0.358263	−	0.933621i	$-0.383369\pi$
$211$	151.187			0.716526			0.358263	+	0.933621i	$0.383369\pi$
$212$	14.5402	+	25.1843i	0.0685858	+	0.118794i
$213$		0			0
$214$	60.0836	−	104.068i	0.280765	−	0.486298i
$215$	−65.8775	+	38.0344i	−0.306407	+	0.176904i
$216$		0			0
$217$	8.43417	+	1.27282i	0.0388671	+	0.00586552i
$218$	−244.458			−1.12137
$219$		0			0
$220$	47.7311	+	27.5575i	0.216959	+	0.125262i
$221$	33.7274	−	58.4176i	0.152613	−	0.264333i
$222$		0			0
$223$		−	308.586i		−	1.38379i	−0.721997	−	0.691896i	$-0.756776\pi$
$223$		−	308.586i		−	1.38379i	0.721997	−	0.691896i	$-0.243224\pi$
$224$	5.90890	−	39.1546i	0.0263790	−	0.174797i
$225$		0			0
$226$	−58.0263	−	100.505i	−0.256754	−	0.444710i
$227$	−86.9683	−	50.2112i	−0.383120	−	0.221195i	0.296055	−	0.955171i	$-0.404329\pi$
$227$	−86.9683	−	50.2112i	−0.383120	−	0.221195i	−0.679175	+	0.733976i	$0.737662\pi$
$228$		0			0
$229$	277.125	−	159.998i	1.21015	−	0.698682i	0.247361	−	0.968923i	$-0.420437\pi$
$229$	277.125	−	159.998i	1.21015	−	0.698682i	0.962793	+	0.270241i	$0.0871034\pi$
$230$			7.11603i			0.0309392i
$231$		0			0
$232$	−119.394			−0.514630
$233$	155.395	+	269.151i	0.666929	+	1.15516i	0.978758	+	0.205017i	$0.0657251\pi$
$233$	155.395	+	269.151i	0.666929	+	1.15516i	−0.311829	+	0.950138i	$0.600942\pi$
$234$		0			0
$235$	−63.8282	+	110.554i	−0.271609	+	0.470441i
$236$	100.213	−	57.8582i	0.424633	−	0.245162i
$237$		0			0
$238$	−33.5879	−	85.6264i	−0.141126	−	0.359775i
$239$	−136.263			−0.570139			−0.285069	−	0.958507i	$-0.592017\pi$
$239$	−136.263			−0.570139			−0.285069	+	0.958507i	$0.592017\pi$
$240$		0			0
$241$	334.441	+	193.090i	1.38772	+	0.801202i	0.993058	−	0.117623i	$-0.0375274\pi$
$241$	334.441	+	193.090i	1.38772	+	0.801202i	0.394665	+	0.918825i	$0.370861\pi$
$242$	−21.8380	+	37.8246i	−0.0902398	+	0.156300i
$243$		0			0
$244$		−	11.7239i		−	0.0480486i
$245$	32.3337	−	104.688i	0.131974	−	0.427297i
$246$		0			0
$247$	22.0577	+	38.2050i	0.0893024	+	0.154676i
$248$	−2.98476	−	1.72325i	−0.0120353	−	0.00694860i
$249$		0			0
$250$	−13.6931	+	7.90569i	−0.0547723	+	0.0316228i
$251$			99.3717i			0.395903i	0.980212	+	0.197952i	$0.0634289\pi$
$251$			99.3717i			0.395903i	−0.980212	+	0.197952i	$0.936571\pi$
$252$		0			0
$253$	−27.7328			−0.109616
$254$	136.811	+	236.964i	0.538626	+	0.932928i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−18.2886	+	10.5589i	−0.0711617	+	0.0410852i	−0.535159	−	0.844752i	$-0.679748\pi$
$257$	−18.2886	+	10.5589i	−0.0711617	+	0.0410852i	0.463997	+	0.885837i	$0.346415\pi$
$258$		0			0
$259$	191.845	+	153.049i	0.740715	+	0.590921i
$260$	−32.4680			−0.124877
$261$		0			0
$262$	−221.819	−	128.067i	−0.846637	−	0.488806i
$263$	−190.259	+	329.538i	−0.723417	+	1.25299i	0.236205	+	0.971703i	$0.424096\pi$
$263$	−190.259	+	329.538i	−0.723417	+	1.25299i	−0.959622	+	0.281292i	$0.909237\pi$
$264$		0			0
$265$		−	32.5128i		−	0.122690i
$266$	59.4802	+	8.97628i	0.223610	+	0.0337454i
$267$		0			0
$268$	−49.4709	−	85.6862i	−0.184593	−	0.319725i
$269$	−14.5415	−	8.39551i	−0.0540574	−	0.0312101i	0.472728	−	0.881209i	$-0.343269\pi$
$269$	−14.5415	−	8.39551i	−0.0540574	−	0.0312101i	−0.526785	+	0.849998i	$0.676603\pi$
$270$		0			0
$271$	320.146	−	184.836i	1.18135	−	0.682052i	0.225023	−	0.974353i	$-0.427754\pi$
$271$	320.146	−	184.836i	1.18135	−	0.682052i	0.956326	+	0.292301i	$0.0944209\pi$
$272$			37.1649i			0.136636i
$273$		0			0
$274$	−1.78662			−0.00652051
$275$	−30.8103	−	53.3650i	−0.112037	−	0.194054i
$276$		0			0
$277$	−242.912	+	420.736i	−0.876940	+	1.51890i	−0.0222577	+	0.999752i	$0.507085\pi$
$277$	−242.912	+	420.736i	−0.876940	+	1.51890i	−0.854682	+	0.519152i	$0.826248\pi$
$278$	14.8595	−	8.57912i	0.0534513	−	0.0308601i
$279$		0			0
$280$	−27.6094	+	34.6081i	−0.0986049	+	0.123600i
$281$	−360.234			−1.28197			−0.640986	−	0.767553i	$-0.721474\pi$
$281$	−360.234			−1.28197			−0.640986	+	0.767553i	$0.721474\pi$
$282$		0			0
$283$	234.261	+	135.251i	0.827778	+	0.477918i	0.853091	−	0.521762i	$-0.174725\pi$
$283$	234.261	+	135.251i	0.827778	+	0.477918i	−0.0253131	+	0.999680i	$0.508058\pi$
$284$	101.986	−	176.646i	0.359107	−	0.621992i
$285$		0			0
$286$		−	126.535i		−	0.442431i
$287$	147.956	+	377.187i	0.515525	+	1.31424i
$288$		0			0
$289$	−101.337	−	175.520i	−0.350646	−	0.607336i
$290$	115.603	+	66.7434i	0.398631	+	0.230150i
$291$		0			0
$292$	−142.557	+	82.3051i	−0.488207	+	0.281867i
$293$			9.63230i			0.0328747i	0.999865	+	0.0164374i	$0.00523241\pi$
$293$			9.63230i			0.0328747i	−0.999865	+	0.0164374i	$0.994768\pi$
$294$		0			0
$295$	−129.375			−0.438559
$296$	−49.5813	−	85.8773i	−0.167504	−	0.290126i
$297$		0			0
$298$	204.867	−	354.840i	0.687472	−	1.19074i
$299$	14.1484	−	8.16861i	0.0473192	−	0.0273198i
$300$		0			0
$301$	221.688	−	86.9594i	0.736504	−	0.288902i
$302$	165.892			0.549310
$303$		0			0
$304$	−21.0494	−	12.1529i	−0.0692415	−	0.0399766i
$305$	−6.55383	+	11.3516i	−0.0214880	+	0.0372183i
$306$		0			0
$307$		−	46.0412i		−	0.149971i	−0.997185	−	0.0749857i	$-0.976109\pi$
$307$		−	46.0412i		−	0.149971i	0.997185	−	0.0749857i	$-0.0238911\pi$
$308$	−134.876	−	107.600i	−0.437908	−	0.349350i
$309$		0			0
$310$	1.92666	+	3.33707i	0.00621502	+	0.0107647i
$311$	378.160	+	218.331i	1.21595	+	0.702029i	0.964049	−	0.265724i	$-0.0856110\pi$
$311$	378.160	+	218.331i	1.21595	+	0.702029i	0.251901	+	0.967753i	$0.418944\pi$
$312$		0			0
$313$	248.135	−	143.261i	0.792764	−	0.457703i	−0.0481706	−	0.998839i	$-0.515339\pi$
$313$	248.135	−	143.261i	0.792764	−	0.457703i	0.840935	+	0.541137i	$0.182006\pi$
$314$		−	259.844i		−	0.827529i
$315$		0			0
$316$	223.412			0.707001
$317$	−0.684418	−	1.18545i	−0.00215905	−	0.00373958i	0.864944	−	0.501869i	$-0.167354\pi$
$317$	−0.684418	−	1.18545i	−0.00215905	−	0.00373958i	−0.867103	+	0.498129i	$0.834021\pi$
$318$		0			0
$319$	−260.114	+	450.531i	−0.815404	+	1.41232i
$320$	15.4919	−	8.94427i	0.0484123	−	0.0279508i
$321$		0			0
$322$	3.32418	−	22.0273i	0.0103235	−	0.0684077i
$323$	−56.4575			−0.174791
$324$		0			0
$325$	31.4370	+	18.1502i	0.0967293	+	0.0558467i
$326$	−85.9636	+	148.893i	−0.263692	+	0.456728i
$327$		0			0
$328$		−	163.712i		−	0.499123i
$329$	249.221	−	312.396i	0.757510	−	0.949533i
$330$		0			0
$331$	192.017	+	332.583i	0.580111	+	1.00478i	0.995466	+	0.0951223i	$0.0303242\pi$
$331$	192.017	+	332.583i	0.580111	+	1.00478i	−0.415354	+	0.909660i	$0.636342\pi$
$332$	158.697	+	91.6237i	0.478003	+	0.275975i
$333$		0			0
$334$	−115.927	+	66.9304i	−0.347087	+	0.200391i
$335$			110.620i			0.330210i
$336$		0			0
$337$	−141.948			−0.421211			−0.210606	−	0.977571i	$-0.567544\pi$
$337$	−141.948			−0.421211			−0.210606	+	0.977571i	$0.567544\pi$
$338$	−82.2305	−	142.427i	−0.243285	−	0.421383i
$339$		0			0
$340$	20.7758	−	35.9847i	0.0611053	−	0.105837i
$341$	−13.0053	+	7.50861i	−0.0381387	+	0.0220194i
$342$		0			0
$343$	−148.991	+	308.951i	−0.434376	+	0.900732i
$344$	−96.2203			−0.279710
$345$		0			0
$346$	−319.281	−	184.337i	−0.922778	−	0.532766i
$347$	−125.176	+	216.811i	−0.360737	+	0.624815i	−0.988082	−	0.153926i	$-0.950808\pi$
$347$	−125.176	+	216.811i	−0.360737	+	0.624815i	0.627345	+	0.778741i	$0.284142\pi$
$348$		0			0
$349$			195.188i			0.559277i	0.960105	+	0.279639i	$0.0902147\pi$
$349$			195.188i			0.559277i	−0.960105	+	0.279639i	$0.909785\pi$
$350$	46.0792	−	18.0751i	0.131655	−	0.0516431i
$351$		0			0
$352$	34.8578	+	60.3756i	0.0990280	+	0.171521i
$353$	−123.148	−	71.0997i	−0.348862	−	0.201416i	0.315322	−	0.948985i	$-0.397887\pi$
$353$	−123.148	−	71.0997i	−0.348862	−	0.201416i	−0.664184	+	0.747569i	$0.731221\pi$
$354$		0			0
$355$	−197.496	+	114.024i	−0.556326	+	0.321195i
$356$		−	255.589i		−	0.717947i
$357$		0			0
$358$	−433.497			−1.21089
$359$	−328.443	−	568.880i	−0.914884	−	1.58462i	−0.807072	−	0.590453i	$-0.798949\pi$
$359$	−328.443	−	568.880i	−0.914884	−	1.58462i	−0.107812	−	0.994171i	$-0.534384\pi$
$360$		0			0
$361$	−162.038	+	280.659i	−0.448860	+	0.777448i
$362$	−385.654	+	222.658i	−1.06534	+	0.615076i
$363$		0			0
$364$	100.503	+	15.1671i	0.276107	+	0.0416678i
$365$	184.040			0.504218
$366$		0			0
$367$	−444.403	−	256.576i	−1.21091	−	0.699117i	−0.247950	−	0.968773i	$-0.579757\pi$
$367$	−444.403	−	256.576i	−1.21091	−	0.699117i	−0.962957	+	0.269655i	$0.913090\pi$
$368$	−4.50057	+	7.79522i	−0.0122298	+	0.0211827i
$369$		0			0
$370$			110.867i			0.299641i
$371$	−15.1880	+	100.642i	−0.0409381	+	0.271271i
$372$		0			0
$373$	316.262	+	547.782i	0.847887	+	1.46858i	0.883090	+	0.469204i	$0.155459\pi$
$373$	316.262	+	547.782i	0.847887	+	1.46858i	−0.0352027	+	0.999380i	$0.511208\pi$
$374$	140.241	+	80.9679i	0.374975	+	0.216492i
$375$		0			0
$376$	−139.841	+	80.7370i	−0.371916	+	0.214726i
$377$		−	306.463i		−	0.812900i
$378$		0			0
$379$	−617.180			−1.62844			−0.814222	−	0.580553i	$-0.802836\pi$
$379$	−617.180			−1.62844			−0.814222	+	0.580553i	$0.802836\pi$
$380$	13.5873	+	23.5340i	0.0357562	+	0.0619315i
$381$		0			0
$382$	−64.1976	+	111.193i	−0.168057	+	0.291082i
$383$	−150.642	+	86.9735i	−0.393322	+	0.227085i	−0.683599	−	0.729858i	$-0.739586\pi$
$383$	−150.642	+	86.9735i	−0.393322	+	0.227085i	0.290276	+	0.956943i	$0.406253\pi$
$384$		0			0
$385$	70.4426	+	179.581i	0.182968	+	0.466444i
$386$	−324.781			−0.841402
$387$		0			0
$388$	−106.427	−	61.4455i	−0.274296	−	0.158365i
$389$	98.0961	−	169.907i	0.252175	−	0.436780i	−0.711949	−	0.702231i	$-0.752187\pi$
$389$	98.0961	−	169.907i	0.252175	−	0.436780i	0.964124	+	0.265451i	$0.0855208\pi$
$390$		0			0
$391$			20.9079i			0.0534729i
$392$	101.630	−	94.2301i	0.259261	−	0.240383i
$393$		0			0
$394$	161.213	+	279.228i	0.409169	+	0.708702i
$395$	−216.318	−	124.891i	−0.547640	−	0.316180i
$396$		0			0
$397$	−345.285	+	199.350i	−0.869736	+	0.502142i	−0.867260	−	0.497855i	$-0.834121\pi$
$397$	−345.285	+	199.350i	−0.869736	+	0.502142i	−0.00247542	+	0.999997i	$0.500788\pi$
$398$		−	15.6216i		−	0.0392502i
$399$		0			0
$400$	−20.0000			−0.0500000
$401$	173.599	+	300.683i	0.432916	+	0.749833i	0.997123	−	0.0758008i	$-0.0241513\pi$
$401$	173.599	+	300.683i	0.432916	+	0.749833i	−0.564207	+	0.825633i	$0.690818\pi$
$402$		0			0
$403$	4.42328	−	7.66135i	0.0109759	−	0.0190108i
$404$	107.628	−	62.1392i	0.266407	−	0.153810i
$405$		0			0
$406$	−326.664	−	260.603i	−0.804591	−	0.641880i
$407$	−432.074			−1.06161
$408$		0			0
$409$	293.397	+	169.393i	0.717352	+	0.414163i	0.813777	−	0.581177i	$-0.197408\pi$
$409$	293.397	+	169.393i	0.717352	+	0.414163i	−0.0964252	+	0.995340i	$0.530741\pi$
$410$	−91.5180	+	158.514i	−0.223215	+	0.386619i
$411$		0			0
$412$		−	355.884i		−	0.863795i
$413$	400.473	+	60.4361i	0.969668	+	0.146334i
$414$		0			0
$415$	−102.438	−	177.429i	−0.246840	−	0.427539i
$416$	−35.5669	−	20.5346i	−0.0854974	−	0.0493619i
$417$		0			0
$418$	−91.7171	+	52.9529i	−0.219419	+	0.126682i
$419$		−	369.514i		−	0.881894i	−0.897533	−	0.440947i	$-0.854643\pi$
$419$		−	369.514i		−	0.881894i	0.897533	−	0.440947i	$-0.145357\pi$
$420$		0			0
$421$	−217.571			−0.516797			−0.258398	−	0.966038i	$-0.583195\pi$
$421$	−217.571			−0.516797			−0.258398	+	0.966038i	$0.583195\pi$
$422$	−106.905	−	185.166i	−0.253330	−	0.438781i
$423$		0			0
$424$	20.5629	−	35.6160i	0.0484975	−	0.0840001i
$425$	−40.2322	+	23.2280i	−0.0946639	+	0.0546542i
$426$		0			0
$427$	25.5898	−	32.0766i	0.0599293	−	0.0751209i
$428$	−169.942			−0.397061
$429$		0			0
$430$	93.1649	+	53.7888i	0.216663	+	0.125090i
$431$	−142.916	+	247.537i	−0.331591	+	0.574332i	−0.982824	−	0.184546i	$-0.940919\pi$
$431$	−142.916	+	247.537i	−0.331591	+	0.574332i	0.651233	+	0.758878i	$0.274252\pi$
$432$		0			0
$433$		−	643.490i		−	1.48612i	−0.669224	−	0.743060i	$-0.733374\pi$
$433$		−	643.490i		−	1.48612i	0.669224	−	0.743060i	$-0.266626\pi$
$434$	−4.40498	−	11.2297i	−0.0101497	−	0.0258749i
$435$		0			0
$436$	172.858	+	299.399i	0.396464	+	0.686695i
$437$	−11.8418	−	6.83686i	−0.0270979	−	0.0156450i
$438$		0			0
$439$	494.013	−	285.218i	1.12531	−	0.649700i	0.182562	−	0.983194i	$-0.441561\pi$
$439$	494.013	−	285.218i	1.12531	−	0.649700i	0.942752	+	0.333494i	$0.108228\pi$
$440$		−	77.9445i		−	0.177147i
$441$		0			0
$442$	−95.3956			−0.215827
$443$	−33.0074	−	57.1705i	−0.0745089	−	0.129053i	0.826364	−	0.563137i	$-0.190406\pi$
$443$	−33.0074	−	57.1705i	−0.0745089	−	0.129053i	−0.900873	+	0.434084i	$0.857072\pi$
$444$		0			0
$445$	−142.879	+	247.473i	−0.321076	+	0.556120i
$446$	−377.939	+	218.203i	−0.847396	+	0.489244i
$447$		0			0
$448$	−52.1327	+	20.4496i	−0.116368	+	0.0456464i
$449$	−515.072			−1.14715			−0.573577	−	0.819152i	$-0.694445\pi$
$449$	−515.072			−1.14715			−0.573577	+	0.819152i	$0.694445\pi$
$450$		0			0
$451$	−617.764	−	356.666i	−1.36977	−	0.790834i
$452$	−82.0616	+	142.135i	−0.181552	+	0.314458i
$453$		0			0
$454$			142.019i			0.312816i
$455$	−88.8329	−	70.8683i	−0.195237	−	0.155755i
$456$		0			0
$457$	−39.5136	−	68.4395i	−0.0864629	−	0.149758i	0.819551	−	0.573007i	$-0.194223\pi$
$457$	−39.5136	−	68.4395i	−0.0864629	−	0.149758i	−0.906014	+	0.423248i	$0.860890\pi$
$458$	−391.914	−	226.272i	−0.855708	−	0.494043i
$459$		0			0
$460$	8.71532	−	5.03179i	0.0189463	−	0.0109387i
$461$			9.58316i			0.0207878i	0.999946	+	0.0103939i	$0.00330854\pi$
$461$			9.58316i			0.0207878i	−0.999946	+	0.0103939i	$0.996691\pi$
$462$		0			0
$463$	−232.103			−0.501303			−0.250652	−	0.968077i	$-0.580645\pi$
$463$	−232.103			−0.501303			−0.250652	+	0.968077i	$0.580645\pi$
$464$	84.4244	+	146.227i	0.181949	+	0.315145i
$465$		0			0
$466$	219.761	−	380.637i	0.471590	−	0.816818i
$467$	−593.692	+	342.768i	−1.27129	+	0.733979i	−0.975230	−	0.221191i	$-0.929006\pi$
$467$	−593.692	+	342.768i	−1.27129	+	0.733979i	−0.296058	+	0.955170i	$0.595672\pi$
$468$		0			0
$469$	51.6752	−	342.419i	0.110182	−	0.730105i
$470$	180.533			0.384114
$471$		0			0
$472$	−141.723	−	81.8238i	−0.300261	−	0.173356i
$473$	−209.627	+	363.085i	−0.443186	+	0.767621i
$474$		0			0
$475$		−	30.3822i		−	0.0639626i
$476$	−81.1202	+	101.684i	−0.170421	+	0.213621i
$477$		0			0
$478$	96.3526	+	166.888i	0.201575	+	0.349137i
$479$	544.818	+	314.551i	1.13741	+	0.656682i	0.945787	−	0.324787i	$-0.105293\pi$
$479$	544.818	+	314.551i	1.13741	+	0.656682i	0.191619	+	0.981469i	$0.438626\pi$
$480$		0			0
$481$	220.432	−	127.266i	0.458278	−	0.264587i
$482$		−	546.140i		−	1.13307i
$483$		0			0
$484$	61.7673			0.127618
$485$	68.6982	+	118.989i	0.141646	+	0.245338i
$486$		0			0
$487$	249.384	−	431.946i	0.512083	−	0.886953i	−0.487819	−	0.872945i	$-0.662207\pi$
$487$	249.384	−	431.946i	0.512083	−	0.886953i	0.999902	−	0.0140085i	$-0.00445918\pi$
$488$	−14.3587	+	8.29002i	−0.0294236	+	0.0169877i
$489$		0			0
$490$	−151.079	+	34.4250i	−0.308325	+	0.0702550i
$491$	−166.583			−0.339274			−0.169637	−	0.985507i	$-0.554259\pi$
$491$	−166.583			−0.339274			−0.169637	+	0.985507i	$0.554259\pi$
$492$		0			0
$493$	339.658	+	196.101i	0.688961	+	0.397772i
$494$	31.1943	−	54.0301i	0.0631463	−	0.109373i
$495$		0			0
$496$			4.87410i			0.00982681i
$497$	664.603	−	260.698i	1.33723	−	0.524543i
$498$		0			0
$499$	−18.1531	−	31.4421i	−0.0363790	−	0.0630102i	0.847263	−	0.531174i	$-0.178249\pi$
$499$	−18.1531	−	31.4421i	−0.0363790	−	0.0630102i	−0.883642	+	0.468164i	$0.844916\pi$
$500$	19.3649	+	11.1803i	0.0387298	+	0.0223607i
$501$		0			0
$502$	121.705	−	70.2664i	0.242440	−	0.139973i
$503$			634.940i			1.26231i	0.775658	+	0.631153i	$0.217418\pi$
$503$			634.940i			1.26231i	−0.775658	+	0.631153i	$0.782582\pi$
$504$		0			0
$505$	−138.947			−0.275143
$506$	19.6100	+	33.9656i	0.0387550	+	0.0671256i
$507$		0			0
$508$	193.480	−	335.117i	0.380866	−	0.659680i
$509$	−500.864	+	289.174i	−0.984015	+	0.568121i	−0.903480	−	0.428631i	$-0.858996\pi$
$509$	−500.864	+	289.174i	−0.984015	+	0.568121i	−0.0805350	+	0.996752i	$0.525663\pi$
$510$		0			0
$511$	−569.685	−	85.9723i	−1.11484	−	0.168243i
$512$	22.6274			0.0441942
$513$		0			0
$514$	25.8639	+	14.9325i	0.0503189	+	0.0290516i
$515$	−198.945	+	344.583i	−0.386301	+	0.669093i
$516$		0			0
$517$			703.579i			1.36089i
$518$	51.7904	−	343.183i	0.0999815	−	0.662516i
$519$		0			0
$520$	22.9583	+	39.7650i	0.0441507	+	0.0764712i
$521$	550.974	+	318.105i	1.05753	+	0.610566i	0.924748	−	0.380579i	$-0.124275\pi$
$521$	550.974	+	318.105i	1.05753	+	0.610566i	0.132783	+	0.991145i	$0.457609\pi$
$522$		0			0
$523$	392.868	−	226.823i	0.751182	−	0.433695i	−0.0749389	−	0.997188i	$-0.523876\pi$
$523$	392.868	−	226.823i	0.751182	−	0.433695i	0.826121	+	0.563493i	$0.190543\pi$
$524$			362.229i			0.691276i
$525$		0			0
$526$	538.133			1.02307
$527$	5.66079	+	9.80477i	0.0107415	+	0.0186049i
$528$		0			0
$529$	261.968	−	453.742i	0.495214	−	0.857735i
$530$	−39.8199	+	22.9901i	−0.0751320	+	0.0433775i
$531$		0			0
$532$	−31.0652	−	79.1953i	−0.0583933	−	0.148863i
$533$	420.220			0.788406
$534$		0			0
$535$	164.546	+	95.0005i	0.307562	+	0.177571i
$536$	−69.9625	+	121.179i	−0.130527	+	0.226079i
$537$		0			0
$538$			23.7461i			0.0441377i
$539$	−134.162	−	588.790i	−0.248909	−	1.09237i
$540$		0			0
$541$	288.159	+	499.106i	0.532641	+	0.922562i	0.999274	+	0.0381102i	$0.0121338\pi$
$541$	288.159	+	499.106i	0.532641	+	0.922562i	−0.466632	+	0.884451i	$0.654533\pi$
$542$	−452.754	−	261.398i	−0.835340	−	0.482284i
$543$		0			0
$544$	45.5175	−	26.2795i	0.0836718	−	0.0483080i
$545$		−	386.523i		−	0.709216i
$546$		0			0
$547$	481.306			0.879901			0.439950	−	0.898022i	$-0.354996\pi$
$547$	481.306			0.879901			0.439950	+	0.898022i	$0.354996\pi$
$548$	1.26333	+	2.18815i	0.00230535	+	0.00399298i
$549$		0			0
$550$	−43.5723	+	75.4694i	−0.0792224	+	0.137217i
$551$	−222.136	+	128.250i	−0.403150	+	0.232759i
$552$		0			0
$553$	611.259	+	487.645i	1.10535	+	0.881817i
$554$	687.060			1.24018
$555$		0			0
$556$	−21.0145	−	12.1327i	−0.0377958	−	0.0218214i
$557$	54.4056	−	94.2333i	0.0976762	−	0.169180i	−0.813046	−	0.582199i	$-0.802192\pi$
$557$	54.4056	−	94.2333i	0.0976762	−	0.169180i	0.910722	+	0.413019i	$0.135526\pi$
$558$		0			0
$559$		−	246.980i		−	0.441825i
$560$	61.9089	+	9.34279i	0.110552	+	0.0166836i
$561$		0			0
$562$	254.724	+	441.195i	0.453245	+	0.785044i
$563$	−521.516	−	301.097i	−0.926316	−	0.534809i	−0.0406717	−	0.999173i	$-0.512950\pi$
$563$	−521.516	−	301.097i	−0.926316	−	0.534809i	−0.885645	+	0.464364i	$0.846283\pi$
$564$		0			0
$565$	158.912	−	91.7477i	0.281260	−	0.162385i
$566$		−	382.547i		−	0.675878i
$567$		0			0
$568$	−288.461			−0.507854
$569$	−4.76685	−	8.25642i	−0.00837759	−	0.0145104i	0.861806	−	0.507238i	$-0.169333\pi$
$569$	−4.76685	−	8.25642i	−0.00837759	−	0.0145104i	−0.870184	+	0.492727i	$0.836000\pi$
$570$		0			0
$571$	−491.103	+	850.615i	−0.860075	+	1.48969i	0.0117813	+	0.999931i	$0.496250\pi$
$571$	−491.103	+	850.615i	−0.860075	+	1.48969i	−0.871856	+	0.489762i	$0.837084\pi$
$572$	−154.973	+	89.4739i	−0.270932	+	0.156423i
$573$		0			0
$574$	357.337	−	447.919i	0.622538	−	0.780347i
$575$	−11.2514			−0.0195677
$576$		0			0
$577$	−454.001	−	262.117i	−0.786830	−	0.454276i	0.0520155	−	0.998646i	$-0.483435\pi$
$577$	−454.001	−	262.117i	−0.786830	−	0.454276i	−0.838845	+	0.544370i	$0.816769\pi$
$578$	−143.312	+	248.223i	−0.247944	+	0.429452i
$579$		0			0
$580$		−	188.779i		−	0.325481i
$581$	234.209	+	597.073i	0.403113	+	1.02767i
$582$		0			0
$583$	−89.5974	−	155.187i	−0.153683	−	0.266187i
$584$	201.605	+	116.397i	0.345215	+	0.199310i
$585$		0			0
$586$	11.7971	−	6.81106i	0.0201316	−	0.0116230i
$587$		−	651.322i		−	1.10958i	−0.831991	−	0.554789i	$-0.812799\pi$
$587$		−	651.322i		−	1.10958i	0.831991	−	0.554789i	$-0.187201\pi$
$588$		0			0
$589$	−7.40429			−0.0125710
$590$	91.4818	+	158.451i	0.155054	+	0.268561i
$591$		0			0
$592$	−70.1185	+	121.449i	−0.118443	+	0.205150i
$593$	610.904	−	352.706i	1.03019	−	0.594782i	0.113152	−	0.993578i	$-0.463905\pi$
$593$	610.904	−	352.706i	1.03019	−	0.594782i	0.917040	+	0.398796i	$0.130572\pi$
$594$		0			0
$595$	135.387	−	53.1071i	0.227541	−	0.0892556i
$596$	−579.451			−0.972233
$597$		0			0
$598$	−20.0089	−	11.5522i	−0.0334597	−	0.0193180i
$599$	−296.910	+	514.263i	−0.495676	+	0.858535i	−0.999988	−	0.00498610i	$-0.998413\pi$
$599$	−296.910	+	514.263i	−0.495676	+	0.858535i	0.504312	+	0.863522i	$0.331746\pi$
$600$		0			0
$601$			12.1644i			0.0202403i	0.999949	+	0.0101202i	$0.00322140\pi$
$601$			12.1644i			0.0202403i	−0.999949	+	0.0101202i	$0.996779\pi$
$602$	−263.260	−	210.021i	−0.437309	−	0.348873i
$603$		0			0
$604$	−117.303	−	203.175i	−0.194211	−	0.336383i
$605$	−59.8059	−	34.5290i	−0.0988528	−	0.0570727i
$606$		0			0
$607$	698.521	−	403.291i	1.15078	−	0.664401i	0.201700	−	0.979447i	$-0.435353\pi$
$607$	698.521	−	403.291i	1.15078	−	0.664401i	0.949076	+	0.315047i	$0.102020\pi$
$608$			34.3736i			0.0565354i
$609$		0			0
$610$	18.5370			0.0303886
$611$	−207.237	−	358.946i	−0.339178	−	0.587473i
$612$		0			0
$613$	397.237	−	688.035i	0.648021	−	1.12241i	−0.335574	−	0.942014i	$-0.608930\pi$
$613$	397.237	−	688.035i	0.648021	−	1.12241i	0.983595	−	0.180392i	$-0.0577365\pi$
$614$	−56.3887	+	32.5560i	−0.0918383	+	0.0530229i
$615$		0			0
$616$	−36.4110	+	241.273i	−0.0591087	+	0.391677i
$617$	−108.982			−0.176633			−0.0883164	−	0.996092i	$-0.528149\pi$
$617$	−108.982			−0.176633			−0.0883164	+	0.996092i	$0.528149\pi$
$618$		0			0
$619$	−310.725	−	179.397i	−0.501979	−	0.289818i	0.227551	−	0.973766i	$-0.426928\pi$
$619$	−310.725	−	179.397i	−0.501979	−	0.289818i	−0.729531	+	0.683948i	$0.760261\pi$
$620$	2.72470	−	4.71932i	0.00439468	−	0.00761181i
$621$		0			0
$622$		−	617.533i		−	0.992819i
$623$	557.878	−	699.296i	0.895470	−	1.12246i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−350.916	−	202.602i	−0.560569	−	0.323645i
$627$		0			0
$628$	−318.243	+	183.737i	−0.506756	+	0.292576i
$629$			325.743i			0.517875i
$630$		0			0
$631$	−612.351			−0.970446			−0.485223	−	0.874391i	$-0.661262\pi$
$631$	−612.351			−0.970446			−0.485223	+	0.874391i	$0.661262\pi$
$632$	−157.976	−	273.623i	−0.249962	−	0.432948i
$633$		0			0
$634$	−0.967913	+	1.67647i	−0.00152668	+	0.00264428i
$635$	−374.672	+	216.317i	−0.590035	+	0.340657i
$636$		0			0
$637$	241.872	+	260.866i	0.379705	+	0.409523i
$638$	735.713			1.15316
$639$		0			0
$640$	−21.9089	−	12.6491i	−0.0342327	−	0.0197642i
$641$	459.706	−	796.233i	0.717169	−	1.24217i	−0.244947	−	0.969536i	$-0.578771\pi$
$641$	459.706	−	796.233i	0.717169	−	1.24217i	0.962117	−	0.272637i	$-0.0878959\pi$
$642$		0			0
$643$			835.879i			1.29997i	0.759948	+	0.649984i	$0.225224\pi$
$643$			835.879i			1.29997i	−0.759948	+	0.649984i	$0.774776\pi$
$644$	−29.3283	+	11.5044i	−0.0455409	+	0.0178639i
$645$		0			0
$646$	39.9215	+	69.1461i	0.0617980	+	0.107037i
$647$	492.933	+	284.595i	0.761876	+	0.439869i	0.829969	−	0.557810i	$-0.188358\pi$
$647$	492.933	+	284.595i	0.761876	+	0.439869i	−0.0680932	+	0.997679i	$0.521692\pi$
$648$		0			0
$649$	−617.520	+	356.525i	−0.951495	+	0.549346i
$650$		−	51.3364i		−	0.0789791i
$651$		0			0
$652$	243.142			0.372917
$653$	196.162	+	339.763i	0.300402	+	0.520311i	0.976227	−	0.216751i	$-0.0695460\pi$
$653$	196.162	+	339.763i	0.300402	+	0.520311i	−0.675825	+	0.737062i	$0.736213\pi$
$654$		0			0
$655$	202.492	−	350.727i	0.309148	−	0.535460i
$656$	−200.506	+	115.762i	−0.305649	+	0.176467i
$657$		0			0
$658$	−558.831	−	84.3343i	−0.849288	−	0.128168i
$659$	−505.063			−0.766408			−0.383204	−	0.923664i	$-0.625179\pi$
$659$	−505.063			−0.766408			−0.383204	+	0.923664i	$0.625179\pi$
$660$		0			0
$661$	−255.815	−	147.695i	−0.387013	−	0.223442i	0.293852	−	0.955851i	$-0.405063\pi$
$661$	−255.815	−	147.695i	−0.387013	−	0.223442i	−0.680865	+	0.732409i	$0.738396\pi$
$662$	271.553	−	470.343i	0.410201	−	0.710488i
$663$		0			0
$664$		−	259.151i		−	0.390288i
$665$	−14.1927	+	94.0465i	−0.0213425	+	0.141423i
$666$		0			0
$667$	47.4948	+	82.2633i	0.0712065	+	0.123333i
$668$	163.945	+	94.6539i	0.245427	+	0.141698i
$669$		0			0
$670$	135.482	−	78.2204i	0.202212	−	0.116747i
$671$			72.2430i			0.107665i
$672$		0			0
$673$	−624.569			−0.928038			−0.464019	−	0.885825i	$-0.653593\pi$
$673$	−624.569			−0.928038			−0.464019	+	0.885825i	$0.653593\pi$
$674$	100.373	+	173.850i	0.148921	+	0.257938i
$675$		0			0
$676$	−116.291	+	201.423i	−0.172029	+	0.297963i
$677$	676.847	−	390.778i	0.999774	−	0.577220i	0.0915926	−	0.995797i	$-0.470804\pi$
$677$	676.847	−	390.778i	0.999774	−	0.577220i	0.908181	+	0.418577i	$0.137471\pi$
$678$		0			0
$679$	−157.067	−	400.415i	−0.231321	−	0.589712i
$680$	−58.7628			−0.0864159
$681$		0			0
$682$	18.3923	+	10.6188i	0.0269681	+	0.0155701i
$683$	50.8525	−	88.0791i	0.0744546	−	0.128959i	−0.826394	−	0.563092i	$-0.809612\pi$
$683$	50.8525	−	88.0791i	0.0744546	−	0.128959i	0.900849	+	0.434133i	$0.142945\pi$
$684$		0			0
$685$		−	2.82490i		−	0.00412393i
$686$	483.739	−	35.9855i	0.705158	−	0.0524570i
$687$		0			0
$688$	68.0380	+	117.845i	0.0988925	+	0.171287i
$689$	91.4200	+	52.7814i	0.132685	+	0.0766057i
$690$		0			0
$691$	634.684	−	366.435i	0.918501	−	0.530297i	0.0353446	−	0.999375i	$-0.488747\pi$
$691$	634.684	−	366.435i	0.918501	−	0.530297i	0.883157	+	0.469078i	$0.155414\pi$
$692$			521.384i			0.753445i
$693$		0			0
$694$	354.051			0.510160
$695$	13.5648	+	23.4949i	0.0195177	+	0.0338056i
$696$		0			0
$697$	−268.893	+	465.736i	−0.385786	+	0.668201i
$698$	239.055	−	138.019i	0.342486	−	0.197734i
$699$		0			0
$700$	−54.7203	−	43.6543i	−0.0781718	−	0.0623632i
$701$	795.928			1.13542			0.567709	−	0.823229i	$-0.307830\pi$
$701$	795.928			1.13542			0.567709	+	0.823229i	$0.307830\pi$
$702$		0			0
$703$	−184.494	−	106.518i	−0.262438	−	0.151519i
$704$	49.2964	−	85.3839i	0.0700233	−	0.121284i
$705$		0			0
$706$			201.100i			0.284845i
$707$	430.104	+	64.9079i	0.608351	+	0.0918075i
$708$		0			0
$709$	−514.532	−	891.196i	−0.725715	−	1.25698i	−0.958679	−	0.284490i	$-0.908176\pi$
$709$	−514.532	−	891.196i	−0.725715	−	1.25698i	0.232964	−	0.972485i	$-0.425158\pi$
$710$	279.301	+	161.255i	0.393382	+	0.227119i
$711$		0			0
$712$	−313.032	+	180.729i	−0.439651	+	0.253833i
$713$			2.74203i			0.00384576i
$714$		0			0
$715$	200.070			0.279818
$716$	306.529	+	530.923i	0.428113	+	0.741513i
$717$		0			0
$718$	−464.489	+	804.518i	−0.646920	+	1.12050i
$719$	136.549	−	78.8367i	0.189915	−	0.109648i	−0.402028	−	0.915628i	$-0.631694\pi$
$719$	136.549	−	78.8367i	0.189915	−	0.109648i	0.591943	+	0.805980i	$0.298361\pi$
$720$		0			0
$721$	776.792	−	973.702i	1.07738	−	1.35049i
$722$	458.314			0.634784
$723$		0			0
$724$	545.397	+	314.885i	0.753311	+	0.434925i
$725$	−105.531	+	182.784i	−0.145559	+	0.252116i
$726$		0			0
$727$		−	13.5224i		−	0.0186003i	−0.999957	−	0.00930013i	$-0.997040\pi$
$727$		−	13.5224i		−	0.0186003i	0.999957	−	0.00930013i	$-0.00296037\pi$
$728$	−52.4905	−	133.815i	−0.0721023	−	0.183812i
$729$		0			0
$730$	−130.136	−	225.402i	−0.178268	−	0.308769i
$731$	273.732	+	158.039i	0.374462	+	0.216196i
$732$		0			0
$733$	341.622	−	197.235i	0.466060	−	0.269080i	−0.248529	−	0.968624i	$-0.579947\pi$
$733$	341.622	−	197.235i	0.466060	−	0.269080i	0.714589	+	0.699545i	$0.246614\pi$
$734$			725.707i			0.988701i
$735$		0			0
$736$	12.7295			0.0172956
$737$	304.843	+	528.003i	0.413626	+	0.716422i
$738$		0			0
$739$	−475.080	+	822.863i	−0.642869	+	1.11348i	0.341920	+	0.939729i	$0.388923\pi$
$739$	−475.080	+	822.863i	−0.642869	+	1.11348i	−0.984789	+	0.173753i	$0.944411\pi$
$740$	135.784	−	78.3949i	0.183492	−	0.105939i
$741$		0			0
$742$	134.000	−	52.5630i	0.180593	−	0.0708396i
$743$	−425.883			−0.573194			−0.286597	−	0.958051i	$-0.592524\pi$
$743$	−425.883			−0.573194			−0.286597	+	0.958051i	$0.592524\pi$
$744$		0			0
$745$	561.051	+	323.923i	0.753088	+	0.434796i
$746$	447.262	−	774.680i	0.599547	−	1.03845i
$747$		0			0
$748$		−	229.012i		−	0.306166i
$749$	−464.964	−	370.935i	−0.620779	−	0.495240i
$750$		0			0
$751$	315.874	+	547.109i	0.420604	+	0.728508i	0.995999	−	0.0893683i	$-0.0284848\pi$
$751$	315.874	+	547.109i	0.420604	+	0.728508i	−0.575395	+	0.817876i	$0.695151\pi$
$752$	197.764	+	114.179i	0.262985	+	0.151834i
$753$		0			0
$754$	−375.340	+	216.702i	−0.497798	+	0.287404i
$755$			262.298i			0.347414i
$756$		0			0
$757$	882.903			1.16632			0.583159	−	0.812358i	$-0.301816\pi$
$757$	882.903			1.16632			0.583159	+	0.812358i	$0.301816\pi$
$758$	436.412	+	755.889i	0.575742	+	0.997214i
$759$		0			0
$760$	19.2154	−	33.2820i	0.0252834	−	0.0437922i
$761$	981.049	−	566.409i	1.28916	−	0.744295i	0.310653	−	0.950523i	$-0.399452\pi$
$761$	981.049	−	566.409i	1.28916	−	0.744295i	0.978504	+	0.206228i	$0.0661189\pi$
$762$		0			0
$763$	−180.560	+	1196.46i	−0.236645	+	1.56810i
$764$	181.578			0.237668
$765$		0			0
$766$	213.041	+	122.999i	0.278121	+	0.160573i
$767$	210.027	−	363.778i	0.273829	−	0.474287i
$768$		0			0
$769$		−	41.6421i		−	0.0541510i	−0.999633	−	0.0270755i	$-0.991381\pi$
$769$		−	41.6421i		−	0.0541510i	0.999633	−	0.0270755i	$-0.00861944\pi$
$770$	170.130	−	213.257i	0.220949	−	0.276957i
$771$		0			0
$772$	229.655	+	397.774i	0.297481	+	0.515252i
$773$	−1114.00	−	643.167i	−1.44114	−	0.832041i	−0.443211	−	0.896417i	$-0.646161\pi$
$773$	−1114.00	−	643.167i	−1.44114	−	0.832041i	−0.997926	+	0.0643767i	$0.979494\pi$
$774$		0			0
$775$	−5.27637	+	3.04631i	−0.00680821	+	0.00393072i
$776$			173.794i			0.223962i
$777$		0			0
$778$	−277.458			−0.356629
$779$	−175.855	−	304.591i	−0.225745	−	0.391002i
$780$		0			0
$781$	−628.446	+	1088.50i	−0.804668	+	1.39373i
$782$	25.6068	−	14.7841i	0.0327453	−	0.0189055i
$783$		0			0
$784$	−187.271	−	57.8402i	−0.238866	−	0.0737758i
$785$	410.850			0.523375
$786$		0			0
$787$	−863.836	−	498.736i	−1.09763	−	0.633718i	−0.162034	−	0.986785i	$-0.551805\pi$
$787$	−863.836	−	498.736i	−1.09763	−	0.633718i	−0.935598	+	0.353067i	$0.885139\pi$
$788$	227.989	−	394.889i	0.289326	−	0.501128i
$789$		0			0
$790$			353.246i			0.447146i
$791$	−534.761	+	209.766i	−0.676057	+	0.265191i
$792$		0			0
$793$	−21.2790	−	36.8563i	−0.0268335	−	0.0464770i
$794$	488.307	+	281.924i	0.614996	+	0.355068i
$795$		0			0
$796$	−19.1325	+	11.0461i	−0.0240358	+	0.0138771i
$797$		−	971.547i		−	1.21901i	−0.792784	−	0.609503i	$-0.791369\pi$
$797$		−	971.547i		−	1.21901i	0.792784	−	0.609503i	$-0.208631\pi$
$798$		0			0
$799$	530.433			0.663871
$800$	14.1421	+	24.4949i	0.0176777	+	0.0306186i
$801$		0			0
$802$	245.507	−	425.230i	0.306118	−	0.530212i
$803$	878.441	−	507.168i	1.09395	−	0.631592i
$804$		0			0
$805$	34.8282	+	5.25599i	0.0432648	+	0.00652918i
$806$	−12.5109			−0.0155223
$807$		0			0
$808$	−152.209	−	87.8781i	−0.188378	−	0.108760i
$809$	−652.112	+	1129.49i	−0.806072	+	1.39616i	0.109493	+	0.993988i	$0.465077\pi$
$809$	−652.112	+	1129.49i	−0.806072	+	1.39616i	−0.915565	+	0.402170i	$0.868256\pi$
$810$		0			0
$811$		−	210.763i		−	0.259880i	−0.991522	−	0.129940i	$-0.958521\pi$
$811$		−	210.763i		−	0.259880i	0.991522	−	0.129940i	$-0.0414785\pi$
$812$	−88.1861	+	584.354i	−0.108604	+	0.719648i
$813$		0			0
$814$	305.523	+	529.181i	0.375335	+	0.650099i
$815$	−235.421	−	135.920i	−0.288860	−	0.166773i
$816$		0			0
$817$	−179.020	+	103.357i	−0.219119	+	0.126508i
$818$		−	479.115i		−	0.585716i
$819$		0			0
$820$	258.852			0.315673
$821$	−362.253	−	627.440i	−0.441234	−	0.764239i	0.556548	−	0.830816i	$-0.312126\pi$
$821$	−362.253	−	627.440i	−0.441234	−	0.764239i	−0.997781	+	0.0665766i	$0.978792\pi$
$822$		0			0
$823$	223.018	−	386.279i	0.270982	−	0.469355i	−0.698131	−	0.715970i	$-0.745985\pi$
$823$	223.018	−	386.279i	0.270982	−	0.469355i	0.969114	+	0.246615i	$0.0793182\pi$
$824$	−435.867	+	251.648i	−0.528964	+	0.305398i
$825$		0			0
$826$	−209.158	−	533.212i	−0.253218	−	0.645535i
$827$	702.737			0.849743			0.424871	−	0.905254i	$-0.360319\pi$
$827$	702.737			0.849743			0.424871	+	0.905254i	$0.360319\pi$
$828$		0			0
$829$	−361.023	−	208.437i	−0.435492	−	0.251431i	0.266192	−	0.963920i	$-0.414235\pi$
$829$	−361.023	−	208.437i	−0.435492	−	0.251431i	−0.701683	+	0.712489i	$0.747568\pi$
$830$	−144.870	+	250.922i	−0.174542	+	0.302316i
$831$		0			0
$832$			58.0805i			0.0698083i
$833$	−443.892	+	101.145i	−0.532883	+	0.121423i
$834$		0			0
$835$	−105.826	−	183.297i	−0.126738	−	0.219517i
$836$	129.708	+	74.8867i	0.155153	+	0.0895774i
$837$		0			0
$838$	−452.560	+	261.286i	−0.540047	+	0.311797i
$839$			359.231i			0.428166i	0.976815	+	0.214083i	$0.0686763\pi$
$839$			359.231i			0.428166i	−0.976815	+	0.214083i	$0.931324\pi$
$840$		0			0
$841$	940.871			1.11875
$842$	153.846	+	266.469i	0.182715	+	0.316472i
$843$		0			0
$844$	−151.187	+	261.864i	−0.179132	+	0.310265i
$845$	225.197	−	130.018i	0.266506	−	0.153867i
$846$		0			0
$847$	168.996	+	134.820i	0.199523	+	0.159174i
$848$	−58.1607			−0.0685858
$849$		0			0
$850$	56.8969	+	32.8494i	0.0669375	+	0.0386464i
$851$	−39.4467	+	68.3236i	−0.0463533	+	0.0802863i
$852$		0			0
$853$			988.948i			1.15938i	0.814838	+	0.579688i	$0.196826\pi$
$853$			988.948i			1.15938i	−0.814838	+	0.579688i	$0.803174\pi$
$854$	−57.3804	−	8.65939i	−0.0671902	−	0.0101398i
$855$		0			0
$856$	120.167	+	208.136i	0.140382	+	0.243149i
$857$	−312.893	−	180.649i	−0.365103	−	0.210792i	0.306214	−	0.951963i	$-0.400938\pi$
$857$	−312.893	−	180.649i	−0.365103	−	0.210792i	−0.671317	+	0.741170i	$0.734271\pi$
$858$		0			0
$859$	−608.464	+	351.297i	−0.708339	+	0.408960i	−0.810446	−	0.585814i	$-0.800775\pi$
$859$	−608.464	+	351.297i	−0.708339	+	0.408960i	0.102106	+	0.994773i	$0.467442\pi$
$860$		−	152.138i		−	0.176904i
$861$		0			0
$862$	404.226			0.468940
$863$	551.208	+	954.720i	0.638711	+	1.10628i	0.985716	+	0.168417i	$0.0538655\pi$
$863$	551.208	+	954.720i	0.638711	+	1.10628i	−0.347005	+	0.937863i	$0.612801\pi$
$864$		0			0
$865$	291.462	−	504.828i	0.336951	−	0.583616i
$866$	−788.111	+	455.016i	−0.910059	+	0.525423i
$867$		0			0
$868$	−10.6388	+	13.3356i	−0.0122566	+	0.0153636i
$869$	−1376.68			−1.58421
$870$		0			0
$871$	−311.044	−	179.581i	−0.357111	−	0.206178i
$872$	244.458	−	423.414i	0.280342	−	0.485567i
$873$		0			0
$874$			19.3376i			0.0221254i
$875$	28.5792	+	72.8576i	0.0326619	+	0.0832658i
$876$		0			0
$877$	−334.061	−	578.610i	−0.380913	−	0.659761i	0.610280	−	0.792186i	$-0.291057\pi$
$877$	−334.061	−	578.610i	−0.380913	−	0.659761i	−0.991193	+	0.132425i	$0.957724\pi$
$878$	−698.640	−	403.360i	−0.795717	−	0.459408i
$879$		0			0
$880$	−95.4621	+	55.1151i	−0.108480	+	0.0626308i
$881$		−	15.3854i		−	0.0174636i	−0.999962	−	0.00873178i	$-0.997221\pi$
$881$		−	15.3854i		−	0.0174636i	0.999962	−	0.00873178i	$-0.00277945\pi$
$882$		0			0
$883$	51.0884			0.0578577			0.0289289	−	0.999581i	$-0.490790\pi$
$883$	51.0884			0.0578577			0.0289289	+	0.999581i	$0.490790\pi$
$884$	67.4549	+	116.835i	0.0763064	+	0.132167i
$885$		0			0
$886$	−46.6796	+	80.8514i	−0.0526857	+	0.0912543i
$887$	−26.3653	+	15.2220i	−0.0297241	+	0.0171612i	−0.514788	−	0.857317i	$-0.672130\pi$
$887$	−26.3653	+	15.2220i	−0.0297241	+	0.0171612i	0.485064	+	0.874478i	$0.338796\pi$
$888$		0			0
$889$	1260.83	−	494.574i	1.41825	−	0.556326i
$890$	404.122			0.454070
$891$		0			0
$892$	534.486	+	308.586i	0.599200	+	0.345948i
$893$	−173.451	+	300.426i	−0.194234	+	0.336423i
$894$		0			0
$895$		−	685.419i		−	0.765831i
$896$	61.9089	+	49.3891i	0.0690948	+	0.0551218i
$897$		0			0
$898$	364.211	+	630.832i	0.405580	+	0.702485i
$899$	44.5454	+	25.7183i	0.0495500	+	0.0286077i
$900$		0			0
$901$	−116.997	+	67.5480i	−0.129852	+	0.0749700i
$902$			1008.80i			1.11841i
$903$		0			0
$904$	232.105			0.256754
$905$	−352.053	−	609.773i	−0.389008	−	0.673782i
$906$		0			0
$907$	345.008	−	597.571i	0.380384	−	0.658844i	−0.610733	−	0.791836i	$-0.709125\pi$
$907$	345.008	−	597.571i	0.380384	−	0.658844i	0.991117	+	0.132993i	$0.0424586\pi$
$908$	173.937	−	100.422i	0.191560	−	0.110597i
$909$		0			0
$910$	−23.9813	+	158.909i	−0.0263531	+	0.174625i
$911$	264.542			0.290386			0.145193	−	0.989403i	$-0.453620\pi$
$911$	264.542			0.290386			0.145193	+	0.989403i	$0.453620\pi$
$912$		0			0
$913$	−977.899	−	564.590i	−1.07108	−	0.618390i
$914$	−55.8806	+	96.7881i	−0.0611385	+	0.105895i
$915$		0			0
$916$			639.993i			0.698682i
$917$	−790.641	+	991.063i	−0.862204	+	1.08077i
$918$		0			0
$919$	−269.068	−	466.039i	−0.292783	−	0.507115i	0.681684	−	0.731647i	$-0.261248\pi$
$919$	−269.068	−	466.039i	−0.292783	−	0.507115i	−0.974467	+	0.224532i	$0.927915\pi$
$920$	−12.3253	−	7.11603i	−0.0133971	−	0.00773481i
$921$		0			0
$922$	11.7369	−	6.77632i	0.0127299	−	0.00734959i
$923$		−	740.428i		−	0.802198i
$924$		0			0
$925$	−175.296			−0.189510
$926$	164.122	+	284.267i	0.177237	+	0.306984i
$927$		0			0
$928$	119.394	−	206.797i	0.128658	−	0.222841i
$929$	770.069	−	444.600i	0.828922	−	0.478579i	−0.0245611	−	0.999698i	$-0.507819\pi$
$929$	770.069	−	444.600i	0.828922	−	0.478579i	0.853484	+	0.521120i	$0.174485\pi$
$930$		0			0
$931$	87.8657	−	284.486i	0.0943778	−	0.305570i
$932$	−621.578			−0.666929
$933$		0			0
$934$	839.607	+	484.747i	0.898937	+	0.519001i
$935$	−128.022	+	221.740i	−0.136921	+	0.237155i
$936$		0			0
$937$		−	997.355i		−	1.06441i	−0.846615	−	0.532206i	$-0.821363\pi$
$937$		−	997.355i		−	1.06441i	0.846615	−	0.532206i	$-0.178637\pi$
$938$	−455.916	+	178.838i	−0.486051	+	0.190659i
$939$		0			0
$940$	−127.656	−	221.107i	−0.135805	−	0.235221i
$941$	959.098	+	553.735i	1.01923	+	0.588454i	0.913882	−	0.405981i	$-0.133070\pi$
$941$	959.098	+	553.735i	1.01923	+	0.588454i	0.105351	+	0.994435i	$0.466403\pi$
$942$		0			0
$943$	−112.799	+	65.1245i	−0.119617	+	0.0690609i
$944$			231.433i			0.245162i
$945$		0			0
$946$	592.915			0.626760
$947$	293.801	+	508.878i	0.310244	+	0.537358i	0.978415	−	0.206650i	$-0.0662560\pi$
$947$	293.801	+	508.878i	0.310244	+	0.537358i	−0.668171	+	0.744008i	$0.732923\pi$
$948$		0			0
$949$	−298.770	+	517.485i	−0.314826	+	0.545295i
$950$	−37.2105	+	21.4835i	−0.0391689	+	0.0226142i
$951$		0			0
$952$	181.897	+	27.4504i	0.191068	+	0.0288345i
$953$	−441.771			−0.463558			−0.231779	−	0.972768i	$-0.574455\pi$
$953$	−441.771			−0.463558			−0.231779	+	0.972768i	$0.574455\pi$
$954$		0			0
$955$	−175.812	−	101.505i	−0.184097	−	0.106288i
$956$	136.263	−	236.015i	0.142535	−	0.246877i
$957$		0			0
$958$		−	889.684i		−	0.928688i
$959$	−1.31962	+	8.74431i	−0.00137604	+	0.00911815i
$960$		0			0
$961$	−479.758	−	830.965i	−0.499227	−	0.864687i
$962$	−311.738	−	179.982i	−0.324051	−	0.187091i
$963$		0			0
$964$	−668.883	+	386.179i	−0.693862	+	0.400601i
$965$		−	513.524i		−	0.532150i
$966$		0			0
$967$	1581.63			1.63561			0.817804	−	0.575497i	$-0.195191\pi$
$967$	1581.63			1.63561			0.817804	+	0.575497i	$0.195191\pi$
$968$	−43.6761	−	75.6492i	−0.0451199	−	0.0781500i
$969$		0			0
$970$	97.1539	−	168.275i	0.100159	−	0.173480i
$971$	−517.033	+	298.509i	−0.532475	+	0.307425i	−0.742024	−	0.670374i	$-0.766134\pi$
$971$	−517.033	+	298.509i	−0.532475	+	0.307425i	0.209549	+	0.977798i	$0.432801\pi$
$972$		0			0
$973$	−31.0136	−	79.0638i	−0.0318742	−	0.0812577i
$974$	−705.365			−0.724194
$975$		0			0
$976$	20.3063	+	11.7239i	0.0208056	+	0.0120121i
$977$	−105.721	+	183.114i	−0.108210	+	0.187425i	−0.915045	−	0.403351i	$-0.867845\pi$
$977$	−105.721	+	183.114i	−0.108210	+	0.187425i	0.806835	+	0.590777i	$0.201179\pi$
$978$		0			0
$979$			1574.96i			1.60874i
$980$	148.991	+	160.691i	0.152032	+	0.163971i
$981$		0			0
$982$	117.792	+	204.022i	0.119951	+	0.207762i
$983$	513.418	+	296.422i	0.522297	+	0.301548i	0.737874	−	0.674939i	$-0.235830\pi$
$983$	513.418	+	296.422i	0.522297	+	0.301548i	−0.215577	+	0.976487i	$0.569163\pi$
$984$		0			0
$985$	−441.499	+	254.899i	−0.448222	+	0.258781i
$986$		−	554.659i		−	0.562534i
$987$		0			0
$988$	−88.2308			−0.0893024
$989$	38.2762	+	66.2964i	0.0387020	+	0.0670338i
$990$		0			0
$991$	189.970	−	329.038i	0.191696	−	0.332027i	−0.754117	−	0.656740i	$-0.771935\pi$
$991$	189.970	−	329.038i	0.191696	−	0.332027i	0.945812	+	0.324714i	$0.105268\pi$
$992$	5.96953	−	3.44651i	0.00601767	−	0.00347430i
$993$		0			0
$994$	−789.233	−	629.628i	−0.793997	−	0.633428i
$995$	24.6999			0.0248240
$996$		0			0
$997$	178.950	+	103.317i	0.179489	+	0.103628i	0.587052	−	0.809549i	$-0.300288\pi$
$997$	178.950	+	103.317i	0.179489	+	0.103628i	−0.407564	+	0.913177i	$0.633622\pi$
$998$	−25.6724	+	44.4658i	−0.0257238	+	0.0445550i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.v.b.451.2		8
3.2	odd	2		210.3.o.a.31.3	✓	8
7.5	odd	6	inner	630.3.v.b.271.2		8
15.2	even	4		1050.3.q.c.199.4		16
15.8	even	4		1050.3.q.c.199.5		16
15.14	odd	2		1050.3.p.b.451.2		8
21.5	even	6		210.3.o.a.61.3	yes	8
21.11	odd	6		1470.3.f.a.391.1		8
21.17	even	6		1470.3.f.a.391.4		8
105.47	odd	12		1050.3.q.c.649.5		16
105.68	odd	12		1050.3.q.c.649.4		16
105.89	even	6		1050.3.p.b.901.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.a.31.3	✓	8	3.2	odd	2
210.3.o.a.61.3	yes	8	21.5	even	6
630.3.v.b.271.2		8	7.5	odd	6	inner
630.3.v.b.451.2		8	1.1	even	1	trivial
1050.3.p.b.451.2		8	15.14	odd	2
1050.3.p.b.901.2		8	105.89	even	6
1050.3.q.c.199.4		16	15.2	even	4
1050.3.q.c.199.5		16	15.8	even	4
1050.3.q.c.649.4		16	105.68	odd	12
1050.3.q.c.649.5		16	105.47	odd	12
1470.3.f.a.391.1		8	21.11	odd	6
1470.3.f.a.391.4		8	21.17	even	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	630.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-6.51658 + 2.55620i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-6.51658 + 2.55620i) q^{7} +2.82843 q^{8} +(-2.73861 - 1.58114i) q^{10} +(6.16205 - 10.6730i) q^{11} +7.26007i q^{13} +(7.73861 + 6.17364i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-8.04643 - 4.64561i) q^{17} +(5.26235 - 3.03822i) q^{19} +4.47214i q^{20} -17.4289 q^{22} +(-1.12514 - 1.94880i) q^{23} +(2.50000 - 4.33013i) q^{25} +(8.89173 - 5.13364i) q^{26} +(2.08911 - 13.8433i) q^{28} -42.2122 q^{29} +(-1.05527 - 0.609262i) q^{31} +(-2.82843 + 4.89898i) q^{32} +13.1398i q^{34} +(-9.76139 + 12.2358i) q^{35} +(-17.5296 - 30.3622i) q^{37} +(-7.44209 - 4.29669i) q^{38} +(5.47723 - 3.16228i) q^{40} -57.8811i q^{41} -34.0190 q^{43} +(12.3241 + 21.3460i) q^{44} +(-1.59119 + 2.75603i) q^{46} +(-49.4411 + 28.5448i) q^{47} +(35.9317 - 33.3154i) q^{49} -7.07107 q^{50} +(-12.5748 - 7.26007i) q^{52} +(7.27009 - 12.5922i) q^{53} -27.5575i q^{55} +(-18.4317 + 7.23003i) q^{56} +(29.8485 + 51.6992i) q^{58} +(-50.1067 - 28.9291i) q^{59} +(-5.07658 + 2.93096i) q^{61} +1.72325i q^{62} +8.00000 q^{64} +(8.11700 + 14.0591i) q^{65} +(-24.7355 + 42.8431i) q^{67} +(16.0929 - 9.29122i) q^{68} +(21.8881 + 3.30318i) q^{70} -101.986 q^{71} +(71.2783 + 41.1525i) q^{73} +(-24.7906 + 42.9387i) q^{74} +12.1529i q^{76} +(-12.8732 + 85.3029i) q^{77} +(-55.8530 - 96.7403i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(-70.8895 + 40.9281i) q^{82} -91.6237i q^{83} -20.7758 q^{85} +(24.0551 + 41.6646i) q^{86} +(17.4289 - 30.1878i) q^{88} +(-110.673 + 63.8973i) q^{89} +(-18.5582 - 47.3108i) q^{91} +4.50057 q^{92} +(69.9203 + 40.3685i) q^{94} +(6.79367 - 11.7670i) q^{95} +61.4455i q^{97} +(-66.2104 - 20.4496i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 8 * q - 8 * q^4	\( 8 q - 8 q^{4} + 4 q^{11} + 40 q^{14} - 16 q^{16} - 84 q^{17} + 108 q^{19} - 48 q^{22} - 12 q^{23} + 20 q^{25} + 96 q^{26} - 72 q^{29} - 132 q^{31} - 100 q^{35} - 96 q^{37} + 168 q^{38} - 112 q^{43} + 8 q^{44} + 8 q^{46} + 24 q^{47} + 156 q^{49} + 48 q^{52} - 32 q^{53} - 16 q^{56} + 104 q^{58} - 132 q^{59} + 96 q^{61} + 64 q^{64} - 20 q^{65} - 120 q^{67} + 168 q^{68} - 8 q^{71} + 24 q^{73} + 16 q^{74} + 216 q^{77} + 12 q^{79} + 24 q^{82} + 120 q^{85} + 40 q^{86} + 48 q^{88} - 492 q^{89} - 308 q^{91} + 48 q^{92} + 480 q^{94} + 40 q^{95}+O(q^{100}) \) 8 * q - 8 * q^4 + 4 * q^11 + 40 * q^14 - 16 * q^16 - 84 * q^17 + 108 * q^19 - 48 * q^22 - 12 * q^23 + 20 * q^25 + 96 * q^26 - 72 * q^29 - 132 * q^31 - 100 * q^35 - 96 * q^37 + 168 * q^38 - 112 * q^43 + 8 * q^44 + 8 * q^46 + 24 * q^47 + 156 * q^49 + 48 * q^52 - 32 * q^53 - 16 * q^56 + 104 * q^58 - 132 * q^59 + 96 * q^61 + 64 * q^64 - 20 * q^65 - 120 * q^67 + 168 * q^68 - 8 * q^71 + 24 * q^73 + 16 * q^74 + 216 * q^77 + 12 * q^79 + 24 * q^82 + 120 * q^85 + 40 * q^86 + 48 * q^88 - 492 * q^89 - 308 * q^91 + 48 * q^92 + 480 * q^94 + 40 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more