LMFDB - Embedded newform 630.3.v.c.451.7

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + \cdots + 101626561 $ x^16 + 92x^14 - 112x^13 + 5846x^12 - 7728x^11 + 197216x^10 - 298200x^9 + 4836403x^8 - 6808704x^7 + 64376800x^6 - 91953512x^5 + 595763862x^4 - 630430976x^3 + 1087013404x^2 + 294123256x + 101626561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 7 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.7
Root			$-3.67087 + 6.35814i$ of defining polynomial
Character	$\chi$	$=$	630.451
Dual form			630.3.v.c.271.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-2.59373 - 6.50174i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-2.59373 - 6.50174i) q^{7} -2.82843 q^{8} +(2.73861 + 1.58114i) q^{10} +(5.13478 - 8.89370i) q^{11} +7.02340i q^{13} +(6.12892 - 7.77408i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-27.4947 - 15.8741i) q^{17} +(-26.9408 + 15.5543i) q^{19} +4.47214i q^{20} +14.5234 q^{22} +(-11.8441 - 20.5146i) q^{23} +(2.50000 - 4.33013i) q^{25} +(-8.60187 + 4.96629i) q^{26} +(13.8551 + 2.00927i) q^{28} -9.19673 q^{29} +(17.4511 + 10.0754i) q^{31} +(2.82843 - 4.89898i) q^{32} -44.8986i q^{34} +(-12.2919 - 9.69068i) q^{35} +(-24.0823 - 41.7118i) q^{37} +(-38.1001 - 21.9971i) q^{38} +(-5.47723 + 3.16228i) q^{40} -65.1226i q^{41} -3.03497 q^{43} +(10.2696 + 17.7874i) q^{44} +(16.7501 - 29.0120i) q^{46} +(53.6472 - 30.9732i) q^{47} +(-35.5451 + 33.7275i) q^{49} +7.07107 q^{50} +(-12.1649 - 7.02340i) q^{52} +(0.690751 - 1.19642i) q^{53} -22.9634i q^{55} +(7.33617 + 18.3897i) q^{56} +(-6.50307 - 11.2636i) q^{58} +(95.1064 + 54.9097i) q^{59} +(-34.3741 + 19.8459i) q^{61} +28.4976i q^{62} +8.00000 q^{64} +(7.85240 + 13.6008i) q^{65} +(-7.95952 + 13.7863i) q^{67} +(54.9893 - 31.7481i) q^{68} +(3.17693 - 21.9068i) q^{70} -53.3489 q^{71} +(62.6830 + 36.1901i) q^{73} +(34.0576 - 58.9894i) q^{74} -62.2172i q^{76} +(-71.1427 - 10.3171i) q^{77} +(-53.2229 - 92.1847i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(79.7586 - 46.0486i) q^{82} +49.4298i q^{83} -70.9909 q^{85} +(-2.14605 - 3.71707i) q^{86} +(-14.5234 + 25.1552i) q^{88} +(142.807 - 82.4499i) q^{89} +(45.6643 - 18.2168i) q^{91} +47.3765 q^{92} +(75.8686 + 43.8027i) q^{94} +(-34.7805 + 60.2416i) q^{95} -49.4799i q^{97} +(-66.4418 - 19.6848i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 4 q^{7}+O(q^{10}) $ 16 * q - 16 * q^4 + 4 * q^7	$ 16 q - 16 q^{4} + 4 q^{7} + 4 q^{11} - 8 q^{14} - 32 q^{16} - 12 q^{17} - 72 q^{19} - 48 q^{22} + 12 q^{23} + 40 q^{25} + 32 q^{28} - 72 q^{29} + 120 q^{31} + 20 q^{35} + 44 q^{37} + 72 q^{38} - 56 q^{43} + 8 q^{44} + 8 q^{46} + 24 q^{47} - 40 q^{49} - 72 q^{52} - 32 q^{53} - 16 q^{56} - 88 q^{58} - 132 q^{59} + 96 q^{61} + 128 q^{64} - 20 q^{65} - 164 q^{67} + 24 q^{68} + 136 q^{71} - 348 q^{73} + 112 q^{74} - 96 q^{77} + 280 q^{79} + 264 q^{82} + 120 q^{85} + 88 q^{86} + 48 q^{88} + 300 q^{89} - 272 q^{91} - 48 q^{92} - 200 q^{95} - 384 q^{98}+O(q^{100}) $ 16 * q - 16 * q^4 + 4 * q^7 + 4 * q^11 - 8 * q^14 - 32 * q^16 - 12 * q^17 - 72 * q^19 - 48 * q^22 + 12 * q^23 + 40 * q^25 + 32 * q^28 - 72 * q^29 + 120 * q^31 + 20 * q^35 + 44 * q^37 + 72 * q^38 - 56 * q^43 + 8 * q^44 + 8 * q^46 + 24 * q^47 - 40 * q^49 - 72 * q^52 - 32 * q^53 - 16 * q^56 - 88 * q^58 - 132 * q^59 + 96 * q^61 + 128 * q^64 - 20 * q^65 - 164 * q^67 + 24 * q^68 + 136 * q^71 - 348 * q^73 + 112 * q^74 - 96 * q^77 + 280 * q^79 + 264 * q^82 + 120 * q^85 + 88 * q^86 + 48 * q^88 + 300 * q^89 - 272 * q^91 - 48 * q^92 - 200 * q^95 - 384 * q^98

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
$7$	−2.59373	−	6.50174i	−0.370533	−	0.928819i
$7$	−2.59373	−	6.50174i	−0.370533	−	0.928819i
$8$	−2.82843			−0.353553
$9$		0			0
$10$	2.73861	+	1.58114i	0.273861	+	0.158114i
$11$	5.13478	−	8.89370i	0.466798	−	0.808518i	−0.532482	−	0.846441i	$-0.678741\pi$
$11$	5.13478	−	8.89370i	0.466798	−	0.808518i	0.999281	+	0.0379228i	$0.0120741\pi$
$12$		0			0
$13$			7.02340i			0.540261i	0.962824	+	0.270131i	$0.0870669\pi$
$13$			7.02340i			0.540261i	−0.962824	+	0.270131i	$0.912933\pi$
$14$	6.12892	−	7.77408i	0.437780	−	0.555291i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−27.4947	−	15.8741i	−1.61733	−	0.933768i	−0.987606	−	0.156951i	$-0.949833\pi$
$17$	−27.4947	−	15.8741i	−1.61733	−	0.933768i	−0.629727	−	0.776816i	$-0.716833\pi$
$18$		0			0
$19$	−26.9408	+	15.5543i	−1.41794	+	0.818648i	−0.996118	−	0.0880311i	$-0.971943\pi$
$19$	−26.9408	+	15.5543i	−1.41794	+	0.818648i	−0.421822	+	0.906679i	$0.638609\pi$
$20$			4.47214i			0.223607i
$21$		0			0
$22$	14.5234			0.660152
$23$	−11.8441	−	20.5146i	−0.514962	−	0.891940i	−0.999849	−	0.0173632i	$-0.994473\pi$
$23$	−11.8441	−	20.5146i	−0.514962	−	0.891940i	0.484888	−	0.874576i	$-0.338860\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	−8.60187	+	4.96629i	−0.330841	+	0.191011i
$27$		0			0
$28$	13.8551	+	2.00927i	0.494824	+	0.0717595i
$29$	−9.19673			−0.317129			−0.158564	−	0.987349i	$-0.550687\pi$
$29$	−9.19673			−0.317129			−0.158564	+	0.987349i	$0.550687\pi$
$30$		0			0
$31$	17.4511	+	10.0754i	0.562940	+	0.325013i	0.754325	−	0.656502i	$-0.227965\pi$
$31$	17.4511	+	10.0754i	0.562940	+	0.325013i	−0.191385	+	0.981515i	$0.561298\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$		0			0
$34$		−	44.8986i		−	1.32055i
$35$	−12.2919	−	9.69068i	−0.351197	−	0.276877i
$36$		0			0
$37$	−24.0823	−	41.7118i	−0.650874	−	1.12735i	−0.982911	−	0.184081i	$-0.941069\pi$
$37$	−24.0823	−	41.7118i	−0.650874	−	1.12735i	0.332037	−	0.943266i	$-0.392264\pi$
$38$	−38.1001	−	21.9971i	−1.00263	−	0.578871i
$39$		0			0
$40$	−5.47723	+	3.16228i	−0.136931	+	0.0790569i
$41$		−	65.1226i		−	1.58836i	−0.607685	−	0.794178i	$-0.707902\pi$
$41$		−	65.1226i		−	1.58836i	0.607685	−	0.794178i	$-0.292098\pi$
$42$		0			0
$43$	−3.03497			−0.0705807			−0.0352904	−	0.999377i	$-0.511236\pi$
$43$	−3.03497			−0.0705807			−0.0352904	+	0.999377i	$0.511236\pi$
$44$	10.2696	+	17.7874i	0.233399	+	0.404259i
$45$		0			0
$46$	16.7501	−	29.0120i	0.364133	−	0.630697i
$47$	53.6472	−	30.9732i	1.14143	−	0.659005i	0.194645	−	0.980874i	$-0.437644\pi$
$47$	53.6472	−	30.9732i	1.14143	−	0.659005i	0.946784	+	0.321869i	$0.104311\pi$
$48$		0			0
$49$	−35.5451	+	33.7275i	−0.725411	+	0.688316i
$50$	7.07107			0.141421
$51$		0			0
$52$	−12.1649	−	7.02340i	−0.233940	−	0.135065i
$53$	0.690751	−	1.19642i	0.0130330	−	0.0225739i	−0.859435	−	0.511244i	$-0.829185\pi$
$53$	0.690751	−	1.19642i	0.0130330	−	0.0225739i	0.872468	+	0.488671i	$0.162518\pi$
$54$		0			0
$55$		−	22.9634i		−	0.417517i
$56$	7.33617	+	18.3897i	0.131003	+	0.328387i
$57$		0			0
$58$	−6.50307	−	11.2636i	−0.112122	−	0.194201i
$59$	95.1064	+	54.9097i	1.61197	+	0.930673i	0.988912	+	0.148500i	$0.0474445\pi$
$59$	95.1064	+	54.9097i	1.61197	+	0.930673i	0.623061	+	0.782173i	$0.285889\pi$
$60$		0			0
$61$	−34.3741	+	19.8459i	−0.563510	+	0.325343i	−0.754553	−	0.656239i	$-0.772146\pi$
$61$	−34.3741	+	19.8459i	−0.563510	+	0.325343i	0.191043	+	0.981582i	$0.438813\pi$
$62$			28.4976i			0.459638i
$63$		0			0
$64$	8.00000			0.125000
$65$	7.85240	+	13.6008i	0.120806	+	0.209242i
$66$		0			0
$67$	−7.95952	+	13.7863i	−0.118799	+	0.205765i	−0.919292	−	0.393576i	$-0.871238\pi$
$67$	−7.95952	+	13.7863i	−0.118799	+	0.205765i	0.800493	+	0.599342i	$0.204571\pi$
$68$	54.9893	−	31.7481i	0.808667	−	0.466884i
$69$		0			0
$70$	3.17693	−	21.9068i	0.0453847	−	0.312954i
$71$	−53.3489			−0.751393			−0.375696	−	0.926743i	$-0.622596\pi$
$71$	−53.3489			−0.751393			−0.375696	+	0.926743i	$0.622596\pi$
$72$		0			0
$73$	62.6830	+	36.1901i	0.858672	+	0.495754i	0.863567	−	0.504234i	$-0.168225\pi$
$73$	62.6830	+	36.1901i	0.858672	+	0.495754i	−0.00489557	+	0.999988i	$0.501558\pi$
$74$	34.0576	−	58.9894i	0.460237	−	0.797155i
$75$		0			0
$76$		−	62.2172i		−	0.818648i
$77$	−71.1427	−	10.3171i	−0.923931	−	0.133989i
$78$		0			0
$79$	−53.2229	−	92.1847i	−0.673707	−	1.16690i	−0.976845	−	0.213948i	$-0.931368\pi$
$79$	−53.2229	−	92.1847i	−0.673707	−	1.16690i	0.303138	−	0.952947i	$-0.401966\pi$
$80$	−7.74597	−	4.47214i	−0.0968246	−	0.0559017i
$81$		0			0
$82$	79.7586	−	46.0486i	0.972666	−	0.561569i
$83$			49.4298i			0.595540i	0.954638	+	0.297770i	$0.0962429\pi$
$83$			49.4298i			0.595540i	−0.954638	+	0.297770i	$0.903757\pi$
$84$		0			0
$85$	−70.9909			−0.835187
$86$	−2.14605	−	3.71707i	−0.0249541	−	0.0432217i
$87$		0			0
$88$	−14.5234	+	25.1552i	−0.165038	+	0.285854i
$89$	142.807	−	82.4499i	1.60458	−	0.926403i	0.614022	−	0.789289i	$-0.289551\pi$
$89$	142.807	−	82.4499i	1.60458	−	0.926403i	0.990555	−	0.137114i	$-0.0437826\pi$
$90$		0			0
$91$	45.6643	−	18.2168i	0.501805	−	0.200185i
$92$	47.3765			0.514962
$93$		0			0
$94$	75.8686	+	43.8027i	0.807113	+	0.465987i
$95$	−34.7805	+	60.2416i	−0.366110	+	0.634122i
$96$		0			0
$97$		−	49.4799i		−	0.510102i	−0.966928	−	0.255051i	$-0.917908\pi$
$97$		−	49.4799i		−	0.510102i	0.966928	−	0.255051i	$-0.0820922\pi$
$98$	−66.4418	−	19.6848i	−0.677977	−	0.200865i
$99$		0			0
$100$	5.00000	+	8.66025i	0.0500000	+	0.0866025i
$101$	−116.803	−	67.4364i	−1.15647	−	0.667687i	−0.206012	−	0.978549i	$-0.566049\pi$
$101$	−116.803	−	67.4364i	−1.15647	−	0.667687i	−0.950455	+	0.310863i	$0.899382\pi$
$102$		0			0
$103$	−32.3911	+	18.7010i	−0.314477	+	0.181563i	−0.648928	−	0.760850i	$-0.724782\pi$
$103$	−32.3911	+	18.7010i	−0.314477	+	0.181563i	0.334451	+	0.942413i	$0.391449\pi$
$104$		−	19.8652i		−	0.191011i
$105$		0			0
$106$	1.95374			0.0184315
$107$	−12.3980	−	21.4739i	−0.115869	−	0.200691i	0.802258	−	0.596978i	$-0.203632\pi$
$107$	−12.3980	−	21.4739i	−0.115869	−	0.200691i	−0.918127	+	0.396287i	$0.870299\pi$
$108$		0			0
$109$	28.1448	−	48.7483i	0.258209	−	0.447232i	−0.707553	−	0.706660i	$-0.750201\pi$
$109$	28.1448	−	48.7483i	0.258209	−	0.447232i	0.965762	+	0.259429i	$0.0835342\pi$
$110$	28.1243	−	16.2376i	0.255676	−	0.147615i
$111$		0			0
$112$	−17.3352	+	21.9884i	−0.154779	+	0.196325i
$113$	−74.9910			−0.663637			−0.331818	−	0.943343i	$-0.607662\pi$
$113$	−74.9910			−0.663637			−0.331818	+	0.943343i	$0.607662\pi$
$114$		0			0
$115$	−45.8721	−	26.4843i	−0.398888	−	0.230298i
$116$	9.19673	−	15.9292i	0.0792822	−	0.137321i
$117$		0			0
$118$			155.308i			1.31617i
$119$	−31.8952	+	219.936i	−0.268027	+	1.84820i
$120$		0			0
$121$	7.76807	+	13.4547i	0.0641989	+	0.111196i
$122$	−48.6124	−	28.0664i	−0.398462	−	0.230052i
$123$		0			0
$124$	−34.9023	+	20.1508i	−0.281470	+	0.162507i
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	128.504			1.01184			0.505921	−	0.862580i	$-0.331153\pi$
$127$	128.504			1.01184			0.505921	+	0.862580i	$0.331153\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−11.1050	+	19.2344i	−0.0854228	+	0.147957i
$131$	−65.3818	+	37.7482i	−0.499098	+	0.288154i	−0.728341	−	0.685215i	$-0.759708\pi$
$131$	−65.3818	+	37.7482i	−0.499098	+	0.288154i	0.229243	+	0.973369i	$0.426375\pi$
$132$		0			0
$133$	171.007	+	134.819i	1.28577	+	1.01367i
$134$	−22.5129			−0.168007
$135$		0			0
$136$	77.7667	+	44.8986i	0.571814	+	0.330137i
$137$	53.7583	−	93.1121i	0.392396	−	0.679650i	−0.600369	−	0.799723i	$-0.704980\pi$
$137$	53.7583	−	93.1121i	0.392396	−	0.679650i	0.992765	+	0.120073i	$0.0383129\pi$
$138$		0			0
$139$			272.004i			1.95686i	0.206576	+	0.978431i	$0.433768\pi$
$139$			272.004i			1.95686i	−0.206576	+	0.978431i	$0.566232\pi$
$140$	29.0766	−	11.5995i	0.207690	−	0.0828536i
$141$		0			0
$142$	−37.7234	−	65.3388i	−0.265658	−	0.460132i
$143$	62.4640	+	36.0636i	0.436811	+	0.252193i
$144$		0			0
$145$	−17.8094	+	10.2823i	−0.122823	+	0.0709121i
$146$			102.361i			0.701102i
$147$		0			0
$148$	96.3294			0.650874
$149$	−41.7135	−	72.2498i	−0.279956	−	0.484898i	0.691417	−	0.722456i	$-0.256987\pi$
$149$	−41.7135	−	72.2498i	−0.279956	−	0.484898i	−0.971374	+	0.237557i	$0.923653\pi$
$150$		0			0
$151$	−63.3973	+	109.807i	−0.419850	+	0.727201i	−0.995924	−	0.0901962i	$-0.971251\pi$
$151$	−63.3973	+	109.807i	−0.419850	+	0.727201i	0.576074	+	0.817397i	$0.304584\pi$
$152$	76.2002	−	43.9942i	0.501317	−	0.289436i
$153$		0			0
$154$	−37.6696	−	94.4270i	−0.244608	−	0.613162i
$155$	45.0586			0.290701
$156$		0			0
$157$	−85.9416	−	49.6184i	−0.547399	−	0.316041i	0.200673	−	0.979658i	$-0.435687\pi$
$157$	−85.9416	−	49.6184i	−0.547399	−	0.316041i	−0.748072	+	0.663617i	$0.769020\pi$
$158$	75.2685	−	130.369i	0.476383	−	0.825120i
$159$		0			0
$160$		−	12.6491i		−	0.0790569i
$161$	−102.660	+	130.217i	−0.637641	+	0.808799i
$162$		0			0
$163$	−139.490	−	241.603i	−0.855765	−	1.48223i	−0.875933	−	0.482433i	$-0.839753\pi$
$163$	−139.490	−	241.603i	−0.855765	−	1.48223i	0.0201678	−	0.999797i	$-0.493580\pi$
$164$	112.796	+	65.1226i	0.687779	+	0.397089i
$165$		0			0
$166$	−60.5389	+	34.9522i	−0.364692	+	0.210555i
$167$		−	29.9435i		−	0.179302i	−0.995973	−	0.0896511i	$-0.971425\pi$
$167$		−	29.9435i		−	0.179302i	0.995973	−	0.0896511i	$-0.0285752\pi$
$168$		0			0
$169$	119.672			0.708118
$170$	−50.1982	−	86.9458i	−0.295283	−	0.511446i
$171$		0			0
$172$	3.03497	−	5.25673i	0.0176452	−	0.0305624i
$173$	−92.2369	+	53.2530i	−0.533161	+	0.307821i	−0.742303	−	0.670065i	$-0.766266\pi$
$173$	−92.2369	+	53.2530i	−0.533161	+	0.307821i	0.209142	+	0.977885i	$0.432933\pi$
$174$		0			0
$175$	−34.6377	−	5.02316i	−0.197930	−	0.0287038i
$176$	−41.0782			−0.233399
$177$		0			0
$178$	201.960	+	116.602i	1.13461	+	0.655066i
$179$	−119.986	+	207.822i	−0.670315	+	1.16102i	0.307500	+	0.951548i	$0.400508\pi$
$179$	−119.986	+	207.822i	−0.670315	+	1.16102i	−0.977815	+	0.209471i	$0.932826\pi$
$180$		0			0
$181$			309.322i			1.70896i	0.519482	+	0.854482i	$0.326125\pi$
$181$			309.322i			1.70896i	−0.519482	+	0.854482i	$0.673875\pi$
$182$	54.6004	+	43.0459i	0.300002	+	0.236516i
$183$		0			0
$184$	33.5002	+	58.0241i	0.182066	+	0.315348i
$185$	−93.2705	−	53.8497i	−0.504165	−	0.291080i
$186$		0			0
$187$	−282.358	+	163.020i	−1.50994	+	0.871762i
$188$			123.893i			0.659005i
$189$		0			0
$190$	−98.3741			−0.517758
$191$	1.54480	+	2.67567i	0.00808796	+	0.0140088i	0.870041	−	0.492979i	$-0.164092\pi$
$191$	1.54480	+	2.67567i	0.00808796	+	0.0140088i	−0.861953	+	0.506988i	$0.830759\pi$
$192$		0			0
$193$	119.349	−	206.718i	0.618387	−	1.07108i	−0.371393	−	0.928476i	$-0.621120\pi$
$193$	119.349	−	206.718i	0.618387	−	1.07108i	0.989780	−	0.142602i	$-0.0455469\pi$
$194$	60.6002	−	34.9875i	0.312372	−	0.180348i
$195$		0			0
$196$	−22.8726	−	95.2935i	−0.116697	−	0.486191i
$197$	291.539			1.47989			0.739946	−	0.672666i	$-0.234851\pi$
$197$	291.539			1.47989			0.739946	+	0.672666i	$0.234851\pi$
$198$		0			0
$199$	209.224	+	120.796i	1.05138	+	0.607013i	0.923034	−	0.384717i	$-0.125701\pi$
$199$	209.224	+	120.796i	1.05138	+	0.607013i	0.128342	+	0.991730i	$0.459034\pi$
$200$	−7.07107	+	12.2474i	−0.0353553	+	0.0612372i
$201$		0			0
$202$		−	190.739i		−	0.944252i
$203$	23.8538	+	59.7947i	0.117507	+	0.294555i
$204$		0			0
$205$	−72.8093	−	126.109i	−0.355167	−	0.615168i
$206$	−45.8080	−	26.4473i	−0.222369	−	0.128385i
$207$		0			0
$208$	24.3298	−	14.0468i	0.116970	−	0.0675327i
$209$			319.472i			1.52857i
$210$		0			0
$211$	−263.018			−1.24653			−0.623266	−	0.782010i	$-0.714195\pi$
$211$	−263.018			−1.24653			−0.623266	+	0.782010i	$0.714195\pi$
$212$	1.38150	+	2.39283i	0.00651652	+	0.0112869i
$213$		0			0
$214$	17.5334	−	30.3688i	0.0819318	−	0.141910i
$215$	−5.87720	+	3.39320i	−0.0273358	+	0.0157823i
$216$		0			0
$217$	20.2442	−	139.596i	0.0932911	−	0.643297i
$218$	79.6056			0.365163
$219$		0			0
$220$	39.7738	+	22.9634i	0.180790	+	0.104379i
$221$	111.490	−	193.106i	0.504479	−	0.873783i
$222$		0			0
$223$			112.658i			0.505193i	0.967572	+	0.252597i	$0.0812845\pi$
$223$			112.658i			0.505193i	−0.967572	+	0.252597i	$0.918715\pi$
$224$	−39.1880	−	5.68306i	−0.174947	−	0.0253708i
$225$		0			0
$226$	−53.0266	−	91.8448i	−0.234631	−	0.406393i
$227$	−42.4529	−	24.5102i	−0.187017	−	0.107974i	0.403568	−	0.914950i	$-0.367770\pi$
$227$	−42.4529	−	24.5102i	−0.187017	−	0.107974i	−0.590585	+	0.806975i	$0.701103\pi$
$228$		0			0
$229$	24.3476	−	14.0571i	0.106321	−	0.0613846i	−0.445896	−	0.895085i	$-0.647115\pi$
$229$	24.3476	−	14.0571i	0.106321	−	0.0613846i	0.552218	+	0.833700i	$0.313782\pi$
$230$		−	74.9088i		−	0.325690i
$231$		0			0
$232$	26.0123			0.112122
$233$	88.1014	+	152.596i	0.378117	+	0.654919i	0.990788	−	0.135420i	$-0.0432382\pi$
$233$	88.1014	+	152.596i	0.378117	+	0.654919i	−0.612671	+	0.790338i	$0.709905\pi$
$234$		0			0
$235$	69.2582	−	119.959i	0.294716	−	0.510463i
$236$	−190.213	+	109.819i	−0.805987	+	0.465337i
$237$		0			0
$238$	−291.919	+	116.455i	−1.22655	+	0.489306i
$239$	−34.7150			−0.145251			−0.0726255	−	0.997359i	$-0.523138\pi$
$239$	−34.7150			−0.145251			−0.0726255	+	0.997359i	$0.523138\pi$
$240$		0			0
$241$	−229.871	−	132.716i	−0.953823	−	0.550690i	−0.0595563	−	0.998225i	$-0.518969\pi$
$241$	−229.871	−	132.716i	−0.953823	−	0.550690i	−0.894266	+	0.447535i	$0.852302\pi$
$242$	−10.9857	+	19.0278i	−0.0453955	+	0.0786273i
$243$		0			0
$244$		−	79.3837i		−	0.325343i
$245$	−31.1244	+	105.054i	−0.127038	+	0.428790i
$246$		0			0
$247$	−109.244	−	189.216i	−0.442284	−	0.766058i
$248$	−49.3592	−	28.4976i	−0.199029	−	0.114910i
$249$		0			0
$250$	13.6931	−	7.90569i	0.0547723	−	0.0316228i
$251$		−	24.1723i		−	0.0963040i	−0.998840	−	0.0481520i	$-0.984667\pi$
$251$		−	24.1723i		−	0.0963040i	0.998840	−	0.0481520i	$-0.0153332\pi$
$252$		0			0
$253$	−243.268			−0.961533
$254$	90.8659	+	157.384i	0.357740	+	0.619624i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	8.25969	−	4.76874i	0.0321389	−	0.0185554i	−0.483844	−	0.875154i	$-0.660760\pi$
$257$	8.25969	−	4.76874i	0.0321389	−	0.0185554i	0.515983	+	0.856599i	$0.327427\pi$
$258$		0			0
$259$	−208.736	+	264.766i	−0.805932	+	1.02226i
$260$	−31.4096			−0.120806
$261$		0			0
$262$	−92.4639	−	53.3840i	−0.352916	−	0.203756i
$263$	−65.9316	+	114.197i	−0.250691	+	0.434209i	−0.963716	−	0.266929i	$-0.913991\pi$
$263$	−65.9316	+	114.197i	−0.250691	+	0.434209i	0.713026	+	0.701138i	$0.247324\pi$
$264$		0			0
$265$		−	3.08913i		−	0.0116571i
$266$	−44.1980	+	304.771i	−0.166158	+	1.14576i
$267$		0			0
$268$	−15.9190	−	27.5726i	−0.0593994	−	0.102883i
$269$	32.8041	+	18.9395i	0.121949	+	0.0704070i	0.559733	−	0.828673i	$-0.310904\pi$
$269$	32.8041	+	18.9395i	0.121949	+	0.0704070i	−0.437785	+	0.899080i	$0.644237\pi$
$270$		0			0
$271$	313.801	−	181.173i	1.15794	−	0.668535i	0.207128	−	0.978314i	$-0.433588\pi$
$271$	313.801	−	181.173i	1.15794	−	0.668535i	0.950809	+	0.309779i	$0.100255\pi$
$272$			126.992i			0.466884i
$273$		0			0
$274$	152.051			0.554932
$275$	−25.6739	−	44.4685i	−0.0933596	−	0.161704i
$276$		0			0
$277$	56.6495	−	98.1197i	0.204511	−	0.354223i	−0.745466	−	0.666544i	$-0.767773\pi$
$277$	56.6495	−	98.1197i	0.204511	−	0.354223i	0.949977	+	0.312321i	$0.101106\pi$
$278$	−333.135	+	192.336i	−1.19833	+	0.691855i
$279$		0			0
$280$	34.7667	+	27.4094i	0.124167	+	0.0978907i
$281$	178.735			0.636069			0.318034	−	0.948079i	$-0.396977\pi$
$281$	178.735			0.636069			0.318034	+	0.948079i	$0.396977\pi$
$282$		0			0
$283$	37.3850	+	21.5843i	0.132103	+	0.0762695i	0.564595	−	0.825368i	$-0.309032\pi$
$283$	37.3850	+	21.5843i	0.132103	+	0.0762695i	−0.432492	+	0.901638i	$0.642366\pi$
$284$	53.3489	−	92.4030i	0.187848	−	0.325363i
$285$		0			0
$286$			102.003i			0.356655i
$287$	−423.410	+	168.910i	−1.47530	+	0.588538i
$288$		0			0
$289$	359.471	+	622.622i	1.24384	+	2.15440i
$290$	−25.1863	−	14.5413i	−0.0868493	−	0.0501424i
$291$		0			0
$292$	−125.366	+	72.3801i	−0.429336	+	0.247877i
$293$		−	15.4426i		−	0.0527050i	−0.999653	−	0.0263525i	$-0.991611\pi$
$293$		−	15.4426i		−	0.0527050i	0.999653	−	0.0263525i	$-0.00838923\pi$
$294$		0			0
$295$	245.564			0.832420
$296$	68.1151	+	117.979i	0.230119	+	0.398577i
$297$		0			0
$298$	58.9917	−	102.177i	0.197959	−	0.342875i
$299$	144.082	−	83.1859i	0.481881	−	0.278214i
$300$		0			0
$301$	7.87189	+	19.7326i	0.0261525	+	0.0655568i
$302$	−179.315			−0.593757
$303$		0			0
$304$	107.763	+	62.2172i	0.354485	+	0.204662i
$305$	−44.3768	+	76.8629i	−0.145498	+	0.252009i
$306$		0			0
$307$		−	234.648i		−	0.764327i	−0.924095	−	0.382163i	$-0.875179\pi$
$307$		−	234.648i		−	0.764327i	0.924095	−	0.382163i	$-0.124821\pi$
$308$	89.0125	−	112.906i	0.289002	−	0.366577i
$309$		0			0
$310$	31.8613	+	55.1853i	0.102778	+	0.178017i
$311$	345.352	+	199.389i	1.11045	+	0.641121i	0.938947	−	0.344061i	$-0.111803\pi$
$311$	345.352	+	199.389i	1.11045	+	0.641121i	0.171508	+	0.985183i	$0.445136\pi$
$312$		0			0
$313$	111.891	−	64.6002i	0.357479	−	0.206390i	−0.310495	−	0.950575i	$-0.600495\pi$
$313$	111.891	−	64.6002i	0.357479	−	0.206390i	0.667974	+	0.744184i	$0.267162\pi$
$314$		−	140.342i		−	0.446949i
$315$		0			0
$316$	212.892			0.673707
$317$	−201.283	−	348.632i	−0.634961	−	1.09979i	−0.986523	−	0.163621i	$-0.947683\pi$
$317$	−201.283	−	348.632i	−0.634961	−	1.09979i	0.351562	−	0.936165i	$-0.385651\pi$
$318$		0			0
$319$	−47.2232	+	81.7930i	−0.148035	+	0.256404i
$320$	15.4919	−	8.94427i	0.0484123	−	0.0279508i
$321$		0			0
$322$	−232.074	−	33.6554i	−0.720726	−	0.104520i
$323$	987.640			3.05771
$324$		0			0
$325$	30.4122	+	17.5585i	0.0935760	+	0.0540261i
$326$	197.268	−	341.679i	0.605118	−	1.04809i
$327$		0			0
$328$			184.195i			0.561569i
$329$	−340.526	−	268.464i	−1.03503	−	0.815999i
$330$		0			0
$331$	83.4463	+	144.533i	0.252104	+	0.436656i	0.964105	−	0.265522i	$-0.0855443\pi$
$331$	83.4463	+	144.533i	0.252104	+	0.436656i	−0.712001	+	0.702178i	$0.752211\pi$
$332$	−85.6150	−	49.4298i	−0.257876	−	0.148885i
$333$		0			0
$334$	36.6731	−	21.1732i	0.109800	−	0.0633929i
$335$			35.5960i			0.106257i
$336$		0			0
$337$	−541.392			−1.60651			−0.803253	−	0.595638i	$-0.796899\pi$
$337$	−541.392			−1.60651			−0.803253	+	0.595638i	$0.796899\pi$
$338$	84.6208	+	146.568i	0.250357	+	0.433632i
$339$		0			0
$340$	70.9909	−	122.960i	0.208797	−	0.361647i
$341$	179.215	−	103.470i	0.525558	−	0.303431i
$342$		0			0
$343$	311.482	+	143.625i	0.908110	+	0.418732i
$344$	8.58420			0.0249541
$345$		0			0
$346$	−130.443	−	75.3111i	−0.377002	−	0.217662i
$347$	214.342	−	371.251i	0.617700	−	1.06989i	−0.372204	−	0.928151i	$-0.621398\pi$
$347$	214.342	−	371.251i	0.617700	−	1.06989i	0.989904	−	0.141737i	$-0.0452687\pi$
$348$		0			0
$349$			74.6851i			0.213998i	0.994259	+	0.106999i	$0.0341241\pi$
$349$			74.6851i			0.213998i	−0.994259	+	0.106999i	$0.965876\pi$
$350$	−18.3404	−	45.9742i	−0.0524012	−	0.131355i
$351$		0			0
$352$	−29.0467	−	50.3104i	−0.0825190	−	0.142927i
$353$	−316.890	−	182.956i	−0.897705	−	0.518290i	−0.0212499	−	0.999774i	$-0.506765\pi$
$353$	−316.890	−	182.956i	−0.897705	−	0.518290i	−0.876455	+	0.481484i	$0.840098\pi$
$354$		0			0
$355$	−103.310	+	59.6459i	−0.291013	+	0.168017i
$356$			329.799i			0.926403i
$357$		0			0
$358$	−339.373			−0.947968
$359$	−248.793	−	430.922i	−0.693017	−	1.20034i	−0.970845	−	0.239710i	$-0.922948\pi$
$359$	−248.793	−	430.922i	−0.693017	−	1.20034i	0.277828	−	0.960631i	$-0.410386\pi$
$360$		0			0
$361$	303.373	−	525.457i	0.840368	−	1.45556i
$362$	−378.841	+	218.724i	−1.04652	+	0.604210i
$363$		0			0
$364$	−14.1119	+	97.3096i	−0.0387689	+	0.267334i
$365$	161.847			0.443416
$366$		0			0
$367$	120.700	+	69.6861i	0.328882	+	0.189880i	0.655345	−	0.755330i	$-0.272523\pi$
$367$	120.700	+	69.6861i	0.328882	+	0.189880i	−0.326462	+	0.945210i	$0.605857\pi$
$368$	−47.3765	+	82.0584i	−0.128740	+	0.222985i
$369$		0			0
$370$		−	152.310i		−	0.411649i
$371$	−9.57040	−	1.38790i	−0.0257962	−	0.00374098i
$372$		0			0
$373$	−173.760	−	300.961i	−0.465844	−	0.806865i	0.533395	−	0.845866i	$-0.320916\pi$
$373$	−173.760	−	300.961i	−0.465844	−	0.806865i	−0.999239	+	0.0390009i	$0.987582\pi$
$374$	−399.315	−	230.544i	−1.06769	−	0.616429i
$375$		0			0
$376$	−151.737	+	87.6055i	−0.403556	+	0.232993i
$377$		−	64.5923i		−	0.171332i
$378$		0			0
$379$	307.387			0.811048			0.405524	−	0.914084i	$-0.367089\pi$
$379$	307.387			0.811048			0.405524	+	0.914084i	$0.367089\pi$
$380$	−69.5610	−	120.483i	−0.183055	−	0.317061i
$381$		0			0
$382$	−2.18468	+	3.78397i	−0.00571905	+	0.00990569i
$383$	440.572	−	254.364i	1.15032	−	0.664136i	0.201353	−	0.979519i	$-0.435466\pi$
$383$	440.572	−	254.364i	1.15032	−	0.664136i	0.948965	+	0.315382i	$0.102133\pi$
$384$		0			0
$385$	−149.302	+	59.5609i	−0.387798	+	0.154704i
$386$	337.569			0.874531
$387$		0			0
$388$	85.7016	+	49.4799i	0.220880	+	0.127525i
$389$	−85.4840	+	148.063i	−0.219753	+	0.380624i	−0.954732	−	0.297466i	$-0.903859\pi$
$389$	−85.4840	+	148.063i	−0.219753	+	0.380624i	0.734979	+	0.678090i	$0.237192\pi$
$390$		0			0
$391$			752.057i			1.92342i
$392$	100.537	−	95.3957i	0.256472	−	0.243356i
$393$		0			0
$394$	206.149	+	357.061i	0.523221	+	0.906245i
$395$	−206.131	−	119.010i	−0.521851	−	0.301291i
$396$		0			0
$397$	551.223	−	318.249i	1.38847	−	0.801634i	0.395328	−	0.918540i	$-0.370631\pi$
$397$	551.223	−	318.249i	1.38847	−	0.801634i	0.993143	+	0.116906i	$0.0372975\pi$
$398$			341.661i			0.858446i
$399$		0			0
$400$	−20.0000			−0.0500000
$401$	−296.110	−	512.878i	−0.738429	−	1.27900i	−0.953202	−	0.302333i	$-0.902235\pi$
$401$	−296.110	−	512.878i	−0.738429	−	1.27900i	0.214773	−	0.976664i	$-0.431099\pi$
$402$		0			0
$403$	−70.7636	+	122.566i	−0.175592	+	0.304135i
$404$	233.606	−	134.873i	0.578234	−	0.333843i
$405$		0			0
$406$	−56.3661	+	71.4961i	−0.138833	+	0.176099i
$407$	−494.630			−1.21531
$408$		0			0
$409$	−245.717	−	141.865i	−0.600776	−	0.346858i	0.168571	−	0.985690i	$-0.446085\pi$
$409$	−245.717	−	141.865i	−0.600776	−	0.346858i	−0.769347	+	0.638831i	$0.779418\pi$
$410$	102.968	−	178.346i	0.251141	−	0.434989i
$411$		0			0
$412$		−	74.8041i		−	0.181563i
$413$	110.328	−	760.778i	0.267138	−	1.84208i
$414$		0			0
$415$	55.2642	+	95.7204i	0.133167	+	0.230652i
$416$	34.4075	+	19.8652i	0.0827103	+	0.0477528i
$417$		0			0
$418$	−391.271	+	225.901i	−0.936056	+	0.540432i
$419$			482.511i			1.15158i	0.817599	+	0.575789i	$0.195305\pi$
$419$			482.511i			1.15158i	−0.817599	+	0.575789i	$0.804695\pi$
$420$		0			0
$421$	762.080			1.81017			0.905083	−	0.425234i	$-0.139808\pi$
$421$	762.080			1.81017			0.905083	+	0.425234i	$0.139808\pi$
$422$	−185.982	−	322.130i	−0.440716	−	0.763342i
$423$		0			0
$424$	−1.95374	+	3.38397i	−0.00460787	+	0.00798107i
$425$	−137.473	+	79.3703i	−0.323467	+	0.186754i
$426$		0			0
$427$	218.190	+	172.017i	0.510984	+	0.402849i
$428$	49.5920			0.115869
$429$		0			0
$430$	−8.31161	−	4.79871i	−0.0193293	−	0.0111598i
$431$	128.008	−	221.717i	0.297003	−	0.514424i	−0.678446	−	0.734650i	$-0.737346\pi$
$431$	128.008	−	221.717i	0.297003	−	0.514424i	0.975449	+	0.220226i	$0.0706795\pi$
$432$		0			0
$433$		−	646.579i		−	1.49325i	−0.665243	−	0.746627i	$-0.731672\pi$
$433$		−	646.579i		−	1.49325i	0.665243	−	0.746627i	$-0.268328\pi$
$434$	185.284	−	73.9150i	0.426921	−	0.170311i
$435$		0			0
$436$	56.2897	+	97.4966i	0.129105	+	0.223616i
$437$	638.181	+	368.454i	1.46037	+	0.843144i
$438$		0			0
$439$	290.352	−	167.635i	0.661394	−	0.381856i	−0.131414	−	0.991328i	$-0.541952\pi$
$439$	290.352	−	167.635i	0.661394	−	0.381856i	0.792808	+	0.609472i	$0.208618\pi$
$440$			64.9504i			0.147615i
$441$		0			0
$442$	315.341			0.713441
$443$	−140.527	−	243.400i	−0.317216	−	0.549435i	0.662690	−	0.748894i	$-0.269415\pi$
$443$	−140.527	−	243.400i	−0.317216	−	0.549435i	−0.979906	+	0.199459i	$0.936081\pi$
$444$		0			0
$445$	184.363	−	319.327i	0.414300	−	0.717589i
$446$	−137.977	+	79.6613i	−0.309366	+	0.178613i
$447$		0			0
$448$	−20.7498	−	52.0139i	−0.0463166	−	0.116102i
$449$	−47.2320			−0.105194			−0.0525969	−	0.998616i	$-0.516750\pi$
$449$	−47.2320			−0.105194			−0.0525969	+	0.998616i	$0.516750\pi$
$450$		0			0
$451$	−579.181	−	334.390i	−1.28422	−	0.741442i
$452$	74.9910	−	129.888i	0.165909	−	0.287363i
$453$		0			0
$454$		−	69.3253i		−	0.152699i
$455$	68.0615	−	86.3309i	0.149586	−	0.189738i
$456$		0			0
$457$	−294.396	−	509.909i	−0.644193	−	1.11578i	−0.984487	−	0.175456i	$-0.943860\pi$
$457$	−294.396	−	509.909i	−0.644193	−	1.11578i	0.340294	−	0.940319i	$-0.389473\pi$
$458$	34.4327	+	19.8797i	0.0751805	+	0.0434055i
$459$		0			0
$460$	91.7441	−	52.9685i	0.199444	−	0.115149i
$461$			60.5606i			0.131368i	0.997840	+	0.0656839i	$0.0209229\pi$
$461$			60.5606i			0.131368i	−0.997840	+	0.0656839i	$0.979077\pi$
$462$		0			0
$463$	88.7592			0.191704			0.0958522	−	0.995396i	$-0.469442\pi$
$463$	88.7592			0.191704			0.0958522	+	0.995396i	$0.469442\pi$
$464$	18.3935	+	31.8584i	0.0396411	+	0.0686604i
$465$		0			0
$466$	−124.594	+	215.803i	−0.267369	+	0.463097i
$467$	−261.733	+	151.112i	−0.560457	+	0.323580i	−0.753329	−	0.657644i	$-0.771553\pi$
$467$	−261.733	+	151.112i	−0.560457	+	0.323580i	0.192872	+	0.981224i	$0.438220\pi$
$468$		0			0
$469$	110.280	+	15.9928i	0.235138	+	0.0340997i
$470$	195.892			0.416791
$471$		0			0
$472$	−269.002	−	155.308i	−0.569919	−	0.329043i
$473$	−15.5839	+	26.9921i	−0.0329470	+	0.0570658i
$474$		0			0
$475$			155.543i			0.327459i
$476$	−349.045	−	275.180i	−0.733288	−	0.578110i
$477$		0			0
$478$	−24.5472	−	42.5170i	−0.0513540	−	0.0889478i
$479$	−30.4237	−	17.5651i	−0.0635151	−	0.0366704i	0.467906	−	0.883778i	$-0.345009\pi$
$479$	−30.4237	−	17.5651i	−0.0635151	−	0.0366704i	−0.531421	+	0.847108i	$0.678342\pi$
$480$		0			0
$481$	292.959	−	169.140i	0.609062	−	0.351642i
$482$		−	375.378i		−	0.778793i
$483$		0			0
$484$	−31.0723			−0.0641989
$485$	−55.3202	−	95.8173i	−0.114062	−	0.197561i
$486$		0			0
$487$	−32.3167	+	55.9741i	−0.0663586	+	0.114937i	−0.897296	−	0.441430i	$-0.854471\pi$
$487$	−32.3167	+	55.9741i	−0.0663586	+	0.114937i	0.830937	+	0.556366i	$0.187805\pi$
$488$	97.2247	−	56.1327i	0.199231	−	0.115026i
$489$		0			0
$490$	−150.672	+	36.1647i	−0.307494	+	0.0738056i
$491$	−241.365			−0.491578			−0.245789	−	0.969323i	$-0.579047\pi$
$491$	−241.365			−0.491578			−0.245789	+	0.969323i	$0.579047\pi$
$492$		0			0
$493$	252.861	+	145.989i	0.512903	+	0.296125i
$494$	154.494	−	267.592i	0.312742	−	0.541685i
$495$		0			0
$496$		−	80.6033i		−	0.162507i
$497$	138.373	+	346.860i	0.278416	+	0.697908i
$498$		0			0
$499$	95.8123	+	165.952i	0.192009	+	0.332569i	0.945916	−	0.324412i	$-0.105166\pi$
$499$	95.8123	+	165.952i	0.192009	+	0.332569i	−0.753907	+	0.656981i	$0.771833\pi$
$500$	19.3649	+	11.1803i	0.0387298	+	0.0223607i
$501$		0			0
$502$	29.6049	−	17.0924i	0.0589739	−	0.0340486i
$503$			919.711i			1.82845i	0.405205	+	0.914226i	$0.367200\pi$
$503$			919.711i			1.82845i	−0.405205	+	0.914226i	$0.632800\pi$
$504$		0			0
$505$	−301.585			−0.597197
$506$	−172.016	−	297.941i	−0.339953	−	0.588816i
$507$		0			0
$508$	−128.504	+	222.575i	−0.252960	+	0.438140i
$509$	−250.976	+	144.901i	−0.493076	+	0.284678i	−0.725850	−	0.687853i	$-0.758553\pi$
$509$	−250.976	+	144.901i	−0.493076	+	0.284678i	0.232773	+	0.972531i	$0.425220\pi$
$510$		0			0
$511$	72.7154	−	501.416i	0.142300	−	0.981244i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	11.6810	+	6.74401i	0.0227256	+	0.0131206i
$515$	−41.8168	+	72.4288i	−0.0811976	+	0.140638i
$516$		0			0
$517$		−	636.163i		−	1.23049i
$518$	−471.870	−	68.4307i	−0.910946	−	0.132106i
$519$		0			0
$520$	−22.2099	−	38.4687i	−0.0427114	−	0.0739783i
$521$	653.176	+	377.112i	1.25370	+	0.723823i	0.971842	−	0.235634i	$-0.0757167\pi$
$521$	653.176	+	377.112i	1.25370	+	0.723823i	0.281856	+	0.959457i	$0.409050\pi$
$522$		0			0
$523$	65.5821	−	37.8638i	0.125396	−	0.0723974i	−0.435990	−	0.899952i	$-0.643602\pi$
$523$	65.5821	−	37.8638i	0.125396	−	0.0723974i	0.561386	+	0.827554i	$0.310268\pi$
$524$		−	150.993i		−	0.288154i
$525$		0			0
$526$	−186.483			−0.354530
$527$	−319.875	−	554.040i	−0.606974	−	1.05131i
$528$		0			0
$529$	−16.0662	+	27.8275i	−0.0303709	+	0.0526039i
$530$	3.78340	−	2.18435i	0.00713849	−	0.00412141i
$531$		0			0
$532$	−404.520	+	161.375i	−0.760376	+	0.303336i
$533$	457.382			0.858128
$534$		0			0
$535$	−48.0172	−	27.7228i	−0.0897518	−	0.0518182i
$536$	22.5129	−	38.9935i	0.0420017	−	0.0727491i
$537$		0			0
$538$			53.5689i			0.0995705i
$539$	117.446	+	489.311i	0.217895	+	0.907813i
$540$		0			0
$541$	−493.177	−	854.207i	−0.911602	−	1.57894i	−0.811802	−	0.583933i	$-0.801513\pi$
$541$	−493.177	−	854.207i	−0.911602	−	1.57894i	−0.0998002	−	0.995007i	$-0.531820\pi$
$542$	443.782	+	256.217i	0.818785	+	0.472726i
$543$		0			0
$544$	−155.533	+	89.7972i	−0.285907	+	0.165068i
$545$		−	125.868i		−	0.230950i
$546$		0			0
$547$	346.700			0.633820			0.316910	−	0.948456i	$-0.397355\pi$
$547$	346.700			0.633820			0.316910	+	0.948456i	$0.397355\pi$
$548$	107.517	+	186.224i	0.196198	+	0.339825i
$549$		0			0
$550$	36.3084	−	62.8880i	0.0660152	−	0.114342i
$551$	247.768	−	143.049i	0.449669	−	0.259617i
$552$		0			0
$553$	−461.315	+	585.143i	−0.834204	+	1.05813i
$554$	160.229			0.289222
$555$		0			0
$556$	−471.124	−	272.004i	−0.847346	−	0.489215i
$557$	−76.7246	+	132.891i	−0.137746	+	0.238583i	−0.926643	−	0.375942i	$-0.877319\pi$
$557$	−76.7246	+	132.891i	−0.137746	+	0.238583i	0.788897	+	0.614525i	$0.210652\pi$
$558$		0			0
$559$		−	21.3158i		−	0.0381320i
$560$	−8.98571	+	61.9617i	−0.0160459	+	0.110646i
$561$		0			0
$562$	126.385	+	218.905i	0.224884	+	0.389511i
$563$	−150.809	−	87.0695i	−0.267866	−	0.154653i	0.360051	−	0.932933i	$-0.382759\pi$
$563$	−150.809	−	87.0695i	−0.267866	−	0.154653i	−0.627918	+	0.778280i	$0.716093\pi$
$564$		0			0
$565$	−145.219	+	83.8424i	−0.257025	+	0.148394i
$566$			61.0495i			0.107861i
$567$		0			0
$568$	150.893			0.265658
$569$	−109.591	−	189.817i	−0.192603	−	0.333597i	0.753509	−	0.657437i	$-0.228359\pi$
$569$	−109.591	−	189.817i	−0.192603	−	0.333597i	−0.946112	+	0.323840i	$0.895026\pi$
$570$		0			0
$571$	−478.914	+	829.504i	−0.838729	+	1.45272i	0.0522282	+	0.998635i	$0.483368\pi$
$571$	−478.914	+	829.504i	−0.838729	+	1.45272i	−0.890958	+	0.454087i	$0.849966\pi$
$572$	−124.928	+	72.1272i	−0.218406	+	0.126097i
$573$		0			0
$574$	−506.268	−	399.132i	−0.882001	−	0.695351i
$575$	−118.441			−0.205985
$576$		0			0
$577$	−898.838	−	518.944i	−1.55778	−	0.899384i	−0.997469	−	0.0710997i	$-0.977349\pi$
$577$	−898.838	−	518.944i	−1.55778	−	0.899384i	−0.560309	−	0.828284i	$-0.689318\pi$
$578$	−508.369	+	880.521i	−0.879531	+	1.52339i
$579$		0			0
$580$		−	41.1290i		−	0.0709121i
$581$	321.380	−	128.208i	0.553149	−	0.220667i
$582$		0			0
$583$	−7.09371	−	12.2867i	−0.0121676	−	0.0210749i
$584$	−177.294	−	102.361i	−0.303586	−	0.175276i
$585$		0			0
$586$	18.9132	−	10.9195i	0.0322751	−	0.0186340i
$587$		−	819.162i		−	1.39551i	−0.716339	−	0.697753i	$-0.754183\pi$
$587$		−	819.162i		−	1.39551i	0.716339	−	0.697753i	$-0.245817\pi$
$588$		0			0
$589$	−626.864			−1.06429
$590$	173.640	+	300.753i	0.294305	+	0.509751i
$591$		0			0
$592$	−96.3294	+	166.847i	−0.162719	+	0.281837i
$593$	−461.919	+	266.689i	−0.778953	+	0.449729i	−0.836059	−	0.548639i	$-0.815146\pi$
$593$	−461.919	+	266.689i	−0.778953	+	0.449729i	0.0571059	+	0.998368i	$0.481813\pi$
$594$		0			0
$595$	184.131	+	461.564i	0.309464	+	0.775738i
$596$	166.854			0.279956
$597$		0			0
$598$	203.763	+	117.643i	0.340741	+	0.196727i
$599$	−171.452	+	296.963i	−0.286230	+	0.495765i	−0.972907	−	0.231198i	$-0.925735\pi$
$599$	−171.452	+	296.963i	−0.286230	+	0.495765i	0.686677	+	0.726963i	$0.259069\pi$
$600$		0			0
$601$		−	418.941i		−	0.697073i	−0.937295	−	0.348536i	$-0.886679\pi$
$601$		−	418.941i		−	0.697073i	0.937295	−	0.348536i	$-0.113321\pi$
$602$	−18.6011	+	23.5941i	−0.0308989	+	0.0391929i
$603$		0			0
$604$	−126.795	−	219.615i	−0.209925	−	0.363601i
$605$	30.0856	+	17.3699i	0.0497282	+	0.0287106i
$606$		0			0
$607$	122.608	−	70.7875i	0.201989	−	0.116619i	−0.395594	−	0.918426i	$-0.629461\pi$
$607$	122.608	−	70.7875i	0.201989	−	0.116619i	0.597583	+	0.801807i	$0.296128\pi$
$608$			175.977i			0.289436i
$609$		0			0
$610$	−125.517			−0.205765
$611$	217.537	+	376.786i	0.356035	+	0.616670i
$612$		0			0
$613$	148.520	−	257.244i	0.242284	−	0.419647i	−0.719081	−	0.694926i	$-0.755437\pi$
$613$	148.520	−	257.244i	0.242284	−	0.419647i	0.961364	+	0.275279i	$0.0887703\pi$
$614$	287.384	−	165.921i	0.468053	−	0.270230i
$615$		0			0
$616$	201.222	+	29.1813i	0.326659	+	0.0473722i
$617$	674.329			1.09292			0.546458	−	0.837486i	$-0.315976\pi$
$617$	674.329			1.09292			0.546458	+	0.837486i	$0.315976\pi$
$618$		0			0
$619$	−833.055	−	480.965i	−1.34581	−	0.777003i	−0.358156	−	0.933662i	$-0.616594\pi$
$619$	−833.055	−	480.965i	−1.34581	−	0.777003i	−0.987653	+	0.156659i	$0.949928\pi$
$620$	−45.0586	+	78.0438i	−0.0726752	+	0.125877i
$621$		0			0
$622$			563.957i			0.906683i
$623$	−906.471	−	714.643i	−1.45501	−	1.14710i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	158.238	+	91.3585i	0.252776	+	0.145940i
$627$		0			0
$628$	171.883	−	99.2368i	0.273699	−	0.158020i
$629$			1529.14i			2.43106i
$630$		0			0
$631$	1185.17			1.87824			0.939122	−	0.343584i	$-0.111641\pi$
$631$	1185.17			1.87824			0.939122	+	0.343584i	$0.111641\pi$
$632$	150.537	+	260.738i	0.238191	+	0.412560i
$633$		0			0
$634$	284.657	−	493.040i	0.448985	−	0.777666i
$635$	248.847	−	143.672i	0.391884	−	0.226255i
$636$		0			0
$637$	−236.882	−	249.648i	−0.371871	−	0.391912i
$638$	−133.567			−0.209353
$639$		0			0
$640$	21.9089	+	12.6491i	0.0342327	+	0.0197642i
$641$	203.549	−	352.557i	0.317549	−	0.550011i	−0.662427	−	0.749126i	$-0.730474\pi$
$641$	203.549	−	352.557i	0.317549	−	0.550011i	0.979976	+	0.199115i	$0.0638068\pi$
$642$		0			0
$643$			1077.83i			1.67626i	0.545474	+	0.838128i	$0.316350\pi$
$643$			1077.83i			1.67626i	−0.545474	+	0.838128i	$0.683650\pi$
$644$	−122.882	−	308.029i	−0.190810	−	0.478306i
$645$		0			0
$646$	698.367	+	1209.61i	1.08106	+	1.87246i
$647$	−1019.05	−	588.349i	−1.57504	−	0.909350i	−0.995536	−	0.0943805i	$-0.969913\pi$
$647$	−1019.05	−	588.349i	−1.57504	−	0.909350i	−0.579504	−	0.814969i	$-0.696754\pi$
$648$		0			0
$649$	976.701	−	563.899i	1.50493	−	0.868873i
$650$			49.6629i			0.0764045i
$651$		0			0
$652$	557.959			0.855765
$653$	−439.563	−	761.345i	−0.673144	−	1.16592i	−0.977008	−	0.213204i	$-0.931610\pi$
$653$	−439.563	−	761.345i	−0.673144	−	1.16592i	0.303864	−	0.952715i	$-0.401723\pi$
$654$		0			0
$655$	−84.4076	+	146.198i	−0.128867	+	0.223203i
$656$	−225.591	+	130.245i	−0.343889	+	0.198545i
$657$		0			0
$658$	88.0113	−	606.890i	0.133756	−	0.922325i
$659$	−65.1550			−0.0988696			−0.0494348	−	0.998777i	$-0.515742\pi$
$659$	−65.1550			−0.0988696			−0.0494348	+	0.998777i	$0.515742\pi$
$660$		0			0
$661$	22.0376	+	12.7234i	0.0333397	+	0.0192487i	0.516577	−	0.856241i	$-0.327206\pi$
$661$	22.0376	+	12.7234i	0.0333397	+	0.0192487i	−0.483237	+	0.875489i	$0.660539\pi$
$662$	−118.011	+	204.401i	−0.178264	+	0.308762i
$663$		0			0
$664$		−	139.809i		−	0.210555i
$665$	481.886	+	69.8832i	0.724641	+	0.105088i
$666$		0			0
$667$	108.927	+	188.667i	0.163309	+	0.282860i
$668$	51.8636	+	29.9435i	0.0776401	+	0.0448256i
$669$		0			0
$670$	−43.5961	+	25.1702i	−0.0650688	+	0.0375675i
$671$			407.618i			0.607478i
$672$		0			0
$673$	23.1893			0.0344566			0.0172283	−	0.999852i	$-0.494516\pi$
$673$	23.1893			0.0344566			0.0172283	+	0.999852i	$0.494516\pi$
$674$	−382.822	−	663.068i	−0.567986	−	0.983780i
$675$		0			0
$676$	−119.672	+	207.278i	−0.177029	+	0.306624i
$677$	123.090	−	71.0658i	0.181816	−	0.104972i	−0.406330	−	0.913727i	$-0.633191\pi$
$677$	123.090	−	71.0658i	0.181816	−	0.104972i	0.588146	+	0.808755i	$0.299858\pi$
$678$		0			0
$679$	−321.705	+	128.337i	−0.473792	+	0.189009i
$680$	200.793			0.295283
$681$		0			0
$682$	253.449	+	146.329i	0.371626	+	0.214558i
$683$	328.352	−	568.722i	0.480749	−	0.832682i	−0.519007	−	0.854770i	$-0.673698\pi$
$683$	328.352	−	568.722i	0.480749	−	0.832682i	0.999756	+	0.0220879i	$0.00703137\pi$
$684$		0			0
$685$		−	240.414i		−	0.350970i
$686$	44.3466	+	483.044i	0.0646452	+	0.704146i
$687$		0			0
$688$	6.06994	+	10.5135i	0.00882259	+	0.0152812i
$689$	8.40290	+	4.85142i	0.0121958	+	0.00704125i
$690$		0			0
$691$	212.350	−	122.600i	0.307308	−	0.177425i	−0.338413	−	0.940998i	$-0.609890\pi$
$691$	212.350	−	122.600i	0.307308	−	0.177425i	0.645721	+	0.763573i	$0.276557\pi$
$692$		−	213.012i		−	0.307821i
$693$		0			0
$694$	606.250			0.873560
$695$	304.109	+	526.733i	0.437567	+	0.757889i
$696$		0			0
$697$	−1033.76	+	1790.52i	−1.48316	+	2.56890i
$698$	−91.4702	+	52.8104i	−0.131046	+	0.0756595i
$699$		0			0
$700$	43.3380	−	54.9710i	0.0619115	−	0.0785300i
$701$	−379.419			−0.541254			−0.270627	−	0.962684i	$-0.587231\pi$
$701$	−379.419			−0.541254			−0.270627	+	0.962684i	$0.587231\pi$
$702$		0			0
$703$	1297.60	+	749.168i	1.84580	+	1.06567i
$704$	41.0782	−	71.1496i	0.0583498	−	0.101065i
$705$		0			0
$706$		−	517.479i		−	0.732973i
$707$	−135.498	+	934.335i	−0.191651	+	1.32155i
$708$		0			0
$709$	442.054	+	765.661i	0.623490	+	1.07992i	0.988831	+	0.149042i	$0.0476191\pi$
$709$	442.054	+	765.661i	0.623490	+	1.07992i	−0.365341	+	0.930874i	$0.619048\pi$
$710$	−146.102	−	84.3520i	−0.205777	−	0.118806i
$711$		0			0
$712$	−403.920	+	233.203i	−0.567304	+	0.327533i
$713$		−	477.337i		−	0.669477i
$714$		0			0
$715$	161.281			0.225568
$716$	−239.973	−	415.645i	−0.335157	−	0.580510i
$717$		0			0
$718$	351.847	−	609.416i	0.490037	−	0.848769i
$719$	825.831	−	476.794i	1.14858	−	0.663135i	0.200042	−	0.979787i	$-0.435892\pi$
$719$	825.831	−	476.794i	1.14858	−	0.663135i	0.948542	+	0.316653i	$0.102559\pi$
$720$		0			0
$721$	205.603	+	162.093i	0.285164	+	0.224817i
$722$	858.068			1.18846
$723$		0			0
$724$	−535.762	−	309.322i	−0.740003	−	0.427241i
$725$	−22.9918	+	39.8230i	−0.0317129	+	0.0549283i
$726$		0			0
$727$			1110.82i			1.52795i	0.645248	+	0.763974i	$0.276754\pi$
$727$			1110.82i			1.52795i	−0.645248	+	0.763974i	$0.723246\pi$
$728$	−129.158	+	51.5249i	−0.177415	+	0.0707759i
$729$		0			0
$730$	114.443	+	198.221i	0.156771	+	0.271536i
$731$	83.4455	+	48.1773i	0.114153	+	0.0659060i
$732$		0			0
$733$	35.2595	−	20.3571i	0.0481029	−	0.0277722i	−0.475756	−	0.879577i	$-0.657825\pi$
$733$	35.2595	−	20.3571i	0.0481029	−	0.0277722i	0.523859	+	0.851805i	$0.324492\pi$
$734$			197.102i			0.268531i
$735$		0			0
$736$	−134.001			−0.182066
$737$	81.7407	+	141.579i	0.110910	+	0.192102i
$738$		0			0
$739$	−422.735	+	732.199i	−0.572037	+	0.990797i	0.424320	+	0.905512i	$0.360513\pi$
$739$	−422.735	+	732.199i	−0.572037	+	0.990797i	−0.996357	+	0.0852847i	$0.972820\pi$
$740$	186.541	−	107.699i	0.252082	−	0.145540i
$741$		0			0
$742$	−5.06747	−	12.7027i	−0.00682947	−	0.0171195i
$743$	−355.319			−0.478222			−0.239111	−	0.970992i	$-0.576856\pi$
$743$	−355.319			−0.478222			−0.239111	+	0.970992i	$0.576856\pi$
$744$		0			0
$745$	−161.556	−	93.2741i	−0.216853	−	0.125200i
$746$	245.733	−	425.623i	0.329401	−	0.570540i
$747$		0			0
$748$		−	652.078i		−	0.871762i
$749$	−107.461	+	136.306i	−0.143473	+	0.181984i
$750$		0			0
$751$	−108.768	−	188.392i	−0.144831	−	0.250855i	0.784479	−	0.620156i	$-0.212931\pi$
$751$	−108.768	−	188.392i	−0.144831	−	0.250855i	−0.929310	+	0.369300i	$0.879597\pi$
$752$	−214.589	−	123.893i	−0.285357	−	0.164751i
$753$		0			0
$754$	79.1091	−	45.6737i	0.104919	−	0.0605751i
$755$			283.521i			0.375525i
$756$		0			0
$757$	1178.25			1.55647			0.778233	−	0.627975i	$-0.216116\pi$
$757$	1178.25			1.55647			0.778233	+	0.627975i	$0.216116\pi$
$758$	217.356	+	376.471i	0.286749	+	0.496663i
$759$		0			0
$760$	98.3741	−	170.389i	0.129440	−	0.224196i
$761$	−711.636	+	410.863i	−0.935133	+	0.539899i	−0.888431	−	0.459010i	$-0.848204\pi$
$761$	−711.636	+	410.863i	−0.935133	+	0.539899i	−0.0467017	+	0.998909i	$0.514871\pi$
$762$		0			0
$763$	−389.948	−	56.5504i	−0.511073	−	0.0741159i
$764$	−6.17920			−0.00808796
$765$		0			0
$766$	623.063	+	359.725i	0.813398	+	0.469615i
$767$	−385.653	+	667.970i	−0.502807	+	0.870887i
$768$		0			0
$769$		−	230.888i		−	0.300244i	−0.988667	−	0.150122i	$-0.952033\pi$
$769$		−	230.888i		−	0.300244i	0.988667	−	0.150122i	$-0.0479667\pi$
$770$	−178.520	−	140.741i	−0.231844	−	0.182781i
$771$		0			0
$772$	238.697	+	413.436i	0.309193	+	0.535539i
$773$	−584.107	−	337.234i	−0.755636	−	0.436267i	0.0720908	−	0.997398i	$-0.477033\pi$
$773$	−584.107	−	337.234i	−0.755636	−	0.436267i	−0.827727	+	0.561131i	$0.810366\pi$
$774$		0			0
$775$	87.2556	−	50.3771i	0.112588	−	0.0650027i
$776$			139.950i			0.180348i
$777$		0			0
$778$	−241.785			−0.310778
$779$	1012.94	+	1754.46i	1.30030	+	2.25219i
$780$		0			0
$781$	−273.935	+	474.469i	−0.350749	+	0.607515i
$782$	−921.077	+	531.784i	−1.17785	+	0.680031i
$783$		0			0
$784$	187.926	+	55.6770i	0.239701	+	0.0710166i
$785$	−221.900			−0.282676
$786$		0			0
$787$	539.438	+	311.445i	0.685436	+	0.395737i	0.801900	−	0.597458i	$-0.203823\pi$
$787$	539.438	+	311.445i	0.685436	+	0.395737i	−0.116464	+	0.993195i	$0.537156\pi$
$788$	−291.539	+	504.960i	−0.369973	+	0.640812i
$789$		0			0
$790$		−	336.611i		−	0.426090i
$791$	194.506	+	487.571i	0.245899	+	0.616399i
$792$		0			0
$793$	−139.386	−	241.423i	−0.175770	−	0.304443i
$794$	779.547	+	450.072i	0.981797	+	0.566841i
$795$		0			0
$796$	−418.448	+	241.591i	−0.525688	+	0.303506i
$797$			1322.28i			1.65907i	0.558452	+	0.829537i	$0.311396\pi$
$797$			1322.28i			1.65907i	−0.558452	+	0.829537i	$0.688604\pi$
$798$		0			0
$799$	−1966.68			−2.46143
$800$	−14.1421	−	24.4949i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	418.763	−	725.319i	0.522148	−	0.904387i
$803$	643.727	−	371.656i	0.801653	−	0.462834i
$804$		0			0
$805$	−53.2139	+	366.941i	−0.0661042	+	0.455827i
$806$	−200.150			−0.248325
$807$		0			0
$808$	330.369	+	190.739i	0.408873	+	0.236063i
$809$	521.105	−	902.581i	0.644135	−	1.11567i	−0.340366	−	0.940293i	$-0.610551\pi$
$809$	521.105	−	902.581i	0.644135	−	1.11567i	0.984501	−	0.175381i	$-0.0561158\pi$
$810$		0			0
$811$			782.292i			0.964602i	0.876006	+	0.482301i	$0.160199\pi$
$811$			782.292i			0.964602i	−0.876006	+	0.482301i	$0.839801\pi$
$812$	−127.421	−	18.4787i	−0.156923	−	0.0227570i
$813$		0			0
$814$	−349.756	−	605.796i	−0.429676	−	0.744221i
$815$	−540.242	−	311.909i	−0.662873	−	0.382710i
$816$		0			0
$817$	81.7647	−	47.2069i	0.100079	−	0.0577808i
$818$		−	401.255i		−	0.490532i
$819$		0			0
$820$	291.237			0.355167
$821$	−505.805	−	876.080i	−0.616084	−	1.06709i	−0.990193	−	0.139704i	$-0.955385\pi$
$821$	−505.805	−	876.080i	−0.616084	−	1.06709i	0.374109	−	0.927385i	$-0.377949\pi$
$822$		0			0
$823$	557.204	−	965.106i	0.677040	−	1.17267i	−0.298828	−	0.954307i	$-0.596596\pi$
$823$	557.204	−	965.106i	0.677040	−	1.17267i	0.975868	−	0.218361i	$-0.0700711\pi$
$824$	91.6160	−	52.8945i	0.111184	−	0.0641924i
$825$		0			0
$826$	1009.77	−	402.827i	1.22249	−	0.487684i
$827$	1267.52			1.53267			0.766336	−	0.642440i	$-0.222078\pi$
$827$	1267.52			1.53267			0.766336	+	0.642440i	$0.222078\pi$
$828$		0			0
$829$	−180.535	−	104.232i	−0.217775	−	0.125732i	0.387145	−	0.922019i	$-0.373461\pi$
$829$	−180.535	−	104.232i	−0.217775	−	0.125732i	−0.604919	+	0.796287i	$0.706795\pi$
$830$	−78.1554	+	135.369i	−0.0941632	+	0.163095i
$831$		0			0
$832$			56.1872i			0.0675327i
$833$	1512.69	−	363.081i	1.81596	−	0.435871i
$834$		0			0
$835$	−33.4778	−	57.9853i	−0.0400932	−	0.0694435i
$836$	−553.341	−	319.472i	−0.661892	−	0.382143i
$837$		0			0
$838$	−590.953	+	341.187i	−0.705194	+	0.407144i
$839$		−	389.239i		−	0.463932i	−0.972724	−	0.231966i	$-0.925484\pi$
$839$		−	389.239i		−	0.463932i	0.972724	−	0.231966i	$-0.0745159\pi$
$840$		0			0
$841$	−756.420			−0.899429
$842$	538.872	+	933.354i	0.639991	+	1.10850i
$843$		0			0
$844$	263.018	−	455.561i	0.311633	−	0.539764i
$845$	231.744	−	133.797i	0.274253	−	0.158340i
$846$		0			0
$847$	67.3305	−	85.4037i	0.0794930	−	0.100831i
$848$	−5.52601			−0.00651652
$849$		0			0
$850$	−194.417	−	112.247i	−0.228725	−	0.132055i
$851$	−570.468	+	988.080i	−0.670350	+	1.16108i
$852$		0			0
$853$			1239.21i			1.45277i	0.687287	+	0.726386i	$0.258801\pi$
$853$			1239.21i			1.45277i	−0.687287	+	0.726386i	$0.741199\pi$
$854$	−56.3928	+	388.861i	−0.0660337	+	0.455341i
$855$		0			0
$856$	35.0668	+	60.7375i	0.0409659	+	0.0709550i
$857$	−157.848	−	91.1334i	−0.184186	−	0.106340i	0.405072	−	0.914285i	$-0.367247\pi$
$857$	−157.848	−	91.1334i	−0.184186	−	0.106340i	−0.589258	+	0.807945i	$0.700580\pi$
$858$		0			0
$859$	−366.992	+	211.883i	−0.427232	+	0.246662i	−0.698167	−	0.715935i	$-0.746001\pi$
$859$	−366.992	+	211.883i	−0.427232	+	0.246662i	0.270935	+	0.962598i	$0.412667\pi$
$860$		−	13.5728i		−	0.0157823i
$861$		0			0
$862$	362.062			0.420026
$863$	−8.63152	−	14.9502i	−0.0100018	−	0.0173236i	0.860981	−	0.508637i	$-0.169850\pi$
$863$	−8.63152	−	14.9502i	−0.0100018	−	0.0173236i	−0.870983	+	0.491313i	$0.836517\pi$
$864$		0			0
$865$	−119.077	+	206.248i	−0.137662	+	0.238437i
$866$	791.895	−	457.201i	0.914428	−	0.527945i
$867$		0			0
$868$	221.542	+	174.659i	0.255233	+	0.201221i
$869$	−1093.15			−1.25794
$870$		0			0
$871$	−96.8266	−	55.9028i	−0.111167	−	0.0641824i
$872$	−79.6056	+	137.881i	−0.0912908	+	0.158120i
$873$		0			0
$874$			1042.15i			1.19239i
$875$	−72.6916	+	28.9988i	−0.0830761	+	0.0331415i
$876$		0			0
$877$	183.668	+	318.122i	0.209428	+	0.362739i	0.951534	−	0.307542i	$-0.0995066\pi$
$877$	183.668	+	318.122i	0.209428	+	0.362739i	−0.742107	+	0.670282i	$0.766173\pi$
$878$	410.620	+	237.071i	0.467676	+	0.270013i
$879$		0			0
$880$	−79.5477	+	45.9269i	−0.0903951	+	0.0521896i
$881$		−	376.890i		−	0.427798i	−0.976856	−	0.213899i	$-0.931384\pi$
$881$		−	376.890i		−	0.427798i	0.976856	−	0.213899i	$-0.0686164\pi$
$882$		0			0
$883$	−1101.06			−1.24695			−0.623476	−	0.781842i	$-0.714280\pi$
$883$	−1101.06			−1.24695			−0.623476	+	0.781842i	$0.714280\pi$
$884$	222.980	+	386.212i	0.252239	+	0.436891i
$885$		0			0
$886$	198.735	−	344.219i	0.224306	−	0.388509i
$887$	105.113	−	60.6873i	0.118504	−	0.0684186i	−0.439576	−	0.898205i	$-0.644871\pi$
$887$	105.113	−	60.6873i	0.118504	−	0.0684186i	0.558081	+	0.829787i	$0.311538\pi$
$888$		0			0
$889$	−333.304	−	835.498i	−0.374920	−	0.939818i
$890$	521.459			0.585909
$891$		0			0
$892$	−195.129	−	112.658i	−0.218755	−	0.126298i
$893$	−963.534	+	1668.89i	−1.07899	+	1.86886i
$894$		0			0
$895$			536.595i			0.599548i
$896$	49.0314	−	62.1926i	0.0547225	−	0.0694114i
$897$		0			0
$898$	−33.3981	−	57.8472i	−0.0371916	−	0.0644178i
$899$	−160.493	−	92.6609i	−0.178524	−	0.103071i
$900$		0			0
$901$	−37.9839	+	21.9300i	−0.0421575	+	0.0243397i
$902$		−	945.799i		−	1.04856i
$903$		0			0
$904$	212.106			0.234631
$905$	345.833	+	599.000i	0.382136	+	0.661879i
$906$		0			0
$907$	−39.0554	+	67.6459i	−0.0430599	+	0.0745820i	−0.886752	−	0.462245i	$-0.847044\pi$
$907$	−39.0554	+	67.6459i	−0.0430599	+	0.0745820i	0.843692	+	0.536827i	$0.180377\pi$
$908$	84.9058	−	49.0204i	0.0935086	−	0.0539872i
$909$		0			0
$910$	153.860	+	22.3128i	0.169077	+	0.0245196i
$911$	−863.281			−0.947619			−0.473809	−	0.880627i	$-0.657121\pi$
$911$	−863.281			−0.947619			−0.473809	+	0.880627i	$0.657121\pi$
$912$		0			0
$913$	439.614	+	253.811i	0.481505	+	0.277997i
$914$	416.339	−	721.121i	0.455513	−	0.788973i
$915$		0			0
$916$			56.2283i			0.0613846i
$917$	415.012	+	327.187i	0.452575	+	0.356801i
$918$		0			0
$919$	−678.926	−	1175.93i	−0.738766	−	1.27958i	−0.953051	−	0.302810i	$-0.902075\pi$
$919$	−678.926	−	1175.93i	−0.738766	−	1.27958i	0.214285	−	0.976771i	$-0.431258\pi$
$920$	129.746	+	74.9088i	0.141028	+	0.0814226i
$921$		0			0
$922$	−74.1712	+	42.8228i	−0.0804460	+	0.0464455i
$923$		−	374.691i		−	0.405949i
$924$		0			0
$925$	−240.823			−0.260350
$926$	62.7622	+	108.707i	0.0677778	+	0.117395i
$927$		0			0
$928$	−26.0123	+	45.0546i	−0.0280305	+	0.0485502i
$929$	−800.920	+	462.411i	−0.862131	+	0.497752i	−0.864725	−	0.502245i	$-0.832508\pi$
$929$	−800.920	+	462.411i	−0.862131	+	0.497752i	0.00259410	+	0.999997i	$0.499174\pi$
$930$		0			0
$931$	433.009	−	1461.53i	0.465101	−	1.56985i
$932$	−352.405			−0.378117
$933$		0			0
$934$	−370.147	−	213.704i	−0.396303	−	0.228806i
$935$	−364.523	+	631.372i	−0.389864	+	0.675264i
$936$		0			0
$937$			270.668i			0.288867i	0.989515	+	0.144433i	$0.0461359\pi$
$937$			270.668i			0.288867i	−0.989515	+	0.144433i	$0.953864\pi$
$938$	58.3924	+	146.373i	0.0622520	+	0.156048i
$939$		0			0
$940$	138.516	+	239.918i	0.147358	+	0.255231i
$941$	395.174	+	228.154i	0.419952	+	0.242459i	0.695057	−	0.718955i	$-0.255379\pi$
$941$	395.174	+	228.154i	0.419952	+	0.242459i	−0.275105	+	0.961414i	$0.588713\pi$
$942$		0			0
$943$	−1335.97	+	771.320i	−1.41672	+	0.817943i
$944$		−	439.278i		−	0.465337i
$945$		0			0
$946$	−44.0780			−0.0465940
$947$	−496.787	−	860.460i	−0.524590	−	0.908617i	−0.999590	−	0.0286308i	$-0.990885\pi$
$947$	−496.787	−	860.460i	−0.524590	−	0.908617i	0.475000	−	0.879986i	$-0.342448\pi$
$948$		0			0
$949$	−254.177	+	440.248i	−0.267837	+	0.463907i
$950$	−190.501	+	109.986i	−0.200527	+	0.115774i
$951$		0			0
$952$	90.2132	−	622.073i	0.0947618	−	0.653438i
$953$	206.385			0.216563			0.108281	−	0.994120i	$-0.465465\pi$
$953$	206.385			0.216563			0.108281	+	0.994120i	$0.465465\pi$
$954$		0			0
$955$	5.98299	+	3.45428i	0.00626491	+	0.00361705i
$956$	34.7150	−	60.1282i	0.0363128	−	0.0628956i
$957$		0			0
$958$		−	49.6817i		−	0.0518598i
$959$	−744.825	−	108.015i	−0.776668	−	0.112633i
$960$		0			0
$961$	−277.472	−	480.596i	−0.288733	−	0.500100i
$962$	414.306	+	239.200i	0.430672	+	0.248649i
$963$		0			0
$964$	459.743	−	265.432i	0.476911	−	0.275345i
$965$		−	533.744i		−	0.553102i
$966$		0			0
$967$	169.282			0.175058			0.0875292	−	0.996162i	$-0.472103\pi$
$967$	169.282			0.175058			0.0875292	+	0.996162i	$0.472103\pi$
$968$	−21.9714	−	38.0556i	−0.0226977	−	0.0393136i
$969$		0			0
$970$	78.2345	−	135.506i	0.0806541	−	0.139697i
$971$	122.891	−	70.9512i	0.126561	−	0.0730702i	−0.435383	−	0.900245i	$-0.643387\pi$
$971$	122.891	−	70.9512i	0.126561	−	0.0730702i	0.561944	+	0.827175i	$0.310054\pi$
$972$		0			0
$973$	1768.50	−	705.504i	1.81757	−	0.725081i
$974$	−91.4053			−0.0938453
$975$		0			0
$976$	137.497	+	79.3837i	0.140878	+	0.0813357i
$977$	−703.901	+	1219.19i	−0.720472	+	1.24789i	0.240339	+	0.970689i	$0.422741\pi$
$977$	−703.901	+	1219.19i	−0.720472	+	1.24789i	−0.960811	+	0.277204i	$0.910592\pi$
$978$		0			0
$979$		−	1693.45i		−	1.72977i
$980$	−150.834	−	158.963i	−0.153912	−	0.162207i
$981$		0			0
$982$	−170.671	−	295.610i	−0.173799	−	0.301029i
$983$	−777.500	−	448.890i	−0.790946	−	0.456653i	0.0493494	−	0.998782i	$-0.484285\pi$
$983$	−777.500	−	448.890i	−0.790946	−	0.456653i	−0.840296	+	0.542129i	$0.817619\pi$
$984$		0			0
$985$	564.562	−	325.950i	0.573160	−	0.330914i
$986$			412.920i			0.418783i
$987$		0			0
$988$	436.976			0.442284
$989$	35.9466	+	62.2613i	0.0363464	+	0.0629538i
$990$		0			0
$991$	−762.140	+	1320.06i	−0.769061	+	1.33205i	0.169011	+	0.985614i	$0.445943\pi$
$991$	−762.140	+	1320.06i	−0.769061	+	1.33205i	−0.938072	+	0.346439i	$0.887391\pi$
$992$	98.7185	−	56.9951i	0.0995146	−	0.0574548i
$993$		0			0
$994$	−326.971	+	414.739i	−0.328945	+	0.417242i
$995$	540.214			0.542929
$996$		0			0
$997$	770.649	+	444.935i	0.772968	+	0.446273i	0.833932	−	0.551866i	$-0.186084\pi$
$997$	770.649	+	444.935i	0.772968	+	0.446273i	−0.0609641	+	0.998140i	$0.519418\pi$
$998$	−135.499	+	234.691i	−0.135771	+	0.235162i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.v.c.451.7		16
3.2	odd	2		210.3.o.b.31.1	✓	16
7.5	odd	6	inner	630.3.v.c.271.7		16
15.2	even	4		1050.3.q.e.199.14		32
15.8	even	4		1050.3.q.e.199.3		32
15.14	odd	2		1050.3.p.i.451.7		16
21.5	even	6		210.3.o.b.61.1	yes	16
21.11	odd	6		1470.3.f.d.391.14		16
21.17	even	6		1470.3.f.d.391.12		16
105.47	odd	12		1050.3.q.e.649.3		32
105.68	odd	12		1050.3.q.e.649.13		32
105.89	even	6		1050.3.p.i.901.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.1	✓	16	3.2	odd	2
210.3.o.b.61.1	yes	16	21.5	even	6
630.3.v.c.271.7		16	7.5	odd	6	inner
630.3.v.c.451.7		16	1.1	even	1	trivial
1050.3.p.i.451.7		16	15.14	odd	2
1050.3.p.i.901.7		16	105.89	even	6
1050.3.q.e.199.3		32	15.8	even	4
1050.3.q.e.199.14		32	15.2	even	4
1050.3.q.e.649.3		32	105.47	odd	12
1050.3.q.e.649.13		32	105.68	odd	12
1470.3.f.d.391.12		16	21.17	even	6
1470.3.f.d.391.14		16	21.11	odd	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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-2.59373 - 6.50174i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-2.59373 - 6.50174i) q^{7} -2.82843 q^{8} +(2.73861 + 1.58114i) q^{10} +(5.13478 - 8.89370i) q^{11} +7.02340i q^{13} +(6.12892 - 7.77408i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-27.4947 - 15.8741i) q^{17} +(-26.9408 + 15.5543i) q^{19} +4.47214i q^{20} +14.5234 q^{22} +(-11.8441 - 20.5146i) q^{23} +(2.50000 - 4.33013i) q^{25} +(-8.60187 + 4.96629i) q^{26} +(13.8551 + 2.00927i) q^{28} -9.19673 q^{29} +(17.4511 + 10.0754i) q^{31} +(2.82843 - 4.89898i) q^{32} -44.8986i q^{34} +(-12.2919 - 9.69068i) q^{35} +(-24.0823 - 41.7118i) q^{37} +(-38.1001 - 21.9971i) q^{38} +(-5.47723 + 3.16228i) q^{40} -65.1226i q^{41} -3.03497 q^{43} +(10.2696 + 17.7874i) q^{44} +(16.7501 - 29.0120i) q^{46} +(53.6472 - 30.9732i) q^{47} +(-35.5451 + 33.7275i) q^{49} +7.07107 q^{50} +(-12.1649 - 7.02340i) q^{52} +(0.690751 - 1.19642i) q^{53} -22.9634i q^{55} +(7.33617 + 18.3897i) q^{56} +(-6.50307 - 11.2636i) q^{58} +(95.1064 + 54.9097i) q^{59} +(-34.3741 + 19.8459i) q^{61} +28.4976i q^{62} +8.00000 q^{64} +(7.85240 + 13.6008i) q^{65} +(-7.95952 + 13.7863i) q^{67} +(54.9893 - 31.7481i) q^{68} +(3.17693 - 21.9068i) q^{70} -53.3489 q^{71} +(62.6830 + 36.1901i) q^{73} +(34.0576 - 58.9894i) q^{74} -62.2172i q^{76} +(-71.1427 - 10.3171i) q^{77} +(-53.2229 - 92.1847i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(79.7586 - 46.0486i) q^{82} +49.4298i q^{83} -70.9909 q^{85} +(-2.14605 - 3.71707i) q^{86} +(-14.5234 + 25.1552i) q^{88} +(142.807 - 82.4499i) q^{89} +(45.6643 - 18.2168i) q^{91} +47.3765 q^{92} +(75.8686 + 43.8027i) q^{94} +(-34.7805 + 60.2416i) q^{95} -49.4799i q^{97} +(-66.4418 - 19.6848i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 4 q^{7}+O(q^{10}) \) 16 * q - 16 * q^4 + 4 * q^7	\( 16 q - 16 q^{4} + 4 q^{7} + 4 q^{11} - 8 q^{14} - 32 q^{16} - 12 q^{17} - 72 q^{19} - 48 q^{22} + 12 q^{23} + 40 q^{25} + 32 q^{28} - 72 q^{29} + 120 q^{31} + 20 q^{35} + 44 q^{37} + 72 q^{38} - 56 q^{43} + 8 q^{44} + 8 q^{46} + 24 q^{47} - 40 q^{49} - 72 q^{52} - 32 q^{53} - 16 q^{56} - 88 q^{58} - 132 q^{59} + 96 q^{61} + 128 q^{64} - 20 q^{65} - 164 q^{67} + 24 q^{68} + 136 q^{71} - 348 q^{73} + 112 q^{74} - 96 q^{77} + 280 q^{79} + 264 q^{82} + 120 q^{85} + 88 q^{86} + 48 q^{88} + 300 q^{89} - 272 q^{91} - 48 q^{92} - 200 q^{95} - 384 q^{98}+O(q^{100}) \) 16 * q - 16 * q^4 + 4 * q^7 + 4 * q^11 - 8 * q^14 - 32 * q^16 - 12 * q^17 - 72 * q^19 - 48 * q^22 + 12 * q^23 + 40 * q^25 + 32 * q^28 - 72 * q^29 + 120 * q^31 + 20 * q^35 + 44 * q^37 + 72 * q^38 - 56 * q^43 + 8 * q^44 + 8 * q^46 + 24 * q^47 - 40 * q^49 - 72 * q^52 - 32 * q^53 - 16 * q^56 - 88 * q^58 - 132 * q^59 + 96 * q^61 + 128 * q^64 - 20 * q^65 - 164 * q^67 + 24 * q^68 + 136 * q^71 - 348 * q^73 + 112 * q^74 - 96 * q^77 + 280 * q^79 + 264 * q^82 + 120 * q^85 + 88 * q^86 + 48 * q^88 + 300 * q^89 - 272 * q^91 - 48 * q^92 - 200 * q^95 - 384 * q^98

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