LMFDB - Embedded newform 630.3.v.c.451.4

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			451.4
Root			$2.81422 - 4.87437i$ of defining polynomial
Character	$\chi$	$=$	630.451
Dual form			630.3.v.c.271.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(6.99242 - 0.325616i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(6.99242 - 0.325616i) q^{7} +2.82843 q^{8} +(-2.73861 - 1.58114i) q^{10} +(6.09582 - 10.5583i) q^{11} +25.3938i q^{13} +(-5.34319 - 8.33369i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(24.9196 + 14.3873i) q^{17} +(-13.9147 + 8.03365i) q^{19} +4.47214i q^{20} -17.2416 q^{22} +(-11.8709 - 20.5610i) q^{23} +(2.50000 - 4.33013i) q^{25} +(31.1010 - 17.9562i) q^{26} +(-6.42844 + 12.4368i) q^{28} -27.9121 q^{29} +(20.0480 + 11.5747i) q^{31} +(-2.82843 + 4.89898i) q^{32} -40.6936i q^{34} +(13.1767 - 8.44832i) q^{35} +(14.5321 + 25.1703i) q^{37} +(19.6783 + 11.3613i) q^{38} +(5.47723 - 3.16228i) q^{40} +56.9065i q^{41} +7.83839 q^{43} +(12.1916 + 21.1165i) q^{44} +(-16.7880 + 29.0777i) q^{46} +(19.7390 - 11.3963i) q^{47} +(48.7879 - 4.55369i) q^{49} -7.07107 q^{50} +(-43.9834 - 25.3938i) q^{52} +(24.2781 - 42.0510i) q^{53} -27.2613i q^{55} +(19.7776 - 0.920981i) q^{56} +(19.7368 + 34.1852i) q^{58} +(62.3779 + 36.0139i) q^{59} +(99.2512 - 57.3027i) q^{61} -32.7382i q^{62} +8.00000 q^{64} +(28.3912 + 49.1750i) q^{65} +(35.2674 - 61.0850i) q^{67} +(-49.8392 + 28.7747i) q^{68} +(-19.6644 - 10.1643i) q^{70} -6.41501 q^{71} +(-34.2569 - 19.7782i) q^{73} +(20.5514 - 35.5961i) q^{74} -32.1346i q^{76} +(39.1866 - 75.8127i) q^{77} +(27.3985 + 47.4555i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(69.6960 - 40.2390i) q^{82} -135.934i q^{83} +64.3422 q^{85} +(-5.54258 - 9.60002i) q^{86} +(17.2416 - 29.8633i) q^{88} +(-124.905 + 72.1140i) q^{89} +(8.26863 + 177.564i) q^{91} +47.4837 q^{92} +(-27.9152 - 16.1168i) q^{94} +(-17.9638 + 31.1142i) q^{95} -78.9980i q^{97} +(-40.0754 - 56.5328i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	6.99242	−	0.325616i	0.998918	−	0.0465165i
$7$	6.99242	−	0.325616i	0.998918	−	0.0465165i
$8$	2.82843			0.353553
$9$		0			0
$10$	−2.73861	−	1.58114i	−0.273861	−	0.158114i
$11$	6.09582	−	10.5583i	0.554165	−	0.959842i	−0.443803	−	0.896125i	$-0.646371\pi$
$11$	6.09582	−	10.5583i	0.554165	−	0.959842i	0.997968	−	0.0637178i	$-0.0202958\pi$
$12$		0			0
$13$			25.3938i			1.95337i	0.214672	+	0.976686i	$0.431132\pi$
$13$			25.3938i			1.95337i	−0.214672	+	0.976686i	$0.568868\pi$
$14$	−5.34319	−	8.33369i	−0.381656	−	0.595263i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	24.9196	+	14.3873i	1.46586	+	0.846315i	0.999272	−	0.0381599i	$-0.0121496\pi$
$17$	24.9196	+	14.3873i	1.46586	+	0.846315i	0.466588	+	0.884475i	$0.345483\pi$
$18$		0			0
$19$	−13.9147	+	8.03365i	−0.732352	+	0.422824i	−0.819282	−	0.573391i	$-0.805628\pi$
$19$	−13.9147	+	8.03365i	−0.732352	+	0.422824i	0.0869298	+	0.996214i	$0.472294\pi$
$20$			4.47214i			0.223607i
$21$		0			0
$22$	−17.2416			−0.783708
$23$	−11.8709	−	20.5610i	−0.516127	−	0.893958i	−0.999825	−	0.0187231i	$-0.994040\pi$
$23$	−11.8709	−	20.5610i	−0.516127	−	0.893958i	0.483698	−	0.875235i	$-0.339293\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	31.1010	−	17.9562i	1.19619	−	0.690621i
$27$		0			0
$28$	−6.42844	+	12.4368i	−0.229587	+	0.444173i
$29$	−27.9121			−0.962486			−0.481243	−	0.876587i	$-0.659815\pi$
$29$	−27.9121			−0.962486			−0.481243	+	0.876587i	$0.659815\pi$
$30$		0			0
$31$	20.0480	+	11.5747i	0.646709	+	0.373378i	0.787194	−	0.616705i	$-0.211533\pi$
$31$	20.0480	+	11.5747i	0.646709	+	0.373378i	−0.140485	+	0.990083i	$0.544866\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$		0			0
$34$		−	40.6936i		−	1.19687i
$35$	13.1767	−	8.44832i	0.376478	−	0.241381i
$36$		0			0
$37$	14.5321	+	25.1703i	0.392758	+	0.680277i	0.992812	−	0.119682i	$-0.0381876\pi$
$37$	14.5321	+	25.1703i	0.392758	+	0.680277i	−0.600054	+	0.799960i	$0.704854\pi$
$38$	19.6783	+	11.3613i	0.517851	+	0.298982i
$39$		0			0
$40$	5.47723	−	3.16228i	0.136931	−	0.0790569i
$41$			56.9065i			1.38796i	0.719992	+	0.693982i	$0.244145\pi$
$41$			56.9065i			1.38796i	−0.719992	+	0.693982i	$0.755855\pi$
$42$		0			0
$43$	7.83839			0.182288			0.0911440	−	0.995838i	$-0.470948\pi$
$43$	7.83839			0.182288			0.0911440	+	0.995838i	$0.470948\pi$
$44$	12.1916	+	21.1165i	0.277083	+	0.479921i
$45$		0			0
$46$	−16.7880	+	29.0777i	−0.364957	+	0.632124i
$47$	19.7390	−	11.3963i	0.419979	−	0.242475i	−0.275089	−	0.961419i	$-0.588707\pi$
$47$	19.7390	−	11.3963i	0.419979	−	0.242475i	0.695068	+	0.718944i	$0.255374\pi$
$48$		0			0
$49$	48.7879	−	4.55369i	0.995672	−	0.0929324i
$50$	−7.07107			−0.141421
$51$		0			0
$52$	−43.9834	−	25.3938i	−0.845835	−	0.488343i
$53$	24.2781	−	42.0510i	0.458078	−	0.793414i	−0.540781	−	0.841163i	$-0.681871\pi$
$53$	24.2781	−	42.0510i	0.458078	−	0.793414i	0.998859	+	0.0477489i	$0.0152047\pi$
$54$		0			0
$55$		−	27.2613i		−	0.495660i
$56$	19.7776	−	0.920981i	0.353171	−	0.0164461i
$57$		0			0
$58$	19.7368	+	34.1852i	0.340290	+	0.589400i
$59$	62.3779	+	36.0139i	1.05725	+	0.610405i	0.924671	−	0.380767i	$-0.124340\pi$
$59$	62.3779	+	36.0139i	1.05725	+	0.610405i	0.132581	+	0.991172i	$0.457673\pi$
$60$		0			0
$61$	99.2512	−	57.3027i	1.62707	−	0.939388i	0.642107	−	0.766615i	$-0.278060\pi$
$61$	99.2512	−	57.3027i	1.62707	−	0.939388i	0.984962	−	0.172773i	$-0.0552729\pi$
$62$		−	32.7382i		−	0.528036i
$63$		0			0
$64$	8.00000			0.125000
$65$	28.3912	+	49.1750i	0.436787	+	0.756538i
$66$		0			0
$67$	35.2674	−	61.0850i	0.526380	−	0.911716i	−0.473148	−	0.880983i	$-0.656882\pi$
$67$	35.2674	−	61.0850i	0.526380	−	0.911716i	0.999528	−	0.0307332i	$-0.00978424\pi$
$68$	−49.8392	+	28.7747i	−0.732930	+	0.423157i
$69$		0			0
$70$	−19.6644	−	10.1643i	−0.280920	−	0.145204i
$71$	−6.41501			−0.0903522			−0.0451761	−	0.998979i	$-0.514385\pi$
$71$	−6.41501			−0.0903522			−0.0451761	+	0.998979i	$0.514385\pi$
$72$		0			0
$73$	−34.2569	−	19.7782i	−0.469272	−	0.270934i	0.246663	−	0.969101i	$-0.420666\pi$
$73$	−34.2569	−	19.7782i	−0.469272	−	0.270934i	−0.715935	+	0.698167i	$0.753999\pi$
$74$	20.5514	−	35.5961i	0.277722	−	0.481029i
$75$		0			0
$76$		−	32.1346i		−	0.422824i
$77$	39.1866	−	75.8127i	0.508917	−	0.984581i
$78$		0			0
$79$	27.3985	+	47.4555i	0.346816	+	0.600703i	0.985682	−	0.168615i	$-0.0539295\pi$
$79$	27.3985	+	47.4555i	0.346816	+	0.600703i	−0.638866	+	0.769318i	$0.720596\pi$
$80$	−7.74597	−	4.47214i	−0.0968246	−	0.0559017i
$81$		0			0
$82$	69.6960	−	40.2390i	0.849951	−	0.490719i
$83$		−	135.934i		−	1.63775i	−0.573969	−	0.818877i	$-0.694597\pi$
$83$		−	135.934i		−	1.63775i	0.573969	−	0.818877i	$-0.305403\pi$
$84$		0			0
$85$	64.3422			0.756967
$86$	−5.54258	−	9.60002i	−0.0644486	−	0.111628i
$87$		0			0
$88$	17.2416	−	29.8633i	0.195927	−	0.339356i
$89$	−124.905	+	72.1140i	−1.40343	+	0.810270i	−0.994743	−	0.102405i	$-0.967346\pi$
$89$	−124.905	+	72.1140i	−1.40343	+	0.810270i	−0.408686	+	0.912675i	$0.634013\pi$
$90$		0			0
$91$	8.26863	+	177.564i	0.0908641	+	1.95126i
$92$	47.4837			0.516127
$93$		0			0
$94$	−27.9152	−	16.1168i	−0.296970	−	0.171456i
$95$	−17.9638	+	31.1142i	−0.189093	+	0.327518i
$96$		0			0
$97$		−	78.9980i		−	0.814412i	−0.913336	−	0.407206i	$-0.866503\pi$
$97$		−	78.9980i		−	0.814412i	0.913336	−	0.407206i	$-0.133497\pi$
$98$	−40.0754	−	56.5328i	−0.408933	−	0.576866i
$99$		0			0
$100$	5.00000	+	8.66025i	0.0500000	+	0.0866025i
$101$	40.4728	+	23.3670i	0.400721	+	0.231356i	0.686795	−	0.726851i	$-0.259017\pi$
$101$	40.4728	+	23.3670i	0.400721	+	0.231356i	−0.286074	+	0.958208i	$0.592350\pi$
$102$		0			0
$103$	−144.022	+	83.1514i	−1.39828	+	0.807295i	−0.994212	−	0.107435i	$-0.965736\pi$
$103$	−144.022	+	83.1514i	−1.39828	+	0.807295i	−0.404064	+	0.914731i	$0.632403\pi$
$104$			71.8246i			0.690621i
$105$		0			0
$106$	−68.6689			−0.647820
$107$	−16.4908	−	28.5629i	−0.154120	−	0.266943i	0.778618	−	0.627498i	$-0.215921\pi$
$107$	−16.4908	−	28.5629i	−0.154120	−	0.266943i	−0.932738	+	0.360554i	$0.882587\pi$
$108$		0			0
$109$	75.8575	−	131.389i	0.695940	−	1.20540i	−0.273923	−	0.961752i	$-0.588321\pi$
$109$	75.8575	−	131.389i	0.695940	−	1.20540i	0.969863	−	0.243652i	$-0.0783454\pi$
$110$	−33.3882	+	19.2767i	−0.303529	+	0.175242i
$111$		0			0
$112$	−15.1128	−	23.5712i	−0.134936	−	0.210457i
$113$	42.1910			0.373372			0.186686	−	0.982420i	$-0.440225\pi$
$113$	42.1910			0.373372			0.186686	+	0.982420i	$0.440225\pi$
$114$		0			0
$115$	−45.9759	−	26.5442i	−0.399790	−	0.230819i
$116$	27.9121	−	48.3452i	0.240622	−	0.416769i
$117$		0			0
$118$		−	101.863i		−	0.863243i
$119$	178.933	+	92.4882i	1.50364	+	0.777212i
$120$		0			0
$121$	−13.8180	−	23.9334i	−0.114198	−	0.197797i
$122$	−140.362	−	81.0383i	−1.15051	−	0.664248i
$123$		0			0
$124$	−40.0960	+	23.1494i	−0.323354	+	0.186689i
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	49.3159			0.388314			0.194157	−	0.980970i	$-0.437803\pi$
$127$	49.3159			0.388314			0.194157	+	0.980970i	$0.437803\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	40.1512	−	69.5439i	0.308855	−	0.534953i
$131$	12.6892	−	7.32612i	0.0968642	−	0.0559246i	−0.450785	−	0.892632i	$-0.648856\pi$
$131$	12.6892	−	7.32612i	0.0968642	−	0.0559246i	0.547650	+	0.836708i	$0.315523\pi$
$132$		0			0
$133$	−94.6815	+	60.7055i	−0.711891	+	0.456433i
$134$	−99.7514			−0.744413
$135$		0			0
$136$	70.4833	+	40.6936i	0.518260	+	0.299217i
$137$	−8.61062	+	14.9140i	−0.0628512	+	0.108862i	−0.895739	−	0.444581i	$-0.853353\pi$
$137$	−8.61062	+	14.9140i	−0.0628512	+	0.108862i	0.832888	+	0.553442i	$0.186686\pi$
$138$		0			0
$139$		−	31.2612i		−	0.224901i	−0.993657	−	0.112450i	$-0.964130\pi$
$139$		−	31.2612i		−	0.224901i	0.993657	−	0.112450i	$-0.0358699\pi$
$140$	1.45620	+	31.2711i	0.0104014	+	0.223365i
$141$		0			0
$142$	4.53610	+	7.85675i	0.0319443	+	0.0553292i
$143$	268.115	+	154.796i	1.87493	+	1.08249i
$144$		0			0
$145$	−54.0516	+	31.2067i	−0.372769	+	0.215218i
$146$			55.9412i			0.383159i
$147$		0			0
$148$	−58.1282			−0.392758
$149$	−71.5886	−	123.995i	−0.480460	−	0.832182i	0.519288	−	0.854599i	$-0.326197\pi$
$149$	−71.5886	−	123.995i	−0.480460	−	0.832182i	−0.999749	+	0.0224175i	$0.992864\pi$
$150$		0			0
$151$	−23.1788	+	40.1468i	−0.153502	+	0.265873i	−0.932512	−	0.361138i	$-0.882388\pi$
$151$	−23.1788	+	40.1468i	−0.153502	+	0.265873i	0.779011	+	0.627011i	$0.215722\pi$
$152$	−39.3567	+	22.7226i	−0.258926	+	0.149491i
$153$		0			0
$154$	−120.560	+	5.61413i	−0.782860	+	0.0364554i
$155$	51.7637			0.333959
$156$		0			0
$157$	71.4553	+	41.2548i	0.455130	+	0.262769i	0.709994	−	0.704208i	$-0.248698\pi$
$157$	71.4553	+	41.2548i	0.455130	+	0.262769i	−0.254865	+	0.966977i	$0.582031\pi$
$158$	38.7473	−	67.1122i	0.245236	−	0.424761i
$159$		0			0
$160$			12.6491i			0.0790569i
$161$	−89.7015	−	139.906i	−0.557152	−	0.868982i
$162$		0			0
$163$	123.208	+	213.403i	0.755879	+	1.30922i	0.944936	+	0.327254i	$0.106123\pi$
$163$	123.208	+	213.403i	0.755879	+	1.30922i	−0.189058	+	0.981966i	$0.560543\pi$
$164$	−98.5650	−	56.9065i	−0.601006	−	0.346991i
$165$		0			0
$166$	−166.484	+	96.1195i	−1.00292	+	0.579033i
$167$		−	287.387i		−	1.72088i	−0.509549	−	0.860441i	$-0.670188\pi$
$167$		−	287.387i		−	1.72088i	0.509549	−	0.860441i	$-0.329812\pi$
$168$		0			0
$169$	−475.847			−2.81566
$170$	−45.4968	−	78.8028i	−0.267628	−	0.463546i
$171$		0			0
$172$	−7.83839	+	13.5765i	−0.0455720	+	0.0789330i
$173$	−236.901	+	136.775i	−1.36937	+	0.790605i	−0.990847	−	0.134988i	$-0.956900\pi$
$173$	−236.901	+	136.775i	−1.36937	+	0.790605i	−0.378521	+	0.925593i	$0.623567\pi$
$174$		0			0
$175$	16.0711	−	31.0921i	0.0918349	−	0.177669i
$176$	−48.7665			−0.277083
$177$		0			0
$178$	176.643	+	101.985i	0.992374	+	0.572948i
$179$	−50.3990	+	87.2936i	−0.281558	+	0.487674i	−0.971769	−	0.235935i	$-0.924185\pi$
$179$	−50.3990	+	87.2936i	−0.281558	+	0.487674i	0.690210	+	0.723609i	$0.257518\pi$
$180$		0			0
$181$			135.147i			0.746667i	0.927697	+	0.373333i	$0.121785\pi$
$181$			135.147i			0.746667i	−0.927697	+	0.373333i	$0.878215\pi$
$182$	211.624	−	135.684i	1.16277	−	0.745516i
$183$		0			0
$184$	−33.5760	−	58.1554i	−0.182478	−	0.316062i
$185$	56.2824	+	32.4947i	0.304229	+	0.175647i
$186$		0			0
$187$	303.811	−	175.405i	1.62466	−	0.937996i
$188$			45.5853i			0.242475i
$189$		0			0
$190$	50.8093			0.267417
$191$	89.0902	+	154.309i	0.466441	+	0.807900i	0.999265	−	0.0383263i	$-0.0122026\pi$
$191$	89.0902	+	154.309i	0.466441	+	0.807900i	−0.532824	+	0.846226i	$0.678869\pi$
$192$		0			0
$193$	−67.5577	+	117.013i	−0.350040	+	0.606287i	−0.986256	−	0.165224i	$-0.947165\pi$
$193$	−67.5577	+	117.013i	−0.350040	+	0.606287i	0.636216	+	0.771511i	$0.280499\pi$
$194$	−96.7523	+	55.8600i	−0.498723	+	0.287938i
$195$		0			0
$196$	−40.9007	+	89.0569i	−0.208677	+	0.454372i
$197$	−64.7529			−0.328695			−0.164347	−	0.986403i	$-0.552552\pi$
$197$	−64.7529			−0.328695			−0.164347	+	0.986403i	$0.552552\pi$
$198$		0			0
$199$	116.757	+	67.4097i	0.586719	+	0.338742i	0.763799	−	0.645454i	$-0.223332\pi$
$199$	116.757	+	67.4097i	0.586719	+	0.338742i	−0.177080	+	0.984196i	$0.556665\pi$
$200$	7.07107	−	12.2474i	0.0353553	−	0.0612372i
$201$		0			0
$202$		−	66.0918i		−	0.327187i
$203$	−195.173	+	9.08862i	−0.961444	+	0.0447715i
$204$		0			0
$205$	63.6234	+	110.199i	0.310358	+	0.537556i
$206$	203.679	+	117.594i	0.988731	+	0.570844i
$207$		0			0
$208$	87.9668	−	50.7877i	0.422917	−	0.244172i
$209$			195.887i			0.937257i
$210$		0			0
$211$	−116.352			−0.551432			−0.275716	−	0.961239i	$-0.588915\pi$
$211$	−116.352			−0.551432			−0.275716	+	0.961239i	$0.588915\pi$
$212$	48.5563	+	84.1019i	0.229039	+	0.396707i
$213$		0			0
$214$	−23.3215	+	40.3941i	−0.108979	+	0.188757i
$215$	15.1790	−	8.76358i	0.0705999	−	0.0407608i
$216$		0			0
$217$	143.953	+	74.4073i	0.663377	+	0.342891i
$218$	−214.557			−0.984208
$219$		0			0
$220$	47.2180	+	27.2613i	0.214627	+	0.123915i
$221$	−365.350	+	632.805i	−1.65317	+	2.86337i
$222$		0			0
$223$			30.0511i			0.134758i	0.997727	+	0.0673791i	$0.0214637\pi$
$223$			30.0511i			0.134758i	−0.997727	+	0.0673791i	$0.978536\pi$
$224$	−18.1824	+	35.1767i	−0.0811713	+	0.157039i
$225$		0			0
$226$	−29.8335	−	51.6732i	−0.132007	−	0.228642i
$227$	−122.698	−	70.8400i	−0.540522	−	0.312070i	0.204769	−	0.978810i	$-0.434356\pi$
$227$	−122.698	−	70.8400i	−0.540522	−	0.312070i	−0.745290	+	0.666740i	$0.767689\pi$
$228$		0			0
$229$	−188.648	+	108.916i	−0.823792	+	0.475617i	−0.851722	−	0.523993i	$-0.824442\pi$
$229$	−188.648	+	108.916i	−0.823792	+	0.475617i	0.0279303	+	0.999610i	$0.491108\pi$
$230$			75.0783i			0.326427i
$231$		0			0
$232$	−78.9473			−0.340290
$233$	−2.12597	−	3.68229i	−0.00912435	−	0.0158038i	0.861427	−	0.507881i	$-0.169571\pi$
$233$	−2.12597	−	3.68229i	−0.00912435	−	0.0158038i	−0.870552	+	0.492077i	$0.836238\pi$
$234$		0			0
$235$	25.4830	−	44.1378i	0.108438	−	0.187820i
$236$	−124.756	+	72.0278i	−0.528626	+	0.305202i
$237$		0			0
$238$	−13.2505	−	284.547i	−0.0556742	−	1.19557i
$239$	−261.513			−1.09419			−0.547097	−	0.837069i	$-0.684267\pi$
$239$	−261.513			−1.09419			−0.547097	+	0.837069i	$0.684267\pi$
$240$		0			0
$241$	−86.5156	−	49.9498i	−0.358986	−	0.207261i	0.309650	−	0.950851i	$-0.399788\pi$
$241$	−86.5156	−	49.9498i	−0.358986	−	0.207261i	−0.668636	+	0.743590i	$0.733121\pi$
$242$	−19.5416	+	33.8470i	−0.0807503	+	0.139864i
$243$		0			0
$244$			229.211i			0.939388i
$245$	89.3863	−	63.3648i	0.364842	−	0.258632i
$246$		0			0
$247$	−204.005	−	353.347i	−0.825932	−	1.43056i
$248$	56.7042	+	32.7382i	0.228646	+	0.132009i
$249$		0			0
$250$	−13.6931	+	7.90569i	−0.0547723	+	0.0316228i
$251$		−	250.563i		−	0.998258i	−0.866528	−	0.499129i	$-0.833653\pi$
$251$		−	250.563i		−	0.998258i	0.866528	−	0.499129i	$-0.166347\pi$
$252$		0			0
$253$	−289.452			−1.14408
$254$	−34.8716	−	60.3993i	−0.137290	−	0.237793i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−151.261	+	87.3305i	−0.588563	+	0.339807i	−0.764529	−	0.644589i	$-0.777029\pi$
$257$	−151.261	+	87.3305i	−0.588563	+	0.339807i	0.175966	+	0.984396i	$0.443695\pi$
$258$		0			0
$259$	109.810	+	171.269i	0.423977	+	0.661271i
$260$	−113.565			−0.436787
$261$		0			0
$262$	−17.9452	−	10.3607i	−0.0684933	−	0.0395446i
$263$	10.4417	−	18.0856i	0.0397023	−	0.0687664i	−0.845491	−	0.533989i	$-0.820692\pi$
$263$	10.4417	−	18.0856i	0.0397023	−	0.0687664i	0.885194	+	0.465223i	$0.154026\pi$
$264$		0			0
$265$		−	108.575i		−	0.409717i
$266$	141.299	+	73.0354i	0.531198	+	0.274569i
$267$		0			0
$268$	70.5349	+	122.170i	0.263190	+	0.455858i
$269$	−0.255741	−	0.147652i	−0.000950712	−	0.000548894i	0.499525	−	0.866300i	$-0.333508\pi$
$269$	−0.255741	−	0.147652i	−0.000950712	−	0.000548894i	−0.500475	+	0.865751i	$0.666841\pi$
$270$		0			0
$271$	284.141	−	164.049i	1.04849	−	0.605346i	0.126264	−	0.991997i	$-0.459702\pi$
$271$	284.141	−	164.049i	1.04849	−	0.605346i	0.922226	+	0.386651i	$0.126368\pi$
$272$		−	115.099i		−	0.423157i
$273$		0			0
$274$	24.3545			0.0888851
$275$	−30.4791	−	52.7913i	−0.110833	−	0.191968i
$276$		0			0
$277$	251.485	−	435.585i	0.907888	−	1.57251i	0.0908951	−	0.995860i	$-0.471027\pi$
$277$	251.485	−	435.585i	0.907888	−	1.57251i	0.816993	−	0.576648i	$-0.195639\pi$
$278$	−38.2870	+	22.1050i	−0.137723	+	0.0795144i
$279$		0			0
$280$	37.2694	−	23.8955i	0.133105	−	0.0853409i
$281$	−264.481			−0.941213			−0.470607	−	0.882343i	$-0.655965\pi$
$281$	−264.481			−0.941213			−0.470607	+	0.882343i	$0.655965\pi$
$282$		0			0
$283$	−399.801	−	230.825i	−1.41272	−	0.815636i	−0.417079	−	0.908870i	$-0.636946\pi$
$283$	−399.801	−	230.825i	−1.41272	−	0.815636i	−0.995644	+	0.0932336i	$0.970280\pi$
$284$	6.41501	−	11.1111i	0.0225881	−	0.0391237i
$285$		0			0
$286$		−	437.830i		−	1.53087i
$287$	18.5297	+	397.914i	0.0645633	+	1.38646i
$288$		0			0
$289$	269.492	+	466.773i	0.932497	+	1.61513i
$290$	76.4404	+	44.1329i	0.263588	+	0.152182i
$291$		0			0
$292$	68.5137	−	39.5564i	0.234636	−	0.135467i
$293$		−	134.788i		−	0.460027i	−0.973187	−	0.230014i	$-0.926123\pi$
$293$		−	134.788i		−	0.460027i	0.973187	−	0.230014i	$-0.0738771\pi$
$294$		0			0
$295$	161.059			0.545963
$296$	41.1029	+	71.1922i	0.138861	+	0.240514i
$297$		0			0
$298$	−101.242	+	175.355i	−0.339737	+	0.588441i
$299$	522.124	−	301.448i	1.74623	−	1.00819i
$300$		0			0
$301$	54.8093	−	2.55230i	0.182091	−	0.00847941i
$302$	65.5595			0.217084
$303$		0			0
$304$	55.6588	+	32.1346i	0.183088	+	0.105706i
$305$	128.133	−	221.932i	0.420107	−	0.727647i
$306$		0			0
$307$			23.7237i			0.0772760i	0.999253	+	0.0386380i	$0.0123019\pi$
$307$			23.7237i			0.0772760i	−0.999253	+	0.0386380i	$0.987698\pi$
$308$	92.1249	+	143.686i	0.299107	+	0.466513i
$309$		0			0
$310$	−36.6024	−	63.3973i	−0.118072	−	0.204507i
$311$	−245.097	−	141.507i	−0.788092	−	0.455005i	0.0511984	−	0.998689i	$-0.483696\pi$
$311$	−245.097	−	141.507i	−0.788092	−	0.455005i	−0.839290	+	0.543683i	$0.817029\pi$
$312$		0			0
$313$	367.522	−	212.189i	1.17419	−	0.677920i	0.219528	−	0.975606i	$-0.429548\pi$
$313$	367.522	−	212.189i	1.17419	−	0.677920i	0.954664	+	0.297687i	$0.0962150\pi$
$314$		−	116.686i		−	0.371612i
$315$		0			0
$316$	−109.594			−0.346816
$317$	−14.0641	−	24.3597i	−0.0443661	−	0.0768444i	0.842990	−	0.537930i	$-0.180793\pi$
$317$	−14.0641	−	24.3597i	−0.0443661	−	0.0768444i	−0.887356	+	0.461085i	$0.847460\pi$
$318$		0			0
$319$	−170.147	+	294.703i	−0.533376	+	0.923835i
$320$	15.4919	−	8.94427i	0.0484123	−	0.0279508i
$321$		0			0
$322$	−107.921	+	208.790i	−0.335158	+	0.648416i
$323$	−462.332			−1.43137
$324$		0			0
$325$	109.959	+	63.4846i	0.338334	+	0.195337i
$326$	174.243	−	301.797i	0.534487	−	0.925758i
$327$		0			0
$328$			160.956i			0.490719i
$329$	134.313	−	86.1153i	0.408245	−	0.261749i
$330$		0			0
$331$	−130.940	−	226.795i	−0.395590	−	0.685182i	0.597586	−	0.801805i	$-0.296127\pi$
$331$	−130.940	−	226.795i	−0.395590	−	0.685182i	−0.993176	+	0.116623i	$0.962793\pi$
$332$	235.444	+	135.934i	0.709168	+	0.409438i
$333$		0			0
$334$	−351.976	+	203.214i	−1.05382	+	0.608424i
$335$		−	157.721i		−	0.470808i
$336$		0			0
$337$	−539.998			−1.60237			−0.801185	−	0.598417i	$-0.795796\pi$
$337$	−539.998			−1.60237			−0.801185	+	0.598417i	$0.795796\pi$
$338$	336.475	+	582.791i	0.995487	+	1.72423i
$339$		0			0
$340$	−64.3422	+	111.444i	−0.189242	+	0.327776i
$341$	244.418	−	141.115i	0.716767	−	0.413826i
$342$		0			0
$343$	339.663	−	47.7274i	0.990272	−	0.139147i
$344$	22.1703			0.0644486
$345$		0			0
$346$	335.028	+	193.429i	0.968289	+	0.559042i
$347$	−19.9273	+	34.5150i	−0.0574273	+	0.0994670i	−0.893310	−	0.449441i	$-0.851623\pi$
$347$	−19.9273	+	34.5150i	−0.0574273	+	0.0994670i	0.835883	+	0.548908i	$0.184956\pi$
$348$		0			0
$349$			326.000i			0.934099i	0.884231	+	0.467049i	$0.154683\pi$
$349$			326.000i			0.934099i	−0.884231	+	0.467049i	$0.845317\pi$
$350$	−49.4439	+	2.30245i	−0.141268	+	0.00657843i
$351$		0			0
$352$	34.4832	+	59.7266i	0.0979635	+	0.169678i
$353$	126.505	+	73.0374i	0.358370	+	0.206905i	0.668365	−	0.743833i	$-0.266994\pi$
$353$	126.505	+	73.0374i	0.358370	+	0.206905i	−0.309996	+	0.950738i	$0.600328\pi$
$354$		0			0
$355$	−12.4226	+	7.17220i	−0.0349933	+	0.0202034i
$356$		−	288.456i		−	0.810270i
$357$		0			0
$358$	142.550			0.398184
$359$	10.7785	+	18.6689i	0.0300237	+	0.0520026i	0.880647	−	0.473773i	$-0.157108\pi$
$359$	10.7785	+	18.6689i	0.0300237	+	0.0520026i	−0.850623	+	0.525776i	$0.823775\pi$
$360$		0			0
$361$	−51.4209	+	89.0636i	−0.142440	+	0.246714i
$362$	165.520	−	95.5632i	0.457238	−	0.263987i
$363$		0			0
$364$	−315.819	−	163.243i	−0.867635	−	0.448469i
$365$	−88.4508			−0.242331
$366$		0			0
$367$	176.974	+	102.176i	0.482217	+	0.278408i	0.721340	−	0.692581i	$-0.243527\pi$
$367$	176.974	+	102.176i	0.482217	+	0.278408i	−0.239123	+	0.970989i	$0.576860\pi$
$368$	−47.4837	+	82.2442i	−0.129032	+	0.223490i
$369$		0			0
$370$		−	91.9088i		−	0.248402i
$371$	156.070	−	301.943i	0.420675	−	0.813864i
$372$		0			0
$373$	−281.632	−	487.800i	−0.755045	−	1.30778i	−0.945352	−	0.326051i	$-0.894282\pi$
$373$	−281.632	−	487.800i	−0.755045	−	1.30778i	0.190308	−	0.981724i	$-0.439051\pi$
$374$	−429.654	−	248.061i	−1.14881	−	0.663264i
$375$		0			0
$376$	55.8304	−	32.2337i	0.148485	−	0.0857279i
$377$		−	708.795i		−	1.88009i
$378$		0			0
$379$	300.642			0.793250			0.396625	−	0.917981i	$-0.370181\pi$
$379$	300.642			0.793250			0.396625	+	0.917981i	$0.370181\pi$
$380$	−35.9276	−	62.2284i	−0.0945463	−	0.163759i
$381$		0			0
$382$	125.993	−	218.226i	0.329824	−	0.571271i
$383$	9.34543	−	5.39559i	0.0244006	−	0.0140877i	−0.487750	−	0.872983i	$-0.662182\pi$
$383$	9.34543	−	5.39559i	0.0244006	−	0.0140877i	0.512151	+	0.858896i	$0.328849\pi$
$384$		0			0
$385$	−8.87672	−	190.623i	−0.0230564	−	0.495124i
$386$	191.082			0.495031
$387$		0			0
$388$	136.828	+	78.9980i	0.352651	+	0.203603i
$389$	−65.7124	+	113.817i	−0.168927	+	0.292589i	−0.938043	−	0.346520i	$-0.887363\pi$
$389$	−65.7124	+	113.817i	−0.168927	+	0.292589i	0.769116	+	0.639109i	$0.220697\pi$
$390$		0			0
$391$		−	683.164i		−	1.74722i
$392$	137.993	−	12.8798i	0.352023	−	0.0328566i
$393$		0			0
$394$	45.7872	+	79.3058i	0.116211	+	0.201284i
$395$	106.114	+	61.2648i	0.268642	+	0.155101i
$396$		0			0
$397$	−485.778	+	280.464i	−1.22362	+	0.706459i	−0.965689	−	0.259703i	$-0.916375\pi$
$397$	−485.778	+	280.464i	−1.22362	+	0.706459i	−0.257935	+	0.966162i	$0.583042\pi$
$398$		−	190.664i		−	0.479054i
$399$		0			0
$400$	−20.0000			−0.0500000
$401$	170.877	+	295.967i	0.426126	+	0.738072i	0.996525	−	0.0832958i	$-0.0265446\pi$
$401$	170.877	+	295.967i	0.426126	+	0.738072i	−0.570399	+	0.821368i	$0.693211\pi$
$402$		0			0
$403$	−293.926	+	509.095i	−0.729345	+	1.26326i
$404$	−80.9456	+	46.7340i	−0.200360	+	0.115678i
$405$		0			0
$406$	149.140	+	232.611i	0.367339	+	0.572933i
$407$	354.339			0.870612
$408$		0			0
$409$	19.6793	+	11.3619i	0.0481157	+	0.0277796i	0.523865	−	0.851801i	$-0.324490\pi$
$409$	19.6793	+	11.3619i	0.0481157	+	0.0277796i	−0.475749	+	0.879581i	$0.657823\pi$
$410$	89.9771	−	155.845i	0.219456	−	0.380110i
$411$		0			0
$412$		−	332.606i		−	0.807295i
$413$	447.899	+	231.513i	1.08450	+	0.560564i
$414$		0			0
$415$	−151.978	−	263.234i	−0.366213	−	0.634299i
$416$	−124.404	−	71.8246i	−0.299048	−	0.172655i
$417$		0			0
$418$	239.911	−	138.513i	0.573950	−	0.331370i
$419$		−	347.375i		−	0.829057i	−0.910036	−	0.414529i	$-0.863946\pi$
$419$		−	347.375i		−	0.829057i	0.910036	−	0.414529i	$-0.136054\pi$
$420$		0			0
$421$	−340.381			−0.808507			−0.404253	−	0.914647i	$-0.632469\pi$
$421$	−340.381			−0.808507			−0.404253	+	0.914647i	$0.632469\pi$
$422$	82.2734	+	142.502i	0.194961	+	0.337682i
$423$		0			0
$424$	68.6689	−	118.938i	0.161955	−	0.280514i
$425$	124.598	−	71.9367i	0.293172	−	0.169263i
$426$		0			0
$427$	675.348	−	433.002i	1.58161	−	1.01406i
$428$	65.9632			0.154120
$429$		0			0
$430$	−21.4663	−	12.3936i	−0.0499216	−	0.0288223i
$431$	−21.7871	+	37.7363i	−0.0505500	+	0.0875552i	−0.890193	−	0.455583i	$-0.849431\pi$
$431$	−21.7871	+	37.7363i	−0.0505500	+	0.0875552i	0.839643	+	0.543138i	$0.182764\pi$
$432$		0			0
$433$		−	304.620i		−	0.703509i	−0.936092	−	0.351755i	$-0.885585\pi$
$433$		−	304.620i		−	0.703509i	0.936092	−	0.351755i	$-0.114415\pi$
$434$	−10.6601	−	228.919i	−0.0245624	−	0.527464i
$435$		0			0
$436$	151.715	+	262.778i	0.347970	+	0.602702i
$437$	330.360	+	190.734i	0.755974	+	0.436462i
$438$		0			0
$439$	−539.136	+	311.270i	−1.22810	+	0.709044i	−0.966632	−	0.256168i	$-0.917540\pi$
$439$	−539.136	+	311.270i	−1.22810	+	0.709044i	−0.261468	+	0.965212i	$0.584207\pi$
$440$		−	77.1067i		−	0.175242i
$441$		0			0
$442$	1033.37			2.33793
$443$	−42.8024	−	74.1360i	−0.0966195	−	0.167350i	0.813664	−	0.581336i	$-0.197470\pi$
$443$	−42.8024	−	74.1360i	−0.0966195	−	0.167350i	−0.910283	+	0.413986i	$0.864136\pi$
$444$		0			0
$445$	−161.252	+	279.297i	−0.362364	+	0.627633i
$446$	36.8049	−	21.2493i	0.0825222	−	0.0476442i
$447$		0			0
$448$	55.9394	−	2.60493i	0.124865	−	0.00581457i
$449$	143.625			0.319876			0.159938	−	0.987127i	$-0.448871\pi$
$449$	143.625			0.319876			0.159938	+	0.987127i	$0.448871\pi$
$450$		0			0
$451$	600.834	+	346.892i	1.33223	+	0.769161i
$452$	−42.1910	+	73.0769i	−0.0933429	+	0.161675i
$453$		0			0
$454$			200.366i			0.441334i
$455$	214.535	+	334.607i	0.471506	+	0.735401i
$456$		0			0
$457$	11.7226	+	20.3041i	0.0256512	+	0.0444292i	0.878566	−	0.477621i	$-0.158501\pi$
$457$	11.7226	+	20.3041i	0.0256512	+	0.0444292i	−0.852915	+	0.522050i	$0.825167\pi$
$458$	266.789	+	154.031i	0.582509	+	0.336312i
$459$		0			0
$460$	91.9518	−	53.0884i	0.199895	−	0.115410i
$461$		−	170.444i		−	0.369728i	−0.982764	−	0.184864i	$-0.940816\pi$
$461$		−	170.444i		−	0.369728i	0.982764	−	0.184864i	$-0.0591844\pi$
$462$		0			0
$463$	475.871			1.02780			0.513899	−	0.857850i	$-0.328200\pi$
$463$	475.871			1.02780			0.513899	+	0.857850i	$0.328200\pi$
$464$	55.8242	+	96.6904i	0.120311	+	0.208384i
$465$		0			0
$466$	−3.00658	+	5.20755i	−0.00645189	+	0.0111750i
$467$	188.847	−	109.031i	0.404384	−	0.233471i	−0.283990	−	0.958827i	$-0.591658\pi$
$467$	188.847	−	109.031i	0.404384	−	0.233471i	0.688374	+	0.725356i	$0.258325\pi$
$468$		0			0
$469$	226.715	−	438.616i	0.483400	−	0.935215i
$470$	−72.0767			−0.153355
$471$		0			0
$472$	176.431	+	101.863i	0.373795	+	0.215811i
$473$	47.7814	−	82.7598i	0.101018	−	0.174968i
$474$		0			0
$475$			80.3365i			0.169130i
$476$	−339.128	+	217.433i	−0.712453	+	0.456793i
$477$		0			0
$478$	184.917	+	320.286i	0.386856	+	0.670055i
$479$	482.916	+	278.812i	1.00817	+	0.582070i	0.910657	−	0.413164i	$-0.135576\pi$
$479$	482.916	+	278.812i	1.00817	+	0.582070i	0.0975181	+	0.995234i	$0.468910\pi$
$480$		0			0
$481$	−639.170	+	369.025i	−1.32883	+	0.767203i
$482$			141.279i			0.293111i
$483$		0			0
$484$	55.2719			0.114198
$485$	−88.3224	−	152.979i	−0.182108	−	0.315420i
$486$		0			0
$487$	258.122	−	447.080i	0.530024	−	0.918029i	−0.469362	−	0.883006i	$-0.655516\pi$
$487$	258.122	−	447.080i	0.530024	−	0.918029i	0.999386	−	0.0350234i	$-0.0111506\pi$
$488$	280.725	−	162.077i	0.575256	−	0.332124i
$489$		0			0
$490$	−140.811	−	64.6697i	−0.287370	−	0.131979i
$491$	−122.586			−0.249666			−0.124833	−	0.992178i	$-0.539839\pi$
$491$	−122.586			−0.249666			−0.124833	+	0.992178i	$0.539839\pi$
$492$		0			0
$493$	−695.559	−	401.581i	−1.41087	−	0.814566i
$494$	−288.507	+	499.709i	−0.584022	+	1.01156i
$495$		0			0
$496$		−	92.5976i		−	0.186689i
$497$	−44.8565	+	2.08883i	−0.0902544	+	0.00420287i
$498$		0			0
$499$	−187.525	−	324.802i	−0.375801	−	0.650906i	0.614646	−	0.788803i	$-0.289299\pi$
$499$	−187.525	−	324.802i	−0.375801	−	0.650906i	−0.990447	+	0.137897i	$0.955966\pi$
$500$	19.3649	+	11.1803i	0.0387298	+	0.0223607i
$501$		0			0
$502$	−306.875	+	177.175i	−0.611306	+	0.352938i
$503$			303.836i			0.604048i	0.953300	+	0.302024i	$0.0976622\pi$
$503$			303.836i			0.604048i	−0.953300	+	0.302024i	$0.902338\pi$
$504$		0			0
$505$	104.500			0.206931
$506$	204.673	+	354.505i	0.404493	+	0.700602i
$507$		0			0
$508$	−49.3159	+	85.4176i	−0.0970784	+	0.168145i
$509$	161.864	−	93.4522i	0.318004	−	0.183600i	−0.332499	−	0.943104i	$-0.607892\pi$
$509$	161.864	−	93.4522i	0.318004	−	0.183600i	0.650503	+	0.759504i	$0.274558\pi$
$510$		0			0
$511$	−245.978	−	127.143i	−0.481367	−	0.248812i
$512$	22.6274			0.0441942
$513$		0			0
$514$	213.915	+	123.504i	0.416177	+	0.240280i
$515$	−185.932	+	322.044i	−0.361033	+	0.625328i
$516$		0			0
$517$		−	277.880i		−	0.537485i
$518$	132.114	−	255.595i	0.255046	−	0.493427i
$519$		0			0
$520$	80.3024	+	139.088i	0.154428	+	0.267477i
$521$	−518.758	−	299.505i	−0.995697	−	0.574866i	−0.0887246	−	0.996056i	$-0.528279\pi$
$521$	−518.758	−	299.505i	−0.995697	−	0.574866i	−0.906972	+	0.421190i	$0.861612\pi$
$522$		0			0
$523$	132.497	−	76.4975i	0.253341	−	0.146267i	−0.367952	−	0.929845i	$-0.619941\pi$
$523$	132.497	−	76.4975i	0.253341	−	0.146267i	0.621293	+	0.783578i	$0.286608\pi$
$524$			29.3045i			0.0559246i
$525$		0			0
$526$	−29.5336			−0.0561475
$527$	333.059	+	576.875i	0.631990	+	1.09464i
$528$		0			0
$529$	−17.3376	+	30.0295i	−0.0327742	+	0.0567666i
$530$	−132.977	+	76.7742i	−0.250900	+	0.144857i
$531$		0			0
$532$	−10.4635	−	224.699i	−0.0196683	−	0.422366i
$533$	−1445.07			−2.71121
$534$		0			0
$535$	−63.8686	−	36.8746i	−0.119381	−	0.0689244i
$536$	99.7514	−	172.774i	0.186103	−	0.322340i
$537$		0			0
$538$			0.417624i			0.000776253i
$539$	249.323	−	542.875i	0.462567	−	1.00719i
$540$		0			0
$541$	−71.7086	−	124.203i	−0.132548	−	0.229580i	0.792110	−	0.610378i	$-0.208983\pi$
$541$	−71.7086	−	124.203i	−0.132548	−	0.229580i	−0.924658	+	0.380798i	$0.875649\pi$
$542$	−401.836	−	232.000i	−0.741394	−	0.428044i
$543$		0			0
$544$	−140.967	+	81.3871i	−0.259130	+	0.149609i
$545$		−	339.245i		−	0.622468i
$546$		0			0
$547$	−103.778			−0.189721			−0.0948607	−	0.995491i	$-0.530241\pi$
$547$	−103.778			−0.189721			−0.0948607	+	0.995491i	$0.530241\pi$
$548$	−17.2212	−	29.8281i	−0.0314256	−	0.0544308i
$549$		0			0
$550$	−43.1039	+	74.6582i	−0.0783708	+	0.135742i
$551$	388.388	−	224.236i	0.704879	−	0.406962i
$552$		0			0
$553$	207.034	+	322.908i	0.374383	+	0.583920i
$554$	−711.307			−1.28395
$555$		0			0
$556$	54.1460	+	31.2612i	0.0973848	+	0.0562251i
$557$	412.613	−	714.666i	0.740777	−	1.28306i	−0.211366	−	0.977407i	$-0.567791\pi$
$557$	412.613	−	714.666i	0.740777	−	1.28306i	0.952142	−	0.305656i	$-0.0988756\pi$
$558$		0			0
$559$			199.047i			0.356076i
$560$	−55.6193	−	28.7489i	−0.0993201	−	0.0513372i
$561$		0			0
$562$	187.016	+	323.922i	0.332769	+	0.576373i
$563$	−331.959	−	191.657i	−0.589626	−	0.340421i	0.175324	−	0.984511i	$-0.443903\pi$
$563$	−331.959	−	191.657i	−0.589626	−	0.340421i	−0.764949	+	0.644090i	$0.777236\pi$
$564$		0			0
$565$	81.7025	−	47.1710i	0.144606	−	0.0834884i
$566$			652.872i			1.15348i
$567$		0			0
$568$	−18.1444			−0.0319443
$569$	377.462	+	653.783i	0.663377	+	1.14900i	0.979723	+	0.200359i	$0.0642108\pi$
$569$	377.462	+	653.783i	0.663377	+	1.14900i	−0.316345	+	0.948644i	$0.602456\pi$
$570$		0			0
$571$	345.652	−	598.687i	0.605346	−	1.04849i	−0.386651	−	0.922226i	$-0.626368\pi$
$571$	345.652	−	598.687i	0.605346	−	1.04849i	0.991997	−	0.126263i	$-0.0402984\pi$
$572$	−536.230	+	309.592i	−0.937465	+	0.541245i
$573$		0			0
$574$	474.241	−	304.062i	0.826204	−	0.529725i
$575$	−118.709			−0.206451
$576$		0			0
$577$	338.973	+	195.706i	0.587476	+	0.339179i	0.764099	−	0.645099i	$-0.223184\pi$
$577$	338.973	+	195.706i	0.587476	+	0.339179i	−0.176623	+	0.984279i	$0.556517\pi$
$578$	381.119	−	660.117i	0.659375	−	1.14207i
$579$		0			0
$580$		−	124.827i		−	0.215218i
$581$	−44.2621	−	950.505i	−0.0761826	−	1.63598i
$582$		0			0
$583$	−295.990	−	512.670i	−0.507702	−	0.879365i
$584$	−96.8930	−	55.9412i	−0.165913	−	0.0957897i
$585$		0			0
$586$	−165.081	+	95.3095i	−0.281708	+	0.162644i
$587$			1027.13i			1.74979i	0.484312	+	0.874896i	$0.339070\pi$
$587$			1027.13i			1.74979i	−0.484312	+	0.874896i	$0.660930\pi$
$588$		0			0
$589$	−371.949			−0.631492
$590$	−113.886	−	197.256i	−0.193027	−	0.334332i
$591$		0			0
$592$	58.1282	−	100.681i	0.0981896	−	0.170069i
$593$	−116.894	+	67.4886i	−0.197123	+	0.113809i	−0.595313	−	0.803494i	$-0.702972\pi$
$593$	−116.894	+	67.4886i	−0.197123	+	0.113809i	0.398190	+	0.917303i	$0.369638\pi$
$594$		0			0
$595$	449.908	−	20.9508i	0.756147	−	0.0352115i
$596$	286.354			0.480460
$597$		0			0
$598$	−738.394	−	426.312i	−1.23477	−	0.712897i
$599$	−380.159	+	658.455i	−0.634656	+	1.09926i	0.351932	+	0.936026i	$0.385525\pi$
$599$	−380.159	+	658.455i	−0.634656	+	1.09926i	−0.986588	+	0.163231i	$0.947808\pi$
$600$		0			0
$601$			604.796i			1.00632i	0.864194	+	0.503158i	$0.167829\pi$
$601$			604.796i			1.00632i	−0.864194	+	0.503158i	$0.832171\pi$
$602$	−41.8820	−	65.3227i	−0.0695714	−	0.108509i
$603$		0			0
$604$	−46.3575	−	80.2936i	−0.0767509	−	0.132936i
$605$	−53.5168	−	30.8979i	−0.0884575	−	0.0510710i
$606$		0			0
$607$	11.2280	−	6.48250i	0.0184976	−	0.0106796i	−0.490723	−	0.871316i	$-0.663267\pi$
$607$	11.2280	−	6.48250i	0.0184976	−	0.0106796i	0.509220	+	0.860636i	$0.329934\pi$
$608$		−	90.8904i		−	0.149491i
$609$		0			0
$610$	−362.414			−0.594121
$611$	289.396	+	501.249i	0.473644	+	0.820375i
$612$		0			0
$613$	−566.514	+	981.231i	−0.924167	+	1.60070i	−0.131271	+	0.991347i	$0.541906\pi$
$613$	−566.514	+	981.231i	−0.924167	+	1.60070i	−0.792896	+	0.609357i	$0.791428\pi$
$614$	29.0555	−	16.7752i	0.0473217	−	0.0273212i
$615$		0			0
$616$	110.836	−	214.431i	0.179929	−	0.348102i
$617$	−19.5534			−0.0316910			−0.0158455	−	0.999874i	$-0.505044\pi$
$617$	−19.5534			−0.0316910			−0.0158455	+	0.999874i	$0.505044\pi$
$618$		0			0
$619$	574.387	+	331.623i	0.927928	+	0.535739i	0.886156	−	0.463388i	$-0.153366\pi$
$619$	574.387	+	331.623i	0.927928	+	0.535739i	0.0417724	+	0.999127i	$0.486700\pi$
$620$	−51.7637	+	89.6573i	−0.0834898	+	0.144609i
$621$		0			0
$622$			400.241i			0.643474i
$623$	−849.908	+	544.923i	−1.36422	+	0.874676i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−519.754	−	300.080i	−0.830279	−	0.479362i
$627$		0			0
$628$	−142.911	+	82.5095i	−0.227565	+	0.131385i
$629$			836.311i			1.32959i
$630$		0			0
$631$	−303.828			−0.481503			−0.240752	−	0.970587i	$-0.577394\pi$
$631$	−303.828			−0.481503			−0.240752	+	0.970587i	$0.577394\pi$
$632$	77.4945	+	134.224i	0.122618	+	0.212380i
$633$		0			0
$634$	−19.8896	+	34.4498i	−0.0313716	+	0.0543372i
$635$	95.4997	−	55.1368i	0.150393	−	0.0868296i
$636$		0			0
$637$	115.636	+	1238.91i	0.181532	+	1.94492i
$638$	481.249			0.754308
$639$		0			0
$640$	−21.9089	−	12.6491i	−0.0342327	−	0.0197642i
$641$	−470.134	+	814.296i	−0.733439	+	1.27035i	0.221967	+	0.975054i	$0.428752\pi$
$641$	−470.134	+	814.296i	−0.733439	+	1.27035i	−0.955405	+	0.295298i	$0.904581\pi$
$642$		0			0
$643$			1143.40i			1.77823i	0.457681	+	0.889116i	$0.348680\pi$
$643$			1143.40i			1.77823i	−0.457681	+	0.889116i	$0.651320\pi$
$644$	332.026	−	15.4614i	0.515568	−	0.0240084i
$645$		0			0
$646$	326.918	+	566.239i	0.506065	+	0.876530i
$647$	−790.146	−	456.191i	−1.22125	−	0.705087i	−0.256063	−	0.966660i	$-0.582425\pi$
$647$	−790.146	−	456.191i	−1.22125	−	0.705087i	−0.965184	+	0.261573i	$0.915759\pi$
$648$		0			0
$649$	760.488	−	439.068i	1.17178	−	0.676530i
$650$		−	179.562i		−	0.276249i
$651$		0			0
$652$	−492.833			−0.755879
$653$	109.628	+	189.881i	0.167884	+	0.290783i	0.937676	−	0.347512i	$-0.112973\pi$
$653$	109.628	+	189.881i	0.167884	+	0.290783i	−0.769792	+	0.638295i	$0.779640\pi$
$654$		0			0
$655$	16.3817	−	28.3739i	0.0250102	−	0.0433190i
$656$	197.130	−	113.813i	0.300503	−	0.173495i
$657$		0			0
$658$	−200.443	−	103.606i	−0.304624	−	0.157456i
$659$	−661.525			−1.00383			−0.501916	−	0.864916i	$-0.667371\pi$
$659$	−661.525			−1.00383			−0.501916	+	0.864916i	$0.667371\pi$
$660$		0			0
$661$	−481.878	−	278.212i	−0.729013	−	0.420896i	0.0890478	−	0.996027i	$-0.471618\pi$
$661$	−481.878	−	278.212i	−0.729013	−	0.420896i	−0.818061	+	0.575131i	$0.804951\pi$
$662$	−185.178	+	320.737i	−0.279724	+	0.484497i
$663$		0			0
$664$		−	384.478i		−	0.579033i
$665$	−115.479	+	223.413i	−0.173653	+	0.335959i
$666$		0			0
$667$	331.342	+	573.902i	0.496765	+	0.860423i
$668$	497.770	+	287.387i	0.745164	+	0.430221i
$669$		0			0
$670$	−193.168	+	111.525i	−0.288310	+	0.166456i
$671$		−	1397.23i		−	2.08231i
$672$		0			0
$673$	−153.903			−0.228682			−0.114341	−	0.993442i	$-0.536476\pi$
$673$	−153.903			−0.228682			−0.114341	+	0.993442i	$0.536476\pi$
$674$	381.837	+	661.360i	0.566523	+	0.981247i
$675$		0			0
$676$	475.847	−	824.191i	0.703916	−	1.21922i
$677$	362.794	−	209.459i	0.535886	−	0.309394i	−0.207524	−	0.978230i	$-0.566541\pi$
$677$	362.794	−	209.459i	0.535886	−	0.309394i	0.743410	+	0.668836i	$0.233207\pi$
$678$		0			0
$679$	−25.7230	−	552.387i	−0.0378836	−	0.813530i
$680$	181.987			0.267628
$681$		0			0
$682$	−345.659	−	199.566i	−0.506831	−	0.292619i
$683$	614.628	−	1064.57i	0.899895	−	1.55866i	0.0722678	−	0.997385i	$-0.476976\pi$
$683$	614.628	−	1064.57i	0.899895	−	1.55866i	0.827627	−	0.561278i	$-0.189690\pi$
$684$		0			0
$685$			38.5079i			0.0562158i
$686$	−298.632	−	382.252i	−0.435324	−	0.557219i
$687$		0			0
$688$	−15.6768	−	27.1530i	−0.0227860	−	0.0394665i
$689$	1067.84	+	616.515i	1.54983	+	0.894797i
$690$		0			0
$691$	314.293	−	181.457i	0.454838	−	0.262601i	−0.255033	−	0.966932i	$-0.582086\pi$
$691$	314.293	−	181.457i	0.454838	−	0.262601i	0.709871	+	0.704331i	$0.248753\pi$
$692$		−	547.099i		−	0.790605i
$693$		0			0
$694$	56.3628			0.0812144
$695$	−34.9511	−	60.5370i	−0.0502893	−	0.0871036i
$696$		0			0
$697$	−818.734	+	1418.09i	−1.17465	+	2.03456i
$698$	399.267	−	230.517i	0.572016	−	0.330254i
$699$		0			0
$700$	37.7820	+	58.9281i	0.0539743	+	0.0841830i
$701$	319.012			0.455081			0.227541	−	0.973769i	$-0.426932\pi$
$701$	319.012			0.455081			0.227541	+	0.973769i	$0.426932\pi$
$702$		0			0
$703$	−404.418	−	233.491i	−0.575275	−	0.332135i
$704$	48.7665	−	84.4661i	0.0692707	−	0.119980i
$705$		0			0
$706$		−	206.581i		−	0.292608i
$707$	290.612	+	150.213i	0.411049	+	0.212466i
$708$		0			0
$709$	−565.639	−	979.716i	−0.797799	−	1.38183i	−0.921047	−	0.389452i	$-0.872664\pi$
$709$	−565.639	−	979.716i	−0.797799	−	1.38183i	0.123248	−	0.992376i	$-0.460669\pi$
$710$	17.5682	+	10.1430i	0.0247440	+	0.0142859i
$711$		0			0
$712$	−353.285	+	203.969i	−0.496187	+	0.286474i
$713$		−	549.610i		−	0.770841i
$714$		0			0
$715$	692.270			0.968209
$716$	−100.798	−	174.587i	−0.140779	−	0.243837i
$717$		0			0
$718$	15.2431	−	26.4018i	0.0212300	−	0.0367714i
$719$	243.094	−	140.350i	0.338100	−	0.195202i	−0.321332	−	0.946967i	$-0.604130\pi$
$719$	243.094	−	140.350i	0.338100	−	0.195202i	0.659431	+	0.751765i	$0.270797\pi$
$720$		0			0
$721$	−979.991	+	628.326i	−1.35921	+	0.871464i
$722$	145.440			0.201441
$723$		0			0
$724$	−234.081	−	135.147i	−0.323316	−	0.186667i
$725$	−69.7803	+	120.863i	−0.0962486	+	0.166708i
$726$		0			0
$727$		−	737.233i		−	1.01408i	−0.861924	−	0.507038i	$-0.830740\pi$
$727$		−	737.233i		−	1.01408i	0.861924	−	0.507038i	$-0.169260\pi$
$728$	23.3872	+	502.228i	0.0321253	+	0.689874i
$729$		0			0
$730$	62.5442	+	108.330i	0.0856769	+	0.148397i
$731$	195.330	+	112.774i	0.267209	+	0.154273i
$732$		0			0
$733$	1172.96	−	677.208i	1.60022	−	0.923886i	0.608775	−	0.793343i	$-0.291661\pi$
$733$	1172.96	−	677.208i	1.60022	−	0.923886i	0.991443	−	0.130543i	$-0.0416719\pi$
$734$		−	288.997i		−	0.393728i
$735$		0			0
$736$	134.304			0.182478
$737$	−429.968	−	744.726i	−0.583403	−	1.01048i
$738$		0			0
$739$	−2.66286	+	4.61222i	−0.00360333	+	0.00624116i	−0.867821	−	0.496876i	$-0.834480\pi$
$739$	−2.66286	+	4.61222i	−0.00360333	+	0.00624116i	0.864218	+	0.503117i	$0.167814\pi$
$740$	−112.565	+	64.9893i	−0.152115	+	0.0878234i
$741$		0			0
$742$	−480.162	+	22.3597i	−0.647119	+	0.0301343i
$743$	−58.3655			−0.0785539			−0.0392769	−	0.999228i	$-0.512505\pi$
$743$	−58.3655			−0.0785539			−0.0392769	+	0.999228i	$0.512505\pi$
$744$		0			0
$745$	−277.261	−	160.077i	−0.372163	−	0.214868i
$746$	−398.287	+	689.854i	−0.533897	+	0.924737i
$747$		0			0
$748$			701.621i			0.937996i
$749$	−124.611	−	194.354i	−0.166370	−	0.259485i
$750$		0			0
$751$	−139.145	−	241.006i	−0.185279	−	0.320913i	0.758391	−	0.651800i	$-0.225986\pi$
$751$	−139.145	−	241.006i	−0.185279	−	0.320913i	−0.943671	+	0.330886i	$0.892652\pi$
$752$	−78.9561	−	45.5853i	−0.104995	−	0.0606188i
$753$		0			0
$754$	−868.094	+	501.194i	−1.15132	+	0.664714i
$755$			103.659i			0.137296i
$756$		0			0
$757$	−59.2916			−0.0783244			−0.0391622	−	0.999233i	$-0.512469\pi$
$757$	−59.2916			−0.0783244			−0.0391622	+	0.999233i	$0.512469\pi$
$758$	−212.586	−	368.209i	−0.280456	−	0.485764i
$759$		0			0
$760$	−50.8093	+	88.0042i	−0.0668543	+	0.115795i
$761$	−788.790	+	455.408i	−1.03652	+	0.598434i	−0.918845	−	0.394619i	$-0.870877\pi$
$761$	−788.790	+	455.408i	−1.03652	+	0.598434i	−0.117673	+	0.993052i	$0.537543\pi$
$762$		0			0
$763$	487.645	−	943.428i	0.639115	−	1.23647i
$764$	−356.361			−0.466441
$765$		0			0
$766$	−13.2164	−	7.63051i	−0.0172538	−	0.00996150i
$767$	−914.531	+	1584.01i	−1.19235	+	2.06521i
$768$		0			0
$769$		−	660.381i		−	0.858753i	−0.903126	−	0.429376i	$-0.858733\pi$
$769$		−	660.381i		−	0.858753i	0.903126	−	0.429376i	$-0.141267\pi$
$770$	−227.187	+	145.662i	−0.295049	+	0.189172i
$771$		0			0
$772$	−135.115	−	234.027i	−0.175020	−	0.303143i
$773$	−1201.60	−	693.744i	−1.55446	−	0.897469i	−0.997770	−	0.0667508i	$-0.978737\pi$
$773$	−1201.60	−	693.744i	−1.55446	−	0.897469i	−0.556693	−	0.830718i	$-0.687930\pi$
$774$		0			0
$775$	100.240	−	57.8735i	0.129342	−	0.0746755i
$776$		−	223.440i		−	0.287938i
$777$		0			0
$778$	185.863			0.238898
$779$	−457.167	−	791.837i	−0.586864	−	1.01648i
$780$		0			0
$781$	−39.1047	+	67.7314i	−0.0500701	+	0.0867239i
$782$	−836.702	+	483.070i	−1.06995	+	0.617737i
$783$		0			0
$784$	−113.350	−	159.899i	−0.144580	−	0.203953i
$785$	184.497			0.235028
$786$		0			0
$787$	−1188.71	−	686.304i	−1.51044	−	0.872050i	−0.999926	−	0.0121785i	$-0.996123\pi$
$787$	−1188.71	−	686.304i	−1.51044	−	0.872050i	−0.510510	−	0.859872i	$-0.670543\pi$
$788$	64.7529	−	112.155i	0.0821737	−	0.142329i
$789$		0			0
$790$		−	173.283i		−	0.219346i
$791$	295.017	−	13.7381i	0.372967	−	0.0173680i
$792$		0			0
$793$	1455.14	+	2520.37i	1.83498	+	3.17827i
$794$	686.995	+	396.636i	0.865232	+	0.499542i
$795$		0			0
$796$	−233.514	+	134.819i	−0.293359	+	0.169371i
$797$		−	64.7049i		−	0.0811855i	−0.999176	−	0.0405928i	$-0.987075\pi$
$797$		−	64.7049i		−	0.0811855i	0.999176	−	0.0405928i	$-0.0129246\pi$
$798$		0			0
$799$	655.852			0.820841
$800$	14.1421	+	24.4949i	0.0176777	+	0.0306186i
$801$		0			0
$802$	241.656	−	418.560i	0.301317	−	0.521896i
$803$	−417.647	+	241.129i	−0.520108	+	0.300285i
$804$		0			0
$805$	−330.126	−	170.638i	−0.410094	−	0.211972i
$806$	831.349			1.03145
$807$		0			0
$808$	114.474	+	66.0918i	0.141676	+	0.0817968i
$809$	268.427	−	464.929i	0.331801	−	0.574696i	−0.651064	−	0.759023i	$-0.725677\pi$
$809$	268.427	−	464.929i	0.331801	−	0.574696i	0.982865	+	0.184327i	$0.0590104\pi$
$810$		0			0
$811$			1472.44i			1.81559i	0.419418	+	0.907793i	$0.362234\pi$
$811$			1472.44i			1.81559i	−0.419418	+	0.907793i	$0.637766\pi$
$812$	179.431	−	347.139i	0.220974	−	0.427511i
$813$		0			0
$814$	−250.556	−	433.975i	−0.307808	−	0.533139i
$815$	477.183	+	275.502i	0.585501	+	0.338039i
$816$		0			0
$817$	−109.069	+	62.9709i	−0.133499	+	0.0770757i
$818$		−	32.1362i		−	0.0392863i
$819$		0			0
$820$	−254.494			−0.310358
$821$	−114.603	−	198.498i	−0.139590	−	0.241776i	0.787752	−	0.615993i	$-0.211245\pi$
$821$	−114.603	−	198.498i	−0.139590	−	0.241776i	−0.927341	+	0.374217i	$0.877912\pi$
$822$		0			0
$823$	7.10905	−	12.3132i	0.00863797	−	0.0149614i	−0.861674	−	0.507462i	$-0.830584\pi$
$823$	7.10905	−	12.3132i	0.00863797	−	0.0149614i	0.870312	+	0.492501i	$0.163917\pi$
$824$	−407.357	+	235.188i	−0.494365	+	0.285422i
$825$		0			0
$826$	−33.1681	−	712.267i	−0.0401551	−	0.862308i
$827$	136.480			0.165030			0.0825151	−	0.996590i	$-0.473705\pi$
$827$	136.480			0.165030			0.0825151	+	0.996590i	$0.473705\pi$
$828$		0			0
$829$	254.554	+	146.967i	0.307061	+	0.177282i	0.645611	−	0.763667i	$-0.276603\pi$
$829$	254.554	+	146.967i	0.307061	+	0.177282i	−0.338549	+	0.940949i	$0.609936\pi$
$830$	−214.930	+	372.269i	−0.258952	+	0.448517i
$831$		0			0
$832$			203.151i			0.244172i
$833$	1281.29	+	588.453i	1.53817	+	0.706426i
$834$		0			0
$835$	−321.309	−	556.523i	−0.384801	−	0.666495i
$836$	−339.286	−	195.887i	−0.405844	−	0.234314i
$837$		0			0
$838$	−425.446	+	245.631i	−0.507692	+	0.293116i
$839$			658.476i			0.784834i	0.919787	+	0.392417i	$0.128361\pi$
$839$			658.476i			0.784834i	−0.919787	+	0.392417i	$0.871639\pi$
$840$		0			0
$841$	−61.9146			−0.0736202
$842$	240.686	+	416.880i	0.285850	+	0.495107i
$843$		0			0
$844$	116.352	−	201.528i	0.137858	−	0.238777i
$845$	−921.474	+	532.013i	−1.09050	+	0.629601i
$846$		0			0
$847$	−104.414	−	162.853i	−0.123275	−	0.192271i
$848$	−194.225			−0.229039
$849$		0			0
$850$	−176.208	−	101.734i	−0.207304	−	0.119687i
$851$	345.018	−	597.588i	0.405426	−	0.702219i
$852$		0			0
$853$		−	1026.25i		−	1.20310i	−0.798834	−	0.601552i	$-0.794549\pi$
$853$		−	1026.25i		−	1.20310i	0.798834	−	0.601552i	$-0.205451\pi$
$854$	−1007.86	−	520.950i	−1.18016	−	0.610011i
$855$		0			0
$856$	−46.6431	−	80.7881i	−0.0544896	−	0.0943787i
$857$	−1405.85	−	811.667i	−1.64043	−	0.947103i	−0.980680	−	0.195619i	$-0.937328\pi$
$857$	−1405.85	−	811.667i	−1.64043	−	0.947103i	−0.659751	−	0.751484i	$-0.729338\pi$
$858$		0			0
$859$	894.833	−	516.632i	1.04171	−	0.601434i	0.121396	−	0.992604i	$-0.461263\pi$
$859$	894.833	−	516.632i	1.04171	−	0.601434i	0.920318	+	0.391170i	$0.127930\pi$
$860$			35.0543i			0.0407608i
$861$		0			0
$862$	61.6231			0.0714885
$863$	−141.684	−	245.403i	−0.164176	−	0.284361i	0.772187	−	0.635396i	$-0.219163\pi$
$863$	−141.684	−	245.403i	−0.164176	−	0.284361i	−0.936362	+	0.351035i	$0.885830\pi$
$864$		0			0
$865$	−305.837	+	529.726i	−0.353569	+	0.612400i
$866$	−373.081	+	215.399i	−0.430810	+	0.248728i
$867$		0			0
$868$	−272.830	+	174.926i	−0.314320	+	0.201528i
$869$	668.064			0.768773
$870$		0			0
$871$	1551.18	+	895.575i	1.78092	+	1.02822i
$872$	214.557	−	371.624i	0.246052	−	0.426174i
$873$		0			0
$874$		−	539.476i		−	0.617250i
$875$	−3.64050	−	78.1777i	−0.00416057	−	0.0893459i
$876$		0			0
$877$	254.904	+	441.507i	0.290655	+	0.503429i	0.973965	−	0.226700i	$-0.0727935\pi$
$877$	254.904	+	441.507i	0.290655	+	0.503429i	−0.683310	+	0.730128i	$0.739460\pi$
$878$	762.454	+	440.203i	0.868398	+	0.501370i
$879$		0			0
$880$	−94.4360	+	54.5226i	−0.107314	+	0.0619576i
$881$			846.387i			0.960711i	0.877074	+	0.480356i	$0.159492\pi$
$881$			846.387i			0.960711i	−0.877074	+	0.480356i	$0.840508\pi$
$882$		0			0
$883$	−350.886			−0.397379			−0.198690	−	0.980062i	$-0.563669\pi$
$883$	−350.886			−0.397379			−0.198690	+	0.980062i	$0.563669\pi$
$884$	−730.700	−	1265.61i	−0.826584	−	1.43169i
$885$		0			0
$886$	−60.5318	+	104.844i	−0.0683203	+	0.118334i
$887$	−434.565	+	250.896i	−0.489927	+	0.282859i	−0.724544	−	0.689228i	$-0.757950\pi$
$887$	−434.565	+	250.896i	−0.489927	+	0.282859i	0.234617	+	0.972088i	$0.424616\pi$
$888$		0			0
$889$	344.837	−	16.0580i	0.387893	−	0.0180630i
$890$	456.089			0.512460
$891$		0			0
$892$	−52.0500	−	30.0511i	−0.0583520	−	0.0336896i
$893$	−183.108	+	317.153i	−0.205048	+	0.355154i
$894$		0			0
$895$			225.391i			0.251834i
$896$	−42.7455	−	66.6695i	−0.0477070	−	0.0744079i
$897$		0			0
$898$	−101.558	−	175.903i	−0.113093	−	0.195883i
$899$	−559.581	−	323.074i	−0.622448	−	0.359371i
$900$		0			0
$901$	1210.00	−	698.596i	1.34296	−	0.775356i
$902$		−	981.158i		−	1.08776i
$903$		0			0
$904$	119.334			0.132007
$905$	151.099	+	261.711i	0.166960	+	0.289183i
$906$		0			0
$907$	−831.238	+	1439.75i	−0.916470	+	1.58737i	−0.111735	+	0.993738i	$0.535641\pi$
$907$	−831.238	+	1439.75i	−0.916470	+	1.58737i	−0.804735	+	0.593634i	$0.797693\pi$
$908$	245.397	−	141.680i	0.270261	−	0.156035i
$909$		0			0
$910$	258.109	−	499.354i	0.283637	−	0.548741i
$911$	143.213			0.157204			0.0786019	−	0.996906i	$-0.474954\pi$
$911$	143.213			0.157204			0.0786019	+	0.996906i	$0.474954\pi$
$912$		0			0
$913$	−1435.22	−	828.626i	−1.57199	−	0.907586i
$914$	16.5783	−	28.7144i	0.0181381	−	0.0314162i
$915$		0			0
$916$		−	435.665i		−	0.475617i
$917$	86.3428	−	55.3591i	0.0941579	−	0.0603698i
$918$		0			0
$919$	−435.504	−	754.315i	−0.473889	−	0.820800i	0.525664	−	0.850692i	$-0.323817\pi$
$919$	−435.504	−	754.315i	−0.473889	−	0.820800i	−0.999553	+	0.0298922i	$0.990484\pi$
$920$	−130.039	−	75.0783i	−0.141347	−	0.0816068i
$921$		0			0
$922$	−208.751	+	120.522i	−0.226411	+	0.130718i
$923$		−	162.902i		−	0.176492i
$924$		0			0
$925$	145.321			0.157103
$926$	−336.492	−	582.820i	−0.363382	−	0.629396i
$927$		0			0
$928$	78.9473	−	136.741i	0.0850726	−	0.147350i
$929$	−1308.36	+	755.381i	−1.40835	+	0.813112i	−0.995229	−	0.0975629i	$-0.968895\pi$
$929$	−1308.36	+	755.381i	−1.40835	+	0.813112i	−0.413123	+	0.910675i	$0.635562\pi$
$930$		0			0
$931$	−642.287	+	455.309i	−0.689889	+	0.489053i
$932$	8.50390			0.00912435
$933$		0			0
$934$	−267.071	−	154.193i	−0.285943	−	0.165089i
$935$	392.218	−	679.342i	0.419485	−	0.726569i
$936$		0			0
$937$		−	485.168i		−	0.517788i	−0.965906	−	0.258894i	$-0.916642\pi$
$937$		−	485.168i		−	0.517788i	0.965906	−	0.258894i	$-0.0833581\pi$
$938$	−697.504	+	32.4806i	−0.743607	+	0.0346275i
$939$		0			0
$940$	50.9659	+	88.2756i	0.0542191	+	0.0939102i
$941$	−215.272	−	124.288i	−0.228770	−	0.132080i	0.381235	−	0.924478i	$-0.375499\pi$
$941$	−215.272	−	124.288i	−0.228770	−	0.132080i	−0.610004	+	0.792398i	$0.708832\pi$
$942$		0			0
$943$	1170.06	−	675.533i	1.24078	−	0.716366i
$944$		−	288.111i		−	0.305202i
$945$		0			0
$946$	−135.146			−0.142861
$947$	681.531	+	1180.45i	0.719674	+	1.24651i	0.961129	+	0.276100i	$0.0890421\pi$
$947$	681.531	+	1180.45i	0.719674	+	1.24651i	−0.241455	+	0.970412i	$0.577625\pi$
$948$		0			0
$949$	502.244	−	869.913i	0.529235	−	0.916663i
$950$	98.3917	−	56.8065i	0.103570	−	0.0597963i
$951$		0			0
$952$	506.100	+	261.596i	0.531617	+	0.274786i
$953$	−879.838			−0.923230			−0.461615	−	0.887080i	$-0.652730\pi$
$953$	−879.838			−0.923230			−0.461615	+	0.887080i	$0.652730\pi$
$954$		0			0
$955$	345.045	+	199.212i	0.361304	+	0.208599i
$956$	261.513	−	452.953i	0.273549	−	0.473800i
$957$		0			0
$958$		−	788.598i		−	0.823171i
$959$	−55.3528	+	107.089i	−0.0577193	+	0.111667i
$960$		0			0
$961$	−212.552	−	368.152i	−0.221178	−	0.383092i
$962$	903.922	+	521.880i	0.939628	+	0.542495i
$963$		0			0
$964$	173.031	−	99.8996i	0.179493	−	0.103630i
$965$			302.127i			0.313085i
$966$		0			0
$967$	−186.884			−0.193262			−0.0966310	−	0.995320i	$-0.530807\pi$
$967$	−186.884			−0.193262			−0.0966310	+	0.995320i	$0.530807\pi$
$968$	−39.0832	−	67.6940i	−0.0403752	−	0.0699318i
$969$		0			0
$970$	−124.907	+	216.345i	−0.128770	+	0.223036i
$971$	159.547	−	92.1145i	0.164312	−	0.0948656i	−0.415589	−	0.909553i	$-0.636425\pi$
$971$	159.547	−	92.1145i	0.164312	−	0.0948656i	0.579901	+	0.814687i	$0.303091\pi$
$972$		0			0
$973$	−10.1791	−	218.591i	−0.0104616	−	0.224657i
$974$	−730.079			−0.749568
$975$		0			0
$976$	−397.005	−	229.211i	−0.406767	−	0.234847i
$977$	−554.021	+	959.592i	−0.567063	+	0.982183i	0.429791	+	0.902928i	$0.358587\pi$
$977$	−554.021	+	959.592i	−0.567063	+	0.982183i	−0.996854	+	0.0792543i	$0.974746\pi$
$978$		0			0
$979$			1758.38i			1.79609i
$980$	20.3647	+	218.186i	0.0207803	+	0.222639i
$981$		0			0
$982$	86.6813	+	150.136i	0.0882702	+	0.152888i
$983$	1216.86	+	702.557i	1.23791	+	0.714707i	0.968666	−	0.248365i	$-0.0798934\pi$
$983$	1216.86	+	702.557i	1.23791	+	0.714707i	0.269242	+	0.963072i	$0.413227\pi$
$984$		0			0
$985$	−125.393	+	72.3959i	−0.127303	+	0.0734984i
$986$			1135.84i			1.15197i
$987$		0			0
$988$	816.021			0.825932
$989$	−93.0489	−	161.165i	−0.0940838	−	0.162958i
$990$		0			0
$991$	−218.084	+	377.732i	−0.220064	+	0.381162i	−0.954827	−	0.297161i	$-0.903960\pi$
$991$	−218.084	+	377.732i	−0.220064	+	0.381162i	0.734763	+	0.678324i	$0.237293\pi$
$992$	−113.408	+	65.4764i	−0.114323	+	0.0660045i
$993$		0			0
$994$	34.2766	+	53.4607i	0.0344835	+	0.0537834i
$995$	301.465			0.302980
$996$		0			0
$997$	−77.2090	−	44.5767i	−0.0774414	−	0.0447108i	0.460779	−	0.887515i	$-0.347570\pi$
$997$	−77.2090	−	44.5767i	−0.0774414	−	0.0447108i	−0.538221	+	0.842804i	$0.680903\pi$
$998$	−265.200	+	459.340i	−0.265731	+	0.460260i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.v.c.451.4		16
3.2	odd	2		210.3.o.b.31.6	✓	16
7.5	odd	6	inner	630.3.v.c.271.4		16
15.2	even	4		1050.3.q.e.199.8		32
15.8	even	4		1050.3.q.e.199.9		32
15.14	odd	2		1050.3.p.i.451.1		16
21.5	even	6		210.3.o.b.61.6	yes	16
21.11	odd	6		1470.3.f.d.391.6		16
21.17	even	6		1470.3.f.d.391.4		16
105.47	odd	12		1050.3.q.e.649.9		32
105.68	odd	12		1050.3.q.e.649.8		32
105.89	even	6		1050.3.p.i.901.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.6	✓	16	3.2	odd	2
210.3.o.b.61.6	yes	16	21.5	even	6
630.3.v.c.271.4		16	7.5	odd	6	inner
630.3.v.c.451.4		16	1.1	even	1	trivial
1050.3.p.i.451.1		16	15.14	odd	2
1050.3.p.i.901.1		16	105.89	even	6
1050.3.q.e.199.8		32	15.2	even	4
1050.3.q.e.199.9		32	15.8	even	4
1050.3.q.e.649.8		32	105.68	odd	12
1050.3.q.e.649.9		32	105.47	odd	12
1470.3.f.d.391.4		16	21.17	even	6
1470.3.f.d.391.6		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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(6.99242 - 0.325616i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(6.99242 - 0.325616i) q^{7} +2.82843 q^{8} +(-2.73861 - 1.58114i) q^{10} +(6.09582 - 10.5583i) q^{11} +25.3938i q^{13} +(-5.34319 - 8.33369i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(24.9196 + 14.3873i) q^{17} +(-13.9147 + 8.03365i) q^{19} +4.47214i q^{20} -17.2416 q^{22} +(-11.8709 - 20.5610i) q^{23} +(2.50000 - 4.33013i) q^{25} +(31.1010 - 17.9562i) q^{26} +(-6.42844 + 12.4368i) q^{28} -27.9121 q^{29} +(20.0480 + 11.5747i) q^{31} +(-2.82843 + 4.89898i) q^{32} -40.6936i q^{34} +(13.1767 - 8.44832i) q^{35} +(14.5321 + 25.1703i) q^{37} +(19.6783 + 11.3613i) q^{38} +(5.47723 - 3.16228i) q^{40} +56.9065i q^{41} +7.83839 q^{43} +(12.1916 + 21.1165i) q^{44} +(-16.7880 + 29.0777i) q^{46} +(19.7390 - 11.3963i) q^{47} +(48.7879 - 4.55369i) q^{49} -7.07107 q^{50} +(-43.9834 - 25.3938i) q^{52} +(24.2781 - 42.0510i) q^{53} -27.2613i q^{55} +(19.7776 - 0.920981i) q^{56} +(19.7368 + 34.1852i) q^{58} +(62.3779 + 36.0139i) q^{59} +(99.2512 - 57.3027i) q^{61} -32.7382i q^{62} +8.00000 q^{64} +(28.3912 + 49.1750i) q^{65} +(35.2674 - 61.0850i) q^{67} +(-49.8392 + 28.7747i) q^{68} +(-19.6644 - 10.1643i) q^{70} -6.41501 q^{71} +(-34.2569 - 19.7782i) q^{73} +(20.5514 - 35.5961i) q^{74} -32.1346i q^{76} +(39.1866 - 75.8127i) q^{77} +(27.3985 + 47.4555i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(69.6960 - 40.2390i) q^{82} -135.934i q^{83} +64.3422 q^{85} +(-5.54258 - 9.60002i) q^{86} +(17.2416 - 29.8633i) q^{88} +(-124.905 + 72.1140i) q^{89} +(8.26863 + 177.564i) q^{91} +47.4837 q^{92} +(-27.9152 - 16.1168i) q^{94} +(-17.9638 + 31.1142i) q^{95} -78.9980i q^{97} +(-40.0754 - 56.5328i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 4 q^{7}+O(q^{10}) \) 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

Introduction

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