LMFDB - Embedded newform 630.3.v.c.451.3

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			451.3
Root			$-2.10711 + 3.64962i$ of defining polynomial
Character	$\chi$	$=$	630.451
Dual form			630.3.v.c.271.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-5.26304 - 4.61524i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-5.26304 - 4.61524i) q^{7} +2.82843 q^{8} +(-2.73861 - 1.58114i) q^{10} +(-5.41099 + 9.37211i) q^{11} -19.2715i q^{13} +(-1.93096 + 9.70935i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(8.89730 + 5.13686i) q^{17} +(-18.0756 + 10.4359i) q^{19} +4.47214i q^{20} +15.3046 q^{22} +(10.5373 + 18.2511i) q^{23} +(2.50000 - 4.33013i) q^{25} +(-23.6026 + 13.6270i) q^{26} +(13.2569 - 4.50061i) q^{28} -19.0888 q^{29} +(-34.6556 - 20.0084i) q^{31} +(-2.82843 + 4.89898i) q^{32} -14.5292i q^{34} +(-15.3518 - 3.05312i) q^{35} +(25.1827 + 43.6177i) q^{37} +(25.5627 + 14.7586i) q^{38} +(5.47723 - 3.16228i) q^{40} -22.7706i q^{41} -48.4307 q^{43} +(-10.8220 - 18.7442i) q^{44} +(14.9020 - 25.8110i) q^{46} +(-57.6236 + 33.2690i) q^{47} +(6.39913 + 48.5804i) q^{49} -7.07107 q^{50} +(33.3792 + 19.2715i) q^{52} +(2.47531 - 4.28736i) q^{53} +24.1987i q^{55} +(-14.8861 - 13.0539i) q^{56} +(13.4978 + 23.3789i) q^{58} +(24.4105 + 14.0934i) q^{59} +(-60.6988 + 35.0445i) q^{61} +56.5924i q^{62} +8.00000 q^{64} +(-21.5462 - 37.3191i) q^{65} +(-9.65287 + 16.7193i) q^{67} +(-17.7946 + 10.2737i) q^{68} +(7.11609 + 20.9609i) q^{70} -49.4968 q^{71} +(-115.159 - 66.4872i) q^{73} +(35.6137 - 61.6848i) q^{74} -41.7437i q^{76} +(71.7328 - 24.3527i) q^{77} +(45.0404 + 78.0122i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(-27.8882 + 16.1013i) q^{82} +101.045i q^{83} +22.9727 q^{85} +(34.2456 + 59.3152i) q^{86} +(-15.3046 + 26.5083i) q^{88} +(-34.3077 + 19.8075i) q^{89} +(-88.9425 + 101.427i) q^{91} -42.1492 q^{92} +(81.4920 + 47.0495i) q^{94} +(-23.3355 + 40.4182i) q^{95} +68.6944i q^{97} +(54.9737 - 42.1888i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−5.26304	−	4.61524i	−0.751863	−	0.659320i
$7$	−5.26304	−	4.61524i	−0.751863	−	0.659320i
$8$	2.82843			0.353553
$9$		0			0
$10$	−2.73861	−	1.58114i	−0.273861	−	0.158114i
$11$	−5.41099	+	9.37211i	−0.491908	+	0.852010i	−0.999957	−	0.00931868i	$-0.997034\pi$
$11$	−5.41099	+	9.37211i	−0.491908	+	0.852010i	0.508049	+	0.861328i	$0.330367\pi$
$12$		0			0
$13$		−	19.2715i		−	1.48242i	−0.671273	−	0.741211i	$-0.734252\pi$
$13$		−	19.2715i		−	1.48242i	0.671273	−	0.741211i	$-0.265748\pi$
$14$	−1.93096	+	9.70935i	−0.137926	+	0.693525i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	8.89730	+	5.13686i	0.523371	+	0.302168i	0.738313	−	0.674459i	$-0.235623\pi$
$17$	8.89730	+	5.13686i	0.523371	+	0.302168i	−0.214942	+	0.976627i	$0.568956\pi$
$18$		0			0
$19$	−18.0756	+	10.4359i	−0.951346	+	0.549260i	−0.893499	−	0.449066i	$-0.851757\pi$
$19$	−18.0756	+	10.4359i	−0.951346	+	0.549260i	−0.0578471	+	0.998325i	$0.518424\pi$
$20$			4.47214i			0.223607i
$21$		0			0
$22$	15.3046			0.695663
$23$	10.5373	+	18.2511i	0.458143	+	0.793527i	0.998863	−	0.0476755i	$-0.0151813\pi$
$23$	10.5373	+	18.2511i	0.458143	+	0.793527i	−0.540720	+	0.841203i	$0.681848\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	−23.6026	+	13.6270i	−0.907794	+	0.524115i
$27$		0			0
$28$	13.2569	−	4.50061i	0.473460	−	0.160736i
$29$	−19.0888			−0.658235			−0.329118	−	0.944289i	$-0.606751\pi$
$29$	−19.0888			−0.658235			−0.329118	+	0.944289i	$0.606751\pi$
$30$		0			0
$31$	−34.6556	−	20.0084i	−1.11792	−	0.645434i	−0.177054	−	0.984201i	$-0.556657\pi$
$31$	−34.6556	−	20.0084i	−1.11792	−	0.645434i	−0.940870	+	0.338768i	$0.889990\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$		0			0
$34$		−	14.5292i		−	0.427330i
$35$	−15.3518	−	3.05312i	−0.438624	−	0.0872319i
$36$		0			0
$37$	25.1827	+	43.6177i	0.680614	+	1.17886i	0.974794	+	0.223107i	$0.0716201\pi$
$37$	25.1827	+	43.6177i	0.680614	+	1.17886i	−0.294180	+	0.955750i	$0.595047\pi$
$38$	25.5627	+	14.7586i	0.672703	+	0.388385i
$39$		0			0
$40$	5.47723	−	3.16228i	0.136931	−	0.0790569i
$41$		−	22.7706i		−	0.555382i	−0.960671	−	0.277691i	$-0.910431\pi$
$41$		−	22.7706i		−	0.555382i	0.960671	−	0.277691i	$-0.0895691\pi$
$42$		0			0
$43$	−48.4307			−1.12629			−0.563147	−	0.826357i	$-0.690410\pi$
$43$	−48.4307			−1.12629			−0.563147	+	0.826357i	$0.690410\pi$
$44$	−10.8220	−	18.7442i	−0.245954	−	0.426005i
$45$		0			0
$46$	14.9020	−	25.8110i	0.323956	−	0.561109i
$47$	−57.6236	+	33.2690i	−1.22603	+	0.707851i	−0.966198	−	0.257802i	$-0.917002\pi$
$47$	−57.6236	+	33.2690i	−1.22603	+	0.707851i	−0.259836	+	0.965653i	$0.583668\pi$
$48$		0			0
$49$	6.39913	+	48.5804i	0.130595	+	0.991436i
$50$	−7.07107			−0.141421
$51$		0			0
$52$	33.3792	+	19.2715i	0.641907	+	0.370605i
$53$	2.47531	−	4.28736i	0.0467040	−	0.0808937i	−0.841728	−	0.539901i	$-0.818462\pi$
$53$	2.47531	−	4.28736i	0.0467040	−	0.0808937i	0.888432	+	0.459008i	$0.151795\pi$
$54$		0			0
$55$			24.1987i			0.439976i
$56$	−14.8861	−	13.0539i	−0.265824	−	0.233105i
$57$		0			0
$58$	13.4978	+	23.3789i	0.232721	+	0.403085i
$59$	24.4105	+	14.0934i	0.413737	+	0.238871i	0.692394	−	0.721520i	$-0.256556\pi$
$59$	24.4105	+	14.0934i	0.413737	+	0.238871i	−0.278657	+	0.960391i	$0.589889\pi$
$60$		0			0
$61$	−60.6988	+	35.0445i	−0.995062	+	0.574499i	−0.906784	−	0.421596i	$-0.861470\pi$
$61$	−60.6988	+	35.0445i	−0.995062	+	0.574499i	−0.0882785	+	0.996096i	$0.528137\pi$
$62$			56.5924i			0.912781i
$63$		0			0
$64$	8.00000			0.125000
$65$	−21.5462	−	37.3191i	−0.331479	−	0.574139i
$66$		0			0
$67$	−9.65287	+	16.7193i	−0.144073	+	0.249541i	−0.929027	−	0.370013i	$-0.879353\pi$
$67$	−9.65287	+	16.7193i	−0.144073	+	0.249541i	0.784954	+	0.619554i	$0.212687\pi$
$68$	−17.7946	+	10.2737i	−0.261685	+	0.151084i
$69$		0			0
$70$	7.11609	+	20.9609i	0.101658	+	0.299442i
$71$	−49.4968			−0.697138			−0.348569	−	0.937283i	$-0.613332\pi$
$71$	−49.4968			−0.697138			−0.348569	+	0.937283i	$0.613332\pi$
$72$		0			0
$73$	−115.159	−	66.4872i	−1.57752	−	0.910783i	−0.995204	−	0.0978221i	$-0.968812\pi$
$73$	−115.159	−	66.4872i	−1.57752	−	0.910783i	−0.582318	−	0.812961i	$-0.697854\pi$
$74$	35.6137	−	61.6848i	0.481266	−	0.833578i
$75$		0			0
$76$		−	41.7437i		−	0.549260i
$77$	71.7328	−	24.3527i	0.931594	−	0.316269i
$78$		0			0
$79$	45.0404	+	78.0122i	0.570132	+	0.987497i	0.996552	+	0.0829717i	$0.0264411\pi$
$79$	45.0404	+	78.0122i	0.570132	+	0.987497i	−0.426420	+	0.904525i	$0.640226\pi$
$80$	−7.74597	−	4.47214i	−0.0968246	−	0.0559017i
$81$		0			0
$82$	−27.8882	+	16.1013i	−0.340100	+	0.196357i
$83$			101.045i			1.21741i	0.793396	+	0.608706i	$0.208311\pi$
$83$			101.045i			1.21741i	−0.793396	+	0.608706i	$0.791689\pi$
$84$		0			0
$85$	22.9727			0.270267
$86$	34.2456	+	59.3152i	0.398205	+	0.689712i
$87$		0			0
$88$	−15.3046	+	26.5083i	−0.173916	+	0.301231i
$89$	−34.3077	+	19.8075i	−0.385479	+	0.222557i	−0.680200	−	0.733027i	$-0.738107\pi$
$89$	−34.3077	+	19.8075i	−0.385479	+	0.222557i	0.294720	+	0.955584i	$0.404774\pi$
$90$		0			0
$91$	−88.9425	+	101.427i	−0.977390	+	1.11458i
$92$	−42.1492			−0.458143
$93$		0			0
$94$	81.4920	+	47.0495i	0.866937	+	0.500526i
$95$	−23.3355	+	40.4182i	−0.245636	+	0.425455i
$96$		0			0
$97$			68.6944i			0.708190i	0.935210	+	0.354095i	$0.115211\pi$
$97$			68.6944i			0.708190i	−0.935210	+	0.354095i	$0.884789\pi$
$98$	54.9737	−	42.1888i	0.560956	−	0.430498i
$99$		0			0
$100$	5.00000	+	8.66025i	0.0500000	+	0.0866025i
$101$	6.96199	+	4.01951i	0.0689306	+	0.0397971i	0.534069	−	0.845441i	$-0.320662\pi$
$101$	6.96199	+	4.01951i	0.0689306	+	0.0397971i	−0.465139	+	0.885238i	$0.653996\pi$
$102$		0			0
$103$	177.158	−	102.282i	1.71998	−	0.993033i	0.801072	−	0.598568i	$-0.204263\pi$
$103$	177.158	−	102.282i	1.71998	−	0.993033i	0.918911	−	0.394465i	$-0.129070\pi$
$104$		−	54.5080i		−	0.524115i
$105$		0			0
$106$	−7.00124			−0.0660494
$107$	82.2769	+	142.508i	0.768943	+	1.33185i	0.938136	+	0.346266i	$0.112551\pi$
$107$	82.2769	+	142.508i	0.768943	+	1.33185i	−0.169193	+	0.985583i	$0.554116\pi$
$108$		0			0
$109$	39.5050	−	68.4247i	0.362432	−	0.627750i	−0.625929	−	0.779880i	$-0.715280\pi$
$109$	39.5050	−	68.4247i	0.362432	−	0.627750i	0.988360	+	0.152130i	$0.0486133\pi$
$110$	29.6372	−	17.1110i	0.269429	−	0.155555i
$111$		0			0
$112$	−5.46158	+	27.4622i	−0.0487641	+	0.245198i
$113$	−84.5690			−0.748398			−0.374199	−	0.927348i	$-0.622082\pi$
$113$	−84.5690			−0.748398			−0.374199	+	0.927348i	$0.622082\pi$
$114$		0			0
$115$	40.8108	+	23.5621i	0.354876	+	0.204888i
$116$	19.0888	−	33.0628i	0.164559	−	0.285024i
$117$		0			0
$118$		−	39.8621i		−	0.337815i
$119$	−23.1190	−	68.0987i	−0.194277	−	0.572258i
$120$		0			0
$121$	1.94240	+	3.36434i	0.0160529	+	0.0278044i
$122$	85.8410	+	49.5603i	0.703615	+	0.406232i
$123$		0			0
$124$	69.3113	−	40.0169i	0.558962	−	0.322717i
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	−101.777			−0.801393			−0.400697	−	0.916211i	$-0.631232\pi$
$127$	−101.777			−0.801393			−0.400697	+	0.916211i	$0.631232\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−30.4709	+	52.7771i	−0.234391	+	0.405978i
$131$	−61.2264	+	35.3491i	−0.467377	+	0.269840i	−0.715141	−	0.698980i	$-0.753638\pi$
$131$	−61.2264	+	35.3491i	−0.467377	+	0.269840i	0.247764	+	0.968820i	$0.420304\pi$
$132$		0			0
$133$	143.297	+	28.4984i	1.07742	+	0.214273i
$134$	27.3024			0.203750
$135$		0			0
$136$	25.1654	+	14.5292i	0.185039	+	0.106833i
$137$	−58.9138	+	102.042i	−0.430027	+	0.744829i	−0.996875	−	0.0789932i	$-0.974829\pi$
$137$	−58.9138	+	102.042i	−0.430027	+	0.744829i	0.566848	+	0.823823i	$0.308163\pi$
$138$		0			0
$139$		−	158.507i		−	1.14034i	−0.821528	−	0.570168i	$-0.806878\pi$
$139$		−	158.507i		−	1.14034i	0.821528	−	0.570168i	$-0.193122\pi$
$140$	20.6400	−	23.5370i	0.147428	−	0.168122i
$141$		0			0
$142$	34.9995	+	60.6209i	0.246475	+	0.426908i
$143$	180.614	+	104.278i	1.26304	+	0.729215i
$144$		0			0
$145$	−36.9653	+	21.3419i	−0.254933	+	0.147186i
$146$			188.054i			1.28804i
$147$		0			0
$148$	−100.731			−0.680614
$149$	−147.948	−	256.254i	−0.992940	−	1.71982i	−0.599193	−	0.800604i	$-0.704512\pi$
$149$	−147.948	−	256.254i	−0.992940	−	1.71982i	−0.393747	−	0.919219i	$-0.628821\pi$
$150$		0			0
$151$	62.6478	−	108.509i	0.414886	−	0.718604i	−0.580530	−	0.814239i	$-0.697155\pi$
$151$	62.6478	−	108.509i	0.414886	−	0.718604i	0.995417	+	0.0956344i	$0.0304880\pi$
$152$	−51.1254	+	29.5173i	−0.336352	+	0.194193i
$153$		0			0
$154$	−80.5486	−	70.6343i	−0.523043	−	0.458665i
$155$	−89.4805			−0.577293
$156$		0			0
$157$	4.61909	+	2.66684i	0.0294210	+	0.0169862i	0.514638	−	0.857407i	$-0.327926\pi$
$157$	4.61909	+	2.66684i	0.0294210	+	0.0169862i	−0.485217	+	0.874394i	$0.661260\pi$
$158$	63.6967	−	110.326i	0.403144	−	0.698266i
$159$		0			0
$160$			12.6491i			0.0790569i
$161$	28.7752	−	144.689i	0.178728	−	0.898686i
$162$		0			0
$163$	−119.623	−	207.193i	−0.733883	−	1.27112i	−0.955212	−	0.295923i	$-0.904373\pi$
$163$	−119.623	−	207.193i	−0.733883	−	1.27112i	0.221329	−	0.975199i	$-0.428961\pi$
$164$	39.4399	+	22.7706i	0.240487	+	0.138845i
$165$		0			0
$166$	123.754	−	71.4497i	0.745509	−	0.430420i
$167$		−	310.440i		−	1.85892i	−0.368918	−	0.929462i	$-0.620272\pi$
$167$		−	310.440i		−	1.85892i	0.368918	−	0.929462i	$-0.379728\pi$
$168$		0			0
$169$	−202.390			−1.19757
$170$	−16.2442	−	28.1357i	−0.0955540	−	0.165504i
$171$		0			0
$172$	48.4307	−	83.8844i	0.281574	−	0.487700i
$173$	−78.7285	+	45.4539i	−0.455078	+	0.262739i	−0.709972	−	0.704230i	$-0.751293\pi$
$173$	−78.7285	+	45.4539i	−0.455078	+	0.262739i	0.254894	+	0.966969i	$0.417959\pi$
$174$		0			0
$175$	−33.1422	+	11.2515i	−0.189384	+	0.0642944i
$176$	43.2879			0.245954
$177$		0			0
$178$	48.5184	+	28.0121i	0.272575	+	0.157371i
$179$	−121.577	+	210.577i	−0.679200	+	1.17641i	0.296022	+	0.955181i	$0.404340\pi$
$179$	−121.577	+	210.577i	−0.679200	+	1.17641i	−0.975222	+	0.221228i	$0.928993\pi$
$180$		0			0
$181$		−	245.993i		−	1.35907i	−0.733641	−	0.679537i	$-0.762181\pi$
$181$		−	245.993i		−	1.35907i	0.733641	−	0.679537i	$-0.237819\pi$
$182$	187.113	+	37.2125i	1.02810	+	0.204464i
$183$		0			0
$184$	29.8040	+	51.6220i	0.161978	+	0.280554i
$185$	97.5322	+	56.3102i	0.527201	+	0.304380i
$186$		0			0
$187$	−96.2864	+	55.5910i	−0.514901	+	0.297278i
$188$		−	133.076i		−	0.707851i
$189$		0			0
$190$	66.0027			0.347382
$191$	−20.6108	−	35.6989i	−0.107910	−	0.186905i	0.807014	−	0.590533i	$-0.201082\pi$
$191$	−20.6108	−	35.6989i	−0.107910	−	0.186905i	−0.914923	+	0.403628i	$0.867749\pi$
$192$		0			0
$193$	94.8727	−	164.324i	0.491568	−	0.851422i	−0.508384	−	0.861130i	$-0.669757\pi$
$193$	94.8727	−	164.324i	0.491568	−	0.851422i	0.999953	+	0.00970872i	$0.00309043\pi$
$194$	84.1331	−	48.5743i	0.433676	−	0.250383i
$195$		0			0
$196$	−90.5428	−	37.4967i	−0.461953	−	0.191310i
$197$	362.318			1.83918			0.919589	−	0.392882i	$-0.128522\pi$
$197$	362.318			1.83918			0.919589	+	0.392882i	$0.128522\pi$
$198$		0			0
$199$	−33.4433	−	19.3085i	−0.168057	−	0.0970278i	0.413612	−	0.910453i	$-0.364267\pi$
$199$	−33.4433	−	19.3085i	−0.168057	−	0.0970278i	−0.581669	+	0.813425i	$0.697600\pi$
$200$	7.07107	−	12.2474i	0.0353553	−	0.0612372i
$201$		0			0
$202$		−	11.3689i		−	0.0562816i
$203$	100.465	+	88.0995i	0.494902	+	0.433987i
$204$		0			0
$205$	−25.4584	−	44.0952i	−0.124187	−	0.215098i
$206$	−250.540	−	144.649i	−1.21621	−	0.702180i
$207$		0			0
$208$	−66.7584	+	38.5430i	−0.320954	+	0.185303i
$209$		−	225.875i		−	1.08074i
$210$		0			0
$211$	−136.551			−0.647163			−0.323581	−	0.946200i	$-0.604887\pi$
$211$	−136.551			−0.647163			−0.323581	+	0.946200i	$0.604887\pi$
$212$	4.95062	+	8.57473i	0.0233520	+	0.0404468i
$213$		0			0
$214$	116.357	−	201.537i	0.543725	−	0.941760i
$215$	−93.7856	+	54.1471i	−0.436212	+	0.251847i
$216$		0			0
$217$	90.0502	+	265.249i	0.414978	+	1.22235i
$218$	−111.737			−0.512556
$219$		0			0
$220$	−41.9133	−	24.1987i	−0.190515	−	0.109994i
$221$	98.9949	−	171.464i	0.447941	−	0.775856i
$222$		0			0
$223$			154.949i			0.694839i	0.937710	+	0.347419i	$0.112942\pi$
$223$			154.949i			0.694839i	−0.937710	+	0.347419i	$0.887058\pi$
$224$	37.4961	−	12.7296i	0.167393	−	0.0568288i
$225$		0			0
$226$	59.7993	+	103.575i	0.264599	+	0.458299i
$227$	−19.3590	−	11.1769i	−0.0852818	−	0.0492375i	0.456753	−	0.889594i	$-0.349012\pi$
$227$	−19.3590	−	11.1769i	−0.0852818	−	0.0492375i	−0.542034	+	0.840356i	$0.682346\pi$
$228$		0			0
$229$	25.9105	−	14.9594i	0.113146	−	0.0653250i	−0.442359	−	0.896838i	$-0.645858\pi$
$229$	25.9105	−	14.9594i	0.113146	−	0.0653250i	0.555505	+	0.831513i	$0.312525\pi$
$230$		−	66.6437i		−	0.289755i
$231$		0			0
$232$	−53.9913			−0.232721
$233$	−126.541	−	219.176i	−0.543095	−	0.940669i	−0.998724	−	0.0504987i	$-0.983919\pi$
$233$	−126.541	−	219.176i	−0.543095	−	0.940669i	0.455629	−	0.890170i	$-0.349414\pi$
$234$		0			0
$235$	−74.3917	+	128.850i	−0.316561	+	0.548299i
$236$	−48.8209	+	28.1868i	−0.206868	+	0.119436i
$237$		0			0
$238$	−67.0559	+	76.4679i	−0.281747	+	0.321294i
$239$	−121.009			−0.506315			−0.253158	−	0.967425i	$-0.581469\pi$
$239$	−121.009			−0.506315			−0.253158	+	0.967425i	$0.581469\pi$
$240$		0			0
$241$	249.755	+	144.196i	1.03633	+	0.598323i	0.918791	−	0.394745i	$-0.129167\pi$
$241$	249.755	+	144.196i	1.03633	+	0.598323i	0.117536	+	0.993069i	$0.462501\pi$
$242$	2.74697	−	4.75789i	0.0113511	−	0.0196607i
$243$		0			0
$244$		−	140.178i		−	0.574499i
$245$	66.7064	+	86.9210i	0.272271	+	0.354780i
$246$		0			0
$247$	201.116	+	348.343i	0.814234	+	1.41030i
$248$	−98.0209	−	56.5924i	−0.395246	−	0.228195i
$249$		0			0
$250$	−13.6931	+	7.90569i	−0.0547723	+	0.0316228i
$251$		−	422.260i		−	1.68231i	−0.540795	−	0.841155i	$-0.681876\pi$
$251$		−	422.260i		−	1.68231i	0.540795	−	0.841155i	$-0.318124\pi$
$252$		0			0
$253$	−228.069			−0.901457
$254$	71.9672	+	124.651i	0.283335	+	0.490751i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−64.5077	+	37.2435i	−0.251003	+	0.144916i	−0.620223	−	0.784425i	$-0.712958\pi$
$257$	−64.5077	+	37.2435i	−0.251003	+	0.144916i	0.369221	+	0.929342i	$0.379625\pi$
$258$		0			0
$259$	68.7687	−	345.786i	0.265516	−	1.33508i
$260$	86.1847			0.331479
$261$		0			0
$262$	86.5872	+	49.9911i	0.330486	+	0.190806i
$263$	156.637	−	271.304i	0.595579	−	1.03157i	−0.397885	−	0.917435i	$-0.630256\pi$
$263$	156.637	−	271.304i	0.595579	−	1.03157i	0.993465	−	0.114139i	$-0.0364108\pi$
$264$		0			0
$265$		−	11.0699i		−	0.0417733i
$266$	−66.4229	−	195.653i	−0.249710	−	0.735539i
$267$		0			0
$268$	−19.3057	−	33.4385i	−0.0720363	−	0.124771i
$269$	138.011	+	79.6809i	0.513053	+	0.296211i	0.734088	−	0.679055i	$-0.237610\pi$
$269$	138.011	+	79.6809i	0.513053	+	0.296211i	−0.221035	+	0.975266i	$0.570943\pi$
$270$		0			0
$271$	−163.041	+	94.1320i	−0.601629	+	0.347350i	−0.769682	−	0.638427i	$-0.779585\pi$
$271$	−163.041	+	94.1320i	−0.601629	+	0.347350i	0.168053	+	0.985778i	$0.446252\pi$
$272$		−	41.0949i		−	0.151084i
$273$		0			0
$274$	166.633			0.608151
$275$	27.0549	+	46.8605i	0.0983816	+	0.170402i
$276$		0			0
$277$	−3.52372	+	6.10326i	−0.0127210	+	0.0220334i	−0.872316	−	0.488943i	$-0.837383\pi$
$277$	−3.52372	+	6.10326i	−0.0127210	+	0.0220334i	0.859595	+	0.510976i	$0.170716\pi$
$278$	−194.130	+	112.081i	−0.698311	+	0.403170i
$279$		0			0
$280$	−43.4215	−	8.63552i	−0.155077	−	0.0308411i
$281$	−198.386			−0.705998			−0.352999	−	0.935624i	$-0.614838\pi$
$281$	−198.386			−0.705998			−0.352999	+	0.935624i	$0.614838\pi$
$282$		0			0
$283$	−163.790	−	94.5641i	−0.578763	−	0.334149i	0.181879	−	0.983321i	$-0.441782\pi$
$283$	−163.790	−	94.5641i	−0.578763	−	0.334149i	−0.760641	+	0.649172i	$0.775115\pi$
$284$	49.4968	−	85.7309i	0.174284	−	0.301869i
$285$		0			0
$286$		−	294.942i		−	1.03127i
$287$	−105.092	+	119.843i	−0.366174	+	0.417571i
$288$		0			0
$289$	−91.7253	−	158.873i	−0.317389	−	0.549733i
$290$	52.2769	+	30.1821i	0.180265	+	0.104076i
$291$		0			0
$292$	230.318	−	132.974i	0.788761	−	0.455391i
$293$		−	486.090i		−	1.65901i	−0.558499	−	0.829505i	$-0.688622\pi$
$293$		−	486.090i		−	1.65901i	0.558499	−	0.829505i	$-0.311378\pi$
$294$		0			0
$295$	63.0276			0.213653
$296$	71.2274	+	123.370i	0.240633	+	0.416789i
$297$		0			0
$298$	−209.230	+	362.397i	−0.702115	+	1.21610i
$299$	351.726	−	203.069i	1.17634	−	0.679161i
$300$		0			0
$301$	254.892	+	223.519i	0.846818	+	0.742588i
$302$	−177.195			−0.586738
$303$		0			0
$304$	72.3023	+	41.7437i	0.237836	+	0.137315i
$305$	−78.3618	+	135.727i	−0.256924	+	0.445005i
$306$		0			0
$307$			427.589i			1.39280i	0.717655	+	0.696399i	$0.245216\pi$
$307$			427.589i			1.39280i	−0.717655	+	0.696399i	$0.754784\pi$
$308$	−29.5526	+	148.598i	−0.0959499	+	0.482460i
$309$		0			0
$310$	63.2723	+	109.591i	0.204104	+	0.353519i
$311$	311.852	+	180.048i	1.00274	+	0.578931i	0.909057	−	0.416671i	$-0.136803\pi$
$311$	311.852	+	180.048i	1.00274	+	0.578931i	0.0936811	+	0.995602i	$0.470137\pi$
$312$		0			0
$313$	505.696	−	291.964i	1.61564	−	0.932792i	0.627614	−	0.778525i	$-0.284032\pi$
$313$	505.696	−	291.964i	1.61564	−	0.932792i	0.988029	−	0.154267i	$-0.0493016\pi$
$314$		−	7.54295i		−	0.0240221i
$315$		0			0
$316$	−180.162			−0.570132
$317$	180.700	+	312.982i	0.570032	+	0.987324i	0.996562	+	0.0828508i	$0.0264025\pi$
$317$	180.700	+	312.982i	0.570032	+	0.987324i	−0.426530	+	0.904473i	$0.640264\pi$
$318$		0			0
$319$	103.289	−	178.902i	0.323791	−	0.560823i
$320$	15.4919	−	8.94427i	0.0484123	−	0.0279508i
$321$		0			0
$322$	−197.554	+	67.0680i	−0.613521	+	0.208286i
$323$	−214.432			−0.663875
$324$		0			0
$325$	−83.4479	−	48.1787i	−0.256763	−	0.148242i
$326$	−169.172	+	293.015i	−0.518934	+	0.898819i
$327$		0			0
$328$		−	64.4051i		−	0.196357i
$329$	456.819	+	90.8507i	1.38851	+	0.276142i
$330$		0			0
$331$	−147.993	−	256.331i	−0.447108	−	0.774415i	0.551088	−	0.834447i	$-0.314213\pi$
$331$	−147.993	−	256.331i	−0.447108	−	0.774415i	−0.998196	+	0.0600326i	$0.980880\pi$
$332$	−175.015	−	101.045i	−0.527154	−	0.304353i
$333$		0			0
$334$	−380.210	+	219.514i	−1.13835	+	0.657229i
$335$			43.1689i			0.128863i
$336$		0			0
$337$	−22.0162			−0.0653300			−0.0326650	−	0.999466i	$-0.510399\pi$
$337$	−22.0162			−0.0653300			−0.0326650	+	0.999466i	$0.510399\pi$
$338$	143.111	+	247.876i	0.423406	+	0.733361i
$339$		0			0
$340$	−22.9727	+	39.7899i	−0.0675669	+	0.117029i
$341$	375.043	−	216.531i	1.09983	−	0.634988i
$342$		0			0
$343$	190.531	−	285.214i	0.555484	−	0.831527i
$344$	−136.983			−0.398205
$345$		0			0
$346$	111.339	+	64.2815i	0.321789	+	0.185785i
$347$	−141.953	+	245.870i	−0.409086	+	0.708559i	−0.994788	−	0.101969i	$-0.967486\pi$
$347$	−141.953	+	245.870i	−0.409086	+	0.708559i	0.585701	+	0.810527i	$0.300819\pi$
$348$		0			0
$349$		−	317.175i		−	0.908811i	−0.890795	−	0.454406i	$-0.849852\pi$
$349$		−	317.175i		−	0.908811i	0.890795	−	0.454406i	$-0.150148\pi$
$350$	37.2153	+	32.6347i	0.106329	+	0.0932419i
$351$		0			0
$352$	−30.6092	−	53.0166i	−0.0869579	−	0.150615i
$353$	101.275	+	58.4712i	0.286898	+	0.165641i	0.636542	−	0.771242i	$-0.280364\pi$
$353$	101.275	+	58.4712i	0.286898	+	0.165641i	−0.349644	+	0.936883i	$0.613697\pi$
$354$		0			0
$355$	−95.8501	+	55.3391i	−0.270000	+	0.155885i
$356$		−	79.2302i		−	0.222557i
$357$		0			0
$358$	343.871			0.960534
$359$	116.793	+	202.291i	0.325329	+	0.563486i	0.981579	−	0.191058i	$-0.0611918\pi$
$359$	116.793	+	202.291i	0.325329	+	0.563486i	−0.656250	+	0.754543i	$0.727858\pi$
$360$		0			0
$361$	37.3175	−	64.6359i	0.103373	−	0.179047i
$362$	−301.278	+	173.943i	−0.832260	+	0.480505i
$363$		0			0
$364$	−86.7334	−	255.479i	−0.238279	−	0.701866i
$365$	−297.340			−0.814629
$366$		0			0
$367$	443.469	+	256.037i	1.20836	+	0.697648i	0.962401	−	0.271632i	$-0.0875634\pi$
$367$	443.469	+	256.037i	1.20836	+	0.697648i	0.245960	+	0.969280i	$0.420897\pi$
$368$	42.1492	−	73.0045i	0.114536	−	0.198382i
$369$		0			0
$370$		−	159.269i		−	0.430458i
$371$	−32.8149	+	11.1404i	−0.0884498	+	0.0300280i
$372$		0			0
$373$	278.204	+	481.863i	0.745854	+	1.29186i	0.949795	+	0.312874i	$0.101292\pi$
$373$	278.204	+	481.863i	0.745854	+	1.29186i	−0.203941	+	0.978983i	$0.565375\pi$
$374$	136.170	+	78.6175i	0.364090	+	0.210207i
$375$		0			0
$376$	−162.984	+	94.0989i	−0.433468	+	0.250263i
$377$			367.870i			0.975782i
$378$		0			0
$379$	−536.301			−1.41504			−0.707521	−	0.706692i	$-0.750187\pi$
$379$	−536.301			−1.41504			−0.707521	+	0.706692i	$0.750187\pi$
$380$	−46.6709	−	80.8364i	−0.122818	−	0.212727i
$381$		0			0
$382$	−29.1480	+	50.4859i	−0.0763038	+	0.132162i
$383$	−25.4184	+	14.6753i	−0.0663666	+	0.0383168i	−0.532816	−	0.846231i	$-0.678866\pi$
$383$	−25.4184	+	14.6753i	−0.0663666	+	0.0383168i	0.466450	+	0.884548i	$0.345533\pi$
$384$		0			0
$385$	111.683	−	127.359i	0.290085	−	0.330801i
$386$	−268.341			−0.695183
$387$		0			0
$388$	−118.982	−	68.6944i	−0.306655	−	0.177047i
$389$	−349.242	+	604.905i	−0.897795	+	1.55503i	−0.0674875	+	0.997720i	$0.521498\pi$
$389$	−349.242	+	604.905i	−0.897795	+	1.55503i	−0.830307	+	0.557306i	$0.811835\pi$
$390$		0			0
$391$			216.514i			0.553745i
$392$	18.0995	+	137.406i	0.0461721	+	0.350526i
$393$		0			0
$394$	−256.198	−	443.747i	−0.650248	−	1.12626i
$395$	174.441	+	100.713i	0.441622	+	0.254971i
$396$		0			0
$397$	−177.270	+	102.347i	−0.446525	+	0.257801i	−0.706361	−	0.707851i	$-0.749665\pi$
$397$	−177.270	+	102.347i	−0.446525	+	0.257801i	0.259837	+	0.965653i	$0.416331\pi$
$398$			54.6127i			0.137218i
$399$		0			0
$400$	−20.0000			−0.0500000
$401$	214.984	+	372.363i	0.536119	+	0.928585i	0.999108	+	0.0422215i	$0.0134435\pi$
$401$	214.984	+	372.363i	0.536119	+	0.928585i	−0.462989	+	0.886364i	$0.653223\pi$
$402$		0			0
$403$	−385.592	+	667.865i	−0.956805	+	1.65723i
$404$	−13.9240	+	8.03902i	−0.0344653	+	0.0198986i
$405$		0			0
$406$	36.8598	−	185.340i	0.0907876	−	0.456502i
$407$	−545.053			−1.33920
$408$		0			0
$409$	15.3567	+	8.86618i	0.0375469	+	0.0216777i	0.518656	−	0.854983i	$-0.326433\pi$
$409$	15.3567	+	8.86618i	0.0375469	+	0.0216777i	−0.481109	+	0.876661i	$0.659766\pi$
$410$	−36.0035	+	62.3600i	−0.0878135	+	0.152097i
$411$		0			0
$412$			409.129i			0.993033i
$413$	−63.4289	−	186.834i	−0.153581	−	0.452383i
$414$		0			0
$415$	112.972	+	195.673i	0.272221	+	0.471501i
$416$	94.4106	+	54.5080i	0.226948	+	0.131029i
$417$		0			0
$418$	−276.639	+	159.718i	−0.661816	+	0.382100i
$419$			440.768i			1.05195i	0.850499	+	0.525977i	$0.176300\pi$
$419$			440.768i			1.05195i	−0.850499	+	0.525977i	$0.823700\pi$
$420$		0			0
$421$	−143.012			−0.339696			−0.169848	−	0.985470i	$-0.554328\pi$
$421$	−143.012			−0.339696			−0.169848	+	0.985470i	$0.554328\pi$
$422$	96.5564	+	167.241i	0.228807	+	0.396305i
$423$		0			0
$424$	7.00124	−	12.1265i	0.0165123	−	0.0286002i
$425$	44.4865	−	25.6843i	0.104674	−	0.0604336i
$426$		0			0
$427$	481.199	+	95.6991i	1.12693	+	0.224120i
$428$	−329.108			−0.768943
$429$		0			0
$430$	132.633	+	76.5756i	0.308448	+	0.178083i
$431$	−391.608	+	678.285i	−0.908604	+	1.57375i	−0.0925988	+	0.995704i	$0.529517\pi$
$431$	−391.608	+	678.285i	−0.908604	+	1.57375i	−0.816005	+	0.578045i	$0.803816\pi$
$432$		0			0
$433$		−	286.669i		−	0.662053i	−0.943622	−	0.331026i	$-0.892605\pi$
$433$		−	286.669i		−	0.662053i	0.943622	−	0.331026i	$-0.107395\pi$
$434$	261.188	−	297.848i	0.601815	−	0.686286i
$435$		0			0
$436$	79.0101	+	136.849i	0.181216	+	0.313875i
$437$	−380.935	−	219.933i	−0.871705	−	0.503279i
$438$		0			0
$439$	−295.016	+	170.328i	−0.672018	+	0.387990i	−0.796841	−	0.604189i	$-0.793497\pi$
$439$	−295.016	+	170.328i	−0.672018	+	0.387990i	0.124823	+	0.992179i	$0.460164\pi$
$440$			68.4442i			0.155555i
$441$		0			0
$442$	−280.000			−0.633484
$443$	197.629	+	342.304i	0.446116	+	0.772696i	0.998129	−	0.0611396i	$-0.0194735\pi$
$443$	197.629	+	342.304i	0.446116	+	0.772696i	−0.552013	+	0.833835i	$0.686140\pi$
$444$		0			0
$445$	−44.2910	+	76.7143i	−0.0995304	+	0.172392i
$446$	189.773	−	109.566i	0.425500	−	0.245663i
$447$		0			0
$448$	−42.1043	−	36.9219i	−0.0939828	−	0.0824150i
$449$	−665.078			−1.48124			−0.740621	−	0.671923i	$-0.765469\pi$
$449$	−665.078			−1.48124			−0.740621	+	0.671923i	$0.765469\pi$
$450$		0			0
$451$	213.409	+	123.212i	0.473190	+	0.273197i
$452$	84.5690	−	146.478i	0.187100	−	0.324066i
$453$		0			0
$454$			31.6131i			0.0696323i
$455$	−58.8381	+	295.852i	−0.129314	+	0.650225i
$456$		0			0
$457$	−255.468	−	442.484i	−0.559012	−	0.968236i	−0.997579	−	0.0695382i	$-0.977847\pi$
$457$	−255.468	−	442.484i	−0.559012	−	0.968236i	0.438568	−	0.898698i	$-0.355486\pi$
$458$	−36.6429	−	21.1558i	−0.0800064	−	0.0461917i
$459$		0			0
$460$	−81.6215	+	47.1242i	−0.177438	+	0.102444i
$461$		−	174.303i		−	0.378097i	−0.981968	−	0.189049i	$-0.939460\pi$
$461$		−	174.303i		−	0.378097i	0.981968	−	0.189049i	$-0.0605404\pi$
$462$		0			0
$463$	755.187			1.63107			0.815537	−	0.578705i	$-0.196442\pi$
$463$	755.187			1.63107			0.815537	+	0.578705i	$0.196442\pi$
$464$	38.1776	+	66.1256i	0.0822794	+	0.142512i
$465$		0			0
$466$	−178.956	+	309.961i	−0.384026	+	0.665153i
$467$	490.666	−	283.286i	1.05068	−	0.606609i	0.127839	−	0.991795i	$-0.459196\pi$
$467$	490.666	−	283.286i	1.05068	−	0.606609i	0.922839	+	0.385186i	$0.125863\pi$
$468$		0			0
$469$	127.967	−	43.4438i	0.272850	−	0.0926307i
$470$	210.412			0.447684
$471$		0			0
$472$	69.0432	+	39.8621i	0.146278	+	0.0844537i
$473$	262.058	−	453.897i	0.554033	−	0.959614i
$474$		0			0
$475$			104.359i			0.219704i
$476$	141.069	+	28.0554i	0.296364	+	0.0589399i
$477$		0			0
$478$	85.5665	+	148.206i	0.179009	+	0.310053i
$479$	−445.286	−	257.086i	−0.929615	−	0.536714i	−0.0429255	−	0.999078i	$-0.513668\pi$
$479$	−445.286	−	257.086i	−0.929615	−	0.536714i	−0.886690	+	0.462365i	$0.847001\pi$
$480$		0			0
$481$	840.578	−	485.308i	1.74756	−	1.00896i
$482$		−	407.848i		−	0.846157i
$483$		0			0
$484$	−7.76960			−0.0160529
$485$	76.8027	+	133.026i	0.158356	+	0.274281i
$486$		0			0
$487$	−163.663	+	283.473i	−0.336064	+	0.582081i	−0.983689	−	0.179879i	$-0.942429\pi$
$487$	−163.663	+	283.473i	−0.336064	+	0.582081i	0.647624	+	0.761960i	$0.275763\pi$
$488$	−171.682	+	99.1207i	−0.351808	+	0.203116i
$489$		0			0
$490$	59.2875	−	143.161i	0.120995	−	0.292165i
$491$	41.8889			0.0853134			0.0426567	−	0.999090i	$-0.486418\pi$
$491$	41.8889			0.0853134			0.0426567	+	0.999090i	$0.486418\pi$
$492$		0			0
$493$	−169.839	−	98.0566i	−0.344501	−	0.198898i
$494$	284.421	−	492.631i	0.575751	−	0.997229i
$495$		0			0
$496$			160.068i			0.322717i
$497$	260.503	+	228.439i	0.524152	+	0.459637i
$498$		0			0
$499$	−207.685	−	359.721i	−0.416203	−	0.720885i	0.579351	−	0.815078i	$-0.303306\pi$
$499$	−207.685	−	359.721i	−0.416203	−	0.720885i	−0.995554	+	0.0941936i	$0.969973\pi$
$500$	19.3649	+	11.1803i	0.0387298	+	0.0223607i
$501$		0			0
$502$	−517.160	+	298.583i	−1.03020	+	0.594786i
$503$		−	51.7604i		−	0.102903i	−0.998675	−	0.0514517i	$-0.983615\pi$
$503$		−	51.7604i		−	0.102903i	0.998675	−	0.0514517i	$-0.0163848\pi$
$504$		0			0
$505$	17.9758			0.0355956
$506$	161.269	+	279.326i	0.318713	+	0.552028i
$507$		0			0
$508$	101.777	−	176.283i	0.200348	−	0.347014i
$509$	−136.916	+	79.0486i	−0.268991	+	0.155302i	−0.628429	−	0.777867i	$-0.716302\pi$
$509$	−136.916	+	79.0486i	−0.268991	+	0.155302i	0.359438	+	0.933169i	$0.382968\pi$
$510$		0			0
$511$	299.233	+	881.411i	0.585583	+	1.72488i
$512$	22.6274			0.0441942
$513$		0			0
$514$	91.2276	+	52.6703i	0.177486	+	0.102471i
$515$	228.710	−	396.138i	0.444098	−	0.769200i
$516$		0			0
$517$		−	720.073i		−	1.39279i
$518$	−472.126	+	160.283i	−0.911441	+	0.309428i
$519$		0			0
$520$	−60.9418	−	105.554i	−0.117196	−	0.202989i
$521$	−306.214	−	176.793i	−0.587744	−	0.339334i	0.176461	−	0.984308i	$-0.443535\pi$
$521$	−306.214	−	176.793i	−0.587744	−	0.339334i	−0.764205	+	0.644974i	$0.776868\pi$
$522$		0			0
$523$	−103.534	+	59.7756i	−0.197962	+	0.114294i	−0.595705	−	0.803204i	$-0.703127\pi$
$523$	−103.534	+	59.7756i	−0.197962	+	0.114294i	0.397742	+	0.917497i	$0.369794\pi$
$524$		−	141.396i		−	0.269840i
$525$		0			0
$526$	−443.037			−0.842277
$527$	−205.561	−	356.042i	−0.390059	−	0.675602i
$528$		0			0
$529$	42.4308	−	73.4924i	0.0802095	−	0.138927i
$530$	−13.5578	+	7.82762i	−0.0255808	+	0.0147691i
$531$		0			0
$532$	−192.657	+	219.699i	−0.362138	+	0.412968i
$533$	−438.824			−0.823309
$534$		0			0
$535$	318.657	+	183.977i	0.595621	+	0.343882i
$536$	−27.3024	+	47.2892i	−0.0509374	+	0.0882261i
$537$		0			0
$538$		−	225.372i		−	0.418906i
$539$	−489.926	−	202.894i	−0.908954	−	0.376427i
$540$		0			0
$541$	−272.691	−	472.315i	−0.504051	−	0.873041i	−0.999989	−	0.00468349i	$-0.998509\pi$
$541$	−272.691	−	472.315i	−0.504051	−	0.873041i	0.495938	−	0.868358i	$-0.334824\pi$
$542$	230.575	+	133.123i	0.425416	+	0.245614i
$543$		0			0
$544$	−50.3307	+	29.0585i	−0.0925197	+	0.0534163i
$545$		−	176.672i		−	0.324169i
$546$		0			0
$547$	−117.783			−0.215325			−0.107663	−	0.994188i	$-0.534337\pi$
$547$	−117.783			−0.215325			−0.107663	+	0.994188i	$0.534337\pi$
$548$	−117.828	−	204.083i	−0.215014	−	0.372415i
$549$		0			0
$550$	38.2615	−	66.2708i	0.0695663	−	0.120492i
$551$	345.041	−	199.210i	0.626209	−	0.361542i
$552$		0			0
$553$	122.996	−	618.454i	0.222416	−	1.11836i
$554$	9.96659			0.0179902
$555$		0			0
$556$	274.542	+	158.507i	0.493780	+	0.285084i
$557$	−307.744	+	533.028i	−0.552503	+	0.956963i	0.445590	+	0.895237i	$0.352994\pi$
$557$	−307.744	+	533.028i	−0.552503	+	0.956963i	−0.998093	+	0.0617258i	$0.980340\pi$
$558$		0			0
$559$			933.330i			1.66964i
$560$	20.1273	+	59.2865i	0.0359417	+	0.105869i
$561$		0			0
$562$	140.280	+	242.972i	0.249608	+	0.432334i
$563$	415.047	+	239.628i	0.737207	+	0.425626i	0.821053	−	0.570852i	$-0.193387\pi$
$563$	415.047	+	239.628i	0.737207	+	0.425626i	−0.0838462	+	0.996479i	$0.526720\pi$
$564$		0			0
$565$	−163.767	+	94.5510i	−0.289853	+	0.167347i
$566$			267.468i			0.472558i
$567$		0			0
$568$	−139.998			−0.246475
$569$	−228.674	−	396.074i	−0.401887	−	0.696088i	0.592067	−	0.805889i	$-0.298312\pi$
$569$	−228.674	−	396.074i	−0.401887	−	0.696088i	−0.993954	+	0.109800i	$0.964979\pi$
$570$		0			0
$571$	−186.601	+	323.203i	−0.326797	+	0.566029i	−0.981874	−	0.189532i	$-0.939303\pi$
$571$	−186.601	+	323.203i	−0.326797	+	0.566029i	0.655077	+	0.755562i	$0.272636\pi$
$572$	−361.229	+	208.555i	−0.631519	+	0.364607i
$573$		0			0
$574$	221.088	+	43.9692i	0.385171	+	0.0766014i
$575$	105.373			0.183257
$576$		0			0
$577$	−772.108	−	445.777i	−1.33814	−	0.772577i	−0.351611	−	0.936146i	$-0.614366\pi$
$577$	−772.108	−	445.777i	−1.33814	−	0.772577i	−0.986532	+	0.163569i	$0.947699\pi$
$578$	−129.719	+	224.680i	−0.224428	+	0.388720i
$579$		0			0
$580$		−	85.3678i		−	0.147186i
$581$	466.347	−	531.804i	0.802663	−	0.915326i
$582$		0			0
$583$	26.7878	+	46.3978i	0.0459481	+	0.0795845i
$584$	−325.719	−	188.054i	−0.557738	−	0.322010i
$585$		0			0
$586$	−595.336	+	343.718i	−1.01593	+	0.586549i
$587$		−	786.758i		−	1.34030i	−0.742224	−	0.670151i	$-0.766229\pi$
$587$		−	786.758i		−	1.34030i	0.742224	−	0.670151i	$-0.233771\pi$
$588$		0			0
$589$	835.227			1.41804
$590$	−44.5672	−	77.1927i	−0.0755377	−	0.130835i
$591$		0			0
$592$	100.731	−	174.471i	0.170153	−	0.294714i
$593$	541.571	−	312.676i	0.913273	−	0.527278i	0.0317903	−	0.999495i	$-0.489879\pi$
$593$	541.571	−	312.676i	0.913273	−	0.527278i	0.881483	+	0.472216i	$0.156546\pi$
$594$		0			0
$595$	−120.906	−	106.025i	−0.203204	−	0.178193i
$596$	591.792			0.992940
$597$		0			0
$598$	−497.416	−	287.183i	−0.831799	−	0.480240i
$599$	75.2476	−	130.333i	0.125622	−	0.217584i	−0.796354	−	0.604831i	$-0.793241\pi$
$599$	75.2476	−	130.333i	0.125622	−	0.217584i	0.921976	+	0.387247i	$0.126574\pi$
$600$		0			0
$601$		−	521.601i		−	0.867888i	−0.900940	−	0.433944i	$-0.857122\pi$
$601$		−	521.601i		−	0.867888i	0.900940	−	0.433944i	$-0.142878\pi$
$602$	93.5177	−	470.230i	0.155345	−	0.781113i
$603$		0			0
$604$	125.296	+	217.019i	0.207443	+	0.359302i
$605$	7.52288	+	4.34334i	0.0124345	+	0.00717907i
$606$		0			0
$607$	−603.404	+	348.375i	−0.994075	+	0.573930i	−0.906490	−	0.422228i	$-0.861248\pi$
$607$	−603.404	+	348.375i	−0.994075	+	0.573930i	−0.0875852	+	0.996157i	$0.527915\pi$
$608$		−	118.069i		−	0.194193i
$609$		0			0
$610$	221.641			0.363345
$611$	641.143	+	1110.49i	1.04933	+	1.81750i
$612$		0			0
$613$	−27.1244	+	46.9809i	−0.0442487	+	0.0766410i	−0.887302	−	0.461190i	$-0.847423\pi$
$613$	−27.1244	+	46.9809i	−0.0442487	+	0.0766410i	0.843053	+	0.537831i	$0.180756\pi$
$614$	523.687	−	302.351i	0.852911	−	0.492428i
$615$		0			0
$616$	202.891	−	68.8800i	0.329368	−	0.111818i
$617$	969.852			1.57188			0.785941	−	0.618301i	$-0.212179\pi$
$617$	969.852			1.57188			0.785941	+	0.618301i	$0.212179\pi$
$618$		0			0
$619$	−111.240	−	64.2247i	−0.179710	−	0.103756i	0.407446	−	0.913229i	$-0.366419\pi$
$619$	−111.240	−	64.2247i	−0.179710	−	0.103756i	−0.587156	+	0.809474i	$0.699753\pi$
$620$	89.4805	−	154.985i	0.144323	−	0.249975i
$621$		0			0
$622$		−	509.252i		−	0.818733i
$623$	271.979	+	54.0903i	0.436564	+	0.0868223i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−715.163	−	412.899i	−1.14243	−	0.659584i
$627$		0			0
$628$	−9.23819	+	5.33367i	−0.0147105	+	0.00849311i
$629$			517.440i			0.822639i
$630$		0			0
$631$	115.457			0.182975			0.0914877	−	0.995806i	$-0.470838\pi$
$631$	115.457			0.182975			0.0914877	+	0.995806i	$0.470838\pi$
$632$	127.393	+	220.652i	0.201572	+	0.349133i
$633$		0			0
$634$	255.549	−	442.623i	0.403073	−	0.698144i
$635$	−197.090	+	113.790i	−0.310378	+	0.179197i
$636$		0			0
$637$	936.215	−	123.321i	1.46973	−	0.193596i
$638$	−292.146			−0.457910
$639$		0			0
$640$	−21.9089	−	12.6491i	−0.0342327	−	0.0197642i
$641$	−476.249	+	824.887i	−0.742978	+	1.28688i	0.208156	+	0.978096i	$0.433254\pi$
$641$	−476.249	+	824.887i	−0.742978	+	1.28688i	−0.951134	+	0.308780i	$0.900079\pi$
$642$		0			0
$643$			253.254i			0.393863i	0.980417	+	0.196931i	$0.0630976\pi$
$643$			253.254i			0.393863i	−0.980417	+	0.196931i	$0.936902\pi$
$644$	221.833	+	194.529i	0.344461	+	0.302063i
$645$		0			0
$646$	151.626	+	262.624i	0.234715	+	0.406539i
$647$	−870.161	−	502.388i	−1.34492	−	0.776488i	−0.357393	−	0.933954i	$-0.616334\pi$
$647$	−870.161	−	502.388i	−1.34492	−	0.776488i	−0.987524	+	0.157466i	$0.949668\pi$
$648$		0			0
$649$	−264.170	+	152.518i	−0.407041	+	0.235005i
$650$			136.270i			0.209646i
$651$		0			0
$652$	478.492			0.733883
$653$	532.797	+	922.831i	0.815922	+	1.41322i	0.908664	+	0.417528i	$0.137103\pi$
$653$	532.797	+	922.831i	0.815922	+	1.41322i	−0.0927422	+	0.995690i	$0.529563\pi$
$654$		0			0
$655$	−79.0429	+	136.906i	−0.120676	+	0.209017i
$656$	−78.8798	+	45.5413i	−0.120244	+	0.0694227i
$657$		0			0
$658$	−211.751	−	623.728i	−0.321810	−	0.947915i
$659$	−432.265			−0.655941			−0.327970	−	0.944688i	$-0.606365\pi$
$659$	−432.265			−0.655941			−0.327970	+	0.944688i	$0.606365\pi$
$660$		0			0
$661$	327.626	+	189.155i	0.495652	+	0.286165i	0.726916	−	0.686726i	$-0.240953\pi$
$661$	327.626	+	189.155i	0.495652	+	0.286165i	−0.231264	+	0.972891i	$0.574286\pi$
$662$	−209.294	+	362.507i	−0.316153	+	0.547594i
$663$		0			0
$664$			285.799i			0.430420i
$665$	309.355	−	105.024i	0.465196	−	0.157931i
$666$		0			0
$667$	−201.144	−	348.392i	−0.301566	−	0.522328i
$668$	537.698	+	310.440i	0.804937	+	0.464731i
$669$		0			0
$670$	52.8709	−	30.5251i	0.0789119	−	0.0455598i
$671$		−	758.501i		−	1.13040i
$672$		0			0
$673$	−689.666			−1.02476			−0.512382	−	0.858758i	$-0.671237\pi$
$673$	−689.666			−1.02476			−0.512382	+	0.858758i	$0.671237\pi$
$674$	15.5678	+	26.9642i	0.0230976	+	0.0400063i
$675$		0			0
$676$	202.390	−	350.549i	0.299393	−	0.518564i
$677$	−328.663	+	189.754i	−0.485470	+	0.280286i	−0.722693	−	0.691169i	$-0.757096\pi$
$677$	−328.663	+	189.754i	−0.485470	+	0.280286i	0.237223	+	0.971455i	$0.423763\pi$
$678$		0			0
$679$	317.041	−	361.541i	0.466924	−	0.532461i
$680$	64.9767			0.0955540
$681$		0			0
$682$	−530.390	−	306.221i	−0.777698	−	0.449004i
$683$	373.753	−	647.360i	0.547223	−	0.947818i	−0.451240	−	0.892403i	$-0.649018\pi$
$683$	373.753	−	647.360i	0.547223	−	0.947818i	0.998463	−	0.0554159i	$-0.0176485\pi$
$684$		0			0
$685$			263.470i			0.384628i
$686$	−484.040	−	31.6754i	−0.705598	−	0.0461740i
$687$		0			0
$688$	96.8613	+	167.769i	0.140787	+	0.243850i
$689$	−82.6238	−	47.7029i	−0.119918	−	0.0692350i
$690$		0			0
$691$	771.026	−	445.152i	1.11581	−	0.644214i	0.175483	−	0.984482i	$-0.443851\pi$
$691$	771.026	−	445.152i	1.11581	−	0.644214i	0.940328	+	0.340268i	$0.110518\pi$
$692$		−	181.816i		−	0.262739i
$693$		0			0
$694$	401.504			0.578536
$695$	−177.216	−	306.947i	−0.254987	−	0.441650i
$696$		0			0
$697$	116.970	−	202.597i	0.167819	−	0.290670i
$698$	−388.459	+	224.277i	−0.556531	+	0.321313i
$699$		0			0
$700$	13.6540	−	68.6554i	0.0195057	−	0.0980792i
$701$	650.703			0.928250			0.464125	−	0.885770i	$-0.346369\pi$
$701$	650.703			0.928250			0.464125	+	0.885770i	$0.346369\pi$
$702$		0			0
$703$	−910.384	−	525.610i	−1.29500	−	0.747667i
$704$	−43.2879	+	74.9769i	−0.0614885	+	0.106501i
$705$		0			0
$706$		−	165.382i		−	0.234251i
$707$	−18.0902	−	53.2861i	−0.0255873	−	0.0753693i
$708$		0			0
$709$	196.427	+	340.222i	0.277048	+	0.479862i	0.970650	−	0.240497i	$-0.0773105\pi$
$709$	196.427	+	340.222i	0.277048	+	0.479862i	−0.693602	+	0.720359i	$0.743977\pi$
$710$	135.553	+	78.2613i	0.190919	+	0.110227i
$711$		0			0
$712$	−97.0368	+	56.0242i	−0.136288	+	0.0786857i
$713$		−	843.339i		−	1.18280i
$714$		0			0
$715$	466.344			0.652230
$716$	−243.154	−	421.155i	−0.339600	−	0.588205i
$717$		0			0
$718$	165.170	−	286.083i	0.230042	−	0.398444i
$719$	−899.919	+	519.569i	−1.25163	+	0.722627i	−0.971432	−	0.237317i	$-0.923732\pi$
$719$	−899.919	+	519.569i	−1.25163	+	0.722627i	−0.280194	+	0.959943i	$0.590399\pi$
$720$		0			0
$721$	−1404.45	−	279.312i	−1.94792	−	0.387395i
$722$	−105.550			−0.146191
$723$		0			0
$724$	426.072	+	245.993i	0.588497	+	0.339769i
$725$	−47.7220	+	82.6570i	−0.0658235	+	0.114010i
$726$		0			0
$727$		−	610.568i		−	0.839846i	−0.907560	−	0.419923i	$-0.862057\pi$
$727$		−	610.568i		−	0.839846i	0.907560	−	0.419923i	$-0.137943\pi$
$728$	−251.567	+	286.877i	−0.345559	+	0.394062i
$729$		0			0
$730$	210.251	+	364.165i	0.288015	+	0.498856i
$731$	−430.902	−	248.781i	−0.589469	−	0.340330i
$732$		0			0
$733$	934.574	−	539.576i	1.27500	−	0.736121i	0.299074	−	0.954230i	$-0.403322\pi$
$733$	934.574	−	539.576i	1.27500	−	0.736121i	0.975924	+	0.218109i	$0.0699889\pi$
$734$		−	724.181i		−	0.986623i
$735$		0			0
$736$	−119.216			−0.161978
$737$	−104.463	−	180.935i	−0.141741	−	0.245503i
$738$		0			0
$739$	−378.082	+	654.857i	−0.511613	+	0.886139i	0.488297	+	0.872678i	$0.337618\pi$
$739$	−378.082	+	654.857i	−0.511613	+	0.886139i	−0.999909	+	0.0134615i	$0.995715\pi$
$740$	−195.064	+	112.620i	−0.263601	+	0.152190i
$741$		0			0
$742$	36.8478	+	32.3124i	0.0496601	+	0.0435477i
$743$	−963.993			−1.29743			−0.648717	−	0.761030i	$-0.724694\pi$
$743$	−963.993			−1.29743			−0.648717	+	0.761030i	$0.724694\pi$
$744$		0			0
$745$	−573.001	−	330.822i	−0.769128	−	0.444056i
$746$	393.439	−	681.457i	0.527398	−	0.913481i
$747$		0			0
$748$		−	222.364i		−	0.297278i
$749$	224.681	−	1129.75i	0.299975	−	1.50835i
$750$		0			0
$751$	−416.806	−	721.929i	−0.555001	−	0.961290i	−0.997903	−	0.0647203i	$-0.979384\pi$
$751$	−416.806	−	721.929i	−0.555001	−	0.961290i	0.442902	−	0.896570i	$-0.353949\pi$
$752$	230.494	+	133.076i	0.306508	+	0.176963i
$753$		0			0
$754$	450.547	−	260.123i	0.597542	−	0.344991i
$755$		−	280.170i		−	0.371086i
$756$		0			0
$757$	−744.966			−0.984103			−0.492051	−	0.870566i	$-0.663753\pi$
$757$	−744.966			−0.984103			−0.492051	+	0.870566i	$0.663753\pi$
$758$	379.222	+	656.832i	0.500293	+	0.866533i
$759$		0			0
$760$	−66.0027	+	114.320i	−0.0868456	+	0.150421i
$761$	64.1518	−	37.0381i	0.0842993	−	0.0486702i	−0.457258	−	0.889334i	$-0.651168\pi$
$761$	64.1518	−	37.0381i	0.0842993	−	0.0486702i	0.541557	+	0.840664i	$0.317835\pi$
$762$		0			0
$763$	−523.713	+	177.797i	−0.686387	+	0.233023i
$764$	82.4431			0.107910
$765$		0			0
$766$	35.9471	+	20.7540i	0.0469283	+	0.0270941i
$767$	271.601	−	470.426i	0.354108	−	0.613332i
$768$		0			0
$769$			961.553i			1.25039i	0.780467	+	0.625197i	$0.214981\pi$
$769$			961.553i			1.25039i	−0.780467	+	0.625197i	$0.785019\pi$
$770$	−234.953	−	46.7267i	−0.305134	−	0.0606840i
$771$		0			0
$772$	189.745	+	328.649i	0.245784	+	0.425711i
$773$	1191.17	+	687.723i	1.54097	+	0.889680i	0.998778	+	0.0494271i	$0.0157395\pi$
$773$	1191.17	+	687.723i	1.54097	+	0.889680i	0.542194	+	0.840253i	$0.317594\pi$
$774$		0			0
$775$	−173.278	+	100.042i	−0.223585	+	0.129087i
$776$			194.297i			0.250383i
$777$		0			0
$778$	987.806			1.26967
$779$	237.633	+	411.592i	0.305049	+	0.528360i
$780$		0			0
$781$	267.826	−	463.889i	0.342928	−	0.593968i
$782$	265.175	−	153.099i	0.339098	−	0.195779i
$783$		0			0
$784$	155.489	−	119.328i	0.198328	−	0.152204i
$785$	11.9264			0.0151929
$786$		0			0
$787$	329.679	+	190.340i	0.418906	+	0.241856i	0.694609	−	0.719387i	$-0.255577\pi$
$787$	329.679	+	190.340i	0.418906	+	0.241856i	−0.275703	+	0.961243i	$0.588911\pi$
$788$	−362.318	+	627.553i	−0.459795	+	0.796387i
$789$		0			0
$790$		−	284.860i		−	0.360583i
$791$	445.090	+	390.306i	0.562693	+	0.493434i
$792$		0			0
$793$	675.358	+	1169.76i	0.851650	+	1.47510i
$794$	250.698	+	144.741i	0.315741	+	0.182293i
$795$		0			0
$796$	66.8867	−	38.6170i	0.0840285	−	0.0485139i
$797$			511.440i			0.641706i	0.947129	+	0.320853i	$0.103970\pi$
$797$			511.440i			0.641706i	−0.947129	+	0.320853i	$0.896030\pi$
$798$		0			0
$799$	−683.593			−0.855560
$800$	14.1421	+	24.4949i	0.0176777	+	0.0306186i
$801$		0			0
$802$	304.033	−	526.600i	0.379093	−	0.656609i
$803$	1246.25	−	719.522i	1.55199	−	0.896043i
$804$		0			0
$805$	−106.044	−	312.360i	−0.131731	−	0.388024i
$806$	1090.62			1.35313
$807$		0			0
$808$	19.6915	+	11.3689i	0.0243707	+	0.0140704i
$809$	579.187	−	1003.18i	0.715930	−	1.24003i	−0.246670	−	0.969099i	$-0.579336\pi$
$809$	579.187	−	1003.18i	0.715930	−	1.24003i	0.962600	−	0.270927i	$-0.0873302\pi$
$810$		0			0
$811$			92.0692i			0.113526i	0.998388	+	0.0567628i	$0.0180779\pi$
$811$			92.0692i			0.113526i	−0.998388	+	0.0567628i	$0.981922\pi$
$812$	−253.058	+	85.9113i	−0.311648	+	0.105802i
$813$		0			0
$814$	385.411	+	667.551i	0.473478	+	0.820088i
$815$	−463.298	−	267.485i	−0.568463	−	0.328202i
$816$		0			0
$817$	875.412	−	505.419i	1.07150	−	0.618628i
$818$		−	25.0774i		−	0.0306569i
$819$		0			0
$820$	101.833			0.124187
$821$	−493.467	−	854.711i	−0.601057	−	1.04106i	−0.992661	−	0.120927i	$-0.961413\pi$
$821$	−493.467	−	854.711i	−0.601057	−	1.04106i	0.391605	−	0.920134i	$-0.371920\pi$
$822$		0			0
$823$	−277.748	+	481.074i	−0.337483	+	0.584537i	−0.983959	−	0.178397i	$-0.942909\pi$
$823$	−277.748	+	481.074i	−0.337483	+	0.584537i	0.646476	+	0.762935i	$0.276242\pi$
$824$	501.079	−	289.298i	0.608106	−	0.351090i
$825$		0			0
$826$	−183.973	+	209.796i	−0.222728	+	0.253990i
$827$	1323.46			1.60032			0.800160	−	0.599787i	$-0.204748\pi$
$827$	1323.46			1.60032			0.800160	+	0.599787i	$0.204748\pi$
$828$		0			0
$829$	911.903	+	526.488i	1.10000	+	0.635088i	0.936222	−	0.351409i	$-0.114297\pi$
$829$	911.903	+	526.488i	1.10000	+	0.635088i	0.163782	+	0.986497i	$0.447631\pi$
$830$	159.766	−	276.723i	0.192490	−	0.333402i
$831$		0			0
$832$		−	154.172i		−	0.185303i
$833$	−192.615	+	465.106i	−0.231231	+	0.558350i
$834$		0			0
$835$	−347.083	−	601.165i	−0.415668	−	0.719958i
$836$	391.227	+	225.875i	0.467975	+	0.270185i
$837$		0			0
$838$	539.829	−	311.670i	0.644187	−	0.371922i
$839$			1254.98i			1.49580i	0.663810	+	0.747901i	$0.268938\pi$
$839$			1254.98i			1.49580i	−0.663810	+	0.747901i	$0.731062\pi$
$840$		0			0
$841$	−476.617			−0.566727
$842$	101.125	+	175.153i	0.120101	+	0.208020i
$843$		0			0
$844$	136.551	−	236.514i	0.161791	−	0.280230i
$845$	−391.926	+	226.279i	−0.463818	+	0.267785i
$846$		0			0
$847$	5.30429	−	26.6713i	0.00626244	−	0.0314891i
$848$	−19.8025			−0.0233520
$849$		0			0
$850$	−62.9134	−	36.3231i	−0.0740158	−	0.0427330i
$851$	−530.715	+	919.226i	−0.623637	+	1.08017i
$852$		0			0
$853$			454.825i			0.533207i	0.963806	+	0.266603i	$0.0859014\pi$
$853$			454.825i			0.533207i	−0.963806	+	0.266603i	$0.914099\pi$
$854$	−223.052	−	657.015i	−0.261185	−	0.769338i
$855$		0			0
$856$	232.714	+	403.073i	0.271863	+	0.470880i
$857$	146.132	+	84.3691i	0.170515	+	0.0984470i	0.582829	−	0.812595i	$-0.301946\pi$
$857$	146.132	+	84.3691i	0.170515	+	0.0984470i	−0.412314	+	0.911042i	$0.635279\pi$
$858$		0			0
$859$	−707.715	+	408.599i	−0.823882	+	0.475669i	−0.851753	−	0.523943i	$-0.824461\pi$
$859$	−707.715	+	408.599i	−0.823882	+	0.475669i	0.0278711	+	0.999612i	$0.491127\pi$
$860$		−	216.588i		−	0.251847i
$861$		0			0
$862$	1107.64			1.28496
$863$	−616.950	−	1068.59i	−0.714890	−	1.23823i	−0.963002	−	0.269495i	$-0.913143\pi$
$863$	−616.950	−	1068.59i	−0.714890	−	1.23823i	0.248112	−	0.968731i	$-0.420190\pi$
$864$		0			0
$865$	−101.638	+	176.042i	−0.117501	+	0.203517i
$866$	−351.096	+	202.705i	−0.405423	+	0.234071i
$867$		0			0
$868$	−549.475	−	109.278i	−0.633036	−	0.125896i
$869$	−974.852			−1.12181
$870$		0			0
$871$	322.205	+	186.025i	0.369925	+	0.213576i
$872$	111.737	−	193.534i	0.128139	−	0.221943i
$873$		0			0
$874$			622.065i			0.711744i
$875$	−51.5999	+	58.8426i	−0.0589714	+	0.0672486i
$876$		0			0
$877$	−37.4779	−	64.9136i	−0.0427342	−	0.0740177i	0.843867	−	0.536552i	$-0.180274\pi$
$877$	−37.4779	−	64.9136i	−0.0427342	−	0.0740177i	−0.886601	+	0.462534i	$0.846940\pi$
$878$	417.216	+	240.880i	0.475189	+	0.274350i
$879$		0			0
$880$	83.8267	−	48.3974i	0.0952576	−	0.0549970i
$881$			461.343i			0.523658i	0.965114	+	0.261829i	$0.0843257\pi$
$881$			461.343i			0.523658i	−0.965114	+	0.261829i	$0.915674\pi$
$882$		0			0
$883$	237.840			0.269354			0.134677	−	0.990890i	$-0.457000\pi$
$883$	237.840			0.269354			0.134677	+	0.990890i	$0.457000\pi$
$884$	197.990	+	342.928i	0.223970	+	0.387928i
$885$		0			0
$886$	279.490	−	484.091i	0.315452	−	0.546379i
$887$	−7.89260	+	4.55679i	−0.00889808	+	0.00513731i	−0.504442	−	0.863445i	$-0.668302\pi$
$887$	−7.89260	+	4.55679i	−0.00889808	+	0.00513731i	0.495544	+	0.868583i	$0.334969\pi$
$888$		0			0
$889$	535.656	+	469.725i	0.602538	+	0.528375i
$890$	125.274			0.140757
$891$		0			0
$892$	−268.380	−	154.949i	−0.300874	−	0.173710i
$893$	694.386	−	1202.71i	0.777588	−	1.34682i
$894$		0			0
$895$			543.708i			0.607495i
$896$	−15.4477	+	77.6748i	−0.0172407	+	0.0866906i
$897$		0			0
$898$	470.281	+	814.551i	0.523698	+	0.907072i
$899$	661.535	+	381.938i	0.735857	+	0.424847i
$900$		0			0
$901$	44.0472	−	25.4306i	0.0488870	−	0.0282249i
$902$		−	348.495i		−	0.386358i
$903$		0			0
$904$	−239.197			−0.264599
$905$	−275.028	−	476.362i	−0.303898	−	0.526367i
$906$		0			0
$907$	−420.352	+	728.070i	−0.463453	+	0.802723i	−0.999130	−	0.0416991i	$-0.986723\pi$
$907$	−420.352	+	728.070i	−0.463453	+	0.802723i	0.535678	+	0.844423i	$0.320056\pi$
$908$	38.7179	−	22.3538i	0.0426409	−	0.0246187i
$909$		0			0
$910$	403.948	−	137.138i	0.443899	−	0.150701i
$911$	35.4735			0.0389390			0.0194695	−	0.999810i	$-0.493802\pi$
$911$	35.4735			0.0389390			0.0194695	+	0.999810i	$0.493802\pi$
$912$		0			0
$913$	−947.006	−	546.754i	−1.03725	−	0.598854i
$914$	−361.287	+	625.767i	−0.395281	+	0.684646i
$915$		0			0
$916$			59.8377i			0.0653250i
$917$	485.381	+	96.5310i	0.529314	+	0.105268i
$918$		0			0
$919$	−215.680	−	373.569i	−0.234690	−	0.406495i	0.724493	−	0.689282i	$-0.242074\pi$
$919$	−215.680	−	373.569i	−0.234690	−	0.406495i	−0.959182	+	0.282788i	$0.908741\pi$
$920$	115.430	+	66.6437i	0.125468	+	0.0724388i
$921$		0			0
$922$	−213.477	+	123.251i	−0.231536	+	0.133678i
$923$			953.876i			1.03345i
$924$		0			0
$925$	251.827			0.272245
$926$	−533.998	−	924.911i	−0.576671	−	0.998824i
$927$		0			0
$928$	53.9913	−	93.5157i	0.0581803	−	0.100771i
$929$	−531.053	+	306.603i	−0.571639	+	0.330036i	−0.757804	−	0.652483i	$-0.773728\pi$
$929$	−531.053	+	306.603i	−0.571639	+	0.330036i	0.186165	+	0.982519i	$0.440394\pi$
$930$		0			0
$931$	−622.649	−	811.337i	−0.668796	−	0.871468i
$932$	506.165			0.543095
$933$		0			0
$934$	−693.907	−	400.627i	−0.742941	−	0.428937i
$935$	−124.305	+	215.303i	−0.132947	+	0.230271i
$936$		0			0
$937$		−	1360.68i		−	1.45216i	−0.687609	−	0.726081i	$-0.741340\pi$
$937$		−	1360.68i		−	1.45216i	0.687609	−	0.726081i	$-0.258660\pi$
$938$	−143.694	−	126.007i	−0.153192	−	0.134336i
$939$		0			0
$940$	−148.783	−	257.700i	−0.158280	−	0.274149i
$941$	146.671	+	84.6806i	0.155867	+	0.0899900i	0.575905	−	0.817517i	$-0.304650\pi$
$941$	146.671	+	84.6806i	0.155867	+	0.0899900i	−0.420038	+	0.907507i	$0.637983\pi$
$942$		0			0
$943$	415.590	−	239.941i	0.440710	−	0.254444i
$944$		−	112.747i		−	0.119436i
$945$		0			0
$946$	−741.211			−0.783521
$947$	−639.583	−	1107.79i	−0.675378	−	1.16979i	−0.976358	−	0.216158i	$-0.930647\pi$
$947$	−639.583	−	1107.79i	−0.675378	−	1.16979i	0.300981	−	0.953630i	$-0.402686\pi$
$948$		0			0
$949$	−1281.31	+	2219.29i	−1.35016	+	2.33855i
$950$	127.814	−	73.7932i	0.134541	−	0.0776771i
$951$		0			0
$952$	−65.3904	−	192.612i	−0.0686874	−	0.202324i
$953$	1.43779			0.00150870			0.000754349	−	1.00000i	$-0.499760\pi$
$953$	1.43779			0.00150870			0.000754349		1.00000i	$0.499760\pi$
$954$		0			0
$955$	−79.8252	−	46.0871i	−0.0835866	−	0.0482587i
$956$	121.009	−	209.594i	0.126579	−	0.219241i
$957$		0			0
$958$			727.149i			0.759028i
$959$	781.012	−	265.148i	0.814402	−	0.276484i
$960$		0			0
$961$	320.176	+	554.560i	0.333169	+	0.577066i
$962$	−1188.76	−	686.329i	−1.23571	−	0.713440i
$963$		0			0
$964$	−499.509	+	288.392i	−0.518163	+	0.299162i
$965$		−	424.284i		−	0.439672i
$966$		0			0
$967$	486.815			0.503428			0.251714	−	0.967802i	$-0.419006\pi$
$967$	486.815			0.503428			0.251714	+	0.967802i	$0.419006\pi$
$968$	5.49394	+	9.51578i	0.00567556	+	0.00983035i
$969$		0			0
$970$	108.615	−	188.127i	0.111975	−	0.193946i
$971$	−378.215	+	218.362i	−0.389511	+	0.224884i	−0.681948	−	0.731401i	$-0.738867\pi$
$971$	−378.215	+	218.362i	−0.389511	+	0.224884i	0.292437	+	0.956285i	$0.405534\pi$
$972$		0			0
$973$	−731.547	+	834.227i	−0.751847	+	0.857376i
$974$	462.910			0.475267
$975$		0			0
$976$	242.795	+	140.178i	0.248766	+	0.143625i
$977$	127.517	−	220.866i	0.130519	−	0.226066i	−0.793358	−	0.608756i	$-0.791669\pi$
$977$	127.517	−	220.866i	0.130519	−	0.226066i	0.923877	+	0.382690i	$0.125002\pi$
$978$		0			0
$979$		−	428.714i		−	0.437910i
$980$	−217.258	+	28.6178i	−0.221692	+	0.0292018i
$981$		0			0
$982$	−29.6199	−	51.3032i	−0.0301628	−	0.0522436i
$983$	−1195.88	−	690.443i	−1.21656	−	0.702383i	−0.252383	−	0.967628i	$-0.581214\pi$
$983$	−1195.88	−	690.443i	−1.21656	−	0.702383i	−0.964181	+	0.265244i	$0.914547\pi$
$984$		0			0
$985$	701.626	−	405.084i	0.712311	−	0.411253i
$986$			277.346i			0.281284i
$987$		0			0
$988$	−804.464			−0.814234
$989$	−510.328	−	883.914i	−0.516004	−	0.893745i
$990$		0			0
$991$	311.554	−	539.628i	0.314384	−	0.544528i	−0.664923	−	0.746912i	$-0.731535\pi$
$991$	311.554	−	539.628i	0.314384	−	0.544528i	0.979306	+	0.202384i	$0.0648688\pi$
$992$	196.042	−	113.185i	0.197623	−	0.114098i
$993$		0			0
$994$	95.5763	−	480.581i	0.0961533	−	0.483482i
$995$	−86.3503			−0.0867843
$996$		0			0
$997$	485.248	+	280.158i	0.486708	+	0.281001i	0.723208	−	0.690630i	$-0.242667\pi$
$997$	485.248	+	280.158i	0.486708	+	0.281001i	−0.236499	+	0.971632i	$0.576000\pi$
$998$	−293.711	+	508.723i	−0.294300	+	0.509742i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.v.c.451.3		16
3.2	odd	2		210.3.o.b.31.5	✓	16
7.5	odd	6	inner	630.3.v.c.271.3		16
15.2	even	4		1050.3.q.e.199.7		32
15.8	even	4		1050.3.q.e.199.16		32
15.14	odd	2		1050.3.p.i.451.3		16
21.5	even	6		210.3.o.b.61.5	yes	16
21.11	odd	6		1470.3.f.d.391.5		16
21.17	even	6		1470.3.f.d.391.3		16
105.47	odd	12		1050.3.q.e.649.16		32
105.68	odd	12		1050.3.q.e.649.7		32
105.89	even	6		1050.3.p.i.901.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.5	✓	16	3.2	odd	2
210.3.o.b.61.5	yes	16	21.5	even	6
630.3.v.c.271.3		16	7.5	odd	6	inner
630.3.v.c.451.3		16	1.1	even	1	trivial
1050.3.p.i.451.3		16	15.14	odd	2
1050.3.p.i.901.3		16	105.89	even	6
1050.3.q.e.199.7		32	15.2	even	4
1050.3.q.e.199.16		32	15.8	even	4
1050.3.q.e.649.7		32	105.68	odd	12
1050.3.q.e.649.16		32	105.47	odd	12
1470.3.f.d.391.3		16	21.17	even	6
1470.3.f.d.391.5		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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-5.26304 - 4.61524i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-5.26304 - 4.61524i) q^{7} +2.82843 q^{8} +(-2.73861 - 1.58114i) q^{10} +(-5.41099 + 9.37211i) q^{11} -19.2715i q^{13} +(-1.93096 + 9.70935i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(8.89730 + 5.13686i) q^{17} +(-18.0756 + 10.4359i) q^{19} +4.47214i q^{20} +15.3046 q^{22} +(10.5373 + 18.2511i) q^{23} +(2.50000 - 4.33013i) q^{25} +(-23.6026 + 13.6270i) q^{26} +(13.2569 - 4.50061i) q^{28} -19.0888 q^{29} +(-34.6556 - 20.0084i) q^{31} +(-2.82843 + 4.89898i) q^{32} -14.5292i q^{34} +(-15.3518 - 3.05312i) q^{35} +(25.1827 + 43.6177i) q^{37} +(25.5627 + 14.7586i) q^{38} +(5.47723 - 3.16228i) q^{40} -22.7706i q^{41} -48.4307 q^{43} +(-10.8220 - 18.7442i) q^{44} +(14.9020 - 25.8110i) q^{46} +(-57.6236 + 33.2690i) q^{47} +(6.39913 + 48.5804i) q^{49} -7.07107 q^{50} +(33.3792 + 19.2715i) q^{52} +(2.47531 - 4.28736i) q^{53} +24.1987i q^{55} +(-14.8861 - 13.0539i) q^{56} +(13.4978 + 23.3789i) q^{58} +(24.4105 + 14.0934i) q^{59} +(-60.6988 + 35.0445i) q^{61} +56.5924i q^{62} +8.00000 q^{64} +(-21.5462 - 37.3191i) q^{65} +(-9.65287 + 16.7193i) q^{67} +(-17.7946 + 10.2737i) q^{68} +(7.11609 + 20.9609i) q^{70} -49.4968 q^{71} +(-115.159 - 66.4872i) q^{73} +(35.6137 - 61.6848i) q^{74} -41.7437i q^{76} +(71.7328 - 24.3527i) q^{77} +(45.0404 + 78.0122i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(-27.8882 + 16.1013i) q^{82} +101.045i q^{83} +22.9727 q^{85} +(34.2456 + 59.3152i) q^{86} +(-15.3046 + 26.5083i) q^{88} +(-34.3077 + 19.8075i) q^{89} +(-88.9425 + 101.427i) q^{91} -42.1492 q^{92} +(81.4920 + 47.0495i) q^{94} +(-23.3355 + 40.4182i) q^{95} +68.6944i q^{97} +(54.9737 - 42.1888i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 4 q^{7}+O(q^{10}) \) 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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