LMFDB - Embedded newform 630.3.bc.a.199.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,3,Mod(19,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.19"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 3, names="a")

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

Newform invariants

comment:select newform

sage:traces = [16,0,0,16,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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} + 42x^{14} + 1322x^{12} + 17616x^{10} + 175407x^{8} + 205392x^{6} + 203018x^{4} + 23226x^{2} + 2401 $ x^16 + 42x^14 + 1322x^12 + 17616x^10 + 175407x^8 + 205392x^6 + 203018x^4 + 23226*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.8
Root			$2.51048 - 4.34828i$ of defining polynomial
Character	$\chi$	$=$	630.199
Dual form			630.3.bc.a.19.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(4.93710 + 0.790609i) q^{5} +(2.74755 - 6.43824i) q^{7} -2.82843i q^{8} +(6.60573 - 2.52276i) q^{10} +(4.76531 - 8.25377i) q^{11} -15.1849 q^{13} +(-1.18747 - 9.82802i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(11.6790 - 20.2287i) q^{17} +(-9.15855 + 5.28769i) q^{19} +(6.30647 - 7.76070i) q^{20} -13.4783i q^{22} +(-18.2632 + 10.5443i) q^{23} +(23.7499 + 7.80663i) q^{25} +(-18.5976 + 10.7373i) q^{26} +(-8.40380 - 11.1971i) q^{28} +37.0510 q^{29} +(13.4505 + 7.76565i) q^{31} +(-4.89898 - 2.82843i) q^{32} -33.0333i q^{34} +(18.6551 - 29.6140i) q^{35} +(-16.9168 + 9.76693i) q^{37} +(-7.47792 + 12.9521i) q^{38} +(2.23618 - 13.9642i) q^{40} -37.7426i q^{41} +18.2540i q^{43} +(-9.53063 - 16.5075i) q^{44} +(-14.9119 + 25.8281i) q^{46} +(-0.155040 - 0.268537i) q^{47} +(-33.9019 - 35.3788i) q^{49} +(34.6077 - 7.23256i) q^{50} +(-15.1849 + 26.3010i) q^{52} +(-8.87784 - 5.12562i) q^{53} +(30.0523 - 36.9821i) q^{55} +(-18.2101 - 7.77126i) q^{56} +(45.3780 - 26.1990i) q^{58} +(3.10758 + 1.79416i) q^{59} +(96.8741 - 55.9303i) q^{61} +21.9646 q^{62} -8.00000 q^{64} +(-74.9693 - 12.0053i) q^{65} +(11.0746 + 6.39394i) q^{67} +(-23.3581 - 40.4573i) q^{68} +(1.90747 - 49.4607i) q^{70} +32.7865 q^{71} +(-30.1530 + 52.2266i) q^{73} +(-13.8125 + 23.9240i) q^{74} +21.1508i q^{76} +(-40.0468 - 53.3579i) q^{77} +(45.6617 + 79.0884i) q^{79} +(-7.13544 - 18.6838i) q^{80} +(-26.6881 - 46.2251i) q^{82} -103.825 q^{83} +(73.6535 - 90.6374i) q^{85} +(12.9075 + 22.3565i) q^{86} +(-23.3452 - 13.4783i) q^{88} +(52.3329 - 30.2144i) q^{89} +(-41.7213 + 97.7639i) q^{91} +42.1771i q^{92} +(-0.379769 - 0.219259i) q^{94} +(-49.3972 + 18.8650i) q^{95} -130.271 q^{97} +(-66.5378 - 19.3578i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} + 6 q^{5} + 24 q^{10} + 12 q^{11} - 32 q^{14} - 32 q^{16} - 12 q^{19} - 42 q^{25} + 48 q^{26} + 136 q^{29} + 84 q^{31} + 190 q^{35} + 48 q^{40} - 24 q^{44} - 68 q^{46} + 296 q^{49} + 96 q^{50}+ \cdots + 310 q^{95}+O(q^{100}) $ 16 * q + 16 * q^4 + 6 * q^5 + 24 * q^10 + 12 * q^11 - 32 * q^14 - 32 * q^16 - 12 * q^19 - 42 * q^25 + 48 * q^26 + 136 * q^29 + 84 * q^31 + 190 * q^35 + 48 * q^40 - 24 * q^44 - 68 * q^46 + 296 * q^49 + 96 * q^50 - 56 * q^56 + 372 * q^59 + 348 * q^61 - 128 * q^64 + 104 * q^65 - 296 * q^70 + 384 * q^71 - 208 * q^74 + 148 * q^79 - 24 * q^80 + 580 * q^85 + 188 * q^86 + 912 * q^89 - 616 * q^91 - 600 * q^94 + 310 * q^95

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	4.93710	+	0.790609i	0.987420	+	0.158122i
$5$	4.93710	+	0.790609i	0.987420	+	0.158122i
$6$		0			0
$7$	2.74755	−	6.43824i	0.392508	−	0.919749i
$7$	2.74755	−	6.43824i	0.392508	−	0.919749i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	6.60573	−	2.52276i	0.660573	−	0.252276i
$11$	4.76531	−	8.25377i	0.433210	−	0.750342i	−0.563937	−	0.825818i	$-0.690714\pi$
$11$	4.76531	−	8.25377i	0.433210	−	0.750342i	0.997148	+	0.0754753i	$0.0240474\pi$
$12$		0			0
$13$	−15.1849			−1.16807			−0.584034	−	0.811729i	$-0.698527\pi$
$13$	−15.1849			−1.16807			−0.584034	+	0.811729i	$0.698527\pi$
$14$	−1.18747	−	9.82802i	−0.0848193	−	0.702001i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	11.6790	−	20.2287i	0.687002	−	1.18992i	−0.285802	−	0.958289i	$-0.592260\pi$
$17$	11.6790	−	20.2287i	0.687002	−	1.18992i	0.972803	−	0.231633i	$-0.0744068\pi$
$18$		0			0
$19$	−9.15855	+	5.28769i	−0.482029	+	0.278300i	−0.721262	−	0.692663i	$-0.756437\pi$
$19$	−9.15855	+	5.28769i	−0.482029	+	0.278300i	0.239233	+	0.970962i	$0.423104\pi$
$20$	6.30647	−	7.76070i	0.315324	−	0.388035i
$21$		0			0
$22$		−	13.4783i		−	0.612652i
$23$	−18.2632	+	10.5443i	−0.794053	+	0.458447i	−0.841387	−	0.540432i	$-0.818261\pi$
$23$	−18.2632	+	10.5443i	−0.794053	+	0.458447i	0.0473345	+	0.998879i	$0.484927\pi$
$24$		0			0
$25$	23.7499	+	7.80663i	0.949995	+	0.312265i
$26$	−18.5976	+	10.7373i	−0.715293	+	0.412974i
$27$		0			0
$28$	−8.40380	−	11.1971i	−0.300136	−	0.399898i
$29$	37.0510			1.27762			0.638810	−	0.769365i	$-0.279427\pi$
$29$	37.0510			1.27762			0.638810	+	0.769365i	$0.279427\pi$
$30$		0			0
$31$	13.4505	+	7.76565i	0.433887	+	0.250505i	0.701001	−	0.713160i	$-0.252737\pi$
$31$	13.4505	+	7.76565i	0.433887	+	0.250505i	−0.267114	+	0.963665i	$0.586070\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$		0			0
$34$		−	33.0333i		−	0.971567i
$35$	18.6551	−	29.6140i	0.533002	−	0.846114i
$36$		0			0
$37$	−16.9168	+	9.76693i	−0.457212	+	0.263971i	−0.710871	−	0.703322i	$-0.751699\pi$
$37$	−16.9168	+	9.76693i	−0.457212	+	0.263971i	0.253660	+	0.967294i	$0.418366\pi$
$38$	−7.47792	+	12.9521i	−0.196787	+	0.340846i
$39$		0			0
$40$	2.23618	−	13.9642i	0.0559045	−	0.349106i
$41$		−	37.7426i		−	0.920552i	−0.887776	−	0.460276i	$-0.847751\pi$
$41$		−	37.7426i		−	0.920552i	0.887776	−	0.460276i	$-0.152249\pi$
$42$		0			0
$43$			18.2540i			0.424512i	0.977214	+	0.212256i	$0.0680810\pi$
$43$			18.2540i			0.424512i	−0.977214	+	0.212256i	$0.931919\pi$
$44$	−9.53063	−	16.5075i	−0.216605	−	0.375171i
$45$		0			0
$46$	−14.9119	+	25.8281i	−0.324171	+	0.561480i
$47$	−0.155040	−	0.268537i	−0.00329872	−	0.00571355i	0.864371	−	0.502854i	$-0.167717\pi$
$47$	−0.155040	−	0.268537i	−0.00329872	−	0.00571355i	−0.867670	+	0.497141i	$0.834383\pi$
$48$		0			0
$49$	−33.9019	−	35.3788i	−0.691875	−	0.722017i
$50$	34.6077	−	7.23256i	0.692153	−	0.144651i
$51$		0			0
$52$	−15.1849	+	26.3010i	−0.292017	+	0.505788i
$53$	−8.87784	−	5.12562i	−0.167506	−	0.0967099i	0.413903	−	0.910321i	$-0.364165\pi$
$53$	−8.87784	−	5.12562i	−0.167506	−	0.0967099i	−0.581410	+	0.813611i	$0.697499\pi$
$54$		0			0
$55$	30.0523	−	36.9821i	0.546406	−	0.672403i
$56$	−18.2101	−	7.77126i	−0.325180	−	0.138772i
$57$		0			0
$58$	45.3780	−	26.1990i	0.782379	−	0.451707i
$59$	3.10758	+	1.79416i	0.0526708	+	0.0304095i	0.526104	−	0.850420i	$-0.323652\pi$
$59$	3.10758	+	1.79416i	0.0526708	+	0.0304095i	−0.473433	+	0.880830i	$0.656986\pi$
$60$		0			0
$61$	96.8741	−	55.9303i	1.58810	−	0.916890i	0.594480	−	0.804111i	$-0.297358\pi$
$61$	96.8741	−	55.9303i	1.58810	−	0.916890i	0.993620	−	0.112779i	$-0.0359753\pi$
$62$	21.9646			0.354267
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−74.9693	−	12.0053i	−1.15337	−	0.184697i
$66$		0			0
$67$	11.0746	+	6.39394i	0.165293	+	0.0954319i	0.580364	−	0.814357i	$-0.302910\pi$
$67$	11.0746	+	6.39394i	0.165293	+	0.0954319i	−0.415072	+	0.909789i	$0.636243\pi$
$68$	−23.3581	−	40.4573i	−0.343501	−	0.594961i
$69$		0			0
$70$	1.90747	−	49.4607i	0.0272495	−	0.706582i
$71$	32.7865			0.461781			0.230891	−	0.972980i	$-0.425836\pi$
$71$	32.7865			0.461781			0.230891	+	0.972980i	$0.425836\pi$
$72$		0			0
$73$	−30.1530	+	52.2266i	−0.413055	+	0.715433i	−0.995222	−	0.0976365i	$-0.968872\pi$
$73$	−30.1530	+	52.2266i	−0.413055	+	0.715433i	0.582167	+	0.813069i	$0.302205\pi$
$74$	−13.8125	+	23.9240i	−0.186656	+	0.323297i
$75$		0			0
$76$			21.1508i			0.278300i
$77$	−40.0468	−	53.3579i	−0.520088	−	0.692960i
$78$		0			0
$79$	45.6617	+	79.0884i	0.577997	+	1.00112i	0.995709	+	0.0925400i	$0.0294986\pi$
$79$	45.6617	+	79.0884i	0.577997	+	1.00112i	−0.417712	+	0.908579i	$0.637168\pi$
$80$	−7.13544	−	18.6838i	−0.0891931	−	0.233548i
$81$		0			0
$82$	−26.6881	−	46.2251i	−0.325464	−	0.563720i
$83$	−103.825			−1.25091			−0.625453	−	0.780262i	$-0.715086\pi$
$83$	−103.825			−1.25091			−0.625453	+	0.780262i	$0.715086\pi$
$84$		0			0
$85$	73.6535	−	90.6374i	0.866512	−	1.06632i
$86$	12.9075	+	22.3565i	0.150088	+	0.259959i
$87$		0			0
$88$	−23.3452	−	13.4783i	−0.265286	−	0.153163i
$89$	52.3329	−	30.2144i	0.588010	−	0.339488i	−0.176300	−	0.984336i	$-0.556413\pi$
$89$	52.3329	−	30.2144i	0.588010	−	0.339488i	0.764310	+	0.644849i	$0.223080\pi$
$90$		0			0
$91$	−41.7213	+	97.7639i	−0.458476	+	1.07433i
$92$			42.1771i			0.458447i
$93$		0			0
$94$	−0.379769	−	0.219259i	−0.00404009	−	0.00233255i
$95$	−49.3972	+	18.8650i	−0.519970	+	0.198579i
$96$		0			0
$97$	−130.271			−1.34300			−0.671501	−	0.741003i	$-0.734350\pi$
$97$	−130.271			−1.34300			−0.671501	+	0.741003i	$0.734350\pi$
$98$	−66.5378	−	19.3578i	−0.678957	−	0.197529i
$99$		0			0
$100$	37.2714	−	33.3294i	0.372714	−	0.333294i
$101$	124.520	+	71.8914i	1.23287	+	0.711796i	0.967627	−	0.252386i	$-0.0812153\pi$
$101$	124.520	+	71.8914i	1.23287	+	0.711796i	0.265241	+	0.964182i	$0.414549\pi$
$102$		0			0
$103$	−26.8014	−	46.4213i	−0.260207	−	0.450692i	0.706090	−	0.708123i	$-0.250458\pi$
$103$	−26.8014	−	46.4213i	−0.260207	−	0.450692i	−0.966297	+	0.257430i	$0.917124\pi$
$104$			42.9493i			0.412974i
$105$		0			0
$106$	−14.4975			−0.136768
$107$	94.2108	−	54.3926i	0.880475	−	0.508342i	0.00965987	−	0.999953i	$-0.496925\pi$
$107$	94.2108	−	54.3926i	0.880475	−	0.508342i	0.870815	+	0.491611i	$0.163592\pi$
$108$		0			0
$109$	30.6519	−	53.0907i	0.281210	−	0.487071i	−0.690473	−	0.723358i	$-0.742597\pi$
$109$	30.6519	−	53.0907i	0.281210	−	0.487071i	0.971683	+	0.236288i	$0.0759308\pi$
$110$	10.6561	−	66.5439i	0.0968737	−	0.604945i
$111$		0			0
$112$	−27.7978	+	3.35867i	−0.248195	+	0.0299881i
$113$			95.2204i			0.842658i	0.906908	+	0.421329i	$0.138436\pi$
$113$			95.2204i			0.842658i	−0.906908	+	0.421329i	$0.861564\pi$
$114$		0			0
$115$	−98.5037	+	37.6190i	−0.856554	+	0.327122i
$116$	37.0510	−	64.1742i	0.319405	−	0.553226i
$117$		0			0
$118$	5.07465			0.0430055
$119$	−98.1483	−	130.772i	−0.824775	−	1.09892i
$120$		0			0
$121$	15.0836	+	26.1255i	0.124658	+	0.215913i
$122$	79.0974	−	137.001i	0.648339	−	1.12296i
$123$		0			0
$124$	26.9010	−	15.5313i	0.216944	−	0.125252i
$125$	111.083	+	57.3190i	0.888668	+	0.458552i
$126$		0			0
$127$			116.435i			0.916812i	0.888743	+	0.458406i	$0.151580\pi$
$127$			116.435i			0.916812i	−0.888743	+	0.458406i	$0.848420\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−100.307	+	38.3078i	−0.771594	+	0.294676i
$131$	−142.914	+	82.5112i	−1.09094	+	0.629857i	−0.933828	−	0.357723i	$-0.883553\pi$
$131$	−142.914	+	82.5112i	−1.09094	+	0.629857i	−0.157116	+	0.987580i	$0.550220\pi$
$132$		0			0
$133$	8.87981	+	73.4932i	0.0667655	+	0.552580i
$134$	18.0848			0.134961
$135$		0			0
$136$	−57.2153	−	33.0333i	−0.420701	−	0.242892i
$137$	184.822	+	106.707i	1.34907	+	0.778884i	0.988117	−	0.153702i	$-0.0491195\pi$
$137$	184.822	+	106.707i	1.34907	+	0.778884i	0.360949	+	0.932586i	$0.382453\pi$
$138$		0			0
$139$			53.0872i			0.381922i	0.981598	+	0.190961i	$0.0611604\pi$
$139$			53.0872i			0.381922i	−0.981598	+	0.190961i	$0.938840\pi$
$140$	−32.6378	−	61.9255i	−0.233127	−	0.442325i
$141$		0			0
$142$	40.1551	−	23.1835i	0.282782	−	0.163264i
$143$	−72.3607	+	125.332i	−0.506019	+	0.876451i
$144$		0			0
$145$	182.924	+	29.2928i	1.26155	+	0.202020i
$146$			85.2857i			0.584149i
$147$		0			0
$148$			39.0677i			0.263971i
$149$	0.00284218	+	0.00492280i	1.90750e−5	+	3.30389e-5i	0.866035	−	0.499983i	$-0.166661\pi$
$149$	0.00284218	+	0.00492280i	1.90750e−5	+	3.30389e-5i	−0.866016	+	0.500017i	$0.833327\pi$
$150$		0			0
$151$	−114.888	+	198.993i	−0.760851	+	1.31783i	0.181562	+	0.983380i	$0.441885\pi$
$151$	−114.888	+	198.993i	−0.760851	+	1.31783i	−0.942412	+	0.334453i	$0.891448\pi$
$152$	14.9558	+	25.9043i	0.0983937	+	0.170423i
$153$		0			0
$154$	−86.7768	−	37.0325i	−0.563486	−	0.240471i
$155$	60.2669	+	48.9739i	0.388818	+	0.315961i
$156$		0			0
$157$	−22.0591	+	38.2074i	−0.140504	+	0.243360i	−0.927686	−	0.373360i	$-0.878206\pi$
$157$	−22.0591	+	38.2074i	−0.140504	+	0.243360i	0.787183	+	0.616720i	$0.211539\pi$
$158$	111.848	+	64.5754i	0.707898	+	0.408705i
$159$		0			0
$160$	−21.9506	−	17.8374i	−0.137191	−	0.111484i
$161$	17.7074	+	146.554i	0.109984	+	0.910273i
$162$		0			0
$163$	26.4560	−	15.2744i	0.162307	−	0.0937079i	−0.416646	−	0.909069i	$-0.636795\pi$
$163$	26.4560	−	15.2744i	0.162307	−	0.0937079i	0.578953	+	0.815361i	$0.303461\pi$
$164$	−65.3721	−	37.7426i	−0.398611	−	0.230138i
$165$		0			0
$166$	−127.159	+	73.4155i	−0.766021	+	0.442262i
$167$	−102.148			−0.611665			−0.305833	−	0.952085i	$-0.598935\pi$
$167$	−102.148			−0.611665			−0.305833	+	0.952085i	$0.598935\pi$
$168$		0			0
$169$	61.5807			0.364383
$170$	26.1164	−	163.089i	0.153626	−	0.959344i
$171$		0			0
$172$	31.6169	+	18.2540i	0.183819	+	0.106128i
$173$	136.689	+	236.753i	0.790111	+	1.36851i	0.925898	+	0.377774i	$0.123311\pi$
$173$	136.689	+	236.753i	0.790111	+	1.36851i	−0.135787	+	0.990738i	$0.543356\pi$
$174$		0			0
$175$	115.515	−	131.458i	0.660086	−	0.751190i
$176$	−38.1225			−0.216605
$177$		0			0
$178$	42.7296	−	74.0098i	0.240054	−	0.415786i
$179$	−4.82428	+	8.35590i	−0.0269513	+	0.0466810i	−0.879186	−	0.476478i	$-0.841913\pi$
$179$	−4.82428	+	8.35590i	−0.0269513	+	0.0466810i	0.852235	+	0.523159i	$0.175247\pi$
$180$		0			0
$181$			221.537i			1.22396i	0.790873	+	0.611980i	$0.209627\pi$
$181$			221.537i			1.22396i	−0.790873	+	0.611980i	$0.790373\pi$
$182$	18.0316	+	149.237i	0.0990747	+	0.819985i
$183$		0			0
$184$	29.8237	+	51.6562i	0.162085	+	0.280740i
$185$	−91.2419	+	34.8457i	−0.493199	+	0.188355i
$186$		0			0
$187$	−111.308	−	192.792i	−0.595232	−	1.03097i
$188$	−0.620160			−0.00329872
$189$		0			0
$190$	−47.1593	+	58.0339i	−0.248207	+	0.305442i
$191$	−104.905	−	181.701i	−0.549241	−	0.951313i	−0.998327	−	0.0578244i	$-0.981584\pi$
$191$	−104.905	−	181.701i	−0.549241	−	0.951313i	0.449086	−	0.893489i	$-0.351750\pi$
$192$		0			0
$193$	217.576	+	125.618i	1.12734	+	0.650868i	0.943264	−	0.332044i	$-0.107738\pi$
$193$	217.576	+	125.618i	1.12734	+	0.650868i	0.184073	+	0.982913i	$0.441072\pi$
$194$	−159.549	+	92.1157i	−0.822418	+	0.474823i
$195$		0			0
$196$	−95.1798	+	23.3409i	−0.485611	+	0.119086i
$197$		−	128.792i		−	0.653768i	−0.945065	−	0.326884i	$-0.894001\pi$
$197$		−	128.792i		−	0.653768i	0.945065	−	0.326884i	$-0.105999\pi$
$198$		0			0
$199$	−173.384	−	100.103i	−0.871275	−	0.503031i	−0.00350309	−	0.999994i	$-0.501115\pi$
$199$	−173.384	−	100.103i	−0.871275	−	0.503031i	−0.867772	+	0.496963i	$0.834448\pi$
$200$	22.0805	−	67.1748i	0.110402	−	0.335874i
$201$		0			0
$202$	203.340			1.00663
$203$	101.800	−	238.543i	0.501476	−	1.17509i
$204$		0			0
$205$	29.8397	−	186.339i	0.145559	−	0.908971i
$206$	−65.6497	−	37.9028i	−0.318688	−	0.183994i
$207$		0			0
$208$	30.3698	+	52.6020i	0.146008	+	0.252894i
$209$			100.790i			0.482249i
$210$		0			0
$211$	167.518			0.793924			0.396962	−	0.917835i	$-0.370064\pi$
$211$	167.518			0.793924			0.396962	+	0.917835i	$0.370064\pi$
$212$	−17.7557	+	10.2512i	−0.0837532	+	0.0483549i
$213$		0			0
$214$	76.9228	−	133.234i	0.359452	−	0.622590i
$215$	−14.4318	+	90.1218i	−0.0671246	+	0.419171i
$216$		0			0
$217$	86.9531	−	65.2610i	0.400706	−	0.300742i
$218$		−	86.6967i		−	0.397691i
$219$		0			0
$220$	−34.0026	−	89.0343i	−0.154557	−	0.404701i
$221$	−177.345	+	307.170i	−0.802465	+	1.38991i
$222$		0			0
$223$	−66.6389			−0.298829			−0.149415	−	0.988775i	$-0.547739\pi$
$223$	−66.6389			−0.298829			−0.149415	+	0.988775i	$0.547739\pi$
$224$	−31.6703	+	23.7695i	−0.141385	+	0.106114i
$225$		0			0
$226$	67.3310	+	116.621i	0.297925	+	0.516021i
$227$	−25.9245	+	44.9026i	−0.114205	+	0.197809i	−0.917462	−	0.397824i	$-0.869765\pi$
$227$	−25.9245	+	44.9026i	−0.114205	+	0.197809i	0.803257	+	0.595633i	$0.203099\pi$
$228$		0			0
$229$	63.0828	−	36.4209i	0.275471	−	0.159043i	−0.355900	−	0.934524i	$-0.615826\pi$
$229$	63.0828	−	36.4209i	0.275471	−	0.159043i	0.631371	+	0.775481i	$0.282492\pi$
$230$	−94.0412	+	115.726i	−0.408875	+	0.503158i
$231$		0			0
$232$		−	104.796i		−	0.451707i
$233$	−119.380	+	68.9243i	−0.512362	+	0.295813i	−0.733804	−	0.679361i	$-0.762257\pi$
$233$	−119.380	+	68.9243i	−0.512362	+	0.295813i	0.221442	+	0.975174i	$0.428924\pi$
$234$		0			0
$235$	−0.553139	−	1.44837i	−0.00235378	−	0.00616327i
$236$	6.21515	−	3.58832i	0.0263354	−	0.0152048i
$237$		0			0
$238$	−212.676	−	90.7607i	−0.893597	−	0.381348i
$239$	350.640			1.46711			0.733557	−	0.679628i	$-0.237859\pi$
$239$	350.640			1.46711			0.733557	+	0.679628i	$0.237859\pi$
$240$		0			0
$241$	−264.464	−	152.688i	−1.09736	−	0.633561i	−0.161833	−	0.986818i	$-0.551741\pi$
$241$	−264.464	−	152.688i	−1.09736	−	0.633561i	−0.935526	+	0.353257i	$0.885074\pi$
$242$	36.9470	+	21.3314i	0.152674	+	0.0881462i
$243$		0			0
$244$		−	223.721i		−	0.916890i
$245$	−139.406	−	201.472i	−0.569004	−	0.822334i
$246$		0			0
$247$	139.072	−	80.2930i	0.563043	−	0.325073i
$248$	21.9646	−	38.0438i	0.0885669	−	0.153402i
$249$		0			0
$250$	176.580	−	8.34674i	0.706318	−	0.0333870i
$251$			419.508i			1.67135i	0.549228	+	0.835673i	$0.314922\pi$
$251$			419.508i			1.67135i	−0.549228	+	0.835673i	$0.685078\pi$
$252$		0			0
$253$			200.987i			0.794415i
$254$	82.3321	+	142.603i	0.324142	+	0.561431i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−3.64460	−	6.31263i	−0.0141813	−	0.0245628i	0.858848	−	0.512231i	$-0.171181\pi$
$257$	−3.64460	−	6.31263i	−0.0141813	−	0.0245628i	−0.873029	+	0.487668i	$0.837848\pi$
$258$		0			0
$259$	16.4020	+	135.750i	0.0633280	+	0.524130i
$260$	−95.7631	+	117.845i	−0.368319	+	0.453251i
$261$		0			0
$262$	−116.689	+	202.110i	−0.445376	+	0.771414i
$263$	118.435	+	68.3785i	0.450323	+	0.259994i	0.707967	−	0.706246i	$-0.249613\pi$
$263$	118.435	+	68.3785i	0.450323	+	0.259994i	−0.257643	+	0.966240i	$0.582946\pi$
$264$		0			0
$265$	−39.7784	−	32.3246i	−0.150107	−	0.121980i
$266$	62.8430	+	83.7314i	0.236252	+	0.314780i
$267$		0			0
$268$	22.1493	−	12.7879i	0.0826465	−	0.0477160i
$269$	−216.274	−	124.866i	−0.803993	−	0.464186i	0.0408722	−	0.999164i	$-0.486986\pi$
$269$	−216.274	−	124.866i	−0.803993	−	0.464186i	−0.844866	+	0.534979i	$0.820320\pi$
$270$		0			0
$271$	−388.441	+	224.266i	−1.43336	+	0.827551i	−0.997375	−	0.0724033i	$-0.976933\pi$
$271$	−388.441	+	224.266i	−1.43336	+	0.827551i	−0.435985	+	0.899954i	$0.643600\pi$
$272$	−93.4322			−0.343501
$273$		0			0
$274$	301.813			1.10151
$275$	177.610	−	158.825i	0.645853	−	0.577545i
$276$		0			0
$277$	424.679	+	245.188i	1.53314	+	0.885157i	0.999215	+	0.0396228i	$0.0126156\pi$
$277$	424.679	+	245.188i	1.53314	+	0.885157i	0.533922	+	0.845534i	$0.320718\pi$
$278$	37.5383	+	65.0183i	0.135030	+	0.233879i
$279$		0			0
$280$	−83.7610	−	52.7645i	−0.299146	−	0.188445i
$281$	54.0733			0.192432			0.0962158	−	0.995360i	$-0.469326\pi$
$281$	54.0733			0.192432			0.0962158	+	0.995360i	$0.469326\pi$
$282$		0			0
$283$	81.2503	−	140.730i	0.287104	−	0.497278i	−0.686014	−	0.727589i	$-0.740641\pi$
$283$	81.2503	−	140.730i	0.287104	−	0.497278i	0.973117	+	0.230311i	$0.0739743\pi$
$284$	32.7865	−	56.7878i	0.115445	−	0.199957i
$285$		0			0
$286$			204.667i			0.715619i
$287$	−242.996	−	103.700i	−0.846676	−	0.361324i
$288$		0			0
$289$	−128.299	−	222.221i	−0.443942	−	0.768931i
$290$	244.749	−	93.4707i	0.843961	−	0.322313i
$291$		0			0
$292$	60.3061	+	104.453i	0.206528	+	0.357716i
$293$	−298.153			−1.01759			−0.508794	−	0.860888i	$-0.669909\pi$
$293$	−298.153			−1.01759			−0.508794	+	0.860888i	$0.669909\pi$
$294$		0			0
$295$	13.9239	+	11.3148i	0.0471998	+	0.0383553i
$296$	27.6251	+	47.8480i	0.0933279	+	0.161649i
$297$		0			0
$298$	0.00696189	+	0.00401945i	2.33620e−5	+	1.34881e-5i
$299$	277.325	−	160.114i	0.927508	−	0.535497i
$300$		0			0
$301$	117.524	+	50.1539i	0.390444	+	0.166624i
$302$			324.954i			1.07601i
$303$		0			0
$304$	36.6342	+	21.1508i	0.120507	+	0.0695749i
$305$	522.496	−	199.544i	1.71310	−	0.654242i
$306$		0			0
$307$	−197.369			−0.642895			−0.321447	−	0.946927i	$-0.604169\pi$
$307$	−197.369			−0.642895			−0.321447	+	0.946927i	$0.604169\pi$
$308$	−132.465	+	16.0051i	−0.430082	+	0.0519647i
$309$		0			0
$310$	108.441	+	17.3654i	0.349811	+	0.0560174i
$311$	−277.559	−	160.249i	−0.892474	−	0.515270i	−0.0177229	−	0.999843i	$-0.505642\pi$
$311$	−277.559	−	160.249i	−0.892474	−	0.515270i	−0.874751	+	0.484573i	$0.838975\pi$
$312$		0			0
$313$	−108.403	−	187.760i	−0.346337	−	0.599873i	0.639259	−	0.768992i	$-0.279241\pi$
$313$	−108.403	−	187.760i	−0.346337	−	0.599873i	−0.985596	+	0.169119i	$0.945908\pi$
$314$			62.3925i			0.198702i
$315$		0			0
$316$	182.647			0.577997
$317$	339.651	−	196.098i	1.07145	−	0.618605i	0.142876	−	0.989741i	$-0.454365\pi$
$317$	339.651	−	196.098i	1.07145	−	0.618605i	0.928579	+	0.371136i	$0.121032\pi$
$318$		0			0
$319$	176.560	−	305.810i	0.553478	−	0.958652i
$320$	−39.4968	−	6.32487i	−0.123427	−	0.0197652i
$321$		0			0
$322$	125.316	+	166.970i	0.389181	+	0.518541i
$323$			247.020i			0.764769i
$324$		0			0
$325$	−360.639	−	118.543i	−1.10966	−	0.364747i
$326$	21.6013	−	37.4145i	0.0662615	−	0.114768i
$327$		0			0
$328$	−106.752			−0.325464
$329$	−2.15489	+	0.260364i	−0.00654981	+	0.000791380i
$330$		0			0
$331$	171.860	+	297.670i	0.519214	+	0.899304i	0.999751	+	0.0223298i	$0.00710839\pi$
$331$	171.860	+	297.670i	0.519214	+	0.899304i	−0.480537	+	0.876974i	$0.659558\pi$
$332$	−103.825	+	179.831i	−0.312727	+	0.541659i
$333$		0			0
$334$	−125.105	+	72.2296i	−0.374567	+	0.216256i
$335$	49.6214	+	40.3232i	0.148124	+	0.120368i
$336$		0			0
$337$		−	86.0226i		−	0.255260i	−0.991822	−	0.127630i	$-0.959263\pi$
$337$		−	86.0226i		−	0.255260i	0.991822	−	0.127630i	$-0.0407370\pi$
$338$	75.4206	−	43.5441i	0.223138	−	0.128829i
$339$		0			0
$340$	−83.3351	−	218.209i	−0.245103	−	0.641791i
$341$	128.192	−	74.0115i	0.375929	−	0.217043i
$342$		0			0
$343$	−320.925	+	121.063i	−0.935641	+	0.352954i
$344$	51.6301			0.150088
$345$		0			0
$346$	334.819	+	193.308i	0.967685	+	0.558693i
$347$	−531.356	−	306.778i	−1.53129	−	0.884088i	−0.999303	−	0.0373324i	$-0.988114\pi$
$347$	−531.356	−	306.778i	−1.53129	−	0.884088i	−0.531982	−	0.846756i	$-0.678553\pi$
$348$		0			0
$349$			202.068i			0.578990i	0.957180	+	0.289495i	$0.0934874\pi$
$349$			202.068i			0.578990i	−0.957180	+	0.289495i	$0.906513\pi$
$350$	48.5215	−	242.684i	0.138633	−	0.693384i
$351$		0			0
$352$	−46.6903	+	26.9567i	−0.132643	+	0.0765815i
$353$	255.952	−	443.323i	0.725078	−	1.25587i	−0.233864	−	0.972269i	$-0.575137\pi$
$353$	255.952	−	443.323i	0.725078	−	1.25587i	0.958942	−	0.283602i	$-0.0915296\pi$
$354$		0			0
$355$	161.870	+	25.9213i	0.455972	+	0.0730177i
$356$		−	120.858i		−	0.339488i
$357$		0			0
$358$			13.6451i			0.0381149i
$359$	−79.2023	−	137.182i	−0.220619	−	0.382124i	0.734377	−	0.678742i	$-0.237475\pi$
$359$	−79.2023	−	137.182i	−0.220619	−	0.382124i	−0.954996	+	0.296618i	$0.904141\pi$
$360$		0			0
$361$	−124.581	+	215.780i	−0.345099	+	0.597729i
$362$	156.650	+	271.326i	0.432736	+	0.749520i
$363$		0			0
$364$	127.611	+	170.027i	0.350579	+	0.467108i
$365$	−190.159	+	234.009i	−0.520985	+	0.641119i
$366$		0			0
$367$	163.167	−	282.613i	0.444596	−	0.770062i	−0.553428	−	0.832897i	$-0.686681\pi$
$367$	163.167	−	282.613i	0.444596	−	0.770062i	0.998024	+	0.0628347i	$0.0200141\pi$
$368$	73.0529	+	42.1771i	0.198513	+	0.114612i
$369$		0			0
$370$	−87.1084	+	107.195i	−0.235428	+	0.289716i
$371$	−57.3923	+	43.0747i	−0.154696	+	0.116104i
$372$		0			0
$373$	−252.630	+	145.856i	−0.677292	+	0.391035i	−0.798834	−	0.601551i	$-0.794549\pi$
$373$	−252.630	+	145.856i	−0.677292	+	0.391035i	0.121542	+	0.992586i	$0.461216\pi$
$374$	−272.649	−	157.414i	−0.729008	−	0.420893i
$375$		0			0
$376$	−0.759537	+	0.438519i	−0.00202005	+	0.00116627i
$377$	−562.615			−1.49235
$378$		0			0
$379$	−677.228			−1.78688			−0.893441	−	0.449181i	$-0.851716\pi$
$379$	−677.228			−1.78688			−0.893441	+	0.449181i	$0.851716\pi$
$380$	−16.7220	+	104.423i	−0.0440052	+	0.274798i
$381$		0			0
$382$	−256.964	−	148.358i	−0.672680	−	0.388372i
$383$	−124.602	−	215.817i	−0.325332	−	0.563491i	0.656248	−	0.754545i	$-0.272143\pi$
$383$	−124.602	−	215.817i	−0.325332	−	0.563491i	−0.981579	+	0.191055i	$0.938809\pi$
$384$		0			0
$385$	−155.530	−	295.095i	−0.403973	−	0.766479i
$386$	355.300			0.920467
$387$		0			0
$388$	−130.271	+	225.636i	−0.335751	+	0.581537i
$389$	−14.3803	+	24.9074i	−0.0369673	+	0.0640293i	−0.883917	−	0.467644i	$-0.845103\pi$
$389$	−14.3803	+	24.9074i	−0.0369673	+	0.0640293i	0.846950	+	0.531673i	$0.178436\pi$
$390$		0			0
$391$			492.587i			1.25981i
$392$	−100.066	+	95.8890i	−0.255272	+	0.244615i
$393$		0			0
$394$	−91.0699	−	157.738i	−0.231142	−	0.400349i
$395$	162.908	+	426.568i	0.412426	+	1.07992i
$396$		0			0
$397$	−126.465	−	219.043i	−0.318550	−	0.551746i	0.661635	−	0.749826i	$-0.269863\pi$
$397$	−126.465	−	219.043i	−0.318550	−	0.551746i	−0.980186	+	0.198080i	$0.936529\pi$
$398$	−283.134			−0.711393
$399$		0			0
$400$	−20.4568	−	97.8852i	−0.0511420	−	0.244713i
$401$	−103.441	−	179.165i	−0.257958	−	0.446796i	0.707737	−	0.706476i	$-0.249716\pi$
$401$	−103.441	−	179.165i	−0.257958	−	0.446796i	−0.965695	+	0.259680i	$0.916383\pi$
$402$		0			0
$403$	−204.244	−	117.921i	−0.506810	−	0.292607i
$404$	249.039	−	143.783i	0.616434	−	0.355898i
$405$		0			0
$406$	−43.9969	−	364.138i	−0.108367	−	0.896891i
$407$			186.170i			0.457420i
$408$		0			0
$409$	577.695	+	333.532i	1.41246	+	0.815483i	0.995619	−	0.0934983i	$-0.0298050\pi$
$409$	577.695	+	333.532i	1.41246	+	0.815483i	0.416838	+	0.908981i	$0.363138\pi$
$410$	−95.2156	−	249.318i	−0.232233	−	0.608092i
$411$		0			0
$412$	−107.205			−0.260207
$413$	20.0895	−	15.0778i	0.0486428	−	0.0365079i
$414$		0			0
$415$	−512.595	−	82.0852i	−1.23517	−	0.197796i
$416$	74.3904	+	42.9493i	0.178823	+	0.103244i
$417$		0			0
$418$	71.2693	+	123.442i	0.170501	+	0.295316i
$419$			82.9914i			0.198070i	0.995084	+	0.0990350i	$0.0315756\pi$
$419$			82.9914i			0.198070i	−0.995084	+	0.0990350i	$0.968424\pi$
$420$		0			0
$421$	155.483			0.369319			0.184659	−	0.982803i	$-0.440882\pi$
$421$	155.483			0.369319			0.184659	+	0.982803i	$0.440882\pi$
$422$	205.167	−	118.453i	0.486177	−	0.280695i
$423$		0			0
$424$	−14.4975	+	25.1103i	−0.0341921	+	0.0592225i
$425$	435.293	−	389.254i	1.02422	−	0.915893i
$426$		0			0
$427$	−93.9257	−	777.370i	−0.219967	−	1.82054i
$428$		−	217.571i		−	0.508342i
$429$		0			0
$430$	46.0505	+	120.581i	0.107094	+	0.280421i
$431$	−17.6114	+	30.5039i	−0.0408618	+	0.0707748i	−0.885733	−	0.464195i	$-0.846344\pi$
$431$	−17.6114	+	30.5039i	−0.0408618	+	0.0707748i	0.844871	+	0.534970i	$0.179677\pi$
$432$		0			0
$433$	98.0262			0.226388			0.113194	−	0.993573i	$-0.463892\pi$
$433$	98.0262			0.226388			0.113194	+	0.993573i	$0.463892\pi$
$434$	60.3489	−	141.413i	0.139053	−	0.325837i
$435$		0			0
$436$	−61.3038	−	106.181i	−0.140605	−	0.243535i
$437$	111.510	−	193.141i	0.255171	−	0.441969i
$438$		0			0
$439$	356.391	−	205.763i	0.811826	−	0.468708i	−0.0357638	−	0.999360i	$-0.511386\pi$
$439$	356.391	−	205.763i	0.811826	−	0.468708i	0.847589	+	0.530653i	$0.178053\pi$
$440$	−104.601	−	85.0008i	−0.237730	−	0.193184i
$441$		0			0
$442$			501.606i			1.13486i
$443$	656.457	−	379.006i	1.48184	−	0.855543i	0.482057	−	0.876140i	$-0.339890\pi$
$443$	656.457	−	379.006i	1.48184	−	0.855543i	0.999788	+	0.0205969i	$0.00655665\pi$
$444$		0			0
$445$	282.260	−	107.797i	0.634293	−	0.242239i
$446$	−81.6157	+	47.1208i	−0.182995	+	0.105652i
$447$		0			0
$448$	−21.9804	+	51.5059i	−0.0490635	+	0.114969i
$449$	49.9480			0.111243			0.0556213	−	0.998452i	$-0.482286\pi$
$449$	49.9480			0.111243			0.0556213	+	0.998452i	$0.482286\pi$
$450$		0			0
$451$	−311.519	−	179.855i	−0.690729	−	0.398792i
$452$	164.926	+	95.2204i	0.364882	+	0.210665i
$453$		0			0
$454$			73.3256i			0.161510i
$455$	−283.275	+	449.685i	−0.622583	+	0.988318i
$456$		0			0
$457$	350.458	−	202.337i	0.766866	−	0.442750i	−0.0648896	−	0.997892i	$-0.520670\pi$
$457$	350.458	−	202.337i	0.766866	−	0.442750i	0.831755	+	0.555142i	$0.187336\pi$
$458$	51.5069	−	89.2126i	0.112461	−	0.194787i
$459$		0			0
$460$	−33.3456	+	208.232i	−0.0724904	+	0.452679i
$461$		−	41.4395i		−	0.0898904i	−0.998989	−	0.0449452i	$-0.985689\pi$
$461$		−	41.4395i		−	0.0898904i	0.998989	−	0.0449452i	$-0.0143113\pi$
$462$		0			0
$463$		−	668.770i		−	1.44443i	−0.691670	−	0.722213i	$-0.743125\pi$
$463$		−	668.770i		−	1.44443i	0.691670	−	0.722213i	$-0.256875\pi$
$464$	−74.1019	−	128.348i	−0.159702	−	0.276613i
$465$		0			0
$466$	−97.4737	+	168.829i	−0.209171	+	0.362295i
$467$	−248.677	−	430.721i	−0.532498	−	0.922314i	−0.999280	−	0.0379417i	$-0.987920\pi$
$467$	−248.677	−	430.721i	−0.532498	−	0.922314i	0.466782	−	0.884373i	$-0.345413\pi$
$468$		0			0
$469$	71.5939	−	53.7334i	0.152652	−	0.114570i
$470$	−1.70161	−	1.38275i	−0.00362044	−	0.00294203i
$471$		0			0
$472$	5.07465	−	8.78956i	0.0107514	−	0.0186219i
$473$	150.664	+	86.9860i	0.318529	+	0.183903i
$474$		0			0
$475$	−258.793	+	54.0846i	−0.544828	+	0.113862i
$476$	−324.652	+	39.2260i	−0.682041	+	0.0824076i
$477$		0			0
$478$	429.445	−	247.940i	0.898420	−	0.518703i
$479$	−383.598	−	221.470i	−0.800830	−	0.462360i	0.0429311	−	0.999078i	$-0.486330\pi$
$479$	−383.598	−	221.470i	−0.800830	−	0.462360i	−0.843761	+	0.536718i	$0.819664\pi$
$480$		0			0
$481$	256.880	−	148.310i	0.534054	−	0.308336i
$482$	−431.867			−0.895990
$483$		0			0
$484$	60.3343			0.124658
$485$	−643.162	−	102.994i	−1.32611	−	0.212358i
$486$		0			0
$487$	−97.2891	−	56.1699i	−0.199772	−	0.115339i	0.396777	−	0.917915i	$-0.370129\pi$
$487$	−97.2891	−	56.1699i	−0.199772	−	0.115339i	−0.596549	+	0.802576i	$0.703462\pi$
$488$	−158.195	−	274.001i	−0.324170	−	0.561478i
$489$		0			0
$490$	−313.199	−	148.177i	−0.639182	−	0.302402i
$491$	677.177			1.37918			0.689590	−	0.724200i	$-0.257791\pi$
$491$	677.177			1.37918			0.689590	+	0.724200i	$0.257791\pi$
$492$		0			0
$493$	432.719	−	749.492i	0.877727	−	1.52027i
$494$	113.551	−	196.677i	0.229861	−	0.398131i
$495$		0			0
$496$		−	62.1252i		−	0.125252i
$497$	90.0826	−	211.087i	0.181253	−	0.424723i
$498$		0			0
$499$	−461.215	−	798.848i	−0.924279	−	1.60090i	−0.792717	−	0.609590i	$-0.791334\pi$
$499$	−461.215	−	798.848i	−0.924279	−	1.60090i	−0.131562	−	0.991308i	$-0.541999\pi$
$500$	210.363	−	135.083i	0.420726	−	0.270166i
$501$		0			0
$502$	296.637	+	513.790i	0.590910	+	1.02349i
$503$	136.712			0.271793			0.135896	−	0.990723i	$-0.456609\pi$
$503$	136.712			0.271793			0.135896	+	0.990723i	$0.456609\pi$
$504$		0			0
$505$	557.927	+	453.381i	1.10481	+	0.897785i
$506$	142.119	+	246.158i	0.280868	+	0.486478i
$507$		0			0
$508$	201.672	+	116.435i	0.396991	+	0.229203i
$509$	619.262	−	357.531i	1.21662	−	0.702418i	0.252430	−	0.967615i	$-0.418770\pi$
$509$	619.262	−	357.531i	1.21662	−	0.702418i	0.964194	+	0.265197i	$0.0854370\pi$
$510$		0			0
$511$	253.400	+	337.628i	0.495891	+	0.660720i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	−8.92741	−	5.15424i	−0.0173685	−	0.0100277i
$515$	−95.6198	−	250.376i	−0.185670	−	0.486167i
$516$		0			0
$517$	−2.95525			−0.00571616
$518$	116.078	+	154.661i	0.224088	+	0.298573i
$519$		0			0
$520$	−33.9561	+	212.045i	−0.0653003	+	0.407779i
$521$	−14.6765	−	8.47346i	−0.0281698	−	0.0162638i	0.485849	−	0.874043i	$-0.338510\pi$
$521$	−14.6765	−	8.47346i	−0.0281698	−	0.0162638i	−0.514019	+	0.857779i	$0.671844\pi$
$522$		0			0
$523$	351.622	+	609.027i	0.672317	+	1.16449i	0.977245	+	0.212113i	$0.0680343\pi$
$523$	351.622	+	609.027i	0.672317	+	1.16449i	−0.304928	+	0.952375i	$0.598632\pi$
$524$			330.045i			0.629857i
$525$		0			0
$526$	193.404			0.367687
$527$	314.178	−	181.391i	0.596162	−	0.344195i
$528$		0			0
$529$	−42.1366	+	72.9828i	−0.0796533	+	0.137964i
$530$	−71.5753	−	11.4618i	−0.135048	−	0.0216261i
$531$		0			0
$532$	136.174	+	58.1129i	0.255966	+	0.109235i
$533$			573.117i			1.07527i
$534$		0			0
$535$	508.131	−	194.058i	0.949778	−	0.362725i
$536$	18.0848	−	31.3238i	0.0337403	−	0.0584399i
$537$		0			0
$538$	−353.174			−0.656458
$539$	−453.562	+	111.227i	−0.841488	+	0.206358i
$540$		0			0
$541$	−473.725	−	820.515i	−0.875647	−	1.51666i	−0.856072	−	0.516856i	$-0.827102\pi$
$541$	−473.725	−	820.515i	−0.875647	−	1.51666i	−0.0195742	−	0.999808i	$-0.506231\pi$
$542$	−317.160	+	549.338i	−0.585167	+	1.01354i
$543$		0			0
$544$	−114.431	+	66.0666i	−0.210350	+	0.121446i
$545$	193.306	−	237.880i	0.354689	−	0.436478i
$546$		0			0
$547$			451.960i			0.826252i	0.910674	+	0.413126i	$0.135563\pi$
$547$			451.960i			0.826252i	−0.910674	+	0.413126i	$0.864437\pi$
$548$	369.644	−	213.414i	0.674533	−	0.389442i
$549$		0			0
$550$	105.220	−	320.109i	0.191310	−	0.582016i
$551$	−339.333	+	195.914i	−0.615850	+	0.355561i
$552$		0			0
$553$	634.648	−	76.6814i	1.14765	−	0.138664i
$554$	693.498			1.25180
$555$		0			0
$556$	91.9497	+	53.0872i	0.165377	+	0.0954806i
$557$	−331.417	−	191.344i	−0.595004	−	0.343526i	0.172069	−	0.985085i	$-0.444955\pi$
$557$	−331.417	−	191.344i	−0.595004	−	0.343526i	−0.767074	+	0.641559i	$0.778288\pi$
$558$		0			0
$559$		−	277.185i		−	0.495858i
$560$	−139.896	−	5.39513i	−0.249814	−	0.00963417i
$561$		0			0
$562$	66.2260	−	38.2356i	0.117840	−	0.0680349i
$563$	−22.9940	+	39.8268i	−0.0408419	+	0.0707402i	−0.885724	−	0.464213i	$-0.846337\pi$
$563$	−22.9940	+	39.8268i	−0.0408419	+	0.0707402i	0.844882	+	0.534953i	$0.179671\pi$
$564$		0			0
$565$	−75.2821	+	470.112i	−0.133243	+	0.832057i
$566$		−	229.811i		−	0.406026i
$567$		0			0
$568$		−	92.7341i		−	0.163264i
$569$	−15.4807	−	26.8133i	−0.0272068	−	0.0471236i	0.852101	−	0.523377i	$-0.175328\pi$
$569$	−15.4807	−	26.8133i	−0.0272068	−	0.0471236i	−0.879308	+	0.476253i	$0.841995\pi$
$570$		0			0
$571$	−200.579	+	347.414i	−0.351277	+	0.608430i	−0.986474	−	0.163921i	$-0.947586\pi$
$571$	−200.579	+	347.414i	−0.351277	+	0.608430i	0.635196	+	0.772351i	$0.280919\pi$
$572$	144.721	+	250.665i	0.253010	+	0.438225i
$573$		0			0
$574$	−370.935	+	44.8182i	−0.646228	+	0.0780805i
$575$	−516.064	+	107.851i	−0.897503	+	0.187567i
$576$		0			0
$577$	−388.494	+	672.891i	−0.673300	+	1.16619i	0.303663	+	0.952780i	$0.401790\pi$
$577$	−388.494	+	672.891i	−0.673300	+	1.16619i	−0.976963	+	0.213410i	$0.931543\pi$
$578$	−314.268	−	181.443i	−0.543716	−	0.313915i
$579$		0			0
$580$	233.661	−	287.541i	0.402864	−	0.495761i
$581$	−285.266	+	668.452i	−0.490991	+	1.15052i
$582$		0			0
$583$	−84.6114	+	48.8504i	−0.145131	+	0.0837914i
$584$	147.719	+	85.2857i	0.252944	+	0.146037i
$585$		0			0
$586$	−365.162	+	210.826i	−0.623143	+	0.359772i
$587$	123.033			0.209596			0.104798	−	0.994494i	$-0.466580\pi$
$587$	123.033			0.209596			0.104798	+	0.994494i	$0.466580\pi$
$588$		0			0
$589$	−164.249			−0.278862
$590$	25.0541	+	4.01207i	0.0424645	+	0.00680011i
$591$		0			0
$592$	67.6673	+	39.0677i	0.114303	+	0.0659928i
$593$	−211.024	−	365.504i	−0.355858	−	0.616364i	0.631407	−	0.775452i	$-0.282478\pi$
$593$	−211.024	−	365.504i	−0.355858	−	0.616364i	−0.987264	+	0.159088i	$0.949145\pi$
$594$		0			0
$595$	−381.178	−	723.230i	−0.640636	−	1.21551i
$596$	0.0113687			1.90750e−5
$597$		0			0
$598$	226.435	−	392.196i	0.378653	−	0.655847i
$599$	−414.355	+	717.684i	−0.691745	+	1.19814i	0.279521	+	0.960140i	$0.409824\pi$
$599$	−414.355	+	717.684i	−0.691745	+	1.19814i	−0.971266	+	0.237998i	$0.923509\pi$
$600$		0			0
$601$		−	675.102i		−	1.12330i	−0.827376	−	0.561649i	$-0.810167\pi$
$601$		−	675.102i		−	1.12330i	0.827376	−	0.561649i	$-0.189833\pi$
$602$	179.401	−	21.6761i	0.298008	−	0.0360068i
$603$		0			0
$604$	229.777	+	397.985i	0.380425	+	0.658916i
$605$	53.8140	+	140.909i	0.0889487	+	0.232908i
$606$		0			0
$607$	−491.492	−	851.289i	−0.809707	−	1.40245i	−0.913067	−	0.407809i	$-0.866293\pi$
$607$	−491.492	−	851.289i	−0.809707	−	1.40245i	0.103360	−	0.994644i	$-0.467041\pi$
$608$	59.8234			0.0983937
$609$		0			0
$610$	498.825	−	613.851i	0.817747	−	1.00631i
$611$	2.35426	+	4.07770i	0.00385313	+	0.00667382i
$612$		0			0
$613$	418.163	+	241.427i	0.682159	+	0.393844i	0.800668	−	0.599108i	$-0.204478\pi$
$613$	418.163	+	241.427i	0.682159	+	0.393844i	−0.118509	+	0.992953i	$0.537812\pi$
$614$	−241.726	+	139.561i	−0.393691	+	0.227298i
$615$		0			0
$616$	−150.919	+	113.269i	−0.244998	+	0.183879i
$617$			550.193i			0.891722i	0.895102	+	0.445861i	$0.147103\pi$
$617$			550.193i			0.891722i	−0.895102	+	0.445861i	$0.852897\pi$
$618$		0			0
$619$	535.910	+	309.408i	0.865767	+	0.499851i	0.865939	−	0.500149i	$-0.166721\pi$
$619$	535.910	+	309.408i	0.865767	+	0.499851i	−0.000172089		1.00000i	$0.500055\pi$
$620$	145.092	−	55.4114i	0.234020	−	0.0893732i
$621$		0			0
$622$	−453.252			−0.728702
$623$	−50.7401	−	419.947i	−0.0814448	−	0.674073i
$624$		0			0
$625$	503.113	+	370.813i	0.804981	+	0.593301i
$626$	−265.533	−	153.306i	−0.424174	−	0.244897i
$627$		0			0
$628$	44.1182	+	76.4149i	0.0702518	+	0.121680i
$629$			456.273i			0.725395i
$630$		0			0
$631$	−167.847			−0.266001			−0.133000	−	0.991116i	$-0.542461\pi$
$631$	−167.847			−0.266001			−0.133000	+	0.991116i	$0.542461\pi$
$632$	223.696	−	129.151i	0.353949	−	0.204353i
$633$		0			0
$634$	277.324	−	480.339i	0.437420	−	0.757633i
$635$	−92.0547	+	574.852i	−0.144968	+	0.905279i
$636$		0			0
$637$	514.796	+	537.224i	0.808157	+	0.843365i
$638$		−	499.386i		−	0.782736i
$639$		0			0
$640$	−52.8458	+	20.1821i	−0.0825716	+	0.0315345i
$641$	529.087	−	916.406i	0.825409	−	1.42965i	−0.0761967	−	0.997093i	$-0.524278\pi$
$641$	529.087	−	916.406i	0.825409	−	1.42965i	0.901606	−	0.432558i	$-0.142389\pi$
$642$		0			0
$643$	−68.2597			−0.106158			−0.0530791	−	0.998590i	$-0.516904\pi$
$643$	−68.2597			−0.106158			−0.0530791	+	0.998590i	$0.516904\pi$
$644$	271.546	+	115.884i	0.421656	+	0.179944i
$645$		0			0
$646$	174.670	+	302.537i	0.270387	+	0.468323i
$647$	−26.7770	+	46.3792i	−0.0413865	+	0.0716835i	−0.885977	−	0.463730i	$-0.846511\pi$
$647$	−26.7770	+	46.3792i	−0.0413865	+	0.0716835i	0.844590	+	0.535413i	$0.179844\pi$
$648$		0			0
$649$	29.6172	−	17.0995i	0.0456351	−	0.0263474i
$650$	−525.513	+	109.826i	−0.808482	+	0.168963i
$651$		0			0
$652$		−	61.0976i		−	0.0937079i
$653$	−39.7204	+	22.9326i	−0.0608276	+	0.0351188i	−0.530105	−	0.847932i	$-0.677848\pi$
$653$	−39.7204	+	22.9326i	−0.0608276	+	0.0351188i	0.469278	+	0.883051i	$0.344514\pi$
$654$		0			0
$655$	−770.813	+	294.377i	−1.17681	+	0.449431i
$656$	−130.744	+	75.4852i	−0.199305	+	0.115069i
$657$		0			0
$658$	−2.45508	+	1.84261i	−0.00373113	+	0.00280033i
$659$	−997.845			−1.51418			−0.757090	−	0.653310i	$-0.773380\pi$
$659$	−997.845			−1.51418			−0.757090	+	0.653310i	$0.773380\pi$
$660$		0			0
$661$	229.919	+	132.744i	0.347836	+	0.200823i	0.663732	−	0.747971i	$-0.268972\pi$
$661$	229.919	+	132.744i	0.347836	+	0.200823i	−0.315896	+	0.948794i	$0.602305\pi$
$662$	420.969	+	243.046i	0.635904	+	0.367139i
$663$		0			0
$664$			293.662i			0.442262i
$665$	−14.2639	+	369.863i	−0.0214495	+	0.556186i
$666$		0			0
$667$	−676.670	+	390.676i	−1.01450	+	0.585720i
$668$	−102.148	+	176.926i	−0.152916	+	0.264859i
$669$		0			0
$670$	89.2864	+	14.2980i	0.133263	+	0.0213403i
$671$		−	1066.10i		−	1.58882i
$672$		0			0
$673$			859.611i			1.27728i	0.769505	+	0.638641i	$0.220503\pi$
$673$			859.611i			1.27728i	−0.769505	+	0.638641i	$0.779497\pi$
$674$	−60.8271	−	105.356i	−0.0902480	−	0.156314i
$675$		0			0
$676$	61.5807	−	106.661i	0.0910956	−	0.157782i
$677$	−35.7345	−	61.8940i	−0.0527836	−	0.0914239i	0.838426	−	0.545015i	$-0.183476\pi$
$677$	−35.7345	−	61.8940i	−0.0527836	−	0.0914239i	−0.891210	+	0.453591i	$0.850143\pi$
$678$		0			0
$679$	−357.927	+	838.718i	−0.527139	+	1.23522i
$680$	−256.361	−	208.323i	−0.377002	−	0.306358i
$681$		0			0
$682$	104.668	−	181.291i	0.153472	−	0.265822i
$683$	832.644	+	480.727i	1.21910	+	0.703847i	0.964725	−	0.263259i	$-0.0847975\pi$
$683$	832.644	+	480.727i	1.21910	+	0.703847i	0.254373	+	0.967106i	$0.418131\pi$
$684$		0			0
$685$	828.121	+	672.945i	1.20894	+	0.982402i
$686$	−307.446	+	375.200i	−0.448173	+	0.546938i
$687$		0			0
$688$	63.2337	−	36.5080i	0.0919095	−	0.0530639i
$689$	134.809	+	77.8320i	0.195659	+	0.112964i
$690$		0			0
$691$	433.591	−	250.334i	0.627483	−	0.362277i	−0.152294	−	0.988335i	$-0.548666\pi$
$691$	433.591	−	250.334i	0.627483	−	0.362277i	0.779777	+	0.626058i	$0.215333\pi$
$692$	546.757			0.790111
$693$		0			0
$694$	−867.701			−1.25029
$695$	−41.9712	+	262.097i	−0.0603903	+	0.377117i
$696$		0			0
$697$	−763.483	−	440.797i	−1.09538	−	0.632420i
$698$	142.883	+	247.481i	0.204704	+	0.354558i
$699$		0			0
$700$	−112.177	−	331.536i	−0.160253	−	0.473623i
$701$	913.148			1.30264			0.651318	−	0.758805i	$-0.274216\pi$
$701$	913.148			1.30264			0.651318	+	0.758805i	$0.274216\pi$
$702$		0			0
$703$	103.289	−	178.902i	0.146926	−	0.254484i
$704$	−38.1225	+	66.0301i	−0.0541513	+	0.0937928i
$705$		0			0
$706$		−	723.943i		−	1.02541i
$707$	804.979	−	604.161i	1.13858	−	0.854542i
$708$		0			0
$709$	−573.474	−	993.286i	−0.808849	−	1.40097i	−0.913661	−	0.406476i	$-0.866757\pi$
$709$	−573.474	−	993.286i	−0.808849	−	1.40097i	0.104812	−	0.994492i	$-0.466576\pi$
$710$	216.579	−	82.7124i	0.305040	−	0.116496i
$711$		0			0
$712$	−85.4592	−	148.020i	−0.120027	−	0.207893i
$713$	−327.533			−0.459373
$714$		0			0
$715$	−456.341	+	561.570i	−0.638239	+	0.785412i
$716$	9.64856	+	16.7118i	0.0134756	+	0.0233405i
$717$		0			0
$718$	−194.005	−	112.009i	−0.270202	−	0.156001i
$719$	84.0179	−	48.5077i	0.116854	−	0.0674656i	−0.440434	−	0.897785i	$-0.645175\pi$
$719$	84.0179	−	48.5077i	0.116854	−	0.0674656i	0.557288	+	0.830319i	$0.311842\pi$
$720$		0			0
$721$	−372.510	+	45.0085i	−0.516657	+	0.0624251i
$722$			352.367i			0.488043i
$723$		0			0
$724$	383.713	+	221.537i	0.529991	+	0.305990i
$725$	879.956	+	289.243i	1.21373	+	0.398956i
$726$		0			0
$727$	175.776			0.241782			0.120891	−	0.992666i	$-0.461425\pi$
$727$	175.776			0.241782			0.120891	+	0.992666i	$0.461425\pi$
$728$	276.518	+	118.006i	0.379833	+	0.162096i
$729$		0			0
$730$	−67.4277	+	421.064i	−0.0923667	+	0.576800i
$731$	369.254	+	213.189i	0.505136	+	0.291640i
$732$		0			0
$733$	−346.840	−	600.745i	−0.473179	−	0.819570i	0.526350	−	0.850268i	$-0.323560\pi$
$733$	−346.840	−	600.745i	−0.473179	−	0.819570i	−0.999529	+	0.0306981i	$0.990227\pi$
$734$		−	461.505i		−	0.628753i
$735$		0			0
$736$	119.295			0.162085
$737$	105.548	−	60.9383i	0.143213	−	0.0826842i
$738$		0			0
$739$	−10.2585	+	17.7682i	−0.0138816	+	0.0240436i	−0.872883	−	0.487930i	$-0.837752\pi$
$739$	−10.2585	+	17.7682i	−0.0138816	+	0.0240436i	0.859001	+	0.511974i	$0.171085\pi$
$740$	−30.8873	+	192.881i	−0.0417396	+	0.260650i
$741$		0			0
$742$	−39.8325	+	93.3381i	−0.0536827	+	0.125793i
$743$			896.676i			1.20683i	0.797427	+	0.603416i	$0.206194\pi$
$743$			896.676i			1.20683i	−0.797427	+	0.603416i	$0.793806\pi$
$744$		0			0
$745$	0.0101401	+	0.0265514i	1.36109e−5	+	3.56394e-5i
$746$	−206.272	+	357.273i	−0.276503	+	0.478918i
$747$		0			0
$748$	−445.234			−0.595232
$749$	−91.3435	−	755.999i	−0.121954	−	1.00934i
$750$		0			0
$751$	298.227	+	516.545i	0.397107	+	0.687809i	0.993368	−	0.114982i	$-0.0366809\pi$
$751$	298.227	+	516.545i	0.397107	+	0.687809i	−0.596261	+	0.802791i	$0.703348\pi$
$752$	−0.620160	+	1.07415i	−0.000824680	+	0.00142839i
$753$		0			0
$754$	−689.059	+	397.829i	−0.913872	+	0.527624i
$755$	−724.541	+	891.615i	−0.959657	+	1.18095i
$756$		0			0
$757$			118.056i			0.155952i	0.996955	+	0.0779761i	$0.0248458\pi$
$757$			118.056i			0.155952i	−0.996955	+	0.0779761i	$0.975154\pi$
$758$	−829.432	+	478.873i	−1.09424	+	0.631758i
$759$		0			0
$760$	53.3583	+	139.716i	0.0702083	+	0.183837i
$761$	−695.093	+	401.312i	−0.913395	+	0.527349i	−0.881522	−	0.472143i	$-0.843480\pi$
$761$	−695.093	+	401.312i	−0.913395	+	0.527349i	−0.0318728	+	0.999492i	$0.510147\pi$
$762$		0			0
$763$	−257.593	−	343.214i	−0.337605	−	0.449822i
$764$	−419.620			−0.549241
$765$		0			0
$766$	−305.211	−	176.214i	−0.398448	−	0.230044i
$767$	−47.1882	−	27.2441i	−0.0615231	−	0.0355204i
$768$		0			0
$769$			1022.31i			1.32940i	0.747109	+	0.664701i	$0.231441\pi$
$769$			1022.31i			1.32940i	−0.747109	+	0.664701i	$0.768559\pi$
$770$	−399.147	−	251.440i	−0.518373	−	0.326545i
$771$		0			0
$772$	435.152	−	251.235i	0.563669	−	0.325434i
$773$	343.943	−	595.726i	0.444945	−	0.770668i	−0.553103	−	0.833113i	$-0.686556\pi$
$773$	343.943	−	595.726i	0.444945	−	0.770668i	0.998048	+	0.0624449i	$0.0198898\pi$
$774$		0			0
$775$	258.824	+	289.436i	0.333967	+	0.373466i
$776$			368.463i			0.474823i
$777$		0			0
$778$			40.6736i			0.0522797i
$779$	199.571	+	345.668i	0.256189	+	0.443733i
$780$		0			0
$781$	156.238	−	270.612i	0.200048	−	0.346494i
$782$	348.312	+	603.294i	0.445412	+	0.771476i
$783$		0			0
$784$	−54.7521	+	188.197i	−0.0698369	+	0.240048i
$785$	−139.115	+	171.194i	−0.177217	+	0.218081i
$786$		0			0
$787$	−612.772	+	1061.35i	−0.778618	+	1.34861i	0.154121	+	0.988052i	$0.450745\pi$
$787$	−612.772	+	1061.35i	−0.778618	+	1.34861i	−0.932739	+	0.360553i	$0.882588\pi$
$788$	−223.075	−	128.792i	−0.283090	−	0.163442i
$789$		0			0
$790$	501.150	+	407.243i	0.634367	+	0.515498i
$791$	613.052	+	261.623i	0.775034	+	0.330750i
$792$		0			0
$793$	−1471.02	+	849.295i	−1.85501	+	1.07099i
$794$	−309.774	−	178.848i	−0.390143	−	0.225249i
$795$		0			0
$796$	−346.767	+	200.206i	−0.435637	+	0.251515i
$797$	691.172			0.867217			0.433608	−	0.901101i	$-0.357240\pi$
$797$	691.172			0.867217			0.433608	+	0.901101i	$0.357240\pi$
$798$		0			0
$799$	−7.24286			−0.00906491
$800$	−94.2697	−	105.419i	−0.117837	−	0.131774i
$801$		0			0
$802$	−253.378	−	146.288i	−0.315932	−	0.182404i
$803$	287.377	+	497.752i	0.357880	+	0.619866i
$804$		0			0
$805$	−28.4439	+	737.551i	−0.0353340	+	0.916212i
$806$	−333.530			−0.413808
$807$		0			0
$808$	203.340	−	352.195i	0.251658	−	0.435884i
$809$	−511.628	+	886.165i	−0.632420	+	1.09538i	0.354636	+	0.935005i	$0.384605\pi$
$809$	−511.628	+	886.165i	−0.632420	+	1.09538i	−0.987056	+	0.160379i	$0.948728\pi$
$810$		0			0
$811$		−	346.588i		−	0.427359i	−0.976904	−	0.213679i	$-0.931455\pi$
$811$		−	346.588i		−	0.427359i	0.976904	−	0.213679i	$-0.0685448\pi$
$812$	−311.369	−	414.865i	−0.383460	−	0.510918i
$813$		0			0
$814$	131.642	+	228.011i	0.161722	+	0.280112i
$815$	142.692	−	54.4948i	0.175082	−	0.0668648i
$816$		0			0
$817$	−96.5215	−	167.180i	−0.118141	−	0.204627i
$818$	943.372			1.15327
$819$		0			0
$820$	−292.909	−	238.023i	−0.357206	−	0.290272i
$821$	−302.304	−	523.605i	−0.368214	−	0.637765i	0.621072	−	0.783753i	$-0.286697\pi$
$821$	−302.304	−	523.605i	−0.368214	−	0.637765i	−0.989286	+	0.145988i	$0.953364\pi$
$822$		0			0
$823$	1002.77	+	578.951i	1.21844	+	0.703464i	0.964583	−	0.263779i	$-0.0849689\pi$
$823$	1002.77	+	578.951i	1.21844	+	0.703464i	0.253853	+	0.967243i	$0.418302\pi$
$824$	−131.299	+	75.8057i	−0.159344	+	0.0919972i
$825$		0			0
$826$	13.9429	−	32.6718i	0.0168800	−	0.0395543i
$827$		−	248.293i		−	0.300234i	−0.988668	−	0.150117i	$-0.952035\pi$
$827$		−	248.293i		−	0.300234i	0.988668	−	0.150117i	$-0.0479650\pi$
$828$		0			0
$829$	808.027	+	466.515i	0.974701	+	0.562744i	0.900666	−	0.434512i	$-0.143079\pi$
$829$	808.027	+	466.515i	0.974701	+	0.562744i	0.0740349	+	0.997256i	$0.476412\pi$
$830$	−685.842	+	261.926i	−0.826315	+	0.315574i
$831$		0			0
$832$	121.479			0.146008
$833$	−1111.61	+	272.600i	−1.33446	+	0.327250i
$834$		0			0
$835$	−504.315	−	80.7592i	−0.603970	−	0.0967176i
$836$	174.573	+	100.790i	0.208820	+	0.120562i
$837$		0			0
$838$	58.6838	+	101.643i	0.0700283	+	0.121293i
$839$			1426.14i			1.69981i	0.526934	+	0.849906i	$0.323341\pi$
$839$			1426.14i			1.69981i	−0.526934	+	0.849906i	$0.676659\pi$
$840$		0			0
$841$	531.775			0.632312
$842$	190.427	−	109.943i	0.226161	−	0.130574i
$843$		0			0
$844$	167.518	−	290.150i	0.198481	−	0.343779i
$845$	304.030	+	48.6862i	0.359798	+	0.0576169i
$846$		0			0
$847$	209.645	−	25.3304i	0.247515	−	0.0299060i
$848$			41.0050i			0.0483549i
$849$		0			0
$850$	257.879	−	784.536i	0.303387	−	0.922984i
$851$	205.970	−	356.751i	0.242033	−	0.419214i
$852$		0			0
$853$	350.268			0.410631			0.205315	−	0.978696i	$-0.434178\pi$
$853$	350.268			0.410631			0.205315	+	0.978696i	$0.434178\pi$
$854$	−664.719	−	885.665i	−0.778359	−	1.03708i
$855$		0			0
$856$	−153.846	−	266.468i	−0.179726	−	0.311295i
$857$	15.1063	−	26.1649i	0.0176269	−	0.0305308i	−0.857077	−	0.515188i	$-0.827722\pi$
$857$	15.1063	−	26.1649i	0.0176269	−	0.0305308i	0.874704	+	0.484657i	$0.161056\pi$
$858$		0			0
$859$	370.864	−	214.119i	0.431740	−	0.249265i	−0.268348	−	0.963322i	$-0.586478\pi$
$859$	370.864	−	214.119i	0.431740	−	0.249265i	0.700087	+	0.714057i	$0.253144\pi$
$860$	141.664	+	115.118i	0.164725	+	0.133859i
$861$		0			0
$862$			49.8127i			0.0577874i
$863$	−1021.22	+	589.602i	−1.18334	+	0.683200i	−0.956784	−	0.290798i	$-0.906079\pi$
$863$	−1021.22	+	589.602i	−1.18334	+	0.683200i	−0.226553	+	0.973999i	$0.572746\pi$
$864$		0			0
$865$	487.669	+	1276.94i	0.563779	+	1.47623i
$866$	120.057	−	69.3150i	0.138634	−	0.0800404i
$867$		0			0
$868$	−26.0823	−	215.868i	−0.0300487	−	0.248696i
$869$	870.370			1.00158
$870$		0			0
$871$	−168.167	−	97.0912i	−0.193073	−	0.111471i
$872$	−150.163	−	86.6967i	−0.172205	−	0.0994229i
$873$		0			0
$874$		−	315.397i		−	0.360866i
$875$	674.241	−	557.695i	0.770561	−	0.637366i
$876$		0			0
$877$	1423.08	−	821.617i	1.62267	−	0.936850i	0.636470	−	0.771302i	$-0.280394\pi$
$877$	1423.08	−	821.617i	1.62267	−	0.936850i	0.986202	−	0.165548i	$-0.0529393\pi$
$878$	290.992	−	504.014i	0.331426	−	0.574047i
$879$		0			0
$880$	−188.215	−	30.1400i	−0.213880	−	0.0342500i
$881$			571.268i			0.648431i	0.945983	+	0.324216i	$0.105100\pi$
$881$			571.268i			0.648431i	−0.945983	+	0.324216i	$0.894900\pi$
$882$		0			0
$883$		−	13.3627i		−	0.0151333i	−0.999971	−	0.00756666i	$-0.997591\pi$
$883$		−	13.3627i		−	0.0151333i	0.999971	−	0.00756666i	$-0.00240856\pi$
$884$	354.689	+	614.340i	0.401232	+	0.694955i
$885$		0			0
$886$	535.995	−	928.370i	0.604960	−	1.04782i
$887$	−662.731	−	1147.88i	−0.747160	−	1.29412i	−0.949179	−	0.314738i	$-0.898083\pi$
$887$	−662.731	−	1147.88i	−0.747160	−	1.29412i	0.202018	−	0.979382i	$-0.435250\pi$
$888$		0			0
$889$	749.638	+	319.912i	0.843237	+	0.359856i
$890$	269.473	−	331.611i	0.302779	−	0.372597i
$891$		0			0
$892$	−66.6389	+	115.422i	−0.0747073	+	0.129397i
$893$	2.83988	+	1.63961i	0.00318016	+	0.00183607i
$894$		0			0
$895$	−30.4242	+	37.4398i	−0.0339935	+	0.0418321i
$896$	9.49976	+	78.6241i	0.0106024	+	0.0877502i
$897$		0			0
$898$	61.1735	−	35.3185i	0.0681219	−	0.0393302i
$899$	498.354	+	287.725i	0.554343	+	0.320050i
$900$		0			0
$901$	−207.369	+	119.725i	−0.230154	+	0.132880i
$902$	−508.708			−0.563978
$903$		0			0
$904$	269.324			0.297925
$905$	−175.149	+	1093.75i	−0.193535	+	1.20856i
$906$		0			0
$907$	−417.494	−	241.041i	−0.460303	−	0.265756i	0.251869	−	0.967761i	$-0.418955\pi$
$907$	−417.494	−	241.041i	−0.460303	−	0.265756i	−0.712171	+	0.702006i	$0.752288\pi$
$908$	51.8490	+	89.8052i	0.0571025	+	0.0989044i
$909$		0			0
$910$	−28.9647	+	751.055i	−0.0318293	+	0.825335i
$911$	−1582.96			−1.73761			−0.868806	−	0.495153i	$-0.835112\pi$
$911$	−1582.96			−1.73761			−0.868806	+	0.495153i	$0.835112\pi$
$912$		0			0
$913$	−494.760	+	856.949i	−0.541906	+	0.938608i
$914$	286.148	−	495.622i	0.313072	−	0.542256i
$915$		0			0
$916$		−	145.684i		−	0.159043i
$917$	138.564	+	1146.82i	0.151106	+	1.25062i
$918$		0			0
$919$	669.468	+	1159.55i	0.728474	+	1.26175i	0.957528	+	0.288340i	$0.0931034\pi$
$919$	669.468	+	1159.55i	0.728474	+	1.26175i	−0.229054	+	0.973414i	$0.573563\pi$
$920$	106.403	+	278.611i	0.115655	+	0.302838i
$921$		0			0
$922$	−29.3021	−	50.7528i	−0.0317811	−	0.0550464i
$923$	−497.859			−0.539392
$924$		0			0
$925$	−478.019	+	99.9000i	−0.516778	+	0.108000i
$926$	−472.892	−	819.072i	−0.510682	−	0.884527i
$927$		0			0
$928$	−181.512	−	104.796i	−0.195595	−	0.112927i
$929$	−641.135	+	370.159i	−0.690135	+	0.398449i	−0.803662	−	0.595085i	$-0.797118\pi$
$929$	−641.135	+	370.159i	−0.690135	+	0.398449i	0.113528	+	0.993535i	$0.463785\pi$
$930$		0			0
$931$	497.564	+	144.756i	0.534441	+	0.155485i
$932$			275.697i			0.295813i
$933$		0			0
$934$	−609.131	−	351.682i	−0.652175	−	0.376533i
$935$	−397.118	−	1039.83i	−0.424725	−	1.11212i
$936$		0			0
$937$	−272.107			−0.290402			−0.145201	−	0.989402i	$-0.546383\pi$
$937$	−272.107			−0.290402			−0.145201	+	0.989402i	$0.546383\pi$
$938$	49.6890	−	116.434i	0.0529733	−	0.124130i
$939$		0			0
$940$	−3.06179	−	0.490304i	−0.00325722	−	0.000521600i
$941$	−203.843	−	117.689i	−0.216623	−	0.125068i	0.387762	−	0.921759i	$-0.373248\pi$
$941$	−203.843	−	117.689i	−0.216623	−	0.125068i	−0.604386	+	0.796692i	$0.706581\pi$
$942$		0			0
$943$	397.968	+	689.302i	0.422024	+	0.730967i
$944$		−	14.3533i		−	0.0152048i
$945$		0			0
$946$	246.034			0.260078
$947$	−526.514	+	303.983i	−0.555981	+	0.320996i	−0.751531	−	0.659698i	$-0.770684\pi$
$947$	−526.514	+	303.983i	−0.555981	+	0.320996i	0.195550	+	0.980694i	$0.437351\pi$
$948$		0			0
$949$	457.870	−	793.055i	0.482477	−	0.835674i
$950$	−278.712	+	249.234i	−0.293381	+	0.262352i
$951$		0			0
$952$	−369.878	+	277.605i	−0.388528	+	0.291602i
$953$		−	188.561i		−	0.197860i	−0.995094	−	0.0989302i	$-0.968458\pi$
$953$		−	188.561i		−	0.197860i	0.995094	−	0.0989302i	$-0.0315421\pi$
$954$		0			0
$955$	−374.272	−	980.013i	−0.391908	−	1.02619i
$956$	350.640	−	607.327i	0.366779	−	0.635279i
$957$		0			0
$958$	−626.412			−0.653875
$959$	1194.81	−	896.745i	1.24590	−	0.935084i
$960$		0			0
$961$	−359.889	−	623.347i	−0.374495	−	0.648644i
$962$	209.742	−	363.283i	0.218027	−	0.377633i
$963$		0			0
$964$	−528.927	+	305.376i	−0.548680	+	0.316780i
$965$	974.880	+	792.204i	1.01024	+	0.820937i
$966$		0			0
$967$			1088.32i			1.12546i	0.826640	+	0.562732i	$0.190250\pi$
$967$			1088.32i			1.12546i	−0.826640	+	0.562732i	$0.809750\pi$
$968$	73.8941	−	42.6628i	0.0763369	−	0.0440731i
$969$		0			0
$970$	−860.537	+	328.643i	−0.887151	+	0.338807i
$971$	164.230	−	94.8183i	0.169135	−	0.0976501i	−0.413043	−	0.910712i	$-0.635534\pi$
$971$	164.230	−	94.8183i	0.169135	−	0.0976501i	0.582178	+	0.813061i	$0.302201\pi$
$972$		0			0
$973$	341.788	+	145.860i	0.351272	+	0.149907i
$974$	−158.872			−0.163113
$975$		0			0
$976$	−387.496	−	223.721i	−0.397025	−	0.229222i
$977$	687.092	+	396.693i	0.703267	+	0.406032i	0.808563	−	0.588409i	$-0.200246\pi$
$977$	687.092	+	396.693i	0.703267	+	0.406032i	−0.105296	+	0.994441i	$0.533579\pi$
$978$		0			0
$979$		−	575.924i		−	0.588278i
$980$	−488.366	+	39.9865i	−0.498332	+	0.0408025i
$981$		0			0
$982$	829.369	−	478.837i	0.844572	−	0.487614i
$983$	26.9121	−	46.6132i	0.0273775	−	0.0474193i	−0.852012	−	0.523522i	$-0.824618\pi$
$983$	26.9121	−	46.6132i	0.0273775	−	0.0474193i	0.879390	+	0.476103i	$0.157951\pi$
$984$		0			0
$985$	101.824	−	635.860i	0.103375	−	0.645543i
$986$		−	1223.92i		−	1.24129i
$987$		0			0
$988$		−	321.172i		−	0.325073i
$989$	−192.475	−	333.377i	−0.194616	−	0.337085i
$990$		0			0
$991$	718.340	−	1244.20i	0.724864	−	1.25550i	−0.234166	−	0.972197i	$-0.575236\pi$
$991$	718.340	−	1244.20i	0.724864	−	1.25550i	0.959030	−	0.283304i	$-0.0914306\pi$
$992$	−43.9292	−	76.0875i	−0.0442834	−	0.0767012i
$993$		0			0
$994$	−38.9329	−	322.226i	−0.0391680	−	0.324171i
$995$	−776.870	−	631.298i	−0.780774	−	0.634470i
$996$		0			0
$997$	110.002	−	190.529i	0.110333	−	0.191102i	−0.805572	−	0.592499i	$-0.798142\pi$
$997$	110.002	−	190.529i	0.110333	−	0.191102i	0.915905	+	0.401396i	$0.131475\pi$
$998$	−1129.74	−	652.257i	−1.13201	−	0.653564i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.bc.a.199.8		16
3.2	odd	2		70.3.h.a.59.1	yes	16
5.4	even	2	inner	630.3.bc.a.199.3		16
7.5	odd	6	inner	630.3.bc.a.19.3		16
12.11	even	2		560.3.br.b.129.8		16
15.2	even	4		350.3.k.e.101.4		16
15.8	even	4		350.3.k.e.101.5		16
15.14	odd	2		70.3.h.a.59.8	yes	16
21.2	odd	6		490.3.h.b.19.5		16
21.5	even	6		70.3.h.a.19.8	yes	16
21.11	odd	6		490.3.d.a.489.8		16
21.17	even	6		490.3.d.a.489.1		16
21.20	even	2		490.3.h.b.129.4		16
35.19	odd	6	inner	630.3.bc.a.19.8		16
60.59	even	2		560.3.br.b.129.1		16
84.47	odd	6		560.3.br.b.369.1		16
105.44	odd	6		490.3.h.b.19.4		16
105.47	odd	12		350.3.k.e.201.4		16
105.59	even	6		490.3.d.a.489.16		16
105.68	odd	12		350.3.k.e.201.5		16
105.74	odd	6		490.3.d.a.489.9		16
105.89	even	6		70.3.h.a.19.1	✓	16
105.104	even	2		490.3.h.b.129.5		16
420.299	odd	6		560.3.br.b.369.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.h.a.19.1	✓	16	105.89	even	6
70.3.h.a.19.8	yes	16	21.5	even	6
70.3.h.a.59.1	yes	16	3.2	odd	2
70.3.h.a.59.8	yes	16	15.14	odd	2
350.3.k.e.101.4		16	15.2	even	4
350.3.k.e.101.5		16	15.8	even	4
350.3.k.e.201.4		16	105.47	odd	12
350.3.k.e.201.5		16	105.68	odd	12
490.3.d.a.489.1		16	21.17	even	6
490.3.d.a.489.8		16	21.11	odd	6
490.3.d.a.489.9		16	105.74	odd	6
490.3.d.a.489.16		16	105.59	even	6
490.3.h.b.19.4		16	105.44	odd	6
490.3.h.b.19.5		16	21.2	odd	6
490.3.h.b.129.4		16	21.20	even	2
490.3.h.b.129.5		16	105.104	even	2
560.3.br.b.129.1		16	60.59	even	2
560.3.br.b.129.8		16	12.11	even	2
560.3.br.b.369.1		16	84.47	odd	6
560.3.br.b.369.8		16	420.299	odd	6
630.3.bc.a.19.3		16	7.5	odd	6	inner
630.3.bc.a.19.8		16	35.19	odd	6	inner
630.3.bc.a.199.3		16	5.4	even	2	inner
630.3.bc.a.199.8		16	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(4.93710 + 0.790609i) q^{5} +(2.74755 - 6.43824i) q^{7} -2.82843i q^{8} +(6.60573 - 2.52276i) q^{10} +(4.76531 - 8.25377i) q^{11} -15.1849 q^{13} +(-1.18747 - 9.82802i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(11.6790 - 20.2287i) q^{17} +(-9.15855 + 5.28769i) q^{19} +(6.30647 - 7.76070i) q^{20} -13.4783i q^{22} +(-18.2632 + 10.5443i) q^{23} +(23.7499 + 7.80663i) q^{25} +(-18.5976 + 10.7373i) q^{26} +(-8.40380 - 11.1971i) q^{28} +37.0510 q^{29} +(13.4505 + 7.76565i) q^{31} +(-4.89898 - 2.82843i) q^{32} -33.0333i q^{34} +(18.6551 - 29.6140i) q^{35} +(-16.9168 + 9.76693i) q^{37} +(-7.47792 + 12.9521i) q^{38} +(2.23618 - 13.9642i) q^{40} -37.7426i q^{41} +18.2540i q^{43} +(-9.53063 - 16.5075i) q^{44} +(-14.9119 + 25.8281i) q^{46} +(-0.155040 - 0.268537i) q^{47} +(-33.9019 - 35.3788i) q^{49} +(34.6077 - 7.23256i) q^{50} +(-15.1849 + 26.3010i) q^{52} +(-8.87784 - 5.12562i) q^{53} +(30.0523 - 36.9821i) q^{55} +(-18.2101 - 7.77126i) q^{56} +(45.3780 - 26.1990i) q^{58} +(3.10758 + 1.79416i) q^{59} +(96.8741 - 55.9303i) q^{61} +21.9646 q^{62} -8.00000 q^{64} +(-74.9693 - 12.0053i) q^{65} +(11.0746 + 6.39394i) q^{67} +(-23.3581 - 40.4573i) q^{68} +(1.90747 - 49.4607i) q^{70} +32.7865 q^{71} +(-30.1530 + 52.2266i) q^{73} +(-13.8125 + 23.9240i) q^{74} +21.1508i q^{76} +(-40.0468 - 53.3579i) q^{77} +(45.6617 + 79.0884i) q^{79} +(-7.13544 - 18.6838i) q^{80} +(-26.6881 - 46.2251i) q^{82} -103.825 q^{83} +(73.6535 - 90.6374i) q^{85} +(12.9075 + 22.3565i) q^{86} +(-23.3452 - 13.4783i) q^{88} +(52.3329 - 30.2144i) q^{89} +(-41.7213 + 97.7639i) q^{91} +42.1771i q^{92} +(-0.379769 - 0.219259i) q^{94} +(-49.3972 + 18.8650i) q^{95} -130.271 q^{97} +(-66.5378 - 19.3578i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} + 6 q^{5} + 24 q^{10} + 12 q^{11} - 32 q^{14} - 32 q^{16} - 12 q^{19} - 42 q^{25} + 48 q^{26} + 136 q^{29} + 84 q^{31} + 190 q^{35} + 48 q^{40} - 24 q^{44} - 68 q^{46} + 296 q^{49} + 96 q^{50}+ \cdots + 310 q^{95}+O(q^{100}) \) 16 * q + 16 * q^4 + 6 * q^5 + 24 * q^10 + 12 * q^11 - 32 * q^14 - 32 * q^16 - 12 * q^19 - 42 * q^25 + 48 * q^26 + 136 * q^29 + 84 * q^31 + 190 * q^35 + 48 * q^40 - 24 * q^44 - 68 * q^46 + 296 * q^49 + 96 * q^50 - 56 * q^56 + 372 * q^59 + 348 * q^61 - 128 * q^64 + 104 * q^65 - 296 * q^70 + 384 * q^71 - 208 * q^74 + 148 * q^79 - 24 * q^80 + 580 * q^85 + 188 * q^86 + 912 * q^89 - 616 * q^91 - 600 * q^94 + 310 * q^95

Introduction

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