LMFDB - Embedded newform 76.3.j.a.21.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,3,Mod(13,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([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("76.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, degree $6$, 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:	$2.07085000914$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 93 x^{16} + 3429 x^{14} + 64261 x^{12} + 647217 x^{10} + 3386277 x^{8} + 8232133 x^{6} + \cdots + 69312 $ x^18 + 93x^16 + 3429x^14 + 64261x^12 + 647217x^10 + 3386277x^8 + 8232133x^6 + 8319228x^4 + 2467872x^2 + 69312
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			21.3
Root			$5.44868i$ of defining polynomial
Character	$\chi$	$=$	76.21
Dual form			76.3.j.a.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.23630 - 2.66512i) q^{3} +(1.62283 - 0.590661i) q^{5} +(-1.87959 - 3.25555i) q^{7} +(-0.538989 - 3.05676i) q^{9} +O(q^{10})$	\(q+(2.23630 - 2.66512i) q^{3} +(1.62283 - 0.590661i) q^{5} +(-1.87959 - 3.25555i) q^{7} +(-0.538989 - 3.05676i) q^{9} +(2.58396 - 4.47556i) q^{11} +(3.02160 + 3.60100i) q^{13} +(2.05495 - 5.64593i) q^{15} +(-2.43654 + 13.8183i) q^{17} +(10.2978 + 15.9673i) q^{19} +(-12.8798 - 2.27105i) q^{21} +(-11.1854 - 4.07116i) q^{23} +(-16.8664 + 14.1526i) q^{25} +(17.7647 + 10.2564i) q^{27} +(-52.5255 + 9.26166i) q^{29} +(4.93716 - 2.85047i) q^{31} +(-6.14938 - 16.8953i) q^{33} +(-4.97317 - 4.17299i) q^{35} +35.7995i q^{37} +16.3543 q^{39} +(11.8339 - 14.1031i) q^{41} +(72.4831 - 26.3817i) q^{43} +(-2.68020 - 4.64223i) q^{45} +(-6.56111 - 37.2099i) q^{47} +(17.4343 - 30.1971i) q^{49} +(31.3787 + 37.3956i) q^{51} +(16.1770 - 44.4460i) q^{53} +(1.54979 - 8.78930i) q^{55} +(65.5838 + 8.26284i) q^{57} +(-86.2842 - 15.2142i) q^{59} +(-19.7588 - 7.19161i) q^{61} +(-8.93835 + 7.50016i) q^{63} +(7.03050 + 4.05906i) q^{65} +(-46.1336 + 8.13459i) q^{67} +(-35.8641 + 20.7062i) q^{69} +(-30.2932 - 83.2298i) q^{71} +(57.7624 + 48.4684i) q^{73} +76.6006i q^{75} -19.4272 q^{77} +(-10.5650 + 12.5908i) q^{79} +(93.3124 - 33.9629i) q^{81} +(-17.5572 - 30.4100i) q^{83} +(4.20785 + 23.8639i) q^{85} +(-92.7794 + 160.699i) q^{87} +(18.1327 + 21.6097i) q^{89} +(6.04386 - 16.6054i) q^{91} +(3.44413 - 19.5326i) q^{93} +(26.1428 + 19.8297i) q^{95} +(39.0070 + 6.87798i) q^{97} +(-15.0734 - 5.48628i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9}+O(q^{10}) $ 18 * q - 6 * q^3 + 9 * q^7 + 6 * q^9	$ 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9} - 15 q^{11} + 51 q^{13} + 21 q^{15} - 45 q^{17} + 30 q^{19} - 63 q^{21} + 48 q^{23} - 54 q^{25} - 198 q^{27} - 39 q^{29} - 108 q^{31} - 105 q^{33} + 51 q^{35} + 48 q^{39} + 54 q^{41} + 75 q^{43} + 288 q^{45} + 339 q^{47} - 24 q^{49} + 360 q^{51} + 69 q^{53} - 51 q^{55} + 510 q^{57} - 483 q^{59} - 36 q^{61} - 267 q^{63} - 585 q^{65} - 87 q^{67} - 351 q^{69} - 234 q^{71} - 132 q^{73} + 108 q^{77} + 363 q^{79} + 258 q^{81} + 279 q^{83} + 666 q^{85} + 600 q^{89} + 270 q^{91} - 456 q^{93} - 39 q^{95} - 801 q^{97} - 267 q^{99}+O(q^{100}) $ 18 * q - 6 * q^3 + 9 * q^7 + 6 * q^9 - 15 * q^11 + 51 * q^13 + 21 * q^15 - 45 * q^17 + 30 * q^19 - 63 * q^21 + 48 * q^23 - 54 * q^25 - 198 * q^27 - 39 * q^29 - 108 * q^31 - 105 * q^33 + 51 * q^35 + 48 * q^39 + 54 * q^41 + 75 * q^43 + 288 * q^45 + 339 * q^47 - 24 * q^49 + 360 * q^51 + 69 * q^53 - 51 * q^55 + 510 * q^57 - 483 * q^59 - 36 * q^61 - 267 * q^63 - 585 * q^65 - 87 * q^67 - 351 * q^69 - 234 * q^71 - 132 * q^73 + 108 * q^77 + 363 * q^79 + 258 * q^81 + 279 * q^83 + 666 * q^85 + 600 * q^89 + 270 * q^91 - 456 * q^93 - 39 * q^95 - 801 * q^97 - 267 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$1$

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			0
$2$		0			0
$3$	2.23630	−	2.66512i	0.745434	−	0.888374i	−0.251400	−	0.967883i	$-0.580891\pi$
$3$	2.23630	−	2.66512i	0.745434	−	0.888374i	0.996834	+	0.0795096i	$0.0253354\pi$
$4$		0			0
$5$	1.62283	−	0.590661i	0.324565	−	0.118132i	−0.174599	−	0.984640i	$-0.555863\pi$
$5$	1.62283	−	0.590661i	0.324565	−	0.118132i	0.499164	+	0.866508i	$0.333641\pi$
$6$		0			0
$7$	−1.87959	−	3.25555i	−0.268513	−	0.465078i	0.699965	−	0.714177i	$-0.253199\pi$
$7$	−1.87959	−	3.25555i	−0.268513	−	0.465078i	−0.968478	+	0.249099i	$0.919866\pi$
$8$		0			0
$9$	−0.538989	−	3.05676i	−0.0598877	−	0.339640i
$10$		0			0
$11$	2.58396	−	4.47556i	0.234906	−	0.406869i	−0.724339	−	0.689444i	$-0.757855\pi$
$11$	2.58396	−	4.47556i	0.234906	−	0.406869i	0.959245	+	0.282575i	$0.0911885\pi$
$12$		0			0
$13$	3.02160	+	3.60100i	0.232431	+	0.277000i	0.869635	−	0.493694i	$-0.164354\pi$
$13$	3.02160	+	3.60100i	0.232431	+	0.277000i	−0.637205	+	0.770695i	$0.719909\pi$
$14$		0			0
$15$	2.05495	−	5.64593i	0.136997	−	0.376395i
$16$		0			0
$17$	−2.43654	+	13.8183i	−0.143326	+	0.812843i	0.825370	+	0.564593i	$0.190967\pi$
$17$	−2.43654	+	13.8183i	−0.143326	+	0.812843i	−0.968696	+	0.248250i	$0.920144\pi$
$18$		0			0
$19$	10.2978	+	15.9673i	0.541990	+	0.840385i
$19$	10.2978	+	15.9673i	0.541990	+	0.840385i
$20$		0			0
$21$	−12.8798	−	2.27105i	−0.613322	−	0.108145i
$22$		0			0
$23$	−11.1854	−	4.07116i	−0.486323	−	0.177007i	0.0872094	−	0.996190i	$-0.472205\pi$
$23$	−11.1854	−	4.07116i	−0.486323	−	0.177007i	−0.573532	+	0.819183i	$0.694427\pi$
$24$		0			0
$25$	−16.8664	+	14.1526i	−0.674657	+	0.566104i
$26$		0			0
$27$	17.7647	+	10.2564i	0.657951	+	0.379868i
$28$		0			0
$29$	−52.5255	+	9.26166i	−1.81122	+	0.319367i	−0.973837	−	0.227246i	$-0.927028\pi$
$29$	−52.5255	+	9.26166i	−1.81122	+	0.319367i	−0.837385	+	0.546613i	$0.815917\pi$
$30$		0			0
$31$	4.93716	−	2.85047i	0.159263	−	0.0919506i	−0.418250	−	0.908332i	$-0.637356\pi$
$31$	4.93716	−	2.85047i	0.159263	−	0.0919506i	0.577513	+	0.816381i	$0.304023\pi$
$32$		0			0
$33$	−6.14938	−	16.8953i	−0.186345	−	0.511978i
$34$		0			0
$35$	−4.97317	−	4.17299i	−0.142091	−	0.119228i
$36$		0			0
$37$			35.7995i			0.967555i	0.875191	+	0.483778i	$0.160736\pi$
$37$			35.7995i			0.967555i	−0.875191	+	0.483778i	$0.839264\pi$
$38$		0			0
$39$	16.3543			0.419341
$40$		0			0
$41$	11.8339	−	14.1031i	0.288633	−	0.343979i	−0.602171	−	0.798367i	$-0.705698\pi$
$41$	11.8339	−	14.1031i	0.288633	−	0.343979i	0.890804	+	0.454388i	$0.150142\pi$
$42$		0			0
$43$	72.4831	−	26.3817i	1.68565	−	0.613528i	0.691587	−	0.722294i	$-0.256912\pi$
$43$	72.4831	−	26.3817i	1.68565	−	0.613528i	0.994067	+	0.108766i	$0.0346898\pi$
$44$		0			0
$45$	−2.68020	−	4.64223i	−0.0595599	−	0.103161i
$46$		0			0
$47$	−6.56111	−	37.2099i	−0.139598	−	0.791699i	−0.971547	−	0.236847i	$-0.923886\pi$
$47$	−6.56111	−	37.2099i	−0.139598	−	0.791699i	0.831949	−	0.554852i	$-0.187225\pi$
$48$		0			0
$49$	17.4343	−	30.1971i	0.355802	−	0.616266i
$50$		0			0
$51$	31.3787	+	37.3956i	0.615268	+	0.733248i
$52$		0			0
$53$	16.1770	−	44.4460i	0.305227	−	0.838603i	−0.688344	−	0.725385i	$-0.741662\pi$
$53$	16.1770	−	44.4460i	0.305227	−	0.838603i	0.993570	−	0.113218i	$-0.0361159\pi$
$54$		0			0
$55$	1.54979	−	8.78930i	0.0281780	−	0.159806i
$56$		0			0
$57$	65.5838	+	8.26284i	1.15059	+	0.144962i
$58$		0			0
$59$	−86.2842	−	15.2142i	−1.46244	−	0.257868i	−0.614905	−	0.788601i	$-0.710806\pi$
$59$	−86.2842	−	15.2142i	−1.46244	−	0.257868i	−0.847539	+	0.530733i	$0.821917\pi$
$60$		0			0
$61$	−19.7588	−	7.19161i	−0.323915	−	0.117895i	0.174945	−	0.984578i	$-0.444025\pi$
$61$	−19.7588	−	7.19161i	−0.323915	−	0.117895i	−0.498859	+	0.866683i	$0.666248\pi$
$62$		0			0
$63$	−8.93835	+	7.50016i	−0.141879	+	0.119050i
$64$		0			0
$65$	7.03050	+	4.05906i	0.108162	+	0.0624471i
$66$		0			0
$67$	−46.1336	+	8.13459i	−0.688560	+	0.121412i	−0.506972	−	0.861963i	$-0.669235\pi$
$67$	−46.1336	+	8.13459i	−0.688560	+	0.121412i	−0.181589	+	0.983375i	$0.558124\pi$
$68$		0			0
$69$	−35.8641	+	20.7062i	−0.519770	+	0.300089i
$70$		0			0
$71$	−30.2932	−	83.2298i	−0.426665	−	1.17225i	−0.947825	−	0.318792i	$-0.896723\pi$
$71$	−30.2932	−	83.2298i	−0.426665	−	1.17225i	0.521160	−	0.853459i	$-0.325499\pi$
$72$		0			0
$73$	57.7624	+	48.4684i	0.791266	+	0.663951i	0.946059	−	0.323996i	$-0.105026\pi$
$73$	57.7624	+	48.4684i	0.791266	+	0.663951i	−0.154792	+	0.987947i	$0.549471\pi$
$74$		0			0
$75$			76.6006i			1.02134i
$76$		0			0
$77$	−19.4272			−0.252301
$78$		0			0
$79$	−10.5650	+	12.5908i	−0.133734	+	0.159378i	−0.828755	−	0.559611i	$-0.810950\pi$
$79$	−10.5650	+	12.5908i	−0.133734	+	0.159378i	0.695021	+	0.718989i	$0.255395\pi$
$80$		0			0
$81$	93.3124	−	33.9629i	1.15200	−	0.419295i
$82$		0			0
$83$	−17.5572	−	30.4100i	−0.211533	−	0.366386i	0.740662	−	0.671878i	$-0.234512\pi$
$83$	−17.5572	−	30.4100i	−0.211533	−	0.366386i	−0.952194	+	0.305493i	$0.901179\pi$
$84$		0			0
$85$	4.20785	+	23.8639i	0.0495042	+	0.280752i
$86$		0			0
$87$	−92.7794	+	160.699i	−1.06643	+	1.84711i
$88$		0			0
$89$	18.1327	+	21.6097i	0.203738	+	0.242805i	0.858232	−	0.513262i	$-0.171563\pi$
$89$	18.1327	+	21.6097i	0.203738	+	0.242805i	−0.654495	+	0.756067i	$0.727119\pi$
$90$		0			0
$91$	6.04386	−	16.6054i	0.0664160	−	0.182477i
$92$		0			0
$93$	3.44413	−	19.5326i	0.0370337	−	0.210028i
$94$		0			0
$95$	26.1428	+	19.8297i	0.275188	+	0.208734i
$96$		0			0
$97$	39.0070	+	6.87798i	0.402134	+	0.0709070i	0.371057	−	0.928610i	$-0.378995\pi$
$97$	39.0070	+	6.87798i	0.402134	+	0.0709070i	0.0310764	+	0.999517i	$0.490106\pi$
$98$		0			0
$99$	−15.0734	−	5.48628i	−0.152257	−	0.0554170i
$100$		0			0
$101$	−108.963	+	91.4309i	−1.07884	+	0.905257i	−0.995824	−	0.0912913i	$-0.970901\pi$
$101$	−108.963	+	91.4309i	−1.07884	+	0.905257i	−0.0830187	+	0.996548i	$0.526456\pi$
$102$		0			0
$103$	−65.8869	−	38.0398i	−0.639678	−	0.369318i	0.144812	−	0.989459i	$-0.453742\pi$
$103$	−65.8869	−	38.0398i	−0.639678	−	0.369318i	−0.784491	+	0.620141i	$0.787075\pi$
$104$		0			0
$105$	−22.2430	+	3.92205i	−0.211838	+	0.0373528i
$106$		0			0
$107$	−91.1219	+	52.6092i	−0.851606	+	0.491675i	−0.861193	−	0.508279i	$-0.830282\pi$
$107$	−91.1219	+	52.6092i	−0.851606	+	0.491675i	0.00958612	+	0.999954i	$0.496949\pi$
$108$		0			0
$109$	−57.2122	−	157.189i	−0.524882	−	1.44210i	−0.865025	−	0.501729i	$-0.832698\pi$
$109$	−57.2122	−	157.189i	−0.524882	−	1.44210i	0.340142	−	0.940374i	$-0.389525\pi$
$110$		0			0
$111$	95.4101	+	80.0586i	0.859551	+	0.721249i
$112$		0			0
$113$		−	121.409i		−	1.07441i	−0.843451	−	0.537207i	$-0.819480\pi$
$113$		−	121.409i		−	1.07441i	0.843451	−	0.537207i	$-0.180520\pi$
$114$		0			0
$115$	−20.5567			−0.178754
$116$		0			0
$117$	9.37879	−	11.1772i	0.0801606	−	0.0955317i
$118$		0			0
$119$	49.5659	−	18.0405i	0.416520	−	0.151601i
$120$		0			0
$121$	47.1463	+	81.6597i	0.389638	+	0.674874i
$122$		0			0
$123$	−11.1223	−	63.0777i	−0.0904253	−	0.512827i
$124$		0			0
$125$	−40.5991	+	70.3197i	−0.324793	+	0.562558i
$126$		0			0
$127$	142.132	+	169.387i	1.11915	+	1.33375i	0.936537	+	0.350567i	$0.114011\pi$
$127$	142.132	+	169.387i	1.11915	+	1.33375i	0.182614	+	0.983185i	$0.441544\pi$
$128$		0			0
$129$	91.7837	−	252.174i	0.711502	−	1.95484i
$130$		0			0
$131$	28.1211	−	159.483i	0.214665	−	1.21742i	−0.666823	−	0.745217i	$-0.732346\pi$
$131$	28.1211	−	159.483i	0.214665	−	1.21742i	0.881487	−	0.472208i	$-0.156543\pi$
$132$		0			0
$133$	32.6267	−	63.5370i	0.245313	−	0.477722i
$134$		0			0
$135$	34.8871	+	6.15153i	0.258423	+	0.0455669i
$136$		0			0
$137$	165.933	+	60.3948i	1.21119	+	0.440838i	0.867117	−	0.498104i	$-0.165970\pi$
$137$	165.933	+	60.3948i	1.21119	+	0.440838i	0.344075	+	0.938942i	$0.388192\pi$
$138$		0			0
$139$	78.7451	−	66.0750i	0.566512	−	0.475360i	−0.313975	−	0.949431i	$-0.601661\pi$
$139$	78.7451	−	66.0750i	0.566512	−	0.475360i	0.880486	+	0.474072i	$0.157216\pi$
$140$		0			0
$141$	−113.841	−	65.7264i	−0.807386	−	0.466145i
$142$		0			0
$143$	23.9242	−	4.21848i	0.167302	−	0.0294999i
$144$		0			0
$145$	−79.7692	+	46.0548i	−0.550133	+	0.317619i
$146$		0			0
$147$	−41.4905	−	113.994i	−0.282248	−	0.775471i
$148$		0			0
$149$	203.127	+	170.444i	1.36327	+	1.14392i	0.974959	+	0.222387i	$0.0713848\pi$
$149$	203.127	+	170.444i	1.36327	+	1.14392i	0.388308	+	0.921530i	$0.373060\pi$
$150$		0			0
$151$		−	81.7629i		−	0.541476i	−0.962653	−	0.270738i	$-0.912732\pi$
$151$		−	81.7629i		−	0.541476i	0.962653	−	0.270738i	$-0.0872677\pi$
$152$		0			0
$153$	43.5526			0.284658
$154$		0			0
$155$	6.32849	−	7.54200i	0.0408290	−	0.0486581i
$156$		0			0
$157$	−71.7181	+	26.1033i	−0.456803	+	0.166263i	−0.560165	−	0.828381i	$-0.689262\pi$
$157$	−71.7181	+	26.1033i	−0.456803	+	0.166263i	0.103362	+	0.994644i	$0.467040\pi$
$158$		0			0
$159$	−82.2772	−	142.508i	−0.517467	−	0.896278i
$160$		0			0
$161$	7.77017	+	44.0668i	0.0482619	+	0.273707i
$162$		0			0
$163$	−157.116	+	272.133i	−0.963903	+	1.66953i	−0.251370	+	0.967891i	$0.580881\pi$
$163$	−157.116	+	272.133i	−0.963903	+	1.66953i	−0.712533	+	0.701638i	$0.752452\pi$
$164$		0			0
$165$	−19.9588	−	23.7859i	−0.120962	−	0.144157i
$166$		0			0
$167$	−25.8348	+	70.9804i	−0.154699	+	0.425032i	−0.992696	−	0.120643i	$-0.961504\pi$
$167$	−25.8348	+	70.9804i	−0.154699	+	0.425032i	0.837997	+	0.545675i	$0.183727\pi$
$168$		0			0
$169$	25.5094	−	144.671i	0.150943	−	0.856041i
$170$		0			0
$171$	43.2579	−	40.0841i	0.252970	−	0.234410i
$172$		0			0
$173$	−28.4830	−	5.02233i	−0.164642	−	0.0290308i	0.0907195	−	0.995876i	$-0.471083\pi$
$173$	−28.4830	−	5.02233i	−0.164642	−	0.0290308i	−0.255361	+	0.966846i	$0.582194\pi$
$174$		0			0
$175$	77.7765	+	28.3083i	0.444437	+	0.161762i
$176$		0			0
$177$	−233.505	+	195.934i	−1.31924	+	1.10697i
$178$		0			0
$179$	−152.955	−	88.3085i	−0.854496	−	0.493344i	0.00766916	−	0.999971i	$-0.497559\pi$
$179$	−152.955	−	88.3085i	−0.854496	−	0.493344i	−0.862165	+	0.506627i	$0.830892\pi$
$180$		0			0
$181$	−198.928	+	35.0764i	−1.09905	+	0.193792i	−0.693626	−	0.720335i	$-0.743988\pi$
$181$	−198.928	+	35.0764i	−1.09905	+	0.193792i	−0.405426	+	0.914128i	$0.632877\pi$
$182$		0			0
$183$	−63.3532	+	36.5770i	−0.346192	+	0.199874i
$184$		0			0
$185$	21.1454	+	58.0965i	0.114299	+	0.314035i
$186$		0			0
$187$	55.5488	+	46.6110i	0.297052	+	0.249257i
$188$		0			0
$189$		−	77.1116i		−	0.407998i
$190$		0			0
$191$	35.5679			0.186219			0.0931097	−	0.995656i	$-0.470319\pi$
$191$	35.5679			0.186219			0.0931097	+	0.995656i	$0.470319\pi$
$192$		0			0
$193$	−25.5263	+	30.4210i	−0.132260	+	0.157622i	−0.828110	−	0.560566i	$-0.810584\pi$
$193$	−25.5263	+	30.4210i	−0.132260	+	0.157622i	0.695849	+	0.718188i	$0.255028\pi$
$194$		0			0
$195$	26.5402	−	9.65985i	0.136104	−	0.0495377i
$196$		0			0
$197$	172.127	+	298.132i	0.873739	+	1.51336i	0.858100	+	0.513483i	$0.171645\pi$
$197$	172.127	+	298.132i	0.873739	+	1.51336i	0.0156396	+	0.999878i	$0.495022\pi$
$198$		0			0
$199$	−12.9894	−	73.6666i	−0.0652735	−	0.370184i	−0.999894	−	0.0145385i	$-0.995372\pi$
$199$	−12.9894	−	73.6666i	−0.0652735	−	0.370184i	0.934621	−	0.355646i	$-0.115739\pi$
$200$		0			0
$201$	−81.4889	+	141.143i	−0.405417	+	0.702203i
$202$		0			0
$203$	128.878	+	153.591i	0.634868	+	0.756606i
$204$		0			0
$205$	10.8743	−	29.8768i	0.0530452	−	0.145740i
$206$		0			0
$207$	−6.41574	+	36.3855i	−0.0309939	+	0.175775i
$208$		0			0
$209$	98.0718	−	4.82945i	0.469243	−	0.0231074i
$210$		0			0
$211$	−11.9068	−	2.09948i	−0.0564301	−	0.00995015i	0.145362	−	0.989379i	$-0.453565\pi$
$211$	−11.9068	−	2.09948i	−0.0564301	−	0.00995015i	−0.201792	+	0.979428i	$0.564676\pi$
$212$		0			0
$213$	−289.562	−	105.392i	−1.35945	−	0.494798i
$214$		0			0
$215$	102.045	−	85.6259i	0.474628	−	0.398260i
$216$		0			0
$217$	−18.5597	−	10.7154i	−0.0855284	−	0.0493799i
$218$		0			0
$219$	258.349	−	45.5538i	1.17967	−	0.208008i
$220$		0			0
$221$	−57.1221	+	32.9794i	−0.258471	+	0.149228i
$222$		0			0
$223$	−77.1612	−	211.999i	−0.346014	−	0.950667i	−0.983612	−	0.180297i	$-0.942294\pi$
$223$	−77.1612	−	211.999i	−0.346014	−	0.950667i	0.637598	−	0.770369i	$-0.279928\pi$
$224$		0			0
$225$	52.3520	+	43.9285i	0.232675	+	0.195238i
$226$		0			0
$227$			99.1388i			0.436735i	0.975867	+	0.218367i	$0.0700731\pi$
$227$			99.1388i			0.436735i	−0.975867	+	0.218367i	$0.929927\pi$
$228$		0			0
$229$	−73.3690			−0.320389			−0.160194	−	0.987086i	$-0.551212\pi$
$229$	−73.3690			−0.320389			−0.160194	+	0.987086i	$0.551212\pi$
$230$		0			0
$231$	−43.4450	+	51.7758i	−0.188074	+	0.224138i
$232$		0			0
$233$	96.3134	−	35.0552i	0.413362	−	0.150452i	−0.126964	−	0.991907i	$-0.540523\pi$
$233$	96.3134	−	35.0552i	0.413362	−	0.150452i	0.540326	+	0.841456i	$0.318301\pi$
$234$		0			0
$235$	−32.6260	−	56.5098i	−0.138834	−	0.240467i
$236$		0			0
$237$	9.92965	+	56.3139i	0.0418973	+	0.237611i
$238$		0			0
$239$	103.142	−	178.648i	0.431558	−	0.747481i	−0.565449	−	0.824783i	$-0.691297\pi$
$239$	103.142	−	178.648i	0.431558	−	0.747481i	0.997008	+	0.0773020i	$0.0246306\pi$
$240$		0			0
$241$	−201.345	−	239.954i	−0.835457	−	0.995659i	−0.999957	−	0.00928168i	$-0.997046\pi$
$241$	−201.345	−	239.954i	−0.835457	−	0.995659i	0.164500	−	0.986377i	$-0.447399\pi$
$242$		0			0
$243$	55.0170	−	151.158i	0.226407	−	0.622049i
$244$		0			0
$245$	10.4566	−	59.3023i	0.0426800	−	0.242050i
$246$		0			0
$247$	−26.3825	+	85.3292i	−0.106812	+	0.345462i
$248$		0			0
$249$	−120.310	−	21.2138i	−0.483171	−	0.0851961i
$250$		0			0
$251$	197.035	+	71.7149i	0.785001	+	0.285717i	0.703256	−	0.710937i	$-0.251729\pi$
$251$	197.035	+	71.7149i	0.785001	+	0.285717i	0.0817443	+	0.996653i	$0.473951\pi$
$252$		0			0
$253$	−47.1235	+	39.5413i	−0.186259	+	0.156290i
$254$		0			0
$255$	73.0103	+	42.1525i	0.286315	+	0.165304i
$256$		0			0
$257$	−150.440	+	26.5267i	−0.585371	+	0.103217i	−0.458487	−	0.888701i	$-0.651609\pi$
$257$	−150.440	+	26.5267i	−0.585371	+	0.103217i	−0.126884	+	0.991918i	$0.540497\pi$
$258$		0			0
$259$	116.547	−	67.2885i	0.449989	−	0.259801i
$260$		0			0
$261$	56.6213	+	155.566i	0.216940	+	0.596038i
$262$		0			0
$263$	−123.404	−	103.548i	−0.469216	−	0.393719i	0.377293	−	0.926094i	$-0.376855\pi$
$263$	−123.404	−	103.548i	−0.469216	−	0.393719i	−0.846508	+	0.532375i	$0.821299\pi$
$264$		0			0
$265$		−	81.6832i		−	0.308239i
$266$		0			0
$267$	98.1424			0.367575
$268$		0			0
$269$	278.090	−	331.415i	1.03379	−	1.23203i	0.0615377	−	0.998105i	$-0.480400\pi$
$269$	278.090	−	331.415i	1.03379	−	1.23203i	0.972255	−	0.233922i	$-0.0751560\pi$
$270$		0			0
$271$	301.996	−	109.918i	1.11438	−	0.405600i	0.281779	−	0.959479i	$-0.409075\pi$
$271$	301.996	−	109.918i	1.11438	−	0.405600i	0.832597	+	0.553879i	$0.186853\pi$
$272$		0			0
$273$	−30.7394	−	53.2422i	−0.112599	−	0.195026i
$274$		0			0
$275$	19.7586	+	112.056i	0.0718494	+	0.407478i
$276$		0			0
$277$	187.838	−	325.345i	0.678115	−	1.17453i	−0.297433	−	0.954743i	$-0.596131\pi$
$277$	187.838	−	325.345i	0.678115	−	1.17453i	0.975548	−	0.219787i	$-0.0705361\pi$
$278$		0			0
$279$	−11.3743	−	13.5553i	−0.0407680	−	0.0485854i
$280$		0			0
$281$	−78.1955	+	214.840i	−0.278276	+	0.764556i	0.719283	+	0.694718i	$0.244471\pi$
$281$	−78.1955	+	214.840i	−0.278276	+	0.764556i	−0.997558	+	0.0698386i	$0.977752\pi$
$282$		0			0
$283$	−21.5662	+	122.308i	−0.0762058	+	0.432184i	0.922704	+	0.385508i	$0.125974\pi$
$283$	−21.5662	+	122.308i	−0.0762058	+	0.432184i	−0.998910	+	0.0466759i	$0.985137\pi$
$284$		0			0
$285$	111.312	−	25.3286i	0.390568	−	0.0888724i
$286$		0			0
$287$	−68.1564	−	12.0178i	−0.237479	−	0.0418739i
$288$		0			0
$289$	86.5617	+	31.5059i	0.299521	+	0.109017i
$290$		0			0
$291$	105.562	−	88.5770i	0.362756	−	0.304388i
$292$		0			0
$293$	351.093	+	202.704i	1.19827	+	0.691821i	0.960169	−	0.279419i	$-0.0901419\pi$
$293$	351.093	+	202.704i	1.19827	+	0.691821i	0.238100	+	0.971241i	$0.423475\pi$
$294$		0			0
$295$	−149.011	+	26.2746i	−0.505121	+	0.0890665i
$296$		0			0
$297$	91.8066	−	53.0046i	0.309113	−	0.178467i
$298$		0			0
$299$	−19.1376	−	52.5802i	−0.0640054	−	0.175853i
$300$		0			0
$301$	−222.125	−	186.385i	−0.737958	−	0.619221i
$302$		0			0
$303$			494.867i			1.63322i
$304$		0			0
$305$	−36.3129			−0.119059
$306$		0			0
$307$	−256.739	+	305.969i	−0.836283	+	0.996643i	0.163666	+	0.986516i	$0.447668\pi$
$307$	−256.739	+	305.969i	−0.836283	+	0.996643i	−0.999949	+	0.0101272i	$0.996776\pi$
$308$		0			0
$309$	−248.724	+	90.5280i	−0.804931	+	0.292971i
$310$		0			0
$311$	−236.487	−	409.607i	−0.760407	−	1.31706i	−0.942641	−	0.333808i	$-0.891666\pi$
$311$	−236.487	−	409.607i	−0.760407	−	1.31706i	0.182234	−	0.983255i	$-0.441667\pi$
$312$		0			0
$313$	−47.1130	−	267.191i	−0.150521	−	0.853646i	−0.962767	−	0.270332i	$-0.912867\pi$
$313$	−47.1130	−	267.191i	−0.150521	−	0.853646i	0.812246	−	0.583314i	$-0.198244\pi$
$314$		0			0
$315$	−10.0753	+	17.4510i	−0.0319852	+	0.0554000i
$316$		0			0
$317$	174.153	+	207.547i	0.549378	+	0.654724i	0.967263	−	0.253777i	$-0.0816728\pi$
$317$	174.153	+	207.547i	0.549378	+	0.654724i	−0.417885	+	0.908500i	$0.637228\pi$
$318$		0			0
$319$	−94.2728	+	259.013i	−0.295526	+	0.811951i
$320$		0			0
$321$	−63.5661	+	360.501i	−0.198025	+	1.12306i
$322$		0			0
$323$	−245.733	+	103.393i	−0.760782	+	0.320103i
$324$		0			0
$325$	−101.927	−	17.9725i	−0.313622	−	0.0553000i
$326$		0			0
$327$	−546.872	−	199.045i	−1.67239	−	0.608701i
$328$		0			0
$329$	−108.806	+	91.2993i	−0.330718	+	0.277506i
$330$		0			0
$331$	237.042	+	136.856i	0.716139	+	0.413463i	0.813330	−	0.581803i	$-0.197652\pi$
$331$	237.042	+	136.856i	0.716139	+	0.413463i	−0.0971909	+	0.995266i	$0.530986\pi$
$332$		0			0
$333$	109.431	−	19.2956i	0.328621	−	0.0579447i
$334$		0			0
$335$	−70.0620	+	40.4503i	−0.209140	+	0.120747i
$336$		0			0
$337$	123.097	+	338.206i	0.365272	+	1.00358i	0.977136	+	0.212614i	$0.0681978\pi$
$337$	123.097	+	338.206i	0.365272	+	1.00358i	−0.611864	+	0.790963i	$0.709580\pi$
$338$		0			0
$339$	−323.569	−	271.507i	−0.954480	−	0.800904i
$340$		0			0
$341$		−	29.4620i		−	0.0863990i
$342$		0			0
$343$	−315.277			−0.919175
$344$		0			0
$345$	−45.9710	+	54.7861i	−0.133249	+	0.158800i
$346$		0			0
$347$	−143.155	+	52.1043i	−0.412552	+	0.150156i	−0.539954	−	0.841695i	$-0.681558\pi$
$347$	−143.155	+	52.1043i	−0.412552	+	0.150156i	0.127402	+	0.991851i	$0.459336\pi$
$348$		0			0
$349$	162.592	+	281.617i	0.465879	+	0.806927i	0.999241	−	0.0389607i	$-0.0124047\pi$
$349$	162.592	+	281.617i	0.465879	+	0.806927i	−0.533361	+	0.845888i	$0.679071\pi$
$350$		0			0
$351$	16.7443	+	94.9614i	0.0477045	+	0.270545i
$352$		0			0
$353$	303.741	−	526.095i	0.860456	−	1.49035i	−0.0110341	−	0.999939i	$-0.503512\pi$
$353$	303.741	−	526.095i	0.860456	−	1.49035i	0.871490	−	0.490414i	$-0.163154\pi$
$354$		0			0
$355$	−98.3212	−	117.175i	−0.276961	−	0.330069i
$356$		0			0
$357$	62.7642	−	172.443i	0.175810	−	0.483034i
$358$		0			0
$359$	−58.4549	+	331.514i	−0.162827	+	0.923438i	0.788449	+	0.615100i	$0.210884\pi$
$359$	−58.4549	+	331.514i	−0.162827	+	0.923438i	−0.951277	+	0.308339i	$0.900227\pi$
$360$		0			0
$361$	−148.910	+	328.857i	−0.412494	+	0.910960i
$362$		0			0
$363$	323.066	+	56.9653i	0.889990	+	0.156929i
$364$		0			0
$365$	122.367	+	44.5379i	0.335252	+	0.122022i
$366$		0			0
$367$	335.139	−	281.215i	0.913186	−	0.766254i	−0.0595366	−	0.998226i	$-0.518962\pi$
$367$	335.139	−	281.215i	0.913186	−	0.766254i	0.972722	+	0.231972i	$0.0745178\pi$
$368$		0			0
$369$	−49.4883	−	28.5721i	−0.134115	−	0.0774311i
$370$		0			0
$371$	−175.102	+	30.8752i	−0.471973	+	0.0832216i
$372$		0			0
$373$	467.732	−	270.045i	1.25397	−	0.723981i	0.282076	−	0.959392i	$-0.408977\pi$
$373$	467.732	−	270.045i	1.25397	−	0.723981i	0.971896	+	0.235411i	$0.0756436\pi$
$374$		0			0
$375$	96.6187	+	265.458i	0.257650	+	0.707887i
$376$		0			0
$377$	−192.062	−	161.159i	−0.509448	−	0.427478i
$378$		0			0
$379$			333.773i			0.880668i	0.897834	+	0.440334i	$0.145140\pi$
$379$			333.773i			0.880668i	−0.897834	+	0.440334i	$0.854860\pi$
$380$		0			0
$381$	769.286			2.01912
$382$		0			0
$383$	−13.9067	+	16.5733i	−0.0363099	+	0.0432724i	−0.783894	−	0.620895i	$-0.786769\pi$
$383$	−13.9067	+	16.5733i	−0.0363099	+	0.0432724i	0.747584	+	0.664167i	$0.231214\pi$
$384$		0			0
$385$	−31.5270	+	11.4749i	−0.0818882	+	0.0298049i
$386$		0			0
$387$	−119.710	−	207.344i	−0.309329	−	0.535773i
$388$		0			0
$389$	−3.22122	−	18.2685i	−0.00828078	−	0.0469626i	0.980387	−	0.197080i	$-0.0631459\pi$
$389$	−3.22122	−	18.2685i	−0.00828078	−	0.0469626i	−0.988668	+	0.150117i	$0.952035\pi$
$390$		0			0
$391$	83.5105	−	144.644i	0.213582	−	0.369934i
$392$		0			0
$393$	−362.153	−	431.597i	−0.921509	−	1.09821i
$394$		0			0
$395$	−9.70821	+	26.6731i	−0.0245777	+	0.0675268i
$396$		0			0
$397$	−9.77687	+	55.4474i	−0.0246269	+	0.139666i	−0.994642	−	0.103378i	$-0.967035\pi$
$397$	−9.77687	+	55.4474i	−0.0246269	+	0.139666i	0.970015	+	0.243044i	$0.0781460\pi$
$398$		0			0
$399$	−96.3707	−	229.042i	−0.241531	−	0.574040i
$400$		0			0
$401$	−37.0196	−	6.52756i	−0.0923183	−	0.0162782i	0.127298	−	0.991864i	$-0.459369\pi$
$401$	−37.0196	−	6.52756i	−0.0923183	−	0.0162782i	−0.219616	+	0.975586i	$0.570481\pi$
$402$		0			0
$403$	25.1827	+	9.16574i	0.0624880	+	0.0227438i
$404$		0			0
$405$	131.369	−	110.232i	0.324369	−	0.272178i
$406$		0			0
$407$	160.223	+	92.5048i	0.393668	+	0.227284i
$408$		0			0
$409$	−13.2294	+	2.33270i	−0.0323457	+	0.00570342i	−0.189798	−	0.981823i	$-0.560783\pi$
$409$	−13.2294	+	2.33270i	−0.0323457	+	0.00570342i	0.157452	+	0.987527i	$0.449672\pi$
$410$		0			0
$411$	532.037	−	307.171i	1.29449	−	0.747376i
$412$		0			0
$413$	112.648	+	309.499i	0.272756	+	0.749392i
$414$		0			0
$415$	−46.4543	−	38.9798i	−0.111938	−	0.0939273i
$416$		0			0
$417$		−	357.629i		−	0.857623i
$418$		0			0
$419$	−784.559			−1.87245			−0.936227	−	0.351395i	$-0.885708\pi$
$419$	−784.559			−1.87245			−0.936227	+	0.351395i	$0.885708\pi$
$420$		0			0
$421$	349.429	−	416.434i	0.829998	−	0.989153i	−0.169995	−	0.985445i	$-0.554375\pi$
$421$	349.429	−	416.434i	0.829998	−	0.989153i	0.999993	−	0.00370830i	$-0.00118039\pi$
$422$		0			0
$423$	−110.205	+	40.1115i	−0.260533	+	0.0948261i
$424$		0			0
$425$	−154.470	−	267.549i	−0.363458	−	0.629528i
$426$		0			0
$427$	13.7258	+	77.8430i	0.0321448	+	0.182302i
$428$		0			0
$429$	42.2590	−	73.1947i	0.0985057	−	0.170617i
$430$		0			0
$431$	−222.339	−	264.974i	−0.515868	−	0.614788i	0.443730	−	0.896160i	$-0.353655\pi$
$431$	−222.339	−	264.974i	−0.515868	−	0.614788i	−0.959599	+	0.281373i	$0.909210\pi$
$432$		0			0
$433$	−185.662	+	510.102i	−0.428781	+	1.17807i	0.517773	+	0.855518i	$0.326761\pi$
$433$	−185.662	+	510.102i	−0.428781	+	1.17807i	−0.946553	+	0.322547i	$0.895461\pi$
$434$		0			0
$435$	−55.6465	+	315.587i	−0.127923	+	0.725488i
$436$		0			0
$437$	−50.1798	−	220.525i	−0.114828	−	0.504635i
$438$		0			0
$439$	496.329	+	87.5162i	1.13059	+	0.199354i	0.707486	−	0.706727i	$-0.249829\pi$
$439$	496.329	+	87.5162i	1.13059	+	0.199354i	0.423104	+	0.906081i	$0.360940\pi$
$440$		0			0
$441$	−101.702	−	37.0165i	−0.230617	−	0.0839377i
$442$		0			0
$443$	308.416	−	258.791i	0.696198	−	0.584179i	−0.224491	−	0.974476i	$-0.572072\pi$
$443$	308.416	−	258.791i	0.696198	−	0.584179i	0.920689	+	0.390297i	$0.127628\pi$
$444$		0			0
$445$	42.1901	+	24.3585i	0.0948093	+	0.0547382i
$446$		0			0
$447$	908.505	−	160.194i	2.03245	−	0.358376i
$448$		0			0
$449$	−411.423	+	237.535i	−0.916309	+	0.529031i	−0.882456	−	0.470396i	$-0.844111\pi$
$449$	−411.423	+	237.535i	−0.916309	+	0.529031i	−0.0338533	+	0.999427i	$0.510778\pi$
$450$		0			0
$451$	−32.5409	−	89.4055i	−0.0721528	−	0.198238i
$452$		0			0
$453$	−217.908	−	182.846i	−0.481033	−	0.403635i
$454$		0			0
$455$		−	30.5175i		−	0.0670714i
$456$		0			0
$457$	169.918			0.371813			0.185906	−	0.982567i	$-0.440478\pi$
$457$	169.918			0.371813			0.185906	+	0.982567i	$0.440478\pi$
$458$		0			0
$459$	−185.011	+	220.488i	−0.403075	+	0.480366i
$460$		0			0
$461$	−647.342	+	235.613i	−1.40421	+	0.511091i	−0.929426	−	0.369010i	$-0.879697\pi$
$461$	−647.342	+	235.613i	−1.40421	+	0.511091i	−0.474786	+	0.880101i	$0.657475\pi$
$462$		0			0
$463$	324.936	+	562.805i	0.701805	+	1.21556i	0.967832	+	0.251596i	$0.0809554\pi$
$463$	324.936	+	562.805i	0.701805	+	1.21556i	−0.266028	+	0.963965i	$0.585711\pi$
$464$		0			0
$465$	−5.94793	−	33.7324i	−0.0127913	−	0.0725428i
$466$		0			0
$467$	368.835	−	638.841i	0.789797	−	1.36797i	−0.136294	−	0.990668i	$-0.543519\pi$
$467$	368.835	−	638.841i	0.789797	−	1.36797i	0.926091	−	0.377300i	$-0.123147\pi$
$468$		0			0
$469$	113.195	+	134.900i	0.241353	+	0.287634i
$470$		0			0
$471$	−90.8150	+	249.512i	−0.192813	+	0.529750i
$472$		0			0
$473$	69.2210	−	392.572i	0.146345	−	0.829962i
$474$		0			0
$475$	−399.666	−	123.571i	−0.841403	−	0.260149i
$476$		0			0
$477$	−144.580	−	25.4933i	−0.303103	−	0.0534452i
$478$		0			0
$479$	356.818	+	129.871i	0.744923	+	0.271130i	0.686468	−	0.727160i	$-0.259160\pi$
$479$	356.818	+	129.871i	0.744923	+	0.271130i	0.0584553	+	0.998290i	$0.481383\pi$
$480$		0			0
$481$	−128.914	+	108.172i	−0.268013	+	0.224890i
$482$		0			0
$483$	134.820	+	77.8382i	0.279130	+	0.161156i
$484$		0			0
$485$	67.3641	−	11.8781i	0.138895	−	0.0244910i
$486$		0			0
$487$	−92.9634	+	53.6724i	−0.190890	+	0.110210i	−0.592399	−	0.805645i	$-0.701819\pi$
$487$	−92.9634	+	53.6724i	−0.190890	+	0.110210i	0.401509	+	0.915855i	$0.368486\pi$
$488$		0			0
$489$	373.909	+	1027.31i	0.764640	+	2.10083i
$490$		0			0
$491$	91.7009	+	76.9462i	0.186763	+	0.156713i	0.731376	−	0.681975i	$-0.238879\pi$
$491$	91.7009	+	76.9462i	0.186763	+	0.156713i	−0.544612	+	0.838688i	$0.683323\pi$
$492$		0			0
$493$		−	748.381i		−	1.51801i
$494$		0			0
$495$	−27.7021			−0.0559639
$496$		0			0
$497$	−214.020	+	255.059i	−0.430623	+	0.513197i
$498$		0			0
$499$	−419.529	+	152.696i	−0.840740	+	0.306004i	−0.726259	−	0.687421i	$-0.758743\pi$
$499$	−419.529	+	152.696i	−0.840740	+	0.306004i	−0.114481	+	0.993425i	$0.536520\pi$
$500$		0			0
$501$	131.397	+	227.586i	0.262270	+	0.454264i
$502$		0			0
$503$	30.3025	+	171.854i	0.0602435	+	0.341658i	1.00000		0.000186740i	$-5.94411e-5\pi$
$503$	30.3025	+	171.854i	0.0602435	+	0.341658i	−0.939756	+	0.341845i	$0.888948\pi$
$504$		0			0
$505$	−122.824	+	212.737i	−0.243215	+	0.421261i
$506$		0			0
$507$	−328.519	−	391.514i	−0.647966	−	0.772216i
$508$		0			0
$509$	−331.344	+	910.361i	−0.650971	+	1.78853i	−0.0368442	+	0.999321i	$0.511731\pi$
$509$	−331.344	+	910.361i	−0.650971	+	1.78853i	−0.614127	+	0.789207i	$0.710492\pi$
$510$		0			0
$511$	49.2215	−	279.149i	0.0963239	−	0.546280i
$512$		0			0
$513$	19.1694	+	389.273i	0.0373672	+	0.758817i
$514$		0			0
$515$	−129.392	−	22.8152i	−0.251246	−	0.0443014i
$516$		0			0
$517$	−183.489	−	66.7844i	−0.354910	−	0.129177i
$518$		0			0
$519$	−77.0818	+	64.6793i	−0.148520	+	0.124623i
$520$		0			0
$521$	−847.732	−	489.438i	−1.62713	−	0.939421i	−0.984945	−	0.172867i	$-0.944697\pi$
$521$	−847.732	−	489.438i	−1.62713	−	0.939421i	−0.642180	−	0.766554i	$-0.721970\pi$
$522$		0			0
$523$	467.583	−	82.4475i	0.894040	−	0.157643i	0.292292	−	0.956329i	$-0.405582\pi$
$523$	467.583	−	82.4475i	0.894040	−	0.157643i	0.601748	+	0.798686i	$0.294471\pi$
$524$		0			0
$525$	249.377	−	143.978i	0.475003	−	0.274243i
$526$		0			0
$527$	27.3591	+	75.1686i	0.0519148	+	0.142635i
$528$		0			0
$529$	−296.698	−	248.959i	−0.560866	−	0.470622i
$530$		0			0
$531$			271.951i			0.512148i
$532$		0			0
$533$	86.5428			0.162369
$534$		0			0
$535$	−116.801	+	139.198i	−0.218319	+	0.260183i
$536$		0			0
$537$	−577.406	+	210.159i	−1.07524	+	0.391357i
$538$		0			0
$539$	−90.0991	−	156.056i	−0.167160	−	0.289529i
$540$		0			0
$541$	174.061	+	987.148i	0.321739	+	1.82467i	0.531665	+	0.846955i	$0.321567\pi$
$541$	174.061	+	987.148i	0.321739	+	1.82467i	−0.209926	+	0.977717i	$0.567322\pi$
$542$		0			0
$543$	−351.381	+	608.610i	−0.647110	+	1.12083i
$544$		0			0
$545$	−185.691	−	221.298i	−0.340717	−	0.406051i
$546$		0			0
$547$	190.375	−	523.051i	0.348035	−	0.956218i	−0.634954	−	0.772550i	$-0.718981\pi$
$547$	190.375	−	523.051i	0.348035	−	0.956218i	0.982988	−	0.183667i	$-0.0587969\pi$
$548$		0			0
$549$	−11.3333	+	64.2741i	−0.0206435	+	0.117075i
$550$		0			0
$551$	−688.781	−	743.316i	−1.25006	−	1.34903i
$552$		0			0
$553$	60.8479	+	10.7291i	0.110032	+	0.0194017i
$554$		0			0
$555$	202.122	+	73.5662i	0.364183	+	0.132552i
$556$		0			0
$557$	441.858	−	370.763i	0.793282	−	0.665642i	−0.153274	−	0.988184i	$-0.548982\pi$
$557$	441.858	−	370.763i	0.793282	−	0.665642i	0.946555	+	0.322541i	$0.104537\pi$
$558$		0			0
$559$	314.015	+	181.297i	0.561745	+	0.324324i
$560$		0			0
$561$	248.448	−	43.8080i	0.442866	−	0.0780892i
$562$		0			0
$563$	−217.337	+	125.479i	−0.386033	+	0.222876i	−0.680440	−	0.732804i	$-0.738211\pi$
$563$	−217.337	+	125.479i	−0.386033	+	0.222876i	0.294407	+	0.955680i	$0.404878\pi$
$564$		0			0
$565$	−71.7114	−	197.025i	−0.126923	−	0.348717i
$566$		0			0
$567$	−285.957	−	239.946i	−0.504333	−	0.423186i
$568$		0			0
$569$		−	336.315i		−	0.591063i	−0.955333	−	0.295532i	$-0.904503\pi$
$569$		−	336.315i		−	0.591063i	0.955333	−	0.295532i	$-0.0954967\pi$
$570$		0			0
$571$	8.08871			0.0141659			0.00708294	−	0.999975i	$-0.497745\pi$
$571$	8.08871			0.0141659			0.00708294	+	0.999975i	$0.497745\pi$
$572$		0			0
$573$	79.5406	−	94.7928i	0.138814	−	0.165432i
$574$		0			0
$575$	246.276	−	89.6370i	0.428306	−	0.155891i
$576$		0			0
$577$	282.888	+	489.976i	0.490274	+	0.849179i	0.999937	−	0.0111946i	$-0.00356343\pi$
$577$	282.888	+	489.976i	0.490274	+	0.849179i	−0.509663	+	0.860374i	$0.670230\pi$
$578$		0			0
$579$	23.9913	+	136.061i	0.0414357	+	0.234993i
$580$		0			0
$581$	−66.0008	+	114.317i	−0.113599	+	0.196759i
$582$		0			0
$583$	−157.120	−	187.248i	−0.269502	−	0.321180i
$584$		0			0
$585$	8.61822	−	23.6784i	0.0147320	−	0.0404758i
$586$		0			0
$587$	52.0032	−	294.925i	0.0885915	−	0.502427i	−0.907932	−	0.419117i	$-0.862340\pi$
$587$	52.0032	−	294.925i	0.0885915	−	0.502427i	0.996524	−	0.0833102i	$-0.0265492\pi$
$588$		0			0
$589$	96.3562	+	49.4796i	0.163593	+	0.0840061i
$590$		0			0
$591$	1179.49	+	207.975i	1.99574	+	0.351904i
$592$		0			0
$593$	744.241	+	270.882i	1.25504	+	0.456799i	0.882103	−	0.471056i	$-0.156127\pi$
$593$	744.241	+	270.882i	1.25504	+	0.456799i	0.372941	+	0.927855i	$0.378349\pi$
$594$		0			0
$595$	69.7811	−	58.5533i	0.117279	−	0.0984089i
$596$		0			0
$597$	−225.379	−	130.123i	−0.377519	−	0.217961i
$598$		0			0
$599$	682.243	−	120.298i	1.13897	−	0.200831i	0.427815	−	0.903866i	$-0.359283\pi$
$599$	682.243	−	120.298i	1.13897	−	0.200831i	0.711155	+	0.703035i	$0.248172\pi$
$600$		0			0
$601$	582.555	−	336.338i	0.969309	−	0.559631i	0.0702836	−	0.997527i	$-0.477610\pi$
$601$	582.555	−	336.338i	0.969309	−	0.559631i	0.899026	+	0.437896i	$0.144276\pi$
$602$		0			0
$603$	49.7310	+	136.635i	0.0824726	+	0.226592i
$604$		0			0
$605$	124.743	+	104.672i	0.206187	+	0.173012i
$606$		0			0
$607$		−	655.314i		−	1.07960i	−0.841795	−	0.539798i	$-0.818501\pi$
$607$		−	655.314i		−	1.07960i	0.841795	−	0.539798i	$-0.181499\pi$
$608$		0			0
$609$	697.549			1.14540
$610$		0			0
$611$	114.168	−	136.060i	0.186854	−	0.222684i
$612$		0			0
$613$	−744.718	+	271.055i	−1.21487	+	0.442178i	−0.868392	−	0.495879i	$-0.834846\pi$
$613$	−744.718	+	271.055i	−1.21487	+	0.442178i	−0.346482	+	0.938057i	$0.612624\pi$
$614$		0			0
$615$	−55.3071	−	95.7948i	−0.0899303	−	0.155764i
$616$		0			0
$617$	−143.509	−	813.879i	−0.232591	−	1.31909i	−0.847628	−	0.530592i	$-0.821970\pi$
$617$	−143.509	−	813.879i	−0.232591	−	1.31909i	0.615036	−	0.788499i	$-0.289141\pi$
$618$		0			0
$619$	117.442	−	203.416i	0.189729	−	0.328621i	−0.755431	−	0.655229i	$-0.772572\pi$
$619$	117.442	−	203.416i	0.189729	−	0.328621i	0.945160	+	0.326608i	$0.105906\pi$
$620$		0			0
$621$	−156.950	−	187.046i	−0.252737	−	0.301201i
$622$		0			0
$623$	36.2693	−	99.6490i	0.0582171	−	0.159950i
$624$		0			0
$625$	71.2325	−	403.979i	0.113972	−	0.646367i
$626$		0			0
$627$	206.447	−	272.173i	0.329262	−	0.434088i
$628$		0			0
$629$	−494.690	−	87.2272i	−0.786470	−	0.138676i
$630$		0			0
$631$	−259.957	−	94.6165i	−0.411976	−	0.149947i	0.127714	−	0.991811i	$-0.459236\pi$
$631$	−259.957	−	94.6165i	−0.411976	−	0.149947i	−0.539689	+	0.841864i	$0.681458\pi$
$632$		0			0
$633$	−32.2225	+	27.0379i	−0.0509044	+	0.0427138i
$634$		0			0
$635$	330.706	+	190.933i	0.520797	+	0.300682i
$636$		0			0
$637$	161.419	−	28.4625i	0.253405	−	0.0446821i
$638$		0			0
$639$	−238.086	+	137.459i	−0.372592	+	0.215116i
$640$		0			0
$641$	176.948	+	486.162i	0.276050	+	0.758442i	0.997800	+	0.0662886i	$0.0211158\pi$
$641$	176.948	+	486.162i	0.276050	+	0.758442i	−0.721750	+	0.692154i	$0.756662\pi$
$642$		0			0
$643$	198.821	+	166.830i	0.309208	+	0.259456i	0.784165	−	0.620553i	$-0.213092\pi$
$643$	198.821	+	166.830i	0.309208	+	0.259456i	−0.474957	+	0.880009i	$0.657536\pi$
$644$		0			0
$645$		−	463.447i		−	0.718523i
$646$		0			0
$647$	−922.026			−1.42508			−0.712539	−	0.701632i	$-0.752455\pi$
$647$	−922.026			−1.42508			−0.712539	+	0.701632i	$0.752455\pi$
$648$		0			0
$649$	−291.048	+	346.857i	−0.448455	+	0.534448i
$650$		0			0
$651$	−70.0629	+	25.5008i	−0.107624	+	0.0391718i
$652$		0			0
$653$	−54.7347	−	94.8034i	−0.0838204	−	0.145181i	0.821068	−	0.570831i	$-0.193379\pi$
$653$	−54.7347	−	94.8034i	−0.0838204	−	0.145181i	−0.904888	+	0.425650i	$0.860046\pi$
$654$		0			0
$655$	−48.5644	−	275.423i	−0.0741442	−	0.420493i
$656$		0			0
$657$	117.023	−	202.690i	0.178117	−	0.308508i
$658$		0			0
$659$	396.936	+	473.050i	0.602330	+	0.717829i	0.977925	−	0.208954i	$-0.0670061\pi$
$659$	396.936	+	473.050i	0.602330	+	0.717829i	−0.375595	+	0.926784i	$0.622562\pi$
$660$		0			0
$661$	−107.714	+	295.941i	−0.162956	+	0.447717i	−0.994117	−	0.108315i	$-0.965455\pi$
$661$	−107.714	+	295.941i	−0.162956	+	0.447717i	0.831161	+	0.556032i	$0.187677\pi$
$662$		0			0
$663$	−39.8480	+	225.989i	−0.0601026	+	0.340859i
$664$		0			0
$665$	15.4186	−	122.381i	0.0231859	−	0.184031i
$666$		0			0
$667$	625.225	+	110.244i	0.937370	+	0.165284i
$668$		0			0
$669$	−737.558	−	268.449i	−1.10248	−	0.401269i
$670$		0			0
$671$	−83.2425	+	69.8488i	−0.124057	+	0.104097i
$672$		0			0
$673$	−520.089	−	300.274i	−0.772793	−	0.446172i	0.0610773	−	0.998133i	$-0.480546\pi$
$673$	−520.089	−	300.274i	−0.772793	−	0.446172i	−0.833870	+	0.551961i	$0.813880\pi$
$674$		0			0
$675$	−444.782	+	78.4270i	−0.658936	+	0.116188i
$676$		0			0
$677$	−473.739	+	273.513i	−0.699762	+	0.404008i	−0.807259	−	0.590198i	$-0.799050\pi$
$677$	−473.739	+	273.513i	−0.699762	+	0.404008i	0.107497	+	0.994205i	$0.465716\pi$
$678$		0			0
$679$	−50.9255	−	139.917i	−0.0750008	−	0.206063i
$680$		0			0
$681$	264.217	+	221.704i	0.387984	+	0.325557i
$682$		0			0
$683$			970.166i			1.42045i	0.703976	+	0.710224i	$0.251406\pi$
$683$			970.166i			1.42045i	−0.703976	+	0.710224i	$0.748594\pi$
$684$		0			0
$685$	304.954			0.445188
$686$		0			0
$687$	−164.075	+	195.537i	−0.238829	+	0.284625i
$688$		0			0
$689$	208.930	−	76.0444i	0.303237	−	0.110369i
$690$		0			0
$691$	−372.204	−	644.676i	−0.538646	−	0.932961i	−0.998977	−	0.0452145i	$-0.985603\pi$
$691$	−372.204	−	644.676i	−0.538646	−	0.932961i	0.460332	−	0.887747i	$-0.347730\pi$
$692$		0			0
$693$	10.4710	+	59.3843i	0.0151097	+	0.0856916i
$694$		0			0
$695$	88.7618	−	153.740i	0.127715	−	0.221209i
$696$		0			0
$697$	166.048	+	197.888i	0.238232	+	0.283914i
$698$		0			0
$699$	121.959	−	335.081i	0.174477	−	0.479372i
$700$		0			0
$701$	−94.2397	+	534.460i	−0.134436	+	0.762425i	0.840815	+	0.541323i	$0.182076\pi$
$701$	−94.2397	+	534.460i	−0.134436	+	0.762425i	−0.975251	+	0.221102i	$0.929035\pi$
$702$		0			0
$703$	−571.623	+	368.657i	−0.813119	+	0.524405i
$704$		0			0
$705$	−223.567	−	39.4209i	−0.317116	−	0.0559162i
$706$		0			0
$707$	502.464	+	182.882i	0.710698	+	0.258673i
$708$		0			0
$709$	126.356	−	106.025i	0.178217	−	0.149542i	−0.549315	−	0.835615i	$-0.685111\pi$
$709$	126.356	−	106.025i	0.178217	−	0.149542i	0.727533	+	0.686073i	$0.240667\pi$
$710$		0			0
$711$	44.1816	+	25.5083i	0.0621401	+	0.0358766i
$712$		0			0
$713$	−66.8290	+	11.7837i	−0.0937292	+	0.0165270i
$714$		0			0
$715$	36.3331	−	20.9769i	0.0508156	−	0.0293384i
$716$		0			0
$717$	−245.461	−	674.398i	−0.342344	−	0.940583i
$718$		0			0
$719$	812.523	+	681.788i	1.13007	+	0.948245i	0.999069	−	0.0431372i	$-0.0137353\pi$
$719$	812.523	+	681.788i	1.13007	+	0.948245i	0.131005	+	0.991382i	$0.458180\pi$
$720$		0			0
$721$			285.997i			0.396667i
$722$		0			0
$723$	−1089.77			−1.50729
$724$		0			0
$725$	754.840	−	899.583i	1.04116	−	1.24080i
$726$		0			0
$727$	562.409	−	204.700i	0.773603	−	0.281568i	0.0751003	−	0.997176i	$-0.476072\pi$
$727$	562.409	−	204.700i	0.773603	−	0.281568i	0.698503	+	0.715608i	$0.253850\pi$
$728$		0			0
$729$	167.035	+	289.313i	0.229129	+	0.396862i
$730$		0			0
$731$	187.943	+	1065.88i	0.257104	+	1.45811i
$732$		0			0
$733$	−364.997	+	632.193i	−0.497949	+	0.862474i	−0.999997	−	0.00236619i	$-0.999247\pi$
$733$	−364.997	+	632.193i	−0.497949	+	0.862474i	0.502048	+	0.864840i	$0.332580\pi$
$734$		0			0
$735$	−134.664	−	160.486i	−0.183216	−	0.218348i
$736$		0			0
$737$	−82.8006	+	227.493i	−0.112348	+	0.308674i
$738$		0			0
$739$	−104.267	+	591.327i	−0.141092	+	0.800172i	0.829330	+	0.558758i	$0.188722\pi$
$739$	−104.267	+	591.327i	−0.141092	+	0.800172i	−0.970422	+	0.241413i	$0.922389\pi$
$740$		0			0
$741$	168.414	+	261.134i	0.227279	+	0.352408i
$742$		0			0
$743$	−473.851	−	83.5527i	−0.637753	−	0.112453i	−0.154583	−	0.987980i	$-0.549404\pi$
$743$	−473.851	−	83.5527i	−0.637753	−	0.112453i	−0.483170	+	0.875527i	$0.660515\pi$
$744$		0			0
$745$	430.314	+	156.621i	0.577602	+	0.210230i
$746$		0			0
$747$	−83.4929	+	70.0589i	−0.111771	+	0.0937870i
$748$		0			0
$749$	342.544	+	197.768i	0.457335	+	0.264042i
$750$		0			0
$751$	−1264.86	+	223.029i	−1.68423	+	0.296975i	−0.932144	−	0.362088i	$-0.882064\pi$
$751$	−1264.86	+	223.029i	−1.68423	+	0.296975i	−0.752087	+	0.659063i	$0.770953\pi$
$752$		0			0
$753$	631.759	−	364.746i	0.838989	−	0.484391i
$754$		0			0
$755$	−48.2941	−	132.687i	−0.0639657	−	0.175744i
$756$		0			0
$757$	−861.349	−	722.757i	−1.13784	−	0.954765i	−0.138479	−	0.990365i	$-0.544221\pi$
$757$	−861.349	−	722.757i	−1.13784	−	0.954765i	−0.999366	+	0.0356002i	$0.988666\pi$
$758$		0			0
$759$			214.016i			0.281971i
$760$		0			0
$761$	464.910			0.610920			0.305460	−	0.952205i	$-0.401190\pi$
$761$	464.910			0.610920			0.305460	+	0.952205i	$0.401190\pi$
$762$		0			0
$763$	−404.201	+	481.708i	−0.529753	+	0.631335i
$764$		0			0
$765$	70.6783	−	25.7248i	0.0923900	−	0.0336272i
$766$		0			0
$767$	−205.930	−	356.681i	−0.268487	−	0.465034i
$768$		0			0
$769$	−90.2830	−	512.020i	−0.117403	−	0.665826i	−0.985532	−	0.169488i	$-0.945789\pi$
$769$	−90.2830	−	512.020i	−0.117403	−	0.665826i	0.868129	−	0.496338i	$-0.165322\pi$
$770$		0			0
$771$	−265.733	+	460.263i	−0.344660	+	0.596969i
$772$		0			0
$773$	670.945	+	799.601i	0.867975	+	1.03441i	0.999073	+	0.0430433i	$0.0137053\pi$
$773$	670.945	+	799.601i	0.867975	+	1.03441i	−0.131098	+	0.991369i	$0.541850\pi$
$774$		0			0
$775$	−42.9306	+	117.951i	−0.0553943	+	0.152195i
$776$		0			0
$777$	81.3025	−	461.089i	0.104636	−	0.593423i
$778$		0			0
$779$	347.053	+	43.7248i	0.445511	+	0.0561294i
$780$		0			0
$781$	−450.776	−	79.4841i	−0.577179	−	0.101772i
$782$		0			0
$783$	−1028.09	−	374.194i	−1.31301	−	0.477898i
$784$		0			0
$785$	−100.968	+	84.7221i	−0.128622	+	0.107926i
$786$		0			0
$787$	−265.038	−	153.020i	−0.336770	−	0.194434i	0.322073	−	0.946715i	$-0.395620\pi$
$787$	−265.038	−	153.020i	−0.336770	−	0.194434i	−0.658843	+	0.752281i	$0.728954\pi$
$788$		0			0
$789$	−551.936	+	97.3212i	−0.699538	+	0.123348i
$790$		0			0
$791$	−395.252	+	228.199i	−0.499686	+	0.288494i
$792$		0			0
$793$	−33.8061	−	92.8816i	−0.0426307	−	0.117127i
$794$		0			0
$795$	−217.696	−	182.668i	−0.273831	−	0.229772i
$796$		0			0
$797$			629.223i			0.789489i	0.918791	+	0.394745i	$0.129167\pi$
$797$			629.223i			0.789489i	−0.918791	+	0.394745i	$0.870833\pi$
$798$		0			0
$799$	530.165			0.663535
$800$		0			0
$801$	56.2822	−	67.0746i	0.0702650	−	0.0837385i
$802$		0			0
$803$	366.179	−	133.278i	0.456014	−	0.165976i
$804$		0			0
$805$	38.6382	+	66.9233i	0.0479977	+	0.0831345i
$806$		0			0
$807$	−261.367	−	1482.29i	−0.323875	−	1.83679i
$808$		0			0
$809$	508.334	−	880.460i	0.628349	−	1.08833i	−0.359534	−	0.933132i	$-0.617064\pi$
$809$	508.334	−	880.460i	0.628349	−	1.08833i	0.987883	−	0.155200i	$-0.0496022\pi$
$810$		0			0
$811$	−469.178	−	559.145i	−0.578518	−	0.689451i	0.394838	−	0.918751i	$-0.370801\pi$
$811$	−469.178	−	559.145i	−0.578518	−	0.689451i	−0.973356	+	0.229300i	$0.926356\pi$
$812$		0			0
$813$	382.411	−	1050.66i	0.470370	−	1.29233i
$814$		0			0
$815$	−94.2340	+	534.428i	−0.115625	+	0.655739i
$816$		0			0
$817$	1167.66	+	885.687i	1.42921	+	1.08407i
$818$		0			0
$819$	−54.0162	−	9.52451i	−0.0659538	−	0.0116294i
$820$		0			0
$821$	286.345	+	104.221i	0.348776	+	0.126944i	0.510467	−	0.859897i	$-0.329473\pi$
$821$	286.345	+	104.221i	0.348776	+	0.126944i	−0.161691	+	0.986841i	$0.551695\pi$
$822$		0			0
$823$	−319.242	+	267.876i	−0.387901	+	0.325488i	−0.815795	−	0.578341i	$-0.803700\pi$
$823$	−319.242	+	267.876i	−0.387901	+	0.325488i	0.427894	+	0.903829i	$0.359256\pi$
$824$		0			0
$825$	342.830	+	197.933i	0.415552	+	0.239919i
$826$		0			0
$827$	367.526	−	64.8048i	0.444409	−	0.0783613i	0.0530342	−	0.998593i	$-0.483111\pi$
$827$	367.526	−	64.8048i	0.444409	−	0.0783613i	0.391375	+	0.920231i	$0.372000\pi$
$828$		0			0
$829$	−370.307	+	213.797i	−0.446691	+	0.257897i	−0.706432	−	0.707781i	$-0.749696\pi$
$829$	−370.307	+	213.797i	−0.446691	+	0.257897i	0.259741	+	0.965678i	$0.416363\pi$
$830$		0			0
$831$	−447.021	−	1228.18i	−0.537931	−	1.47795i
$832$		0			0
$833$	374.793	+	314.489i	0.449932	+	0.377538i
$834$		0			0
$835$			130.448i			0.156226i
$836$		0			0
$837$	116.943			0.139716
$838$		0			0
$839$	121.054	−	144.266i	0.144284	−	0.171950i	−0.689063	−	0.724702i	$-0.741978\pi$
$839$	121.054	−	144.266i	0.144284	−	0.171950i	0.833346	+	0.552751i	$0.186422\pi$
$840$		0			0
$841$	1882.86	−	685.306i	2.23884	−	0.814871i
$842$		0			0
$843$	397.707	+	688.848i	0.471775	+	0.817139i
$844$		0			0
$845$	−44.0541	−	249.843i	−0.0521351	−	0.295673i
$846$		0			0
$847$	177.231	−	306.974i	0.209246	−	0.362425i
$848$		0			0
$849$	277.737	+	330.995i	0.327135	+	0.389864i
$850$		0			0
$851$	145.746	−	400.433i	0.171264	−	0.470544i
$852$		0			0
$853$	69.5191	−	394.262i	0.0814995	−	0.462206i	−0.916558	−	0.399902i	$-0.869044\pi$
$853$	69.5191	−	394.262i	0.0814995	−	0.462206i	0.998057	−	0.0623041i	$-0.0198449\pi$
$854$		0			0
$855$	46.5239	−	90.6004i	0.0544139	−	0.105965i
$856$		0			0
$857$	−419.466	−	73.9631i	−0.489458	−	0.0863047i	−0.0765282	−	0.997067i	$-0.524384\pi$
$857$	−419.466	−	73.9631i	−0.489458	−	0.0863047i	−0.412930	+	0.910763i	$0.635495\pi$
$858$		0			0
$859$	−652.245	−	237.398i	−0.759307	−	0.276365i	−0.0667903	−	0.997767i	$-0.521276\pi$
$859$	−652.245	−	237.398i	−0.759307	−	0.276365i	−0.692517	+	0.721402i	$0.743498\pi$
$860$		0			0
$861$	−184.447	+	154.770i	−0.214224	+	0.179756i
$862$		0			0
$863$	1067.21	+	616.154i	1.23663	+	0.713968i	0.968404	−	0.249388i	$-0.0802295\pi$
$863$	1067.21	+	616.154i	1.23663	+	0.713968i	0.268225	+	0.963356i	$0.413563\pi$
$864$		0			0
$865$	−49.1895	+	8.67344i	−0.0568665	+	0.0100271i
$866$		0			0
$867$	277.545	−	160.241i	0.320121	−	0.184822i
$868$		0			0
$869$	29.0515	+	79.8184i	0.0334310	+	0.0918509i
$870$		0			0
$871$	−168.690	−	141.548i	−0.193674	−	0.162511i
$872$		0			0
$873$		−	122.942i		−	0.140827i
$874$		0			0
$875$	305.239			0.348844
$876$		0			0
$877$	−66.5831	+	79.3507i	−0.0759215	+	0.0904797i	−0.802668	−	0.596426i	$-0.796587\pi$
$877$	−66.5831	+	79.3507i	−0.0759215	+	0.0904797i	0.726747	+	0.686906i	$0.241031\pi$
$878$		0			0
$879$	1325.38	−	482.399i	1.50783	−	0.548804i
$880$		0			0
$881$	−786.786	−	1362.75i	−0.893060	−	1.54683i	−0.836187	−	0.548444i	$-0.815220\pi$
$881$	−786.786	−	1362.75i	−0.893060	−	1.54683i	−0.0568725	−	0.998381i	$-0.518113\pi$
$882$		0			0
$883$	40.3265	+	228.703i	0.0456699	+	0.259007i	0.999091	−	0.0426369i	$-0.0135759\pi$
$883$	40.3265	+	228.703i	0.0456699	+	0.259007i	−0.953421	+	0.301644i	$0.902465\pi$
$884$		0			0
$885$	−263.208	+	455.890i	−0.297410	+	0.515130i
$886$		0			0
$887$	1113.80	+	1327.37i	1.25569	+	1.49647i	0.792062	+	0.610440i	$0.209008\pi$
$887$	1113.80	+	1327.37i	1.25569	+	1.49647i	0.463626	+	0.886031i	$0.346548\pi$
$888$		0			0
$889$	284.295	−	781.095i	0.319792	−	0.878622i
$890$		0			0
$891$	89.1128	−	505.384i	0.100014	−	0.567210i
$892$		0			0
$893$	526.577	−	487.943i	0.589672	−	0.546409i
$894$		0			0
$895$	−300.380	−	52.9650i	−0.335620	−	0.0591788i
$896$		0			0
$897$	−182.930	−	66.5811i	−0.203935	−	0.0742264i
$898$		0			0
$899$	−232.926	+	195.448i	−0.259095	+	0.217407i
$900$		0			0
$901$	574.753	+	331.834i	0.637906	+	0.368295i
$902$		0			0
$903$	−993.479	+	175.177i	−1.10020	+	0.193995i
$904$		0			0
$905$	−302.108	+	174.422i	−0.333821	+	0.192732i
$906$		0			0
$907$	−360.985	−	991.799i	−0.397999	−	1.09349i	−0.963257	−	0.268580i	$-0.913446\pi$
$907$	−360.985	−	991.799i	−0.397999	−	1.09349i	0.565258	−	0.824914i	$-0.308777\pi$
$908$		0			0
$909$	338.212	+	283.794i	0.372071	+	0.312205i
$910$		0			0
$911$			765.235i			0.839995i	0.907525	+	0.419997i	$0.137969\pi$
$911$			765.235i			0.839995i	−0.907525	+	0.419997i	$0.862031\pi$
$912$		0			0
$913$	−181.469			−0.198761
$914$		0			0
$915$	−81.2066	+	96.7783i	−0.0887504	+	0.105769i
$916$		0			0
$917$	−572.059	+	208.212i	−0.623838	+	0.227058i
$918$		0			0
$919$	−70.5236	−	122.151i	−0.0767395	−	0.132917i	0.825102	−	0.564984i	$-0.191118\pi$
$919$	−70.5236	−	122.151i	−0.0767395	−	0.132917i	−0.901841	+	0.432067i	$0.857784\pi$
$920$		0			0
$921$	241.300	+	1368.48i	0.261998	+	1.48586i
$922$		0			0
$923$	208.177	−	360.573i	0.225544	−	0.390653i
$924$		0			0
$925$	−506.657	−	603.810i	−0.547737	−	0.652768i
$926$		0			0
$927$	−80.7662	+	221.903i	−0.0871265	+	0.239378i
$928$		0			0
$929$	76.8896	−	436.063i	0.0827660	−	0.469389i	−0.915050	−	0.403340i	$-0.867849\pi$
$929$	76.8896	−	436.063i	0.0827660	−	0.469389i	0.997816	−	0.0660497i	$-0.0210396\pi$
$930$		0			0
$931$	661.701	−	32.5848i	0.710742	−	0.0349998i
$932$		0			0
$933$	−1620.51	−	285.739i	−1.73688	−	0.306258i
$934$		0			0
$935$	117.677	+	42.8311i	0.125858	+	0.0458086i
$936$		0			0
$937$	−1288.21	+	1080.94i	−1.37482	+	1.15361i	−0.403739	+	0.914874i	$0.632290\pi$
$937$	−1288.21	+	1080.94i	−1.37482	+	1.15361i	−0.971084	+	0.238739i	$0.923266\pi$
$938$		0			0
$939$	−817.456	−	471.958i	−0.870560	−	0.502618i
$940$		0			0
$941$	−1623.23	+	286.219i	−1.72501	+	0.304165i	−0.946316	−	0.323243i	$-0.895227\pi$
$941$	−1623.23	+	286.219i	−1.72501	+	0.304165i	−0.778690	+	0.627408i	$0.784116\pi$
$942$		0			0
$943$	−189.784	+	109.572i	−0.201255	+	0.116195i
$944$		0			0
$945$	−45.5468	−	125.139i	−0.0481977	−	0.132422i
$946$		0			0
$947$	559.654	+	469.605i	0.590975	+	0.495887i	0.888531	−	0.458817i	$-0.151727\pi$
$947$	559.654	+	469.605i	0.590975	+	0.495887i	−0.297555	+	0.954705i	$0.596171\pi$
$948$		0			0
$949$			354.455i			0.373504i
$950$		0			0
$951$	942.597			0.991164
$952$		0			0
$953$	817.829	−	974.651i	0.858163	−	1.02272i	−0.141301	−	0.989967i	$-0.545128\pi$
$953$	817.829	−	974.651i	0.858163	−	1.02272i	0.999464	−	0.0327519i	$-0.0104271\pi$
$954$		0			0
$955$	57.7206	−	21.0086i	0.0604404	−	0.0219985i
$956$		0			0
$957$	479.477	+	830.479i	0.501021	+	0.867794i
$958$		0			0
$959$	−115.269	−	653.721i	−0.120197	−	0.681670i
$960$		0			0
$961$	−464.250	+	804.104i	−0.483090	+	0.836737i
$962$		0			0
$963$	209.928	+	250.182i	0.217993	+	0.259794i
$964$		0			0
$965$	−23.4562	+	64.4454i	−0.0243070	+	0.0667828i
$966$		0			0
$967$	−128.633	+	729.513i	−0.133023	+	0.754409i	0.843194	+	0.537610i	$0.180673\pi$
$967$	−128.633	+	729.513i	−0.133023	+	0.754409i	−0.976216	+	0.216799i	$0.930438\pi$
$968$		0			0
$969$	−273.977	+	886.126i	−0.282742	+	0.914475i
$970$		0			0
$971$	−1006.39	−	177.454i	−1.03645	−	0.182754i	−0.370563	−	0.928807i	$-0.620835\pi$
$971$	−1006.39	−	177.454i	−1.03645	−	0.182754i	−0.665886	+	0.746053i	$0.731946\pi$
$972$		0			0
$973$	−363.119	−	132.164i	−0.373195	−	0.135832i
$974$		0			0
$975$	−275.839	+	231.456i	−0.282912	+	0.237391i
$976$		0			0
$977$	−1153.54	−	665.998i	−1.18070	−	0.681677i	−0.224523	−	0.974469i	$-0.572082\pi$
$977$	−1153.54	−	665.998i	−1.18070	−	0.681677i	−0.956176	+	0.292792i	$0.905416\pi$
$978$		0			0
$979$	143.569	−	25.3152i	0.146649	−	0.0258582i
$980$		0			0
$981$	−449.653	+	259.607i	−0.458362	+	0.264635i
$982$		0			0
$983$	397.788	+	1092.91i	0.404667	+	1.11181i	0.959955	+	0.280156i	$0.0903861\pi$
$983$	397.788	+	1092.91i	0.404667	+	1.11181i	−0.555287	+	0.831659i	$0.687392\pi$
$984$		0			0
$985$	455.427	+	382.148i	0.462362	+	0.387968i
$986$		0			0
$987$			494.155i			0.500663i
$988$		0			0
$989$	−918.159			−0.928371
$990$		0			0
$991$	146.942	−	175.119i	0.148277	−	0.176709i	−0.686794	−	0.726852i	$-0.740982\pi$
$991$	146.942	−	175.119i	0.148277	−	0.176709i	0.835070	+	0.550143i	$0.185427\pi$
$992$		0			0
$993$	894.836	−	325.694i	0.901144	−	0.327990i
$994$		0			0
$995$	−64.5916	−	111.876i	−0.0649162	−	0.112438i
$996$		0			0
$997$	−78.4445	−	444.881i	−0.0786805	−	0.446219i	−0.998542	−	0.0539765i	$-0.982810\pi$
$997$	−78.4445	−	444.881i	−0.0786805	−	0.446219i	0.919862	−	0.392243i	$-0.128301\pi$
$998$		0			0
$999$	−367.176	+	635.967i	−0.367543	+	0.636604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.j.a.21.3	✓	18
4.3	odd	2		304.3.z.b.97.1		18
19.3	odd	18		1444.3.c.c.721.15		18
19.10	odd	18	inner	76.3.j.a.29.3	yes	18
19.16	even	9		1444.3.c.c.721.4		18
76.67	even	18		304.3.z.b.257.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.j.a.21.3	✓	18	1.1	even	1	trivial
76.3.j.a.29.3	yes	18	19.10	odd	18	inner
304.3.z.b.97.1		18	4.3	odd	2
304.3.z.b.257.1		18	76.67	even	18
1444.3.c.c.721.4		18	19.16	even	9
1444.3.c.c.721.15		18	19.3	odd	18

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.23630 - 2.66512i) q^{3} +(1.62283 - 0.590661i) q^{5} +(-1.87959 - 3.25555i) q^{7} +(-0.538989 - 3.05676i) q^{9} +O(q^{10})\)	\(q+(2.23630 - 2.66512i) q^{3} +(1.62283 - 0.590661i) q^{5} +(-1.87959 - 3.25555i) q^{7} +(-0.538989 - 3.05676i) q^{9} +(2.58396 - 4.47556i) q^{11} +(3.02160 + 3.60100i) q^{13} +(2.05495 - 5.64593i) q^{15} +(-2.43654 + 13.8183i) q^{17} +(10.2978 + 15.9673i) q^{19} +(-12.8798 - 2.27105i) q^{21} +(-11.1854 - 4.07116i) q^{23} +(-16.8664 + 14.1526i) q^{25} +(17.7647 + 10.2564i) q^{27} +(-52.5255 + 9.26166i) q^{29} +(4.93716 - 2.85047i) q^{31} +(-6.14938 - 16.8953i) q^{33} +(-4.97317 - 4.17299i) q^{35} +35.7995i q^{37} +16.3543 q^{39} +(11.8339 - 14.1031i) q^{41} +(72.4831 - 26.3817i) q^{43} +(-2.68020 - 4.64223i) q^{45} +(-6.56111 - 37.2099i) q^{47} +(17.4343 - 30.1971i) q^{49} +(31.3787 + 37.3956i) q^{51} +(16.1770 - 44.4460i) q^{53} +(1.54979 - 8.78930i) q^{55} +(65.5838 + 8.26284i) q^{57} +(-86.2842 - 15.2142i) q^{59} +(-19.7588 - 7.19161i) q^{61} +(-8.93835 + 7.50016i) q^{63} +(7.03050 + 4.05906i) q^{65} +(-46.1336 + 8.13459i) q^{67} +(-35.8641 + 20.7062i) q^{69} +(-30.2932 - 83.2298i) q^{71} +(57.7624 + 48.4684i) q^{73} +76.6006i q^{75} -19.4272 q^{77} +(-10.5650 + 12.5908i) q^{79} +(93.3124 - 33.9629i) q^{81} +(-17.5572 - 30.4100i) q^{83} +(4.20785 + 23.8639i) q^{85} +(-92.7794 + 160.699i) q^{87} +(18.1327 + 21.6097i) q^{89} +(6.04386 - 16.6054i) q^{91} +(3.44413 - 19.5326i) q^{93} +(26.1428 + 19.8297i) q^{95} +(39.0070 + 6.87798i) q^{97} +(-15.0734 - 5.48628i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9}+O(q^{10}) \) 18 * q - 6 * q^3 + 9 * q^7 + 6 * q^9	\( 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9} - 15 q^{11} + 51 q^{13} + 21 q^{15} - 45 q^{17} + 30 q^{19} - 63 q^{21} + 48 q^{23} - 54 q^{25} - 198 q^{27} - 39 q^{29} - 108 q^{31} - 105 q^{33} + 51 q^{35} + 48 q^{39} + 54 q^{41} + 75 q^{43} + 288 q^{45} + 339 q^{47} - 24 q^{49} + 360 q^{51} + 69 q^{53} - 51 q^{55} + 510 q^{57} - 483 q^{59} - 36 q^{61} - 267 q^{63} - 585 q^{65} - 87 q^{67} - 351 q^{69} - 234 q^{71} - 132 q^{73} + 108 q^{77} + 363 q^{79} + 258 q^{81} + 279 q^{83} + 666 q^{85} + 600 q^{89} + 270 q^{91} - 456 q^{93} - 39 q^{95} - 801 q^{97} - 267 q^{99}+O(q^{100}) \) 18 * q - 6 * q^3 + 9 * q^7 + 6 * q^9 - 15 * q^11 + 51 * q^13 + 21 * q^15 - 45 * q^17 + 30 * q^19 - 63 * q^21 + 48 * q^23 - 54 * q^25 - 198 * q^27 - 39 * q^29 - 108 * q^31 - 105 * q^33 + 51 * q^35 + 48 * q^39 + 54 * q^41 + 75 * q^43 + 288 * q^45 + 339 * q^47 - 24 * q^49 + 360 * q^51 + 69 * q^53 - 51 * q^55 + 510 * q^57 - 483 * q^59 - 36 * q^61 - 267 * q^63 - 585 * q^65 - 87 * q^67 - 351 * q^69 - 234 * q^71 - 132 * q^73 + 108 * q^77 + 363 * q^79 + 258 * q^81 + 279 * q^83 + 666 * q^85 + 600 * q^89 + 270 * q^91 - 456 * q^93 - 39 * q^95 - 801 * q^97 - 267 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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