LMFDB - Embedded newform 76.3.j.a.13.3

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			13.3
Root			$-4.19502i$ of defining polynomial
Character	$\chi$	$=$	76.13
Dual form			76.3.j.a.41.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.87447 - 5.15008i) q^{3} +(0.722564 + 4.09786i) q^{5} +(2.33853 - 4.05046i) q^{7} +(-16.1152 - 13.5223i) q^{9} +O(q^{10})$	\(q+(1.87447 - 5.15008i) q^{3} +(0.722564 + 4.09786i) q^{5} +(2.33853 - 4.05046i) q^{7} +(-16.1152 - 13.5223i) q^{9} +(-4.49006 - 7.77701i) q^{11} +(7.53942 + 20.7144i) q^{13} +(22.4587 + 3.96008i) q^{15} +(2.56611 - 2.15322i) q^{17} +(15.9032 + 10.3965i) q^{19} +(-16.4766 - 19.6361i) q^{21} +(-6.25588 + 35.4788i) q^{23} +(7.22192 - 2.62856i) q^{25} +(-57.1314 + 32.9848i) q^{27} +(-1.48437 + 1.76901i) q^{29} +(-4.89112 - 2.82389i) q^{31} +(-48.4687 + 8.54634i) q^{33} +(18.2880 + 6.65627i) q^{35} -62.7609i q^{37} +120.813 q^{39} +(-23.6361 + 64.9396i) q^{41} +(-4.30442 - 24.4116i) q^{43} +(43.7682 - 75.8088i) q^{45} +(-3.19164 - 2.67810i) q^{47} +(13.5625 + 23.4910i) q^{49} +(-6.27916 - 17.2518i) q^{51} +(-58.6464 - 10.3409i) q^{53} +(28.6248 - 24.0190i) q^{55} +(83.3530 - 62.4149i) q^{57} +(-60.9767 - 72.6691i) q^{59} +(-0.775508 + 4.39813i) q^{61} +(-92.4575 + 33.6518i) q^{63} +(-79.4371 + 45.8630i) q^{65} +(-22.5407 + 26.8630i) q^{67} +(170.992 + 98.7224i) q^{69} +(-8.23814 + 1.45261i) q^{71} +(-58.9706 - 21.4635i) q^{73} -42.1206i q^{75} -42.0006 q^{77} +(24.3697 - 66.9552i) q^{79} +(29.9058 + 169.604i) q^{81} +(24.7388 - 42.8489i) q^{83} +(10.6778 + 8.95974i) q^{85} +(6.32810 + 10.9606i) q^{87} +(-0.257321 - 0.706985i) q^{89} +(101.534 + 17.9032i) q^{91} +(-23.7116 + 19.8964i) q^{93} +(-31.1124 + 72.6814i) q^{95} +(24.0440 + 28.6545i) q^{97} +(-32.8046 + 186.044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$

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
$3$	1.87447	−	5.15008i	0.624825	−	1.71669i	−0.0700324	−	0.997545i	$-0.522310\pi$
$3$	1.87447	−	5.15008i	0.624825	−	1.71669i	0.694857	−	0.719148i	$-0.255468\pi$
$4$		0			0
$5$	0.722564	+	4.09786i	0.144513	+	0.819573i	0.967757	+	0.251886i	$0.0810507\pi$
$5$	0.722564	+	4.09786i	0.144513	+	0.819573i	−0.823244	+	0.567687i	$0.807838\pi$
$6$		0			0
$7$	2.33853	−	4.05046i	0.334076	−	0.578637i	−0.649231	−	0.760591i	$-0.724909\pi$
$7$	2.33853	−	4.05046i	0.334076	−	0.578637i	0.983307	+	0.181955i	$0.0582424\pi$
$8$		0			0
$9$	−16.1152	−	13.5223i	−1.79058	−	1.50248i
$10$		0			0
$11$	−4.49006	−	7.77701i	−0.408187	−	0.707001i	0.586499	−	0.809950i	$-0.300506\pi$
$11$	−4.49006	−	7.77701i	−0.408187	−	0.707001i	−0.994687	+	0.102949i	$0.967172\pi$
$12$		0			0
$13$	7.53942	+	20.7144i	0.579956	+	1.59342i	0.788254	+	0.615350i	$0.210985\pi$
$13$	7.53942	+	20.7144i	0.579956	+	1.59342i	−0.208298	+	0.978065i	$0.566793\pi$
$14$		0			0
$15$	22.4587	+	3.96008i	1.49725	+	0.264006i
$16$		0			0
$17$	2.56611	−	2.15322i	0.150948	−	0.126660i	−0.564186	−	0.825648i	$-0.690810\pi$
$17$	2.56611	−	2.15322i	0.150948	−	0.126660i	0.715134	+	0.698987i	$0.246366\pi$
$18$		0			0
$19$	15.9032	+	10.3965i	0.837012	+	0.547184i
$19$	15.9032	+	10.3965i	0.837012	+	0.547184i
$20$		0			0
$21$	−16.4766	−	19.6361i	−0.784602	−	0.935052i
$22$		0			0
$23$	−6.25588	+	35.4788i	−0.271995	+	1.54256i	0.476355	+	0.879253i	$0.341958\pi$
$23$	−6.25588	+	35.4788i	−0.271995	+	1.54256i	−0.748349	+	0.663305i	$0.769153\pi$
$24$		0			0
$25$	7.22192	−	2.62856i	0.288877	−	0.105143i
$26$		0			0
$27$	−57.1314	+	32.9848i	−2.11598	+	1.22166i
$28$		0			0
$29$	−1.48437	+	1.76901i	−0.0511853	+	0.0610002i	−0.791030	−	0.611778i	$-0.790455\pi$
$29$	−1.48437	+	1.76901i	−0.0511853	+	0.0610002i	0.739844	+	0.672778i	$0.234899\pi$
$30$		0			0
$31$	−4.89112	−	2.82389i	−0.157778	−	0.0910933i	0.419032	−	0.907971i	$-0.362369\pi$
$31$	−4.89112	−	2.82389i	−0.157778	−	0.0910933i	−0.576810	+	0.816878i	$0.695703\pi$
$32$		0			0
$33$	−48.4687	+	8.54634i	−1.46875	+	0.258980i
$34$		0			0
$35$	18.2880	+	6.65627i	0.522513	+	0.190179i
$36$		0			0
$37$		−	62.7609i		−	1.69624i	−0.529804	−	0.848120i	$-0.677735\pi$
$37$		−	62.7609i		−	1.69624i	0.529804	−	0.848120i	$-0.322265\pi$
$38$		0			0
$39$	120.813			3.09777
$40$		0			0
$41$	−23.6361	+	64.9396i	−0.576490	+	1.58389i	0.217564	+	0.976046i	$0.430189\pi$
$41$	−23.6361	+	64.9396i	−0.576490	+	1.58389i	−0.794054	+	0.607847i	$0.792033\pi$
$42$		0			0
$43$	−4.30442	−	24.4116i	−0.100103	−	0.567711i	−0.993064	−	0.117577i	$-0.962487\pi$
$43$	−4.30442	−	24.4116i	−0.100103	−	0.567711i	0.892961	−	0.450134i	$-0.148624\pi$
$44$		0			0
$45$	43.7682	−	75.8088i	0.972627	−	1.68464i
$46$		0			0
$47$	−3.19164	−	2.67810i	−0.0679072	−	0.0569809i	0.608202	−	0.793782i	$-0.291891\pi$
$47$	−3.19164	−	2.67810i	−0.0679072	−	0.0569809i	−0.676109	+	0.736801i	$0.736335\pi$
$48$		0			0
$49$	13.5625	+	23.4910i	0.276786	+	0.479408i
$50$		0			0
$51$	−6.27916	−	17.2518i	−0.123121	−	0.338271i
$52$		0			0
$53$	−58.6464	−	10.3409i	−1.10653	−	0.195112i	−0.409613	−	0.912259i	$-0.634336\pi$
$53$	−58.6464	−	10.3409i	−1.10653	−	0.195112i	−0.696922	+	0.717147i	$0.745447\pi$
$54$		0			0
$55$	28.6248	−	24.0190i	0.520451	−	0.436710i
$56$		0			0
$57$	83.3530	−	62.4149i	1.46233	−	1.09500i
$58$		0			0
$59$	−60.9767	−	72.6691i	−1.03350	−	1.23168i	−0.972344	−	0.233552i	$-0.924965\pi$
$59$	−60.9767	−	72.6691i	−1.03350	−	1.23168i	−0.0611584	−	0.998128i	$-0.519479\pi$
$60$		0			0
$61$	−0.775508	+	4.39813i	−0.0127133	+	0.0721004i	−0.990504	−	0.137482i	$-0.956099\pi$
$61$	−0.775508	+	4.39813i	−0.0127133	+	0.0721004i	0.977791	+	0.209582i	$0.0672103\pi$
$62$		0			0
$63$	−92.4575	+	33.6518i	−1.46758	+	0.534155i
$64$		0			0
$65$	−79.4371	+	45.8630i	−1.22211	+	0.705585i
$66$		0			0
$67$	−22.5407	+	26.8630i	−0.336428	+	0.400940i	−0.907562	−	0.419917i	$-0.862059\pi$
$67$	−22.5407	+	26.8630i	−0.336428	+	0.400940i	0.571134	+	0.820857i	$0.306504\pi$
$68$		0			0
$69$	170.992	+	98.7224i	2.47815	+	1.43076i
$70$		0			0
$71$	−8.23814	+	1.45261i	−0.116030	+	0.0204592i	−0.231362	−	0.972868i	$-0.574318\pi$
$71$	−8.23814	+	1.45261i	−0.116030	+	0.0204592i	0.115332	+	0.993327i	$0.463207\pi$
$72$		0			0
$73$	−58.9706	−	21.4635i	−0.807817	−	0.294021i	−0.0950949	−	0.995468i	$-0.530315\pi$
$73$	−58.9706	−	21.4635i	−0.807817	−	0.294021i	−0.712722	+	0.701447i	$0.752538\pi$
$74$		0			0
$75$		−	42.1206i		−	0.561608i
$76$		0			0
$77$	−42.0006			−0.545462
$78$		0			0
$79$	24.3697	−	66.9552i	0.308477	−	0.847534i	−0.684477	−	0.729034i	$-0.739969\pi$
$79$	24.3697	−	66.9552i	0.308477	−	0.847534i	0.992954	−	0.118499i	$-0.0378084\pi$
$80$		0			0
$81$	29.9058	+	169.604i	0.369208	+	2.09388i
$82$		0			0
$83$	24.7388	−	42.8489i	0.298058	−	0.516251i	−0.677634	−	0.735400i	$-0.736994\pi$
$83$	24.7388	−	42.8489i	0.298058	−	0.516251i	0.975692	+	0.219148i	$0.0703278\pi$
$84$		0			0
$85$	10.6778	+	8.95974i	0.125621	+	0.105409i
$86$		0			0
$87$	6.32810	+	10.9606i	0.0727368	+	0.125984i
$88$		0			0
$89$	−0.257321	−	0.706985i	−0.00289125	−	0.00794365i	0.938239	−	0.345989i	$-0.112457\pi$
$89$	−0.257321	−	0.706985i	−0.00289125	−	0.00794365i	−0.941130	+	0.338045i	$0.890234\pi$
$90$		0			0
$91$	101.534	+	17.9032i	1.11576	+	0.196738i
$92$		0			0
$93$	−23.7116	+	19.8964i	−0.254963	+	0.213939i
$94$		0			0
$95$	−31.1124	+	72.6814i	−0.327499	+	0.765068i
$96$		0			0
$97$	24.0440	+	28.6545i	0.247876	+	0.295407i	0.875608	−	0.483022i	$-0.160461\pi$
$97$	24.0440	+	28.6545i	0.247876	+	0.295407i	−0.627732	+	0.778430i	$0.716017\pi$
$98$		0			0
$99$	−32.8046	+	186.044i	−0.331360	+	1.87924i
$100$		0			0
$101$	22.8980	−	8.33417i	0.226712	−	0.0825166i	−0.226166	−	0.974089i	$-0.572619\pi$
$101$	22.8980	−	8.33417i	0.226712	−	0.0825166i	0.452879	+	0.891572i	$0.350397\pi$
$102$		0			0
$103$	−0.515749	+	0.297768i	−0.00500727	+	0.00289095i	−0.502502	−	0.864576i	$-0.667587\pi$
$103$	−0.515749	+	0.297768i	−0.00500727	+	0.00289095i	0.497494	+	0.867467i	$0.334254\pi$
$104$		0			0
$105$	68.5606	−	81.7074i	0.652959	−	0.778166i
$106$		0			0
$107$	−100.858	−	58.2307i	−0.942603	−	0.544212i	−0.0518275	−	0.998656i	$-0.516505\pi$
$107$	−100.858	−	58.2307i	−0.942603	−	0.544212i	−0.890775	+	0.454444i	$0.849838\pi$
$108$		0			0
$109$	−70.3529	+	12.4051i	−0.645440	+	0.113808i	−0.486780	−	0.873525i	$-0.661829\pi$
$109$	−70.3529	+	12.4051i	−0.645440	+	0.113808i	−0.158660	+	0.987333i	$0.550717\pi$
$110$		0			0
$111$	−323.223	−	117.644i	−2.91192	−	1.05985i
$112$		0			0
$113$			178.424i			1.57898i	0.613767	+	0.789488i	$0.289654\pi$
$113$			178.424i			1.57898i	−0.613767	+	0.789488i	$0.710346\pi$
$114$		0			0
$115$	−149.908			−1.30355
$116$		0			0
$117$	158.606	−	435.768i	1.35561	−	3.72451i
$118$		0			0
$119$	−2.72060	−	15.4293i	−0.0228622	−	0.129658i
$120$		0			0
$121$	20.1787	−	34.9506i	0.166766	−	0.288848i
$122$		0			0
$123$	290.139	+	243.455i	2.35885	+	1.97931i
$124$		0			0
$125$	68.0033	+	117.785i	0.544026	+	0.942281i
$126$		0			0
$127$	22.0360	+	60.5435i	0.173512	+	0.476720i	0.995715	−	0.0924739i	$-0.0294775\pi$
$127$	22.0360	+	60.5435i	0.173512	+	0.476720i	−0.822203	+	0.569194i	$0.807255\pi$
$128$		0			0
$129$	−133.790	−	23.5908i	−1.03713	−	0.182874i
$130$		0			0
$131$	116.297	−	97.5848i	0.887764	−	0.744922i	−0.0799966	−	0.996795i	$-0.525491\pi$
$131$	116.297	−	97.5848i	0.887764	−	0.744922i	0.967760	+	0.251873i	$0.0810465\pi$
$132$		0			0
$133$	79.3008	−	40.1028i	0.596247	−	0.301525i
$134$		0			0
$135$	−176.449	−	210.283i	−1.30703	−	1.55765i
$136$		0			0
$137$	20.0100	−	113.482i	0.146059	−	0.828339i	−0.820453	−	0.571714i	$-0.806279\pi$
$137$	20.0100	−	113.482i	0.146059	−	0.828339i	0.966511	−	0.256625i	$-0.0826104\pi$
$138$		0			0
$139$	177.954	−	64.7701i	1.28025	−	0.465972i	0.389733	−	0.920928i	$-0.372567\pi$
$139$	177.954	−	64.7701i	1.28025	−	0.465972i	0.890514	+	0.454956i	$0.150345\pi$
$140$		0			0
$141$	−19.7751	+	11.4171i	−0.140249	+	0.0809727i
$142$		0			0
$143$	127.244	−	151.643i	0.889816	−	1.06044i
$144$		0			0
$145$	−8.32171	−	4.80454i	−0.0573911	−	0.0331348i
$146$		0			0
$147$	146.403	−	25.8148i	0.995939	−	0.175611i
$148$		0			0
$149$	49.2334	+	17.9195i	0.330425	+	0.120265i	0.501905	−	0.864923i	$-0.332633\pi$
$149$	49.2334	+	17.9195i	0.330425	+	0.120265i	−0.171480	+	0.985188i	$0.554855\pi$
$150$		0			0
$151$			141.246i			0.935403i	0.883887	+	0.467701i	$0.154918\pi$
$151$			141.246i			0.935403i	−0.883887	+	0.467701i	$0.845082\pi$
$152$		0			0
$153$	−70.4700			−0.460589
$154$		0			0
$155$	8.03778	−	22.0836i	0.0518566	−	0.142475i
$156$		0			0
$157$	−3.96829	−	22.5053i	−0.0252757	−	0.143346i	0.969558	−	0.244861i	$-0.0787422\pi$
$157$	−3.96829	−	22.5053i	−0.0252757	−	0.143346i	−0.994834	+	0.101515i	$0.967631\pi$
$158$		0			0
$159$	−163.188	+	282.649i	−1.02634	+	1.77767i
$160$		0			0
$161$	129.076	+	108.308i	0.801714	+	0.672718i
$162$		0			0
$163$	15.5651	+	26.9596i	0.0954915	+	0.165396i	0.909814	−	0.415017i	$-0.136224\pi$
$163$	15.5651	+	26.9596i	0.0954915	+	0.165396i	−0.814322	+	0.580413i	$0.802891\pi$
$164$		0			0
$165$	−70.0435	−	192.443i	−0.424506	−	1.16632i
$166$		0			0
$167$	−137.657	−	24.2727i	−0.824295	−	0.145345i	−0.254438	−	0.967089i	$-0.581890\pi$
$167$	−137.657	−	24.2727i	−0.824295	−	0.145345i	−0.569857	+	0.821744i	$0.693001\pi$
$168$		0			0
$169$	−242.782	+	203.718i	−1.43658	+	1.20543i
$170$		0			0
$171$	−115.700	−	382.590i	−0.676607	−	2.23737i
$172$		0			0
$173$	84.3144	+	100.482i	0.487366	+	0.580821i	0.952546	−	0.304396i	$-0.0984546\pi$
$173$	84.3144	+	100.482i	0.487366	+	0.580821i	−0.465179	+	0.885216i	$0.654010\pi$
$174$		0			0
$175$	6.24181	−	35.3990i	0.0356675	−	0.202280i
$176$		0			0
$177$	−488.551	+	177.818i	−2.76017	+	1.00462i
$178$		0			0
$179$	−166.677	+	96.2309i	−0.931155	+	0.537603i	−0.887177	−	0.461430i	$-0.847337\pi$
$179$	−166.677	+	96.2309i	−0.931155	+	0.537603i	−0.0439785	+	0.999032i	$0.514003\pi$
$180$		0			0
$181$	82.1346	−	97.8842i	0.453782	−	0.540797i	−0.489844	−	0.871810i	$-0.662946\pi$
$181$	82.1346	−	97.8842i	0.453782	−	0.540797i	0.943626	+	0.331014i	$0.107391\pi$
$182$		0			0
$183$	21.1970	+	12.2381i	0.115831	+	0.0668749i
$184$		0			0
$185$	257.186	−	45.3487i	1.39019	−	0.245128i
$186$		0			0
$187$	−28.2677	−	10.2886i	−0.151164	−	0.0550192i
$188$		0			0
$189$			308.544i			1.63251i
$190$		0			0
$191$	215.217			1.12679			0.563396	−	0.826187i	$-0.309494\pi$
$191$	215.217			1.12679			0.563396	+	0.826187i	$0.309494\pi$
$192$		0			0
$193$	41.0419	−	112.762i	0.212652	−	0.584257i	−0.786805	−	0.617202i	$-0.788266\pi$
$193$	41.0419	−	112.762i	0.212652	−	0.584257i	0.999457	+	0.0329447i	$0.0104885\pi$
$194$		0			0
$195$	87.2953	+	495.076i	0.447668	+	2.53885i
$196$		0			0
$197$	−55.7053	+	96.4844i	−0.282768	+	0.489769i	−0.972065	−	0.234710i	$-0.924586\pi$
$197$	−55.7053	+	96.4844i	−0.282768	+	0.489769i	0.689297	+	0.724478i	$0.257919\pi$
$198$		0			0
$199$	237.350	+	199.160i	1.19271	+	1.00081i	0.999808	+	0.0195891i	$0.00623581\pi$
$199$	237.350	+	199.160i	1.19271	+	1.00081i	0.192906	+	0.981217i	$0.438209\pi$
$200$		0			0
$201$	96.0943	+	166.440i	0.478081	+	0.828061i
$202$		0			0
$203$	3.69403	+	10.1493i	0.0181972	+	0.0499964i
$204$		0			0
$205$	−283.192	−	49.9344i	−1.38143	−	0.243583i
$206$		0			0
$207$	580.570	−	487.156i	2.80469	−	2.35341i
$208$		0			0
$209$	9.44728	−	170.361i	0.0452023	−	0.815122i
$210$		0			0
$211$	−49.2423	−	58.6847i	−0.233376	−	0.278127i	0.636628	−	0.771171i	$-0.280329\pi$
$211$	−49.2423	−	58.6847i	−0.233376	−	0.278127i	−0.870004	+	0.493044i	$0.835884\pi$
$212$		0			0
$213$	−7.96115	+	45.1499i	−0.0373763	+	0.211971i
$214$		0			0
$215$	96.9252	−	35.2779i	0.450815	−	0.164083i
$216$		0			0
$217$	−22.8761	+	13.2075i	−0.105420	+	0.0608642i
$218$		0			0
$219$	−221.078	+	263.470i	−1.00949	+	1.20306i
$220$		0			0
$221$	63.9498	+	36.9214i	0.289365	+	0.167065i
$222$		0			0
$223$	−249.888	+	44.0620i	−1.12057	+	0.197587i	−0.703092	−	0.711099i	$-0.748198\pi$
$223$	−249.888	+	44.0620i	−1.12057	+	0.197587i	−0.417481	+	0.908686i	$0.637087\pi$
$224$		0			0
$225$	−151.927	−	55.2970i	−0.675232	−	0.245764i
$226$		0			0
$227$		−	363.124i		−	1.59967i	−0.600222	−	0.799833i	$-0.704921\pi$
$227$		−	363.124i		−	1.59967i	0.600222	−	0.799833i	$-0.295079\pi$
$228$		0			0
$229$	−71.8239			−0.313641			−0.156821	−	0.987627i	$-0.550124\pi$
$229$	−71.8239			−0.313641			−0.156821	+	0.987627i	$0.550124\pi$
$230$		0			0
$231$	−78.7291	+	216.306i	−0.340818	+	0.936391i
$232$		0			0
$233$	−56.5012	−	320.434i	−0.242495	−	1.37526i	−0.826240	−	0.563318i	$-0.809524\pi$
$233$	−56.5012	−	320.434i	−0.242495	−	1.37526i	0.583745	−	0.811937i	$-0.301587\pi$
$234$		0			0
$235$	8.66834	−	15.0140i	0.0368865	−	0.0638894i
$236$		0			0
$237$	−299.144	−	251.012i	−1.26221	−	1.05912i
$238$		0			0
$239$	−19.1218	−	33.1199i	−0.0800076	−	0.138577i	0.823245	−	0.567686i	$-0.192161\pi$
$239$	−19.1218	−	33.1199i	−0.0800076	−	0.138577i	−0.903253	+	0.429109i	$0.858828\pi$
$240$		0			0
$241$	75.2472	+	206.740i	0.312229	+	0.857842i	0.992206	+	0.124608i	$0.0397675\pi$
$241$	75.2472	+	206.740i	0.312229	+	0.857842i	−0.679977	+	0.733233i	$0.738010\pi$
$242$		0			0
$243$	344.826	+	60.8021i	1.41904	+	0.250214i
$244$		0			0
$245$	−86.4631	+	72.5512i	−0.352911	+	0.296127i
$246$		0			0
$247$	−95.4561	+	407.809i	−0.386462	+	1.65105i
$248$		0			0
$249$	−174.303	−	207.726i	−0.700011	−	0.834241i
$250$		0			0
$251$	24.6657	−	139.886i	0.0982698	−	0.557316i	−0.895426	−	0.445210i	$-0.853129\pi$
$251$	24.6657	−	139.886i	0.0982698	−	0.557316i	0.993696	−	0.112106i	$-0.0357597\pi$
$252$		0			0
$253$	304.009	−	110.650i	1.20162	−	0.437352i
$254$		0			0
$255$	66.1586	−	38.1967i	0.259446	−	0.149791i
$256$		0			0
$257$	188.654	−	224.829i	0.734062	−	0.874821i	−0.261854	−	0.965108i	$-0.584334\pi$
$257$	188.654	−	224.829i	0.734062	−	0.874821i	0.995916	+	0.0902863i	$0.0287782\pi$
$258$		0			0
$259$	−254.210	−	146.768i	−0.981506	−	0.566673i
$260$		0			0
$261$	47.8421	−	8.43585i	0.183303	−	0.0323212i
$262$		0			0
$263$	72.7607	+	26.4827i	0.276657	+	0.100695i	0.476622	−	0.879108i	$-0.341861\pi$
$263$	72.7607	+	26.4827i	0.276657	+	0.100695i	−0.199966	+	0.979803i	$0.564083\pi$
$264$		0			0
$265$		−	247.797i		−	0.935082i
$266$		0			0
$267$	−4.12337			−0.0154433
$268$		0			0
$269$	22.7680	−	62.5545i	0.0846393	−	0.232545i	−0.890152	−	0.455664i	$-0.849402\pi$
$269$	22.7680	−	62.5545i	0.0846393	−	0.232545i	0.974791	+	0.223120i	$0.0716240\pi$
$270$		0			0
$271$	8.86168	+	50.2571i	0.0326999	+	0.185450i	0.996783	−	0.0801515i	$-0.0255404\pi$
$271$	8.86168	+	50.2571i	0.0326999	+	0.185450i	−0.964083	+	0.265602i	$0.914429\pi$
$272$		0			0
$273$	282.526	−	489.349i	1.03489	−	1.79249i
$274$		0			0
$275$	−52.8692	−	44.3625i	−0.192252	−	0.161318i
$276$		0			0
$277$	−178.941	−	309.935i	−0.645997	−	1.11890i	−0.984070	−	0.177780i	$-0.943108\pi$
$277$	−178.941	−	309.935i	−0.645997	−	1.11890i	0.338073	−	0.941120i	$-0.390225\pi$
$278$		0			0
$279$	40.6362	+	111.647i	0.145649	+	0.400168i
$280$		0			0
$281$	347.696	+	61.3081i	1.23735	+	0.218178i	0.753780	−	0.657127i	$-0.228228\pi$
$281$	347.696	+	61.3081i	1.23735	+	0.218178i	0.483571	+	0.875305i	$0.339339\pi$
$282$		0			0
$283$	−250.331	+	210.053i	−0.884563	+	0.742236i	−0.967112	−	0.254351i	$-0.918138\pi$
$283$	−250.331	+	210.053i	−0.884563	+	0.742236i	0.0825494	+	0.996587i	$0.473694\pi$
$284$		0			0
$285$	315.996	+	296.471i	1.10876	+	1.04025i
$286$		0			0
$287$	207.761	+	247.600i	0.723907	+	0.862719i
$288$		0			0
$289$	−48.2358	+	273.559i	−0.166906	+	0.946570i
$290$		0			0
$291$	192.643	−	70.1162i	0.662002	−	0.240949i
$292$		0			0
$293$	−204.358	+	117.986i	−0.697468	+	0.402683i	−0.806404	−	0.591365i	$-0.798589\pi$
$293$	−204.358	+	117.986i	−0.697468	+	0.402683i	0.108936	+	0.994049i	$0.465256\pi$
$294$		0			0
$295$	253.729	−	302.382i	0.860098	−	1.02502i
$296$		0			0
$297$	513.047	+	296.208i	1.72743	+	0.997333i
$298$		0			0
$299$	−782.088	+	137.903i	−2.61568	+	0.461215i
$300$		0			0
$301$	−108.944	−	39.6524i	−0.361941	−	0.131736i
$302$		0			0
$303$		−	133.548i		−	0.440754i
$304$		0			0
$305$	−18.5833			−0.0609288
$306$		0			0
$307$	−3.26213	+	8.96263i	−0.0106258	+	0.0291942i	−0.944892	−	0.327382i	$-0.893834\pi$
$307$	−3.26213	+	8.96263i	−0.0106258	+	0.0291942i	0.934266	+	0.356576i	$0.116056\pi$
$308$		0			0
$309$	0.566769	+	3.21430i	0.00183420	+	0.0104023i
$310$		0			0
$311$	104.437	−	180.890i	0.335810	−	0.581639i	−0.647830	−	0.761785i	$-0.724323\pi$
$311$	104.437	−	180.890i	0.335810	−	0.581639i	0.983640	+	0.180145i	$0.0576568\pi$
$312$		0			0
$313$	−253.421	−	212.645i	−0.809650	−	0.679377i	0.140874	−	0.990028i	$-0.455009\pi$
$313$	−253.421	−	212.645i	−0.809650	−	0.679377i	−0.950524	+	0.310650i	$0.899453\pi$
$314$		0			0
$315$	−204.707	−	354.563i	−0.649863	−	1.12560i
$316$		0			0
$317$	52.6194	+	144.571i	0.165992	+	0.456058i	0.994602	−	0.103768i	$-0.0330900\pi$
$317$	52.6194	+	144.571i	0.165992	+	0.456058i	−0.828610	+	0.559827i	$0.810868\pi$
$318$		0			0
$319$	20.4225	+	3.60104i	0.0640204	+	0.0112885i
$320$		0			0
$321$	−488.949	+	410.277i	−1.52321	+	1.27812i
$322$		0			0
$323$	63.1955	−	7.56462i	0.195652	−	0.0234199i
$324$		0			0
$325$	108.898	+	129.780i	0.335071	+	0.399323i
$326$		0			0
$327$	−67.9875	+	385.576i	−0.207913	+	1.17913i
$328$		0			0
$329$	−18.3113	+	6.66476i	−0.0556574	+	0.0202576i
$330$		0			0
$331$	−226.517	+	130.779i	−0.684340	+	0.395104i	−0.801488	−	0.598011i	$-0.795958\pi$
$331$	−226.517	+	130.779i	−0.684340	+	0.395104i	0.117148	+	0.993114i	$0.462625\pi$
$332$		0			0
$333$	−848.671	+	1011.41i	−2.54856	+	3.03726i
$334$		0			0
$335$	−126.368	−	72.9585i	−0.377217	−	0.217787i
$336$		0			0
$337$	101.555	−	17.9069i	0.301350	−	0.0531362i	−0.0209286	−	0.999781i	$-0.506662\pi$
$337$	101.555	−	17.9069i	0.301350	−	0.0531362i	0.322279	+	0.946645i	$0.395551\pi$
$338$		0			0
$339$	918.898	+	334.452i	2.71061	+	0.986583i
$340$		0			0
$341$			50.7178i			0.148732i
$342$		0			0
$343$	356.042			1.03802
$344$		0			0
$345$	−280.998	+	772.036i	−0.814488	+	2.23779i
$346$		0			0
$347$	−118.388	−	671.412i	−0.341176	−	1.93490i	−0.354660	−	0.934995i	$-0.615403\pi$
$347$	−118.388	−	671.412i	−0.341176	−	1.93490i	0.0134844	−	0.999909i	$-0.495708\pi$
$348$		0			0
$349$	229.837	−	398.089i	0.658558	−	1.14066i	−0.322432	−	0.946593i	$-0.604500\pi$
$349$	229.837	−	398.089i	0.658558	−	1.14066i	0.980989	−	0.194062i	$-0.0621664\pi$
$350$		0			0
$351$	−1114.00	−	934.756i	−3.17379	−	2.66312i
$352$		0			0
$353$	268.371	+	464.832i	0.760257	+	1.31680i	0.942718	+	0.333590i	$0.108260\pi$
$353$	268.371	+	464.832i	0.760257	+	1.31680i	−0.182461	+	0.983213i	$0.558406\pi$
$354$		0			0
$355$	−11.9052	−	32.7092i	−0.0335357	−	0.0921385i
$356$		0			0
$357$	−84.5619	−	14.9105i	−0.236868	−	0.0417662i
$358$		0			0
$359$	−61.1230	+	51.2883i	−0.170259	+	0.142864i	−0.723936	−	0.689867i	$-0.757669\pi$
$359$	−61.1230	+	51.2883i	−0.170259	+	0.142864i	0.553677	+	0.832732i	$0.313224\pi$
$360$		0			0
$361$	144.825	+	330.676i	0.401178	+	0.916000i
$362$		0			0
$363$	−142.174	−	169.436i	−0.391663	−	0.466766i
$364$		0			0
$365$	45.3447	−	257.162i	0.124232	−	0.704554i
$366$		0			0
$367$	−325.654	+	118.528i	−0.887341	+	0.322966i	−0.745169	−	0.666876i	$-0.767631\pi$
$367$	−325.654	+	118.528i	−0.887341	+	0.322966i	−0.142173	+	0.989842i	$0.545409\pi$
$368$		0			0
$369$	1259.03	−	726.903i	3.41201	−	1.96993i
$370$		0			0
$371$	−179.032	+	213.362i	−0.482566	+	0.575099i
$372$		0			0
$373$	242.499	+	140.007i	0.650130	+	0.375353i	0.788506	−	0.615027i	$-0.210855\pi$
$373$	242.499	+	140.007i	0.650130	+	0.375353i	−0.138376	+	0.990380i	$0.544188\pi$
$374$		0			0
$375$	734.073	−	129.437i	1.95753	−	0.345165i
$376$		0			0
$377$	−47.8352	−	17.4106i	−0.126884	−	0.0461820i
$378$		0			0
$379$		−	108.639i		−	0.286647i	−0.989676	−	0.143324i	$-0.954221\pi$
$379$		−	108.639i		−	0.286647i	0.989676	−	0.143324i	$-0.0457790\pi$
$380$		0			0
$381$	353.110			0.926797
$382$		0			0
$383$	−129.614	+	356.112i	−0.338418	+	0.929796i	0.647426	+	0.762129i	$0.275846\pi$
$383$	−129.614	+	356.112i	−0.338418	+	0.929796i	−0.985844	+	0.167667i	$0.946377\pi$
$384$		0			0
$385$	−30.3481	−	172.113i	−0.0788263	−	0.447046i
$386$		0			0
$387$	−260.734	+	451.604i	−0.673731	+	1.16694i
$388$		0			0
$389$	534.696	+	448.663i	1.37454	+	1.15338i	0.971183	+	0.238333i	$0.0766011\pi$
$389$	534.696	+	448.663i	1.37454	+	1.15338i	0.403357	+	0.915043i	$0.367843\pi$
$390$		0			0
$391$	60.3406	+	104.513i	0.154324	+	0.267297i
$392$		0			0
$393$	−284.573	−	781.859i	−0.724105	−	1.98946i
$394$		0			0
$395$	291.982	+	51.4843i	0.739195	+	0.130340i
$396$		0			0
$397$	459.550	−	385.608i	1.15756	−	0.971304i	0.157686	−	0.987489i	$-0.449596\pi$
$397$	459.550	−	385.608i	1.15756	−	0.971304i	0.999869	+	0.0161848i	$0.00515202\pi$
$398$		0			0
$399$	−57.8851	−	483.577i	−0.145075	−	1.21197i
$400$		0			0
$401$	121.256	+	144.508i	0.302385	+	0.360368i	0.895744	−	0.444569i	$-0.146643\pi$
$401$	121.256	+	144.508i	0.302385	+	0.360368i	−0.593360	+	0.804937i	$0.702199\pi$
$402$		0			0
$403$	21.6190	−	122.607i	0.0536451	−	0.304236i
$404$		0			0
$405$	−673.407	+	245.100i	−1.66273	+	0.605185i
$406$		0			0
$407$	−488.092	+	281.800i	−1.19924	+	0.692383i
$408$		0			0
$409$	108.192	−	128.939i	0.264529	−	0.315254i	−0.617387	−	0.786659i	$-0.711809\pi$
$409$	108.192	−	128.939i	0.264529	−	0.315254i	0.881916	+	0.471406i	$0.156253\pi$
$410$		0			0
$411$	−546.935	−	315.773i	−1.33074	−	0.768304i
$412$		0			0
$413$	−436.939	+	77.0441i	−1.05796	+	0.186548i
$414$		0			0
$415$	193.464	+	70.4152i	0.466179	+	0.169675i
$416$		0			0
$417$		−	1037.89i		−	2.48894i
$418$		0			0
$419$	329.021			0.785254			0.392627	−	0.919698i	$-0.371566\pi$
$419$	329.021			0.785254			0.392627	+	0.919698i	$0.371566\pi$
$420$		0			0
$421$	−162.580	+	446.685i	−0.386176	+	1.06101i	0.582532	+	0.812808i	$0.302062\pi$
$421$	−162.580	+	446.685i	−0.386176	+	1.06101i	−0.968708	+	0.248202i	$0.920160\pi$
$422$		0			0
$423$	15.2199	+	86.3165i	0.0359809	+	0.204058i
$424$		0			0
$425$	12.8724	−	22.2956i	0.0302879	−	0.0524602i
$426$		0			0
$427$	16.0009	+	13.4263i	0.0374728	+	0.0314434i
$428$		0			0
$429$	−542.459	−	939.566i	−1.26447	−	2.19013i
$430$		0			0
$431$	−108.340	−	297.662i	−0.251369	−	0.690630i	−0.999629	−	0.0272251i	$-0.991333\pi$
$431$	−108.340	−	297.662i	−0.251369	−	0.690630i	0.748261	−	0.663405i	$-0.230889\pi$
$432$		0			0
$433$	−100.575	−	17.7341i	−0.232275	−	0.0409564i	0.0562987	−	0.998414i	$-0.482070\pi$
$433$	−100.575	−	17.7341i	−0.232275	−	0.0409564i	−0.288574	+	0.957458i	$0.593181\pi$
$434$		0			0
$435$	−40.3426	+	33.8514i	−0.0927416	+	0.0778194i
$436$		0			0
$437$	−468.345	+	499.189i	−1.07173	+	1.14231i
$438$		0			0
$439$	222.022	+	264.595i	0.505745	+	0.602723i	0.957149	−	0.289597i	$-0.0935211\pi$
$439$	222.022	+	264.595i	0.505745	+	0.602723i	−0.451404	+	0.892320i	$0.649077\pi$
$440$		0			0
$441$	99.0886	−	561.960i	0.224691	−	1.27428i
$442$		0			0
$443$	129.768	−	47.2318i	0.292931	−	0.106618i	−0.191375	−	0.981517i	$-0.561295\pi$
$443$	129.768	−	47.2318i	0.292931	−	0.106618i	0.484306	+	0.874899i	$0.339072\pi$
$444$		0			0
$445$	2.71120	−	1.56531i	0.00609258	−	0.00351755i
$446$		0			0
$447$	184.573	−	219.966i	0.412916	−	0.492094i
$448$		0			0
$449$	−190.819	−	110.170i	−0.424987	−	0.245366i	0.272222	−	0.962235i	$-0.412242\pi$
$449$	−190.819	−	110.170i	−0.424987	−	0.245366i	−0.697209	+	0.716868i	$0.745575\pi$
$450$		0			0
$451$	611.164	−	107.765i	1.35513	−	0.238946i
$452$		0			0
$453$	727.427	+	264.762i	1.60580	+	0.584463i
$454$		0			0
$455$			429.009i			0.942876i
$456$		0			0
$457$	−456.166			−0.998175			−0.499088	−	0.866552i	$-0.666331\pi$
$457$	−456.166			−0.998175			−0.499088	+	0.866552i	$0.666331\pi$
$458$		0			0
$459$	−75.5819	+	207.660i	−0.164666	+	0.452417i
$460$		0			0
$461$	−97.5134	−	553.026i	−0.211526	−	1.19962i	−0.886834	−	0.462088i	$-0.847101\pi$
$461$	−97.5134	−	553.026i	−0.211526	−	1.19962i	0.675308	−	0.737535i	$-0.264011\pi$
$462$		0			0
$463$	−392.058	+	679.064i	−0.846777	+	1.46666i	0.0372912	+	0.999304i	$0.488127\pi$
$463$	−392.058	+	679.064i	−0.846777	+	1.46666i	−0.884069	+	0.467357i	$0.845206\pi$
$464$		0			0
$465$	−98.6657	−	82.7903i	−0.212184	−	0.178044i
$466$		0			0
$467$	332.463	+	575.843i	0.711912	+	1.23307i	0.964138	+	0.265400i	$0.0855040\pi$
$467$	332.463	+	575.843i	0.711912	+	1.23307i	−0.252226	+	0.967668i	$0.581163\pi$
$468$		0			0
$469$	56.0951	+	154.120i	0.119606	+	0.328614i
$470$		0			0
$471$	−123.342	−	21.7486i	−0.261873	−	0.0461754i
$472$		0			0
$473$	−170.522	+	143.085i	−0.360512	+	0.302505i
$474$		0			0
$475$	142.180	+	33.2801i	0.299326	+	0.0700633i
$476$		0			0
$477$	805.267	+	959.680i	1.68819	+	2.01191i
$478$		0			0
$479$	50.5312	−	286.577i	0.105493	−	0.598281i	−0.885529	−	0.464584i	$-0.846204\pi$
$479$	50.5312	−	286.577i	0.105493	−	0.598281i	0.991022	−	0.133697i	$-0.0426850\pi$
$480$		0			0
$481$	1300.05	−	473.181i	2.70281	−	0.983744i
$482$		0			0
$483$	799.742	−	461.731i	1.65578	−	0.955965i
$484$		0			0
$485$	−100.049	+	119.234i	−0.206286	+	0.245843i
$486$		0			0
$487$	−444.391	−	256.569i	−0.912506	−	0.526836i	−0.0312697	−	0.999511i	$-0.509955\pi$
$487$	−444.391	−	256.569i	−0.912506	−	0.526836i	−0.881237	+	0.472675i	$0.843288\pi$
$488$		0			0
$489$	168.020	−	29.6265i	0.343600	−	0.0605859i
$490$		0			0
$491$	−152.339	−	55.4467i	−0.310262	−	0.112926i	0.182196	−	0.983262i	$-0.441679\pi$
$491$	−152.339	−	55.4467i	−0.310262	−	0.112926i	−0.492458	+	0.870336i	$0.663902\pi$
$492$		0			0
$493$			7.73566i			0.0156910i
$494$		0			0
$495$	−786.088			−1.58806
$496$		0			0
$497$	−13.3814	+	36.7652i	−0.0269244	+	0.0739742i
$498$		0			0
$499$	−51.5086	−	292.120i	−0.103224	−	0.585410i	−0.991915	−	0.126904i	$-0.959496\pi$
$499$	−51.5086	−	292.120i	−0.103224	−	0.585410i	0.888691	−	0.458506i	$-0.151615\pi$
$500$		0			0
$501$	−383.041	+	663.447i	−0.764553	+	1.32425i
$502$		0			0
$503$	−359.049	−	301.278i	−0.713815	−	0.598962i	0.211852	−	0.977302i	$-0.432051\pi$
$503$	−359.049	−	301.278i	−0.713815	−	0.598962i	−0.925667	+	0.378340i	$0.876495\pi$
$504$		0			0
$505$	50.6975	+	87.8107i	0.100391	+	0.173883i
$506$		0			0
$507$	594.076	+	1632.21i	1.17175	+	3.21935i
$508$		0			0
$509$	−203.264	−	35.8409i	−0.399340	−	0.0704144i	−0.0296285	−	0.999561i	$-0.509432\pi$
$509$	−203.264	−	35.8409i	−0.399340	−	0.0704144i	−0.369712	+	0.929147i	$0.620544\pi$
$510$		0			0
$511$	−224.842	+	188.665i	−0.440004	+	0.369207i
$512$		0			0
$513$	−1251.50	−	69.4015i	−2.43957	−	0.135286i
$514$		0			0
$515$	−1.59287	−	1.89831i	−0.00309296	−	0.00368604i
$516$		0			0
$517$	−6.49699	+	36.8462i	−0.0125667	+	0.0712693i
$518$		0			0
$519$	675.535	−	245.875i	1.30161	−	0.473747i
$520$		0			0
$521$	−78.7091	+	45.4427i	−0.151073	+	0.0872221i	−0.573631	−	0.819114i	$-0.694466\pi$
$521$	−78.7091	+	45.4427i	−0.151073	+	0.0872221i	0.422558	+	0.906336i	$0.361132\pi$
$522$		0			0
$523$	391.924	−	467.077i	0.749377	−	0.893073i	−0.247750	−	0.968824i	$-0.579691\pi$
$523$	391.924	−	467.077i	0.749377	−	0.893073i	0.997127	+	0.0757515i	$0.0241356\pi$
$524$		0			0
$525$	−170.608	−	98.5004i	−0.324967	−	0.187620i
$526$		0			0
$527$	−18.6317	+	3.28526i	−0.0353542	+	0.00623390i
$528$		0			0
$529$	−722.515	−	262.974i	−1.36581	−	0.497115i
$530$		0			0
$531$			1995.62i			3.75824i
$532$		0			0
$533$	−1523.39			−2.85814
$534$		0			0
$535$	165.745	−	455.380i	0.309803	−	0.851177i
$536$		0			0
$537$	183.165	+	1038.78i	0.341090	+	1.93441i
$538$		0			0
$539$	121.793	−	210.952i	0.225961	−	0.391377i
$540$		0			0
$541$	720.024	+	604.172i	1.33091	+	1.11677i	0.983863	+	0.178922i	$0.0572609\pi$
$541$	720.024	+	604.172i	1.33091	+	1.11677i	0.347050	+	0.937847i	$0.387184\pi$
$542$		0			0
$543$	−350.152	−	606.481i	−0.644847	−	1.11691i
$544$		0			0
$545$	−101.669	−	279.333i	−0.186549	−	0.512538i
$546$		0			0
$547$	−879.472	−	155.075i	−1.60781	−	0.283500i	−0.703602	−	0.710594i	$-0.748426\pi$
$547$	−879.472	−	155.075i	−1.60781	−	0.283500i	−0.904207	+	0.427094i	$0.859538\pi$
$548$		0			0
$549$	71.9703	−	60.3902i	0.131093	−	0.110000i
$550$		0			0
$551$	−41.9978	+	12.7006i	−0.0762211	+	0.0230502i
$552$		0			0
$553$	−214.210	−	255.285i	−0.387359	−	0.461637i
$554$		0			0
$555$	248.538	−	1409.53i	0.447817	−	2.53969i
$556$		0			0
$557$	−202.594	+	73.7382i	−0.363724	+	0.132385i	−0.517416	−	0.855734i	$-0.673106\pi$
$557$	−202.594	+	73.7382i	−0.363724	+	0.132385i	0.153692	+	0.988119i	$0.450884\pi$
$558$		0			0
$559$	473.218	−	273.213i	0.846545	−	0.488753i
$560$		0			0
$561$	−105.974	+	126.295i	−0.188902	+	0.225125i
$562$		0			0
$563$	157.169	+	90.7417i	0.279164	+	0.161175i	0.633045	−	0.774115i	$-0.281805\pi$
$563$	157.169	+	90.7417i	0.279164	+	0.161175i	−0.353881	+	0.935290i	$0.615138\pi$
$564$		0			0
$565$	−731.158	+	128.923i	−1.29409	+	0.228182i
$566$		0			0
$567$	756.911	+	275.493i	1.33494	+	0.485878i
$568$		0			0
$569$			549.429i			0.965605i	0.875729	+	0.482803i	$0.160381\pi$
$569$			549.429i			0.965605i	−0.875729	+	0.482803i	$0.839619\pi$
$570$		0			0
$571$	505.826			0.885861			0.442930	−	0.896556i	$-0.353939\pi$
$571$	505.826			0.885861			0.442930	+	0.896556i	$0.353939\pi$
$572$		0			0
$573$	403.419	−	1108.39i	0.704048	−	1.93436i
$574$		0			0
$575$	48.0790	+	272.669i	0.0836156	+	0.474207i
$576$		0			0
$577$	−101.129	+	175.161i	−0.175267	+	0.303572i	−0.940254	−	0.340475i	$-0.889412\pi$
$577$	−101.129	+	175.161i	−0.175267	+	0.303572i	0.764987	+	0.644046i	$0.222746\pi$
$578$		0			0
$579$	−503.799	−	422.738i	−0.870119	−	0.730117i
$580$		0			0
$581$	−115.705	−	200.407i	−0.199148	−	0.344934i
$582$		0			0
$583$	182.904	+	502.525i	0.313729	+	0.861964i
$584$		0			0
$585$	1900.32	+	335.078i	3.24841	+	0.572783i
$586$		0			0
$587$	60.5305	−	50.7912i	0.103118	−	0.0865267i	−0.589771	−	0.807571i	$-0.700782\pi$
$587$	60.5305	−	50.7912i	0.103118	−	0.0865267i	0.692889	+	0.721044i	$0.256337\pi$
$588$		0			0
$589$	−48.4261	−	95.7596i	−0.0822174	−	0.162580i
$590$		0			0
$591$	392.484	+	467.744i	0.664102	+	0.791445i
$592$		0			0
$593$	−62.4626	+	354.243i	−0.105333	+	0.597374i	0.885753	+	0.464156i	$0.153642\pi$
$593$	−62.4626	+	354.243i	−0.105333	+	0.597374i	−0.991087	+	0.133218i	$0.957469\pi$
$594$		0			0
$595$	61.2614	−	22.2973i	0.102960	−	0.0374745i
$596$		0			0
$597$	1470.60	−	849.051i	2.46331	−	1.42220i
$598$		0			0
$599$	395.844	−	471.749i	0.660842	−	0.787561i	−0.326664	−	0.945140i	$-0.605925\pi$
$599$	395.844	−	471.749i	0.660842	−	0.787561i	0.987506	+	0.157580i	$0.0503691\pi$
$600$		0			0
$601$	−743.458	−	429.235i	−1.23703	−	0.714202i	−0.268547	−	0.963266i	$-0.586544\pi$
$601$	−743.458	−	429.235i	−1.23703	−	0.714202i	−0.968487	+	0.249064i	$0.919877\pi$
$602$		0			0
$603$	726.497	−	128.101i	1.20480	−	0.212440i
$604$		0			0
$605$	157.803	+	57.4357i	0.260832	+	0.0949350i
$606$		0			0
$607$		−	498.085i		−	0.820569i	−0.911958	−	0.410284i	$-0.865429\pi$
$607$		−	498.085i		−	0.820569i	0.911958	−	0.410284i	$-0.134571\pi$
$608$		0			0
$609$	59.1939			0.0971985
$610$		0			0
$611$	31.4122	−	86.3042i	0.0514111	−	0.141251i
$612$		0			0
$613$	−66.7175	−	378.374i	−0.108838	−	0.617249i	−0.989618	−	0.143724i	$-0.954092\pi$
$613$	−66.7175	−	378.374i	−0.108838	−	0.617249i	0.880780	−	0.473525i	$-0.157019\pi$
$614$		0			0
$615$	−788.003	+	1364.86i	−1.28131	+	2.21929i
$616$		0			0
$617$	219.295	+	184.010i	0.355421	+	0.298234i	0.802962	−	0.596030i	$-0.203256\pi$
$617$	219.295	+	184.010i	0.355421	+	0.298234i	−0.447542	+	0.894263i	$0.647700\pi$
$618$		0			0
$619$	−420.938	−	729.086i	−0.680029	−	1.17784i	−0.974972	−	0.222330i	$-0.928634\pi$
$619$	−420.938	−	729.086i	−0.680029	−	1.17784i	0.294943	−	0.955515i	$-0.404699\pi$
$620$		0			0
$621$	−812.857	−	2233.31i	−1.30895	−	3.59631i
$622$		0			0
$623$	−3.46537	−	0.611038i	−0.00556239	−	0.000980799i
$624$		0			0
$625$	−286.347	+	240.274i	−0.458155	+	0.384438i
$626$		0			0
$627$	−859.661	−	367.991i	−1.37107	−	0.586907i
$628$		0			0
$629$	−135.138	−	161.051i	−0.214846	−	0.256044i
$630$		0			0
$631$	97.9506	−	555.505i	0.155231	−	0.880357i	−0.803344	−	0.595516i	$-0.796948\pi$
$631$	97.9506	−	555.505i	0.155231	−	0.880357i	0.958575	−	0.284842i	$-0.0919411\pi$
$632$		0			0
$633$	−394.534	+	143.599i	−0.623277	+	0.226854i
$634$		0			0
$635$	−232.177	+	134.047i	−0.365632	+	0.211098i
$636$		0			0
$637$	−384.348	+	458.048i	−0.603372	+	0.719071i
$638$		0			0
$639$	152.402	+	87.9894i	0.238501	+	0.137699i
$640$		0			0
$641$	1189.34	−	209.712i	1.85544	−	0.327164i	0.869458	−	0.494007i	$-0.164468\pi$
$641$	1189.34	−	209.712i	1.85544	−	0.327164i	0.985983	+	0.166843i	$0.0533573\pi$
$642$		0			0
$643$	303.003	+	110.284i	0.471233	+	0.171515i	0.566711	−	0.823917i	$-0.308216\pi$
$643$	303.003	+	110.284i	0.471233	+	0.171515i	−0.0954776	+	0.995432i	$0.530438\pi$
$644$		0			0
$645$		−	565.300i		−	0.876433i
$646$		0			0
$647$	−1020.25			−1.57689			−0.788443	−	0.615107i	$-0.789113\pi$
$647$	−1020.25			−1.57689			−0.788443	+	0.615107i	$0.789113\pi$
$648$		0			0
$649$	−291.360	+	800.505i	−0.448937	+	1.23344i
$650$		0			0
$651$	25.1391	+	142.571i	0.0386161	+	0.219003i
$652$		0			0
$653$	274.634	−	475.680i	0.420573	−	0.728454i	−0.575423	−	0.817856i	$-0.695162\pi$
$653$	274.634	−	475.680i	0.420573	−	0.728454i	0.995996	+	0.0894026i	$0.0284958\pi$
$654$		0			0
$655$	483.921	+	406.058i	0.738811	+	0.619936i
$656$		0			0
$657$	660.089	+	1143.31i	1.00470	+	1.74019i
$658$		0			0
$659$	−84.8900	−	233.233i	−0.128816	−	0.353920i	0.858472	−	0.512861i	$-0.171414\pi$
$659$	−84.8900	−	233.233i	−0.128816	−	0.353920i	−0.987288	+	0.158941i	$0.949192\pi$
$660$		0			0
$661$	−584.806	−	103.117i	−0.884730	−	0.156002i	−0.287221	−	0.957864i	$-0.592731\pi$
$661$	−584.806	−	103.117i	−0.884730	−	0.156002i	−0.597508	+	0.801863i	$0.703843\pi$
$662$		0			0
$663$	310.020	−	260.138i	0.467602	−	0.392365i
$664$		0			0
$665$	221.636	+	295.987i	0.333287	+	0.445093i
$666$		0			0
$667$	−53.4763	−	63.7305i	−0.0801743	−	0.0955480i
$668$		0			0
$669$	−241.486	+	1369.53i	−0.360965	+	2.04714i
$670$		0			0
$671$	37.6864	−	13.7167i	0.0561645	−	0.0204422i
$672$		0			0
$673$	310.092	−	179.032i	0.460761	−	0.266021i	−0.251603	−	0.967831i	$-0.580958\pi$
$673$	310.092	−	179.032i	0.460761	−	0.266021i	0.712364	+	0.701810i	$0.247624\pi$
$674$		0			0
$675$	−325.896	+	388.387i	−0.482809	+	0.575389i
$676$		0			0
$677$	46.5794	+	26.8926i	0.0688026	+	0.0397232i	0.534007	−	0.845480i	$-0.320686\pi$
$677$	46.5794	+	26.8926i	0.0688026	+	0.0397232i	−0.465204	+	0.885203i	$0.654019\pi$
$678$		0			0
$679$	172.291	−	30.3796i	0.253743	−	0.0447417i
$680$		0			0
$681$	−1870.12	−	680.668i	−2.74614	−	0.999512i
$682$		0			0
$683$			375.775i			0.550182i	0.961418	+	0.275091i	$0.0887080\pi$
$683$			375.775i			0.550182i	−0.961418	+	0.275091i	$0.911292\pi$
$684$		0			0
$685$	479.494			0.699992
$686$		0			0
$687$	−134.632	+	369.899i	−0.195971	+	0.538426i
$688$		0			0
$689$	−227.953	−	1292.79i	−0.330847	−	1.87633i
$690$		0			0
$691$	−63.1359	+	109.355i	−0.0913689	+	0.158256i	−0.908087	−	0.418781i	$-0.862458\pi$
$691$	−63.1359	+	109.355i	−0.0913689	+	0.158256i	0.816718	+	0.577036i	$0.195791\pi$
$692$		0			0
$693$	676.850	+	567.944i	0.976695	+	0.819544i
$694$		0			0
$695$	394.002	+	682.432i	0.566910	+	0.981917i
$696$		0			0
$697$	79.1767	+	217.536i	0.113596	+	0.312104i
$698$		0			0
$699$	−1756.17	−	309.661i	−2.51241	−	0.443005i
$700$		0			0
$701$	873.909	−	733.296i	1.24666	−	1.04607i	0.249687	−	0.968327i	$-0.419672\pi$
$701$	873.909	−	733.296i	1.24666	−	1.04607i	0.996973	−	0.0777452i	$-0.0247721\pi$
$702$		0			0
$703$	652.494	−	998.100i	0.928156	−	1.41977i
$704$		0			0
$705$	−61.0747	−	72.7860i	−0.0866307	−	0.103243i
$706$		0			0
$707$	19.7904	−	112.237i	0.0279921	−	0.158751i
$708$		0			0
$709$	−902.523	+	328.492i	−1.27295	+	0.463317i	−0.888095	−	0.459659i	$-0.847971\pi$
$709$	−902.523	+	328.492i	−1.27295	+	0.463317i	−0.384857	+	0.922976i	$0.625749\pi$
$710$		0			0
$711$	−1298.11	+	749.465i	−1.82575	+	1.05410i
$712$		0			0
$713$	130.787	−	155.866i	0.183432	−	0.218605i
$714$		0			0
$715$	713.354	+	411.855i	0.997699	+	0.576022i
$716$		0			0
$717$	−206.414	+	36.3963i	−0.287885	+	0.0507619i
$718$		0			0
$719$	878.849	+	319.875i	1.22232	+	0.444889i	0.870961	−	0.491352i	$-0.163497\pi$
$719$	878.849	+	319.875i	1.22232	+	0.444889i	0.351360	+	0.936240i	$0.385719\pi$
$720$		0			0
$721$			2.78536i			0.00386319i
$722$		0			0
$723$	1205.78			1.66774
$724$		0			0
$725$	−6.07008	+	16.6774i	−0.00837252	+	0.0230033i
$726$		0			0
$727$	4.17491	+	23.6771i	0.00574265	+	0.0325682i	0.987544	−	0.157340i	$-0.0502920\pi$
$727$	4.17491	+	23.6771i	0.00574265	+	0.0325682i	−0.981802	+	0.189909i	$0.939181\pi$
$728$		0			0
$729$	184.510	−	319.580i	0.253100	−	0.438382i
$730$		0			0
$731$	−63.6093	−	53.3745i	−0.0870168	−	0.0730157i
$732$		0			0
$733$	555.448	+	962.064i	0.757774	+	1.31250i	0.943983	+	0.329993i	$0.107046\pi$
$733$	555.448	+	962.064i	0.757774	+	1.31250i	−0.186210	+	0.982510i	$0.559620\pi$
$734$		0			0
$735$	211.571	+	581.287i	0.287852	+	0.790867i
$736$		0			0
$737$	310.123	+	54.6830i	0.420790	+	0.0741967i
$738$		0			0
$739$	−874.713	+	733.971i	−1.18364	+	0.993195i	−0.183696	+	0.982983i	$0.558806\pi$
$739$	−874.713	+	733.971i	−1.18364	+	0.993195i	−0.999948	+	0.0102116i	$0.996749\pi$
$740$		0			0
$741$	1921.32	+	1256.03i	2.59287	+	1.69505i
$742$		0			0
$743$	690.911	+	823.396i	0.929894	+	1.10820i	0.993903	+	0.110255i	$0.0351669\pi$
$743$	690.911	+	823.396i	0.929894	+	1.10820i	−0.0640091	+	0.997949i	$0.520389\pi$
$744$		0			0
$745$	−37.8574	+	214.700i	−0.0508152	+	0.288188i
$746$		0			0
$747$	−978.087	+	355.994i	−1.30935	+	0.476566i
$748$		0			0
$749$	−471.722	+	272.349i	−0.629802	+	0.363616i
$750$		0			0
$751$	−438.106	+	522.115i	−0.583364	+	0.695226i	−0.974316	−	0.225185i	$-0.927701\pi$
$751$	−438.106	+	522.115i	−0.583364	+	0.695226i	0.390952	+	0.920411i	$0.372146\pi$
$752$		0			0
$753$	−674.190	−	389.244i	−0.895338	−	0.516924i
$754$		0			0
$755$	−578.806	+	102.059i	−0.766631	+	0.135178i
$756$		0			0
$757$	1158.15	+	421.533i	1.52993	+	0.556847i	0.963603	−	0.267337i	$-0.0861436\pi$
$757$	1158.15	+	421.533i	1.52993	+	0.556847i	0.566322	+	0.824184i	$0.308366\pi$
$758$		0			0
$759$		−	1773.08i		−	2.33607i
$760$		0			0
$761$	577.794			0.759256			0.379628	−	0.925139i	$-0.376052\pi$
$761$	577.794			0.759256			0.379628	+	0.925139i	$0.376052\pi$
$762$		0			0
$763$	−114.276	+	313.971i	−0.149772	+	0.411496i
$764$		0			0
$765$	−50.9191	−	288.777i	−0.0665609	−	0.377486i
$766$		0			0
$767$	1045.57	−	1810.98i	1.36319	−	2.36112i
$768$		0			0
$769$	−505.628	−	424.272i	−0.657513	−	0.551719i	0.251827	−	0.967772i	$-0.418969\pi$
$769$	−505.628	−	424.272i	−0.657513	−	0.551719i	−0.909340	+	0.416053i	$0.863413\pi$
$770$		0			0
$771$	−804.260	−	1393.02i	−1.04314	−	1.80677i
$772$		0			0
$773$	−203.079	−	557.954i	−0.262715	−	0.721803i	−0.998982	−	0.0451121i	$-0.985636\pi$
$773$	−203.079	−	557.954i	−0.262715	−	0.721803i	0.736267	−	0.676691i	$-0.236587\pi$
$774$		0			0
$775$	−42.7461	−	7.53729i	−0.0551562	−	0.00972553i
$776$		0			0
$777$	−1232.38	+	1034.09i	−1.58607	+	1.33087i
$778$		0			0
$779$	−1051.03	+	787.017i	−1.34921	+	1.01029i
$780$		0			0
$781$	48.2867	+	57.5458i	0.0618267	+	0.0736822i
$782$		0			0
$783$	26.4539	−	150.028i	0.0337854	−	0.191606i
$784$		0			0
$785$	89.3563	−	32.5230i	0.113830	−	0.0414306i
$786$		0			0
$787$	−538.312	+	310.795i	−0.684005	+	0.394911i	−0.801362	−	0.598179i	$-0.795891\pi$
$787$	−538.312	+	310.795i	−0.684005	+	0.394911i	0.117357	+	0.993090i	$0.462558\pi$
$788$		0			0
$789$	272.776	−	325.082i	0.345724	−	0.412018i
$790$		0			0
$791$	722.699	+	417.251i	0.913653	+	0.527498i
$792$		0			0
$793$	−96.9514	+	17.0952i	−0.122259	+	0.0215576i
$794$		0			0
$795$	−1276.17	−	464.489i	−1.60525	−	0.584263i
$796$		0			0
$797$			387.289i			0.485933i	0.970035	+	0.242967i	$0.0781206\pi$
$797$			387.289i			0.485933i	−0.970035	+	0.242967i	$0.921879\pi$
$798$		0			0
$799$	−13.9567			−0.0174677
$800$		0			0
$801$	−5.41326	+	14.8728i	−0.00675813	+	0.0185678i
$802$		0			0
$803$	97.8593	+	554.988i	0.121867	+	0.691143i
$804$		0			0
$805$	−350.564	+	607.195i	−0.435483	+	0.754279i
$806$		0			0
$807$	−279.483	−	234.514i	−0.346323	−	0.290599i
$808$		0			0
$809$	488.293	+	845.749i	0.603576	+	1.04543i	0.992275	+	0.124060i	$0.0395915\pi$
$809$	488.293	+	845.749i	0.603576	+	1.04543i	−0.388698	+	0.921365i	$0.627075\pi$
$810$		0			0
$811$	−70.4203	−	193.478i	−0.0868315	−	0.238568i	0.888675	−	0.458537i	$-0.151626\pi$
$811$	−70.4203	−	193.478i	−0.0868315	−	0.238568i	−0.975507	+	0.219970i	$0.929404\pi$
$812$		0			0
$813$	275.439	+	48.5673i	0.338793	+	0.0597384i
$814$		0			0
$815$	−99.2299	+	83.2638i	−0.121754	+	0.102164i
$816$		0			0
$817$	185.341	−	432.974i	0.226856	−	0.529956i
$818$		0			0
$819$	−1394.15	−	1661.49i	−1.70226	−	2.02868i
$820$		0			0
$821$	79.8984	−	453.126i	0.0973184	−	0.551920i	−0.896694	−	0.442651i	$-0.854038\pi$
$821$	79.8984	−	453.126i	0.0973184	−	0.551920i	0.994012	−	0.109269i	$-0.0348509\pi$
$822$		0			0
$823$	308.028	−	112.113i	0.374274	−	0.136225i	−0.148032	−	0.988983i	$-0.547294\pi$
$823$	308.028	−	112.113i	0.374274	−	0.136225i	0.522307	+	0.852758i	$0.325072\pi$
$824$		0			0
$825$	−327.573	+	189.124i	−0.397058	+	0.229241i
$826$		0			0
$827$	860.552	−	1025.57i	1.04057	−	1.24010i	0.0704406	−	0.997516i	$-0.477559\pi$
$827$	860.552	−	1025.57i	1.04057	−	1.24010i	0.970130	−	0.242587i	$-0.0779961\pi$
$828$		0			0
$829$	909.088	+	524.862i	1.09661	+	0.633127i	0.935328	−	0.353782i	$-0.115105\pi$
$829$	909.088	+	524.862i	1.09661	+	0.633127i	0.161280	+	0.986909i	$0.448438\pi$
$830$		0			0
$831$	−1931.61	+	340.595i	−2.32444	+	0.409862i
$832$		0			0
$833$	85.3844	+	31.0774i	0.102502	+	0.0373078i
$834$		0			0
$835$		−	581.639i		−	0.696574i
$836$		0			0
$837$	372.583			0.445140
$838$		0			0
$839$	394.655	−	1084.30i	0.470387	−	1.29238i	−0.447055	−	0.894507i	$-0.647527\pi$
$839$	394.655	−	1084.30i	0.470387	−	1.29238i	0.917442	−	0.397871i	$-0.130251\pi$
$840$		0			0
$841$	145.112	+	822.972i	0.172547	+	0.978563i
$842$		0			0
$843$	967.489	−	1675.74i	1.14767	−	1.98783i
$844$		0			0
$845$	−1010.23	−	847.688i	−1.19554	−	1.00318i
$846$		0			0
$847$	−94.3772	−	163.466i	−0.111425	−	0.192994i
$848$		0			0
$849$	612.549	+	1682.96i	0.721494	+	1.98229i
$850$		0			0
$851$	2226.68	+	392.624i	2.61655	+	0.461368i
$852$		0			0
$853$	958.780	−	804.512i	1.12401	−	0.943156i	0.125209	−	0.992130i	$-0.460040\pi$
$853$	958.780	−	804.512i	1.12401	−	0.943156i	0.998800	+	0.0489745i	$0.0155953\pi$
$854$		0			0
$855$	1484.20	−	750.568i	1.73591	−	0.877857i
$856$		0			0
$857$	−930.794	−	1109.28i	−1.08611	−	1.29437i	−0.952900	−	0.303283i	$-0.901917\pi$
$857$	−930.794	−	1109.28i	−1.08611	−	1.29437i	−0.133206	−	0.991088i	$-0.542527\pi$
$858$		0			0
$859$	−111.169	+	630.471i	−0.129417	+	0.733959i	0.849169	+	0.528121i	$0.177103\pi$
$859$	−111.169	+	630.471i	−0.129417	+	0.733959i	−0.978586	+	0.205838i	$0.934008\pi$
$860$		0			0
$861$	1664.60	−	605.866i	1.93334	−	0.703677i
$862$		0			0
$863$	−687.219	+	396.766i	−0.796314	+	0.459752i	−0.842181	−	0.539195i	$-0.818728\pi$
$863$	−687.219	+	396.766i	−0.796314	+	0.459752i	0.0458667	+	0.998948i	$0.485395\pi$
$864$		0			0
$865$	−350.839	+	418.114i	−0.405594	+	0.483368i
$866$		0			0
$867$	1318.43	+	761.197i	1.52068	+	0.877966i
$868$		0			0
$869$	−630.133	+	111.109i	−0.725124	+	0.127859i
$870$		0			0
$871$	−726.394	−	264.386i	−0.833977	−	0.303543i
$872$		0			0
$873$		−	786.904i		−	0.901379i
$874$		0			0
$875$	636.112			0.726985
$876$		0			0
$877$	166.088	−	456.324i	0.189382	−	0.520324i	−0.808269	−	0.588813i	$-0.799596\pi$
$877$	166.088	−	456.324i	0.189382	−	0.520324i	0.997652	+	0.0684888i	$0.0218177\pi$
$878$		0			0
$879$	224.574	+	1273.62i	0.255488	+	1.44894i
$880$		0			0
$881$	691.692	−	1198.05i	0.785121	−	1.35987i	−0.143805	−	0.989606i	$-0.545934\pi$
$881$	691.692	−	1198.05i	0.785121	−	1.35987i	0.928927	−	0.370264i	$-0.120733\pi$
$882$		0			0
$883$	−272.402	−	228.573i	−0.308496	−	0.258859i	0.475374	−	0.879784i	$-0.342313\pi$
$883$	−272.402	−	228.573i	−0.308496	−	0.258859i	−0.783870	+	0.620925i	$0.786757\pi$
$884$		0			0
$885$	−1081.68	−	1873.53i	−1.22224	−	2.11698i
$886$		0			0
$887$	138.840	+	381.459i	0.156527	+	0.430055i	0.993023	−	0.117918i	$-0.0376220\pi$
$887$	138.840	+	381.459i	0.156527	+	0.430055i	−0.836496	+	0.547973i	$0.815400\pi$
$888$		0			0
$889$	296.761	+	52.3269i	0.333814	+	0.0588604i
$890$		0			0
$891$	1184.74	−	994.111i	1.32967	−	1.11573i
$892$		0			0
$893$	−22.9144	−	75.7723i	−0.0256601	−	0.0848514i
$894$		0			0
$895$	−514.776	−	613.486i	−0.575169	−	0.685459i
$896$		0			0
$897$	−755.792	+	4286.31i	−0.842578	+	4.77850i
$898$		0			0
$899$	12.2557	−	4.46072i	0.0136326	−	0.00496187i
$900$		0			0
$901$	−172.760	+	99.7427i	−0.191742	+	0.110702i
$902$		0			0
$903$	−408.426	+	486.743i	−0.452299	+	0.539029i
$904$		0			0
$905$	460.464	+	265.849i	0.508800	+	0.293756i
$906$		0			0
$907$	412.544	−	72.7426i	0.454845	−	0.0802014i	0.0584678	−	0.998289i	$-0.481379\pi$
$907$	412.544	−	72.7426i	0.454845	−	0.0802014i	0.396377	+	0.918088i	$0.370267\pi$
$908$		0			0
$909$	−481.703	−	175.326i	−0.529926	−	0.192877i
$910$		0			0
$911$			1515.82i			1.66390i	0.554847	+	0.831952i	$0.312777\pi$
$911$			1515.82i			1.66390i	−0.554847	+	0.831952i	$0.687223\pi$
$912$		0			0
$913$	−444.315			−0.486654
$914$		0			0
$915$	−34.8339	+	95.7053i	−0.0380698	+	0.104596i
$916$		0			0
$917$	−123.299	−	699.261i	−0.134459	−	0.762553i
$918$		0			0
$919$	26.3189	−	45.5857i	0.0286387	−	0.0496036i	−0.851351	−	0.524597i	$-0.824216\pi$
$919$	26.3189	−	45.5857i	0.0286387	−	0.0496036i	0.879990	+	0.474993i	$0.157549\pi$
$920$		0			0
$921$	40.0435	+	33.6004i	0.0434782	+	0.0364826i
$922$		0			0
$923$	−92.2007	−	159.696i	−0.0998924	−	0.173019i
$924$		0			0
$925$	−164.971	−	453.254i	−0.178347	−	0.490004i
$926$		0			0
$927$	12.3379	+	2.17551i	0.0133095	+	0.00234683i
$928$		0			0
$929$	814.935	−	683.812i	0.877217	−	0.736073i	−0.0883877	−	0.996086i	$-0.528171\pi$
$929$	814.935	−	683.812i	0.877217	−	0.736073i	0.965605	+	0.260013i	$0.0837270\pi$
$930$		0			0
$931$	−28.5362	+	514.586i	−0.0306511	+	0.552724i
$932$		0			0
$933$	−735.832	−	876.931i	−0.788674	−	0.939905i
$934$		0			0
$935$	21.7360	−	123.271i	0.0232471	−	0.131841i
$936$		0			0
$937$	−972.861	+	354.093i	−1.03827	+	0.377900i	−0.804225	−	0.594325i	$-0.797419\pi$
$937$	−972.861	+	354.093i	−1.03827	+	0.377900i	−0.234048	+	0.972225i	$0.575197\pi$
$938$		0			0
$939$	−1570.17	+	906.537i	−1.67217	+	0.965429i
$940$		0			0
$941$	−1051.65	+	1253.31i	−1.11759	+	1.33189i	−0.180195	+	0.983631i	$0.557673\pi$
$941$	−1051.65	+	1253.31i	−1.11759	+	1.33189i	−0.937397	+	0.348263i	$0.886772\pi$
$942$		0			0
$943$	−2156.12	−	1244.83i	−2.28644	−	1.32008i
$944$		0			0
$945$	−1264.37	+	222.943i	−1.33796	+	0.235919i
$946$		0			0
$947$	−8.66816	−	3.15495i	−0.00915328	−	0.00333152i	0.337439	−	0.941347i	$-0.390439\pi$
$947$	−8.66816	−	3.15495i	−0.00915328	−	0.00333152i	−0.346593	+	0.938016i	$0.612661\pi$
$948$		0			0
$949$		−	1383.36i		−	1.45771i
$950$		0			0
$951$	843.183			0.886628
$952$		0			0
$953$	−166.619	+	457.782i	−0.174836	+	0.480358i	−0.995898	−	0.0904806i	$-0.971160\pi$
$953$	−166.619	+	457.782i	−0.174836	+	0.480358i	0.821062	+	0.570839i	$0.193382\pi$
$954$		0			0
$955$	155.508	+	881.931i	0.162836	+	0.923488i
$956$		0			0
$957$	56.8271	−	98.4275i	0.0593805	−	0.102850i
$958$		0			0
$959$	−412.862	−	346.432i	−0.430513	−	0.361243i
$960$		0			0
$961$	−464.551	−	804.626i	−0.483404	−	0.837280i
$962$		0			0
$963$	837.947	+	2302.24i	0.870142	+	2.39069i
$964$		0			0
$965$	491.737	+	86.7065i	0.509572	+	0.0898513i
$966$		0			0
$967$	−381.357	+	319.997i	−0.394372	+	0.330917i	−0.818313	−	0.574772i	$-0.805091\pi$
$967$	−381.357	+	319.997i	−0.394372	+	0.330917i	0.423942	+	0.905690i	$0.360646\pi$
$968$		0			0
$969$	79.5000	−	339.641i	0.0820433	−	0.350507i
$970$		0			0
$971$	411.544	+	490.459i	0.423835	+	0.505107i	0.935133	−	0.354296i	$-0.115280\pi$
$971$	411.544	+	490.459i	0.423835	+	0.505107i	−0.511298	+	0.859403i	$0.670835\pi$
$972$		0			0
$973$	153.804	−	872.263i	0.158071	−	0.896468i
$974$		0			0
$975$	872.503	−	317.565i	0.894875	−	0.325708i
$976$		0			0
$977$	−14.8192	+	8.55589i	−0.0151681	+	0.00875731i	−0.507565	−	0.861614i	$-0.669454\pi$
$977$	−14.8192	+	8.55589i	−0.0151681	+	0.00875731i	0.492397	+	0.870371i	$0.336121\pi$
$978$		0			0
$979$	−4.34284	+	5.17560i	−0.00443600	+	0.00528662i
$980$		0			0
$981$	1301.50	+	751.421i	1.32671	+	0.765975i
$982$		0			0
$983$	−1019.86	+	179.829i	−1.03750	+	0.182939i	−0.666354	−	0.745636i	$-0.732146\pi$
$983$	−1019.86	+	179.829i	−1.03750	+	0.182939i	−0.371145	+	0.928575i	$0.621035\pi$
$984$		0			0
$985$	−435.631	−	158.557i	−0.442265	−	0.160971i
$986$		0			0
$987$			106.797i			0.108204i
$988$		0			0
$989$	893.023			0.902955
$990$		0			0
$991$	−226.041	+	621.043i	−0.228094	+	0.626683i	−0.999959	−	0.00910368i	$-0.997102\pi$
$991$	−226.041	+	621.043i	−0.228094	+	0.626683i	0.771864	+	0.635787i	$0.219324\pi$
$992$		0			0
$993$	248.924	+	1411.72i	0.250679	+	1.42167i
$994$		0			0
$995$	−644.632	+	1116.54i	−0.647871	+	1.12215i
$996$		0			0
$997$	763.278	+	640.467i	0.765575	+	0.642394i	0.939572	−	0.342353i	$-0.111224\pi$
$997$	763.278	+	640.467i	0.765575	+	0.642394i	−0.173997	+	0.984746i	$0.555668\pi$
$998$		0			0
$999$	2070.16	+	3585.62i	2.07223	+	3.58921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.j.a.13.3	✓	18
4.3	odd	2		304.3.z.b.241.1		18
19.3	odd	18	inner	76.3.j.a.41.3	yes	18
19.4	even	9		1444.3.c.c.721.18		18
19.15	odd	18		1444.3.c.c.721.1		18
76.3	even	18		304.3.z.b.193.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.j.a.13.3	✓	18	1.1	even	1	trivial
76.3.j.a.41.3	yes	18	19.3	odd	18	inner
304.3.z.b.193.1		18	76.3	even	18
304.3.z.b.241.1		18	4.3	odd	2
1444.3.c.c.721.1		18	19.15	odd	18
1444.3.c.c.721.18		18	19.4	even	9

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)

\(f(q)\)	\(=\)	\(q+(1.87447 - 5.15008i) q^{3} +(0.722564 + 4.09786i) q^{5} +(2.33853 - 4.05046i) q^{7} +(-16.1152 - 13.5223i) q^{9} +O(q^{10})\)	\(q+(1.87447 - 5.15008i) q^{3} +(0.722564 + 4.09786i) q^{5} +(2.33853 - 4.05046i) q^{7} +(-16.1152 - 13.5223i) q^{9} +(-4.49006 - 7.77701i) q^{11} +(7.53942 + 20.7144i) q^{13} +(22.4587 + 3.96008i) q^{15} +(2.56611 - 2.15322i) q^{17} +(15.9032 + 10.3965i) q^{19} +(-16.4766 - 19.6361i) q^{21} +(-6.25588 + 35.4788i) q^{23} +(7.22192 - 2.62856i) q^{25} +(-57.1314 + 32.9848i) q^{27} +(-1.48437 + 1.76901i) q^{29} +(-4.89112 - 2.82389i) q^{31} +(-48.4687 + 8.54634i) q^{33} +(18.2880 + 6.65627i) q^{35} -62.7609i q^{37} +120.813 q^{39} +(-23.6361 + 64.9396i) q^{41} +(-4.30442 - 24.4116i) q^{43} +(43.7682 - 75.8088i) q^{45} +(-3.19164 - 2.67810i) q^{47} +(13.5625 + 23.4910i) q^{49} +(-6.27916 - 17.2518i) q^{51} +(-58.6464 - 10.3409i) q^{53} +(28.6248 - 24.0190i) q^{55} +(83.3530 - 62.4149i) q^{57} +(-60.9767 - 72.6691i) q^{59} +(-0.775508 + 4.39813i) q^{61} +(-92.4575 + 33.6518i) q^{63} +(-79.4371 + 45.8630i) q^{65} +(-22.5407 + 26.8630i) q^{67} +(170.992 + 98.7224i) q^{69} +(-8.23814 + 1.45261i) q^{71} +(-58.9706 - 21.4635i) q^{73} -42.1206i q^{75} -42.0006 q^{77} +(24.3697 - 66.9552i) q^{79} +(29.9058 + 169.604i) q^{81} +(24.7388 - 42.8489i) q^{83} +(10.6778 + 8.95974i) q^{85} +(6.32810 + 10.9606i) q^{87} +(-0.257321 - 0.706985i) q^{89} +(101.534 + 17.9032i) q^{91} +(-23.7116 + 19.8964i) q^{93} +(-31.1124 + 72.6814i) q^{95} +(24.0440 + 28.6545i) q^{97} +(-32.8046 + 186.044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9}+O(q^{10}) \) 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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