LMFDB - Embedded newform 315.3.bi.c.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(19,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("315.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 180x^{8} - 669x^{6} + 1980x^{4} - 135x^{2} + 9 $ x^12 - 15x^10 + 180x^8 - 669x^6 + 1980x^4 - 135*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.3
Root			$-0.226181 - 0.130586i$ of defining polynomial
Character	$\chi$	$=$	315.19
Dual form			315.3.bi.c.199.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.226181 - 0.130586i) q^{2} +(-1.96589 - 3.40503i) q^{4} +(-2.11218 - 4.53196i) q^{5} +(-1.66053 - 6.80019i) q^{7} +2.07156i q^{8} +O(q^{10})$	\(q+(-0.226181 - 0.130586i) q^{2} +(-1.96589 - 3.40503i) q^{4} +(-2.11218 - 4.53196i) q^{5} +(-1.66053 - 6.80019i) q^{7} +2.07156i q^{8} +(-0.114075 + 1.30086i) q^{10} +(3.04653 + 5.27675i) q^{11} -13.0886 q^{13} +(-0.512426 + 1.75492i) q^{14} +(-7.59306 + 13.1516i) q^{16} +(5.05373 + 8.75332i) q^{17} +(19.5373 + 11.2799i) q^{19} +(-11.2792 + 16.1014i) q^{20} -1.59133i q^{22} +(-30.2957 - 17.4912i) q^{23} +(-16.0774 + 19.1446i) q^{25} +(2.96039 + 1.70918i) q^{26} +(-19.8904 + 19.0226i) q^{28} +16.3474 q^{29} +(-23.4907 + 13.5624i) q^{31} +(10.6109 - 6.12620i) q^{32} -2.63978i q^{34} +(-27.3109 + 21.8887i) q^{35} +(-14.4349 - 8.33401i) q^{37} +(-2.94598 - 5.10258i) q^{38} +(9.38822 - 4.37550i) q^{40} -19.7267i q^{41} -53.4739i q^{43} +(11.9783 - 20.7471i) q^{44} +(4.56821 + 7.91237i) q^{46} +(18.3385 - 31.7632i) q^{47} +(-43.4852 + 22.5839i) q^{49} +(6.13642 - 2.23067i) q^{50} +(25.7308 + 44.5671i) q^{52} +(-31.9730 + 18.4596i) q^{53} +(17.4792 - 24.9522i) q^{55} +(14.0870 - 3.43989i) q^{56} +(-3.69747 - 2.13474i) q^{58} +(-92.4861 + 53.3969i) q^{59} +(-18.4211 - 10.6354i) q^{61} +7.08422 q^{62} +57.5445 q^{64} +(27.6455 + 59.3171i) q^{65} +(5.33016 - 3.07737i) q^{67} +(19.8702 - 34.4162i) q^{68} +(9.03556 - 1.38440i) q^{70} +48.1133 q^{71} +(-2.82277 - 4.88919i) q^{73} +(2.17660 + 3.76999i) q^{74} -88.7000i q^{76} +(30.8240 - 29.4792i) q^{77} +(19.1607 - 33.1873i) q^{79} +(75.6404 + 6.63304i) q^{80} +(-2.57602 + 4.46180i) q^{82} -102.359 q^{83} +(28.9953 - 41.3919i) q^{85} +(-6.98292 + 12.0948i) q^{86} +(-10.9311 + 6.31106i) q^{88} +(34.1003 + 19.6878i) q^{89} +(21.7341 + 89.0050i) q^{91} +137.544i q^{92} +(-8.29564 + 4.78949i) q^{94} +(9.85369 - 112.367i) q^{95} +33.5609 q^{97} +(12.7847 + 0.570497i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4}+O(q^{10}) $ 12 * q + 6 * q^4	$ 12 q + 6 q^{4} - 54 q^{10} - 6 q^{11} + 66 q^{14} - 6 q^{16} + 18 q^{19} + 18 q^{25} - 18 q^{26} - 108 q^{31} - 222 q^{35} - 162 q^{40} + 42 q^{44} + 114 q^{46} - 324 q^{49} + 192 q^{50} - 336 q^{56} - 396 q^{59} - 108 q^{61} + 372 q^{64} + 54 q^{65} + 300 q^{70} - 192 q^{71} + 594 q^{74} - 192 q^{79} + 504 q^{80} - 192 q^{85} + 384 q^{86} - 684 q^{89} - 72 q^{91} + 990 q^{94} - 288 q^{95}+O(q^{100}) $ 12 * q + 6 * q^4 - 54 * q^10 - 6 * q^11 + 66 * q^14 - 6 * q^16 + 18 * q^19 + 18 * q^25 - 18 * q^26 - 108 * q^31 - 222 * q^35 - 162 * q^40 + 42 * q^44 + 114 * q^46 - 324 * q^49 + 192 * q^50 - 336 * q^56 - 396 * q^59 - 108 * q^61 + 372 * q^64 + 54 * q^65 + 300 * q^70 - 192 * q^71 + 594 * q^74 - 192 * q^79 + 504 * q^80 - 192 * q^85 + 384 * q^86 - 684 * q^89 - 72 * q^91 + 990 * q^94 - 288 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.226181	−	0.130586i	−0.113091	−	0.0652929i	0.442388	−	0.896824i	$-0.354131\pi$
$2$	−0.226181	−	0.130586i	−0.113091	−	0.0652929i	−0.555478	+	0.831531i	$0.687465\pi$
$3$		0			0
$3$		0			0
$4$	−1.96589	−	3.40503i	−0.491474	−	0.851257i
$5$	−2.11218	−	4.53196i	−0.422436	−	0.906393i
$5$	−2.11218	−	4.53196i	−0.422436	−	0.906393i
$6$		0			0
$7$	−1.66053	−	6.80019i	−0.237219	−	0.971456i
$7$	−1.66053	−	6.80019i	−0.237219	−	0.971456i
$8$			2.07156i			0.258945i
$9$		0			0
$10$	−0.114075	+	1.30086i	−0.0114075	+	0.130086i
$11$	3.04653	+	5.27675i	0.276957	+	0.479704i	0.970627	−	0.240589i	$-0.0773406\pi$
$11$	3.04653	+	5.27675i	0.276957	+	0.479704i	−0.693670	+	0.720293i	$0.744007\pi$
$12$		0			0
$13$	−13.0886			−1.00682			−0.503408	−	0.864049i	$-0.667921\pi$
$13$	−13.0886			−1.00682			−0.503408	+	0.864049i	$0.667921\pi$
$14$	−0.512426	+	1.75492i	−0.0366019	+	0.125351i
$15$		0			0
$16$	−7.59306	+	13.1516i	−0.474566	+	0.821973i
$17$	5.05373	+	8.75332i	0.297278	+	0.514901i	0.975512	−	0.219945i	$-0.0705878\pi$
$17$	5.05373	+	8.75332i	0.297278	+	0.514901i	−0.678234	+	0.734846i	$0.737254\pi$
$18$		0			0
$19$	19.5373	+	11.2799i	1.02828	+	0.593676i	0.916491	−	0.400056i	$-0.131009\pi$
$19$	19.5373	+	11.2799i	1.02828	+	0.593676i	0.111787	+	0.993732i	$0.464343\pi$
$20$	−11.2792	+	16.1014i	−0.563958	+	0.805070i
$21$		0			0
$22$		−	1.59133i		−	0.0723334i
$23$	−30.2957	−	17.4912i	−1.31720	−	0.760488i	−0.333927	−	0.942599i	$-0.608374\pi$
$23$	−30.2957	−	17.4912i	−1.31720	−	0.760488i	−0.983278	+	0.182111i	$0.941707\pi$
$24$		0			0
$25$	−16.0774	+	19.1446i	−0.643096	+	0.765785i
$26$	2.96039	+	1.70918i	0.113861	+	0.0657379i
$27$		0			0
$28$	−19.8904	+	19.0226i	−0.710372	+	0.679380i
$29$	16.3474			0.563703			0.281852	−	0.959458i	$-0.409051\pi$
$29$	16.3474			0.563703			0.281852	+	0.959458i	$0.409051\pi$
$30$		0			0
$31$	−23.4907	+	13.5624i	−0.757766	+	0.437496i	−0.828493	−	0.559999i	$-0.810801\pi$
$31$	−23.4907	+	13.5624i	−0.757766	+	0.437496i	0.0707270	+	0.997496i	$0.477468\pi$
$32$	10.6109	−	6.12620i	0.331591	−	0.191444i
$33$		0			0
$34$		−	2.63978i		−	0.0776406i
$35$	−27.3109	+	21.8887i	−0.780311	+	0.625391i
$36$		0			0
$37$	−14.4349	−	8.33401i	−0.390133	−	0.225243i	0.292085	−	0.956392i	$-0.405651\pi$
$37$	−14.4349	−	8.33401i	−0.390133	−	0.225243i	−0.682218	+	0.731149i	$0.738984\pi$
$38$	−2.94598	−	5.10258i	−0.0775257	−	0.134278i
$39$		0			0
$40$	9.38822	−	4.37550i	0.234706	−	0.109387i
$41$		−	19.7267i		−	0.481139i	−0.970632	−	0.240569i	$-0.922666\pi$
$41$		−	19.7267i		−	0.481139i	0.970632	−	0.240569i	$-0.0773341\pi$
$42$		0			0
$43$		−	53.4739i		−	1.24358i	−0.783185	−	0.621789i	$-0.786406\pi$
$43$		−	53.4739i		−	1.24358i	0.783185	−	0.621789i	$-0.213594\pi$
$44$	11.9783	−	20.7471i	0.272235	−	0.471524i
$45$		0			0
$46$	4.56821	+	7.91237i	0.0993089	+	0.172008i
$47$	18.3385	−	31.7632i	0.390181	−	0.675813i	−0.602293	−	0.798275i	$-0.705746\pi$
$47$	18.3385	−	31.7632i	0.390181	−	0.675813i	0.992473	+	0.122463i	$0.0390792\pi$
$48$		0			0
$49$	−43.4852	+	22.5839i	−0.887454	+	0.460896i
$50$	6.13642	−	2.23067i	0.122728	−	0.0446135i
$51$		0			0
$52$	25.7308	+	44.5671i	0.494823	+	0.857059i
$53$	−31.9730	+	18.4596i	−0.603264	+	0.348294i	−0.770324	−	0.637652i	$-0.779906\pi$
$53$	−31.9730	+	18.4596i	−0.603264	+	0.348294i	0.167061	+	0.985947i	$0.446572\pi$
$54$		0			0
$55$	17.4792	−	24.9522i	0.317804	−	0.453676i
$56$	14.0870	−	3.43989i	0.251553	−	0.0614266i
$57$		0			0
$58$	−3.69747	−	2.13474i	−0.0637495	−	0.0368058i
$59$	−92.4861	+	53.3969i	−1.56756	+	0.905032i	−0.571108	+	0.820875i	$0.693486\pi$
$59$	−92.4861	+	53.3969i	−1.56756	+	0.905032i	−0.996452	+	0.0841571i	$0.973180\pi$
$60$		0			0
$61$	−18.4211	−	10.6354i	−0.301985	−	0.174351i	0.341349	−	0.939937i	$-0.389116\pi$
$61$	−18.4211	−	10.6354i	−0.301985	−	0.174351i	−0.643334	+	0.765585i	$0.722450\pi$
$62$	7.08422			0.114262
$63$		0			0
$64$	57.5445			0.899133
$65$	27.6455	+	59.3171i	0.425315	+	0.912571i
$66$		0			0
$67$	5.33016	−	3.07737i	0.0795546	−	0.0459309i	−0.459695	−	0.888077i	$-0.652041\pi$
$67$	5.33016	−	3.07737i	0.0795546	−	0.0459309i	0.539250	+	0.842146i	$0.318708\pi$
$68$	19.8702	−	34.4162i	0.292209	−	0.506121i
$69$		0			0
$70$	9.03556	−	1.38440i	0.129079	−	0.0197771i
$71$	48.1133			0.677652			0.338826	−	0.940849i	$-0.389970\pi$
$71$	48.1133			0.677652			0.338826	+	0.940849i	$0.389970\pi$
$72$		0			0
$73$	−2.82277	−	4.88919i	−0.0386681	−	0.0669752i	0.846044	−	0.533114i	$-0.178978\pi$
$73$	−2.82277	−	4.88919i	−0.0386681	−	0.0669752i	−0.884712	+	0.466138i	$0.845645\pi$
$74$	2.17660	+	3.76999i	0.0294136	+	0.0509458i
$75$		0			0
$76$		−	88.7000i		−	1.16711i
$77$	30.8240	−	29.4792i	0.400312	−	0.382847i
$78$		0			0
$79$	19.1607	−	33.1873i	0.242540	−	0.420092i	−0.718897	−	0.695117i	$-0.755353\pi$
$79$	19.1607	−	33.1873i	0.242540	−	0.420092i	0.961437	+	0.275024i	$0.0886860\pi$
$80$	75.6404	+	6.63304i	0.945504	+	0.0829130i
$81$		0			0
$82$	−2.57602	+	4.46180i	−0.0314149	+	0.0544122i
$83$	−102.359			−1.23325			−0.616623	−	0.787259i	$-0.711500\pi$
$83$	−102.359			−1.23325			−0.616623	+	0.787259i	$0.711500\pi$
$84$		0			0
$85$	28.9953	−	41.3919i	0.341122	−	0.486963i
$86$	−6.98292	+	12.0948i	−0.0811968	+	0.140637i
$87$		0			0
$88$	−10.9311	+	6.31106i	−0.124217	+	0.0717166i
$89$	34.1003	+	19.6878i	0.383149	+	0.221211i	0.679187	−	0.733965i	$-0.262332\pi$
$89$	34.1003	+	19.6878i	0.383149	+	0.221211i	−0.296038	+	0.955176i	$0.595666\pi$
$90$		0			0
$91$	21.7341	+	89.0050i	0.238836	+	0.978077i
$92$			137.544i			1.49504i
$93$		0			0
$94$	−8.29564	+	4.78949i	−0.0882515	+	0.0509520i
$95$	9.85369	−	112.367i	0.103723	−	1.18281i
$96$		0			0
$97$	33.5609			0.345989			0.172994	−	0.984923i	$-0.444656\pi$
$97$	33.5609			0.345989			0.172994	+	0.984923i	$0.444656\pi$
$98$	12.7847	+	0.570497i	0.130456	+	0.00582140i
$99$		0			0
$100$	96.7945	+	17.1077i	0.967945	+	0.171077i
$101$	16.5905	−	9.57851i	0.164262	−	0.0948367i	−0.415615	−	0.909540i	$-0.636434\pi$
$101$	16.5905	−	9.57851i	0.164262	−	0.0948367i	0.579877	+	0.814704i	$0.303100\pi$
$102$		0			0
$103$	−11.1967	+	19.3933i	−0.108706	+	0.188285i	−0.915246	−	0.402895i	$-0.868004\pi$
$103$	−11.1967	+	19.3933i	−0.108706	+	0.188285i	0.806540	+	0.591179i	$0.201337\pi$
$104$		−	27.1138i		−	0.260709i
$105$		0			0
$106$	9.64224			0.0909646
$107$	44.9916	+	25.9759i	0.420482	+	0.242766i	0.695284	−	0.718735i	$-0.255279\pi$
$107$	44.9916	+	25.9759i	0.420482	+	0.242766i	−0.274801	+	0.961501i	$0.588612\pi$
$108$		0			0
$109$	−90.8644	−	157.382i	−0.833619	−	1.44387i	−0.895150	−	0.445765i	$-0.852932\pi$
$109$	−90.8644	−	157.382i	−0.833619	−	1.44387i	0.0615316	−	0.998105i	$-0.480401\pi$
$110$	−7.21187	+	3.36118i	−0.0655624	+	0.0305562i
$111$		0			0
$112$	102.042	+	29.7957i	0.911087	+	0.266033i
$113$		−	195.000i		−	1.72566i	−0.505492	−	0.862831i	$-0.668689\pi$
$113$		−	195.000i		−	1.72566i	0.505492	−	0.862831i	$-0.331311\pi$
$114$		0			0
$115$	−15.2797	+	174.244i	−0.132867	+	1.51516i
$116$	−32.1373	−	55.6634i	−0.277045	−	0.479857i
$117$		0			0
$118$	27.8915			0.236368
$119$	51.1323	−	48.9015i	0.429684	−	0.410937i
$120$		0			0
$121$	41.9373	−	72.6375i	0.346589	−	0.600310i
$122$	2.77767	+	4.81107i	0.0227678	+	0.0394350i
$123$		0			0
$124$	92.3607	+	53.3245i	0.744844	+	0.430036i
$125$	120.721	+	32.4254i	0.965769	+	0.259403i
$126$		0			0
$127$		−	67.3739i		−	0.530503i	−0.964179	−	0.265252i	$-0.914545\pi$
$127$		−	67.3739i		−	0.530503i	0.964179	−	0.265252i	$-0.0854550\pi$
$128$	−55.4591	−	32.0193i	−0.433274	−	0.250151i
$129$		0			0
$130$	1.49308	−	17.0265i	0.0114853	−	0.130973i
$131$	−82.1026	−	47.4019i	−0.626737	−	0.361847i	0.152750	−	0.988265i	$-0.451187\pi$
$131$	−82.1026	−	47.4019i	−0.626737	−	0.361847i	−0.779487	+	0.626418i	$0.784520\pi$
$132$		0			0
$133$	44.2628	−	151.588i	0.332803	−	1.13976i
$134$	−1.60744			−0.0119958
$135$		0			0
$136$	−18.1330	+	10.4691i	−0.133331	+	0.0769786i
$137$	−141.017	+	81.4160i	−1.02932	+	0.594278i	−0.916789	−	0.399371i	$-0.869229\pi$
$137$	−141.017	+	81.4160i	−1.02932	+	0.594278i	−0.112529	+	0.993648i	$0.535895\pi$
$138$		0			0
$139$			120.304i			0.865495i	0.901515	+	0.432747i	$0.142456\pi$
$139$			120.304i			0.865495i	−0.901515	+	0.432747i	$0.857544\pi$
$140$	128.222	+	49.9635i	0.915872	+	0.356882i
$141$		0			0
$142$	−10.8823	−	6.28290i	−0.0766360	−	0.0442458i
$143$	−39.8748	−	69.0653i	−0.278845	−	0.482974i
$144$		0			0
$145$	−34.5286	−	74.0858i	−0.238128	−	0.510937i
$146$			1.47446i			0.0100990i
$147$		0			0
$148$			65.5351i			0.442805i
$149$	107.789	−	186.696i	0.723414	−	1.25299i	−0.236209	−	0.971702i	$-0.575905\pi$
$149$	107.789	−	186.696i	0.723414	−	1.25299i	0.959623	−	0.281288i	$-0.0907616\pi$
$150$		0			0
$151$	−58.8121	−	101.866i	−0.389484	−	0.674607i	0.602896	−	0.797820i	$-0.294013\pi$
$151$	−58.8121	−	101.866i	−0.389484	−	0.674607i	−0.992380	+	0.123213i	$0.960680\pi$
$152$	−23.3669	+	40.4726i	−0.153729	+	0.266267i
$153$		0			0
$154$	−10.8214	+	2.64247i	−0.0702687	+	0.0171589i
$155$	111.081	+	77.8131i	0.716651	+	0.502020i
$156$		0			0
$157$	−12.4693	−	21.5974i	−0.0794222	−	0.137563i	0.823579	−	0.567202i	$-0.191974\pi$
$157$	−12.4693	−	21.5974i	−0.0794222	−	0.137563i	−0.903001	+	0.429639i	$0.858641\pi$
$158$	−8.66757	+	5.00423i	−0.0548581	+	0.0316723i
$159$		0			0
$160$	−50.1758	−	35.1486i	−0.313599	−	0.219679i
$161$	−68.6367	+	235.061i	−0.426315	+	1.46001i
$162$		0			0
$163$	−112.324	−	64.8502i	−0.689103	−	0.397854i	0.114173	−	0.993461i	$-0.463578\pi$
$163$	−112.324	−	64.8502i	−0.689103	−	0.397854i	−0.803276	+	0.595607i	$0.796912\pi$
$164$	−67.1699	+	38.7806i	−0.409573	+	0.236467i
$165$		0			0
$166$	23.1518	+	13.3667i	0.139468	+	0.0805222i
$167$	65.7030			0.393431			0.196716	−	0.980461i	$-0.436972\pi$
$167$	65.7030			0.393431			0.196716	+	0.980461i	$0.436972\pi$
$168$		0			0
$169$	2.31155			0.0136778
$170$	−11.9634	+	5.57568i	−0.0703729	+	0.0327981i
$171$		0			0
$172$	−182.080	+	105.124i	−1.05860	+	0.611186i
$173$	−49.9582	+	86.5301i	−0.288775	+	0.500174i	−0.973518	−	0.228612i	$-0.926581\pi$
$173$	−49.9582	+	86.5301i	−0.288775	+	0.500174i	0.684742	+	0.728785i	$0.259915\pi$
$174$		0			0
$175$	156.884	+	77.5392i	0.896482	+	0.443081i
$176$	−92.5300			−0.525739
$177$		0			0
$178$	−5.14189	−	8.90601i	−0.0288870	−	0.0500338i
$179$	72.1529	+	124.972i	0.403089	+	0.698170i	0.994097	−	0.108495i	$-0.0346033\pi$
$179$	72.1529	+	124.972i	0.403089	+	0.698170i	−0.591008	+	0.806665i	$0.701270\pi$
$180$		0			0
$181$			62.7672i			0.346780i	0.984853	+	0.173390i	$0.0554722\pi$
$181$			62.7672i			0.346780i	−0.984853	+	0.173390i	$0.944528\pi$
$182$	6.70695	−	22.9694i	0.0368514	−	0.126206i
$183$		0			0
$184$	36.2341	−	62.7593i	0.196924	−	0.341083i
$185$	−7.28030	+	83.0215i	−0.0393530	+	0.448765i
$186$		0			0
$187$	−30.7927	+	53.3345i	−0.164667	+	0.285211i
$188$	−144.206			−0.767054
$189$		0			0
$190$	−16.9023	+	24.1286i	−0.0889594	+	0.126993i
$191$	−28.7734	+	49.8369i	−0.150646	+	0.260926i	−0.931465	−	0.363831i	$-0.881469\pi$
$191$	−28.7734	+	49.8369i	−0.150646	+	0.260926i	0.780819	+	0.624757i	$0.214802\pi$
$192$		0			0
$193$	−213.940	+	123.518i	−1.10850	+	0.639991i	−0.938440	−	0.345444i	$-0.887728\pi$
$193$	−213.940	+	123.518i	−1.10850	+	0.639991i	−0.170057	+	0.985434i	$0.554395\pi$
$194$	−7.59084	−	4.38258i	−0.0391281	−	0.0225906i
$195$		0			0
$196$	162.386	+	103.671i	0.828502	+	0.528933i
$197$		−	225.394i		−	1.14413i	−0.820207	−	0.572067i	$-0.806142\pi$
$197$		−	225.394i		−	1.14413i	0.820207	−	0.572067i	$-0.193858\pi$
$198$		0			0
$199$	−159.406	+	92.0330i	−0.801034	+	0.462477i	−0.843833	−	0.536606i	$-0.819706\pi$
$199$	−159.406	+	92.0330i	−0.801034	+	0.462477i	0.0427985	+	0.999084i	$0.486373\pi$
$200$	−39.6592	−	33.3053i	−0.198296	−	0.166526i
$201$		0			0
$202$	−5.00327			−0.0247686
$203$	−27.1454	−	111.165i	−0.133721	−	0.547613i
$204$		0			0
$205$	−89.4006	+	41.6663i	−0.436101	+	0.203250i
$206$	5.06498	−	2.92427i	0.0245873	−	0.0141955i
$207$		0			0
$208$	99.3826	−	172.136i	0.477801	−	0.827576i
$209$			137.458i			0.657692i
$210$		0			0
$211$	189.894			0.899972			0.449986	−	0.893036i	$-0.351429\pi$
$211$	189.894			0.899972			0.449986	+	0.893036i	$0.351429\pi$
$212$	125.711	+	72.5793i	0.592977	+	0.342355i
$213$		0			0
$214$	−6.78416	−	11.7505i	−0.0317017	−	0.0549090i
$215$	−242.342	+	112.946i	−1.12717	+	0.525332i
$216$		0			0
$217$	131.234	+	137.221i	0.604765	+	0.632354i
$218$			47.4624i			0.217717i
$219$		0			0
$220$	−119.325	−	10.4638i	−0.542388	−	0.0475630i
$221$	−66.1463	−	114.569i	−0.299304	−	0.518410i
$222$		0			0
$223$	−310.730			−1.39341			−0.696703	−	0.717360i	$-0.745350\pi$
$223$	−310.730			−1.39341			−0.696703	+	0.717360i	$0.745350\pi$
$224$	−59.2791	−	61.9834i	−0.264639	−	0.276711i
$225$		0			0
$226$	−25.4642	+	44.1053i	−0.112673	+	0.195156i
$227$	81.9716	+	141.979i	0.361108	+	0.625458i	0.988144	−	0.153533i	$-0.0490651\pi$
$227$	81.9716	+	141.979i	0.361108	+	0.625458i	−0.627035	+	0.778991i	$0.715732\pi$
$228$		0			0
$229$	−13.5862	−	7.84399i	−0.0593283	−	0.0342532i	0.470042	−	0.882644i	$-0.344239\pi$
$229$	−13.5862	−	7.84399i	−0.0593283	−	0.0342532i	−0.529371	+	0.848391i	$0.677572\pi$
$230$	26.2097	−	37.4153i	0.113955	−	0.162675i
$231$		0			0
$232$			33.8646i			0.145968i
$233$	−236.940	−	136.798i	−1.01691	−	0.587114i	−0.103704	−	0.994608i	$-0.533069\pi$
$233$	−236.940	−	136.798i	−1.01691	−	0.587114i	−0.913208	+	0.407494i	$0.866403\pi$
$234$		0			0
$235$	−182.684	−	16.0199i	−0.777378	−	0.0681697i
$236$	363.636	+	209.945i	1.54083	+	0.889599i
$237$		0			0
$238$	−17.9510	+	4.38345i	−0.0754244	+	0.0184178i
$239$	−87.2116			−0.364902			−0.182451	−	0.983215i	$-0.558403\pi$
$239$	−87.2116			−0.364902			−0.182451	+	0.983215i	$0.558403\pi$
$240$		0			0
$241$	−121.507	+	70.1522i	−0.504179	+	0.291088i	−0.730438	−	0.682979i	$-0.760684\pi$
$241$	−121.507	+	70.1522i	−0.504179	+	0.291088i	0.226259	+	0.974067i	$0.427351\pi$
$242$	−18.9708	+	10.9528i	−0.0783919	+	0.0452596i
$243$		0			0
$244$			83.6326i			0.342756i
$245$	194.198	+	149.372i	0.792645	+	0.609683i
$246$		0			0
$247$	−255.716	−	147.638i	−1.03529	−	0.597723i
$248$	−28.0953	−	48.6624i	−0.113287	−	0.196219i
$249$		0			0
$250$	−23.0705	−	23.0985i	−0.0922822	−	0.0923939i
$251$		−	252.962i		−	1.00782i	−0.863757	−	0.503909i	$-0.831895\pi$
$251$		−	252.962i		−	1.00782i	0.863757	−	0.503909i	$-0.168105\pi$
$252$		0			0
$253$		−	213.150i		−	0.842492i
$254$	−8.79807	+	15.2387i	−0.0346381	+	0.0599949i
$255$		0			0
$256$	−106.727	−	184.856i	−0.416900	−	0.722093i
$257$	188.929	−	327.234i	0.735132	−	1.27329i	−0.219534	−	0.975605i	$-0.570454\pi$
$257$	188.929	−	327.234i	0.735132	−	1.27329i	0.954666	−	0.297680i	$-0.0962129\pi$
$258$		0			0
$259$	−32.7032	+	111.999i	−0.126267	+	0.432429i
$260$	147.628	−	210.745i	0.567802	−	0.810557i
$261$		0			0
$262$	12.3800	+	21.4428i	0.0472520	+	0.0818429i
$263$	−194.747	+	112.437i	−0.740484	+	0.427518i	−0.822245	−	0.569133i	$-0.807279\pi$
$263$	−194.747	+	112.437i	−0.740484	+	0.427518i	0.0817614	+	0.996652i	$0.473945\pi$
$264$		0			0
$265$	151.191	+	105.910i	0.570532	+	0.399662i
$266$	−29.8066	+	28.5062i	−0.112055	+	0.107166i
$267$		0			0
$268$	−20.9571	−	12.0996i	−0.0781980	−	0.0451476i
$269$	−224.966	+	129.884i	−0.836305	+	0.482841i	−0.856007	−	0.516965i	$-0.827062\pi$
$269$	−224.966	+	129.884i	−0.836305	+	0.482841i	0.0197015	+	0.999806i	$0.493728\pi$
$270$		0			0
$271$	142.862	+	82.4817i	0.527168	+	0.304360i	0.739862	−	0.672758i	$-0.234891\pi$
$271$	142.862	+	82.4817i	0.527168	+	0.304360i	−0.212695	+	0.977119i	$0.568224\pi$
$272$	−153.493			−0.564313
$273$		0			0
$274$	42.5271			0.155208
$275$	−150.002	−	26.5117i	−0.545461	−	0.0964062i
$276$		0			0
$277$	437.005	−	252.305i	1.57764	−	0.910848i	0.582447	−	0.812869i	$-0.302095\pi$
$277$	437.005	−	252.305i	1.57764	−	0.910848i	0.995188	−	0.0979797i	$-0.0312380\pi$
$278$	15.7100	−	27.2104i	0.0565106	−	0.0978793i
$279$		0			0
$280$	−45.3437	−	56.5761i	−0.161942	−	0.202057i
$281$	−119.284			−0.424498			−0.212249	−	0.977216i	$-0.568079\pi$
$281$	−119.284			−0.424498			−0.212249	+	0.977216i	$0.568079\pi$
$282$		0			0
$283$	194.704	+	337.236i	0.687998	+	1.19165i	0.972484	+	0.232968i	$0.0748437\pi$
$283$	194.704	+	337.236i	0.687998	+	1.19165i	−0.284486	+	0.958680i	$0.591823\pi$
$284$	−94.5856	−	163.827i	−0.333048	−	0.576856i
$285$		0			0
$286$			20.8283i			0.0728264i
$287$	−134.145	+	32.7569i	−0.467405	+	0.114135i
$288$		0			0
$289$	93.4196	−	161.808i	0.323251	−	0.559888i
$290$	−1.86483	+	21.2658i	−0.00643046	+	0.0733302i
$291$		0			0
$292$	−11.0986	+	19.2233i	−0.0380088	+	0.0658331i
$293$	482.593			1.64708			0.823538	−	0.567261i	$-0.191997\pi$
$293$	482.593			1.64708			0.823538	+	0.567261i	$0.191997\pi$
$294$		0			0
$295$	437.340	+	306.360i	1.48251	+	1.03851i
$296$	17.2644	−	29.9028i	0.0583256	−	0.101023i
$297$		0			0
$298$	−48.7595	+	28.1513i	−0.163623	+	0.0944675i
$299$	396.529	+	228.936i	1.32618	+	0.765672i
$300$		0			0
$301$	−363.633	+	88.7952i	−1.20808	+	0.295001i
$302$			30.7201i			0.101722i
$303$		0			0
$304$	−296.696	+	171.297i	−0.975972	+	0.563478i
$305$	−9.29075	+	105.948i	−0.0304615	+	0.347370i
$306$		0			0
$307$	−87.6642			−0.285551			−0.142776	−	0.989755i	$-0.545603\pi$
$307$	−87.6642			−0.285551			−0.142776	+	0.989755i	$0.545603\pi$
$308$	−160.974	−	47.0037i	−0.522644	−	0.152609i
$309$		0			0
$310$	−14.9631	−	32.1054i	−0.0482681	−	0.103566i
$311$	149.803	−	86.4888i	0.481681	−	0.278099i	−0.239435	−	0.970912i	$-0.576962\pi$
$311$	149.803	−	86.4888i	0.481681	−	0.278099i	0.721117	+	0.692813i	$0.243629\pi$
$312$		0			0
$313$	31.1714	−	53.9905i	0.0995891	−	0.172493i	−0.811926	−	0.583761i	$-0.801580\pi$
$313$	31.1714	−	53.9905i	0.0995891	−	0.172493i	0.911515	+	0.411268i	$0.134914\pi$
$314$			6.51324i			0.0207428i
$315$		0			0
$316$	−150.672			−0.476809
$317$	143.150	+	82.6479i	0.451578	+	0.260719i	0.708497	−	0.705714i	$-0.249374\pi$
$317$	143.150	+	82.6479i	0.451578	+	0.260719i	−0.256918	+	0.966433i	$0.582707\pi$
$318$		0			0
$319$	49.8029	+	86.2611i	0.156122	+	0.270411i
$320$	−121.544	−	260.790i	−0.379826	−	0.814968i
$321$		0			0
$322$	46.2200	−	44.2035i	0.143540	−	0.137278i
$323$			228.021i			0.705948i
$324$		0			0
$325$	210.431	−	250.576i	0.647480	−	0.771005i
$326$	16.9370	+	29.3358i	0.0519541	+	0.0899871i
$327$		0			0
$328$	40.8649			0.124588
$329$	−246.448	−	71.9614i	−0.749081	−	0.218728i
$330$		0			0
$331$	166.380	−	288.178i	0.502657	−	0.870628i	−0.497338	−	0.867557i	$-0.665689\pi$
$331$	166.380	−	288.178i	0.502657	−	0.870628i	0.999995	−	0.00307088i	$-0.000977494\pi$
$332$	201.228	+	348.537i	0.606108	+	1.04981i
$333$		0			0
$334$	−14.8608	−	8.57988i	−0.0444934	−	0.0256882i
$335$	−25.2048	−	17.6561i	−0.0752381	−	0.0527049i
$336$		0			0
$337$		−	313.978i		−	0.931685i	−0.884868	−	0.465842i	$-0.845751\pi$
$337$		−	313.978i		−	0.931685i	0.884868	−	0.465842i	$-0.154249\pi$
$338$	−0.522828	−	0.301855i	−0.00154683	−	0.000893062i
$339$		0			0
$340$	−197.942	−	17.3579i	−0.582184	−	0.0510527i
$341$	−143.131	−	82.6365i	−0.419738	−	0.242336i
$342$		0			0
$343$	225.784	+	258.207i	0.658262	+	0.752789i
$344$	110.774			0.322018
$345$		0			0
$346$	22.5992	−	13.0476i	0.0653156	−	0.0377100i
$347$	188.880	−	109.050i	0.544322	−	0.314264i	−0.202507	−	0.979281i	$-0.564909\pi$
$347$	188.880	−	109.050i	0.544322	−	0.314264i	0.746829	+	0.665017i	$0.231576\pi$
$348$		0			0
$349$		−	452.923i		−	1.29777i	−0.760885	−	0.648886i	$-0.775235\pi$
$349$		−	452.923i		−	1.29777i	0.760885	−	0.648886i	$-0.224765\pi$
$350$	−25.3587	−	38.0247i	−0.0724536	−	0.108642i
$351$		0			0
$352$	64.6529	+	37.3274i	0.183673	+	0.106044i
$353$	113.487	+	196.565i	0.321493	+	0.556842i	0.980796	−	0.195035i	$-0.0624821\pi$
$353$	113.487	+	196.565i	0.321493	+	0.556842i	−0.659304	+	0.751877i	$0.729149\pi$
$354$		0			0
$355$	−101.624	−	218.048i	−0.286264	−	0.614219i
$356$		−	154.817i		−	0.434878i
$357$		0			0
$358$		−	37.6885i		−	0.105275i
$359$	124.724	−	216.028i	0.347420	−	0.601748i	−0.638371	−	0.769729i	$-0.720391\pi$
$359$	124.724	−	216.028i	0.347420	−	0.601748i	0.985790	+	0.167981i	$0.0537246\pi$
$360$		0			0
$361$	73.9702	+	128.120i	0.204904	+	0.354903i
$362$	8.19650	−	14.1968i	0.0226423	−	0.0392176i
$363$		0			0
$364$	260.338	−	248.980i	0.715214	−	0.684010i
$365$	−16.1954	+	23.1196i	−0.0443710	+	0.0633412i
$366$		0			0
$367$	152.029	+	263.322i	0.414247	+	0.717497i	0.995349	−	0.0963334i	$-0.0307115\pi$
$367$	152.029	+	263.322i	0.414247	+	0.717497i	−0.581102	+	0.813831i	$0.697378\pi$
$368$	460.074	−	265.624i	1.25020	−	0.721805i
$369$		0			0
$370$	12.4881	−	17.8272i	0.0337516	−	0.0481816i
$371$	178.621	+	186.770i	0.481459	+	0.503422i
$372$		0			0
$373$	306.192	+	176.780i	0.820889	+	0.473940i	0.850723	−	0.525614i	$-0.176165\pi$
$373$	306.192	+	176.780i	0.820889	+	0.473940i	−0.0298340	+	0.999555i	$0.509498\pi$
$374$	13.9294	−	8.04217i	0.0372445	−	0.0215031i
$375$		0			0
$376$	65.7993	+	37.9892i	0.174998	+	0.101035i
$377$	−213.965			−0.567545
$378$		0			0
$379$	435.916			1.15017			0.575087	−	0.818092i	$-0.304968\pi$
$379$	435.916			1.15017			0.575087	+	0.818092i	$0.304968\pi$
$380$	−401.985	+	187.350i	−1.05786	+	0.493027i
$381$		0			0
$382$	13.0160	−	7.51478i	0.0340733	−	0.0196722i
$383$	−104.085	+	180.281i	−0.271764	+	0.470708i	−0.969314	−	0.245828i	$-0.920940\pi$
$383$	−104.085	+	180.281i	−0.271764	+	0.470708i	0.697550	+	0.716536i	$0.254274\pi$
$384$		0			0
$385$	−198.705	−	77.4280i	−0.516116	−	0.201112i
$386$	64.5188			0.167147
$387$		0			0
$388$	−65.9772	−	114.276i	−0.170044	−	0.294525i
$389$	−284.349	−	492.507i	−0.730975	−	1.26609i	−0.956467	−	0.291840i	$-0.905732\pi$
$389$	−284.349	−	492.507i	−0.730975	−	1.26609i	0.225493	−	0.974245i	$-0.427601\pi$
$390$		0			0
$391$		−	353.584i		−	0.904307i
$392$	−46.7839	−	90.0822i	−0.119347	−	0.229801i
$393$		0			0
$394$	−29.4333	+	50.9799i	−0.0747038	+	0.129391i
$395$	−190.874	−	16.7381i	−0.483226	−	0.0423750i
$396$		0			0
$397$	−142.678	+	247.125i	−0.359390	+	0.622482i	−0.987859	−	0.155353i	$-0.950349\pi$
$397$	−142.678	+	247.125i	−0.359390	+	0.622482i	0.628469	+	0.777835i	$0.283682\pi$
$398$	48.0728			0.120786
$399$		0			0
$400$	−129.705	−	356.810i	−0.324263	−	0.892024i
$401$	140.086	−	242.635i	0.349341	−	0.605076i	−0.636792	−	0.771036i	$-0.719739\pi$
$401$	140.086	−	242.635i	0.349341	−	0.605076i	0.986132	+	0.165960i	$0.0530723\pi$
$402$		0			0
$403$	307.461	−	177.513i	0.762931	−	0.440478i
$404$	−65.2302	−	37.6607i	−0.161461	−	0.0932195i
$405$		0			0
$406$	−8.37684	+	28.6883i	−0.0206326	+	0.0706609i
$407$		−	101.559i		−	0.249531i
$408$		0			0
$409$	−62.2921	+	35.9644i	−0.152303	+	0.0879325i	−0.574215	−	0.818705i	$-0.694693\pi$
$409$	−62.2921	+	35.9644i	−0.152303	+	0.0879325i	0.421911	+	0.906637i	$0.361359\pi$
$410$	25.6618	+	2.25033i	0.0625896	+	0.00548860i
$411$		0			0
$412$	88.0465			0.213705
$413$	516.685	+	540.256i	1.25105	+	1.30813i
$414$		0			0
$415$	216.201	+	463.889i	0.520967	+	1.11781i
$416$	−138.882	+	80.1835i	−0.333851	+	0.192749i
$417$		0			0
$418$	17.9500	−	31.0903i	0.0429426	−	0.0743788i
$419$			465.475i			1.11092i	0.831544	+	0.555459i	$0.187458\pi$
$419$			465.475i			1.11092i	−0.831544	+	0.555459i	$0.812542\pi$
$420$		0			0
$421$	−368.126			−0.874410			−0.437205	−	0.899362i	$-0.644032\pi$
$421$	−368.126			−0.874410			−0.437205	+	0.899362i	$0.644032\pi$
$422$	−42.9505	−	24.7975i	−0.101778	−	0.0587618i
$423$		0			0
$424$	−38.2401	−	66.2338i	−0.0901890	−	0.156212i
$425$	−248.830	−	43.9789i	−0.585482	−	0.103480i
$426$		0			0
$427$	−41.7341	+	142.928i	−0.0977379	+	0.334725i
$428$		−	204.264i		−	0.477251i
$429$		0			0
$430$	69.5623	+	6.10004i	0.161773	+	0.0141861i
$431$	379.314	+	656.992i	0.880080	+	1.52434i	0.851251	+	0.524758i	$0.175844\pi$
$431$	379.314	+	656.992i	0.880080	+	1.52434i	0.0288283	+	0.999584i	$0.490822\pi$
$432$		0			0
$433$	423.683			0.978482			0.489241	−	0.872149i	$-0.337274\pi$
$433$	423.683			0.978482			0.489241	+	0.872149i	$0.337274\pi$
$434$	−11.7636	−	48.1740i	−0.0271050	−	0.111000i
$435$		0			0
$436$	−357.260	+	618.792i	−0.819403	+	1.41925i
$437$	−394.597	−	683.462i	−0.902968	−	1.56399i
$438$		0			0
$439$	−63.4357	−	36.6246i	−0.144500	−	0.0834273i	0.426007	−	0.904720i	$-0.359920\pi$
$439$	−63.4357	−	36.6246i	−0.144500	−	0.0834273i	−0.570507	+	0.821293i	$0.693253\pi$
$440$	51.6899	+	36.2092i	0.117477	+	0.0822936i
$441$		0			0
$442$			34.5510i			0.0781697i
$443$	499.601	+	288.445i	1.12777	+	0.651117i	0.943372	−	0.331736i	$-0.107634\pi$
$443$	499.601	+	288.445i	1.12777	+	0.651117i	0.184395	+	0.982852i	$0.440968\pi$
$444$		0			0
$445$	17.1986	−	196.125i	0.0386485	−	0.440731i
$446$	70.2811	+	40.5768i	0.157581	+	0.0909794i
$447$		0			0
$448$	−95.5547	−	391.314i	−0.213292	−	0.873469i
$449$	652.932			1.45419			0.727095	−	0.686537i	$-0.240870\pi$
$449$	652.932			1.45419			0.727095	+	0.686537i	$0.240870\pi$
$450$		0			0
$451$	104.093	−	60.0980i	0.230804	−	0.133255i
$452$	−663.980	+	383.349i	−1.46898	+	0.848118i
$453$		0			0
$454$		−	42.8173i		−	0.0943112i
$455$	357.461	−	286.493i	0.785629	−	0.629654i
$456$		0			0
$457$	−108.778	−	62.8031i	−0.238027	−	0.137425i	0.376243	−	0.926521i	$-0.377216\pi$
$457$	−108.778	−	62.8031i	−0.238027	−	0.137425i	−0.614269	+	0.789096i	$0.710549\pi$
$458$	2.04863	+	3.54832i	0.00447298	+	0.00774743i
$459$		0			0
$460$	623.343	−	290.517i	1.35509	−	0.631558i
$461$		−	695.270i		−	1.50818i	−0.656773	−	0.754089i	$-0.728079\pi$
$461$		−	695.270i		−	1.50818i	0.656773	−	0.754089i	$-0.271921\pi$
$462$		0			0
$463$			438.632i			0.947370i	0.880694	+	0.473685i	$0.157076\pi$
$463$			438.632i			0.947370i	−0.880694	+	0.473685i	$0.842924\pi$
$464$	−124.127	+	214.994i	−0.267515	+	0.463349i
$465$		0			0
$466$	35.7276	+	61.8821i	0.0766687	+	0.132794i
$467$	−41.6921	+	72.2129i	−0.0892765	+	0.154631i	−0.907206	−	0.420688i	$-0.861789\pi$
$467$	−41.6921	+	72.2129i	−0.0892765	+	0.154631i	0.817929	+	0.575319i	$0.195122\pi$
$468$		0			0
$469$	−29.7776	−	31.1360i	−0.0634917	−	0.0663881i
$470$	39.2277	+	27.4793i	0.0834631	+	0.0584666i
$471$		0			0
$472$	−110.615	−	191.590i	−0.234353	−	0.405911i
$473$	282.168	−	162.910i	0.596550	−	0.344418i
$474$		0			0
$475$	−530.057	+	192.683i	−1.11591	+	0.405649i
$476$	−267.032	−	77.9719i	−0.560991	−	0.163807i
$477$		0			0
$478$	19.7256	+	11.3886i	0.0412670	+	0.0238255i
$479$	270.669	−	156.271i	0.565071	−	0.326244i	−0.190108	−	0.981763i	$-0.560884\pi$
$479$	270.669	−	156.271i	0.565071	−	0.326244i	0.755178	+	0.655520i	$0.227550\pi$
$480$		0			0
$481$	188.933	+	109.081i	0.392792	+	0.226779i
$482$	36.6435			0.0760239
$483$		0			0
$484$	−329.777			−0.681358
$485$	−70.8866	−	152.097i	−0.146158	−	0.313602i
$486$		0			0
$487$	−425.683	+	245.768i	−0.874093	+	0.504658i	−0.868706	−	0.495328i	$-0.835048\pi$
$487$	−425.683	+	245.768i	−0.874093	+	0.504658i	−0.00538659	+	0.999985i	$0.501715\pi$
$488$	22.0319	−	38.1604i	0.0451473	−	0.0781975i
$489$		0			0
$490$	−24.4180	−	59.1447i	−0.0498327	−	0.120703i
$491$	−693.987			−1.41342			−0.706708	−	0.707506i	$-0.749820\pi$
$491$	−693.987			−1.41342			−0.706708	+	0.707506i	$0.749820\pi$
$492$		0			0
$493$	82.6153	+	143.094i	0.167577	+	0.290251i
$494$	38.5587	+	66.7856i	0.0780541	+	0.135194i
$495$		0			0
$496$		−	411.920i		−	0.830485i
$497$	−79.8938	−	327.179i	−0.160752	−	0.658309i
$498$		0			0
$499$	35.7821	−	61.9763i	0.0717075	−	0.124201i	−0.827942	−	0.560813i	$-0.810489\pi$
$499$	35.7821	−	61.9763i	0.0717075	−	0.124201i	0.899650	+	0.436612i	$0.143822\pi$
$500$	−126.916	−	474.804i	−0.253831	−	0.949608i
$501$		0			0
$502$	−33.0333	+	57.2153i	−0.0658033	+	0.113975i
$503$	−573.959			−1.14107			−0.570535	−	0.821273i	$-0.693264\pi$
$503$	−573.959			−1.14107			−0.570535	+	0.821273i	$0.693264\pi$
$504$		0			0
$505$	−78.4515	−	54.9559i	−0.155349	−	0.108824i
$506$	−27.8344	+	48.2106i	−0.0550087	+	0.0952778i
$507$		0			0
$508$	−229.410	+	132.450i	−0.451595	+	0.260728i
$509$	−394.898	−	227.995i	−0.775832	−	0.447927i	0.0591192	−	0.998251i	$-0.481171\pi$
$509$	−394.898	−	227.995i	−0.775832	−	0.447927i	−0.834951	+	0.550324i	$0.814504\pi$
$510$		0			0
$511$	−28.5601	+	27.3141i	−0.0558906	+	0.0534522i
$512$			311.902i			0.609184i
$513$		0			0
$514$	−85.4642	+	49.3428i	−0.166273	+	0.0959977i
$515$	111.539	+	9.78109i	0.216581	+	0.0189924i
$516$		0			0
$517$	223.475			0.432254
$518$	22.0223	−	21.0615i	0.0425142	−	0.0406593i
$519$		0			0
$520$	−122.879	+	57.2691i	−0.236305	+	0.110133i
$521$	318.552	−	183.916i	0.611424	−	0.353006i	−0.162098	−	0.986775i	$-0.551826\pi$
$521$	318.552	−	183.916i	0.611424	−	0.353006i	0.773523	+	0.633769i	$0.218493\pi$
$522$		0			0
$523$	−329.927	+	571.450i	−0.630835	+	1.09264i	0.356546	+	0.934278i	$0.383954\pi$
$523$	−329.927	+	571.450i	−0.630835	+	1.09264i	−0.987381	+	0.158361i	$0.949379\pi$
$524$			372.749i			0.711353i
$525$		0			0
$526$	58.7308			0.111656
$527$	−237.432	−	137.081i	−0.450535	−	0.260116i
$528$		0			0
$529$	347.387	+	601.691i	0.656685	+	1.13741i
$530$	−20.3661	−	43.6983i	−0.0384267	−	0.0824496i
$531$		0			0
$532$	−603.177	+	147.289i	−1.13379	+	0.276860i
$533$			258.195i			0.484418i
$534$		0			0
$535$	22.6917	−	258.766i	0.0424143	−	0.483675i
$536$	6.37494	+	11.0417i	0.0118935	+	0.0206002i
$537$		0			0
$538$	67.8441			0.126104
$539$	−251.649	−	160.658i	−0.466881	−	0.298067i
$540$		0			0
$541$	237.101	−	410.672i	0.438265	−	0.759098i	−0.559291	−	0.828972i	$-0.688926\pi$
$541$	237.101	−	410.672i	0.438265	−	0.759098i	0.997556	+	0.0698740i	$0.0222597\pi$
$542$	−21.5419	−	37.3116i	−0.0397451	−	0.0688406i
$543$		0			0
$544$	107.249	+	61.9204i	0.197149	+	0.113824i
$545$	−521.327	+	744.213i	−0.956563	+	1.36553i
$546$		0			0
$547$		−	401.484i		−	0.733975i	−0.930226	−	0.366987i	$-0.880389\pi$
$547$		−	401.484i		−	0.733975i	0.930226	−	0.366987i	$-0.119611\pi$
$548$	554.448	+	320.111i	1.01177	+	0.584144i
$549$		0			0
$550$	30.4655	+	25.5845i	0.0553918	+	0.0465173i
$551$	319.384	+	184.396i	0.579644	+	0.334657i
$552$		0			0
$553$	−257.497	−	75.1878i	−0.465637	−	0.135963i
$554$	−131.790			−0.237888
$555$		0			0
$556$	409.638	−	236.505i	0.736759	−	0.425368i
$557$	35.2935	−	20.3767i	0.0633636	−	0.0365830i	−0.467984	−	0.883737i	$-0.655019\pi$
$557$	35.2935	−	20.3767i	0.0633636	−	0.0365830i	0.531347	+	0.847154i	$0.321686\pi$
$558$		0			0
$559$			699.898i			1.25205i
$560$	−80.4975	−	525.383i	−0.143746	−	0.938185i
$561$		0			0
$562$	26.9797	+	15.5768i	0.0480067	+	0.0277167i
$563$	368.838	+	638.845i	0.655129	+	1.13472i	0.981861	+	0.189600i	$0.0607190\pi$
$563$	368.838	+	638.845i	0.655129	+	1.13472i	−0.326733	+	0.945117i	$0.605948\pi$
$564$		0			0
$565$	−883.733	+	411.874i	−1.56413	+	0.728981i
$566$		−	101.702i		−	0.179685i
$567$		0			0
$568$			99.6694i			0.175474i
$569$	−255.233	+	442.077i	−0.448564	+	0.776936i	−0.998293	−	0.0584072i	$-0.981398\pi$
$569$	−255.233	+	442.077i	−0.448564	+	0.776936i	0.549729	+	0.835343i	$0.314731\pi$
$570$		0			0
$571$	328.855	+	569.594i	0.575928	+	0.997537i	0.995940	+	0.0900183i	$0.0286925\pi$
$571$	328.855	+	569.594i	0.575928	+	0.997537i	−0.420012	+	0.907519i	$0.637974\pi$
$572$	−156.779	+	271.550i	−0.274090	+	0.474738i
$573$		0			0
$574$	34.6187	+	10.1085i	0.0603113	+	0.0176106i
$575$	821.940	−	298.786i	1.42946	−	0.519628i
$576$		0			0
$577$	−517.946	−	897.109i	−0.897654	−	1.55478i	−0.830485	−	0.557041i	$-0.811937\pi$
$577$	−517.946	−	897.109i	−0.897654	−	1.55478i	−0.0671686	−	0.997742i	$-0.521397\pi$
$578$	−42.2595	+	24.3985i	−0.0731133	+	0.0422120i
$579$		0			0
$580$	−184.385	+	263.216i	−0.317905	+	0.453821i
$581$	169.971	+	696.064i	0.292550	+	1.19804i
$582$		0			0
$583$	−194.813	−	112.476i	−0.334157	−	0.192925i
$584$	10.1282	−	5.84754i	0.0173429	−	0.0100129i
$585$		0			0
$586$	−109.153	−	63.0198i	−0.186269	−	0.107542i
$587$	18.0678			0.0307799			0.0153900	−	0.999882i	$-0.495101\pi$
$587$	18.0678			0.0307799			0.0153900	+	0.999882i	$0.495101\pi$
$588$		0			0
$589$	−611.927			−1.03893
$590$	−58.9117	−	126.403i	−0.0998504	−	0.214243i
$591$		0			0
$592$	219.211	−	126.561i	0.370288	−	0.213786i
$593$	1.41323	−	2.44778i	0.00238318	−	0.00412779i	−0.864831	−	0.502062i	$-0.832575\pi$
$593$	1.41323	−	2.44778i	0.00238318	−	0.00412779i	0.867215	+	0.497935i	$0.165908\pi$
$594$		0			0
$595$	−329.621	−	128.441i	−0.553984	−	0.215868i
$596$	−847.605			−1.42216
$597$		0			0
$598$	−59.7915	−	103.562i	−0.0999858	−	0.173180i
$599$	158.480	+	274.495i	0.264574	+	0.458256i	0.967452	−	0.253055i	$-0.0814353\pi$
$599$	158.480	+	274.495i	0.264574	+	0.458256i	−0.702878	+	0.711310i	$0.748102\pi$
$600$		0			0
$601$			479.510i			0.797854i	0.916983	+	0.398927i	$0.130617\pi$
$601$			479.510i			0.797854i	−0.916983	+	0.398927i	$0.869383\pi$
$602$	93.8422	+	27.4014i	0.155884	+	0.0455173i
$603$		0			0
$604$	−231.237	+	400.514i	−0.382843	+	0.663103i
$605$	−417.770	−	36.6350i	−0.690528	−	0.0605537i
$606$		0			0
$607$	−142.302	+	246.475i	−0.234436	+	0.406054i	−0.959108	−	0.283039i	$-0.908658\pi$
$607$	−142.302	+	246.475i	−0.234436	+	0.406054i	0.724673	+	0.689093i	$0.241991\pi$
$608$	276.411			0.454623
$609$		0			0
$610$	15.9367	−	22.7501i	0.0261257	−	0.0372953i
$611$	−240.025	+	415.736i	−0.392840	+	0.680419i
$612$		0			0
$613$	820.234	−	473.562i	1.33807	−	0.772533i	0.351545	−	0.936171i	$-0.385656\pi$
$613$	820.234	−	473.562i	1.33807	−	0.772533i	0.986520	+	0.163638i	$0.0523230\pi$
$614$	19.8280	+	11.4477i	0.0322931	+	0.0186444i
$615$		0			0
$616$	61.0679	+	63.8537i	0.0991362	+	0.103659i
$617$			626.960i			1.01614i	0.861315	+	0.508071i	$0.169641\pi$
$617$			626.960i			1.01614i	−0.861315	+	0.508071i	$0.830359\pi$
$618$		0			0
$619$	826.701	−	477.296i	1.33554	−	0.771076i	0.349399	−	0.936974i	$-0.386386\pi$
$619$	826.701	−	477.296i	1.33554	−	0.771076i	0.986143	+	0.165898i	$0.0530523\pi$
$620$	46.5824	−	531.206i	0.0751329	−	0.856784i
$621$		0			0
$622$	−45.1768			−0.0726315
$623$	77.2561	−	264.581i	0.124007	−	0.424688i
$624$		0			0
$625$	−108.034	−	615.592i	−0.172854	−	0.984947i
$626$	−14.1008	+	8.14108i	−0.0225252	+	0.0130049i
$627$		0			0
$628$	−49.0266	+	84.9166i	−0.0780678	+	0.135217i
$629$		−	168.471i		−	0.267840i
$630$		0			0
$631$	−773.291			−1.22550			−0.612751	−	0.790276i	$-0.709937\pi$
$631$	−773.291			−1.22550			−0.612751	+	0.790276i	$0.709937\pi$
$632$	68.7494	+	39.6925i	0.108781	+	0.0628045i
$633$		0			0
$634$	−21.5853	−	37.3868i	−0.0340462	−	0.0589697i
$635$	−305.336	+	142.306i	−0.480844	+	0.224103i
$636$		0			0
$637$	569.161	−	295.592i	0.893503	−	0.464038i
$638$		−	26.0142i		−	0.0407746i
$639$		0			0
$640$	−27.9710	+	318.969i	−0.0437046	+	0.498389i
$641$	−85.9409	−	148.854i	−0.134073	−	0.232222i	0.791170	−	0.611597i	$-0.209472\pi$
$641$	−85.9409	−	148.854i	−0.134073	−	0.232222i	−0.925243	+	0.379375i	$0.876139\pi$
$642$		0			0
$643$	−301.390			−0.468725			−0.234363	−	0.972149i	$-0.575300\pi$
$643$	−301.390			−0.468725			−0.234363	+	0.972149i	$0.575300\pi$
$644$	935.324	−	228.396i	1.45237	−	0.354652i
$645$		0			0
$646$	29.7763	−	51.5741i	0.0460934	−	0.0798361i
$647$	−347.837	−	602.471i	−0.537615	−	0.931177i	−0.999032	−	0.0439931i	$-0.985992\pi$
$647$	−347.837	−	602.471i	−0.537615	−	0.931177i	0.461417	−	0.887184i	$-0.347341\pi$
$648$		0			0
$649$	−563.524	−	325.351i	−0.868295	−	0.501311i
$650$	−80.3172	+	29.1964i	−0.123565	+	0.0449175i
$651$		0			0
$652$			509.955i			0.782139i
$653$	−522.355	−	301.582i	−0.799930	−	0.461840i	0.0435164	−	0.999053i	$-0.486144\pi$
$653$	−522.355	−	301.582i	−0.799930	−	0.461840i	−0.843447	+	0.537213i	$0.819477\pi$
$654$		0			0
$655$	−41.4087	+	472.207i	−0.0632194	+	0.720927i
$656$	259.437	+	149.786i	0.395483	+	0.228332i
$657$		0			0
$658$	46.3446	+	48.4588i	0.0704326	+	0.0736456i
$659$	−403.838			−0.612804			−0.306402	−	0.951902i	$-0.599125\pi$
$659$	−403.838			−0.612804			−0.306402	+	0.951902i	$0.599125\pi$
$660$		0			0
$661$	680.021	−	392.610i	1.02878	−	0.593964i	0.112142	−	0.993692i	$-0.464229\pi$
$661$	680.021	−	392.610i	1.02878	−	0.593964i	0.916634	+	0.399728i	$0.130896\pi$
$662$	−75.2638	+	43.4536i	−0.113692	+	0.0656398i
$663$		0			0
$664$		−	212.043i		−	0.319342i
$665$	−780.482	+	119.583i	−1.17366	+	0.179824i
$666$		0			0
$667$	−495.256	−	285.936i	−0.742513	−	0.428690i
$668$	−129.165	−	223.721i	−0.193361	−	0.334911i
$669$		0			0
$670$	3.39520	+	7.28487i	0.00506746	+	0.0108729i
$671$		−	129.605i		−	0.193152i
$672$		0			0
$673$			374.318i			0.556193i	0.960553	+	0.278096i	$0.0897035\pi$
$673$			374.318i			0.556193i	−0.960553	+	0.278096i	$0.910297\pi$
$674$	−41.0010	+	71.0158i	−0.0608324	+	0.105365i
$675$		0			0
$676$	−4.54426	−	7.87089i	−0.00672228	−	0.0116433i
$677$	470.298	−	814.579i	0.694679	−	1.20322i	−0.275610	−	0.961270i	$-0.588880\pi$
$677$	470.298	−	814.579i	0.694679	−	1.20322i	0.970289	−	0.241950i	$-0.0777869\pi$
$678$		0			0
$679$	−55.7291	−	228.221i	−0.0820752	−	0.336113i
$680$	85.7456	+	60.0655i	0.126097	+	0.0883316i
$681$		0			0
$682$	21.5823	+	37.3816i	0.0316456	+	0.0548118i
$683$	−0.311813	+	0.180026i	−0.000456535	+	0.000263581i	−0.500228	−	0.865894i	$-0.666751\pi$
$683$	−0.311813	+	0.180026i	−0.000456535	+	0.000263581i	0.499772	+	0.866157i	$0.333417\pi$
$684$		0			0
$685$	666.827	+	467.118i	0.973470	+	0.681923i
$686$	−17.3499	−	87.8856i	−0.0252914	−	0.128113i
$687$		0			0
$688$	703.265	+	406.030i	1.02219	+	0.590160i
$689$	418.482	−	241.610i	0.607375	−	0.350668i
$690$		0			0
$691$	−64.7660	−	37.3927i	−0.0937280	−	0.0541139i	0.452403	−	0.891813i	$-0.350567\pi$
$691$	−64.7660	−	37.3927i	−0.0937280	−	0.0541139i	−0.546131	+	0.837700i	$0.683900\pi$
$692$	392.850			0.567702
$693$		0			0
$694$	−56.9613			−0.0820768
$695$	545.212	−	254.103i	0.784478	−	0.365616i
$696$		0			0
$697$	172.674	−	99.6933i	0.247739	−	0.143032i
$698$	−59.1452	+	102.443i	−0.0847353	+	0.146766i
$699$		0			0
$700$	−44.3948	−	686.629i	−0.0634212	−	0.980899i
$701$	−661.374			−0.943472			−0.471736	−	0.881740i	$-0.656372\pi$
$701$	−661.374			−0.943472			−0.471736	+	0.881740i	$0.656372\pi$
$702$		0			0
$703$	−188.013	−	325.648i	−0.267444	−	0.463226i
$704$	175.311	+	303.648i	0.249022	+	0.431318i
$705$		0			0
$706$		−	59.2791i		−	0.0839647i
$707$	−92.6848	−	96.9129i	−0.131096	−	0.137076i
$708$		0			0
$709$	−33.3002	+	57.6776i	−0.0469678	+	0.0813506i	−0.888554	−	0.458773i	$-0.848289\pi$
$709$	−33.3002	+	57.6776i	−0.0469678	+	0.0813506i	0.841586	+	0.540124i	$0.181622\pi$
$710$	−5.48853	+	62.5889i	−0.00773032	+	0.0881533i
$711$		0			0
$712$	−40.7844	+	70.6406i	−0.0572814	+	0.0992144i
$713$	948.892			1.33084
$714$		0			0
$715$	−228.779	+	326.589i	−0.319970	+	0.456769i
$716$	283.690	−	491.365i	0.396215	−	0.686264i
$717$		0			0
$718$	−56.4202	+	32.5742i	−0.0785797	+	0.0453680i
$719$	−963.069	−	556.028i	−1.33946	−	0.773336i	−0.352730	−	0.935725i	$-0.614747\pi$
$719$	−963.069	−	556.028i	−1.33946	−	0.773336i	−0.986727	+	0.162390i	$0.948080\pi$
$720$		0			0
$721$	150.471	+	43.9367i	0.208698	+	0.0609386i
$722$		−	38.6378i		−	0.0535150i
$723$		0			0
$724$	213.724	−	123.394i	0.295199	−	0.170433i
$725$	−262.824	+	312.965i	−0.362516	+	0.431676i
$726$		0			0
$727$	1077.98			1.48278			0.741391	−	0.671073i	$-0.234166\pi$
$727$	1077.98			1.48278			0.741391	+	0.671073i	$0.234166\pi$
$728$	−184.379	+	45.0234i	−0.253268	+	0.0618453i
$729$		0			0
$730$	6.68218	−	3.11431i	0.00915368	−	0.00426618i
$731$	468.074	−	270.242i	0.640320	−	0.369689i
$732$		0			0
$733$	414.302	−	717.592i	0.565214	−	0.978980i	−0.431815	−	0.901962i	$-0.642127\pi$
$733$	414.302	−	717.592i	0.565214	−	0.978980i	0.997030	−	0.0770179i	$-0.0245398\pi$
$734$		−	79.4111i		−	0.108190i
$735$		0			0
$736$	−428.620			−0.582363
$737$	32.4770	+	18.7506i	0.0440665	+	0.0254418i
$738$		0			0
$739$	22.9967	+	39.8315i	0.0311187	+	0.0538992i	0.881165	−	0.472808i	$-0.156760\pi$
$739$	22.9967	+	39.8315i	0.0311187	+	0.0538992i	−0.850047	+	0.526707i	$0.823426\pi$
$740$	297.003	−	138.422i	0.401355	−	0.187057i
$741$		0			0
$742$	−16.0113	−	65.5691i	−0.0215785	−	0.0883681i
$743$			1104.41i			1.48642i	0.669060	+	0.743209i	$0.266697\pi$
$743$			1104.41i			1.48642i	−0.669060	+	0.743209i	$0.733303\pi$
$744$		0			0
$745$	−1073.77	−	94.1605i	−1.44130	−	0.126390i
$746$	−46.1698	−	79.9685i	−0.0618899	−	0.107196i
$747$		0			0
$748$	242.141			0.323718
$749$	101.931	−	349.085i	0.136090	−	0.466069i
$750$		0			0
$751$	−78.7995	+	136.485i	−0.104926	+	0.181737i	−0.913708	−	0.406371i	$-0.866794\pi$
$751$	−78.7995	+	136.485i	−0.104926	+	0.181737i	0.808782	+	0.588109i	$0.200127\pi$
$752$	278.491	+	482.360i	0.370333	+	0.641436i
$753$		0			0
$754$	48.3948	+	27.9407i	0.0641840	+	0.0370567i
$755$	−337.430	+	481.693i	−0.446927	+	0.638004i
$756$		0			0
$757$			1148.34i			1.51696i	0.651695	+	0.758481i	$0.274058\pi$
$757$			1148.34i			1.51696i	−0.651695	+	0.758481i	$0.725942\pi$
$758$	−98.5960	−	56.9244i	−0.130074	−	0.0750982i
$759$		0			0
$760$	232.775	+	20.4125i	0.306283	+	0.0268585i
$761$	761.832	+	439.844i	1.00109	+	0.577981i	0.908571	−	0.417729i	$-0.137174\pi$
$761$	761.832	+	439.844i	1.00109	+	0.577981i	0.0925215	+	0.995711i	$0.470507\pi$
$762$		0			0
$763$	−919.343	+	879.234i	−1.20491	+	1.15234i
$764$	226.262			0.296154
$765$		0			0
$766$	47.0843	−	27.1841i	0.0614678	−	0.0354884i
$767$	1210.51	−	698.890i	1.57824	−	0.911200i
$768$		0			0
$769$			725.749i			0.943757i	0.881664	+	0.471879i	$0.156424\pi$
$769$			725.749i			0.943757i	−0.881664	+	0.471879i	$0.843576\pi$
$770$	34.8322	+	43.4607i	0.0452367	+	0.0564425i
$771$		0			0
$772$	841.166	+	485.648i	1.08959	+	0.629077i
$773$	−82.5496	−	142.980i	−0.106791	−	0.184968i	0.807677	−	0.589625i	$-0.200724\pi$
$773$	−82.5496	−	142.980i	−0.106791	−	0.184968i	−0.914469	+	0.404657i	$0.867391\pi$
$774$		0			0
$775$	118.023	−	667.770i	0.152288	−	0.861638i
$776$			69.5233i			0.0895919i
$777$		0			0
$778$			148.528i			0.190910i
$779$	222.514	−	385.406i	0.285641	−	0.494744i
$780$		0			0
$781$	146.579	+	253.882i	0.187681	+	0.325072i
$782$	−46.1730	+	79.9740i	−0.0590448	+	0.102269i
$783$		0			0
$784$	33.1722	−	743.380i	0.0423115	−	0.948189i
$785$	−71.5415	+	102.128i	−0.0911356	+	0.130099i
$786$		0			0
$787$	99.1839	+	171.792i	0.126028	+	0.218287i	0.922134	−	0.386870i	$-0.126444\pi$
$787$	99.1839	+	171.792i	0.126028	+	0.218287i	−0.796106	+	0.605157i	$0.793110\pi$
$788$	−767.474	+	443.102i	−0.973952	+	0.562312i
$789$		0			0
$790$	40.9864	+	28.7113i	0.0518816	+	0.0363434i
$791$	−1326.04	+	323.804i	−1.67641	+	0.409360i
$792$		0			0
$793$	241.107	+	139.203i	0.304044	+	0.175540i
$794$	64.5420	−	37.2634i	0.0812872	−	0.0469312i
$795$		0			0
$796$	626.750	+	361.854i	0.787374	+	0.454591i
$797$	266.357			0.334199			0.167100	−	0.985940i	$-0.446560\pi$
$797$	266.357			0.334199			0.167100	+	0.985940i	$0.446560\pi$
$798$		0			0
$799$	370.711			0.463969
$800$	−53.3118	+	301.635i	−0.0666398	+	0.377044i
$801$		0			0
$802$	−63.3694	+	36.5863i	−0.0790142	+	0.0456189i
$803$	17.1993	−	29.7901i	0.0214189	−	0.0370986i
$804$		0			0
$805$	1210.26	−	185.433i	1.50343	−	0.230351i
$806$	−92.7225			−0.115040
$807$		0			0
$808$	19.8424	+	34.3681i	0.0245575	+	0.0425348i
$809$	472.741	+	818.812i	0.584352	+	1.01213i	0.994956	+	0.100314i	$0.0319847\pi$
$809$	472.741	+	818.812i	0.584352	+	1.01213i	−0.410603	+	0.911814i	$0.634682\pi$
$810$		0			0
$811$		−	1402.01i		−	1.72875i	−0.502850	−	0.864374i	$-0.667715\pi$
$811$		−	1402.01i		−	1.72875i	0.502850	−	0.864374i	$-0.332285\pi$
$812$	−325.157	+	310.971i	−0.400439	+	0.382969i
$813$		0			0
$814$	−13.2622	+	22.9708i	−0.0162926	+	0.0282196i
$815$	−56.6509	+	646.023i	−0.0695103	+	0.792666i
$816$		0			0
$817$	603.177	−	1044.73i	0.738283	−	1.27874i
$818$	18.7857			0.0229654
$819$		0			0
$820$	317.627	+	222.500i	0.387350	+	0.271342i
$821$	224.015	−	388.005i	0.272856	−	0.472601i	−0.696736	−	0.717328i	$-0.745365\pi$
$821$	224.015	−	388.005i	0.272856	−	0.472601i	0.969592	+	0.244727i	$0.0786983\pi$
$822$		0			0
$823$	325.923	−	188.172i	0.396018	−	0.228641i	−0.288746	−	0.957406i	$-0.593238\pi$
$823$	325.923	−	188.172i	0.396018	−	0.228641i	0.684764	+	0.728765i	$0.259905\pi$
$824$	−40.1744	−	23.1947i	−0.0487553	−	0.0281489i
$825$		0			0
$826$	−46.3148	−	189.667i	−0.0560711	−	0.229622i
$827$		−	1506.52i		−	1.82166i	−0.412778	−	0.910832i	$-0.635441\pi$
$827$		−	1506.52i		−	1.82166i	0.412778	−	0.910832i	$-0.364559\pi$
$828$		0			0
$829$	1072.01	−	618.925i	1.29313	−	0.746592i	0.313926	−	0.949447i	$-0.398356\pi$
$829$	1072.01	−	618.925i	1.29313	−	0.746592i	0.979209	+	0.202856i	$0.0650222\pi$
$830$	11.6767	−	133.156i	0.0140683	−	0.160429i
$831$		0			0
$832$	−753.178			−0.905261
$833$	−417.447	−	266.507i	−0.501137	−	0.319937i
$834$		0			0
$835$	−138.776	−	297.764i	−0.166199	−	0.356603i
$836$	468.048	−	270.227i	0.559866	−	0.323239i
$837$		0			0
$838$	60.7844	−	105.282i	0.0725350	−	0.125634i
$839$		−	158.707i		−	0.189162i	−0.995517	−	0.0945808i	$-0.969849\pi$
$839$		−	158.707i		−	0.189162i	0.995517	−	0.0945808i	$-0.0301511\pi$
$840$		0			0
$841$	−573.762			−0.682238
$842$	83.2632	+	48.0721i	0.0988875	+	0.0570927i
$843$		0			0
$844$	−373.312	−	646.595i	−0.442313	−	0.766108i
$845$	−4.88240	−	10.4758i	−0.00577799	−	0.0123975i
$846$		0			0
$847$	−563.587	−	164.565i	−0.665393	−	0.194291i
$848$		−	560.660i		−	0.661156i
$849$		0			0
$850$	50.5376	+	42.4408i	0.0594560	+	0.0499304i
$851$	291.544	+	504.969i	0.342590	+	0.593384i
$852$		0			0
$853$	−329.313			−0.386064			−0.193032	−	0.981192i	$-0.561832\pi$
$853$	−329.313			−0.386064			−0.193032	+	0.981192i	$0.561832\pi$
$854$	28.1038	−	26.8776i	0.0329084	−	0.0314727i
$855$		0			0
$856$	−53.8106	+	93.2026i	−0.0628628	+	0.108882i
$857$	336.964	+	583.639i	0.393190	+	0.681025i	0.992868	−	0.119216i	$-0.0380381\pi$
$857$	336.964	+	583.639i	0.393190	+	0.681025i	−0.599678	+	0.800241i	$0.704705\pi$
$858$		0			0
$859$	−717.735	−	414.384i	−0.835547	−	0.482403i	0.0202012	−	0.999796i	$-0.493569\pi$
$859$	−717.735	−	414.384i	−0.835547	−	0.482403i	−0.855748	+	0.517393i	$0.826903\pi$
$860$	861.004	+	603.140i	1.00117	+	0.701325i
$861$		0			0
$862$		−	198.132i		−	0.229852i
$863$	−89.2709	−	51.5406i	−0.103443	−	0.0597226i	0.447386	−	0.894341i	$-0.352355\pi$
$863$	−89.2709	−	51.5406i	−0.103443	−	0.0597226i	−0.550829	+	0.834618i	$0.685688\pi$
$864$		0			0
$865$	497.672	+	43.6417i	0.575343	+	0.0504529i
$866$	−95.8290	−	55.3269i	−0.110657	−	0.0638879i
$867$		0			0
$868$	209.248	−	716.618i	0.241070	−	0.825596i
$869$	233.495			0.268694
$870$		0			0
$871$	−69.7643	+	40.2784i	−0.0800968	+	0.0462439i
$872$	326.025	−	188.231i	0.373882	−	0.215861i
$873$		0			0
$874$			206.115i			0.235829i
$875$	20.0373	−	874.771i	0.0228997	−	0.999738i
$876$		0			0
$877$	−46.5819	−	26.8941i	−0.0531151	−	0.0306660i	0.473207	−	0.880951i	$-0.343096\pi$
$877$	−46.5819	−	26.8941i	−0.0531151	−	0.0306660i	−0.526322	+	0.850285i	$0.676429\pi$
$878$	9.56530	+	16.5676i	0.0108944	+	0.0188697i
$879$		0			0
$880$	195.440	+	419.343i	0.222091	+	0.476526i
$881$		−	1300.77i		−	1.47647i	−0.674545	−	0.738234i	$-0.735660\pi$
$881$		−	1300.77i		−	1.47647i	0.674545	−	0.738234i	$-0.264340\pi$
$882$		0			0
$883$		−	525.467i		−	0.595093i	−0.954707	−	0.297546i	$-0.903832\pi$
$883$		−	525.467i		−	0.595093i	0.954707	−	0.297546i	$-0.0961683\pi$
$884$	−260.073	+	450.460i	−0.294200	+	0.509570i
$885$		0			0
$886$	−75.3335	−	130.481i	−0.0850265	−	0.147270i
$887$	−698.419	+	1209.70i	−0.787395	+	1.36381i	0.140164	+	0.990128i	$0.455237\pi$
$887$	−698.419	+	1209.70i	−0.787395	+	1.36381i	−0.927558	+	0.373679i	$0.878096\pi$
$888$		0			0
$889$	−458.156	+	111.877i	−0.515361	+	0.125846i
$890$	−29.5012	+	42.1139i	−0.0331474	+	0.0473190i
$891$		0			0
$892$	610.862	+	1058.04i	0.684822	+	1.18615i
$893$	716.568	−	413.711i	0.802428	−	0.463282i
$894$		0			0
$895$	413.971	−	590.958i	0.462537	−	0.660289i
$896$	−125.646	+	430.302i	−0.140230	+	0.480247i
$897$		0			0
$898$	−147.681	−	85.2635i	−0.164455	−	0.0949483i
$899$	−384.013	+	221.710i	−0.427155	+	0.246618i
$900$		0			0
$901$	−323.166	−	186.580i	−0.358674	−	0.207081i
$902$	−31.3917			−0.0348024
$903$		0			0
$904$	403.953			0.446851
$905$	284.459	−	132.576i	0.314319	−	0.146492i
$906$		0			0
$907$	1436.20	−	829.191i	1.58346	−	0.914213i	0.589114	−	0.808050i	$-0.299477\pi$
$907$	1436.20	−	829.191i	1.58346	−	0.914213i	0.994349	−	0.106162i	$-0.0338564\pi$
$908$	322.295	−	558.231i	0.354950	−	0.614792i
$909$		0			0
$910$	−118.263	+	18.1198i	−0.129959	+	0.0199119i
$911$	−891.683			−0.978796			−0.489398	−	0.872061i	$-0.662783\pi$
$911$	−891.683			−0.978796			−0.489398	+	0.872061i	$0.662783\pi$
$912$		0			0
$913$	−311.841	−	540.125i	−0.341557	−	0.591593i
$914$	16.4024	+	28.4097i	0.0179457	+	0.0310829i
$915$		0			0
$916$			61.6818i			0.0673383i
$917$	−186.008	+	637.026i	−0.202844	+	0.694685i
$918$		0			0
$919$	−476.682	+	825.638i	−0.518697	+	0.898409i	0.481067	+	0.876684i	$0.340249\pi$
$919$	−476.682	+	825.638i	−0.518697	+	0.898409i	−0.999764	+	0.0217255i	$0.993084\pi$
$920$	−360.956	−	31.6528i	−0.392343	−	0.0344053i
$921$		0			0
$922$	−90.7923	+	157.257i	−0.0984732	+	0.170561i
$923$	−629.735			−0.682270
$924$		0			0
$925$	391.628	−	142.362i	0.423381	−	0.153905i
$926$	57.2791	−	99.2103i	0.0618565	−	0.107139i
$927$		0			0
$928$	173.461	−	100.148i	0.186919	−	0.107918i
$929$	−1235.66	−	713.408i	−1.33010	−	0.767931i	−0.344782	−	0.938683i	$-0.612047\pi$
$929$	−1235.66	−	713.408i	−1.33010	−	0.767931i	−0.985314	+	0.170751i	$0.945381\pi$
$930$		0			0
$931$	−1104.33	−	49.2789i	−1.18617	−	0.0529312i
$932$			1075.72i			1.15420i
$933$		0			0
$934$	18.8599	−	10.8888i	0.0201927	−	0.0116582i
$935$	306.750	+	26.8994i	0.328075	+	0.0287695i
$936$		0			0
$937$	−1775.21			−1.89456			−0.947282	−	0.320400i	$-0.896183\pi$
$937$	−1775.21			−1.89456			−0.947282	+	0.320400i	$0.896183\pi$
$938$	2.66921	+	10.9309i	0.00284564	+	0.0116534i
$939$		0			0
$940$	304.589	+	653.537i	0.324031	+	0.695252i
$941$	1361.38	−	785.994i	1.44674	−	0.835275i	0.448453	−	0.893806i	$-0.351975\pi$
$941$	1361.38	−	785.994i	1.44674	−	0.835275i	0.998286	+	0.0585313i	$0.0186417\pi$
$942$		0			0
$943$	−345.044	+	597.634i	−0.365900	+	0.633758i
$944$		−	1621.78i		−	1.71799i
$945$		0			0
$946$	−85.0948			−0.0899522
$947$	−477.980	−	275.962i	−0.504731	−	0.291407i	0.225934	−	0.974143i	$-0.427457\pi$
$947$	−477.980	−	275.962i	−0.504731	−	0.291407i	−0.730665	+	0.682736i	$0.760790\pi$
$948$		0			0
$949$	36.9462	+	63.9927i	0.0389317	+	0.0674317i
$950$	145.051	+	25.6366i	0.152685	+	0.0269859i
$951$		0			0
$952$	101.302	+	105.924i	0.106410	+	0.111264i
$953$		−	1328.92i		−	1.39446i	−0.716846	−	0.697232i	$-0.754415\pi$
$953$		−	1328.92i		−	1.39446i	0.716846	−	0.697232i	$-0.245585\pi$
$954$		0			0
$955$	286.634	+	25.1354i	0.300140	+	0.0263198i
$956$	171.449	+	296.958i	0.179340	+	0.310626i
$957$		0			0
$958$	−81.6269			−0.0852055
$959$	787.808	+	823.747i	0.821489	+	0.858964i
$960$		0			0
$961$	−112.623	+	195.069i	−0.117194	+	0.202986i
$962$	−28.4887	−	49.3439i	−0.0296141	−	0.0512930i
$963$		0			0
$964$	477.741	+	275.824i	0.495582	+	0.286124i
$965$	1011.66	+	708.675i	1.04835	+	0.734378i
$966$		0			0
$967$		−	380.091i		−	0.393062i	−0.980498	−	0.196531i	$-0.937032\pi$
$967$		−	380.091i		−	0.393062i	0.980498	−	0.196531i	$-0.0629676\pi$
$968$	150.473	+	86.8755i	0.155447	+	0.0897474i
$969$		0			0
$970$	−3.82847	+	43.6582i	−0.00394687	+	0.0450085i
$971$	1539.11	+	888.604i	1.58508	+	0.915144i	0.994102	+	0.108453i	$0.0345896\pi$
$971$	1539.11	+	888.604i	1.58508	+	0.915144i	0.590974	+	0.806691i	$0.298744\pi$
$972$		0			0
$973$	818.089	−	199.769i	0.840790	−	0.205312i
$974$	128.375			0.131802
$975$		0			0
$976$	279.745	−	161.511i	0.286624	−	0.165483i
$977$	−842.114	+	486.195i	−0.861939	+	0.497641i	−0.864661	−	0.502356i	$-0.832467\pi$
$977$	−842.114	+	486.195i	−0.861939	+	0.497641i	0.00272235	+	0.999996i	$0.499133\pi$
$978$		0			0
$979$			239.918i			0.245064i
$980$	126.844	−	954.901i	0.129433	−	0.974388i
$981$		0			0
$982$	156.967	+	90.6248i	0.159844	+	0.0922859i
$983$	−693.763	−	1201.63i	−0.705761	−	1.22241i	−0.966416	−	0.256982i	$-0.917272\pi$
$983$	−693.763	−	1201.63i	−0.705761	−	1.22241i	0.260655	−	0.965432i	$-0.416061\pi$
$984$		0			0
$985$	−1021.48	+	476.073i	−1.03703	+	0.483323i
$986$		−	43.1535i		−	0.0437663i
$987$		0			0
$988$			1160.96i			1.17506i
$989$	−935.324	+	1620.03i	−0.945727	+	1.63805i
$990$		0			0
$991$	963.975	+	1669.65i	0.972730	+	1.68482i	0.687231	+	0.726439i	$0.258826\pi$
$991$	963.975	+	1669.65i	0.972730	+	1.68482i	0.285499	+	0.958379i	$0.407841\pi$
$992$	−166.172	+	287.818i	−0.167512	+	0.290139i
$993$		0			0
$994$	−24.6545	+	84.4348i	−0.0248033	+	0.0849445i
$995$	753.784	+	528.031i	0.757571	+	0.530685i
$996$		0			0
$997$	−666.163	−	1153.83i	−0.668167	−	1.15730i	−0.978416	−	0.206644i	$-0.933746\pi$
$997$	−666.163	−	1153.83i	−0.668167	−	1.15730i	0.310249	−	0.950655i	$-0.399588\pi$
$998$	−16.1864	+	9.34525i	−0.0162189	+	0.00936398i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.bi.c.19.3		12
3.2	odd	2		35.3.i.a.19.4	yes	12
5.4	even	2	inner	315.3.bi.c.19.4		12
7.3	odd	6	inner	315.3.bi.c.199.4		12
12.11	even	2		560.3.br.a.369.2		12
15.2	even	4		175.3.i.c.26.3		12
15.8	even	4		175.3.i.c.26.4		12
15.14	odd	2		35.3.i.a.19.3	✓	12
21.2	odd	6		245.3.c.a.244.5		12
21.5	even	6		245.3.c.a.244.6		12
21.11	odd	6		245.3.i.d.129.3		12
21.17	even	6		35.3.i.a.24.3	yes	12
21.20	even	2		245.3.i.d.19.4		12
35.24	odd	6	inner	315.3.bi.c.199.3		12
60.59	even	2		560.3.br.a.369.5		12
84.59	odd	6		560.3.br.a.129.5		12
105.17	odd	12		175.3.i.c.101.3		12
105.38	odd	12		175.3.i.c.101.4		12
105.44	odd	6		245.3.c.a.244.8		12
105.59	even	6		35.3.i.a.24.4	yes	12
105.74	odd	6		245.3.i.d.129.4		12
105.89	even	6		245.3.c.a.244.7		12
105.104	even	2		245.3.i.d.19.3		12
420.59	odd	6		560.3.br.a.129.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.i.a.19.3	✓	12	15.14	odd	2
35.3.i.a.19.4	yes	12	3.2	odd	2
35.3.i.a.24.3	yes	12	21.17	even	6
35.3.i.a.24.4	yes	12	105.59	even	6
175.3.i.c.26.3		12	15.2	even	4
175.3.i.c.26.4		12	15.8	even	4
175.3.i.c.101.3		12	105.17	odd	12
175.3.i.c.101.4		12	105.38	odd	12
245.3.c.a.244.5		12	21.2	odd	6
245.3.c.a.244.6		12	21.5	even	6
245.3.c.a.244.7		12	105.89	even	6
245.3.c.a.244.8		12	105.44	odd	6
245.3.i.d.19.3		12	105.104	even	2
245.3.i.d.19.4		12	21.20	even	2
245.3.i.d.129.3		12	21.11	odd	6
245.3.i.d.129.4		12	105.74	odd	6
315.3.bi.c.19.3		12	1.1	even	1	trivial
315.3.bi.c.19.4		12	5.4	even	2	inner
315.3.bi.c.199.3		12	35.24	odd	6	inner
315.3.bi.c.199.4		12	7.3	odd	6	inner
560.3.br.a.129.2		12	420.59	odd	6
560.3.br.a.129.5		12	84.59	odd	6
560.3.br.a.369.2		12	12.11	even	2
560.3.br.a.369.5		12	60.59	even	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.226181 - 0.130586i) q^{2} +(-1.96589 - 3.40503i) q^{4} +(-2.11218 - 4.53196i) q^{5} +(-1.66053 - 6.80019i) q^{7} +2.07156i q^{8} +O(q^{10})\)	\(q+(-0.226181 - 0.130586i) q^{2} +(-1.96589 - 3.40503i) q^{4} +(-2.11218 - 4.53196i) q^{5} +(-1.66053 - 6.80019i) q^{7} +2.07156i q^{8} +(-0.114075 + 1.30086i) q^{10} +(3.04653 + 5.27675i) q^{11} -13.0886 q^{13} +(-0.512426 + 1.75492i) q^{14} +(-7.59306 + 13.1516i) q^{16} +(5.05373 + 8.75332i) q^{17} +(19.5373 + 11.2799i) q^{19} +(-11.2792 + 16.1014i) q^{20} -1.59133i q^{22} +(-30.2957 - 17.4912i) q^{23} +(-16.0774 + 19.1446i) q^{25} +(2.96039 + 1.70918i) q^{26} +(-19.8904 + 19.0226i) q^{28} +16.3474 q^{29} +(-23.4907 + 13.5624i) q^{31} +(10.6109 - 6.12620i) q^{32} -2.63978i q^{34} +(-27.3109 + 21.8887i) q^{35} +(-14.4349 - 8.33401i) q^{37} +(-2.94598 - 5.10258i) q^{38} +(9.38822 - 4.37550i) q^{40} -19.7267i q^{41} -53.4739i q^{43} +(11.9783 - 20.7471i) q^{44} +(4.56821 + 7.91237i) q^{46} +(18.3385 - 31.7632i) q^{47} +(-43.4852 + 22.5839i) q^{49} +(6.13642 - 2.23067i) q^{50} +(25.7308 + 44.5671i) q^{52} +(-31.9730 + 18.4596i) q^{53} +(17.4792 - 24.9522i) q^{55} +(14.0870 - 3.43989i) q^{56} +(-3.69747 - 2.13474i) q^{58} +(-92.4861 + 53.3969i) q^{59} +(-18.4211 - 10.6354i) q^{61} +7.08422 q^{62} +57.5445 q^{64} +(27.6455 + 59.3171i) q^{65} +(5.33016 - 3.07737i) q^{67} +(19.8702 - 34.4162i) q^{68} +(9.03556 - 1.38440i) q^{70} +48.1133 q^{71} +(-2.82277 - 4.88919i) q^{73} +(2.17660 + 3.76999i) q^{74} -88.7000i q^{76} +(30.8240 - 29.4792i) q^{77} +(19.1607 - 33.1873i) q^{79} +(75.6404 + 6.63304i) q^{80} +(-2.57602 + 4.46180i) q^{82} -102.359 q^{83} +(28.9953 - 41.3919i) q^{85} +(-6.98292 + 12.0948i) q^{86} +(-10.9311 + 6.31106i) q^{88} +(34.1003 + 19.6878i) q^{89} +(21.7341 + 89.0050i) q^{91} +137.544i q^{92} +(-8.29564 + 4.78949i) q^{94} +(9.85369 - 112.367i) q^{95} +33.5609 q^{97} +(12.7847 + 0.570497i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4}+O(q^{10}) \) 12 * q + 6 * q^4	\( 12 q + 6 q^{4} - 54 q^{10} - 6 q^{11} + 66 q^{14} - 6 q^{16} + 18 q^{19} + 18 q^{25} - 18 q^{26} - 108 q^{31} - 222 q^{35} - 162 q^{40} + 42 q^{44} + 114 q^{46} - 324 q^{49} + 192 q^{50} - 336 q^{56} - 396 q^{59} - 108 q^{61} + 372 q^{64} + 54 q^{65} + 300 q^{70} - 192 q^{71} + 594 q^{74} - 192 q^{79} + 504 q^{80} - 192 q^{85} + 384 q^{86} - 684 q^{89} - 72 q^{91} + 990 q^{94} - 288 q^{95}+O(q^{100}) \) 12 * q + 6 * q^4 - 54 * q^10 - 6 * q^11 + 66 * q^14 - 6 * q^16 + 18 * q^19 + 18 * q^25 - 18 * q^26 - 108 * q^31 - 222 * q^35 - 162 * q^40 + 42 * q^44 + 114 * q^46 - 324 * q^49 + 192 * q^50 - 336 * q^56 - 396 * q^59 - 108 * q^61 + 372 * q^64 + 54 * q^65 + 300 * q^70 - 192 * q^71 + 594 * q^74 - 192 * q^79 + 504 * q^80 - 192 * q^85 + 384 * q^86 - 684 * q^89 - 72 * q^91 + 990 * q^94 - 288 * q^95

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