LMFDB - Embedded newform 315.3.bi.a.199.1

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Root			$-1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	315.199
Dual form			315.3.bi.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-5.29150 - 4.58258i) q^{7} -8.66025i q^{8} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-5.29150 - 4.58258i) q^{7} -8.66025i q^{8} +(-7.50000 - 4.33013i) q^{10} +(9.26013 - 16.0390i) q^{11} -18.5203 q^{13} +(11.9059 + 2.29129i) q^{14} +(5.50000 + 9.52628i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(19.5000 - 11.2583i) q^{19} -5.00000 q^{20} +32.0780i q^{22} +(4.50000 - 2.59808i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(27.7804 - 16.0390i) q^{26} +(6.61438 - 2.29129i) q^{28} +37.0405 q^{29} +(-33.0000 - 19.0526i) q^{31} +(13.5000 + 7.79423i) q^{32} -3.46410i q^{34} +(6.61438 - 34.3693i) q^{35} +(27.7804 - 16.0390i) q^{37} +(-19.5000 + 33.7750i) q^{38} +(37.5000 - 21.6506i) q^{40} -32.0780i q^{41} -64.1561i q^{43} +(9.26013 + 16.0390i) q^{44} +(-4.50000 + 7.79423i) q^{46} +(-20.5000 - 35.5070i) q^{47} +(7.00000 + 48.4974i) q^{49} -43.3013i q^{50} +(9.26013 - 16.0390i) q^{52} +(19.5000 + 11.2583i) q^{53} +92.6013 q^{55} +(-39.6863 + 45.8258i) q^{56} +(-55.5608 + 32.0780i) q^{58} +(55.5608 + 32.0780i) q^{59} +(48.0000 - 27.7128i) q^{61} +66.0000 q^{62} -71.0000 q^{64} +(-46.3006 - 80.1951i) q^{65} +(55.5608 + 32.0780i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(19.8431 + 57.2822i) q^{70} -74.0810 q^{71} +(-18.5203 + 32.0780i) q^{73} +(-27.7804 + 48.1170i) q^{74} +22.5167i q^{76} +(-122.500 + 42.4352i) q^{77} +(-52.0000 - 90.0666i) q^{79} +(-27.5000 + 47.6314i) q^{80} +(27.7804 + 48.1170i) q^{82} +32.0000 q^{83} -10.0000 q^{85} +(55.5608 + 96.2341i) q^{86} +(-138.902 - 80.1951i) q^{88} +(-55.5608 + 32.0780i) q^{89} +(98.0000 + 84.8705i) q^{91} +5.19615i q^{92} +(61.5000 + 35.5070i) q^{94} +(97.5000 + 56.2917i) q^{95} -74.0810 q^{97} +(-52.5000 - 66.6840i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} - 2 q^{4} + 10 q^{5}+O(q^{10}) $ 4 * q - 6 * q^2 - 2 * q^4 + 10 * q^5	$ 4 q - 6 q^{2} - 2 q^{4} + 10 q^{5} - 30 q^{10} + 22 q^{16} - 4 q^{17} + 78 q^{19} - 20 q^{20} + 18 q^{23} - 50 q^{25} - 132 q^{31} + 54 q^{32} - 78 q^{38} + 150 q^{40} - 18 q^{46} - 82 q^{47} + 28 q^{49} + 78 q^{53} + 192 q^{61} + 264 q^{62} - 284 q^{64} - 4 q^{68} - 490 q^{77} - 208 q^{79} - 110 q^{80} + 128 q^{83} - 40 q^{85} + 392 q^{91} + 246 q^{94} + 390 q^{95} - 210 q^{98}+O(q^{100}) $ 4 * q - 6 * q^2 - 2 * q^4 + 10 * q^5 - 30 * q^10 + 22 * q^16 - 4 * q^17 + 78 * q^19 - 20 * q^20 + 18 * q^23 - 50 * q^25 - 132 * q^31 + 54 * q^32 - 78 * q^38 + 150 * q^40 - 18 * q^46 - 82 * q^47 + 28 * q^49 + 78 * q^53 + 192 * q^61 + 264 * q^62 - 284 * q^64 - 4 * q^68 - 490 * q^77 - 208 * q^79 - 110 * q^80 + 128 * q^83 - 40 * q^85 + 392 * q^91 + 246 * q^94 + 390 * q^95 - 210 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.50000	+	0.866025i	−0.750000	+	0.433013i	−0.825694	−	0.564118i	$-0.809216\pi$
$2$	−1.50000	+	0.866025i	−0.750000	+	0.433013i	0.0756939	+	0.997131i	$0.475883\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$5$	2.50000	+	4.33013i	0.500000	+	0.866025i
$5$	2.50000	+	4.33013i	0.500000	+	0.866025i
$6$		0			0
$7$	−5.29150	−	4.58258i	−0.755929	−	0.654654i
$7$	−5.29150	−	4.58258i	−0.755929	−	0.654654i
$8$		−	8.66025i		−	1.08253i
$9$		0			0
$10$	−7.50000	−	4.33013i	−0.750000	−	0.433013i
$11$	9.26013	−	16.0390i	0.841830	−	1.45809i	−0.0465160	−	0.998918i	$-0.514812\pi$
$11$	9.26013	−	16.0390i	0.841830	−	1.45809i	0.888346	−	0.459175i	$-0.151855\pi$
$12$		0			0
$13$	−18.5203			−1.42464			−0.712318	−	0.701857i	$-0.752354\pi$
$13$	−18.5203			−1.42464			−0.712318	+	0.701857i	$0.752354\pi$
$14$	11.9059	+	2.29129i	0.850420	+	0.163663i
$15$		0			0
$16$	5.50000	+	9.52628i	0.343750	+	0.595392i
$17$	−1.00000	+	1.73205i	−0.0588235	+	0.101885i	−0.893938	−	0.448192i	$-0.852068\pi$
$17$	−1.00000	+	1.73205i	−0.0588235	+	0.101885i	0.835114	+	0.550077i	$0.185402\pi$
$18$		0			0
$19$	19.5000	−	11.2583i	1.02632	−	0.592544i	0.110389	−	0.993888i	$-0.464790\pi$
$19$	19.5000	−	11.2583i	1.02632	−	0.592544i	0.915927	+	0.401345i	$0.131457\pi$
$20$	−5.00000			−0.250000
$21$		0			0
$22$			32.0780i			1.45809i
$23$	4.50000	−	2.59808i	0.195652	−	0.112960i	−0.398974	−	0.916962i	$-0.630634\pi$
$23$	4.50000	−	2.59808i	0.195652	−	0.112960i	0.594626	+	0.804003i	$0.297300\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$26$	27.7804	−	16.0390i	1.06848	−	0.616885i
$27$		0			0
$28$	6.61438	−	2.29129i	0.236228	−	0.0818317i
$29$	37.0405			1.27726			0.638630	−	0.769514i	$-0.279502\pi$
$29$	37.0405			1.27726			0.638630	+	0.769514i	$0.279502\pi$
$30$		0			0
$31$	−33.0000	−	19.0526i	−1.06452	−	0.614599i	−0.137838	−	0.990455i	$-0.544015\pi$
$31$	−33.0000	−	19.0526i	−1.06452	−	0.614599i	−0.926678	+	0.375856i	$0.877349\pi$
$32$	13.5000	+	7.79423i	0.421875	+	0.243570i
$33$		0			0
$34$		−	3.46410i		−	0.101885i
$35$	6.61438	−	34.3693i	0.188982	−	0.981981i
$36$		0			0
$37$	27.7804	−	16.0390i	0.750821	−	0.433487i	−0.0751693	−	0.997171i	$-0.523950\pi$
$37$	27.7804	−	16.0390i	0.750821	−	0.433487i	0.825991	+	0.563684i	$0.190616\pi$
$38$	−19.5000	+	33.7750i	−0.513158	+	0.888816i
$39$		0			0
$40$	37.5000	−	21.6506i	0.937500	−	0.541266i
$41$		−	32.0780i		−	0.782391i	−0.920308	−	0.391195i	$-0.872062\pi$
$41$		−	32.0780i		−	0.782391i	0.920308	−	0.391195i	$-0.127938\pi$
$42$		0			0
$43$		−	64.1561i		−	1.49200i	−0.665945	−	0.746001i	$-0.731972\pi$
$43$		−	64.1561i		−	1.49200i	0.665945	−	0.746001i	$-0.268028\pi$
$44$	9.26013	+	16.0390i	0.210457	+	0.364523i
$45$		0			0
$46$	−4.50000	+	7.79423i	−0.0978261	+	0.169440i
$47$	−20.5000	−	35.5070i	−0.436170	−	0.755469i	0.561220	−	0.827667i	$-0.310332\pi$
$47$	−20.5000	−	35.5070i	−0.436170	−	0.755469i	−0.997390	+	0.0721976i	$0.976999\pi$
$48$		0			0
$49$	7.00000	+	48.4974i	0.142857	+	0.989743i
$50$		−	43.3013i		−	0.866025i
$51$		0			0
$52$	9.26013	−	16.0390i	0.178079	−	0.308443i
$53$	19.5000	+	11.2583i	0.367925	+	0.212421i	0.672551	−	0.740050i	$-0.265198\pi$
$53$	19.5000	+	11.2583i	0.367925	+	0.212421i	−0.304627	+	0.952472i	$0.598532\pi$
$54$		0			0
$55$	92.6013			1.68366
$56$	−39.6863	+	45.8258i	−0.708683	+	0.818317i
$57$		0			0
$58$	−55.5608	+	32.0780i	−0.957944	+	0.553069i
$59$	55.5608	+	32.0780i	0.941708	+	0.543695i	0.890495	−	0.454992i	$-0.150358\pi$
$59$	55.5608	+	32.0780i	0.941708	+	0.543695i	0.0512127	+	0.998688i	$0.483691\pi$
$60$		0			0
$61$	48.0000	−	27.7128i	0.786885	−	0.454308i	−0.0519796	−	0.998648i	$-0.516553\pi$
$61$	48.0000	−	27.7128i	0.786885	−	0.454308i	0.838865	+	0.544340i	$0.183220\pi$
$62$	66.0000			1.06452
$63$		0			0
$64$	−71.0000			−1.10938
$65$	−46.3006	−	80.1951i	−0.712318	−	1.23377i
$66$		0			0
$67$	55.5608	+	32.0780i	0.829265	+	0.478777i	0.853601	−	0.520927i	$-0.174414\pi$
$67$	55.5608	+	32.0780i	0.829265	+	0.478777i	−0.0243357	+	0.999704i	$0.507747\pi$
$68$	−1.00000	−	1.73205i	−0.0147059	−	0.0254713i
$69$		0			0
$70$	19.8431	+	57.2822i	0.283473	+	0.818317i
$71$	−74.0810			−1.04339			−0.521697	−	0.853131i	$-0.674701\pi$
$71$	−74.0810			−1.04339			−0.521697	+	0.853131i	$0.674701\pi$
$72$		0			0
$73$	−18.5203	+	32.0780i	−0.253702	+	0.439425i	−0.964542	−	0.263929i	$-0.914982\pi$
$73$	−18.5203	+	32.0780i	−0.253702	+	0.439425i	0.710840	+	0.703354i	$0.248315\pi$
$74$	−27.7804	+	48.1170i	−0.375411	+	0.650230i
$75$		0			0
$76$			22.5167i			0.296272i
$77$	−122.500	+	42.4352i	−1.59091	+	0.551107i
$78$		0			0
$79$	−52.0000	−	90.0666i	−0.658228	−	1.14008i	−0.981074	−	0.193633i	$-0.937973\pi$
$79$	−52.0000	−	90.0666i	−0.658228	−	1.14008i	0.322846	−	0.946451i	$-0.395360\pi$
$80$	−27.5000	+	47.6314i	−0.343750	+	0.595392i
$81$		0			0
$82$	27.7804	+	48.1170i	0.338785	+	0.586793i
$83$	32.0000			0.385542			0.192771	−	0.981244i	$-0.438253\pi$
$83$	32.0000			0.385542			0.192771	+	0.981244i	$0.438253\pi$
$84$		0			0
$85$	−10.0000			−0.117647
$86$	55.5608	+	96.2341i	0.646056	+	1.11900i
$87$		0			0
$88$	−138.902	−	80.1951i	−1.57843	−	0.911308i
$89$	−55.5608	+	32.0780i	−0.624278	+	0.360427i	−0.778533	−	0.627604i	$-0.784036\pi$
$89$	−55.5608	+	32.0780i	−0.624278	+	0.360427i	0.154254	+	0.988031i	$0.450702\pi$
$90$		0			0
$91$	98.0000	+	84.8705i	1.07692	+	0.932643i
$92$			5.19615i			0.0564799i
$93$		0			0
$94$	61.5000	+	35.5070i	0.654255	+	0.377734i
$95$	97.5000	+	56.2917i	1.02632	+	0.592544i
$96$		0			0
$97$	−74.0810			−0.763722			−0.381861	−	0.924220i	$-0.624717\pi$
$97$	−74.0810			−0.763722			−0.381861	+	0.924220i	$0.624717\pi$
$98$	−52.5000	−	66.6840i	−0.535714	−	0.680449i
$99$		0			0
$100$	−12.5000	−	21.6506i	−0.125000	−	0.216506i
$101$	−166.682	−	96.2341i	−1.65032	−	0.952813i	−0.976939	−	0.213517i	$-0.931508\pi$
$101$	−166.682	−	96.2341i	−1.65032	−	0.952813i	−0.673381	−	0.739296i	$-0.735159\pi$
$102$		0			0
$103$	−74.0810	−	128.312i	−0.719233	−	1.24575i	−0.961304	−	0.275490i	$-0.911160\pi$
$103$	−74.0810	−	128.312i	−0.719233	−	1.24575i	0.242071	−	0.970259i	$-0.422173\pi$
$104$			160.390i			1.54221i
$105$		0			0
$106$	−39.0000			−0.367925
$107$	96.0000	−	55.4256i	0.897196	−	0.517997i	0.0209068	−	0.999781i	$-0.493345\pi$
$107$	96.0000	−	55.4256i	0.897196	−	0.517997i	0.876289	+	0.481785i	$0.160011\pi$
$108$		0			0
$109$	−28.0000	+	48.4974i	−0.256881	+	0.444930i	−0.965405	−	0.260756i	$-0.916028\pi$
$109$	−28.0000	+	48.4974i	−0.256881	+	0.444930i	0.708524	+	0.705687i	$0.249361\pi$
$110$	−138.902	+	80.1951i	−1.26274	+	0.729046i
$111$		0			0
$112$	14.5516	−	75.6125i	0.129925	−	0.675112i
$113$		−	162.813i		−	1.44082i	−0.693548	−	0.720411i	$-0.743953\pi$
$113$		−	162.813i		−	1.44082i	0.693548	−	0.720411i	$-0.256047\pi$
$114$		0			0
$115$	22.5000	+	12.9904i	0.195652	+	0.112960i
$116$	−18.5203	+	32.0780i	−0.159657	+	0.276535i
$117$		0			0
$118$	−111.122			−0.941708
$119$	13.2288	−	4.58258i	0.111166	−	0.0385090i
$120$		0			0
$121$	−111.000	−	192.258i	−0.917355	−	1.58891i
$122$	−48.0000	+	83.1384i	−0.393443	+	0.681463i
$123$		0			0
$124$	33.0000	−	19.0526i	0.266129	−	0.153650i
$125$	−125.000			−1.00000
$126$		0			0
$127$			96.2341i			0.757749i	0.925448	+	0.378874i	$0.123689\pi$
$127$			96.2341i			0.757749i	−0.925448	+	0.378874i	$0.876311\pi$
$128$	52.5000	−	30.3109i	0.410156	−	0.236804i
$129$		0			0
$130$	138.902	+	80.1951i	1.06848	+	0.616885i
$131$	83.3412	−	48.1170i	0.636192	−	0.367306i	−0.146954	−	0.989143i	$-0.546947\pi$
$131$	83.3412	−	48.1170i	0.636192	−	0.367306i	0.783146	+	0.621838i	$0.213614\pi$
$132$		0			0
$133$	−154.776	−	29.7867i	−1.16373	−	0.223960i
$134$	−111.122			−0.829265
$135$		0			0
$136$	15.0000	+	8.66025i	0.110294	+	0.0636783i
$137$	144.000	+	83.1384i	1.05109	+	0.606850i	0.922956	−	0.384906i	$-0.125766\pi$
$137$	144.000	+	83.1384i	1.05109	+	0.606850i	0.128139	+	0.991756i	$0.459100\pi$
$138$		0			0
$139$			117.779i			0.847334i	0.905818	+	0.423667i	$0.139257\pi$
$139$			117.779i			0.847334i	−0.905818	+	0.423667i	$0.860743\pi$
$140$	26.4575	+	22.9129i	0.188982	+	0.163663i
$141$		0			0
$142$	111.122	−	64.1561i	0.782546	−	0.451803i
$143$	−171.500	+	297.047i	−1.19930	+	2.07725i
$144$		0			0
$145$	92.6013	+	160.390i	0.638630	+	1.10614i
$146$		−	64.1561i		−	0.439425i
$147$		0			0
$148$			32.0780i			0.216743i
$149$	−18.5203	−	32.0780i	−0.124297	−	0.215289i	0.797161	−	0.603767i	$-0.206334\pi$
$149$	−18.5203	−	32.0780i	−0.124297	−	0.215289i	−0.921458	+	0.388478i	$0.873001\pi$
$150$		0			0
$151$	−85.0000	+	147.224i	−0.562914	+	0.974995i	0.434326	+	0.900756i	$0.356986\pi$
$151$	−85.0000	+	147.224i	−0.562914	+	0.974995i	−0.997240	+	0.0742400i	$0.976347\pi$
$152$	−97.5000	−	168.875i	−0.641447	−	1.11102i
$153$		0			0
$154$	147.000	−	169.741i	0.954545	−	1.10221i
$155$		−	190.526i		−	1.22920i
$156$		0			0
$157$	9.26013	−	16.0390i	0.0589817	−	0.102159i	−0.835027	−	0.550209i	$-0.814548\pi$
$157$	9.26013	−	16.0390i	0.0589817	−	0.102159i	0.894009	+	0.448050i	$0.147881\pi$
$158$	156.000	+	90.0666i	0.987342	+	0.570042i
$159$		0			0
$160$			77.9423i			0.487139i
$161$	−35.7176	−	6.87386i	−0.221849	−	0.0426948i
$162$		0			0
$163$	−55.5608	+	32.0780i	−0.340864	+	0.196798i	−0.660654	−	0.750691i	$-0.729721\pi$
$163$	−55.5608	+	32.0780i	−0.340864	+	0.196798i	0.319790	+	0.947488i	$0.396388\pi$
$164$	27.7804	+	16.0390i	0.169393	+	0.0977989i
$165$		0			0
$166$	−48.0000	+	27.7128i	−0.289157	+	0.166945i
$167$	89.0000			0.532934			0.266467	−	0.963844i	$-0.414144\pi$
$167$	89.0000			0.532934			0.266467	+	0.963844i	$0.414144\pi$
$168$		0			0
$169$	174.000			1.02959
$170$	15.0000	−	8.66025i	0.0882353	−	0.0509427i
$171$		0			0
$172$	55.5608	+	32.0780i	0.323028	+	0.186500i
$173$	48.5000	+	84.0045i	0.280347	+	0.485575i	0.971470	−	0.237162i	$-0.0762172\pi$
$173$	48.5000	+	84.0045i	0.280347	+	0.485575i	−0.691123	+	0.722737i	$0.742884\pi$
$174$		0			0
$175$	165.359	−	57.2822i	0.944911	−	0.327327i
$176$	203.723			1.15752
$177$		0			0
$178$	55.5608	−	96.2341i	0.312139	−	0.540641i
$179$	64.8209	−	112.273i	0.362128	−	0.627224i	−0.626183	−	0.779676i	$-0.715384\pi$
$179$	64.8209	−	112.273i	0.362128	−	0.627224i	0.988311	+	0.152452i	$0.0487170\pi$
$180$		0			0
$181$		−	103.923i		−	0.574160i	−0.957907	−	0.287080i	$-0.907315\pi$
$181$		−	103.923i		−	0.574160i	0.957907	−	0.287080i	$-0.0926846\pi$
$182$	−220.500	−	42.4352i	−1.21154	−	0.233161i
$183$		0			0
$184$	−22.5000	−	38.9711i	−0.122283	−	0.211800i
$185$	138.902	+	80.1951i	0.750821	+	0.433487i
$186$		0			0
$187$	18.5203	+	32.0780i	0.0990388	+	0.171540i
$188$	41.0000			0.218085
$189$		0			0
$190$	−195.000			−1.02632
$191$	−18.5203	−	32.0780i	−0.0969647	−	0.167948i	0.813462	−	0.581618i	$-0.197580\pi$
$191$	−18.5203	−	32.0780i	−0.0969647	−	0.167948i	−0.910427	+	0.413670i	$0.864247\pi$
$192$		0			0
$193$	−111.122	−	64.1561i	−0.575759	−	0.332415i	0.183687	−	0.982985i	$-0.441197\pi$
$193$	−111.122	−	64.1561i	−0.575759	−	0.332415i	−0.759446	+	0.650570i	$0.774530\pi$
$194$	111.122	−	64.1561i	0.572792	−	0.330701i
$195$		0			0
$196$	−45.5000	−	18.1865i	−0.232143	−	0.0927884i
$197$		−	77.9423i		−	0.395646i	−0.980238	−	0.197823i	$-0.936613\pi$
$197$		−	77.9423i		−	0.395646i	0.980238	−	0.197823i	$-0.0633871\pi$
$198$		0			0
$199$	−165.000	−	95.2628i	−0.829146	−	0.478708i	0.0244144	−	0.999702i	$-0.492228\pi$
$199$	−165.000	−	95.2628i	−0.829146	−	0.478708i	−0.853560	+	0.520994i	$0.825561\pi$
$200$	187.500	+	108.253i	0.937500	+	0.541266i
$201$		0			0
$202$	333.365			1.65032
$203$	−196.000	−	169.741i	−0.965517	−	0.836162i
$204$		0			0
$205$	138.902	−	80.1951i	0.677570	−	0.391195i
$206$	222.243	+	128.312i	1.07885	+	0.622874i
$207$		0			0
$208$	−101.861	−	176.429i	−0.489718	−	0.848217i
$209$		−	417.014i		−	1.99528i
$210$		0			0
$211$	287.000			1.36019			0.680095	−	0.733124i	$-0.261939\pi$
$211$	287.000			1.36019			0.680095	+	0.733124i	$0.261939\pi$
$212$	−19.5000	+	11.2583i	−0.0919811	+	0.0531053i
$213$		0			0
$214$	−96.0000	+	166.277i	−0.448598	+	0.776995i
$215$	277.804	−	160.390i	1.29211	−	0.746001i
$216$		0			0
$217$	87.3098	+	252.042i	0.402349	+	1.16148i
$218$		−	96.9948i		−	0.444930i
$219$		0			0
$220$	−46.3006	+	80.1951i	−0.210457	+	0.364523i
$221$	18.5203	−	32.0780i	0.0838021	−	0.145149i
$222$		0			0
$223$	−74.0810			−0.332202			−0.166101	−	0.986109i	$-0.553118\pi$
$223$	−74.0810			−0.332202			−0.166101	+	0.986109i	$0.553118\pi$
$224$	−35.7176	−	103.108i	−0.159454	−	0.460303i
$225$		0			0
$226$	141.000	+	244.219i	0.623894	+	1.08062i
$227$	−67.0000	+	116.047i	−0.295154	+	0.511222i	−0.975021	−	0.222114i	$-0.928704\pi$
$227$	−67.0000	+	116.047i	−0.295154	+	0.511222i	0.679867	+	0.733336i	$0.262038\pi$
$228$		0			0
$229$	−27.0000	+	15.5885i	−0.117904	+	0.0680719i	−0.557792	−	0.829981i	$-0.688351\pi$
$229$	−27.0000	+	15.5885i	−0.117904	+	0.0680719i	0.439888	+	0.898053i	$0.355018\pi$
$230$	−45.0000			−0.195652
$231$		0			0
$232$		−	320.780i		−	1.38267i
$233$	321.000	−	185.329i	1.37768	−	0.795405i	0.385802	−	0.922581i	$-0.373925\pi$
$233$	321.000	−	185.329i	1.37768	−	0.795405i	0.991880	+	0.127176i	$0.0405914\pi$
$234$		0			0
$235$	102.500	−	177.535i	0.436170	−	0.755469i
$236$	−55.5608	+	32.0780i	−0.235427	+	0.135924i
$237$		0			0
$238$	−15.8745	+	18.3303i	−0.0666996	+	0.0770181i
$239$	259.284			1.08487			0.542434	−	0.840098i	$-0.317503\pi$
$239$	259.284			1.08487			0.542434	+	0.840098i	$0.317503\pi$
$240$		0			0
$241$	−13.5000	−	7.79423i	−0.0560166	−	0.0323412i	0.471730	−	0.881743i	$-0.343630\pi$
$241$	−13.5000	−	7.79423i	−0.0560166	−	0.0323412i	−0.527747	+	0.849402i	$0.676963\pi$
$242$	333.000	+	192.258i	1.37603	+	0.794453i
$243$		0			0
$244$			55.4256i			0.227154i
$245$	−192.500	+	151.554i	−0.785714	+	0.618590i
$246$		0			0
$247$	−361.145	+	208.507i	−1.46213	+	0.844159i
$248$	−165.000	+	285.788i	−0.665323	+	1.15237i
$249$		0			0
$250$	187.500	−	108.253i	0.750000	−	0.433013i
$251$			288.702i			1.15021i	0.818080	+	0.575104i	$0.195038\pi$
$251$			288.702i			1.15021i	−0.818080	+	0.575104i	$0.804962\pi$
$252$		0			0
$253$		−	96.2341i		−	0.380372i
$254$	−83.3412	−	144.351i	−0.328115	−	0.568312i
$255$		0			0
$256$	89.5000	−	155.019i	0.349609	−	0.605541i
$257$	−28.0000	−	48.4974i	−0.108949	−	0.188706i	0.806396	−	0.591377i	$-0.201415\pi$
$257$	−28.0000	−	48.4974i	−0.108949	−	0.188706i	−0.915345	+	0.402671i	$0.868082\pi$
$258$		0			0
$259$	−220.500	−	42.4352i	−0.851351	−	0.163843i
$260$	92.6013			0.356159
$261$		0			0
$262$	−83.3412	+	144.351i	−0.318096	+	0.550959i
$263$	−270.000	−	155.885i	−1.02662	−	0.592717i	−0.110603	−	0.993865i	$-0.535278\pi$
$263$	−270.000	−	155.885i	−1.02662	−	0.592717i	−0.916013	+	0.401148i	$0.868611\pi$
$264$		0			0
$265$			112.583i			0.424843i
$266$	257.961	−	89.3602i	0.969777	−	0.335941i
$267$		0			0
$268$	−55.5608	+	32.0780i	−0.207316	+	0.119694i
$269$	−388.925	−	224.546i	−1.44582	−	0.834744i	−0.447591	−	0.894238i	$-0.647718\pi$
$269$	−388.925	−	224.546i	−1.44582	−	0.834744i	−0.998229	+	0.0594942i	$0.981051\pi$
$270$		0			0
$271$	−219.000	+	126.440i	−0.808118	+	0.466567i	−0.846302	−	0.532704i	$-0.821176\pi$
$271$	−219.000	+	126.440i	−0.808118	+	0.466567i	0.0381838	+	0.999271i	$0.487843\pi$
$272$	−22.0000			−0.0808824
$273$		0			0
$274$	−288.000			−1.05109
$275$	231.503	+	400.975i	0.841830	+	1.45809i
$276$		0			0
$277$	−166.682	−	96.2341i	−0.601741	−	0.347415i	0.167985	−	0.985790i	$-0.446274\pi$
$277$	−166.682	−	96.2341i	−0.601741	−	0.347415i	−0.769726	+	0.638374i	$0.779607\pi$
$278$	−102.000	−	176.669i	−0.366906	−	0.635501i
$279$		0			0
$280$	−297.647	−	57.2822i	−1.06303	−	0.204579i
$281$	−240.763			−0.856809			−0.428405	−	0.903587i	$-0.640924\pi$
$281$	−240.763			−0.856809			−0.428405	+	0.903587i	$0.640924\pi$
$282$		0			0
$283$	−74.0810	+	128.312i	−0.261770	+	0.453400i	−0.966712	−	0.255865i	$-0.917640\pi$
$283$	−74.0810	+	128.312i	−0.261770	+	0.453400i	0.704942	+	0.709265i	$0.250973\pi$
$284$	37.0405	−	64.1561i	0.130424	−	0.225902i
$285$		0			0
$286$		−	594.093i		−	2.07725i
$287$	−147.000	+	169.741i	−0.512195	+	0.591432i
$288$		0			0
$289$	142.500	+	246.817i	0.493080	+	0.854039i
$290$	−277.804	−	160.390i	−0.957944	−	0.553069i
$291$		0			0
$292$	−18.5203	−	32.0780i	−0.0634255	−	0.109856i
$293$	455.000			1.55290			0.776451	−	0.630178i	$-0.217018\pi$
$293$	455.000			1.55290			0.776451	+	0.630178i	$0.217018\pi$
$294$		0			0
$295$			320.780i			1.08739i
$296$	−138.902	−	240.585i	−0.469263	−	0.812788i
$297$		0			0
$298$	55.5608	+	32.0780i	0.186446	+	0.107644i
$299$	−83.3412	+	48.1170i	−0.278733	+	0.160927i
$300$		0			0
$301$	−294.000	+	339.482i	−0.976744	+	1.12785i
$302$		−	294.449i		−	0.974995i
$303$		0			0
$304$	214.500	+	123.842i	0.705592	+	0.407374i
$305$	240.000	+	138.564i	0.786885	+	0.454308i
$306$		0			0
$307$	−74.0810			−0.241306			−0.120653	−	0.992695i	$-0.538499\pi$
$307$	−74.0810			−0.241306			−0.120653	+	0.992695i	$0.538499\pi$
$308$	24.5000	−	127.306i	0.0795455	−	0.413330i
$309$		0			0
$310$	165.000	+	285.788i	0.532258	+	0.921898i
$311$	388.925	+	224.546i	1.25056	+	0.722014i	0.971222	−	0.238178i	$-0.0765502\pi$
$311$	388.925	+	224.546i	1.25056	+	0.722014i	0.279343	+	0.960191i	$0.409883\pi$
$312$		0			0
$313$	148.162	+	256.624i	0.473361	+	0.819886i	0.999535	−	0.0304913i	$-0.00970719\pi$
$313$	148.162	+	256.624i	0.473361	+	0.819886i	−0.526174	+	0.850377i	$0.676374\pi$
$314$			32.0780i			0.102159i
$315$		0			0
$316$	104.000			0.329114
$317$	174.000	−	100.459i	0.548896	−	0.316905i	−0.199781	−	0.979841i	$-0.564023\pi$
$317$	174.000	−	100.459i	0.548896	−	0.316905i	0.748677	+	0.662935i	$0.230690\pi$
$318$		0			0
$319$	343.000	−	594.093i	1.07524	−	1.86236i
$320$	−177.500	−	307.439i	−0.554688	−	0.960747i
$321$		0			0
$322$	59.5294	−	20.6216i	0.184874	−	0.0640422i
$323$			45.0333i			0.139422i
$324$		0			0
$325$	231.503	−	400.975i	0.712318	−	1.23377i
$326$	55.5608	−	96.2341i	0.170432	−	0.295197i
$327$		0			0
$328$	−277.804			−0.846963
$329$	−54.2379	+	281.828i	−0.164857	+	0.856621i
$330$		0			0
$331$	87.5000	+	151.554i	0.264350	+	0.457868i	0.967393	−	0.253279i	$-0.0815091\pi$
$331$	87.5000	+	151.554i	0.264350	+	0.457868i	−0.703043	+	0.711148i	$0.748176\pi$
$332$	−16.0000	+	27.7128i	−0.0481928	+	0.0834723i
$333$		0			0
$334$	−133.500	+	77.0763i	−0.399701	+	0.230767i
$335$			320.780i			0.957553i
$336$		0			0
$337$			64.1561i			0.190374i	0.995459	+	0.0951870i	$0.0303449\pi$
$337$			64.1561i			0.190374i	−0.995459	+	0.0951870i	$0.969655\pi$
$338$	−261.000	+	150.688i	−0.772189	+	0.445824i
$339$		0			0
$340$	5.00000	−	8.66025i	0.0147059	−	0.0254713i
$341$	−611.169	+	352.858i	−1.79228	+	1.03478i
$342$		0			0
$343$	185.203	−	288.702i	0.539949	−	0.841698i
$344$	−555.608			−1.61514
$345$		0			0
$346$	−145.500	−	84.0045i	−0.420520	−	0.242787i
$347$	75.0000	+	43.3013i	0.216138	+	0.124788i	0.604161	−	0.796862i	$-0.293508\pi$
$347$	75.0000	+	43.3013i	0.216138	+	0.124788i	−0.388023	+	0.921650i	$0.626842\pi$
$348$		0			0
$349$			6.92820i			0.0198516i	0.999951	+	0.00992579i	$0.00315953\pi$
$349$			6.92820i			0.0198516i	−0.999951	+	0.00992579i	$0.996840\pi$
$350$	−198.431	+	229.129i	−0.566947	+	0.654654i
$351$		0			0
$352$	250.023	−	144.351i	0.710294	−	0.410088i
$353$	−259.000	+	448.601i	−0.733711	+	1.27082i	0.221576	+	0.975143i	$0.428880\pi$
$353$	−259.000	+	448.601i	−0.733711	+	1.27082i	−0.955287	+	0.295682i	$0.904453\pi$
$354$		0			0
$355$	−185.203	−	320.780i	−0.521697	−	0.903606i
$356$		−	64.1561i		−	0.180214i
$357$		0			0
$358$			224.546i			0.627224i
$359$	92.6013	+	160.390i	0.257942	+	0.446769i	0.965691	−	0.259696i	$-0.0836222\pi$
$359$	92.6013	+	160.390i	0.257942	+	0.446769i	−0.707748	+	0.706465i	$0.750289\pi$
$360$		0			0
$361$	73.0000	−	126.440i	0.202216	−	0.350249i
$362$	90.0000	+	155.885i	0.248619	+	0.430620i
$363$		0			0
$364$	−122.500	+	42.4352i	−0.336538	+	0.116580i
$365$	−185.203			−0.507404
$366$		0			0
$367$	9.26013	−	16.0390i	0.0252320	−	0.0437030i	−0.853134	−	0.521692i	$-0.825301\pi$
$367$	9.26013	−	16.0390i	0.0252320	−	0.0437030i	0.878366	+	0.477989i	$0.158634\pi$
$368$	49.5000	+	28.5788i	0.134511	+	0.0776599i
$369$		0			0
$370$	−277.804			−0.750821
$371$	−51.5922	−	148.934i	−0.139062	−	0.401439i
$372$		0			0
$373$	500.047	−	288.702i	1.34061	−	0.774001i	0.353712	−	0.935354i	$-0.384919\pi$
$373$	500.047	−	288.702i	1.34061	−	0.774001i	0.986897	+	0.161354i	$0.0515860\pi$
$374$	−55.5608	−	32.0780i	−0.148558	−	0.0857701i
$375$		0			0
$376$	−307.500	+	177.535i	−0.817819	+	0.472168i
$377$	−686.000			−1.81963
$378$		0			0
$379$	−67.0000			−0.176781			−0.0883905	−	0.996086i	$-0.528172\pi$
$379$	−67.0000			−0.176781			−0.0883905	+	0.996086i	$0.528172\pi$
$380$	−97.5000	+	56.2917i	−0.256579	+	0.148136i
$381$		0			0
$382$	55.5608	+	32.0780i	0.145447	+	0.0839739i
$383$	273.500	+	473.716i	0.714099	+	1.23686i	0.963306	+	0.268406i	$0.0864968\pi$
$383$	273.500	+	473.716i	0.714099	+	1.23686i	−0.249207	+	0.968450i	$0.580170\pi$
$384$		0			0
$385$	−490.000	−	424.352i	−1.27273	−	1.10221i
$386$	222.243			0.575759
$387$		0			0
$388$	37.0405	−	64.1561i	0.0954653	−	0.165351i
$389$	−240.763	+	417.014i	−0.618929	+	1.07202i	0.370753	+	0.928732i	$0.379100\pi$
$389$	−240.763	+	417.014i	−0.618929	+	1.07202i	−0.989682	+	0.143285i	$0.954234\pi$
$390$		0			0
$391$			10.3923i			0.0265788i
$392$	420.000	−	60.6218i	1.07143	−	0.154647i
$393$		0			0
$394$	67.5000	+	116.913i	0.171320	+	0.296735i
$395$	260.000	−	450.333i	0.658228	−	1.14008i
$396$		0			0
$397$	−74.0810	−	128.312i	−0.186602	−	0.323204i	0.757513	−	0.652820i	$-0.226414\pi$
$397$	−74.0810	−	128.312i	−0.186602	−	0.323204i	−0.944115	+	0.329616i	$0.893081\pi$
$398$	330.000			0.829146
$399$		0			0
$400$	−275.000			−0.687500
$401$	−157.422	−	272.663i	−0.392574	−	0.679958i	0.600214	−	0.799839i	$-0.295082\pi$
$401$	−157.422	−	272.663i	−0.392574	−	0.679958i	−0.992788	+	0.119881i	$0.961749\pi$
$402$		0			0
$403$	611.169	+	352.858i	1.51655	+	0.875579i
$404$	166.682	−	96.2341i	0.412580	−	0.238203i
$405$		0			0
$406$	441.000	+	84.8705i	1.08621	+	0.209041i
$407$		−	594.093i		−	1.45969i
$408$		0			0
$409$	444.000	+	256.344i	1.08557	+	0.626757i	0.932395	−	0.361442i	$-0.117715\pi$
$409$	444.000	+	256.344i	1.08557	+	0.626757i	0.153180	+	0.988198i	$0.451049\pi$
$410$	−138.902	+	240.585i	−0.338785	+	0.586793i
$411$		0			0
$412$	148.162			0.359617
$413$	−147.000	−	424.352i	−0.355932	−	1.02749i
$414$		0			0
$415$	80.0000	+	138.564i	0.192771	+	0.333889i
$416$	−250.023	−	144.351i	−0.601018	−	0.346998i
$417$		0			0
$418$	361.145	+	625.522i	0.863983	+	1.49646i
$419$			352.858i			0.842144i	0.907027	+	0.421072i	$0.138346\pi$
$419$			352.858i			0.842144i	−0.907027	+	0.421072i	$0.861654\pi$
$420$		0			0
$421$	752.000			1.78622			0.893112	−	0.449835i	$-0.148517\pi$
$421$	752.000			1.78622			0.893112	+	0.449835i	$0.148517\pi$
$422$	−430.500	+	248.549i	−1.02014	+	0.588979i
$423$		0			0
$424$	97.5000	−	168.875i	0.229953	−	0.398290i
$425$	−25.0000	−	43.3013i	−0.0588235	−	0.101885i
$426$		0			0
$427$	−380.988	−	73.3212i	−0.892244	−	0.171712i
$428$			110.851i			0.258998i
$429$		0			0
$430$	−277.804	+	481.170i	−0.646056	+	1.11900i
$431$	−351.885	+	609.483i	−0.816438	+	1.41411i	0.0918522	+	0.995773i	$0.470721\pi$
$431$	−351.885	+	609.483i	−0.816438	+	1.41411i	−0.908290	+	0.418340i	$0.862612\pi$
$432$		0			0
$433$	703.770			1.62533			0.812667	−	0.582728i	$-0.198015\pi$
$433$	703.770			1.62533			0.812667	+	0.582728i	$0.198015\pi$
$434$	−349.239	−	302.450i	−0.804699	−	0.696889i
$435$		0			0
$436$	−28.0000	−	48.4974i	−0.0642202	−	0.111233i
$437$	58.5000	−	101.325i	0.133867	−	0.231865i
$438$		0			0
$439$	−132.000	+	76.2102i	−0.300683	+	0.173600i	−0.642750	−	0.766076i	$-0.722207\pi$
$439$	−132.000	+	76.2102i	−0.300683	+	0.173600i	0.342066	+	0.939676i	$0.388873\pi$
$440$		−	801.951i		−	1.82262i
$441$		0			0
$442$			64.1561i			0.145149i
$443$	390.000	−	225.167i	0.880361	−	0.508277i	0.00958369	−	0.999954i	$-0.496949\pi$
$443$	390.000	−	225.167i	0.880361	−	0.508277i	0.870777	+	0.491677i	$0.163616\pi$
$444$		0			0
$445$	−277.804	−	160.390i	−0.624278	−	0.360427i
$446$	111.122	−	64.1561i	0.249151	−	0.143848i
$447$		0			0
$448$	375.697	+	325.363i	0.838609	+	0.726256i
$449$	203.723			0.453726			0.226863	−	0.973927i	$-0.427153\pi$
$449$	203.723			0.453726			0.226863	+	0.973927i	$0.427153\pi$
$450$		0			0
$451$	−514.500	−	297.047i	−1.14080	−	0.658640i
$452$	141.000	+	81.4064i	0.311947	+	0.180103i
$453$		0			0
$454$		−	232.095i		−	0.511222i
$455$	−122.500	+	636.529i	−0.269231	+	1.39896i
$456$		0			0
$457$	−277.804	+	160.390i	−0.607886	+	0.350963i	−0.772138	−	0.635455i	$-0.780812\pi$
$457$	−277.804	+	160.390i	−0.607886	+	0.350963i	0.164252	+	0.986418i	$0.447479\pi$
$458$	27.0000	−	46.7654i	0.0589520	−	0.102108i
$459$		0			0
$460$	−22.5000	+	12.9904i	−0.0489130	+	0.0282400i
$461$			128.312i			0.278334i	0.990269	+	0.139167i	$0.0444425\pi$
$461$			128.312i			0.278334i	−0.990269	+	0.139167i	$0.955557\pi$
$462$		0			0
$463$		−	224.546i		−	0.484981i	−0.970154	−	0.242491i	$-0.922036\pi$
$463$		−	224.546i		−	0.484981i	0.970154	−	0.242491i	$-0.0779643\pi$
$464$	203.723	+	352.858i	0.439058	+	0.760471i
$465$		0			0
$466$	−321.000	+	555.988i	−0.688841	+	1.19311i
$467$	170.000	+	294.449i	0.364026	+	0.630511i	0.988619	−	0.150439i	$-0.0480687\pi$
$467$	170.000	+	294.449i	0.364026	+	0.630511i	−0.624594	+	0.780950i	$0.714735\pi$
$468$		0			0
$469$	−147.000	−	424.352i	−0.313433	−	0.904803i
$470$			355.070i			0.755469i
$471$		0			0
$472$	277.804	−	481.170i	0.588568	−	1.01943i
$473$	−1029.00	−	594.093i	−2.17548	−	1.25601i
$474$		0			0
$475$			562.917i			1.18509i
$476$	−2.64575	+	13.7477i	−0.00555830	+	0.0288818i
$477$		0			0
$478$	−388.925	+	224.546i	−0.813652	+	0.469762i
$479$	666.729	+	384.936i	1.39192	+	0.803625i	0.993528	−	0.113590i	$-0.0362352\pi$
$479$	666.729	+	384.936i	1.39192	+	0.803625i	0.398392	+	0.917215i	$0.369569\pi$
$480$		0			0
$481$	−514.500	+	297.047i	−1.06965	+	0.617561i
$482$	27.0000			0.0560166
$483$		0			0
$484$	222.000			0.458678
$485$	−185.203	−	320.780i	−0.381861	−	0.661403i
$486$		0			0
$487$	−388.925	−	224.546i	−0.798615	−	0.461081i	0.0443717	−	0.999015i	$-0.485871\pi$
$487$	−388.925	−	224.546i	−0.798615	−	0.461081i	−0.842987	+	0.537935i	$0.819205\pi$
$488$	−240.000	−	415.692i	−0.491803	−	0.851828i
$489$		0			0
$490$	157.500	−	394.042i	0.321429	−	0.804166i
$491$	148.162			0.301756			0.150878	−	0.988552i	$-0.451790\pi$
$491$	148.162			0.301756			0.150878	+	0.988552i	$0.451790\pi$
$492$		0			0
$493$	−37.0405	+	64.1561i	−0.0751329	+	0.130134i
$494$	361.145	−	625.522i	0.731063	−	1.26624i
$495$		0			0
$496$		−	419.156i		−	0.845073i
$497$	392.000	+	339.482i	0.788732	+	0.683062i
$498$		0			0
$499$	−109.000	−	188.794i	−0.218437	−	0.378344i	0.735893	−	0.677097i	$-0.236762\pi$
$499$	−109.000	−	188.794i	−0.218437	−	0.378344i	−0.954330	+	0.298754i	$0.903429\pi$
$500$	62.5000	−	108.253i	0.125000	−	0.216506i
$501$		0			0
$502$	−250.023	−	433.053i	−0.498055	−	0.862656i
$503$	290.000			0.576541			0.288270	−	0.957549i	$-0.406920\pi$
$503$	290.000			0.576541			0.288270	+	0.957549i	$0.406920\pi$
$504$		0			0
$505$		−	962.341i		−	1.90563i
$506$	83.3412	+	144.351i	0.164706	+	0.285279i
$507$		0			0
$508$	−83.3412	−	48.1170i	−0.164057	−	0.0947186i
$509$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$509$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$510$		0			0
$511$	245.000	−	84.8705i	0.479452	−	0.166087i
$512$			552.524i			1.07915i
$513$		0			0
$514$	84.0000	+	48.4974i	0.163424	+	0.0943530i
$515$	370.405	−	641.561i	0.719233	−	1.24575i
$516$		0			0
$517$	−759.331			−1.46872
$518$	367.500	−	127.306i	0.709459	−	0.245764i
$519$		0			0
$520$	−694.510	+	400.975i	−1.33560	+	0.771106i
$521$	−305.584	−	176.429i	−0.586534	−	0.338636i	0.177192	−	0.984176i	$-0.443299\pi$
$521$	−305.584	−	176.429i	−0.586534	−	0.338636i	−0.763726	+	0.645541i	$0.776632\pi$
$522$		0			0
$523$	−185.203	−	320.780i	−0.354116	−	0.613347i	0.632850	−	0.774274i	$-0.281885\pi$
$523$	−185.203	−	320.780i	−0.354116	−	0.613347i	−0.986966	+	0.160927i	$0.948551\pi$
$524$			96.2341i			0.183653i
$525$		0			0
$526$	540.000			1.02662
$527$	66.0000	−	38.1051i	0.125237	−	0.0723057i
$528$		0			0
$529$	−251.000	+	434.745i	−0.474480	+	0.821824i
$530$	−97.5000	−	168.875i	−0.183962	−	0.318632i
$531$		0			0
$532$	103.184	−	119.147i	0.193955	−	0.223960i
$533$			594.093i			1.11462i
$534$		0			0
$535$	480.000	+	277.128i	0.897196	+	0.517997i
$536$	277.804	−	481.170i	0.518291	−	0.897706i
$537$		0			0
$538$	777.851			1.44582
$539$	842.672	+	336.819i	1.56340	+	0.624897i
$540$		0			0
$541$	−235.000	−	407.032i	−0.434381	−	0.752370i	0.562864	−	0.826549i	$-0.309699\pi$
$541$	−235.000	−	407.032i	−0.434381	−	0.752370i	−0.997245	+	0.0741799i	$0.976366\pi$
$542$	219.000	−	379.319i	0.404059	−	0.699851i
$543$		0			0
$544$	−27.0000	+	15.5885i	−0.0496324	+	0.0286553i
$545$	−280.000			−0.513761
$546$		0			0
$547$			128.312i			0.234574i	0.993098	+	0.117287i	$0.0374198\pi$
$547$			128.312i			0.234574i	−0.993098	+	0.117287i	$0.962580\pi$
$548$	−144.000	+	83.1384i	−0.262774	+	0.151712i
$549$		0			0
$550$	−694.510	−	400.975i	−1.26274	−	0.729046i
$551$	722.290	−	417.014i	1.31087	−	0.756832i
$552$		0			0
$553$	−137.579	+	714.882i	−0.248787	+	1.29273i
$554$	333.365			0.601741
$555$		0			0
$556$	−102.000	−	58.8897i	−0.183453	−	0.105917i
$557$	−223.500	−	129.038i	−0.401257	−	0.231666i	0.285769	−	0.958298i	$-0.407751\pi$
$557$	−223.500	−	129.038i	−0.401257	−	0.231666i	−0.687026	+	0.726633i	$0.741084\pi$
$558$		0			0
$559$			1188.19i			2.12556i
$560$	363.791	−	126.021i	0.649626	−	0.225037i
$561$		0			0
$562$	361.145	−	208.507i	0.642607	−	0.371009i
$563$	113.000	−	195.722i	0.200710	−	0.347641i	−0.748047	−	0.663646i	$-0.769008\pi$
$563$	113.000	−	195.722i	0.200710	−	0.347641i	0.948758	+	0.316005i	$0.102342\pi$
$564$		0			0
$565$	705.000	−	407.032i	1.24779	−	0.720411i
$566$		−	256.624i		−	0.453400i
$567$		0			0
$568$			641.561i			1.12951i
$569$	−46.3006	−	80.1951i	−0.0813720	−	0.140940i	0.822468	−	0.568812i	$-0.192597\pi$
$569$	−46.3006	−	80.1951i	−0.0813720	−	0.140940i	−0.903839	+	0.427872i	$0.859264\pi$
$570$		0			0
$571$	203.000	−	351.606i	0.355517	−	0.615773i	−0.631690	−	0.775221i	$-0.717638\pi$
$571$	203.000	−	351.606i	0.355517	−	0.615773i	0.987206	+	0.159449i	$0.0509716\pi$
$572$	−171.500	−	297.047i	−0.299825	−	0.519312i
$573$		0			0
$574$	73.5000	−	381.917i	0.128049	−	0.665361i
$575$			129.904i			0.225920i
$576$		0			0
$577$	−518.567	+	898.185i	−0.898730	+	1.55665i	−0.0696109	+	0.997574i	$0.522176\pi$
$577$	−518.567	+	898.185i	−0.898730	+	1.55665i	−0.829119	+	0.559072i	$0.811158\pi$
$578$	−427.500	−	246.817i	−0.739619	−	0.427019i
$579$		0			0
$580$	−185.203			−0.319315
$581$	−169.328	−	146.642i	−0.291442	−	0.252397i
$582$		0			0
$583$	361.145	−	208.507i	0.619460	−	0.357645i
$584$	277.804	+	160.390i	0.475692	+	0.274641i
$585$		0			0
$586$	−682.500	+	394.042i	−1.16468	+	0.672426i
$587$	−556.000			−0.947189			−0.473595	−	0.880743i	$-0.657044\pi$
$587$	−556.000			−0.947189			−0.473595	+	0.880743i	$0.657044\pi$
$588$		0			0
$589$	−858.000			−1.45671
$590$	−277.804	−	481.170i	−0.470854	−	0.815543i
$591$		0			0
$592$	305.584	+	176.429i	0.516190	+	0.298022i
$593$	446.000	+	772.495i	0.752108	+	1.30269i	0.946799	+	0.321825i	$0.104296\pi$
$593$	446.000	+	772.495i	0.752108	+	1.30269i	−0.194691	+	0.980865i	$0.562371\pi$
$594$		0			0
$595$	52.9150	+	45.8258i	0.0889328	+	0.0770181i
$596$	37.0405			0.0621485
$597$		0			0
$598$	83.3412	−	144.351i	0.139366	−	0.241390i
$599$	−74.0810	+	128.312i	−0.123675	+	0.214211i	−0.921214	−	0.389056i	$-0.872801\pi$
$599$	−74.0810	+	128.312i	−0.123675	+	0.214211i	0.797540	+	0.603267i	$0.206135\pi$
$600$		0			0
$601$		−	658.179i		−	1.09514i	−0.836760	−	0.547570i	$-0.815553\pi$
$601$		−	658.179i		−	1.09514i	0.836760	−	0.547570i	$-0.184447\pi$
$602$	147.000	−	763.834i	0.244186	−	1.26883i
$603$		0			0
$604$	−85.0000	−	147.224i	−0.140728	−	0.243749i
$605$	555.000	−	961.288i	0.917355	−	1.58891i
$606$		0			0
$607$	342.625	+	593.444i	0.564456	+	0.977666i	0.997100	+	0.0761017i	$0.0242474\pi$
$607$	342.625	+	593.444i	0.564456	+	0.977666i	−0.432644	+	0.901565i	$0.642419\pi$
$608$	351.000			0.577303
$609$		0			0
$610$	−480.000			−0.786885
$611$	379.665	+	657.600i	0.621383	+	1.07627i
$612$		0			0
$613$	694.510	+	400.975i	1.13297	+	0.654120i	0.944680	−	0.327994i	$-0.106373\pi$
$613$	694.510	+	400.975i	1.13297	+	0.654120i	0.188289	+	0.982114i	$0.439706\pi$
$614$	111.122	−	64.1561i	0.180980	−	0.104489i
$615$		0			0
$616$	367.500	+	1060.88i	0.596591	+	1.72221i
$617$			263.272i			0.426696i	0.976976	+	0.213348i	$0.0684369\pi$
$617$			263.272i			0.426696i	−0.976976	+	0.213348i	$0.931563\pi$
$618$		0			0
$619$	−580.500	−	335.152i	−0.937803	−	0.541441i	−0.0485320	−	0.998822i	$-0.515454\pi$
$619$	−580.500	−	335.152i	−0.937803	−	0.541441i	−0.889271	+	0.457381i	$0.848788\pi$
$620$	165.000	+	95.2628i	0.266129	+	0.153650i
$621$		0			0
$622$	−777.851			−1.25056
$623$	441.000	+	84.8705i	0.707865	+	0.136229i
$624$		0			0
$625$	−312.500	−	541.266i	−0.500000	−	0.866025i
$626$	−444.486	−	256.624i	−0.710042	−	0.409943i
$627$		0			0
$628$	9.26013	+	16.0390i	0.0147454	+	0.0255398i
$629$			64.1561i			0.101997i
$630$		0			0
$631$	662.000			1.04913			0.524564	−	0.851371i	$-0.324228\pi$
$631$	662.000			1.04913			0.524564	+	0.851371i	$0.324228\pi$
$632$	−780.000	+	450.333i	−1.23418	+	0.712553i
$633$		0			0
$634$	−174.000	+	301.377i	−0.274448	+	0.475358i
$635$	−416.706	+	240.585i	−0.656230	+	0.378874i
$636$		0			0
$637$	−129.642	−	898.185i	−0.203519	−	1.41002i
$638$			1188.19i			1.86236i
$639$		0			0
$640$	262.500	+	151.554i	0.410156	+	0.236804i
$641$	453.746	−	785.912i	0.707873	−	1.22607i	−0.257772	−	0.966206i	$-0.582988\pi$
$641$	453.746	−	785.912i	0.707873	−	1.22607i	0.965645	−	0.259866i	$-0.0836783\pi$
$642$		0			0
$643$	481.527			0.748875			0.374438	−	0.927252i	$-0.377836\pi$
$643$	481.527			0.748875			0.374438	+	0.927252i	$0.377836\pi$
$644$	23.8118	−	27.4955i	0.0369748	−	0.0426948i
$645$		0			0
$646$	−39.0000	−	67.5500i	−0.0603715	−	0.104567i
$647$	504.500	−	873.820i	0.779753	−	1.35057i	−0.152331	−	0.988329i	$-0.548678\pi$
$647$	504.500	−	873.820i	0.779753	−	1.35057i	0.932084	−	0.362242i	$-0.117989\pi$
$648$		0			0
$649$	1029.00	−	594.093i	1.58552	−	0.915398i
$650$			801.951i			1.23377i
$651$		0			0
$652$		−	64.1561i		−	0.0983989i
$653$	−211.500	+	122.110i	−0.323890	+	0.186998i	−0.653125	−	0.757250i	$-0.726542\pi$
$653$	−211.500	+	122.110i	−0.323890	+	0.186998i	0.329235	+	0.944248i	$0.393209\pi$
$654$		0			0
$655$	416.706	+	240.585i	0.636192	+	0.367306i
$656$	305.584	−	176.429i	0.465830	−	0.268947i
$657$		0			0
$658$	−162.714	−	469.714i	−0.247285	−	0.713851i
$659$	592.648			0.899315			0.449657	−	0.893201i	$-0.351546\pi$
$659$	592.648			0.899315			0.449657	+	0.893201i	$0.351546\pi$
$660$		0			0
$661$	516.000	+	297.913i	0.780635	+	0.450700i	0.836655	−	0.547730i	$-0.184508\pi$
$661$	516.000	+	297.913i	0.780635	+	0.450700i	−0.0560200	+	0.998430i	$0.517841\pi$
$662$	−262.500	−	151.554i	−0.396526	−	0.228934i
$663$		0			0
$664$		−	277.128i		−	0.417362i
$665$	−257.961	−	744.669i	−0.387911	−	1.11980i
$666$		0			0
$667$	166.682	−	96.2341i	0.249899	−	0.144279i
$668$	−44.5000	+	77.0763i	−0.0666168	+	0.115384i
$669$		0			0
$670$	−277.804	−	481.170i	−0.414633	−	0.718165i
$671$		−	1026.50i		−	1.52980i
$672$		0			0
$673$			513.248i			0.762628i	0.924446	+	0.381314i	$0.124528\pi$
$673$			513.248i			0.762628i	−0.924446	+	0.381314i	$0.875472\pi$
$674$	−55.5608	−	96.2341i	−0.0824344	−	0.142781i
$675$		0			0
$676$	−87.0000	+	150.688i	−0.128698	+	0.222912i
$677$	339.500	+	588.031i	0.501477	+	0.868584i	0.999999	+	0.00170645i	$0.000543182\pi$
$677$	339.500	+	588.031i	0.501477	+	0.868584i	−0.498521	+	0.866877i	$0.666123\pi$
$678$		0			0
$679$	392.000	+	339.482i	0.577320	+	0.499973i
$680$			86.6025i			0.127357i
$681$		0			0
$682$	611.169	−	1058.57i	0.896142	−	1.55216i
$683$	−1101.00	−	635.663i	−1.61201	−	0.930692i	−0.988905	−	0.148551i	$-0.952539\pi$
$683$	−1101.00	−	635.663i	−1.61201	−	0.930692i	−0.623101	−	0.782141i	$-0.714127\pi$
$684$		0			0
$685$			831.384i			1.21370i
$686$	−27.7804	+	593.444i	−0.0404962	+	0.865078i
$687$		0			0
$688$	611.169	−	352.858i	0.888326	−	0.512875i
$689$	−361.145	−	208.507i	−0.524158	−	0.302623i
$690$		0			0
$691$	12.0000	−	6.92820i	0.0173661	−	0.0100263i	−0.491292	−	0.870995i	$-0.663475\pi$
$691$	12.0000	−	6.92820i	0.0173661	−	0.0100263i	0.508658	+	0.860969i	$0.330142\pi$
$692$	−97.0000			−0.140173
$693$		0			0
$694$	−150.000			−0.216138
$695$	−510.000	+	294.449i	−0.733813	+	0.423667i
$696$		0			0
$697$	55.5608	+	32.0780i	0.0797142	+	0.0460230i
$698$	−6.00000	−	10.3923i	−0.00859599	−	0.0148887i
$699$		0			0
$700$	−33.0719	+	171.847i	−0.0472456	+	0.245495i
$701$	−740.810			−1.05679			−0.528395	−	0.848998i	$-0.677206\pi$
$701$	−740.810			−1.05679			−0.528395	+	0.848998i	$0.677206\pi$
$702$		0			0
$703$	361.145	−	625.522i	0.513720	−	0.889789i
$704$	−657.469	+	1138.77i	−0.933905	+	1.61757i
$705$		0			0
$706$		−	897.202i		−	1.27082i
$707$	441.000	+	1273.06i	0.623762	+	1.80065i
$708$		0			0
$709$	−73.0000	−	126.440i	−0.102962	−	0.178335i	0.809942	−	0.586510i	$-0.199499\pi$
$709$	−73.0000	−	126.440i	−0.102962	−	0.178335i	−0.912904	+	0.408175i	$0.866165\pi$
$710$	555.608	+	320.780i	0.782546	+	0.451803i
$711$		0			0
$712$	277.804	+	481.170i	0.390174	+	0.675801i
$713$	−198.000			−0.277700
$714$		0			0
$715$	−1715.00			−2.39860
$716$	64.8209	+	112.273i	0.0905320	+	0.156806i
$717$		0			0
$718$	−277.804	−	160.390i	−0.386913	−	0.223385i
$719$	−555.608	+	320.780i	−0.772751	+	0.446148i	−0.833855	−	0.551984i	$-0.813871\pi$
$719$	−555.608	+	320.780i	−0.772751	+	0.446148i	0.0611043	+	0.998131i	$0.480538\pi$
$720$		0			0
$721$	−196.000	+	1018.45i	−0.271845	+	1.41255i
$722$			252.879i			0.350249i
$723$		0			0
$724$	90.0000	+	51.9615i	0.124309	+	0.0717701i
$725$	−463.006	+	801.951i	−0.638630	+	1.10614i
$726$		0			0
$727$	−240.763			−0.331174			−0.165587	−	0.986195i	$-0.552952\pi$
$727$	−240.763			−0.331174			−0.165587	+	0.986195i	$0.552952\pi$
$728$	735.000	−	848.705i	1.00962	−	1.16580i
$729$		0			0
$730$	277.804	−	160.390i	0.380553	−	0.219713i
$731$	111.122	+	64.1561i	0.152013	+	0.0877648i
$732$		0			0
$733$	342.625	+	593.444i	0.467428	+	0.809609i	0.999307	−	0.0372109i	$-0.0118473\pi$
$733$	342.625	+	593.444i	0.467428	+	0.809609i	−0.531879	+	0.846820i	$0.678514\pi$
$734$			32.0780i			0.0437030i
$735$		0			0
$736$	81.0000			0.110054
$737$	1029.00	−	594.093i	1.39620	−	0.806097i
$738$		0			0
$739$	126.500	−	219.104i	0.171177	−	0.296488i	−0.767654	−	0.640864i	$-0.778576\pi$
$739$	126.500	−	219.104i	0.171177	−	0.296488i	0.938832	+	0.344376i	$0.111910\pi$
$740$	−138.902	+	80.1951i	−0.187705	+	0.108372i
$741$		0			0
$742$	206.369	+	178.720i	0.278125	+	0.240863i
$743$		−	718.801i		−	0.967431i	−0.875225	−	0.483715i	$-0.839287\pi$
$743$		−	718.801i		−	0.967431i	0.875225	−	0.483715i	$-0.160713\pi$
$744$		0			0
$745$	92.6013	−	160.390i	0.124297	−	0.215289i
$746$	−500.047	+	866.107i	−0.670304	+	1.16100i
$747$		0			0
$748$	−37.0405			−0.0495194
$749$	−761.976	−	146.642i	−1.01732	−	0.195784i
$750$		0			0
$751$	−310.000	−	536.936i	−0.412783	−	0.714961i	0.582410	−	0.812895i	$-0.302110\pi$
$751$	−310.000	−	536.936i	−0.412783	−	0.714961i	−0.995193	+	0.0979342i	$0.968777\pi$
$752$	225.500	−	390.577i	0.299867	−	0.519385i
$753$		0			0
$754$	1029.00	−	594.093i	1.36472	−	0.787922i
$755$	−850.000			−1.12583
$756$		0			0
$757$			962.341i			1.27126i	0.771995	+	0.635628i	$0.219259\pi$
$757$			962.341i			1.27126i	−0.771995	+	0.635628i	$0.780741\pi$
$758$	100.500	−	58.0237i	0.132586	−	0.0765484i
$759$		0			0
$760$	487.500	−	844.375i	0.641447	−	1.11102i
$761$	416.706	−	240.585i	0.547577	−	0.316144i	−0.200567	−	0.979680i	$-0.564279\pi$
$761$	416.706	−	240.585i	0.547577	−	0.316144i	0.748144	+	0.663536i	$0.230945\pi$
$762$		0			0
$763$	370.405	−	128.312i	0.485459	−	0.168168i
$764$	37.0405			0.0484824
$765$		0			0
$766$	−820.500	−	473.716i	−1.07115	−	0.618428i
$767$	−1029.00	−	594.093i	−1.34159	−	0.774568i
$768$		0			0
$769$			299.645i			0.389655i	0.980838	+	0.194828i	$0.0624147\pi$
$769$			299.645i			0.389655i	−0.980838	+	0.194828i	$0.937585\pi$
$770$	1102.50	+	212.176i	1.43182	+	0.275554i
$771$		0			0
$772$	111.122	−	64.1561i	0.143940	−	0.0831037i
$773$	219.500	−	380.185i	0.283959	−	0.491831i	−0.688398	−	0.725334i	$-0.741686\pi$
$773$	219.500	−	380.185i	0.283959	−	0.491831i	0.972356	+	0.233503i	$0.0750188\pi$
$774$		0			0
$775$	825.000	−	476.314i	1.06452	−	0.614599i
$776$			641.561i			0.826753i
$777$		0			0
$778$		−	834.029i		−	1.07202i
$779$	−361.145	−	625.522i	−0.463601	−	0.802980i
$780$		0			0
$781$	−686.000	+	1188.19i	−0.878361	+	1.52137i
$782$	−9.00000	−	15.5885i	−0.0115090	−	0.0199341i
$783$		0			0
$784$	−423.500	+	333.420i	−0.540179	+	0.425280i
$785$	92.6013			0.117963
$786$		0			0
$787$	−407.446	+	705.717i	−0.517720	+	0.896717i	0.482068	+	0.876134i	$0.339886\pi$
$787$	−407.446	+	705.717i	−0.517720	+	0.896717i	−0.999788	+	0.0205837i	$0.993448\pi$
$788$	67.5000	+	38.9711i	0.0856599	+	0.0494558i
$789$		0			0
$790$			900.666i			1.14008i
$791$	−746.102	+	861.524i	−0.943239	+	1.08916i
$792$		0			0
$793$	−888.972	+	513.248i	−1.12102	+	0.647224i
$794$	222.243	+	128.312i	0.279903	+	0.161602i
$795$		0			0
$796$	165.000	−	95.2628i	0.207286	−	0.119677i
$797$	−46.0000			−0.0577164			−0.0288582	−	0.999584i	$-0.509187\pi$
$797$	−46.0000			−0.0577164			−0.0288582	+	0.999584i	$0.509187\pi$
$798$		0			0
$799$	82.0000			0.102628
$800$	−337.500	+	194.856i	−0.421875	+	0.243570i
$801$		0			0
$802$	472.267	+	272.663i	0.588861	+	0.339979i
$803$	343.000	+	594.093i	0.427148	+	0.739842i
$804$		0			0
$805$	−59.5294	−	171.847i	−0.0739496	−	0.213474i
$806$	−1222.34			−1.51655
$807$		0			0
$808$	−833.412	+	1443.51i	−1.03145	+	1.78652i
$809$	398.186	−	689.678i	0.492195	−	0.852506i	−0.507765	−	0.861496i	$-0.669528\pi$
$809$	398.186	−	689.678i	0.492195	−	0.852506i	0.999960	+	0.00898937i	$0.00286144\pi$
$810$		0			0
$811$		−	1148.35i		−	1.41597i	−0.706229	−	0.707984i	$-0.749605\pi$
$811$		−	1148.35i		−	1.41597i	0.706229	−	0.707984i	$-0.250395\pi$
$812$	245.000	−	84.8705i	0.301724	−	0.104520i
$813$		0			0
$814$	514.500	+	891.140i	0.632064	+	1.09477i
$815$	−277.804	−	160.390i	−0.340864	−	0.196798i
$816$		0			0
$817$	−722.290	−	1251.04i	−0.884076	−	1.53126i
$818$	−888.000			−1.08557
$819$		0			0
$820$			160.390i			0.195598i
$821$	203.723	+	352.858i	0.248140	+	0.429791i	0.963010	−	0.269467i	$-0.0868474\pi$
$821$	203.723	+	352.858i	0.248140	+	0.429791i	−0.714870	+	0.699258i	$0.753514\pi$
$822$		0			0
$823$	−944.533	−	545.327i	−1.14767	−	0.662608i	−0.199352	−	0.979928i	$-0.563884\pi$
$823$	−944.533	−	545.327i	−1.14767	−	0.662608i	−0.948319	+	0.317320i	$0.897217\pi$
$824$	−1111.22	+	641.561i	−1.34856	+	0.778593i
$825$		0			0
$826$	588.000	+	509.223i	0.711864	+	0.616493i
$827$			1423.75i			1.72158i	0.508961	+	0.860789i	$0.330030\pi$
$827$			1423.75i			1.72158i	−0.508961	+	0.860789i	$0.669970\pi$
$828$		0			0
$829$	−201.000	−	116.047i	−0.242461	−	0.139985i	0.373846	−	0.927491i	$-0.378039\pi$
$829$	−201.000	−	116.047i	−0.242461	−	0.139985i	−0.616307	+	0.787506i	$0.711372\pi$
$830$	−240.000	−	138.564i	−0.289157	−	0.166945i
$831$		0			0
$832$	1314.94			1.58045
$833$	−91.0000	−	36.3731i	−0.109244	−	0.0436651i
$834$		0			0
$835$	222.500	+	385.381i	0.266467	+	0.461534i
$836$	361.145	+	208.507i	0.431992	+	0.249411i
$837$		0			0
$838$	−305.584	−	529.287i	−0.364659	−	0.631608i
$839$		−	641.561i		−	0.764673i	−0.924023	−	0.382336i	$-0.875120\pi$
$839$		−	641.561i		−	0.764673i	0.924023	−	0.382336i	$-0.124880\pi$
$840$		0			0
$841$	531.000			0.631391
$842$	−1128.00	+	651.251i	−1.33967	+	0.773457i
$843$		0			0
$844$	−143.500	+	248.549i	−0.170024	+	0.294490i
$845$	435.000	+	753.442i	0.514793	+	0.891647i
$846$		0			0
$847$	−293.678	+	1526.00i	−0.346728	+	1.80165i
$848$			247.683i			0.292079i
$849$		0			0
$850$	75.0000	+	43.3013i	0.0882353	+	0.0509427i
$851$	83.3412	−	144.351i	0.0979332	−	0.169625i
$852$		0			0
$853$	−1463.10			−1.71524			−0.857620	−	0.514283i	$-0.828058\pi$
$853$	−1463.10			−1.71524			−0.857620	+	0.514283i	$0.828058\pi$
$854$	634.980	−	219.964i	0.743537	−	0.257569i
$855$		0			0
$856$	−480.000	−	831.384i	−0.560748	−	0.971243i
$857$	365.000	−	632.199i	0.425904	−	0.737688i	−0.570600	−	0.821228i	$-0.693289\pi$
$857$	365.000	−	632.199i	0.425904	−	0.737688i	0.996504	+	0.0835401i	$0.0266227\pi$
$858$		0			0
$859$	594.000	−	342.946i	0.691502	−	0.399239i	−0.112673	−	0.993632i	$-0.535941\pi$
$859$	594.000	−	342.946i	0.691502	−	0.399239i	0.804174	+	0.594393i	$0.202608\pi$
$860$			320.780i			0.373000i
$861$		0			0
$862$		−	1218.97i		−	1.41411i
$863$	208.500	−	120.378i	0.241599	−	0.139487i	−0.374312	−	0.927303i	$-0.622121\pi$
$863$	208.500	−	120.378i	0.241599	−	0.139487i	0.615911	+	0.787815i	$0.288788\pi$
$864$		0			0
$865$	−242.500	+	420.022i	−0.280347	+	0.485575i
$866$	−1055.65	+	609.483i	−1.21900	+	0.703790i
$867$		0			0
$868$	−261.929	−	50.4083i	−0.301762	−	0.0580741i
$869$	−1926.11			−2.21646
$870$		0			0
$871$	−1029.00	−	594.093i	−1.18140	−	0.682082i
$872$	420.000	+	242.487i	0.481651	+	0.278082i
$873$		0			0
$874$			202.650i			0.231865i
$875$	661.438	+	572.822i	0.755929	+	0.654654i
$876$		0			0
$877$	−916.753	+	529.287i	−1.04533	+	0.603521i	−0.921338	−	0.388763i	$-0.872903\pi$
$877$	−916.753	+	529.287i	−1.04533	+	0.603521i	−0.123990	+	0.992283i	$0.539569\pi$
$878$	132.000	−	228.631i	0.150342	−	0.260399i
$879$		0			0
$880$	509.307	+	882.146i	0.578758	+	1.00244i
$881$			866.107i			0.983095i	0.870851	+	0.491548i	$0.163569\pi$
$881$			866.107i			0.983095i	−0.870851	+	0.491548i	$0.836431\pi$
$882$		0			0
$883$		−	962.341i		−	1.08985i	−0.838484	−	0.544927i	$-0.816557\pi$
$883$		−	962.341i		−	1.08985i	0.838484	−	0.544927i	$-0.183443\pi$
$884$	18.5203	+	32.0780i	0.0209505	+	0.0362874i
$885$		0			0
$886$	−390.000	+	675.500i	−0.440181	+	0.762415i
$887$	−535.000	−	926.647i	−0.603157	−	1.04470i	−0.992340	−	0.123538i	$-0.960576\pi$
$887$	−535.000	−	926.647i	−0.603157	−	1.04470i	0.389183	−	0.921160i	$-0.372757\pi$
$888$		0			0
$889$	441.000	−	509.223i	0.496063	−	0.572804i
$890$	555.608			0.624278
$891$		0			0
$892$	37.0405	−	64.1561i	0.0415252	−	0.0719238i
$893$	−799.500	−	461.592i	−0.895297	−	0.516900i
$894$		0			0
$895$	648.209			0.724256
$896$	−416.706	−	80.1951i	−0.465073	−	0.0895034i
$897$		0			0
$898$	−305.584	+	176.429i	−0.340294	+	0.196469i
$899$	−1222.34	−	705.717i	−1.35966	−	0.785002i
$900$		0			0
$901$	−39.0000	+	22.5167i	−0.0432852	+	0.0249907i
$902$	1029.00			1.14080
$903$		0			0
$904$	−1410.00			−1.55973
$905$	450.000	−	259.808i	0.497238	−	0.287080i
$906$		0			0
$907$	−1166.78	−	673.639i	−1.28641	−	0.742711i	−0.308400	−	0.951257i	$-0.599794\pi$
$907$	−1166.78	−	673.639i	−1.28641	−	0.742711i	−0.978013	+	0.208546i	$0.933127\pi$
$908$	−67.0000	−	116.047i	−0.0737885	−	0.127806i
$909$		0			0
$910$	−367.500	−	1060.88i	−0.403846	−	1.16580i
$911$	1592.74			1.74834			0.874172	−	0.485616i	$-0.161404\pi$
$911$	1592.74			1.74834			0.874172	+	0.485616i	$0.161404\pi$
$912$		0			0
$913$	296.324	−	513.248i	0.324561	−	0.562156i
$914$	277.804	−	481.170i	0.303943	−	0.526445i
$915$		0			0
$916$		−	31.1769i		−	0.0340359i
$917$	−661.500	−	127.306i	−0.721374	−	0.138828i
$918$		0			0
$919$	−175.000	−	303.109i	−0.190424	−	0.329825i	0.754967	−	0.655763i	$-0.227653\pi$
$919$	−175.000	−	303.109i	−0.190424	−	0.329825i	−0.945391	+	0.325939i	$0.894320\pi$
$920$	112.500	−	194.856i	0.122283	−	0.211800i
$921$		0			0
$922$	−111.122	−	192.468i	−0.120522	−	0.208751i
$923$	1372.00			1.48646
$924$		0			0
$925$			801.951i			0.866974i
$926$	194.463	+	336.819i	0.210003	+	0.363736i
$927$		0			0
$928$	500.047	+	288.702i	0.538844	+	0.311102i
$929$	1305.68	−	753.834i	1.40547	−	0.811446i	0.410520	−	0.911852i	$-0.365347\pi$
$929$	1305.68	−	753.834i	1.40547	−	0.811446i	0.994947	+	0.100405i	$0.0320139\pi$
$930$		0			0
$931$	682.500	+	866.891i	0.733083	+	0.931140i
$932$			370.659i			0.397703i
$933$		0			0
$934$	−510.000	−	294.449i	−0.546039	−	0.315256i
$935$	−92.6013	+	160.390i	−0.0990388	+	0.171540i
$936$		0			0
$937$	1592.74			1.69983			0.849916	−	0.526918i	$-0.176653\pi$
$937$	1592.74			1.69983			0.849916	+	0.526918i	$0.176653\pi$
$938$	588.000	+	509.223i	0.626866	+	0.542882i
$939$		0			0
$940$	102.500	+	177.535i	0.109043	+	0.188867i
$941$	−611.169	−	352.858i	−0.649488	−	0.374982i	0.138772	−	0.990324i	$-0.455685\pi$
$941$	−611.169	−	352.858i	−0.649488	−	0.374982i	−0.788260	+	0.615342i	$0.789018\pi$
$942$		0			0
$943$	−83.3412	−	144.351i	−0.0883788	−	0.153076i
$944$			705.717i			0.747581i
$945$		0			0
$946$	2058.00			2.17548
$947$	−51.0000	+	29.4449i	−0.0538543	+	0.0310928i	−0.526685	−	0.850060i	$-0.676565\pi$
$947$	−51.0000	+	29.4449i	−0.0538543	+	0.0310928i	0.472831	+	0.881153i	$0.343232\pi$
$948$		0			0
$949$	343.000	−	594.093i	0.361433	−	0.626020i
$950$	−487.500	−	844.375i	−0.513158	−	0.888816i
$951$		0			0
$952$	−39.6863	−	114.564i	−0.0416873	−	0.120341i
$953$			696.284i			0.730624i	0.930885	+	0.365312i	$0.119038\pi$
$953$			696.284i			0.730624i	−0.930885	+	0.365312i	$0.880962\pi$
$954$		0			0
$955$	92.6013	−	160.390i	0.0969647	−	0.167948i
$956$	−129.642	+	224.546i	−0.135609	+	0.234881i
$957$		0			0
$958$	−1333.46			−1.39192
$959$	−380.988	−	1099.82i	−0.397277	−	1.14684i
$960$		0			0
$961$	245.500	+	425.218i	0.255463	+	0.442475i
$962$	514.500	−	891.140i	0.534823	−	0.926341i
$963$		0			0
$964$	13.5000	−	7.79423i	0.0140041	−	0.00808530i
$965$		−	641.561i		−	0.664830i
$966$		0			0
$967$		−	320.780i		−	0.331727i	−0.986149	−	0.165864i	$-0.946959\pi$
$967$		−	320.780i		−	0.331727i	0.986149	−	0.165864i	$-0.0530412\pi$
$968$	−1665.00	+	961.288i	−1.72004	+	0.993066i
$969$		0			0
$970$	555.608	+	320.780i	0.572792	+	0.330701i
$971$	194.463	−	112.273i	0.200271	−	0.115626i	−0.396511	−	0.918030i	$-0.629779\pi$
$971$	194.463	−	112.273i	0.200271	−	0.115626i	0.596782	+	0.802404i	$0.296446\pi$
$972$		0			0
$973$	539.733	−	623.230i	0.554710	−	0.640524i
$974$	777.851			0.798615
$975$		0			0
$976$	528.000	+	304.841i	0.540984	+	0.312337i
$977$	−789.000	−	455.529i	−0.807574	−	0.466253i	0.0385386	−	0.999257i	$-0.487730\pi$
$977$	−789.000	−	455.529i	−0.807574	−	0.466253i	−0.846113	+	0.533004i	$0.821063\pi$
$978$		0			0
$979$			1188.19i			1.21367i
$980$	−35.0000	−	242.487i	−0.0357143	−	0.247436i
$981$		0			0
$982$	−222.243	+	128.312i	−0.226317	+	0.130664i
$983$	−143.500	+	248.549i	−0.145982	+	0.252848i	−0.929739	−	0.368220i	$-0.879967\pi$
$983$	−143.500	+	248.549i	−0.145982	+	0.252848i	0.783757	+	0.621067i	$0.213301\pi$
$984$		0			0
$985$	337.500	−	194.856i	0.342640	−	0.197823i
$986$		−	128.312i		−	0.130134i
$987$		0			0
$988$		−	417.014i		−	0.422079i
$989$	−166.682	−	288.702i	−0.168536	−	0.291913i
$990$		0			0
$991$	−550.000	+	952.628i	−0.554995	+	0.961279i	0.442909	+	0.896567i	$0.353946\pi$
$991$	−550.000	+	952.628i	−0.554995	+	0.961279i	−0.997904	+	0.0647129i	$0.979387\pi$
$992$	−297.000	−	514.419i	−0.299395	−	0.518568i
$993$		0			0
$994$	−882.000	−	169.741i	−0.887324	−	0.170766i
$995$		−	952.628i		−	0.957415i
$996$		0			0
$997$	370.405	−	641.561i	0.371520	−	0.643491i	−0.618280	−	0.785958i	$-0.712170\pi$
$997$	370.405	−	641.561i	0.371520	−	0.643491i	0.989800	+	0.142467i	$0.0455035\pi$
$998$	327.000	+	188.794i	0.327655	+	0.189172i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.bi.a.199.1	yes	4
3.2	odd	2		315.3.bi.b.199.1	yes	4
5.4	even	2		315.3.bi.b.199.2	yes	4
7.5	odd	6		315.3.bi.b.19.2	yes	4
15.14	odd	2	inner	315.3.bi.a.199.2	yes	4
21.5	even	6	inner	315.3.bi.a.19.2	yes	4
35.19	odd	6	inner	315.3.bi.a.19.1	✓	4
105.89	even	6		315.3.bi.b.19.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.3.bi.a.19.1	✓	4	35.19	odd	6	inner
315.3.bi.a.19.2	yes	4	21.5	even	6	inner
315.3.bi.a.199.1	yes	4	1.1	even	1	trivial
315.3.bi.a.199.2	yes	4	15.14	odd	2	inner
315.3.bi.b.19.1	yes	4	105.89	even	6
315.3.bi.b.19.2	yes	4	7.5	odd	6
315.3.bi.b.199.1	yes	4	3.2	odd	2
315.3.bi.b.199.2	yes	4	5.4	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)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-5.29150 - 4.58258i) q^{7} -8.66025i q^{8} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-5.29150 - 4.58258i) q^{7} -8.66025i q^{8} +(-7.50000 - 4.33013i) q^{10} +(9.26013 - 16.0390i) q^{11} -18.5203 q^{13} +(11.9059 + 2.29129i) q^{14} +(5.50000 + 9.52628i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(19.5000 - 11.2583i) q^{19} -5.00000 q^{20} +32.0780i q^{22} +(4.50000 - 2.59808i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(27.7804 - 16.0390i) q^{26} +(6.61438 - 2.29129i) q^{28} +37.0405 q^{29} +(-33.0000 - 19.0526i) q^{31} +(13.5000 + 7.79423i) q^{32} -3.46410i q^{34} +(6.61438 - 34.3693i) q^{35} +(27.7804 - 16.0390i) q^{37} +(-19.5000 + 33.7750i) q^{38} +(37.5000 - 21.6506i) q^{40} -32.0780i q^{41} -64.1561i q^{43} +(9.26013 + 16.0390i) q^{44} +(-4.50000 + 7.79423i) q^{46} +(-20.5000 - 35.5070i) q^{47} +(7.00000 + 48.4974i) q^{49} -43.3013i q^{50} +(9.26013 - 16.0390i) q^{52} +(19.5000 + 11.2583i) q^{53} +92.6013 q^{55} +(-39.6863 + 45.8258i) q^{56} +(-55.5608 + 32.0780i) q^{58} +(55.5608 + 32.0780i) q^{59} +(48.0000 - 27.7128i) q^{61} +66.0000 q^{62} -71.0000 q^{64} +(-46.3006 - 80.1951i) q^{65} +(55.5608 + 32.0780i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(19.8431 + 57.2822i) q^{70} -74.0810 q^{71} +(-18.5203 + 32.0780i) q^{73} +(-27.7804 + 48.1170i) q^{74} +22.5167i q^{76} +(-122.500 + 42.4352i) q^{77} +(-52.0000 - 90.0666i) q^{79} +(-27.5000 + 47.6314i) q^{80} +(27.7804 + 48.1170i) q^{82} +32.0000 q^{83} -10.0000 q^{85} +(55.5608 + 96.2341i) q^{86} +(-138.902 - 80.1951i) q^{88} +(-55.5608 + 32.0780i) q^{89} +(98.0000 + 84.8705i) q^{91} +5.19615i q^{92} +(61.5000 + 35.5070i) q^{94} +(97.5000 + 56.2917i) q^{95} -74.0810 q^{97} +(-52.5000 - 66.6840i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} - 2 q^{4} + 10 q^{5}+O(q^{10}) \) 4 * q - 6 * q^2 - 2 * q^4 + 10 * q^5	\( 4 q - 6 q^{2} - 2 q^{4} + 10 q^{5} - 30 q^{10} + 22 q^{16} - 4 q^{17} + 78 q^{19} - 20 q^{20} + 18 q^{23} - 50 q^{25} - 132 q^{31} + 54 q^{32} - 78 q^{38} + 150 q^{40} - 18 q^{46} - 82 q^{47} + 28 q^{49} + 78 q^{53} + 192 q^{61} + 264 q^{62} - 284 q^{64} - 4 q^{68} - 490 q^{77} - 208 q^{79} - 110 q^{80} + 128 q^{83} - 40 q^{85} + 392 q^{91} + 246 q^{94} + 390 q^{95} - 210 q^{98}+O(q^{100}) \) 4 * q - 6 * q^2 - 2 * q^4 + 10 * q^5 - 30 * q^10 + 22 * q^16 - 4 * q^17 + 78 * q^19 - 20 * q^20 + 18 * q^23 - 50 * q^25 - 132 * q^31 + 54 * q^32 - 78 * q^38 + 150 * q^40 - 18 * q^46 - 82 * q^47 + 28 * q^49 + 78 * q^53 + 192 * q^61 + 264 * q^62 - 284 * q^64 - 4 * q^68 - 490 * q^77 - 208 * q^79 - 110 * q^80 + 128 * q^83 - 40 * q^85 + 392 * q^91 + 246 * q^94 + 390 * q^95 - 210 * q^98

Introduction

L-functions

Modular forms

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