LMFDB - Embedded newform 108.3.d.d.55.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(55,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("108.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.207360000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 $ x^8 + 6x^6 + 32x^4 + 24*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.4
Root			$-1.14412 + 1.98168i$ of defining polynomial
Character	$\chi$	$=$	108.55
Dual form			108.3.d.d.55.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.270091 + 1.98168i) q^{2} +(-3.85410 - 1.07047i) q^{4} -7.40492 q^{5} -9.47802i q^{7} +(3.16228 - 7.34847i) q^{8} +O(q^{10})$	\(q+(-0.270091 + 1.98168i) q^{2} +(-3.85410 - 1.07047i) q^{4} -7.40492 q^{5} -9.47802i q^{7} +(3.16228 - 7.34847i) q^{8} +(2.00000 - 14.6742i) q^{10} +6.77022i q^{11} -14.4164 q^{13} +(18.7824 + 2.55992i) q^{14} +(13.7082 + 8.25137i) q^{16} -17.8933 q^{17} +5.19615i q^{19} +(28.5393 + 7.92672i) q^{20} +(-13.4164 - 1.82857i) q^{22} -24.9366i q^{23} +29.8328 q^{25} +(3.89374 - 28.5687i) q^{26} +(-10.1459 + 36.5292i) q^{28} -29.6197 q^{29} +17.1275i q^{31} +(-20.0540 + 24.9366i) q^{32} +(4.83282 - 35.4588i) q^{34} +70.1839i q^{35} +6.41641 q^{37} +(-10.2971 - 1.40343i) q^{38} +(-23.4164 + 54.4148i) q^{40} -8.64290 q^{41} +50.1329i q^{43} +(7.24730 - 26.0931i) q^{44} +(49.4164 + 6.73516i) q^{46} -52.0175i q^{47} -40.8328 q^{49} +(-8.05757 + 59.1191i) q^{50} +(55.5623 + 15.4323i) q^{52} +82.6921 q^{53} -50.1329i q^{55} +(-69.6489 - 29.9721i) q^{56} +(8.00000 - 58.6967i) q^{58} -83.7244i q^{59} -8.41641 q^{61} +(-33.9411 - 4.62597i) q^{62} +(-44.0000 - 46.4758i) q^{64} +106.752 q^{65} -29.0588i q^{67} +(68.9626 + 19.1542i) q^{68} +(-139.082 - 18.9560i) q^{70} +113.287i q^{71} +2.16718 q^{73} +(-1.73301 + 12.7153i) q^{74} +(5.56231 - 20.0265i) q^{76} +64.1683 q^{77} -149.485i q^{79} +(-101.508 - 61.1007i) q^{80} +(2.33437 - 17.1275i) q^{82} -13.5404i q^{83} +132.498 q^{85} +(-99.3474 - 13.5404i) q^{86} +(49.7508 + 21.4093i) q^{88} -17.8933 q^{89} +136.639i q^{91} +(-26.6938 + 96.1083i) q^{92} +(103.082 + 14.0495i) q^{94} -38.4771i q^{95} -138.331 q^{97} +(11.0286 - 80.9175i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4}+O(q^{10}) $ 8 * q - 4 * q^4	$ 8 q - 4 q^{4} + 16 q^{10} - 8 q^{13} + 56 q^{16} + 24 q^{25} - 108 q^{28} - 176 q^{34} - 56 q^{37} - 80 q^{40} + 288 q^{46} - 112 q^{49} + 364 q^{52} + 64 q^{58} + 40 q^{61} - 352 q^{64} - 576 q^{70} + 232 q^{73} - 36 q^{76} + 448 q^{82} + 416 q^{85} + 720 q^{88} + 288 q^{94} - 248 q^{97}+O(q^{100}) $ 8 * q - 4 * q^4 + 16 * q^10 - 8 * q^13 + 56 * q^16 + 24 * q^25 - 108 * q^28 - 176 * q^34 - 56 * q^37 - 80 * q^40 + 288 * q^46 - 112 * q^49 + 364 * q^52 + 64 * q^58 + 40 * q^61 - 352 * q^64 - 576 * q^70 + 232 * q^73 - 36 * q^76 + 448 * q^82 + 416 * q^85 + 720 * q^88 + 288 * q^94 - 248 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$1$	$-1$

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 $

$2$	−0.270091	+	1.98168i	−0.135045	+	0.990839i
$2$	−0.270091	+	1.98168i	−0.135045	+	0.990839i
$3$		0			0
$3$		0			0
$4$	−3.85410	−	1.07047i	−0.963525	−	0.267617i
$5$	−7.40492			−1.48098			−0.740492	−	0.672065i	$-0.765407\pi$
$5$	−7.40492			−1.48098			−0.740492	+	0.672065i	$0.765407\pi$
$6$		0			0
$7$		−	9.47802i		−	1.35400i	−0.735982	−	0.677001i	$-0.763279\pi$
$7$		−	9.47802i		−	1.35400i	0.735982	−	0.677001i	$-0.236721\pi$
$8$	3.16228	−	7.34847i	0.395285	−	0.918559i
$9$		0			0
$10$	2.00000	−	14.6742i	0.200000	−	1.46742i
$11$			6.77022i			0.615475i	0.951471	+	0.307737i	$0.0995718\pi$
$11$			6.77022i			0.615475i	−0.951471	+	0.307737i	$0.900428\pi$
$12$		0			0
$13$	−14.4164			−1.10895			−0.554477	−	0.832199i	$-0.687082\pi$
$13$	−14.4164			−1.10895			−0.554477	+	0.832199i	$0.687082\pi$
$14$	18.7824	+	2.55992i	1.34160	+	0.182852i
$15$		0			0
$16$	13.7082	+	8.25137i	0.856763	+	0.515711i
$17$	−17.8933			−1.05255			−0.526274	−	0.850315i	$-0.676411\pi$
$17$	−17.8933			−1.05255			−0.526274	+	0.850315i	$0.676411\pi$
$18$		0			0
$19$			5.19615i			0.273482i	0.990607	+	0.136741i	$0.0436628\pi$
$19$			5.19615i			0.273482i	−0.990607	+	0.136741i	$0.956337\pi$
$20$	28.5393	+	7.92672i	1.42697	+	0.396336i
$21$		0			0
$22$	−13.4164	−	1.82857i	−0.609837	−	0.0831170i
$23$		−	24.9366i		−	1.08420i	−0.840313	−	0.542101i	$-0.817629\pi$
$23$		−	24.9366i		−	1.08420i	0.840313	−	0.542101i	$-0.182371\pi$
$24$		0			0
$25$	29.8328			1.19331
$26$	3.89374	−	28.5687i	0.149759	−	1.09880i
$27$		0			0
$28$	−10.1459	+	36.5292i	−0.362354	+	1.30462i
$29$	−29.6197			−1.02137			−0.510684	−	0.859768i	$-0.670608\pi$
$29$	−29.6197			−1.02137			−0.510684	+	0.859768i	$0.670608\pi$
$30$		0			0
$31$			17.1275i			0.552499i	0.961086	+	0.276249i	$0.0890916\pi$
$31$			17.1275i			0.552499i	−0.961086	+	0.276249i	$0.910908\pi$
$32$	−20.0540	+	24.9366i	−0.626688	+	0.779270i
$33$		0			0
$34$	4.83282	−	35.4588i	0.142142	−	1.04291i
$35$			70.1839i			2.00526i
$36$		0			0
$37$	6.41641			0.173416			0.0867082	−	0.996234i	$-0.472365\pi$
$37$	6.41641			0.173416			0.0867082	+	0.996234i	$0.472365\pi$
$38$	−10.2971	−	1.40343i	−0.270976	−	0.0369324i
$39$		0			0
$40$	−23.4164	+	54.4148i	−0.585410	+	1.36037i
$41$	−8.64290			−0.210803			−0.105401	−	0.994430i	$-0.533613\pi$
$41$	−8.64290			−0.210803			−0.105401	+	0.994430i	$0.533613\pi$
$42$		0			0
$43$			50.1329i			1.16588i	0.812514	+	0.582941i	$0.198098\pi$
$43$			50.1329i			1.16588i	−0.812514	+	0.582941i	$0.801902\pi$
$44$	7.24730	−	26.0931i	0.164711	−	0.593026i
$45$		0			0
$46$	49.4164	+	6.73516i	1.07427	+	0.146416i
$47$		−	52.0175i		−	1.10676i	−0.832930	−	0.553378i	$-0.813339\pi$
$47$		−	52.0175i		−	1.10676i	0.832930	−	0.553378i	$-0.186661\pi$
$48$		0			0
$49$	−40.8328			−0.833323
$50$	−8.05757	+	59.1191i	−0.161151	+	1.18238i
$51$		0			0
$52$	55.5623	+	15.4323i	1.06851	+	0.296775i
$53$	82.6921			1.56023			0.780114	−	0.625637i	$-0.215161\pi$
$53$	82.6921			1.56023			0.780114	+	0.625637i	$0.215161\pi$
$54$		0			0
$55$		−	50.1329i		−	0.911508i
$56$	−69.6489	−	29.9721i	−1.24373	−	0.535216i
$57$		0			0
$58$	8.00000	−	58.6967i	0.137931	−	1.01201i
$59$		−	83.7244i		−	1.41906i	−0.704676	−	0.709529i	$-0.748908\pi$
$59$		−	83.7244i		−	1.41906i	0.704676	−	0.709529i	$-0.251092\pi$
$60$		0			0
$61$	−8.41641			−0.137974			−0.0689869	−	0.997618i	$-0.521977\pi$
$61$	−8.41641			−0.137974			−0.0689869	+	0.997618i	$0.521977\pi$
$62$	−33.9411	−	4.62597i	−0.547438	−	0.0746124i
$63$		0			0
$64$	−44.0000	−	46.4758i	−0.687500	−	0.726184i
$65$	106.752			1.64234
$66$		0			0
$67$		−	29.0588i		−	0.433713i	−0.976203	−	0.216856i	$-0.930420\pi$
$67$		−	29.0588i		−	0.433713i	0.976203	−	0.216856i	$-0.0695804\pi$
$68$	68.9626	+	19.1542i	1.01416	+	0.281679i
$69$		0			0
$70$	−139.082	−	18.9560i	−1.98689	−	0.270800i
$71$			113.287i			1.59559i	0.602928	+	0.797796i	$0.294001\pi$
$71$			113.287i			1.59559i	−0.602928	+	0.797796i	$0.705999\pi$
$72$		0			0
$73$	2.16718			0.0296875			0.0148437	−	0.999890i	$-0.495275\pi$
$73$	2.16718			0.0296875			0.0148437	+	0.999890i	$0.495275\pi$
$74$	−1.73301	+	12.7153i	−0.0234191	+	0.171828i
$75$		0			0
$76$	5.56231	−	20.0265i	0.0731882	−	0.263507i
$77$	64.1683			0.833354
$78$		0			0
$79$		−	149.485i		−	1.89221i	−0.323861	−	0.946105i	$-0.604981\pi$
$79$		−	149.485i		−	1.89221i	0.323861	−	0.946105i	$-0.395019\pi$
$80$	−101.508	−	61.1007i	−1.26885	−	0.763759i
$81$		0			0
$82$	2.33437	−	17.1275i	0.0284679	−	0.208871i
$83$		−	13.5404i		−	0.163138i	−0.996668	−	0.0815690i	$-0.974007\pi$
$83$		−	13.5404i		−	0.163138i	0.996668	−	0.0815690i	$-0.0259931\pi$
$84$		0			0
$85$	132.498			1.55881
$86$	−99.3474	−	13.5404i	−1.15520	−	0.157447i
$87$		0			0
$88$	49.7508	+	21.4093i	0.565350	+	0.243288i
$89$	−17.8933			−0.201048			−0.100524	−	0.994935i	$-0.532052\pi$
$89$	−17.8933			−0.201048			−0.100524	+	0.994935i	$0.532052\pi$
$90$		0			0
$91$			136.639i			1.50153i
$92$	−26.6938	+	96.1083i	−0.290150	+	1.04466i
$93$		0			0
$94$	103.082	+	14.0495i	1.09662	+	0.149462i
$95$		−	38.4771i		−	0.405022i
$96$		0			0
$97$	−138.331			−1.42610			−0.713048	−	0.701115i	$-0.752686\pi$
$97$	−138.331			−1.42610			−0.713048	+	0.701115i	$0.752686\pi$
$98$	11.0286	−	80.9175i	0.112536	−	0.825689i
$99$		0			0
$100$	−114.979	−	31.9350i	−1.14979	−	0.319350i
$101$	−97.5019			−0.965366			−0.482683	−	0.875795i	$-0.660338\pi$
$101$	−97.5019			−0.965366			−0.482683	+	0.875795i	$0.660338\pi$
$102$		0			0
$103$		−	42.4835i		−	0.412461i	−0.978503	−	0.206231i	$-0.933880\pi$
$103$		−	42.4835i		−	0.412461i	0.978503	−	0.206231i	$-0.0661197\pi$
$104$	−45.5887	+	105.939i	−0.438353	+	1.01864i
$105$		0			0
$106$	−22.3344	+	163.869i	−0.210702	+	1.54594i
$107$		−	97.2648i		−	0.909017i	−0.890742	−	0.454509i	$-0.849815\pi$
$107$		−	97.2648i		−	0.909017i	0.890742	−	0.454509i	$-0.150185\pi$
$108$		0			0
$109$	−96.8328			−0.888374			−0.444187	−	0.895934i	$-0.646507\pi$
$109$	−96.8328			−0.888374			−0.444187	+	0.895934i	$0.646507\pi$
$110$	99.3474	+	13.5404i	0.903158	+	0.123095i
$111$		0			0
$112$	78.2067	−	129.927i	0.698274	−	1.16006i
$113$	−38.8701			−0.343983			−0.171991	−	0.985098i	$-0.555020\pi$
$113$	−38.8701			−0.343983			−0.171991	+	0.985098i	$0.555020\pi$
$114$		0			0
$115$			184.654i			1.60568i
$116$	114.157	+	31.7069i	0.984114	+	0.273335i
$117$		0			0
$118$	165.915	+	22.6132i	1.40606	+	0.191637i
$119$			169.593i			1.42515i
$120$		0			0
$121$	75.1641			0.621191
$122$	2.27319	−	16.6786i	0.0186327	−	0.136710i
$123$		0			0
$124$	18.3344	−	66.0110i	0.147858	−	0.532347i
$125$	−35.7866			−0.286293
$126$		0			0
$127$		−	99.0165i		−	0.779657i	−0.920887	−	0.389829i	$-0.872534\pi$
$127$		−	99.0165i		−	0.779657i	0.920887	−	0.389829i	$-0.127466\pi$
$128$	103.984	−	74.6412i	0.812376	−	0.583134i
$129$		0			0
$130$	−28.8328	+	211.549i	−0.221791	+	1.62730i
$131$			54.1618i			0.413449i	0.978399	+	0.206724i	$0.0662803\pi$
$131$			54.1618i			0.413449i	−0.978399	+	0.206724i	$0.933720\pi$
$132$		0			0
$133$	49.2492			0.370295
$134$	57.5851	+	7.84850i	0.429740	+	0.0585709i
$135$		0			0
$136$	−56.5836	+	131.488i	−0.416056	+	0.966826i
$137$	5.55944			0.0405798			0.0202899	−	0.999794i	$-0.493541\pi$
$137$	5.55944			0.0405798			0.0202899	+	0.999794i	$0.493541\pi$
$138$		0			0
$139$			152.517i			1.09724i	0.836070	+	0.548622i	$0.184847\pi$
$139$			152.517i			1.09724i	−0.836070	+	0.548622i	$0.815153\pi$
$140$	75.1295	−	270.496i	0.536640	−	1.93211i
$141$		0			0
$142$	−224.498	−	30.5978i	−1.58097	−	0.215477i
$143$		−	97.6023i		−	0.682534i
$144$		0			0
$145$	219.331			1.51263
$146$	−0.585336	+	4.29466i	−0.00400915	+	0.0294155i
$147$		0			0
$148$	−24.7295	−	6.86855i	−0.167091	−	0.0464091i
$149$	−136.979			−0.919325			−0.459663	−	0.888094i	$-0.652030\pi$
$149$	−136.979			−0.919325			−0.459663	+	0.888094i	$0.652030\pi$
$150$		0			0
$151$			77.9879i			0.516476i	0.966081	+	0.258238i	$0.0831419\pi$
$151$			77.9879i			0.516476i	−0.966081	+	0.258238i	$0.916858\pi$
$152$	38.1838	+	16.4317i	0.251209	+	0.108103i
$153$		0			0
$154$	−17.3313	+	127.161i	−0.112541	+	0.825720i
$155$		−	126.827i		−	0.818242i
$156$		0			0
$157$	−72.1641			−0.459644			−0.229822	−	0.973233i	$-0.573814\pi$
$157$	−72.1641			−0.459644			−0.229822	+	0.973233i	$0.573814\pi$
$158$	296.230	+	40.3744i	1.87488	+	0.255534i
$159$		0			0
$160$	148.498	−	184.654i	0.928115	−	1.15409i
$161$	−236.350			−1.46801
$162$		0			0
$163$		−	56.5785i		−	0.347108i	−0.984824	−	0.173554i	$-0.944475\pi$
$163$		−	56.5785i		−	0.347108i	0.984824	−	0.173554i	$-0.0555250\pi$
$164$	33.3106	+	9.25194i	0.203114	+	0.0564143i
$165$		0			0
$166$	26.8328	+	3.65715i	0.161643	+	0.0220310i
$167$			201.637i			1.20741i	0.797208	+	0.603705i	$0.206309\pi$
$167$			201.637i			1.20741i	−0.797208	+	0.603705i	$0.793691\pi$
$168$		0			0
$169$	38.8328			0.229780
$170$	−35.7866	+	262.569i	−0.210509	+	1.54453i
$171$		0			0
$172$	53.6656	−	193.217i	0.312009	−	1.12336i
$173$	−92.5500			−0.534971			−0.267485	−	0.963562i	$-0.586193\pi$
$173$	−92.5500			−0.534971			−0.267485	+	0.963562i	$0.586193\pi$
$174$		0			0
$175$		−	282.756i		−	1.61575i
$176$	−55.8636	+	92.8076i	−0.317407	+	0.527316i
$177$		0			0
$178$	4.83282	−	35.4588i	0.0271507	−	0.199207i
$179$			4.28851i			0.0239581i	0.999928	+	0.0119791i	$0.00381315\pi$
$179$			4.28851i			0.0239581i	−0.999928	+	0.0119791i	$0.996187\pi$
$180$		0			0
$181$	−289.748			−1.60082			−0.800408	−	0.599456i	$-0.795384\pi$
$181$	−289.748			−1.60082			−0.800408	+	0.599456i	$0.795384\pi$
$182$	−270.775	−	36.9049i	−1.48777	−	0.202774i
$183$		0			0
$184$	−183.246	−	78.8566i	−0.995903	−	0.428568i
$185$	−47.5130			−0.256827
$186$		0			0
$187$		−	121.142i		−	0.647816i
$188$	−55.6830	+	200.481i	−0.296186	+	1.06639i
$189$		0			0
$190$	76.2492	+	10.3923i	0.401312	+	0.0546963i
$191$		−	92.6389i		−	0.485020i	−0.970149	−	0.242510i	$-0.922029\pi$
$191$		−	92.6389i		−	0.485020i	0.970149	−	0.242510i	$-0.0779708\pi$
$192$		0			0
$193$	−243.164			−1.25992			−0.629959	−	0.776629i	$-0.716928\pi$
$193$	−243.164			−1.25992			−0.629959	+	0.776629i	$0.716928\pi$
$194$	37.3620	−	274.128i	0.192588	−	1.41303i
$195$		0			0
$196$	157.374	+	43.7102i	0.802928	+	0.223011i
$197$	139.432			0.707779			0.353890	−	0.935287i	$-0.384859\pi$
$197$	139.432			0.707779			0.353890	+	0.935287i	$0.384859\pi$
$198$		0			0
$199$		−	110.993i		−	0.557756i	−0.960327	−	0.278878i	$-0.910038\pi$
$199$		−	110.993i		−	0.557756i	0.960327	−	0.278878i	$-0.0899624\pi$
$200$	94.3396	−	219.226i	0.471698	−	1.09613i
$201$		0			0
$202$	26.3344	−	193.217i	0.130368	−	0.956522i
$203$			280.736i			1.38293i
$204$		0			0
$205$	64.0000			0.312195
$206$	84.1887	+	11.4744i	0.408683	+	0.0557010i
$207$		0			0
$208$	−197.623	−	118.955i	−0.950111	−	0.571900i
$209$	−35.1791			−0.168321
$210$		0			0
$211$			265.095i			1.25637i	0.778062	+	0.628187i	$0.216203\pi$
$211$			265.095i			1.25637i	−0.778062	+	0.628187i	$0.783797\pi$
$212$	−318.704	−	88.5191i	−1.50332	−	0.417543i
$213$		0			0
$214$	192.748	+	26.2703i	0.900690	+	0.122759i
$215$		−	371.230i		−	1.72665i
$216$		0			0
$217$	162.334			0.748085
$218$	26.1536	−	191.892i	0.119971	−	0.880236i
$219$		0			0
$220$	−53.6656	+	193.217i	−0.243935	+	0.878261i
$221$	257.957			1.16723
$222$		0			0
$223$		−	317.925i		−	1.42567i	−0.701330	−	0.712837i	$-0.747410\pi$
$223$		−	317.925i		−	1.42567i	0.701330	−	0.712837i	$-0.252590\pi$
$224$	236.350	+	190.072i	1.05513	+	0.848538i
$225$		0			0
$226$	10.4984	−	77.0280i	0.0464533	−	0.340832i
$227$			249.366i			1.09853i	0.835648	+	0.549265i	$0.185092\pi$
$227$			249.366i			1.09853i	−0.835648	+	0.549265i	$0.814908\pi$
$228$		0			0
$229$	152.334			0.665216			0.332608	−	0.943065i	$-0.392071\pi$
$229$	152.334			0.665216			0.332608	+	0.943065i	$0.392071\pi$
$230$	−365.924	−	49.8733i	−1.59098	−	0.216840i
$231$		0			0
$232$	−93.6656	+	217.659i	−0.403731	+	0.938186i
$233$	346.793			1.48838			0.744191	−	0.667966i	$-0.232835\pi$
$233$	346.793			1.48838			0.744191	+	0.667966i	$0.232835\pi$
$234$		0			0
$235$			385.186i			1.63909i
$236$	−89.6241	+	322.682i	−0.379763	+	1.36730i
$237$		0			0
$238$	−336.079	−	45.8055i	−1.41210	−	0.192460i
$239$		−	104.035i		−	0.435293i	−0.976028	−	0.217647i	$-0.930162\pi$
$239$		−	104.035i		−	0.435293i	0.976028	−	0.217647i	$-0.0698380\pi$
$240$		0			0
$241$	281.827			1.16940			0.584702	−	0.811248i	$-0.301211\pi$
$241$	281.827			1.16940			0.584702	+	0.811248i	$0.301211\pi$
$242$	−20.3011	+	148.951i	−0.0838889	+	0.615500i
$243$		0			0
$244$	32.4377	+	9.00948i	0.132941	+	0.0369241i
$245$	302.364			1.23414
$246$		0			0
$247$		−	74.9099i		−	0.303279i
$248$	125.861	+	54.1618i	0.507502	+	0.218394i
$249$		0			0
$250$	9.66563	−	70.9176i	0.0386625	−	0.283670i
$251$		−	271.484i		−	1.08161i	−0.841148	−	0.540804i	$-0.818120\pi$
$251$		−	271.484i		−	1.08161i	0.841148	−	0.540804i	$-0.181880\pi$
$252$		0			0
$253$	168.827			0.667299
$254$	196.219	+	26.7434i	0.772515	+	0.105289i
$255$		0			0
$256$	119.830	+	226.223i	0.468085	+	0.883684i
$257$	459.105			1.78640			0.893200	−	0.449659i	$-0.148455\pi$
$257$	459.105			1.78640			0.893200	+	0.449659i	$0.148455\pi$
$258$		0			0
$259$		−	60.8148i		−	0.234806i
$260$	−411.434	−	114.275i	−1.58244	−	0.439518i
$261$		0			0
$262$	−107.331	−	14.6286i	−0.409661	−	0.0558343i
$263$		−	203.782i		−	0.774835i	−0.921904	−	0.387418i	$-0.873367\pi$
$263$		−	203.782i		−	0.774835i	0.921904	−	0.387418i	$-0.126633\pi$
$264$		0			0
$265$	−612.328			−2.31067
$266$	−13.3018	+	97.5961i	−0.0500066	+	0.366903i
$267$		0			0
$268$	−31.1064	+	111.995i	−0.116069	+	0.417893i
$269$	−323.363			−1.20209			−0.601047	−	0.799213i	$-0.705250\pi$
$269$	−323.363			−1.20209			−0.601047	+	0.799213i	$0.705250\pi$
$270$		0			0
$271$			104.928i			0.387190i	0.981082	+	0.193595i	$0.0620148\pi$
$271$			104.928i			0.387190i	−0.981082	+	0.193595i	$0.937985\pi$
$272$	−245.285	−	147.644i	−0.901783	−	0.542810i
$273$		0			0
$274$	−1.50155	+	11.0170i	−0.00548012	+	0.0402081i
$275$			201.975i			0.734454i
$276$		0			0
$277$	−48.8328			−0.176292			−0.0881459	−	0.996108i	$-0.528094\pi$
$277$	−48.8328			−0.176292			−0.0881459	+	0.996108i	$0.528094\pi$
$278$	−302.240	−	41.1934i	−1.08719	−	0.148178i
$279$		0			0
$280$	515.745	+	221.941i	1.84194	+	0.792647i
$281$	−29.6197			−0.105408			−0.0527040	−	0.998610i	$-0.516784\pi$
$281$	−29.6197			−0.105408			−0.0527040	+	0.998610i	$0.516784\pi$
$282$		0			0
$283$			385.186i			1.36108i	0.732711	+	0.680540i	$0.238255\pi$
$283$			385.186i			1.36108i	−0.732711	+	0.680540i	$0.761745\pi$
$284$	121.270	−	436.620i	0.427007	−	1.53739i
$285$		0			0
$286$	193.416	+	26.3615i	0.676281	+	0.0921730i
$287$			81.9176i			0.285427i
$288$		0			0
$289$	31.1703			0.107856
$290$	−59.2393	+	434.644i	−0.204274	+	1.49877i
$291$		0			0
$292$	−8.35255	−	2.31990i	−0.0286046	−	0.00794486i
$293$	−281.410			−0.960443			−0.480222	−	0.877147i	$-0.659444\pi$
$293$	−281.410			−0.960443			−0.480222	+	0.877147i	$0.659444\pi$
$294$		0			0
$295$			619.972i			2.10160i
$296$	20.2905	−	47.1508i	0.0685489	−	0.159293i
$297$		0			0
$298$	36.9969	−	271.449i	0.124151	−	0.910904i
$299$			359.497i			1.20233i
$300$		0			0
$301$	475.161			1.57861
$302$	−154.547	−	21.0638i	−0.511745	−	0.0697477i
$303$		0			0
$304$	−42.8754	+	71.2299i	−0.141037	+	0.234309i
$305$	62.3228			0.204337
$306$		0			0
$307$		−	553.961i		−	1.80443i	−0.431282	−	0.902217i	$-0.641939\pi$
$307$		−	553.961i		−	1.80443i	0.431282	−	0.902217i	$-0.358061\pi$
$308$	−247.311	−	68.6900i	−0.802958	−	0.223019i
$309$		0			0
$310$	251.331	+	34.2549i	0.810746	+	0.110500i
$311$			15.6847i			0.0504331i	0.999682	+	0.0252166i	$0.00802753\pi$
$311$			15.6847i			0.0504331i	−0.999682	+	0.0252166i	$0.991972\pi$
$312$		0			0
$313$	−308.161			−0.984540			−0.492270	−	0.870443i	$-0.663833\pi$
$313$	−308.161			−0.984540			−0.492270	+	0.870443i	$0.663833\pi$
$314$	19.4909	−	143.006i	0.0620728	−	0.455433i
$315$		0			0
$316$	−160.018	+	576.129i	−0.506387	+	1.82319i
$317$	496.107			1.56500			0.782502	−	0.622648i	$-0.213943\pi$
$317$	496.107			1.56500			0.782502	+	0.622648i	$0.213943\pi$
$318$		0			0
$319$		−	200.532i		−	0.628626i
$320$	325.816	+	344.150i	1.01818	+	1.07547i
$321$		0			0
$322$	63.8359	−	468.370i	0.198248	−	1.45456i
$323$		−	92.9763i		−	0.287852i
$324$		0			0
$325$	−430.082			−1.32333
$326$	112.120	+	15.2813i	0.343928	+	0.0468753i
$327$		0			0
$328$	−27.3313	+	63.5121i	−0.0833270	+	0.193634i
$329$	−493.023			−1.49855
$330$		0			0
$331$			86.5060i			0.261347i	0.991425	+	0.130674i	$0.0417140\pi$
$331$			86.5060i			0.261347i	−0.991425	+	0.130674i	$0.958286\pi$
$332$	−14.4946	+	52.1863i	−0.0436584	+	0.157188i
$333$		0			0
$334$	−399.580	−	54.4604i	−1.19635	−	0.163055i
$335$			215.178i			0.642322i
$336$		0			0
$337$	320.659			0.951512			0.475756	−	0.879577i	$-0.342175\pi$
$337$	320.659			0.951512			0.475756	+	0.879577i	$0.342175\pi$
$338$	−10.4884	+	76.9542i	−0.0310307	+	0.227675i
$339$		0			0
$340$	−510.663	−	141.835i	−1.50195	−	0.417162i
$341$	−115.957			−0.340049
$342$		0			0
$343$		−	77.4087i		−	0.225681i
$344$	368.400	+	158.534i	1.07093	+	0.460856i
$345$		0			0
$346$	24.9969	−	183.404i	0.0722454	−	0.530070i
$347$		−	674.759i		−	1.94455i	−0.233842	−	0.972275i	$-0.575130\pi$
$347$		−	674.759i		−	1.94455i	0.233842	−	0.972275i	$-0.424870\pi$
$348$		0			0
$349$	153.918			0.441026			0.220513	−	0.975384i	$-0.429227\pi$
$349$	153.918			0.441026			0.220513	+	0.975384i	$0.429227\pi$
$350$	560.331	+	76.3698i	1.60095	+	0.218199i
$351$		0			0
$352$	−168.827	−	135.770i	−0.479621	−	0.385711i
$353$	−623.228			−1.76552			−0.882759	−	0.469825i	$-0.844317\pi$
$353$	−623.228			−1.76552			−0.882759	+	0.469825i	$0.844317\pi$
$354$		0			0
$355$		−	838.881i		−	2.36305i
$356$	68.9626	+	19.1542i	0.193715	+	0.0538039i
$357$		0			0
$358$	−8.49845	−	1.15829i	−0.0237387	−	0.00323544i
$359$			160.341i			0.446633i	0.974746	+	0.223316i	$0.0716883\pi$
$359$			160.341i			0.446633i	−0.974746	+	0.223316i	$0.928312\pi$
$360$		0			0
$361$	334.000			0.925208
$362$	78.2582	−	574.187i	0.216183	−	1.58615i
$363$		0			0
$364$	146.267	−	526.621i	0.401834	−	1.44676i
$365$	−16.0478			−0.0439666
$366$		0			0
$367$		−	284.585i		−	0.775435i	−0.921778	−	0.387717i	$-0.873264\pi$
$367$		−	284.585i		−	0.775435i	0.921778	−	0.387717i	$-0.126736\pi$
$368$	205.761	−	341.837i	0.559134	−	0.928904i
$369$		0			0
$370$	12.8328	−	94.1555i	0.0346833	−	0.254474i
$371$		−	783.757i		−	2.11255i
$372$		0			0
$373$	301.420			0.808095			0.404048	−	0.914738i	$-0.367603\pi$
$373$	301.420			0.808095			0.404048	+	0.914738i	$0.367603\pi$
$374$	240.064	+	32.7192i	0.641882	+	0.0874846i
$375$		0			0
$376$	−382.249	−	164.494i	−1.01662	−	0.437484i
$377$	427.009			1.13265
$378$		0			0
$379$			248.547i			0.655796i	0.944713	+	0.327898i	$0.106340\pi$
$379$			248.547i			0.655796i	−0.944713	+	0.327898i	$0.893660\pi$
$380$	−41.1884	+	148.295i	−0.108391	+	0.390249i
$381$		0			0
$382$	183.580	+	25.0209i	0.480577	+	0.0654997i
$383$			488.131i			1.27449i	0.770660	+	0.637247i	$0.219927\pi$
$383$			488.131i			1.27449i	−0.770660	+	0.637247i	$0.780073\pi$
$384$		0			0
$385$	−475.161			−1.23418
$386$	65.6764	−	481.873i	0.170146	−	1.24838i
$387$		0			0
$388$	533.143	+	148.079i	1.37408	+	0.381647i
$389$	−415.867			−1.06907			−0.534534	−	0.845147i	$-0.679513\pi$
$389$	−415.867			−1.06907			−0.534534	+	0.845147i	$0.679513\pi$
$390$		0			0
$391$			446.199i			1.14117i
$392$	−129.125	+	300.059i	−0.329400	+	0.765456i
$393$		0			0
$394$	−37.6594	+	276.310i	−0.0955823	+	0.701295i
$395$			1106.92i			2.80233i
$396$		0			0
$397$	−670.827			−1.68974			−0.844870	−	0.534972i	$-0.820322\pi$
$397$	−670.827			−1.68974			−0.844870	+	0.534972i	$0.820322\pi$
$398$	219.953	+	29.9783i	0.552646	+	0.0753223i
$399$		0			0
$400$	408.954	+	246.162i	1.02239	+	0.615404i
$401$	114.742			0.286139			0.143070	−	0.989713i	$-0.454303\pi$
$401$	114.742			0.286139			0.143070	+	0.989713i	$0.454303\pi$
$402$		0			0
$403$		−	246.916i		−	0.612696i
$404$	375.782	+	104.373i	0.930154	+	0.258348i
$405$		0			0
$406$	−556.328	−	75.8241i	−1.37027	−	0.186759i
$407$			43.4405i			0.106733i
$408$		0			0
$409$	−146.672			−0.358611			−0.179305	−	0.983793i	$-0.557385\pi$
$409$	−146.672			−0.358611			−0.179305	+	0.983793i	$0.557385\pi$
$410$	−17.2858	+	126.827i	−0.0421605	+	0.309335i
$411$		0			0
$412$	−45.4772	+	163.736i	−0.110381	+	0.397417i
$413$	−793.541			−1.92141
$414$		0			0
$415$			100.266i			0.241605i
$416$	289.107	−	359.497i	0.694969	−	0.864175i
$417$		0			0
$418$	9.50155	−	69.7137i	0.0227310	−	0.166779i
$419$		−	536.872i		−	1.28132i	−0.767825	−	0.640659i	$-0.778661\pi$
$419$		−	536.872i		−	1.28132i	0.767825	−	0.640659i	$-0.221339\pi$
$420$		0			0
$421$	−367.413			−0.872716			−0.436358	−	0.899773i	$-0.643732\pi$
$421$	−367.413			−0.872716			−0.436358	+	0.899773i	$0.643732\pi$
$422$	−525.333	−	71.5997i	−1.24486	−	0.169668i
$423$		0			0
$424$	261.495	−	607.660i	0.616734	−	1.43316i
$425$	−533.808			−1.25602
$426$		0			0
$427$			79.7709i			0.186817i
$428$	−104.119	+	374.869i	−0.243268	+	0.875861i
$429$		0			0
$430$	735.659	+	100.266i	1.71084	+	0.233177i
$431$			735.353i			1.70616i	0.521784	+	0.853078i	$0.325267\pi$
$431$			735.353i			1.70616i	−0.521784	+	0.853078i	$0.674733\pi$
$432$		0			0
$433$	765.161			1.76712			0.883558	−	0.468322i	$-0.155141\pi$
$433$	765.161			1.76712			0.883558	+	0.468322i	$0.155141\pi$
$434$	−43.8450	+	321.695i	−0.101025	+	0.741232i
$435$		0			0
$436$	373.204	+	103.656i	0.855971	+	0.237744i
$437$	129.575			0.296509
$438$		0			0
$439$			46.3847i			0.105660i	0.998604	+	0.0528299i	$0.0168241\pi$
$439$			46.3847i			0.105660i	−0.998604	+	0.0528299i	$0.983176\pi$
$440$	−368.400	−	158.534i	−0.837274	−	0.360305i
$441$		0			0
$442$	−69.6718	+	511.188i	−0.157629	+	1.15653i
$443$		−	139.693i		−	0.315334i	−0.987492	−	0.157667i	$-0.949603\pi$
$443$		−	139.693i		−	0.315334i	0.987492	−	0.157667i	$-0.0503973\pi$
$444$		0			0
$445$	132.498			0.297749
$446$	630.026	+	85.8686i	1.41261	+	0.192531i
$447$		0			0
$448$	−440.498	+	417.033i	−0.983255	+	0.930877i
$449$	−267.139			−0.594963			−0.297482	−	0.954728i	$-0.596147\pi$
$449$	−267.139			−0.594963			−0.297482	+	0.954728i	$0.596147\pi$
$450$		0			0
$451$		−	58.5144i		−	0.129744i
$452$	149.809	+	41.6091i	0.331436	+	0.0920555i
$453$		0			0
$454$	−494.164	−	67.3516i	−1.08847	−	0.148351i
$455$		−	1011.80i		−	2.22374i
$456$		0			0
$457$	237.830			0.520415			0.260208	−	0.965553i	$-0.416209\pi$
$457$	237.830			0.520415			0.260208	+	0.965553i	$0.416209\pi$
$458$	−41.1441	+	301.878i	−0.0898343	+	0.659122i
$459$		0			0
$460$	197.666	−	711.674i	0.429708	−	1.54712i
$461$	298.650			0.647830			0.323915	−	0.946086i	$-0.395001\pi$
$461$	298.650			0.647830			0.323915	+	0.946086i	$0.395001\pi$
$462$		0			0
$463$			489.535i			1.05731i	0.848837	+	0.528655i	$0.177304\pi$
$463$			489.535i			1.05731i	−0.848837	+	0.528655i	$0.822696\pi$
$464$	−406.033	−	244.403i	−0.875070	−	0.526731i
$465$		0			0
$466$	−93.6656	+	687.233i	−0.200999	+	1.47475i
$467$		−	454.280i		−	0.972762i	−0.873747	−	0.486381i	$-0.838317\pi$
$467$		−	454.280i		−	0.972762i	0.873747	−	0.486381i	$-0.161683\pi$
$468$		0			0
$469$	−275.420			−0.587248
$470$	−763.314	−	104.035i	−1.62407	−	0.221351i
$471$		0			0
$472$	−615.246	−	264.760i	−1.30349	−	0.560932i
$473$	−339.411			−0.717571
$474$		0			0
$475$			155.016i			0.326349i
$476$	181.544	−	653.629i	0.381394	−	1.37317i
$477$		0			0
$478$	206.164	+	28.0989i	0.431306	+	0.0587843i
$479$			3.61359i			0.00754403i	0.999993	+	0.00377201i	$0.00120067\pi$
$479$			3.61359i			0.00754403i	−0.999993	+	0.00377201i	$0.998799\pi$
$480$		0			0
$481$	−92.5016			−0.192311
$482$	−76.1188	+	558.490i	−0.157923	+	1.15869i
$483$		0			0
$484$	−289.690	−	80.4606i	−0.598533	−	0.166241i
$485$	1024.33			2.11202
$486$		0			0
$487$			874.538i			1.79577i	0.440234	+	0.897883i	$0.354896\pi$
$487$			874.538i			1.79577i	−0.440234	+	0.897883i	$0.645104\pi$
$488$	−26.6150	+	61.8477i	−0.0545390	+	0.126737i
$489$		0			0
$490$	−81.6656	+	599.188i	−0.166665	+	1.22283i
$491$			645.196i			1.31404i	0.753871	+	0.657022i	$0.228184\pi$
$491$			645.196i			1.31404i	−0.753871	+	0.657022i	$0.771816\pi$
$492$		0			0
$493$	529.994			1.07504
$494$	148.447	+	20.2325i	0.300501	+	0.0409564i
$495$		0			0
$496$	−141.325	+	234.787i	−0.284930	+	0.473360i
$497$	1073.74			2.16043
$498$		0			0
$499$		−	564.842i		−	1.13195i	−0.824423	−	0.565974i	$-0.808500\pi$
$499$		−	564.842i		−	1.13195i	0.824423	−	0.565974i	$-0.191500\pi$
$500$	137.925	+	38.3084i	0.275850	+	0.0766167i
$501$		0			0
$502$	537.994	+	73.3253i	1.07170	+	0.146066i
$503$			483.048i			0.960334i	0.877177	+	0.480167i	$0.159424\pi$
$503$			483.048i			0.960334i	−0.877177	+	0.480167i	$0.840576\pi$
$504$		0			0
$505$	721.994			1.42969
$506$	−45.5985	+	334.560i	−0.0901156	+	0.661186i
$507$		0			0
$508$	−105.994	+	381.620i	−0.208649	+	0.751220i
$509$	−216.004			−0.424369			−0.212184	−	0.977230i	$-0.568058\pi$
$509$	−216.004			−0.424369			−0.212184	+	0.977230i	$0.568058\pi$
$510$		0			0
$511$		−	20.5406i		−	0.0401969i
$512$	−480.666	+	176.363i	−0.938801	+	0.344459i
$513$		0			0
$514$	−124.000	+	909.799i	−0.241245	+	1.77004i
$515$			314.587i			0.610848i
$516$		0			0
$517$	352.170			0.681180
$518$	120.515	+	16.4255i	0.232655	+	0.0317095i
$519$		0			0
$520$	337.580	−	784.466i	0.649193	−	1.50859i
$521$	454.806			0.872949			0.436475	−	0.899717i	$-0.356227\pi$
$521$	454.806			0.872949			0.436475	+	0.899717i	$0.356227\pi$
$522$		0			0
$523$		−	325.041i		−	0.621493i	−0.950493	−	0.310747i	$-0.899421\pi$
$523$		−	325.041i		−	0.621493i	0.950493	−	0.310747i	$-0.100579\pi$
$524$	57.9784	−	208.745i	0.110646	−	0.398368i
$525$		0			0
$526$	403.830	+	55.0395i	0.767737	+	0.104638i
$527$		−	306.467i		−	0.581531i
$528$		0			0
$529$	−92.8359			−0.175493
$530$	165.384	−	1213.44i	0.312046	−	2.28951i
$531$		0			0
$532$	−189.812	−	52.7196i	−0.356789	−	0.0990971i
$533$	124.600			0.233770
$534$		0			0
$535$			720.238i			1.34624i
$536$	−213.537	−	91.8919i	−0.398391	−	0.171440i
$537$		0			0
$538$	87.3375	−	640.802i	0.162337	−	1.19108i
$539$		−	276.447i		−	0.512889i
$540$		0			0
$541$	−962.574			−1.77925			−0.889625	−	0.456692i	$-0.849034\pi$
$541$	−962.574			−1.77925			−0.889625	+	0.456692i	$0.849034\pi$
$542$	−207.935	−	28.3402i	−0.383643	−	0.0522882i
$543$		0			0
$544$	358.833	−	446.199i	0.659619	−	0.820218i
$545$	717.039			1.31567
$546$		0			0
$547$		−	133.470i		−	0.244003i	−0.992530	−	0.122002i	$-0.961069\pi$
$547$		−	133.470i		−	0.244003i	0.992530	−	0.122002i	$-0.0389313\pi$
$548$	−21.4266	−	5.95119i	−0.0390997	−	0.0108598i
$549$		0			0
$550$	−400.249	−	54.5515i	−0.727726	−	0.0991846i
$551$		−	153.908i		−	0.279325i
$552$		0			0
$553$	−1416.82			−2.56206
$554$	13.1893	−	96.7710i	0.0238074	−	0.174677i
$555$		0			0
$556$	163.264	−	587.816i	0.293641	−	1.05722i
$557$	413.437			0.742258			0.371129	−	0.928581i	$-0.378971\pi$
$557$	413.437			0.742258			0.371129	+	0.928581i	$0.378971\pi$
$558$		0			0
$559$		−	722.737i		−	1.29291i
$560$	−579.114	+	962.096i	−1.03413	+	1.71803i
$561$		0			0
$562$	8.00000	−	58.6967i	0.0142349	−	0.104442i
$563$		−	516.562i		−	0.917516i	−0.888561	−	0.458758i	$-0.848294\pi$
$563$		−	516.562i		−	0.917516i	0.888561	−	0.458758i	$-0.151706\pi$
$564$		0			0
$565$	287.830			0.509433
$566$	−763.314	−	104.035i	−1.34861	−	0.183808i
$567$		0			0
$568$	832.486	+	358.245i	1.46564	+	0.630713i
$569$	468.355			0.823120			0.411560	−	0.911383i	$-0.364984\pi$
$569$	468.355			0.823120			0.411560	+	0.911383i	$0.364984\pi$
$570$		0			0
$571$		−	675.972i		−	1.18384i	−0.805997	−	0.591919i	$-0.798370\pi$
$571$		−	675.972i		−	1.18384i	0.805997	−	0.591919i	$-0.201630\pi$
$572$	−104.480	+	376.169i	−0.182657	+	0.657638i
$573$		0			0
$574$	−162.334	−	22.1252i	−0.282812	−	0.0385456i
$575$		−	743.930i		−	1.29379i
$576$		0			0
$577$	−354.823			−0.614945			−0.307473	−	0.951557i	$-0.599483\pi$
$577$	−354.823			−0.614945			−0.307473	+	0.951557i	$0.599483\pi$
$578$	−8.41881	+	61.7695i	−0.0145654	+	0.106868i
$579$		0			0
$580$	−845.325	−	234.787i	−1.45746	−	0.404805i
$581$	−128.337			−0.220889
$582$		0			0
$583$			559.844i			0.960281i
$584$	6.85324	−	15.9255i	0.0117350	−	0.0272697i
$585$		0			0
$586$	76.0062	−	557.664i	0.129703	−	0.951645i
$587$			220.479i			0.375603i	0.982207	+	0.187801i	$0.0601361\pi$
$587$			220.479i			0.375603i	−0.982207	+	0.187801i	$0.939864\pi$
$588$		0			0
$589$	−88.9969			−0.151098
$590$	−1228.59	−	167.449i	−2.08235	−	0.283811i
$591$		0			0
$592$	87.9574	+	52.9442i	0.148577	+	0.0894327i
$593$	−993.520			−1.67541			−0.837707	−	0.546121i	$-0.816104\pi$
$593$	−993.520			−1.67541			−0.837707	+	0.546121i	$0.816104\pi$
$594$		0			0
$595$		−	1255.82i		−	2.11063i
$596$	527.933	+	146.632i	0.885793	+	0.246027i
$597$		0			0
$598$	−712.407	−	97.0967i	−1.19132	−	0.162369i
$599$			280.736i			0.468674i	0.972155	+	0.234337i	$0.0752919\pi$
$599$			280.736i			0.468674i	−0.972155	+	0.234337i	$0.924708\pi$
$600$		0			0
$601$	561.830			0.934825			0.467412	−	0.884039i	$-0.345186\pi$
$601$	561.830			0.934825			0.467412	+	0.884039i	$0.345186\pi$
$602$	−128.337	+	941.616i	−0.213184	+	1.56415i
$603$		0			0
$604$	83.4834	−	300.573i	0.138218	−	0.497638i
$605$	−556.584			−0.919973
$606$		0			0
$607$		−	84.0527i		−	0.138472i	−0.997600	−	0.0692362i	$-0.977944\pi$
$607$		−	84.0527i		−	0.138472i	0.997600	−	0.0692362i	$-0.0220562\pi$
$608$	−129.575	−	104.204i	−0.213116	−	0.171388i
$609$		0			0
$610$	−16.8328	+	123.504i	−0.0275948	+	0.202465i
$611$			749.906i			1.22734i
$612$		0			0
$613$	730.234			1.19125			0.595623	−	0.803264i	$-0.296905\pi$
$613$	730.234			1.19125			0.595623	+	0.803264i	$0.296905\pi$
$614$	1097.77	+	149.620i	1.78790	+	0.243681i
$615$		0			0
$616$	202.918	−	471.539i	0.329412	−	0.765485i
$617$	549.786			0.891064			0.445532	−	0.895266i	$-0.353015\pi$
$617$	549.786			0.891064			0.445532	+	0.895266i	$0.353015\pi$
$618$		0			0
$619$		−	73.1269i		−	0.118137i	−0.998254	−	0.0590685i	$-0.981187\pi$
$619$		−	73.1269i		−	0.118137i	0.998254	−	0.0590685i	$-0.0188131\pi$
$620$	−135.765	+	488.806i	−0.218975	+	0.788397i
$621$		0			0
$622$	−31.0820	−	4.23629i	−0.0499711	−	0.00681076i
$623$			169.593i			0.272220i
$624$		0			0
$625$	−480.823			−0.769318
$626$	83.2314	−	610.676i	0.132958	−	0.975521i
$627$		0			0
$628$	278.128	+	77.2492i	0.442879	+	0.123008i
$629$	−114.811			−0.182529
$630$		0			0
$631$			779.849i			1.23589i	0.786220	+	0.617947i	$0.212035\pi$
$631$			779.849i			1.23589i	−0.786220	+	0.617947i	$0.787965\pi$
$632$	−1098.48	−	472.712i	−1.73811	−	0.747962i
$633$		0			0
$634$	−133.994	+	983.124i	−0.211347	+	1.55067i
$635$			733.209i			1.15466i
$636$		0			0
$637$	588.663			0.924117
$638$	397.390	+	54.1618i	0.622868	+	0.0848931i
$639$		0			0
$640$	−769.994	+	552.712i	−1.20312	+	0.863612i
$641$	−444.341			−0.693200			−0.346600	−	0.938013i	$-0.612664\pi$
$641$	−444.341			−0.693200			−0.346600	+	0.938013i	$0.612664\pi$
$642$		0			0
$643$		−	446.199i		−	0.693933i	−0.937878	−	0.346966i	$-0.887212\pi$
$643$		−	446.199i		−	0.693933i	0.937878	−	0.346966i	$-0.112788\pi$
$644$	910.917	+	253.005i	1.41447	+	0.392864i
$645$		0			0
$646$	184.249	+	25.1120i	0.285216	+	0.0388731i
$647$		−	861.386i		−	1.33135i	−0.746240	−	0.665677i	$-0.768143\pi$
$647$		−	861.386i		−	1.33135i	0.746240	−	0.665677i	$-0.231857\pi$
$648$		0			0
$649$	566.833			0.873394
$650$	116.161	−	852.284i	0.178710	−	1.31121i
$651$		0			0
$652$	−60.5654	+	218.059i	−0.0928917	+	0.334447i
$653$	876.302			1.34196			0.670982	−	0.741474i	$-0.265873\pi$
$653$	876.302			1.34196			0.670982	+	0.741474i	$0.265873\pi$
$654$		0			0
$655$		−	401.064i		−	0.612311i
$656$	−118.479	−	71.3158i	−0.180608	−	0.108713i
$657$		0			0
$658$	133.161	−	977.013i	0.202372	−	1.48482i
$659$			565.760i			0.858513i	0.903183	+	0.429257i	$0.141224\pi$
$659$			565.760i			0.858513i	−0.903183	+	0.429257i	$0.858776\pi$
$660$		0			0
$661$	632.580			0.957005			0.478503	−	0.878086i	$-0.341180\pi$
$661$	632.580			0.957005			0.478503	+	0.878086i	$0.341180\pi$
$662$	−171.427	−	23.3645i	−0.258953	−	0.0352938i
$663$		0			0
$664$	−99.5016	−	42.8187i	−0.149852	−	0.0644859i
$665$	−364.686			−0.548401
$666$		0			0
$667$			738.615i			1.10737i
$668$	215.846	−	777.131i	0.323123	−	1.16337i
$669$		0			0
$670$	−426.413	−	58.1175i	−0.636438	−	0.0867426i
$671$		−	56.9810i		−	0.0849195i
$672$		0			0
$673$	−1072.66			−1.59385			−0.796924	−	0.604080i	$-0.793541\pi$
$673$	−1072.66			−1.59385			−0.796924	+	0.604080i	$0.793541\pi$
$674$	−86.6071	+	635.444i	−0.128497	+	0.942795i
$675$		0			0
$676$	−149.666	−	41.5692i	−0.221399	−	0.0614929i
$677$	−478.798			−0.707234			−0.353617	−	0.935390i	$-0.615048\pi$
$677$	−478.798			−0.707234			−0.353617	+	0.935390i	$0.615048\pi$
$678$		0			0
$679$			1311.11i			1.93094i
$680$	418.997	−	973.661i	0.616172	−	1.43185i
$681$		0			0
$682$	31.3188	−	229.789i	0.0459221	−	0.336934i
$683$		−	318.418i		−	0.466206i	−0.972452	−	0.233103i	$-0.925112\pi$
$683$		−	318.418i		−	0.466206i	0.972452	−	0.233103i	$-0.0748879\pi$
$684$		0			0
$685$	−41.1672			−0.0600981
$686$	153.399	+	20.9074i	0.223614	+	0.0304772i
$687$		0			0
$688$	−413.666	+	687.233i	−0.601258	+	0.998885i
$689$	−1192.12			−1.73022
$690$		0			0
$691$		−	1121.30i		−	1.62272i	−0.584545	−	0.811362i	$-0.698727\pi$
$691$		−	1121.30i		−	1.62272i	0.584545	−	0.811362i	$-0.301273\pi$
$692$	356.697	+	99.0716i	0.515458	+	0.143167i
$693$		0			0
$694$	1337.15	+	182.246i	1.92674	+	0.262602i
$695$		−	1129.38i		−	1.62500i
$696$		0			0
$697$	154.650			0.221880
$698$	−41.5718	+	305.016i	−0.0595585	+	0.436986i
$699$		0			0
$700$	−302.681	+	1089.77i	−0.432401	+	1.55681i
$701$	413.437			0.589782			0.294891	−	0.955531i	$-0.404717\pi$
$701$	413.437			0.589782			0.294891	+	0.955531i	$0.404717\pi$
$702$		0			0
$703$			33.3406i			0.0474262i
$704$	314.652	−	297.890i	0.446948	−	0.423139i
$705$		0			0
$706$	168.328	−	1235.04i	0.238425	−	1.74935i
$707$			924.125i			1.30711i
$708$		0			0
$709$	−682.915			−0.963209			−0.481604	−	0.876389i	$-0.659946\pi$
$709$	−682.915			−0.963209			−0.481604	+	0.876389i	$0.659946\pi$
$710$	1662.39	+	226.574i	2.34140	+	0.319118i
$711$		0			0
$712$	−56.5836	+	131.488i	−0.0794713	+	0.184675i
$713$	427.101			0.599020
$714$		0			0
$715$			722.737i			1.01082i
$716$	4.59070	−	16.5284i	0.00641160	−	0.0230843i
$717$		0			0
$718$	−317.745	−	43.3066i	−0.442541	−	0.0603157i
$719$		−	286.374i		−	0.398295i	−0.979970	−	0.199148i	$-0.936183\pi$
$719$		−	286.374i		−	0.398295i	0.979970	−	0.199148i	$-0.0638173\pi$
$720$		0			0
$721$	−402.659			−0.558474
$722$	−90.2103	+	661.881i	−0.124945	+	0.916732i
$723$		0			0
$724$	1116.72	+	310.165i	1.54243	+	0.428405i
$725$	−883.638			−1.21881
$726$		0			0
$727$			322.923i			0.444186i	0.975026	+	0.222093i	$0.0712888\pi$
$727$			322.923i			0.444186i	−0.975026	+	0.222093i	$0.928711\pi$
$728$	1004.09	+	432.090i	1.37924	+	0.593531i
$729$		0			0
$730$	4.33437	−	31.8016i	0.00593749	−	0.0435639i
$731$		−	897.044i		−	1.22715i
$732$		0			0
$733$	−521.830			−0.711910			−0.355955	−	0.934503i	$-0.615844\pi$
$733$	−521.830			−0.711910			−0.355955	+	0.934503i	$0.615844\pi$
$734$	563.955	+	76.8636i	0.768331	+	0.104719i
$735$		0			0
$736$	621.836	+	500.080i	0.844886	+	0.679457i
$737$	196.734			0.266939
$738$		0			0
$739$			965.020i			1.30585i	0.757424	+	0.652923i	$0.226458\pi$
$739$			965.020i			1.30585i	−0.757424	+	0.652923i	$0.773542\pi$
$740$	183.120	+	50.8610i	0.247459	+	0.0687311i
$741$		0			0
$742$	1553.15	+	211.686i	2.09320	+	0.285290i
$743$			1097.33i			1.47689i	0.674312	+	0.738447i	$0.264440\pi$
$743$			1097.33i			1.47689i	−0.674312	+	0.738447i	$0.735560\pi$
$744$		0			0
$745$	1014.32			1.36151
$746$	−81.4106	+	597.317i	−0.109130	+	0.800693i
$747$		0			0
$748$	−129.678	+	466.892i	−0.173366	+	0.624188i
$749$	−921.878			−1.23081
$750$		0			0
$751$		−	1381.05i		−	1.83894i	−0.393154	−	0.919472i	$-0.628616\pi$
$751$		−	1381.05i		−	1.83894i	0.393154	−	0.919472i	$-0.371384\pi$
$752$	429.216	−	713.067i	0.570766	−	0.948227i
$753$		0			0
$754$	−115.331	+	846.195i	−0.152959	+	1.12227i
$755$		−	577.494i		−	0.764892i
$756$		0			0
$757$	−516.252			−0.681971			−0.340986	−	0.940068i	$-0.610761\pi$
$757$	−516.252			−0.681971			−0.340986	+	0.940068i	$0.610761\pi$
$758$	−492.540	−	67.1301i	−0.649788	−	0.0885622i
$759$		0			0
$760$	−282.748	−	121.675i	−0.372036	−	0.160099i
$761$	−1216.18			−1.59814			−0.799069	−	0.601239i	$-0.794674\pi$
$761$	−1216.18			−1.59814			−0.799069	+	0.601239i	$0.794674\pi$
$762$		0			0
$763$			917.783i			1.20286i
$764$	−99.1668	+	357.040i	−0.129799	+	0.467329i
$765$		0			0
$766$	−967.319	−	131.840i	−1.26282	−	0.172114i
$767$			1207.00i			1.57367i
$768$		0			0
$769$	1004.33			1.30601			0.653007	−	0.757352i	$-0.273507\pi$
$769$	1004.33			1.30601			0.653007	+	0.757352i	$0.273507\pi$
$770$	128.337	−	941.616i	0.166671	−	1.22288i
$771$		0			0
$772$	937.179	+	260.299i	1.21396	+	0.337175i
$773$	−382.580			−0.494929			−0.247464	−	0.968897i	$-0.579597\pi$
$773$	−382.580			−0.494929			−0.247464	+	0.968897i	$0.579597\pi$
$774$		0			0
$775$			510.960i			0.659304i
$776$	−437.442	+	1016.52i	−0.563714	+	1.30995i
$777$		0			0
$778$	112.322	−	824.116i	0.144373	−	1.05927i
$779$		−	44.9098i		−	0.0576506i
$780$		0			0
$781$	−766.978			−0.982046
$782$	−884.223	−	120.514i	−1.13072	−	0.154110i
$783$		0			0
$784$	−559.745	−	336.927i	−0.713960	−	0.429754i
$785$	534.369			0.680725
$786$		0			0
$787$			477.268i			0.606440i	0.952921	+	0.303220i	$0.0980617\pi$
$787$			477.268i			0.606440i	−0.952921	+	0.303220i	$0.901938\pi$
$788$	−537.387	−	149.258i	−0.681963	−	0.189413i
$789$		0			0
$790$	−2193.56	−	298.969i	−2.77666	−	0.378442i
$791$			368.411i			0.465754i
$792$		0			0
$793$	121.334			0.153007
$794$	181.184	−	1329.36i	0.228192	−	1.67426i
$795$		0			0
$796$	−118.815	+	427.780i	−0.149265	+	0.537412i
$797$	514.607			0.645680			0.322840	−	0.946453i	$-0.395362\pi$
$797$	514.607			0.645680			0.322840	+	0.946453i	$0.395362\pi$
$798$		0			0
$799$			930.765i			1.16491i
$800$	−598.268	+	743.930i	−0.747835	+	0.929913i
$801$		0			0
$802$	−30.9907	+	227.381i	−0.0386417	+	0.283518i
$803$			14.6723i			0.0182719i
$804$		0			0
$805$	1750.15			2.17410
$806$	489.309	+	66.6899i	0.607083	+	0.0827418i
$807$		0			0
$808$	−308.328	+	716.490i	−0.381594	+	0.886745i
$809$	−1463.74			−1.80932			−0.904662	−	0.426129i	$-0.859877\pi$
$809$	−1463.74			−1.80932			−0.904662	+	0.426129i	$0.859877\pi$
$810$		0			0
$811$		−	1163.05i		−	1.43410i	−0.697023	−	0.717049i	$-0.745492\pi$
$811$		−	1163.05i		−	1.43410i	0.697023	−	0.717049i	$-0.254508\pi$
$812$	300.518	−	1081.98i	0.370096	−	1.33249i
$813$		0			0
$814$	−86.0851	−	11.7329i	−0.105756	−	0.0144139i
$815$			418.959i			0.514061i
$816$		0			0
$817$	−260.498			−0.318848
$818$	39.6147	−	290.656i	0.0484287	−	0.355326i
$819$		0			0
$820$	−246.663	−	68.5098i	−0.300808	−	0.0835486i
$821$	−392.553			−0.478140			−0.239070	−	0.971002i	$-0.576842\pi$
$821$	−392.553			−0.478140			−0.239070	+	0.971002i	$0.576842\pi$
$822$		0			0
$823$		−	1248.84i		−	1.51743i	−0.651424	−	0.758714i	$-0.725828\pi$
$823$		−	1248.84i		−	1.51743i	0.651424	−	0.758714i	$-0.274172\pi$
$824$	−312.189	−	134.345i	−0.378870	−	0.163040i
$825$		0			0
$826$	214.328	−	1572.54i	0.259477	−	1.90381i
$827$		−	1369.15i		−	1.65557i	−0.561049	−	0.827783i	$-0.689602\pi$
$827$		−	1369.15i		−	1.65557i	0.561049	−	0.827783i	$-0.310398\pi$
$828$		0			0
$829$	−73.7477			−0.0889598			−0.0444799	−	0.999010i	$-0.514163\pi$
$829$	−73.7477			−0.0889598			−0.0444799	+	0.999010i	$0.514163\pi$
$830$	−198.695	−	27.0809i	−0.239391	−	0.0326276i
$831$		0			0
$832$	634.322	+	670.014i	0.762406	+	0.805305i
$833$	730.634			0.877112
$834$		0			0
$835$		−	1493.11i		−	1.78815i
$836$	135.584	+	37.6581i	0.162182	+	0.0450455i
$837$		0			0
$838$	1063.91	+	145.004i	1.26958	+	0.173036i
$839$			1200.57i			1.43096i	0.698635	+	0.715478i	$0.253791\pi$
$839$			1200.57i			1.43096i	−0.698635	+	0.715478i	$0.746209\pi$
$840$		0			0
$841$	36.3251			0.0431927
$842$	99.2349	−	728.095i	0.117856	−	0.864721i
$843$		0			0
$844$	283.775	−	1021.70i	0.336227	−	1.21055i
$845$	−287.554			−0.340300
$846$		0			0
$847$		−	712.406i		−	0.841094i
$848$	1133.56	+	682.323i	1.33675	+	0.804626i
$849$		0			0
$850$	144.177	−	1057.84i	0.169619	−	1.24451i
$851$		−	160.004i		−	0.188018i
$852$		0			0
$853$	−439.079			−0.514747			−0.257373	−	0.966312i	$-0.582857\pi$
$853$	−439.079			−0.514747			−0.257373	+	0.966312i	$0.582857\pi$
$854$	−158.080	−	21.5454i	−0.185106	−	0.0252288i
$855$		0			0
$856$	−714.748	−	307.578i	−0.834986	−	0.359321i
$857$	510.962			0.596222			0.298111	−	0.954531i	$-0.403643\pi$
$857$	510.962			0.596222			0.298111	+	0.954531i	$0.403643\pi$
$858$		0			0
$859$			176.776i			0.205793i	0.994692	+	0.102897i	$0.0328111\pi$
$859$			176.776i			0.205793i	−0.994692	+	0.102897i	$0.967189\pi$
$860$	−397.390	+	1430.76i	−0.462081	+	1.66367i
$861$		0			0
$862$	−1457.23	−	198.612i	−1.69053	−	0.230408i
$863$		−	1028.28i		−	1.19152i	−0.803163	−	0.595759i	$-0.796851\pi$
$863$		−	1028.28i		−	1.19152i	0.803163	−	0.595759i	$-0.203149\pi$
$864$		0			0
$865$	685.325			0.792283
$866$	−206.663	+	1516.30i	−0.238641	+	1.75093i
$867$		0			0
$868$	−625.653	−	173.773i	−0.720799	−	0.200200i
$869$	1012.04			1.16461
$870$		0			0
$871$			418.923i			0.480968i
$872$	−306.212	+	711.573i	−0.351161	+	0.816024i
$873$		0			0
$874$	−34.9969	+	256.775i	−0.0400422	+	0.293793i
$875$			339.186i			0.387641i
$876$		0			0
$877$	−940.915			−1.07288			−0.536439	−	0.843939i	$-0.680231\pi$
$877$	−940.915			−1.07288			−0.536439	+	0.843939i	$0.680231\pi$
$878$	−91.9195	−	12.5281i	−0.104692	−	0.0142689i
$879$		0			0
$880$	413.666	−	687.233i	0.470075	−	0.780946i
$881$	1065.75			1.20970			0.604851	−	0.796339i	$-0.293233\pi$
$881$	1065.75			1.20970			0.604851	+	0.796339i	$0.293233\pi$
$882$		0			0
$883$		−	1001.97i		−	1.13474i	−0.823464	−	0.567368i	$-0.807962\pi$
$883$		−	1001.97i		−	1.13474i	0.823464	−	0.567368i	$-0.192038\pi$
$884$	−994.193	−	276.134i	−1.12465	−	0.312369i
$885$		0			0
$886$	276.827	+	37.7298i	0.312445	+	0.0425844i
$887$			674.084i			0.759959i	0.924995	+	0.379980i	$0.124069\pi$
$887$			674.084i			0.759959i	−0.924995	+	0.379980i	$0.875931\pi$
$888$		0			0
$889$	−938.480			−1.05566
$890$	−35.7866	+	262.569i	−0.0402097	+	0.295022i
$891$		0			0
$892$	−340.328	+	1225.32i	−0.381534	+	1.37367i
$893$	270.291			0.302678
$894$		0			0
$895$		−	31.7561i		−	0.0354816i
$896$	−707.450	−	985.563i	−0.789565	−	1.09996i
$897$		0			0
$898$	72.1517	−	529.383i	0.0803471	−	0.589513i
$899$		−	507.310i		−	0.564305i
$900$		0			0
$901$	−1479.63			−1.64221
$902$	115.957	+	15.8042i	0.128555	+	0.0175213i
$903$		0			0
$904$	−122.918	+	285.636i	−0.135971	+	0.315969i
$905$	2145.56			2.37078
$906$		0			0
$907$			1181.45i			1.30259i	0.758826	+	0.651293i	$0.225773\pi$
$907$			1181.45i			1.30259i	−0.758826	+	0.651293i	$0.774227\pi$
$908$	266.938	−	961.083i	0.293985	−	1.05846i
$909$		0			0
$910$	2005.06	+	273.278i	2.20337	+	0.300305i
$911$		−	1394.43i		−	1.53066i	−0.643641	−	0.765328i	$-0.722577\pi$
$911$		−	1394.43i		−	1.53066i	0.643641	−	0.765328i	$-0.277423\pi$
$912$		0			0
$913$	91.6718			0.100407
$914$	−64.2356	+	471.302i	−0.0702797	+	0.515648i
$915$		0			0
$916$	−587.112	−	163.069i	−0.640952	−	0.178023i
$917$	513.346			0.559811
$918$		0			0
$919$		−	210.163i		−	0.228686i	−0.993441	−	0.114343i	$-0.963524\pi$
$919$		−	210.163i		−	0.228686i	0.993441	−	0.114343i	$-0.0364763\pi$
$920$	1356.92	+	583.926i	1.47492	+	0.634703i
$921$		0			0
$922$	−80.6625	+	591.828i	−0.0874865	+	0.641896i
$923$		−	1633.19i		−	1.76944i
$924$		0			0
$925$	191.420			0.206940
$926$	−970.101	−	132.219i	−1.04763	−	0.142785i
$927$		0			0
$928$	593.994	−	738.615i	0.640080	−	0.795921i
$929$	166.599			0.179332			0.0896659	−	0.995972i	$-0.471420\pi$
$929$	166.599			0.179332			0.0896659	+	0.995972i	$0.471420\pi$
$930$		0			0
$931$		−	212.174i		−	0.227899i
$932$	−1336.58	−	371.230i	−1.43409	−	0.398316i
$933$		0			0
$934$	900.237	+	122.697i	0.963851	+	0.131367i
$935$			897.044i			0.959405i
$936$		0			0
$937$	251.158			0.268045			0.134022	−	0.990978i	$-0.457211\pi$
$937$	251.158			0.268045			0.134022	+	0.990978i	$0.457211\pi$
$938$	74.3883	−	545.793i	0.0793052	−	0.581869i
$939$		0			0
$940$	412.328	−	1484.54i	0.438647	−	1.57930i
$941$	−814.564			−0.865637			−0.432818	−	0.901481i	$-0.642481\pi$
$941$	−814.564			−0.865637			−0.432818	+	0.901481i	$0.642481\pi$
$942$		0			0
$943$			215.525i			0.228552i
$944$	690.841	−	1147.71i	0.731823	−	1.21580i
$945$		0			0
$946$	91.6718	−	672.604i	0.0969047	−	0.710998i
$947$			592.384i			0.625537i	0.949829	+	0.312769i	$0.101256\pi$
$947$			592.384i			0.625537i	−0.949829	+	0.312769i	$0.898744\pi$
$948$		0			0
$949$	−31.2430			−0.0329220
$950$	−307.192	−	41.8684i	−0.323360	−	0.0440719i
$951$		0			0
$952$	1246.25	+	536.300i	1.30909	+	0.563341i
$953$	844.768			0.886430			0.443215	−	0.896415i	$-0.353838\pi$
$953$	844.768			0.886430			0.443215	+	0.896415i	$0.353838\pi$
$954$		0			0
$955$			685.983i			0.718307i
$956$	−111.366	+	400.962i	−0.116492	+	0.419416i
$957$		0			0
$958$	−7.16097	−	0.975997i	−0.00747492	−	0.00101879i
$959$		−	52.6925i		−	0.0549452i
$960$		0			0
$961$	667.650			0.694745
$962$	24.9838	−	183.308i	0.0259707	−	0.190549i
$963$		0			0
$964$	−1086.19	−	301.686i	−1.12675	−	0.312952i
$965$	1800.61			1.86592
$966$		0			0
$967$		−	180.173i		−	0.186322i	−0.995651	−	0.0931611i	$-0.970303\pi$
$967$		−	180.173i		−	0.186322i	0.995651	−	0.0931611i	$-0.0296971\pi$
$968$	237.690	−	552.341i	0.245547	−	0.570600i
$969$		0			0
$970$	−276.663	+	2029.90i	−0.285219	+	2.09268i
$971$			411.395i			0.423682i	0.977304	+	0.211841i	$0.0679458\pi$
$971$			411.395i			0.423682i	−0.977304	+	0.211841i	$0.932054\pi$
$972$		0			0
$973$	1445.56			1.48567
$974$	−1733.05	−	236.205i	−1.77932	−	0.242510i
$975$		0			0
$976$	−115.374	−	69.4469i	−0.118211	−	0.0711546i
$977$	−1756.25			−1.79759			−0.898797	−	0.438365i	$-0.855558\pi$
$977$	−1756.25			−1.79759			−0.898797	+	0.438365i	$0.855558\pi$
$978$		0			0
$979$		−	121.142i		−	0.123740i
$980$	−1165.34	−	323.670i	−1.18912	−	0.330276i
$981$		0			0
$982$	−1278.57	−	174.261i	−1.30201	−	0.177456i
$983$			803.055i			0.816943i	0.912771	+	0.408472i	$0.133938\pi$
$983$			803.055i			0.816943i	−0.912771	+	0.408472i	$0.866062\pi$
$984$		0			0
$985$	−1032.49			−1.04821
$986$	−143.146	+	1050.28i	−0.145179	+	1.06519i
$987$		0			0
$988$	−80.1885	+	288.710i	−0.0811624	+	0.292217i
$989$	1250.15			1.26405
$990$		0			0
$991$		−	338.466i		−	0.341540i	−0.985311	−	0.170770i	$-0.945375\pi$
$991$		−	338.466i		−	0.341540i	0.985311	−	0.170770i	$-0.0546254\pi$
$992$	−427.101	−	343.475i	−0.430546	−	0.346245i
$993$		0			0
$994$	−290.006	+	2127.80i	−0.291757	+	2.14064i
$995$			821.897i			0.826027i
$996$		0			0
$997$	591.811			0.593592			0.296796	−	0.954941i	$-0.404082\pi$
$997$	591.811			0.593592			0.296796	+	0.954941i	$0.404082\pi$
$998$	1119.33	+	152.558i	1.12158	+	0.152864i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.d.d.55.4	yes	8
3.2	odd	2	inner	108.3.d.d.55.5	yes	8
4.3	odd	2	inner	108.3.d.d.55.3	✓	8
8.3	odd	2		1728.3.g.l.703.8		8
8.5	even	2		1728.3.g.l.703.7		8
9.2	odd	6		324.3.f.o.271.1		8
9.4	even	3		324.3.f.p.55.1		8
9.5	odd	6		324.3.f.p.55.4		8
9.7	even	3		324.3.f.o.271.4		8
12.11	even	2	inner	108.3.d.d.55.6	yes	8
24.5	odd	2		1728.3.g.l.703.1		8
24.11	even	2		1728.3.g.l.703.2		8
36.7	odd	6		324.3.f.p.271.2		8
36.11	even	6		324.3.f.p.271.3		8
36.23	even	6		324.3.f.o.55.1		8
36.31	odd	6		324.3.f.o.55.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.d.d.55.3	✓	8	4.3	odd	2	inner
108.3.d.d.55.4	yes	8	1.1	even	1	trivial
108.3.d.d.55.5	yes	8	3.2	odd	2	inner
108.3.d.d.55.6	yes	8	12.11	even	2	inner
324.3.f.o.55.1		8	36.23	even	6
324.3.f.o.55.4		8	36.31	odd	6
324.3.f.o.271.1		8	9.2	odd	6
324.3.f.o.271.4		8	9.7	even	3
324.3.f.p.55.1		8	9.4	even	3
324.3.f.p.55.4		8	9.5	odd	6
324.3.f.p.271.2		8	36.7	odd	6
324.3.f.p.271.3		8	36.11	even	6
1728.3.g.l.703.1		8	24.5	odd	2
1728.3.g.l.703.2		8	24.11	even	2
1728.3.g.l.703.7		8	8.5	even	2
1728.3.g.l.703.8		8	8.3	odd	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.270091 + 1.98168i) q^{2} +(-3.85410 - 1.07047i) q^{4} -7.40492 q^{5} -9.47802i q^{7} +(3.16228 - 7.34847i) q^{8} +O(q^{10})\)	\(q+(-0.270091 + 1.98168i) q^{2} +(-3.85410 - 1.07047i) q^{4} -7.40492 q^{5} -9.47802i q^{7} +(3.16228 - 7.34847i) q^{8} +(2.00000 - 14.6742i) q^{10} +6.77022i q^{11} -14.4164 q^{13} +(18.7824 + 2.55992i) q^{14} +(13.7082 + 8.25137i) q^{16} -17.8933 q^{17} +5.19615i q^{19} +(28.5393 + 7.92672i) q^{20} +(-13.4164 - 1.82857i) q^{22} -24.9366i q^{23} +29.8328 q^{25} +(3.89374 - 28.5687i) q^{26} +(-10.1459 + 36.5292i) q^{28} -29.6197 q^{29} +17.1275i q^{31} +(-20.0540 + 24.9366i) q^{32} +(4.83282 - 35.4588i) q^{34} +70.1839i q^{35} +6.41641 q^{37} +(-10.2971 - 1.40343i) q^{38} +(-23.4164 + 54.4148i) q^{40} -8.64290 q^{41} +50.1329i q^{43} +(7.24730 - 26.0931i) q^{44} +(49.4164 + 6.73516i) q^{46} -52.0175i q^{47} -40.8328 q^{49} +(-8.05757 + 59.1191i) q^{50} +(55.5623 + 15.4323i) q^{52} +82.6921 q^{53} -50.1329i q^{55} +(-69.6489 - 29.9721i) q^{56} +(8.00000 - 58.6967i) q^{58} -83.7244i q^{59} -8.41641 q^{61} +(-33.9411 - 4.62597i) q^{62} +(-44.0000 - 46.4758i) q^{64} +106.752 q^{65} -29.0588i q^{67} +(68.9626 + 19.1542i) q^{68} +(-139.082 - 18.9560i) q^{70} +113.287i q^{71} +2.16718 q^{73} +(-1.73301 + 12.7153i) q^{74} +(5.56231 - 20.0265i) q^{76} +64.1683 q^{77} -149.485i q^{79} +(-101.508 - 61.1007i) q^{80} +(2.33437 - 17.1275i) q^{82} -13.5404i q^{83} +132.498 q^{85} +(-99.3474 - 13.5404i) q^{86} +(49.7508 + 21.4093i) q^{88} -17.8933 q^{89} +136.639i q^{91} +(-26.6938 + 96.1083i) q^{92} +(103.082 + 14.0495i) q^{94} -38.4771i q^{95} -138.331 q^{97} +(11.0286 - 80.9175i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4}+O(q^{10}) \) 8 * q - 4 * q^4	\( 8 q - 4 q^{4} + 16 q^{10} - 8 q^{13} + 56 q^{16} + 24 q^{25} - 108 q^{28} - 176 q^{34} - 56 q^{37} - 80 q^{40} + 288 q^{46} - 112 q^{49} + 364 q^{52} + 64 q^{58} + 40 q^{61} - 352 q^{64} - 576 q^{70} + 232 q^{73} - 36 q^{76} + 448 q^{82} + 416 q^{85} + 720 q^{88} + 288 q^{94} - 248 q^{97}+O(q^{100}) \) 8 * q - 4 * q^4 + 16 * q^10 - 8 * q^13 + 56 * q^16 + 24 * q^25 - 108 * q^28 - 176 * q^34 - 56 * q^37 - 80 * q^40 + 288 * q^46 - 112 * q^49 + 364 * q^52 + 64 * q^58 + 40 * q^61 - 352 * q^64 - 576 * q^70 + 232 * q^73 - 36 * q^76 + 448 * q^82 + 416 * q^85 + 720 * q^88 + 288 * q^94 - 248 * q^97

Introduction

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