LMFDB - Embedded newform 108.3.d.d.55.5

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			55.5
Root			$1.14412 - 1.98168i$ of defining polynomial
Character	$\chi$	$=$	108.55
Dual form			108.3.d.d.55.6

$q$-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	$-0.234593\pi$
$5$	7.40492			1.48098			0.740492	+	0.672065i	$0.234593\pi$
$6$		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	$-0.900428\pi$
$11$		−	6.77022i		−	0.615475i	0.951471	−	0.307737i	$-0.0995718\pi$
$12$		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	$-0.323589\pi$
$17$	17.8933			1.05255			0.526274	+	0.850315i	$0.323589\pi$
$18$		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	$0.182371\pi$
$23$			24.9366i			1.08420i	−0.840313	+	0.542101i	$0.817629\pi$
$24$		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	$-0.329392\pi$
$29$	29.6197			1.02137			0.510684	+	0.859768i	$0.329392\pi$
$30$		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	$-0.466387\pi$
$41$	8.64290			0.210803			0.105401	+	0.994430i	$0.466387\pi$
$42$		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	$0.186661\pi$
$47$			52.0175i			1.10676i	−0.832930	+	0.553378i	$0.813339\pi$
$48$		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	$-0.784839\pi$
$53$	−82.6921			−1.56023			−0.780114	+	0.625637i	$0.784839\pi$
$54$		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	$0.251092\pi$
$59$			83.7244i			1.41906i	−0.704676	+	0.709529i	$0.748908\pi$
$60$		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	$-0.705999\pi$
$71$		−	113.287i		−	1.59559i	0.602928	−	0.797796i	$-0.294001\pi$
$72$		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	$0.0259931\pi$
$83$			13.5404i			0.163138i	−0.996668	+	0.0815690i	$0.974007\pi$
$84$		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	$-0.467948\pi$
$89$	17.8933			0.201048			0.100524	+	0.994935i	$0.467948\pi$
$90$		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	$-0.339662\pi$
$101$	97.5019			0.965366			0.482683	+	0.875795i	$0.339662\pi$
$102$		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	$0.150185\pi$
$107$			97.2648i			0.909017i	−0.890742	+	0.454509i	$0.849815\pi$
$108$		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	$-0.444980\pi$
$113$	38.8701			0.343983			0.171991	+	0.985098i	$0.444980\pi$
$114$		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	$-0.933720\pi$
$131$		−	54.1618i		−	0.413449i	0.978399	−	0.206724i	$-0.0662803\pi$
$132$		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	$-0.506459\pi$
$137$	−5.55944			−0.0405798			−0.0202899	+	0.999794i	$0.506459\pi$
$138$		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	$-0.347970\pi$
$149$	136.979			0.919325			0.459663	+	0.888094i	$0.347970\pi$
$150$		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	$-0.793691\pi$
$167$		−	201.637i		−	1.20741i	0.797208	−	0.603705i	$-0.206309\pi$
$168$		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	$-0.413807\pi$
$173$	92.5500			0.534971			0.267485	+	0.963562i	$0.413807\pi$
$174$		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	$-0.996187\pi$
$179$		−	4.28851i		−	0.0239581i	0.999928	−	0.0119791i	$-0.00381315\pi$
$180$		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	$0.0779708\pi$
$191$			92.6389i			0.485020i	−0.970149	+	0.242510i	$0.922029\pi$
$192$		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	$-0.615141\pi$
$197$	−139.432			−0.707779			−0.353890	+	0.935287i	$0.615141\pi$
$198$		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	$-0.814908\pi$
$227$		−	249.366i		−	1.09853i	0.835648	−	0.549265i	$-0.185092\pi$
$228$		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	$-0.767165\pi$
$233$	−346.793			−1.48838			−0.744191	+	0.667966i	$0.767165\pi$
$234$		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	$0.0698380\pi$
$239$			104.035i			0.435293i	−0.976028	+	0.217647i	$0.930162\pi$
$240$		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	$0.181880\pi$
$251$			271.484i			1.08161i	−0.841148	+	0.540804i	$0.818120\pi$
$252$		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	$-0.851545\pi$
$257$	−459.105			−1.78640			−0.893200	+	0.449659i	$0.851545\pi$
$258$		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	$0.126633\pi$
$263$			203.782i			0.774835i	−0.921904	+	0.387418i	$0.873367\pi$
$264$		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	$-0.294750\pi$
$269$	323.363			1.20209			0.601047	+	0.799213i	$0.294750\pi$
$270$		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	$-0.483216\pi$
$281$	29.6197			0.105408			0.0527040	+	0.998610i	$0.483216\pi$
$282$		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	$-0.340556\pi$
$293$	281.410			0.960443			0.480222	+	0.877147i	$0.340556\pi$
$294$		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	$-0.991972\pi$
$311$		−	15.6847i		−	0.0504331i	0.999682	−	0.0252166i	$-0.00802753\pi$
$312$		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	$-0.786057\pi$
$317$	−496.107			−1.56500			−0.782502	+	0.622648i	$0.786057\pi$
$318$		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	$0.424870\pi$
$347$			674.759i			1.94455i	−0.233842	+	0.972275i	$0.575130\pi$
$348$		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	$-0.155683\pi$
$353$	623.228			1.76552			0.882759	+	0.469825i	$0.155683\pi$
$354$		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	$-0.928312\pi$
$359$		−	160.341i		−	0.446633i	0.974746	−	0.223316i	$-0.0716883\pi$
$360$		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	$-0.780073\pi$
$383$		−	488.131i		−	1.27449i	0.770660	−	0.637247i	$-0.219927\pi$
$384$		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	$-0.320487\pi$
$389$	415.867			1.06907			0.534534	+	0.845147i	$0.320487\pi$
$390$		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	$-0.545697\pi$
$401$	−114.742			−0.286139			−0.143070	+	0.989713i	$0.545697\pi$
$402$		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	$0.221339\pi$
$419$			536.872i			1.28132i	−0.767825	+	0.640659i	$0.778661\pi$
$420$		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	$-0.674733\pi$
$431$		−	735.353i		−	1.70616i	0.521784	−	0.853078i	$-0.325267\pi$
$432$		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	$0.0503973\pi$
$443$			139.693i			0.315334i	−0.987492	+	0.157667i	$0.949603\pi$
$444$		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	$-0.403853\pi$
$449$	267.139			0.594963			0.297482	+	0.954728i	$0.403853\pi$
$450$		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	$-0.604999\pi$
$461$	−298.650			−0.647830			−0.323915	+	0.946086i	$0.604999\pi$
$462$		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	$0.161683\pi$
$467$			454.280i			0.972762i	−0.873747	+	0.486381i	$0.838317\pi$
$468$		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	$-0.998799\pi$
$479$		−	3.61359i		−	0.00754403i	0.999993	−	0.00377201i	$-0.00120067\pi$
$480$		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	$-0.771816\pi$
$491$		−	645.196i		−	1.31404i	0.753871	−	0.657022i	$-0.228184\pi$
$492$		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	$-0.840576\pi$
$503$		−	483.048i		−	0.960334i	0.877177	−	0.480167i	$-0.159424\pi$
$504$		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	$-0.431942\pi$
$509$	216.004			0.424369			0.212184	+	0.977230i	$0.431942\pi$
$510$		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	$-0.643773\pi$
$521$	−454.806			−0.872949			−0.436475	+	0.899717i	$0.643773\pi$
$522$		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	$-0.621029\pi$
$557$	−413.437			−0.742258			−0.371129	+	0.928581i	$0.621029\pi$
$558$		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	$0.151706\pi$
$563$			516.562i			0.917516i	−0.888561	+	0.458758i	$0.848294\pi$
$564$		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	$-0.635016\pi$
$569$	−468.355			−0.823120			−0.411560	+	0.911383i	$0.635016\pi$
$570$		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	$-0.939864\pi$
$587$		−	220.479i		−	0.375603i	0.982207	−	0.187801i	$-0.0601361\pi$
$588$		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	$-0.183896\pi$
$593$	993.520			1.67541			0.837707	+	0.546121i	$0.183896\pi$
$594$		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	$-0.924708\pi$
$599$		−	280.736i		−	0.468674i	0.972155	−	0.234337i	$-0.0752919\pi$
$600$		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	$-0.646985\pi$
$617$	−549.786			−0.891064			−0.445532	+	0.895266i	$0.646985\pi$
$618$		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	$-0.387336\pi$
$641$	444.341			0.693200			0.346600	+	0.938013i	$0.387336\pi$
$642$		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	$0.231857\pi$
$647$			861.386i			1.33135i	−0.746240	+	0.665677i	$0.768143\pi$
$648$		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	$-0.734127\pi$
$653$	−876.302			−1.34196			−0.670982	+	0.741474i	$0.734127\pi$
$654$		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	$-0.858776\pi$
$659$		−	565.760i		−	0.858513i	0.903183	−	0.429257i	$-0.141224\pi$
$660$		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	$-0.384952\pi$
$677$	478.798			0.707234			0.353617	+	0.935390i	$0.384952\pi$
$678$		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	$0.0748879\pi$
$683$			318.418i			0.466206i	−0.972452	+	0.233103i	$0.925112\pi$
$684$		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	$-0.595283\pi$
$701$	−413.437			−0.589782			−0.294891	+	0.955531i	$0.595283\pi$
$702$		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	$0.0638173\pi$
$719$			286.374i			0.398295i	−0.979970	+	0.199148i	$0.936183\pi$
$720$		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	$-0.735560\pi$
$743$		−	1097.33i		−	1.47689i	0.674312	−	0.738447i	$-0.264440\pi$
$744$		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	$-0.205326\pi$
$761$	1216.18			1.59814			0.799069	+	0.601239i	$0.205326\pi$
$762$		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	$-0.420403\pi$
$773$	382.580			0.494929			0.247464	+	0.968897i	$0.420403\pi$
$774$		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	$-0.604638\pi$
$797$	−514.607			−0.645680			−0.322840	+	0.946453i	$0.604638\pi$
$798$		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	$-0.140123\pi$
$809$	1463.74			1.80932			0.904662	+	0.426129i	$0.140123\pi$
$810$		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	$-0.423158\pi$
$821$	392.553			0.478140			0.239070	+	0.971002i	$0.423158\pi$
$822$		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	$0.310398\pi$
$827$			1369.15i			1.65557i	−0.561049	+	0.827783i	$0.689602\pi$
$828$		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	$-0.746209\pi$
$839$		−	1200.57i		−	1.43096i	0.698635	−	0.715478i	$-0.253791\pi$
$840$		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	$-0.596357\pi$
$857$	−510.962			−0.596222			−0.298111	+	0.954531i	$0.596357\pi$
$858$		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	$0.203149\pi$
$863$			1028.28i			1.19152i	−0.803163	+	0.595759i	$0.796851\pi$
$864$		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	$-0.706767\pi$
$881$	−1065.75			−1.20970			−0.604851	+	0.796339i	$0.706767\pi$
$882$		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	$-0.875931\pi$
$887$		−	674.084i		−	0.759959i	0.924995	−	0.379980i	$-0.124069\pi$
$888$		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	$0.277423\pi$
$911$			1394.43i			1.53066i	−0.643641	+	0.765328i	$0.722577\pi$
$912$		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	$-0.528580\pi$
$929$	−166.599			−0.179332			−0.0896659	+	0.995972i	$0.528580\pi$
$930$		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	$-0.357519\pi$
$941$	814.564			0.865637			0.432818	+	0.901481i	$0.357519\pi$
$942$		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	$-0.898744\pi$
$947$		−	592.384i		−	0.625537i	0.949829	−	0.312769i	$-0.101256\pi$
$948$		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	$-0.646162\pi$
$953$	−844.768			−0.886430			−0.443215	+	0.896415i	$0.646162\pi$
$954$		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	$-0.932054\pi$
$971$		−	411.395i		−	0.423682i	0.977304	−	0.211841i	$-0.0679458\pi$
$972$		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	$-0.144442\pi$
$977$	1756.25			1.79759			0.898797	+	0.438365i	$0.144442\pi$
$978$		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	$-0.866062\pi$
$983$		−	803.055i		−	0.816943i	0.912771	−	0.408472i	$-0.133938\pi$
$984$		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.55.5	yes	8
3.2	odd	2	inner	108.3.d.d.55.4	yes	8
4.3	odd	2	inner	108.3.d.d.55.6	yes	8
8.3	odd	2		1728.3.g.l.703.2		8
8.5	even	2		1728.3.g.l.703.1		8
9.2	odd	6		324.3.f.o.271.4		8
9.4	even	3		324.3.f.p.55.4		8
9.5	odd	6		324.3.f.p.55.1		8
9.7	even	3		324.3.f.o.271.1		8
12.11	even	2	inner	108.3.d.d.55.3	✓	8
24.5	odd	2		1728.3.g.l.703.7		8
24.11	even	2		1728.3.g.l.703.8		8
36.7	odd	6		324.3.f.p.271.3		8
36.11	even	6		324.3.f.p.271.2		8
36.23	even	6		324.3.f.o.55.4		8
36.31	odd	6		324.3.f.o.55.1		8

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