LMFDB - Embedded newform 384.4.k.b.95.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,4,Mod(95,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("384.95");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	384.k (of order $4$, degree $2$, not 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:	$22.6567334422$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			95.1
Character	$\chi$	$=$	384.95
Dual form			384.4.k.b.287.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.19396 - 0.151014i) q^{3} +(-4.66675 - 4.66675i) q^{5} +0.405799 q^{7} +(26.9544 + 1.56872i) q^{9} +O(q^{10})$	\(q+(-5.19396 - 0.151014i) q^{3} +(-4.66675 - 4.66675i) q^{5} +0.405799 q^{7} +(26.9544 + 1.56872i) q^{9} +(5.82048 - 5.82048i) q^{11} +(35.2429 + 35.2429i) q^{13} +(23.5341 + 24.9436i) q^{15} +49.3434i q^{17} +(-108.402 + 108.402i) q^{19} +(-2.10770 - 0.0612813i) q^{21} -130.212i q^{23} -81.4430i q^{25} +(-139.763 - 12.2184i) q^{27} +(172.328 - 172.328i) q^{29} +36.1724i q^{31} +(-31.1103 + 29.3524i) q^{33} +(-1.89376 - 1.89376i) q^{35} +(257.830 - 257.830i) q^{37} +(-177.728 - 188.372i) q^{39} -5.87635 q^{41} +(-170.580 - 170.580i) q^{43} +(-118.468 - 133.110i) q^{45} -181.338 q^{47} -342.835 q^{49} +(7.45153 - 256.287i) q^{51} +(148.916 + 148.916i) q^{53} -54.3254 q^{55} +(579.404 - 546.664i) q^{57} +(567.816 - 567.816i) q^{59} +(-481.074 - 481.074i) q^{61} +(10.9381 + 0.636585i) q^{63} -328.939i q^{65} +(-296.210 + 296.210i) q^{67} +(-19.6638 + 676.314i) q^{69} -533.975i q^{71} -178.769i q^{73} +(-12.2990 + 423.011i) q^{75} +(2.36194 - 2.36194i) q^{77} -528.133i q^{79} +(724.078 + 84.5678i) q^{81} +(-713.160 - 713.160i) q^{83} +(230.273 - 230.273i) q^{85} +(-921.090 + 869.042i) q^{87} +204.984 q^{89} +(14.3015 + 14.3015i) q^{91} +(5.46254 - 187.878i) q^{93} +1011.77 q^{95} +275.409 q^{97} +(166.018 - 147.757i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{3} - 8 q^{7}+O(q^{10}) $ 44 * q + 2 * q^3 - 8 * q^7	$ 44 q + 2 q^{3} - 8 q^{7} + 4 q^{13} - 20 q^{19} + 56 q^{21} + 134 q^{27} - 4 q^{33} + 4 q^{37} + 596 q^{39} + 436 q^{43} + 252 q^{45} + 972 q^{49} + 648 q^{51} + 280 q^{55} + 916 q^{61} + 1636 q^{67} - 52 q^{69} - 1454 q^{75} - 4 q^{81} - 736 q^{85} + 1284 q^{87} - 424 q^{91} + 2084 q^{93} - 8 q^{97} - 1196 q^{99}+O(q^{100}) $ 44 * q + 2 * q^3 - 8 * q^7 + 4 * q^13 - 20 * q^19 + 56 * q^21 + 134 * q^27 - 4 * q^33 + 4 * q^37 + 596 * q^39 + 436 * q^43 + 252 * q^45 + 972 * q^49 + 648 * q^51 + 280 * q^55 + 916 * q^61 + 1636 * q^67 - 52 * q^69 - 1454 * q^75 - 4 * q^81 - 736 * q^85 + 1284 * q^87 - 424 * q^91 + 2084 * q^93 - 8 * q^97 - 1196 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−5.19396	−	0.151014i	−0.999578	−	0.0290626i
$3$	−5.19396	−	0.151014i	−0.999578	−	0.0290626i
$4$		0			0
$5$	−4.66675	−	4.66675i	−0.417407	−	0.417407i	0.466902	−	0.884309i	$-0.345370\pi$
$5$	−4.66675	−	4.66675i	−0.417407	−	0.417407i	−0.884309	+	0.466902i	$0.845370\pi$
$6$		0			0
$7$	0.405799			0.0219111			0.0109555	−	0.999940i	$-0.496513\pi$
$7$	0.405799			0.0219111			0.0109555	+	0.999940i	$0.496513\pi$
$8$		0			0
$9$	26.9544	+	1.56872i	0.998311	+	0.0581007i
$10$		0			0
$11$	5.82048	−	5.82048i	0.159540	−	0.159540i	−0.622823	−	0.782363i	$-0.714014\pi$
$11$	5.82048	−	5.82048i	0.159540	−	0.159540i	0.782363	+	0.622823i	$0.214014\pi$
$12$		0			0
$13$	35.2429	+	35.2429i	0.751893	+	0.751893i	0.974832	−	0.222939i	$-0.0715652\pi$
$13$	35.2429	+	35.2429i	0.751893	+	0.751893i	−0.222939	+	0.974832i	$0.571565\pi$
$14$		0			0
$15$	23.5341	+	24.9436i	0.405099	+	0.429361i
$16$		0			0
$17$			49.3434i			0.703972i	0.936005	+	0.351986i	$0.114494\pi$
$17$			49.3434i			0.703972i	−0.936005	+	0.351986i	$0.885506\pi$
$18$		0			0
$19$	−108.402	+	108.402i	−1.30890	+	1.30890i	−0.386687	+	0.922211i	$0.626381\pi$
$19$	−108.402	+	108.402i	−1.30890	+	1.30890i	−0.922211	+	0.386687i	$0.873619\pi$
$20$		0			0
$21$	−2.10770	−	0.0612813i	−0.0219018	−	0.000636794i
$22$		0			0
$23$		−	130.212i		−	1.18048i	−0.807228	−	0.590240i	$-0.799033\pi$
$23$		−	130.212i		−	1.18048i	0.807228	−	0.590240i	$-0.200967\pi$
$24$		0			0
$25$		−	81.4430i		−	0.651544i
$26$		0			0
$27$	−139.763	−	12.2184i	−0.996200	−	0.0870897i
$28$		0			0
$29$	172.328	−	172.328i	1.10347	−	1.10347i	0.109478	−	0.993989i	$-0.465082\pi$
$29$	172.328	−	172.328i	1.10347	−	1.10347i	0.993989	−	0.109478i	$-0.0349180\pi$
$30$		0			0
$31$			36.1724i			0.209573i	0.994495	+	0.104786i	$0.0334159\pi$
$31$			36.1724i			0.209573i	−0.994495	+	0.104786i	$0.966584\pi$
$32$		0			0
$33$	−31.1103	+	29.3524i	−0.164109	+	0.154836i
$34$		0			0
$35$	−1.89376	−	1.89376i	−0.00914583	−	0.00914583i
$36$		0			0
$37$	257.830	−	257.830i	1.14560	−	1.14560i	0.158186	−	0.987409i	$-0.449435\pi$
$37$	257.830	−	257.830i	1.14560	−	1.14560i	0.987409	−	0.158186i	$-0.0505647\pi$
$38$		0			0
$39$	−177.728	−	188.372i	−0.729723	−	0.773427i
$40$		0			0
$41$	−5.87635			−0.0223837			−0.0111919	−	0.999937i	$-0.503563\pi$
$41$	−5.87635			−0.0223837			−0.0111919	+	0.999937i	$0.503563\pi$
$42$		0			0
$43$	−170.580	−	170.580i	−0.604959	−	0.604959i	0.336665	−	0.941624i	$-0.390701\pi$
$43$	−170.580	−	170.580i	−0.604959	−	0.604959i	−0.941624	+	0.336665i	$0.890701\pi$
$44$		0			0
$45$	−118.468	−	133.110i	−0.392450	−	0.440953i
$46$		0			0
$47$	−181.338			−0.562784			−0.281392	−	0.959593i	$-0.590796\pi$
$47$	−181.338			−0.562784			−0.281392	+	0.959593i	$0.590796\pi$
$48$		0			0
$49$	−342.835			−0.999520
$50$		0			0
$51$	7.45153	−	256.287i	0.0204593	−	0.703675i
$52$		0			0
$53$	148.916	+	148.916i	0.385947	+	0.385947i	0.873239	−	0.487292i	$-0.162015\pi$
$53$	148.916	+	148.916i	0.385947	+	0.385947i	−0.487292	+	0.873239i	$0.662015\pi$
$54$		0			0
$55$	−54.3254			−0.133186
$56$		0			0
$57$	579.404	−	546.664i	1.34639	−	1.27031i
$58$		0			0
$59$	567.816	−	567.816i	1.25294	−	1.25294i	0.298542	−	0.954396i	$-0.403500\pi$
$59$	567.816	−	567.816i	1.25294	−	1.25294i	0.954396	−	0.298542i	$-0.0965003\pi$
$60$		0			0
$61$	−481.074	−	481.074i	−1.00976	−	1.00976i	−0.999952	−	0.00980553i	$-0.996879\pi$
$61$	−481.074	−	481.074i	−1.00976	−	1.00976i	−0.00980553	−	0.999952i	$-0.503121\pi$
$62$		0			0
$63$	10.9381	+	0.636585i	0.0218741	+	0.00127305i
$64$		0			0
$65$		−	328.939i		−	0.627690i
$66$		0			0
$67$	−296.210	+	296.210i	−0.540117	+	0.540117i	−0.923563	−	0.383446i	$-0.874737\pi$
$67$	−296.210	+	296.210i	−0.540117	+	0.540117i	0.383446	+	0.923563i	$0.374737\pi$
$68$		0			0
$69$	−19.6638	+	676.314i	−0.0343079	+	1.17998i
$70$		0			0
$71$		−	533.975i		−	0.892552i	−0.894895	−	0.446276i	$-0.852750\pi$
$71$		−	533.975i		−	0.892552i	0.894895	−	0.446276i	$-0.147250\pi$
$72$		0			0
$73$		−	178.769i		−	0.286621i	−0.989678	−	0.143311i	$-0.954225\pi$
$73$		−	178.769i		−	0.286621i	0.989678	−	0.143311i	$-0.0457748\pi$
$74$		0			0
$75$	−12.2990	+	423.011i	−0.0189356	+	0.651268i
$76$		0			0
$77$	2.36194	−	2.36194i	0.00349570	−	0.00349570i
$78$		0			0
$79$		−	528.133i		−	0.752146i	−0.926590	−	0.376073i	$-0.877274\pi$
$79$		−	528.133i		−	0.752146i	0.926590	−	0.376073i	$-0.122726\pi$
$80$		0			0
$81$	724.078	+	84.5678i	0.993249	+	0.116005i
$82$		0			0
$83$	−713.160	−	713.160i	−0.943126	−	0.943126i	0.0553412	−	0.998468i	$-0.482375\pi$
$83$	−713.160	−	713.160i	−0.943126	−	0.943126i	−0.998468	+	0.0553412i	$0.982375\pi$
$84$		0			0
$85$	230.273	−	230.273i	0.293842	−	0.293842i
$86$		0			0
$87$	−921.090	+	869.042i	−1.13507	+	1.07093i
$88$		0			0
$89$	204.984			0.244138			0.122069	−	0.992522i	$-0.461047\pi$
$89$	204.984			0.244138			0.122069	+	0.992522i	$0.461047\pi$
$90$		0			0
$91$	14.3015	+	14.3015i	0.0164748	+	0.0164748i
$92$		0			0
$93$	5.46254	−	187.878i	0.00609074	−	0.209484i
$94$		0			0
$95$	1011.77			1.09269
$96$		0			0
$97$	275.409			0.288284			0.144142	−	0.989557i	$-0.453958\pi$
$97$	275.409			0.288284			0.144142	+	0.989557i	$0.453958\pi$
$98$		0			0
$99$	166.018	−	147.757i	0.168540	−	0.150001i
$100$		0			0
$101$	−759.307	−	759.307i	−0.748058	−	0.748058i	0.226056	−	0.974114i	$-0.427417\pi$
$101$	−759.307	−	759.307i	−0.748058	−	0.748058i	−0.974114	+	0.226056i	$0.927417\pi$
$102$		0			0
$103$	−367.357			−0.351425			−0.175712	−	0.984442i	$-0.556223\pi$
$103$	−367.357			−0.351425			−0.175712	+	0.984442i	$0.556223\pi$
$104$		0			0
$105$	9.55013	+	10.1221i	0.00887616	+	0.00940777i
$106$		0			0
$107$	80.5577	−	80.5577i	0.0727833	−	0.0727833i	−0.669778	−	0.742561i	$-0.733611\pi$
$107$	80.5577	−	80.5577i	0.0727833	−	0.0727833i	0.742561	+	0.669778i	$0.233611\pi$
$108$		0			0
$109$	569.823	+	569.823i	0.500726	+	0.500726i	0.911663	−	0.410938i	$-0.134799\pi$
$109$	569.823	+	569.823i	0.500726	+	0.500726i	−0.410938	+	0.911663i	$0.634799\pi$
$110$		0			0
$111$	−1378.10	+	1300.22i	−1.17841	+	1.11182i
$112$		0			0
$113$		−	999.419i		−	0.832013i	−0.909362	−	0.416006i	$-0.863429\pi$
$113$		−	999.419i		−	0.832013i	0.909362	−	0.416006i	$-0.136571\pi$
$114$		0			0
$115$	−607.665	+	607.665i	−0.492740	+	0.492740i
$116$		0			0
$117$	894.664	+	1005.24i	0.706937	+	0.794308i
$118$		0			0
$119$			20.0235i			0.0154248i
$120$		0			0
$121$			1263.24i			0.949094i
$122$		0			0
$123$	30.5215	+	0.887411i	0.0223743	+	0.000650530i
$124$		0			0
$125$	−963.417	+	963.417i	−0.689365	+	0.689365i
$126$		0			0
$127$		−	84.8717i		−	0.0593004i	−0.999560	−	0.0296502i	$-0.990561\pi$
$127$		−	84.8717i		−	0.0593004i	0.999560	−	0.0296502i	$-0.00943933\pi$
$128$		0			0
$129$	860.227	+	911.747i	0.587122	+	0.622285i
$130$		0			0
$131$	1300.38	+	1300.38i	0.867288	+	0.867288i	0.992171	−	0.124883i	$-0.0398556\pi$
$131$	1300.38	+	1300.38i	0.867288	+	0.867288i	−0.124883	+	0.992171i	$0.539856\pi$
$132$		0			0
$133$	−43.9893	+	43.9893i	−0.0286794	+	0.0286794i
$134$		0			0
$135$	595.219	+	709.259i	0.379469	+	0.452172i
$136$		0			0
$137$	−1889.62			−1.17840			−0.589201	−	0.807986i	$-0.700558\pi$
$137$	−1889.62			−1.17840			−0.589201	+	0.807986i	$0.700558\pi$
$138$		0			0
$139$	241.475	+	241.475i	0.147350	+	0.147350i	0.776933	−	0.629583i	$-0.216774\pi$
$139$	241.475	+	241.475i	0.147350	+	0.147350i	−0.629583	+	0.776933i	$0.716774\pi$
$140$		0			0
$141$	941.862	+	27.3846i	0.562547	+	0.0163560i
$142$		0			0
$143$	410.261			0.239914
$144$		0			0
$145$	−1608.42			−0.921189
$146$		0			0
$147$	1780.67	+	51.7729i	0.999098	+	0.0290487i
$148$		0			0
$149$	−1223.18	−	1223.18i	−0.672527	−	0.672527i	0.285771	−	0.958298i	$-0.407750\pi$
$149$	−1223.18	−	1223.18i	−0.672527	−	0.672527i	−0.958298	+	0.285771i	$0.907750\pi$
$150$		0			0
$151$	2720.26			1.46604			0.733018	−	0.680209i	$-0.238111\pi$
$151$	2720.26			1.46604			0.733018	+	0.680209i	$0.238111\pi$
$152$		0			0
$153$	−77.4059	+	1330.02i	−0.0409013	+	0.702783i
$154$		0			0
$155$	168.807	−	168.807i	0.0874770	−	0.0874770i
$156$		0			0
$157$	914.088	+	914.088i	0.464663	+	0.464663i	0.900180	−	0.435517i	$-0.143434\pi$
$157$	914.088	+	914.088i	0.464663	+	0.464663i	−0.435517	+	0.900180i	$0.643434\pi$
$158$		0			0
$159$	−750.974	−	795.951i	−0.374567	−	0.397000i
$160$		0			0
$161$		−	52.8398i		−	0.0258656i
$162$		0			0
$163$	1570.14	−	1570.14i	0.754497	−	0.754497i	−0.220818	−	0.975315i	$-0.570873\pi$
$163$	1570.14	−	1570.14i	0.754497	−	0.754497i	0.975315	+	0.220818i	$0.0708726\pi$
$164$		0			0
$165$	282.164	+	8.20389i	0.133130	+	0.00387074i
$166$		0			0
$167$		−	2185.45i		−	1.01267i	−0.862338	−	0.506333i	$-0.831001\pi$
$167$		−	2185.45i		−	1.01267i	0.862338	−	0.506333i	$-0.168999\pi$
$168$		0			0
$169$			287.118i			0.130686i
$170$		0			0
$171$	−3091.95	+	2751.85i	−1.38274	+	1.23064i
$172$		0			0
$173$	217.067	−	217.067i	0.0953948	−	0.0953948i	−0.657799	−	0.753194i	$-0.728512\pi$
$173$	217.067	−	217.067i	0.0953948	−	0.0953948i	0.753194	+	0.657799i	$0.228512\pi$
$174$		0			0
$175$		−	33.0495i		−	0.0142760i
$176$		0			0
$177$	−3034.96	+	2863.47i	−1.28882	+	1.21600i
$178$		0			0
$179$	−651.988	−	651.988i	−0.272245	−	0.272245i	0.557758	−	0.830003i	$-0.311662\pi$
$179$	−651.988	−	651.988i	−0.272245	−	0.272245i	−0.830003	+	0.557758i	$0.811662\pi$
$180$		0			0
$181$	−898.471	+	898.471i	−0.368966	+	0.368966i	−0.867100	−	0.498134i	$-0.834019\pi$
$181$	−898.471	+	898.471i	−0.368966	+	0.368966i	0.498134	+	0.867100i	$0.334019\pi$
$182$		0			0
$183$	2426.03	+	2571.33i	0.979985	+	1.03868i
$184$		0			0
$185$	−2406.46			−0.956358
$186$		0			0
$187$	287.202	+	287.202i	0.112312	+	0.112312i
$188$		0			0
$189$	−56.7157	−	4.95819i	−0.0218278	−	0.00190823i
$190$		0			0
$191$	3594.58			1.36175			0.680877	−	0.732398i	$-0.261599\pi$
$191$	3594.58			1.36175			0.680877	+	0.732398i	$0.261599\pi$
$192$		0			0
$193$	1074.49			0.400744			0.200372	−	0.979720i	$-0.435785\pi$
$193$	1074.49			0.400744			0.200372	+	0.979720i	$0.435785\pi$
$194$		0			0
$195$	−49.6744	+	1708.50i	−0.0182423	+	0.627425i
$196$		0			0
$197$	−3405.92	−	3405.92i	−1.23179	−	1.23179i	−0.963277	−	0.268510i	$-0.913469\pi$
$197$	−3405.92	−	3405.92i	−1.23179	−	1.23179i	−0.268510	−	0.963277i	$-0.586531\pi$
$198$		0			0
$199$	2379.94			0.847786			0.423893	−	0.905712i	$-0.360663\pi$
$199$	2379.94			0.847786			0.423893	+	0.905712i	$0.360663\pi$
$200$		0			0
$201$	1583.23	−	1493.77i	0.555586	−	0.524191i
$202$		0			0
$203$	69.9306	−	69.9306i	0.0241782	−	0.0241782i
$204$		0			0
$205$	27.4234	+	27.4234i	0.00934311	+	0.00934311i
$206$		0			0
$207$	204.266	−	3509.78i	0.0685867	−	1.17849i
$208$		0			0
$209$			1261.90i			0.417643i
$210$		0			0
$211$	1309.41	−	1309.41i	0.427220	−	0.427220i	−0.460460	−	0.887680i	$-0.652316\pi$
$211$	1309.41	−	1309.41i	0.427220	−	0.427220i	0.887680	+	0.460460i	$0.152316\pi$
$212$		0			0
$213$	−80.6377	+	2773.44i	−0.0259399	+	0.892175i
$214$		0			0
$215$			1592.11i			0.505028i
$216$		0			0
$217$			14.6787i			0.00459197i
$218$		0			0
$219$	−26.9966	+	928.520i	−0.00832997	+	0.286500i
$220$		0			0
$221$	−1739.00	+	1739.00i	−0.529312	+	0.529312i
$222$		0			0
$223$			1400.11i			0.420440i	0.977654	+	0.210220i	$0.0674181\pi$
$223$			1400.11i			0.420440i	−0.977654	+	0.210220i	$0.932582\pi$
$224$		0			0
$225$	127.761	−	2195.25i	0.0378552	−	0.650443i
$226$		0			0
$227$	1494.96	+	1494.96i	0.437111	+	0.437111i	0.891038	−	0.453928i	$-0.149978\pi$
$227$	1494.96	+	1494.96i	0.437111	+	0.437111i	−0.453928	+	0.891038i	$0.649978\pi$
$228$		0			0
$229$	−247.702	+	247.702i	−0.0714786	+	0.0714786i	−0.741942	−	0.670464i	$-0.766095\pi$
$229$	−247.702	+	247.702i	−0.0714786	+	0.0714786i	0.670464	+	0.741942i	$0.266095\pi$
$230$		0			0
$231$	−12.6245	+	11.9112i	−0.00359581	+	0.00339263i
$232$		0			0
$233$	−3504.28			−0.985293			−0.492647	−	0.870229i	$-0.663970\pi$
$233$	−3504.28			−0.985293			−0.492647	+	0.870229i	$0.663970\pi$
$234$		0			0
$235$	846.259	+	846.259i	0.234910	+	0.234910i
$236$		0			0
$237$	−79.7554	+	2743.10i	−0.0218594	+	0.751829i
$238$		0			0
$239$	−4389.56			−1.18802			−0.594010	−	0.804458i	$-0.702456\pi$
$239$	−4389.56			−1.18802			−0.594010	+	0.804458i	$0.702456\pi$
$240$		0			0
$241$	4549.03			1.21589			0.607944	−	0.793980i	$-0.291995\pi$
$241$	4549.03			1.21589			0.607944	+	0.793980i	$0.291995\pi$
$242$		0			0
$243$	−3748.06	−	548.587i	−0.989458	−	0.144823i
$244$		0			0
$245$	1599.93	+	1599.93i	0.417206	+	0.417206i
$246$		0			0
$247$	−7640.77			−1.96830
$248$		0			0
$249$	3596.43	+	3811.82i	0.915318	+	0.970138i
$250$		0			0
$251$	3546.61	−	3546.61i	0.891872	−	0.891872i	−0.102827	−	0.994699i	$-0.532789\pi$
$251$	3546.61	−	3546.61i	0.891872	−	0.891872i	0.994699	+	0.102827i	$0.0327888\pi$
$252$		0			0
$253$	−757.895	−	757.895i	−0.188334	−	0.188334i
$254$		0			0
$255$	−1230.80	+	1161.25i	−0.302258	+	0.285178i
$256$		0			0
$257$		−	6362.20i		−	1.54421i	−0.635493	−	0.772107i	$-0.719203\pi$
$257$		−	6362.20i		−	1.54421i	0.635493	−	0.772107i	$-0.280797\pi$
$258$		0			0
$259$	104.627	−	104.627i	0.0251012	−	0.0251012i
$260$		0			0
$261$	4915.34	−	4374.67i	1.16572	−	1.03749i
$262$		0			0
$263$			1319.81i			0.309441i	0.987958	+	0.154720i	$0.0494477\pi$
$263$			1319.81i			0.309441i	−0.987958	+	0.154720i	$0.950552\pi$
$264$		0			0
$265$		−	1389.91i		−	0.322193i
$266$		0			0
$267$	−1064.68	−	30.9555i	−0.244035	−	0.00709530i
$268$		0			0
$269$	3795.13	−	3795.13i	0.860198	−	0.860198i	−0.131163	−	0.991361i	$-0.541871\pi$
$269$	3795.13	−	3795.13i	0.860198	−	0.860198i	0.991361	+	0.131163i	$0.0418710\pi$
$270$		0			0
$271$			3647.13i			0.817517i	0.912643	+	0.408759i	$0.134038\pi$
$271$			3647.13i			0.817517i	−0.912643	+	0.408759i	$0.865962\pi$
$272$		0			0
$273$	−72.1217	−	76.4412i	−0.0159890	−	0.0169466i
$274$		0			0
$275$	−474.037	−	474.037i	−0.103947	−	0.103947i
$276$		0			0
$277$	−3570.65	+	3570.65i	−0.774511	+	0.774511i	−0.978891	−	0.204381i	$-0.934482\pi$
$277$	−3570.65	+	3570.65i	−0.774511	+	0.774511i	0.204381	+	0.978891i	$0.434482\pi$
$278$		0			0
$279$	−56.7444	+	975.005i	−0.0121763	+	0.209219i
$280$		0			0
$281$	3787.24			0.804014			0.402007	−	0.915637i	$-0.368313\pi$
$281$	3787.24			0.804014			0.402007	+	0.915637i	$0.368313\pi$
$282$		0			0
$283$	−121.369	−	121.369i	−0.0254935	−	0.0254935i	0.694245	−	0.719739i	$-0.255738\pi$
$283$	−121.369	−	121.369i	−0.0254935	−	0.0254935i	−0.719739	+	0.694245i	$0.755738\pi$
$284$		0			0
$285$	−5255.07	−	152.791i	−1.09222	−	0.0317563i
$286$		0			0
$287$	−2.38462			−0.000490451
$288$		0			0
$289$	2478.23			0.504424
$290$		0			0
$291$	−1430.46	−	41.5905i	−0.288162	−	0.00837829i
$292$		0			0
$293$	3924.62	+	3924.62i	0.782521	+	0.782521i	0.980256	−	0.197734i	$-0.0633583\pi$
$293$	3924.62	+	3924.62i	0.782521	+	0.782521i	−0.197734	+	0.980256i	$0.563358\pi$
$294$		0			0
$295$	−5299.71			−1.04597
$296$		0			0
$297$	−884.605	+	742.371i	−0.172828	+	0.145040i
$298$		0			0
$299$	4589.04	−	4589.04i	0.887595	−	0.887595i
$300$		0			0
$301$	−69.2213	−	69.2213i	−0.0132553	−	0.0132553i
$302$		0			0
$303$	3829.14	+	4058.47i	0.726001	+	0.769482i
$304$		0			0
$305$			4490.10i			0.842959i
$306$		0			0
$307$	420.586	−	420.586i	0.0781893	−	0.0781893i	−0.666931	−	0.745120i	$-0.732392\pi$
$307$	420.586	−	420.586i	0.0781893	−	0.0781893i	0.745120	+	0.666931i	$0.232392\pi$
$308$		0			0
$309$	1908.04	+	55.4760i	0.351276	+	0.0102133i
$310$		0			0
$311$		−	7577.80i		−	1.38166i	−0.723015	−	0.690832i	$-0.757244\pi$
$311$		−	7577.80i		−	1.38166i	0.723015	−	0.690832i	$-0.242756\pi$
$312$		0			0
$313$		−	1198.81i		−	0.216489i	−0.994124	−	0.108244i	$-0.965477\pi$
$313$		−	1198.81i		−	0.216489i	0.994124	−	0.108244i	$-0.0345229\pi$
$314$		0			0
$315$	−48.0744	−	54.0160i	−0.00859900	−	0.00966176i
$316$		0			0
$317$	−145.999	+	145.999i	−0.0258679	+	0.0258679i	−0.719922	−	0.694055i	$-0.755823\pi$
$317$	−145.999	+	145.999i	−0.0258679	+	0.0258679i	0.694055	+	0.719922i	$0.255823\pi$
$318$		0			0
$319$		−	2006.07i		−	0.352095i
$320$		0			0
$321$	−430.579	+	406.248i	−0.0748678	+	0.0706372i
$322$		0			0
$323$	−5348.91	−	5348.91i	−0.921428	−	0.921428i
$324$		0			0
$325$	2870.28	−	2870.28i	0.489891	−	0.489891i
$326$		0			0
$327$	−2873.58	−	3045.69i	−0.485962	−	0.515067i
$328$		0			0
$329$	−73.5868			−0.0123312
$330$		0			0
$331$	973.884	+	973.884i	0.161721	+	0.161721i	0.783329	−	0.621608i	$-0.213520\pi$
$331$	973.884	+	973.884i	0.161721	+	0.161721i	−0.621608	+	0.783329i	$0.713520\pi$
$332$		0			0
$333$	7354.12	−	6545.20i	1.21022	−	1.07710i
$334$		0			0
$335$	2764.68			0.450897
$336$		0			0
$337$	−6066.21			−0.980557			−0.490278	−	0.871566i	$-0.663105\pi$
$337$	−6066.21			−0.980557			−0.490278	+	0.871566i	$0.663105\pi$
$338$		0			0
$339$	−150.926	+	5190.94i	−0.0241805	+	0.831661i
$340$		0			0
$341$	210.541	+	210.541i	0.0334352	+	0.0334352i
$342$		0			0
$343$	−278.311			−0.0438117
$344$		0			0
$345$	3247.95	−	3064.42i	0.506852	−	0.478211i
$346$		0			0
$347$	−5808.66	+	5808.66i	−0.898632	+	0.898632i	−0.995315	−	0.0966836i	$-0.969177\pi$
$347$	−5808.66	+	5808.66i	−0.898632	+	0.898632i	0.0966836	+	0.995315i	$0.469177\pi$
$348$		0			0
$349$	−8153.57	−	8153.57i	−1.25057	−	1.25057i	−0.955463	−	0.295112i	$-0.904643\pi$
$349$	−8153.57	−	8153.57i	−1.25057	−	1.25057i	−0.295112	−	0.955463i	$-0.595357\pi$
$350$		0			0
$351$	−4495.04	−	5356.26i	−0.683554	−	0.814518i
$352$		0			0
$353$		−	4088.22i		−	0.616413i	−0.951319	−	0.308206i	$-0.900271\pi$
$353$		−	4088.22i		−	0.616413i	0.951319	−	0.308206i	$-0.0997288\pi$
$354$		0			0
$355$	−2491.93	+	2491.93i	−0.372557	+	0.372557i
$356$		0			0
$357$	3.02382	−	104.001i	0.000448285	−	0.0154183i
$358$		0			0
$359$			2932.72i			0.431150i	0.976487	+	0.215575i	$0.0691626\pi$
$359$			2932.72i			0.431150i	−0.976487	+	0.215575i	$0.930837\pi$
$360$		0			0
$361$		−	16642.9i		−	2.42643i
$362$		0			0
$363$	190.767	−	6561.24i	0.0275832	−	0.948693i
$364$		0			0
$365$	−834.271	+	834.271i	−0.119638	+	0.119638i
$366$		0			0
$367$		−	7806.79i		−	1.11038i	−0.831722	−	0.555192i	$-0.812645\pi$
$367$		−	7806.79i		−	1.11038i	0.831722	−	0.555192i	$-0.187355\pi$
$368$		0			0
$369$	−158.393	−	9.21835i	−0.0223459	−	0.00130051i
$370$		0			0
$371$	60.4299	+	60.4299i	0.00845651	+	0.00845651i
$372$		0			0
$373$	−2207.72	+	2207.72i	−0.306465	+	0.306465i	−0.843537	−	0.537072i	$-0.819530\pi$
$373$	−2207.72	+	2207.72i	−0.306465	+	0.306465i	0.537072	+	0.843537i	$0.319530\pi$
$374$		0			0
$375$	5149.44	−	4858.46i	0.709109	−	0.669039i
$376$		0			0
$377$	12146.7			1.65938
$378$		0			0
$379$	−9215.05	−	9215.05i	−1.24893	−	1.24893i	−0.956192	−	0.292741i	$-0.905433\pi$
$379$	−9215.05	−	9215.05i	−1.24893	−	1.24893i	−0.292741	−	0.956192i	$-0.594567\pi$
$380$		0			0
$381$	−12.8168	+	440.820i	−0.00172343	+	0.0592753i
$382$		0			0
$383$	−3924.08			−0.523528			−0.261764	−	0.965132i	$-0.584304\pi$
$383$	−3924.08			−0.523528			−0.261764	+	0.965132i	$0.584304\pi$
$384$		0			0
$385$	−22.0452			−0.00291825
$386$		0			0
$387$	−4330.29	−	4865.48i	−0.568789	−	0.639086i
$388$		0			0
$389$	−6777.56	−	6777.56i	−0.883383	−	0.883383i	0.110494	−	0.993877i	$-0.464757\pi$
$389$	−6777.56	−	6777.56i	−0.883383	−	0.883383i	−0.993877	+	0.110494i	$0.964757\pi$
$390$		0			0
$391$	6425.09			0.831025
$392$		0			0
$393$	−6557.75	−	6950.50i	−0.841716	−	0.892128i
$394$		0			0
$395$	−2464.66	+	2464.66i	−0.313951	+	0.313951i
$396$		0			0
$397$	6040.61	+	6040.61i	0.763651	+	0.763651i	0.976980	−	0.213329i	$-0.0684306\pi$
$397$	6040.61	+	6040.61i	0.763651	+	0.763651i	−0.213329	+	0.976980i	$0.568431\pi$
$398$		0			0
$399$	235.122	−	221.836i	0.0295008	−	0.0278338i
$400$		0			0
$401$			8980.43i			1.11836i	0.829047	+	0.559179i	$0.188884\pi$
$401$			8980.43i			1.11836i	−0.829047	+	0.559179i	$0.811116\pi$
$402$		0			0
$403$	−1274.82	+	1274.82i	−0.157576	+	0.157576i
$404$		0			0
$405$	−2984.43	−	3773.75i	−0.366167	−	0.463010i
$406$		0			0
$407$		−	3001.39i		−	0.365537i
$408$		0			0
$409$			12981.1i			1.56937i	0.619893	+	0.784687i	$0.287176\pi$
$409$			12981.1i			1.56937i	−0.619893	+	0.784687i	$0.712824\pi$
$410$		0			0
$411$	9814.61	+	285.359i	1.17790	+	0.0342475i
$412$		0			0
$413$	230.419	−	230.419i	0.0274532	−	0.0274532i
$414$		0			0
$415$			6656.27i			0.787334i
$416$		0			0
$417$	−1217.74	−	1290.67i	−0.143005	−	0.151570i
$418$		0			0
$419$	2795.25	+	2795.25i	0.325911	+	0.325911i	0.851029	−	0.525118i	$-0.175979\pi$
$419$	2795.25	+	2795.25i	0.325911	+	0.325911i	−0.525118	+	0.851029i	$0.675979\pi$
$420$		0			0
$421$	10585.9	−	10585.9i	1.22548	−	1.22548i	0.259823	−	0.965656i	$-0.416336\pi$
$421$	10585.9	−	10585.9i	1.22548	−	1.22548i	0.965656	−	0.259823i	$-0.0836643\pi$
$422$		0			0
$423$	−4887.86	−	284.469i	−0.561834	−	0.0326982i
$424$		0			0
$425$	4018.67			0.458668
$426$		0			0
$427$	−195.219	−	195.219i	−0.0221249	−	0.0221249i
$428$		0			0
$429$	−2130.88	−	61.9551i	−0.239813	−	0.00697254i
$430$		0			0
$431$	5849.75			0.653765			0.326882	−	0.945065i	$-0.394002\pi$
$431$	5849.75			0.653765			0.326882	+	0.945065i	$0.394002\pi$
$432$		0			0
$433$	−14016.2			−1.55561			−0.777804	−	0.628507i	$-0.783666\pi$
$433$	−14016.2			−1.55561			−0.777804	+	0.628507i	$0.783666\pi$
$434$		0			0
$435$	8354.09	+	242.895i	0.920800	+	0.0267722i
$436$		0			0
$437$	14115.2	+	14115.2i	1.54513	+	1.54513i
$438$		0			0
$439$	815.498			0.0886596			0.0443298	−	0.999017i	$-0.485885\pi$
$439$	815.498			0.0886596			0.0443298	+	0.999017i	$0.485885\pi$
$440$		0			0
$441$	−9240.92	−	537.812i	−0.997831	−	0.0580728i
$442$		0			0
$443$	−9194.09	+	9194.09i	−0.986060	+	0.986060i	−0.999904	−	0.0138442i	$-0.995593\pi$
$443$	−9194.09	+	9194.09i	−0.986060	+	0.986060i	0.0138442	+	0.999904i	$0.495593\pi$
$444$		0			0
$445$	−956.610	−	956.610i	−0.101905	−	0.101905i
$446$		0			0
$447$	6168.41	+	6537.85i	0.652698	+	0.691789i
$448$		0			0
$449$			4760.01i			0.500309i	0.968206	+	0.250154i	$0.0804814\pi$
$449$			4760.01i			0.500309i	−0.968206	+	0.250154i	$0.919519\pi$
$450$		0			0
$451$	−34.2032	+	34.2032i	−0.00357110	+	0.00357110i
$452$		0			0
$453$	−14128.9	−	410.797i	−1.46542	−	0.0426069i
$454$		0			0
$455$		−	133.483i		−	0.0137534i
$456$		0			0
$457$			10036.1i			1.02728i	0.858005	+	0.513642i	$0.171704\pi$
$457$			10036.1i			1.02728i	−0.858005	+	0.513642i	$0.828296\pi$
$458$		0			0
$459$	602.894	−	6896.38i	0.0613087	−	0.701297i
$460$		0			0
$461$	9685.06	−	9685.06i	0.978478	−	0.978478i	−0.0212957	−	0.999773i	$-0.506779\pi$
$461$	9685.06	−	9685.06i	0.978478	−	0.978478i	0.999773	+	0.0212957i	$0.00677914\pi$
$462$		0			0
$463$			4061.81i			0.407707i	0.979001	+	0.203854i	$0.0653467\pi$
$463$			4061.81i			0.407707i	−0.979001	+	0.203854i	$0.934653\pi$
$464$		0			0
$465$	−902.271	+	851.286i	−0.0899824	+	0.0848978i
$466$		0			0
$467$	3720.85	+	3720.85i	0.368695	+	0.368695i	0.867001	−	0.498306i	$-0.166044\pi$
$467$	3720.85	+	3720.85i	0.368695	+	0.368695i	−0.498306	+	0.867001i	$0.666044\pi$
$468$		0			0
$469$	−120.202	+	120.202i	−0.0118345	+	0.0118345i
$470$		0			0
$471$	−4609.69	−	4885.77i	−0.450963	−	0.477971i
$472$		0			0
$473$	−1985.72			−0.193030
$474$		0			0
$475$	8828.56	+	8828.56i	0.852804	+	0.852804i
$476$		0			0
$477$	3780.33	+	4247.54i	0.362871	+	0.407718i
$478$		0			0
$479$	−9242.13			−0.881594			−0.440797	−	0.897607i	$-0.645304\pi$
$479$	−9242.13			−0.881594			−0.440797	+	0.897607i	$0.645304\pi$
$480$		0			0
$481$	18173.4			1.72273
$482$		0			0
$483$	−7.97955	+	274.448i	−0.000751722	+	0.0258547i
$484$		0			0
$485$	−1285.26	−	1285.26i	−0.120332	−	0.120332i
$486$		0			0
$487$	10165.4			0.945867			0.472933	−	0.881098i	$-0.343195\pi$
$487$	10165.4			0.945867			0.472933	+	0.881098i	$0.343195\pi$
$488$		0			0
$489$	−8392.37	+	7918.14i	−0.776106	+	0.732251i
$490$		0			0
$491$	−2662.06	+	2662.06i	−0.244678	+	0.244678i	−0.818782	−	0.574104i	$-0.805351\pi$
$491$	−2662.06	+	2662.06i	−0.244678	+	0.244678i	0.574104	+	0.818782i	$0.305351\pi$
$492$		0			0
$493$	8503.26	+	8503.26i	0.776810	+	0.776810i
$494$		0			0
$495$	−1464.31	−	85.2213i	−0.132961	−	0.00773821i
$496$		0			0
$497$		−	216.687i		−	0.0195568i
$498$		0			0
$499$	−9435.03	+	9435.03i	−0.846433	+	0.846433i	−0.989686	−	0.143253i	$-0.954244\pi$
$499$	−9435.03	+	9435.03i	−0.846433	+	0.846433i	0.143253	+	0.989686i	$0.454244\pi$
$500$		0			0
$501$	−330.034	+	11351.1i	−0.0294308	+	1.01224i
$502$		0			0
$503$			10737.0i			0.951764i	0.879509	+	0.475882i	$0.157871\pi$
$503$			10737.0i			0.951764i	−0.879509	+	0.475882i	$0.842129\pi$
$504$		0			0
$505$			7086.98i			0.624488i
$506$		0			0
$507$	43.3588	−	1491.28i	0.00379809	−	0.130631i
$508$		0			0
$509$	−15372.5	+	15372.5i	−1.33865	+	1.33865i	−0.441279	+	0.897370i	$0.645475\pi$
$509$	−15372.5	+	15372.5i	−1.33865	+	1.33865i	−0.897370	+	0.441279i	$0.854525\pi$
$510$		0			0
$511$		−	72.5444i		−	0.00628019i
$512$		0			0
$513$	16475.0	−	13826.1i	1.41792	−	1.18993i
$514$		0			0
$515$	1714.36	+	1714.36i	0.146687	+	0.146687i
$516$		0			0
$517$	−1055.47	+	1055.47i	−0.0897867	+	0.0897867i
$518$		0			0
$519$	−1160.22	+	1094.66i	−0.0981270	+	0.0925821i
$520$		0			0
$521$	−12415.9			−1.04405			−0.522027	−	0.852929i	$-0.674824\pi$
$521$	−12415.9			−1.04405			−0.522027	+	0.852929i	$0.674824\pi$
$522$		0			0
$523$	2505.05	+	2505.05i	0.209442	+	0.209442i	0.804030	−	0.594588i	$-0.202685\pi$
$523$	2505.05	+	2505.05i	0.209442	+	0.209442i	−0.594588	+	0.804030i	$0.702685\pi$
$524$		0			0
$525$	−4.99093	+	171.658i	−0.000414899	+	0.0142700i
$526$		0			0
$527$	−1784.87			−0.147533
$528$		0			0
$529$	−4788.11			−0.393532
$530$		0			0
$531$	16195.9	−	14414.4i	1.32362	−	1.17803i
$532$		0			0
$533$	−207.099	−	207.099i	−0.0168302	−	0.0168302i
$534$		0			0
$535$	−751.885			−0.0607604
$536$		0			0
$537$	3287.94	+	3484.86i	0.264218	+	0.280042i
$538$		0			0
$539$	−1995.47	+	1995.47i	−0.159463	+	0.159463i
$540$		0			0
$541$	5592.06	+	5592.06i	0.444402	+	0.444402i	0.893488	−	0.449086i	$-0.148250\pi$
$541$	5592.06	+	5592.06i	0.444402	+	0.444402i	−0.449086	+	0.893488i	$0.648250\pi$
$542$		0			0
$543$	4802.30	−	4530.94i	0.379533	−	0.358087i
$544$		0			0
$545$		−	5318.44i		−	0.418012i
$546$		0			0
$547$	7535.39	−	7535.39i	0.589012	−	0.589012i	−0.348352	−	0.937364i	$-0.613258\pi$
$547$	7535.39	−	7535.39i	0.589012	−	0.589012i	0.937364	+	0.348352i	$0.113258\pi$
$548$		0			0
$549$	−12212.4	−	13721.7i	−0.949384	−	1.06672i
$550$		0			0
$551$			37361.4i			2.88865i
$552$		0			0
$553$		−	214.316i		−	0.0164803i
$554$		0			0
$555$	12499.0	+	363.409i	0.955954	+	0.0277943i
$556$		0			0
$557$	−9660.53	+	9660.53i	−0.734883	+	0.734883i	−0.971583	−	0.236700i	$-0.923934\pi$
$557$	−9660.53	+	9660.53i	−0.734883	+	0.734883i	0.236700	+	0.971583i	$0.423934\pi$
$558$		0			0
$559$		−	12023.5i		−	0.909729i
$560$		0			0
$561$	−1448.34	−	1535.09i	−0.109000	−	0.115528i
$562$		0			0
$563$	438.805	+	438.805i	0.0328480	+	0.0328480i	0.723340	−	0.690492i	$-0.242606\pi$
$563$	438.805	+	438.805i	0.0328480	+	0.0328480i	−0.690492	+	0.723340i	$0.742606\pi$
$564$		0			0
$565$	−4664.03	+	4664.03i	−0.347287	+	0.347287i
$566$		0			0
$567$	293.830	+	34.3175i	0.0217632	+	0.00254180i
$568$		0			0
$569$	15726.9			1.15871			0.579356	−	0.815075i	$-0.303304\pi$
$569$	15726.9			1.15871			0.579356	+	0.815075i	$0.303304\pi$
$570$		0			0
$571$	4315.78	+	4315.78i	0.316304	+	0.316304i	0.847346	−	0.531042i	$-0.178199\pi$
$571$	4315.78	+	4315.78i	0.316304	+	0.316304i	−0.531042	+	0.847346i	$0.678199\pi$
$572$		0			0
$573$	−18670.1	−	542.832i	−1.36118	−	0.0395761i
$574$		0			0
$575$	−10604.8			−0.769134
$576$		0			0
$577$	−230.069			−0.0165995			−0.00829973	−	0.999966i	$-0.502642\pi$
$577$	−230.069			−0.0165995			−0.00829973	+	0.999966i	$0.502642\pi$
$578$		0			0
$579$	−5580.87	−	162.263i	−0.400575	−	0.0116467i
$580$		0			0
$581$	−289.400	−	289.400i	−0.0206649	−	0.0206649i
$582$		0			0
$583$	1733.52			0.123148
$584$		0			0
$585$	516.013	−	8866.35i	0.0364693	−	0.626630i
$586$		0			0
$587$	2558.02	−	2558.02i	0.179865	−	0.179865i	−0.611432	−	0.791297i	$-0.709406\pi$
$587$	2558.02	−	2558.02i	0.179865	−	0.179865i	0.791297	+	0.611432i	$0.209406\pi$
$588$		0			0
$589$	−3921.15	−	3921.15i	−0.274309	−	0.274309i
$590$		0			0
$591$	17175.9	+	18204.6i	1.19547	+	1.26707i
$592$		0			0
$593$			7843.65i			0.543171i	0.962414	+	0.271585i	$0.0875479\pi$
$593$			7843.65i			0.543171i	−0.962414	+	0.271585i	$0.912452\pi$
$594$		0			0
$595$	93.4445	−	93.4445i	0.00643841	−	0.00643841i
$596$		0			0
$597$	−12361.3	−	359.404i	−0.847428	−	0.0246389i
$598$		0			0
$599$			3723.46i			0.253984i	0.991904	+	0.126992i	$0.0405322\pi$
$599$			3723.46i			0.253984i	−0.991904	+	0.126992i	$0.959468\pi$
$600$		0			0
$601$			4258.35i			0.289021i	0.989503	+	0.144510i	$0.0461607\pi$
$601$			4258.35i			0.289021i	−0.989503	+	0.144510i	$0.953839\pi$
$602$		0			0
$603$	−8448.83	+	7519.49i	−0.570586	+	0.507823i
$604$		0			0
$605$	5895.24	−	5895.24i	0.396158	−	0.396158i
$606$		0			0
$607$		−	16079.7i		−	1.07521i	−0.843196	−	0.537607i	$-0.819328\pi$
$607$		−	16079.7i		−	1.07521i	0.843196	−	0.537607i	$-0.180672\pi$
$608$		0			0
$609$	−373.777	+	352.656i	−0.0248706	+	0.0234653i
$610$		0			0
$611$	−6390.87	−	6390.87i	−0.423154	−	0.423154i
$612$		0			0
$613$	−8932.52	+	8932.52i	−0.588550	+	0.588550i	−0.937239	−	0.348689i	$-0.886627\pi$
$613$	−8932.52	+	8932.52i	−0.588550	+	0.588550i	0.348689	+	0.937239i	$0.386627\pi$
$614$		0			0
$615$	−138.295	−	146.578i	−0.00906762	−	0.00961069i
$616$		0			0
$617$	−13786.6			−0.899561			−0.449781	−	0.893139i	$-0.648498\pi$
$617$	−13786.6			−0.899561			−0.449781	+	0.893139i	$0.648498\pi$
$618$		0			0
$619$	8515.92	+	8515.92i	0.552962	+	0.552962i	0.927295	−	0.374332i	$-0.122128\pi$
$619$	8515.92	+	8515.92i	0.552962	+	0.552962i	−0.374332	+	0.927295i	$0.622128\pi$
$620$		0			0
$621$	−1590.97	+	18198.8i	−0.102808	+	1.17599i
$622$		0			0
$623$	83.1824			0.00534933
$624$		0			0
$625$	−1188.32			−0.0760527
$626$		0			0
$627$	190.564	−	6554.26i	0.0121378	−	0.417467i
$628$		0			0
$629$	12722.2	+	12722.2i	0.806467	+	0.806467i
$630$		0			0
$631$	18050.1			1.13877			0.569384	−	0.822072i	$-0.307182\pi$
$631$	18050.1			1.13877			0.569384	+	0.822072i	$0.307182\pi$
$632$		0			0
$633$	−6998.76	+	6603.28i	−0.439456	+	0.414624i
$634$		0			0
$635$	−396.075	+	396.075i	−0.0247524	+	0.0247524i
$636$		0			0
$637$	−12082.5	−	12082.5i	−0.751532	−	0.751532i
$638$		0			0
$639$	837.657	−	14393.0i	0.0518579	−	0.891044i
$640$		0			0
$641$			3074.43i			0.189443i	0.995504	+	0.0947214i	$0.0301960\pi$
$641$			3074.43i			0.189443i	−0.995504	+	0.0947214i	$0.969804\pi$
$642$		0			0
$643$	12329.7	−	12329.7i	0.756201	−	0.756201i	−0.219428	−	0.975629i	$-0.570419\pi$
$643$	12329.7	−	12329.7i	0.756201	−	0.756201i	0.975629	+	0.219428i	$0.0704191\pi$
$644$		0			0
$645$	240.431	−	8269.35i	0.0146774	−	0.504815i
$646$		0			0
$647$		−	15254.8i		−	0.926935i	−0.886114	−	0.463467i	$-0.846605\pi$
$647$		−	15254.8i		−	0.926935i	0.886114	−	0.463467i	$-0.153395\pi$
$648$		0			0
$649$		−	6609.93i		−	0.399788i
$650$		0			0
$651$	2.21669	−	76.2407i	0.000133455	−	0.00459003i
$652$		0			0
$653$	17233.8	−	17233.8i	1.03279	−	1.03279i	0.0333418	−	0.999444i	$-0.489385\pi$
$653$	17233.8	−	17233.8i	1.03279	−	1.03279i	0.999444	−	0.0333418i	$-0.0106150\pi$
$654$		0			0
$655$		−	12137.1i		−	0.724024i
$656$		0			0
$657$	280.439	−	4818.62i	0.0166529	−	0.286137i
$658$		0			0
$659$	17880.8	+	17880.8i	1.05696	+	1.05696i	0.998277	+	0.0586826i	$0.0186900\pi$
$659$	17880.8	+	17880.8i	1.05696	+	1.05696i	0.0586826	+	0.998277i	$0.481310\pi$
$660$		0			0
$661$	4067.01	−	4067.01i	0.239317	−	0.239317i	−0.577250	−	0.816567i	$-0.695874\pi$
$661$	4067.01	−	4067.01i	0.239317	−	0.239317i	0.816567	+	0.577250i	$0.195874\pi$
$662$		0			0
$663$	9294.91	−	8769.68i	0.544471	−	0.513705i
$664$		0			0
$665$	410.574			0.0239419
$666$		0			0
$667$	−22439.2	−	22439.2i	−1.30262	−	1.30262i
$668$		0			0
$669$	211.436	−	7272.11i	0.0122191	−	0.420263i
$670$		0			0
$671$	−5600.16			−0.322194
$672$		0			0
$673$	−14736.5			−0.844055			−0.422028	−	0.906583i	$-0.638681\pi$
$673$	−14736.5			−0.844055			−0.422028	+	0.906583i	$0.638681\pi$
$674$		0			0
$675$	−995.099	+	11382.7i	−0.0567428	+	0.649068i
$676$		0			0
$677$	7537.37	+	7537.37i	0.427894	+	0.427894i	0.887911	−	0.460016i	$-0.152156\pi$
$677$	7537.37	+	7537.37i	0.427894	+	0.427894i	−0.460016	+	0.887911i	$0.652156\pi$
$678$		0			0
$679$	111.761			0.00631661
$680$		0			0
$681$	−7539.01	−	7990.53i	−0.424223	−	0.449630i
$682$		0			0
$683$	−13047.9	+	13047.9i	−0.730988	+	0.730988i	−0.970816	−	0.239827i	$-0.922909\pi$
$683$	−13047.9	+	13047.9i	−0.730988	+	0.730988i	0.239827	+	0.970816i	$0.422909\pi$
$684$		0			0
$685$	8818.38	+	8818.38i	0.491873	+	0.491873i
$686$		0			0
$687$	1323.96	−	1249.15i	0.0735257	−	0.0693710i
$688$		0			0
$689$			10496.4i			0.580381i
$690$		0			0
$691$	−219.408	+	219.408i	−0.0120791	+	0.0120791i	−0.713121	−	0.701041i	$-0.752719\pi$
$691$	−219.408	+	219.408i	−0.0120791	+	0.0120791i	0.701041	+	0.713121i	$0.252719\pi$
$692$		0			0
$693$	67.3700	−	59.9595i	0.00369289	−	0.00328669i
$694$		0			0
$695$		−	2253.80i		−	0.123009i
$696$		0			0
$697$		−	289.959i		−	0.0157575i
$698$		0			0
$699$	18201.1	+	529.196i	0.984877	+	0.0286352i
$700$		0			0
$701$	1627.72	−	1627.72i	0.0877008	−	0.0877008i	−0.661895	−	0.749596i	$-0.730248\pi$
$701$	1627.72	−	1627.72i	0.0877008	−	0.0877008i	0.749596	+	0.661895i	$0.230248\pi$
$702$		0			0
$703$			55898.5i			2.99894i
$704$		0			0
$705$	−4267.63	−	4523.23i	−0.227984	−	0.241638i
$706$		0			0
$707$	−308.126	−	308.126i	−0.0163908	−	0.0163908i
$708$		0			0
$709$	12014.9	−	12014.9i	0.636431	−	0.636431i	−0.313242	−	0.949673i	$-0.601415\pi$
$709$	12014.9	−	12014.9i	0.636431	−	0.636431i	0.949673	+	0.313242i	$0.101415\pi$
$710$		0			0
$711$	828.492	−	14235.5i	0.0437003	−	0.750876i
$712$		0			0
$713$	4710.07			0.247396
$714$		0			0
$715$	−1914.58	−	1914.58i	−0.100142	−	0.100142i
$716$		0			0
$717$	22799.2	+	662.884i	1.18752	+	0.0345270i
$718$		0			0
$719$	−10643.1			−0.552044			−0.276022	−	0.961151i	$-0.589016\pi$
$719$	−10643.1			−0.552044			−0.276022	+	0.961151i	$0.589016\pi$
$720$		0			0
$721$	−149.073			−0.00770010
$722$		0			0
$723$	−23627.5	−	686.967i	−1.21537	−	0.0353369i
$724$		0			0
$725$	−14034.9	−	14034.9i	−0.718957	−	0.718957i
$726$		0			0
$727$	−37024.9			−1.88883			−0.944414	−	0.328759i	$-0.893370\pi$
$727$	−37024.9			−1.88883			−0.944414	+	0.328759i	$0.893370\pi$
$728$		0			0
$729$	19384.4	+	3415.35i	0.984831	+	0.173518i
$730$		0			0
$731$	8417.00	−	8417.00i	0.425874	−	0.425874i
$732$		0			0
$733$	−7748.42	−	7748.42i	−0.390443	−	0.390443i	0.484403	−	0.874845i	$-0.339037\pi$
$733$	−7748.42	−	7748.42i	−0.390443	−	0.390443i	−0.874845	+	0.484403i	$0.839037\pi$
$734$		0			0
$735$	−8068.33	−	8551.56i	−0.404905	−	0.429155i
$736$		0			0
$737$			3448.17i			0.172341i
$738$		0			0
$739$	−3104.56	+	3104.56i	−0.154537	+	0.154537i	−0.780141	−	0.625604i	$-0.784853\pi$
$739$	−3104.56	+	3104.56i	−0.154537	+	0.154537i	0.625604	+	0.780141i	$0.284853\pi$
$740$		0			0
$741$	39685.9	+	1153.86i	1.96747	+	0.0572041i
$742$		0			0
$743$		−	26472.4i		−	1.30710i	−0.756882	−	0.653552i	$-0.773278\pi$
$743$		−	26472.4i		−	1.30710i	0.756882	−	0.653552i	$-0.226722\pi$
$744$		0			0
$745$			11416.5i			0.561435i
$746$		0			0
$747$	−18104.0	−	20341.5i	−0.886737	−	0.996329i
$748$		0			0
$749$	32.6902	−	32.6902i	0.00159476	−	0.00159476i
$750$		0			0
$751$		−	3504.42i		−	0.170277i	−0.996369	−	0.0851386i	$-0.972867\pi$
$751$		−	3504.42i		−	0.170277i	0.996369	−	0.0851386i	$-0.0271333\pi$
$752$		0			0
$753$	−18956.5	+	17885.3i	−0.917416	+	0.865575i
$754$		0			0
$755$	−12694.8	−	12694.8i	−0.611933	−	0.611933i
$756$		0			0
$757$	−1584.85	+	1584.85i	−0.0760929	+	0.0760929i	−0.744129	−	0.668036i	$-0.767135\pi$
$757$	−1584.85	+	1584.85i	−0.0760929	+	0.0760929i	0.668036	+	0.744129i	$0.267135\pi$
$758$		0			0
$759$	3822.02	+	4050.93i	0.182781	+	0.193728i
$760$		0			0
$761$	8268.32			0.393858			0.196929	−	0.980418i	$-0.436903\pi$
$761$	8268.32			0.393858			0.196929	+	0.980418i	$0.436903\pi$
$762$		0			0
$763$	231.233	+	231.233i	0.0109714	+	0.0109714i
$764$		0			0
$765$	6568.10	−	5845.63i	0.310419	−	0.276274i
$766$		0			0
$767$	40022.9			1.88415
$768$		0			0
$769$	4645.29			0.217833			0.108916	−	0.994051i	$-0.465262\pi$
$769$	4645.29			0.217833			0.108916	+	0.994051i	$0.465262\pi$
$770$		0			0
$771$	−960.780	+	33045.0i	−0.0448789	+	1.54356i
$772$		0			0
$773$	−10938.2	−	10938.2i	−0.508952	−	0.508952i	0.405253	−	0.914205i	$-0.367184\pi$
$773$	−10938.2	−	10938.2i	−0.508952	−	0.508952i	−0.914205	+	0.405253i	$0.867184\pi$
$774$		0			0
$775$	2945.99			0.136546
$776$		0			0
$777$	−559.230	+	527.629i	−0.0258202	+	0.0243611i
$778$		0			0
$779$	637.007	−	637.007i	0.0292980	−	0.0292980i
$780$		0			0
$781$	−3107.99	−	3107.99i	−0.142398	−	0.142398i
$782$		0			0
$783$	−26190.7	+	21979.6i	−1.19538	+	1.00317i
$784$		0			0
$785$		−	8531.63i		−	0.387907i
$786$		0			0
$787$	−15406.3	+	15406.3i	−0.697810	+	0.697810i	−0.963938	−	0.266128i	$-0.914256\pi$
$787$	−15406.3	+	15406.3i	−0.697810	+	0.697810i	0.266128	+	0.963938i	$0.414256\pi$
$788$		0			0
$789$	199.310	−	6855.04i	0.00899317	−	0.309310i
$790$		0			0
$791$		−	405.563i		−	0.0182303i
$792$		0			0
$793$		−	33908.8i		−	1.51846i
$794$		0			0
$795$	−209.895	+	7219.11i	−0.00936379	+	0.322057i
$796$		0			0
$797$	−8248.05	+	8248.05i	−0.366576	+	0.366576i	−0.866227	−	0.499651i	$-0.833462\pi$
$797$	−8248.05	+	8248.05i	−0.366576	+	0.366576i	0.499651	+	0.866227i	$0.333462\pi$
$798$		0			0
$799$		−	8947.83i		−	0.396184i
$800$		0			0
$801$	5525.23	+	321.563i	0.243726	+	0.0141846i
$802$		0			0
$803$	−1040.52	−	1040.52i	−0.0457276	−	0.0457276i
$804$		0			0
$805$	−246.590	+	246.590i	−0.0107965	+	0.0107965i
$806$		0			0
$807$	−20284.9	+	19138.6i	−0.884835	+	0.834835i
$808$		0			0
$809$	22258.0			0.967304			0.483652	−	0.875260i	$-0.339310\pi$
$809$	22258.0			0.967304			0.483652	+	0.875260i	$0.339310\pi$
$810$		0			0
$811$	−10862.2	−	10862.2i	−0.470314	−	0.470314i	0.431702	−	0.902016i	$-0.357913\pi$
$811$	−10862.2	−	10862.2i	−0.470314	−	0.470314i	−0.902016	+	0.431702i	$0.857913\pi$
$812$		0			0
$813$	550.767	−	18943.0i	0.0237592	−	0.817172i
$814$		0			0
$815$	−14654.9			−0.629864
$816$		0			0
$817$	36982.4			1.58366
$818$		0			0
$819$	363.054	+	407.924i	0.0154898	+	0.0174042i
$820$		0			0
$821$	7722.94	+	7722.94i	0.328298	+	0.328298i	0.851939	−	0.523641i	$-0.175427\pi$
$821$	7722.94	+	7722.94i	0.328298	+	0.328298i	−0.523641	+	0.851939i	$0.675427\pi$
$822$		0			0
$823$	−18227.8			−0.772030			−0.386015	−	0.922493i	$-0.626149\pi$
$823$	−18227.8			−0.772030			−0.386015	+	0.922493i	$0.626149\pi$
$824$		0			0
$825$	2390.54	+	2533.71i	0.100882	+	0.106924i
$826$		0			0
$827$	12130.6	−	12130.6i	0.510064	−	0.510064i	−0.404482	−	0.914546i	$-0.632548\pi$
$827$	12130.6	−	12130.6i	0.510064	−	0.510064i	0.914546	+	0.404482i	$0.132548\pi$
$828$		0			0
$829$	23901.9	+	23901.9i	1.00138	+	1.00138i	0.999999	+	0.00138493i	$0.000440837\pi$
$829$	23901.9	+	23901.9i	1.00138	+	1.00138i	0.00138493	+	0.999999i	$0.499559\pi$
$830$		0			0
$831$	19085.0	−	18006.6i	0.796693	−	0.751674i
$832$		0			0
$833$		−	16916.6i		−	0.703634i
$834$		0			0
$835$	−10199.0	+	10199.0i	−0.422694	+	0.422694i
$836$		0			0
$837$	441.967	−	5055.57i	0.0182516	−	0.208776i
$838$		0			0
$839$		−	39073.9i		−	1.60784i	−0.594734	−	0.803922i	$-0.702743\pi$
$839$		−	39073.9i		−	1.60784i	0.594734	−	0.803922i	$-0.297257\pi$
$840$		0			0
$841$		−	35005.1i		−	1.43528i
$842$		0			0
$843$	−19670.8	−	571.926i	−0.803674	−	0.0233668i
$844$		0			0
$845$	1339.91	−	1339.91i	0.0545493	−	0.0545493i
$846$		0			0
$847$			512.623i			0.0207957i
$848$		0			0
$849$	612.059	+	648.716i	0.0247418	+	0.0262237i
$850$		0			0
$851$	−33572.5	−	33572.5i	−1.35235	−	1.35235i
$852$		0			0
$853$	−16425.2	+	16425.2i	−0.659306	+	0.659306i	−0.955216	−	0.295910i	$-0.904377\pi$
$853$	−16425.2	+	16425.2i	−0.659306	+	0.659306i	0.295910	+	0.955216i	$0.404377\pi$
$854$		0			0
$855$	27271.6	+	1587.18i	1.09084	+	0.0634858i
$856$		0			0
$857$	−816.193			−0.0325328			−0.0162664	−	0.999868i	$-0.505178\pi$
$857$	−816.193			−0.0325328			−0.0162664	+	0.999868i	$0.505178\pi$
$858$		0			0
$859$	7666.85	+	7666.85i	0.304528	+	0.304528i	0.842782	−	0.538254i	$-0.180916\pi$
$859$	7666.85	+	7666.85i	0.304528	+	0.304528i	−0.538254	+	0.842782i	$0.680916\pi$
$860$		0			0
$861$	12.3856	+	0.360110i	0.000490244	+	1.42538e-5i
$862$		0			0
$863$	−2649.99			−0.104527			−0.0522634	−	0.998633i	$-0.516644\pi$
$863$	−2649.99			−0.104527			−0.0522634	+	0.998633i	$0.516644\pi$
$864$		0			0
$865$	−2025.99			−0.0796368
$866$		0			0
$867$	−12871.8	−	374.248i	−0.504211	−	0.0146599i
$868$		0			0
$869$	−3073.99	−	3073.99i	−0.119997	−	0.119997i
$870$		0			0
$871$	−20878.6			−0.812220
$872$		0			0
$873$	7423.47	+	432.039i	0.287797	+	0.0167495i
$874$		0			0
$875$	−390.954	+	390.954i	−0.0151047	+	0.0151047i
$876$		0			0
$877$	−25276.8	−	25276.8i	−0.973247	−	0.973247i	0.0264043	−	0.999651i	$-0.491594\pi$
$877$	−25276.8	−	25276.8i	−0.973247	−	0.973247i	−0.999651	+	0.0264043i	$0.991594\pi$
$878$		0			0
$879$	−19791.6	−	20977.0i	−0.759449	−	0.804933i
$880$		0			0
$881$		−	7497.28i		−	0.286708i	−0.989671	−	0.143354i	$-0.954211\pi$
$881$		−	7497.28i		−	0.286708i	0.989671	−	0.143354i	$-0.0457888\pi$
$882$		0			0
$883$	3891.20	−	3891.20i	0.148301	−	0.148301i	−0.629058	−	0.777358i	$-0.716559\pi$
$883$	3891.20	−	3891.20i	0.148301	−	0.148301i	0.777358	+	0.629058i	$0.216559\pi$
$884$		0			0
$885$	27526.5	+	800.330i	1.04553	+	0.0303986i
$886$		0			0
$887$			12695.2i			0.480567i	0.970703	+	0.240284i	$0.0772404\pi$
$887$			12695.2i			0.480567i	−0.970703	+	0.240284i	$0.922760\pi$
$888$		0			0
$889$		−	34.4409i		−	0.00129934i
$890$		0			0
$891$	4706.71	−	3722.26i	0.176970	−	0.139955i
$892$		0			0
$893$	19657.4	−	19657.4i	0.736628	−	0.736628i
$894$		0			0
$895$			6085.32i			0.227274i
$896$		0			0
$897$	−24528.3	+	23142.2i	−0.913015	+	0.861424i
$898$		0			0
$899$	6233.53	+	6233.53i	0.231257	+	0.231257i
$900$		0			0
$901$	−7348.01	+	7348.01i	−0.271696	+	0.271696i
$902$		0			0
$903$	349.079	+	369.986i	0.0128645	+	0.0136349i
$904$		0			0
$905$	8385.87			0.308017
$906$		0			0
$907$	27470.7	+	27470.7i	1.00568	+	1.00568i	0.999984	+	0.00569203i	$0.00181184\pi$
$907$	27470.7	+	27470.7i	1.00568	+	1.00568i	0.00569203	+	0.999984i	$0.498188\pi$
$908$		0			0
$909$	−19275.5	−	21657.8i	−0.703331	−	0.790257i
$910$		0			0
$911$	49872.0			1.81376			0.906878	−	0.421392i	$-0.138458\pi$
$911$	49872.0			1.81376			0.906878	+	0.421392i	$0.138458\pi$
$912$		0			0
$913$	−8301.87			−0.300933
$914$		0			0
$915$	678.068	−	23321.4i	0.0244986	−	0.842603i
$916$		0			0
$917$	527.693	+	527.693i	0.0190032	+	0.0190032i
$918$		0			0
$919$	−21222.5			−0.761768			−0.380884	−	0.924623i	$-0.624380\pi$
$919$	−21222.5			−0.761768			−0.380884	+	0.924623i	$0.624380\pi$
$920$		0			0
$921$	−2248.02	+	2120.99i	−0.0804286	+	0.0758839i
$922$		0			0
$923$	18818.8	−	18818.8i	0.671104	−	0.671104i
$924$		0			0
$925$	−20998.5	−	20998.5i	−0.746406	−	0.746406i
$926$		0			0
$927$	−9901.88	−	576.280i	−0.350831	−	0.0204180i
$928$		0			0
$929$		−	37120.6i		−	1.31097i	−0.755210	−	0.655483i	$-0.772465\pi$
$929$		−	37120.6i		−	1.31097i	0.755210	−	0.655483i	$-0.227535\pi$
$930$		0			0
$931$	37163.9	−	37163.9i	1.30827	−	1.30827i
$932$		0			0
$933$	−1144.35	+	39358.8i	−0.0401548	+	1.38108i
$934$		0			0
$935$		−	2680.60i		−	0.0937593i
$936$		0			0
$937$		−	9079.21i		−	0.316547i	−0.987395	−	0.158274i	$-0.949407\pi$
$937$		−	9079.21i		−	0.316547i	0.987395	−	0.158274i	$-0.0505928\pi$
$938$		0			0
$939$	−181.038	+	6226.59i	−0.00629173	+	0.216397i
$940$		0			0
$941$	−30272.6	+	30272.6i	−1.04874	+	1.04874i	−0.0499850	+	0.998750i	$0.515917\pi$
$941$	−30272.6	+	30272.6i	−1.04874	+	1.04874i	−0.998750	+	0.0499850i	$0.984083\pi$
$942$		0			0
$943$			765.170i			0.0264235i
$944$		0			0
$945$	241.539	+	287.816i	0.00831457	+	0.00990759i
$946$		0			0
$947$	21273.7	+	21273.7i	0.729993	+	0.729993i	0.970618	−	0.240625i	$-0.0773523\pi$
$947$	21273.7	+	21273.7i	0.729993	+	0.729993i	−0.240625	+	0.970618i	$0.577352\pi$
$948$		0			0
$949$	6300.34	−	6300.34i	0.215509	−	0.215509i
$950$		0			0
$951$	780.361	−	736.265i	0.0266088	−	0.0251052i
$952$		0			0
$953$	−38299.3			−1.30182			−0.650911	−	0.759154i	$-0.725613\pi$
$953$	−38299.3			−1.30182			−0.650911	+	0.759154i	$0.725613\pi$
$954$		0			0
$955$	−16775.0	−	16775.0i	−0.568405	−	0.568405i
$956$		0			0
$957$	−302.944	+	10419.4i	−0.0102328	+	0.351946i
$958$		0			0
$959$	−766.806			−0.0258201
$960$		0			0
$961$	28482.6			0.956079
$962$		0			0
$963$	2297.76	−	2045.01i	0.0768891	−	0.0684315i
$964$		0			0
$965$	−5014.38	−	5014.38i	−0.167273	−	0.167273i
$966$		0			0
$967$	44091.4			1.46627			0.733136	−	0.680082i	$-0.238056\pi$
$967$	44091.4			1.46627			0.733136	+	0.680082i	$0.238056\pi$
$968$		0			0
$969$	26974.2	+	28589.7i	0.894259	+	0.947817i
$970$		0			0
$971$	12841.6	−	12841.6i	0.424413	−	0.424413i	−0.462307	−	0.886720i	$-0.652978\pi$
$971$	12841.6	−	12841.6i	0.424413	−	0.424413i	0.886720	+	0.462307i	$0.152978\pi$
$972$		0			0
$973$	97.9901	+	97.9901i	0.00322859	+	0.00322859i
$974$		0			0
$975$	−15341.6	+	14474.7i	−0.503922	+	0.475447i
$976$		0			0
$977$			23887.3i			0.782215i	0.920345	+	0.391107i	$0.127908\pi$
$977$			23887.3i			0.782215i	−0.920345	+	0.391107i	$0.872092\pi$
$978$		0			0
$979$	1193.11	−	1193.11i	0.0389498	−	0.0389498i
$980$		0			0
$981$	14465.3	+	16253.1i	0.470787	+	0.528973i
$982$		0			0
$983$			32053.2i			1.04002i	0.854160	+	0.520010i	$0.174072\pi$
$983$			32053.2i			1.04002i	−0.854160	+	0.520010i	$0.825928\pi$
$984$		0			0
$985$			31789.2i			1.02831i
$986$		0			0
$987$	382.207	+	11.1126i	0.0123260	+	0.000358378i
$988$		0			0
$989$	−22211.6	+	22211.6i	−0.714142	+	0.714142i
$990$		0			0
$991$		−	9896.44i		−	0.317226i	−0.987341	−	0.158613i	$-0.949298\pi$
$991$		−	9896.44i		−	0.317226i	0.987341	−	0.158613i	$-0.0507022\pi$
$992$		0			0
$993$	−4911.24	−	5205.38i	−0.156952	−	0.166352i
$994$		0			0
$995$	−11106.6	−	11106.6i	−0.353871	−	0.353871i
$996$		0			0
$997$	2246.47	−	2246.47i	0.0713604	−	0.0713604i	−0.670526	−	0.741886i	$-0.733931\pi$
$997$	2246.47	−	2246.47i	0.0713604	−	0.0713604i	0.741886	+	0.670526i	$0.233931\pi$
$998$		0			0
$999$	−39185.4	+	32884.9i	−1.24101	+	1.04147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.4.k.b.95.1		44
3.2	odd	2	inner	384.4.k.b.95.12		44
4.3	odd	2		384.4.k.a.95.22		44
8.3	odd	2		192.4.k.a.47.1		44
8.5	even	2		48.4.k.a.35.13	yes	44
12.11	even	2		384.4.k.a.95.11		44
16.3	odd	4		48.4.k.a.11.10	✓	44
16.5	even	4		384.4.k.a.287.11		44
16.11	odd	4	inner	384.4.k.b.287.12		44
16.13	even	4		192.4.k.a.143.12		44
24.5	odd	2		48.4.k.a.35.10	yes	44
24.11	even	2		192.4.k.a.47.12		44
48.5	odd	4		384.4.k.a.287.22		44
48.11	even	4	inner	384.4.k.b.287.1		44
48.29	odd	4		192.4.k.a.143.1		44
48.35	even	4		48.4.k.a.11.13	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.k.a.11.10	✓	44	16.3	odd	4
48.4.k.a.11.13	yes	44	48.35	even	4
48.4.k.a.35.10	yes	44	24.5	odd	2
48.4.k.a.35.13	yes	44	8.5	even	2
192.4.k.a.47.1		44	8.3	odd	2
192.4.k.a.47.12		44	24.11	even	2
192.4.k.a.143.1		44	48.29	odd	4
192.4.k.a.143.12		44	16.13	even	4
384.4.k.a.95.11		44	12.11	even	2
384.4.k.a.95.22		44	4.3	odd	2
384.4.k.a.287.11		44	16.5	even	4
384.4.k.a.287.22		44	48.5	odd	4
384.4.k.b.95.1		44	1.1	even	1	trivial
384.4.k.b.95.12		44	3.2	odd	2	inner
384.4.k.b.287.1		44	48.11	even	4	inner
384.4.k.b.287.12		44	16.11	odd	4	inner

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	384.k (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.19396 - 0.151014i) q^{3} +(-4.66675 - 4.66675i) q^{5} +0.405799 q^{7} +(26.9544 + 1.56872i) q^{9} +O(q^{10})\)	\(q+(-5.19396 - 0.151014i) q^{3} +(-4.66675 - 4.66675i) q^{5} +0.405799 q^{7} +(26.9544 + 1.56872i) q^{9} +(5.82048 - 5.82048i) q^{11} +(35.2429 + 35.2429i) q^{13} +(23.5341 + 24.9436i) q^{15} +49.3434i q^{17} +(-108.402 + 108.402i) q^{19} +(-2.10770 - 0.0612813i) q^{21} -130.212i q^{23} -81.4430i q^{25} +(-139.763 - 12.2184i) q^{27} +(172.328 - 172.328i) q^{29} +36.1724i q^{31} +(-31.1103 + 29.3524i) q^{33} +(-1.89376 - 1.89376i) q^{35} +(257.830 - 257.830i) q^{37} +(-177.728 - 188.372i) q^{39} -5.87635 q^{41} +(-170.580 - 170.580i) q^{43} +(-118.468 - 133.110i) q^{45} -181.338 q^{47} -342.835 q^{49} +(7.45153 - 256.287i) q^{51} +(148.916 + 148.916i) q^{53} -54.3254 q^{55} +(579.404 - 546.664i) q^{57} +(567.816 - 567.816i) q^{59} +(-481.074 - 481.074i) q^{61} +(10.9381 + 0.636585i) q^{63} -328.939i q^{65} +(-296.210 + 296.210i) q^{67} +(-19.6638 + 676.314i) q^{69} -533.975i q^{71} -178.769i q^{73} +(-12.2990 + 423.011i) q^{75} +(2.36194 - 2.36194i) q^{77} -528.133i q^{79} +(724.078 + 84.5678i) q^{81} +(-713.160 - 713.160i) q^{83} +(230.273 - 230.273i) q^{85} +(-921.090 + 869.042i) q^{87} +204.984 q^{89} +(14.3015 + 14.3015i) q^{91} +(5.46254 - 187.878i) q^{93} +1011.77 q^{95} +275.409 q^{97} +(166.018 - 147.757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{3} - 8 q^{7}+O(q^{10}) \) 44 * q + 2 * q^3 - 8 * q^7	\( 44 q + 2 q^{3} - 8 q^{7} + 4 q^{13} - 20 q^{19} + 56 q^{21} + 134 q^{27} - 4 q^{33} + 4 q^{37} + 596 q^{39} + 436 q^{43} + 252 q^{45} + 972 q^{49} + 648 q^{51} + 280 q^{55} + 916 q^{61} + 1636 q^{67} - 52 q^{69} - 1454 q^{75} - 4 q^{81} - 736 q^{85} + 1284 q^{87} - 424 q^{91} + 2084 q^{93} - 8 q^{97} - 1196 q^{99}+O(q^{100}) \) 44 * q + 2 * q^3 - 8 * q^7 + 4 * q^13 - 20 * q^19 + 56 * q^21 + 134 * q^27 - 4 * q^33 + 4 * q^37 + 596 * q^39 + 436 * q^43 + 252 * q^45 + 972 * q^49 + 648 * q^51 + 280 * q^55 + 916 * q^61 + 1636 * q^67 - 52 * q^69 - 1454 * q^75 - 4 * q^81 - 736 * q^85 + 1284 * q^87 - 424 * q^91 + 2084 * q^93 - 8 * q^97 - 1196 * q^99

Introduction

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