LMFDB - Embedded newform 384.4.k.b.95.12

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			95.12
Character	$\chi$	$=$	384.95
Dual form			384.4.k.b.287.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.151014 + 5.19396i) q^{3} +(4.66675 + 4.66675i) q^{5} +0.405799 q^{7} +(-26.9544 + 1.56872i) q^{9} +O(q^{10})$	\(q+(0.151014 + 5.19396i) q^{3} +(4.66675 + 4.66675i) q^{5} +0.405799 q^{7} +(-26.9544 + 1.56872i) q^{9} +(-5.82048 + 5.82048i) q^{11} +(35.2429 + 35.2429i) q^{13} +(-23.5341 + 24.9436i) q^{15} -49.3434i q^{17} +(-108.402 + 108.402i) q^{19} +(0.0612813 + 2.10770i) q^{21} +130.212i q^{23} -81.4430i q^{25} +(-12.2184 - 139.763i) q^{27} +(-172.328 + 172.328i) q^{29} +36.1724i q^{31} +(-31.1103 - 29.3524i) q^{33} +(1.89376 + 1.89376i) q^{35} +(257.830 - 257.830i) q^{37} +(-177.728 + 188.372i) q^{39} +5.87635 q^{41} +(-170.580 - 170.580i) q^{43} +(-133.110 - 118.468i) q^{45} +181.338 q^{47} -342.835 q^{49} +(256.287 - 7.45153i) q^{51} +(-148.916 - 148.916i) q^{53} -54.3254 q^{55} +(-579.404 - 546.664i) q^{57} +(-567.816 + 567.816i) q^{59} +(-481.074 - 481.074i) q^{61} +(-10.9381 + 0.636585i) q^{63} +328.939i q^{65} +(-296.210 + 296.210i) q^{67} +(-676.314 + 19.6638i) q^{69} +533.975i q^{71} -178.769i q^{73} +(423.011 - 12.2990i) q^{75} +(-2.36194 + 2.36194i) q^{77} -528.133i q^{79} +(724.078 - 84.5678i) q^{81} +(713.160 + 713.160i) q^{83} +(230.273 - 230.273i) q^{85} +(-921.090 - 869.042i) q^{87} -204.984 q^{89} +(14.3015 + 14.3015i) q^{91} +(-187.878 + 5.46254i) q^{93} -1011.77 q^{95} +275.409 q^{97} +(147.757 - 166.018i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.151014	+	5.19396i	0.0290626	+	0.999578i
$3$	0.151014	+	5.19396i	0.0290626	+	0.999578i
$4$		0			0
$5$	4.66675	+	4.66675i	0.417407	+	0.417407i	0.884309	−	0.466902i	$-0.154630\pi$
$5$	4.66675	+	4.66675i	0.417407	+	0.417407i	−0.466902	+	0.884309i	$0.654630\pi$
$6$		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	−0.782363	−	0.622823i	$-0.785986\pi$
$11$	−5.82048	+	5.82048i	−0.159540	+	0.159540i	0.622823	+	0.782363i	$0.285986\pi$
$12$		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	$-0.885506\pi$
$17$		−	49.3434i		−	0.703972i	0.936005	−	0.351986i	$-0.114494\pi$
$18$		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
$21$	0.0612813	+	2.10770i	0.000636794	+	0.0219018i
$22$		0			0
$23$			130.212i			1.18048i	0.807228	+	0.590240i	$0.200967\pi$
$23$			130.212i			1.18048i	−0.807228	+	0.590240i	$0.799033\pi$
$24$		0			0
$25$		−	81.4430i		−	0.651544i
$26$		0			0
$27$	−12.2184	−	139.763i	−0.0870897	−	0.996200i
$28$		0			0
$29$	−172.328	+	172.328i	−1.10347	+	1.10347i	−0.109478	+	0.993989i	$0.534918\pi$
$29$	−172.328	+	172.328i	−1.10347	+	1.10347i	−0.993989	+	0.109478i	$0.965082\pi$
$30$		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	$-0.496437\pi$
$41$	5.87635			0.0223837			0.0111919	+	0.999937i	$0.496437\pi$
$42$		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
$45$	−133.110	−	118.468i	−0.440953	−	0.392450i
$46$		0			0
$47$	181.338			0.562784			0.281392	−	0.959593i	$-0.409204\pi$
$47$	181.338			0.562784			0.281392	+	0.959593i	$0.409204\pi$
$48$		0			0
$49$	−342.835			−0.999520
$50$		0			0
$51$	256.287	−	7.45153i	0.703675	−	0.0204593i
$52$		0			0
$53$	−148.916	−	148.916i	−0.385947	−	0.385947i	0.487292	−	0.873239i	$-0.337985\pi$
$53$	−148.916	−	148.916i	−0.385947	−	0.385947i	−0.873239	+	0.487292i	$0.837985\pi$
$54$		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	$0.596500\pi$
$59$	−567.816	+	567.816i	−1.25294	+	1.25294i	−0.954396	+	0.298542i	$0.903500\pi$
$60$		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
$69$	−676.314	+	19.6638i	−1.17998	+	0.0343079i
$70$		0			0
$71$			533.975i			0.892552i	0.894895	+	0.446276i	$0.147250\pi$
$71$			533.975i			0.892552i	−0.894895	+	0.446276i	$0.852750\pi$
$72$		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
$75$	423.011	−	12.2990i	0.651268	−	0.0189356i
$76$		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	0.998468	−	0.0553412i	$-0.0176246\pi$
$83$	713.160	+	713.160i	0.943126	+	0.943126i	−0.0553412	+	0.998468i	$0.517625\pi$
$84$		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	$-0.538953\pi$
$89$	−204.984			−0.244138			−0.122069	+	0.992522i	$0.538953\pi$
$90$		0			0
$91$	14.3015	+	14.3015i	0.0164748	+	0.0164748i
$92$		0			0
$93$	−187.878	+	5.46254i	−0.209484	+	0.00609074i
$94$		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
$99$	147.757	−	166.018i	0.150001	−	0.168540i
$100$		0			0
$101$	759.307	+	759.307i	0.748058	+	0.748058i	0.974114	−	0.226056i	$-0.0725834\pi$
$101$	759.307	+	759.307i	0.748058	+	0.748058i	−0.226056	+	0.974114i	$0.572583\pi$
$102$		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	−0.742561	−	0.669778i	$-0.766389\pi$
$107$	−80.5577	+	80.5577i	−0.0727833	+	0.0727833i	0.669778	+	0.742561i	$0.266389\pi$
$108$		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	$0.136571\pi$
$113$			999.419i			0.832013i	−0.909362	+	0.416006i	$0.863429\pi$
$114$		0			0
$115$	−607.665	+	607.665i	−0.492740	+	0.492740i
$116$		0			0
$117$	−1005.24	−	894.664i	−0.794308	−	0.706937i
$118$		0			0
$119$		−	20.0235i		−	0.0154248i
$120$		0			0
$121$			1263.24i			0.949094i
$122$		0			0
$123$	0.887411	+	30.5215i	0.000650530	+	0.0223743i
$124$		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	0.124883	−	0.992171i	$-0.460144\pi$
$131$	−1300.38	−	1300.38i	−0.867288	−	0.867288i	−0.992171	+	0.124883i	$0.960144\pi$
$132$		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	$-0.299442\pi$
$137$	1889.62			1.17840			0.589201	+	0.807986i	$0.299442\pi$
$138$		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
$141$	27.3846	+	941.862i	0.0163560	+	0.562547i
$142$		0			0
$143$	−410.261			−0.239914
$144$		0			0
$145$	−1608.42			−0.921189
$146$		0			0
$147$	−51.7729	−	1780.67i	−0.0290487	−	0.999098i
$148$		0			0
$149$	1223.18	+	1223.18i	0.672527	+	0.672527i	0.958298	−	0.285771i	$-0.0922496\pi$
$149$	1223.18	+	1223.18i	0.672527	+	0.672527i	−0.285771	+	0.958298i	$0.592250\pi$
$150$		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
$165$	−8.20389	−	282.164i	−0.00387074	−	0.133130i
$166$		0			0
$167$			2185.45i			1.01267i	0.862338	+	0.506333i	$0.168999\pi$
$167$			2185.45i			1.01267i	−0.862338	+	0.506333i	$0.831001\pi$
$168$		0			0
$169$			287.118i			0.130686i
$170$		0			0
$171$	2751.85	−	3091.95i	1.23064	−	1.38274i
$172$		0			0
$173$	−217.067	+	217.067i	−0.0953948	+	0.0953948i	−0.753194	−	0.657799i	$-0.771488\pi$
$173$	−217.067	+	217.067i	−0.0953948	+	0.0953948i	0.657799	+	0.753194i	$0.271488\pi$
$174$		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	0.830003	−	0.557758i	$-0.188338\pi$
$179$	651.988	+	651.988i	0.272245	+	0.272245i	−0.557758	+	0.830003i	$0.688338\pi$
$180$		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
$189$	−4.95819	−	56.7157i	−0.00190823	−	0.0218278i
$190$		0			0
$191$	−3594.58			−1.36175			−0.680877	−	0.732398i	$-0.738401\pi$
$191$	−3594.58			−1.36175			−0.680877	+	0.732398i	$0.738401\pi$
$192$		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
$195$	−1708.50	+	49.6744i	−0.627425	+	0.0182423i
$196$		0			0
$197$	3405.92	+	3405.92i	1.23179	+	1.23179i	0.963277	+	0.268510i	$0.0865311\pi$
$197$	3405.92	+	3405.92i	1.23179	+	1.23179i	0.268510	+	0.963277i	$0.413469\pi$
$198$		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
$213$	−2773.44	+	80.6377i	−0.892175	+	0.0259399i
$214$		0			0
$215$		−	1592.11i		−	0.505028i
$216$		0			0
$217$			14.6787i			0.00459197i
$218$		0			0
$219$	928.520	−	26.9966i	0.286500	−	0.00832997i
$220$		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	0.453928	−	0.891038i	$-0.350022\pi$
$227$	−1494.96	−	1494.96i	−0.437111	−	0.437111i	−0.891038	+	0.453928i	$0.850022\pi$
$228$		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	$-0.336030\pi$
$233$	3504.28			0.985293			0.492647	+	0.870229i	$0.336030\pi$
$234$		0			0
$235$	846.259	+	846.259i	0.234910	+	0.234910i
$236$		0			0
$237$	2743.10	−	79.7554i	0.751829	−	0.0218594i
$238$		0			0
$239$	4389.56			1.18802			0.594010	−	0.804458i	$-0.297544\pi$
$239$	4389.56			1.18802			0.594010	+	0.804458i	$0.297544\pi$
$240$		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
$243$	548.587	+	3748.06i	0.144823	+	0.989458i
$244$		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	−0.994699	−	0.102827i	$-0.967211\pi$
$251$	−3546.61	+	3546.61i	−0.891872	+	0.891872i	0.102827	+	0.994699i	$0.467211\pi$
$252$		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	$0.280797\pi$
$257$			6362.20i			1.54421i	−0.635493	+	0.772107i	$0.719203\pi$
$258$		0			0
$259$	104.627	−	104.627i	0.0251012	−	0.0251012i
$260$		0			0
$261$	4374.67	−	4915.34i	1.03749	−	1.16572i
$262$		0			0
$263$		−	1319.81i		−	0.309441i	−0.987958	−	0.154720i	$-0.950552\pi$
$263$		−	1319.81i		−	0.309441i	0.987958	−	0.154720i	$-0.0494477\pi$
$264$		0			0
$265$		−	1389.91i		−	0.322193i
$266$		0			0
$267$	−30.9555	−	1064.68i	−0.00709530	−	0.244035i
$268$		0			0
$269$	−3795.13	+	3795.13i	−0.860198	+	0.860198i	−0.991361	−	0.131163i	$-0.958129\pi$
$269$	−3795.13	+	3795.13i	−0.860198	+	0.860198i	0.131163	+	0.991361i	$0.458129\pi$
$270$		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	$-0.631687\pi$
$281$	−3787.24			−0.804014			−0.402007	+	0.915637i	$0.631687\pi$
$282$		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
$285$	−152.791	−	5255.07i	−0.0317563	−	1.09222i
$286$		0			0
$287$	2.38462			0.000490451
$288$		0			0
$289$	2478.23			0.504424
$290$		0			0
$291$	41.5905	+	1430.46i	0.00837829	+	0.288162i
$292$		0			0
$293$	−3924.62	−	3924.62i	−0.782521	−	0.782521i	0.197734	−	0.980256i	$-0.436642\pi$
$293$	−3924.62	−	3924.62i	−0.782521	−	0.782521i	−0.980256	+	0.197734i	$0.936642\pi$
$294$		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
$309$	−55.4760	−	1908.04i	−0.0102133	−	0.351276i
$310$		0			0
$311$			7577.80i			1.38166i	0.723015	+	0.690832i	$0.242756\pi$
$311$			7577.80i			1.38166i	−0.723015	+	0.690832i	$0.757244\pi$
$312$		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
$315$	−54.0160	−	48.0744i	−0.00966176	−	0.00859900i
$316$		0			0
$317$	145.999	−	145.999i	0.0258679	−	0.0258679i	−0.694055	−	0.719922i	$-0.744177\pi$
$317$	145.999	−	145.999i	0.0258679	−	0.0258679i	0.719922	+	0.694055i	$0.244177\pi$
$318$		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
$333$	−6545.20	+	7354.12i	−1.07710	+	1.21022i
$334$		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
$339$	−5190.94	+	150.926i	−0.831661	+	0.0241805i
$340$		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	−0.0966836	−	0.995315i	$-0.530823\pi$
$347$	5808.66	−	5808.66i	0.898632	−	0.898632i	0.995315	+	0.0966836i	$0.0308235\pi$
$348$		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	$0.0997288\pi$
$353$			4088.22i			0.616413i	−0.951319	+	0.308206i	$0.900271\pi$
$354$		0			0
$355$	−2491.93	+	2491.93i	−0.372557	+	0.372557i
$356$		0			0
$357$	104.001	−	3.02382i	0.0154183	−	0.000448285i
$358$		0			0
$359$		−	2932.72i		−	0.431150i	−0.976487	−	0.215575i	$-0.930837\pi$
$359$		−	2932.72i		−	0.431150i	0.976487	−	0.215575i	$-0.0691626\pi$
$360$		0			0
$361$		−	16642.9i		−	2.42643i
$362$		0			0
$363$	−6561.24	+	190.767i	−0.948693	+	0.0275832i
$364$		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
$381$	440.820	−	12.8168i	0.0592753	−	0.00172343i
$382$		0			0
$383$	3924.08			0.523528			0.261764	−	0.965132i	$-0.415696\pi$
$383$	3924.08			0.523528			0.261764	+	0.965132i	$0.415696\pi$
$384$		0			0
$385$	−22.0452			−0.00291825
$386$		0			0
$387$	4865.48	+	4330.29i	0.639086	+	0.568789i
$388$		0			0
$389$	6777.56	+	6777.56i	0.883383	+	0.883383i	0.993877	−	0.110494i	$-0.0352433\pi$
$389$	6777.56	+	6777.56i	0.883383	+	0.883383i	−0.110494	+	0.993877i	$0.535243\pi$
$390$		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	$-0.811116\pi$
$401$		−	8980.43i		−	1.11836i	0.829047	−	0.559179i	$-0.188884\pi$
$402$		0			0
$403$	−1274.82	+	1274.82i	−0.157576	+	0.157576i
$404$		0			0
$405$	3773.75	+	2984.43i	0.463010	+	0.366167i
$406$		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
$411$	285.359	+	9814.61i	0.0342475	+	1.17790i
$412$		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	0.525118	−	0.851029i	$-0.324021\pi$
$419$	−2795.25	−	2795.25i	−0.325911	−	0.325911i	−0.851029	+	0.525118i	$0.824021\pi$
$420$		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
$429$	−61.9551	−	2130.88i	−0.00697254	−	0.239813i
$430$		0			0
$431$	−5849.75			−0.653765			−0.326882	−	0.945065i	$-0.605998\pi$
$431$	−5849.75			−0.653765			−0.326882	+	0.945065i	$0.605998\pi$
$432$		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
$435$	−242.895	−	8354.09i	−0.0267722	−	0.920800i
$436$		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	−0.0138442	−	0.999904i	$-0.504407\pi$
$443$	9194.09	−	9194.09i	0.986060	−	0.986060i	0.999904	+	0.0138442i	$0.00440687\pi$
$444$		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	$-0.919519\pi$
$449$		−	4760.01i		−	0.500309i	0.968206	−	0.250154i	$-0.0804814\pi$
$450$		0			0
$451$	−34.2032	+	34.2032i	−0.00357110	+	0.00357110i
$452$		0			0
$453$	410.797	+	14128.9i	0.0426069	+	1.46542i
$454$		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
$459$	−6896.38	+	602.894i	−0.701297	+	0.0613087i
$460$		0			0
$461$	−9685.06	+	9685.06i	−0.978478	+	0.978478i	−0.999773	−	0.0212957i	$-0.993221\pi$
$461$	−9685.06	+	9685.06i	−0.978478	+	0.978478i	0.0212957	+	0.999773i	$0.493221\pi$
$462$		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	0.498306	−	0.867001i	$-0.333956\pi$
$467$	−3720.85	−	3720.85i	−0.368695	−	0.368695i	−0.867001	+	0.498306i	$0.833956\pi$
$468$		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
$477$	4247.54	+	3780.33i	0.407718	+	0.362871i
$478$		0			0
$479$	9242.13			0.881594			0.440797	−	0.897607i	$-0.354696\pi$
$479$	9242.13			0.881594			0.440797	+	0.897607i	$0.354696\pi$
$480$		0			0
$481$	18173.4			1.72273
$482$		0			0
$483$	−274.448	+	7.97955i	−0.0258547	+	0.000751722i
$484$		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	−0.574104	−	0.818782i	$-0.694649\pi$
$491$	2662.06	−	2662.06i	0.244678	−	0.244678i	0.818782	+	0.574104i	$0.194649\pi$
$492$		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
$501$	−11351.1	+	330.034i	−1.01224	+	0.0294308i
$502$		0			0
$503$		−	10737.0i		−	0.951764i	−0.879509	−	0.475882i	$-0.842129\pi$
$503$		−	10737.0i		−	0.951764i	0.879509	−	0.475882i	$-0.157871\pi$
$504$		0			0
$505$			7086.98i			0.624488i
$506$		0			0
$507$	−1491.28	+	43.3588i	−0.130631	+	0.00379809i
$508$		0			0
$509$	15372.5	−	15372.5i	1.33865	−	1.33865i	0.441279	−	0.897370i	$-0.354525\pi$
$509$	15372.5	−	15372.5i	1.33865	−	1.33865i	0.897370	−	0.441279i	$-0.145475\pi$
$510$		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	$-0.325176\pi$
$521$	12415.9			1.04405			0.522027	+	0.852929i	$0.325176\pi$
$522$		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
$525$	171.658	−	4.99093i	0.0142700	−	0.000414899i
$526$		0			0
$527$	1784.87			0.147533
$528$		0			0
$529$	−4788.11			−0.393532
$530$		0			0
$531$	14414.4	−	16195.9i	1.17803	−	1.32362i
$532$		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
$549$	13721.7	+	12212.4i	1.06672	+	0.949384i
$550$		0			0
$551$		−	37361.4i		−	2.88865i
$552$		0			0
$553$		−	214.316i		−	0.0164803i
$554$		0			0
$555$	363.409	+	12499.0i	0.0277943	+	0.955954i
$556$		0			0
$557$	9660.53	−	9660.53i	0.734883	−	0.734883i	−0.236700	−	0.971583i	$-0.576066\pi$
$557$	9660.53	−	9660.53i	0.734883	−	0.734883i	0.971583	+	0.236700i	$0.0760658\pi$
$558$		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	0.690492	−	0.723340i	$-0.257394\pi$
$563$	−438.805	−	438.805i	−0.0328480	−	0.0328480i	−0.723340	+	0.690492i	$0.757394\pi$
$564$		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	$-0.696696\pi$
$569$	−15726.9			−1.15871			−0.579356	+	0.815075i	$0.696696\pi$
$570$		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
$573$	−542.832	−	18670.1i	−0.0395761	−	1.36118i
$574$		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
$579$	162.263	+	5580.87i	0.0116467	+	0.400575i
$580$		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	−0.791297	−	0.611432i	$-0.790594\pi$
$587$	−2558.02	+	2558.02i	−0.179865	+	0.179865i	0.611432	+	0.791297i	$0.290594\pi$
$588$		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	$-0.912452\pi$
$593$		−	7843.65i		−	0.543171i	0.962414	−	0.271585i	$-0.0875479\pi$
$594$		0			0
$595$	93.4445	−	93.4445i	0.00643841	−	0.00643841i
$596$		0			0
$597$	359.404	+	12361.3i	0.0246389	+	0.847428i
$598$		0			0
$599$		−	3723.46i		−	0.253984i	−0.991904	−	0.126992i	$-0.959468\pi$
$599$		−	3723.46i		−	0.253984i	0.991904	−	0.126992i	$-0.0405322\pi$
$600$		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
$603$	7519.49	−	8448.83i	0.507823	−	0.570586i
$604$		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	$-0.351502\pi$
$617$	13786.6			0.899561			0.449781	+	0.893139i	$0.351502\pi$
$618$		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
$621$	18198.8	−	1590.97i	1.17599	−	0.102808i
$622$		0			0
$623$	−83.1824			−0.00534933
$624$		0			0
$625$	−1188.32			−0.0760527
$626$		0			0
$627$	6554.26	−	190.564i	0.417467	−	0.0121378i
$628$		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	$-0.969804\pi$
$641$		−	3074.43i		−	0.189443i	0.995504	−	0.0947214i	$-0.0301960\pi$
$642$		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
$645$	8269.35	−	240.431i	0.504815	−	0.0146774i
$646$		0			0
$647$			15254.8i			0.926935i	0.886114	+	0.463467i	$0.153395\pi$
$647$			15254.8i			0.926935i	−0.886114	+	0.463467i	$0.846605\pi$
$648$		0			0
$649$		−	6609.93i		−	0.399788i
$650$		0			0
$651$	−76.2407	+	2.21669i	−0.00459003	+	0.000133455i
$652$		0			0
$653$	−17233.8	+	17233.8i	−1.03279	+	1.03279i	−0.0333418	+	0.999444i	$0.510615\pi$
$653$	−17233.8	+	17233.8i	−1.03279	+	1.03279i	−0.999444	+	0.0333418i	$0.989385\pi$
$654$		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	$-0.981310\pi$
$659$	−17880.8	−	17880.8i	−1.05696	−	1.05696i	−0.0586826	−	0.998277i	$-0.518690\pi$
$660$		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
$669$	−7272.11	+	211.436i	−0.420263	+	0.0122191i
$670$		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
$675$	−11382.7	+	995.099i	−0.649068	+	0.0567428i
$676$		0			0
$677$	−7537.37	−	7537.37i	−0.427894	−	0.427894i	0.460016	−	0.887911i	$-0.347844\pi$
$677$	−7537.37	−	7537.37i	−0.427894	−	0.427894i	−0.887911	+	0.460016i	$0.847844\pi$
$678$		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	−0.239827	−	0.970816i	$-0.577091\pi$
$683$	13047.9	−	13047.9i	0.730988	−	0.730988i	0.970816	+	0.239827i	$0.0770908\pi$
$684$		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
$693$	59.9595	−	67.3700i	0.00328669	−	0.00369289i
$694$		0			0
$695$			2253.80i			0.123009i
$696$		0			0
$697$		−	289.959i		−	0.0157575i
$698$		0			0
$699$	529.196	+	18201.1i	0.0286352	+	0.984877i
$700$		0			0
$701$	−1627.72	+	1627.72i	−0.0877008	+	0.0877008i	−0.749596	−	0.661895i	$-0.769752\pi$
$701$	−1627.72	+	1627.72i	−0.0877008	+	0.0877008i	0.661895	+	0.749596i	$0.269752\pi$
$702$		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
$717$	662.884	+	22799.2i	0.0345270	+	1.18752i
$718$		0			0
$719$	10643.1			0.552044			0.276022	−	0.961151i	$-0.410984\pi$
$719$	10643.1			0.552044			0.276022	+	0.961151i	$0.410984\pi$
$720$		0			0
$721$	−149.073			−0.00770010
$722$		0			0
$723$	686.967	+	23627.5i	0.0353369	+	1.21537i
$724$		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
$741$	−1153.86	−	39685.9i	−0.0572041	−	1.96747i
$742$		0			0
$743$			26472.4i			1.30710i	0.756882	+	0.653552i	$0.226722\pi$
$743$			26472.4i			1.30710i	−0.756882	+	0.653552i	$0.773278\pi$
$744$		0			0
$745$			11416.5i			0.561435i
$746$		0			0
$747$	−20341.5	−	18104.0i	−0.996329	−	0.886737i
$748$		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	$-0.563097\pi$
$761$	−8268.32			−0.393858			−0.196929	+	0.980418i	$0.563097\pi$
$762$		0			0
$763$	231.233	+	231.233i	0.0109714	+	0.0109714i
$764$		0			0
$765$	−5845.63	+	6568.10i	−0.276274	+	0.310419i
$766$		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
$771$	−33045.0	+	960.780i	−1.54356	+	0.0448789i
$772$		0			0
$773$	10938.2	+	10938.2i	0.508952	+	0.508952i	0.914205	−	0.405253i	$-0.132816\pi$
$773$	10938.2	+	10938.2i	0.508952	+	0.508952i	−0.405253	+	0.914205i	$0.632816\pi$
$774$		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
$789$	6855.04	−	199.310i	0.309310	−	0.00899317i
$790$		0			0
$791$			405.563i			0.0182303i
$792$		0			0
$793$		−	33908.8i		−	1.51846i
$794$		0			0
$795$	7219.11	−	209.895i	0.322057	−	0.00936379i
$796$		0			0
$797$	8248.05	−	8248.05i	0.366576	−	0.366576i	−0.499651	−	0.866227i	$-0.666538\pi$
$797$	8248.05	−	8248.05i	0.366576	−	0.366576i	0.866227	+	0.499651i	$0.166538\pi$
$798$		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	$-0.660690\pi$
$809$	−22258.0			−0.967304			−0.483652	+	0.875260i	$0.660690\pi$
$810$		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
$813$	−18943.0	+	550.767i	−0.817172	+	0.0237592i
$814$		0			0
$815$	14654.9			0.629864
$816$		0			0
$817$	36982.4			1.58366
$818$		0			0
$819$	−407.924	−	363.054i	−0.0174042	−	0.0154898i
$820$		0			0
$821$	−7722.94	−	7722.94i	−0.328298	−	0.328298i	0.523641	−	0.851939i	$-0.324573\pi$
$821$	−7722.94	−	7722.94i	−0.328298	−	0.328298i	−0.851939	+	0.523641i	$0.824573\pi$
$822$		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	−0.914546	−	0.404482i	$-0.867452\pi$
$827$	−12130.6	+	12130.6i	−0.510064	+	0.510064i	0.404482	+	0.914546i	$0.367452\pi$
$828$		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
$837$	5055.57	−	441.967i	0.208776	−	0.0182516i
$838$		0			0
$839$			39073.9i			1.60784i	0.594734	+	0.803922i	$0.297257\pi$
$839$			39073.9i			1.60784i	−0.594734	+	0.803922i	$0.702743\pi$
$840$		0			0
$841$		−	35005.1i		−	1.43528i
$842$		0			0
$843$	−571.926	−	19670.8i	−0.0233668	−	0.803674i
$844$		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	$-0.494822\pi$
$857$	816.193			0.0325328			0.0162664	+	0.999868i	$0.494822\pi$
$858$		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
$861$	0.360110	+	12.3856i	1.42538e−5	+	0.000490244i
$862$		0			0
$863$	2649.99			0.104527			0.0522634	−	0.998633i	$-0.483356\pi$
$863$	2649.99			0.104527			0.0522634	+	0.998633i	$0.483356\pi$
$864$		0			0
$865$	−2025.99			−0.0796368
$866$		0			0
$867$	374.248	+	12871.8i	0.0146599	+	0.504211i
$868$		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	$0.0457888\pi$
$881$			7497.28i			0.286708i	−0.989671	+	0.143354i	$0.954211\pi$
$882$		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
$885$	−800.330	−	27526.5i	−0.0303986	−	1.04553i
$886$		0			0
$887$		−	12695.2i		−	0.480567i	−0.970703	−	0.240284i	$-0.922760\pi$
$887$		−	12695.2i		−	0.480567i	0.970703	−	0.240284i	$-0.0772404\pi$
$888$		0			0
$889$		−	34.4409i		−	0.00129934i
$890$		0			0
$891$	−3722.26	+	4706.71i	−0.139955	+	0.176970i
$892$		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
$909$	−21657.8	−	19275.5i	−0.790257	−	0.703331i
$910$		0			0
$911$	−49872.0			−1.81376			−0.906878	−	0.421392i	$-0.861542\pi$
$911$	−49872.0			−1.81376			−0.906878	+	0.421392i	$0.861542\pi$
$912$		0			0
$913$	−8301.87			−0.300933
$914$		0			0
$915$	23321.4	−	678.068i	0.842603	−	0.0244986i
$916$		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	$0.227535\pi$
$929$			37120.6i			1.31097i	−0.755210	+	0.655483i	$0.772465\pi$
$930$		0			0
$931$	37163.9	−	37163.9i	1.30827	−	1.30827i
$932$		0			0
$933$	−39358.8	+	1144.35i	−1.38108	+	0.0401548i
$934$		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
$939$	6226.59	−	181.038i	0.216397	−	0.00629173i
$940$		0			0
$941$	30272.6	−	30272.6i	1.04874	−	1.04874i	0.0499850	−	0.998750i	$-0.484083\pi$
$941$	30272.6	−	30272.6i	1.04874	−	1.04874i	0.998750	−	0.0499850i	$-0.0159174\pi$
$942$		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	0.240625	−	0.970618i	$-0.422648\pi$
$947$	−21273.7	−	21273.7i	−0.729993	−	0.729993i	−0.970618	+	0.240625i	$0.922648\pi$
$948$		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	$-0.274387\pi$
$953$	38299.3			1.30182			0.650911	+	0.759154i	$0.274387\pi$
$954$		0			0
$955$	−16775.0	−	16775.0i	−0.568405	−	0.568405i
$956$		0			0
$957$	10419.4	−	302.944i	0.351946	−	0.0102328i
$958$		0			0
$959$	766.806			0.0258201
$960$		0			0
$961$	28482.6			0.956079
$962$		0			0
$963$	2045.01	−	2297.76i	0.0684315	−	0.0768891i
$964$		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	−0.886720	−	0.462307i	$-0.847022\pi$
$971$	−12841.6	+	12841.6i	−0.424413	+	0.424413i	0.462307	+	0.886720i	$0.347022\pi$
$972$		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	$-0.872092\pi$
$977$		−	23887.3i		−	0.782215i	0.920345	−	0.391107i	$-0.127908\pi$
$978$		0			0
$979$	1193.11	−	1193.11i	0.0389498	−	0.0389498i
$980$		0			0
$981$	−16253.1	−	14465.3i	−0.528973	−	0.470787i
$982$		0			0
$983$		−	32053.2i		−	1.04002i	−0.854160	−	0.520010i	$-0.825928\pi$
$983$		−	32053.2i		−	1.04002i	0.854160	−	0.520010i	$-0.174072\pi$
$984$		0			0
$985$			31789.2i			1.02831i
$986$		0			0
$987$	11.1126	+	382.207i	0.000358378	+	0.0123260i
$988$		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.95.12		44
3.2	odd	2	inner	384.4.k.b.95.1		44
4.3	odd	2		384.4.k.a.95.11		44
8.3	odd	2		192.4.k.a.47.12		44
8.5	even	2		48.4.k.a.35.10	yes	44
12.11	even	2		384.4.k.a.95.22		44
16.3	odd	4		48.4.k.a.11.13	yes	44
16.5	even	4		384.4.k.a.287.22		44
16.11	odd	4	inner	384.4.k.b.287.1		44
16.13	even	4		192.4.k.a.143.1		44
24.5	odd	2		48.4.k.a.35.13	yes	44
24.11	even	2		192.4.k.a.47.1		44
48.5	odd	4		384.4.k.a.287.11		44
48.11	even	4	inner	384.4.k.b.287.12		44
48.29	odd	4		192.4.k.a.143.12		44
48.35	even	4		48.4.k.a.11.10	✓	44

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

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