LMFDB - Embedded newform 275.3.f.c.232.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(232,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.232"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			232.12
Character	$\chi$	$=$	275.232
Dual form			275.3.f.c.243.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.61911 + 2.61911i) q^{2} +(-3.50488 + 3.50488i) q^{3} +9.71948i q^{4} -18.3593 q^{6} +(6.89960 + 6.89960i) q^{7} +(-14.9800 + 14.9800i) q^{8} -15.5684i q^{9} +3.31662 q^{11} +(-34.0656 - 34.0656i) q^{12} +(3.74323 - 3.74323i) q^{13} +36.1416i q^{14} -39.5904 q^{16} +(8.33513 + 8.33513i) q^{17} +(40.7753 - 40.7753i) q^{18} -24.9955i q^{19} -48.3645 q^{21} +(8.68661 + 8.68661i) q^{22} +(26.1029 - 26.1029i) q^{23} -105.006i q^{24} +19.6078 q^{26} +(23.0213 + 23.0213i) q^{27} +(-67.0605 + 67.0605i) q^{28} +31.2821i q^{29} -2.56038 q^{31} +(-43.7718 - 43.7718i) q^{32} +(-11.6244 + 11.6244i) q^{33} +43.6613i q^{34} +151.316 q^{36} +(7.48687 + 7.48687i) q^{37} +(65.4659 - 65.4659i) q^{38} +26.2391i q^{39} -27.3750 q^{41} +(-126.672 - 126.672i) q^{42} +(-33.0693 + 33.0693i) q^{43} +32.2359i q^{44} +136.733 q^{46} +(-17.6292 - 17.6292i) q^{47} +(138.760 - 138.760i) q^{48} +46.2090i q^{49} -58.4273 q^{51} +(36.3822 + 36.3822i) q^{52} +(-47.0174 + 47.0174i) q^{53} +120.591i q^{54} -206.711 q^{56} +(87.6061 + 87.6061i) q^{57} +(-81.9312 + 81.9312i) q^{58} -44.3951i q^{59} +0.515535 q^{61} +(-6.70593 - 6.70593i) q^{62} +(107.416 - 107.416i) q^{63} -70.9247i q^{64} -60.8910 q^{66} +(-5.39673 - 5.39673i) q^{67} +(-81.0132 + 81.0132i) q^{68} +182.975i q^{69} +75.9918 q^{71} +(233.213 + 233.213i) q^{72} +(-21.1155 + 21.1155i) q^{73} +39.2179i q^{74} +242.943 q^{76} +(22.8834 + 22.8834i) q^{77} +(-68.7232 + 68.7232i) q^{78} -80.1381i q^{79} -21.2587 q^{81} +(-71.6982 - 71.6982i) q^{82} +(79.3669 - 79.3669i) q^{83} -470.078i q^{84} -173.224 q^{86} +(-109.640 - 109.640i) q^{87} +(-49.6829 + 49.6829i) q^{88} -104.142i q^{89} +51.6535 q^{91} +(253.707 + 253.707i) q^{92} +(8.97384 - 8.97384i) q^{93} -92.3456i q^{94} +306.830 q^{96} +(103.728 + 103.728i) q^{97} +(-121.027 + 121.027i) q^{98} -51.6344i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 128 q^{16} - 88 q^{21} + 96 q^{26} + 360 q^{31} + 176 q^{36} - 152 q^{41} + 56 q^{46} - 512 q^{51} - 1048 q^{56} + 784 q^{61} - 440 q^{66} + 728 q^{71} + 1704 q^{76} - 568 q^{81} - 328 q^{86}+ \cdots + 1568 q^{96}+O(q^{100}) $ 24 * q - 8 * q^6 - 128 * q^16 - 88 * q^21 + 96 * q^26 + 360 * q^31 + 176 * q^36 - 152 * q^41 + 56 * q^46 - 512 * q^51 - 1048 * q^56 + 784 * q^61 - 440 * q^66 + 728 * q^71 + 1704 * q^76 - 568 * q^81 - 328 * q^86 - 968 * q^91 + 1568 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.61911	+	2.61911i	1.30956	+	1.30956i	0.921735	+	0.387820i	$0.126772\pi$
$2$	2.61911	+	2.61911i	1.30956	+	1.30956i	0.387820	+	0.921735i	$0.373228\pi$
$3$	−3.50488	+	3.50488i	−1.16829	+	1.16829i	−0.185684	+	0.982610i	$0.559450\pi$
$3$	−3.50488	+	3.50488i	−1.16829	+	1.16829i	−0.982610	+	0.185684i	$0.940550\pi$
$4$			9.71948i			2.42987i
$5$		0			0
$5$		0			0
$6$	−18.3593			−3.05989
$7$	6.89960	+	6.89960i	0.985657	+	0.985657i	0.999899	−	0.0142412i	$-0.00453327\pi$
$7$	6.89960	+	6.89960i	0.985657	+	0.985657i	−0.0142412	+	0.999899i	$0.504533\pi$
$8$	−14.9800	+	14.9800i	−1.87249	+	1.87249i
$9$		−	15.5684i		−	1.72982i
$10$		0			0
$11$	3.31662			0.301511
$11$	3.31662			0.301511
$12$	−34.0656	−	34.0656i	−2.83880	−	2.83880i
$13$	3.74323	−	3.74323i	0.287940	−	0.287940i	−0.548325	−	0.836265i	$-0.684734\pi$
$13$	3.74323	−	3.74323i	0.287940	−	0.287940i	0.836265	+	0.548325i	$0.184734\pi$
$14$			36.1416i			2.58155i
$15$		0			0
$16$	−39.5904			−2.47440
$17$	8.33513	+	8.33513i	0.490302	+	0.490302i	0.908401	−	0.418099i	$-0.137304\pi$
$17$	8.33513	+	8.33513i	0.490302	+	0.490302i	−0.418099	+	0.908401i	$0.637304\pi$
$18$	40.7753	−	40.7753i	2.26529	−	2.26529i
$19$		−	24.9955i		−	1.31555i	−0.753214	−	0.657776i	$-0.771498\pi$
$19$		−	24.9955i		−	1.31555i	0.753214	−	0.657776i	$-0.228502\pi$
$20$		0			0
$21$	−48.3645			−2.30307
$22$	8.68661	+	8.68661i	0.394846	+	0.394846i
$23$	26.1029	−	26.1029i	1.13491	−	1.13491i	0.145561	−	0.989349i	$-0.453501\pi$
$23$	26.1029	−	26.1029i	1.13491	−	1.13491i	0.989349	−	0.145561i	$-0.0464987\pi$
$24$		−	105.006i		−	4.37524i
$25$		0			0
$26$	19.6078			0.754148
$27$	23.0213	+	23.0213i	0.852642	+	0.852642i
$28$	−67.0605	+	67.0605i	−2.39502	+	2.39502i
$29$			31.2821i			1.07869i	0.842084	+	0.539346i	$0.181329\pi$
$29$			31.2821i			1.07869i	−0.842084	+	0.539346i	$0.818671\pi$
$30$		0			0
$31$	−2.56038			−0.0825930			−0.0412965	−	0.999147i	$-0.513149\pi$
$31$	−2.56038			−0.0825930			−0.0412965	+	0.999147i	$0.513149\pi$
$32$	−43.7718	−	43.7718i	−1.36787	−	1.36787i
$33$	−11.6244	+	11.6244i	−0.352254	+	0.352254i
$34$			43.6613i			1.28416i
$35$		0			0
$36$	151.316			4.20323
$37$	7.48687	+	7.48687i	0.202348	+	0.202348i	0.801005	−	0.598657i	$-0.204299\pi$
$37$	7.48687	+	7.48687i	0.202348	+	0.202348i	−0.598657	+	0.801005i	$0.704299\pi$
$38$	65.4659	−	65.4659i	1.72279	−	1.72279i
$39$			26.2391i			0.672798i
$40$		0			0
$41$	−27.3750			−0.667684			−0.333842	−	0.942629i	$-0.608345\pi$
$41$	−27.3750			−0.667684			−0.333842	+	0.942629i	$0.608345\pi$
$42$	−126.672	−	126.672i	−3.01600	−	3.01600i
$43$	−33.0693	+	33.0693i	−0.769053	+	0.769053i	−0.977940	−	0.208887i	$-0.933016\pi$
$43$	−33.0693	+	33.0693i	−0.769053	+	0.769053i	0.208887	+	0.977940i	$0.433016\pi$
$44$			32.2359i			0.732633i
$45$		0			0
$46$	136.733			2.97246
$47$	−17.6292	−	17.6292i	−0.375089	−	0.375089i	0.494238	−	0.869327i	$-0.335447\pi$
$47$	−17.6292	−	17.6292i	−0.375089	−	0.375089i	−0.869327	+	0.494238i	$0.835447\pi$
$48$	138.760	−	138.760i	2.89082	−	2.89082i
$49$			46.2090i			0.943041i
$50$		0			0
$51$	−58.4273			−1.14563
$52$	36.3822	+	36.3822i	0.699658	+	0.699658i
$53$	−47.0174	+	47.0174i	−0.887121	+	0.887121i	−0.994246	−	0.107125i	$-0.965836\pi$
$53$	−47.0174	+	47.0174i	−0.887121	+	0.887121i	0.107125	+	0.994246i	$0.465836\pi$
$54$			120.591i			2.23316i
$55$		0			0
$56$	−206.711			−3.69128
$57$	87.6061	+	87.6061i	1.53695	+	1.53695i
$58$	−81.9312	+	81.9312i	−1.41261	+	1.41261i
$59$		−	44.3951i		−	0.752460i	−0.926526	−	0.376230i	$-0.877220\pi$
$59$		−	44.3951i		−	0.752460i	0.926526	−	0.376230i	$-0.122780\pi$
$60$		0			0
$61$	0.515535			0.00845139			0.00422570	−	0.999991i	$-0.498655\pi$
$61$	0.515535			0.00845139			0.00422570	+	0.999991i	$0.498655\pi$
$62$	−6.70593	−	6.70593i	−0.108160	−	0.108160i
$63$	107.416	−	107.416i	1.70501	−	1.70501i
$64$		−	70.9247i		−	1.10820i
$65$		0			0
$66$	−60.8910			−0.922591
$67$	−5.39673	−	5.39673i	−0.0805482	−	0.0805482i	0.665685	−	0.746233i	$-0.268140\pi$
$67$	−5.39673	−	5.39673i	−0.0805482	−	0.0805482i	−0.746233	+	0.665685i	$0.768140\pi$
$68$	−81.0132	+	81.0132i	−1.19137	+	1.19137i
$69$			182.975i			2.65182i
$70$		0			0
$71$	75.9918			1.07031			0.535154	−	0.844755i	$-0.320254\pi$
$71$	75.9918			1.07031			0.535154	+	0.844755i	$0.320254\pi$
$72$	233.213	+	233.213i	3.23907	+	3.23907i
$73$	−21.1155	+	21.1155i	−0.289253	+	0.289253i	−0.836785	−	0.547532i	$-0.815568\pi$
$73$	−21.1155	+	21.1155i	−0.289253	+	0.289253i	0.547532	+	0.836785i	$0.315568\pi$
$74$			39.2179i			0.529971i
$75$		0			0
$76$	242.943			3.19662
$77$	22.8834	+	22.8834i	0.297187	+	0.297187i
$78$	−68.7232	+	68.7232i	−0.881066	+	0.881066i
$79$		−	80.1381i		−	1.01441i	−0.861826	−	0.507203i	$-0.830679\pi$
$79$		−	80.1381i		−	1.01441i	0.861826	−	0.507203i	$-0.169321\pi$
$80$		0			0
$81$	−21.2587			−0.262453
$82$	−71.6982	−	71.6982i	−0.874368	−	0.874368i
$83$	79.3669	−	79.3669i	0.956228	−	0.956228i	−0.0428532	−	0.999081i	$-0.513645\pi$
$83$	79.3669	−	79.3669i	0.956228	−	0.956228i	0.999081	+	0.0428532i	$0.0136448\pi$
$84$		−	470.078i		−	5.59617i
$85$		0			0
$86$	−173.224			−2.01424
$87$	−109.640	−	109.640i	−1.26023	−	1.26023i
$88$	−49.6829	+	49.6829i	−0.564578	+	0.564578i
$89$		−	104.142i		−	1.17014i	−0.810983	−	0.585070i	$-0.801067\pi$
$89$		−	104.142i		−	1.17014i	0.810983	−	0.585070i	$-0.198933\pi$
$90$		0			0
$91$	51.6535			0.567621
$92$	253.707	+	253.707i	2.75768	+	2.75768i
$93$	8.97384	−	8.97384i	0.0964929	−	0.0964929i
$94$		−	92.3456i		−	0.982401i
$95$		0			0
$96$	306.830			3.19614
$97$	103.728	+	103.728i	1.06937	+	1.06937i	0.997408	+	0.0719575i	$0.0229246\pi$
$97$	103.728	+	103.728i	1.06937	+	1.06937i	0.0719575	+	0.997408i	$0.477075\pi$
$98$	−121.027	+	121.027i	−1.23496	+	1.23496i
$99$		−	51.6344i		−	0.521560i
$100$		0			0
$101$	−89.2137			−0.883304			−0.441652	−	0.897186i	$-0.645607\pi$
$101$	−89.2137			−0.883304			−0.441652	+	0.897186i	$0.645607\pi$
$102$	−153.028	−	153.028i	−1.50027	−	1.50027i
$103$	−63.6584	+	63.6584i	−0.618043	+	0.618043i	−0.945029	−	0.326986i	$-0.893967\pi$
$103$	−63.6584	+	63.6584i	−0.618043	+	0.618043i	0.326986	+	0.945029i	$0.393967\pi$
$104$			112.147i			1.07833i
$105$		0			0
$106$	−246.288			−2.32347
$107$	76.6723	+	76.6723i	0.716563	+	0.716563i	0.967900	−	0.251337i	$-0.0808701\pi$
$107$	76.6723	+	76.6723i	0.716563	+	0.716563i	−0.251337	+	0.967900i	$0.580870\pi$
$108$	−223.755	+	223.755i	−2.07181	+	2.07181i
$109$		−	116.933i		−	1.07278i	−0.843969	−	0.536392i	$-0.819787\pi$
$109$		−	116.933i		−	1.07278i	0.843969	−	0.536392i	$-0.180213\pi$
$110$		0			0
$111$	−52.4812			−0.472803
$112$	−273.158	−	273.158i	−2.43891	−	2.43891i
$113$	68.9982	−	68.9982i	0.610604	−	0.610604i	−0.332500	−	0.943103i	$-0.607892\pi$
$113$	68.9982	−	68.9982i	0.610604	−	0.610604i	0.943103	+	0.332500i	$0.107892\pi$
$114$			458.900i			4.02544i
$115$		0			0
$116$	−304.046			−2.62108
$117$	−58.2759	−	58.2759i	−0.498085	−	0.498085i
$118$	116.276	−	116.276i	0.985387	−	0.985387i
$119$			115.018i			0.966540i
$120$		0			0
$121$	11.0000			0.0909091
$122$	1.35024	+	1.35024i	0.0110676	+	0.0110676i
$123$	95.9462	−	95.9462i	0.780050	−	0.780050i
$124$		−	24.8856i		−	0.200690i
$125$		0			0
$126$	562.666			4.46561
$127$	−103.423	−	103.423i	−0.814356	−	0.814356i	0.170928	−	0.985284i	$-0.445323\pi$
$127$	−103.423	−	103.423i	−0.814356	−	0.814356i	−0.985284	+	0.170928i	$0.945323\pi$
$128$	10.6726	−	10.6726i	0.0833797	−	0.0833797i
$129$		−	231.808i		−	1.79696i
$130$		0			0
$131$	106.139			0.810221			0.405110	−	0.914268i	$-0.367233\pi$
$131$	106.139			0.810221			0.405110	+	0.914268i	$0.367233\pi$
$132$	−112.983	−	112.983i	−0.855931	−	0.855931i
$133$	172.459	−	172.459i	1.29668	−	1.29668i
$134$		−	28.2692i		−	0.210965i
$135$		0			0
$136$	−249.720			−1.83618
$137$	91.0791	+	91.0791i	0.664811	+	0.664811i	0.956510	−	0.291699i	$-0.0942206\pi$
$137$	91.0791	+	91.0791i	0.664811	+	0.664811i	−0.291699	+	0.956510i	$0.594221\pi$
$138$	−479.233	+	479.233i	−3.47270	+	3.47270i
$139$		−	86.3737i		−	0.621394i	−0.950509	−	0.310697i	$-0.899438\pi$
$139$		−	86.3737i		−	0.621394i	0.950509	−	0.310697i	$-0.100562\pi$
$140$		0			0
$141$	123.576			0.876429
$142$	199.031	+	199.031i	1.40163	+	1.40163i
$143$	12.4149	−	12.4149i	0.0868173	−	0.0868173i
$144$			616.358i			4.28026i
$145$		0			0
$146$	−110.608			−0.757586
$147$	−161.957	−	161.957i	−1.10175	−	1.10175i
$148$	−72.7685	+	72.7685i	−0.491679	+	0.491679i
$149$			34.0435i			0.228480i	0.993453	+	0.114240i	$0.0364433\pi$
$149$			34.0435i			0.228480i	−0.993453	+	0.114240i	$0.963557\pi$
$150$		0			0
$151$	189.253			1.25333			0.626666	−	0.779288i	$-0.284419\pi$
$151$	189.253			1.25333			0.626666	+	0.779288i	$0.284419\pi$
$152$	374.431	+	374.431i	2.46336	+	2.46336i
$153$	129.764	−	129.764i	0.848133	−	0.848133i
$154$			119.868i			0.778365i
$155$		0			0
$156$	−255.031			−1.63481
$157$	1.71034	+	1.71034i	0.0108939	+	0.0108939i	0.712533	−	0.701639i	$-0.247548\pi$
$157$	1.71034	+	1.71034i	0.0108939	+	0.0108939i	−0.701639	+	0.712533i	$0.747548\pi$
$158$	209.891	−	209.891i	1.32842	−	1.32842i
$159$		−	329.581i		−	2.07283i
$160$		0			0
$161$	360.200			2.23727
$162$	−55.6789	−	55.6789i	−0.343697	−	0.343697i
$163$	−178.008	+	178.008i	−1.09207	+	1.09207i	−0.0967643	+	0.995307i	$0.530849\pi$
$163$	−178.008	+	178.008i	−1.09207	+	1.09207i	−0.995307	+	0.0967643i	$0.969151\pi$
$164$		−	266.071i		−	1.62238i
$165$		0			0
$166$	415.742			2.50447
$167$	−21.9696	−	21.9696i	−0.131554	−	0.131554i	0.638264	−	0.769818i	$-0.279653\pi$
$167$	−21.9696	−	21.9696i	−0.131554	−	0.131554i	−0.769818	+	0.638264i	$0.779653\pi$
$168$	724.499	−	724.499i	4.31249	−	4.31249i
$169$			140.977i			0.834181i
$170$		0			0
$171$	−389.139			−2.27566
$172$	−321.416	−	321.416i	−1.86870	−	1.86870i
$173$	176.125	−	176.125i	1.01806	−	1.01806i	0.0182302	−	0.999834i	$-0.494197\pi$
$173$	176.125	−	176.125i	1.01806	−	1.01806i	0.999834	−	0.0182302i	$-0.00580318\pi$
$174$		−	574.318i		−	3.30068i
$175$		0			0
$176$	−131.306			−0.746059
$177$	155.600	+	155.600i	0.879093	+	0.879093i
$178$	272.761	−	272.761i	1.53236	−	1.53236i
$179$			218.626i			1.22137i	0.791872	+	0.610687i	$0.209107\pi$
$179$			218.626i			1.22137i	−0.791872	+	0.610687i	$0.790893\pi$
$180$		0			0
$181$	−244.373			−1.35013			−0.675063	−	0.737760i	$-0.735884\pi$
$181$	−244.373			−1.35013			−0.675063	+	0.737760i	$0.735884\pi$
$182$	135.286	+	135.286i	0.743332	+	0.743332i
$183$	−1.80689	+	1.80689i	−0.00987371	+	0.00987371i
$184$			782.041i			4.25023i
$185$		0			0
$186$	47.0069			0.252725
$187$	27.6445	+	27.6445i	0.147832	+	0.147832i
$188$	171.347	−	171.347i	0.911418	−	0.911418i
$189$			317.676i			1.68083i
$190$		0			0
$191$	349.751			1.83116			0.915578	−	0.402140i	$-0.131734\pi$
$191$	349.751			1.83116			0.915578	+	0.402140i	$0.131734\pi$
$192$	248.583	+	248.583i	1.29470	+	1.29470i
$193$	−117.795	+	117.795i	−0.610335	+	0.610335i	−0.943033	−	0.332698i	$-0.892041\pi$
$193$	−117.795	+	117.795i	−0.610335	+	0.610335i	0.332698	+	0.943033i	$0.392041\pi$
$194$			543.352i			2.80079i
$195$		0			0
$196$	−449.128			−2.29147
$197$	−0.103007	−	0.103007i	−0.000522877	−	0.000522877i	0.706845	−	0.707368i	$-0.250118\pi$
$197$	−0.103007	−	0.103007i	−0.000522877	−	0.000522877i	−0.707368	+	0.706845i	$0.750118\pi$
$198$	135.236	−	135.236i	0.683011	−	0.683011i
$199$		−	336.943i		−	1.69318i	−0.532246	−	0.846590i	$-0.678652\pi$
$199$		−	336.943i		−	1.69318i	0.532246	−	0.846590i	$-0.321348\pi$
$200$		0			0
$201$	37.8298			0.188208
$202$	−233.661	−	233.661i	−1.15674	−	1.15674i
$203$	−215.834	+	215.834i	−1.06322	+	1.06322i
$204$		−	567.883i		−	2.78374i
$205$		0			0
$206$	−333.457			−1.61872
$207$	−406.380	−	406.380i	−1.96319	−	1.96319i
$208$	−148.196	+	148.196i	−0.712480	+	0.712480i
$209$		−	82.9006i		−	0.396654i
$210$		0			0
$211$	−378.745			−1.79500			−0.897501	−	0.441013i	$-0.854619\pi$
$211$	−378.745			−1.79500			−0.897501	+	0.441013i	$0.854619\pi$
$212$	−456.985	−	456.985i	−2.15559	−	2.15559i
$213$	−266.342	+	266.342i	−1.25043	+	1.25043i
$214$			401.626i			1.87676i
$215$		0			0
$216$	−689.717			−3.19313
$217$	−17.6656	−	17.6656i	−0.0814084	−	0.0814084i
$218$	306.262	−	306.262i	1.40487	−	1.40487i
$219$		−	148.014i		−	0.675865i
$220$		0			0
$221$	62.4006			0.282356
$222$	−137.454	−	137.454i	−0.619162	−	0.619162i
$223$	−149.378	+	149.378i	−0.669856	+	0.669856i	−0.957683	−	0.287826i	$-0.907067\pi$
$223$	−149.378	+	149.378i	−0.669856	+	0.669856i	0.287826	+	0.957683i	$0.407067\pi$
$224$		−	604.016i		−	2.69650i
$225$		0			0
$226$	361.428			1.59924
$227$	−116.922	−	116.922i	−0.515073	−	0.515073i	0.401003	−	0.916077i	$-0.368662\pi$
$227$	−116.922	−	116.922i	−0.515073	−	0.515073i	−0.916077	+	0.401003i	$0.868662\pi$
$228$	−851.486	+	851.486i	−3.73459	+	3.73459i
$229$		−	375.142i		−	1.63817i	−0.573670	−	0.819087i	$-0.694481\pi$
$229$		−	375.142i		−	1.63817i	0.573670	−	0.819087i	$-0.305519\pi$
$230$		0			0
$231$	−160.407			−0.694403
$232$	−468.604	−	468.604i	−2.01984	−	2.01984i
$233$	−257.342	+	257.342i	−1.10447	+	1.10447i	−0.110608	+	0.993864i	$0.535280\pi$
$233$	−257.342	+	257.342i	−1.10447	+	1.10447i	−0.993864	+	0.110608i	$0.964720\pi$
$234$		−	305.262i		−	1.30454i
$235$		0			0
$236$	431.497			1.82838
$237$	280.874	+	280.874i	1.18512	+	1.18512i
$238$	−301.245	+	301.245i	−1.26574	+	1.26574i
$239$			109.604i			0.458595i	0.973356	+	0.229297i	$0.0736428\pi$
$239$			109.604i			0.458595i	−0.973356	+	0.229297i	$0.926357\pi$
$240$		0			0
$241$	105.255			0.436744			0.218372	−	0.975866i	$-0.429925\pi$
$241$	105.255			0.436744			0.218372	+	0.975866i	$0.429925\pi$
$242$	28.8102	+	28.8102i	0.119050	+	0.119050i
$243$	−132.683	+	132.683i	−0.546020	+	0.546020i
$244$			5.01073i			0.0205358i
$245$		0			0
$246$	502.587			2.04304
$247$	−93.5637	−	93.5637i	−0.378800	−	0.378800i
$248$	38.3544	−	38.3544i	0.154655	−	0.154655i
$249$			556.343i			2.23431i
$250$		0			0
$251$	61.9229			0.246705			0.123352	−	0.992363i	$-0.460635\pi$
$251$	61.9229			0.246705			0.123352	+	0.992363i	$0.460635\pi$
$252$	1044.02	+	1044.02i	4.14295	+	4.14295i
$253$	86.5736	−	86.5736i	0.342188	−	0.342188i
$254$		−	541.753i		−	2.13289i
$255$		0			0
$256$	−227.793			−0.889818
$257$	−143.603	−	143.603i	−0.558768	−	0.558768i	0.370188	−	0.928957i	$-0.379293\pi$
$257$	−143.603	−	143.603i	−0.558768	−	0.558768i	−0.928957	+	0.370188i	$0.879293\pi$
$258$	607.130	−	607.130i	2.35322	−	2.35322i
$259$			103.313i			0.398891i
$260$		0			0
$261$	487.011			1.86594
$262$	277.989	+	277.989i	1.06103	+	1.06103i
$263$	94.1800	−	94.1800i	0.358099	−	0.358099i	−0.505013	−	0.863112i	$-0.668512\pi$
$263$	94.1800	−	94.1800i	0.358099	−	0.358099i	0.863112	+	0.505013i	$0.168512\pi$
$264$		−	348.265i		−	1.31919i
$265$		0			0
$266$	903.377			3.39616
$267$	365.007	+	365.007i	1.36707	+	1.36707i
$268$	52.4534	−	52.4534i	0.195722	−	0.195722i
$269$			69.9106i			0.259891i	0.991521	+	0.129945i	$0.0414802\pi$
$269$			69.9106i			0.259891i	−0.991521	+	0.129945i	$0.958520\pi$
$270$		0			0
$271$	−167.707			−0.618845			−0.309423	−	0.950925i	$-0.600136\pi$
$271$	−167.707			−0.618845			−0.309423	+	0.950925i	$0.600136\pi$
$272$	−329.991	−	329.991i	−1.21320	−	1.21320i
$273$	−181.039	+	181.039i	−0.663148	+	0.663148i
$274$			477.093i			1.74121i
$275$		0			0
$276$	−1778.42			−6.44357
$277$	49.9803	+	49.9803i	0.180434	+	0.180434i	0.791545	−	0.611111i	$-0.209277\pi$
$277$	49.9803	+	49.9803i	0.180434	+	0.180434i	−0.611111	+	0.791545i	$0.709277\pi$
$278$	226.222	−	226.222i	0.813749	−	0.813749i
$279$			39.8610i			0.142871i
$280$		0			0
$281$	384.296			1.36760			0.683801	−	0.729669i	$-0.260326\pi$
$281$	384.296			1.36760			0.683801	+	0.729669i	$0.260326\pi$
$282$	323.660	+	323.660i	1.14773	+	1.14773i
$283$	339.698	−	339.698i	1.20035	−	1.20035i	0.226284	−	0.974061i	$-0.427342\pi$
$283$	339.698	−	339.698i	1.20035	−	1.20035i	0.974061	−	0.226284i	$-0.0726578\pi$
$284$			738.601i			2.60071i
$285$		0			0
$286$	65.0319			0.227384
$287$	−188.877	−	188.877i	−0.658107	−	0.658107i
$288$	−681.455	+	681.455i	−2.36616	+	2.36616i
$289$		−	150.051i		−	0.519208i
$290$		0			0
$291$	−727.111			−2.49866
$292$	−205.231	−	205.231i	−0.702848	−	0.702848i
$293$	−363.407	+	363.407i	−1.24030	+	1.24030i	−0.280420	+	0.959877i	$0.590474\pi$
$293$	−363.407	+	363.407i	−1.24030	+	1.24030i	−0.959877	+	0.280420i	$0.909526\pi$
$294$		−	848.367i		−	2.88560i
$295$		0			0
$296$	−224.306			−0.757790
$297$	76.3531	+	76.3531i	0.257081	+	0.257081i
$298$	−89.1637	+	89.1637i	−0.299207	+	0.299207i
$299$		−	195.418i		−	0.653573i
$300$		0			0
$301$	−456.330			−1.51605
$302$	495.675	+	495.675i	1.64131	+	1.64131i
$303$	312.683	−	312.683i	1.03196	−	1.03196i
$304$			989.580i			3.25520i
$305$		0			0
$306$	679.735			2.22136
$307$	−424.575	−	424.575i	−1.38298	−	1.38298i	−0.839277	−	0.543705i	$-0.817021\pi$
$307$	−424.575	−	424.575i	−1.38298	−	1.38298i	−0.543705	−	0.839277i	$-0.682979\pi$
$308$	−222.415	+	222.415i	−0.722126	+	0.722126i
$309$		−	446.230i		−	1.44411i
$310$		0			0
$311$	32.0702			0.103120			0.0515598	−	0.998670i	$-0.483581\pi$
$311$	32.0702			0.103120			0.0515598	+	0.998670i	$0.483581\pi$
$312$	−393.061	−	393.061i	−1.25981	−	1.25981i
$313$	33.8691	−	33.8691i	0.108208	−	0.108208i	−0.650930	−	0.759138i	$-0.725621\pi$
$313$	33.8691	−	33.8691i	0.108208	−	0.108208i	0.759138	+	0.650930i	$0.225621\pi$
$314$			8.95915i			0.0285323i
$315$		0			0
$316$	778.901			2.46488
$317$	−64.3362	−	64.3362i	−0.202953	−	0.202953i	0.598311	−	0.801264i	$-0.295839\pi$
$317$	−64.3362	−	64.3362i	−0.202953	−	0.202953i	−0.801264	+	0.598311i	$0.795839\pi$
$318$	863.208	−	863.208i	2.71449	−	2.71449i
$319$			103.751i			0.325238i
$320$		0			0
$321$	−537.454			−1.67431
$322$	943.403	+	943.403i	2.92982	+	2.92982i
$323$	208.341	−	208.341i	0.645017	−	0.645017i
$324$		−	206.624i		−	0.637727i
$325$		0			0
$326$	−932.444			−2.86026
$327$	409.838	+	409.838i	1.25333	+	1.25333i
$328$	410.077	−	410.077i	1.25023	−	1.25023i
$329$		−	243.269i		−	0.739419i
$330$		0			0
$331$	294.825			0.890711			0.445356	−	0.895354i	$-0.353077\pi$
$331$	294.825			0.890711			0.445356	+	0.895354i	$0.353077\pi$
$332$	771.405	+	771.405i	2.32351	+	2.32351i
$333$	116.558	−	116.558i	0.350025	−	0.350025i
$334$		−	115.082i		−	0.344555i
$335$		0			0
$336$	1914.77			5.69872
$337$	54.3054	+	54.3054i	0.161143	+	0.161143i	0.783073	−	0.621930i	$-0.213651\pi$
$337$	54.3054	+	54.3054i	0.161143	+	0.161143i	−0.621930	+	0.783073i	$0.713651\pi$
$338$	−369.233	+	369.233i	−1.09241	+	1.09241i
$339$			483.661i			1.42673i
$340$		0			0
$341$	−8.49183			−0.0249027
$342$	−1019.20	−	1019.20i	−2.98011	−	2.98011i
$343$	19.2567	−	19.2567i	0.0561421	−	0.0561421i
$344$		−	990.753i		−	2.88010i
$345$		0			0
$346$	922.582			2.66642
$347$	57.3163	+	57.3163i	0.165177	+	0.165177i	0.784855	−	0.619679i	$-0.212737\pi$
$347$	57.3163	+	57.3163i	0.165177	+	0.165177i	−0.619679	+	0.784855i	$0.712737\pi$
$348$	1065.64	−	1065.64i	3.06219	−	3.06219i
$349$			389.915i			1.11724i	0.829425	+	0.558618i	$0.188668\pi$
$349$			389.915i			1.11724i	−0.829425	+	0.558618i	$0.811332\pi$
$350$		0			0
$351$	172.348			0.491020
$352$	−145.175	−	145.175i	−0.412428	−	0.412428i
$353$	58.1497	−	58.1497i	0.164730	−	0.164730i	−0.619928	−	0.784658i	$-0.712838\pi$
$353$	58.1497	−	58.1497i	0.164730	−	0.164730i	0.784658	+	0.619928i	$0.212838\pi$
$354$			815.065i			2.30244i
$355$		0			0
$356$	1012.21			2.84329
$357$	−403.125	−	403.125i	−1.12920	−	1.12920i
$358$	−572.606	+	572.606i	−1.59946	+	1.59946i
$359$			67.8984i			0.189132i	0.995519	+	0.0945660i	$0.0301464\pi$
$359$			67.8984i			0.189132i	−0.995519	+	0.0945660i	$0.969854\pi$
$360$		0			0
$361$	−263.774			−0.730675
$362$	−640.039	−	640.039i	−1.76806	−	1.76806i
$363$	−38.5537	+	38.5537i	−0.106208	+	0.106208i
$364$			502.046i			1.37925i
$365$		0			0
$366$	−9.46488			−0.0258603
$367$	269.376	+	269.376i	0.733994	+	0.733994i	0.971409	−	0.237414i	$-0.0762998\pi$
$367$	269.376	+	269.376i	0.733994	+	0.733994i	−0.237414	+	0.971409i	$0.576300\pi$
$368$	−1033.43	+	1033.43i	−2.80822	+	2.80822i
$369$			426.184i			1.15497i
$370$		0			0
$371$	−648.803			−1.74879
$372$	87.2210	+	87.2210i	0.234465	+	0.234465i
$373$	−216.865	+	216.865i	−0.581406	+	0.581406i	−0.935290	−	0.353883i	$-0.884861\pi$
$373$	−216.865	+	216.865i	−0.581406	+	0.581406i	0.353883	+	0.935290i	$0.384861\pi$
$374$			144.808i			0.387187i
$375$		0			0
$376$	528.169			1.40471
$377$	117.096	+	117.096i	0.310599	+	0.310599i
$378$	−832.029	+	832.029i	−2.20113	+	2.20113i
$379$			18.5329i			0.0488994i	0.999701	+	0.0244497i	$0.00778336\pi$
$379$			18.5329i			0.0488994i	−0.999701	+	0.0244497i	$0.992217\pi$
$380$		0			0
$381$	724.971			1.90281
$382$	916.036	+	916.036i	2.39800	+	2.39800i
$383$	450.630	−	450.630i	1.17658	−	1.17658i	0.195970	−	0.980610i	$-0.437214\pi$
$383$	450.630	−	450.630i	1.17658	−	1.17658i	0.980610	−	0.195970i	$-0.0627856\pi$
$384$			74.8123i			0.194824i
$385$		0			0
$386$	−617.034			−1.59853
$387$	514.835	+	514.835i	1.33032	+	1.33032i
$388$	−1008.19	+	1008.19i	−2.59842	+	2.59842i
$389$			29.1385i			0.0749063i	0.999298	+	0.0374531i	$0.0119245\pi$
$389$			29.1385i			0.0749063i	−0.999298	+	0.0374531i	$0.988076\pi$
$390$		0			0
$391$	435.143			1.11290
$392$	−692.209	−	692.209i	−1.76584	−	1.76584i
$393$	−372.004	+	372.004i	−0.946575	+	0.946575i
$394$		−	0.539573i		−	0.00136947i
$395$		0			0
$396$	501.860			1.26732
$397$	−11.9239	−	11.9239i	−0.0300349	−	0.0300349i	0.691930	−	0.721965i	$-0.256761\pi$
$397$	−11.9239	−	11.9239i	−0.0300349	−	0.0300349i	−0.721965	+	0.691930i	$0.756761\pi$
$398$	882.490	−	882.490i	2.21731	−	2.21731i
$399$			1208.89i			3.02981i
$400$		0			0
$401$	473.602			1.18105			0.590526	−	0.807018i	$-0.298920\pi$
$401$	473.602			1.18105			0.590526	+	0.807018i	$0.298920\pi$
$402$	99.0803	+	99.0803i	0.246468	+	0.246468i
$403$	−9.58409	+	9.58409i	−0.0237819	+	0.0237819i
$404$		−	867.111i		−	2.14631i
$405$		0			0
$406$	−1130.59			−2.78469
$407$	24.8311	+	24.8311i	0.0610102	+	0.0610102i
$408$	875.238	−	875.238i	2.14519	−	2.14519i
$409$			555.961i			1.35932i	0.733528	+	0.679659i	$0.237872\pi$
$409$			555.961i			1.35932i	−0.733528	+	0.679659i	$0.762128\pi$
$410$		0			0
$411$	−638.443			−1.55339
$412$	−618.727	−	618.727i	−1.50176	−	1.50176i
$413$	306.309	−	306.309i	0.741667	−	0.741667i
$414$		−	2128.71i		−	5.14181i
$415$		0			0
$416$	−327.695			−0.787729
$417$	302.729	+	302.729i	0.725970	+	0.725970i
$418$	217.126	−	217.126i	0.519440	−	0.519440i
$419$			539.043i			1.28650i	0.765656	+	0.643250i	$0.222414\pi$
$419$			539.043i			1.28650i	−0.765656	+	0.643250i	$0.777586\pi$
$420$		0			0
$421$	191.827			0.455645			0.227823	−	0.973703i	$-0.426839\pi$
$421$	191.827			0.455645			0.227823	+	0.973703i	$0.426839\pi$
$422$	−991.976	−	991.976i	−2.35065	−	2.35065i
$423$	−274.458	+	274.458i	−0.648836	+	0.648836i
$424$		−	1408.64i		−	3.32226i
$425$		0			0
$426$	−1395.16			−3.27502
$427$	3.55699	+	3.55699i	0.00833018	+	0.00833018i
$428$	−745.215	+	745.215i	−1.74116	+	1.74116i
$429$			87.0253i			0.202856i
$430$		0			0
$431$	188.577			0.437533			0.218766	−	0.975777i	$-0.429797\pi$
$431$	188.577			0.437533			0.218766	+	0.975777i	$0.429797\pi$
$432$	−911.423	−	911.423i	−2.10978	−	2.10978i
$433$	−50.5654	+	50.5654i	−0.116779	+	0.116779i	−0.763081	−	0.646302i	$-0.776315\pi$
$433$	−50.5654	+	50.5654i	−0.116779	+	0.116779i	0.646302	+	0.763081i	$0.276315\pi$
$434$		−	92.5365i		−	0.213218i
$435$		0			0
$436$	1136.53			2.60673
$437$	−652.455	−	652.455i	−1.49303	−	1.49303i
$438$	387.666	−	387.666i	0.885083	−	0.885083i
$439$			430.188i			0.979927i	0.871743	+	0.489964i	$0.162990\pi$
$439$			430.188i			0.979927i	−0.871743	+	0.489964i	$0.837010\pi$
$440$		0			0
$441$	719.399			1.63129
$442$	163.434	+	163.434i	0.369760	+	0.369760i
$443$	95.3705	−	95.3705i	0.215283	−	0.215283i	−0.591224	−	0.806507i	$-0.701355\pi$
$443$	95.3705	−	95.3705i	0.215283	−	0.215283i	0.806507	+	0.591224i	$0.201355\pi$
$444$		−	510.090i		−	1.14885i
$445$		0			0
$446$	−782.475			−1.75443
$447$	−119.318	−	119.318i	−0.266932	−	0.266932i
$448$	489.352	−	489.352i	1.09230	−	1.09230i
$449$		−	551.659i		−	1.22864i	−0.789057	−	0.614320i	$-0.789431\pi$
$449$		−	551.659i		−	1.22864i	0.789057	−	0.614320i	$-0.210569\pi$
$450$		0			0
$451$	−90.7927			−0.201314
$452$	670.627	+	670.627i	1.48369	+	1.48369i
$453$	−663.310	+	663.310i	−1.46426	+	1.46426i
$454$		−	612.461i		−	1.34903i
$455$		0			0
$456$	−2624.67			−5.75586
$457$	228.779	+	228.779i	0.500610	+	0.500610i	0.911627	−	0.411018i	$-0.134827\pi$
$457$	228.779	+	228.779i	0.500610	+	0.500610i	−0.411018	+	0.911627i	$0.634827\pi$
$458$	982.538	−	982.538i	2.14528	−	2.14528i
$459$			383.772i			0.836104i
$460$		0			0
$461$	15.5314			0.0336906			0.0168453	−	0.999858i	$-0.494638\pi$
$461$	15.5314			0.0336906			0.0168453	+	0.999858i	$0.494638\pi$
$462$	−420.124	−	420.124i	−0.909359	−	0.909359i
$463$	464.253	−	464.253i	1.00271	−	1.00271i	0.00270954	−	0.999996i	$-0.499138\pi$
$463$	464.253	−	464.253i	1.00271	−	1.00271i	0.999996	−	0.00270954i	$-0.000862474\pi$
$464$		−	1238.47i		−	2.66911i
$465$		0			0
$466$	−1348.01			−2.89274
$467$	−152.863	−	152.863i	−0.327330	−	0.327330i	0.524241	−	0.851570i	$-0.324349\pi$
$467$	−152.863	−	152.863i	−0.327330	−	0.327330i	−0.851570	+	0.524241i	$0.824349\pi$
$468$	566.412	−	566.412i	1.21028	−	1.21028i
$469$		−	74.4705i		−	0.158786i
$470$		0			0
$471$	−11.9891			−0.0254545
$472$	665.037	+	665.037i	1.40898	+	1.40898i
$473$	−109.678	+	109.678i	−0.231878	+	0.231878i
$474$			1471.28i			3.10397i
$475$		0			0
$476$	−1117.92			−2.34857
$477$	731.984	+	731.984i	1.53456	+	1.53456i
$478$	−287.065	+	287.065i	−0.600555	+	0.600555i
$479$			161.273i			0.336686i	0.985728	+	0.168343i	$0.0538416\pi$
$479$			161.273i			0.336686i	−0.985728	+	0.168343i	$0.946158\pi$
$480$		0			0
$481$	56.0501			0.116528
$482$	275.675	+	275.675i	0.571941	+	0.571941i
$483$	−1262.46	+	1262.46i	−2.61378	+	2.61378i
$484$			106.914i			0.220897i
$485$		0			0
$486$	−695.022			−1.43009
$487$	−634.318	−	634.318i	−1.30250	−	1.30250i	−0.926701	−	0.375800i	$-0.877368\pi$
$487$	−634.318	−	634.318i	−1.30250	−	1.30250i	−0.375800	−	0.926701i	$-0.622632\pi$
$488$	−7.72269	+	7.72269i	−0.0158252	+	0.0158252i
$489$		−	1247.79i		−	2.55172i
$490$		0			0
$491$	−8.03136			−0.0163572			−0.00817858	−	0.999967i	$-0.502603\pi$
$491$	−8.03136			−0.0163572			−0.00817858	+	0.999967i	$0.502603\pi$
$492$	932.547	+	932.547i	1.89542	+	1.89542i
$493$	−260.740	+	260.740i	−0.528885	+	0.528885i
$494$		−	490.107i		−	0.992120i
$495$		0			0
$496$	101.367			0.204368
$497$	524.313	+	524.313i	1.05496	+	1.05496i
$498$	−1457.12	+	1457.12i	−2.92595	+	2.92595i
$499$		−	812.378i		−	1.62801i	−0.580856	−	0.814006i	$-0.697282\pi$
$499$		−	812.378i		−	1.62801i	0.580856	−	0.814006i	$-0.302718\pi$
$500$		0			0
$501$	154.001			0.307388
$502$	162.183	+	162.183i	0.323074	+	0.323074i
$503$	493.267	−	493.267i	0.980650	−	0.980650i	−0.0191662	−	0.999816i	$-0.506101\pi$
$503$	493.267	−	493.267i	0.980650	−	0.980650i	0.999816	+	0.0191662i	$0.00610116\pi$
$504$			3218.16i			6.38524i
$505$		0			0
$506$	453.492			0.896229
$507$	−494.106	−	494.106i	−0.974568	−	0.974568i
$508$	1005.22	−	1005.22i	1.97878	−	1.97878i
$509$			269.355i			0.529184i	0.964360	+	0.264592i	$0.0852373\pi$
$509$			269.355i			0.529184i	−0.964360	+	0.264592i	$0.914763\pi$
$510$		0			0
$511$	−291.377			−0.570209
$512$	−639.307	−	639.307i	−1.24865	−	1.24865i
$513$	575.429	−	575.429i	1.12169	−	1.12169i
$514$		−	752.227i		−	1.46348i
$515$		0			0
$516$	2253.05			4.36638
$517$	−58.4694	−	58.4694i	−0.113094	−	0.113094i
$518$	−270.588	+	270.588i	−0.522370	+	0.522370i
$519$			1234.59i			2.37879i
$520$		0			0
$521$	−122.573			−0.235265			−0.117633	−	0.993057i	$-0.537531\pi$
$521$	−122.573			−0.235265			−0.117633	+	0.993057i	$0.537531\pi$
$522$	1275.54	+	1275.54i	2.44355	+	2.44355i
$523$	−13.3025	+	13.3025i	−0.0254349	+	0.0254349i	−0.719710	−	0.694275i	$-0.755725\pi$
$523$	−13.3025	+	13.3025i	−0.0254349	+	0.0254349i	0.694275	+	0.719710i	$0.255725\pi$
$524$			1031.61i			1.96873i
$525$		0			0
$526$	493.336			0.937901
$527$	−21.3411	−	21.3411i	−0.0404955	−	0.0404955i
$528$	460.213	−	460.213i	0.871616	−	0.871616i
$529$		−	833.726i		−	1.57604i
$530$		0			0
$531$	−691.159			−1.30162
$532$	1676.21	+	1676.21i	3.15077	+	3.15077i
$533$	−102.471	+	102.471i	−0.192253	+	0.192253i
$534$			1911.99i			3.58050i
$535$		0			0
$536$	161.685			0.301652
$537$	−766.258	−	766.258i	−1.42692	−	1.42692i
$538$	−183.104	+	183.104i	−0.340341	+	0.340341i
$539$			153.258i			0.284338i
$540$		0			0
$541$	−282.495			−0.522171			−0.261086	−	0.965316i	$-0.584081\pi$
$541$	−282.495			−0.522171			−0.261086	+	0.965316i	$0.584081\pi$
$542$	−439.243	−	439.243i	−0.810412	−	0.810412i
$543$	856.497	−	856.497i	1.57734	−	1.57734i
$544$		−	729.687i		−	1.34134i
$545$		0			0
$546$	−948.325			−1.73686
$547$	−615.503	−	615.503i	−1.12523	−	1.12523i	−0.990942	−	0.134292i	$-0.957124\pi$
$547$	−615.503	−	615.503i	−1.12523	−	1.12523i	−0.134292	−	0.990942i	$-0.542876\pi$
$548$	−885.242	+	885.242i	−1.61540	+	1.61540i
$549$		−	8.02604i		−	0.0146194i
$550$		0			0
$551$	781.910			1.41907
$552$	−2740.96	−	2740.96i	−4.96551	−	4.96551i
$553$	552.921	−	552.921i	0.999857	−	0.999857i
$554$			261.808i			0.472577i
$555$		0			0
$556$	839.508			1.50991
$557$	−274.816	−	274.816i	−0.493386	−	0.493386i	0.415985	−	0.909371i	$-0.363437\pi$
$557$	−274.816	−	274.816i	−0.493386	−	0.493386i	−0.909371	+	0.415985i	$0.863437\pi$
$558$	−104.400	+	104.400i	−0.187097	+	0.187097i
$559$			247.572i			0.442883i
$560$		0			0
$561$	−193.781			−0.345421
$562$	1006.51	+	1006.51i	1.79095	+	1.79095i
$563$	49.6753	−	49.6753i	0.0882331	−	0.0882331i	−0.661613	−	0.749846i	$-0.730128\pi$
$563$	49.6753	−	49.6753i	0.0882331	−	0.0882331i	0.749846	+	0.661613i	$0.230128\pi$
$564$			1201.10i			2.12961i
$565$		0			0
$566$	1779.41			3.14384
$567$	−146.677	−	146.677i	−0.258689	−	0.258689i
$568$	−1138.35	+	1138.35i	−2.00414	+	2.00414i
$569$		−	121.110i		−	0.212847i	−0.994321	−	0.106423i	$-0.966060\pi$
$569$		−	121.110i		−	0.212847i	0.994321	−	0.106423i	$-0.0339399\pi$
$570$		0			0
$571$	−446.350			−0.781699			−0.390849	−	0.920455i	$-0.627819\pi$
$571$	−446.350			−0.781699			−0.390849	+	0.920455i	$0.627819\pi$
$572$	120.666	+	120.666i	0.210955	+	0.210955i
$573$	−1225.83	+	1225.83i	−2.13933	+	2.13933i
$574$		−	989.378i		−	1.72366i
$575$		0			0
$576$	−1104.18			−1.91698
$577$	−484.478	−	484.478i	−0.839650	−	0.839650i	0.149162	−	0.988813i	$-0.452342\pi$
$577$	−484.478	−	484.478i	−0.839650	−	0.839650i	−0.988813	+	0.149162i	$0.952342\pi$
$578$	393.000	−	393.000i	0.679932	−	0.679932i
$579$		−	825.712i		−	1.42610i
$580$		0			0
$581$	1095.20			1.88503
$582$	−1904.38	−	1904.38i	−3.27214	−	3.27214i
$583$	−155.939	+	155.939i	−0.267477	+	0.267477i
$584$		−	632.618i		−	1.08325i
$585$		0			0
$586$	−1903.61			−3.24848
$587$	702.982	+	702.982i	1.19758	+	1.19758i	0.974888	+	0.222696i	$0.0714857\pi$
$587$	702.982	+	702.982i	1.19758	+	1.19758i	0.222696	+	0.974888i	$0.428514\pi$
$588$	1574.14	−	1574.14i	2.67711	−	2.67711i
$589$			63.9980i			0.108655i
$590$		0			0
$591$	0.722053			0.00122175
$592$	−296.408	−	296.408i	−0.500689	−	0.500689i
$593$	487.169	−	487.169i	0.821533	−	0.821533i	−0.164795	−	0.986328i	$-0.552696\pi$
$593$	487.169	−	487.169i	0.821533	−	0.821533i	0.986328	+	0.164795i	$0.0526962\pi$
$594$			399.955i			0.673324i
$595$		0			0
$596$	−330.885			−0.555176
$597$	1180.94	+	1180.94i	1.97813	+	1.97813i
$598$	511.822	−	511.822i	0.855890	−	0.855890i
$599$		−	448.859i		−	0.749347i	−0.927157	−	0.374673i	$-0.877755\pi$
$599$		−	448.859i		−	0.749347i	0.927157	−	0.374673i	$-0.122245\pi$
$600$		0			0
$601$	−46.2237			−0.0769113			−0.0384556	−	0.999260i	$-0.512244\pi$
$601$	−46.2237			−0.0769113			−0.0384556	+	0.999260i	$0.512244\pi$
$602$	−1195.18	−	1195.18i	−1.98535	−	1.98535i
$603$	−84.0182	+	84.0182i	−0.139334	+	0.139334i
$604$			1839.44i			3.04543i
$605$		0			0
$606$	1637.90			2.70281
$607$	−388.855	−	388.855i	−0.640618	−	0.640618i	0.310089	−	0.950707i	$-0.399641\pi$
$607$	−388.855	−	388.855i	−0.640618	−	0.640618i	−0.950707	+	0.310089i	$0.899641\pi$
$608$	−1094.10	+	1094.10i	−1.79950	+	1.79950i
$609$		−	1512.94i		−	2.48431i
$610$		0			0
$611$	−131.980			−0.216007
$612$	1261.24	+	1261.24i	2.06085	+	2.06085i
$613$	−488.824	+	488.824i	−0.797430	+	0.797430i	−0.982690	−	0.185260i	$-0.940687\pi$
$613$	−488.824	+	488.824i	−0.797430	+	0.797430i	0.185260	+	0.982690i	$0.440687\pi$
$614$		−	2224.02i		−	3.62218i
$615$		0			0
$616$	−685.584			−1.11296
$617$	−476.985	−	476.985i	−0.773071	−	0.773071i	0.205571	−	0.978642i	$-0.434095\pi$
$617$	−476.985	−	476.985i	−0.773071	−	0.773071i	−0.978642	+	0.205571i	$0.934095\pi$
$618$	1168.73	−	1168.73i	1.89114	−	1.89114i
$619$		−	377.724i		−	0.610217i	−0.952318	−	0.305108i	$-0.901307\pi$
$619$		−	377.724i		−	0.610217i	0.952318	−	0.305108i	$-0.0986927\pi$
$620$		0			0
$621$	1201.85			1.93534
$622$	83.9954	+	83.9954i	0.135041	+	0.135041i
$623$	718.541	−	718.541i	1.15336	−	1.15336i
$624$		−	1038.82i		−	1.66477i
$625$		0			0
$626$	177.414			0.283409
$627$	290.557	+	290.557i	0.463408	+	0.463408i
$628$	−16.6236	+	16.6236i	−0.0264708	+	0.0264708i
$629$			124.808i			0.198423i
$630$		0			0
$631$	−404.178			−0.640536			−0.320268	−	0.947327i	$-0.603773\pi$
$631$	−404.178			−0.640536			−0.320268	+	0.947327i	$0.603773\pi$
$632$	1200.47	+	1200.47i	1.89947	+	1.89947i
$633$	1327.46	−	1327.46i	2.09709	−	2.09709i
$634$		−	337.007i		−	0.531557i
$635$		0			0
$636$	3203.35			5.03672
$637$	172.971	+	172.971i	0.271540	+	0.271540i
$638$	−271.735	+	271.735i	−0.425917	+	0.425917i
$639$		−	1183.07i		−	1.85144i
$640$		0			0
$641$	−811.838			−1.26652			−0.633259	−	0.773940i	$-0.718283\pi$
$641$	−811.838			−1.26652			−0.633259	+	0.773940i	$0.718283\pi$
$642$	−1407.65	−	1407.65i	−2.19260	−	2.19260i
$643$	−412.116	+	412.116i	−0.640927	+	0.640927i	−0.950783	−	0.309857i	$-0.899719\pi$
$643$	−412.116	+	412.116i	−0.640927	+	0.640927i	0.309857	+	0.950783i	$0.399719\pi$
$644$			3500.95i			5.43626i
$645$		0			0
$646$	1091.33			1.68937
$647$	539.084	+	539.084i	0.833205	+	0.833205i	0.987954	−	0.154749i	$-0.0494567\pi$
$647$	539.084	+	539.084i	0.833205	+	0.833205i	−0.154749	+	0.987954i	$0.549457\pi$
$648$	318.454	−	318.454i	0.491442	−	0.491442i
$649$		−	147.242i		−	0.226875i
$650$		0			0
$651$	123.832			0.190218
$652$	−1730.14	−	1730.14i	−2.65359	−	2.65359i
$653$	−266.585	+	266.585i	−0.408247	+	0.408247i	−0.881127	−	0.472880i	$-0.843215\pi$
$653$	−266.585	+	266.585i	−0.408247	+	0.408247i	0.472880	+	0.881127i	$0.343215\pi$
$654$			2146.82i			3.28260i
$655$		0			0
$656$	1083.79			1.65212
$657$	328.733	+	328.733i	0.500355	+	0.500355i
$658$	637.148	−	637.148i	0.968310	−	0.968310i
$659$		−	219.013i		−	0.332342i	−0.986097	−	0.166171i	$-0.946860\pi$
$659$		−	219.013i		−	0.332342i	0.986097	−	0.166171i	$-0.0531403\pi$
$660$		0			0
$661$	−988.567			−1.49556			−0.747781	−	0.663945i	$-0.768881\pi$
$661$	−988.567			−1.49556			−0.747781	+	0.663945i	$0.768881\pi$
$662$	772.180	+	772.180i	1.16644	+	1.16644i
$663$	−218.707	+	218.707i	−0.329874	+	0.329874i
$664$			2377.83i			3.58106i
$665$		0			0
$666$	610.558			0.916754
$667$	816.554	+	816.554i	1.22422	+	1.22422i
$668$	213.533	−	213.533i	0.319660	−	0.319660i
$669$		−	1047.10i		−	1.56518i
$670$		0			0
$671$	1.70984			0.00254819
$672$	2117.00	+	2117.00i	3.15030	+	3.15030i
$673$	−59.4777	+	59.4777i	−0.0883770	+	0.0883770i	−0.749913	−	0.661536i	$-0.769905\pi$
$673$	−59.4777	+	59.4777i	−0.0883770	+	0.0883770i	0.661536	+	0.749913i	$0.269905\pi$
$674$			284.463i			0.422053i
$675$		0			0
$676$	−1370.22			−2.02695
$677$	34.1769	+	34.1769i	0.0504829	+	0.0504829i	0.731898	−	0.681415i	$-0.238635\pi$
$677$	34.1769	+	34.1769i	0.0504829	+	0.0504829i	−0.681415	+	0.731898i	$0.738635\pi$
$678$	−1266.76	+	1266.76i	−1.86838	+	1.86838i
$679$			1431.37i			2.10806i
$680$		0			0
$681$	819.592			1.20351
$682$	−22.2410	−	22.2410i	−0.0326115	−	0.0326115i
$683$	−562.268	+	562.268i	−0.823233	+	0.823233i	−0.986570	−	0.163337i	$-0.947774\pi$
$683$	−562.268	+	562.268i	−0.823233	+	0.823233i	0.163337	+	0.986570i	$0.447774\pi$
$684$		−	3782.23i		−	5.52957i
$685$		0			0
$686$	100.871			0.147042
$687$	1314.83	+	1314.83i	1.91387	+	1.91387i
$688$	1309.23	−	1309.23i	1.90294	−	1.90294i
$689$			351.994i			0.510876i
$690$		0			0
$691$	94.1456			0.136245			0.0681227	−	0.997677i	$-0.478299\pi$
$691$	94.1456			0.136245			0.0681227	+	0.997677i	$0.478299\pi$
$692$	1711.84	+	1711.84i	2.47376	+	2.47376i
$693$	356.257	−	356.257i	0.514079	−	0.514079i
$694$			300.235i			0.432616i
$695$		0			0
$696$	3284.80			4.71954
$697$	−228.174	−	228.174i	−0.327367	−	0.327367i
$698$	−1021.23	+	1021.23i	−1.46308	+	1.46308i
$699$		−	1803.91i		−	2.58070i
$700$		0			0
$701$	212.516			0.303161			0.151580	−	0.988445i	$-0.451564\pi$
$701$	212.516			0.303161			0.151580	+	0.988445i	$0.451564\pi$
$702$	451.399	+	451.399i	0.643018	+	0.643018i
$703$	187.138	−	187.138i	0.266199	−	0.266199i
$704$		−	235.231i		−	0.334135i
$705$		0			0
$706$	304.601			0.431446
$707$	−615.539	−	615.539i	−0.870635	−	0.870635i
$708$	−1512.35	+	1512.35i	−2.13608	+	2.13608i
$709$		−	440.572i		−	0.621399i	−0.950508	−	0.310700i	$-0.899437\pi$
$709$		−	440.572i		−	0.621399i	0.950508	−	0.310700i	$-0.100563\pi$
$710$		0			0
$711$	−1247.62			−1.75474
$712$	1560.05	+	1560.05i	2.19108	+	2.19108i
$713$	−66.8335	+	66.8335i	−0.0937357	+	0.0937357i
$714$		−	2111.66i		−	2.95750i
$715$		0			0
$716$	−2124.93			−2.96778
$717$	−384.149	−	384.149i	−0.535773	−	0.535773i
$718$	−177.833	+	177.833i	−0.247679	+	0.247679i
$719$		−	787.071i		−	1.09467i	−0.836912	−	0.547337i	$-0.815642\pi$
$719$		−	787.071i		−	1.09467i	0.836912	−	0.547337i	$-0.184358\pi$
$720$		0			0
$721$	−878.435			−1.21836
$722$	−690.852	−	690.852i	−0.956859	−	0.956859i
$723$	−368.907	+	368.907i	−0.510245	+	0.510245i
$724$		−	2375.18i		−	3.28063i
$725$		0			0
$726$	−201.953			−0.278172
$727$	−883.293	−	883.293i	−1.21498	−	1.21498i	−0.969367	−	0.245616i	$-0.921010\pi$
$727$	−883.293	−	883.293i	−1.21498	−	1.21498i	−0.245616	−	0.969367i	$-0.578990\pi$
$728$	−773.768	+	773.768i	−1.06287	+	1.06287i
$729$		−	1121.40i		−	1.53828i
$730$		0			0
$731$	−551.274			−0.754137
$732$	−17.5620	−	17.5620i	−0.0239918	−	0.0239918i
$733$	351.167	−	351.167i	0.479082	−	0.479082i	−0.425756	−	0.904838i	$-0.639992\pi$
$733$	351.167	−	351.167i	0.479082	−	0.479082i	0.904838	+	0.425756i	$0.139992\pi$
$734$			1411.05i			1.92241i
$735$		0			0
$736$	−2285.14			−3.10481
$737$	−17.8989	−	17.8989i	−0.0242862	−	0.0242862i
$738$	−1116.22	+	1116.22i	−1.51250	+	1.51250i
$739$			315.768i			0.427291i	0.976911	+	0.213646i	$0.0685338\pi$
$739$			315.768i			0.427291i	−0.976911	+	0.213646i	$0.931466\pi$
$740$		0			0
$741$	655.859			0.885100
$742$	−1699.29	−	1699.29i	−2.29014	−	2.29014i
$743$	−499.908	+	499.908i	−0.672824	+	0.672824i	−0.958366	−	0.285542i	$-0.907826\pi$
$743$	−499.908	+	499.908i	−0.672824	+	0.672824i	0.285542	+	0.958366i	$0.407826\pi$
$744$			268.855i			0.361365i
$745$		0			0
$746$	−1135.98			−1.52277
$747$	−1235.61	−	1235.61i	−1.65410	−	1.65410i
$748$	−268.690	+	268.690i	−0.359212	+	0.359212i
$749$			1058.02i			1.41257i
$750$		0			0
$751$	50.9789			0.0678813			0.0339407	−	0.999424i	$-0.489194\pi$
$751$	50.9789			0.0678813			0.0339407	+	0.999424i	$0.489194\pi$
$752$	697.947	+	697.947i	0.928121	+	0.928121i
$753$	−217.032	+	217.032i	−0.288224	+	0.288224i
$754$			613.374i			0.813494i
$755$		0			0
$756$	−3087.65			−4.08419
$757$	−765.183	−	765.183i	−1.01081	−	1.01081i	−0.999941	−	0.0108684i	$-0.996540\pi$
$757$	−765.183	−	765.183i	−1.01081	−	1.01081i	−0.0108684	−	0.999941i	$-0.503460\pi$
$758$	−48.5397	+	48.5397i	−0.0640365	+	0.0640365i
$759$			606.860i			0.799553i
$760$		0			0
$761$	−92.9924			−0.122198			−0.0610988	−	0.998132i	$-0.519460\pi$
$761$	−92.9924			−0.122198			−0.0610988	+	0.998132i	$0.519460\pi$
$762$	1898.78	+	1898.78i	2.49184	+	2.49184i
$763$	806.794	−	806.794i	1.05740	−	1.05740i
$764$			3399.40i			4.44947i
$765$		0			0
$766$	2360.50			3.08159
$767$	−166.181	−	166.181i	−0.216664	−	0.216664i
$768$	798.389	−	798.389i	1.03957	−	1.03957i
$769$			1381.20i			1.79610i	0.439892	+	0.898051i	$0.355017\pi$
$769$			1381.20i			1.79610i	−0.439892	+	0.898051i	$0.644983\pi$
$770$		0			0
$771$	1006.63			1.30561
$772$	−1144.90	−	1144.90i	−1.48303	−	1.48303i
$773$	240.787	−	240.787i	0.311497	−	0.311497i	−0.533993	−	0.845489i	$-0.679309\pi$
$773$	240.787	−	240.787i	0.311497	−	0.311497i	0.845489	+	0.533993i	$0.179309\pi$
$774$			2696.82i			3.48426i
$775$		0			0
$776$	−3107.69			−4.00476
$777$	−362.099	−	362.099i	−0.466022	−	0.466022i
$778$	−76.3171	+	76.3171i	−0.0980939	+	0.0980939i
$779$			684.252i			0.878372i
$780$		0			0
$781$	252.036			0.322710
$782$	1139.69	+	1139.69i	1.45740	+	1.45740i
$783$	−720.155	+	720.155i	−0.919738	+	0.919738i
$784$		−	1829.43i		−	2.33346i
$785$		0			0
$786$	−1948.64			−2.47919
$787$	122.762	+	122.762i	0.155988	+	0.155988i	0.780786	−	0.624798i	$-0.214819\pi$
$787$	122.762	+	122.762i	0.155988	+	0.155988i	−0.624798	+	0.780786i	$0.714819\pi$
$788$	1.00117	−	1.00117i	0.00127052	−	0.00127052i
$789$			660.179i			0.836729i
$790$		0			0
$791$	952.121			1.20369
$792$	773.481	+	773.481i	0.976618	+	0.976618i
$793$	1.92976	−	1.92976i	0.00243350	−	0.00243350i
$794$		−	62.4598i		−	0.0786647i
$795$		0			0
$796$	3274.91			4.11421
$797$	174.178	+	174.178i	0.218543	+	0.218543i	0.807884	−	0.589341i	$-0.200613\pi$
$797$	174.178	+	174.178i	0.218543	+	0.218543i	−0.589341	+	0.807884i	$0.700613\pi$
$798$	−3166.23	+	3166.23i	−3.96771	+	3.96771i
$799$		−	293.883i		−	0.367814i
$800$		0			0
$801$	−1621.33			−2.02413
$802$	1240.42	+	1240.42i	1.54665	+	1.54665i
$803$	−70.0321	+	70.0321i	−0.0872131	+	0.0872131i
$804$			367.686i			0.457320i
$805$		0			0
$806$	−50.2036			−0.0622874
$807$	−245.028	−	245.028i	−0.303629	−	0.303629i
$808$	1336.42	−	1336.42i	1.65398	−	1.65398i
$809$		−	272.806i		−	0.337213i	−0.985683	−	0.168607i	$-0.946073\pi$
$809$		−	272.806i		−	0.337213i	0.985683	−	0.168607i	$-0.0539268\pi$
$810$		0			0
$811$	−764.856			−0.943102			−0.471551	−	0.881839i	$-0.656306\pi$
$811$	−764.856			−0.943102			−0.471551	+	0.881839i	$0.656306\pi$
$812$	−2097.79	−	2097.79i	−2.58349	−	2.58349i
$813$	587.793	−	587.793i	0.722992	−	0.722992i
$814$			130.071i			0.159792i
$815$		0			0
$816$	2313.16			2.83475
$817$	826.583	+	826.583i	1.01173	+	1.01173i
$818$	−1456.12	+	1456.12i	−1.78010	+	1.78010i
$819$		−	804.161i		−	0.981882i
$820$		0			0
$821$	376.669			0.458793			0.229396	−	0.973333i	$-0.426325\pi$
$821$	376.669			0.458793			0.229396	+	0.973333i	$0.426325\pi$
$822$	−1672.15	−	1672.15i	−2.03425	−	2.03425i
$823$	159.477	−	159.477i	0.193775	−	0.193775i	−0.603550	−	0.797325i	$-0.706248\pi$
$823$	159.477	−	159.477i	0.193775	−	0.193775i	0.797325	+	0.603550i	$0.206248\pi$
$824$		−	1907.20i		−	2.31456i
$825$		0			0
$826$	1604.51			1.94251
$827$	612.569	+	612.569i	0.740713	+	0.740713i	0.972715	−	0.232003i	$-0.0745278\pi$
$827$	612.569	+	612.569i	0.740713	+	0.740713i	−0.232003	+	0.972715i	$0.574528\pi$
$828$	3949.80	−	3949.80i	4.77029	−	4.77029i
$829$			767.065i			0.925289i	0.886544	+	0.462645i	$0.153099\pi$
$829$			767.065i			0.925289i	−0.886544	+	0.462645i	$0.846901\pi$
$830$		0			0
$831$	−350.350			−0.421600
$832$	−265.487	−	265.487i	−0.319095	−	0.319095i
$833$	−385.158	+	385.158i	−0.462375	+	0.462375i
$834$			1585.76i			1.90140i
$835$		0			0
$836$	805.751			0.963817
$837$	−58.9434	−	58.9434i	−0.0704223	−	0.0704223i
$838$	−1411.81	+	1411.81i	−1.68474	+	1.68474i
$839$			599.820i			0.714922i	0.933928	+	0.357461i	$0.116358\pi$
$839$			599.820i			0.714922i	−0.933928	+	0.357461i	$0.883642\pi$
$840$		0			0
$841$	−137.568			−0.163577
$842$	502.415	+	502.415i	0.596693	+	0.596693i
$843$	−1346.91	+	1346.91i	−1.59776	+	1.59776i
$844$		−	3681.21i		−	4.36162i
$845$		0			0
$846$	−1437.67			−1.69937
$847$	75.8956	+	75.8956i	0.0896052	+	0.0896052i
$848$	1861.44	−	1861.44i	2.19509	−	2.19509i
$849$			2381.20i			2.80471i
$850$		0			0
$851$	390.859			0.459293
$852$	−2588.71	−	2588.71i	−3.03839	−	3.03839i
$853$	−608.322	+	608.322i	−0.713156	+	0.713156i	−0.967194	−	0.254038i	$-0.918241\pi$
$853$	−608.322	+	608.322i	−0.713156	+	0.713156i	0.254038	+	0.967194i	$0.418241\pi$
$854$			18.6323i			0.0218177i
$855$		0			0
$856$	−2297.09			−2.68352
$857$	157.546	+	157.546i	0.183834	+	0.183834i	0.793024	−	0.609190i	$-0.208505\pi$
$857$	157.546	+	157.546i	0.183834	+	0.183834i	−0.609190	+	0.793024i	$0.708505\pi$
$858$	−227.929	+	227.929i	−0.265651	+	0.265651i
$859$		−	1249.31i		−	1.45438i	−0.686435	−	0.727191i	$-0.740826\pi$
$859$		−	1249.31i		−	1.45438i	0.686435	−	0.727191i	$-0.259174\pi$
$860$		0			0
$861$	1323.98			1.53772
$862$	493.903	+	493.903i	0.572973	+	0.572973i
$863$	487.037	−	487.037i	0.564354	−	0.564354i	−0.366187	−	0.930541i	$-0.619337\pi$
$863$	487.037	−	487.037i	0.564354	−	0.564354i	0.930541	+	0.366187i	$0.119337\pi$
$864$		−	2015.37i		−	2.33260i
$865$		0			0
$866$	−264.873			−0.305857
$867$	525.911	+	525.911i	0.606587	+	0.606587i
$868$	171.701	−	171.701i	0.197812	−	0.197812i
$869$		−	265.788i		−	0.305855i
$870$		0			0
$871$	−40.4023			−0.0463862
$872$	1751.66	+	1751.66i	2.00878	+	2.00878i
$873$	1614.88	−	1614.88i	1.84981	−	1.84981i
$874$		−	3417.70i		−	3.91042i
$875$		0			0
$876$	1438.62			1.64226
$877$	623.403	+	623.403i	0.710836	+	0.710836i	0.966710	−	0.255874i	$-0.0823632\pi$
$877$	623.403	+	623.403i	0.710836	+	0.710836i	−0.255874	+	0.966710i	$0.582363\pi$
$878$	−1126.71	+	1126.71i	−1.28327	+	1.28327i
$879$		−	2547.40i		−	2.89806i
$880$		0			0
$881$	−454.861			−0.516301			−0.258151	−	0.966105i	$-0.583113\pi$
$881$	−454.861			−0.516301			−0.258151	+	0.966105i	$0.583113\pi$
$882$	1884.18	+	1884.18i	2.13626	+	2.13626i
$883$	1004.76	−	1004.76i	1.13789	−	1.13789i	0.149060	−	0.988828i	$-0.452375\pi$
$883$	1004.76	−	1004.76i	1.13789	−	1.13789i	0.988828	−	0.149060i	$-0.0476249\pi$
$884$			606.501i			0.686087i
$885$		0			0
$886$	499.572			0.563851
$887$	−541.833	−	541.833i	−0.610861	−	0.610861i	0.332310	−	0.943170i	$-0.392172\pi$
$887$	−541.833	−	541.833i	−0.610861	−	0.610861i	−0.943170	+	0.332310i	$0.892172\pi$
$888$	786.165	−	786.165i	0.885321	−	0.885321i
$889$		−	1427.16i		−	1.60535i
$890$		0			0
$891$	−70.5072			−0.0791326
$892$	−1451.88	−	1451.88i	−1.62766	−	1.62766i
$893$	−440.650	+	440.650i	−0.493449	+	0.493449i
$894$		−	625.016i		−	0.699123i
$895$		0			0
$896$	147.273			0.164368
$897$	684.918	+	684.918i	0.763565	+	0.763565i
$898$	1444.86	−	1444.86i	1.60897	−	1.60897i
$899$		−	80.0941i		−	0.0890924i
$900$		0			0
$901$	−783.793			−0.869914
$902$	−237.796	−	237.796i	−0.263632	−	0.263632i
$903$	1599.38	−	1599.38i	1.77119	−	1.77119i
$904$			2067.18i			2.28670i
$905$		0			0
$906$	−3474.56			−3.83506
$907$	−1233.67	−	1233.67i	−1.36016	−	1.36016i	−0.873706	−	0.486454i	$-0.838290\pi$
$907$	−1233.67	−	1233.67i	−1.36016	−	1.36016i	−0.486454	−	0.873706i	$-0.661710\pi$
$908$	1136.42	−	1136.42i	1.25156	−	1.25156i
$909$			1388.91i			1.52796i
$910$		0			0
$911$	1576.82			1.73087			0.865434	−	0.501024i	$-0.167043\pi$
$911$	1576.82			1.73087			0.865434	+	0.501024i	$0.167043\pi$
$912$	−3468.36	−	3468.36i	−3.80303	−	3.80303i
$913$	263.230	−	263.230i	0.288314	−	0.288314i
$914$			1198.39i			1.31115i
$915$		0			0
$916$	3646.18			3.98055
$917$	732.316	+	732.316i	0.798600	+	0.798600i
$918$	−1005.14	+	1005.14i	−1.09492	+	1.09492i
$919$			288.943i			0.314410i	0.987566	+	0.157205i	$0.0502483\pi$
$919$			288.943i			0.314410i	−0.987566	+	0.157205i	$0.949752\pi$
$920$		0			0
$921$	2976.17			3.23146
$922$	40.6784	+	40.6784i	0.0441197	+	0.0441197i
$923$	284.455	−	284.455i	0.308185	−	0.308185i
$924$		−	1559.07i		−	1.68731i
$925$		0			0
$926$	2431.86			2.62620
$927$	991.058	+	991.058i	1.06910	+	1.06910i
$928$	1369.27	−	1369.27i	1.47551	−	1.47551i
$929$			264.227i			0.284421i	0.989836	+	0.142211i	$0.0454210\pi$
$929$			264.227i			0.284421i	−0.989836	+	0.142211i	$0.954579\pi$
$930$		0			0
$931$	1155.02			1.24062
$932$	−2501.23	−	2501.23i	−2.68372	−	2.68372i
$933$	−112.402	+	112.402i	−0.120474	+	0.120474i
$934$		−	800.730i		−	0.857313i
$935$		0			0
$936$	1745.94			1.86532
$937$	372.874	+	372.874i	0.397944	+	0.397944i	0.877507	−	0.479563i	$-0.159205\pi$
$937$	372.874	+	372.874i	0.397944	+	0.397944i	−0.479563	+	0.877507i	$0.659205\pi$
$938$	195.047	−	195.047i	0.207939	−	0.207939i
$939$			237.415i			0.252838i
$940$		0			0
$941$	−1180.10			−1.25409			−0.627047	−	0.778981i	$-0.715737\pi$
$941$	−1180.10			−1.25409			−0.627047	+	0.778981i	$0.715737\pi$
$942$	−31.4008	−	31.4008i	−0.0333341	−	0.0333341i
$943$	−714.568	+	714.568i	−0.757761	+	0.757761i
$944$			1757.62i			1.86188i
$945$		0			0
$946$	−574.520			−0.607315
$947$	101.650	+	101.650i	0.107339	+	0.107339i	0.758737	−	0.651398i	$-0.225817\pi$
$947$	101.650	+	101.650i	0.107339	+	0.107339i	−0.651398	+	0.758737i	$0.725817\pi$
$948$	−2729.95	+	2729.95i	−2.87970	+	2.87970i
$949$			158.080i			0.166575i
$950$		0			0
$951$	450.981			0.474218
$952$	−1722.97	−	1722.97i	−1.80984	−	1.80984i
$953$	−892.133	+	892.133i	−0.936131	+	0.936131i	−0.998079	−	0.0619483i	$-0.980269\pi$
$953$	−892.133	+	892.133i	−0.936131	+	0.936131i	0.0619483	+	0.998079i	$0.480269\pi$
$954$			3834.30i			4.01918i
$955$		0			0
$956$	−1065.30			−1.11433
$957$	−363.634	−	363.634i	−0.379973	−	0.379973i
$958$	−422.391	+	422.391i	−0.440909	+	0.440909i
$959$			1256.82i			1.31055i
$960$		0			0
$961$	−954.444			−0.993178
$962$	146.801	+	146.801i	0.152600	+	0.152600i
$963$	1193.66	−	1193.66i	1.23952	−	1.23952i
$964$			1023.03i			1.06123i
$965$		0			0
$966$	−6613.03			−6.84578
$967$	19.5447	+	19.5447i	0.0202117	+	0.0202117i	0.717140	−	0.696929i	$-0.245451\pi$
$967$	19.5447	+	19.5447i	0.0202117	+	0.0202117i	−0.696929	+	0.717140i	$0.745451\pi$
$968$	−164.779	+	164.779i	−0.170227	+	0.170227i
$969$			1460.42i			1.50714i
$970$		0			0
$971$	−954.386			−0.982890			−0.491445	−	0.870909i	$-0.663531\pi$
$971$	−954.386			−0.982890			−0.491445	+	0.870909i	$0.663531\pi$
$972$	−1289.61	−	1289.61i	−1.32676	−	1.32676i
$973$	595.944	−	595.944i	0.612481	−	0.612481i
$974$		−	3322.70i		−	3.41139i
$975$		0			0
$976$	−20.4102			−0.0209121
$977$	579.740	+	579.740i	0.593388	+	0.593388i	0.938545	−	0.345157i	$-0.112174\pi$
$977$	579.740	+	579.740i	0.593388	+	0.593388i	−0.345157	+	0.938545i	$0.612174\pi$
$978$	3268.10	−	3268.10i	3.34162	−	3.34162i
$979$		−	345.401i		−	0.352810i
$980$		0			0
$981$	−1820.46			−1.85572
$982$	−21.0350	−	21.0350i	−0.0214206	−	0.0214206i
$983$	515.818	−	515.818i	0.524738	−	0.524738i	−0.394260	−	0.918999i	$-0.628999\pi$
$983$	515.818	−	515.818i	0.524738	−	0.524738i	0.918999	+	0.394260i	$0.128999\pi$
$984$			2874.54i			2.92128i
$985$		0			0
$986$	−1365.82			−1.38521
$987$	852.628	+	852.628i	0.863858	+	0.863858i
$988$	909.391	−	909.391i	0.920436	−	0.920436i
$989$			1726.41i			1.74561i
$990$		0			0
$991$	−1588.85			−1.60328			−0.801639	−	0.597809i	$-0.796038\pi$
$991$	−1588.85			−1.60328			−0.801639	+	0.597809i	$0.796038\pi$
$992$	112.073	+	112.073i	0.112976	+	0.112976i
$993$	−1033.33	+	1033.33i	−1.04061	+	1.04061i
$994$			2746.47i			2.76305i
$995$		0			0
$996$	−5407.37			−5.42908
$997$	−330.956	−	330.956i	−0.331951	−	0.331951i	0.521376	−	0.853327i	$-0.325419\pi$
$997$	−330.956	−	330.956i	−0.331951	−	0.331951i	−0.853327	+	0.521376i	$0.825419\pi$
$998$	2127.71	−	2127.71i	2.13197	−	2.13197i
$999$			344.715i			0.345061i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.f.c.232.12	yes	24
5.2	odd	4	inner	275.3.f.c.243.1	yes	24
5.3	odd	4	inner	275.3.f.c.243.12	yes	24
5.4	even	2	inner	275.3.f.c.232.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.f.c.232.1	✓	24	5.4	even	2	inner
275.3.f.c.232.12	yes	24	1.1	even	1	trivial
275.3.f.c.243.1	yes	24	5.2	odd	4	inner
275.3.f.c.243.12	yes	24	5.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.61911 + 2.61911i) q^{2} +(-3.50488 + 3.50488i) q^{3} +9.71948i q^{4} -18.3593 q^{6} +(6.89960 + 6.89960i) q^{7} +(-14.9800 + 14.9800i) q^{8} -15.5684i q^{9} +3.31662 q^{11} +(-34.0656 - 34.0656i) q^{12} +(3.74323 - 3.74323i) q^{13} +36.1416i q^{14} -39.5904 q^{16} +(8.33513 + 8.33513i) q^{17} +(40.7753 - 40.7753i) q^{18} -24.9955i q^{19} -48.3645 q^{21} +(8.68661 + 8.68661i) q^{22} +(26.1029 - 26.1029i) q^{23} -105.006i q^{24} +19.6078 q^{26} +(23.0213 + 23.0213i) q^{27} +(-67.0605 + 67.0605i) q^{28} +31.2821i q^{29} -2.56038 q^{31} +(-43.7718 - 43.7718i) q^{32} +(-11.6244 + 11.6244i) q^{33} +43.6613i q^{34} +151.316 q^{36} +(7.48687 + 7.48687i) q^{37} +(65.4659 - 65.4659i) q^{38} +26.2391i q^{39} -27.3750 q^{41} +(-126.672 - 126.672i) q^{42} +(-33.0693 + 33.0693i) q^{43} +32.2359i q^{44} +136.733 q^{46} +(-17.6292 - 17.6292i) q^{47} +(138.760 - 138.760i) q^{48} +46.2090i q^{49} -58.4273 q^{51} +(36.3822 + 36.3822i) q^{52} +(-47.0174 + 47.0174i) q^{53} +120.591i q^{54} -206.711 q^{56} +(87.6061 + 87.6061i) q^{57} +(-81.9312 + 81.9312i) q^{58} -44.3951i q^{59} +0.515535 q^{61} +(-6.70593 - 6.70593i) q^{62} +(107.416 - 107.416i) q^{63} -70.9247i q^{64} -60.8910 q^{66} +(-5.39673 - 5.39673i) q^{67} +(-81.0132 + 81.0132i) q^{68} +182.975i q^{69} +75.9918 q^{71} +(233.213 + 233.213i) q^{72} +(-21.1155 + 21.1155i) q^{73} +39.2179i q^{74} +242.943 q^{76} +(22.8834 + 22.8834i) q^{77} +(-68.7232 + 68.7232i) q^{78} -80.1381i q^{79} -21.2587 q^{81} +(-71.6982 - 71.6982i) q^{82} +(79.3669 - 79.3669i) q^{83} -470.078i q^{84} -173.224 q^{86} +(-109.640 - 109.640i) q^{87} +(-49.6829 + 49.6829i) q^{88} -104.142i q^{89} +51.6535 q^{91} +(253.707 + 253.707i) q^{92} +(8.97384 - 8.97384i) q^{93} -92.3456i q^{94} +306.830 q^{96} +(103.728 + 103.728i) q^{97} +(-121.027 + 121.027i) q^{98} -51.6344i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 128 q^{16} - 88 q^{21} + 96 q^{26} + 360 q^{31} + 176 q^{36} - 152 q^{41} + 56 q^{46} - 512 q^{51} - 1048 q^{56} + 784 q^{61} - 440 q^{66} + 728 q^{71} + 1704 q^{76} - 568 q^{81} - 328 q^{86}+ \cdots + 1568 q^{96}+O(q^{100}) \) 24 * q - 8 * q^6 - 128 * q^16 - 88 * q^21 + 96 * q^26 + 360 * q^31 + 176 * q^36 - 152 * q^41 + 56 * q^46 - 512 * q^51 - 1048 * q^56 + 784 * q^61 - 440 * q^66 + 728 * q^71 + 1704 * q^76 - 568 * q^81 - 328 * q^86 - 968 * q^91 + 1568 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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