LMFDB - Embedded newform 1008.2.bh.c.191.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(95,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1008.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.bh (of order $6$, degree $2$, 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.2
Character	$\chi$	$=$	1008.191
Dual form			1008.2.bh.c.95.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64852 - 0.531401i) q^{3} +0.911520i q^{5} +(-2.19821 - 1.47237i) q^{7} +(2.43522 + 1.75205i) q^{9} +O(q^{10})$	\(q+(-1.64852 - 0.531401i) q^{3} +0.911520i q^{5} +(-2.19821 - 1.47237i) q^{7} +(2.43522 + 1.75205i) q^{9} +4.51559 q^{11} +(0.317553 + 0.550018i) q^{13} +(0.484383 - 1.50266i) q^{15} +(-5.33837 + 3.08211i) q^{17} +(-6.27974 - 3.62561i) q^{19} +(2.84137 + 3.59536i) q^{21} -1.06200 q^{23} +4.16913 q^{25} +(-3.08347 - 4.18237i) q^{27} +(3.77247 + 2.17804i) q^{29} +(9.09549 + 5.25129i) q^{31} +(-7.44403 - 2.39959i) q^{33} +(1.34209 - 2.00371i) q^{35} +(-0.869958 + 1.50681i) q^{37} +(-0.231211 - 1.07546i) q^{39} +(8.50356 - 4.90953i) q^{41} +(5.62021 + 3.24483i) q^{43} +(-1.59703 + 2.21976i) q^{45} +(4.68099 + 8.10771i) q^{47} +(2.66425 + 6.47316i) q^{49} +(10.4382 - 2.24409i) q^{51} +(8.64955 - 4.99382i) q^{53} +4.11605i q^{55} +(8.42561 + 9.31394i) q^{57} +(6.63767 - 11.4968i) q^{59} +(0.739024 + 1.28003i) q^{61} +(-2.77347 - 7.43693i) q^{63} +(-0.501352 + 0.289456i) q^{65} +(-4.72497 - 2.72796i) q^{67} +(1.75073 + 0.564348i) q^{69} +8.00517 q^{71} +(4.39305 + 7.60899i) q^{73} +(-6.87289 - 2.21548i) q^{75} +(-9.92621 - 6.64862i) q^{77} +(-12.8756 + 7.43373i) q^{79} +(2.86064 + 8.53327i) q^{81} +(-3.51817 + 6.09365i) q^{83} +(-2.80940 - 4.86603i) q^{85} +(-5.06157 - 5.59523i) q^{87} +(3.61630 + 2.08787i) q^{89} +(0.111782 - 1.67661i) q^{91} +(-12.2035 - 13.4902i) q^{93} +(3.30481 - 5.72410i) q^{95} +(3.10677 - 5.38109i) q^{97} +(10.9965 + 7.91153i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 2 q^{7} - q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 2 * q^7 - q^9	$ 30 q - 3 q^{3} - 2 q^{7} - q^{9} + 6 q^{11} + 12 q^{17} + 9 q^{19} + 14 q^{21} - 24 q^{23} - 36 q^{25} + 27 q^{27} + 27 q^{29} + 6 q^{31} - 20 q^{33} - 6 q^{35} + 6 q^{37} - 15 q^{39} + 9 q^{41} - 21 q^{43} - 8 q^{45} + 12 q^{49} - 15 q^{51} - 3 q^{53} + 20 q^{57} + 3 q^{59} - 3 q^{61} + 24 q^{63} - 39 q^{67} + 10 q^{69} + 18 q^{71} + 21 q^{73} + 21 q^{75} + 36 q^{77} - 33 q^{79} - 17 q^{81} - 15 q^{83} - 3 q^{85} + 78 q^{87} + 6 q^{89} - 26 q^{91} - 3 q^{93} - 27 q^{95} - 6 q^{97} - 48 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 2 * q^7 - q^9 + 6 * q^11 + 12 * q^17 + 9 * q^19 + 14 * q^21 - 24 * q^23 - 36 * q^25 + 27 * q^27 + 27 * q^29 + 6 * q^31 - 20 * q^33 - 6 * q^35 + 6 * q^37 - 15 * q^39 + 9 * q^41 - 21 * q^43 - 8 * q^45 + 12 * q^49 - 15 * q^51 - 3 * q^53 + 20 * q^57 + 3 * q^59 - 3 * q^61 + 24 * q^63 - 39 * q^67 + 10 * q^69 + 18 * q^71 + 21 * q^73 + 21 * q^75 + 36 * q^77 - 33 * q^79 - 17 * q^81 - 15 * q^83 - 3 * q^85 + 78 * q^87 + 6 * q^89 - 26 * q^91 - 3 * q^93 - 27 * q^95 - 6 * q^97 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−1.64852	−	0.531401i	−0.951772	−	0.306805i
$3$	−1.64852	−	0.531401i	−0.951772	−	0.306805i
$4$		0			0
$5$			0.911520i			0.407644i	0.979008	+	0.203822i	$0.0653364\pi$
$5$			0.911520i			0.407644i	−0.979008	+	0.203822i	$0.934664\pi$
$6$		0			0
$7$	−2.19821	−	1.47237i	−0.830845	−	0.556504i
$7$	−2.19821	−	1.47237i	−0.830845	−	0.556504i
$8$		0			0
$9$	2.43522	+	1.75205i	0.811742	+	0.584017i
$10$		0			0
$11$	4.51559			1.36150			0.680750	−	0.732516i	$-0.261654\pi$
$11$	4.51559			1.36150			0.680750	+	0.732516i	$0.261654\pi$
$12$		0			0
$13$	0.317553	+	0.550018i	0.0880733	+	0.152547i	0.906697	−	0.421783i	$-0.138596\pi$
$13$	0.317553	+	0.550018i	0.0880733	+	0.152547i	−0.818623	+	0.574331i	$0.805262\pi$
$14$		0			0
$15$	0.484383	−	1.50266i	0.125067	−	0.387984i
$16$		0			0
$17$	−5.33837	+	3.08211i	−1.29474	+	0.747521i	−0.979491	−	0.201487i	$-0.935423\pi$
$17$	−5.33837	+	3.08211i	−1.29474	+	0.747521i	−0.315253	+	0.949008i	$0.602089\pi$
$18$		0			0
$19$	−6.27974	−	3.62561i	−1.44067	−	0.831771i	−0.442776	−	0.896632i	$-0.646006\pi$
$19$	−6.27974	−	3.62561i	−1.44067	−	0.831771i	−0.997894	+	0.0648609i	$0.979340\pi$
$20$		0			0
$21$	2.84137	+	3.59536i	0.620038	+	0.784572i
$22$		0			0
$23$	−1.06200			−0.221442			−0.110721	−	0.993852i	$-0.535316\pi$
$23$	−1.06200			−0.221442			−0.110721	+	0.993852i	$0.535316\pi$
$24$		0			0
$25$	4.16913			0.833826
$26$		0			0
$27$	−3.08347	−	4.18237i	−0.593414	−	0.804897i
$28$		0			0
$29$	3.77247	+	2.17804i	0.700530	+	0.404451i	0.807545	−	0.589806i	$-0.200796\pi$
$29$	3.77247	+	2.17804i	0.700530	+	0.404451i	−0.107015	+	0.994257i	$0.534129\pi$
$30$		0			0
$31$	9.09549	+	5.25129i	1.63360	+	0.943159i	0.982971	+	0.183762i	$0.0588277\pi$
$31$	9.09549	+	5.25129i	1.63360	+	0.943159i	0.650628	+	0.759396i	$0.274506\pi$
$32$		0			0
$33$	−7.44403	−	2.39959i	−1.29584	−	0.417715i
$34$		0			0
$35$	1.34209	−	2.00371i	0.226855	−	0.338689i
$36$		0			0
$37$	−0.869958	+	1.50681i	−0.143020	+	0.247718i	−0.928633	−	0.371001i	$-0.879015\pi$
$37$	−0.869958	+	1.50681i	−0.143020	+	0.247718i	0.785612	+	0.618719i	$0.212348\pi$
$38$		0			0
$39$	−0.231211	−	1.07546i	−0.0370235	−	0.172212i
$40$		0			0
$41$	8.50356	−	4.90953i	1.32803	−	0.766740i	0.343038	−	0.939321i	$-0.388544\pi$
$41$	8.50356	−	4.90953i	1.32803	−	0.766740i	0.984995	+	0.172581i	$0.0552106\pi$
$42$		0			0
$43$	5.62021	+	3.24483i	0.857074	+	0.494832i	0.863031	−	0.505150i	$-0.168563\pi$
$43$	5.62021	+	3.24483i	0.857074	+	0.494832i	−0.00595744	+	0.999982i	$0.501896\pi$
$44$		0			0
$45$	−1.59703	+	2.21976i	−0.238071	+	0.330902i
$46$		0			0
$47$	4.68099	+	8.10771i	0.682793	+	1.18263i	0.974125	+	0.226010i	$0.0725681\pi$
$47$	4.68099	+	8.10771i	0.682793	+	1.18263i	−0.291332	+	0.956622i	$0.594099\pi$
$48$		0			0
$49$	2.66425	+	6.47316i	0.380607	+	0.924737i
$50$		0			0
$51$	10.4382	−	2.24409i	1.46164	−	0.314236i
$52$		0			0
$53$	8.64955	−	4.99382i	1.18811	−	0.685954i	0.230231	−	0.973136i	$-0.426052\pi$
$53$	8.64955	−	4.99382i	1.18811	−	0.685954i	0.957876	+	0.287182i	$0.0927184\pi$
$54$		0			0
$55$			4.11605i			0.555007i
$56$		0			0
$57$	8.42561	+	9.31394i	1.11600	+	1.23366i
$58$		0			0
$59$	6.63767	−	11.4968i	0.864151	−	1.49675i	−0.00373578	−	0.999993i	$-0.501189\pi$
$59$	6.63767	−	11.4968i	0.864151	−	1.49675i	0.867887	−	0.496761i	$-0.165478\pi$
$60$		0			0
$61$	0.739024	+	1.28003i	0.0946223	+	0.163891i	0.909451	−	0.415811i	$-0.136502\pi$
$61$	0.739024	+	1.28003i	0.0946223	+	0.163891i	−0.814829	+	0.579702i	$0.803169\pi$
$62$		0			0
$63$	−2.77347	−	7.43693i	−0.349424	−	0.936965i
$64$		0			0
$65$	−0.501352	+	0.289456i	−0.0621850	+	0.0359025i
$66$		0			0
$67$	−4.72497	−	2.72796i	−0.577247	−	0.333274i	0.182792	−	0.983152i	$-0.441487\pi$
$67$	−4.72497	−	2.72796i	−0.577247	−	0.333274i	−0.760039	+	0.649878i	$0.774820\pi$
$68$		0			0
$69$	1.75073	+	0.564348i	0.210763	+	0.0679396i
$70$		0			0
$71$	8.00517			0.950038			0.475019	−	0.879975i	$-0.342441\pi$
$71$	8.00517			0.950038			0.475019	+	0.879975i	$0.342441\pi$
$72$		0			0
$73$	4.39305	+	7.60899i	0.514168	+	0.890564i	0.999865	+	0.0164373i	$0.00523240\pi$
$73$	4.39305	+	7.60899i	0.514168	+	0.890564i	−0.485697	+	0.874127i	$0.661434\pi$
$74$		0			0
$75$	−6.87289	−	2.21548i	−0.793613	−	0.255822i
$76$		0			0
$77$	−9.92621	−	6.64862i	−1.13120	−	0.757680i
$78$		0			0
$79$	−12.8756	+	7.43373i	−1.44862	+	0.836360i	−0.998399	−	0.0565575i	$-0.981988\pi$
$79$	−12.8756	+	7.43373i	−1.44862	+	0.836360i	−0.450219	+	0.892918i	$0.648654\pi$
$80$		0			0
$81$	2.86064	+	8.53327i	0.317849	+	0.948141i
$82$		0			0
$83$	−3.51817	+	6.09365i	−0.386169	+	0.668865i	−0.991931	−	0.126782i	$-0.959535\pi$
$83$	−3.51817	+	6.09365i	−0.386169	+	0.668865i	0.605761	+	0.795646i	$0.292869\pi$
$84$		0			0
$85$	−2.80940	−	4.86603i	−0.304722	−	0.527795i
$86$		0			0
$87$	−5.06157	−	5.59523i	−0.542658	−	0.599872i
$88$		0			0
$89$	3.61630	+	2.08787i	0.383327	+	0.221314i	0.679265	−	0.733893i	$-0.262299\pi$
$89$	3.61630	+	2.08787i	0.383327	+	0.221314i	−0.295938	+	0.955207i	$0.595632\pi$
$90$		0			0
$91$	0.111782	−	1.67661i	0.0117179	−	0.175756i
$92$		0			0
$93$	−12.2035	−	13.4902i	−1.26545	−	1.39887i
$94$		0			0
$95$	3.30481	−	5.72410i	0.339067	−	0.587280i
$96$		0			0
$97$	3.10677	−	5.38109i	0.315445	−	0.546367i	−0.664087	−	0.747655i	$-0.731179\pi$
$97$	3.10677	−	5.38109i	0.315445	−	0.546367i	0.979532	+	0.201288i	$0.0645128\pi$
$98$		0			0
$99$	10.9965	+	7.91153i	1.10519	+	0.795139i
$100$		0			0
$101$		−	7.91303i		−	0.787376i	−0.919244	−	0.393688i	$-0.871199\pi$
$101$		−	7.91303i		−	0.787376i	0.919244	−	0.393688i	$-0.128801\pi$
$102$		0			0
$103$			12.9620i			1.27718i	0.769547	+	0.638590i	$0.220482\pi$
$103$			12.9620i			1.27718i	−0.769547	+	0.638590i	$0.779518\pi$
$104$		0			0
$105$	−3.27724	+	2.58996i	−0.319826	+	0.252755i
$106$		0			0
$107$	2.57785	−	4.46497i	0.249210	−	0.431645i	−0.714097	−	0.700047i	$-0.753162\pi$
$107$	2.57785	−	4.46497i	0.249210	−	0.431645i	0.963307	+	0.268402i	$0.0864957\pi$
$108$		0			0
$109$	1.70897	+	2.96003i	0.163690	+	0.283520i	0.936189	−	0.351496i	$-0.114327\pi$
$109$	1.70897	+	2.96003i	0.163690	+	0.283520i	−0.772499	+	0.635016i	$0.780994\pi$
$110$		0			0
$111$	2.23486	−	2.02171i	0.212124	−	0.191892i
$112$		0			0
$113$	−0.535953	+	0.309433i	−0.0504182	+	0.0291090i	−0.524997	−	0.851104i	$-0.675934\pi$
$113$	−0.535953	+	0.309433i	−0.0504182	+	0.0291090i	0.474579	+	0.880213i	$0.342600\pi$
$114$		0			0
$115$		−	0.968034i		−	0.0902696i
$116$		0			0
$117$	−0.190346	+	1.89578i	−0.0175975	+	0.175265i
$118$		0			0
$119$	16.2729	+	1.08493i	1.49173	+	0.0994558i
$120$		0			0
$121$	9.39052			0.853684
$122$		0			0
$123$	−16.6272	+	3.57465i	−1.49923	+	0.322315i
$124$		0			0
$125$			8.35784i			0.747548i
$126$		0			0
$127$			1.88454i			0.167226i	0.996498	+	0.0836131i	$0.0266460\pi$
$127$			1.88454i			0.167226i	−0.996498	+	0.0836131i	$0.973354\pi$
$128$		0			0
$129$	−7.54071	−	8.33575i	−0.663923	−	0.733922i
$130$		0			0
$131$	−4.90526			−0.428574			−0.214287	−	0.976771i	$-0.568743\pi$
$131$	−4.90526			−0.428574			−0.214287	+	0.976771i	$0.568743\pi$
$132$		0			0
$133$	8.46594	+	17.2159i	0.734090	+	1.49281i
$134$		0			0
$135$	3.81231	−	2.81064i	0.328111	−	0.241902i
$136$		0			0
$137$		−	6.83751i		−	0.584168i	−0.956393	−	0.292084i	$-0.905651\pi$
$137$		−	6.83751i		−	0.584168i	0.956393	−	0.292084i	$-0.0943486\pi$
$138$		0			0
$139$	10.7893	−	6.22923i	0.915140	−	0.528356i	0.0330587	−	0.999453i	$-0.489475\pi$
$139$	10.7893	−	6.22923i	0.915140	−	0.528356i	0.882081	+	0.471097i	$0.156142\pi$
$140$		0			0
$141$	−3.40825	−	15.8532i	−0.287026	−	1.33508i
$142$		0			0
$143$	1.43394	+	2.48365i	0.119912	+	0.207693i
$144$		0			0
$145$	−1.98532	+	3.43868i	−0.164872	+	0.285567i
$146$		0			0
$147$	−0.952221	−	12.0869i	−0.0785379	−	0.996911i
$148$		0			0
$149$		−	14.1182i		−	1.15660i	−0.815823	−	0.578302i	$-0.803715\pi$
$149$		−	14.1182i		−	1.15660i	0.815823	−	0.578302i	$-0.196285\pi$
$150$		0			0
$151$			18.5326i			1.50817i	0.656780	+	0.754083i	$0.271918\pi$
$151$			18.5326i			1.50817i	−0.656780	+	0.754083i	$0.728082\pi$
$152$		0			0
$153$	−18.4001	−	1.84746i	−1.48756	−	0.149358i
$154$		0			0
$155$	−4.78665	+	8.29072i	−0.384473	+	0.665927i
$156$		0			0
$157$	−0.464999	+	0.805402i	−0.0371110	+	0.0642781i	−0.883984	−	0.467517i	$-0.845149\pi$
$157$	−0.464999	+	0.805402i	−0.0371110	+	0.0642781i	0.846873	+	0.531795i	$0.178482\pi$
$158$		0			0
$159$	−16.9127	+	3.63602i	−1.34126	+	0.288355i
$160$		0			0
$161$	2.33450	+	1.56366i	0.183984	+	0.123233i
$162$		0			0
$163$	0.651181	+	0.375960i	0.0510045	+	0.0294474i	0.525285	−	0.850926i	$-0.323959\pi$
$163$	0.651181	+	0.375960i	0.0510045	+	0.0294474i	−0.474281	+	0.880374i	$0.657292\pi$
$164$		0			0
$165$	2.18727	−	6.78538i	0.170279	−	0.528241i
$166$		0			0
$167$	−1.41671	−	2.45382i	−0.109628	−	0.189882i	0.805991	−	0.591927i	$-0.201633\pi$
$167$	−1.41671	−	2.45382i	−0.109628	−	0.189882i	−0.915620	+	0.402045i	$0.868299\pi$
$168$		0			0
$169$	6.29832	−	10.9090i	0.484486	−	0.839155i
$170$		0			0
$171$	−8.94032	−	19.8316i	−0.683684	−	1.51656i
$172$		0			0
$173$	−4.78611	+	2.76326i	−0.363881	+	0.210087i	−0.670782	−	0.741655i	$-0.734041\pi$
$173$	−4.78611	+	2.76326i	−0.363881	+	0.210087i	0.306901	+	0.951742i	$0.400708\pi$
$174$		0			0
$175$	−9.16463	−	6.13851i	−0.692781	−	0.464027i
$176$		0			0
$177$	−17.0517	+	15.4254i	−1.28169	+	1.15944i
$178$		0			0
$179$	−1.65203	−	2.86140i	−0.123478	−	0.213871i	0.797659	−	0.603109i	$-0.206072\pi$
$179$	−1.65203	−	2.86140i	−0.123478	−	0.213871i	−0.921137	+	0.389238i	$0.872738\pi$
$180$		0			0
$181$	−11.7692			−0.874795			−0.437398	−	0.899268i	$-0.644100\pi$
$181$	−11.7692			−0.874795			−0.437398	+	0.899268i	$0.644100\pi$
$182$		0			0
$183$	−0.538086	−	2.50287i	−0.0397765	−	0.185017i
$184$		0			0
$185$	−1.37349	−	0.792984i	−0.100981	−	0.0583013i
$186$		0			0
$187$	−24.1059	+	13.9175i	−1.76279	+	1.01775i
$188$		0			0
$189$	0.620119	+	13.7337i	0.0451070	+	0.998982i
$190$		0			0
$191$	4.87967	+	8.45184i	0.353081	+	0.611553i	0.986788	−	0.162020i	$-0.0518008\pi$
$191$	4.87967	+	8.45184i	0.353081	+	0.611553i	−0.633707	+	0.773573i	$0.718467\pi$
$192$		0			0
$193$	7.30962	−	12.6606i	0.526158	−	0.911333i	−0.473377	−	0.880860i	$-0.656965\pi$
$193$	7.30962	−	12.6606i	0.526158	−	0.911333i	0.999536	−	0.0304731i	$-0.00970138\pi$
$194$		0			0
$195$	0.980305	−	0.210754i	0.0702011	−	0.0150924i
$196$		0			0
$197$			22.4670i			1.60071i	0.599526	+	0.800355i	$0.295356\pi$
$197$			22.4670i			1.60071i	−0.599526	+	0.800355i	$0.704644\pi$
$198$		0			0
$199$	−7.67719	+	4.43243i	−0.544221	+	0.314206i	−0.746788	−	0.665062i	$-0.768405\pi$
$199$	−7.67719	+	4.43243i	−0.544221	+	0.314206i	0.202567	+	0.979268i	$0.435072\pi$
$200$		0			0
$201$	6.33956	+	7.00795i	0.447158	+	0.494303i
$202$		0			0
$203$	−5.08580	−	10.3423i	−0.356953	−	0.725884i
$204$		0			0
$205$	4.47514	+	7.75116i	0.312557	+	0.541365i
$206$		0			0
$207$	−2.58621	−	1.86068i	−0.179754	−	0.129326i
$208$		0			0
$209$	−28.3567	−	16.3717i	−1.96147	−	1.13246i
$210$		0			0
$211$	−11.6175	+	6.70738i	−0.799783	+	0.461755i	−0.843395	−	0.537294i	$-0.819447\pi$
$211$	−11.6175	+	6.70738i	−0.799783	+	0.461755i	0.0436123	+	0.999049i	$0.486113\pi$
$212$		0			0
$213$	−13.1967	−	4.25396i	−0.904220	−	0.291476i
$214$		0			0
$215$	−2.95773	+	5.12293i	−0.201715	+	0.349381i
$216$		0			0
$217$	−12.2620	−	24.9354i	−0.832396	−	1.69272i
$218$		0			0
$219$	−3.19860	−	14.8780i	−0.216141	−	1.00536i
$220$		0			0
$221$	−3.39043	−	1.95746i	−0.228065	−	0.131673i
$222$		0			0
$223$	0.901983	+	0.520760i	0.0604013	+	0.0348727i	0.529897	−	0.848062i	$-0.322231\pi$
$223$	0.901983	+	0.520760i	0.0604013	+	0.0348727i	−0.469495	+	0.882935i	$0.655564\pi$
$224$		0			0
$225$	10.1528	+	7.30453i	0.676852	+	0.486969i
$226$		0			0
$227$	3.26115			0.216450			0.108225	−	0.994126i	$-0.465483\pi$
$227$	3.26115			0.216450			0.108225	+	0.994126i	$0.465483\pi$
$228$		0			0
$229$	−15.1064			−0.998259			−0.499130	−	0.866527i	$-0.666347\pi$
$229$	−15.1064			−0.998259			−0.499130	+	0.866527i	$0.666347\pi$
$230$		0			0
$231$	12.8304	+	16.2352i	0.844181	+	1.06820i
$232$		0			0
$233$	−8.34972	−	4.82071i	−0.547008	−	0.315815i	0.200906	−	0.979610i	$-0.435611\pi$
$233$	−8.34972	−	4.82071i	−0.547008	−	0.315815i	−0.747914	+	0.663795i	$0.768945\pi$
$234$		0			0
$235$	−7.39034	+	4.26681i	−0.482093	+	0.278336i
$236$		0			0
$237$	25.1760	−	5.41253i	1.63535	−	0.351582i
$238$		0			0
$239$	13.7549	+	23.8242i	0.889731	+	1.54106i	0.840194	+	0.542286i	$0.182441\pi$
$239$	13.7549	+	23.8242i	0.889731	+	1.54106i	0.0495367	+	0.998772i	$0.484226\pi$
$240$		0			0
$241$	−13.0727			−0.842089			−0.421045	−	0.907040i	$-0.638336\pi$
$241$	−13.0727			−0.842089			−0.421045	+	0.907040i	$0.638336\pi$
$242$		0			0
$243$	−0.181225	−	15.5874i	−0.0116256	−	0.999932i
$244$		0			0
$245$	−5.90041	+	2.42852i	−0.376963	+	0.155152i
$246$		0			0
$247$		−	4.60529i		−	0.293027i
$248$		0			0
$249$	9.03794	−	8.17593i	0.572756	−	0.518128i
$250$		0			0
$251$	−5.42523			−0.342438			−0.171219	−	0.985233i	$-0.554770\pi$
$251$	−5.42523			−0.342438			−0.171219	+	0.985233i	$0.554770\pi$
$252$		0			0
$253$	−4.79555			−0.301494
$254$		0			0
$255$	2.04554	+	9.51465i	0.128096	+	0.595831i
$256$		0			0
$257$		−	12.7030i		−	0.792392i	−0.918166	−	0.396196i	$-0.870330\pi$
$257$		−	12.7030i		−	0.792392i	0.918166	−	0.396196i	$-0.129670\pi$
$258$		0			0
$259$	4.13093	−	2.03139i	0.256684	−	0.126224i
$260$		0			0
$261$	5.37078	+	11.9136i	0.332443	+	0.737431i
$262$		0			0
$263$	2.44953			0.151045			0.0755224	−	0.997144i	$-0.475938\pi$
$263$	2.44953			0.151045			0.0755224	+	0.997144i	$0.475938\pi$
$264$		0			0
$265$	4.55197	+	7.88423i	0.279625	+	0.484325i
$266$		0			0
$267$	−4.85203	−	5.36360i	−0.296940	−	0.328247i
$268$		0			0
$269$	14.0278	−	8.09898i	0.855293	−	0.493803i	−0.00714047	−	0.999975i	$-0.502273\pi$
$269$	14.0278	−	8.09898i	0.855293	−	0.493803i	0.862433	+	0.506171i	$0.168940\pi$
$270$		0			0
$271$	−8.08183	−	4.66605i	−0.490936	−	0.283442i	0.234027	−	0.972230i	$-0.424810\pi$
$271$	−8.08183	−	4.66605i	−0.490936	−	0.283442i	−0.724963	+	0.688788i	$0.758143\pi$
$272$		0			0
$273$	−1.07523	+	2.70452i	−0.0650757	+	0.163685i
$274$		0			0
$275$	18.8261			1.13526
$276$		0			0
$277$	−10.4879			−0.630157			−0.315079	−	0.949066i	$-0.602031\pi$
$277$	−10.4879			−0.630157			−0.315079	+	0.949066i	$0.602031\pi$
$278$		0			0
$279$	12.9491	+	28.7238i	0.775240	+	1.71965i
$280$		0			0
$281$	−22.2238	−	12.8309i	−1.32576	−	0.765427i	−0.341118	−	0.940020i	$-0.610806\pi$
$281$	−22.2238	−	12.8309i	−1.32576	−	0.765427i	−0.984641	+	0.174593i	$0.944139\pi$
$282$		0			0
$283$	−3.45322	−	1.99372i	−0.205273	−	0.118514i	0.393840	−	0.919179i	$-0.371147\pi$
$283$	−3.45322	−	1.99372i	−0.205273	−	0.118514i	−0.599113	+	0.800665i	$0.704480\pi$
$284$		0			0
$285$	−8.48984	+	7.68010i	−0.502895	+	0.454930i
$286$		0			0
$287$	−25.9213	−	1.72821i	−1.53008	−	0.102013i
$288$		0			0
$289$	10.4988	−	18.1844i	0.617575	−	1.06967i
$290$		0			0
$291$	−7.98110	+	7.21988i	−0.467860	+	0.423237i
$292$		0			0
$293$	23.8239	−	13.7548i	1.39181	−	0.803561i	0.398293	−	0.917258i	$-0.369603\pi$
$293$	23.8239	−	13.7548i	1.39181	−	0.803561i	0.993515	+	0.113697i	$0.0362693\pi$
$294$		0			0
$295$	10.4795	+	6.05037i	0.610143	+	0.352266i
$296$		0			0
$297$	−13.9237	−	18.8858i	−0.807934	−	1.09587i
$298$		0			0
$299$	−0.337241	−	0.584118i	−0.0195031	−	0.0337804i
$300$		0			0
$301$	−7.57681	−	15.4078i	−0.436720	−	0.888093i
$302$		0			0
$303$	−4.20500	+	13.0448i	−0.241571	+	0.749403i
$304$		0			0
$305$	−1.16677	+	0.673635i	−0.0668090	+	0.0385722i
$306$		0			0
$307$			13.5995i			0.776163i	0.921625	+	0.388081i	$0.126862\pi$
$307$			13.5995i			0.776163i	−0.921625	+	0.388081i	$0.873138\pi$
$308$		0			0
$309$	6.88800	−	21.3680i	0.391845	−	1.21558i
$310$		0			0
$311$	9.43448	−	16.3410i	0.534980	−	0.926613i	−0.464184	−	0.885739i	$-0.653652\pi$
$311$	9.43448	−	16.3410i	0.534980	−	0.926613i	0.999164	−	0.0408740i	$-0.0130142\pi$
$312$		0			0
$313$	10.7670	+	18.6490i	0.608586	+	1.05410i	0.991474	+	0.130307i	$0.0415962\pi$
$313$	10.7670	+	18.6490i	0.608586	+	1.05410i	−0.382888	+	0.923795i	$0.625071\pi$
$314$		0			0
$315$	6.77890	−	2.52807i	0.381948	−	0.142441i
$316$		0			0
$317$	11.5701	−	6.67999i	0.649840	−	0.375185i	−0.138555	−	0.990355i	$-0.544246\pi$
$317$	11.5701	−	6.67999i	0.649840	−	0.375185i	0.788395	+	0.615169i	$0.210912\pi$
$318$		0			0
$319$	17.0349	+	9.83511i	0.953772	+	0.550661i
$320$		0			0
$321$	−6.62232	+	5.99071i	−0.369622	+	0.334369i
$322$		0			0
$323$	44.6980			2.48707
$324$		0			0
$325$	1.32392	+	2.29310i	0.0734378	+	0.127198i
$326$		0			0
$327$	−1.24431	−	5.78782i	−0.0688106	−	0.320067i
$328$		0			0
$329$	1.64776	−	24.7146i	0.0908439	−	1.36256i
$330$		0			0
$331$	26.0423	−	15.0355i	1.43141	−	0.826427i	0.434184	−	0.900824i	$-0.357037\pi$
$331$	26.0423	−	15.0355i	1.43141	−	0.826427i	0.997229	+	0.0743976i	$0.0237034\pi$
$332$		0			0
$333$	−4.75855	+	2.14521i	−0.260767	+	0.117557i
$334$		0			0
$335$	2.48659	−	4.30690i	0.135857	−	0.235311i
$336$		0			0
$337$	−6.06592	−	10.5065i	−0.330432	−	0.572324i	0.652165	−	0.758077i	$-0.273861\pi$
$337$	−6.06592	−	10.5065i	−0.330432	−	0.572324i	−0.982597	+	0.185753i	$0.940528\pi$
$338$		0			0
$339$	1.04796	−	0.225299i	0.0569174	−	0.0122366i
$340$		0			0
$341$	41.0715	+	23.7126i	2.22415	+	1.28411i
$342$		0			0
$343$	3.67430	−	18.1521i	0.198394	−	0.980122i
$344$		0			0
$345$	−0.514414	+	1.59582i	−0.0276951	+	0.0859161i
$346$		0			0
$347$	−12.1039	+	20.9647i	−0.649774	+	1.12544i	0.333403	+	0.942785i	$0.391803\pi$
$347$	−12.1039	+	20.9647i	−0.649774	+	1.12544i	−0.983177	+	0.182657i	$0.941530\pi$
$348$		0			0
$349$	−1.53901	+	2.66564i	−0.0823812	+	0.142688i	−0.904272	−	0.426956i	$-0.859586\pi$
$349$	−1.53901	+	2.66564i	−0.0823812	+	0.142688i	0.821891	+	0.569645i	$0.192919\pi$
$350$		0			0
$351$	1.32121	−	3.02409i	0.0705210	−	0.161414i
$352$		0			0
$353$			22.4953i			1.19730i	0.801010	+	0.598652i	$0.204297\pi$
$353$			22.4953i			1.19730i	−0.801010	+	0.598652i	$0.795703\pi$
$354$		0			0
$355$			7.29687i			0.387277i
$356$		0			0
$357$	−26.2496	−	10.4360i	−1.38927	−	0.552329i
$358$		0			0
$359$	2.88125	−	4.99047i	0.152067	−	0.263387i	−0.779920	−	0.625879i	$-0.784741\pi$
$359$	2.88125	−	4.99047i	0.152067	−	0.263387i	0.931987	+	0.362492i	$0.118074\pi$
$360$		0			0
$361$	16.7901	+	29.0812i	0.883687	+	1.53059i
$362$		0			0
$363$	−15.4804	−	4.99014i	−0.812513	−	0.261914i
$364$		0			0
$365$	−6.93574	+	4.00435i	−0.363033	+	0.209597i
$366$		0			0
$367$		−	21.0694i		−	1.09981i	−0.835226	−	0.549906i	$-0.814663\pi$
$367$		−	21.0694i		−	1.09981i	0.835226	−	0.549906i	$-0.185337\pi$
$368$		0			0
$369$	29.3098	+	2.94285i	1.52581	+	0.153199i
$370$		0			0
$371$	−26.3663	−	1.75788i	−1.36887	−	0.0912645i
$372$		0			0
$373$	14.2143			0.735987			0.367994	−	0.929828i	$-0.380045\pi$
$373$	14.2143			0.735987			0.367994	+	0.929828i	$0.380045\pi$
$374$		0			0
$375$	4.44137	−	13.7781i	0.229351	−	0.711496i
$376$		0			0
$377$			2.76657i			0.142485i
$378$		0			0
$379$			6.14836i			0.315820i	0.987454	+	0.157910i	$0.0504756\pi$
$379$			6.14836i			0.315820i	−0.987454	+	0.157910i	$0.949524\pi$
$380$		0			0
$381$	1.00145	−	3.10671i	0.0513058	−	0.159161i
$382$		0			0
$383$	−29.8228			−1.52388			−0.761938	−	0.647650i	$-0.775752\pi$
$383$	−29.8228			−1.52388			−0.761938	+	0.647650i	$0.775752\pi$
$384$		0			0
$385$	6.06034	−	9.04793i	0.308864	−	0.461125i
$386$		0			0
$387$	8.00137	+	17.7488i	0.406732	+	0.902221i
$388$		0			0
$389$			9.26817i			0.469915i	0.972006	+	0.234957i	$0.0754951\pi$
$389$			9.26817i			0.469915i	−0.972006	+	0.234957i	$0.924505\pi$
$390$		0			0
$391$	5.66934	−	3.27320i	0.286711	−	0.165533i
$392$		0			0
$393$	8.08640	+	2.60666i	0.407905	+	0.131489i
$394$		0			0
$395$	−6.77599	−	11.7364i	−0.340937	−	0.590521i
$396$		0			0
$397$	−10.6644	+	18.4712i	−0.535228	+	0.927043i	0.463924	+	0.885875i	$0.346441\pi$
$397$	−10.6644	+	18.4712i	−0.535228	+	0.927043i	−0.999152	+	0.0411677i	$0.986892\pi$
$398$		0			0
$399$	−4.80768	−	32.8796i	−0.240685	−	1.64604i
$400$		0			0
$401$		−	7.76840i		−	0.387935i	−0.981008	−	0.193968i	$-0.937864\pi$
$401$		−	7.76840i		−	0.387935i	0.981008	−	0.193968i	$-0.0621357\pi$
$402$		0			0
$403$			6.67024i			0.332268i
$404$		0			0
$405$	−7.77824	+	2.60753i	−0.386504	+	0.129569i
$406$		0			0
$407$	−3.92837	+	6.80414i	−0.194722	+	0.337269i
$408$		0			0
$409$	−11.4439	+	19.8214i	−0.565864	+	0.980105i	0.431105	+	0.902302i	$0.358124\pi$
$409$	−11.4439	+	19.8214i	−0.565864	+	0.980105i	−0.996969	+	0.0778033i	$0.975209\pi$
$410$		0			0
$411$	−3.63346	+	11.2718i	−0.179225	+	0.555995i
$412$		0			0
$413$	−31.5185	+	15.4992i	−1.55093	+	0.762668i
$414$		0			0
$415$	−5.55448	−	3.20688i	−0.272659	−	0.157420i
$416$		0			0
$417$	−21.0966	+	4.53553i	−1.03311	+	0.222106i
$418$		0			0
$419$	−3.40785	−	5.90256i	−0.166484	−	0.288359i	0.770697	−	0.637202i	$-0.219908\pi$
$419$	−3.40785	−	5.90256i	−0.166484	−	0.288359i	−0.937181	+	0.348843i	$0.886575\pi$
$420$		0			0
$421$	9.22429	−	15.9769i	0.449564	−	0.778668i	−0.548793	−	0.835958i	$-0.684913\pi$
$421$	9.22429	−	15.9769i	0.449564	−	0.778668i	0.998358	+	0.0572900i	$0.0182460\pi$
$422$		0			0
$423$	−2.80586	+	27.9454i	−0.136425	+	1.35875i
$424$		0			0
$425$	−22.2564	+	12.8497i	−1.07959	+	0.623303i
$426$		0			0
$427$	0.260144	−	3.90188i	0.0125893	−	0.188825i
$428$		0			0
$429$	−1.04405	−	4.85634i	−0.0504074	−	0.234466i
$430$		0			0
$431$	0.962293	+	1.66674i	0.0463520	+	0.0802840i	0.888271	−	0.459321i	$-0.151907\pi$
$431$	0.962293	+	1.66674i	0.0463520	+	0.0802840i	−0.841919	+	0.539605i	$0.818574\pi$
$432$		0			0
$433$	19.5159			0.937875			0.468938	−	0.883231i	$-0.344637\pi$
$433$	19.5159			0.937875			0.468938	+	0.883231i	$0.344637\pi$
$434$		0			0
$435$	5.10016	−	4.61372i	0.244534	−	0.221211i
$436$		0			0
$437$	6.66908	+	3.85039i	0.319025	+	0.184189i
$438$		0			0
$439$	2.73160	−	1.57709i	0.130372	−	0.0752704i	−0.433396	−	0.901204i	$-0.642685\pi$
$439$	2.73160	−	1.57709i	0.130372	−	0.0752704i	0.563768	+	0.825933i	$0.309351\pi$
$440$		0			0
$441$	−4.85325	+	20.4315i	−0.231107	+	0.972928i
$442$		0			0
$443$	9.91615	+	17.1753i	0.471131	+	0.816022i	0.999455	−	0.0330206i	$-0.0105127\pi$
$443$	9.91615	+	17.1753i	0.471131	+	0.816022i	−0.528324	+	0.849043i	$0.677179\pi$
$444$		0			0
$445$	−1.90313	+	3.29632i	−0.0902172	+	0.156261i
$446$		0			0
$447$	−7.50241	+	23.2740i	−0.354852	+	1.10082i
$448$		0			0
$449$			10.7923i			0.509320i	0.967031	+	0.254660i	$0.0819635\pi$
$449$			10.7923i			0.509320i	−0.967031	+	0.254660i	$0.918036\pi$
$450$		0			0
$451$	38.3986	−	22.1694i	1.80812	−	1.04392i
$452$		0			0
$453$	9.84828	−	30.5514i	0.462712	−	1.43543i
$454$		0			0
$455$	1.52826	+	0.101891i	0.0716460	+	0.00477674i
$456$		0			0
$457$	−16.0669	−	27.8287i	−0.751579	−	1.30177i	−0.947057	−	0.321065i	$-0.895959\pi$
$457$	−16.0669	−	27.8287i	−0.751579	−	1.30177i	0.195478	−	0.980708i	$-0.437374\pi$
$458$		0			0
$459$	29.3512	+	12.8234i	1.37000	+	0.598546i
$460$		0			0
$461$	20.9889	+	12.1179i	0.977550	+	0.564389i	0.901529	−	0.432718i	$-0.142445\pi$
$461$	20.9889	+	12.1179i	0.977550	+	0.564389i	0.0760202	+	0.997106i	$0.475779\pi$
$462$		0			0
$463$	−13.6304	+	7.86952i	−0.633459	+	0.365728i	−0.782091	−	0.623165i	$-0.785847\pi$
$463$	−13.6304	+	7.86952i	−0.633459	+	0.365728i	0.148631	+	0.988893i	$0.452513\pi$
$464$		0			0
$465$	12.2966	−	11.1238i	0.570240	−	0.515853i
$466$		0			0
$467$	7.77171	−	13.4610i	0.359632	−	0.622901i	−0.628267	−	0.777997i	$-0.716236\pi$
$467$	7.77171	−	13.4610i	0.359632	−	0.622901i	0.987899	+	0.155097i	$0.0495690\pi$
$468$		0			0
$469$	6.36990	+	12.9535i	0.294135	+	0.598139i
$470$		0			0
$471$	1.19455	−	1.08062i	0.0550420	−	0.0497923i
$472$		0			0
$473$	25.3785	+	14.6523i	1.16691	+	0.673714i
$474$		0			0
$475$	−26.1811	−	15.1156i	−1.20127	−	0.693553i
$476$		0			0
$477$	29.8130	+	2.99337i	1.36504	+	0.137057i
$478$		0			0
$479$	−1.77509			−0.0811059			−0.0405529	−	0.999177i	$-0.512912\pi$
$479$	−1.77509			−0.0811059			−0.0405529	+	0.999177i	$0.512912\pi$
$480$		0			0
$481$	−1.10503			−0.0503850
$482$		0			0
$483$	−3.01753	−	3.81827i	−0.137303	−	0.173737i
$484$		0			0
$485$	4.90497	+	2.83189i	0.222723	+	0.128589i
$486$		0			0
$487$	12.0166	−	6.93776i	0.544522	−	0.314380i	−0.202387	−	0.979306i	$-0.564870\pi$
$487$	12.0166	−	6.93776i	0.544522	−	0.314380i	0.746910	+	0.664925i	$0.231537\pi$
$488$		0			0
$489$	−0.873699	−	0.965815i	−0.0395100	−	0.0436757i
$490$		0			0
$491$	−18.8330	−	32.6196i	−0.849919	−	1.47210i	−0.881280	−	0.472595i	$-0.843317\pi$
$491$	−18.8330	−	32.6196i	−0.849919	−	1.47210i	0.0313601	−	0.999508i	$-0.490016\pi$
$492$		0			0
$493$	−26.8518			−1.20934
$494$		0			0
$495$	−7.21152	+	10.0235i	−0.324134	+	0.450523i
$496$		0			0
$497$	−17.5970	−	11.7866i	−0.789335	−	0.528700i
$498$		0			0
$499$		−	22.0430i		−	0.986779i	−0.869808	−	0.493389i	$-0.835758\pi$
$499$		−	22.0430i		−	0.986779i	0.869808	−	0.493389i	$-0.164242\pi$
$500$		0			0
$501$	1.03151	+	4.79800i	0.0460846	+	0.214359i
$502$		0			0
$503$	21.2154			0.945949			0.472974	−	0.881076i	$-0.343180\pi$
$503$	21.2154			0.945949			0.472974	+	0.881076i	$0.343180\pi$
$504$		0			0
$505$	7.21288			0.320969
$506$		0			0
$507$	−16.1800	+	14.6368i	−0.718577	+	0.650042i
$508$		0			0
$509$			35.6126i			1.57850i	0.614072	+	0.789250i	$0.289530\pi$
$509$			35.6126i			1.57850i	−0.614072	+	0.789250i	$0.710470\pi$
$510$		0			0
$511$	1.54640	−	23.1943i	0.0684087	−	1.02606i
$512$		0			0
$513$	4.19976	+	37.4436i	0.185424	+	1.65318i
$514$		0			0
$515$	−11.8151			−0.520635
$516$		0			0
$517$	21.1374	+	36.6111i	0.929623	+	1.61015i
$518$		0			0
$519$	9.35840	−	2.01194i	0.410788	−	0.0883145i
$520$		0			0
$521$	29.7881	−	17.1982i	1.30504	−	0.753466i	0.323777	−	0.946133i	$-0.395047\pi$
$521$	29.7881	−	17.1982i	1.30504	−	0.753466i	0.981264	+	0.192668i	$0.0617139\pi$
$522$		0			0
$523$	−4.38233	−	2.53014i	−0.191626	−	0.110635i	0.401118	−	0.916027i	$-0.368622\pi$
$523$	−4.38233	−	2.53014i	−0.191626	−	0.110635i	−0.592743	+	0.805391i	$0.701955\pi$
$524$		0			0
$525$	11.8460	+	14.9895i	0.517004	+	0.654197i
$526$		0			0
$527$	−64.7401			−2.82012
$528$		0			0
$529$	−21.8722			−0.950963
$530$		0			0
$531$	36.3072	−	16.3677i	1.57560	−	0.710299i
$532$		0			0
$533$	5.40066	+	3.11807i	0.233929	+	0.135059i
$534$		0			0
$535$	4.06991	+	2.34976i	0.175957	+	0.101589i
$536$		0			0
$537$	1.20285	+	5.59496i	0.0519068	+	0.241440i
$538$		0			0
$539$	12.0307	+	29.2301i	0.518197	+	1.25903i
$540$		0			0
$541$	−10.6221	+	18.3980i	−0.456679	+	0.790992i	−0.998783	−	0.0493196i	$-0.984295\pi$
$541$	−10.6221	+	18.3980i	−0.456679	+	0.790992i	0.542104	+	0.840312i	$0.317628\pi$
$542$		0			0
$543$	19.4017	+	6.25415i	0.832606	+	0.268391i
$544$		0			0
$545$	−2.69813	+	1.55776i	−0.115575	+	0.0667273i
$546$		0			0
$547$	−5.03897	−	2.90925i	−0.215451	−	0.124390i	0.388391	−	0.921495i	$-0.373031\pi$
$547$	−5.03897	−	2.90925i	−0.215451	−	0.124390i	−0.603842	+	0.797104i	$0.706364\pi$
$548$		0			0
$549$	−0.442982	+	4.41196i	−0.0189060	+	0.188298i
$550$		0			0
$551$	−15.7934	−	27.3550i	−0.672822	−	1.16536i
$552$		0			0
$553$	39.2485	+	2.61675i	1.66902	+	0.111276i
$554$		0			0
$555$	1.84283	+	2.03712i	0.0782237	+	0.0864710i
$556$		0			0
$557$	−13.4790	+	7.78211i	−0.571124	+	0.329739i	−0.757598	−	0.652721i	$-0.773627\pi$
$557$	−13.4790	+	7.78211i	−0.571124	+	0.329739i	0.186474	+	0.982460i	$0.440294\pi$
$558$		0			0
$559$			4.12162i			0.174326i
$560$		0			0
$561$	47.1347	−	10.1334i	1.99003	−	0.427833i
$562$		0			0
$563$	10.7171	−	18.5625i	0.451670	−	0.782315i	−0.546820	−	0.837250i	$-0.684162\pi$
$563$	10.7171	−	18.5625i	0.451670	−	0.782315i	0.998490	+	0.0549349i	$0.0174951\pi$
$564$		0			0
$565$	−0.282054	−	0.488532i	−0.0118661	−	0.0205527i
$566$		0			0
$567$	6.27585	−	22.9698i	0.263561	−	0.964643i
$568$		0			0
$569$	−24.9498	+	14.4048i	−1.04595	+	0.603879i	−0.921512	−	0.388349i	$-0.873046\pi$
$569$	−24.9498	+	14.4048i	−1.04595	+	0.603879i	−0.124436	+	0.992228i	$0.539712\pi$
$570$		0			0
$571$	−7.64577	−	4.41429i	−0.319966	−	0.184732i	0.331412	−	0.943486i	$-0.392475\pi$
$571$	−7.64577	−	4.41429i	−0.319966	−	0.184732i	−0.651377	+	0.758754i	$0.725808\pi$
$572$		0			0
$573$	−3.55291	−	16.5261i	−0.148425	−	0.690387i
$574$		0			0
$575$	−4.42762			−0.184644
$576$		0			0
$577$	5.83225	+	10.1017i	0.242800	+	0.420541i	0.961511	−	0.274768i	$-0.0886009\pi$
$577$	5.83225	+	10.1017i	0.242800	+	0.420541i	−0.718711	+	0.695309i	$0.755268\pi$
$578$		0			0
$579$	−18.7779	+	16.9870i	−0.780384	+	0.705954i
$580$		0			0
$581$	16.7058	−	8.21507i	0.693072	−	0.340818i
$582$		0			0
$583$	39.0578	−	22.5500i	1.61761	−	0.933927i
$584$		0			0
$585$	−1.72804	−	0.173504i	−0.0714459	−	0.00717351i
$586$		0			0
$587$	9.27599	−	16.0665i	0.382861	−	0.663135i	−0.608609	−	0.793470i	$-0.708272\pi$
$587$	9.27599	−	16.0665i	0.382861	−	0.663135i	0.991470	+	0.130336i	$0.0416055\pi$
$588$		0			0
$589$	−38.0782	−	65.9534i	−1.56898	−	2.71756i
$590$		0			0
$591$	11.9390	−	37.0373i	0.491106	−	1.52351i
$592$		0			0
$593$	2.35329	+	1.35867i	0.0966380	+	0.0557940i	0.547540	−	0.836779i	$-0.315564\pi$
$593$	2.35329	+	1.35867i	0.0966380	+	0.0557940i	−0.450902	+	0.892573i	$0.648898\pi$
$594$		0			0
$595$	−0.988939	+	14.8330i	−0.0405425	+	0.608095i
$596$		0			0
$597$	15.0114	−	3.22727i	0.614375	−	0.132083i
$598$		0			0
$599$	−9.36817	+	16.2262i	−0.382773	+	0.662983i	−0.991458	−	0.130430i	$-0.958364\pi$
$599$	−9.36817	+	16.2262i	−0.382773	+	0.662983i	0.608684	+	0.793412i	$0.291698\pi$
$600$		0			0
$601$	−13.0782	+	22.6521i	−0.533471	+	0.923999i	0.465765	+	0.884909i	$0.345779\pi$
$601$	−13.0782	+	22.6521i	−0.533471	+	0.923999i	−0.999236	+	0.0390904i	$0.987554\pi$
$602$		0			0
$603$	−6.72684	−	14.9216i	−0.273938	−	0.607654i
$604$		0			0
$605$			8.55964i			0.347999i
$606$		0			0
$607$		−	11.8809i		−	0.482230i	−0.970497	−	0.241115i	$-0.922487\pi$
$607$		−	11.8809i		−	0.482230i	0.970497	−	0.241115i	$-0.0775131\pi$
$608$		0			0
$609$	2.88815	+	19.7520i	0.117034	+	0.800391i
$610$		0			0
$611$	−2.97292	+	5.14925i	−0.120272	+	0.208317i
$612$		0			0
$613$	−22.0844	−	38.2514i	−0.891982	−	1.54496i	−0.837496	−	0.546443i	$-0.815981\pi$
$613$	−22.0844	−	38.2514i	−0.891982	−	1.54496i	−0.0544856	−	0.998515i	$-0.517352\pi$
$614$		0			0
$615$	−3.25836	−	15.1560i	−0.131390	−	0.611150i
$616$		0			0
$617$	21.3973	−	12.3538i	0.861425	−	0.497344i	−0.00306450	−	0.999995i	$-0.500975\pi$
$617$	21.3973	−	12.3538i	0.861425	−	0.497344i	0.864489	+	0.502652i	$0.167642\pi$
$618$		0			0
$619$			17.8004i			0.715460i	0.933825	+	0.357730i	$0.116449\pi$
$619$			17.8004i			0.715460i	−0.933825	+	0.357730i	$0.883551\pi$
$620$		0			0
$621$	3.27465	+	4.44167i	0.131407	+	0.178238i
$622$		0			0
$623$	−4.87526	−	9.91410i	−0.195323	−	0.397200i
$624$		0			0
$625$	13.2273			0.529093
$626$		0			0
$627$	38.0466	+	42.0579i	1.51943	+	1.67963i
$628$		0			0
$629$		−	10.7252i		−	0.427642i
$630$		0			0
$631$			17.4695i			0.695448i	0.937597	+	0.347724i	$0.113045\pi$
$631$			17.4695i			0.695448i	−0.937597	+	0.347724i	$0.886955\pi$
$632$		0			0
$633$	22.7160	−	4.88367i	0.902880	−	0.194108i
$634$		0			0
$635$	−1.71780			−0.0681688
$636$		0			0
$637$	−2.71431	+	3.52095i	−0.107545	+	0.139505i
$638$		0			0
$639$	19.4944	+	14.0255i	0.771186	+	0.554838i
$640$		0			0
$641$			33.1328i			1.30867i	0.756206	+	0.654334i	$0.227051\pi$
$641$			33.1328i			1.30867i	−0.756206	+	0.654334i	$0.772949\pi$
$642$		0			0
$643$	6.20797	−	3.58417i	0.244819	−	0.141346i	−0.372571	−	0.928004i	$-0.621524\pi$
$643$	6.20797	−	3.58417i	0.244819	−	0.141346i	0.617389	+	0.786658i	$0.288190\pi$
$644$		0			0
$645$	7.59820	−	6.87350i	0.299179	−	0.270644i
$646$		0			0
$647$	−14.4804	−	25.0808i	−0.569284	−	0.986028i	−0.996637	−	0.0819437i	$-0.973887\pi$
$647$	−14.4804	−	25.0808i	−0.569284	−	0.986028i	0.427353	−	0.904085i	$-0.359446\pi$
$648$		0			0
$649$	29.9730	−	51.9147i	1.17654	−	2.03783i
$650$		0			0
$651$	6.96338	+	47.6224i	0.272917	+	1.86647i
$652$		0			0
$653$		−	35.7463i		−	1.39886i	−0.714701	−	0.699430i	$-0.753437\pi$
$653$		−	35.7463i		−	1.39886i	0.714701	−	0.699430i	$-0.246563\pi$
$654$		0			0
$655$		−	4.47124i		−	0.174706i
$656$		0			0
$657$	−2.63326	+	26.2264i	−0.102733	+	1.02319i
$658$		0			0
$659$	−15.3084	+	26.5149i	−0.596330	+	1.03287i	0.397028	+	0.917806i	$0.370042\pi$
$659$	−15.3084	+	26.5149i	−0.596330	+	1.03287i	−0.993358	+	0.115067i	$0.963292\pi$
$660$		0			0
$661$	−17.1782	+	29.7536i	−0.668156	+	1.15728i	0.310264	+	0.950650i	$0.399583\pi$
$661$	−17.1782	+	29.7536i	−0.668156	+	1.15728i	−0.978419	+	0.206629i	$0.933751\pi$
$662$		0			0
$663$	4.54898	+	5.02859i	0.176668	+	0.195294i
$664$		0			0
$665$	−15.6927	+	7.71687i	−0.608536	+	0.299247i
$666$		0			0
$667$	−4.00636	−	2.31307i	−0.155127	−	0.0895626i
$668$		0			0
$669$	−1.21020	−	1.33780i	−0.0467891	−	0.0517223i
$670$		0			0
$671$	3.33713	+	5.78007i	0.128828	+	0.223137i
$672$		0			0
$673$	6.51290	−	11.2807i	0.251054	−	0.434838i	−0.712762	−	0.701406i	$-0.752556\pi$
$673$	6.51290	−	11.2807i	0.251054	−	0.434838i	0.963816	+	0.266568i	$0.0858895\pi$
$674$		0			0
$675$	−12.8554	−	17.4368i	−0.494804	−	0.671145i
$676$		0			0
$677$	−3.76850	+	2.17575i	−0.144835	+	0.0836207i	−0.570666	−	0.821182i	$-0.693315\pi$
$677$	−3.76850	+	2.17575i	−0.144835	+	0.0836207i	0.425831	+	0.904803i	$0.359982\pi$
$678$		0			0
$679$	−14.7523	+	7.25444i	−0.566141	+	0.278400i
$680$		0			0
$681$	−5.37607	−	1.73298i	−0.206011	−	0.0664080i
$682$		0			0
$683$	0.0912485	+	0.158047i	0.00349153	+	0.00604750i	0.867766	−	0.496973i	$-0.165555\pi$
$683$	0.0912485	+	0.158047i	0.00349153	+	0.00604750i	−0.864274	+	0.503021i	$0.832222\pi$
$684$		0			0
$685$	6.23252			0.238132
$686$		0			0
$687$	24.9032	+	8.02756i	0.950116	+	0.306271i
$688$		0			0
$689$	5.49338	+	3.17160i	0.209281	+	0.120828i
$690$		0			0
$691$	22.1734	−	12.8018i	0.843517	−	0.487005i	−0.0149410	−	0.999888i	$-0.504756\pi$
$691$	22.1734	−	12.8018i	0.843517	−	0.487005i	0.858458	+	0.512883i	$0.171423\pi$
$692$		0			0
$693$	−12.5238	−	33.5821i	−0.475741	−	1.27568i
$694$		0			0
$695$	5.67806	+	9.83470i	0.215381	+	0.373051i
$696$		0			0
$697$	−30.2634	+	52.4178i	−1.14631	+	1.98547i
$698$		0			0
$699$	11.2029	+	12.3841i	0.423734	+	0.468409i
$700$		0			0
$701$			44.5999i			1.68451i	0.539076	+	0.842257i	$0.318774\pi$
$701$			44.5999i			1.68451i	−0.539076	+	0.842257i	$0.681226\pi$
$702$		0			0
$703$	10.9262	−	6.30825i	0.412090	−	0.237920i
$704$		0			0
$705$	14.4505	−	3.10668i	0.544237	−	0.117004i
$706$		0			0
$707$	−11.6509	+	17.3945i	−0.438178	+	0.654187i
$708$		0			0
$709$	0.541446	+	0.937811i	0.0203344	+	0.0352202i	0.876014	−	0.482286i	$-0.160194\pi$
$709$	0.541446	+	0.937811i	0.0203344	+	0.0352202i	−0.855679	+	0.517507i	$0.826860\pi$
$710$		0			0
$711$	−44.3793	−	4.45589i	−1.66435	−	0.167109i
$712$		0			0
$713$	−9.65941	−	5.57686i	−0.361748	−	0.208855i
$714$		0			0
$715$	−2.26390	+	1.30706i	−0.0846649	+	0.0488813i
$716$		0			0
$717$	−10.0150	−	46.5840i	−0.374017	−	1.73971i
$718$		0			0
$719$	12.0240	−	20.8261i	0.448419	−	0.776684i	−0.549865	−	0.835254i	$-0.685321\pi$
$719$	12.0240	−	20.8261i	0.448419	−	0.776684i	0.998283	+	0.0585698i	$0.0186540\pi$
$720$		0			0
$721$	19.0848	−	28.4931i	0.710755	−	1.06114i
$722$		0			0
$723$	21.5506	+	6.94687i	0.801477	+	0.258357i
$724$		0			0
$725$	15.7279	+	9.08052i	0.584121	+	0.337242i
$726$		0			0
$727$	31.2889	+	18.0647i	1.16044	+	0.669981i	0.951410	−	0.307928i	$-0.0996354\pi$
$727$	31.2889	+	18.0647i	1.16044	+	0.669981i	0.209032	+	0.977909i	$0.432969\pi$
$728$		0			0
$729$	−7.98442	+	25.7924i	−0.295719	+	0.955275i
$730$		0			0
$731$	−40.0036			−1.47959
$732$		0			0
$733$	−10.3045			−0.380604			−0.190302	−	0.981726i	$-0.560947\pi$
$733$	−10.3045			−0.380604			−0.190302	+	0.981726i	$0.560947\pi$
$734$		0			0
$735$	11.0174	−	0.867968i	0.406385	−	0.0320155i
$736$		0			0
$737$	−21.3360	−	12.3184i	−0.785922	−	0.453752i
$738$		0			0
$739$	26.0884	−	15.0621i	0.959676	−	0.554069i	0.0636026	−	0.997975i	$-0.479741\pi$
$739$	26.0884	−	15.0621i	0.959676	−	0.554069i	0.896073	+	0.443906i	$0.146408\pi$
$740$		0			0
$741$	−2.44726	+	7.59190i	−0.0899022	+	0.278895i
$742$		0			0
$743$	23.8516	+	41.3122i	0.875031	+	1.51560i	0.856730	+	0.515765i	$0.172492\pi$
$743$	23.8516	+	41.3122i	0.875031	+	1.51560i	0.0183011	+	0.999833i	$0.494174\pi$
$744$		0			0
$745$	12.8690			0.471483
$746$		0			0
$747$	−19.2439	+	8.67539i	−0.704098	+	0.317416i
$748$		0			0
$749$	−12.2407	+	6.01938i	−0.447267	+	0.219944i
$750$		0			0
$751$		−	26.1869i		−	0.955573i	−0.878476	−	0.477787i	$-0.841439\pi$
$751$		−	26.1869i		−	0.955573i	0.878476	−	0.477787i	$-0.158561\pi$
$752$		0			0
$753$	8.94359	+	2.88298i	0.325923	+	0.105061i
$754$		0			0
$755$	−16.8929			−0.614794
$756$		0			0
$757$	−28.8710			−1.04933			−0.524667	−	0.851307i	$-0.675810\pi$
$757$	−28.8710			−1.04933			−0.524667	+	0.851307i	$0.675810\pi$
$758$		0			0
$759$	7.90555	+	2.54836i	0.286953	+	0.0924997i
$760$		0			0
$761$			42.4848i			1.54007i	0.637999	+	0.770037i	$0.279762\pi$
$761$			42.4848i			1.54007i	−0.637999	+	0.770037i	$0.720238\pi$
$762$		0			0
$763$	0.601577	−	9.02301i	0.0217786	−	0.326655i
$764$		0			0
$765$	1.68400	−	16.7721i	0.0608850	−	0.606396i
$766$		0			0
$767$	8.43125			0.304435
$768$		0			0
$769$	−20.3143	−	35.1853i	−0.732551	−	1.26882i	−0.955789	−	0.294052i	$-0.904996\pi$
$769$	−20.3143	−	35.1853i	−0.732551	−	1.26882i	0.223238	−	0.974764i	$-0.428337\pi$
$770$		0			0
$771$	−6.75040	+	20.9412i	−0.243110	+	0.754177i
$772$		0			0
$773$	22.0030	−	12.7035i	0.791395	−	0.456912i	−0.0490586	−	0.998796i	$-0.515622\pi$
$773$	22.0030	−	12.7035i	0.791395	−	0.456912i	0.840453	+	0.541884i	$0.182289\pi$
$774$		0			0
$775$	37.9203	+	21.8933i	1.36214	+	0.786431i
$776$		0			0
$777$	−7.88940	+	1.15359i	−0.283031	+	0.0413849i
$778$		0			0
$779$	−71.2002			−2.55101
$780$		0			0
$781$	36.1480			1.29348
$782$		0			0
$783$	−2.52295	−	22.4938i	−0.0901628	−	0.803862i
$784$		0			0
$785$	−0.734139	−	0.423856i	−0.0262026	−	0.0151281i
$786$		0			0
$787$	9.63371	+	5.56203i	0.343405	+	0.198265i	0.661777	−	0.749701i	$-0.269803\pi$
$787$	9.63371	+	5.56203i	0.343405	+	0.198265i	−0.318372	+	0.947966i	$0.603136\pi$
$788$		0			0
$789$	−4.03810	−	1.30169i	−0.143760	−	0.0463412i
$790$		0			0
$791$	1.63374	+	0.108924i	0.0580890	+	0.00387288i
$792$		0			0
$793$	−0.469358	+	0.812952i	−0.0166674	+	0.0288688i
$794$		0			0
$795$	−3.31430	−	15.4162i	−0.117546	−	0.546757i
$796$		0			0
$797$	4.55233	−	2.62829i	0.161252	−	0.0930988i	−0.417202	−	0.908814i	$-0.636989\pi$
$797$	4.55233	−	2.62829i	0.161252	−	0.0930988i	0.578454	+	0.815715i	$0.303656\pi$
$798$		0			0
$799$	−49.9777	−	28.8546i	−1.76808	−	1.02080i
$800$		0			0
$801$	5.14844	+	11.4204i	0.181911	+	0.403519i
$802$		0			0
$803$	19.8372	+	34.3590i	0.700039	+	1.21250i
$804$		0			0
$805$	−1.42530	+	2.12794i	−0.0502354	+	0.0750001i
$806$		0			0
$807$	−27.4290	+	5.89690i	−0.965545	+	0.207581i
$808$		0			0
$809$	−11.3564	+	6.55663i	−0.399270	+	0.230519i	−0.686169	−	0.727442i	$-0.740709\pi$
$809$	−11.3564	+	6.55663i	−0.399270	+	0.230519i	0.286899	+	0.957961i	$0.407376\pi$
$810$		0			0
$811$		−	28.5667i		−	1.00311i	−0.865125	−	0.501556i	$-0.832761\pi$
$811$		−	28.5667i		−	1.00311i	0.865125	−	0.501556i	$-0.167239\pi$
$812$		0			0
$813$	10.8435	+	11.9868i	0.380298	+	0.420394i
$814$		0			0
$815$	−0.342695	+	0.593564i	−0.0120041	+	0.0207917i
$816$		0			0
$817$	−23.5290	−	40.7533i	−0.823174	−	1.42578i
$818$		0			0
$819$	3.20972	−	3.88707i	0.112157	−	0.135825i
$820$		0			0
$821$	−15.6273	+	9.02242i	−0.545396	+	0.314885i	−0.747263	−	0.664528i	$-0.768633\pi$
$821$	−15.6273	+	9.02242i	−0.545396	+	0.314885i	0.201867	+	0.979413i	$0.435299\pi$
$822$		0			0
$823$	−38.0389	−	21.9618i	−1.32595	−	0.765539i	−0.341281	−	0.939961i	$-0.610861\pi$
$823$	−38.0389	−	21.9618i	−1.32595	−	0.765539i	−0.984671	+	0.174423i	$0.944194\pi$
$824$		0			0
$825$	−31.0351	−	10.0042i	−1.08050	−	0.348302i
$826$		0			0
$827$	33.5698			1.16734			0.583668	−	0.811993i	$-0.301617\pi$
$827$	33.5698			1.16734			0.583668	+	0.811993i	$0.301617\pi$
$828$		0			0
$829$	−9.13344	−	15.8196i	−0.317218	−	0.549437i	0.662689	−	0.748895i	$-0.269415\pi$
$829$	−9.13344	−	15.8196i	−0.317218	−	0.549437i	−0.979906	+	0.199458i	$0.936082\pi$
$830$		0			0
$831$	17.2895	+	5.57329i	0.599766	+	0.193335i
$832$		0			0
$833$	−34.1737	−	26.3446i	−1.18405	−	0.912786i
$834$		0			0
$835$	2.23670	−	1.29136i	0.0774043	−	0.0446894i
$836$		0			0
$837$	−6.08287	−	54.2329i	−0.210255	−	1.87456i
$838$		0			0
$839$	−4.29047	+	7.43130i	−0.148123	+	0.256557i	−0.930534	−	0.366206i	$-0.880657\pi$
$839$	−4.29047	+	7.43130i	−0.148123	+	0.256557i	0.782411	+	0.622763i	$0.213990\pi$
$840$		0			0
$841$	−5.01231	−	8.68158i	−0.172838	−	0.299365i
$842$		0			0
$843$	29.8179	+	32.9617i	1.02698	+	1.13526i
$844$		0			0
$845$	9.94378	+	5.74104i	0.342076	+	0.197498i
$846$		0			0
$847$	−20.6423	−	13.8263i	−0.709279	−	0.475078i
$848$		0			0
$849$	4.63324	+	5.12173i	0.159012	+	0.175777i
$850$		0			0
$851$	0.923895	−	1.60023i	0.0316707	−	0.0548553i
$852$		0			0
$853$	6.83591	−	11.8402i	0.234057	−	0.405399i	−0.724941	−	0.688811i	$-0.758133\pi$
$853$	6.83591	−	11.8402i	0.234057	−	0.405399i	0.958998	+	0.283412i	$0.0914664\pi$
$854$		0			0
$855$	18.0769	−	8.14928i	0.618216	−	0.278699i
$856$		0			0
$857$		−	4.19979i		−	0.143462i	−0.997424	−	0.0717311i	$-0.977148\pi$
$857$		−	4.19979i		−	0.143462i	0.997424	−	0.0717311i	$-0.0228523\pi$
$858$		0			0
$859$			6.51721i			0.222364i	0.993800	+	0.111182i	$0.0354637\pi$
$859$			6.51721i			0.222364i	−0.993800	+	0.111182i	$0.964536\pi$
$860$		0			0
$861$	41.8133	+	16.6236i	1.42499	+	0.566530i
$862$		0			0
$863$	27.0745	−	46.8944i	0.921626	−	1.59630i	0.124726	−	0.992191i	$-0.460195\pi$
$863$	27.0745	−	46.8944i	0.921626	−	1.59630i	0.796900	−	0.604112i	$-0.206472\pi$
$864$		0			0
$865$	−2.51877	−	4.36263i	−0.0856407	−	0.148334i
$866$		0			0
$867$	−26.9706	+	24.3983i	−0.915971	+	0.828608i
$868$		0			0
$869$	−58.1409	+	33.5677i	−1.97230	+	1.13871i
$870$		0			0
$871$		−	3.46509i		−	0.117410i
$872$		0			0
$873$	16.9936	−	7.66094i	0.575148	−	0.259284i
$874$		0			0
$875$	12.3058	−	18.3723i	0.416013	−	0.621097i
$876$		0			0
$877$	42.2534			1.42680			0.713398	−	0.700759i	$-0.247155\pi$
$877$	42.2534			1.42680			0.713398	+	0.700759i	$0.247155\pi$
$878$		0			0
$879$	−46.5835	+	10.0149i	−1.57122	+	0.337794i
$880$		0			0
$881$		−	21.8177i		−	0.735058i	−0.930012	−	0.367529i	$-0.880204\pi$
$881$		−	21.8177i		−	0.735058i	0.930012	−	0.367529i	$-0.119796\pi$
$882$		0			0
$883$			53.8619i			1.81260i	0.422638	+	0.906299i	$0.361104\pi$
$883$			53.8619i			1.81260i	−0.422638	+	0.906299i	$0.638896\pi$
$884$		0			0
$885$	−14.0605	−	15.5430i	−0.472640	−	0.522472i
$886$		0			0
$887$	12.9667			0.435378			0.217689	−	0.976018i	$-0.430148\pi$
$887$	12.9667			0.435378			0.217689	+	0.976018i	$0.430148\pi$
$888$		0			0
$889$	2.77475	−	4.14262i	0.0930620	−	0.138939i
$890$		0			0
$891$	12.9175	+	38.5327i	0.432752	+	1.29089i
$892$		0			0
$893$		−	67.8857i		−	2.27171i
$894$		0			0
$895$	2.60822	−	1.50586i	0.0871832	−	0.0503352i
$896$		0			0
$897$	0.245546	+	1.14214i	0.00819856	+	0.0381350i
$898$		0			0
$899$	22.8750	+	39.6206i	0.762924	+	1.32142i
$900$		0			0
$901$	−30.7830	+	53.3177i	−1.02553	+	1.77627i
$902$		0			0
$903$	4.30275	+	29.4264i	0.143187	+	0.979251i
$904$		0			0
$905$		−	10.7278i		−	0.356605i
$906$		0			0
$907$		−	20.5869i		−	0.683578i	−0.939777	−	0.341789i	$-0.888967\pi$
$907$		−	20.5869i		−	0.683578i	0.939777	−	0.341789i	$-0.111033\pi$
$908$		0			0
$909$	13.8640	−	19.2700i	0.459841	−	0.639146i
$910$		0			0
$911$	9.24843	−	16.0187i	0.306414	−	0.530725i	−0.671161	−	0.741312i	$-0.734204\pi$
$911$	9.24843	−	16.0187i	0.306414	−	0.530725i	0.977575	+	0.210587i	$0.0675374\pi$
$912$		0			0
$913$	−15.8866	+	27.5164i	−0.525770	+	0.910660i
$914$		0			0
$915$	2.28141	−	0.490476i	0.0754211	−	0.0162146i
$916$		0			0
$917$	10.7828	+	7.22235i	0.356079	+	0.238503i
$918$		0			0
$919$	−0.0359304	−	0.0207444i	−0.00118523	−	0.000684295i	0.499407	−	0.866367i	$-0.333551\pi$
$919$	−0.0359304	−	0.0207444i	−0.00118523	−	0.000684295i	−0.500593	+	0.865683i	$0.666884\pi$
$920$		0			0
$921$	7.22678	−	22.4190i	0.238130	−	0.738730i
$922$		0			0
$923$	2.54206	+	4.40298i	0.0836730	+	0.144926i
$924$		0			0
$925$	−3.62697	+	6.28210i	−0.119254	+	0.206554i
$926$		0			0
$927$	−22.7100	+	31.5653i	−0.745894	+	1.03674i
$928$		0			0
$929$	26.3893	−	15.2359i	0.865805	−	0.499873i	−0.000146825	−	1.00000i	$-0.500047\pi$
$929$	26.3893	−	15.2359i	0.865805	−	0.499873i	0.865952	+	0.500127i	$0.166713\pi$
$930$		0			0
$931$	6.73833	−	50.3092i	0.220840	−	1.64882i
$932$		0			0
$933$	−24.2365	+	21.9249i	−0.793469	+	0.717790i
$934$		0			0
$935$	−12.6861	−	21.9730i	−0.414880	−	0.718592i
$936$		0			0
$937$	−2.79007			−0.0911478			−0.0455739	−	0.998961i	$-0.514512\pi$
$937$	−2.79007			−0.0911478			−0.0455739	+	0.998961i	$0.514512\pi$
$938$		0			0
$939$	−7.83948	−	36.4647i	−0.255832	−	1.18998i
$940$		0			0
$941$	30.5158	+	17.6183i	0.994785	+	0.574339i	0.906701	−	0.421774i	$-0.138592\pi$
$941$	30.5158	+	17.6183i	0.994785	+	0.574339i	0.0880839	+	0.996113i	$0.471926\pi$
$942$		0			0
$943$	−9.03078	+	5.21392i	−0.294083	+	0.169789i
$944$		0			0
$945$	−12.5186	+	0.565251i	−0.407229	+	0.0183876i
$946$		0			0
$947$	−9.80418	−	16.9813i	−0.318593	−	0.551820i	0.661602	−	0.749856i	$-0.269877\pi$
$947$	−9.80418	−	16.9813i	−0.318593	−	0.551820i	−0.980195	+	0.198036i	$0.936544\pi$
$948$		0			0
$949$	−2.79005	+	4.83251i	−0.0905689	+	0.156870i
$950$		0			0
$951$	−22.6232	+	4.86372i	−0.733609	+	0.157717i
$952$		0			0
$953$		−	13.7977i		−	0.446950i	−0.974710	−	0.223475i	$-0.928260\pi$
$953$		−	13.7977i		−	0.446950i	0.974710	−	0.223475i	$-0.0717401\pi$
$954$		0			0
$955$	−7.70401	+	4.44791i	−0.249296	+	0.143931i
$956$		0			0
$957$	−22.8560	−	25.2657i	−0.738829	−	0.816725i
$958$		0			0
$959$	−10.0673	+	15.0303i	−0.325091	+	0.485353i
$960$		0			0
$961$	39.6520	+	68.6793i	1.27910	+	2.21546i
$962$		0			0
$963$	14.1005	−	6.35668i	0.454382	−	0.204841i
$964$		0			0
$965$	11.5404	+	6.66286i	0.371499	+	0.214485i
$966$		0			0
$967$	12.3253	−	7.11599i	0.396354	−	0.228835i	−0.288556	−	0.957463i	$-0.593175\pi$
$967$	12.3253	−	7.11599i	0.396354	−	0.228835i	0.684909	+	0.728628i	$0.259842\pi$
$968$		0			0
$969$	−73.6855	−	23.7526i	−2.36712	−	0.763044i
$970$		0			0
$971$	−9.11370	+	15.7854i	−0.292473	+	0.506577i	−0.974394	−	0.224848i	$-0.927811\pi$
$971$	−9.11370	+	15.7854i	−0.292473	+	0.506577i	0.681921	+	0.731426i	$0.261145\pi$
$972$		0			0
$973$	−32.8890	−	2.19276i	−1.05437	−	0.0702965i
$974$		0			0
$975$	−0.963951	−	4.48374i	−0.0308711	−	0.143595i
$976$		0			0
$977$	9.38975	+	5.42117i	0.300405	+	0.173439i	0.642625	−	0.766181i	$-0.277845\pi$
$977$	9.38975	+	5.42117i	0.300405	+	0.173439i	−0.342220	+	0.939620i	$0.611179\pi$
$978$		0			0
$979$	16.3297	+	9.42795i	0.521899	+	0.301319i
$980$		0			0
$981$	−1.02438	+	10.2026i	−0.0327061	+	0.325742i
$982$		0			0
$983$	−53.9525			−1.72082			−0.860408	−	0.509605i	$-0.829792\pi$
$983$	−53.9525			−1.72082			−0.860408	+	0.509605i	$0.829792\pi$
$984$		0			0
$985$	−20.4791			−0.652520
$986$		0			0
$987$	−15.8497	+	39.8669i	−0.504503	+	1.26898i
$988$		0			0
$989$	−5.96866	−	3.44601i	−0.189792	−	0.109577i
$990$		0			0
$991$	−16.3812	+	9.45768i	−0.520366	+	0.300433i	−0.737084	−	0.675801i	$-0.763798\pi$
$991$	−16.3812	+	9.45768i	−0.520366	+	0.300433i	0.216719	+	0.976234i	$0.430465\pi$
$992$		0			0
$993$	−50.9211	+	10.9474i	−1.61593	+	0.347406i
$994$		0			0
$995$	−4.04024	−	6.99791i	−0.128084	−	0.221849i
$996$		0			0
$997$	−56.3212			−1.78371			−0.891855	−	0.452322i	$-0.850596\pi$
$997$	−56.3212			−1.78371			−0.891855	+	0.452322i	$0.850596\pi$
$998$		0			0
$999$	8.98453	−	1.00772i	0.284258	−	0.0318830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.bh.c.191.2	yes	30
3.2	odd	2		3024.2.bh.c.1871.6		30
4.3	odd	2		1008.2.bh.d.191.14	yes	30
7.4	even	3		1008.2.cj.c.767.9	yes	30
9.4	even	3		3024.2.cj.d.2879.10		30
9.5	odd	6		1008.2.cj.d.527.7	yes	30
12.11	even	2		3024.2.bh.d.1871.6		30
21.11	odd	6		3024.2.cj.c.1439.10		30
28.11	odd	6		1008.2.cj.d.767.7	yes	30
36.23	even	6		1008.2.cj.c.527.9	yes	30
36.31	odd	6		3024.2.cj.c.2879.10		30
63.4	even	3		3024.2.bh.d.2447.10		30
63.32	odd	6		1008.2.bh.d.95.14	yes	30
84.11	even	6		3024.2.cj.d.1439.10		30
252.67	odd	6		3024.2.bh.c.2447.10		30
252.95	even	6	inner	1008.2.bh.c.95.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bh.c.95.2	✓	30	252.95	even	6	inner
1008.2.bh.c.191.2	yes	30	1.1	even	1	trivial
1008.2.bh.d.95.14	yes	30	63.32	odd	6
1008.2.bh.d.191.14	yes	30	4.3	odd	2
1008.2.cj.c.527.9	yes	30	36.23	even	6
1008.2.cj.c.767.9	yes	30	7.4	even	3
1008.2.cj.d.527.7	yes	30	9.5	odd	6
1008.2.cj.d.767.7	yes	30	28.11	odd	6
3024.2.bh.c.1871.6		30	3.2	odd	2
3024.2.bh.c.2447.10		30	252.67	odd	6
3024.2.bh.d.1871.6		30	12.11	even	2
3024.2.bh.d.2447.10		30	63.4	even	3
3024.2.cj.c.1439.10		30	21.11	odd	6
3024.2.cj.c.2879.10		30	36.31	odd	6
3024.2.cj.d.1439.10		30	84.11	even	6
3024.2.cj.d.2879.10		30	9.4	even	3

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.64852 - 0.531401i) q^{3} +0.911520i q^{5} +(-2.19821 - 1.47237i) q^{7} +(2.43522 + 1.75205i) q^{9} +O(q^{10})\)	\(q+(-1.64852 - 0.531401i) q^{3} +0.911520i q^{5} +(-2.19821 - 1.47237i) q^{7} +(2.43522 + 1.75205i) q^{9} +4.51559 q^{11} +(0.317553 + 0.550018i) q^{13} +(0.484383 - 1.50266i) q^{15} +(-5.33837 + 3.08211i) q^{17} +(-6.27974 - 3.62561i) q^{19} +(2.84137 + 3.59536i) q^{21} -1.06200 q^{23} +4.16913 q^{25} +(-3.08347 - 4.18237i) q^{27} +(3.77247 + 2.17804i) q^{29} +(9.09549 + 5.25129i) q^{31} +(-7.44403 - 2.39959i) q^{33} +(1.34209 - 2.00371i) q^{35} +(-0.869958 + 1.50681i) q^{37} +(-0.231211 - 1.07546i) q^{39} +(8.50356 - 4.90953i) q^{41} +(5.62021 + 3.24483i) q^{43} +(-1.59703 + 2.21976i) q^{45} +(4.68099 + 8.10771i) q^{47} +(2.66425 + 6.47316i) q^{49} +(10.4382 - 2.24409i) q^{51} +(8.64955 - 4.99382i) q^{53} +4.11605i q^{55} +(8.42561 + 9.31394i) q^{57} +(6.63767 - 11.4968i) q^{59} +(0.739024 + 1.28003i) q^{61} +(-2.77347 - 7.43693i) q^{63} +(-0.501352 + 0.289456i) q^{65} +(-4.72497 - 2.72796i) q^{67} +(1.75073 + 0.564348i) q^{69} +8.00517 q^{71} +(4.39305 + 7.60899i) q^{73} +(-6.87289 - 2.21548i) q^{75} +(-9.92621 - 6.64862i) q^{77} +(-12.8756 + 7.43373i) q^{79} +(2.86064 + 8.53327i) q^{81} +(-3.51817 + 6.09365i) q^{83} +(-2.80940 - 4.86603i) q^{85} +(-5.06157 - 5.59523i) q^{87} +(3.61630 + 2.08787i) q^{89} +(0.111782 - 1.67661i) q^{91} +(-12.2035 - 13.4902i) q^{93} +(3.30481 - 5.72410i) q^{95} +(3.10677 - 5.38109i) q^{97} +(10.9965 + 7.91153i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 2 q^{7} - q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 2 * q^7 - q^9	\( 30 q - 3 q^{3} - 2 q^{7} - q^{9} + 6 q^{11} + 12 q^{17} + 9 q^{19} + 14 q^{21} - 24 q^{23} - 36 q^{25} + 27 q^{27} + 27 q^{29} + 6 q^{31} - 20 q^{33} - 6 q^{35} + 6 q^{37} - 15 q^{39} + 9 q^{41} - 21 q^{43} - 8 q^{45} + 12 q^{49} - 15 q^{51} - 3 q^{53} + 20 q^{57} + 3 q^{59} - 3 q^{61} + 24 q^{63} - 39 q^{67} + 10 q^{69} + 18 q^{71} + 21 q^{73} + 21 q^{75} + 36 q^{77} - 33 q^{79} - 17 q^{81} - 15 q^{83} - 3 q^{85} + 78 q^{87} + 6 q^{89} - 26 q^{91} - 3 q^{93} - 27 q^{95} - 6 q^{97} - 48 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 2 * q^7 - q^9 + 6 * q^11 + 12 * q^17 + 9 * q^19 + 14 * q^21 - 24 * q^23 - 36 * q^25 + 27 * q^27 + 27 * q^29 + 6 * q^31 - 20 * q^33 - 6 * q^35 + 6 * q^37 - 15 * q^39 + 9 * q^41 - 21 * q^43 - 8 * q^45 + 12 * q^49 - 15 * q^51 - 3 * q^53 + 20 * q^57 + 3 * q^59 - 3 * q^61 + 24 * q^63 - 39 * q^67 + 10 * q^69 + 18 * q^71 + 21 * q^73 + 21 * q^75 + 36 * q^77 - 33 * q^79 - 17 * q^81 - 15 * q^83 - 3 * q^85 + 78 * q^87 + 6 * q^89 - 26 * q^91 - 3 * q^93 - 27 * q^95 - 6 * q^97 - 48 * q^99

Introduction

L-functions

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