LMFDB - Embedded newform 270.3.l.b.253.1

Error: no document with id 275815335 found in table mf_hecke_traces.

Error: table True does not exist

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [270,3,Mod(37,270)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("270.37"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(270, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	270.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.35696713773$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			253.1
Character	$\chi$	$=$	270.253
Dual form			270.3.l.b.127.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36603 + 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(-4.54899 + 2.07525i) q^{5} +(-9.78534 - 2.62197i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-6.97363 + 1.16980i) q^{10} +(8.11214 + 14.0506i) q^{11} +(-20.2033 + 5.41347i) q^{13} +(-12.4073 - 7.16337i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-7.49936 + 7.49936i) q^{17} -1.15457i q^{19} +(-9.95434 - 0.954551i) q^{20} +(5.93850 + 22.1628i) q^{22} +(-19.1900 + 5.14194i) q^{23} +(16.3867 - 18.8806i) q^{25} -29.5797 q^{26} +(-14.3267 - 14.3267i) q^{28} +(19.9833 - 11.5374i) q^{29} +(2.50793 - 4.34387i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-12.9893 + 7.49936i) q^{34} +(49.9547 - 8.37971i) q^{35} +(33.0094 - 33.0094i) q^{37} +(0.422601 - 1.57717i) q^{38} +(-13.2485 - 4.94748i) q^{40} +(-26.2476 + 45.4622i) q^{41} +(-8.94107 + 33.3685i) q^{43} +32.4486i q^{44} -28.0961 q^{46} +(-15.5699 - 4.17194i) q^{47} +(46.4429 + 26.8138i) q^{49} +(29.2954 - 19.7935i) q^{50} +(-40.4067 - 10.8269i) q^{52} +(30.1924 + 30.1924i) q^{53} +(-66.0607 - 47.0815i) q^{55} +(-14.3267 - 24.8146i) q^{56} +(31.5207 - 8.44594i) q^{58} +(0.730822 + 0.421940i) q^{59} +(-15.8940 - 27.5292i) q^{61} +(5.01587 - 5.01587i) q^{62} +8.00000i q^{64} +(80.6705 - 66.5529i) q^{65} +(-9.02411 - 33.6785i) q^{67} +(-20.4886 + 5.48991i) q^{68} +(71.3066 + 6.83780i) q^{70} -1.68895 q^{71} +(100.701 + 100.701i) q^{73} +(57.1739 - 33.0094i) q^{74} +(1.15457 - 1.99977i) q^{76} +(-42.5396 - 158.760i) q^{77} +(-9.01283 + 5.20356i) q^{79} +(-16.2869 - 11.6077i) q^{80} +(-52.4953 + 52.4953i) q^{82} +(-6.02023 + 22.4678i) q^{83} +(18.5515 - 49.6776i) q^{85} +(-24.4275 + 42.3096i) q^{86} +(-11.8770 + 44.3256i) q^{88} +102.749i q^{89} +211.891 q^{91} +(-38.3800 - 10.2839i) q^{92} +(-19.7418 - 11.3980i) q^{94} +(2.39602 + 5.25211i) q^{95} +(-21.8580 - 5.85684i) q^{97} +(53.6276 + 53.6276i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} - 6 q^{7} + 48 q^{8} - 12 q^{10} + 12 q^{11} + 48 q^{16} + 36 q^{17} - 12 q^{20} - 12 q^{22} + 54 q^{23} + 54 q^{25} - 24 q^{28} - 72 q^{31} - 48 q^{32} + 336 q^{35} + 132 q^{37} + 36 q^{38}+ \cdots - 24 q^{98}+O(q^{100}) $ 24 * q + 12 * q^2 - 6 * q^7 + 48 * q^8 - 12 * q^10 + 12 * q^11 + 48 * q^16 + 36 * q^17 - 12 * q^20 - 12 * q^22 + 54 * q^23 + 54 * q^25 - 24 * q^28 - 72 * q^31 - 48 * q^32 + 336 * q^35 + 132 * q^37 + 36 * q^38 + 12 * q^40 - 24 * q^41 + 108 * q^43 + 216 * q^46 - 48 * q^47 - 54 * q^50 - 384 * q^53 - 552 * q^55 - 24 * q^56 + 60 * q^58 - 456 * q^61 - 144 * q^62 - 264 * q^65 + 12 * q^67 + 36 * q^68 + 174 * q^70 + 168 * q^71 - 432 * q^73 - 72 * q^76 + 48 * q^77 - 48 * q^82 + 246 * q^83 + 324 * q^85 - 216 * q^86 + 24 * q^88 + 1224 * q^91 + 108 * q^92 - 432 * q^95 - 102 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$	−4.54899	+	2.07525i	−0.909798	+	0.415050i
$5$	−4.54899	+	2.07525i	−0.909798	+	0.415050i
$6$		0			0
$7$	−9.78534	−	2.62197i	−1.39791	−	0.374568i	−0.520313	−	0.853975i	$-0.674185\pi$
$7$	−9.78534	−	2.62197i	−1.39791	−	0.374568i	−0.877592	+	0.479408i	$0.840852\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$		0			0
$10$	−6.97363	+	1.16980i	−0.697363	+	0.116980i
$11$	8.11214	+	14.0506i	0.737467	+	1.27733i	0.953632	+	0.300974i	$0.0973117\pi$
$11$	8.11214	+	14.0506i	0.737467	+	1.27733i	−0.216165	+	0.976357i	$0.569355\pi$
$12$		0			0
$13$	−20.2033	+	5.41347i	−1.55410	+	0.416421i	−0.930791	−	0.365552i	$-0.880880\pi$
$13$	−20.2033	+	5.41347i	−1.55410	+	0.416421i	−0.623312	+	0.781973i	$0.714213\pi$
$14$	−12.4073	−	7.16337i	−0.886237	−	0.511669i
$15$		0			0
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	−7.49936	+	7.49936i	−0.441139	+	0.441139i	−0.892395	−	0.451256i	$-0.850976\pi$
$17$	−7.49936	+	7.49936i	−0.441139	+	0.441139i	0.451256	+	0.892395i	$0.350976\pi$
$18$		0			0
$19$		−	1.15457i		−	0.0607666i	−0.999538	−	0.0303833i	$-0.990327\pi$
$19$		−	1.15457i		−	0.0607666i	0.999538	−	0.0303833i	$-0.00967280\pi$
$20$	−9.95434	−	0.954551i	−0.497717	−	0.0477275i
$21$		0			0
$22$	5.93850	+	22.1628i	0.269932	+	1.00740i
$23$	−19.1900	+	5.14194i	−0.834347	+	0.223563i	−0.650609	−	0.759413i	$-0.725486\pi$
$23$	−19.1900	+	5.14194i	−0.834347	+	0.223563i	−0.183738	+	0.982975i	$0.558820\pi$
$24$		0			0
$25$	16.3867	−	18.8806i	0.655466	−	0.755224i
$26$	−29.5797			−1.13768
$27$		0			0
$28$	−14.3267	−	14.3267i	−0.511669	−	0.511669i
$29$	19.9833	−	11.5374i	0.689080	−	0.397840i	−0.114187	−	0.993459i	$-0.536426\pi$
$29$	19.9833	−	11.5374i	0.689080	−	0.397840i	0.803267	+	0.595619i	$0.203093\pi$
$30$		0			0
$31$	2.50793	−	4.34387i	0.0809011	−	0.140125i	−0.822736	−	0.568423i	$-0.807554\pi$
$31$	2.50793	−	4.34387i	0.0809011	−	0.140125i	0.903637	+	0.428299i	$0.140887\pi$
$32$	1.46410	+	5.46410i	0.0457532	+	0.170753i
$33$		0			0
$34$	−12.9893	+	7.49936i	−0.382038	+	0.220569i
$35$	49.9547	−	8.37971i	1.42728	−	0.239420i
$36$		0			0
$37$	33.0094	−	33.0094i	0.892146	−	0.892146i	−0.102579	−	0.994725i	$-0.532709\pi$
$37$	33.0094	−	33.0094i	0.892146	−	0.892146i	0.994725	+	0.102579i	$0.0327095\pi$
$38$	0.422601	−	1.57717i	0.0111211	−	0.0415044i
$39$		0			0
$40$	−13.2485	−	4.94748i	−0.331212	−	0.123687i
$41$	−26.2476	+	45.4622i	−0.640186	+	1.10883i	0.345205	+	0.938527i	$0.387809\pi$
$41$	−26.2476	+	45.4622i	−0.640186	+	1.10883i	−0.985391	+	0.170307i	$0.945524\pi$
$42$		0			0
$43$	−8.94107	+	33.3685i	−0.207932	+	0.776012i	0.780604	+	0.625026i	$0.214912\pi$
$43$	−8.94107	+	33.3685i	−0.207932	+	0.776012i	−0.988536	+	0.150986i	$0.951755\pi$
$44$			32.4486i			0.737467i
$45$		0			0
$46$	−28.0961			−0.610785
$47$	−15.5699	−	4.17194i	−0.331274	−	0.0887647i	0.0893481	−	0.996000i	$-0.471522\pi$
$47$	−15.5699	−	4.17194i	−0.331274	−	0.0887647i	−0.420622	+	0.907236i	$0.638188\pi$
$48$		0			0
$49$	46.4429	+	26.8138i	0.947814	+	0.547221i
$50$	29.2954	−	19.7935i	0.585908	−	0.395869i
$51$		0			0
$52$	−40.4067	−	10.8269i	−0.777052	−	0.208210i
$53$	30.1924	+	30.1924i	0.569669	+	0.569669i	0.932036	−	0.362367i	$-0.118031\pi$
$53$	30.1924	+	30.1924i	0.569669	+	0.569669i	−0.362367	+	0.932036i	$0.618031\pi$
$54$		0			0
$55$	−66.0607	−	47.0815i	−1.20110	−	0.856027i
$56$	−14.3267	−	24.8146i	−0.255835	−	0.443118i
$57$		0			0
$58$	31.5207	−	8.44594i	0.543460	−	0.145620i
$59$	0.730822	+	0.421940i	0.0123868	+	0.00715153i	0.506181	−	0.862427i	$-0.331057\pi$
$59$	0.730822	+	0.421940i	0.0123868	+	0.00715153i	−0.493794	+	0.869579i	$0.664390\pi$
$60$		0			0
$61$	−15.8940	−	27.5292i	−0.260557	−	0.451298i	0.705833	−	0.708378i	$-0.250573\pi$
$61$	−15.8940	−	27.5292i	−0.260557	−	0.451298i	−0.966390	+	0.257080i	$0.917240\pi$
$62$	5.01587	−	5.01587i	0.0809011	−	0.0809011i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	80.6705	−	66.5529i	1.24109	−	1.02389i
$66$		0			0
$67$	−9.02411	−	33.6785i	−0.134688	−	0.502663i	−0.999999	−	0.00142763i	$-0.999546\pi$
$67$	−9.02411	−	33.6785i	−0.134688	−	0.502663i	0.865311	−	0.501236i	$-0.167121\pi$
$68$	−20.4886	+	5.48991i	−0.301304	+	0.0807340i
$69$		0			0
$70$	71.3066	+	6.83780i	1.01867	+	0.0976828i
$71$	−1.68895			−0.0237880			−0.0118940	−	0.999929i	$-0.503786\pi$
$71$	−1.68895			−0.0237880			−0.0118940	+	0.999929i	$0.503786\pi$
$72$		0			0
$73$	100.701	+	100.701i	1.37946	+	1.37946i	0.845520	+	0.533944i	$0.179291\pi$
$73$	100.701	+	100.701i	1.37946	+	1.37946i	0.533944	+	0.845520i	$0.320709\pi$
$74$	57.1739	−	33.0094i	0.772621	−	0.446073i
$75$		0			0
$76$	1.15457	−	1.99977i	0.0151917	−	0.0263127i
$77$	−42.5396	−	158.760i	−0.552463	−	2.06182i
$78$		0			0
$79$	−9.01283	+	5.20356i	−0.114086	+	0.0658679i	−0.555957	−	0.831211i	$-0.687648\pi$
$79$	−9.01283	+	5.20356i	−0.114086	+	0.0658679i	0.441871	+	0.897079i	$0.354315\pi$
$80$	−16.2869	−	11.6077i	−0.203586	−	0.145096i
$81$		0			0
$82$	−52.4953	+	52.4953i	−0.640186	+	0.640186i
$83$	−6.02023	+	22.4678i	−0.0725329	+	0.270696i	−0.992663	−	0.120917i	$-0.961416\pi$
$83$	−6.02023	+	22.4678i	−0.0725329	+	0.270696i	0.920130	+	0.391614i	$0.128083\pi$
$84$		0			0
$85$	18.5515	−	49.6776i	0.218253	−	0.584442i
$86$	−24.4275	+	42.3096i	−0.284040	+	0.491972i
$87$		0			0
$88$	−11.8770	+	44.3256i	−0.134966	+	0.503699i
$89$			102.749i			1.15449i	0.816572	+	0.577243i	$0.195871\pi$
$89$			102.749i			1.15449i	−0.816572	+	0.577243i	$0.804129\pi$
$90$		0			0
$91$	211.891			2.32847
$92$	−38.3800	−	10.2839i	−0.417174	−	0.111781i
$93$		0			0
$94$	−19.7418	−	11.3980i	−0.210020	−	0.121255i
$95$	2.39602	+	5.25211i	0.0252212	+	0.0552854i
$96$		0			0
$97$	−21.8580	−	5.85684i	−0.225341	−	0.0603798i	0.144382	−	0.989522i	$-0.453881\pi$
$97$	−21.8580	−	5.85684i	−0.225341	−	0.0603798i	−0.369723	+	0.929142i	$0.620547\pi$
$98$	53.6276	+	53.6276i	0.547221	+	0.547221i
$99$		0			0
$100$	47.2631	−	16.3155i	0.472631	−	0.163155i
$101$	−28.6802	−	49.6756i	−0.283963	−	0.491838i	0.688394	−	0.725337i	$-0.258316\pi$
$101$	−28.6802	−	49.6756i	−0.283963	−	0.491838i	−0.972357	+	0.233499i	$0.924983\pi$
$102$		0			0
$103$	−30.7382	+	8.23627i	−0.298429	+	0.0799638i	−0.404927	−	0.914349i	$-0.632703\pi$
$103$	−30.7382	+	8.23627i	−0.298429	+	0.0799638i	0.106498	+	0.994313i	$0.466036\pi$
$104$	−51.2336	−	29.5797i	−0.492631	−	0.284421i
$105$		0			0
$106$	30.1924	+	52.2949i	0.284834	+	0.493348i
$107$	16.8887	−	16.8887i	0.157838	−	0.157838i	−0.623770	−	0.781608i	$-0.714400\pi$
$107$	16.8887	−	16.8887i	0.157838	−	0.157838i	0.781608	+	0.623770i	$0.214400\pi$
$108$		0			0
$109$		−	8.42672i		−	0.0773094i	−0.999253	−	0.0386547i	$-0.987693\pi$
$109$		−	8.42672i		−	0.0773094i	0.999253	−	0.0386547i	$-0.0123072\pi$
$110$	−73.0075	−	88.4944i	−0.663705	−	0.804495i
$111$		0			0
$112$	−10.4879	−	39.1414i	−0.0936419	−	0.349476i
$113$	48.3042	−	12.9431i	0.427471	−	0.114541i	−0.0386677	−	0.999252i	$-0.512311\pi$
$113$	48.3042	−	12.9431i	0.427471	−	0.114541i	0.466139	+	0.884712i	$0.345645\pi$
$114$		0			0
$115$	76.6243	−	63.2147i	0.666298	−	0.549693i
$116$	46.1495			0.397840
$117$		0			0
$118$	0.843880	+	0.843880i	0.00715153	+	0.00715153i
$119$	93.0469	−	53.7207i	0.781907	−	0.451434i
$120$		0			0
$121$	−71.1136	+	123.172i	−0.587716	+	1.01795i
$122$	−11.6352	−	43.4232i	−0.0953705	−	0.355928i
$123$		0			0
$124$	8.68774	−	5.01587i	0.0700624	−	0.0404505i
$125$	−35.3608	+	119.894i	−0.282886	+	0.959153i
$126$		0			0
$127$	−144.508	+	144.508i	−1.13786	+	1.13786i	−0.149025	+	0.988833i	$0.547614\pi$
$127$	−144.508	+	144.508i	−1.13786	+	1.13786i	−0.988833	+	0.149025i	$0.952386\pi$
$128$	−2.92820	+	10.9282i	−0.0228766	+	0.0853766i
$129$		0			0
$130$	134.558	−	61.3854i	1.03506	−	0.472196i
$131$	−52.4476	+	90.8420i	−0.400364	+	0.693450i	−0.993770	−	0.111453i	$-0.964450\pi$
$131$	−52.4476	+	90.8420i	−0.400364	+	0.693450i	0.593406	+	0.804903i	$0.297783\pi$
$132$		0			0
$133$	−3.02724	+	11.2978i	−0.0227612	+	0.0849461i
$134$		−	49.3087i		−	0.367975i
$135$		0			0
$136$	−29.9974			−0.220569
$137$	−55.6524	−	14.9120i	−0.406222	−	0.108847i	0.0499215	−	0.998753i	$-0.484103\pi$
$137$	−55.6524	−	14.9120i	−0.406222	−	0.108847i	−0.456143	+	0.889906i	$0.650770\pi$
$138$		0			0
$139$	−108.159	−	62.4459i	−0.778126	−	0.449251i	0.0576399	−	0.998337i	$-0.481642\pi$
$139$	−108.159	−	62.4459i	−0.778126	−	0.449251i	−0.835766	+	0.549086i	$0.814976\pi$
$140$	94.9038	+	35.4406i	0.677884	+	0.253147i
$141$		0			0
$142$	−2.30714	−	0.618197i	−0.0162475	−	0.00435350i
$143$	−239.955	−	239.955i	−1.67801	−	1.67801i
$144$		0			0
$145$	−66.9610	+	93.9538i	−0.461800	+	0.647958i
$146$	100.701	+	174.419i	0.689732	+	1.19465i
$147$		0			0
$148$	90.1833	−	24.1646i	0.609347	−	0.163274i
$149$	158.796	+	91.6809i	1.06574	+	0.615308i	0.927016	−	0.375022i	$-0.122365\pi$
$149$	158.796	+	91.6809i	1.06574	+	0.615308i	0.138729	+	0.990330i	$0.455698\pi$
$150$		0			0
$151$	−45.6297	−	79.0329i	−0.302183	−	0.523397i	0.674447	−	0.738323i	$-0.264382\pi$
$151$	−45.6297	−	79.0329i	−0.302183	−	0.523397i	−0.976630	+	0.214927i	$0.931049\pi$
$152$	2.30913	−	2.30913i	0.0151917	−	0.0151917i
$153$		0			0
$154$		−	232.441i		−	1.50936i
$155$	−2.39395	+	24.9648i	−0.0154448	+	0.161063i
$156$		0			0
$157$	−9.28597	−	34.6557i	−0.0591463	−	0.220737i	0.930026	−	0.367492i	$-0.119784\pi$
$157$	−9.28597	−	34.6557i	−0.0591463	−	0.220737i	−0.989173	+	0.146755i	$0.953117\pi$
$158$	−14.2164	+	3.80927i	−0.0899772	+	0.0241093i
$159$		0			0
$160$	−17.9996	−	21.8178i	−0.112497	−	0.136361i
$161$	201.263			1.25008
$162$		0			0
$163$	−158.678	−	158.678i	−0.973485	−	0.973485i	0.0261726	−	0.999657i	$-0.491668\pi$
$163$	−158.678	−	158.678i	−0.973485	−	0.973485i	−0.999657	+	0.0261726i	$0.991668\pi$
$164$	−90.9245	+	52.4953i	−0.554417	+	0.320093i
$165$		0			0
$166$	−16.4476	+	28.4880i	−0.0990818	+	0.171615i
$167$	−51.7555	−	193.154i	−0.309913	−	1.15661i	−0.928633	−	0.370999i	$-0.879015\pi$
$167$	−51.7555	−	193.154i	−0.309913	−	1.15661i	0.618720	−	0.785611i	$-0.287651\pi$
$168$		0			0
$169$	232.511	−	134.240i	1.37581	−	0.794322i
$170$	43.5250	−	61.0706i	0.256030	−	0.359239i
$171$		0			0
$172$	−48.8549	+	48.8549i	−0.284040	+	0.284040i
$173$	−63.1904	+	235.830i	−0.365262	+	1.36318i	0.501803	+	0.864982i	$0.332670\pi$
$173$	−63.1904	+	235.830i	−0.365262	+	1.36318i	−0.867065	+	0.498195i	$0.833996\pi$
$174$		0			0
$175$	−209.854	+	141.788i	−1.19916	+	0.810216i
$176$	−32.4486	+	56.2025i	−0.184367	+	0.319333i
$177$		0			0
$178$	−37.6088	+	140.358i	−0.211286	+	0.788529i
$179$			112.194i			0.626781i	0.949624	+	0.313391i	$0.101465\pi$
$179$			112.194i			0.626781i	−0.949624	+	0.313391i	$0.898535\pi$
$180$		0			0
$181$	−11.2065			−0.0619143			−0.0309572	−	0.999521i	$-0.509856\pi$
$181$	−11.2065			−0.0619143			−0.0309572	+	0.999521i	$0.509856\pi$
$182$	289.448	+	77.5573i	1.59037	+	0.426139i
$183$		0			0
$184$	−48.6639	−	28.0961i	−0.264477	−	0.152696i
$185$	−81.6567	+	218.662i	−0.441387	+	1.18196i
$186$		0			0
$187$	−166.207	−	44.5349i	−0.888806	−	0.238155i
$188$	−22.7959	−	22.7959i	−0.121255	−	0.121255i
$189$		0			0
$190$	1.35061	+	8.05152i	0.00710848	+	0.0423764i
$191$	−43.4409	−	75.2419i	−0.227439	−	0.393937i	0.729609	−	0.683864i	$-0.239702\pi$
$191$	−43.4409	−	75.2419i	−0.227439	−	0.393937i	−0.957049	+	0.289928i	$0.906369\pi$
$192$		0			0
$193$	79.8914	−	21.4068i	0.413945	−	0.110916i	−0.0458351	−	0.998949i	$-0.514595\pi$
$193$	79.8914	−	21.4068i	0.413945	−	0.110916i	0.459780	+	0.888033i	$0.347928\pi$
$194$	−27.7149	−	16.0012i	−0.142860	−	0.0824804i
$195$		0			0
$196$	53.6276	+	92.8858i	0.273610	+	0.473907i
$197$	−91.8988	+	91.8988i	−0.466492	+	0.466492i	−0.900776	−	0.434284i	$-0.857001\pi$
$197$	−91.8988	+	91.8988i	−0.466492	+	0.466492i	0.434284	+	0.900776i	$0.357001\pi$
$198$		0			0
$199$			67.5469i			0.339432i	0.985493	+	0.169716i	$0.0542850\pi$
$199$			67.5469i			0.339432i	−0.985493	+	0.169716i	$0.945715\pi$
$200$	70.5345	−	4.98790i	0.352673	−	0.0249395i
$201$		0			0
$202$	−20.9954	−	78.3559i	−0.103938	−	0.387900i
$203$	−225.794	+	60.5014i	−1.11229	+	0.298036i
$204$		0			0
$205$	25.0547	−	261.278i	0.122218	−	1.27453i
$206$	−45.0038			−0.218465
$207$		0			0
$208$	−59.1595	−	59.1595i	−0.284421	−	0.284421i
$209$	16.2224	−	9.36600i	0.0776191	−	0.0448134i
$210$		0			0
$211$	−140.894	+	244.035i	−0.667744	+	1.15657i	0.310790	+	0.950479i	$0.399406\pi$
$211$	−140.894	+	244.035i	−0.667744	+	1.15657i	−0.978534	+	0.206087i	$0.933927\pi$
$212$	22.1024	+	82.4873i	0.104257	+	0.389091i
$213$		0			0
$214$	29.2521	−	16.8887i	0.136692	−	0.0789191i
$215$	−28.5752	−	170.348i	−0.132908	−	0.792317i
$216$		0			0
$217$	−35.9305	+	35.9305i	−0.165578	+	0.165578i
$218$	3.08439	−	11.5111i	0.0141486	−	0.0528033i
$219$		0			0
$220$	−67.3389	−	147.608i	−0.306086	−	0.670947i
$221$	110.915	−	192.110i	0.501876	−	0.869275i
$222$		0			0
$223$	−90.8647	+	339.112i	−0.407465	+	1.52068i	0.391999	+	0.919966i	$0.371784\pi$
$223$	−90.8647	+	339.112i	−0.407465	+	1.52068i	−0.799464	+	0.600714i	$0.794883\pi$
$224$		−	57.3069i		−	0.255835i
$225$		0			0
$226$	70.7223			0.312931
$227$	−323.682	−	86.7303i	−1.42591	−	0.382072i	−0.538335	−	0.842731i	$-0.680946\pi$
$227$	−323.682	−	86.7303i	−1.42591	−	0.382072i	−0.887577	+	0.460659i	$0.847613\pi$
$228$		0			0
$229$	334.125	+	192.907i	1.45906	+	0.842390i	0.998965	−	0.0454788i	$-0.0144814\pi$
$229$	334.125	+	192.907i	1.45906	+	0.842390i	0.460097	+	0.887869i	$0.347815\pi$
$230$	127.809	−	58.3065i	0.555691	−	0.253506i
$231$		0			0
$232$	63.0414	+	16.8919i	0.271730	+	0.0728099i
$233$	30.9334	+	30.9334i	0.132761	+	0.132761i	0.770365	−	0.637603i	$-0.220074\pi$
$233$	30.9334	+	30.9334i	0.132761	+	0.132761i	−0.637603	+	0.770365i	$0.720074\pi$
$234$		0			0
$235$	79.4852	−	13.3333i	0.338235	−	0.0567376i
$236$	0.843880	+	1.46164i	0.00357576	+	0.00619340i
$237$		0			0
$238$	146.768	−	39.3263i	0.616671	−	0.165236i
$239$	−113.445	−	65.4974i	−0.474664	−	0.274048i	0.243526	−	0.969894i	$-0.421696\pi$
$239$	−113.445	−	65.4974i	−0.474664	−	0.274048i	−0.718190	+	0.695847i	$0.755029\pi$
$240$		0			0
$241$	32.6896	+	56.6200i	0.135641	+	0.234938i	0.925842	−	0.377910i	$-0.123357\pi$
$241$	32.6896	+	56.6200i	0.135641	+	0.234938i	−0.790201	+	0.612848i	$0.790024\pi$
$242$	−142.227	+	142.227i	−0.587716	+	0.587716i
$243$		0			0
$244$		−	63.5759i		−	0.260557i
$245$	−266.914	−	25.5951i	−1.08944	−	0.104470i
$246$		0			0
$247$	6.25021	+	23.3261i	0.0253045	+	0.0944376i
$248$	13.7036	−	3.67187i	0.0552565	−	0.0148059i
$249$		0			0
$250$	−92.1880	+	150.836i	−0.368752	+	0.603342i
$251$	−341.145			−1.35914			−0.679572	−	0.733609i	$-0.737834\pi$
$251$	−341.145			−1.35914			−0.679572	+	0.733609i	$0.737834\pi$
$252$		0			0
$253$	−227.919	−	227.919i	−0.900867	−	0.900867i
$254$	−250.295	+	144.508i	−0.985414	+	0.568929i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	84.8755	+	316.760i	0.330255	+	1.23253i	0.908923	+	0.416965i	$0.136906\pi$
$257$	84.8755	+	316.760i	0.330255	+	1.23253i	−0.578668	+	0.815563i	$0.696427\pi$
$258$		0			0
$259$	−409.558	+	236.458i	−1.58130	+	0.912967i
$260$	206.278	−	34.6024i	0.793378	−	0.133086i
$261$		0			0
$262$	−104.895	+	104.895i	−0.400364	+	0.400364i
$263$	−68.1118	+	254.197i	−0.258980	+	0.966527i	0.706853	+	0.707361i	$0.250114\pi$
$263$	−68.1118	+	254.197i	−0.258980	+	0.966527i	−0.965833	+	0.259166i	$0.916552\pi$
$264$		0			0
$265$	−200.002	−	74.6883i	−0.754725	−	0.281843i
$266$	−8.27058	+	14.3251i	−0.0310924	+	0.0538536i
$267$		0			0
$268$	18.0482	−	67.3569i	0.0673441	−	0.251332i
$269$		−	424.447i		−	1.57787i	−0.614476	−	0.788935i	$-0.710633\pi$
$269$		−	424.447i		−	1.57787i	0.614476	−	0.788935i	$-0.289367\pi$
$270$		0			0
$271$	513.264			1.89396			0.946981	−	0.321290i	$-0.104116\pi$
$271$	513.264			1.89396			0.946981	+	0.321290i	$0.104116\pi$
$272$	−40.9773	−	10.9798i	−0.150652	−	0.0403670i
$273$		0			0
$274$	−70.5644	−	40.7404i	−0.257534	−	0.148687i
$275$	398.215	+	77.0809i	1.44806	+	0.280294i
$276$		0			0
$277$	202.878	+	54.3610i	0.732412	+	0.196249i	0.605703	−	0.795691i	$-0.292892\pi$
$277$	202.878	+	54.3610i	0.732412	+	0.196249i	0.126709	+	0.991940i	$0.459559\pi$
$278$	−124.892	−	124.892i	−0.449251	−	0.449251i
$279$		0			0
$280$	116.669	+	83.1500i	0.416674	+	0.296964i
$281$	181.603	+	314.546i	0.646275	+	1.11938i	0.984005	+	0.178139i	$0.0570075\pi$
$281$	181.603	+	314.546i	0.646275	+	1.11938i	−0.337730	+	0.941243i	$0.609659\pi$
$282$		0			0
$283$	114.709	−	30.7362i	0.405333	−	0.108609i	−0.0503917	−	0.998730i	$-0.516047\pi$
$283$	114.709	−	30.7362i	0.405333	−	0.108609i	0.455724	+	0.890121i	$0.349380\pi$
$284$	−2.92534	−	1.68895i	−0.0103005	−	0.00594699i
$285$		0			0
$286$	−239.955	−	415.614i	−0.839004	−	1.45320i
$287$	376.043	−	376.043i	1.31025	−	1.31025i
$288$		0			0
$289$			176.519i			0.610793i
$290$	−125.860	+	103.834i	−0.434000	+	0.358048i
$291$		0			0
$292$	73.7181	+	275.120i	0.252459	+	0.942191i
$293$	481.195	−	128.936i	1.64230	−	0.440054i	0.684859	−	0.728675i	$-0.259864\pi$
$293$	481.195	−	128.936i	1.64230	−	0.440054i	0.957443	+	0.288622i	$0.0931970\pi$
$294$		0			0
$295$	−4.20013	−	0.402763i	−0.0142377	−	0.00136530i
$296$	132.038			0.446073
$297$		0			0
$298$	183.362	+	183.362i	0.615308	+	0.615308i
$299$	359.866	−	207.769i	1.20357	−	0.694879i
$300$		0			0
$301$	174.983	−	303.079i	0.581338	−	1.00691i
$302$	−33.4032	−	124.663i	−0.110607	−	0.412790i
$303$		0			0
$304$	3.99954	−	2.30913i	0.0131564	−	0.00759583i
$305$	129.432	+	92.2460i	0.424366	+	0.302446i
$306$		0			0
$307$	417.932	−	417.932i	1.36134	−	1.36134i	0.489135	−	0.872208i	$-0.337312\pi$
$307$	417.932	−	417.932i	1.36134	−	1.36134i	0.872208	−	0.489135i	$-0.162688\pi$
$308$	85.0793	−	317.520i	0.276231	−	1.03091i
$309$		0			0
$310$	−12.4080	+	33.2263i	−0.0400257	+	0.107182i
$311$	182.970	−	316.913i	0.588328	−	1.01901i	−0.406123	−	0.913818i	$-0.633120\pi$
$311$	182.970	−	316.913i	0.588328	−	1.01901i	0.994452	−	0.105196i	$-0.0335470\pi$
$312$		0			0
$313$	157.443	−	587.584i	0.503012	−	1.87727i	0.0235127	−	0.999724i	$-0.492515\pi$
$313$	157.443	−	587.584i	0.503012	−	1.87727i	0.479499	−	0.877542i	$-0.340818\pi$
$314$		−	50.7395i		−	0.161591i
$315$		0			0
$316$	−20.8142			−0.0658679
$317$	−39.5983	−	10.6103i	−0.124916	−	0.0334710i	0.195820	−	0.980640i	$-0.437263\pi$
$317$	−39.5983	−	10.6103i	−0.124916	−	0.0334710i	−0.320735	+	0.947169i	$0.603930\pi$
$318$		0			0
$319$	324.215	+	187.186i	1.01635	+	0.586789i
$320$	−16.6020	−	36.3919i	−0.0518813	−	0.113725i
$321$		0			0
$322$	274.930	+	73.6672i	0.853819	+	0.228780i
$323$	8.65851	+	8.65851i	0.0268065	+	0.0268065i
$324$		0			0
$325$	−228.856	+	470.160i	−0.704171	+	1.44665i
$326$	−158.678	−	274.838i	−0.486742	−	0.843063i
$327$		0			0
$328$	−143.420	+	38.4292i	−0.437255	+	0.117162i
$329$	141.418	+	81.6477i	0.429842	+	0.248169i
$330$		0			0
$331$	−72.8075	−	126.106i	−0.219962	−	0.380986i	0.734834	−	0.678247i	$-0.237260\pi$
$331$	−72.8075	−	126.106i	−0.219962	−	0.380986i	−0.954796	+	0.297261i	$0.903927\pi$
$332$	−32.8952	+	32.8952i	−0.0990818	+	0.0990818i
$333$		0			0
$334$		−	282.797i		−	0.846698i
$335$	110.942	+	134.476i	0.331170	+	0.401420i
$336$		0			0
$337$	−168.974	−	630.620i	−0.501407	−	1.87128i	−0.490691	−	0.871334i	$-0.663256\pi$
$337$	−168.974	−	630.620i	−0.501407	−	1.87128i	−0.0107157	−	0.999943i	$-0.503411\pi$
$338$	366.751	−	98.2707i	1.08506	−	0.290742i
$339$		0			0
$340$	81.8097	−	67.4927i	0.240617	−	0.198508i
$341$	81.3788			0.238648
$342$		0			0
$343$	−33.1495	−	33.1495i	−0.0966459	−	0.0966459i
$344$	−84.6192	+	48.8549i	−0.245986	+	0.142020i
$345$		0			0
$346$	−172.639	+	299.020i	−0.498958	+	0.864220i
$347$	91.7205	+	342.306i	0.264324	+	0.986472i	0.962663	+	0.270704i	$0.0872565\pi$
$347$	91.7205	+	342.306i	0.264324	+	0.986472i	−0.698338	+	0.715768i	$0.746077\pi$
$348$		0			0
$349$	−422.949	+	244.190i	−1.21189	+	0.699685i	−0.963171	−	0.268891i	$-0.913343\pi$
$349$	−422.949	+	244.190i	−1.21189	+	0.699685i	−0.248719	+	0.968576i	$0.580009\pi$
$350$	−338.563	+	116.874i	−0.967323	+	0.333926i
$351$		0			0
$352$	−64.8971	+	64.8971i	−0.184367	+	0.184367i
$353$	52.4481	−	195.739i	0.148578	−	0.554501i	−0.850992	−	0.525179i	$-0.823998\pi$
$353$	52.4481	−	195.739i	0.148578	−	0.554501i	0.999570	−	0.0293222i	$-0.00933489\pi$
$354$		0			0
$355$	7.68300	−	3.50499i	0.0216423	−	0.00987320i
$356$	−102.749	+	177.967i	−0.288622	+	0.499907i
$357$		0			0
$358$	−41.0658	+	153.260i	−0.114709	+	0.428100i
$359$			416.887i			1.16124i	0.814173	+	0.580622i	$0.197191\pi$
$359$			416.887i			1.16124i	−0.814173	+	0.580622i	$0.802809\pi$
$360$		0			0
$361$	359.667			0.996307
$362$	−15.3084	−	4.10186i	−0.0422883	−	0.0113311i
$363$		0			0
$364$	367.005	+	211.891i	1.00826	+	0.582117i
$365$	−667.067	−	249.108i	−1.82758	−	0.682487i
$366$		0			0
$367$	133.020	+	35.6425i	0.362451	+	0.0971185i	0.435448	−	0.900214i	$-0.356590\pi$
$367$	133.020	+	35.6425i	0.362451	+	0.0971185i	−0.0729974	+	0.997332i	$0.523256\pi$
$368$	−56.1922	−	56.1922i	−0.152696	−	0.152696i
$369$		0			0
$370$	−191.581	+	268.810i	−0.517787	+	0.726513i
$371$	−216.280	−	374.607i	−0.582964	−	1.00972i
$372$		0			0
$373$	−50.7484	+	13.5980i	−0.136055	+	0.0364557i	−0.326204	−	0.945300i	$-0.605770\pi$
$373$	−50.7484	+	13.5980i	−0.136055	+	0.0364557i	0.190149	+	0.981755i	$0.439103\pi$
$374$	−210.742	−	121.672i	−0.563480	−	0.325326i
$375$		0			0
$376$	−22.7959	−	39.4837i	−0.0606274	−	0.105010i
$377$	−341.273	+	341.273i	−0.905232	+	0.905232i
$378$		0			0
$379$		−	430.016i		−	1.13461i	−0.823509	−	0.567303i	$-0.807987\pi$
$379$		−	430.016i		−	1.13461i	0.823509	−	0.567303i	$-0.192013\pi$
$380$	−1.10209	+	11.4929i	−0.00290024	+	0.0302446i
$381$		0			0
$382$	−31.8010	−	118.683i	−0.0832486	−	0.310688i
$383$	292.904	−	78.4834i	0.764763	−	0.204918i	0.144706	−	0.989475i	$-0.453776\pi$
$383$	292.904	−	78.4834i	0.764763	−	0.204918i	0.620057	+	0.784557i	$0.287110\pi$
$384$		0			0
$385$	522.980	+	633.918i	1.35839	+	1.64654i
$386$	116.969			0.303029
$387$		0			0
$388$	−32.0024	−	32.0024i	−0.0824804	−	0.0824804i
$389$	−35.9231	+	20.7402i	−0.0923474	+	0.0533168i	−0.545463	−	0.838135i	$-0.683646\pi$
$389$	−35.9231	+	20.7402i	−0.0923474	+	0.0533168i	0.453115	+	0.891452i	$0.350313\pi$
$390$		0			0
$391$	105.351	−	182.474i	0.269441	−	0.466685i
$392$	39.2582	+	146.513i	0.100148	+	0.373759i
$393$		0			0
$394$	−159.173	+	91.8988i	−0.403994	+	0.233246i
$395$	30.2006	−	42.3748i	0.0764572	−	0.107278i
$396$		0			0
$397$	−26.1316	+	26.1316i	−0.0658226	+	0.0658226i	−0.739252	−	0.673429i	$-0.764821\pi$
$397$	−26.1316	+	26.1316i	−0.0658226	+	0.0658226i	0.673429	+	0.739252i	$0.264821\pi$
$398$	−24.7239	+	92.2708i	−0.0621203	+	0.231836i
$399$		0			0
$400$	98.1777	+	19.0038i	0.245444	+	0.0475096i
$401$	190.145	−	329.342i	0.474178	−	0.821301i	−0.525385	−	0.850865i	$-0.676079\pi$
$401$	190.145	−	329.342i	0.474178	−	0.821301i	0.999563	+	0.0295642i	$0.00941195\pi$
$402$		0			0
$403$	−27.1532	+	101.337i	−0.0673778	+	0.251457i
$404$		−	114.721i		−	0.283963i
$405$		0			0
$406$	−330.586			−0.814251
$407$	731.580	+	196.026i	1.79749	+	0.481637i
$408$		0			0
$409$	−8.26410	−	4.77128i	−0.0202056	−	0.0116657i	0.489863	−	0.871799i	$-0.337047\pi$
$409$	−8.26410	−	4.77128i	−0.0202056	−	0.0116657i	−0.510069	+	0.860134i	$0.670380\pi$
$410$	129.860	−	347.741i	0.316731	−	0.848150i
$411$		0			0
$412$	−61.4764	−	16.4725i	−0.149215	−	0.0399819i
$413$	−6.04502	−	6.04502i	−0.0146369	−	0.0146369i
$414$		0			0
$415$	−19.2404	−	114.699i	−0.0463624	−	0.276384i
$416$	−59.1595	−	102.467i	−0.142210	−	0.246315i
$417$		0			0
$418$	25.5884	−	6.85639i	0.0612163	−	0.0164028i
$419$	−286.594	−	165.465i	−0.683994	−	0.394904i	0.117364	−	0.993089i	$-0.462556\pi$
$419$	−286.594	−	165.465i	−0.683994	−	0.394904i	−0.801358	+	0.598185i	$0.795889\pi$
$420$		0			0
$421$	−89.1896	−	154.481i	−0.211852	−	0.366938i	0.740442	−	0.672120i	$-0.234616\pi$
$421$	−89.1896	−	154.481i	−0.211852	−	0.366938i	−0.952294	+	0.305182i	$0.901283\pi$
$422$	−281.788	+	281.788i	−0.667744	+	0.667744i
$423$		0			0
$424$			120.770i			0.284834i
$425$	18.7030	+	264.482i	0.0440071	+	0.622311i
$426$		0			0
$427$	83.3472	+	311.056i	0.195193	+	0.728469i
$428$	46.1408	−	12.3634i	0.107806	−	0.0288864i
$429$		0			0
$430$	23.3172	−	243.159i	0.0542262	−	0.565487i
$431$	−249.781			−0.579538			−0.289769	−	0.957097i	$-0.593579\pi$
$431$	−249.781			−0.579538			−0.289769	+	0.957097i	$0.593579\pi$
$432$		0			0
$433$	−24.9453	−	24.9453i	−0.0576103	−	0.0576103i	0.677715	−	0.735325i	$-0.262970\pi$
$433$	−24.9453	−	24.9453i	−0.0576103	−	0.0576103i	−0.735325	+	0.677715i	$0.762970\pi$
$434$	−62.2334	+	35.9305i	−0.143395	+	0.0827892i
$435$		0			0
$436$	8.42672	−	14.5955i	0.0193273	−	0.0334759i
$437$	5.93671	+	22.1561i	0.0135852	+	0.0507005i
$438$		0			0
$439$	−94.6999	+	54.6750i	−0.215717	+	0.124544i	−0.603966	−	0.797010i	$-0.706414\pi$
$439$	−94.6999	+	54.6750i	−0.215717	+	0.124544i	0.388248	+	0.921555i	$0.373080\pi$
$440$	−37.9583	−	226.284i	−0.0862689	−	0.514283i
$441$		0			0
$442$	221.829	−	221.829i	0.501876	−	0.501876i
$443$	−95.7040	+	357.172i	−0.216036	+	0.806258i	0.769763	+	0.638330i	$0.220374\pi$
$443$	−95.7040	+	357.172i	−0.216036	+	0.806258i	−0.985799	+	0.167928i	$0.946292\pi$
$444$		0			0
$445$	−213.231	−	467.406i	−0.479170	−	1.05035i
$446$	−248.247	+	429.976i	−0.556608	+	0.964072i
$447$		0			0
$448$	20.9758	−	78.2827i	0.0468210	−	0.174738i
$449$		−	358.178i		−	0.797724i	−0.917011	−	0.398862i	$-0.869405\pi$
$449$		−	358.178i		−	0.797724i	0.917011	−	0.398862i	$-0.130595\pi$
$450$		0			0
$451$	−851.698			−1.88847
$452$	96.6085	+	25.8862i	0.213736	+	0.0572703i
$453$		0			0
$454$	−410.412	−	236.952i	−0.903992	−	0.521920i
$455$	−963.889	+	439.726i	−2.11844	+	0.966431i
$456$		0			0
$457$	847.169	+	226.998i	1.85376	+	0.496714i	0.999724	−	0.0234957i	$-0.00747960\pi$
$457$	847.169	+	226.998i	1.85376	+	0.496714i	0.854038	+	0.520210i	$0.174146\pi$
$458$	385.815	+	385.815i	0.842390	+	0.842390i
$459$		0			0
$460$	195.932	−	32.8668i	0.425939	−	0.0714496i
$461$	107.336	+	185.912i	0.232833	+	0.403279i	0.958641	−	0.284619i	$-0.0918670\pi$
$461$	107.336	+	185.912i	0.232833	+	0.403279i	−0.725807	+	0.687898i	$0.758534\pi$
$462$		0			0
$463$	324.757	−	87.0183i	0.701419	−	0.187945i	0.109553	−	0.993981i	$-0.465058\pi$
$463$	324.757	−	87.0183i	0.701419	−	0.187945i	0.591866	+	0.806036i	$0.298391\pi$
$464$	79.9333	+	46.1495i	0.172270	+	0.0994601i
$465$		0			0
$466$	30.9334	+	53.5783i	0.0663807	+	0.114975i
$467$	551.200	−	551.200i	1.18030	−	1.18030i	0.200632	−	0.979667i	$-0.435700\pi$
$467$	551.200	−	551.200i	1.18030	−	1.18030i	0.979667	−	0.200632i	$-0.0642996\pi$
$468$		0			0
$469$			353.216i			0.753126i
$470$	113.459	+	10.8799i	0.241402	+	0.0231488i
$471$		0			0
$472$	0.617763	+	2.30552i	0.00130882	+	0.00488458i
$473$	−541.380	+	145.062i	−1.14457	+	0.306686i
$474$		0			0
$475$	−21.7989	−	18.9195i	−0.0458925	−	0.0398305i
$476$	214.883			0.451434
$477$		0			0
$478$	−130.995	−	130.995i	−0.274048	−	0.274048i
$479$	−535.392	+	309.109i	−1.11773	+	0.645321i	−0.940820	−	0.338906i	$-0.889943\pi$
$479$	−535.392	+	309.109i	−1.11773	+	0.645321i	−0.176909	+	0.984227i	$0.556610\pi$
$480$		0			0
$481$	−488.205	+	845.595i	−1.01498	+	1.75799i
$482$	23.9304	+	89.3095i	0.0496482	+	0.185289i
$483$		0			0
$484$	−246.345	+	142.227i	−0.508977	+	0.293858i
$485$	111.586	−	18.7182i	0.230075	−	0.0385942i
$486$		0			0
$487$	−418.202	+	418.202i	−0.858732	+	0.858732i	−0.991189	−	0.132457i	$-0.957713\pi$
$487$	−418.202	+	418.202i	−0.858732	+	0.858732i	0.132457	+	0.991189i	$0.457713\pi$
$488$	23.2704	−	86.8463i	0.0476853	−	0.177964i
$489$		0			0
$490$	−355.243	−	132.661i	−0.724985	−	0.270736i
$491$	−163.231	+	282.725i	−0.332447	+	0.575815i	−0.982991	−	0.183653i	$-0.941208\pi$
$491$	−163.231	+	282.725i	−0.332447	+	0.575815i	0.650544	+	0.759468i	$0.274541\pi$
$492$		0			0
$493$	−63.3392	+	236.385i	−0.128477	+	0.479483i
$494$			34.1518i			0.0691332i
$495$		0			0
$496$	20.0635			0.0404505
$497$	16.5269	+	4.42837i	0.0332533	+	0.00891021i
$498$		0			0
$499$	−196.690	−	113.559i	−0.394169	−	0.227574i	0.289796	−	0.957088i	$-0.406413\pi$
$499$	−196.690	−	113.559i	−0.394169	−	0.227574i	−0.683965	+	0.729515i	$0.739746\pi$
$500$	−181.141	+	172.302i	−0.362282	+	0.344604i
$501$		0			0
$502$	−466.013	−	124.868i	−0.928312	−	0.248740i
$503$	521.931	+	521.931i	1.03764	+	1.03764i	0.999264	+	0.0383723i	$0.0122173\pi$
$503$	521.931	+	521.931i	1.03764	+	1.03764i	0.0383723	+	0.999264i	$0.487783\pi$
$504$		0			0
$505$	233.556	+	166.455i	0.462487	+	0.329615i
$506$	−227.919	−	394.768i	−0.450434	−	0.780174i
$507$		0			0
$508$	−394.803	+	105.787i	−0.777172	+	0.208243i
$509$	211.134	+	121.899i	0.414802	+	0.239486i	0.692851	−	0.721081i	$-0.256354\pi$
$509$	211.134	+	121.899i	0.414802	+	0.239486i	−0.278049	+	0.960567i	$0.589688\pi$
$510$		0			0
$511$	−721.357	−	1249.43i	−1.41166	−	2.44506i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			463.768i			0.902273i
$515$	122.735	−	101.256i	0.238321	−	0.196614i
$516$		0			0
$517$	−67.6867	−	252.610i	−0.130922	−	0.488608i
$518$	−646.016	+	173.100i	−1.24714	+	0.334169i
$519$		0			0
$520$	294.447	+	28.2354i	0.566244	+	0.0542988i
$521$	−411.938			−0.790669			−0.395334	−	0.918537i	$-0.629371\pi$
$521$	−411.938			−0.790669			−0.395334	+	0.918537i	$0.629371\pi$
$522$		0			0
$523$	−109.244	−	109.244i	−0.208880	−	0.208880i	0.594911	−	0.803791i	$-0.297187\pi$
$523$	−109.244	−	109.244i	−0.208880	−	0.208880i	−0.803791	+	0.594911i	$0.797187\pi$
$524$	−181.684	+	104.895i	−0.346725	+	0.200182i
$525$		0			0
$526$	−186.085	+	322.308i	−0.353773	+	0.612753i
$527$	13.7683	+	51.3841i	0.0261259	+	0.0975031i
$528$		0			0
$529$	−116.311	+	67.1524i	−0.219870	+	0.126942i
$530$	−245.870	−	175.232i	−0.463906	−	0.330626i
$531$		0			0
$532$	−16.5412	+	16.5412i	−0.0310924	+	0.0310924i
$533$	284.181	−	1060.58i	0.533173	−	1.98983i
$534$		0			0
$535$	−41.7782	+	111.875i	−0.0780901	+	0.209112i
$536$	49.3087	−	85.4051i	0.0919938	−	0.159338i
$537$		0			0
$538$	155.358	−	579.806i	0.288770	−	1.07771i
$539$			870.070i			1.61423i
$540$		0			0
$541$	−944.075			−1.74506			−0.872528	−	0.488565i	$-0.837521\pi$
$541$	−944.075			−1.74506			−0.872528	+	0.488565i	$0.837521\pi$
$542$	701.131	+	187.868i	1.29360	+	0.346619i
$543$		0			0
$544$	−51.9571	−	29.9974i	−0.0955094	−	0.0551424i
$545$	17.4876	+	38.3331i	0.0320873	+	0.0703360i
$546$		0			0
$547$	871.576	+	233.538i	1.59337	+	0.426943i	0.943033	−	0.332699i	$-0.107959\pi$
$547$	871.576	+	233.538i	1.59337	+	0.426943i	0.650341	+	0.759642i	$0.274626\pi$
$548$	−81.4807	−	81.4807i	−0.148687	−	0.148687i
$549$		0			0
$550$	515.759	+	251.051i	0.937743	+	0.456457i
$551$	−13.3207	−	23.0721i	−0.0241754	−	0.0418731i
$552$		0			0
$553$	101.837	−	27.2872i	0.184154	−	0.0493439i
$554$	257.239	+	148.517i	0.464331	+	0.268081i
$555$		0			0
$556$	−124.892	−	216.319i	−0.224626	−	0.389063i
$557$	195.150	−	195.150i	0.350360	−	0.350360i	−0.509884	−	0.860243i	$-0.670312\pi$
$557$	195.150	−	195.150i	0.350360	−	0.350360i	0.860243	+	0.509884i	$0.170312\pi$
$558$		0			0
$559$		−	722.558i		−	1.29259i
$560$	128.938	+	156.289i	0.230246	+	0.279087i
$561$		0			0
$562$	132.943	+	496.150i	0.236553	+	0.882828i
$563$	60.5941	−	16.2361i	0.107627	−	0.0288386i	−0.204604	−	0.978845i	$-0.565591\pi$
$563$	60.5941	−	16.2361i	0.107627	−	0.0288386i	0.312231	+	0.950006i	$0.398924\pi$
$564$		0			0
$565$	−192.875	+	159.121i	−0.341372	+	0.281631i
$566$	167.946			0.296724
$567$		0			0
$568$	−3.37789	−	3.37789i	−0.00594699	−	0.00594699i
$569$	22.5971	−	13.0464i	0.0397136	−	0.0229287i	−0.480012	−	0.877262i	$-0.659368\pi$
$569$	22.5971	−	13.0464i	0.0397136	−	0.0229287i	0.519725	+	0.854333i	$0.326034\pi$
$570$		0			0
$571$	468.026	−	810.645i	0.819660	−	1.41969i	−0.0862725	−	0.996272i	$-0.527496\pi$
$571$	468.026	−	810.645i	0.819660	−	1.41969i	0.905933	−	0.423422i	$-0.139171\pi$
$572$	−175.659	−	655.569i	−0.307097	−	1.14610i
$573$		0			0
$574$	651.325	−	376.043i	1.13471	−	0.655127i
$575$	−217.377	+	446.578i	−0.378047	+	0.776657i
$576$		0			0
$577$	371.244	−	371.244i	0.643405	−	0.643405i	−0.307986	−	0.951391i	$-0.599655\pi$
$577$	371.244	−	371.244i	0.643405	−	0.643405i	0.951391	+	0.307986i	$0.0996551\pi$
$578$	−64.6105	+	241.130i	−0.111783	+	0.417179i
$579$		0			0
$580$	−209.934	+	95.7718i	−0.361955	+	0.165124i
$581$	117.820	−	204.070i	0.202788	−	0.351240i
$582$		0			0
$583$	−179.298	+	669.148i	−0.307543	+	1.14777i
$584$			402.803i			0.689732i
$585$		0			0
$586$	704.518			1.20225
$587$	−600.077	−	160.790i	−1.02228	−	0.273919i	−0.291527	−	0.956563i	$-0.594163\pi$
$587$	−600.077	−	160.790i	−1.02228	−	0.273919i	−0.730751	+	0.682644i	$0.760830\pi$
$588$		0			0
$589$	−5.01528	−	2.89558i	−0.00851491	−	0.00491609i
$590$	−5.59007	−	2.08754i	−0.00947469	−	0.00353820i
$591$		0			0
$592$	180.367	+	48.3291i	0.304673	+	0.0816370i
$593$	−300.303	−	300.303i	−0.506413	−	0.506413i	0.407011	−	0.913423i	$-0.366571\pi$
$593$	−300.303	−	300.303i	−0.506413	−	0.506413i	−0.913423	+	0.407011i	$0.866571\pi$
$594$		0			0
$595$	−311.786	+	437.471i	−0.524010	+	0.735245i
$596$	183.362	+	317.592i	0.307654	+	0.532872i
$597$		0			0
$598$	567.635	−	152.097i	0.949222	−	0.254343i
$599$	−239.651	−	138.363i	−0.400085	−	0.230989i	0.286435	−	0.958100i	$-0.407530\pi$
$599$	−239.651	−	138.363i	−0.400085	−	0.230989i	−0.686521	+	0.727110i	$0.740863\pi$
$600$		0			0
$601$	321.077	+	556.122i	0.534238	+	0.925328i	0.999200	+	0.0399972i	$0.0127349\pi$
$601$	321.077	+	556.122i	0.534238	+	0.925328i	−0.464961	+	0.885331i	$0.653932\pi$
$602$	349.966	−	349.966i	0.581338	−	0.581338i
$603$		0			0
$604$		−	182.519i		−	0.302183i
$605$	67.8815	−	707.889i	0.112201	−	1.17006i
$606$		0			0
$607$	252.760	+	943.312i	0.416408	+	1.55406i	0.781999	+	0.623280i	$0.214200\pi$
$607$	252.760	+	943.312i	0.416408	+	1.55406i	−0.365591	+	0.930776i	$0.619133\pi$
$608$	6.30867	−	1.69040i	0.0103761	−	0.00278027i
$609$		0			0
$610$	143.042	+	173.386i	0.234496	+	0.284239i
$611$	337.149			0.551798
$612$		0			0
$613$	−409.139	−	409.139i	−0.667437	−	0.667437i	0.289685	−	0.957122i	$-0.406450\pi$
$613$	−409.139	−	409.139i	−0.667437	−	0.667437i	−0.957122	+	0.289685i	$0.906450\pi$
$614$	723.880	−	417.932i	1.17896	−	0.680672i
$615$		0			0
$616$	232.441	−	402.599i	0.377339	−	0.653571i
$617$	185.796	+	693.400i	0.301128	+	1.12383i	0.936227	+	0.351395i	$0.114292\pi$
$617$	185.796	+	693.400i	0.301128	+	1.12383i	−0.635099	+	0.772430i	$0.719041\pi$
$618$		0			0
$619$	−7.99592	+	4.61645i	−0.0129175	+	0.00745791i	−0.506445	−	0.862272i	$-0.669041\pi$
$619$	−7.99592	+	4.61645i	−0.0129175	+	0.00745791i	0.493527	+	0.869730i	$0.335707\pi$
$620$	−29.1113	+	40.8464i	−0.0469536	+	0.0658813i
$621$		0			0
$622$	365.940	−	365.940i	0.588328	−	0.588328i
$623$	269.406	−	1005.44i	0.432433	−	1.61386i
$624$		0			0
$625$	−87.9548	−	618.780i	−0.140728	−	0.990048i
$626$	430.142	−	745.027i	0.687127	−	1.19014i
$627$		0			0
$628$	18.5719	−	69.3114i	0.0295732	−	0.110369i
$629$			495.099i			0.787121i
$630$		0			0
$631$	1103.76			1.74923			0.874614	−	0.484820i	$-0.161115\pi$
$631$	1103.76			1.74923			0.874614	+	0.484820i	$0.161115\pi$
$632$	−28.4328	−	7.61854i	−0.0449886	−	0.0120547i
$633$		0			0
$634$	−50.2086	−	28.9879i	−0.0791933	−	0.0457223i
$635$	357.475	−	957.256i	0.562953	−	1.50749i
$636$		0			0
$637$	−1083.46	−	290.312i	−1.70088	−	0.455748i
$638$	374.371	+	374.371i	0.586789	+	0.586789i
$639$		0			0
$640$	−9.35840	−	55.7891i	−0.0146225	−	0.0871704i
$641$	261.993	+	453.785i	0.408726	+	0.707933i	0.994747	−	0.102362i	$-0.0326400\pi$
$641$	261.993	+	453.785i	0.408726	+	0.707933i	−0.586022	+	0.810295i	$0.699307\pi$
$642$		0			0
$643$	394.979	−	105.834i	0.614275	−	0.164595i	0.0617512	−	0.998092i	$-0.480331\pi$
$643$	394.979	−	105.834i	0.614275	−	0.164595i	0.552524	+	0.833497i	$0.313665\pi$
$644$	348.597	+	201.263i	0.541300	+	0.312520i
$645$		0			0
$646$	8.65851	+	14.9970i	0.0134033	+	0.0232151i
$647$	−829.739	+	829.739i	−1.28244	+	1.28244i	−0.343166	+	0.939275i	$0.611499\pi$
$647$	−829.739	+	829.739i	−1.28244	+	1.28244i	−0.939275	+	0.343166i	$0.888501\pi$
$648$		0			0
$649$			13.6913i			0.0210961i
$650$	−484.713	+	558.484i	−0.745713	+	0.859206i
$651$		0			0
$652$	−116.160	−	433.516i	−0.178160	−	0.664903i
$653$	−554.527	+	148.585i	−0.849199	+	0.227542i	−0.657072	−	0.753828i	$-0.728205\pi$
$653$	−554.527	+	148.585i	−0.849199	+	0.227542i	−0.192127	+	0.981370i	$0.561538\pi$
$654$		0			0
$655$	50.0639	−	522.082i	0.0764335	−	0.797071i
$656$	−209.981			−0.320093
$657$		0			0
$658$	163.295	+	163.295i	0.248169	+	0.248169i
$659$	565.064	−	326.240i	0.857456	−	0.495053i	−0.00570347	−	0.999984i	$-0.501815\pi$
$659$	565.064	−	326.240i	0.857456	−	0.495053i	0.863160	+	0.504931i	$0.168482\pi$
$660$		0			0
$661$	−441.648	+	764.957i	−0.668152	+	1.15727i	0.310269	+	0.950649i	$0.399581\pi$
$661$	−441.648	+	764.957i	−0.668152	+	1.15727i	−0.978420	+	0.206624i	$0.933752\pi$
$662$	−53.2988	−	198.914i	−0.0805118	−	0.300474i
$663$		0			0
$664$	−56.9761	+	32.8952i	−0.0858073	+	0.0495409i
$665$	−9.67493	−	57.6760i	−0.0145488	−	0.0867308i
$666$		0			0
$667$	−324.155	+	324.155i	−0.485990	+	0.485990i
$668$	103.511	−	386.308i	0.154956	−	0.578305i
$669$		0			0
$670$	102.328	+	224.305i	0.152728	+	0.334783i
$671$	257.868	−	446.641i	0.384305	−	0.665635i
$672$		0			0
$673$	−152.431	+	568.879i	−0.226494	+	0.845288i	0.755306	+	0.655372i	$0.227488\pi$
$673$	−152.431	+	568.879i	−0.226494	+	0.845288i	−0.981800	+	0.189916i	$0.939178\pi$
$674$		−	923.292i		−	1.36987i
$675$		0			0
$676$	536.961			0.794322
$677$	−1121.40	−	300.478i	−1.65643	−	0.443838i	−0.695024	−	0.718987i	$-0.744606\pi$
$677$	−1121.40	−	300.478i	−1.65643	−	0.443838i	−0.961402	+	0.275149i	$0.911273\pi$
$678$		0			0
$679$	198.532	+	114.622i	0.292389	+	0.168811i
$680$	136.458	−	62.2523i	0.200674	−	0.0915474i
$681$		0			0
$682$	111.166	+	29.7867i	0.162999	+	0.0436755i
$683$	31.6260	+	31.6260i	0.0463045	+	0.0463045i	0.729880	−	0.683575i	$-0.239576\pi$
$683$	31.6260	+	31.6260i	0.0463045	+	0.0463045i	−0.683575	+	0.729880i	$0.739576\pi$
$684$		0			0
$685$	284.108	−	47.6581i	0.414757	−	0.0695738i
$686$	−33.1495	−	57.4167i	−0.0483229	−	0.0836978i
$687$		0			0
$688$	−133.474	+	35.7643i	−0.194003	+	0.0519830i
$689$	−773.434	−	446.542i	−1.12255	−	0.648102i
$690$		0			0
$691$	297.024	+	514.461i	0.429847	+	0.744517i	0.996859	−	0.0791924i	$-0.0252341\pi$
$691$	297.024	+	514.461i	0.429847	+	0.744517i	−0.567012	+	0.823709i	$0.691901\pi$
$692$	−345.279	+	345.279i	−0.498958	+	0.498958i
$693$		0			0
$694$			501.170i			0.722147i
$695$	621.608	+	59.6078i	0.894399	+	0.0857666i
$696$		0			0
$697$	−144.097	−	537.778i	−0.206739	−	0.771561i
$698$	−667.139	+	178.759i	−0.955787	+	0.256102i
$699$		0			0
$700$	−505.265	+	35.7301i	−0.721807	+	0.0510431i
$701$	539.121			0.769075			0.384537	−	0.923109i	$-0.374361\pi$
$701$	539.121			0.769075			0.384537	+	0.923109i	$0.374361\pi$
$702$		0			0
$703$	−38.1115	−	38.1115i	−0.0542127	−	0.0542127i
$704$	−112.405	+	64.8971i	−0.159666	+	0.0921834i
$705$		0			0
$706$	143.291	−	248.187i	0.202961	−	0.351540i
$707$	150.398	+	561.292i	0.212727	+	0.793907i
$708$		0			0
$709$	603.510	−	348.437i	0.851213	−	0.491448i	−0.00984700	−	0.999952i	$-0.503134\pi$
$709$	603.510	−	348.437i	0.851213	−	0.491448i	0.861060	+	0.508504i	$0.169801\pi$
$710$	11.7781	−	1.97573i	0.0165889	−	0.00278272i
$711$		0			0
$712$	−205.499	+	205.499i	−0.288622	+	0.288622i
$713$	−25.7913	+	96.2544i	−0.0361729	+	0.134999i
$714$		0			0
$715$	1589.52	+	593.586i	2.22311	+	0.830191i
$716$	−112.194	+	194.325i	−0.156695	+	0.271404i
$717$		0			0
$718$	−152.591	+	569.478i	−0.212522	+	0.793145i
$719$		−	446.528i		−	0.621041i	−0.950567	−	0.310520i	$-0.899497\pi$
$719$		−	446.528i		−	0.621041i	0.950567	−	0.310520i	$-0.100503\pi$
$720$		0			0
$721$	322.379			0.447128
$722$	491.314	+	131.647i	0.680491	+	0.182337i
$723$		0			0
$724$	−19.4102	−	11.2065i	−0.0268097	−	0.0154786i
$725$	109.627	−	566.356i	0.151210	−	0.781181i
$726$		0			0
$727$	−451.432	−	120.961i	−0.620952	−	0.166384i	−0.0653917	−	0.997860i	$-0.520830\pi$
$727$	−451.432	−	120.961i	−0.620952	−	0.166384i	−0.555561	+	0.831476i	$0.687496\pi$
$728$	423.781	+	423.781i	0.582117	+	0.582117i
$729$		0			0
$730$	−820.051	−	584.451i	−1.12336	−	0.800618i
$731$	−183.190	−	317.295i	−0.250602	−	0.434056i
$732$		0			0
$733$	766.887	−	205.487i	1.04623	−	0.280337i	0.305538	−	0.952180i	$-0.401164\pi$
$733$	766.887	−	205.487i	1.04623	−	0.280337i	0.740693	+	0.671843i	$0.234497\pi$
$734$	168.662	+	97.3771i	0.229785	+	0.132666i
$735$		0			0
$736$	−56.1922	−	97.3277i	−0.0763481	−	0.132239i
$737$	399.999	−	399.999i	0.542739	−	0.542739i
$738$		0			0
$739$			5.34957i			0.00723893i	0.999993	+	0.00361947i	$0.00115211\pi$
$739$			5.34957i			0.00723893i	−0.999993	+	0.00361947i	$0.998848\pi$
$740$	−360.096	+	297.078i	−0.486616	+	0.401456i
$741$		0			0
$742$	−158.328	−	590.887i	−0.213380	−	0.796343i
$743$	1388.28	−	371.988i	1.86848	−	0.500657i	0.868489	−	0.495708i	$-0.165091\pi$
$743$	1388.28	−	371.988i	1.86848	−	0.500657i	0.999988	−	0.00494907i	$-0.00157534\pi$
$744$		0			0
$745$	−912.622	−	87.5140i	−1.22500	−	0.117468i
$746$	−74.3008			−0.0995989
$747$		0			0
$748$	−243.343	−	243.343i	−0.325326	−	0.325326i
$749$	−209.543	+	120.980i	−0.279764	+	0.161522i
$750$		0			0
$751$	−104.684	+	181.317i	−0.139392	+	0.241435i	−0.927267	−	0.374401i	$-0.877848\pi$
$751$	−104.684	+	181.317i	−0.139392	+	0.241435i	0.787874	+	0.615836i	$0.211182\pi$
$752$	−16.6878	−	62.2796i	−0.0221912	−	0.0828186i
$753$		0			0
$754$	−591.101	+	341.273i	−0.783954	+	0.452616i
$755$	371.582	+	264.827i	0.492162	+	0.350764i
$756$		0			0
$757$	−854.924	+	854.924i	−1.12936	+	1.12936i	−0.139076	+	0.990282i	$0.544413\pi$
$757$	−854.924	+	854.924i	−1.12936	+	1.12936i	−0.990282	+	0.139076i	$0.955587\pi$
$758$	157.397	−	587.413i	0.207647	−	0.774951i
$759$		0			0
$760$	−5.71219	+	15.2963i	−0.00751605	+	0.0201267i
$761$	−214.446	+	371.432i	−0.281795	+	0.488084i	−0.971827	−	0.235695i	$-0.924263\pi$
$761$	−214.446	+	371.432i	−0.281795	+	0.488084i	0.690032	+	0.723779i	$0.257597\pi$
$762$		0			0
$763$	−22.0946	+	82.4584i	−0.0289576	+	0.108071i
$764$		−	173.764i		−	0.227439i
$765$		0			0
$766$	428.842			0.559845
$767$	−17.0492	−	4.56832i	−0.0222284	−	0.00595609i
$768$		0			0
$769$	−417.404	−	240.988i	−0.542788	−	0.313379i	0.203420	−	0.979092i	$-0.434794\pi$
$769$	−417.404	−	240.988i	−0.542788	−	0.313379i	−0.746208	+	0.665713i	$0.768128\pi$
$770$	482.373	+	1057.37i	0.626459	+	1.37321i
$771$		0			0
$772$	159.783	+	42.8137i	0.206973	+	0.0554581i
$773$	−398.239	−	398.239i	−0.515187	−	0.515187i	0.400924	−	0.916111i	$-0.368689\pi$
$773$	−398.239	−	398.239i	−0.515187	−	0.515187i	−0.916111	+	0.400924i	$0.868689\pi$
$774$		0			0
$775$	−40.9182	−	118.533i	−0.0527977	−	0.152946i
$776$	−32.0024	−	55.4298i	−0.0412402	−	0.0714301i
$777$		0			0
$778$	−56.6634	+	15.1829i	−0.0728321	+	0.0195153i
$779$	52.4892	+	30.3046i	0.0673802	+	0.0389020i
$780$		0			0
$781$	−13.7010	−	23.7308i	−0.0175428	−	0.0303851i
$782$	210.703	−	210.703i	0.269441	−	0.269441i
$783$		0			0
$784$			214.511i			0.273610i
$785$	114.161	+	138.378i	0.145428	+	0.176278i
$786$		0			0
$787$	−184.125	−	687.164i	−0.233958	−	0.873143i	−0.978616	−	0.205697i	$-0.934054\pi$
$787$	−184.125	−	687.164i	−0.233958	−	0.873143i	0.744658	−	0.667446i	$-0.232613\pi$
$788$	−251.072	+	67.2746i	−0.318620	+	0.0853739i
$789$		0			0
$790$	56.7651	−	46.8309i	0.0718545	−	0.0592797i
$791$	−506.610			−0.640468
$792$		0			0
$793$	470.140	+	470.140i	0.592863	+	0.592863i
$794$	−45.2612	+	26.1316i	−0.0570040	+	0.0329113i
$795$		0			0
$796$	−67.5469	+	116.995i	−0.0848579	+	0.146978i
$797$	−177.694	−	663.163i	−0.222954	−	0.832074i	−0.983214	−	0.182456i	$-0.941595\pi$
$797$	−177.694	−	663.163i	−0.222954	−	0.832074i	0.760261	−	0.649618i	$-0.225071\pi$
$798$		0			0
$799$	148.051	−	85.4774i	0.185296	−	0.106980i
$800$	127.157	+	61.8952i	0.158947	+	0.0773691i
$801$		0			0
$802$	380.291	−	380.291i	0.474178	−	0.474178i
$803$	−598.012	+	2231.81i	−0.744722	+	2.77934i
$804$		0			0
$805$	−915.542	+	417.671i	−1.13732	+	0.518845i
$806$	−74.1840	+	128.491i	−0.0920397	+	0.159418i
$807$		0			0
$808$	41.9908	−	156.712i	0.0519688	−	0.193950i
$809$		−	1351.77i		−	1.67092i	−0.549552	−	0.835459i	$-0.685202\pi$
$809$		−	1351.77i		−	1.67092i	0.549552	−	0.835459i	$-0.314798\pi$
$810$		0			0
$811$	226.208			0.278925			0.139463	−	0.990227i	$-0.455463\pi$
$811$	226.208			0.278925			0.139463	+	0.990227i	$0.455463\pi$
$812$	−451.589	−	121.003i	−0.556144	−	0.149018i
$813$		0			0
$814$	927.606	+	535.554i	1.13957	+	0.657928i
$815$	1051.12	+	392.528i	1.28972	+	0.481630i
$816$		0			0
$817$	38.5262	+	10.3231i	0.0471557	+	0.0126353i
$818$	−9.54256	−	9.54256i	−0.0116657	−	0.0116657i
$819$		0			0
$820$	304.674	−	427.492i	0.371553	−	0.521331i
$821$	311.348	+	539.270i	0.379230	+	0.656846i	0.990950	−	0.134228i	$-0.0428556\pi$
$821$	311.348	+	539.270i	0.379230	+	0.656846i	−0.611720	+	0.791074i	$0.709522\pi$
$822$		0			0
$823$	−1141.41	+	305.841i	−1.38689	+	0.371617i	−0.873621	−	0.486608i	$-0.838234\pi$
$823$	−1141.41	+	305.841i	−1.38689	+	0.371617i	−0.513274	+	0.858225i	$0.671567\pi$
$824$	−77.9489	−	45.0038i	−0.0945982	−	0.0546163i
$825$		0			0
$826$	−6.04502	−	10.4703i	−0.00731843	−	0.0126759i
$827$	269.820	−	269.820i	0.326264	−	0.326264i	−0.524900	−	0.851164i	$-0.675897\pi$
$827$	269.820	−	269.820i	0.326264	−	0.326264i	0.851164	+	0.524900i	$0.175897\pi$
$828$		0			0
$829$			228.498i			0.275630i	0.990458	+	0.137815i	$0.0440080\pi$
$829$			228.498i			0.275630i	−0.990458	+	0.137815i	$0.955992\pi$
$830$	15.7000	−	163.725i	0.0189157	−	0.197259i
$831$		0			0
$832$	−43.3078	−	161.627i	−0.0520526	−	0.194263i
$833$	−549.379	+	147.206i	−0.659518	+	0.176717i
$834$		0			0
$835$	636.278	+	771.250i	0.762010	+	0.923653i
$836$	37.4640			0.0448134
$837$		0			0
$838$	−330.930	−	330.930i	−0.394904	−	0.394904i
$839$	−1178.88	+	680.626i	−1.40510	+	0.811234i	−0.994910	−	0.100766i	$-0.967871\pi$
$839$	−1178.88	+	680.626i	−1.40510	+	0.811234i	−0.410189	+	0.912000i	$0.634537\pi$
$840$		0			0
$841$	−154.278	+	267.217i	−0.183446	+	0.317738i
$842$	−65.2913	−	243.670i	−0.0775431	−	0.289395i
$843$		0			0
$844$	−488.071	+	281.788i	−0.578283	+	0.333872i
$845$	−779.109	+	1093.18i	−0.922022	+	1.29370i
$846$		0			0
$847$	1018.83	−	1018.83i	1.20286	−	1.20286i
$848$	−44.2048	+	164.975i	−0.0521283	+	0.194546i
$849$		0			0
$850$	−71.2583	+	368.135i	−0.0838333	+	0.433100i
$851$	−463.717	+	803.182i	−0.544909	+	0.943810i
$852$		0			0
$853$	212.386	−	792.635i	0.248987	−	0.929233i	−0.722350	−	0.691527i	$-0.756938\pi$
$853$	212.386	−	792.635i	0.248987	−	0.929233i	0.971337	−	0.237705i	$-0.0763952\pi$
$854$			455.418i			0.533276i
$855$		0			0
$856$	67.5548			0.0789191
$857$	−112.046	−	30.0226i	−0.130742	−	0.0350322i	0.192855	−	0.981227i	$-0.438225\pi$
$857$	−112.046	−	30.0226i	−0.130742	−	0.0350322i	−0.323597	+	0.946195i	$0.604892\pi$
$858$		0			0
$859$	963.468	+	556.258i	1.12162	+	0.647565i	0.941813	−	0.336138i	$-0.109121\pi$
$859$	963.468	+	556.258i	1.12162	+	0.647565i	0.179803	+	0.983703i	$0.442454\pi$
$860$	120.854	−	323.627i	0.140528	−	0.376310i
$861$		0			0
$862$	−341.207	−	91.4262i	−0.395832	−	0.106063i
$863$	−354.960	−	354.960i	−0.411309	−	0.411309i	0.470885	−	0.882194i	$-0.343935\pi$
$863$	−354.960	−	354.960i	−0.411309	−	0.411309i	−0.882194	+	0.470885i	$0.843935\pi$
$864$		0			0
$865$	−201.953	−	1203.92i	−0.233472	−	1.39182i
$866$	−24.9453	−	43.2064i	−0.0288051	−	0.0498920i
$867$		0			0
$868$	−98.1639	+	26.3029i	−0.113092	+	0.0303029i
$869$	−146.227	−	84.4240i	−0.168270	−	0.0971508i
$870$		0			0
$871$	364.635	+	631.566i	0.418639	+	0.725104i
$872$	16.8534	−	16.8534i	0.0193273	−	0.0193273i
$873$		0			0
$874$			32.4388i			0.0371153i
$875$	660.377	−	1080.49i	0.754716	−	1.23485i
$876$		0			0
$877$	96.5961	+	360.501i	0.110144	+	0.411062i	0.998878	−	0.0473610i	$-0.0150811\pi$
$877$	96.5961	+	360.501i	0.110144	+	0.411062i	−0.888734	+	0.458423i	$0.848414\pi$
$878$	−149.375	+	40.0249i	−0.170131	+	0.0455864i
$879$		0			0
$880$	30.9738	−	323.004i	0.0351975	−	0.367050i
$881$	−1377.92			−1.56404			−0.782022	−	0.623251i	$-0.785812\pi$
$881$	−1377.92			−1.56404			−0.782022	+	0.623251i	$0.785812\pi$
$882$		0			0
$883$	−25.5579	−	25.5579i	−0.0289444	−	0.0289444i	0.692486	−	0.721431i	$-0.256515\pi$
$883$	−25.5579	−	25.5579i	−0.0289444	−	0.0289444i	−0.721431	+	0.692486i	$0.756515\pi$
$884$	384.219	−	221.829i	0.434637	−	0.250938i
$885$		0			0
$886$	−261.468	+	452.876i	−0.295111	+	0.511147i
$887$	39.5459	+	147.587i	0.0445839	+	0.166389i	0.984628	−	0.174663i	$-0.0558835\pi$
$887$	39.5459	+	147.587i	0.0445839	+	0.166389i	−0.940044	+	0.341052i	$0.889217\pi$
$888$		0			0
$889$	1792.96	−	1035.16i	2.01682	−	1.16441i
$890$	−120.196	−	716.536i	−0.135052	−	0.805096i
$891$		0			0
$892$	−496.494	+	496.494i	−0.556608	+	0.556608i
$893$	−4.81678	+	17.9765i	−0.00539393	+	0.0201304i
$894$		0			0
$895$	−232.830	−	510.369i	−0.260146	−	0.570245i
$896$	57.3069	−	99.2585i	0.0639586	−	0.110780i
$897$		0			0
$898$	131.102	−	489.280i	0.145994	−	0.544855i
$899$		−	115.740i		−	0.128743i
$900$		0			0
$901$	−452.848			−0.502606
$902$	−1163.44	−	311.743i	−1.28985	−	0.345613i
$903$		0			0
$904$	122.495	+	70.7223i	0.135503	+	0.0782326i
$905$	50.9783	−	23.2563i	0.0563296	−	0.0256976i
$906$		0			0
$907$	−1602.13	−	429.289i	−1.76640	−	0.473307i	−0.778405	−	0.627763i	$-0.783971\pi$
$907$	−1602.13	−	429.289i	−1.76640	−	0.473307i	−0.988000	+	0.154456i	$0.950637\pi$
$908$	−473.903	−	473.903i	−0.521920	−	0.521920i
$909$		0			0
$910$	−1477.65	+	247.870i	−1.62379	+	0.272384i
$911$	−79.1611	−	137.111i	−0.0868947	−	0.150506i	0.819302	−	0.573362i	$-0.194361\pi$
$911$	−79.1611	−	137.111i	−0.0868947	−	0.150506i	−0.906197	+	0.422856i	$0.861028\pi$
$912$		0			0
$913$	−364.524	+	97.6739i	−0.399260	+	0.106981i
$914$	1074.17	+	620.171i	1.17524	+	0.678524i
$915$		0			0
$916$	385.815	+	668.250i	0.421195	+	0.729531i
$917$	751.403	−	751.403i	0.819415	−	0.819415i
$918$		0			0
$919$		−	449.294i		−	0.488894i	−0.969663	−	0.244447i	$-0.921394\pi$
$919$		−	449.294i		−	0.488894i	0.969663	−	0.244447i	$-0.0786065\pi$
$920$	279.678	+	26.8191i	0.303998	+	0.0291512i
$921$		0			0
$922$	78.5756	+	293.248i	0.0852230	+	0.318056i
$923$	34.1223	−	9.14306i	0.0369690	−	0.00990580i
$924$		0			0
$925$	−82.3238	−	1164.15i	−0.0889987	−	1.25854i
$926$	475.477			0.513474
$927$		0			0
$928$	92.2990	+	92.2990i	0.0994601	+	0.0994601i
$929$	851.351	−	491.528i	0.916417	−	0.529094i	0.0339268	−	0.999424i	$-0.489199\pi$
$929$	851.351	−	491.528i	0.916417	−	0.529094i	0.882490	+	0.470331i	$0.155865\pi$
$930$		0			0
$931$	30.9583	−	53.6214i	0.0332528	−	0.0575955i
$932$	22.6448	+	84.5117i	0.0242970	+	0.0906778i
$933$		0			0
$934$	954.706	−	551.200i	1.02217	−	0.590149i
$935$	848.494	−	142.332i	0.907480	−	0.152226i
$936$		0			0
$937$	−890.763	+	890.763i	−0.950654	+	0.950654i	−0.998838	−	0.0481843i	$-0.984657\pi$
$937$	−890.763	+	890.763i	−0.950654	+	0.950654i	0.0481843	+	0.998838i	$0.484657\pi$
$938$	−129.286	+	482.502i	−0.137832	+	0.514395i
$939$		0			0
$940$	151.006	+	56.3912i	0.160644	+	0.0599906i
$941$	−141.451	+	245.001i	−0.150320	+	0.260362i	−0.931345	−	0.364137i	$-0.881364\pi$
$941$	−141.451	+	245.001i	−0.150320	+	0.260362i	0.781025	+	0.624500i	$0.214697\pi$
$942$		0			0
$943$	269.928	−	1007.38i	0.286243	−	1.06828i
$944$			3.37552i			0.00357576i
$945$		0			0
$946$	−792.636			−0.837882
$947$	419.826	+	112.492i	0.443322	+	0.118788i	0.473573	−	0.880755i	$-0.342964\pi$
$947$	419.826	+	112.492i	0.443322	+	0.118788i	−0.0302512	+	0.999542i	$0.509631\pi$
$948$		0			0
$949$	−2579.63	−	1489.35i	−2.71827	−	1.56939i
$950$	−22.8529	−	33.8235i	−0.0240556	−	0.0356036i
$951$		0			0
$952$	293.535	+	78.6525i	0.308335	+	0.0826182i
$953$	521.907	+	521.907i	0.547647	+	0.547647i	0.925760	−	0.378113i	$-0.123427\pi$
$953$	521.907	+	521.907i	0.547647	+	0.547647i	−0.378113	+	0.925760i	$0.623427\pi$
$954$		0			0
$955$	353.758	+	252.124i	0.370428	+	0.264004i
$956$	−130.995	−	226.890i	−0.137024	−	0.237332i
$957$		0			0
$958$	−844.501	+	226.283i	−0.881525	+	0.236204i
$959$	505.479	+	291.838i	0.527089	+	0.304315i
$960$		0			0
$961$	467.921	+	810.462i	0.486910	+	0.843353i
$962$	−976.410	+	976.410i	−1.01498	+	1.01498i
$963$		0			0
$964$			130.758i			0.135641i
$965$	−319.001	+	263.174i	−0.330571	+	0.272720i
$966$		0			0
$967$	364.541	+	1360.49i	0.376981	+	1.40691i	0.850428	+	0.526091i	$0.176343\pi$
$967$	364.541	+	1360.49i	0.376981	+	1.40691i	−0.473447	+	0.880822i	$0.656990\pi$
$968$	−388.572	+	104.118i	−0.401417	+	0.107559i
$969$		0			0
$970$	159.281	+	15.2739i	0.164207	+	0.0157463i
$971$	684.172			0.704605			0.352303	−	0.935886i	$-0.385399\pi$
$971$	684.172			0.704605			0.352303	+	0.935886i	$0.385399\pi$
$972$		0			0
$973$	894.646	+	894.646i	0.919472	+	0.919472i
$974$	−724.348	+	418.202i	−0.743684	+	0.429366i
$975$		0			0
$976$	63.5759	−	110.117i	0.0651393	−	0.112825i
$977$	282.136	+	1052.94i	0.288777	+	1.07773i	0.946035	+	0.324066i	$0.105050\pi$
$977$	282.136	+	1052.94i	0.288777	+	1.07773i	−0.657257	+	0.753666i	$0.728283\pi$
$978$		0			0
$979$	−1443.69	+	833.516i	−1.47466	+	0.851396i
$980$	−436.713	−	311.246i	−0.445626	−	0.317598i
$981$		0			0
$982$	−326.463	+	326.463i	−0.332447	+	0.332447i
$983$	−360.626	+	1345.88i	−0.366863	+	1.36915i	0.498015	+	0.867168i	$0.334062\pi$
$983$	−360.626	+	1345.88i	−0.366863	+	1.36915i	−0.864878	+	0.501982i	$0.832604\pi$
$984$		0			0
$985$	227.334	−	608.760i	0.230796	−	0.618031i
$986$	−173.046	+	299.724i	−0.175503	+	0.303980i
$987$		0			0
$988$	−12.5004	+	46.6522i	−0.0126522	+	0.0472188i
$989$		−	686.316i		−	0.693950i
$990$		0			0
$991$	−454.036			−0.458160			−0.229080	−	0.973408i	$-0.573572\pi$
$991$	−454.036			−0.458160			−0.229080	+	0.973408i	$0.573572\pi$
$992$	27.4072	+	7.34374i	0.0276282	+	0.00740296i
$993$		0			0
$994$	20.9553	+	12.0985i	0.0210818	+	0.0121716i
$995$	−140.177	−	307.270i	−0.140881	−	0.308815i
$996$		0			0
$997$	−636.610	−	170.579i	−0.638526	−	0.171092i	−0.0749902	−	0.997184i	$-0.523893\pi$
$997$	−636.610	−	170.579i	−0.638526	−	0.171092i	−0.563536	+	0.826092i	$0.690559\pi$
$998$	−227.119	−	227.119i	−0.227574	−	0.227574i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.3.l.b.253.1		24
3.2	odd	2		90.3.k.a.13.2	yes	24
5.2	odd	4	inner	270.3.l.b.37.3		24
9.2	odd	6		90.3.k.a.43.2	yes	24
9.4	even	3		810.3.g.i.163.5		12
9.5	odd	6		810.3.g.k.163.2		12
9.7	even	3	inner	270.3.l.b.73.3		24
15.2	even	4		90.3.k.a.67.2	yes	24
45.2	even	12		90.3.k.a.7.2	✓	24
45.7	odd	12	inner	270.3.l.b.127.1		24
45.22	odd	12		810.3.g.i.487.5		12
45.32	even	12		810.3.g.k.487.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.k.a.7.2	✓	24	45.2	even	12
90.3.k.a.13.2	yes	24	3.2	odd	2
90.3.k.a.43.2	yes	24	9.2	odd	6
90.3.k.a.67.2	yes	24	15.2	even	4
270.3.l.b.37.3		24	5.2	odd	4	inner
270.3.l.b.73.3		24	9.7	even	3	inner
270.3.l.b.127.1		24	45.7	odd	12	inner
270.3.l.b.253.1		24	1.1	even	1	trivial
810.3.g.i.163.5		12	9.4	even	3
810.3.g.i.487.5		12	45.22	odd	12
810.3.g.k.163.2		12	9.5	odd	6
810.3.g.k.487.2		12	45.32	even	12

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	270.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(-4.54899 + 2.07525i) q^{5} +(-9.78534 - 2.62197i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-6.97363 + 1.16980i) q^{10} +(8.11214 + 14.0506i) q^{11} +(-20.2033 + 5.41347i) q^{13} +(-12.4073 - 7.16337i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-7.49936 + 7.49936i) q^{17} -1.15457i q^{19} +(-9.95434 - 0.954551i) q^{20} +(5.93850 + 22.1628i) q^{22} +(-19.1900 + 5.14194i) q^{23} +(16.3867 - 18.8806i) q^{25} -29.5797 q^{26} +(-14.3267 - 14.3267i) q^{28} +(19.9833 - 11.5374i) q^{29} +(2.50793 - 4.34387i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-12.9893 + 7.49936i) q^{34} +(49.9547 - 8.37971i) q^{35} +(33.0094 - 33.0094i) q^{37} +(0.422601 - 1.57717i) q^{38} +(-13.2485 - 4.94748i) q^{40} +(-26.2476 + 45.4622i) q^{41} +(-8.94107 + 33.3685i) q^{43} +32.4486i q^{44} -28.0961 q^{46} +(-15.5699 - 4.17194i) q^{47} +(46.4429 + 26.8138i) q^{49} +(29.2954 - 19.7935i) q^{50} +(-40.4067 - 10.8269i) q^{52} +(30.1924 + 30.1924i) q^{53} +(-66.0607 - 47.0815i) q^{55} +(-14.3267 - 24.8146i) q^{56} +(31.5207 - 8.44594i) q^{58} +(0.730822 + 0.421940i) q^{59} +(-15.8940 - 27.5292i) q^{61} +(5.01587 - 5.01587i) q^{62} +8.00000i q^{64} +(80.6705 - 66.5529i) q^{65} +(-9.02411 - 33.6785i) q^{67} +(-20.4886 + 5.48991i) q^{68} +(71.3066 + 6.83780i) q^{70} -1.68895 q^{71} +(100.701 + 100.701i) q^{73} +(57.1739 - 33.0094i) q^{74} +(1.15457 - 1.99977i) q^{76} +(-42.5396 - 158.760i) q^{77} +(-9.01283 + 5.20356i) q^{79} +(-16.2869 - 11.6077i) q^{80} +(-52.4953 + 52.4953i) q^{82} +(-6.02023 + 22.4678i) q^{83} +(18.5515 - 49.6776i) q^{85} +(-24.4275 + 42.3096i) q^{86} +(-11.8770 + 44.3256i) q^{88} +102.749i q^{89} +211.891 q^{91} +(-38.3800 - 10.2839i) q^{92} +(-19.7418 - 11.3980i) q^{94} +(2.39602 + 5.25211i) q^{95} +(-21.8580 - 5.85684i) q^{97} +(53.6276 + 53.6276i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} - 6 q^{7} + 48 q^{8} - 12 q^{10} + 12 q^{11} + 48 q^{16} + 36 q^{17} - 12 q^{20} - 12 q^{22} + 54 q^{23} + 54 q^{25} - 24 q^{28} - 72 q^{31} - 48 q^{32} + 336 q^{35} + 132 q^{37} + 36 q^{38}+ \cdots - 24 q^{98}+O(q^{100}) \) 24 * q + 12 * q^2 - 6 * q^7 + 48 * q^8 - 12 * q^10 + 12 * q^11 + 48 * q^16 + 36 * q^17 - 12 * q^20 - 12 * q^22 + 54 * q^23 + 54 * q^25 - 24 * q^28 - 72 * q^31 - 48 * q^32 + 336 * q^35 + 132 * q^37 + 36 * q^38 + 12 * q^40 - 24 * q^41 + 108 * q^43 + 216 * q^46 - 48 * q^47 - 54 * q^50 - 384 * q^53 - 552 * q^55 - 24 * q^56 + 60 * q^58 - 456 * q^61 - 144 * q^62 - 264 * q^65 + 12 * q^67 + 36 * q^68 + 174 * q^70 + 168 * q^71 - 432 * q^73 - 72 * q^76 + 48 * q^77 - 48 * q^82 + 246 * q^83 + 324 * q^85 - 216 * q^86 + 24 * q^88 + 1224 * q^91 + 108 * q^92 - 432 * q^95 - 102 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more