LMFDB - Embedded newform 304.5.r.d.65.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,5,Mod(65,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("304.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	304.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$31.4244687775$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.4
Character	$\chi$	$=$	304.65
Dual form			304.5.r.d.145.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.6119 - 6.12677i) q^{3} +(3.27153 - 5.66646i) q^{5} +87.4966 q^{7} +(34.5747 + 59.8851i) q^{9} +O(q^{10})$	\(q+(-10.6119 - 6.12677i) q^{3} +(3.27153 - 5.66646i) q^{5} +87.4966 q^{7} +(34.5747 + 59.8851i) q^{9} +159.983 q^{11} +(-223.432 + 128.999i) q^{13} +(-69.4342 + 40.0878i) q^{15} +(-151.893 + 263.086i) q^{17} +(-345.743 - 103.841i) q^{19} +(-928.504 - 536.072i) q^{21} +(-60.7531 - 105.227i) q^{23} +(291.094 + 504.190i) q^{25} +145.212i q^{27} +(1032.69 - 596.223i) q^{29} +1124.35i q^{31} +(-1697.72 - 980.179i) q^{33} +(286.248 - 495.796i) q^{35} +2469.60i q^{37} +3161.38 q^{39} +(-700.793 - 404.603i) q^{41} +(1066.38 - 1847.03i) q^{43} +452.448 q^{45} +(1576.10 + 2729.89i) q^{47} +5254.66 q^{49} +(3223.74 - 1861.23i) q^{51} +(-1104.88 + 637.901i) q^{53} +(523.389 - 906.536i) q^{55} +(3032.77 + 3220.24i) q^{57} +(-2531.03 - 1461.29i) q^{59} +(-1308.59 - 2266.55i) q^{61} +(3025.17 + 5239.75i) q^{63} +1688.09i q^{65} +(642.212 - 370.781i) q^{67} +1488.88i q^{69} +(5880.82 + 3395.29i) q^{71} +(422.902 - 732.488i) q^{73} -7133.87i q^{75} +13998.0 q^{77} +(4664.22 + 2692.89i) q^{79} +(3690.23 - 6391.67i) q^{81} -2130.90 q^{83} +(993.844 + 1721.39i) q^{85} -14611.7 q^{87} +(1213.55 - 700.644i) q^{89} +(-19549.6 + 11287.0i) q^{91} +(6888.61 - 11931.4i) q^{93} +(-1719.52 + 1619.42i) q^{95} +(749.210 + 432.556i) q^{97} +(5531.36 + 9580.59i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) $ 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9	$ 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) $ 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9 - 24 * q^11 + 264 * q^13 - 624 * q^15 + 216 * q^17 + 652 * q^19 - 216 * q^21 + 1296 * q^23 - 3044 * q^25 + 288 * q^29 - 6660 * q^33 - 360 * q^35 - 3184 * q^39 + 1260 * q^41 - 632 * q^43 + 256 * q^45 - 1248 * q^47 + 16696 * q^49 + 8064 * q^51 - 3672 * q^53 + 3408 * q^55 - 4552 * q^57 - 12492 * q^59 + 2720 * q^61 - 12472 * q^63 - 16260 * q^67 + 504 * q^71 + 9220 * q^73 - 14688 * q^77 + 28944 * q^79 - 1660 * q^81 + 39192 * q^83 - 18632 * q^85 + 34400 * q^87 + 3456 * q^89 - 54432 * q^91 - 17208 * q^93 - 44520 * q^95 - 30540 * q^97 + 10096 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−10.6119	−	6.12677i	−1.17910	−	0.680753i	−0.223292	−	0.974752i	$-0.571680\pi$
$3$	−10.6119	−	6.12677i	−1.17910	−	0.680753i	−0.955806	+	0.293999i	$0.905014\pi$
$4$		0			0
$5$	3.27153	−	5.66646i	0.130861	−	0.226658i	−0.793148	−	0.609029i	$-0.791559\pi$
$5$	3.27153	−	5.66646i	0.130861	−	0.226658i	0.924009	+	0.382371i	$0.124892\pi$
$6$		0			0
$7$	87.4966			1.78565			0.892823	−	0.450409i	$-0.148722\pi$
$7$	87.4966			1.78565			0.892823	+	0.450409i	$0.148722\pi$
$8$		0			0
$9$	34.5747	+	59.8851i	0.426848	+	0.739322i
$10$		0			0
$11$	159.983			1.32217			0.661086	−	0.750310i	$-0.270096\pi$
$11$	159.983			1.32217			0.661086	+	0.750310i	$0.270096\pi$
$12$		0			0
$13$	−223.432	+	128.999i	−1.32209	+	0.763306i	−0.984061	−	0.177831i	$-0.943092\pi$
$13$	−223.432	+	128.999i	−1.32209	+	0.763306i	−0.338024	+	0.941137i	$0.609759\pi$
$14$		0			0
$15$	−69.4342	+	40.0878i	−0.308596	+	0.178168i
$16$		0			0
$17$	−151.893	+	263.086i	−0.525581	+	0.910333i	0.473975	+	0.880538i	$0.342819\pi$
$17$	−151.893	+	263.086i	−0.525581	+	0.910333i	−0.999556	+	0.0297949i	$0.990515\pi$
$18$		0			0
$19$	−345.743	−	103.841i	−0.957736	−	0.287648i
$19$	−345.743	−	103.841i	−0.957736	−	0.287648i
$20$		0			0
$21$	−928.504	−	536.072i	−2.10545	−	1.21558i
$22$		0			0
$23$	−60.7531	−	105.227i	−0.114845	−	0.198918i	0.802873	−	0.596150i	$-0.203304\pi$
$23$	−60.7531	−	105.227i	−0.114845	−	0.198918i	−0.917718	+	0.397233i	$0.869971\pi$
$24$		0			0
$25$	291.094	+	504.190i	0.465751	+	0.806704i
$26$		0			0
$27$			145.212i			0.199194i
$28$		0			0
$29$	1032.69	−	596.223i	1.22793	−	0.708945i	0.261332	−	0.965249i	$-0.415838\pi$
$29$	1032.69	−	596.223i	1.22793	−	0.708945i	0.966596	+	0.256304i	$0.0825049\pi$
$30$		0			0
$31$			1124.35i			1.16997i	0.811043	+	0.584987i	$0.198900\pi$
$31$			1124.35i			1.16997i	−0.811043	+	0.584987i	$0.801100\pi$
$32$		0			0
$33$	−1697.72	−	980.179i	−1.55897	−	0.900072i
$34$		0			0
$35$	286.248	−	495.796i	0.233672	−	0.404731i
$36$		0			0
$37$			2469.60i			1.80394i	0.431796	+	0.901971i	$0.357880\pi$
$37$			2469.60i			1.80394i	−0.431796	+	0.901971i	$0.642120\pi$
$38$		0			0
$39$	3161.38			2.07849
$40$		0			0
$41$	−700.793	−	404.603i	−0.416891	−	0.240692i	0.276855	−	0.960912i	$-0.410708\pi$
$41$	−700.793	−	404.603i	−0.416891	−	0.240692i	−0.693746	+	0.720220i	$0.744041\pi$
$42$		0			0
$43$	1066.38	−	1847.03i	0.576736	−	0.998935i	−0.419115	−	0.907933i	$-0.637660\pi$
$43$	1066.38	−	1847.03i	0.576736	−	0.998935i	0.995851	−	0.0910022i	$-0.0290070\pi$
$44$		0			0
$45$	452.448			0.223431
$46$		0			0
$47$	1576.10	+	2729.89i	0.713491	+	1.23580i	0.963539	+	0.267569i	$0.0862204\pi$
$47$	1576.10	+	2729.89i	0.713491	+	1.23580i	−0.250048	+	0.968234i	$0.580446\pi$
$48$		0			0
$49$	5254.66			2.18853
$50$		0			0
$51$	3223.74	−	1861.23i	1.23942	−	0.715581i
$52$		0			0
$53$	−1104.88	+	637.901i	−0.393334	+	0.227092i	−0.683604	−	0.729853i	$-0.739588\pi$
$53$	−1104.88	+	637.901i	−0.393334	+	0.227092i	0.290269	+	0.956945i	$0.406255\pi$
$54$		0			0
$55$	523.389	−	906.536i	0.173021	−	0.299681i
$56$		0			0
$57$	3032.77	+	3220.24i	0.933448	+	0.991147i
$58$		0			0
$59$	−2531.03	−	1461.29i	−0.727097	−	0.419790i	0.0902619	−	0.995918i	$-0.471230\pi$
$59$	−2531.03	−	1461.29i	−0.727097	−	0.419790i	−0.817359	+	0.576128i	$0.804563\pi$
$60$		0			0
$61$	−1308.59	−	2266.55i	−0.351677	−	0.609123i	0.634866	−	0.772622i	$-0.281055\pi$
$61$	−1308.59	−	2266.55i	−0.351677	−	0.609123i	−0.986543	+	0.163499i	$0.947722\pi$
$62$		0			0
$63$	3025.17	+	5239.75i	0.762199	+	1.32017i
$64$		0			0
$65$			1688.09i			0.399549i
$66$		0			0
$67$	642.212	−	370.781i	0.143063	−	0.0825977i	−0.426760	−	0.904365i	$-0.640345\pi$
$67$	642.212	−	370.781i	0.143063	−	0.0825977i	0.569823	+	0.821767i	$0.307012\pi$
$68$		0			0
$69$			1488.88i			0.312724i
$70$		0			0
$71$	5880.82	+	3395.29i	1.16660	+	0.673536i	0.952876	−	0.303359i	$-0.0981081\pi$
$71$	5880.82	+	3395.29i	1.16660	+	0.673536i	0.213722	+	0.976895i	$0.431441\pi$
$72$		0			0
$73$	422.902	−	732.488i	0.0793586	−	0.137453i	−0.823615	−	0.567150i	$-0.808046\pi$
$73$	422.902	−	732.488i	0.0793586	−	0.137453i	0.902973	+	0.429696i	$0.141379\pi$
$74$		0			0
$75$		−	7133.87i		−	1.26824i
$76$		0			0
$77$	13998.0			2.36093
$78$		0			0
$79$	4664.22	+	2692.89i	0.747352	+	0.431484i	0.824736	−	0.565518i	$-0.191324\pi$
$79$	4664.22	+	2692.89i	0.747352	+	0.431484i	−0.0773846	+	0.997001i	$0.524657\pi$
$80$		0			0
$81$	3690.23	−	6391.67i	0.562450	−	0.974191i
$82$		0			0
$83$	−2130.90			−0.309319			−0.154659	−	0.987968i	$-0.549428\pi$
$83$	−2130.90			−0.309319			−0.154659	+	0.987968i	$0.549428\pi$
$84$		0			0
$85$	993.844	+	1721.39i	0.137556	+	0.238255i
$86$		0			0
$87$	−14611.7			−1.93046
$88$		0			0
$89$	1213.55	−	700.644i	0.153207	−	0.0884540i	−0.421437	−	0.906858i	$-0.638474\pi$
$89$	1213.55	−	700.644i	0.153207	−	0.0884540i	0.574644	+	0.818404i	$0.305141\pi$
$90$		0			0
$91$	−19549.6	+	11287.0i	−2.36077	+	1.36299i
$92$		0			0
$93$	6888.61	−	11931.4i	0.796463	−	1.37951i
$94$		0			0
$95$	−1719.52	+	1619.42i	−0.190528	+	0.179437i
$96$		0			0
$97$	749.210	+	432.556i	0.0796269	+	0.0459726i	0.539285	−	0.842123i	$-0.318695\pi$
$97$	749.210	+	432.556i	0.0796269	+	0.0459726i	−0.459658	+	0.888096i	$0.652028\pi$
$98$		0			0
$99$	5531.36	+	9580.59i	0.564367	+	0.977512i
$100$		0			0
$101$	6479.55	+	11222.9i	0.635188	+	1.10018i	0.986475	+	0.163910i	$0.0524106\pi$
$101$	6479.55	+	11222.9i	0.635188	+	1.10018i	−0.351287	+	0.936268i	$0.614256\pi$
$102$		0			0
$103$		−	6549.01i		−	0.617307i	−0.951175	−	0.308653i	$-0.900122\pi$
$103$		−	6549.01i		−	0.617307i	0.951175	−	0.308653i	$-0.0998783\pi$
$104$		0			0
$105$	−6075.25	+	3507.55i	−0.551043	+	0.318145i
$106$		0			0
$107$			108.250i			0.00945494i	0.999989	+	0.00472747i	$0.00150481\pi$
$107$			108.250i			0.00945494i	−0.999989	+	0.00472747i	$0.998495\pi$
$108$		0			0
$109$	−5819.33	−	3359.79i	−0.489801	−	0.282787i	0.234691	−	0.972070i	$-0.424592\pi$
$109$	−5819.33	−	3359.79i	−0.489801	−	0.282787i	−0.724492	+	0.689283i	$0.757926\pi$
$110$		0			0
$111$	15130.7	−	26207.1i	1.22804	−	2.12703i
$112$		0			0
$113$			20307.5i			1.59038i	0.606363	+	0.795188i	$0.292628\pi$
$113$			20307.5i			1.59038i	−0.606363	+	0.795188i	$0.707372\pi$
$114$		0			0
$115$	−795.022			−0.0601151
$116$		0			0
$117$	−15450.2	−	8920.18i	−1.12866	−	0.651631i
$118$		0			0
$119$	−13290.1	+	23019.2i	−0.938501	+	1.62553i
$120$		0			0
$121$	10953.5			0.748140
$122$		0			0
$123$	4957.82	+	8587.20i	0.327703	+	0.567599i
$124$		0			0
$125$	7898.70			0.505517
$126$		0			0
$127$	15332.1	−	8852.02i	0.950595	−	0.548826i	0.0573290	−	0.998355i	$-0.481742\pi$
$127$	15332.1	−	8852.02i	0.950595	−	0.548826i	0.893266	+	0.449529i	$0.148408\pi$
$128$		0			0
$129$	−22632.7	+	13067.0i	−1.36006	+	0.785228i
$130$		0			0
$131$	10646.6	−	18440.4i	0.620394	−	1.07455i	−0.369018	−	0.929422i	$-0.620306\pi$
$131$	10646.6	−	18440.4i	0.620394	−	1.07455i	0.989412	−	0.145132i	$-0.0463607\pi$
$132$		0			0
$133$	−30251.3	−	9085.73i	−1.71018	−	0.513637i
$134$		0			0
$135$	822.838	+	475.066i	0.0451489	+	0.0260667i
$136$		0			0
$137$	9797.08	+	16969.0i	0.521982	+	0.904099i	0.999673	+	0.0255711i	$0.00814043\pi$
$137$	9797.08	+	16969.0i	0.521982	+	0.904099i	−0.477691	+	0.878528i	$0.658526\pi$
$138$		0			0
$139$	6161.97	+	10672.8i	0.318926	+	0.552396i	0.980264	−	0.197692i	$-0.0633446\pi$
$139$	6161.97	+	10672.8i	0.318926	+	0.552396i	−0.661338	+	0.750088i	$0.730011\pi$
$140$		0			0
$141$		−	38625.7i		−	1.94284i
$142$		0			0
$143$	−35745.4	+	20637.6i	−1.74802	+	1.00922i
$144$		0			0
$145$		−	7802.24i		−	0.371093i
$146$		0			0
$147$	−55761.8	−	32194.1i	−2.58049	−	1.48985i
$148$		0			0
$149$	−13494.6	+	23373.3i	−0.607838	+	1.05281i	0.383758	+	0.923434i	$0.374630\pi$
$149$	−13494.6	+	23373.3i	−0.607838	+	1.05281i	−0.991596	+	0.129372i	$0.958704\pi$
$150$		0			0
$151$		−	15879.3i		−	0.696429i	−0.937415	−	0.348214i	$-0.886788\pi$
$151$		−	15879.3i		−	0.696429i	0.937415	−	0.348214i	$-0.113212\pi$
$152$		0			0
$153$	−21006.6			−0.897373
$154$		0			0
$155$	6371.05	+	3678.33i	0.265184	+	0.153104i
$156$		0			0
$157$	10064.4	−	17432.0i	0.408309	−	0.707211i	−0.586392	−	0.810028i	$-0.699452\pi$
$157$	10064.4	−	17432.0i	0.408309	−	0.707211i	0.994700	+	0.102816i	$0.0327854\pi$
$158$		0			0
$159$	15633.1			0.618373
$160$		0			0
$161$	−5315.69	−	9207.04i	−0.205073	−	0.355196i
$162$		0			0
$163$	42179.3			1.58754			0.793770	−	0.608218i	$-0.208115\pi$
$163$	42179.3			1.58754			0.793770	+	0.608218i	$0.208115\pi$
$164$		0			0
$165$	−11108.3	+	6413.37i	−0.408018	+	0.235569i
$166$		0			0
$167$	36239.9	−	20923.1i	1.29943	−	0.750227i	0.319126	−	0.947712i	$-0.396611\pi$
$167$	36239.9	−	20923.1i	1.29943	−	0.750227i	0.980306	+	0.197485i	$0.0632773\pi$
$168$		0			0
$169$	19000.9	−	32910.4i	0.665273	−	1.15229i
$170$		0			0
$171$	−5735.42	−	24295.1i	−0.196143	−	0.830858i
$172$		0			0
$173$	−15892.8	−	9175.71i	−0.531017	−	0.306583i	0.210414	−	0.977612i	$-0.432519\pi$
$173$	−15892.8	−	9175.71i	−0.531017	−	0.306583i	−0.741430	+	0.671030i	$0.765852\pi$
$174$		0			0
$175$	25469.8	+	44114.9i	0.831665	+	1.44049i
$176$		0			0
$177$	17906.0	+	31014.0i	0.571546	+	0.989947i
$178$		0			0
$179$		−	10031.8i		−	0.313093i	−0.987671	−	0.156546i	$-0.949964\pi$
$179$		−	10031.8i		−	0.313093i	0.987671	−	0.156546i	$-0.0500361\pi$
$180$		0			0
$181$	−18128.2	+	10466.3i	−0.553346	+	0.319474i	−0.750470	−	0.660904i	$-0.770173\pi$
$181$	−18128.2	+	10466.3i	−0.553346	+	0.319474i	0.197125	+	0.980378i	$0.436840\pi$
$182$		0			0
$183$			32069.8i			0.957621i
$184$		0			0
$185$	13993.9	+	8079.36i	0.408878	+	0.236066i
$186$		0			0
$187$	−24300.3	+	42089.3i	−0.694909	+	1.20362i
$188$		0			0
$189$			12705.6i			0.355689i
$190$		0			0
$191$	−44033.7			−1.20703			−0.603515	−	0.797352i	$-0.706234\pi$
$191$	−44033.7			−1.20703			−0.603515	+	0.797352i	$0.706234\pi$
$192$		0			0
$193$	−13753.4	−	7940.55i	−0.369230	−	0.213175i	0.303892	−	0.952706i	$-0.401714\pi$
$193$	−13753.4	−	7940.55i	−0.369230	−	0.213175i	−0.673122	+	0.739532i	$0.735047\pi$
$194$		0			0
$195$	10342.6	−	17913.8i	0.271994	−	0.471107i
$196$		0			0
$197$	41918.3			1.08012			0.540059	−	0.841627i	$-0.318402\pi$
$197$	41918.3			1.08012			0.540059	+	0.841627i	$0.318402\pi$
$198$		0			0
$199$	−6604.31	−	11439.0i	−0.166771	−	0.288856i	0.770512	−	0.637426i	$-0.220001\pi$
$199$	−6604.31	−	11439.0i	−0.166771	−	0.288856i	−0.937283	+	0.348570i	$0.886667\pi$
$200$		0			0
$201$	−9086.77			−0.224914
$202$		0			0
$203$	90356.7	−	52167.5i	2.19264	−	1.26592i
$204$		0			0
$205$	−4585.33	+	2647.34i	−0.109110	+	0.0629945i
$206$		0			0
$207$	4201.04	−	7276.41i	0.0980428	−	0.169815i
$208$		0			0
$209$	−55312.9	−	16612.8i	−1.26629	−	0.380320i
$210$		0			0
$211$	−56476.4	−	32606.7i	−1.26853	−	0.732389i	−0.293824	−	0.955859i	$-0.594928\pi$
$211$	−56476.4	−	32606.7i	−1.26853	−	0.732389i	−0.974711	+	0.223470i	$0.928261\pi$
$212$		0			0
$213$	−41604.4	−	72060.9i	−0.917022	−	1.58833i
$214$		0			0
$215$	−6977.41	−	12085.2i	−0.150945	−	0.261444i
$216$		0			0
$217$			98376.4i			2.08916i
$218$		0			0
$219$	−8975.58	+	5182.05i	−0.187143	+	0.108047i
$220$		0			0
$221$		−	78376.0i		−	1.60472i
$222$		0			0
$223$	−16703.5	−	9643.79i	−0.335891	−	0.193927i	0.322562	−	0.946548i	$-0.395456\pi$
$223$	−16703.5	−	9643.79i	−0.335891	−	0.193927i	−0.658454	+	0.752621i	$0.728789\pi$
$224$		0			0
$225$	−20129.0	+	34864.4i	−0.397610	+	0.688680i
$226$		0			0
$227$			70874.3i			1.37543i	0.725983	+	0.687713i	$0.241385\pi$
$227$			70874.3i			1.37543i	−0.725983	+	0.687713i	$0.758615\pi$
$228$		0			0
$229$	8279.28			0.157878			0.0789390	−	0.996879i	$-0.474847\pi$
$229$	8279.28			0.157878			0.0789390	+	0.996879i	$0.474847\pi$
$230$		0			0
$231$	−148545.	−	85762.3i	−2.78377	−	1.60721i
$232$		0			0
$233$	−29319.8	+	50783.5i	−0.540070	+	0.935428i	0.458830	+	0.888524i	$0.348269\pi$
$233$	−29319.8	+	50783.5i	−0.540070	+	0.935428i	−0.998899	+	0.0469040i	$0.985065\pi$
$234$		0			0
$235$	20625.1			0.373473
$236$		0			0
$237$	−32997.4	−	57153.2i	−0.587467	−	1.01752i
$238$		0			0
$239$	−54309.7			−0.950783			−0.475391	−	0.879774i	$-0.657694\pi$
$239$	−54309.7			−0.950783			−0.475391	+	0.879774i	$0.657694\pi$
$240$		0			0
$241$	−33546.9	+	19368.3i	−0.577588	+	0.333471i	−0.760174	−	0.649719i	$-0.774887\pi$
$241$	−33546.9	+	19368.3i	−0.577588	+	0.333471i	0.182586	+	0.983190i	$0.441553\pi$
$242$		0			0
$243$	−68134.3	+	39337.3i	−1.15386	+	0.666181i
$244$		0			0
$245$	17190.8	−	29775.3i	0.286393	−	0.496048i
$246$		0			0
$247$	90645.5	−	21398.9i	1.48577	−	0.350751i
$248$		0			0
$249$	22612.8	+	13055.5i	0.364717	+	0.210569i
$250$		0			0
$251$	−28766.7	−	49825.4i	−0.456608	−	0.790868i	0.542171	−	0.840268i	$-0.317602\pi$
$251$	−28766.7	−	49825.4i	−0.456608	−	0.790868i	−0.998779	+	0.0494003i	$0.984269\pi$
$252$		0			0
$253$	−9719.45	−	16834.6i	−0.151845	−	0.263003i
$254$		0			0
$255$		−	24356.2i		−	0.374567i
$256$		0			0
$257$	10498.0	−	6061.03i	0.158943	−	0.0917657i	−0.418419	−	0.908254i	$-0.637416\pi$
$257$	10498.0	−	6061.03i	0.158943	−	0.0917657i	0.577362	+	0.816488i	$0.304082\pi$
$258$		0			0
$259$			216081.i			3.22120i
$260$		0			0
$261$	71409.7	+	41228.4i	1.04828	+	0.605223i
$262$		0			0
$263$	−5627.35	+	9746.85i	−0.0813565	+	0.140914i	−0.903833	−	0.427886i	$-0.859259\pi$
$263$	−5627.35	+	9746.85i	−0.0813565	+	0.140914i	0.822476	+	0.568799i	$0.192592\pi$
$264$		0			0
$265$			8347.64i			0.118870i
$266$		0			0
$267$	−17170.7			−0.240861
$268$		0			0
$269$	35461.0	+	20473.4i	0.490056	+	0.282934i	0.724598	−	0.689172i	$-0.242026\pi$
$269$	35461.0	+	20473.4i	0.490056	+	0.282934i	−0.234542	+	0.972106i	$0.575359\pi$
$270$		0			0
$271$	−16785.0	+	29072.5i	−0.228551	+	0.395862i	−0.957379	−	0.288835i	$-0.906732\pi$
$271$	−16785.0	+	29072.5i	−0.228551	+	0.395862i	0.728828	+	0.684697i	$0.240065\pi$
$272$		0			0
$273$	276610.			3.71145
$274$		0			0
$275$	46570.1	+	80661.8i	0.615803	+	1.06660i
$276$		0			0
$277$	−63920.4			−0.833067			−0.416534	−	0.909120i	$-0.636755\pi$
$277$	−63920.4			−0.833067			−0.416534	+	0.909120i	$0.636755\pi$
$278$		0			0
$279$	−67331.6	+	38873.9i	−0.864988	+	0.499401i
$280$		0			0
$281$	32299.0	−	18647.8i	0.409050	−	0.236165i	−0.281332	−	0.959611i	$-0.590776\pi$
$281$	32299.0	−	18647.8i	0.409050	−	0.236165i	0.690381	+	0.723446i	$0.257443\pi$
$282$		0			0
$283$	19496.8	−	33769.4i	0.243439	−	0.421649i	−0.718253	−	0.695782i	$-0.755058\pi$
$283$	19496.8	−	33769.4i	0.243439	−	0.421649i	0.961692	+	0.274134i	$0.0883911\pi$
$284$		0			0
$285$	28169.1	−	6649.97i	0.346804	−	0.0818709i
$286$		0			0
$287$	−61317.1	−	35401.4i	−0.744419	−	0.429791i
$288$		0			0
$289$	−4382.43	−	7590.60i	−0.0524710	−	0.0908825i
$290$		0			0
$291$	−5300.35	−	9180.48i	−0.0625920	−	0.108412i
$292$		0			0
$293$			66877.6i			0.779014i	0.921023	+	0.389507i	$0.127355\pi$
$293$			66877.6i			0.779014i	−0.921023	+	0.389507i	$0.872645\pi$
$294$		0			0
$295$	−16560.7	+	9561.30i	−0.190298	+	0.109868i
$296$		0			0
$297$			23231.5i			0.263368i
$298$		0			0
$299$	27148.4	+	15674.1i	0.303670	+	0.175324i
$300$		0			0
$301$	93305.0	−	161609.i	1.02985	−	1.78374i
$302$		0			0
$303$		−	158795.i		−	1.72962i
$304$		0			0
$305$	−17124.4			−0.184084
$306$		0			0
$307$	115578.	+	66729.3i	1.22631	+	0.708010i	0.966256	−	0.257584i	$-0.0829263\pi$
$307$	115578.	+	66729.3i	1.22631	+	0.708010i	0.260054	+	0.965594i	$0.416260\pi$
$308$		0			0
$309$	−40124.3	+	69497.3i	−0.420233	+	0.727865i
$310$		0			0
$311$	65162.3			0.673714			0.336857	−	0.941556i	$-0.390636\pi$
$311$	65162.3			0.673714			0.336857	+	0.941556i	$0.390636\pi$
$312$		0			0
$313$	−40456.2	−	70072.3i	−0.412949	−	0.715249i	0.582261	−	0.813002i	$-0.302168\pi$
$313$	−40456.2	−	70072.3i	−0.412949	−	0.715249i	−0.995211	+	0.0977523i	$0.968835\pi$
$314$		0			0
$315$	39587.7			0.398969
$316$		0			0
$317$	107528.	−	62081.5i	1.07005	−	0.617794i	0.141856	−	0.989887i	$-0.454693\pi$
$317$	107528.	−	62081.5i	1.07005	−	0.617794i	0.928195	+	0.372093i	$0.121360\pi$
$318$		0			0
$319$	165212.	−	95385.4i	1.62353	−	0.937347i
$320$		0			0
$321$	663.220	−	1148.73i	0.00643647	−	0.0111483i
$322$		0			0
$323$	79835.0	−	75187.5i	0.765224	−	0.720677i
$324$		0			0
$325$	−130080.	−	75101.6i	−1.23152	−	0.711021i
$326$		0			0
$327$	41169.3	+	71307.4i	0.385016	+	0.666867i
$328$		0			0
$329$	137904.	+	238856.i	1.27404	+	2.20671i
$330$		0			0
$331$			193085.i			1.76235i	0.472786	+	0.881177i	$0.343248\pi$
$331$			193085.i			1.76235i	−0.472786	+	0.881177i	$0.656752\pi$
$332$		0			0
$333$	−147892.	+	85385.6i	−1.33370	+	0.770009i
$334$		0			0
$335$		−	4852.09i		−	0.0432353i
$336$		0			0
$337$	−47212.5	−	27258.1i	−0.415716	−	0.240014i	0.277527	−	0.960718i	$-0.410485\pi$
$337$	−47212.5	−	27258.1i	−0.415716	−	0.240014i	−0.693243	+	0.720704i	$0.743819\pi$
$338$		0			0
$339$	124419.	−	215501.i	1.08265	−	1.87521i
$340$		0			0
$341$			179876.i			1.54691i
$342$		0			0
$343$	249685.			2.12229
$344$		0			0
$345$	8436.67	+	4870.92i	0.0708815	+	0.0409235i
$346$		0			0
$347$	10995.2	−	19044.3i	0.0913157	−	0.158163i	−0.816749	−	0.576993i	$-0.804226\pi$
$347$	10995.2	−	19044.3i	0.0913157	−	0.158163i	0.908065	+	0.418829i	$0.137559\pi$
$348$		0			0
$349$	−76554.7			−0.628522			−0.314261	−	0.949337i	$-0.601757\pi$
$349$	−76554.7			−0.628522			−0.314261	+	0.949337i	$0.601757\pi$
$350$		0			0
$351$	−18732.2	−	32445.1i	−0.152046	−	0.263351i
$352$		0			0
$353$	9417.83			0.0755791			0.0377895	−	0.999286i	$-0.487968\pi$
$353$	9417.83			0.0755791			0.0377895	+	0.999286i	$0.487968\pi$
$354$		0			0
$355$	38478.6	−	22215.6i	0.305325	−	0.176279i
$356$		0			0
$357$	282066.	−	162851.i	2.21317	−	1.27777i
$358$		0			0
$359$	−54377.9	+	94185.2i	−0.421923	+	0.730792i	−0.996128	−	0.0879199i	$-0.971978\pi$
$359$	−54377.9	+	94185.2i	−0.421923	+	0.730792i	0.574205	+	0.818712i	$0.305311\pi$
$360$		0			0
$361$	108755.	+	71804.5i	0.834517	+	0.550982i
$362$		0			0
$363$	−116238.	−	67109.8i	−0.882131	−	0.509299i
$364$		0			0
$365$	−2767.07	−	4792.71i	−0.0207699	−	0.0359746i
$366$		0			0
$367$	23127.8	+	40058.5i	0.171712	+	0.297415i	0.939019	−	0.343866i	$-0.111737\pi$
$367$	23127.8	+	40058.5i	0.171712	+	0.297415i	−0.767306	+	0.641281i	$0.778403\pi$
$368$		0			0
$369$		−	55956.1i		−	0.410956i
$370$		0			0
$371$	−96673.0	+	55814.2i	−0.702356	+	0.405505i
$372$		0			0
$373$		−	224355.i		−	1.61257i	−0.591530	−	0.806283i	$-0.701476\pi$
$373$		−	224355.i		−	1.61257i	0.591530	−	0.806283i	$-0.298524\pi$
$374$		0			0
$375$	−83820.1	−	48393.6i	−0.596054	−	0.344132i
$376$		0			0
$377$	−153824.	+	266431.i	−1.08228	+	1.87457i
$378$		0			0
$379$		−	3761.90i		−	0.0261896i	−0.999914	−	0.0130948i	$-0.995832\pi$
$379$		−	3761.90i		−	0.0261896i	0.999914	−	0.0130948i	$-0.00416832\pi$
$380$		0			0
$381$	−216937.			−1.49446
$382$		0			0
$383$	101734.	+	58736.4i	0.693538	+	0.400414i	0.804936	−	0.593362i	$-0.202200\pi$
$383$	101734.	+	58736.4i	0.693538	+	0.400414i	−0.111398	+	0.993776i	$0.535533\pi$
$384$		0			0
$385$	45794.7	−	79318.8i	0.308954	−	0.535124i
$386$		0			0
$387$	147480.			0.984714
$388$		0			0
$389$	27604.9	+	47813.0i	0.182426	+	0.315971i	0.942706	−	0.333624i	$-0.108272\pi$
$389$	27604.9	+	47813.0i	0.182426	+	0.315971i	−0.760280	+	0.649595i	$0.774938\pi$
$390$		0			0
$391$	36911.8			0.241442
$392$		0			0
$393$	−225961.	+	130458.i	−1.46301	+	0.844670i
$394$		0			0
$395$	30518.3	−	17619.7i	0.195599	−	0.112929i
$396$		0			0
$397$	73678.8	−	127615.i	0.467478	−	0.809696i	−0.531831	−	0.846850i	$-0.678496\pi$
$397$	73678.8	−	127615.i	0.467478	−	0.809696i	0.999310	+	0.0371543i	$0.0118293\pi$
$398$		0			0
$399$	265357.	+	281760.i	1.66681	+	1.76984i
$400$		0			0
$401$	156892.	+	90581.6i	0.975690	+	0.563315i	0.900966	−	0.433889i	$-0.142859\pi$
$401$	156892.	+	90581.6i	0.975690	+	0.563315i	0.0747238	+	0.997204i	$0.476192\pi$
$402$		0			0
$403$	−145039.	−	251215.i	−0.893049	−	1.54681i
$404$		0			0
$405$	−24145.4	−	41821.1i	−0.147206	−	0.254968i
$406$		0			0
$407$			395093.i			2.38512i
$408$		0			0
$409$	−91404.5	+	52772.4i	−0.546413	+	0.315472i	−0.747674	−	0.664066i	$-0.768829\pi$
$409$	−91404.5	+	52772.4i	−0.546413	+	0.315472i	0.201261	+	0.979538i	$0.435496\pi$
$410$		0			0
$411$		−	240098.i		−	1.42136i
$412$		0			0
$413$	−221456.	−	127858.i	−1.29834	−	0.749596i
$414$		0			0
$415$	−6971.29	+	12074.6i	−0.0404778	+	0.0701096i
$416$		0			0
$417$		−	151012.i		−	0.868438i
$418$		0			0
$419$	−194045.			−1.10528			−0.552642	−	0.833419i	$-0.686380\pi$
$419$	−194045.			−1.10528			−0.552642	+	0.833419i	$0.686380\pi$
$420$		0			0
$421$	−20316.6	−	11729.8i	−0.114627	−	0.0661799i	0.441590	−	0.897217i	$-0.354414\pi$
$421$	−20316.6	−	11729.8i	−0.114627	−	0.0661799i	−0.556217	+	0.831037i	$0.687748\pi$
$422$		0			0
$423$	−108986.	+	188770.i	−0.609104	+	1.05500i
$424$		0			0
$425$	−176861.			−0.979159
$426$		0			0
$427$	−114497.	−	198315.i	−0.627971	−	1.08768i
$428$		0			0
$429$	505767.			2.74812
$430$		0			0
$431$	26797.3	−	15471.4i	0.144257	−	0.0832867i	−0.426134	−	0.904660i	$-0.640125\pi$
$431$	26797.3	−	15471.4i	0.144257	−	0.0832867i	0.570391	+	0.821373i	$0.306792\pi$
$432$		0			0
$433$	62325.3	−	35983.5i	0.332421	−	0.191923i	−0.324494	−	0.945888i	$-0.605194\pi$
$433$	62325.3	−	35983.5i	0.332421	−	0.191923i	0.656915	+	0.753964i	$0.271861\pi$
$434$		0			0
$435$	−47802.5	+	82796.4i	−0.252623	+	0.437555i
$436$		0			0
$437$	10078.0	+	42690.3i	0.0527730	+	0.223545i
$438$		0			0
$439$	−236606.	−	136605.i	−1.22771	−	0.708821i	−0.261163	−	0.965295i	$-0.584106\pi$
$439$	−236606.	−	136605.i	−1.22771	−	0.708821i	−0.966551	+	0.256474i	$0.917439\pi$
$440$		0			0
$441$	181678.	+	314676.i	0.934169	+	1.61803i
$442$		0			0
$443$	86761.7	+	150276.i	0.442100	+	0.765740i	0.997845	−	0.0656130i	$-0.0209003\pi$
$443$	86761.7	+	150276.i	0.442100	+	0.765740i	−0.555745	+	0.831353i	$0.687567\pi$
$444$		0			0
$445$		−	9168.71i		−	0.0463008i
$446$		0			0
$447$	286406.	−	165357.i	1.43340	−	0.827574i
$448$		0			0
$449$		−	49069.8i		−	0.243400i	−0.992567	−	0.121700i	$-0.961165\pi$
$449$		−	49069.8i		−	0.243400i	0.992567	−	0.121700i	$-0.0388346\pi$
$450$		0			0
$451$	−112115.	−	64729.6i	−0.551202	−	0.318236i
$452$		0			0
$453$	−97288.7	+	168509.i	−0.474096	+	0.821158i
$454$		0			0
$455$			147702.i			0.713452i
$456$		0			0
$457$	−318103.			−1.52313			−0.761563	−	0.648091i	$-0.775568\pi$
$457$	−318103.			−1.52313			−0.761563	+	0.648091i	$0.775568\pi$
$458$		0			0
$459$	−38203.3	−	22056.7i	−0.181333	−	0.104692i
$460$		0			0
$461$	−115150.	+	199445.i	−0.541827	+	0.938472i	0.456972	+	0.889481i	$0.348934\pi$
$461$	−115150.	+	199445.i	−0.541827	+	0.938472i	−0.998799	+	0.0489911i	$0.984399\pi$
$462$		0			0
$463$	−260720.			−1.21622			−0.608110	−	0.793853i	$-0.708072\pi$
$463$	−260720.			−1.21622			−0.608110	+	0.793853i	$0.708072\pi$
$464$		0			0
$465$	−45072.6	−	78068.0i	−0.208452	−	0.361050i
$466$		0			0
$467$	−264853.			−1.21443			−0.607213	−	0.794539i	$-0.707713\pi$
$467$	−264853.			−1.21443			−0.607213	+	0.794539i	$0.707713\pi$
$468$		0			0
$469$	56191.4	−	32442.1i	0.255461	−	0.147490i
$470$		0			0
$471$	−213604.	+	123325.i	−0.962872	+	0.555914i
$472$		0			0
$473$	170603.	−	295493.i	0.762544	−	1.32076i
$474$		0			0
$475$	−48288.1	−	204548.i	−0.214019	−	0.906582i
$476$		0			0
$477$	−76401.5	−	44110.4i	−0.335788	−	0.193867i
$478$		0			0
$479$	−21172.2	−	36671.4i	−0.0922775	−	0.159829i	0.816192	−	0.577781i	$-0.196081\pi$
$479$	−21172.2	−	36671.4i	−0.0922775	−	0.159829i	−0.908469	+	0.417952i	$0.862748\pi$
$480$		0			0
$481$	−318575.	−	551788.i	−1.37696	−	2.38497i
$482$		0			0
$483$			130272.i			0.558415i
$484$		0			0
$485$	4902.12	−	2830.24i	0.0208401	−	0.0120321i
$486$		0			0
$487$		−	405115.i		−	1.70813i	−0.520167	−	0.854065i	$-0.674130\pi$
$487$		−	405115.i		−	1.70813i	0.520167	−	0.854065i	$-0.325870\pi$
$488$		0			0
$489$	−447602.	−	258423.i	−1.87186	−	1.08072i
$490$		0			0
$491$	69256.6	−	119956.i	0.287275	−	0.497575i	−0.685883	−	0.727712i	$-0.740584\pi$
$491$	69256.6	−	119956.i	0.287275	−	0.497575i	0.973158	+	0.230136i	$0.0739172\pi$
$492$		0			0
$493$			362248.i			1.49043i
$494$		0			0
$495$	72384.0			0.295415
$496$		0			0
$497$	514552.	+	297077.i	2.08313	+	1.20270i
$498$		0			0
$499$	−20069.0	+	34760.4i	−0.0805979	+	0.139600i	−0.903507	−	0.428574i	$-0.859016\pi$
$499$	−20069.0	+	34760.4i	−0.0805979	+	0.139600i	0.822909	+	0.568173i	$0.192350\pi$
$500$		0			0
$501$	−512764.			−2.04288
$502$		0			0
$503$	−96593.3	−	167304.i	−0.381778	−	0.661259i	0.609538	−	0.792756i	$-0.291355\pi$
$503$	−96593.3	−	167304.i	−0.381778	−	0.661259i	−0.991316	+	0.131498i	$0.958021\pi$
$504$		0			0
$505$	84792.2			0.332486
$506$		0			0
$507$	−403270.	+	232828.i	−1.56884	+	0.905772i
$508$		0			0
$509$	−18282.6	+	10555.5i	−0.0705671	+	0.0407419i	−0.534868	−	0.844935i	$-0.679639\pi$
$509$	−18282.6	+	10555.5i	−0.0705671	+	0.0407419i	0.464301	+	0.885677i	$0.346305\pi$
$510$		0			0
$511$	37002.5	−	64090.2i	0.141706	−	0.245443i
$512$		0			0
$513$	15079.0	−	50206.0i	0.0572977	−	0.190775i
$514$		0			0
$515$	−37109.6	−	21425.3i	−0.139918	−	0.0807815i
$516$		0			0
$517$	252149.	+	436735.i	0.943358	+	1.63394i
$518$		0			0
$519$	112435.	+	194743.i	0.417414	+	0.722982i
$520$		0			0
$521$			258409.i			0.951990i	0.879448	+	0.475995i	$0.157912\pi$
$521$			258409.i			0.951990i	−0.879448	+	0.475995i	$0.842088\pi$
$522$		0			0
$523$	−290643.	+	167803.i	−1.06257	+	0.613474i	−0.926142	−	0.377176i	$-0.876895\pi$
$523$	−290643.	+	167803.i	−1.06257	+	0.613474i	−0.136427	+	0.990650i	$0.543562\pi$
$524$		0			0
$525$		−	624190.i		−	2.26463i
$526$		0			0
$527$	−295800.	−	170780.i	−1.06507	−	0.614916i
$528$		0			0
$529$	132539.	−	229564.i	0.473621	−	0.820336i
$530$		0			0
$531$		−	202094.i		−	0.716746i
$532$		0			0
$533$	208773.			0.734887
$534$		0			0
$535$	613.391	+	354.142i	0.00214304	+	0.00123728i
$536$		0			0
$537$	−61462.6	+	106456.i	−0.213139	+	0.369167i
$538$		0			0
$539$	840655.			2.89361
$540$		0			0
$541$	−238134.	−	412461.i	−0.813631	−	1.40925i	−0.910307	−	0.413935i	$-0.864154\pi$
$541$	−238134.	−	412461.i	−0.813631	−	1.40925i	0.0966752	−	0.995316i	$-0.469179\pi$
$542$		0			0
$543$	256499.			0.869932
$544$		0			0
$545$	−38076.2	+	21983.3i	−0.128192	+	0.0740116i
$546$		0			0
$547$	−404094.	+	233304.i	−1.35054	+	0.779736i	−0.988325	−	0.152358i	$-0.951313\pi$
$547$	−404094.	+	233304.i	−1.35054	+	0.779736i	−0.362217	+	0.932094i	$0.617980\pi$
$548$		0			0
$549$	90488.3	−	156730.i	0.300226	−	0.520006i
$550$		0			0
$551$	−418957.	+	98904.3i	−1.37996	+	0.325771i
$552$		0			0
$553$	408104.	+	235619.i	1.33450	+	0.770477i
$554$		0			0
$555$	−99000.8	−	171474.i	−0.321405	−	0.556690i
$556$		0			0
$557$	167744.	+	290541.i	0.540675	+	0.936477i	0.998865	+	0.0476230i	$0.0151646\pi$
$557$	167744.	+	290541.i	0.540675	+	0.936477i	−0.458190	+	0.888854i	$0.651502\pi$
$558$		0			0
$559$			550249.i			1.76090i
$560$		0			0
$561$	515743.	−	297764.i	1.63873	−	0.946122i
$562$		0			0
$563$			88504.2i			0.279220i	0.990207	+	0.139610i	$0.0445850\pi$
$563$			88504.2i			0.279220i	−0.990207	+	0.139610i	$0.955415\pi$
$564$		0			0
$565$	115072.	+	66436.6i	0.360472	+	0.208118i
$566$		0			0
$567$	322883.	−	559249.i	1.00434	−	1.73956i
$568$		0			0
$569$		−	423424.i		−	1.30783i	−0.756569	−	0.653914i	$-0.773126\pi$
$569$		−	423424.i		−	1.30783i	0.756569	−	0.653914i	$-0.226874\pi$
$570$		0			0
$571$	625686.			1.91904			0.959520	−	0.281639i	$-0.0908781\pi$
$571$	625686.			1.91904			0.959520	+	0.281639i	$0.0908781\pi$
$572$		0			0
$573$	467280.	+	269784.i	1.42321	+	0.821689i
$574$		0			0
$575$	35369.7	−	61262.2i	0.106978	−	0.185292i
$576$		0			0
$577$	220061.			0.660985			0.330492	−	0.943809i	$-0.392785\pi$
$577$	220061.			0.660985			0.330492	+	0.943809i	$0.392785\pi$
$578$		0			0
$579$	97299.9	+	168528.i	0.290239	+	0.502708i
$580$		0			0
$581$	−186446.			−0.552333
$582$		0			0
$583$	−176761.	+	102053.i	−0.520056	+	0.300255i
$584$		0			0
$585$	−101092.	+	58365.3i	−0.295395	+	0.170547i
$586$		0			0
$587$	−243910.	+	422465.i	−0.707870	+	1.22607i	0.257775	+	0.966205i	$0.417011\pi$
$587$	−243910.	+	422465.i	−0.707870	+	1.22607i	−0.965646	+	0.259863i	$0.916323\pi$
$588$		0			0
$589$	116753.	−	388734.i	0.336541	−	1.12053i
$590$		0			0
$591$	−444832.	−	256824.i	−1.27357	−	0.735294i
$592$		0			0
$593$	190258.	+	329536.i	0.541045	+	0.937117i	0.998844	+	0.0480614i	$0.0153043\pi$
$593$	190258.	+	329536.i	0.541045	+	0.937117i	−0.457800	+	0.889055i	$0.651362\pi$
$594$		0			0
$595$	86958.0	+	150616.i	0.245627	+	0.425438i
$596$		0			0
$597$			161852.i			0.454120i
$598$		0			0
$599$	417085.	−	240804.i	1.16244	−	0.671135i	0.210553	−	0.977583i	$-0.432474\pi$
$599$	417085.	−	240804.i	1.16244	−	0.671135i	0.951888	+	0.306447i	$0.0991403\pi$
$600$		0			0
$601$		−	197247.i		−	0.546086i	−0.962002	−	0.273043i	$-0.911970\pi$
$601$		−	197247.i		−	0.546086i	0.962002	−	0.273043i	$-0.0880302\pi$
$602$		0			0
$603$	44408.6	+	25639.3i	0.122133	+	0.0705134i
$604$		0			0
$605$	35834.8	−	62067.7i	0.0979025	−	0.169572i
$606$		0			0
$607$		−	90988.1i		−	0.246949i	−0.992348	−	0.123474i	$-0.960596\pi$
$607$		−	90988.1i		−	0.246949i	0.992348	−	0.123474i	$-0.0394037\pi$
$608$		0			0
$609$	−1.27847e6			−3.44712
$610$		0			0
$611$	−704304.	−	406630.i	−1.88659	−	1.08922i
$612$		0			0
$613$	−323328.	+	560020.i	−0.860442	+	1.49033i	0.0110604	+	0.999939i	$0.496479\pi$
$613$	−323328.	+	560020.i	−0.860442	+	1.49033i	−0.871503	+	0.490391i	$0.836854\pi$
$614$		0			0
$615$	64878.7			0.171535
$616$		0			0
$617$	−319989.	−	554236.i	−0.840551	−	1.45588i	−0.889430	−	0.457072i	$-0.848898\pi$
$617$	−319989.	−	554236.i	−0.840551	−	1.45588i	0.0488785	−	0.998805i	$-0.484435\pi$
$618$		0			0
$619$	363100.			0.947643			0.473821	−	0.880621i	$-0.342874\pi$
$619$	363100.			0.947643			0.473821	+	0.880621i	$0.342874\pi$
$620$		0			0
$621$	15280.3	−	8822.08i	0.0396231	−	0.0228764i
$622$		0			0
$623$	106182.	−	61304.0i	0.273573	−	0.157947i
$624$		0			0
$625$	−156093.	+	270361.i	−0.399598	+	0.692124i
$626$		0			0
$627$	485191.	+	515183.i	1.23418	+	1.31047i
$628$		0			0
$629$	−649717.	−	375114.i	−1.64219	−	0.948118i
$630$		0			0
$631$	−299572.	−	518874.i	−0.752390	−	1.30318i	−0.946661	−	0.322230i	$-0.895568\pi$
$631$	−299572.	−	518874.i	−0.752390	−	1.30318i	0.194272	−	0.980948i	$-0.437766\pi$
$632$		0			0
$633$	399548.	+	692037.i	0.997151	+	1.72712i
$634$		0			0
$635$		−	115839.i		−	0.287280i
$636$		0			0
$637$	−1.17406e6	+	677844.i	−2.89342	+	1.67052i
$638$		0			0
$639$			469565.i			1.14999i
$640$		0			0
$641$	−675838.	−	390195.i	−1.64485	−	0.949656i	−0.979074	−	0.203506i	$-0.934766\pi$
$641$	−675838.	−	390195.i	−1.64485	−	0.949656i	−0.665778	−	0.746150i	$-0.731900\pi$
$642$		0			0
$643$	114508.	−	198333.i	0.276957	−	0.479703i	−0.693670	−	0.720293i	$-0.744007\pi$
$643$	114508.	−	198333.i	0.276957	−	0.479703i	0.970627	+	0.240589i	$0.0773408\pi$
$644$		0			0
$645$			170996.i			0.411024i
$646$		0			0
$647$	624912.			1.49283			0.746415	−	0.665481i	$-0.231774\pi$
$647$	624912.			1.49283			0.746415	+	0.665481i	$0.231774\pi$
$648$		0			0
$649$	−404921.	−	233781.i	−0.961348	−	0.555035i
$650$		0			0
$651$	602730.	−	1.04396e6i	1.42220	−	2.46332i
$652$		0			0
$653$	168830.			0.395935			0.197968	−	0.980209i	$-0.436566\pi$
$653$	168830.			0.395935			0.197968	+	0.980209i	$0.436566\pi$
$654$		0			0
$655$	−69661.2	−	120657.i	−0.162371	−	0.281235i
$656$		0			0
$657$	58486.9			0.135496
$658$		0			0
$659$	−384180.	+	221806.i	−0.884633	+	0.510743i	−0.872183	−	0.489179i	$-0.837296\pi$
$659$	−384180.	+	221806.i	−0.884633	+	0.510743i	−0.0124501	+	0.999922i	$0.503963\pi$
$660$		0			0
$661$	582296.	−	336189.i	1.33273	−	0.769449i	0.347009	−	0.937862i	$-0.387197\pi$
$661$	582296.	−	336189.i	1.33273	−	0.769449i	0.985717	+	0.168412i	$0.0538640\pi$
$662$		0			0
$663$	−480192.	+	831717.i	−1.09242	+	1.89212i
$664$		0			0
$665$	−150452.	+	141694.i	−0.340216	+	0.320410i
$666$		0			0
$667$	−125478.	−	72444.7i	−0.282043	−	0.162838i
$668$		0			0
$669$	118171.	+	204677.i	0.264032	+	0.457318i
$670$		0			0
$671$	−209352.	−	362609.i	−0.464978	−	0.805366i
$672$		0			0
$673$			198510.i			0.438280i	0.975693	+	0.219140i	$0.0703252\pi$
$673$			198510.i			0.438280i	−0.975693	+	0.219140i	$0.929675\pi$
$674$		0			0
$675$	−73214.5	+	42270.4i	−0.160690	+	0.0927746i
$676$		0			0
$677$			458372.i			1.00009i	0.865998	+	0.500047i	$0.166684\pi$
$677$			458372.i			1.00009i	−0.865998	+	0.500047i	$0.833316\pi$
$678$		0			0
$679$	65553.3	+	37847.2i	0.142185	+	0.0820908i
$680$		0			0
$681$	434231.	−	752110.i	0.936325	−	1.62176i
$682$		0			0
$683$			724266.i			1.55259i	0.630371	+	0.776294i	$0.282903\pi$
$683$			724266.i			1.55259i	−0.630371	+	0.776294i	$0.717097\pi$
$684$		0			0
$685$	128206.			0.273229
$686$		0			0
$687$	−87858.7	−	50725.2i	−0.186154	−	0.107476i
$688$		0			0
$689$	164577.	−	285055.i	0.346681	−	0.600469i
$690$		0			0
$691$	−77146.3			−0.161569			−0.0807846	−	0.996732i	$-0.525743\pi$
$691$	−77146.3			−0.161569			−0.0807846	+	0.996732i	$0.525743\pi$
$692$		0			0
$693$	483975.	+	838270.i	1.00776	+	1.74549i
$694$		0			0
$695$	80636.2			0.166940
$696$		0			0
$697$	212891.	−	122913.i	0.438220	−	0.253006i
$698$		0			0
$699$	622278.	−	359272.i	1.27359	−	0.735308i
$700$		0			0
$701$	−301911.	+	522925.i	−0.614388	+	1.06415i	0.376104	+	0.926578i	$0.377264\pi$
$701$	−301911.	+	522925.i	−0.614388	+	1.06415i	−0.990492	+	0.137574i	$0.956070\pi$
$702$		0			0
$703$	256445.	−	853846.i	0.518901	−	1.72770i
$704$		0			0
$705$	−218871.	−	126365.i	−0.440361	−	0.254243i
$706$		0			0
$707$	566939.	+	981967.i	1.13422	+	1.96453i
$708$		0			0
$709$	−273486.	−	473692.i	−0.544055	−	0.942331i	−0.998666	−	0.0516408i	$-0.983555\pi$
$709$	−273486.	−	473692.i	−0.544055	−	0.942331i	0.454611	−	0.890690i	$-0.349778\pi$
$710$		0			0
$711$			372423.i			0.736712i
$712$		0			0
$713$	118312.	−	68307.4i	0.232728	−	0.134366i
$714$		0			0
$715$			270066.i			0.528272i
$716$		0			0
$717$	576328.	+	332743.i	1.12107	+	0.647248i
$718$		0			0
$719$	174216.	−	301751.i	0.337000	−	0.583701i	−0.646867	−	0.762603i	$-0.723921\pi$
$719$	174216.	−	301751.i	0.337000	−	0.583701i	0.983867	+	0.178902i	$0.0572545\pi$
$720$		0			0
$721$		−	573016.i		−	1.10229i
$722$		0			0
$723$	474661.			0.908045
$724$		0			0
$725$	601219.	+	347114.i	1.14382	+	0.660383i
$726$		0			0
$727$	74583.2	−	129182.i	0.141115	−	0.244418i	−0.786802	−	0.617206i	$-0.788265\pi$
$727$	74583.2	−	129182.i	0.141115	−	0.244418i	0.927917	+	0.372788i	$0.121598\pi$
$728$		0			0
$729$	366226.			0.689119
$730$		0			0
$731$	323952.	+	561102.i	0.606243	+	1.05004i
$732$		0			0
$733$	683086.			1.27136			0.635679	−	0.771954i	$-0.280720\pi$
$733$	683086.			1.27136			0.635679	+	0.771954i	$0.280720\pi$
$734$		0			0
$735$	−364853.	+	210648.i	−0.675372	+	0.389926i
$736$		0			0
$737$	102743.	−	59318.7i	0.189155	−	0.109208i
$738$		0			0
$739$	33940.9	−	58787.4i	0.0621491	−	0.107645i	−0.833277	−	0.552856i	$-0.813538\pi$
$739$	33940.9	−	58787.4i	0.0621491	−	0.107645i	0.895426	+	0.445211i	$0.146871\pi$
$740$		0			0
$741$	−1.09303e6	−	328281.i	−1.99065	−	0.597874i
$742$		0			0
$743$	−388012.	−	224019.i	−0.702859	−	0.405796i	0.105553	−	0.994414i	$-0.466339\pi$
$743$	−388012.	−	224019.i	−0.702859	−	0.405796i	−0.808411	+	0.588618i	$0.799672\pi$
$744$		0			0
$745$	88296.0	+	152933.i	0.159085	+	0.275543i
$746$		0			0
$747$	−73675.1	−	127609.i	−0.132032	−	0.228686i
$748$		0			0
$749$			9471.47i			0.0168832i
$750$		0			0
$751$	485606.	−	280365.i	0.861001	−	0.497099i	−0.00334616	−	0.999994i	$-0.501065\pi$
$751$	485606.	−	280365.i	0.861001	−	0.497099i	0.864347	+	0.502895i	$0.167732\pi$
$752$		0			0
$753$			704989.i			1.24335i
$754$		0			0
$755$	−89979.2	−	51949.5i	−0.157851	−	0.0911355i
$756$		0			0
$757$	47237.6	−	81818.0i	0.0824321	−	0.142777i	−0.821862	−	0.569687i	$-0.807065\pi$
$757$	47237.6	−	81818.0i	0.0824321	−	0.142777i	0.904294	+	0.426910i	$0.140398\pi$
$758$		0			0
$759$			238195.i			0.413476i
$760$		0			0
$761$	−642030.			−1.10863			−0.554314	−	0.832307i	$-0.687019\pi$
$761$	−642030.			−1.10863			−0.554314	+	0.832307i	$0.687019\pi$
$762$		0			0
$763$	−509171.	−	293970.i	−0.874611	−	0.504957i
$764$		0			0
$765$	−68723.7	+	119033.i	−0.117431	+	0.203397i
$766$		0			0
$767$	754018.			1.28171
$768$		0			0
$769$	370799.	+	642243.i	0.627026	+	1.08604i	0.988145	+	0.153522i	$0.0490615\pi$
$769$	370799.	+	642243.i	0.627026	+	1.08604i	−0.361119	+	0.932520i	$0.617605\pi$
$770$		0			0
$771$	−148538.			−0.249879
$772$		0			0
$773$	950582.	−	548819.i	1.59085	−	0.918480i	0.597694	−	0.801724i	$-0.296084\pi$
$773$	950582.	−	548819.i	1.59085	−	0.918480i	0.993161	−	0.116756i	$-0.0372496\pi$
$774$		0			0
$775$	−566884.	+	327290.i	−0.943823	+	0.544916i
$776$		0			0
$777$	1.32388e6	−	2.29303e6i	2.19284	−	3.79811i
$778$		0			0
$779$	200280.	+	212660.i	0.330037	+	0.350437i
$780$		0			0
$781$	940831.	+	543189.i	1.54244	+	0.890531i
$782$		0			0
$783$	86578.7	+	149959.i	0.141217	+	0.244595i
$784$		0			0
$785$	−65851.9	−	114059.i	−0.106863	−	0.185093i
$786$		0			0
$787$			164853.i			0.266162i	0.991105	+	0.133081i	$0.0424871\pi$
$787$			164853.i			0.266162i	−0.991105	+	0.133081i	$0.957513\pi$
$788$		0			0
$789$	119434.	−	68955.0i	0.191855	−	0.110767i
$790$		0			0
$791$			1.77684e6i			2.83985i
$792$		0			0
$793$	584763.	+	337613.i	0.929895	+	0.536875i
$794$		0			0
$795$	51144.1	−	88584.2i	0.0809210	−	0.140159i
$796$		0			0
$797$			733416.i			1.15461i	0.816530	+	0.577303i	$0.195895\pi$
$797$			733416.i			1.15461i	−0.816530	+	0.577303i	$0.804105\pi$
$798$		0			0
$799$	−957595.			−1.49999
$800$		0			0
$801$	83916.3	+	48449.1i	0.130792	+	0.0755128i
$802$		0			0
$803$	67657.1	−	117186.i	0.104926	−	0.181737i
$804$		0			0
$805$	−69561.7			−0.107344
$806$		0			0
$807$	−250872.	−	434523.i	−0.385216	−	0.667214i
$808$		0			0
$809$	−140499.			−0.214673			−0.107336	−	0.994223i	$-0.534232\pi$
$809$	−140499.			−0.214673			−0.107336	+	0.994223i	$0.534232\pi$
$810$		0			0
$811$	667782.	−	385544.i	1.01530	−	0.586182i	0.102559	−	0.994727i	$-0.467297\pi$
$811$	667782.	−	385544.i	1.01530	−	0.586182i	0.912738	+	0.408545i	$0.133964\pi$
$812$		0			0
$813$	356241.	−	205676.i	0.538968	−	0.311173i
$814$		0			0
$815$	137991.	−	239007.i	0.207747	−	0.359829i
$816$		0			0
$817$	−560492.	+	527863.i	−0.839702	+	0.790820i
$818$		0			0
$819$	−1.35184e6	−	780486.i	−2.01538	−	1.16358i
$820$		0			0
$821$	261740.	+	453346.i	0.388314	+	0.672579i	0.992223	−	0.124474i	$-0.0397243\pi$
$821$	261740.	+	453346.i	0.388314	+	0.672579i	−0.603909	+	0.797053i	$0.706391\pi$
$822$		0			0
$823$	−303281.	−	525298.i	−0.447760	−	0.775543i	0.550480	−	0.834848i	$-0.314445\pi$
$823$	−303281.	−	525298.i	−0.447760	−	0.775543i	−0.998240	+	0.0593054i	$0.981111\pi$
$824$		0			0
$825$		−	1.14130e6i		−	1.67684i
$826$		0			0
$827$	−326130.	+	188291.i	−0.476848	+	0.275309i	−0.719102	−	0.694904i	$-0.755447\pi$
$827$	−326130.	+	188291.i	−0.476848	+	0.275309i	0.242254	+	0.970213i	$0.422113\pi$
$828$		0			0
$829$		−	984280.i		−	1.43222i	−0.697987	−	0.716110i	$-0.745921\pi$
$829$		−	984280.i		−	1.43222i	0.697987	−	0.716110i	$-0.254079\pi$
$830$		0			0
$831$	678316.	+	391626.i	0.982268	+	0.567113i
$832$		0			0
$833$	−798145.	+	1.38243e6i	−1.15025	+	1.99229i
$834$		0			0
$835$		−	273802.i		−	0.392703i
$836$		0			0
$837$	−163269.			−0.233051
$838$		0			0
$839$	750419.	+	433254.i	1.06606	+	0.615487i	0.927101	−	0.374812i	$-0.122293\pi$
$839$	750419.	+	433254.i	1.06606	+	0.615487i	0.138954	+	0.990299i	$0.455626\pi$
$840$		0			0
$841$	357322.	−	618900.i	0.505205	−	0.875041i
$842$		0			0
$843$	−457004.			−0.643080
$844$		0			0
$845$	−124324.	−	215335.i	−0.174117	−	0.301579i
$846$		0			0
$847$	958396.			1.33591
$848$		0			0
$849$	−413795.	+	238905.i	−0.574077	+	0.331443i
$850$		0			0
$851$	259869.	−	150036.i	0.358836	−	0.207174i
$852$		0			0
$853$	−548802.	+	950552.i	−0.754253	+	1.30641i	0.191491	+	0.981494i	$0.438668\pi$
$853$	−548802.	+	950552.i	−0.754253	+	1.30641i	−0.945745	+	0.324911i	$0.894666\pi$
$854$		0			0
$855$	−156431.	−	46982.7i	−0.213988	−	0.0642696i
$856$		0			0
$857$	−134301.	−	77539.0i	−0.182860	−	0.105574i	0.405776	−	0.913973i	$-0.367001\pi$
$857$	−134301.	−	77539.0i	−0.182860	−	0.105574i	−0.588636	+	0.808398i	$0.700335\pi$
$858$		0			0
$859$	−368893.	−	638941.i	−0.499936	−	0.865914i	0.500064	−	0.865988i	$-0.333310\pi$
$859$	−368893.	−	638941.i	−0.499936	−	0.865914i	−1.00000		7.43982e-5i	$0.999976\pi$
$860$		0			0
$861$	433793.	+	751351.i	0.585162	+	1.01353i
$862$		0			0
$863$		−	333186.i		−	0.447368i	−0.974662	−	0.223684i	$-0.928192\pi$
$863$		−	333186.i		−	0.447368i	0.974662	−	0.223684i	$-0.0718084\pi$
$864$		0			0
$865$	−103987.	+	60037.2i	−0.138979	+	0.0802395i
$866$		0			0
$867$			107401.i			0.142879i
$868$		0			0
$869$	746196.	+	430816.i	0.988128	+	0.570496i
$870$		0			0
$871$	−95660.6	+	165689.i	−0.126095	+	0.218402i
$872$		0			0
$873$			59822.0i			0.0784933i
$874$		0			0
$875$	691110.			0.902674
$876$		0			0
$877$	−109433.	−	63181.0i	−0.142281	−	0.0821462i	0.427169	−	0.904172i	$-0.359511\pi$
$877$	−109433.	−	63181.0i	−0.142281	−	0.0821462i	−0.569451	+	0.822025i	$0.692844\pi$
$878$		0			0
$879$	409744.	−	709697.i	0.530316	−	0.918534i
$880$		0			0
$881$	423413.			0.545522			0.272761	−	0.962082i	$-0.412063\pi$
$881$	423413.			0.545522			0.272761	+	0.962082i	$0.412063\pi$
$882$		0			0
$883$	223764.	+	387571.i	0.286992	+	0.497084i	0.973090	−	0.230424i	$-0.0740114\pi$
$883$	223764.	+	387571.i	0.286992	+	0.497084i	−0.686098	+	0.727509i	$0.740678\pi$
$884$		0			0
$885$	234320.			0.299173
$886$		0			0
$887$	383905.	−	221648.i	0.487952	−	0.281719i	−0.235773	−	0.971808i	$-0.575762\pi$
$887$	383905.	−	221648.i	0.487952	−	0.281719i	0.723724	+	0.690089i	$0.242429\pi$
$888$		0			0
$889$	1.34151e6	−	774521.i	1.69742	−	0.980009i
$890$		0			0
$891$	590374.	−	1.02256e6i	0.743655	−	1.28805i
$892$		0			0
$893$	−261451.	−	1.10750e6i	−0.327860	−	1.38881i
$894$		0			0
$895$	−56844.8	−	32819.4i	−0.0709651	−	0.0409717i
$896$		0			0
$897$	−192064.	−	332664.i	−0.238704	−	0.413448i
$898$		0			0
$899$	670360.	+	1.16110e6i	0.829447	+	1.43664i
$900$		0			0
$901$		−	387571.i		−	0.477421i
$902$		0			0
$903$	−1.98028e6	+	1.14332e6i	−2.42858	+	1.40214i
$904$		0			0
$905$			136963.i			0.167227i
$906$		0			0
$907$	425062.	+	245410.i	0.516699	+	0.298316i	0.735583	−	0.677435i	$-0.236908\pi$
$907$	425062.	+	245410.i	0.516699	+	0.298316i	−0.218884	+	0.975751i	$0.570242\pi$
$908$		0			0
$909$	−448057.	+	776057.i	−0.542257	+	0.939217i
$910$		0			0
$911$		−	1.49138e6i		−	1.79701i	−0.438964	−	0.898505i	$-0.644655\pi$
$911$		−	1.49138e6i		−	1.79701i	0.438964	−	0.898505i	$-0.355345\pi$
$912$		0			0
$913$	−340907.			−0.408973
$914$		0			0
$915$	181722.	+	104917.i	0.217053	+	0.125315i
$916$		0			0
$917$	931540.	−	1.61348e6i	1.10780	−	1.91877i
$918$		0			0
$919$	−426250.			−0.504700			−0.252350	−	0.967636i	$-0.581203\pi$
$919$	−426250.			−0.504700			−0.252350	+	0.967636i	$0.581203\pi$
$920$		0			0
$921$	−817670.	−	1.41625e6i	−0.963960	−	1.66963i
$922$		0			0
$923$	−1.75195e6			−2.05646
$924$		0			0
$925$	−1.24515e6	+	718886.i	−1.45525	+	0.840188i
$926$		0			0
$927$	392188.	−	226430.i	0.456389	−	0.263496i
$928$		0			0
$929$	−354996.	+	614871.i	−0.411332	+	0.712447i	−0.995036	−	0.0995192i	$-0.968270\pi$
$929$	−354996.	+	614871.i	−0.411332	+	0.712447i	0.583704	+	0.811967i	$0.301603\pi$
$930$		0			0
$931$	−1.81676e6	−	545649.i	−2.09603	−	0.629526i
$932$		0			0
$933$	−691494.	−	399234.i	−0.794374	−	0.458632i
$934$		0			0
$935$	158998.	+	275393.i	0.181873	+	0.315014i
$936$		0			0
$937$	813410.	+	1.40887e6i	0.926468	+	1.60469i	0.789184	+	0.614157i	$0.210504\pi$
$937$	813410.	+	1.40887e6i	0.926468	+	1.60469i	0.137284	+	0.990532i	$0.456163\pi$
$938$		0			0
$939$			991465.i			1.12447i
$940$		0			0
$941$	−341032.	+	196895.i	−0.385138	+	0.222359i	−0.680051	−	0.733165i	$-0.738042\pi$
$941$	−341032.	+	196895.i	−0.385138	+	0.222359i	0.294914	+	0.955524i	$0.404709\pi$
$942$		0			0
$943$			98323.5i			0.110569i
$944$		0			0
$945$	71995.5	+	41566.6i	0.0806198	+	0.0465459i
$946$		0			0
$947$	−641916.	+	1.11183e6i	−0.715778	+	1.23976i	0.246881	+	0.969046i	$0.420594\pi$
$947$	−641916.	+	1.11183e6i	−0.715778	+	1.23976i	−0.962659	+	0.270717i	$0.912739\pi$
$948$		0			0
$949$			218215.i			0.242300i
$950$		0			0
$951$	−1.52144e6			−1.68226
$952$		0			0
$953$	798550.	+	461043.i	0.879258	+	0.507640i	0.870414	−	0.492321i	$-0.163851\pi$
$953$	798550.	+	461043.i	0.879258	+	0.507640i	0.00884417	+	0.999961i	$0.497185\pi$
$954$		0			0
$955$	−144057.	+	249515.i	−0.157953	+	0.273583i
$956$		0			0
$957$	−2.33762e6			−2.55241
$958$		0			0
$959$	857211.	+	1.48473e6i	0.932074	+	1.61440i
$960$		0			0
$961$	−340632.			−0.368840
$962$		0			0
$963$	−6482.54	+	3742.69i	−0.00699025	+	0.00403582i
$964$		0			0
$965$	−89989.6	+	51955.5i	−0.0966357	+	0.0557926i
$966$		0			0
$967$	−130631.	+	226259.i	−0.139699	+	0.241966i	−0.927383	−	0.374114i	$-0.877947\pi$
$967$	−130631.	+	226259.i	−0.139699	+	0.241966i	0.787684	+	0.616080i	$0.211280\pi$
$968$		0			0
$969$	−1.30786e6	+	308749.i	−1.39288	+	0.328820i
$970$		0			0
$971$	−550548.	−	317859.i	−0.583925	−	0.337129i	0.178767	−	0.983891i	$-0.442789\pi$
$971$	−550548.	−	317859.i	−0.583925	−	0.337129i	−0.762692	+	0.646762i	$0.776123\pi$
$972$		0			0
$973$	539151.	+	933837.i	0.569488	+	0.986383i
$974$		0			0
$975$	920261.	+	1.59394e6i	0.968058	+	1.67673i
$976$		0			0
$977$		−	198508.i		−	0.207964i	−0.994579	−	0.103982i	$-0.966842\pi$
$977$		−	198508.i		−	0.207964i	0.994579	−	0.103982i	$-0.0331585\pi$
$978$		0			0
$979$	194147.	−	112091.i	0.202566	−	0.116951i
$980$		0			0
$981$		−	464655.i		−	0.482828i
$982$		0			0
$983$	−496151.	−	286453.i	−0.513461	−	0.296447i	0.220794	−	0.975320i	$-0.429135\pi$
$983$	−496151.	−	286453.i	−0.513461	−	0.296447i	−0.734255	+	0.678874i	$0.762468\pi$
$984$		0			0
$985$	137137.	−	237528.i	0.141346	−	0.244818i
$986$		0			0
$987$		−	3.37962e6i		−	3.46923i
$988$		0			0
$989$	−259144.			−0.264941
$990$		0			0
$991$	−837652.	−	483619.i	−0.852936	−	0.492443i	0.00870457	−	0.999962i	$-0.497229\pi$
$991$	−837652.	−	483619.i	−0.852936	−	0.492443i	−0.861640	+	0.507519i	$0.830563\pi$
$992$		0			0
$993$	1.18299e6	−	2.04900e6i	1.19973	−	2.07799i
$994$		0			0
$995$	−86424.7			−0.0872955
$996$		0			0
$997$	−187999.	−	325625.i	−0.189133	−	0.327587i	0.755829	−	0.654769i	$-0.227234\pi$
$997$	−187999.	−	325625.i	−0.189133	−	0.327587i	−0.944961	+	0.327182i	$0.893901\pi$
$998$		0			0
$999$	−358616.			−0.359334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.d.65.4		40
4.3	odd	2		152.5.n.a.65.17	✓	40
19.12	odd	6	inner	304.5.r.d.145.4		40
76.31	even	6		152.5.n.a.145.17	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.5.n.a.65.17	✓	40	4.3	odd	2
152.5.n.a.145.17	yes	40	76.31	even	6
304.5.r.d.65.4		40	1.1	even	1	trivial
304.5.r.d.145.4		40	19.12	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	304.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-10.6119 - 6.12677i) q^{3} +(3.27153 - 5.66646i) q^{5} +87.4966 q^{7} +(34.5747 + 59.8851i) q^{9} +O(q^{10})\)	\(q+(-10.6119 - 6.12677i) q^{3} +(3.27153 - 5.66646i) q^{5} +87.4966 q^{7} +(34.5747 + 59.8851i) q^{9} +159.983 q^{11} +(-223.432 + 128.999i) q^{13} +(-69.4342 + 40.0878i) q^{15} +(-151.893 + 263.086i) q^{17} +(-345.743 - 103.841i) q^{19} +(-928.504 - 536.072i) q^{21} +(-60.7531 - 105.227i) q^{23} +(291.094 + 504.190i) q^{25} +145.212i q^{27} +(1032.69 - 596.223i) q^{29} +1124.35i q^{31} +(-1697.72 - 980.179i) q^{33} +(286.248 - 495.796i) q^{35} +2469.60i q^{37} +3161.38 q^{39} +(-700.793 - 404.603i) q^{41} +(1066.38 - 1847.03i) q^{43} +452.448 q^{45} +(1576.10 + 2729.89i) q^{47} +5254.66 q^{49} +(3223.74 - 1861.23i) q^{51} +(-1104.88 + 637.901i) q^{53} +(523.389 - 906.536i) q^{55} +(3032.77 + 3220.24i) q^{57} +(-2531.03 - 1461.29i) q^{59} +(-1308.59 - 2266.55i) q^{61} +(3025.17 + 5239.75i) q^{63} +1688.09i q^{65} +(642.212 - 370.781i) q^{67} +1488.88i q^{69} +(5880.82 + 3395.29i) q^{71} +(422.902 - 732.488i) q^{73} -7133.87i q^{75} +13998.0 q^{77} +(4664.22 + 2692.89i) q^{79} +(3690.23 - 6391.67i) q^{81} -2130.90 q^{83} +(993.844 + 1721.39i) q^{85} -14611.7 q^{87} +(1213.55 - 700.644i) q^{89} +(-19549.6 + 11287.0i) q^{91} +(6888.61 - 11931.4i) q^{93} +(-1719.52 + 1619.42i) q^{95} +(749.210 + 432.556i) q^{97} +(5531.36 + 9580.59i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) \) 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) \) 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9 - 24 * q^11 + 264 * q^13 - 624 * q^15 + 216 * q^17 + 652 * q^19 - 216 * q^21 + 1296 * q^23 - 3044 * q^25 + 288 * q^29 - 6660 * q^33 - 360 * q^35 - 3184 * q^39 + 1260 * q^41 - 632 * q^43 + 256 * q^45 - 1248 * q^47 + 16696 * q^49 + 8064 * q^51 - 3672 * q^53 + 3408 * q^55 - 4552 * q^57 - 12492 * q^59 + 2720 * q^61 - 12472 * q^63 - 16260 * q^67 + 504 * q^71 + 9220 * q^73 - 14688 * q^77 + 28944 * q^79 - 1660 * q^81 + 39192 * q^83 - 18632 * q^85 + 34400 * q^87 + 3456 * q^89 - 54432 * q^91 - 17208 * q^93 - 44520 * q^95 - 30540 * q^97 + 10096 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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