LMFDB - Embedded newform 304.5.r.d.145.3

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			145.3
Character	$\chi$	$=$	304.145
Dual form			304.5.r.d.65.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.4606 + 7.19410i) q^{3} +(-20.6420 - 35.7530i) q^{5} -1.47481 q^{7} +(63.0102 - 109.137i) q^{9} +O(q^{10})$	\(q+(-12.4606 + 7.19410i) q^{3} +(-20.6420 - 35.7530i) q^{5} -1.47481 q^{7} +(63.0102 - 109.137i) q^{9} +101.571 q^{11} +(92.8097 + 53.5837i) q^{13} +(514.422 + 297.002i) q^{15} +(-141.736 - 245.493i) q^{17} +(267.967 - 241.899i) q^{19} +(18.3770 - 10.6100i) q^{21} +(-275.304 + 476.841i) q^{23} +(-539.686 + 934.764i) q^{25} +647.763i q^{27} +(700.077 + 404.189i) q^{29} -545.336i q^{31} +(-1265.63 + 730.712i) q^{33} +(30.4431 + 52.7291i) q^{35} -2530.76i q^{37} -1541.95 q^{39} +(1311.65 - 757.280i) q^{41} +(149.081 + 258.216i) q^{43} -5202.63 q^{45} +(-1063.81 + 1842.57i) q^{47} -2398.82 q^{49} +(3532.21 + 2039.32i) q^{51} +(-3473.59 - 2005.48i) q^{53} +(-2096.63 - 3631.47i) q^{55} +(-1598.77 + 4941.97i) q^{57} +(-950.795 + 548.942i) q^{59} +(2352.29 - 4074.29i) q^{61} +(-92.9283 + 160.957i) q^{63} -4424.30i q^{65} +(-7156.49 - 4131.80i) q^{67} -7922.27i q^{69} +(-5346.10 + 3086.57i) q^{71} +(1676.62 + 2903.99i) q^{73} -15530.2i q^{75} -149.798 q^{77} +(-5903.97 + 3408.66i) q^{79} +(443.754 + 768.604i) q^{81} +5929.78 q^{83} +(-5851.42 + 10135.0i) q^{85} -11631.1 q^{87} +(12457.3 + 7192.23i) q^{89} +(-136.877 - 79.0260i) q^{91} +(3923.21 + 6795.19i) q^{93} +(-14180.0 - 4587.34i) q^{95} +(-8863.99 + 5117.62i) q^{97} +(6400.01 - 11085.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$3$	−12.4606	+	7.19410i	−1.38451	+	0.799345i	−0.992689	−	0.120699i	$-0.961486\pi$
$3$	−12.4606	+	7.19410i	−1.38451	+	0.799345i	−0.391816	+	0.920043i	$0.628153\pi$
$4$		0			0
$5$	−20.6420	−	35.7530i	−0.825681	−	1.43012i	−0.901398	−	0.432992i	$-0.857458\pi$
$5$	−20.6420	−	35.7530i	−0.825681	−	1.43012i	0.0757171	−	0.997129i	$-0.475875\pi$
$6$		0			0
$7$	−1.47481			−0.0300982			−0.0150491	−	0.999887i	$-0.504790\pi$
$7$	−1.47481			−0.0300982			−0.0150491	+	0.999887i	$0.504790\pi$
$8$		0			0
$9$	63.0102	−	109.137i	0.777904	−	1.34737i
$10$		0			0
$11$	101.571			0.839429			0.419715	−	0.907656i	$-0.362130\pi$
$11$	101.571			0.839429			0.419715	+	0.907656i	$0.362130\pi$
$12$		0			0
$13$	92.8097	+	53.5837i	0.549170	+	0.317063i	0.748787	−	0.662811i	$-0.230637\pi$
$13$	92.8097	+	53.5837i	0.549170	+	0.317063i	−0.199617	+	0.979874i	$0.563970\pi$
$14$		0			0
$15$	514.422	+	297.002i	2.28632	+	1.32001i
$16$		0			0
$17$	−141.736	−	245.493i	−0.490434	−	0.849457i	0.509505	−	0.860468i	$-0.329829\pi$
$17$	−141.736	−	245.493i	−0.490434	−	0.849457i	−0.999939	+	0.0110103i	$0.996495\pi$
$18$		0			0
$19$	267.967	−	241.899i	0.742290	−	0.670079i
$19$	267.967	−	241.899i	0.742290	−	0.670079i
$20$		0			0
$21$	18.3770	−	10.6100i	0.0416712	−	0.0240589i
$22$		0			0
$23$	−275.304	+	476.841i	−0.520424	+	0.901401i	0.479294	+	0.877654i	$0.340893\pi$
$23$	−275.304	+	476.841i	−0.520424	+	0.901401i	−0.999718	+	0.0237465i	$0.992441\pi$
$24$		0			0
$25$	−539.686	+	934.764i	−0.863498	+	1.49562i
$26$		0			0
$27$			647.763i			0.888564i
$28$		0			0
$29$	700.077	+	404.189i	0.832433	+	0.480606i	0.854685	−	0.519147i	$-0.173750\pi$
$29$	700.077	+	404.189i	0.832433	+	0.480606i	−0.0222517	+	0.999752i	$0.507084\pi$
$30$		0			0
$31$		−	545.336i		−	0.567468i	−0.958903	−	0.283734i	$-0.908427\pi$
$31$		−	545.336i		−	0.567468i	0.958903	−	0.283734i	$-0.0915732\pi$
$32$		0			0
$33$	−1265.63	+	730.712i	−1.16219	+	0.670993i
$34$		0			0
$35$	30.4431	+	52.7291i	0.0248515	+	0.0430441i
$36$		0			0
$37$		−	2530.76i		−	1.84862i	−0.381642	−	0.924310i	$-0.624641\pi$
$37$		−	2530.76i		−	1.84862i	0.381642	−	0.924310i	$-0.375359\pi$
$38$		0			0
$39$	−1541.95			−1.01377
$40$		0			0
$41$	1311.65	−	757.280i	0.780278	−	0.450494i	−0.0562508	−	0.998417i	$-0.517915\pi$
$41$	1311.65	−	757.280i	0.780278	−	0.450494i	0.836529	+	0.547923i	$0.184581\pi$
$42$		0			0
$43$	149.081	+	258.216i	0.0806279	+	0.139652i	0.903520	−	0.428546i	$-0.140974\pi$
$43$	149.081	+	258.216i	0.0806279	+	0.139652i	−0.822892	+	0.568198i	$0.807641\pi$
$44$		0			0
$45$	−5202.63			−2.56920
$46$		0			0
$47$	−1063.81	+	1842.57i	−0.481580	+	0.834120i	−0.999777	−	0.0211410i	$-0.993270\pi$
$47$	−1063.81	+	1842.57i	−0.481580	+	0.834120i	0.518197	+	0.855261i	$0.326603\pi$
$48$		0			0
$49$	−2398.82			−0.999094
$50$		0			0
$51$	3532.21	+	2039.32i	1.35802	+	0.784052i
$52$		0			0
$53$	−3473.59	−	2005.48i	−1.23659	−	0.713948i	−0.268198	−	0.963364i	$-0.586428\pi$
$53$	−3473.59	−	2005.48i	−1.23659	−	0.713948i	−0.968397	+	0.249416i	$0.919761\pi$
$54$		0			0
$55$	−2096.63	−	3631.47i	−0.693101	−	1.20049i
$56$		0			0
$57$	−1598.77	+	4941.97i	−0.492080	+	1.52107i
$58$		0			0
$59$	−950.795	+	548.942i	−0.273138	+	0.157697i	−0.630313	−	0.776341i	$-0.717073\pi$
$59$	−950.795	+	548.942i	−0.273138	+	0.157697i	0.357175	+	0.934038i	$0.383740\pi$
$60$		0			0
$61$	2352.29	−	4074.29i	0.632166	−	1.09494i	−0.354942	−	0.934888i	$-0.615499\pi$
$61$	2352.29	−	4074.29i	0.632166	−	1.09494i	0.987108	−	0.160055i	$-0.0511673\pi$
$62$		0			0
$63$	−92.9283	+	160.957i	−0.0234135	+	0.0405534i
$64$		0			0
$65$		−	4424.30i		−	1.04717i
$66$		0			0
$67$	−7156.49	−	4131.80i	−1.59423	−	0.920428i	−0.992570	−	0.121675i	$-0.961173\pi$
$67$	−7156.49	−	4131.80i	−1.59423	−	0.920428i	−0.601659	−	0.798753i	$-0.705493\pi$
$68$		0			0
$69$		−	7922.27i		−	1.66399i
$70$		0			0
$71$	−5346.10	+	3086.57i	−1.06052	+	0.612294i	−0.925577	−	0.378559i	$-0.876420\pi$
$71$	−5346.10	+	3086.57i	−1.06052	+	0.612294i	−0.134947	+	0.990853i	$0.543086\pi$
$72$		0			0
$73$	1676.62	+	2903.99i	0.314622	+	0.544941i	0.979357	−	0.202138i	$-0.0647890\pi$
$73$	1676.62	+	2903.99i	0.314622	+	0.544941i	−0.664735	+	0.747079i	$0.731456\pi$
$74$		0			0
$75$		−	15530.2i		−	2.76093i
$76$		0			0
$77$	−149.798			−0.0252654
$78$		0			0
$79$	−5903.97	+	3408.66i	−0.945997	+	0.546172i	−0.891835	−	0.452360i	$-0.850582\pi$
$79$	−5903.97	+	3408.66i	−0.945997	+	0.546172i	−0.0541621	+	0.998532i	$0.517249\pi$
$80$		0			0
$81$	443.754	+	768.604i	0.0676351	+	0.117147i
$82$		0			0
$83$	5929.78			0.860761			0.430381	−	0.902647i	$-0.358379\pi$
$83$	5929.78			0.860761			0.430381	+	0.902647i	$0.358379\pi$
$84$		0			0
$85$	−5851.42	+	10135.0i	−0.809885	+	1.40276i
$86$		0			0
$87$	−11631.1			−1.53668
$88$		0			0
$89$	12457.3	+	7192.23i	1.57269	+	0.907996i	0.995837	+	0.0911507i	$0.0290545\pi$
$89$	12457.3	+	7192.23i	1.57269	+	0.907996i	0.576857	+	0.816845i	$0.304279\pi$
$90$		0			0
$91$	−136.877	−	79.0260i	−0.0165290	−	0.00954305i
$92$		0			0
$93$	3923.21	+	6795.19i	0.453602	+	0.785662i
$94$		0			0
$95$	−14180.0	−	4587.34i	−1.57119	−	0.508293i
$96$		0			0
$97$	−8863.99	+	5117.62i	−0.942075	+	0.543907i	−0.890610	−	0.454767i	$-0.849722\pi$
$97$	−8863.99	+	5117.62i	−0.942075	+	0.543907i	−0.0514650	+	0.998675i	$0.516389\pi$
$98$		0			0
$99$	6400.01	−	11085.1i	0.652995	−	1.13102i
$100$		0			0
$101$	−6849.55	+	11863.8i	−0.671459	+	1.16300i	0.306032	+	0.952021i	$0.400999\pi$
$101$	−6849.55	+	11863.8i	−0.671459	+	1.16300i	−0.977491	+	0.210979i	$0.932335\pi$
$102$		0			0
$103$		−	2565.64i		−	0.241836i	−0.992663	−	0.120918i	$-0.961416\pi$
$103$		−	2565.64i		−	0.241836i	0.992663	−	0.120918i	$-0.0385838\pi$
$104$		0			0
$105$	−758.677	−	438.022i	−0.0688142	−	0.0397299i
$106$		0			0
$107$			15803.0i			1.38029i	0.723670	+	0.690146i	$0.242454\pi$
$107$			15803.0i			1.38029i	−0.723670	+	0.690146i	$0.757546\pi$
$108$		0			0
$109$	8696.16	−	5020.73i	0.731938	−	0.422585i	−0.0871927	−	0.996191i	$-0.527790\pi$
$109$	8696.16	−	5020.73i	0.731938	−	0.422585i	0.819131	+	0.573607i	$0.194456\pi$
$110$		0			0
$111$	18206.6	+	31534.7i	1.47768	+	2.55942i
$112$		0			0
$113$		−	2023.69i		−	0.158485i	−0.996855	−	0.0792423i	$-0.974750\pi$
$113$		−	2023.69i		−	0.158485i	0.996855	−	0.0792423i	$-0.0252501\pi$
$114$		0			0
$115$	22731.4			1.71882
$116$		0			0
$117$	11695.9	−	6752.64i	0.854403	−	0.493290i
$118$		0			0
$119$	209.034	+	362.057i	0.0147612	+	0.0255672i
$120$		0			0
$121$	−4324.34			−0.295358
$122$		0			0
$123$	−10895.9	+	18872.3i	−0.720200	+	1.24742i
$124$		0			0
$125$	18758.3			1.20053
$126$		0			0
$127$	−25920.2	−	14965.0i	−1.60705	−	0.927833i	−0.990025	−	0.140891i	$-0.955003\pi$
$127$	−25920.2	−	14965.0i	−1.60705	−	0.927833i	−0.617028	−	0.786941i	$-0.711663\pi$
$128$		0			0
$129$	−3715.26	−	2145.01i	−0.223260	−	0.128899i
$130$		0			0
$131$	−2698.30	−	4673.60i	−0.157235	−	0.272338i	0.776636	−	0.629950i	$-0.216925\pi$
$131$	−2698.30	−	4673.60i	−0.157235	−	0.272338i	−0.933870	+	0.357611i	$0.883591\pi$
$132$		0			0
$133$	−395.201	+	356.755i	−0.0223416	+	0.0201682i
$134$		0			0
$135$	23159.5	−	13371.1i	1.27075	−	0.733670i
$136$		0			0
$137$	−5579.43	+	9663.86i	−0.297268	+	0.514884i	−0.975510	−	0.219955i	$-0.929409\pi$
$137$	−5579.43	+	9663.86i	−0.297268	+	0.514884i	0.678242	+	0.734839i	$0.262742\pi$
$138$		0			0
$139$	−10264.2	+	17778.1i	−0.531246	+	0.920144i	0.468089	+	0.883681i	$0.344943\pi$
$139$	−10264.2	+	17778.1i	−0.531246	+	0.920144i	−0.999335	+	0.0364632i	$0.988391\pi$
$140$		0			0
$141$		−	30612.6i		−	1.53979i
$142$		0			0
$143$	9426.77	+	5442.55i	0.460989	+	0.266152i
$144$		0			0
$145$		−	33373.1i		−	1.58731i
$146$		0			0
$147$	29890.7	−	17257.4i	1.38325	−	0.798621i
$148$		0			0
$149$	8921.33	+	15452.2i	0.401843	+	0.696013i	0.993948	−	0.109848i	$-0.0350363\pi$
$149$	8921.33	+	15452.2i	0.401843	+	0.696013i	−0.592105	+	0.805861i	$0.701703\pi$
$150$		0			0
$151$		−	25118.5i		−	1.10164i	−0.834624	−	0.550820i	$-0.814315\pi$
$151$		−	25118.5i		−	1.10164i	0.834624	−	0.550820i	$-0.185685\pi$
$152$		0			0
$153$	−35723.2			−1.52604
$154$		0			0
$155$	−19497.4	+	11256.8i	−0.811547	+	0.468547i
$156$		0			0
$157$	−12021.3	−	20821.6i	−0.487701	−	0.844722i	0.512199	−	0.858867i	$-0.328831\pi$
$157$	−12021.3	−	20821.6i	−0.487701	−	0.844722i	−0.999900	+	0.0141443i	$0.995498\pi$
$158$		0			0
$159$	57710.5			2.28276
$160$		0			0
$161$	406.023	−	703.252i	0.0156639	−	0.0271306i
$162$		0			0
$163$	41201.0			1.55072			0.775359	−	0.631521i	$-0.217569\pi$
$163$	41201.0			1.55072			0.775359	+	0.631521i	$0.217569\pi$
$164$		0			0
$165$	52250.3	+	30166.7i	1.91920	+	1.10805i
$166$		0			0
$167$	−25406.3	−	14668.3i	−0.910980	−	0.525955i	−0.0302337	−	0.999543i	$-0.509625\pi$
$167$	−25406.3	−	14668.3i	−0.910980	−	0.525955i	−0.880746	+	0.473588i	$0.842958\pi$
$168$		0			0
$169$	−8538.07	−	14788.4i	−0.298942	−	0.517782i
$170$		0			0
$171$	−9515.43	−	44487.1i	−0.325414	−	1.52140i
$172$		0			0
$173$	8320.87	−	4804.06i	0.278020	−	0.160515i	−0.354506	−	0.935054i	$-0.615351\pi$
$173$	8320.87	−	4804.06i	0.278020	−	0.160515i	0.632527	+	0.774538i	$0.282018\pi$
$174$		0			0
$175$	795.936	−	1378.60i	0.0259898	−	0.0450156i
$176$		0			0
$177$	7898.28	−	13680.2i	0.252108	−	0.436663i
$178$		0			0
$179$			644.867i			0.0201263i	0.999949	+	0.0100631i	$0.00320325\pi$
$179$			644.867i			0.0201263i	−0.999949	+	0.0100631i	$0.996797\pi$
$180$		0			0
$181$	16953.1	+	9787.88i	0.517478	+	0.298766i	0.735902	−	0.677088i	$-0.236758\pi$
$181$	16953.1	+	9787.88i	0.517478	+	0.298766i	−0.218424	+	0.975854i	$0.570092\pi$
$182$		0			0
$183$			67690.4i			2.02127i
$184$		0			0
$185$	−90482.4	+	52240.0i	−2.64375	+	1.52637i
$186$		0			0
$187$	−14396.2	−	24935.0i	−0.411685	−	0.713060i
$188$		0			0
$189$		−	955.330i		−	0.0267442i
$190$		0			0
$191$	−28099.8			−0.770259			−0.385130	−	0.922862i	$-0.625843\pi$
$191$	−28099.8			−0.770259			−0.385130	+	0.922862i	$0.625843\pi$
$192$		0			0
$193$	−40846.2	+	23582.5i	−1.09657	+	0.633106i	−0.935318	−	0.353808i	$-0.884887\pi$
$193$	−40846.2	+	23582.5i	−1.09657	+	0.633106i	−0.161253	+	0.986913i	$0.551553\pi$
$194$		0			0
$195$	31828.9	+	55129.3i	0.837052	+	1.44982i
$196$		0			0
$197$	−13005.0			−0.335102			−0.167551	−	0.985863i	$-0.553586\pi$
$197$	−13005.0			−0.335102			−0.167551	+	0.985863i	$0.553586\pi$
$198$		0			0
$199$	−1346.24	+	2331.76i	−0.0339952	+	0.0588814i	−0.882522	−	0.470270i	$-0.844156\pi$
$199$	−1346.24	+	2331.76i	−0.0339952	+	0.0588814i	0.848527	+	0.529152i	$0.177490\pi$
$200$		0			0
$201$	118898.			2.94296
$202$		0			0
$203$	−1032.48	−	596.104i	−0.0250548	−	0.0144654i
$204$		0			0
$205$	−54150.1	−	31263.6i	−1.28852	−	0.743928i
$206$		0			0
$207$	34694.0	+	60091.7i	0.809680	+	1.40241i
$208$		0			0
$209$	27217.6	−	24569.9i	0.623100	−	0.562484i
$210$		0			0
$211$	−51621.4	+	29803.6i	−1.15948	+	0.669429i	−0.951180	−	0.308635i	$-0.900128\pi$
$211$	−51621.4	+	29803.6i	−1.15948	+	0.669429i	−0.208304	+	0.978064i	$0.566794\pi$
$212$		0			0
$213$	44410.2	−	76920.8i	0.978867	−	1.69545i
$214$		0			0
$215$	6154.66	−	10660.2i	0.133146	−	0.230615i
$216$		0			0
$217$			804.270i			0.0170798i
$218$		0			0
$219$	−41783.2	−	24123.5i	−0.871191	−	0.502982i
$220$		0			0
$221$		−	30378.9i		−	0.621995i
$222$		0			0
$223$	66148.5	−	38190.9i	1.33018	−	0.767980i	0.344853	−	0.938657i	$-0.387929\pi$
$223$	66148.5	−	38190.9i	1.33018	−	0.767980i	0.985327	+	0.170677i	$0.0545953\pi$
$224$		0			0
$225$	68011.5	+	117799.i	1.34344	+	2.32690i
$226$		0			0
$227$			29007.0i			0.562926i	0.959572	+	0.281463i	$0.0908197\pi$
$227$			29007.0i			0.562926i	−0.959572	+	0.281463i	$0.909180\pi$
$228$		0			0
$229$	−70222.4			−1.33907			−0.669537	−	0.742779i	$-0.733508\pi$
$229$	−70222.4			−1.33907			−0.669537	+	0.742779i	$0.733508\pi$
$230$		0			0
$231$	1866.57	−	1077.66i	0.0349800	−	0.0201957i
$232$		0			0
$233$	−10899.4	−	18878.3i	−0.200766	−	0.347737i	0.748009	−	0.663688i	$-0.231010\pi$
$233$	−10899.4	−	18878.3i	−0.200766	−	0.347737i	−0.948775	+	0.315951i	$0.897676\pi$
$234$		0			0
$235$	87836.7			1.59052
$236$		0			0
$237$	49044.5	−	84947.5i	0.873159	−	1.51236i
$238$		0			0
$239$	73538.9			1.28742			0.643712	−	0.765268i	$-0.277394\pi$
$239$	73538.9			1.28742			0.643712	+	0.765268i	$0.277394\pi$
$240$		0			0
$241$	74241.5	+	42863.3i	1.27824	+	0.737992i	0.976525	−	0.215406i	$-0.0691074\pi$
$241$	74241.5	+	42863.3i	1.27824	+	0.737992i	0.301716	+	0.953398i	$0.402441\pi$
$242$		0			0
$243$	−56498.1	−	32619.2i	−0.956801	−	0.552409i
$244$		0			0
$245$	49516.6	+	85765.3i	0.824933	+	1.42883i
$246$		0			0
$247$	37831.7	−	8091.89i	0.620101	−	0.132634i
$248$		0			0
$249$	−73888.4	+	42659.5i	−1.19173	+	0.688045i
$250$		0			0
$251$	−11579.8	+	20056.8i	−0.183804	+	0.318357i	−0.943173	−	0.332303i	$-0.892174\pi$
$251$	−11579.8	+	20056.8i	−0.183804	+	0.318357i	0.759369	+	0.650660i	$0.225508\pi$
$252$		0			0
$253$	−27962.9	+	48433.2i	−0.436859	+	0.756662i
$254$		0			0
$255$		−	168383.i		−	2.58951i
$256$		0			0
$257$	−10147.5	−	5858.66i	−0.153636	−	0.0887017i	0.421211	−	0.906963i	$-0.361605\pi$
$257$	−10147.5	−	5858.66i	−0.153636	−	0.0887017i	−0.574847	+	0.818261i	$0.694938\pi$
$258$		0			0
$259$			3732.40i			0.0556402i
$260$		0			0
$261$	88223.9	−	50936.1i	1.29511	−	0.747730i
$262$		0			0
$263$	6716.09	+	11632.6i	0.0970969	+	0.168177i	0.910482	−	0.413549i	$-0.135711\pi$
$263$	6716.09	+	11632.6i	0.0970969	+	0.168177i	−0.813385	+	0.581726i	$0.802378\pi$
$264$		0			0
$265$			165589.i			2.35797i
$266$		0			0
$267$	−206967.			−2.90321
$268$		0			0
$269$	59354.8	−	34268.5i	0.820259	−	0.473577i	−0.0302468	−	0.999542i	$-0.509629\pi$
$269$	59354.8	−	34268.5i	0.820259	−	0.473577i	0.850506	+	0.525966i	$0.176296\pi$
$270$		0			0
$271$	−21257.9	−	36819.8i	−0.289456	−	0.501352i	0.684224	−	0.729272i	$-0.260141\pi$
$271$	−21257.9	−	36819.8i	−0.289456	−	0.501352i	−0.973680	+	0.227920i	$0.926808\pi$
$272$		0			0
$273$	2274.08			0.0305127
$274$		0			0
$275$	−54816.4	+	94944.8i	−0.724845	+	1.25547i
$276$		0			0
$277$	−122418.			−1.59546			−0.797731	−	0.603014i	$-0.793966\pi$
$277$	−122418.			−1.59546			−0.797731	+	0.603014i	$0.793966\pi$
$278$		0			0
$279$	−59516.3	−	34361.8i	−0.764588	−	0.441435i
$280$		0			0
$281$	56580.0	+	32666.5i	0.716556	+	0.413704i	0.813484	−	0.581588i	$-0.197568\pi$
$281$	56580.0	+	32666.5i	0.716556	+	0.413704i	−0.0969279	+	0.995291i	$0.530902\pi$
$282$		0			0
$283$	55860.0	+	96752.4i	0.697475	+	1.20806i	0.969339	+	0.245726i	$0.0790263\pi$
$283$	55860.0	+	96752.4i	0.697475	+	1.20806i	−0.271865	+	0.962335i	$0.587640\pi$
$284$		0			0
$285$	209692.	−	44851.4i	2.58162	−	0.552187i
$286$		0			0
$287$	−1934.44	+	1116.85i	−0.0234850	+	0.0135591i
$288$		0			0
$289$	1582.56	−	2741.07i	0.0189480	−	0.0328189i
$290$		0			0
$291$	73633.4	−	127537.i	0.869539	−	1.50609i
$292$		0			0
$293$		−	120611.i		−	1.40492i	−0.711725	−	0.702458i	$-0.752086\pi$
$293$		−	120611.i		−	1.40492i	0.711725	−	0.702458i	$-0.247914\pi$
$294$		0			0
$295$	39252.6	+	22662.5i	0.451050	+	0.260414i
$296$		0			0
$297$			65793.9i			0.745887i
$298$		0			0
$299$	−51101.8	+	29503.7i	−0.571602	+	0.330015i
$300$		0			0
$301$	−219.867	−	380.820i	−0.00242676	−	0.00420327i
$302$		0			0
$303$		−	197105.i		−	2.14691i
$304$		0			0
$305$	−194224.			−2.08787
$306$		0			0
$307$	−68525.1	+	39563.0i	−0.727064	+	0.419771i	−0.817347	−	0.576145i	$-0.804556\pi$
$307$	−68525.1	+	39563.0i	−0.727064	+	0.419771i	0.0902830	+	0.995916i	$0.471223\pi$
$308$		0			0
$309$	18457.5	+	31969.3i	0.193310	+	0.334823i
$310$		0			0
$311$	−170202.			−1.75973			−0.879863	−	0.475228i	$-0.842366\pi$
$311$	−170202.			−1.75973			−0.879863	+	0.475228i	$0.842366\pi$
$312$		0			0
$313$	−26875.5	+	46549.7i	−0.274327	+	0.475148i	−0.969965	−	0.243244i	$-0.921788\pi$
$313$	−26875.5	+	46549.7i	−0.274327	+	0.475148i	0.695638	+	0.718392i	$0.255122\pi$
$314$		0			0
$315$	7672.91			0.0773284
$316$		0			0
$317$	−80516.8	−	46486.4i	−0.801250	−	0.462602i	0.0426578	−	0.999090i	$-0.486417\pi$
$317$	−80516.8	−	46486.4i	−0.801250	−	0.462602i	−0.843908	+	0.536488i	$0.819751\pi$
$318$		0			0
$319$	71107.4	+	41053.9i	0.698769	+	0.403435i
$320$		0			0
$321$	−113688.	−	196914.i	−1.10333	−	1.91102i
$322$		0			0
$323$	−97364.9	−	31498.3i	−0.933248	−	0.301914i
$324$		0			0
$325$	−100176.	+	57836.7i	−0.948414	+	0.547567i
$326$		0			0
$327$	−72239.3	+	125122.i	−0.675582	+	1.17014i
$328$		0			0
$329$	1568.92	−	2717.45i	0.0144947	−	0.0251056i
$330$		0			0
$331$		−	160498.i		−	1.46492i	−0.680811	−	0.732459i	$-0.738373\pi$
$331$		−	160498.i		−	1.46492i	0.680811	−	0.732459i	$-0.261627\pi$
$332$		0			0
$333$	−276199.	−	159464.i	−2.49077	−	1.43805i
$334$		0			0
$335$			341155.i			3.03992i
$336$		0			0
$337$	−39739.7	+	22943.7i	−0.349917	+	0.202024i	−0.664649	−	0.747156i	$-0.731419\pi$
$337$	−39739.7	+	22943.7i	−0.349917	+	0.202024i	0.314732	+	0.949181i	$0.398085\pi$
$338$		0			0
$339$	14558.6	+	25216.3i	0.126684	+	0.219423i
$340$		0			0
$341$		−	55390.3i		−	0.476349i
$342$		0			0
$343$	7078.85			0.0601692
$344$		0			0
$345$	−283245.	+	163532.i	−2.37971	+	1.37393i
$346$		0			0
$347$	−85631.1	−	148317.i	−0.711169	−	1.23178i	−0.964419	−	0.264380i	$-0.914833\pi$
$347$	−85631.1	−	148317.i	−0.711169	−	1.23178i	0.253250	−	0.967401i	$-0.418501\pi$
$348$		0			0
$349$	29538.6			0.242515			0.121258	−	0.992621i	$-0.461307\pi$
$349$	29538.6			0.242515			0.121258	+	0.992621i	$0.461307\pi$
$350$		0			0
$351$	−34709.5	+	60118.7i	−0.281731	+	0.487972i
$352$		0			0
$353$	−188864.			−1.51565			−0.757827	−	0.652455i	$-0.773739\pi$
$353$	−188864.			−1.51565			−0.757827	+	0.652455i	$0.773739\pi$
$354$		0			0
$355$	220709.	+	127426.i	1.75131	+	1.01112i
$356$		0			0
$357$	−5209.35	−	3007.62i	−0.0408740	−	0.0235986i
$358$		0			0
$359$	−35234.2	−	61027.4i	−0.273385	−	0.473518i	0.696341	−	0.717711i	$-0.254810\pi$
$359$	−35234.2	−	61027.4i	−0.273385	−	0.473518i	−0.969727	+	0.244194i	$0.921477\pi$
$360$		0			0
$361$	13291.1	−	129641.i	0.101988	−	0.994786i
$362$		0			0
$363$	53883.7	−	31109.8i	0.408925	−	0.236093i
$364$		0			0
$365$	69217.6	−	119888.i	0.519554	−	0.899894i
$366$		0			0
$367$	979.658	−	1696.82i	0.00727348	−	0.0125980i	−0.862366	−	0.506286i	$-0.831018\pi$
$367$	979.658	−	1696.82i	0.00727348	−	0.0125980i	0.869639	+	0.493688i	$0.164351\pi$
$368$		0			0
$369$		−	190865.i		−	1.40176i
$370$		0			0
$371$	5122.90	+	2957.71i	0.0372193	+	0.0214886i
$372$		0			0
$373$		−	44074.7i		−	0.316790i	−0.987376	−	0.158395i	$-0.949368\pi$
$373$		−	44074.7i		−	0.316790i	0.987376	−	0.158395i	$-0.0506319\pi$
$374$		0			0
$375$	−233739.	+	134949.i	−1.66214	+	0.959639i
$376$		0			0
$377$	43315.9	+	75025.4i	0.304765	+	0.527868i
$378$		0			0
$379$		−	108094.i		−	0.752526i	−0.926513	−	0.376263i	$-0.877209\pi$
$379$		−	108094.i		−	0.752526i	0.926513	−	0.376263i	$-0.122791\pi$
$380$		0			0
$381$	430639.			2.96663
$382$		0			0
$383$	9001.88	−	5197.24i	0.0613671	−	0.0354303i	−0.469003	−	0.883197i	$-0.655386\pi$
$383$	9001.88	−	5197.24i	0.0613671	−	0.0354303i	0.530370	+	0.847767i	$0.322053\pi$
$384$		0			0
$385$	3092.14	+	5355.74i	0.0208611	+	0.0361325i
$386$		0			0
$387$	37574.5			0.250883
$388$		0			0
$389$	−129094.	+	223598.i	−0.853115	+	1.47764i	0.0252669	+	0.999681i	$0.491956\pi$
$389$	−129094.	+	223598.i	−0.853115	+	1.47764i	−0.878382	+	0.477959i	$0.841377\pi$
$390$		0			0
$391$	156082.			1.02094
$392$		0			0
$393$	67244.7	+	38823.8i	0.435385	+	0.251369i
$394$		0			0
$395$	243740.	+	140723.i	1.56218	+	0.901927i
$396$		0			0
$397$	123353.	+	213653.i	0.782650	+	1.35559i	0.930393	+	0.366563i	$0.119466\pi$
$397$	123353.	+	213653.i	0.782650	+	1.35559i	−0.147744	+	0.989026i	$0.547201\pi$
$398$		0			0
$399$	2357.88	−	7288.48i	0.0148107	−	0.0457816i
$400$		0			0
$401$	19961.6	−	11524.8i	0.124138	−	0.0716713i	−0.436645	−	0.899634i	$-0.643833\pi$
$401$	19961.6	−	11524.8i	0.124138	−	0.0716713i	0.560783	+	0.827963i	$0.310500\pi$
$402$		0			0
$403$	29221.1	−	50612.5i	0.179923	−	0.311636i
$404$		0			0
$405$	18319.9	−	31731.1i	0.111690	−	0.193453i
$406$		0			0
$407$		−	257052.i		−	1.55179i
$408$		0			0
$409$	−102893.	−	59405.2i	−0.615090	−	0.355122i	0.159865	−	0.987139i	$-0.448894\pi$
$409$	−102893.	−	59405.2i	−0.615090	−	0.355122i	−0.774955	+	0.632016i	$0.782228\pi$
$410$		0			0
$411$		−	160556.i		−	0.950480i
$412$		0			0
$413$	1402.25	−	809.587i	0.00822099	−	0.00474639i
$414$		0			0
$415$	−122403.	−	212008.i	−0.710714	−	1.23099i
$416$		0			0
$417$		−	295367.i		−	1.69859i
$418$		0			0
$419$	−141945.			−0.808523			−0.404262	−	0.914643i	$-0.632471\pi$
$419$	−141945.			−0.808523			−0.404262	+	0.914643i	$0.632471\pi$
$420$		0			0
$421$	−162013.	+	93538.2i	−0.914083	+	0.527746i	−0.881743	−	0.471731i	$-0.843629\pi$
$421$	−162013.	+	93538.2i	−0.914083	+	0.527746i	−0.0323404	+	0.999477i	$0.510296\pi$
$422$		0			0
$423$	134062.	+	232202.i	0.749245	+	1.29773i
$424$		0			0
$425$	305971.			1.69396
$426$		0			0
$427$	−3469.19	+	6008.81i	−0.0190271	+	0.0329559i
$428$		0			0
$429$	−156617.			−0.850990
$430$		0			0
$431$	−14001.5	−	8083.76i	−0.0753737	−	0.0435170i	0.461840	−	0.886964i	$-0.347190\pi$
$431$	−14001.5	−	8083.76i	−0.0753737	−	0.0435170i	−0.537213	+	0.843446i	$0.680523\pi$
$432$		0			0
$433$	163369.	+	94321.0i	0.871351	+	0.503075i	0.867797	−	0.496919i	$-0.165535\pi$
$433$	163369.	+	94321.0i	0.871351	+	0.503075i	0.00355389	+	0.999994i	$0.498869\pi$
$434$		0			0
$435$	240090.	+	415848.i	1.26881	+	2.19764i
$436$		0			0
$437$	41574.8	+	194373.i	0.217705	+	1.01783i
$438$		0			0
$439$	−7150.60	+	4128.40i	−0.0371034	+	0.0214216i	−0.518437	−	0.855116i	$-0.673486\pi$
$439$	−7150.60	+	4128.40i	−0.0371034	+	0.0214216i	0.481334	+	0.876537i	$0.340153\pi$
$440$		0			0
$441$	−151150.	+	261800.i	−0.777199	+	1.34615i
$442$		0			0
$443$	42260.5	−	73197.2i	0.215341	−	0.372982i	−0.738037	−	0.674760i	$-0.764247\pi$
$443$	42260.5	−	73197.2i	0.215341	−	0.372982i	0.953378	+	0.301779i	$0.0975804\pi$
$444$		0			0
$445$		−	593849.i		−	2.99886i
$446$		0			0
$447$	−222329.	−	128362.i	−1.11271	−	0.642423i
$448$		0			0
$449$			171857.i			0.852462i	0.904614	+	0.426231i	$0.140159\pi$
$449$			171857.i			0.852462i	−0.904614	+	0.426231i	$0.859841\pi$
$450$		0			0
$451$	133225.	−	76917.6i	0.654988	−	0.378158i
$452$		0			0
$453$	180705.	+	312990.i	0.880589	+	1.52523i
$454$		0			0
$455$			6525.02i			0.0315181i
$456$		0			0
$457$	208493.			0.998293			0.499147	−	0.866517i	$-0.333647\pi$
$457$	208493.			0.998293			0.499147	+	0.866517i	$0.333647\pi$
$458$		0			0
$459$	159021.	−	91811.1i	0.754797	−	0.435782i
$460$		0			0
$461$	17285.3	+	29939.1i	0.0813346	+	0.140876i	0.903823	−	0.427906i	$-0.140748\pi$
$461$	17285.3	+	29939.1i	0.0813346	+	0.140876i	−0.822489	+	0.568781i	$0.807415\pi$
$462$		0			0
$463$	115112.			0.536979			0.268489	−	0.963283i	$-0.413476\pi$
$463$	115112.			0.536979			0.268489	+	0.963283i	$0.413476\pi$
$464$		0			0
$465$	161966.	−	280533.i	0.749061	−	1.29741i
$466$		0			0
$467$	−2702.30			−0.0123908			−0.00619541	−	0.999981i	$-0.501972\pi$
$467$	−2702.30			−0.0123908			−0.00619541	+	0.999981i	$0.501972\pi$
$468$		0			0
$469$	10554.5	+	6093.64i	0.0479835	+	0.0277033i
$470$		0			0
$471$	299585.	+	172965.i	1.35045	+	0.779682i
$472$		0			0
$473$	15142.3	+	26227.2i	0.0676814	+	0.117228i
$474$		0			0
$475$	81500.2	+	381035.i	0.361220	+	1.68880i
$476$		0			0
$477$	−437744.	+	252731.i	−1.92390	+	1.11077i
$478$		0			0
$479$	44236.3	−	76619.6i	0.192800	−	0.333940i	−0.753377	−	0.657589i	$-0.771576\pi$
$479$	44236.3	−	76619.6i	0.192800	−	0.333940i	0.946177	+	0.323649i	$0.104910\pi$
$480$		0			0
$481$	135608.	−	234879.i	0.586130	−	1.01521i
$482$		0			0
$483$			11683.9i			0.0500833i
$484$		0			0
$485$	365941.	+	211276.i	1.55571	+	0.898188i
$486$		0			0
$487$			62624.5i			0.264050i	0.991246	+	0.132025i	$0.0421480\pi$
$487$			62624.5i			0.264050i	−0.991246	+	0.132025i	$0.957852\pi$
$488$		0			0
$489$	−513387.	+	296404.i	−2.14698	+	1.23956i
$490$		0			0
$491$	24252.9	+	42007.3i	0.100601	+	0.174246i	0.911932	−	0.410341i	$-0.134590\pi$
$491$	24252.9	+	42007.3i	0.100601	+	0.174246i	−0.811332	+	0.584586i	$0.801257\pi$
$492$		0			0
$493$		−	229152.i		−	0.942822i
$494$		0			0
$495$	−528436.			−2.15666
$496$		0			0
$497$	7884.50	−	4552.12i	0.0319199	−	0.0184290i
$498$		0			0
$499$	−230702.	−	399587.i	−0.926509	−	1.60476i	−0.789116	−	0.614245i	$-0.789461\pi$
$499$	−230702.	−	399587.i	−0.926509	−	1.60476i	−0.137394	−	0.990516i	$-0.543873\pi$
$500$		0			0
$501$	422102.			1.68168
$502$		0			0
$503$	−228498.	+	395770.i	−0.903122	+	1.56425i	−0.0797041	+	0.996819i	$0.525398\pi$
$503$	−228498.	+	395770.i	−0.903122	+	1.56425i	−0.823418	+	0.567435i	$0.807936\pi$
$504$		0			0
$505$	565554.			2.21764
$506$		0			0
$507$	212778.	+	122848.i	0.827773	+	0.477915i
$508$		0			0
$509$	26721.8	+	15427.8i	0.103141	+	0.0595483i	0.550683	−	0.834714i	$-0.314367\pi$
$509$	26721.8	+	15427.8i	0.103141	+	0.0595483i	−0.447542	+	0.894263i	$0.647701\pi$
$510$		0			0
$511$	−2472.70	−	4282.84i	−0.00946956	−	0.0164018i
$512$		0			0
$513$	156693.	+	173579.i	0.595408	+	0.659572i
$514$		0			0
$515$	−91729.3	+	52959.9i	−0.345855	+	0.199679i
$516$		0			0
$517$	−108052.	+	187152.i	−0.404252	+	0.700185i
$518$		0			0
$519$	−69121.8	+	119722.i	−0.256614	+	0.444468i
$520$		0			0
$521$		−	89712.6i		−	0.330505i	−0.986251	−	0.165253i	$-0.947156\pi$
$521$		−	89712.6i		−	0.330505i	0.986251	−	0.165253i	$-0.0528439\pi$
$522$		0			0
$523$	−437540.	−	252614.i	−1.59961	−	0.923536i	−0.991562	−	0.129636i	$-0.958619\pi$
$523$	−437540.	−	252614.i	−1.59961	−	0.923536i	−0.608049	−	0.793899i	$-0.708048\pi$
$524$		0			0
$525$			22904.2i			0.0830991i
$526$		0			0
$527$	−133876.	+	77293.6i	−0.482040	+	0.278306i
$528$		0			0
$529$	−11664.5	−	20203.5i	−0.0416825	−	0.0721962i
$530$		0			0
$531$			138356.i			0.490691i
$532$		0			0
$533$	162311.			0.571340
$534$		0			0
$535$	565004.	−	326205.i	1.97398	−	1.13968i
$536$		0			0
$537$	−4639.24	−	8035.39i	−0.0160878	−	0.0278650i
$538$		0			0
$539$	−243651.			−0.838669
$540$		0			0
$541$	−62932.1	+	109002.i	−0.215020	+	0.372425i	−0.953279	−	0.302092i	$-0.902315\pi$
$541$	−62932.1	+	109002.i	−0.215020	+	0.372425i	0.738259	+	0.674517i	$0.235648\pi$
$542$		0			0
$543$	−281660.			−0.955269
$544$		0			0
$545$	−359012.	−	207276.i	−1.20869	−	0.697840i
$546$		0			0
$547$	−32281.2	−	18637.5i	−0.107888	−	0.0622894i	0.445085	−	0.895488i	$-0.353174\pi$
$547$	−32281.2	−	18637.5i	−0.107888	−	0.0622894i	−0.552973	+	0.833199i	$0.686507\pi$
$548$		0			0
$549$	−296437.	−	513443.i	−0.983529	−	1.70352i
$550$		0			0
$551$	285370.	−	61038.3i	0.939951	−	0.201048i
$552$		0			0
$553$	8707.26	−	5027.14i	0.0284729	−	0.0164388i
$554$		0			0
$555$	751640.	−	1.30188e6i	2.44019	−	4.22654i
$556$		0			0
$557$	68381.9	−	118441.i	0.220410	−	0.381761i	−0.734523	−	0.678584i	$-0.762594\pi$
$557$	68381.9	−	118441.i	0.220410	−	0.381761i	0.954932	+	0.296823i	$0.0959272\pi$
$558$		0			0
$559$			31953.2i			0.102257i
$560$		0			0
$561$	358770.	+	207136.i	1.13996	+	0.658157i
$562$		0			0
$563$			48655.6i			0.153503i	0.997050	+	0.0767514i	$0.0244548\pi$
$563$			48655.6i			0.153503i	−0.997050	+	0.0767514i	$0.975545\pi$
$564$		0			0
$565$	−72353.0	+	41773.0i	−0.226652	+	0.130858i
$566$		0			0
$567$	−654.454	−	1133.55i	−0.00203570	−	0.00352593i
$568$		0			0
$569$			448205.i			1.38437i	0.721721	+	0.692184i	$0.243351\pi$
$569$			448205.i			1.38437i	−0.721721	+	0.692184i	$0.756649\pi$
$570$		0			0
$571$	90460.7			0.277452			0.138726	−	0.990331i	$-0.455699\pi$
$571$	90460.7			0.277452			0.138726	+	0.990331i	$0.455699\pi$
$572$		0			0
$573$	350139.	−	202153.i	1.06643	−	0.615703i
$574$		0			0
$575$	−297156.	−	514689.i	−0.898770	−	1.55672i
$576$		0			0
$577$	461592.			1.38646			0.693229	−	0.720717i	$-0.256187\pi$
$577$	461592.			1.38646			0.693229	+	0.720717i	$0.256187\pi$
$578$		0			0
$579$	339311.	−	587703.i	1.01214	−	1.75308i
$580$		0			0
$581$	−8745.33			−0.0259074
$582$		0			0
$583$	−352816.	−	203699.i	−1.03803	−	0.599309i
$584$		0			0
$585$	−482855.	−	278776.i	−1.41093	−	0.814599i
$586$		0			0
$587$	191245.	+	331247.i	0.555028	+	0.961337i	0.997901	+	0.0647524i	$0.0206258\pi$
$587$	191245.	+	331247.i	0.555028	+	0.961337i	−0.442873	+	0.896584i	$0.646041\pi$
$588$		0			0
$589$	−131916.	−	146132.i	−0.380248	−	0.421225i
$590$		0			0
$591$	162049.	−	93559.1i	0.463951	−	0.267862i
$592$		0			0
$593$	−230612.	+	399431.i	−0.655800	+	1.13588i	0.325892	+	0.945407i	$0.394335\pi$
$593$	−230612.	+	399431.i	−0.655800	+	1.13588i	−0.981693	+	0.190472i	$0.938998\pi$
$594$		0			0
$595$	8629.75	−	14947.2i	0.0243761	−	0.0422207i
$596$		0			0
$597$		−	38740.1i		−	0.108696i
$598$		0			0
$599$	279980.	+	161646.i	0.780320	+	0.450518i	0.836544	−	0.547900i	$-0.184573\pi$
$599$	279980.	+	161646.i	0.780320	+	0.450518i	−0.0562237	+	0.998418i	$0.517906\pi$
$600$		0			0
$601$		−	541609.i		−	1.49947i	−0.661740	−	0.749733i	$-0.730182\pi$
$601$		−	541609.i		−	1.49947i	0.661740	−	0.749733i	$-0.269818\pi$
$602$		0			0
$603$	−901864.	+	520692.i	−2.48031	+	1.43201i
$604$		0			0
$605$	89263.1	+	154608.i	0.243872	+	0.422398i
$606$		0			0
$607$			344265.i			0.934362i	0.884162	+	0.467181i	$0.154730\pi$
$607$			344265.i			0.934362i	−0.884162	+	0.467181i	$0.845270\pi$
$608$		0			0
$609$	17153.7			0.0462513
$610$		0			0
$611$	−197464.	+	114006.i	−0.528938	+	0.305382i
$612$		0			0
$613$	41187.6	+	71339.0i	0.109609	+	0.189848i	0.915612	−	0.402063i	$-0.131707\pi$
$613$	41187.6	+	71339.0i	0.109609	+	0.189848i	−0.806003	+	0.591911i	$0.798374\pi$
$614$		0			0
$615$	899653.			2.37862
$616$		0			0
$617$	−156294.	+	270708.i	−0.410554	+	0.711101i	−0.994950	−	0.100368i	$-0.967998\pi$
$617$	−156294.	+	270708.i	−0.410554	+	0.711101i	0.584396	+	0.811469i	$0.301331\pi$
$618$		0			0
$619$	122270.			0.319110			0.159555	−	0.987189i	$-0.448994\pi$
$619$	122270.			0.319110			0.159555	+	0.987189i	$0.448994\pi$
$620$		0			0
$621$	−308880.	−	178332.i	−0.800952	−	0.462430i
$622$		0			0
$623$	−18372.2	−	10607.2i	−0.0473353	−	0.0273291i
$624$		0			0
$625$	−49905.7	−	86439.2i	−0.127759	−	0.221284i
$626$		0			0
$627$	−162388.	+	501960.i	−0.413066	+	1.27683i
$628$		0			0
$629$	−621285.	+	358699.i	−1.57032	+	0.906627i
$630$		0			0
$631$	285388.	−	494307.i	0.716766	−	1.24147i	−0.245509	−	0.969394i	$-0.578955\pi$
$631$	285388.	−	494307.i	0.716766	−	1.24147i	0.962275	−	0.272080i	$-0.0877115\pi$
$632$		0			0
$633$	428821.	−	742740.i	1.07021	−	1.85366i
$634$		0			0
$635$			1.23563e6i			3.06437i
$636$		0			0
$637$	−222634.	−	128538.i	−0.548672	−	0.316776i
$638$		0			0
$639$			777942.i			1.90522i
$640$		0			0
$641$	634323.	−	366227.i	1.54381	−	0.891321i	0.545220	−	0.838293i	$-0.316446\pi$
$641$	634323.	−	366227.i	1.54381	−	0.891321i	0.998593	−	0.0530278i	$-0.0168872\pi$
$642$		0			0
$643$	220412.	+	381764.i	0.533105	+	0.923365i	0.999253	+	0.0386577i	$0.0123082\pi$
$643$	220412.	+	381764.i	0.533105	+	0.923365i	−0.466148	+	0.884707i	$0.654358\pi$
$644$		0			0
$645$			177109.i			0.425718i
$646$		0			0
$647$	−109452.			−0.261466			−0.130733	−	0.991418i	$-0.541733\pi$
$647$	−109452.			−0.261466			−0.130733	+	0.991418i	$0.541733\pi$
$648$		0			0
$649$	−96573.1	+	55756.5i	−0.229280	+	0.132375i
$650$		0			0
$651$	−5786.00	−	10021.6i	−0.0136526	−	0.0236471i
$652$		0			0
$653$	−271766.			−0.637335			−0.318668	−	0.947866i	$-0.603235\pi$
$653$	−271766.			−0.637335			−0.318668	+	0.947866i	$0.603235\pi$
$654$		0			0
$655$	−111397.	+	192945.i	−0.259651	+	0.449729i
$656$		0			0
$657$	422576.			0.978982
$658$		0			0
$659$	269769.	+	155751.i	0.621185	+	0.358641i	0.777330	−	0.629093i	$-0.216574\pi$
$659$	269769.	+	155751.i	0.621185	+	0.358641i	−0.156145	+	0.987734i	$0.549907\pi$
$660$		0			0
$661$	21057.6	+	12157.6i	0.0481955	+	0.0278257i	0.523904	−	0.851777i	$-0.324475\pi$
$661$	21057.6	+	12157.6i	0.0481955	+	0.0278257i	−0.475709	+	0.879603i	$0.657808\pi$
$662$		0			0
$663$	218549.	+	378537.i	0.497189	+	0.861156i
$664$		0			0
$665$	20912.8	+	6765.47i	0.0472900	+	0.0152987i
$666$		0			0
$667$	−385468.	+	222550.i	−0.866437	+	0.500238i
$668$		0			0
$669$	−549498.	+	951759.i	−1.22776	+	2.12655i
$670$		0			0
$671$	238924.	−	413829.i	0.530659	−	0.919128i
$672$		0			0
$673$			465940.i			1.02873i	0.857572	+	0.514364i	$0.171972\pi$
$673$			465940.i			1.02873i	−0.857572	+	0.514364i	$0.828028\pi$
$674$		0			0
$675$	−605505.	−	349589.i	−1.32896	−	0.767273i
$676$		0			0
$677$		−	554556.i		−	1.20995i	−0.796244	−	0.604976i	$-0.793183\pi$
$677$		−	554556.i		−	1.20995i	0.796244	−	0.604976i	$-0.206817\pi$
$678$		0			0
$679$	13072.7	−	7547.54i	0.0283548	−	0.0163707i
$680$		0			0
$681$	−208680.	−	361444.i	−0.449972	−	0.779375i
$682$		0			0
$683$			112690.i			0.241571i	0.992679	+	0.120785i	$0.0385413\pi$
$683$			112690.i			0.241571i	−0.992679	+	0.120785i	$0.961459\pi$
$684$		0			0
$685$	460683.			0.981795
$686$		0			0
$687$	875010.	−	505187.i	1.85396	−	1.07038i
$688$		0			0
$689$	−214922.	−	372256.i	−0.452734	−	0.784158i
$690$		0			0
$691$	6403.46			0.0134109			0.00670546	−	0.999978i	$-0.497866\pi$
$691$	6403.46			0.0134109			0.00670546	+	0.999978i	$0.497866\pi$
$692$		0			0
$693$	−9438.82	+	16348.5i	−0.0196540	+	0.0340418i
$694$		0			0
$695$	847495.			1.75456
$696$		0			0
$697$	−371814.	−	214667.i	−0.765351	−	0.441875i
$698$		0			0
$699$	271625.	+	156823.i	0.555924	+	0.320963i
$700$		0			0
$701$	27682.9	+	47948.3i	0.0563347	+	0.0975746i	0.892817	−	0.450419i	$-0.148725\pi$
$701$	27682.9	+	47948.3i	0.0563347	+	0.0975746i	−0.836483	+	0.547993i	$0.815392\pi$
$702$		0			0
$703$	−612187.	−	678159.i	−1.23872	−	1.37221i
$704$		0			0
$705$	−1.09449e6	+	631906.i	−2.20209	+	1.27138i
$706$		0			0
$707$	10101.8	−	17496.9i	0.0202097	−	0.0350043i
$708$		0			0
$709$	196079.	−	339619.i	0.390067	−	0.675616i	−0.602391	−	0.798201i	$-0.705785\pi$
$709$	196079.	−	339619.i	0.390067	−	0.675616i	0.992458	+	0.122585i	$0.0391185\pi$
$710$		0			0
$711$			859121.i			1.69948i
$712$		0			0
$713$	260039.	+	150133.i	0.511516	+	0.295324i
$714$		0			0
$715$		−	449381.i		−	0.879027i
$716$		0			0
$717$	−916335.	+	529047.i	−1.78245	+	1.02910i
$718$		0			0
$719$	278092.	+	481669.i	0.537936	+	0.931732i	0.999015	+	0.0443729i	$0.0141290\pi$
$719$	278092.	+	481669.i	0.537936	+	0.931732i	−0.461079	+	0.887359i	$0.652538\pi$
$720$		0			0
$721$			3783.84i			0.00727884i
$722$		0			0
$723$	−1.23345e6			−2.35964
$724$		0			0
$725$	−755643.	+	436271.i	−1.43761	+	0.830004i
$726$		0			0
$727$	−221730.	−	384048.i	−0.419524	−	0.726636i	0.576368	−	0.817190i	$-0.304470\pi$
$727$	−221730.	−	384048.i	−0.419524	−	0.726636i	−0.995892	+	0.0905541i	$0.971136\pi$
$728$		0			0
$729$	866776.			1.63099
$730$		0			0
$731$	42260.2	−	73196.7i	0.0790854	−	0.136980i
$732$		0			0
$733$	417064.			0.776237			0.388118	−	0.921610i	$-0.373125\pi$
$733$	417064.			0.776237			0.388118	+	0.921610i	$0.373125\pi$
$734$		0			0
$735$	−1.23401e6	−	712455.i	−2.28425	−	1.31881i
$736$		0			0
$737$	−726892.	−	419671.i	−1.33824	−	0.772635i
$738$		0			0
$739$	37727.0	+	65345.0i	0.0690817	+	0.119653i	0.898497	−	0.438979i	$-0.144660\pi$
$739$	37727.0	+	65345.0i	0.0690817	+	0.119653i	−0.829416	+	0.558632i	$0.811326\pi$
$740$		0			0
$741$	−413190.	+	372995.i	−0.752512	+	0.679307i
$742$		0			0
$743$	−280539.	+	161969.i	−0.508178	+	0.293397i	−0.732085	−	0.681214i	$-0.761452\pi$
$743$	−280539.	+	161969.i	−0.508178	+	0.293397i	0.223906	+	0.974611i	$0.428119\pi$
$744$		0			0
$745$	368308.	−	637929.i	0.663589	−	1.14937i
$746$		0			0
$747$	373637.	−	647158.i	0.669589	−	1.15976i
$748$		0			0
$749$		−	23306.4i		−	0.0415444i
$750$		0			0
$751$	−311259.	−	179706.i	−0.551877	−	0.318626i	0.198002	−	0.980202i	$-0.436555\pi$
$751$	−311259.	−	179706.i	−0.551877	−	0.318626i	−0.749879	+	0.661575i	$0.769888\pi$
$752$		0			0
$753$		−	333226.i		−	0.587690i
$754$		0			0
$755$	−898061.	+	518496.i	−1.57548	+	0.909602i
$756$		0			0
$757$	−100075.	−	173334.i	−0.174635	−	0.302477i	0.765400	−	0.643555i	$-0.222541\pi$
$757$	−100075.	−	173334.i	−0.174635	−	0.302477i	−0.940035	+	0.341078i	$0.889208\pi$
$758$		0			0
$759$		−	804673.i		−	1.39680i
$760$		0			0
$761$	1.04991e6			1.81294			0.906472	−	0.422267i	$-0.138765\pi$
$761$	1.04991e6			1.81294			0.906472	+	0.422267i	$0.138765\pi$
$762$		0			0
$763$	−12825.2	+	7404.64i	−0.0220301	+	0.0127191i
$764$		0			0
$765$	737398.	+	1.27721e6i	1.26002	+	2.18243i
$766$		0			0
$767$	−117657.			−0.199999
$768$		0			0
$769$	212076.	−	367327.i	0.358624	−	0.621155i	−0.629107	−	0.777318i	$-0.716579\pi$
$769$	212076.	−	367327.i	0.358624	−	0.621155i	0.987731	+	0.156164i	$0.0499128\pi$
$770$		0			0
$771$	168591.			0.283613
$772$		0			0
$773$	−292487.	−	168867.i	−0.489493	−	0.282609i	0.234871	−	0.972027i	$-0.424533\pi$
$773$	−292487.	−	168867.i	−0.489493	−	0.282609i	−0.724364	+	0.689417i	$0.757867\pi$
$774$		0			0
$775$	509761.	+	294310.i	0.848717	+	0.490007i
$776$		0			0
$777$	−26851.3	−	46507.8i	−0.0444757	−	0.0770342i
$778$		0			0
$779$	168293.	−	520211.i	0.277326	−	0.857245i
$780$		0			0
$781$	−543009.	+	313506.i	−0.890235	+	0.513977i
$782$		0			0
$783$	−261819.	+	453484.i	−0.427049	+	0.739670i
$784$		0			0
$785$	−496289.	+	859598.i	−0.805370	+	1.39494i
$786$		0			0
$787$		−	54774.7i		−	0.0884363i	−0.999022	−	0.0442182i	$-0.985920\pi$
$787$		−	54774.7i		−	0.0884363i	0.999022	−	0.0442182i	$-0.0140797\pi$
$788$		0			0
$789$	−167372.	−	96632.5i	−0.268862	−	0.155228i
$790$		0			0
$791$			2984.56i			0.00477011i
$792$		0			0
$793$	436631.	−	252089.i	0.694333	−	0.400873i
$794$		0			0
$795$	−1.19126e6	−	2.06333e6i	−1.88483	−	3.26463i
$796$		0			0
$797$		−	205180.i		−	0.323012i	−0.986872	−	0.161506i	$-0.948365\pi$
$797$		−	205180.i		−	0.323012i	0.986872	−	0.161506i	$-0.0516352\pi$
$798$		0			0
$799$	603119.			0.944733
$800$		0			0
$801$	1.56988e6	−	906368.i	2.44681	−	1.41267i
$802$		0			0
$803$	170296.	+	294961.i	0.264103	+	0.457439i
$804$		0			0
$805$	−33524.5			−0.0517334
$806$		0			0
$807$	−493062.	+	854008.i	−0.757102	+	1.31134i
$808$		0			0
$809$	−1.03460e6			−1.58080			−0.790401	−	0.612590i	$-0.790128\pi$
$809$	−1.03460e6			−1.58080			−0.790401	+	0.612590i	$0.790128\pi$
$810$		0			0
$811$	−96318.8	−	55609.7i	−0.146443	−	0.0845490i	0.424988	−	0.905199i	$-0.360278\pi$
$811$	−96318.8	−	55609.7i	−0.146443	−	0.0845490i	−0.571431	+	0.820650i	$0.693612\pi$
$812$		0			0
$813$	529771.	+	305863.i	0.801506	+	0.462750i
$814$		0			0
$815$	−850472.	−	1.47306e6i	−1.28040	−	2.21771i
$816$		0			0
$817$	102411.	+	33130.7i	0.153427	+	0.0496349i
$818$		0			0
$819$	−17249.3	+	9958.89i	−0.0257160	+	0.0148471i
$820$		0			0
$821$	364446.	−	631240.i	0.540689	−	0.936500i	−0.458176	−	0.888862i	$-0.651497\pi$
$821$	364446.	−	631240.i	0.540689	−	0.936500i	0.998865	−	0.0476388i	$-0.0151697\pi$
$822$		0			0
$823$	−407061.	+	705050.i	−0.600980	+	1.04093i	0.391693	+	0.920096i	$0.371889\pi$
$823$	−407061.	+	705050.i	−0.600980	+	1.04093i	−0.992673	+	0.120832i	$0.961444\pi$
$824$		0			0
$825$		−	1.57742e6i		−	2.31760i
$826$		0			0
$827$	−362497.	−	209288.i	−0.530021	−	0.306008i	0.211004	−	0.977485i	$-0.432327\pi$
$827$	−362497.	−	209288.i	−0.530021	−	0.306008i	−0.741025	+	0.671477i	$0.765660\pi$
$828$		0			0
$829$			281852.i			0.410121i	0.978749	+	0.205061i	$0.0657392\pi$
$829$			281852.i			0.410121i	−0.978749	+	0.205061i	$0.934261\pi$
$830$		0			0
$831$	1.52540e6	−	880689.i	2.20893	−	1.27532i
$832$		0			0
$833$	339999.	+	588895.i	0.489990	+	0.848688i
$834$		0			0
$835$			1.21114e6i			1.73708i
$836$		0			0
$837$	353249.			0.504231
$838$		0			0
$839$	−186170.	+	107485.i	−0.264476	+	0.152695i	−0.626375	−	0.779522i	$-0.715462\pi$
$839$	−186170.	+	107485.i	−0.264476	+	0.152695i	0.361899	+	0.932217i	$0.382129\pi$
$840$		0			0
$841$	−26902.4	−	46596.4i	−0.0380364	−	0.0658810i
$842$		0			0
$843$	−940023.			−1.32277
$844$		0			0
$845$	−352486.	+	610524.i	−0.493661	+	0.855046i
$846$		0			0
$847$	6377.60			0.00888977
$848$		0			0
$849$	−1.39209e6	−	803726.i	−1.93131	−	1.11505i
$850$		0			0
$851$	1.20677e6	+	696729.i	1.66635	+	0.962066i
$852$		0			0
$853$	−519887.	−	900471.i	−0.714515	−	1.23758i	−0.963146	−	0.268978i	$-0.913314\pi$
$853$	−519887.	−	900471.i	−0.714515	−	1.23758i	0.248632	−	0.968598i	$-0.420019\pi$
$854$		0			0
$855$	−1.39413e6	+	1.25851e6i	−1.90709	+	1.72157i
$856$		0			0
$857$	−761968.	+	439923.i	−1.03747	+	0.598983i	−0.919115	−	0.393988i	$-0.871095\pi$
$857$	−761968.	+	439923.i	−1.03747	+	0.598983i	−0.118354	+	0.992971i	$0.537762\pi$
$858$		0			0
$859$	136881.	−	237085.i	0.185506	−	0.321306i	−0.758241	−	0.651974i	$-0.773941\pi$
$859$	136881.	−	237085.i	0.185506	−	0.321306i	0.943747	+	0.330669i	$0.107274\pi$
$860$		0			0
$861$	16069.4	−	27833.1i	0.0216767	−	0.0375452i
$862$		0			0
$863$		−	988896.i		−	1.32779i	−0.747826	−	0.663894i	$-0.768902\pi$
$863$		−	988896.i		−	1.32779i	0.747826	−	0.663894i	$-0.231098\pi$
$864$		0			0
$865$	−343519.	−	198331.i	−0.459112	−	0.265069i
$866$		0			0
$867$			45540.3i			0.0605840i
$868$		0			0
$869$	−599672.	+	346221.i	−0.794098	+	0.458473i
$870$		0			0
$871$	−442795.	−	766943.i	−0.583668	−	1.01094i
$872$		0			0
$873$			1.28985e6i			1.69243i
$874$		0			0
$875$	−27665.0			−0.0361339
$876$		0			0
$877$	206093.	−	118988.i	0.267956	−	0.154705i	−0.360002	−	0.932951i	$-0.617224\pi$
$877$	206093.	−	118988.i	0.267956	−	0.154705i	0.627959	+	0.778247i	$0.283891\pi$
$878$		0			0
$879$	867685.	+	1.50287e6i	1.12301	+	1.94511i
$880$		0			0
$881$	−1.10453e6			−1.42307			−0.711534	−	0.702652i	$-0.751999\pi$
$881$	−1.10453e6			−1.42307			−0.711534	+	0.702652i	$0.751999\pi$
$882$		0			0
$883$	−424047.	+	734471.i	−0.543867	+	0.942006i	0.454810	+	0.890588i	$0.349707\pi$
$883$	−424047.	+	734471.i	−0.543867	+	0.942006i	−0.998677	+	0.0514172i	$0.983626\pi$
$884$		0			0
$885$	−652146.			−0.832642
$886$		0			0
$887$	−286658.	−	165502.i	−0.364348	−	0.210356i	0.306639	−	0.951826i	$-0.400796\pi$
$887$	−286658.	−	165502.i	−0.364348	−	0.210356i	−0.670986	+	0.741470i	$0.734129\pi$
$888$		0			0
$889$	38227.4	+	22070.6i	0.0483695	+	0.0279261i
$890$		0			0
$891$	45072.5	+	78067.8i	0.0567749	+	0.0983370i
$892$		0			0
$893$	160650.	+	751082.i	0.201455	+	0.941855i
$894$		0			0
$895$	23055.9	−	13311.4i	0.0287830	−	0.0166179i
$896$		0			0
$897$	424505.	−	735263.i	0.527591	−	0.913815i
$898$		0			0
$899$	220419.	−	381777.i	0.272728	−	0.472379i
$900$		0			0
$901$			1.13699e6i			1.40058i
$902$		0			0
$903$	5479.32	+	3163.49i	0.00671972	+	0.00387963i
$904$		0			0
$905$		−	808166.i		−	0.986742i
$906$		0			0
$907$	412538.	−	238179.i	0.501475	−	0.289527i	−0.227847	−	0.973697i	$-0.573169\pi$
$907$	412538.	−	238179.i	0.501475	−	0.289527i	0.729322	+	0.684170i	$0.239835\pi$
$908$		0			0
$909$	863183.	+	1.49508e6i	1.04466	+	1.80941i
$910$		0			0
$911$		−	834529.i		−	1.00555i	−0.864417	−	0.502776i	$-0.832312\pi$
$911$		−	834529.i		−	1.00555i	0.864417	−	0.502776i	$-0.167688\pi$
$912$		0			0
$913$	602294.			0.722548
$914$		0			0
$915$	2.42014e6	−	1.39727e6i	2.89067	−	1.66893i
$916$		0			0
$917$	3979.50	+	6892.69i	0.00473249	+	0.00819691i
$918$		0			0
$919$	−783926.			−0.928206			−0.464103	−	0.885781i	$-0.653623\pi$
$919$	−783926.			−0.928206			−0.464103	+	0.885781i	$0.653623\pi$
$920$		0			0
$921$	569240.	−	985953.i	0.671083	−	1.16235i
$922$		0			0
$923$	−661560.			−0.776543
$924$		0			0
$925$	2.36566e6	+	1.36582e6i	2.76484	+	1.59628i
$926$		0			0
$927$	−280006.	−	161661.i	−0.325842	−	0.188125i
$928$		0			0
$929$	517535.	+	896397.i	0.599665	+	1.03865i	0.992870	+	0.119199i	$0.0380327\pi$
$929$	517535.	+	896397.i	0.599665	+	1.03865i	−0.393206	+	0.919451i	$0.628634\pi$
$930$		0			0
$931$	−642805.	+	580272.i	−0.741617	+	0.669472i
$932$		0			0
$933$	2.12082e6	−	1.22445e6i	2.43635	−	1.40663i
$934$		0			0
$935$	−594334.	+	1.02942e6i	−0.679841	+	1.17752i
$936$		0			0
$937$	23427.7	−	40577.9i	0.0266839	−	0.0462179i	−0.852375	−	0.522931i	$-0.824839\pi$
$937$	23427.7	−	40577.9i	0.0266839	−	0.0462179i	0.879059	+	0.476713i	$0.158172\pi$
$938$		0			0
$939$		−	773380.i		−	0.877126i
$940$		0			0
$941$	−911004.	−	525968.i	−1.02882	−	0.593992i	−0.112176	−	0.993688i	$-0.535782\pi$
$941$	−911004.	−	525968.i	−1.02882	−	0.593992i	−0.916647	+	0.399697i	$0.869115\pi$
$942$		0			0
$943$			833930.i			0.937791i
$944$		0			0
$945$	−34155.9	+	19719.9i	−0.0382475	+	0.0220822i
$946$		0			0
$947$	471926.	+	817399.i	0.526228	+	0.911453i	0.999533	+	0.0305547i	$0.00972738\pi$
$947$	471926.	+	817399.i	0.526228	+	0.911453i	−0.473305	+	0.880898i	$0.656939\pi$
$948$		0			0
$949$			359358.i			0.399020i
$950$		0			0
$951$	1.33771e6			1.47911
$952$		0			0
$953$	−825995.	+	476888.i	−0.909476	+	0.525086i	−0.880263	−	0.474487i	$-0.842634\pi$
$953$	−825995.	+	476888.i	−0.909476	+	0.525086i	−0.0292138	+	0.999573i	$0.509300\pi$
$954$		0			0
$955$	580037.	+	1.00465e6i	0.635988	+	1.10156i
$956$		0			0
$957$	−1.18138e6			−1.28993
$958$		0			0
$959$	8228.62	−	14252.4i	0.00894726	−	0.0154971i
$960$		0			0
$961$	626129.			0.677980
$962$		0			0
$963$	1.72469e6	+	995748.i	1.85976	+	1.07373i
$964$		0			0
$965$	1.68630e6	+	973583.i	1.81084	+	1.04549i
$966$		0			0
$967$	408078.	+	706812.i	0.436406	+	0.755877i	0.997409	−	0.0719365i	$-0.0229179\pi$
$967$	408078.	+	706812.i	0.436406	+	0.755877i	−0.561003	+	0.827813i	$0.689585\pi$
$968$		0			0
$969$	1.43982e6	−	307966.i	1.53342	−	0.327986i
$970$		0			0
$971$	1.25114e6	−	722349.i	1.32699	−	0.766140i	0.342161	−	0.939642i	$-0.388841\pi$
$971$	1.25114e6	−	722349.i	1.32699	−	0.766140i	0.984834	+	0.173501i	$0.0555080\pi$
$972$		0			0
$973$	15137.8	−	26219.4i	0.0159896	−	0.0276947i
$974$		0			0
$975$	832167.	−	1.44136e6i	0.875389	−	1.51622i
$976$		0			0
$977$			672275.i			0.704300i	0.935944	+	0.352150i	$0.114549\pi$
$977$			672275.i			0.704300i	−0.935944	+	0.352150i	$0.885451\pi$
$978$		0			0
$979$	1.26530e6	+	730522.i	1.32017	+	0.762198i
$980$		0			0
$981$		−	1.26543e6i		−	1.31492i
$982$		0			0
$983$	−645861.	+	372888.i	−0.668393	+	0.385897i	−0.795468	−	0.605996i	$-0.792775\pi$
$983$	−645861.	+	372888.i	−0.668393	+	0.385897i	0.127074	+	0.991893i	$0.459441\pi$
$984$		0			0
$985$	268449.	+	464967.i	0.276687	+	0.479237i
$986$		0			0
$987$			45147.9i			0.0463451i
$988$		0			0
$989$	−164171.			−0.167843
$990$		0			0
$991$	−845740.	+	488288.i	−0.861171	+	0.497197i	−0.864404	−	0.502797i	$-0.832304\pi$
$991$	−845740.	+	488288.i	−0.861171	+	0.497197i	0.00323318	+	0.999995i	$0.498971\pi$
$992$		0			0
$993$	1.15464e6	+	1.99989e6i	1.17097	+	2.02819i
$994$		0			0
$995$	111157.			0.112277
$996$		0			0
$997$	275134.	−	476545.i	0.276792	−	0.479417i	−0.693794	−	0.720174i	$-0.744062\pi$
$997$	275134.	−	476545.i	0.276792	−	0.479417i	0.970586	+	0.240756i	$0.0773954\pi$
$998$		0			0
$999$	1.63933e6			1.64262

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.d.145.3		40
4.3	odd	2		152.5.n.a.145.18	yes	40
19.8	odd	6	inner	304.5.r.d.65.3		40
76.27	even	6		152.5.n.a.65.18	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.5.n.a.65.18	✓	40	76.27	even	6
152.5.n.a.145.18	yes	40	4.3	odd	2
304.5.r.d.65.3		40	19.8	odd	6	inner
304.5.r.d.145.3		40	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-12.4606 + 7.19410i) q^{3} +(-20.6420 - 35.7530i) q^{5} -1.47481 q^{7} +(63.0102 - 109.137i) q^{9} +O(q^{10})\)	\(q+(-12.4606 + 7.19410i) q^{3} +(-20.6420 - 35.7530i) q^{5} -1.47481 q^{7} +(63.0102 - 109.137i) q^{9} +101.571 q^{11} +(92.8097 + 53.5837i) q^{13} +(514.422 + 297.002i) q^{15} +(-141.736 - 245.493i) q^{17} +(267.967 - 241.899i) q^{19} +(18.3770 - 10.6100i) q^{21} +(-275.304 + 476.841i) q^{23} +(-539.686 + 934.764i) q^{25} +647.763i q^{27} +(700.077 + 404.189i) q^{29} -545.336i q^{31} +(-1265.63 + 730.712i) q^{33} +(30.4431 + 52.7291i) q^{35} -2530.76i q^{37} -1541.95 q^{39} +(1311.65 - 757.280i) q^{41} +(149.081 + 258.216i) q^{43} -5202.63 q^{45} +(-1063.81 + 1842.57i) q^{47} -2398.82 q^{49} +(3532.21 + 2039.32i) q^{51} +(-3473.59 - 2005.48i) q^{53} +(-2096.63 - 3631.47i) q^{55} +(-1598.77 + 4941.97i) q^{57} +(-950.795 + 548.942i) q^{59} +(2352.29 - 4074.29i) q^{61} +(-92.9283 + 160.957i) q^{63} -4424.30i q^{65} +(-7156.49 - 4131.80i) q^{67} -7922.27i q^{69} +(-5346.10 + 3086.57i) q^{71} +(1676.62 + 2903.99i) q^{73} -15530.2i q^{75} -149.798 q^{77} +(-5903.97 + 3408.66i) q^{79} +(443.754 + 768.604i) q^{81} +5929.78 q^{83} +(-5851.42 + 10135.0i) q^{85} -11631.1 q^{87} +(12457.3 + 7192.23i) q^{89} +(-136.877 - 79.0260i) q^{91} +(3923.21 + 6795.19i) q^{93} +(-14180.0 - 4587.34i) q^{95} +(-8863.99 + 5117.62i) q^{97} +(6400.01 - 11085.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) \) 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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