LMFDB - Embedded newform 304.5.r.d.145.11

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			145.11
Character	$\chi$	$=$	304.145
Dual form			304.5.r.d.65.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.620551 + 0.358275i) q^{3} +(16.9339 + 29.3305i) q^{5} -38.8265 q^{7} +(-40.2433 + 69.7034i) q^{9} +O(q^{10})$	\(q+(-0.620551 + 0.358275i) q^{3} +(16.9339 + 29.3305i) q^{5} -38.8265 q^{7} +(-40.2433 + 69.7034i) q^{9} -37.5609 q^{11} +(-175.693 - 101.437i) q^{13} +(-21.0167 - 12.1340i) q^{15} +(-1.83186 - 3.17288i) q^{17} +(-56.3584 - 356.574i) q^{19} +(24.0938 - 13.9106i) q^{21} +(211.053 - 365.555i) q^{23} +(-261.017 + 452.095i) q^{25} -115.713i q^{27} +(385.100 + 222.337i) q^{29} -773.065i q^{31} +(23.3085 - 13.4571i) q^{33} +(-657.485 - 1138.80i) q^{35} +1465.59i q^{37} +145.369 q^{39} +(2324.61 - 1342.12i) q^{41} +(-116.536 - 201.846i) q^{43} -2725.91 q^{45} +(925.321 - 1602.70i) q^{47} -893.505 q^{49} +(2.27353 + 1.31262i) q^{51} +(-1868.52 - 1078.79i) q^{53} +(-636.054 - 1101.68i) q^{55} +(162.725 + 201.080i) q^{57} +(879.571 - 507.821i) q^{59} +(-301.488 + 522.192i) q^{61} +(1562.50 - 2706.34i) q^{63} -6870.88i q^{65} +(-5999.45 - 3463.78i) q^{67} +302.460i q^{69} +(-6252.28 + 3609.75i) q^{71} +(-3531.05 - 6115.97i) q^{73} -374.064i q^{75} +1458.36 q^{77} +(-5216.77 + 3011.91i) q^{79} +(-3218.25 - 5574.17i) q^{81} -1064.16 q^{83} +(62.0413 - 107.459i) q^{85} -318.632 q^{87} +(-1617.25 - 933.720i) q^{89} +(6821.55 + 3938.42i) q^{91} +(276.970 + 479.726i) q^{93} +(9504.09 - 7691.22i) q^{95} +(-1210.89 + 699.109i) q^{97} +(1511.57 - 2618.12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.620551	+	0.358275i	−0.0689501	+	0.0398084i	−0.534079	−	0.845435i	$-0.679341\pi$
$3$	−0.620551	+	0.358275i	−0.0689501	+	0.0398084i	0.465129	+	0.885243i	$0.346008\pi$
$4$		0			0
$5$	16.9339	+	29.3305i	0.677358	+	1.17322i	0.975774	+	0.218782i	$0.0702084\pi$
$5$	16.9339	+	29.3305i	0.677358	+	1.17322i	−0.298416	+	0.954436i	$0.596458\pi$
$6$		0			0
$7$	−38.8265			−0.792377			−0.396188	−	0.918169i	$-0.629667\pi$
$7$	−38.8265			−0.792377			−0.396188	+	0.918169i	$0.629667\pi$
$8$		0			0
$9$	−40.2433	+	69.7034i	−0.496831	+	0.860536i
$10$		0			0
$11$	−37.5609			−0.310421			−0.155210	−	0.987881i	$-0.549606\pi$
$11$	−37.5609			−0.310421			−0.155210	+	0.987881i	$0.549606\pi$
$12$		0			0
$13$	−175.693	−	101.437i	−1.03961	−	0.600216i	−0.119884	−	0.992788i	$-0.538252\pi$
$13$	−175.693	−	101.437i	−1.03961	−	0.600216i	−0.919721	+	0.392572i	$0.871585\pi$
$14$		0			0
$15$	−21.0167	−	12.1340i	−0.0934078	−	0.0539290i
$16$		0			0
$17$	−1.83186	−	3.17288i	−0.00633862	−	0.0109788i	0.862839	−	0.505479i	$-0.168684\pi$
$17$	−1.83186	−	3.17288i	−0.00633862	−	0.0109788i	−0.869177	+	0.494501i	$0.835351\pi$
$18$		0			0
$19$	−56.3584	−	356.574i	−0.156118	−	0.987738i
$19$	−56.3584	−	356.574i	−0.156118	−	0.987738i
$20$		0			0
$21$	24.0938	−	13.9106i	0.0546345	−	0.0315432i
$22$		0			0
$23$	211.053	−	365.555i	0.398966	−	0.691030i	−0.594632	−	0.803998i	$-0.702702\pi$
$23$	211.053	−	365.555i	0.398966	−	0.691030i	0.993599	+	0.112968i	$0.0360358\pi$
$24$		0			0
$25$	−261.017	+	452.095i	−0.417627	+	0.723351i
$26$		0			0
$27$		−	115.713i		−	0.158729i
$28$		0			0
$29$	385.100	+	222.337i	0.457907	+	0.264373i	0.711164	−	0.703026i	$-0.248168\pi$
$29$	385.100	+	222.337i	0.457907	+	0.264373i	−0.253257	+	0.967399i	$0.581502\pi$
$30$		0			0
$31$		−	773.065i		−	0.804438i	−0.915543	−	0.402219i	$-0.868239\pi$
$31$		−	773.065i		−	0.804438i	0.915543	−	0.402219i	$-0.131761\pi$
$32$		0			0
$33$	23.3085	−	13.4571i	0.0214035	−	0.0123573i
$34$		0			0
$35$	−657.485	−	1138.80i	−0.536723	−	0.929631i
$36$		0			0
$37$			1465.59i			1.07056i	0.844676	+	0.535278i	$0.179793\pi$
$37$			1465.59i			1.07056i	−0.844676	+	0.535278i	$0.820207\pi$
$38$		0			0
$39$	145.369			0.0955745
$40$		0			0
$41$	2324.61	−	1342.12i	1.38288	−	0.798404i	0.390377	−	0.920655i	$-0.372345\pi$
$41$	2324.61	−	1342.12i	1.38288	−	0.798404i	0.992499	+	0.122252i	$0.0390115\pi$
$42$		0			0
$43$	−116.536	−	201.846i	−0.0630264	−	0.109165i	0.832790	−	0.553588i	$-0.186742\pi$
$43$	−116.536	−	201.846i	−0.0630264	−	0.109165i	−0.895817	+	0.444424i	$0.853409\pi$
$44$		0			0
$45$	−2725.91			−1.34613
$46$		0			0
$47$	925.321	−	1602.70i	0.418887	−	0.725533i	−0.576941	−	0.816786i	$-0.695754\pi$
$47$	925.321	−	1602.70i	0.418887	−	0.725533i	0.995828	+	0.0912525i	$0.0290870\pi$
$48$		0			0
$49$	−893.505			−0.372139
$50$		0			0
$51$	2.27353	+	1.31262i	0.000874097	+	0.000504660i
$52$		0			0
$53$	−1868.52	−	1078.79i	−0.665189	−	0.384047i	0.129062	−	0.991637i	$-0.458803\pi$
$53$	−1868.52	−	1078.79i	−0.665189	−	0.384047i	−0.794251	+	0.607589i	$0.792137\pi$
$54$		0			0
$55$	−636.054	−	1101.68i	−0.210266	−	0.364191i
$56$		0			0
$57$	162.725	+	201.080i	0.0500846	+	0.0618899i
$58$		0			0
$59$	879.571	−	507.821i	0.252678	−	0.145884i	−0.368312	−	0.929702i	$-0.620064\pi$
$59$	879.571	−	507.821i	0.252678	−	0.145884i	0.620990	+	0.783819i	$0.286731\pi$
$60$		0			0
$61$	−301.488	+	522.192i	−0.0810233	+	0.140336i	−0.903690	−	0.428188i	$-0.859152\pi$
$61$	−301.488	+	522.192i	−0.0810233	+	0.140336i	0.822666	+	0.568524i	$0.192485\pi$
$62$		0			0
$63$	1562.50	−	2706.34i	0.393677	−	0.681869i
$64$		0			0
$65$		−	6870.88i		−	1.62624i
$66$		0			0
$67$	−5999.45	−	3463.78i	−1.33648	−	0.771616i	−0.350194	−	0.936677i	$-0.613884\pi$
$67$	−5999.45	−	3463.78i	−1.33648	−	0.771616i	−0.986283	+	0.165061i	$0.947218\pi$
$68$		0			0
$69$			302.460i			0.0635287i
$70$		0			0
$71$	−6252.28	+	3609.75i	−1.24028	+	0.716079i	−0.969152	−	0.246463i	$-0.920732\pi$
$71$	−6252.28	+	3609.75i	−1.24028	+	0.716079i	−0.271133	+	0.962542i	$0.587398\pi$
$72$		0			0
$73$	−3531.05	−	6115.97i	−0.662611	−	1.14768i	−0.979927	−	0.199356i	$-0.936115\pi$
$73$	−3531.05	−	6115.97i	−0.662611	−	1.14768i	0.317316	−	0.948320i	$-0.397218\pi$
$74$		0			0
$75$		−	374.064i		−	0.0665002i
$76$		0			0
$77$	1458.36			0.245970
$78$		0			0
$79$	−5216.77	+	3011.91i	−0.835887	+	0.482600i	−0.855864	−	0.517201i	$-0.826974\pi$
$79$	−5216.77	+	3011.91i	−0.835887	+	0.482600i	0.0199769	+	0.999800i	$0.493641\pi$
$80$		0			0
$81$	−3218.25	−	5574.17i	−0.490512	−	0.849591i
$82$		0			0
$83$	−1064.16			−0.154472			−0.0772358	−	0.997013i	$-0.524609\pi$
$83$	−1064.16			−0.154472			−0.0772358	+	0.997013i	$0.524609\pi$
$84$		0			0
$85$	62.0413	−	107.459i	0.00858703	−	0.0148732i
$86$		0			0
$87$	−318.632			−0.0420970
$88$		0			0
$89$	−1617.25	−	933.720i	−0.204172	−	0.117879i	0.394428	−	0.918927i	$-0.370943\pi$
$89$	−1617.25	−	933.720i	−0.204172	−	0.117879i	−0.598600	+	0.801048i	$0.704276\pi$
$90$		0			0
$91$	6821.55	+	3938.42i	0.823759	+	0.475597i
$92$		0			0
$93$	276.970	+	479.726i	0.0320234	+	0.0554661i
$94$		0			0
$95$	9504.09	−	7691.22i	1.05309	−	0.852212i
$96$		0			0
$97$	−1210.89	+	699.109i	−0.128695	+	0.0743022i	−0.562965	−	0.826480i	$-0.690340\pi$
$97$	−1210.89	+	699.109i	−0.128695	+	0.0743022i	0.434270	+	0.900783i	$0.357006\pi$
$98$		0			0
$99$	1511.57	−	2618.12i	0.154227	−	0.267128i
$100$		0			0
$101$	8623.38	−	14936.1i	0.845347	−	1.46418i	−0.0399730	−	0.999201i	$-0.512727\pi$
$101$	8623.38	−	14936.1i	0.845347	−	1.46418i	0.885320	−	0.464983i	$-0.153939\pi$
$102$		0			0
$103$			10894.7i			1.02693i	0.858110	+	0.513467i	$0.171639\pi$
$103$			10894.7i			1.02693i	−0.858110	+	0.513467i	$0.828361\pi$
$104$		0			0
$105$	816.006	+	471.121i	0.0740142	+	0.0427321i
$106$		0			0
$107$			17083.3i			1.49212i	0.665879	+	0.746060i	$0.268057\pi$
$107$			17083.3i			1.49212i	−0.665879	+	0.746060i	$0.731943\pi$
$108$		0			0
$109$	2647.73	−	1528.67i	0.222854	−	0.128665i	−0.384417	−	0.923160i	$-0.625598\pi$
$109$	2647.73	−	1528.67i	0.222854	−	0.128665i	0.607271	+	0.794495i	$0.292264\pi$
$110$		0			0
$111$	−525.085	−	909.474i	−0.0426171	−	0.0738149i
$112$		0			0
$113$			6485.27i			0.507892i	0.967218	+	0.253946i	$0.0817285\pi$
$113$			6485.27i			0.507892i	−0.967218	+	0.253946i	$0.918272\pi$
$114$		0			0
$115$	14295.8			1.08097
$116$		0			0
$117$	14140.9	−	8164.28i	1.03302	−	0.596412i
$118$		0			0
$119$	71.1247	+	123.192i	0.00502258	+	0.00869936i
$120$		0			0
$121$	−13230.2			−0.903639
$122$		0			0
$123$	−961.694	+	1665.70i	−0.0635663	+	0.110100i
$124$		0			0
$125$	3487.25			0.223184
$126$		0			0
$127$	−24474.5	−	14130.3i	−1.51742	−	0.876082i	−0.999790	−	0.0204773i	$-0.993481\pi$
$127$	−24474.5	−	14130.3i	−1.51742	−	0.876082i	−0.517629	−	0.855605i	$-0.673185\pi$
$128$		0			0
$129$	144.633	+	83.5037i	0.00869135	+	0.00501795i
$130$		0			0
$131$	−12074.0	−	20912.8i	−0.703573	−	1.21862i	−0.967204	−	0.254001i	$-0.918253\pi$
$131$	−12074.0	−	20912.8i	−0.703573	−	1.21862i	0.263631	−	0.964624i	$-0.415080\pi$
$132$		0			0
$133$	2188.20	+	13844.5i	0.123704	+	0.782661i
$134$		0			0
$135$	3393.92	−	1959.48i	0.186223	−	0.107516i
$136$		0			0
$137$	−16525.1	+	28622.3i	−0.880445	+	1.52498i	−0.0295976	+	0.999562i	$0.509423\pi$
$137$	−16525.1	+	28622.3i	−0.880445	+	1.52498i	−0.850847	+	0.525413i	$0.823911\pi$
$138$		0			0
$139$	−3471.93	+	6013.56i	−0.179697	+	0.311245i	−0.941777	−	0.336238i	$-0.890845\pi$
$139$	−3471.93	+	6013.56i	−0.179697	+	0.311245i	0.762080	+	0.647483i	$0.224179\pi$
$140$		0			0
$141$			1326.08i			0.0667008i
$142$		0			0
$143$	6599.20	+	3810.05i	0.322715	+	0.186320i
$144$		0			0
$145$			15060.2i			0.716300i
$146$		0			0
$147$	554.466	−	320.121i	0.0256590	−	0.0148142i
$148$		0			0
$149$	−8271.44	−	14326.6i	−0.372571	−	0.645311i	0.617389	−	0.786658i	$-0.288190\pi$
$149$	−8271.44	−	14326.6i	−0.372571	−	0.645311i	−0.989960	+	0.141346i	$0.954857\pi$
$150$		0			0
$151$			16711.1i			0.732911i	0.930436	+	0.366455i	$0.119429\pi$
$151$			16711.1i			0.732911i	−0.930436	+	0.366455i	$0.880571\pi$
$152$		0			0
$153$	294.880			0.0125969
$154$		0			0
$155$	22674.3	−	13091.0i	0.943781	−	0.544892i
$156$		0			0
$157$	8092.24	+	14016.2i	0.328299	+	0.568630i	0.982174	−	0.187972i	$-0.0601913\pi$
$157$	8092.24	+	14016.2i	0.328299	+	0.568630i	−0.653876	+	0.756602i	$0.726858\pi$
$158$		0			0
$159$	1546.01			0.0611532
$160$		0			0
$161$	−8194.45	+	14193.2i	−0.316132	+	0.547556i
$162$		0			0
$163$	−40440.0			−1.52207			−0.761037	−	0.648709i	$-0.775309\pi$
$163$	−40440.0			−1.52207			−0.761037	+	0.648709i	$0.775309\pi$
$164$		0			0
$165$	789.408	+	455.765i	0.0289957	+	0.0167407i
$166$		0			0
$167$	16732.5	+	9660.52i	0.599968	+	0.346392i	0.769029	−	0.639214i	$-0.220740\pi$
$167$	16732.5	+	9660.52i	0.599968	+	0.346392i	−0.169061	+	0.985606i	$0.554073\pi$
$168$		0			0
$169$	6298.25	+	10908.9i	0.220519	+	0.381950i
$170$		0			0
$171$	27122.4	+	10421.3i	0.927548	+	0.356394i
$172$		0			0
$173$	598.320	−	345.440i	0.0199913	−	0.0115420i	−0.489971	−	0.871739i	$-0.662993\pi$
$173$	598.320	−	345.440i	0.0199913	−	0.0115420i	0.509962	+	0.860197i	$0.329659\pi$
$174$		0			0
$175$	10134.4	−	17553.2i	0.330918	−	0.573167i
$176$		0			0
$177$	−363.879	+	630.257i	−0.0116148	+	0.0201174i
$178$		0			0
$179$			4224.55i			0.131848i	0.997825	+	0.0659242i	$0.0209996\pi$
$179$			4224.55i			0.131848i	−0.997825	+	0.0659242i	$0.979000\pi$
$180$		0			0
$181$	50617.3	+	29223.9i	1.54505	+	0.892033i	0.998508	+	0.0545991i	$0.0173881\pi$
$181$	50617.3	+	29223.9i	1.54505	+	0.892033i	0.546538	+	0.837434i	$0.315945\pi$
$182$		0			0
$183$		−	432.062i		−	0.0129016i
$184$		0			0
$185$	−42986.4	+	24818.2i	−1.25600	+	0.725149i
$186$		0			0
$187$	68.8064	+	119.176i	0.00196764	+	0.00340805i
$188$		0			0
$189$			4492.74i			0.125773i
$190$		0			0
$191$	40680.9			1.11512			0.557562	−	0.830135i	$-0.311737\pi$
$191$	40680.9			1.11512			0.557562	+	0.830135i	$0.311737\pi$
$192$		0			0
$193$	12646.5	−	7301.47i	0.339513	−	0.196018i	−0.320544	−	0.947234i	$-0.603866\pi$
$193$	12646.5	−	7301.47i	0.339513	−	0.196018i	0.660057	+	0.751216i	$0.270532\pi$
$194$		0			0
$195$	2461.67	+	4263.73i	0.0647381	+	0.112130i
$196$		0			0
$197$	15827.6			0.407832			0.203916	−	0.978988i	$-0.434633\pi$
$197$	15827.6			0.407832			0.203916	+	0.978988i	$0.434633\pi$
$198$		0			0
$199$	3521.22	−	6098.93i	0.0889175	−	0.154010i	−0.818136	−	0.575024i	$-0.804993\pi$
$199$	3521.22	−	6098.93i	0.0889175	−	0.154010i	0.907054	+	0.421015i	$0.138326\pi$
$200$		0			0
$201$	4963.95			0.122867
$202$		0			0
$203$	−14952.1	−	8632.58i	−0.362835	−	0.209483i
$204$		0			0
$205$	78729.8	+	45454.7i	1.87340	+	1.08161i
$206$		0			0
$207$	16986.9	+	29422.2i	0.396437	+	0.686649i
$208$		0			0
$209$	2116.87	+	13393.2i	0.0484621	+	0.306615i
$210$		0			0
$211$	−24004.3	+	13858.9i	−0.539167	+	0.311288i	−0.744741	−	0.667353i	$-0.767427\pi$
$211$	−24004.3	+	13858.9i	−0.539167	+	0.311288i	0.205574	+	0.978642i	$0.434094\pi$
$212$		0			0
$213$	2586.57	−	4480.07i	0.0570118	−	0.0987474i
$214$		0			0
$215$	3946.82	−	6836.09i	0.0853828	−	0.147887i
$216$		0			0
$217$			30015.4i			0.637418i
$218$		0			0
$219$	4382.40	+	2530.18i	0.0913742	+	0.0527549i
$220$		0			0
$221$			743.271i			0.0152182i
$222$		0			0
$223$	−14474.6	+	8356.89i	−0.291069	+	0.168049i	−0.638424	−	0.769685i	$-0.720413\pi$
$223$	−14474.6	+	8356.89i	−0.291069	+	0.168049i	0.347355	+	0.937734i	$0.387080\pi$
$224$		0			0
$225$	−21008.4	−	36387.5i	−0.414980	−	0.718766i
$226$		0			0
$227$			36020.6i			0.699035i	0.936930	+	0.349517i	$0.113654\pi$
$227$			36020.6i			0.699035i	−0.936930	+	0.349517i	$0.886346\pi$
$228$		0			0
$229$	16916.2			0.322577			0.161288	−	0.986907i	$-0.448435\pi$
$229$	16916.2			0.322577			0.161288	+	0.986907i	$0.448435\pi$
$230$		0			0
$231$	−904.985	+	522.493i	−0.0169597	+	0.00979167i
$232$		0			0
$233$	−46136.6	−	79910.9i	−0.849833	−	1.47195i	−0.881357	−	0.472451i	$-0.843370\pi$
$233$	−46136.6	−	79910.9i	−0.849833	−	1.47195i	0.0315244	−	0.999503i	$-0.489964\pi$
$234$		0			0
$235$	62677.4			1.13495
$236$		0			0
$237$	2158.18	−	3738.08i	0.0384230	−	0.0665506i
$238$		0			0
$239$	−26468.9			−0.463384			−0.231692	−	0.972789i	$-0.574426\pi$
$239$	−26468.9			−0.463384			−0.231692	+	0.972789i	$0.574426\pi$
$240$		0			0
$241$	−62128.3	−	35869.8i	−1.06968	−	0.617582i	−0.141588	−	0.989926i	$-0.545221\pi$
$241$	−62128.3	−	35869.8i	−1.06968	−	0.617582i	−0.928095	+	0.372344i	$0.878554\pi$
$242$		0			0
$243$	12111.2	+	6992.42i	0.205105	+	0.118417i
$244$		0			0
$245$	−15130.6	−	26206.9i	−0.252071	−	0.436600i
$246$		0			0
$247$	−26267.8	+	68364.4i	−0.430556	+	1.12056i
$248$		0			0
$249$	660.362	−	381.260i	0.0106508	−	0.00614926i
$250$		0			0
$251$	−52362.2	+	90694.0i	−0.831133	+	1.43957i	0.0660069	+	0.997819i	$0.478974\pi$
$251$	−52362.2	+	90694.0i	−0.831133	+	1.43957i	−0.897140	+	0.441746i	$0.854359\pi$
$252$		0			0
$253$	−7927.35	+	13730.6i	−0.123847	+	0.214510i
$254$		0			0
$255$			88.9114i			0.00136734i
$256$		0			0
$257$	−60291.2	−	34809.2i	−0.912826	−	0.527020i	−0.0314864	−	0.999504i	$-0.510024\pi$
$257$	−60291.2	−	34809.2i	−0.912826	−	0.527020i	−0.881339	+	0.472484i	$0.843357\pi$
$258$		0			0
$259$		−	56903.7i		−	0.848283i
$260$		0			0
$261$	−30995.3	+	17895.2i	−0.455004	+	0.262697i
$262$		0			0
$263$	11736.2	+	20327.7i	0.169674	+	0.293885i	0.938305	−	0.345808i	$-0.112395\pi$
$263$	11736.2	+	20327.7i	0.169674	+	0.293885i	−0.768631	+	0.639692i	$0.779062\pi$
$264$		0			0
$265$		−	73072.6i		−	1.04055i
$266$		0			0
$267$	1338.11			0.0187703
$268$		0			0
$269$	76649.5	−	44253.6i	1.05926	−	0.611567i	0.134036	−	0.990976i	$-0.457206\pi$
$269$	76649.5	−	44253.6i	1.05926	−	0.611567i	0.925229	+	0.379410i	$0.123873\pi$
$270$		0			0
$271$	−65270.5	−	113052.i	−0.888747	−	1.53936i	−0.841357	−	0.540479i	$-0.818243\pi$
$271$	−65270.5	−	113052.i	−0.888747	−	1.53936i	−0.0473898	−	0.998876i	$-0.515090\pi$
$272$		0			0
$273$	−5644.16			−0.0757310
$274$		0			0
$275$	9804.03	−	16981.1i	0.129640	−	0.224543i
$276$		0			0
$277$	48239.8			0.628703			0.314352	−	0.949307i	$-0.398213\pi$
$277$	48239.8			0.628703			0.314352	+	0.949307i	$0.398213\pi$
$278$		0			0
$279$	53885.3	+	31110.7i	0.692248	+	0.399669i
$280$		0			0
$281$	9861.96	+	5693.80i	0.124897	+	0.0721090i	0.561147	−	0.827716i	$-0.310360\pi$
$281$	9861.96	+	5693.80i	0.124897	+	0.0721090i	−0.436250	+	0.899825i	$0.643694\pi$
$282$		0			0
$283$	−41851.1	−	72488.2i	−0.522557	−	0.905095i	−0.999656	−	0.0262455i	$-0.991645\pi$
$283$	−41851.1	−	72488.2i	−0.522557	−	0.905095i	0.477098	−	0.878850i	$-0.341689\pi$
$284$		0			0
$285$	−3142.20	+	8177.87i	−0.0386852	+	0.100682i
$286$		0			0
$287$	−90256.6	+	52109.6i	−1.09576	+	0.632637i
$288$		0			0
$289$	41753.8	−	72319.7i	0.499920	−	0.865886i
$290$		0			0
$291$	500.947	−	867.666i	0.00591570	−	0.0102463i
$292$		0			0
$293$			72636.4i			0.846094i	0.906108	+	0.423047i	$0.139040\pi$
$293$			72636.4i			0.846094i	−0.906108	+	0.423047i	$0.860960\pi$
$294$		0			0
$295$	29789.2	+	17198.8i	0.342306	+	0.197631i
$296$		0			0
$297$			4346.30i			0.0492727i
$298$		0			0
$299$	−74161.2	+	42817.0i	−0.829534	+	0.478932i
$300$		0			0
$301$	4524.67	+	7836.96i	0.0499406	+	0.0864997i
$302$		0			0
$303$			12358.2i			0.134607i
$304$		0			0
$305$	−20421.5			−0.219527
$306$		0			0
$307$	100626.	−	58096.5i	1.06766	−	0.616415i	0.140121	−	0.990134i	$-0.455251\pi$
$307$	100626.	−	58096.5i	1.06766	−	0.616415i	0.927542	+	0.373719i	$0.121918\pi$
$308$		0			0
$309$	−3903.31	−	6760.74i	−0.0408805	−	0.0708072i
$310$		0			0
$311$	−46690.1			−0.482730			−0.241365	−	0.970434i	$-0.577595\pi$
$311$	−46690.1			−0.482730			−0.241365	+	0.970434i	$0.577595\pi$
$312$		0			0
$313$	−3689.07	+	6389.66i	−0.0376555	+	0.0652212i	−0.884239	−	0.467035i	$-0.845322\pi$
$313$	−3689.07	+	6389.66i	−0.0376555	+	0.0652212i	0.846583	+	0.532256i	$0.178656\pi$
$314$		0			0
$315$	105837.			1.06664
$316$		0			0
$317$	−119739.	−	69131.4i	−1.19156	−	0.687950i	−0.232903	−	0.972500i	$-0.574822\pi$
$317$	−119739.	−	69131.4i	−1.19156	−	0.687950i	−0.958661	+	0.284550i	$0.908156\pi$
$318$		0			0
$319$	−14464.7	−	8351.20i	−0.142144	−	0.0820668i
$320$		0			0
$321$	−6120.51	−	10601.0i	−0.0593988	−	0.102882i
$322$		0			0
$323$	−1028.12	+	832.012i	−0.00985463	+	0.00797488i
$324$		0			0
$325$	91717.8	−	52953.3i	0.868334	−	0.501333i
$326$		0			0
$327$	−1095.37	+	1897.23i	−0.0102439	+	0.0177429i
$328$		0			0
$329$	−35927.0	+	62227.3i	−0.331916	+	0.574896i
$330$		0			0
$331$		−	43910.6i		−	0.400787i	−0.979716	−	0.200393i	$-0.935778\pi$
$331$		−	43910.6i		−	0.400787i	0.979716	−	0.200393i	$-0.0642220\pi$
$332$		0			0
$333$	−102157.	−	58980.2i	−0.921251	−	0.531885i
$334$		0			0
$335$		−	234622.i		−	2.09064i
$336$		0			0
$337$	62775.6	−	36243.5i	0.552753	−	0.319132i	−0.197479	−	0.980307i	$-0.563275\pi$
$337$	62775.6	−	36243.5i	0.552753	−	0.319132i	0.750231	+	0.661175i	$0.229942\pi$
$338$		0			0
$339$	−2323.51	−	4024.44i	−0.0202183	−	0.0350192i
$340$		0			0
$341$			29037.0i			0.249714i
$342$		0			0
$343$	127914.			1.08725
$344$		0			0
$345$	−8871.30	+	5121.85i	−0.0745331	+	0.0430317i
$346$		0			0
$347$	25828.3	+	44735.9i	0.214504	+	0.371533i	0.953119	−	0.302595i	$-0.0978530\pi$
$347$	25828.3	+	44735.9i	0.214504	+	0.371533i	−0.738615	+	0.674128i	$0.764520\pi$
$348$		0			0
$349$	172502.			1.41626			0.708132	−	0.706080i	$-0.249538\pi$
$349$	172502.			1.41626			0.708132	+	0.706080i	$0.249538\pi$
$350$		0			0
$351$	−11737.6	+	20330.0i	−0.0952716	+	0.165015i
$352$		0			0
$353$	−192519.			−1.54498			−0.772491	−	0.635026i	$-0.780989\pi$
$353$	−192519.			−1.54498			−0.772491	+	0.635026i	$0.780989\pi$
$354$		0			0
$355$	−211751.	−	122255.i	−1.68023	−	0.970083i
$356$		0			0
$357$	−88.2730	−	50.9644i	−0.000692614	−	0.000399881i
$358$		0			0
$359$	−77482.7	−	134204.i	−0.601196	−	1.04130i	−0.992640	−	0.121100i	$-0.961358\pi$
$359$	−77482.7	−	134204.i	−0.601196	−	1.04130i	0.391445	−	0.920202i	$-0.371975\pi$
$360$		0			0
$361$	−123968.	+	40191.9i	−0.951255	+	0.308407i
$362$		0			0
$363$	8210.00	−	4740.04i	0.0623060	−	0.0359724i
$364$		0			0
$365$	119589.	−	207135.i	0.897649	−	1.55477i
$366$		0			0
$367$	79781.4	−	138185.i	0.592338	−	1.02596i	−0.401579	−	0.915825i	$-0.631538\pi$
$367$	79781.4	−	138185.i	0.592338	−	1.02596i	0.993917	−	0.110135i	$-0.0351283\pi$
$368$		0			0
$369$			216045.i			1.58669i
$370$		0			0
$371$	72547.9	+	41885.6i	0.527081	+	0.304310i
$372$		0			0
$373$			70497.7i			0.506707i	0.967374	+	0.253354i	$0.0815336\pi$
$373$			70497.7i			0.506707i	−0.967374	+	0.253354i	$0.918466\pi$
$374$		0			0
$375$	−2164.01	+	1249.39i	−0.0153885	+	0.00888458i
$376$		0			0
$377$	−45106.3	−	78126.4i	−0.317362	−	0.549686i
$378$		0			0
$379$		−	149930.i		−	1.04378i	−0.853013	−	0.521890i	$-0.825227\pi$
$379$		−	149930.i		−	1.04378i	0.853013	−	0.521890i	$-0.174773\pi$
$380$		0			0
$381$	20250.2			0.139502
$382$		0			0
$383$	−90031.5	+	51979.7i	−0.613758	+	0.354353i	−0.774435	−	0.632654i	$-0.781966\pi$
$383$	−90031.5	+	51979.7i	−0.613758	+	0.354353i	0.160677	+	0.987007i	$0.448632\pi$
$384$		0			0
$385$	24695.7	+	42774.3i	0.166610	+	0.288577i
$386$		0			0
$387$	18759.1			0.125254
$388$		0			0
$389$	−48964.6	+	84809.2i	−0.323581	+	0.560459i	−0.981224	−	0.192871i	$-0.938220\pi$
$389$	−48964.6	+	84809.2i	−0.323581	+	0.560459i	0.657643	+	0.753330i	$0.271554\pi$
$390$		0			0
$391$	−1546.48			−0.0101156
$392$		0			0
$393$	14985.1	+	8651.65i	0.0970229	+	0.0560162i
$394$		0			0
$395$	−176681.	−	102007.i	−1.13239	−	0.653785i
$396$		0			0
$397$	144321.	+	249972.i	0.915691	+	1.58602i	0.805886	+	0.592071i	$0.201689\pi$
$397$	144321.	+	249972.i	0.915691	+	1.58602i	0.109805	+	0.993953i	$0.464977\pi$
$398$		0			0
$399$	−6318.03	−	7807.24i	−0.0396859	−	0.0490401i
$400$		0			0
$401$	−168167.	+	97091.1i	−1.04581	+	0.603797i	−0.921472	−	0.388444i	$-0.873013\pi$
$401$	−168167.	+	97091.1i	−1.04581	+	0.603797i	−0.124334	+	0.992240i	$0.539679\pi$
$402$		0			0
$403$	−78417.0	+	135822.i	−0.482837	+	0.836298i
$404$		0			0
$405$	108995.	−	188785.i	0.664504	−	1.15095i
$406$		0			0
$407$		−	55048.9i		−	0.332323i
$408$		0			0
$409$	−100571.	−	58064.4i	−0.601207	−	0.347107i	0.168309	−	0.985734i	$-0.446169\pi$
$409$	−100571.	−	58064.4i	−0.601207	−	0.347107i	−0.769516	+	0.638627i	$0.779503\pi$
$410$		0			0
$411$		−	23682.1i		−	0.140196i
$412$		0			0
$413$	−34150.6	+	19716.9i	−0.200216	+	0.115595i
$414$		0			0
$415$	−18020.3	−	31212.2i	−0.104633	−	0.181229i
$416$		0			0
$417$		−	4975.63i		−	0.0286138i
$418$		0			0
$419$	75236.9			0.428551			0.214276	−	0.976773i	$-0.431261\pi$
$419$	75236.9			0.428551			0.214276	+	0.976773i	$0.431261\pi$
$420$		0			0
$421$	61555.6	−	35539.2i	0.347299	−	0.200513i	−0.316196	−	0.948694i	$-0.602406\pi$
$421$	61555.6	−	35539.2i	0.347299	−	0.200513i	0.663495	+	0.748181i	$0.269072\pi$
$422$		0			0
$423$	74475.9	+	128996.i	0.416232	+	0.720934i
$424$		0			0
$425$	1912.59			0.0105887
$426$		0			0
$427$	11705.7	−	20274.9i	0.0642010	−	0.111199i
$428$		0			0
$429$	−5460.19			−0.0296683
$430$		0			0
$431$	259317.	+	149717.i	1.39597	+	0.805965i	0.993968	−	0.109672i	$-0.0349800\pi$
$431$	259317.	+	149717.i	1.39597	+	0.805965i	0.402005	+	0.915637i	$0.368313\pi$
$432$		0			0
$433$	−5237.16	−	3023.68i	−0.0279332	−	0.0161272i	0.485968	−	0.873976i	$-0.338467\pi$
$433$	−5237.16	−	3023.68i	−0.0279332	−	0.0161272i	−0.513902	+	0.857849i	$0.671800\pi$
$434$		0			0
$435$	−5395.70	−	9345.62i	−0.0285147	−	0.0493889i
$436$		0			0
$437$	−142242.	−	54653.9i	−0.744842	−	0.286192i
$438$		0			0
$439$	−291795.	+	168468.i	−1.51408	+	0.874155i	−0.514217	+	0.857660i	$0.671918\pi$
$439$	−291795.	+	168468.i	−1.51408	+	0.874155i	−0.999864	+	0.0164954i	$0.994749\pi$
$440$		0			0
$441$	35957.6	−	62280.4i	0.184890	−	0.320239i
$442$		0			0
$443$	−9662.61	+	16736.1i	−0.0492365	+	0.0852801i	−0.889593	−	0.456754i	$-0.849012\pi$
$443$	−9662.61	+	16736.1i	−0.0492365	+	0.0852801i	0.840357	+	0.542034i	$0.182345\pi$
$444$		0			0
$445$		−	63246.2i		−	0.319385i
$446$		0			0
$447$	10265.7	+	5926.91i	0.0513776	+	0.0296629i
$448$		0			0
$449$			284873.i			1.41305i	0.707686	+	0.706527i	$0.249739\pi$
$449$			284873.i			1.41305i	−0.707686	+	0.706527i	$0.750261\pi$
$450$		0			0
$451$	−87314.6	+	50411.1i	−0.429273	+	0.247841i
$452$		0			0
$453$	−5987.17	−	10370.1i	−0.0291760	−	0.0505343i
$454$		0			0
$455$			266772.i			1.28860i
$456$		0			0
$457$	−226740.			−1.08567			−0.542833	−	0.839841i	$-0.682648\pi$
$457$	−226740.			−1.08567			−0.542833	+	0.839841i	$0.682648\pi$
$458$		0			0
$459$	−367.144	+	211.971i	−0.00174265	+	0.00100612i
$460$		0			0
$461$	2005.42	+	3473.49i	0.00943634	+	0.0163442i	0.870705	−	0.491806i	$-0.163663\pi$
$461$	2005.42	+	3473.49i	0.00943634	+	0.0163442i	−0.861269	+	0.508150i	$0.830330\pi$
$462$		0			0
$463$	120150.			0.560483			0.280241	−	0.959930i	$-0.409585\pi$
$463$	120150.			0.560483			0.280241	+	0.959930i	$0.409585\pi$
$464$		0			0
$465$	−9380.39	+	16247.3i	−0.0433825	+	0.0751408i
$466$		0			0
$467$	132763.			0.608755			0.304377	−	0.952552i	$-0.401552\pi$
$467$	132763.			0.608755			0.304377	+	0.952552i	$0.401552\pi$
$468$		0			0
$469$	232937.	+	134486.i	1.05899	+	0.611411i
$470$		0			0
$471$	−10043.3	−	5798.50i	−0.0452725	−	0.0261381i
$472$		0			0
$473$	4377.19	+	7581.51i	0.0195647	+	0.0338870i
$474$		0			0
$475$	175915.	+	67592.4i	0.779681	+	0.299578i
$476$		0			0
$477$	150390.	−	86828.0i	0.660973	−	0.381613i
$478$		0			0
$479$	44026.0	−	76255.3i	0.191884	−	0.332352i	−0.753991	−	0.656885i	$-0.771874\pi$
$479$	44026.0	−	76255.3i	0.191884	−	0.332352i	0.945874	+	0.324533i	$0.105207\pi$
$480$		0			0
$481$	148664.	−	257494.i	0.642565	−	1.11295i
$482$		0			0
$483$		−	11743.5i		−	0.0503387i
$484$		0			0
$485$	−41010.4	−	23677.4i	−0.174345	−	0.100658i
$486$		0			0
$487$		−	260375.i		−	1.09784i	−0.835873	−	0.548922i	$-0.815038\pi$
$487$		−	260375.i		−	1.09784i	0.835873	−	0.548922i	$-0.184962\pi$
$488$		0			0
$489$	25095.1	−	14488.6i	0.104947	−	0.0605912i
$490$		0			0
$491$	130693.	+	226367.i	0.542112	+	0.938966i	0.998783	+	0.0493297i	$0.0157085\pi$
$491$	130693.	+	226367.i	0.542112	+	0.938966i	−0.456670	+	0.889636i	$0.650958\pi$
$492$		0			0
$493$		−	1629.17i		−	0.00670303i
$494$		0			0
$495$	102388.			0.417866
$496$		0			0
$497$	242754.	−	140154.i	0.982773	−	0.567404i
$498$		0			0
$499$	235058.	+	407132.i	0.944003	+	1.63506i	0.757735	+	0.652562i	$0.226306\pi$
$499$	235058.	+	407132.i	0.944003	+	1.63506i	0.186268	+	0.982499i	$0.440361\pi$
$500$		0			0
$501$	−13844.5			−0.0551572
$502$		0			0
$503$	39530.3	−	68468.6i	0.156241	−	0.270617i	−0.777269	−	0.629168i	$-0.783396\pi$
$503$	39530.3	−	68468.6i	0.156241	−	0.270617i	0.933510	+	0.358551i	$0.116729\pi$
$504$		0			0
$505$	584111.			2.29041
$506$		0			0
$507$	−7816.76	−	4513.01i	−0.0304096	−	0.0175570i
$508$		0			0
$509$	72386.6	+	41792.4i	0.279398	+	0.161310i	0.633151	−	0.774029i	$-0.281761\pi$
$509$	72386.6	+	41792.4i	0.279398	+	0.161310i	−0.353753	+	0.935339i	$0.615095\pi$
$510$		0			0
$511$	137098.	+	237461.i	0.525038	+	0.909392i
$512$		0			0
$513$	−41260.3	+	6521.42i	−0.156783	+	0.0247803i
$514$		0			0
$515$	−319548.	+	184491.i	−1.20482	+	0.695601i
$516$		0			0
$517$	−34755.9	+	60199.0i	−0.130031	+	0.225221i
$518$		0			0
$519$	−247.525	+	428.726i	−0.000918935	+	0.00159164i
$520$		0			0
$521$		−	94878.0i		−	0.349535i	−0.984610	−	0.174767i	$-0.944083\pi$
$521$		−	94878.0i		−	0.349535i	0.984610	−	0.174767i	$-0.0559173\pi$
$522$		0			0
$523$	−95396.4	−	55077.2i	−0.348762	−	0.201358i	0.315378	−	0.948966i	$-0.397869\pi$
$523$	−95396.4	−	55077.2i	−0.348762	−	0.201358i	−0.664140	+	0.747608i	$0.731202\pi$
$524$		0			0
$525$			14523.6i			0.0526932i
$526$		0			0
$527$	−2452.84	+	1416.15i	−0.00883178	+	0.00509903i
$528$		0			0
$529$	50833.7	+	88046.5i	0.181652	+	0.314631i
$530$		0			0
$531$			81745.5i			0.289918i
$532$		0			0
$533$	−544559.			−1.91686
$534$		0			0
$535$	−501060.	+	289287.i	−1.75058	+	1.01070i
$536$		0			0
$537$	−1513.55	−	2621.55i	−0.00524867	−	0.00909096i
$538$		0			0
$539$	33560.9			0.115520
$540$		0			0
$541$	−87676.3	+	151860.i	−0.299563	+	0.518858i	−0.976036	−	0.217609i	$-0.930174\pi$
$541$	−87676.3	+	151860.i	−0.299563	+	0.518858i	0.676473	+	0.736467i	$0.263507\pi$
$542$		0			0
$543$	−41880.8			−0.142042
$544$		0			0
$545$	89673.0	+	51772.7i	0.301904	+	0.174304i
$546$		0			0
$547$	−43582.3	−	25162.3i	−0.145659	−	0.0840960i	0.425400	−	0.905006i	$-0.360134\pi$
$547$	−43582.3	−	25162.3i	−0.145659	−	0.0840960i	−0.571058	+	0.820910i	$0.693467\pi$
$548$		0			0
$549$	−24265.7	−	42029.4i	−0.0805097	−	0.139447i
$550$		0			0
$551$	57576.0	−	149847.i	0.189644	−	0.493565i
$552$		0			0
$553$	202549.	−	116942.i	0.662338	−	0.382401i
$554$		0			0
$555$	17783.5	−	30801.9i	0.0577340	−	0.0999982i
$556$		0			0
$557$	−120293.	+	208354.i	−0.387730	+	0.671569i	−0.992144	−	0.125102i	$-0.960074\pi$
$557$	−120293.	+	208354.i	−0.387730	+	0.671569i	0.604414	+	0.796671i	$0.293407\pi$
$558$		0			0
$559$			47283.9i			0.151318i
$560$		0			0
$561$	−85.3957	−	49.3032i	−0.000271338	−	0.000156657i
$562$		0			0
$563$			292763.i			0.923632i	0.886976	+	0.461816i	$0.152802\pi$
$563$			292763.i			0.923632i	−0.886976	+	0.461816i	$0.847198\pi$
$564$		0			0
$565$	−190216.	+	109821.i	−0.595868	+	0.344024i
$566$		0			0
$567$	124953.	+	216425.i	0.388670	+	0.673197i
$568$		0			0
$569$			32716.5i			0.101052i	0.998723	+	0.0505258i	$0.0160897\pi$
$569$			32716.5i			0.101052i	−0.998723	+	0.0505258i	$0.983910\pi$
$570$		0			0
$571$	612399.			1.87829			0.939144	−	0.343524i	$-0.111621\pi$
$571$	612399.			1.87829			0.939144	+	0.343524i	$0.111621\pi$
$572$		0			0
$573$	−25244.5	+	14574.9i	−0.0768880	+	0.0443913i
$574$		0			0
$575$	110177.	+	190832.i	0.333238	+	0.577185i
$576$		0			0
$577$	−613892.			−1.84391			−0.921956	−	0.387295i	$-0.873409\pi$
$577$	−613892.			−1.84391			−0.921956	+	0.387295i	$0.873409\pi$
$578$		0			0
$579$	−5231.87	+	9061.87i	−0.0156063	+	0.0270309i
$580$		0			0
$581$	41317.4			0.122400
$582$		0			0
$583$	70183.2	+	40520.3i	0.206489	+	0.119216i
$584$		0			0
$585$	478924.	+	276507.i	1.39944	+	0.807968i
$586$		0			0
$587$	−342258.	−	592808.i	−0.993293	−	1.72043i	−0.596783	−	0.802403i	$-0.703555\pi$
$587$	−342258.	−	592808.i	−0.993293	−	1.72043i	−0.396510	−	0.918031i	$-0.629779\pi$
$588$		0			0
$589$	−275655.	+	43568.7i	−0.794574	+	0.125587i
$590$		0			0
$591$	−9821.81	+	5670.62i	−0.0281201	+	0.0162351i
$592$		0			0
$593$	131478.	−	227726.i	0.373889	−	0.647594i	−0.616271	−	0.787534i	$-0.711358\pi$
$593$	131478.	−	227726.i	0.373889	−	0.647594i	0.990160	+	0.139940i	$0.0446909\pi$
$594$		0			0
$595$	−2408.84	+	4172.24i	−0.00680416	+	0.0117852i
$596$		0			0
$597$			5046.27i			0.0141586i
$598$		0			0
$599$	−386970.	−	223417.i	−1.07851	−	0.622678i	−0.148015	−	0.988985i	$-0.547288\pi$
$599$	−386970.	−	223417.i	−1.07851	−	0.622678i	−0.930494	+	0.366308i	$0.880622\pi$
$600$		0			0
$601$			326926.i			0.905109i	0.891737	+	0.452554i	$0.149487\pi$
$601$			326926.i			0.905109i	−0.891737	+	0.452554i	$0.850513\pi$
$602$		0			0
$603$	482875.	−	278788.i	1.32801	−	0.766725i
$604$		0			0
$605$	−224039.	−	388047.i	−0.612087	−	1.06017i
$606$		0			0
$607$			551691.i			1.49733i	0.662946	+	0.748667i	$0.269306\pi$
$607$			551691.i			1.49733i	−0.662946	+	0.748667i	$0.730694\pi$
$608$		0			0
$609$	12371.4			0.0333567
$610$		0			0
$611$	−325145.	+	187723.i	−0.870954	+	0.502845i
$612$		0			0
$613$	165331.	+	286362.i	0.439981	+	0.762069i	0.997687	−	0.0679691i	$-0.0216519\pi$
$613$	165331.	+	286362.i	0.439981	+	0.762069i	−0.557707	+	0.830038i	$0.688319\pi$
$614$		0			0
$615$	−65141.1			−0.172228
$616$		0			0
$617$	51970.9	−	90016.2i	0.136518	−	0.236456i	−0.789658	−	0.613547i	$-0.789742\pi$
$617$	51970.9	−	90016.2i	0.136518	−	0.236456i	0.926176	+	0.377091i	$0.123076\pi$
$618$		0			0
$619$	−473683.			−1.23625			−0.618126	−	0.786079i	$-0.712108\pi$
$619$	−473683.			−1.23625			−0.618126	+	0.786079i	$0.712108\pi$
$620$		0			0
$621$	−42299.5	−	24421.6i	−0.109686	−	0.0633274i
$622$		0			0
$623$	62792.1	+	36253.0i	0.161782	+	0.0934046i
$624$		0			0
$625$	222188.	+	384842.i	0.568802	+	0.985195i
$626$		0			0
$627$	−6112.09	−	7552.76i	−0.0155473	−	0.0192119i
$628$		0			0
$629$	4650.14	−	2684.76i	0.0117534	−	0.00678585i
$630$		0			0
$631$	312921.	−	541995.i	0.785916	−	1.36125i	−0.142534	−	0.989790i	$-0.545525\pi$
$631$	312921.	−	541995.i	0.785916	−	1.36125i	0.928450	−	0.371457i	$-0.121142\pi$
$632$		0			0
$633$	9930.57	−	17200.3i	0.0247837	−	0.0429267i
$634$		0			0
$635$		−	957129.i		−	2.37368i
$636$		0			0
$637$	156983.	+	90634.1i	0.386877	+	0.223364i
$638$		0			0
$639$		−	581073.i		−	1.42308i
$640$		0			0
$641$	420890.	−	243001.i	1.02436	−	0.591415i	0.108997	−	0.994042i	$-0.465236\pi$
$641$	420890.	−	243001.i	1.02436	−	0.591415i	0.915364	+	0.402627i	$0.131903\pi$
$642$		0			0
$643$	403634.	+	699114.i	0.976260	+	1.69093i	0.675714	+	0.737164i	$0.263836\pi$
$643$	403634.	+	699114.i	0.976260	+	1.69093i	0.300546	+	0.953767i	$0.402831\pi$
$644$		0			0
$645$			5656.19i			0.0135958i
$646$		0			0
$647$	−573211.			−1.36932			−0.684662	−	0.728861i	$-0.740050\pi$
$647$	−573211.			−1.36932			−0.684662	+	0.728861i	$0.740050\pi$
$648$		0			0
$649$	−33037.5	+	19074.2i	−0.0784364	+	0.0452853i
$650$		0			0
$651$	−10753.8	−	18626.1i	−0.0253746	−	0.0439500i
$652$		0			0
$653$	−449978.			−1.05527			−0.527636	−	0.849470i	$-0.676922\pi$
$653$	−449978.			−1.05527			−0.527636	+	0.849470i	$0.676922\pi$
$654$		0			0
$655$	408922.	−	708273.i	0.953142	−	1.65089i
$656$		0			0
$657$	568405.			1.31682
$658$		0			0
$659$	−481262.	−	277857.i	−1.10818	−	0.639808i	−0.169823	−	0.985475i	$-0.554320\pi$
$659$	−481262.	−	277857.i	−1.10818	−	0.639808i	−0.938358	+	0.345666i	$0.887653\pi$
$660$		0			0
$661$	105185.	+	60728.4i	0.240741	+	0.138992i	0.615517	−	0.788124i	$-0.288947\pi$
$661$	105185.	+	60728.4i	0.240741	+	0.138992i	−0.374776	+	0.927115i	$0.622281\pi$
$662$		0			0
$663$	−266.295	−	461.237i	−0.000605810	−	0.00104929i
$664$		0			0
$665$	−369010.	+	298623.i	−0.834440	+	0.675273i
$666$		0			0
$667$	162553.	−	93850.0i	0.365379	−	0.210951i
$668$		0			0
$669$	5988.13	−	10371.8i	0.0133795	−	0.0231739i
$670$		0			0
$671$	11324.1	−	19614.0i	0.0251513	−	0.0435633i
$672$		0			0
$673$		−	664353.i		−	1.46679i	−0.679801	−	0.733397i	$-0.737934\pi$
$673$		−	664353.i		−	1.46679i	0.679801	−	0.733397i	$-0.262066\pi$
$674$		0			0
$675$	52313.3	+	30203.1i	0.114817	+	0.0662894i
$676$		0			0
$677$			38003.5i			0.0829175i	0.999140	+	0.0414587i	$0.0132005\pi$
$677$			38003.5i			0.0829175i	−0.999140	+	0.0414587i	$0.986799\pi$
$678$		0			0
$679$	47014.7	−	27143.9i	0.101975	−	0.0588753i
$680$		0			0
$681$	−12905.3	−	22352.6i	−0.0278274	−	0.0481985i
$682$		0			0
$683$		−	382063.i		−	0.819019i	−0.912306	−	0.409509i	$-0.865700\pi$
$683$		−	382063.i		−	0.819019i	0.912306	−	0.409509i	$-0.134300\pi$
$684$		0			0
$685$	−1.11934e6			−2.38550
$686$		0			0
$687$	−10497.4	+	6060.67i	−0.0222417	+	0.0128412i
$688$		0			0
$689$	218857.	+	379072.i	0.461023	+	0.798515i
$690$		0			0
$691$	466584.			0.977177			0.488589	−	0.872514i	$-0.337512\pi$
$691$	466584.			0.977177			0.488589	+	0.872514i	$0.337512\pi$
$692$		0			0
$693$	−58689.1	+	101652.i	−0.122206	+	0.211666i
$694$		0			0
$695$	−235174.			−0.486878
$696$		0			0
$697$	−8516.74	−	4917.14i	−0.0175310	−	0.0101216i
$698$		0			0
$699$	57260.2	+	33059.2i	0.117192	+	0.0676609i
$700$		0			0
$701$	388230.	+	672435.i	0.790048	+	1.36840i	0.925936	+	0.377679i	$0.123278\pi$
$701$	388230.	+	672435.i	0.790048	+	1.36840i	−0.135888	+	0.990724i	$0.543389\pi$
$702$		0			0
$703$	522591.	−	82598.4i	1.05743	−	0.167132i
$704$		0			0
$705$	−38894.5	+	22455.7i	−0.0782546	+	0.0451803i
$706$		0			0
$707$	−334815.	+	579917.i	−0.669833	+	1.16019i
$708$		0			0
$709$	185822.	−	321854.i	0.369663	−	0.640275i	−0.619850	−	0.784720i	$-0.712807\pi$
$709$	185822.	−	321854.i	0.369663	−	0.640275i	0.989513	+	0.144446i	$0.0461399\pi$
$710$		0			0
$711$		−	484836.i		−	0.959081i
$712$		0			0
$713$	−282598.	−	163158.i	−0.555891	−	0.320944i
$714$		0			0
$715$			258077.i			0.504820i
$716$		0			0
$717$	16425.3	−	9483.17i	0.0319504	−	0.0184465i
$718$		0			0
$719$	223649.	+	387371.i	0.432622	+	0.749324i	0.997098	−	0.0761256i	$-0.0242550\pi$
$719$	223649.	+	387371.i	0.432622	+	0.749324i	−0.564476	+	0.825450i	$0.690922\pi$
$720$		0			0
$721$		−	423004.i		−	0.813718i
$722$		0			0
$723$	51405.0			0.0983397
$724$		0			0
$725$	−201035.	+	116068.i	−0.382469	+	0.220818i
$726$		0			0
$727$	175339.	+	303695.i	0.331748	+	0.574605i	0.982855	−	0.184381i	$-0.0590282\pi$
$727$	175339.	+	303695.i	0.331748	+	0.574605i	−0.651106	+	0.758986i	$0.725695\pi$
$728$		0			0
$729$	511335.			0.962168
$730$		0			0
$731$	−426.955	+	739.507i	−0.000799000	+	0.00138391i
$732$		0			0
$733$	−346926.			−0.645696			−0.322848	−	0.946451i	$-0.604640\pi$
$733$	−346926.			−0.645696			−0.322848	+	0.946451i	$0.604640\pi$
$734$		0			0
$735$	18778.6	+	10841.8i	0.0347607	+	0.0200691i
$736$		0			0
$737$	225345.	+	130103.i	0.414870	+	0.239526i
$738$		0			0
$739$	−384861.	−	666598.i	−0.704717	−	1.22061i	−0.966794	−	0.255558i	$-0.917741\pi$
$739$	−384861.	−	666598.i	−0.704717	−	1.22061i	0.262077	−	0.965047i	$-0.415593\pi$
$740$		0			0
$741$	−8192.76	−	51834.7i	−0.0149209	−	0.0944026i
$742$		0			0
$743$	−742302.	+	428568.i	−1.34463	+	0.776323i	−0.987483	−	0.157725i	$-0.949584\pi$
$743$	−742302.	+	428568.i	−1.34463	+	0.776323i	−0.357148	+	0.934048i	$0.616251\pi$
$744$		0			0
$745$	280136.	−	485210.i	0.504727	−	0.874213i
$746$		0			0
$747$	42825.1	−	74175.2i	0.0767462	−	0.132928i
$748$		0			0
$749$		−	663283.i		−	1.18232i
$750$		0			0
$751$	−30693.4	−	17720.9i	−0.0544208	−	0.0314199i	0.472543	−	0.881308i	$-0.343336\pi$
$751$	−30693.4	−	17720.9i	−0.0544208	−	0.0314199i	−0.526964	+	0.849888i	$0.676670\pi$
$752$		0			0
$753$		−	75040.4i		−	0.132344i
$754$		0			0
$755$	−490144.	+	282985.i	−0.859864	+	0.496443i
$756$		0			0
$757$	−189781.	−	328711.i	−0.331178	−	0.573617i	0.651565	−	0.758593i	$-0.274113\pi$
$757$	−189781.	−	328711.i	−0.331178	−	0.573617i	−0.982743	+	0.184976i	$0.940779\pi$
$758$		0			0
$759$		−	11360.7i		−	0.0197206i
$760$		0			0
$761$	−707632.			−1.22191			−0.610953	−	0.791667i	$-0.709214\pi$
$761$	−707632.			−1.22191			−0.610953	+	0.791667i	$0.709214\pi$
$762$		0			0
$763$	−102802.	+	59352.7i	−0.176584	+	0.101951i
$764$		0			0
$765$	4993.49	+	8648.98i	0.00853260	+	0.0147789i
$766$		0			0
$767$	−206046.			−0.350247
$768$		0			0
$769$	157274.	−	272406.i	0.265952	−	0.460642i	−0.701861	−	0.712314i	$-0.747647\pi$
$769$	157274.	−	272406.i	0.265952	−	0.460642i	0.967813	+	0.251672i	$0.0809804\pi$
$770$		0			0
$771$	49885.0			0.0839192
$772$		0			0
$773$	−865076.	−	499452.i	−1.44776	−	0.835862i	−0.449409	−	0.893326i	$-0.648365\pi$
$773$	−865076.	−	499452.i	−1.44776	−	0.835862i	−0.998348	+	0.0574638i	$0.981699\pi$
$774$		0			0
$775$	349498.	+	201783.i	0.581891	+	0.335955i
$776$		0			0
$777$	20387.2	+	35311.6i	0.0337688	+	0.0584892i
$778$		0			0
$779$	−609575.	−	753256.i	−1.00451	−	1.24127i
$780$		0			0
$781$	234841.	−	135586.i	0.385010	−	0.222286i
$782$		0			0
$783$	25727.4	−	44561.1i	0.0419635	−	0.0726830i
$784$		0			0
$785$	−274067.	+	474698.i	−0.444752	+	0.770332i
$786$		0			0
$787$		−	621498.i		−	1.00344i	−0.865031	−	0.501719i	$-0.832701\pi$
$787$		−	621498.i		−	1.00344i	0.865031	−	0.501719i	$-0.167299\pi$
$788$		0			0
$789$	−14565.8	−	8409.59i	−0.0233981	−	0.0135089i
$790$		0			0
$791$		−	251800.i		−	0.402442i
$792$		0			0
$793$	105939.	−	61163.7i	0.168464	−	0.0972629i
$794$		0			0
$795$	26180.1	+	45345.3i	0.0414226	+	0.0717460i
$796$		0			0
$797$		−	688845.i		−	1.08444i	−0.840237	−	0.542219i	$-0.817584\pi$
$797$		−	688845.i		−	1.08444i	0.840237	−	0.542219i	$-0.182416\pi$
$798$		0			0
$799$	−6780.24			−0.0106207
$800$		0			0
$801$	130167.	−	75151.9i	0.202878	−	0.117132i
$802$		0			0
$803$	132630.	+	229721.i	0.205688	+	0.356263i
$804$		0			0
$805$	−555057.			−0.856537
$806$		0			0
$807$	−31709.9	+	54923.2i	−0.0486909	+	0.0843352i
$808$		0			0
$809$	498894.			0.762274			0.381137	−	0.924519i	$-0.375533\pi$
$809$	498894.			0.762274			0.381137	+	0.924519i	$0.375533\pi$
$810$		0			0
$811$	−613640.	−	354285.i	−0.932979	−	0.538656i	−0.0452263	−	0.998977i	$-0.514401\pi$
$811$	−613640.	−	354285.i	−0.932979	−	0.538656i	−0.887752	+	0.460321i	$0.847734\pi$
$812$		0			0
$813$	81007.3	+	46769.6i	0.122558	+	0.0707591i
$814$		0			0
$815$	−684808.	−	1.18612e6i	−1.03099	−	1.78572i
$816$		0			0
$817$	−65405.1	+	52929.3i	−0.0979868	+	0.0792961i
$818$		0			0
$819$	−549043.	+	316990.i	−0.818537	+	0.472583i
$820$		0			0
$821$	643893.	−	1.11526e6i	0.955273	−	1.65458i	0.221530	−	0.975154i	$-0.428895\pi$
$821$	643893.	−	1.11526e6i	0.955273	−	1.65458i	0.733743	−	0.679428i	$-0.237772\pi$
$822$		0			0
$823$	−72047.6	+	124790.i	−0.106370	+	0.184238i	−0.914297	−	0.405044i	$-0.867256\pi$
$823$	−72047.6	+	124790.i	−0.106370	+	0.184238i	0.807927	+	0.589283i	$0.200589\pi$
$824$		0			0
$825$			14050.2i			0.0206430i
$826$		0			0
$827$	1.15269e6	+	665506.i	1.68539	+	0.973063i	0.957967	+	0.286879i	$0.0926176\pi$
$827$	1.15269e6	+	665506.i	1.68539	+	0.973063i	0.727428	+	0.686184i	$0.240716\pi$
$828$		0			0
$829$			254492.i			0.370310i	0.982709	+	0.185155i	$0.0592788\pi$
$829$			254492.i			0.370310i	−0.982709	+	0.185155i	$0.940721\pi$
$830$		0			0
$831$	−29935.2	+	17283.1i	−0.0433491	+	0.0250276i
$832$		0			0
$833$	1636.78	+	2834.98i	0.00235885	+	0.00408564i
$834$		0			0
$835$			654363.i			0.938525i
$836$		0			0
$837$	−89453.9			−0.127687
$838$		0			0
$839$	−423161.	+	244312.i	−0.601148	+	0.347073i	−0.769493	−	0.638655i	$-0.779491\pi$
$839$	−423161.	+	244312.i	−0.601148	+	0.347073i	0.168345	+	0.985728i	$0.446158\pi$
$840$		0			0
$841$	−254773.	−	441279.i	−0.360214	−	0.623909i
$842$		0			0
$843$	−8159.79			−0.0114822
$844$		0			0
$845$	−213308.	+	369461.i	−0.298741	+	0.517434i
$846$		0			0
$847$	513681.			0.716023
$848$		0			0
$849$	51941.4	+	29988.4i	0.0720607	+	0.0416043i
$850$		0			0
$851$	535753.	+	309317.i	0.739786	+	0.427115i
$852$		0			0
$853$	−541205.	−	937394.i	−0.743812	−	1.28832i	−0.950748	−	0.309966i	$-0.899682\pi$
$853$	−541205.	−	937394.i	−0.743812	−	1.28832i	0.206935	−	0.978355i	$-0.433651\pi$
$854$		0			0
$855$	153628.	+	971987.i	0.210154	+	1.32962i
$856$		0			0
$857$	−404866.	+	233749.i	−0.551251	+	0.318265i	−0.749626	−	0.661861i	$-0.769767\pi$
$857$	−404866.	+	233749.i	−0.551251	+	0.318265i	0.198375	+	0.980126i	$0.436434\pi$
$858$		0			0
$859$	−26462.9	+	45835.1i	−0.0358634	+	0.0621172i	−0.883400	−	0.468620i	$-0.844751\pi$
$859$	−26462.9	+	45835.1i	−0.0358634	+	0.0621172i	0.847537	+	0.530737i	$0.178085\pi$
$860$		0			0
$861$	37339.2	−	64673.4i	0.0503684	−	0.0872407i
$862$		0			0
$863$		−	299062.i		−	0.401549i	−0.979637	−	0.200775i	$-0.935654\pi$
$863$		−	299062.i		−	0.401549i	0.979637	−	0.200775i	$-0.0643459\pi$
$864$		0			0
$865$	20263.8	+	11699.3i	0.0270825	+	0.0156361i
$866$		0			0
$867$			59837.4i			0.0796039i
$868$		0			0
$869$	195947.	−	113130.i	0.259477	−	0.149809i
$870$		0			0
$871$	702708.	+	1.21713e6i	0.926273	+	1.60435i
$872$		0			0
$873$		−	112538.i		−	0.147662i
$874$		0			0
$875$	−135398.			−0.176846
$876$		0			0
$877$	869896.	−	502235.i	1.13101	−	0.652992i	0.186825	−	0.982393i	$-0.440180\pi$
$877$	869896.	−	502235.i	1.13101	−	0.652992i	0.944190	+	0.329402i	$0.106847\pi$
$878$		0			0
$879$	−26023.8	−	45074.6i	−0.0336816	−	0.0583383i
$880$		0			0
$881$	242998.			0.313077			0.156539	−	0.987672i	$-0.449966\pi$
$881$	242998.			0.313077			0.156539	+	0.987672i	$0.449966\pi$
$882$		0			0
$883$	−208863.	+	361762.i	−0.267880	+	0.463982i	−0.968314	−	0.249735i	$-0.919656\pi$
$883$	−208863.	+	361762.i	−0.267880	+	0.463982i	0.700434	+	0.713717i	$0.252990\pi$
$884$		0			0
$885$	−24647.6			−0.0314694
$886$		0			0
$887$	1.11618e6	+	644427.i	1.41869	+	0.819080i	0.996184	−	0.0872806i	$-0.0278177\pi$
$887$	1.11618e6	+	644427.i	1.41869	+	0.819080i	0.422505	+	0.906361i	$0.361151\pi$
$888$		0			0
$889$	950257.	+	548631.i	1.20237	+	0.694188i
$890$		0			0
$891$	120880.	+	209371.i	0.152265	+	0.263731i
$892$		0			0
$893$	−623631.	−	239619.i	−0.782033	−	0.300482i
$894$		0			0
$895$	−123908.	+	71538.4i	−0.154687	+	0.0893085i
$896$		0			0
$897$	30680.5	−	53140.2i	0.0381310	−	0.0660448i
$898$		0			0
$899$	171881.	−	297707.i	0.212671	−	0.368358i
$900$		0			0
$901$			7904.77i			0.00973732i
$902$		0			0
$903$	−5615.58	−	3242.16i	−0.00688682	−	0.00397611i
$904$		0			0
$905$			1.97950e6i			2.41690i
$906$		0			0
$907$	797029.	−	460165.i	0.968857	−	0.559370i	0.0699692	−	0.997549i	$-0.477710\pi$
$907$	797029.	−	460165.i	0.968857	−	0.559370i	0.898888	+	0.438179i	$0.144377\pi$
$908$		0			0
$909$	694066.	+	1.20216e6i	0.839988	+	1.45490i
$910$		0			0
$911$		−	177208.i		−	0.213524i	−0.994285	−	0.106762i	$-0.965952\pi$
$911$		−	177208.i		−	0.213524i	0.994285	−	0.106762i	$-0.0340483\pi$
$912$		0			0
$913$	39970.6			0.0479512
$914$		0			0
$915$	12672.6	−	7316.51i	0.0151364	−	0.00873901i
$916$		0			0
$917$	468792.	+	811971.i	0.557495	+	0.965610i
$918$		0			0
$919$	−1.40002e6			−1.65768			−0.828842	−	0.559483i	$-0.811000\pi$
$919$	−1.40002e6			−1.65768			−0.828842	+	0.559483i	$0.811000\pi$
$920$		0			0
$921$	−41629.1	+	72103.7i	−0.0490770	+	0.0850038i
$922$		0			0
$923$	1.46464e6			1.71921
$924$		0			0
$925$	−662585.	−	382544.i	−0.774388	−	0.447093i
$926$		0			0
$927$	−759400.	−	438440.i	−0.883713	−	0.510212i
$928$		0			0
$929$	−106562.	−	184571.i	−0.123473	−	0.213861i	0.797662	−	0.603104i	$-0.206070\pi$
$929$	−106562.	−	184571.i	−0.123473	−	0.213861i	−0.921135	+	0.389244i	$0.872736\pi$
$930$		0			0
$931$	50356.6	+	318600.i	0.0580974	+	0.367576i
$932$		0			0
$933$	28973.6	−	16727.9i	0.0332843	−	0.0192167i
$934$		0			0
$935$	−2330.33	+	4036.24i	−0.00266559	+	0.00461694i
$936$		0			0
$937$	351248.	−	608380.i	0.400069	−	0.692940i	−0.593665	−	0.804712i	$-0.702319\pi$
$937$	351248.	−	608380.i	0.400069	−	0.692940i	0.993734	+	0.111773i	$0.0356528\pi$
$938$		0			0
$939$		−	5286.81i		−	0.00599601i
$940$		0			0
$941$	−63757.0	−	36810.1i	−0.0720027	−	0.0415708i	0.463566	−	0.886062i	$-0.346570\pi$
$941$	−63757.0	−	36810.1i	−0.0720027	−	0.0415708i	−0.535569	+	0.844491i	$0.679903\pi$
$942$		0			0
$943$		−	1.13303e6i		−	1.27414i
$944$		0			0
$945$	−131774.	+	76079.8i	−0.147559	+	0.0851933i
$946$		0			0
$947$	−467262.	−	809321.i	−0.521027	−	0.902445i	−0.999701	−	0.0244524i	$-0.992216\pi$
$947$	−467262.	−	809321.i	−0.521027	−	0.902445i	0.478674	−	0.877993i	$-0.341118\pi$
$948$		0			0
$949$			1.43271e6i			1.59084i
$950$		0			0
$951$	99072.2			0.109545
$952$		0			0
$953$	530413.	−	306234.i	0.584020	−	0.337184i	−0.178709	−	0.983902i	$-0.557192\pi$
$953$	530413.	−	306234.i	0.584020	−	0.337184i	0.762730	+	0.646718i	$0.223859\pi$
$954$		0			0
$955$	688887.	+	1.19319e6i	0.755338	+	1.30828i
$956$		0			0
$957$	11968.1			0.0130678
$958$		0			0
$959$	641610.	−	1.11130e6i	0.697644	−	1.20836i
$960$		0			0
$961$	325891.			0.352879
$962$		0			0
$963$	−1.19076e6	−	687487.i	−1.28402	−	0.741330i
$964$		0			0
$965$	428311.	+	247285.i	0.459944	+	0.265549i
$966$		0			0
$967$	283177.	+	490477.i	0.302834	+	0.524524i	0.976777	−	0.214260i	$-0.0687339\pi$
$967$	283177.	+	490477.i	0.302834	+	0.524524i	−0.673943	+	0.738784i	$0.735401\pi$
$968$		0			0
$969$	339.914	−	884.657i	0.000362010	−	0.000942166i
$970$		0			0
$971$	−1.03406e6	+	597015.i	−1.09675	+	0.633208i	−0.935365	−	0.353683i	$-0.884929\pi$
$971$	−1.03406e6	+	597015.i	−1.09675	+	0.633208i	−0.161384	+	0.986892i	$0.551596\pi$
$972$		0			0
$973$	134803.	−	233485.i	0.142388	−	0.246623i
$974$		0			0
$975$	−37943.7	+	65720.4i	−0.0399145	+	0.0691339i
$976$		0			0
$977$			597766.i			0.626241i	0.949713	+	0.313121i	$0.101374\pi$
$977$			597766.i			0.626241i	−0.949713	+	0.313121i	$0.898626\pi$
$978$		0			0
$979$	60745.4	+	35071.4i	0.0633794	+	0.0365921i
$980$		0			0
$981$			246074.i			0.255699i
$982$		0			0
$983$	−1.41392e6	+	816326.i	−1.46325	+	0.844805i	−0.999160	−	0.0409851i	$-0.986950\pi$
$983$	−1.41392e6	+	816326.i	−1.46325	+	0.844805i	−0.464086	+	0.885790i	$0.653617\pi$
$984$		0			0
$985$	268023.	+	464230.i	0.276248	+	0.478476i
$986$		0			0
$987$		−	51487.0i		−	0.0528522i
$988$		0			0
$989$	−98380.9			−0.100582
$990$		0			0
$991$	1.38891e6	−	801890.i	1.41426	−	0.816521i	0.418470	−	0.908231i	$-0.362567\pi$
$991$	1.38891e6	−	801890.i	1.41426	−	0.816521i	0.995786	+	0.0917097i	$0.0292332\pi$
$992$		0			0
$993$	15732.1	+	27248.8i	0.0159547	+	0.0276343i
$994$		0			0
$995$	238513.			0.240916
$996$		0			0
$997$	−125533.	+	217429.i	−0.126289	+	0.218740i	−0.922236	−	0.386627i	$-0.873640\pi$
$997$	−125533.	+	217429.i	−0.126289	+	0.218740i	0.795947	+	0.605367i	$0.206973\pi$
$998$		0			0
$999$	169588.			0.169928

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.d.145.11		40
4.3	odd	2		152.5.n.a.145.10	yes	40
19.8	odd	6	inner	304.5.r.d.65.11		40
76.27	even	6		152.5.n.a.65.10	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.5.n.a.65.10	✓	40	76.27	even	6
152.5.n.a.145.10	yes	40	4.3	odd	2
304.5.r.d.65.11		40	19.8	odd	6	inner
304.5.r.d.145.11		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)

\(f(q)\)	\(=\)	\(q+(-0.620551 + 0.358275i) q^{3} +(16.9339 + 29.3305i) q^{5} -38.8265 q^{7} +(-40.2433 + 69.7034i) q^{9} +O(q^{10})\)	\(q+(-0.620551 + 0.358275i) q^{3} +(16.9339 + 29.3305i) q^{5} -38.8265 q^{7} +(-40.2433 + 69.7034i) q^{9} -37.5609 q^{11} +(-175.693 - 101.437i) q^{13} +(-21.0167 - 12.1340i) q^{15} +(-1.83186 - 3.17288i) q^{17} +(-56.3584 - 356.574i) q^{19} +(24.0938 - 13.9106i) q^{21} +(211.053 - 365.555i) q^{23} +(-261.017 + 452.095i) q^{25} -115.713i q^{27} +(385.100 + 222.337i) q^{29} -773.065i q^{31} +(23.3085 - 13.4571i) q^{33} +(-657.485 - 1138.80i) q^{35} +1465.59i q^{37} +145.369 q^{39} +(2324.61 - 1342.12i) q^{41} +(-116.536 - 201.846i) q^{43} -2725.91 q^{45} +(925.321 - 1602.70i) q^{47} -893.505 q^{49} +(2.27353 + 1.31262i) q^{51} +(-1868.52 - 1078.79i) q^{53} +(-636.054 - 1101.68i) q^{55} +(162.725 + 201.080i) q^{57} +(879.571 - 507.821i) q^{59} +(-301.488 + 522.192i) q^{61} +(1562.50 - 2706.34i) q^{63} -6870.88i q^{65} +(-5999.45 - 3463.78i) q^{67} +302.460i q^{69} +(-6252.28 + 3609.75i) q^{71} +(-3531.05 - 6115.97i) q^{73} -374.064i q^{75} +1458.36 q^{77} +(-5216.77 + 3011.91i) q^{79} +(-3218.25 - 5574.17i) q^{81} -1064.16 q^{83} +(62.0413 - 107.459i) q^{85} -318.632 q^{87} +(-1617.25 - 933.720i) q^{89} +(6821.55 + 3938.42i) q^{91} +(276.970 + 479.726i) q^{93} +(9504.09 - 7691.22i) q^{95} +(-1210.89 + 699.109i) q^{97} +(1511.57 - 2618.12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) \) 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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