LMFDB - Embedded newform 304.5.r.d.145.17

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			145.17
Character	$\chi$	$=$	304.145
Dual form			304.5.r.d.65.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.7629 - 6.21398i) q^{3} +(20.5828 + 35.6505i) q^{5} -44.5677 q^{7} +(36.7272 - 63.6134i) q^{9} +O(q^{10})$	\(q+(10.7629 - 6.21398i) q^{3} +(20.5828 + 35.6505i) q^{5} -44.5677 q^{7} +(36.7272 - 63.6134i) q^{9} -201.791 q^{11} +(-5.67551 - 3.27675i) q^{13} +(443.063 + 255.803i) q^{15} +(274.839 + 476.034i) q^{17} +(200.767 + 300.023i) q^{19} +(-479.679 + 276.943i) q^{21} +(-75.0694 + 130.024i) q^{23} +(-534.805 + 926.310i) q^{25} +93.7766i q^{27} +(236.163 + 136.349i) q^{29} -1734.05i q^{31} +(-2171.87 + 1253.93i) q^{33} +(-917.329 - 1588.86i) q^{35} +280.350i q^{37} -81.4468 q^{39} +(-1519.80 + 877.456i) q^{41} +(1241.48 + 2150.31i) q^{43} +3023.80 q^{45} +(-1645.29 + 2849.73i) q^{47} -414.720 q^{49} +(5916.14 + 3415.69i) q^{51} +(-657.198 - 379.434i) q^{53} +(-4153.43 - 7193.96i) q^{55} +(4025.18 + 1981.56i) q^{57} +(1629.06 - 940.536i) q^{59} +(2598.46 - 4500.67i) q^{61} +(-1636.85 + 2835.10i) q^{63} -269.779i q^{65} +(2729.68 + 1575.98i) q^{67} +1865.92i q^{69} +(-1059.75 + 611.845i) q^{71} +(-458.731 - 794.546i) q^{73} +13293.1i q^{75} +8993.37 q^{77} +(6245.99 - 3606.12i) q^{79} +(3557.63 + 6161.99i) q^{81} -7165.18 q^{83} +(-11313.9 + 19596.3i) q^{85} +3389.07 q^{87} +(-1019.11 - 588.384i) q^{89} +(252.944 + 146.037i) q^{91} +(-10775.4 - 18663.5i) q^{93} +(-6563.61 + 13332.8i) q^{95} +(4904.87 - 2831.83i) q^{97} +(-7411.23 + 12836.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	10.7629	−	6.21398i	1.19588	−	0.690443i	0.236247	−	0.971693i	$-0.424082\pi$
$3$	10.7629	−	6.21398i	1.19588	−	0.690443i	0.959634	+	0.281250i	$0.0907491\pi$
$4$		0			0
$5$	20.5828	+	35.6505i	0.823313	+	1.42602i	0.903202	+	0.429216i	$0.141210\pi$
$5$	20.5828	+	35.6505i	0.823313	+	1.42602i	−0.0798890	+	0.996804i	$0.525457\pi$
$6$		0			0
$7$	−44.5677			−0.909545			−0.454772	−	0.890608i	$-0.650279\pi$
$7$	−44.5677			−0.909545			−0.454772	+	0.890608i	$0.650279\pi$
$8$		0			0
$9$	36.7272	−	63.6134i	0.453422	−	0.785350i
$10$		0			0
$11$	−201.791			−1.66770			−0.833848	−	0.551994i	$-0.813867\pi$
$11$	−201.791			−1.66770			−0.833848	+	0.551994i	$0.813867\pi$
$12$		0			0
$13$	−5.67551	−	3.27675i	−0.0335829	−	0.0193891i	0.483115	−	0.875557i	$-0.339505\pi$
$13$	−5.67551	−	3.27675i	−0.0335829	−	0.0193891i	−0.516697	+	0.856168i	$0.672839\pi$
$14$		0			0
$15$	443.063	+	255.803i	1.96917	+	1.13690i
$16$		0			0
$17$	274.839	+	476.034i	0.950999	+	1.64718i	0.743270	+	0.668992i	$0.233274\pi$
$17$	274.839	+	476.034i	0.950999	+	1.64718i	0.207729	+	0.978186i	$0.433393\pi$
$18$		0			0
$19$	200.767	+	300.023i	0.556141	+	0.831088i
$19$	200.767	+	300.023i	0.556141	+	0.831088i
$20$		0			0
$21$	−479.679	+	276.943i	−1.08771	+	0.627989i
$22$		0			0
$23$	−75.0694	+	130.024i	−0.141908	+	0.245792i	−0.928215	−	0.372044i	$-0.878657\pi$
$23$	−75.0694	+	130.024i	−0.141908	+	0.245792i	0.786307	+	0.617836i	$0.211990\pi$
$24$		0			0
$25$	−534.805	+	926.310i	−0.855688	+	1.48210i
$26$		0			0
$27$			93.7766i			0.128637i
$28$		0			0
$29$	236.163	+	136.349i	0.280812	+	0.162127i	0.633791	−	0.773504i	$-0.281498\pi$
$29$	236.163	+	136.349i	0.280812	+	0.162127i	−0.352979	+	0.935631i	$0.614831\pi$
$30$		0			0
$31$		−	1734.05i		−	1.80443i	−0.431290	−	0.902213i	$-0.641941\pi$
$31$		−	1734.05i		−	1.80443i	0.431290	−	0.902213i	$-0.358059\pi$
$32$		0			0
$33$	−2171.87	+	1253.93i	−1.99437	+	1.15145i
$34$		0			0
$35$	−917.329	−	1588.86i	−0.748840	−	1.29703i
$36$		0			0
$37$			280.350i			0.204784i	0.994744	+	0.102392i	$0.0326497\pi$
$37$			280.350i			0.204784i	−0.994744	+	0.102392i	$0.967350\pi$
$38$		0			0
$39$	−81.4468			−0.0535482
$40$		0			0
$41$	−1519.80	+	877.456i	−0.904103	+	0.521984i	−0.878529	−	0.477689i	$-0.841475\pi$
$41$	−1519.80	+	877.456i	−0.904103	+	0.521984i	−0.0255741	+	0.999673i	$0.508141\pi$
$42$		0			0
$43$	1241.48	+	2150.31i	0.671433	+	1.16296i	0.977498	+	0.210945i	$0.0676542\pi$
$43$	1241.48	+	2150.31i	0.671433	+	1.16296i	−0.306065	+	0.952011i	$0.599012\pi$
$44$		0			0
$45$	3023.80			1.49323
$46$		0			0
$47$	−1645.29	+	2849.73i	−0.744814	+	1.29006i	0.205468	+	0.978664i	$0.434128\pi$
$47$	−1645.29	+	2849.73i	−0.744814	+	1.29006i	−0.950282	+	0.311391i	$0.899205\pi$
$48$		0			0
$49$	−414.720			−0.172728
$50$		0			0
$51$	5916.14	+	3415.69i	2.27456	+	1.31322i
$52$		0			0
$53$	−657.198	−	379.434i	−0.233962	−	0.135078i	0.378437	−	0.925627i	$-0.376462\pi$
$53$	−657.198	−	379.434i	−0.233962	−	0.135078i	−0.612398	+	0.790549i	$0.709795\pi$
$54$		0			0
$55$	−4153.43	−	7193.96i	−1.37304	−	2.37817i
$56$		0			0
$57$	4025.18	+	1981.56i	1.23890	+	0.609899i
$58$		0			0
$59$	1629.06	−	940.536i	0.467985	−	0.270191i	−0.247411	−	0.968911i	$-0.579580\pi$
$59$	1629.06	−	940.536i	0.467985	−	0.270191i	0.715396	+	0.698719i	$0.246246\pi$
$60$		0			0
$61$	2598.46	−	4500.67i	0.698323	−	1.20953i	−0.270724	−	0.962657i	$-0.587263\pi$
$61$	2598.46	−	4500.67i	0.698323	−	1.20953i	0.969047	−	0.246874i	$-0.0794035\pi$
$62$		0			0
$63$	−1636.85	+	2835.10i	−0.412408	+	0.714311i
$64$		0			0
$65$		−	269.779i		−	0.0638531i
$66$		0			0
$67$	2729.68	+	1575.98i	0.608082	+	0.351077i	0.772215	−	0.635362i	$-0.219149\pi$
$67$	2729.68	+	1575.98i	0.608082	+	0.351077i	−0.164132	+	0.986438i	$0.552482\pi$
$68$		0			0
$69$			1865.92i			0.391918i
$70$		0			0
$71$	−1059.75	+	611.845i	−0.210226	+	0.121374i	−0.601416	−	0.798936i	$-0.705397\pi$
$71$	−1059.75	+	611.845i	−0.210226	+	0.121374i	0.391191	+	0.920310i	$0.372063\pi$
$72$		0			0
$73$	−458.731	−	794.546i	−0.0860820	−	0.149098i	0.819770	−	0.572693i	$-0.194101\pi$
$73$	−458.731	−	794.546i	−0.0860820	−	0.149098i	−0.905852	+	0.423595i	$0.860768\pi$
$74$		0			0
$75$			13293.1i			2.36321i
$76$		0			0
$77$	8993.37			1.51684
$78$		0			0
$79$	6245.99	−	3606.12i	1.00080	−	0.577812i	0.0923145	−	0.995730i	$-0.470573\pi$
$79$	6245.99	−	3606.12i	1.00080	−	0.577812i	0.908485	+	0.417918i	$0.137240\pi$
$80$		0			0
$81$	3557.63	+	6161.99i	0.542239	+	0.939185i
$82$		0			0
$83$	−7165.18			−1.04009			−0.520045	−	0.854139i	$-0.674085\pi$
$83$	−7165.18			−1.04009			−0.520045	+	0.854139i	$0.674085\pi$
$84$		0			0
$85$	−11313.9	+	19596.3i	−1.56594	+	2.71229i
$86$		0			0
$87$	3389.07			0.447757
$88$		0			0
$89$	−1019.11	−	588.384i	−0.128659	−	0.0742816i	0.434289	−	0.900774i	$-0.357000\pi$
$89$	−1019.11	−	588.384i	−0.128659	−	0.0742816i	−0.562948	+	0.826492i	$0.690333\pi$
$90$		0			0
$91$	252.944	+	146.037i	0.0305451	+	0.0176352i
$92$		0			0
$93$	−10775.4	−	18663.5i	−1.24585	−	2.15788i
$94$		0			0
$95$	−6563.61	+	13332.8i	−0.727270	+	1.47731i
$96$		0			0
$97$	4904.87	−	2831.83i	0.521296	−	0.300970i	−0.216169	−	0.976356i	$-0.569356\pi$
$97$	4904.87	−	2831.83i	0.521296	−	0.300970i	0.737465	+	0.675386i	$0.236023\pi$
$98$		0			0
$99$	−7411.23	+	12836.6i	−0.756170	+	1.30973i
$100$		0			0
$101$	−5256.21	+	9104.02i	−0.515264	+	0.892464i	0.484579	+	0.874748i	$0.338973\pi$
$101$	−5256.21	+	9104.02i	−0.515264	+	0.892464i	−0.999843	+	0.0177162i	$0.994360\pi$
$102$		0			0
$103$			1448.51i			0.136536i	0.997667	+	0.0682682i	$0.0217474\pi$
$103$			1448.51i			0.136536i	−0.997667	+	0.0682682i	$0.978253\pi$
$104$		0			0
$105$	−19746.3	−	11400.5i	−1.79105	−	1.03406i
$106$		0			0
$107$		−	8776.50i		−	0.766573i	−0.923629	−	0.383287i	$-0.874792\pi$
$107$		−	8776.50i		−	0.766573i	0.923629	−	0.383287i	$-0.125208\pi$
$108$		0			0
$109$	19440.7	−	11224.1i	1.63628	−	0.944708i	0.654185	−	0.756335i	$-0.273012\pi$
$109$	19440.7	−	11224.1i	1.63628	−	0.944708i	0.982097	−	0.188373i	$-0.0603215\pi$
$110$		0			0
$111$	1742.09	+	3017.39i	0.141392	+	0.244898i
$112$		0			0
$113$		−	3573.35i		−	0.279846i	−0.990162	−	0.139923i	$-0.955315\pi$
$113$		−	3573.35i		−	0.279846i	0.990162	−	0.139923i	$-0.0446855\pi$
$114$		0			0
$115$	−6180.56			−0.467339
$116$		0			0
$117$	−416.891	+	240.692i	−0.0304544	+	0.0175829i
$118$		0			0
$119$	−12248.9	−	21215.8i	−0.864976	−	1.49818i
$120$		0			0
$121$	26078.7			1.78121
$122$		0			0
$123$	−10905.0	+	18888.0i	−0.720800	+	1.24846i
$124$		0			0
$125$	−18302.7			−1.17137
$126$		0			0
$127$	7354.87	+	4246.33i	0.456003	+	0.263273i	0.710362	−	0.703837i	$-0.248531\pi$
$127$	7354.87	+	4246.33i	0.456003	+	0.263273i	−0.254359	+	0.967110i	$0.581865\pi$
$128$		0			0
$129$	26723.9	+	15429.1i	1.60591	+	0.927172i
$130$		0			0
$131$	1734.52	+	3004.27i	0.101073	+	0.175064i	0.912127	−	0.409908i	$-0.134439\pi$
$131$	1734.52	+	3004.27i	0.101073	+	0.175064i	−0.811054	+	0.584971i	$0.801106\pi$
$132$		0			0
$133$	−8947.72	−	13371.3i	−0.505835	−	0.755912i
$134$		0			0
$135$	−3343.18	+	1930.19i	−0.183439	+	0.105909i
$136$		0			0
$137$	−10968.7	+	18998.4i	−0.584406	+	1.01222i	0.410543	+	0.911841i	$0.365339\pi$
$137$	−10968.7	+	18998.4i	−0.584406	+	1.01222i	−0.994949	+	0.100380i	$0.967994\pi$
$138$		0			0
$139$	9929.04	−	17197.6i	0.513899	−	0.890099i	−0.485971	−	0.873975i	$-0.661534\pi$
$139$	9929.04	−	17197.6i	0.513899	−	0.890099i	0.999870	−	0.0161240i	$-0.00513265\pi$
$140$		0			0
$141$			40895.3i			2.05700i
$142$		0			0
$143$	1145.27	+	661.220i	0.0560060	+	0.0323351i
$144$		0			0
$145$			11225.8i			0.533924i
$146$		0			0
$147$	−4463.61	+	2577.07i	−0.206563	+	0.119259i
$148$		0			0
$149$	−17534.3	−	30370.3i	−0.789797	−	1.36797i	−0.926091	−	0.377300i	$-0.876852\pi$
$149$	−17534.3	−	30370.3i	−0.789797	−	1.36797i	0.136294	−	0.990668i	$-0.456481\pi$
$150$		0			0
$151$		−	16956.9i		−	0.743692i	−0.928294	−	0.371846i	$-0.878725\pi$
$151$		−	16956.9i		−	0.743692i	0.928294	−	0.371846i	$-0.121275\pi$
$152$		0			0
$153$	40376.2			1.72482
$154$		0			0
$155$	61819.9	−	35691.7i	2.57315	−	1.48561i
$156$		0			0
$157$	9938.64	+	17214.2i	0.403207	+	0.698375i	0.994111	−	0.108367i	$-0.0345622\pi$
$157$	9938.64	+	17214.2i	0.403207	+	0.698375i	−0.590904	+	0.806742i	$0.701229\pi$
$158$		0			0
$159$	−9431.18			−0.373054
$160$		0			0
$161$	3345.67	−	5794.87i	0.129072	−	0.223559i
$162$		0			0
$163$	15584.3			0.586560			0.293280	−	0.956027i	$-0.405253\pi$
$163$	15584.3			0.586560			0.293280	+	0.956027i	$0.405253\pi$
$164$		0			0
$165$	−89406.3	−	51618.7i	−3.28398	−	1.89600i
$166$		0			0
$167$	8237.74	+	4756.06i	0.295376	+	0.170535i	0.640364	−	0.768072i	$-0.278784\pi$
$167$	8237.74	+	4756.06i	0.295376	+	0.170535i	−0.344988	+	0.938607i	$0.612117\pi$
$168$		0			0
$169$	−14259.0	−	24697.4i	−0.499248	−	0.864723i
$170$		0			0
$171$	26459.1	−	1752.47i	0.904862	−	0.0599319i
$172$		0			0
$173$	2067.16	−	1193.48i	0.0690689	−	0.0398770i	−0.465068	−	0.885275i	$-0.653970\pi$
$173$	2067.16	−	1193.48i	0.0690689	−	0.0398770i	0.534137	+	0.845398i	$0.320637\pi$
$174$		0			0
$175$	23835.0	−	41283.5i	0.778287	−	1.34803i
$176$		0			0
$177$	11688.9	−	20245.8i	0.373103	−	0.646233i
$178$		0			0
$179$			777.144i			0.0242547i	0.999926	+	0.0121273i	$0.00386035\pi$
$179$			777.144i			0.0242547i	−0.999926	+	0.0121273i	$0.996140\pi$
$180$		0			0
$181$	29545.3	+	17058.0i	0.901843	+	0.520679i	0.877798	−	0.479031i	$-0.159012\pi$
$181$	29545.3	+	17058.0i	0.901843	+	0.520679i	0.0240455	+	0.999711i	$0.492345\pi$
$182$		0			0
$183$		−	64587.2i		−	1.92861i
$184$		0			0
$185$	−9994.61	+	5770.39i	−0.292027	+	0.168602i
$186$		0			0
$187$	−55460.0	−	96059.6i	−1.58598	−	2.74699i
$188$		0			0
$189$		−	4179.41i		−	0.117001i
$190$		0			0
$191$	−10041.3			−0.275248			−0.137624	−	0.990485i	$-0.543947\pi$
$191$	−10041.3			−0.275248			−0.137624	+	0.990485i	$0.543947\pi$
$192$		0			0
$193$	42561.5	−	24572.9i	1.14262	−	0.659693i	0.195543	−	0.980695i	$-0.437353\pi$
$193$	42561.5	−	24572.9i	1.14262	−	0.659693i	0.947079	+	0.321002i	$0.104020\pi$
$194$		0			0
$195$	−1676.41	−	2903.62i	−0.0440869	−	0.0763608i
$196$		0			0
$197$	−3328.41			−0.0857639			−0.0428820	−	0.999080i	$-0.513654\pi$
$197$	−3328.41			−0.0857639			−0.0428820	+	0.999080i	$0.513654\pi$
$198$		0			0
$199$	5520.30	−	9561.44i	0.139398	−	0.241444i	−0.787871	−	0.615840i	$-0.788817\pi$
$199$	5520.30	−	9561.44i	0.139398	−	0.241444i	0.927269	+	0.374396i	$0.122150\pi$
$200$		0			0
$201$	39172.5			0.969593
$202$		0			0
$203$	−10525.2	−	6076.74i	−0.255411	−	0.147462i
$204$		0			0
$205$	−62563.5	−	36121.0i	−1.48872	−	0.859513i
$206$		0			0
$207$	5514.18	+	9550.83i	0.128689	+	0.222895i
$208$		0			0
$209$	−40513.0	−	60542.0i	−0.927474	−	1.38600i
$210$		0			0
$211$	−35581.9	+	20543.2i	−0.799216	+	0.461428i	−0.843197	−	0.537605i	$-0.819329\pi$
$211$	−35581.9	+	20543.2i	−0.799216	+	0.461428i	0.0439809	+	0.999032i	$0.485996\pi$
$212$		0			0
$213$	−7603.99	+	13170.5i	−0.167603	+	0.290297i
$214$		0			0
$215$	−51106.3	+	88518.7i	−1.10560	+	1.91495i
$216$		0			0
$217$			77282.8i			1.64121i
$218$		0			0
$219$	−9874.59	−	5701.10i	−0.205888	−	0.118869i
$220$		0			0
$221$		−	3602.32i		−	0.0737560i
$222$		0			0
$223$	−40784.7	+	23547.1i	−0.820140	+	0.473508i	−0.850465	−	0.526032i	$-0.823679\pi$
$223$	−40784.7	+	23547.1i	−0.820140	+	0.473508i	0.0303249	+	0.999540i	$0.490346\pi$
$224$		0			0
$225$	39283.8	+	68041.5i	0.775976	+	1.34403i
$226$		0			0
$227$			77284.8i			1.49983i	0.661534	+	0.749916i	$0.269906\pi$
$227$			77284.8i			1.49983i	−0.661534	+	0.749916i	$0.730094\pi$
$228$		0			0
$229$	35512.6			0.677192			0.338596	−	0.940932i	$-0.390048\pi$
$229$	35512.6			0.677192			0.338596	+	0.940932i	$0.390048\pi$
$230$		0			0
$231$	96795.1	−	55884.7i	1.81397	−	1.04729i
$232$		0			0
$233$	−26332.7	−	45609.5i	−0.485046	−	0.840125i	0.514806	−	0.857307i	$-0.327864\pi$
$233$	−26332.7	−	45609.5i	−0.485046	−	0.840125i	−0.999852	+	0.0171818i	$0.994531\pi$
$234$		0			0
$235$	−135459.			−2.45286
$236$		0			0
$237$	44816.8	−	77624.9i	0.797892	−	1.38199i
$238$		0			0
$239$	16249.6			0.284477			0.142238	−	0.989832i	$-0.454570\pi$
$239$	16249.6			0.284477			0.142238	+	0.989832i	$0.454570\pi$
$240$		0			0
$241$	−18086.9	−	10442.5i	−0.311409	−	0.179792i	0.336148	−	0.941809i	$-0.390876\pi$
$241$	−18086.9	−	10442.5i	−0.311409	−	0.179792i	−0.647557	+	0.762017i	$0.724209\pi$
$242$		0			0
$243$	70002.8	+	40416.1i	1.18550	+	0.684451i
$244$		0			0
$245$	−8536.12	−	14785.0i	−0.142209	−	0.246314i
$246$		0			0
$247$	−156.353	−	2360.64i	−0.00256279	−	0.0386934i
$248$		0			0
$249$	−77118.3	+	44524.3i	−1.24382	+	0.718122i
$250$		0			0
$251$	3178.47	−	5505.27i	0.0504511	−	0.0873839i	−0.839697	−	0.543055i	$-0.817267\pi$
$251$	3178.47	−	5505.27i	0.0504511	−	0.0873839i	0.890148	+	0.455671i	$0.150601\pi$
$252$		0			0
$253$	15148.3	−	26237.7i	0.236660	−	0.409906i
$254$		0			0
$255$			281218.i			4.32476i
$256$		0			0
$257$	103193.	+	59578.3i	1.56236	+	0.902031i	0.997017	+	0.0771781i	$0.0245910\pi$
$257$	103193.	+	59578.3i	1.56236	+	0.902031i	0.565347	+	0.824853i	$0.308742\pi$
$258$		0			0
$259$		−	12494.5i		−	0.186261i
$260$		0			0
$261$	17347.2	−	10015.4i	0.254653	−	0.147024i
$262$		0			0
$263$	66905.8	+	115884.i	0.967280	+	1.67538i	0.703360	+	0.710834i	$0.251682\pi$
$263$	66905.8	+	115884.i	0.967280	+	1.67538i	0.263920	+	0.964545i	$0.414984\pi$
$264$		0			0
$265$		−	31239.3i		−	0.444845i
$266$		0			0
$267$	−14624.8			−0.205149
$268$		0			0
$269$	43720.0	−	25241.7i	0.604193	−	0.348831i	−0.166497	−	0.986042i	$-0.553245\pi$
$269$	43720.0	−	25241.7i	0.604193	−	0.348831i	0.770689	+	0.637211i	$0.219912\pi$
$270$		0			0
$271$	−29815.1	−	51641.2i	−0.405973	−	0.703166i	0.588461	−	0.808526i	$-0.299734\pi$
$271$	−29815.1	−	51641.2i	−0.405973	−	0.703166i	−0.994434	+	0.105359i	$0.966401\pi$
$272$		0			0
$273$	3629.90			0.0487045
$274$		0			0
$275$	107919.	−	186921.i	1.42703	−	2.47168i
$276$		0			0
$277$	−131537.			−1.71430			−0.857150	−	0.515067i	$-0.827767\pi$
$277$	−131537.			−1.71430			−0.857150	+	0.515067i	$0.827767\pi$
$278$		0			0
$279$	−110309.	−	63686.9i	−1.41711	−	0.818167i
$280$		0			0
$281$	87139.7	+	50310.1i	1.10358	+	0.637152i	0.937159	−	0.348903i	$-0.113446\pi$
$281$	87139.7	+	50310.1i	1.10358	+	0.637152i	0.166420	+	0.986055i	$0.446779\pi$
$282$		0			0
$283$	−5780.54	−	10012.2i	−0.0721765	−	0.125013i	0.827678	−	0.561203i	$-0.189661\pi$
$283$	−5780.54	−	10012.2i	−0.0721765	−	0.125013i	−0.899855	+	0.436189i	$0.856328\pi$
$284$		0			0
$285$	12205.8	+	184286.i	0.150272	+	2.26883i
$286$		0			0
$287$	67733.9	−	39106.2i	0.822323	−	0.474768i
$288$		0			0
$289$	−109312.	+	189334.i	−1.30880	+	2.26690i
$290$		0			0
$291$	35193.9	−	60957.6i	0.415605	−	0.719849i
$292$		0			0
$293$		−	154991.i		−	1.80539i	−0.430283	−	0.902694i	$-0.641586\pi$
$293$		−	154991.i		−	1.80539i	0.430283	−	0.902694i	$-0.358414\pi$
$294$		0			0
$295$	67061.1	+	38717.7i	0.770596	+	0.444904i
$296$		0			0
$297$		−	18923.3i		−	0.214528i
$298$		0			0
$299$	852.114	−	491.968i	0.00953136	−	0.00550294i
$300$		0			0
$301$	−55329.9	−	95834.2i	−0.610698	−	1.05776i
$302$		0			0
$303$			130648.i			1.42304i
$304$		0			0
$305$	213935.			2.29975
$306$		0			0
$307$	−135679.	+	78334.4i	−1.43958	+	0.831143i	−0.997820	−	0.0659887i	$-0.978980\pi$
$307$	−135679.	+	78334.4i	−1.43958	+	0.831143i	−0.441762	+	0.897132i	$0.645647\pi$
$308$		0			0
$309$	9001.05	+	15590.3i	0.0942706	+	0.163281i
$310$		0			0
$311$	−27583.4			−0.285186			−0.142593	−	0.989781i	$-0.545544\pi$
$311$	−27583.4			−0.285186			−0.142593	+	0.989781i	$0.545544\pi$
$312$		0			0
$313$	−15661.3	+	27126.1i	−0.159860	+	0.276885i	−0.934818	−	0.355127i	$-0.884437\pi$
$313$	−15661.3	+	27126.1i	−0.159860	+	0.276885i	0.774958	+	0.632012i	$0.217771\pi$
$314$		0			0
$315$	−134764.			−1.35816
$316$		0			0
$317$	−87806.7	−	50695.2i	−0.873794	−	0.504485i	−0.00518704	−	0.999987i	$-0.501651\pi$
$317$	−87806.7	−	50695.2i	−0.873794	−	0.504485i	−0.868607	+	0.495501i	$0.834984\pi$
$318$		0			0
$319$	−47655.6	−	27514.0i	−0.468309	−	0.270378i
$320$		0			0
$321$	−54537.0	−	94460.9i	−0.529275	−	0.916731i
$322$		0			0
$323$	−87642.6	+	178030.i	−0.840060	+	1.70643i
$324$		0			0
$325$	6070.58	−	3504.85i	0.0574729	−	0.0331820i
$326$		0			0
$327$	139492.	−	241608.i	1.30453	−	2.25952i
$328$		0			0
$329$	73326.9	−	127006.i	0.677441	−	1.17336i
$330$		0			0
$331$			127532.i			1.16403i	0.813179	+	0.582014i	$0.197735\pi$
$331$			127532.i			1.16403i	−0.813179	+	0.582014i	$0.802265\pi$
$332$		0			0
$333$	17834.0	+	10296.5i	0.160827	+	0.0928538i
$334$		0			0
$335$			129753.i			1.15618i
$336$		0			0
$337$	−3840.86	+	2217.52i	−0.0338196	+	0.0195258i	−0.516814	−	0.856097i	$-0.672882\pi$
$337$	−3840.86	+	2217.52i	−0.0338196	+	0.0195258i	0.482995	+	0.875623i	$0.339549\pi$
$338$		0			0
$339$	−22204.7	−	38459.7i	−0.193217	−	0.334662i
$340$		0			0
$341$			349917.i			3.00924i
$342$		0			0
$343$	125490.			1.06665
$344$		0			0
$345$	−66521.0	+	38405.9i	−0.558882	+	0.322671i
$346$		0			0
$347$	26142.1	+	45279.4i	0.217111	+	0.376047i	0.953923	−	0.300050i	$-0.0970034\pi$
$347$	26142.1	+	45279.4i	0.217111	+	0.376047i	−0.736813	+	0.676097i	$0.763670\pi$
$348$		0			0
$349$	48987.9			0.402196			0.201098	−	0.979571i	$-0.435549\pi$
$349$	48987.9			0.402196			0.201098	+	0.979571i	$0.435549\pi$
$350$		0			0
$351$	307.283	−	532.230i	0.00249416	−	0.00432001i
$352$		0			0
$353$	97459.2			0.782120			0.391060	−	0.920365i	$-0.372108\pi$
$353$	97459.2			0.782120			0.391060	+	0.920365i	$0.372108\pi$
$354$		0			0
$355$	−43625.2	−	25187.0i	−0.346163	−	0.199857i
$356$		0			0
$357$	−263669.	−	152229.i	−2.06882	−	1.19443i
$358$		0			0
$359$	−90147.6	−	156140.i	−0.699464	−	1.21151i	−0.968652	−	0.248420i	$-0.920089\pi$
$359$	−90147.6	−	156140.i	−0.699464	−	1.21151i	0.269188	−	0.963088i	$-0.413245\pi$
$360$		0			0
$361$	−49706.3	+	120469.i	−0.381414	+	0.924404i
$362$		0			0
$363$	280683.	−	162053.i	2.13012	−	1.22982i
$364$		0			0
$365$	18884.0	−	32708.0i	0.141745	−	0.245509i
$366$		0			0
$367$	49062.0	−	84977.8i	0.364261	−	0.630919i	−0.624396	−	0.781108i	$-0.714655\pi$
$367$	49062.0	−	84977.8i	0.364261	−	0.630919i	0.988657	+	0.150189i	$0.0479882\pi$
$368$		0			0
$369$			128906.i			0.946717i
$370$		0			0
$371$	29289.8	+	16910.5i	0.212799	+	0.122859i
$372$		0			0
$373$		−	209968.i		−	1.50916i	−0.656206	−	0.754582i	$-0.727840\pi$
$373$		−	209968.i		−	1.50916i	0.656206	−	0.754582i	$-0.272160\pi$
$374$		0			0
$375$	−196990.	+	113732.i	−1.40082	+	0.808764i
$376$		0			0
$377$	−893.562	−	1547.69i	−0.00628698	−	0.0108894i
$378$		0			0
$379$		−	178655.i		−	1.24376i	−0.783112	−	0.621880i	$-0.786369\pi$
$379$		−	178655.i		−	1.24376i	0.783112	−	0.621880i	$-0.213631\pi$
$380$		0			0
$381$	105547.			0.727100
$382$		0			0
$383$	95477.3	−	55123.9i	0.650883	−	0.375787i	−0.137912	−	0.990445i	$-0.544039\pi$
$383$	95477.3	−	55123.9i	0.650883	−	0.375787i	0.788794	+	0.614657i	$0.210706\pi$
$384$		0			0
$385$	185109.	+	320618.i	1.24884	+	2.16305i
$386$		0			0
$387$	182384.			1.21777
$388$		0			0
$389$	−70913.8	+	122826.i	−0.468632	+	0.811694i	−0.999357	−	0.0358497i	$-0.988586\pi$
$389$	−70913.8	+	122826.i	−0.468632	+	0.811694i	0.530725	+	0.847544i	$0.321920\pi$
$390$		0			0
$391$	−82527.9			−0.539818
$392$		0			0
$393$	37337.0	+	21556.5i	0.241743	+	0.139570i
$394$		0			0
$395$	257120.	+	148448.i	1.64794	+	0.951440i
$396$		0			0
$397$	22024.3	+	38147.2i	0.139740	+	0.242037i	0.927398	−	0.374076i	$-0.122040\pi$
$397$	22024.3	+	38147.2i	0.139740	+	0.242037i	−0.787658	+	0.616113i	$0.788707\pi$
$398$		0			0
$399$	−179393.	−	88313.7i	−1.12683	−	0.554731i
$400$		0			0
$401$	53250.9	−	30744.4i	0.331160	−	0.191195i	−0.325196	−	0.945647i	$-0.605430\pi$
$401$	53250.9	−	30744.4i	0.331160	−	0.191195i	0.656356	+	0.754451i	$0.272097\pi$
$402$		0			0
$403$	−5682.07	+	9841.63i	−0.0349862	+	0.0605978i
$404$		0			0
$405$	−146452.	+	253662.i	−0.892864	+	1.54649i
$406$		0			0
$407$		−	56572.2i		−	0.341518i
$408$		0			0
$409$	245356.	+	141656.i	1.46673	+	0.846817i	0.999307	−	0.0372168i	$-0.0118492\pi$
$409$	245356.	+	141656.i	1.46673	+	0.846817i	0.467423	+	0.884034i	$0.345183\pi$
$410$		0			0
$411$			272638.i			1.61400i
$412$		0			0
$413$	−72603.2	+	41917.5i	−0.425653	+	0.245751i
$414$		0			0
$415$	−147480.	−	255442.i	−0.856319	−	1.48319i
$416$		0			0
$417$		−	246796.i		−	1.41927i
$418$		0			0
$419$	96918.9			0.552052			0.276026	−	0.961150i	$-0.410982\pi$
$419$	96918.9			0.552052			0.276026	+	0.961150i	$0.410982\pi$
$420$		0			0
$421$	−193076.	+	111473.i	−1.08934	+	0.628932i	−0.933401	−	0.358834i	$-0.883174\pi$
$421$	−193076.	+	111473.i	−1.08934	+	0.628932i	−0.155941	+	0.987766i	$0.549841\pi$
$422$		0			0
$423$	120854.	+	209325.i	0.675430	+	1.16988i
$424$		0			0
$425$	−587940.			−3.25503
$426$		0			0
$427$	−115807.	+	200584.i	−0.635156	+	1.10012i
$428$		0			0
$429$	16435.3			0.0893021
$430$		0			0
$431$	141619.	+	81763.6i	0.762370	+	0.440155i	0.830146	−	0.557546i	$-0.188257\pi$
$431$	141619.	+	81763.6i	0.762370	+	0.440155i	−0.0677758	+	0.997701i	$0.521590\pi$
$432$		0			0
$433$	236986.	+	136824.i	1.26400	+	0.729771i	0.973846	−	0.227208i	$-0.0729598\pi$
$433$	236986.	+	136824.i	1.26400	+	0.729771i	0.290155	+	0.956980i	$0.406293\pi$
$434$		0			0
$435$	69756.7	+	120822.i	0.368644	+	0.638510i
$436$		0			0
$437$	−54081.6	+	3582.00i	−0.283196	+	0.0187570i
$438$		0			0
$439$	67411.9	−	38920.3i	0.349790	−	0.201952i	−0.314803	−	0.949157i	$-0.601938\pi$
$439$	67411.9	−	38920.3i	0.349790	−	0.201952i	0.664593	+	0.747206i	$0.268605\pi$
$440$		0			0
$441$	−15231.5	+	26381.8i	−0.0783188	+	0.135652i
$442$		0			0
$443$	−59937.6	+	103815.i	−0.305416	+	0.528996i	−0.977354	−	0.211611i	$-0.932129\pi$
$443$	−59937.6	+	103815.i	−0.305416	+	0.528996i	0.671938	+	0.740608i	$0.265462\pi$
$444$		0			0
$445$		−	48442.4i		−	0.244628i
$446$		0			0
$447$	−377441.	−	217916.i	−1.88901	−	1.09062i
$448$		0			0
$449$		−	205693.i		−	1.02030i	−0.860087	−	0.510148i	$-0.829591\pi$
$449$		−	205693.i		−	1.02030i	0.860087	−	0.510148i	$-0.170409\pi$
$450$		0			0
$451$	306682.	−	177063.i	1.50777	−	0.870511i
$452$		0			0
$453$	−105370.	−	182506.i	−0.513477	−	0.889368i
$454$		0			0
$455$			12023.4i			0.0580773i
$456$		0			0
$457$	90733.5			0.434446			0.217223	−	0.976122i	$-0.430300\pi$
$457$	90733.5			0.434446			0.217223	+	0.976122i	$0.430300\pi$
$458$		0			0
$459$	−44640.9	+	25773.4i	−0.211889	+	0.122334i
$460$		0			0
$461$	123505.	+	213917.i	0.581144	+	1.00657i	0.995344	+	0.0963846i	$0.0307279\pi$
$461$	123505.	+	213917.i	0.581144	+	1.00657i	−0.414201	+	0.910186i	$0.635939\pi$
$462$		0			0
$463$	−264222.			−1.23256			−0.616278	−	0.787529i	$-0.711360\pi$
$463$	−264222.			−1.23256			−0.616278	+	0.787529i	$0.711360\pi$
$464$		0			0
$465$	443576.	−	768295.i	2.05145	−	3.55322i
$466$		0			0
$467$	−129467.			−0.593643			−0.296822	−	0.954933i	$-0.595927\pi$
$467$	−129467.			−0.593643			−0.296822	+	0.954933i	$0.595927\pi$
$468$		0			0
$469$	−121656.	−	70237.9i	−0.553078	−	0.319320i
$470$		0			0
$471$	213938.	+	123517.i	0.964375	+	0.556782i
$472$		0			0
$473$	−250520.	−	433913.i	−1.11975	−	1.93946i
$474$		0			0
$475$	−385285.	+	25518.7i	−1.70763	+	0.113102i
$476$		0			0
$477$	−48274.1	+	27871.1i	−0.212167	+	0.122495i
$478$		0			0
$479$	−100.338	+	173.791i	−0.000437315	+	0.000757452i	−0.866244	−	0.499621i	$-0.833473\pi$
$479$	−100.338	+	173.791i	−0.000437315	+	0.000757452i	0.865807	+	0.500379i	$0.166806\pi$
$480$		0			0
$481$	918.638	−	1591.13i	0.00397058	−	0.00687725i
$482$		0			0
$483$		−	83159.8i		−	0.356467i
$484$		0			0
$485$	201912.	+	116574.i	0.858379	+	0.495585i
$486$		0			0
$487$		−	43880.9i		−	0.185019i	−0.995712	−	0.0925097i	$-0.970511\pi$
$487$		−	43880.9i		−	0.185019i	0.995712	−	0.0925097i	$-0.0294889\pi$
$488$		0			0
$489$	167733.	−	96840.7i	0.701457	−	0.404986i
$490$		0			0
$491$	−110719.	−	191770.i	−0.459259	−	0.795461i	0.539663	−	0.841881i	$-0.318552\pi$
$491$	−110719.	−	191770.i	−0.459259	−	0.795461i	−0.998922	+	0.0464207i	$0.985219\pi$
$492$		0			0
$493$			149895.i			0.616729i
$494$		0			0
$495$	−610176.			−2.49026
$496$		0			0
$497$	47230.5	−	27268.5i	0.191210	−	0.110395i
$498$		0			0
$499$	135861.	+	235318.i	0.545624	+	0.945049i	0.998567	+	0.0535095i	$0.0170407\pi$
$499$	135861.	+	235318.i	0.545624	+	0.945049i	−0.452943	+	0.891539i	$0.649626\pi$
$500$		0			0
$501$	118216.			0.470980
$502$		0			0
$503$	−109778.	+	190141.i	−0.433890	+	0.751519i	−0.997204	−	0.0747237i	$-0.976193\pi$
$503$	−109778.	+	190141.i	−0.433890	+	0.751519i	0.563315	+	0.826242i	$0.309526\pi$
$504$		0			0
$505$	−432751.			−1.69689
$506$		0			0
$507$	−306938.	−	177211.i	−1.19408	−	0.689404i
$508$		0			0
$509$	71586.8	+	41330.7i	0.276311	+	0.159528i	0.631752	−	0.775171i	$-0.282336\pi$
$509$	71586.8	+	41330.7i	0.276311	+	0.159528i	−0.355441	+	0.934699i	$0.615669\pi$
$510$		0			0
$511$	20444.6	+	35411.1i	0.0782955	+	0.135612i
$512$		0			0
$513$	−28135.1	+	18827.2i	−0.106909	+	0.0715405i
$514$		0			0
$515$	−51640.3	+	29814.5i	−0.194704	+	0.112412i
$516$		0			0
$517$	332006.	−	575051.i	1.24212	−	2.15142i
$518$		0			0
$519$	14832.5	−	25690.7i	0.0550655	−	0.0953763i
$520$		0			0
$521$			176162.i			0.648987i	0.945888	+	0.324494i	$0.105194\pi$
$521$			176162.i			0.648987i	−0.945888	+	0.324494i	$0.894806\pi$
$522$		0			0
$523$	58279.2	+	33647.5i	0.213064	+	0.123013i	0.602735	−	0.797942i	$-0.294078\pi$
$523$	58279.2	+	33647.5i	0.213064	+	0.123013i	−0.389671	+	0.920954i	$0.627411\pi$
$524$		0			0
$525$		−	592442.i		−	2.14945i
$526$		0			0
$527$	825469.	−	476585.i	2.97221	−	1.71601i
$528$		0			0
$529$	128650.	+	222828.i	0.459724	+	0.796266i
$530$		0			0
$531$		−	138173.i		−	0.490043i
$532$		0			0
$533$	11500.8			0.0404832
$534$		0			0
$535$	312886.	−	180645.i	1.09315	−	0.631130i
$536$		0			0
$537$	4829.16	+	8364.35i	0.0167465	+	0.0290057i
$538$		0			0
$539$	83687.0			0.288058
$540$		0			0
$541$	54973.5	−	95216.9i	0.187827	−	0.325327i	−0.756698	−	0.653764i	$-0.773189\pi$
$541$	54973.5	−	95216.9i	0.187827	−	0.325327i	0.944526	+	0.328438i	$0.106522\pi$
$542$		0			0
$543$	423992.			1.43800
$544$		0			0
$545$	800288.	+	462046.i	2.69434	+	1.55558i
$546$		0			0
$547$	−233361.	−	134731.i	−0.779926	−	0.450291i	0.0564780	−	0.998404i	$-0.482013\pi$
$547$	−233361.	−	134731.i	−0.779926	−	0.450291i	−0.836404	+	0.548113i	$0.815346\pi$
$548$		0			0
$549$	−190868.	−	330594.i	−0.633270	−	1.09686i
$550$		0			0
$551$	6505.99	+	98228.5i	0.0214294	+	0.323545i
$552$		0			0
$553$	−278369.	+	160717.i	−0.910272	+	0.525546i
$554$		0			0
$555$	−71714.2	+	124213.i	−0.232820	+	0.403255i
$556$		0			0
$557$	160748.	−	278423.i	0.518125	−	0.897419i	−0.481653	−	0.876362i	$-0.659963\pi$
$557$	160748.	−	278423.i	0.518125	−	0.897419i	0.999778	−	0.0210574i	$-0.00670326\pi$
$558$		0			0
$559$		−	16272.1i		−	0.0520739i
$560$		0			0
$561$	−1.19383e6	−	689255.i	−3.79328	−	2.19005i
$562$		0			0
$563$			160295.i			0.505712i	0.967504	+	0.252856i	$0.0813698\pi$
$563$			160295.i			0.505712i	−0.967504	+	0.252856i	$0.918630\pi$
$564$		0			0
$565$	127392.	−	73549.6i	0.399066	−	0.230401i
$566$		0			0
$567$	−158555.	−	274626.i	−0.493191	−	0.854231i
$568$		0			0
$569$			316400.i			0.977264i	0.872490	+	0.488632i	$0.162504\pi$
$569$			316400.i			0.977264i	−0.872490	+	0.488632i	$0.837496\pi$
$570$		0			0
$571$	−285002.			−0.874131			−0.437065	−	0.899430i	$-0.643982\pi$
$571$	−285002.			−0.874131			−0.437065	+	0.899430i	$0.643982\pi$
$572$		0			0
$573$	−108074.	+	62396.6i	−0.329164	+	0.190043i
$574$		0			0
$575$	−80295.0	−	139075.i	−0.242858	−	0.420643i
$576$		0			0
$577$	−378157.			−1.13585			−0.567924	−	0.823081i	$-0.692253\pi$
$577$	−378157.			−1.13585			−0.567924	+	0.823081i	$0.692253\pi$
$578$		0			0
$579$	305391.	−	528953.i	0.910961	−	1.57783i
$580$		0			0
$581$	319335.			0.946008
$582$		0			0
$583$	132617.	+	76566.4i	0.390177	+	0.225269i
$584$		0			0
$585$	−17161.6	−	9908.24i	−0.0501471	−	0.0289524i
$586$		0			0
$587$	280821.	+	486396.i	0.814992	+	1.41161i	0.909334	+	0.416067i	$0.136592\pi$
$587$	280821.	+	486396.i	0.814992	+	1.41161i	−0.0943423	+	0.995540i	$0.530075\pi$
$588$		0			0
$589$	520256.	−	348141.i	1.49964	−	1.00352i
$590$		0			0
$591$	−35823.5	+	20682.7i	−0.102564	+	0.0592151i
$592$		0			0
$593$	−79186.7	+	137155.i	−0.225187	+	0.390035i	−0.956375	−	0.292140i	$-0.905633\pi$
$593$	−79186.7	+	137155.i	−0.225187	+	0.390035i	0.731189	+	0.682175i	$0.238966\pi$
$594$		0			0
$595$	504235.	−	873360.i	1.42429	−	2.46695i
$596$		0			0
$597$		−	137212.i		−	0.384985i
$598$		0			0
$599$	400620.	+	231298.i	1.11655	+	0.644641i	0.940518	−	0.339743i	$-0.110340\pi$
$599$	400620.	+	231298.i	1.11655	+	0.644641i	0.176033	+	0.984384i	$0.443674\pi$
$600$		0			0
$601$		−	541788.i		−	1.49996i	−0.661460	−	0.749981i	$-0.730063\pi$
$601$		−	541788.i		−	1.49996i	0.661460	−	0.749981i	$-0.269937\pi$
$602$		0			0
$603$	200507.	−	115763.i	0.551436	−	0.318372i
$604$		0			0
$605$	536773.	+	929719.i	1.46649	+	2.54004i
$606$		0			0
$607$			254651.i			0.691142i	0.938393	+	0.345571i	$0.112315\pi$
$607$			254651.i			0.691142i	−0.938393	+	0.345571i	$0.887685\pi$
$608$		0			0
$609$	−151043.			−0.407255
$610$		0			0
$611$	18675.7	−	10782.4i	0.0500260	−	0.0288825i
$612$		0			0
$613$	111484.	+	193096.i	0.296682	+	0.513869i	0.975375	−	0.220554i	$-0.0707864\pi$
$613$	111484.	+	193096.i	0.296682	+	0.513869i	−0.678692	+	0.734423i	$0.737453\pi$
$614$		0			0
$615$	−897822.			−2.37378
$616$		0			0
$617$	−220727.	+	382310.i	−0.579808	+	1.00426i	0.415693	+	0.909505i	$0.363539\pi$
$617$	−220727.	+	382310.i	−0.579808	+	1.00426i	−0.995501	+	0.0947523i	$0.969794\pi$
$618$		0			0
$619$	364041.			0.950100			0.475050	−	0.879959i	$-0.342430\pi$
$619$	364041.			0.950100			0.475050	+	0.879959i	$0.342430\pi$
$620$		0			0
$621$	−12193.2	−	7039.75i	−0.0316180	−	0.0182547i
$622$		0			0
$623$	45419.5	+	26222.9i	0.117022	+	0.0675624i
$624$		0			0
$625$	−42467.3	−	73555.5i	−0.108716	−	0.188302i
$626$		0			0
$627$	−812246.	−	399862.i	−2.06610	−	1.01713i
$628$		0			0
$629$	−133456.	+	77051.0i	−0.337316	+	0.194750i
$630$		0			0
$631$	−38481.0	+	66651.0i	−0.0966468	+	0.167397i	−0.910295	−	0.413961i	$-0.864145\pi$
$631$	−38481.0	+	66651.0i	−0.0966468	+	0.167397i	0.813648	+	0.581358i	$0.197478\pi$
$632$		0			0
$633$	−255310.	+	442211.i	−0.637179	+	1.10363i
$634$		0			0
$635$			349606.i			0.867025i
$636$		0			0
$637$	2353.75	+	1358.94i	0.00580071	+	0.00334904i
$638$		0			0
$639$			89885.4i			0.220134i
$640$		0			0
$641$	240024.	−	138578.i	0.584170	−	0.337270i	−0.178619	−	0.983918i	$-0.557163\pi$
$641$	240024.	−	138578.i	0.584170	−	0.337270i	0.762789	+	0.646648i	$0.223830\pi$
$642$		0			0
$643$	73649.8	+	127565.i	0.178135	+	0.308539i	0.941242	−	0.337733i	$-0.109660\pi$
$643$	73649.8	+	127565.i	0.178135	+	0.308539i	−0.763107	+	0.646273i	$0.776327\pi$
$644$		0			0
$645$			1.27029e6i			3.05341i
$646$		0			0
$647$	−218686.			−0.522410			−0.261205	−	0.965283i	$-0.584120\pi$
$647$	−218686.			−0.522410			−0.261205	+	0.965283i	$0.584120\pi$
$648$		0			0
$649$	−328729.	+	189792.i	−0.780457	+	0.450597i
$650$		0			0
$651$	480234.	+	831790.i	1.13316	+	1.96269i
$652$		0			0
$653$	364695.			0.855270			0.427635	−	0.903952i	$-0.359347\pi$
$653$	364695.			0.855270			0.427635	+	0.903952i	$0.359347\pi$
$654$		0			0
$655$	−71402.5	+	123673.i	−0.166430	+	0.288264i
$656$		0			0
$657$	−67391.6			−0.156126
$658$		0			0
$659$	−636343.	−	367393.i	−1.46528	−	0.845980i	−0.466033	−	0.884768i	$-0.654317\pi$
$659$	−636343.	−	367393.i	−1.46528	−	0.845980i	−0.999247	+	0.0387877i	$0.987650\pi$
$660$		0			0
$661$	149494.	+	86310.3i	0.342153	+	0.197542i	0.661224	−	0.750189i	$-0.270037\pi$
$661$	149494.	+	86310.3i	0.342153	+	0.197542i	−0.319071	+	0.947731i	$0.603371\pi$
$662$		0			0
$663$	−22384.7	−	38771.5i	−0.0509243	−	0.0882034i
$664$		0			0
$665$	292525.	−	594210.i	0.661484	−	1.34368i
$666$		0			0
$667$	−35457.2	+	20471.2i	−0.0796989	+	0.0460142i
$668$		0			0
$669$	−292642.	+	506871.i	−0.653860	+	1.13252i
$670$		0			0
$671$	−524347.	+	908195.i	−1.16459	+	2.01713i
$672$		0			0
$673$		−	127306.i		−	0.281073i	−0.990075	−	0.140537i	$-0.955117\pi$
$673$		−	127306.i		−	0.281073i	0.990075	−	0.140537i	$-0.0448828\pi$
$674$		0			0
$675$	−86866.2	−	50152.2i	−0.190653	−	0.110073i
$676$		0			0
$677$			248368.i			0.541898i	0.962594	+	0.270949i	$0.0873375\pi$
$677$			248368.i			0.541898i	−0.962594	+	0.270949i	$0.912663\pi$
$678$		0			0
$679$	−218599.	+	126208.i	−0.474142	+	0.273746i
$680$		0			0
$681$	480246.	+	831811.i	1.03555	+	1.79362i
$682$		0			0
$683$		−	704222.i		−	1.50962i	−0.655942	−	0.754811i	$-0.727728\pi$
$683$		−	704222.i		−	1.50962i	0.655942	−	0.754811i	$-0.272272\pi$
$684$		0			0
$685$	−903069.			−1.92460
$686$		0			0
$687$	382220.	−	220675.i	0.809841	−	0.467562i
$688$		0			0
$689$	2486.62	+	4306.96i	0.00523807	+	0.00907260i
$690$		0			0
$691$	131652.			0.275722			0.137861	−	0.990452i	$-0.455977\pi$
$691$	131652.			0.275722			0.137861	+	0.990452i	$0.455977\pi$
$692$		0			0
$693$	330301.	−	572099.i	0.687771	−	1.19125i
$694$		0			0
$695$	817471.			1.69240
$696$		0			0
$697$	−835398.	−	482317.i	−1.71960	−	0.992813i
$698$		0			0
$699$	−566834.	−	327262.i	−1.16012	−	0.669793i
$700$		0			0
$701$	−114253.	−	197892.i	−0.232504	−	0.402709i	0.726040	−	0.687652i	$-0.241359\pi$
$701$	−114253.	−	197892.i	−0.232504	−	0.402709i	−0.958544	+	0.284943i	$0.908025\pi$
$702$		0			0
$703$	−84111.3	+	56285.0i	−0.170194	+	0.113889i
$704$		0			0
$705$	−1.45794e6	+	841741.i	−2.93333	+	1.69356i
$706$		0			0
$707$	234257.	−	405745.i	0.468656	−	0.811736i
$708$		0			0
$709$	13056.1	−	22613.8i	0.0259729	−	0.0449863i	−0.852747	−	0.522324i	$-0.825065\pi$
$709$	13056.1	−	22613.8i	0.0259729	−	0.0449863i	0.878720	+	0.477338i	$0.158398\pi$
$710$		0			0
$711$		−	529771.i		−	1.04797i
$712$		0			0
$713$	225469.	+	130174.i	0.443514	+	0.256063i
$714$		0			0
$715$			54439.1i			0.106488i
$716$		0			0
$717$	174893.	−	100975.i	0.340201	−	0.196415i
$718$		0			0
$719$	191859.	+	332310.i	0.371129	+	0.642815i	0.989740	−	0.142883i	$-0.0456373\pi$
$719$	191859.	+	332310.i	0.371129	+	0.642815i	−0.618610	+	0.785698i	$0.712304\pi$
$720$		0			0
$721$		−	64557.0i		−	0.124186i
$722$		0			0
$723$	−259558.			−0.496544
$724$		0			0
$725$	−252602.	+	145840.i	−0.480575	+	0.277460i
$726$		0			0
$727$	388898.	+	673591.i	0.735812	+	1.27446i	0.954366	+	0.298639i	$0.0965326\pi$
$727$	388898.	+	673591.i	0.735812	+	1.27446i	−0.218554	+	0.975825i	$0.570134\pi$
$728$		0			0
$729$	428245.			0.805819
$730$		0			0
$731$	−682413.	+	1.18197e6i	−1.27706	+	2.21194i
$732$		0			0
$733$	−493900.			−0.919245			−0.459623	−	0.888114i	$-0.652015\pi$
$733$	−493900.			−0.919245			−0.459623	+	0.888114i	$0.652015\pi$
$734$		0			0
$735$	−183747.	−	106087.i	−0.340131	−	0.196375i
$736$		0			0
$737$	−550826.	−	318020.i	−1.01410	−	0.585489i
$738$		0			0
$739$	−49544.6	−	85813.8i	−0.0907210	−	0.157133i	0.817094	−	0.576505i	$-0.195584\pi$
$739$	−49544.6	−	85813.8i	−0.0907210	−	0.157133i	−0.907815	+	0.419372i	$0.862250\pi$
$740$		0			0
$741$	−16351.8	−	24435.9i	−0.0297804	−	0.0445033i
$742$		0			0
$743$	311835.	−	180038.i	0.564868	−	0.326127i	−0.190229	−	0.981740i	$-0.560923\pi$
$743$	311835.	−	180038.i	0.564868	−	0.326127i	0.755097	+	0.655613i	$0.227590\pi$
$744$		0			0
$745$	721810.	−	1.25021e6i	1.30050	−	2.25253i
$746$		0			0
$747$	−263157.	+	455801.i	−0.471600	+	0.816835i
$748$		0			0
$749$			391148.i			0.697233i
$750$		0			0
$751$	769461.	+	444248.i	1.36429	+	0.787673i	0.990192	−	0.139716i	$-0.0446191\pi$
$751$	769461.	+	444248.i	1.36429	+	0.787673i	0.374098	+	0.927389i	$0.377952\pi$
$752$		0			0
$753$		−	79003.9i		−	0.139334i
$754$		0			0
$755$	604523.	−	349021.i	1.06052	−	0.612291i
$756$		0			0
$757$	181444.	+	314271.i	0.316630	+	0.548419i	0.979783	−	0.200065i	$-0.0641154\pi$
$757$	181444.	+	314271.i	0.316630	+	0.548419i	−0.663153	+	0.748484i	$0.730782\pi$
$758$		0			0
$759$		−	376526.i		−	0.653600i
$760$		0			0
$761$	966366.			1.66868			0.834338	−	0.551252i	$-0.185850\pi$
$761$	966366.			1.66868			0.834338	+	0.551252i	$0.185850\pi$
$762$		0			0
$763$	−866426.	+	500231.i	−1.48827	+	0.859254i
$764$		0			0
$765$	831056.	+	1.43943e6i	1.42006	+	2.45962i
$766$		0			0
$767$	−12327.6			−0.0209550
$768$		0			0
$769$	−84892.5	+	147038.i	−0.143554	+	0.248643i	−0.928833	−	0.370499i	$-0.879187\pi$
$769$	−84892.5	+	147038.i	−0.143554	+	0.248643i	0.785278	+	0.619143i	$0.212520\pi$
$770$		0			0
$771$	1.48087e6			2.49120
$772$		0			0
$773$	119326.	+	68892.9i	0.199699	+	0.115296i	0.596515	−	0.802602i	$-0.296552\pi$
$773$	119326.	+	68892.9i	0.199699	+	0.115296i	−0.396816	+	0.917898i	$0.629885\pi$
$774$		0			0
$775$	1.60627e6	+	927381.i	2.67433	+	1.54403i
$776$		0			0
$777$	−77640.9	−	134478.i	−0.128602	−	0.222746i
$778$		0			0
$779$	−568382.	−	279810.i	−0.936624	−	0.461092i
$780$		0			0
$781$	213848.	−	123465.i	0.350592	−	0.202415i
$782$		0			0
$783$	−12786.3	+	22146.5i	−0.0208555	+	0.0361229i
$784$		0			0
$785$	−409131.	+	708635.i	−0.663931	+	1.14996i
$786$		0			0
$787$		−	322446.i		−	0.520605i	−0.965527	−	0.260302i	$-0.916178\pi$
$787$		−	322446.i		−	0.520605i	0.965527	−	0.260302i	$-0.0838223\pi$
$788$		0			0
$789$	1.44021e6	+	831503.i	2.31351	+	1.33570i
$790$		0			0
$791$			159256.i			0.254532i
$792$		0			0
$793$	−29495.2	+	17029.0i	−0.0469034	+	0.0270797i
$794$		0			0
$795$	−194120.	−	336226.i	−0.307140	−	0.531982i
$796$		0			0
$797$		−	295134.i		−	0.464626i	−0.972641	−	0.232313i	$-0.925371\pi$
$797$		−	295134.i		−	0.464626i	0.972641	−	0.232313i	$-0.0746293\pi$
$798$		0			0
$799$	−1.80876e6			−2.83327
$800$		0			0
$801$	−74858.2	+	43219.4i	−0.116674	+	0.0673618i
$802$		0			0
$803$	92567.9	+	160332.i	0.143559	+	0.248651i
$804$		0			0
$805$	275453.			0.425066
$806$		0			0
$807$	313704.	−	543351.i	0.481695	−	0.834321i
$808$		0			0
$809$	1.28150e6			1.95804			0.979019	−	0.203770i	$-0.0653195\pi$
$809$	1.28150e6			1.95804			0.979019	+	0.203770i	$0.0653195\pi$
$810$		0			0
$811$	471028.	+	271948.i	0.716151	+	0.413470i	0.813334	−	0.581796i	$-0.197650\pi$
$811$	471028.	+	271948.i	0.716151	+	0.413470i	−0.0971833	+	0.995267i	$0.530983\pi$
$812$		0			0
$813$	−641796.	−	370541.i	−0.970992	−	0.560603i
$814$		0			0
$815$	320769.	+	555589.i	0.482923	+	0.836447i
$816$		0			0
$817$	−395892.	+	804182.i	−0.593107	+	1.20479i
$818$		0			0
$819$	18579.9	−	10727.1i	0.0276997	−	0.0159924i
$820$		0			0
$821$	−29907.7	+	51801.7i	−0.0443708	+	0.0768525i	−0.887358	−	0.461081i	$-0.847462\pi$
$821$	−29907.7	+	51801.7i	−0.0443708	+	0.0768525i	0.842987	+	0.537934i	$0.180795\pi$
$822$		0			0
$823$	378892.	−	656261.i	0.559392	−	0.968895i	−0.438155	−	0.898899i	$-0.644368\pi$
$823$	378892.	−	656261.i	0.559392	−	0.968895i	0.997547	−	0.0699959i	$-0.0222986\pi$
$824$		0			0
$825$		−	2.68243e6i		−	3.94112i
$826$		0			0
$827$	−976167.	−	563591.i	−1.42729	−	0.824048i	−0.430387	−	0.902644i	$-0.641623\pi$
$827$	−976167.	−	563591.i	−1.42729	−	0.824048i	−0.996907	+	0.0785962i	$0.974956\pi$
$828$		0			0
$829$		−	127248.i		−	0.185158i	−0.995705	−	0.0925789i	$-0.970489\pi$
$829$		−	127248.i		−	0.185158i	0.995705	−	0.0925789i	$-0.0295110\pi$
$830$		0			0
$831$	−1.41572e6	+	817366.i	−2.05010	+	1.18363i
$832$		0			0
$833$	−113981.	−	197421.i	−0.164264	−	0.284514i
$834$		0			0
$835$			391573.i			0.561616i
$836$		0			0
$837$	162614.			0.232117
$838$		0			0
$839$	−613546.	+	354231.i	−0.871612	+	0.503225i	−0.867884	−	0.496768i	$-0.834520\pi$
$839$	−613546.	+	354231.i	−0.871612	+	0.503225i	−0.00372839	+	0.999993i	$0.501187\pi$
$840$		0			0
$841$	−316459.	−	548122.i	−0.447430	−	0.774971i
$842$		0			0
$843$	1.25051e6			1.75967
$844$		0			0
$845$	586982.	−	1.01668e6i	0.822075	−	1.42388i
$846$		0			0
$847$	−1.16227e6			−1.62009
$848$		0			0
$849$	−124431.	−	71840.4i	−0.172629	−	0.0996674i
$850$		0			0
$851$	−36452.2	−	21045.7i	−0.0503344	−	0.0290606i
$852$		0			0
$853$	−441100.	−	764007.i	−0.606232	−	1.05002i	−0.991855	−	0.127368i	$-0.959347\pi$
$853$	−441100.	−	764007.i	−0.606232	−	1.05002i	0.385623	−	0.922656i	$-0.373986\pi$
$854$		0			0
$855$	607079.	+	907208.i	0.830448	+	1.24101i
$856$		0			0
$857$	798313.	−	460906.i	1.08695	−	0.627554i	0.154191	−	0.988041i	$-0.450723\pi$
$857$	798313.	−	460906.i	1.08695	−	0.627554i	0.932764	+	0.360488i	$0.117390\pi$
$858$		0			0
$859$	194147.	−	336273.i	0.263115	−	0.455728i	−0.703953	−	0.710246i	$-0.748584\pi$
$859$	194147.	−	336273.i	0.263115	−	0.455728i	0.967068	+	0.254518i	$0.0819169\pi$
$860$		0			0
$861$	486010.	−	841795.i	0.655600	−	1.13553i
$862$		0			0
$863$		−	832764.i		−	1.11815i	−0.829117	−	0.559075i	$-0.811156\pi$
$863$		−	832764.i		−	1.11815i	0.829117	−	0.559075i	$-0.188844\pi$
$864$		0			0
$865$	85096.2	+	49130.3i	0.113731	+	0.0656625i
$866$		0			0
$867$			2.71705e6i			3.61460i
$868$		0			0
$869$	−1.26039e6	+	727684.i	−1.66903	+	0.963614i
$870$		0			0
$871$	−10328.2	−	17889.0i	−0.0136141	−	0.0235803i
$872$		0			0
$873$		−	416020.i		−	0.545866i
$874$		0			0
$875$	815708.			1.06541
$876$		0			0
$877$	−95547.1	+	55164.2i	−0.124228	+	0.0717229i	−0.560826	−	0.827934i	$-0.689516\pi$
$877$	−95547.1	+	55164.2i	−0.124228	+	0.0717229i	0.436598	+	0.899656i	$0.356183\pi$
$878$		0			0
$879$	−963110.	−	1.66816e6i	−1.24652	−	2.15903i
$880$		0			0
$881$	−722867.			−0.931336			−0.465668	−	0.884959i	$-0.654186\pi$
$881$	−722867.			−0.931336			−0.465668	+	0.884959i	$0.654186\pi$
$882$		0			0
$883$	−510226.	+	883737.i	−0.654396	+	1.13345i	0.327648	+	0.944800i	$0.393744\pi$
$883$	−510226.	+	883737.i	−0.654396	+	1.13345i	−0.982045	+	0.188648i	$0.939589\pi$
$884$		0			0
$885$	962366.			1.22872
$886$		0			0
$887$	393397.	+	227128.i	0.500016	+	0.288684i	0.728720	−	0.684812i	$-0.240116\pi$
$887$	393397.	+	227128.i	0.500016	+	0.288684i	−0.228704	+	0.973496i	$0.573449\pi$
$888$		0			0
$889$	−327789.	−	189249.i	−0.414755	−	0.239459i
$890$		0			0
$891$	−717898.	−	1.24344e6i	−0.904290	−	1.56628i
$892$		0			0
$893$	−1.18530e6	+	78506.6i	−1.48637	+	0.0984471i
$894$		0			0
$895$	−27705.6	+	15995.8i	−0.0345877	+	0.0199692i
$896$		0			0
$897$	6114.16	−	10590.0i	0.00759892	−	0.0131617i
$898$		0			0
$899$	236436.	−	409519.i	0.292546	−	0.506704i
$900$		0			0
$901$		−	417132.i		−	0.513835i
$902$		0			0
$903$	−1.19102e6	−	687638.i	−1.46065	−	0.843304i
$904$		0			0
$905$			1.40441e6i			1.71473i
$906$		0			0
$907$	−1.18350e6	+	683295.i	−1.43865	+	0.830603i	−0.997756	−	0.0669574i	$-0.978671\pi$
$907$	−1.18350e6	+	683295.i	−1.43865	+	0.830603i	−0.440891	+	0.897561i	$0.645338\pi$
$908$		0			0
$909$	386092.	+	668730.i	0.467264	+	0.809326i
$910$		0			0
$911$			1.49105e6i			1.79661i	0.439369	+	0.898306i	$0.355202\pi$
$911$			1.49105e6i			1.79661i	−0.439369	+	0.898306i	$0.644798\pi$
$912$		0			0
$913$	1.44587e6			1.73455
$914$		0			0
$915$	2.30256e6	−	1.32939e6i	2.75023	−	1.58785i
$916$		0			0
$917$	−77303.4	−	133893.i	−0.0919305	−	0.159228i
$918$		0			0
$919$	−813727.			−0.963492			−0.481746	−	0.876311i	$-0.659997\pi$
$919$	−813727.			−0.963492			−0.481746	+	0.876311i	$0.659997\pi$
$920$		0			0
$921$	−973538.	+	1.68622e6i	−1.14771	+	1.98790i
$922$		0			0
$923$	8019.47			0.00941330
$924$		0			0
$925$	−259691.	−	149933.i	−0.303510	−	0.175232i
$926$		0			0
$927$	92144.9	+	53199.9i	0.107229	+	0.0619086i
$928$		0			0
$929$	−423902.	−	734221.i	−0.491173	−	0.850737i	0.508775	−	0.860899i	$-0.330098\pi$
$929$	−423902.	−	734221.i	−0.491173	−	0.850737i	−0.999948	+	0.0101628i	$0.996765\pi$
$930$		0			0
$931$	−83262.2	−	124426.i	−0.0960613	−	0.143552i
$932$		0			0
$933$	−296879.	+	171403.i	−0.341048	+	0.196904i
$934$		0			0
$935$	2.28305e6	−	3.95435e6i	2.61151	−	4.52327i
$936$		0			0
$937$	231918.	−	401694.i	0.264153	−	0.457527i	−0.703188	−	0.711004i	$-0.748241\pi$
$937$	231918.	−	401694.i	0.264153	−	0.457527i	0.967341	+	0.253477i	$0.0815742\pi$
$938$		0			0
$939$			389276.i			0.441495i
$940$		0			0
$941$	−897345.	−	518082.i	−1.01340	−	0.585086i	−0.101214	−	0.994865i	$-0.532273\pi$
$941$	−897345.	−	518082.i	−1.01340	−	0.585086i	−0.912185	+	0.409779i	$0.865606\pi$
$942$		0			0
$943$		−	263480.i		−	0.296295i
$944$		0			0
$945$	148998.	−	86024.0i	0.166846	−	0.0963287i
$946$		0			0
$947$	437526.	+	757817.i	0.487870	+	0.845015i	0.999903	−	0.0139507i	$-0.00444078\pi$
$947$	437526.	+	757817.i	0.487870	+	0.845015i	−0.512033	+	0.858966i	$0.671107\pi$
$948$		0			0
$949$			6012.60i			0.00667621i
$950$		0			0
$951$	−1.26008e6			−1.39327
$952$		0			0
$953$	−44500.9	+	25692.6i	−0.0489985	+	0.0282893i	−0.524299	−	0.851534i	$-0.675673\pi$
$953$	−44500.9	+	25692.6i	−0.0489985	+	0.0282893i	0.475301	+	0.879823i	$0.342339\pi$
$954$		0			0
$955$	−206679.	−	357978.i	−0.226615	−	0.392509i
$956$		0			0
$957$	−683885.			−0.746722
$958$		0			0
$959$	488851.	−	846714.i	0.531544	−	0.920661i
$960$		0			0
$961$	−2.08342e6			−2.25596
$962$		0			0
$963$	−558303.	−	322336.i	−0.602028	−	0.347581i
$964$		0			0
$965$	1.75207e6	+	1.01156e6i	1.88147	+	1.08627i
$966$		0			0
$967$	392078.	+	679099.i	0.419295	+	0.726240i	0.995869	−	0.0908053i	$-0.0289441\pi$
$967$	392078.	+	679099.i	0.419295	+	0.726240i	−0.576574	+	0.817045i	$0.695611\pi$
$968$		0			0
$969$	162982.	+	2.46073e6i	0.173577	+	2.62070i
$970$		0			0
$971$	−1.05745e6	+	610521.i	−1.12156	+	0.647533i	−0.941799	−	0.336177i	$-0.890866\pi$
$971$	−1.05745e6	+	610521.i	−1.12156	+	0.647533i	−0.179761	+	0.983710i	$0.557533\pi$
$972$		0			0
$973$	−442514.	+	766457.i	−0.467414	+	0.809585i
$974$		0			0
$975$	43558.2	−	75445.0i	0.0458206	−	0.0793635i
$976$		0			0
$977$		−	1.82331e6i		−	1.91017i	−0.296337	−	0.955083i	$-0.595765\pi$
$977$		−	1.82331e6i		−	1.91017i	0.296337	−	0.955083i	$-0.404235\pi$
$978$		0			0
$979$	205648.	+	118731.i	0.214565	+	0.123879i
$980$		0			0
$981$		−	1.64892e6i		−	1.71341i
$982$		0			0
$983$	−403220.	+	232799.i	−0.417288	+	0.240921i	−0.693916	−	0.720056i	$-0.744116\pi$
$983$	−403220.	+	232799.i	−0.417288	+	0.240921i	0.276629	+	0.960977i	$0.410783\pi$
$984$		0			0
$985$	−68508.1	−	118660.i	−0.0706106	−	0.122301i
$986$		0			0
$987$		−	1.82261e6i		−	1.87094i
$988$		0			0
$989$	−372788.			−0.381127
$990$		0			0
$991$	1.21291e6	−	700274.i	1.23504	−	0.713051i	0.266964	−	0.963706i	$-0.413979\pi$
$991$	1.21291e6	−	700274.i	1.23504	−	0.713051i	0.968076	+	0.250655i	$0.0806460\pi$
$992$		0			0
$993$	792482.	+	1.37262e6i	0.803694	+	1.39204i
$994$		0			0
$995$	454494.			0.459073
$996$		0			0
$997$	−806934.	+	1.39765e6i	−0.811797	+	1.40607i	0.0998080	+	0.995007i	$0.468177\pi$
$997$	−806934.	+	1.39765e6i	−0.811797	+	1.40607i	−0.911605	+	0.411067i	$0.865156\pi$
$998$		0			0
$999$	−26290.3			−0.0263429

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.5.n.a.65.4	✓	40	76.27	even	6
152.5.n.a.145.4	yes	40	4.3	odd	2
304.5.r.d.65.17		40	19.8	odd	6	inner
304.5.r.d.145.17		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)

\(f(q)\)	\(=\)	\(q+(10.7629 - 6.21398i) q^{3} +(20.5828 + 35.6505i) q^{5} -44.5677 q^{7} +(36.7272 - 63.6134i) q^{9} +O(q^{10})\)	\(q+(10.7629 - 6.21398i) q^{3} +(20.5828 + 35.6505i) q^{5} -44.5677 q^{7} +(36.7272 - 63.6134i) q^{9} -201.791 q^{11} +(-5.67551 - 3.27675i) q^{13} +(443.063 + 255.803i) q^{15} +(274.839 + 476.034i) q^{17} +(200.767 + 300.023i) q^{19} +(-479.679 + 276.943i) q^{21} +(-75.0694 + 130.024i) q^{23} +(-534.805 + 926.310i) q^{25} +93.7766i q^{27} +(236.163 + 136.349i) q^{29} -1734.05i q^{31} +(-2171.87 + 1253.93i) q^{33} +(-917.329 - 1588.86i) q^{35} +280.350i q^{37} -81.4468 q^{39} +(-1519.80 + 877.456i) q^{41} +(1241.48 + 2150.31i) q^{43} +3023.80 q^{45} +(-1645.29 + 2849.73i) q^{47} -414.720 q^{49} +(5916.14 + 3415.69i) q^{51} +(-657.198 - 379.434i) q^{53} +(-4153.43 - 7193.96i) q^{55} +(4025.18 + 1981.56i) q^{57} +(1629.06 - 940.536i) q^{59} +(2598.46 - 4500.67i) q^{61} +(-1636.85 + 2835.10i) q^{63} -269.779i q^{65} +(2729.68 + 1575.98i) q^{67} +1865.92i q^{69} +(-1059.75 + 611.845i) q^{71} +(-458.731 - 794.546i) q^{73} +13293.1i q^{75} +8993.37 q^{77} +(6245.99 - 3606.12i) q^{79} +(3557.63 + 6161.99i) q^{81} -7165.18 q^{83} +(-11313.9 + 19596.3i) q^{85} +3389.07 q^{87} +(-1019.11 - 588.384i) q^{89} +(252.944 + 146.037i) q^{91} +(-10775.4 - 18663.5i) q^{93} +(-6563.61 + 13332.8i) q^{95} +(4904.87 - 2831.83i) q^{97} +(-7411.23 + 12836.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) \) 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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