LMFDB - Embedded newform 308.4.w.a.13.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,4,Mod(13,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("308.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	308.w (of order $10$, degree $4$, 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:	$18.1725882818$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.14
Character	$\chi$	$=$	308.13
Dual form			308.4.w.a.237.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.468867 + 0.645340i) q^{3} +(-18.3612 + 5.96593i) q^{5} +(-5.38402 + 17.7204i) q^{7} +(8.14683 - 25.0734i) q^{9} +(-14.5801 - 33.4428i) q^{11} +(-10.5017 + 32.3210i) q^{13} +(-12.4590 - 9.05201i) q^{15} +(-2.05129 - 6.31322i) q^{17} +(55.3638 - 40.2242i) q^{19} +(-13.9601 + 4.83398i) q^{21} +94.7185 q^{23} +(200.415 - 145.610i) q^{25} +(40.4840 - 13.1540i) q^{27} +(24.4042 - 33.5895i) q^{29} +(240.685 + 78.2034i) q^{31} +(14.7458 - 25.0893i) q^{33} +(-6.86141 - 357.489i) q^{35} +(-18.3996 - 13.3681i) q^{37} +(-25.7820 + 8.37706i) q^{39} +(-81.3985 + 59.1395i) q^{41} -530.645i q^{43} +508.981i q^{45} +(-159.397 - 219.391i) q^{47} +(-285.025 - 190.814i) q^{49} +(3.11239 - 4.28384i) q^{51} +(82.7565 - 254.698i) q^{53} +(467.226 + 527.067i) q^{55} +(51.9165 + 16.8687i) q^{57} +(-421.914 + 580.715i) q^{59} +(-168.728 - 519.292i) q^{61} +(400.447 + 279.360i) q^{63} -656.106i q^{65} +604.494 q^{67} +(44.4103 + 61.1256i) q^{69} +(-8.78097 - 27.0250i) q^{71} +(806.789 + 586.166i) q^{73} +(187.936 + 61.0642i) q^{75} +(671.119 - 78.3089i) q^{77} +(-293.262 - 95.2866i) q^{79} +(-548.404 - 398.439i) q^{81} +(-401.923 - 1236.99i) q^{83} +(75.3285 + 103.681i) q^{85} +33.1190 q^{87} -1130.18i q^{89} +(-516.200 - 360.112i) q^{91} +(62.3816 + 191.991i) q^{93} +(-776.574 + 1068.86i) q^{95} +(930.592 + 302.368i) q^{97} +(-957.305 + 93.1199i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 10 q^{7} + 168 q^{9} + 60 q^{11} - 192 q^{15} - 112 q^{23} + 548 q^{25} - 700 q^{29} - 940 q^{35} + 288 q^{37} + 460 q^{39} + 90 q^{49} - 1420 q^{51} - 2240 q^{53} + 560 q^{57} + 320 q^{63} + 4272 q^{67}+ \cdots - 10212 q^{99}+O(q^{100}) $ 96 * q - 10 * q^7 + 168 * q^9 + 60 * q^11 - 192 * q^15 - 112 * q^23 + 548 * q^25 - 700 * q^29 - 940 * q^35 + 288 * q^37 + 460 * q^39 + 90 * q^49 - 1420 * q^51 - 2240 * q^53 + 560 * q^57 + 320 * q^63 + 4272 * q^67 + 296 * q^71 + 430 * q^77 + 2100 * q^79 - 6088 * q^81 + 5900 * q^85 - 636 * q^91 - 2628 * q^93 + 780 * q^95 - 10212 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$	$1$

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
$3$	0.468867	+	0.645340i	0.0902334	+	0.124196i	0.851747	−	0.523953i	$-0.175543\pi$
$3$	0.468867	+	0.645340i	0.0902334	+	0.124196i	−0.761514	+	0.648149i	$0.775543\pi$
$4$		0			0
$5$	−18.3612	+	5.96593i	−1.64228	+	0.533609i	−0.977046	−	0.213028i	$-0.931668\pi$
$5$	−18.3612	+	5.96593i	−1.64228	+	0.533609i	−0.665232	+	0.746636i	$0.731668\pi$
$6$		0			0
$7$	−5.38402	+	17.7204i	−0.290709	+	0.956811i
$7$	−5.38402	+	17.7204i	−0.290709	+	0.956811i
$8$		0			0
$9$	8.14683	−	25.0734i	0.301735	−	0.928643i
$10$		0			0
$11$	−14.5801	−	33.4428i	−0.399643	−	0.916671i
$11$	−14.5801	−	33.4428i	−0.399643	−	0.916671i
$12$		0			0
$13$	−10.5017	+	32.3210i	−0.224051	+	0.689557i	0.774336	+	0.632775i	$0.218084\pi$
$13$	−10.5017	+	32.3210i	−0.224051	+	0.689557i	−0.998387	+	0.0567821i	$0.981916\pi$
$14$		0			0
$15$	−12.4590	−	9.05201i	−0.214460	−	0.155815i
$16$		0			0
$17$	−2.05129	−	6.31322i	−0.0292654	−	0.0900695i	0.935357	−	0.353705i	$-0.115078\pi$
$17$	−2.05129	−	6.31322i	−0.0292654	−	0.0900695i	−0.964622	+	0.263636i	$0.915078\pi$
$18$		0			0
$19$	55.3638	−	40.2242i	0.668491	−	0.485687i	−0.201029	−	0.979585i	$-0.564428\pi$
$19$	55.3638	−	40.2242i	0.668491	−	0.485687i	0.869520	+	0.493898i	$0.164428\pi$
$20$		0			0
$21$	−13.9601	+	4.83398i	−0.145064	+	0.0502315i
$22$		0			0
$23$	94.7185			0.858703			0.429351	−	0.903137i	$-0.358742\pi$
$23$	94.7185			0.858703			0.429351	+	0.903137i	$0.358742\pi$
$24$		0			0
$25$	200.415	−	145.610i	1.60332	−	1.16488i
$26$		0			0
$27$	40.4840	−	13.1540i	0.288561	−	0.0937591i
$28$		0			0
$29$	24.4042	−	33.5895i	0.156267	−	0.215083i	−0.723704	−	0.690111i	$-0.757562\pi$
$29$	24.4042	−	33.5895i	0.156267	−	0.215083i	0.879971	+	0.475027i	$0.157562\pi$
$30$		0			0
$31$	240.685	+	78.2034i	1.39446	+	0.453089i	0.907396	−	0.420276i	$-0.138067\pi$
$31$	240.685	+	78.2034i	1.39446	+	0.453089i	0.487067	+	0.873365i	$0.338067\pi$
$32$		0			0
$33$	14.7458	−	25.0893i	0.0777854	−	0.132348i
$34$		0			0
$35$	−6.86141	−	357.489i	−0.0331368	−	1.72648i
$36$		0			0
$37$	−18.3996	−	13.3681i	−0.0817535	−	0.0593974i	0.546158	−	0.837682i	$-0.316090\pi$
$37$	−18.3996	−	13.3681i	−0.0817535	−	0.0593974i	−0.627911	+	0.778285i	$0.716090\pi$
$38$		0			0
$39$	−25.7820	+	8.37706i	−0.105857	+	0.0343950i
$40$		0			0
$41$	−81.3985	+	59.1395i	−0.310056	+	0.225269i	−0.731921	−	0.681390i	$-0.761376\pi$
$41$	−81.3985	+	59.1395i	−0.310056	+	0.225269i	0.421864	+	0.906659i	$0.361376\pi$
$42$		0			0
$43$		−	530.645i		−	1.88192i	−0.338514	−	0.940961i	$-0.609924\pi$
$43$		−	530.645i		−	1.88192i	0.338514	−	0.940961i	$-0.390076\pi$
$44$		0			0
$45$			508.981i			1.68610i
$46$		0			0
$47$	−159.397	−	219.391i	−0.494690	−	0.680882i	0.486555	−	0.873650i	$-0.338253\pi$
$47$	−159.397	−	219.391i	−0.494690	−	0.680882i	−0.981244	+	0.192768i	$0.938253\pi$
$48$		0			0
$49$	−285.025	−	190.814i	−0.830976	−	0.556308i
$50$		0			0
$51$	3.11239	−	4.28384i	0.00854553	−	0.0117619i
$52$		0			0
$53$	82.7565	−	254.698i	0.214481	−	0.660104i	−0.784709	−	0.619864i	$-0.787188\pi$
$53$	82.7565	−	254.698i	0.214481	−	0.660104i	0.999190	−	0.0402398i	$-0.0128122\pi$
$54$		0			0
$55$	467.226	+	527.067i	1.14547	+	1.29218i
$56$		0			0
$57$	51.9165	+	16.8687i	0.120641	+	0.0391985i
$58$		0			0
$59$	−421.914	+	580.715i	−0.930992	+	1.28140i	0.0284796	+	0.999594i	$0.490933\pi$
$59$	−421.914	+	580.715i	−0.930992	+	1.28140i	−0.959471	+	0.281806i	$0.909067\pi$
$60$		0			0
$61$	−168.728	−	519.292i	−0.354155	−	1.08998i	−0.956498	−	0.291739i	$-0.905766\pi$
$61$	−168.728	−	519.292i	−0.354155	−	1.08998i	0.602343	−	0.798237i	$-0.294234\pi$
$62$		0			0
$63$	400.447	+	279.360i	0.800819	+	0.558668i
$64$		0			0
$65$		−	656.106i		−	1.25200i
$66$		0			0
$67$	604.494			1.10225			0.551124	−	0.834423i	$-0.314199\pi$
$67$	604.494			1.10225			0.551124	+	0.834423i	$0.314199\pi$
$68$		0			0
$69$	44.4103	+	61.1256i	0.0774837	+	0.106647i
$70$		0			0
$71$	−8.78097	−	27.0250i	−0.0146776	−	0.0451730i	0.943449	−	0.331516i	$-0.107560\pi$
$71$	−8.78097	−	27.0250i	−0.0146776	−	0.0451730i	−0.958127	+	0.286343i	$0.907560\pi$
$72$		0			0
$73$	806.789	+	586.166i	1.29353	+	0.939803i	0.999870	−	0.0161082i	$-0.00512761\pi$
$73$	806.789	+	586.166i	1.29353	+	0.939803i	0.293657	+	0.955911i	$0.405128\pi$
$74$		0			0
$75$	187.936	+	61.0642i	0.289347	+	0.0940145i
$76$		0			0
$77$	671.119	−	78.3089i	0.993261	−	0.115898i
$78$		0			0
$79$	−293.262	−	95.2866i	−0.417652	−	0.135704i	0.0926495	−	0.995699i	$-0.470466\pi$
$79$	−293.262	−	95.2866i	−0.417652	−	0.135704i	−0.510302	+	0.859995i	$0.670466\pi$
$80$		0			0
$81$	−548.404	−	398.439i	−0.752269	−	0.546555i
$82$		0			0
$83$	−401.923	−	1236.99i	−0.531527	−	1.63587i	−0.751035	−	0.660262i	$-0.770445\pi$
$83$	−401.923	−	1236.99i	−0.531527	−	1.63587i	0.219508	−	0.975611i	$-0.429555\pi$
$84$		0			0
$85$	75.3285	+	103.681i	0.0961237	+	0.132303i
$86$		0			0
$87$	33.1190			0.0408130
$88$		0			0
$89$		−	1130.18i		−	1.34606i	−0.739616	−	0.673029i	$-0.764993\pi$
$89$		−	1130.18i		−	1.34606i	0.739616	−	0.673029i	$-0.235007\pi$
$90$		0			0
$91$	−516.200	−	360.112i	−0.594642	−	0.414835i
$92$		0			0
$93$	62.3816	+	191.991i	0.0695556	+	0.214070i
$94$		0			0
$95$	−776.574	+	1068.86i	−0.838682	+	1.15435i
$96$		0			0
$97$	930.592	+	302.368i	0.974096	+	0.316503i	0.752468	−	0.658629i	$-0.228863\pi$
$97$	930.592	+	302.368i	0.974096	+	0.316503i	0.221627	+	0.975131i	$0.428863\pi$
$98$		0			0
$99$	−957.305	+	93.1199i	−0.971846	+	0.0945343i
$100$		0			0
$101$	252.863	−	778.231i	0.249116	−	0.766702i	−0.745816	−	0.666152i	$-0.767940\pi$
$101$	252.863	−	778.231i	0.249116	−	0.766702i	0.994932	−	0.100549i	$-0.0320600\pi$
$102$		0			0
$103$	−573.839	+	789.821i	−0.548952	+	0.755567i	−0.989869	−	0.141980i	$-0.954653\pi$
$103$	−573.839	+	789.821i	−0.548952	+	0.755567i	0.440918	+	0.897547i	$0.354653\pi$
$104$		0			0
$105$	227.485	−	172.043i	0.211431	−	0.159901i
$106$		0			0
$107$	102.709	+	141.367i	0.0927967	+	0.127724i	0.852891	−	0.522089i	$-0.174847\pi$
$107$	102.709	+	141.367i	0.0927967	+	0.127724i	−0.760094	+	0.649813i	$0.774847\pi$
$108$		0			0
$109$			1892.28i			1.66283i	0.555656	+	0.831413i	$0.312467\pi$
$109$			1892.28i			1.66283i	−0.555656	+	0.831413i	$0.687533\pi$
$110$		0			0
$111$		−	18.1419i		−	0.0155131i
$112$		0			0
$113$	1590.42	−	1155.51i	1.32402	−	0.961955i	0.324144	−	0.946008i	$-0.394924\pi$
$113$	1590.42	−	1155.51i	1.32402	−	0.961955i	0.999873	−	0.0159469i	$-0.00507629\pi$
$114$		0			0
$115$	−1739.15	+	565.083i	−1.41023	+	0.458211i
$116$		0			0
$117$	724.841	+	526.628i	0.572748	+	0.416126i
$118$		0			0
$119$	122.917	−	2.35919i	0.0946872	−	0.00181736i
$120$		0			0
$121$	−905.840	+	975.200i	−0.680571	+	0.732682i
$122$		0			0
$123$	−76.3301	−	24.8012i	−0.0559549	−	0.0181809i
$124$		0			0
$125$	−1392.69	+	1916.87i	−0.996529	+	1.37160i
$126$		0			0
$127$	−1488.68	+	483.701i	−1.04015	+	0.337964i	−0.778795	−	0.627279i	$-0.784169\pi$
$127$	−1488.68	+	483.701i	−1.04015	+	0.337964i	−0.261353	+	0.965243i	$0.584169\pi$
$128$		0			0
$129$	342.447	−	248.802i	0.233727	−	0.169812i
$130$		0			0
$131$	−1636.62			−1.09154			−0.545772	−	0.837934i	$-0.683764\pi$
$131$	−1636.62			−1.09154			−0.545772	+	0.837934i	$0.683764\pi$
$132$		0			0
$133$	414.709	+	1197.64i	0.270374	+	0.780814i
$134$		0			0
$135$	−664.859	+	483.049i	−0.423867	+	0.307957i
$136$		0			0
$137$	399.102	+	1228.31i	0.248887	+	0.765996i	0.994973	+	0.100146i	$0.0319310\pi$
$137$	399.102	+	1228.31i	0.248887	+	0.765996i	−0.746086	+	0.665850i	$0.768069\pi$
$138$		0			0
$139$	−723.947	−	525.978i	−0.441758	−	0.320956i	0.344575	−	0.938759i	$-0.388023\pi$
$139$	−723.947	−	525.978i	−0.441758	−	0.320956i	−0.786333	+	0.617803i	$0.788023\pi$
$140$		0			0
$141$	66.8458	−	205.730i	0.0399250	−	0.122877i
$142$		0			0
$143$	1234.02	−	120.037i	0.721637	−	0.0701957i
$144$		0			0
$145$	−247.699	+	762.339i	−0.141864	+	0.436612i
$146$		0			0
$147$	−10.4989	−	273.404i	−0.00589074	−	0.153401i
$148$		0			0
$149$	1554.36	−	505.041i	0.854617	−	0.277682i	0.151238	−	0.988497i	$-0.451674\pi$
$149$	1554.36	−	505.041i	0.854617	−	0.277682i	0.703378	+	0.710816i	$0.251674\pi$
$150$		0			0
$151$	1029.18	+	1416.55i	0.554659	+	0.763423i	0.990635	−	0.136535i	$-0.0435967\pi$
$151$	1029.18	+	1416.55i	0.554659	+	0.763423i	−0.435976	+	0.899958i	$0.643597\pi$
$152$		0			0
$153$	−175.005			−0.0924728
$154$		0			0
$155$	−4885.83			−2.53187
$156$		0			0
$157$	−1663.91	−	2290.18i	−0.845826	−	1.16418i	−0.984767	−	0.173879i	$-0.944370\pi$
$157$	−1663.91	−	2290.18i	−0.845826	−	1.16418i	0.138941	−	0.990301i	$-0.455630\pi$
$158$		0			0
$159$	203.169	−	66.0135i	0.101335	−	0.0329259i
$160$		0			0
$161$	−509.966	+	1678.45i	−0.249633	+	0.821617i
$162$		0			0
$163$	136.769	−	420.931i	0.0657212	−	0.202269i	−0.912803	−	0.408399i	$-0.866087\pi$
$163$	136.769	−	420.931i	0.0657212	−	0.202269i	0.978525	+	0.206130i	$0.0660871\pi$
$164$		0			0
$165$	−121.070	+	548.644i	−0.0571232	+	0.258860i
$166$		0			0
$167$	568.500	−	1749.66i	0.263424	−	0.810737i	−0.728628	−	0.684910i	$-0.759842\pi$
$167$	568.500	−	1749.66i	0.263424	−	0.810737i	0.992052	−	0.125827i	$-0.0401585\pi$
$168$		0			0
$169$	843.048	+	612.511i	0.383727	+	0.278794i
$170$		0			0
$171$	−557.516	−	1715.86i	−0.249323	−	0.767338i
$172$		0			0
$173$	865.198	−	628.603i	0.380230	−	0.276253i	−0.381210	−	0.924488i	$-0.624493\pi$
$173$	865.198	−	628.603i	0.380230	−	0.276253i	0.761440	+	0.648235i	$0.224493\pi$
$174$		0			0
$175$	1501.23	+	4335.41i	0.648472	+	1.87272i
$176$		0			0
$177$	−572.580			−0.243151
$178$		0			0
$179$	−1691.63	+	1229.04i	−0.706359	+	0.513200i	−0.881997	−	0.471255i	$-0.843801\pi$
$179$	−1691.63	+	1229.04i	−0.706359	+	0.513200i	0.175638	+	0.984455i	$0.443801\pi$
$180$		0			0
$181$	1407.03	−	457.173i	0.577812	−	0.187743i	−0.00550791	−	0.999985i	$-0.501753\pi$
$181$	1407.03	−	457.173i	0.577812	−	0.187743i	0.583320	+	0.812242i	$0.301753\pi$
$182$		0			0
$183$	256.009	−	352.366i	0.103414	−	0.142337i
$184$		0			0
$185$	417.593	+	135.684i	0.165957	+	0.0539227i
$186$		0			0
$187$	−181.224	+	160.648i	−0.0708684	+	0.0628223i
$188$		0			0
$189$	15.1284	+	788.213i	0.00582240	+	0.303355i
$190$		0			0
$191$	−41.0945	−	29.8569i	−0.0155680	−	0.0113108i	0.579974	−	0.814635i	$-0.303063\pi$
$191$	−41.0945	−	29.8569i	−0.0155680	−	0.0113108i	−0.595542	+	0.803324i	$0.703063\pi$
$192$		0			0
$193$	4379.13	−	1422.86i	1.63325	−	0.530674i	0.658231	−	0.752816i	$-0.271305\pi$
$193$	4379.13	−	1422.86i	1.63325	−	0.530674i	0.975014	+	0.222142i	$0.0713048\pi$
$194$		0			0
$195$	423.411	−	307.626i	0.155493	−	0.112972i
$196$		0			0
$197$		−	3571.77i		−	1.29177i	−0.763436	−	0.645883i	$-0.776489\pi$
$197$		−	3571.77i		−	1.29177i	0.763436	−	0.645883i	$-0.223511\pi$
$198$		0			0
$199$		−	4050.42i		−	1.44285i	−0.692494	−	0.721424i	$-0.743488\pi$
$199$		−	4050.42i		−	1.44285i	0.692494	−	0.721424i	$-0.256512\pi$
$200$		0			0
$201$	283.427	+	390.104i	0.0994597	+	0.136895i
$202$		0			0
$203$	463.827	+	613.299i	0.160366	+	0.212045i
$204$		0			0
$205$	1141.76	−	1571.49i	0.388993	−	0.535403i
$206$		0			0
$207$	771.655	−	2374.91i	0.259100	−	0.797429i
$208$		0			0
$209$	−2152.42	−	1265.05i	−0.712373	−	0.418685i
$210$		0			0
$211$	−27.5628	−	8.95570i	−0.00899291	−	0.00292197i	0.304517	−	0.952507i	$-0.401505\pi$
$211$	−27.5628	−	8.95570i	−0.00899291	−	0.00292197i	−0.313510	+	0.949585i	$0.601505\pi$
$212$		0			0
$213$	13.3232	−	18.3379i	0.00428588	−	0.00589901i
$214$		0			0
$215$	3165.79	+	9743.30i	1.00421	+	3.09064i
$216$		0			0
$217$	−2681.65	+	3843.99i	−0.838904	+	1.20252i
$218$		0			0
$219$			795.487i			0.245452i
$220$		0			0
$221$	225.592			0.0686650
$222$		0			0
$223$	18.8081	+	25.8871i	0.00564791	+	0.00777368i	0.811832	−	0.583892i	$-0.198471\pi$
$223$	18.8081	+	25.8871i	0.00564791	+	0.00777368i	−0.806184	+	0.591665i	$0.798471\pi$
$224$		0			0
$225$	−2018.19	−	6211.35i	−0.597983	−	1.84040i
$226$		0			0
$227$	−434.390	−	315.603i	−0.127011	−	0.0922788i	0.522466	−	0.852660i	$-0.325012\pi$
$227$	−434.390	−	315.603i	−0.127011	−	0.0922788i	−0.649477	+	0.760381i	$0.725012\pi$
$228$		0			0
$229$	−1097.91	−	356.732i	−0.316820	−	0.102941i	0.146290	−	0.989242i	$-0.453267\pi$
$229$	−1097.91	−	356.732i	−0.316820	−	0.102941i	−0.463110	+	0.886301i	$0.653267\pi$
$230$		0			0
$231$	365.201	+	396.383i	0.104019	+	0.112901i
$232$		0			0
$233$	−3136.67	−	1019.16i	−0.881931	−	0.286557i	−0.167172	−	0.985928i	$-0.553464\pi$
$233$	−3136.67	−	1019.16i	−0.881931	−	0.286557i	−0.714759	+	0.699371i	$0.753464\pi$
$234$		0			0
$235$	4235.59	+	3077.34i	1.17574	+	0.854227i
$236$		0			0
$237$	−76.0086	−	233.930i	−0.0208324	−	0.0641156i
$238$		0			0
$239$	−2416.19	−	3325.60i	−0.653934	−	0.900063i	0.345328	−	0.938482i	$-0.387768\pi$
$239$	−2416.19	−	3325.60i	−0.653934	−	0.900063i	−0.999262	+	0.0384195i	$0.987768\pi$
$240$		0			0
$241$	−4058.30			−1.08472			−0.542361	−	0.840145i	$-0.682470\pi$
$241$	−4058.30			−1.08472			−0.542361	+	0.840145i	$0.682470\pi$
$242$		0			0
$243$		−	1690.04i		−	0.446157i
$244$		0			0
$245$	6371.79	+	1803.14i	1.66154	+	0.470197i
$246$		0			0
$247$	718.670	+	2211.84i	0.185133	+	0.569781i
$248$		0			0
$249$	609.831	−	839.361i	0.155207	−	0.213624i
$250$		0			0
$251$	−39.2178	−	12.7426i	−0.00986216	−	0.00320441i	0.304082	−	0.952646i	$-0.401650\pi$
$251$	−39.2178	−	12.7426i	−0.00986216	−	0.00320441i	−0.313944	+	0.949442i	$0.601650\pi$
$252$		0			0
$253$	−1381.01	−	3167.65i	−0.343174	−	0.787148i
$254$		0			0
$255$	−31.5903	+	97.2249i	−0.00775788	+	0.0238763i
$256$		0			0
$257$	2172.20	−	2989.77i	0.527229	−	0.725668i	−0.459476	−	0.888190i	$-0.651963\pi$
$257$	2172.20	−	2989.77i	0.527229	−	0.725668i	0.986705	+	0.162522i	$0.0519628\pi$
$258$		0			0
$259$	335.952	−	254.075i	0.0805986	−	0.0609553i
$260$		0			0
$261$	−643.386	−	885.544i	−0.152585	−	0.210015i
$262$		0			0
$263$			1424.23i			0.333922i	0.985963	+	0.166961i	$0.0533954\pi$
$263$			1424.23i			0.333922i	−0.985963	+	0.166961i	$0.946605\pi$
$264$		0			0
$265$			5170.29i			1.19852i
$266$		0			0
$267$	729.352	−	529.905i	0.167175	−	0.121460i
$268$		0			0
$269$	6288.93	−	2043.40i	1.42544	−	0.463153i	0.508113	−	0.861290i	$-0.330343\pi$
$269$	6288.93	−	2043.40i	1.42544	−	0.463153i	0.917326	+	0.398137i	$0.130343\pi$
$270$		0			0
$271$	−2836.39	−	2060.76i	−0.635788	−	0.461927i	0.222612	−	0.974907i	$-0.428542\pi$
$271$	−2836.39	−	2060.76i	−0.635788	−	0.461927i	−0.858401	+	0.512980i	$0.828542\pi$
$272$		0			0
$273$	−9.63446	−	501.969i	−0.00213591	−	0.111284i
$274$		0			0
$275$	−7791.70	−	4579.44i	−1.70857	−	1.00418i
$276$		0			0
$277$	−1823.79	−	592.584i	−0.395598	−	0.128538i	0.104461	−	0.994529i	$-0.466688\pi$
$277$	−1823.79	−	592.584i	−0.395598	−	0.128538i	−0.500059	+	0.865991i	$0.666688\pi$
$278$		0			0
$279$	3921.65	−	5397.68i	0.841515	−	1.15825i
$280$		0			0
$281$	1832.92	−	595.551i	0.389120	−	0.126433i	−0.107922	−	0.994159i	$-0.534420\pi$
$281$	1832.92	−	595.551i	0.389120	−	0.126433i	0.497042	+	0.867727i	$0.334420\pi$
$282$		0			0
$283$	−1389.92	+	1009.83i	−0.291950	+	0.212114i	−0.724113	−	0.689681i	$-0.757751\pi$
$283$	−1389.92	+	1009.83i	−0.291950	+	0.212114i	0.432163	+	0.901796i	$0.357751\pi$
$284$		0			0
$285$	−1053.89			−0.219042
$286$		0			0
$287$	−609.724	−	1760.82i	−0.125404	−	0.362153i
$288$		0			0
$289$	3939.05	−	2861.89i	0.801761	−	0.582513i
$290$		0			0
$291$	241.194	+	742.318i	0.0485877	+	0.149538i
$292$		0			0
$293$	−623.201	−	452.782i	−0.124259	−	0.0902792i	0.523920	−	0.851767i	$-0.324469\pi$
$293$	−623.201	−	452.782i	−0.124259	−	0.0902792i	−0.648179	+	0.761488i	$0.724469\pi$
$294$		0			0
$295$	4282.36	−	13179.7i	0.845182	−	2.60120i
$296$		0			0
$297$	−1030.17	−	1162.11i	−0.201267	−	0.227045i
$298$		0			0
$299$	−994.708	+	3061.40i	−0.192393	+	0.592124i
$300$		0			0
$301$	9403.25	+	2857.00i	1.80064	+	0.547093i
$302$		0			0
$303$	620.782	−	201.704i	0.117700	−	0.0382429i
$304$		0			0
$305$	6196.12	+	8528.22i	1.16324	+	1.60106i
$306$		0			0
$307$	8618.72			1.60227			0.801134	−	0.598485i	$-0.204230\pi$
$307$	8618.72			1.60227			0.801134	+	0.598485i	$0.204230\pi$
$308$		0			0
$309$	−778.757			−0.143372
$310$		0			0
$311$	4594.02	+	6323.12i	0.837629	+	1.15290i	0.986455	+	0.164035i	$0.0524509\pi$
$311$	4594.02	+	6323.12i	0.837629	+	1.15290i	−0.148825	+	0.988864i	$0.547549\pi$
$312$		0			0
$313$	9437.86	−	3066.55i	1.70434	−	0.553775i	0.714968	−	0.699158i	$-0.246441\pi$
$313$	9437.86	−	3066.55i	1.70434	−	0.553775i	0.989375	+	0.145383i	$0.0464415\pi$
$314$		0			0
$315$	−9019.35	−	2740.36i	−1.61328	−	0.490165i
$316$		0			0
$317$	2289.05	−	7044.99i	0.405571	−	1.24822i	−0.514846	−	0.857283i	$-0.672151\pi$
$317$	2289.05	−	7044.99i	0.405571	−	1.24822i	0.920417	−	0.390938i	$-0.127849\pi$
$318$		0			0
$319$	−1479.14	−	326.406i	−0.259612	−	0.0572891i
$320$		0			0
$321$	−43.0727	+	132.564i	−0.00748936	+	0.0230499i
$322$		0			0
$323$	−367.511	−	267.013i	−0.0633092	−	0.0459969i
$324$		0			0
$325$	2601.56	+	8006.79i	0.444027	+	1.36658i
$326$		0			0
$327$	−1221.17	+	887.229i	−0.206516	+	0.150042i
$328$		0			0
$329$	4745.89	−	1643.37i	0.795287	−	0.275386i
$330$		0			0
$331$	3635.94			0.603775			0.301887	−	0.953344i	$-0.402383\pi$
$331$	3635.94			0.603775			0.301887	+	0.953344i	$0.402383\pi$
$332$		0			0
$333$	−485.082	+	352.433i	−0.0798269	+	0.0579976i
$334$		0			0
$335$	−11099.3	+	3606.37i	−1.81020	+	0.588170i
$336$		0			0
$337$	−4491.76	+	6182.38i	−0.726059	+	0.999334i	0.273242	+	0.961945i	$0.411904\pi$
$337$	−4491.76	+	6182.38i	−0.726059	+	0.999334i	−0.999301	+	0.0373887i	$0.988096\pi$
$338$		0			0
$339$	1491.39	+	484.581i	0.238941	+	0.0776367i
$340$		0			0
$341$	−893.880	−	9189.40i	−0.141954	−	1.45934i
$342$		0			0
$343$	4915.87	−	4023.41i	0.773855	−	0.633363i
$344$		0			0
$345$	−1180.10	−	857.392i	−0.184158	−	0.133798i
$346$		0			0
$347$	−2994.38	+	972.934i	−0.463247	+	0.150518i	−0.531336	−	0.847161i	$-0.678310\pi$
$347$	−2994.38	+	972.934i	−0.463247	+	0.150518i	0.0680888	+	0.997679i	$0.478310\pi$
$348$		0			0
$349$	−9263.27	+	6730.16i	−1.42078	+	1.03226i	−0.429136	+	0.903240i	$0.641182\pi$
$349$	−9263.27	+	6730.16i	−1.42078	+	1.03226i	−0.991643	+	0.129016i	$0.958818\pi$
$350$		0			0
$351$			1446.62i			0.219986i
$352$		0			0
$353$			2304.55i			0.347475i	0.984792	+	0.173737i	$0.0555844\pi$
$353$			2304.55i			0.347475i	−0.984792	+	0.173737i	$0.944416\pi$
$354$		0			0
$355$	322.459	+	443.827i	0.0482094	+	0.0663545i
$356$		0			0
$357$	59.1542	+	78.2171i	0.00876967	+	0.0115958i
$358$		0			0
$359$	2959.37	−	4073.22i	0.435068	−	0.598819i	−0.534039	−	0.845460i	$-0.679327\pi$
$359$	2959.37	−	4073.22i	0.435068	−	0.598819i	0.969107	+	0.246640i	$0.0793266\pi$
$360$		0			0
$361$	−672.379	+	2069.37i	−0.0980287	+	0.301701i
$362$		0			0
$363$	−1054.05	−	127.336i	−0.152406	−	0.0184116i
$364$		0			0
$365$	−18310.7	−	5949.50i	−2.62582	−	0.853180i
$366$		0			0
$367$	−5103.95	+	7024.99i	−0.725951	+	0.999186i	0.273354	+	0.961914i	$0.411867\pi$
$367$	−5103.95	+	7024.99i	−0.725951	+	0.999186i	−0.999305	+	0.0372726i	$0.988133\pi$
$368$		0			0
$369$	819.686	+	2522.73i	0.115640	+	0.355903i
$370$		0			0
$371$	4067.79	+	2837.78i	0.569243	+	0.397116i
$372$		0			0
$373$			4798.65i			0.666125i	0.942905	+	0.333062i	$0.108082\pi$
$373$			4798.65i			0.666125i	−0.942905	+	0.333062i	$0.891918\pi$
$374$		0			0
$375$	−1890.02			−0.260268
$376$		0			0
$377$	829.361	+	1141.52i	0.113300	+	0.155945i
$378$		0			0
$379$	−2246.27	−	6913.30i	−0.304441	−	0.936972i	−0.979885	−	0.199561i	$-0.936048\pi$
$379$	−2246.27	−	6913.30i	−0.304441	−	0.936972i	0.675445	−	0.737411i	$-0.263952\pi$
$380$		0			0
$381$	−1010.14	−	733.912i	−0.135830	−	0.0986862i
$382$		0			0
$383$	−10901.5	−	3542.12i	−1.45442	−	0.472569i	−0.528058	−	0.849208i	$-0.677080\pi$
$383$	−10901.5	−	3542.12i	−1.45442	−	0.472569i	−0.926360	+	0.376639i	$0.877080\pi$
$384$		0			0
$385$	−11855.4	+	5441.69i	−1.56937	+	0.720349i
$386$		0			0
$387$	−13305.1	−	4323.08i	−1.74763	−	0.567841i
$388$		0			0
$389$	8702.77	+	6322.93i	1.13431	+	0.824127i	0.986317	−	0.164861i	$-0.0527177\pi$
$389$	8702.77	+	6322.93i	1.13431	+	0.824127i	0.147996	+	0.988988i	$0.452718\pi$
$390$		0			0
$391$	−194.295	−	597.979i	−0.0251302	−	0.0773429i
$392$		0			0
$393$	−767.357	−	1056.18i	−0.0984938	−	0.135565i
$394$		0			0
$395$	5953.12			0.758314
$396$		0			0
$397$		−	8334.52i		−	1.05365i	−0.849975	−	0.526823i	$-0.823383\pi$
$397$		−	8334.52i		−	1.05365i	0.849975	−	0.526823i	$-0.176617\pi$
$398$		0			0
$399$	−578.439	+	829.160i	−0.0725769	+	0.104035i
$400$		0			0
$401$	−121.133	−	372.810i	−0.0150851	−	0.0464271i	0.943231	−	0.332138i	$-0.107770\pi$
$401$	−121.133	−	372.810i	−0.0150851	−	0.0464271i	−0.958316	+	0.285711i	$0.907770\pi$
$402$		0			0
$403$	−5055.23	+	6957.92i	−0.624861	+	0.860047i
$404$		0			0
$405$	12446.4	+	4044.09i	1.52708	+	0.496179i
$406$		0			0
$407$	−178.798	+	810.244i	−0.0217757	+	0.0986788i
$408$		0			0
$409$	−1264.73	+	3892.43i	−0.152902	+	0.470583i	−0.997942	−	0.0641194i	$-0.979576\pi$
$409$	−1264.73	+	3892.43i	−0.152902	+	0.470583i	0.845041	+	0.534702i	$0.179576\pi$
$410$		0			0
$411$	−605.551	+	833.469i	−0.0726755	+	0.100029i
$412$		0			0
$413$	−8018.90	−	10603.1i	−0.955410	−	1.26330i
$414$		0			0
$415$	14759.6	+	20314.8i	1.74583	+	2.40293i
$416$		0			0
$417$		−	713.806i		−	0.0838255i
$418$		0			0
$419$		−	2531.21i		−	0.295126i	−0.989053	−	0.147563i	$-0.952857\pi$
$419$		−	2531.21i		−	0.295126i	0.989053	−	0.147563i	$-0.0471429\pi$
$420$		0			0
$421$	−2815.60	+	2045.66i	−0.325948	+	0.236815i	−0.738709	−	0.674024i	$-0.764564\pi$
$421$	−2815.60	+	2045.66i	−0.325948	+	0.236815i	0.412761	+	0.910839i	$0.364564\pi$
$422$		0			0
$423$	−6799.45	+	2209.27i	−0.781561	+	0.253945i
$424$		0			0
$425$	−1330.38	−	966.578i	−0.151842	−	0.110320i
$426$		0			0
$427$	10110.5	−	194.054i	1.14586	−	0.0219928i
$428$		0			0
$429$	656.056	+	740.082i	0.0738338	+	0.0832902i
$430$		0			0
$431$	7530.41	+	2446.78i	0.841594	+	0.273450i	0.697921	−	0.716175i	$-0.254109\pi$
$431$	7530.41	+	2446.78i	0.841594	+	0.273450i	0.143673	+	0.989625i	$0.454109\pi$
$432$		0			0
$433$	3358.43	−	4622.48i	0.372739	−	0.513031i	−0.580904	−	0.813972i	$-0.697301\pi$
$433$	3358.43	−	4622.48i	0.372739	−	0.513031i	0.953643	+	0.300941i	$0.0973008\pi$
$434$		0			0
$435$	−608.105	+	197.585i	−0.0670263	+	0.0217781i
$436$		0			0
$437$	5243.98	−	3809.97i	0.574035	−	0.417061i
$438$		0			0
$439$	−6957.85			−0.756446			−0.378223	−	0.925714i	$-0.623465\pi$
$439$	−6957.85			−0.756446			−0.378223	+	0.925714i	$0.623465\pi$
$440$		0			0
$441$	−7106.39	+	5592.00i	−0.767346	+	0.603823i
$442$		0			0
$443$	−5124.98	+	3723.52i	−0.549651	+	0.399345i	−0.827657	−	0.561235i	$-0.810327\pi$
$443$	−5124.98	+	3723.52i	−0.549651	+	0.399345i	0.278006	+	0.960579i	$0.410327\pi$
$444$		0			0
$445$	6742.59	+	20751.6i	0.718269	+	2.21060i
$446$		0			0
$447$	1054.71	+	766.291i	0.111602	+	0.0810835i
$448$		0			0
$449$	4270.28	−	13142.6i	0.448835	−	1.38137i	−0.429387	−	0.903120i	$-0.641270\pi$
$449$	4270.28	−	13142.6i	0.448835	−	1.38137i	0.878222	−	0.478252i	$-0.158730\pi$
$450$		0			0
$451$	3164.59	+	1859.93i	0.330409	+	0.194192i
$452$		0			0
$453$	−431.605	+	1328.34i	−0.0447650	+	0.137773i
$454$		0			0
$455$	11626.5	+	3532.49i	1.19793	+	0.363968i
$456$		0			0
$457$	5398.38	−	1754.04i	0.552572	−	0.179542i	−0.0194042	−	0.999812i	$-0.506177\pi$
$457$	5398.38	−	1754.04i	0.552572	−	0.179542i	0.571976	+	0.820270i	$0.306177\pi$
$458$		0			0
$459$	−166.089	−	228.602i	−0.0168897	−	0.0232466i
$460$		0			0
$461$	−11380.7			−1.14979			−0.574895	−	0.818227i	$-0.694957\pi$
$461$	−11380.7			−1.14979			−0.574895	+	0.818227i	$0.694957\pi$
$462$		0			0
$463$	164.572			0.0165190			0.00825950	−	0.999966i	$-0.497371\pi$
$463$	164.572			0.0165190			0.00825950	+	0.999966i	$0.497371\pi$
$464$		0			0
$465$	−2290.81	−	3153.02i	−0.228459	−	0.314447i
$466$		0			0
$467$	4752.26	−	1544.10i	0.470896	−	0.153003i	−0.0639496	−	0.997953i	$-0.520370\pi$
$467$	4752.26	−	1544.10i	0.470896	−	0.153003i	0.534846	+	0.844950i	$0.320370\pi$
$468$		0			0
$469$	−3254.60	+	10711.9i	−0.320434	+	1.05464i
$470$		0			0
$471$	697.791	−	2147.58i	0.0682643	−	0.210096i
$472$		0			0
$473$	−17746.3	+	7736.87i	−1.72510	+	0.752097i
$474$		0			0
$475$	5238.71	−	16123.1i	0.506039	−	1.55743i
$476$		0			0
$477$	−5711.94	−	4149.97i	−0.548285	−	0.398352i
$478$		0			0
$479$	−1000.61	−	3079.57i	−0.0954472	−	0.293756i	0.891923	−	0.452188i	$-0.149356\pi$
$479$	−1000.61	−	3079.57i	−0.0954472	−	0.293756i	−0.987370	+	0.158432i	$0.949356\pi$
$480$		0			0
$481$	625.299	−	454.306i	0.0592748	−	0.0430657i
$482$		0			0
$483$	−1322.28	+	457.868i	−0.124567	+	0.0431340i
$484$		0			0
$485$	−18890.7			−1.76863
$486$		0			0
$487$	16816.3	−	12217.7i	1.56472	−	1.13683i	0.632715	−	0.774385i	$-0.281940\pi$
$487$	16816.3	−	12217.7i	1.56472	−	1.13683i	0.932003	−	0.362450i	$-0.118060\pi$
$488$		0			0
$489$	335.770	−	109.098i	0.0310512	−	0.0100891i
$490$		0			0
$491$	−6484.27	+	8924.83i	−0.595990	+	0.820310i	−0.995334	−	0.0964914i	$-0.969238\pi$
$491$	−6484.27	+	8924.83i	−0.595990	+	0.820310i	0.399344	+	0.916801i	$0.369238\pi$
$492$		0			0
$493$	−262.118	−	85.1674i	−0.0239457	−	0.00778042i
$494$		0			0
$495$	17021.8	−	7421.01i	1.54560	−	0.673837i
$496$		0			0
$497$	526.171	−	10.0990i	0.0474890	−	0.000911472i
$498$		0			0
$499$	−4330.11	−	3146.01i	−0.388461	−	0.282234i	0.376363	−	0.926472i	$-0.377174\pi$
$499$	−4330.11	−	3146.01i	−0.388461	−	0.282234i	−0.764825	+	0.644238i	$0.777174\pi$
$500$		0			0
$501$	1395.68	−	453.484i	0.124460	−	0.0404394i
$502$		0			0
$503$	−9006.52	+	6543.62i	−0.798372	+	0.580051i	−0.910436	−	0.413650i	$-0.864254\pi$
$503$	−9006.52	+	6543.62i	−0.798372	+	0.580051i	0.112064	+	0.993701i	$0.464254\pi$
$504$		0			0
$505$			15797.8i			1.39207i
$506$		0			0
$507$			831.239i			0.0728138i
$508$		0			0
$509$	−4731.11	−	6511.81i	−0.411990	−	0.567055i	0.551713	−	0.834034i	$-0.313974\pi$
$509$	−4731.11	−	6511.81i	−0.411990	−	0.567055i	−0.963702	+	0.266979i	$0.913974\pi$
$510$		0			0
$511$	−14730.9	+	11140.7i	−1.27525	+	0.964452i
$512$		0			0
$513$	1712.24	−	2356.69i	0.147363	−	0.202827i
$514$		0			0
$515$	5824.37	−	17925.6i	0.498354	−	1.53378i
$516$		0			0
$517$	−5013.02	+	8529.42i	−0.426446	+	0.725577i
$518$		0			0
$519$	811.325	+	263.615i	0.0686189	+	0.0222956i
$520$		0			0
$521$	−5048.63	+	6948.84i	−0.424538	+	0.584327i	−0.966689	−	0.255954i	$-0.917610\pi$
$521$	−5048.63	+	6948.84i	−0.424538	+	0.584327i	0.542150	+	0.840281i	$0.317610\pi$
$522$		0			0
$523$	7020.42	+	21606.6i	0.586963	+	1.80649i	0.591240	+	0.806496i	$0.298639\pi$
$523$	7020.42	+	21606.6i	0.586963	+	1.80649i	−0.00427704	+	0.999991i	$0.501361\pi$
$524$		0			0
$525$	−2093.93	+	3001.53i	−0.174070	+	0.249519i
$526$		0			0
$527$		−	1679.92i		−	0.138858i
$528$		0			0
$529$	−3195.41			−0.262629
$530$		0			0
$531$	11123.2	+	15309.8i	0.909051	+	1.25120i
$532$		0			0
$533$	−1056.62	−	3251.95i	−0.0858675	−	0.264273i
$534$		0			0
$535$	−2729.24	−	1982.91i	−0.220552	−	0.160241i
$536$		0			0
$537$	−1586.30	−	515.419i	−0.127474	−	0.0414189i
$538$		0			0
$539$	−2225.65	+	12314.1i	−0.177858	+	0.984056i
$540$		0			0
$541$	−8832.49	−	2869.85i	−0.701919	−	0.228067i	−0.0637526	−	0.997966i	$-0.520307\pi$
$541$	−8832.49	−	2869.85i	−0.701919	−	0.228067i	−0.638167	+	0.769898i	$0.720307\pi$
$542$		0			0
$543$	954.744	+	693.662i	0.0754548	+	0.0548211i
$544$		0			0
$545$	−11289.2	−	34744.7i	−0.887298	−	2.73082i
$546$		0			0
$547$	−2552.79	−	3513.62i	−0.199542	−	0.274646i	0.697506	−	0.716579i	$-0.254293\pi$
$547$	−2552.79	−	3513.62i	−0.199542	−	0.274646i	−0.897048	+	0.441933i	$0.854293\pi$
$548$		0			0
$549$	−14395.0			−1.11906
$550$		0			0
$551$		−	2841.28i		−	0.219678i
$552$		0			0
$553$	3267.44	−	4683.69i	0.251258	−	0.360164i
$554$		0			0
$555$	108.233	+	333.107i	0.00827791	+	0.0254768i
$556$		0			0
$557$	3170.16	−	4363.36i	0.241156	−	0.331923i	−0.671233	−	0.741246i	$-0.734235\pi$
$557$	3170.16	−	4363.36i	0.241156	−	0.331923i	0.912390	+	0.409323i	$0.134235\pi$
$558$		0			0
$559$	17151.0	+	5572.70i	1.29769	+	0.421646i
$560$		0			0
$561$	−188.643	−	41.6282i	−0.0141970	−	0.00313288i
$562$		0			0
$563$	2753.19	−	8473.45i	0.206098	−	0.634305i	−0.793568	−	0.608481i	$-0.791779\pi$
$563$	2753.19	−	8473.45i	0.206098	−	0.634305i	0.999667	−	0.0258237i	$-0.00822084\pi$
$564$		0			0
$565$	−22308.4	+	30704.8i	−1.66110	+	2.28630i
$566$		0			0
$567$	10013.1	−	7572.73i	0.741642	−	0.560891i
$568$		0			0
$569$	7187.86	+	9893.25i	0.529580	+	0.728904i	0.987066	−	0.160312i	$-0.0512502\pi$
$569$	7187.86	+	9893.25i	0.529580	+	0.728904i	−0.457486	+	0.889217i	$0.651250\pi$
$570$		0			0
$571$			9819.89i			0.719701i	0.933010	+	0.359851i	$0.117172\pi$
$571$			9819.89i			0.719701i	−0.933010	+	0.359851i	$0.882828\pi$
$572$		0			0
$573$		−	40.5188i		−	0.00295410i
$574$		0			0
$575$	18983.0	−	13792.0i	1.37678	−	1.00029i
$576$		0			0
$577$	9744.77	−	3166.27i	0.703085	−	0.228446i	0.0644110	−	0.997923i	$-0.479483\pi$
$577$	9744.77	−	3166.27i	0.703085	−	0.228446i	0.638674	+	0.769477i	$0.279483\pi$
$578$		0			0
$579$	2971.46	+	2158.89i	0.213281	+	0.154958i
$580$		0			0
$581$	24083.9	−	462.251i	1.71974	−	0.0330076i
$582$		0			0
$583$	−9724.42	+	945.922i	−0.690814	+	0.0671974i
$584$		0			0
$585$	−16450.8	−	5345.19i	−1.16266	−	0.377771i
$586$		0			0
$587$	−5759.30	+	7926.99i	−0.404960	+	0.557380i	−0.961980	−	0.273119i	$-0.911945\pi$
$587$	−5759.30	+	7926.99i	−0.404960	+	0.557380i	0.557020	+	0.830499i	$0.311945\pi$
$588$		0			0
$589$	16470.9	−	5351.73i	1.15225	−	0.374387i
$590$		0			0
$591$	2305.00	−	1674.68i	0.160432	−	0.116561i
$592$		0			0
$593$	−16537.1			−1.14519			−0.572595	−	0.819838i	$-0.694063\pi$
$593$	−16537.1			−1.14519			−0.572595	+	0.819838i	$0.694063\pi$
$594$		0			0
$595$	−2242.83	+	776.631i	−0.154533	+	0.0535106i
$596$		0			0
$597$	2613.90	−	1899.11i	0.179196	−	0.130193i
$598$		0			0
$599$	−7302.36	−	22474.3i	−0.498107	−	1.53302i	−0.812058	−	0.583577i	$-0.801653\pi$
$599$	−7302.36	−	22474.3i	−0.498107	−	1.53302i	0.313951	−	0.949439i	$-0.398347\pi$
$600$		0			0
$601$	7724.98	+	5612.53i	0.524307	+	0.380931i	0.818224	−	0.574900i	$-0.194959\pi$
$601$	7724.98	+	5612.53i	0.524307	+	0.380931i	−0.293917	+	0.955831i	$0.594959\pi$
$602$		0			0
$603$	4924.71	−	15156.7i	0.332587	−	1.02360i
$604$		0			0
$605$	10814.4	−	23310.0i	0.726722	−	1.56643i
$606$		0			0
$607$	897.436	−	2762.03i	0.0600096	−	0.184691i	−0.916558	−	0.399902i	$-0.869044\pi$
$607$	897.436	−	2762.03i	0.0600096	−	0.184691i	0.976567	+	0.215212i	$0.0690441\pi$
$608$		0			0
$609$	−178.313	+	586.881i	−0.0118647	+	0.0390503i
$610$		0			0
$611$	8764.88	−	2847.88i	0.580342	−	0.188565i
$612$		0			0
$613$	7403.26	+	10189.7i	0.487789	+	0.671384i	0.979978	−	0.199104i	$-0.0638031\pi$
$613$	7403.26	+	10189.7i	0.487789	+	0.671384i	−0.492189	+	0.870488i	$0.663803\pi$
$614$		0			0
$615$	1549.48			0.101595
$616$		0			0
$617$	−13684.1			−0.892873			−0.446437	−	0.894815i	$-0.647307\pi$
$617$	−13684.1			−0.892873			−0.446437	+	0.894815i	$0.647307\pi$
$618$		0			0
$619$	−15497.9	−	21331.0i	−1.00632	−	1.38508i	−0.921365	−	0.388699i	$-0.872925\pi$
$619$	−15497.9	−	21331.0i	−1.00632	−	1.38508i	−0.0849571	−	0.996385i	$-0.527075\pi$
$620$		0			0
$621$	3834.58	−	1245.93i	0.247788	−	0.0805112i
$622$		0			0
$623$	20027.3	+	6084.93i	1.28792	+	0.391312i
$624$		0			0
$625$	4566.60	−	14054.6i	0.292263	−	0.899492i
$626$		0			0
$627$	−192.812	−	1982.18i	−0.0122810	−	0.126253i
$628$		0			0
$629$	−46.6529	+	143.583i	−0.00295735	+	0.00910179i
$630$		0			0
$631$	10798.9	+	7845.84i	0.681294	+	0.494989i	0.873787	−	0.486309i	$-0.161657\pi$
$631$	10798.9	+	7845.84i	0.681294	+	0.494989i	−0.192493	+	0.981298i	$0.561657\pi$
$632$		0			0
$633$	−7.14382	−	21.9864i	−0.000448565	−	0.00138054i
$634$		0			0
$635$	24448.2	−	17762.7i	1.52787	−	1.11006i
$636$		0			0
$637$	9160.55	−	7208.42i	0.569787	−	0.448364i
$638$		0			0
$639$	−749.146			−0.0463783
$640$		0			0
$641$	−14093.3	+	10239.4i	−0.868410	+	0.630937i	−0.930160	−	0.367155i	$-0.880332\pi$
$641$	−14093.3	+	10239.4i	−0.868410	+	0.630937i	0.0617497	+	0.998092i	$0.480332\pi$
$642$		0			0
$643$	−9629.38	+	3128.77i	−0.590584	+	0.191892i	−0.589037	−	0.808106i	$-0.700493\pi$
$643$	−9629.38	+	3128.77i	−0.590584	+	0.191892i	−0.00154753	+	0.999999i	$0.500493\pi$
$644$		0			0
$645$	−4803.41	+	6611.32i	−0.293231	+	0.403598i
$646$		0			0
$647$	2385.76	+	775.179i	0.144967	+	0.0471027i	0.380602	−	0.924739i	$-0.375717\pi$
$647$	2385.76	+	775.179i	0.144967	+	0.0471027i	−0.235635	+	0.971842i	$0.575717\pi$
$648$		0			0
$649$	25572.3	+	5643.09i	1.54669	+	0.341311i
$650$		0			0
$651$	−3738.02	+	71.7450i	−0.225045	+	0.00431937i
$652$		0			0
$653$	5623.15	+	4085.46i	0.336984	+	0.244833i	0.743388	−	0.668860i	$-0.233217\pi$
$653$	5623.15	+	4085.46i	0.336984	+	0.244833i	−0.406404	+	0.913693i	$0.633217\pi$
$654$		0			0
$655$	30050.4	−	9763.96i	1.79262	−	0.582457i
$656$		0			0
$657$	21269.9	−	15453.5i	1.26304	−	0.917655i
$658$		0			0
$659$		−	16336.2i		−	0.965658i	−0.875715	−	0.482829i	$-0.839609\pi$
$659$		−	16336.2i		−	0.965658i	0.875715	−	0.482829i	$-0.160391\pi$
$660$		0			0
$661$		−	20076.9i		−	1.18139i	−0.806895	−	0.590695i	$-0.798853\pi$
$661$		−	20076.9i		−	1.18139i	0.806895	−	0.590695i	$-0.201147\pi$
$662$		0			0
$663$	105.773	+	145.583i	0.00619588	+	0.00852789i
$664$		0			0
$665$	−14759.6	−	19516.0i	−0.860679	−	1.13804i
$666$		0			0
$667$	2311.53	−	3181.55i	0.134187	−	0.184693i
$668$		0			0
$669$	−7.88750	+	24.2752i	−0.000455827	+	0.00140289i
$670$		0			0
$671$	−14906.5	+	13214.1i	−0.857614	+	0.760244i
$672$		0			0
$673$	7610.59	+	2472.83i	0.435909	+	0.141635i	0.518747	−	0.854928i	$-0.326398\pi$
$673$	7610.59	+	2472.83i	0.435909	+	0.141635i	−0.0828383	+	0.996563i	$0.526398\pi$
$674$		0			0
$675$	6198.25	−	8531.16i	0.353438	−	0.486466i
$676$		0			0
$677$	10346.5	+	31843.4i	0.587371	+	1.80774i	0.589534	+	0.807743i	$0.299311\pi$
$677$	10346.5	+	31843.4i	0.587371	+	1.80774i	−0.00216379	+	0.999998i	$0.500689\pi$
$678$		0			0
$679$	−10368.4	+	14862.5i	−0.586012	+	0.840015i
$680$		0			0
$681$		−	428.305i		−	0.0241008i
$682$		0			0
$683$	−784.541			−0.0439526			−0.0219763	−	0.999758i	$-0.506996\pi$
$683$	−784.541			−0.0439526			−0.0219763	+	0.999758i	$0.506996\pi$
$684$		0			0
$685$	−14656.0	−	20172.2i	−0.817484	−	1.12517i
$686$		0			0
$687$	−284.559	−	875.783i	−0.0158029	−	0.0486364i
$688$		0			0
$689$	7363.02	+	5349.55i	0.407124	+	0.295793i
$690$		0			0
$691$	−21954.6	−	7133.50i	−1.20867	−	0.392722i	−0.365729	−	0.930721i	$-0.619180\pi$
$691$	−21954.6	−	7133.50i	−1.20867	−	0.392722i	−0.842945	+	0.537999i	$0.819180\pi$
$692$		0			0
$693$	3504.03	−	17465.2i	0.192073	−	0.957356i
$694$		0			0
$695$	16430.5	+	5338.60i	0.896755	+	0.291373i
$696$		0			0
$697$	540.333	+	392.575i	0.0293638	+	0.0213340i
$698$		0			0
$699$	−812.971	−	2502.07i	−0.0439906	−	0.135389i
$700$		0			0
$701$	10815.2	+	14885.9i	0.582719	+	0.802044i	0.993990	−	0.109469i	$-0.0349150\pi$
$701$	10815.2	+	14885.9i	0.582719	+	0.802044i	−0.411271	+	0.911513i	$0.634915\pi$
$702$		0			0
$703$	−1556.40			−0.0835001
$704$		0			0
$705$			4176.26i			0.223102i
$706$		0			0
$707$	12429.1	+	8670.83i	0.661168	+	0.461245i
$708$		0			0
$709$	−3958.78	−	12183.9i	−0.209697	−	0.645380i	−0.999488	−	0.0320041i	$-0.989811\pi$
$709$	−3958.78	−	12183.9i	−0.209697	−	0.645380i	0.789791	−	0.613376i	$-0.210189\pi$
$710$		0			0
$711$	−4778.31	+	6576.78i	−0.252040	+	0.346904i
$712$		0			0
$713$	22797.3	+	7407.31i	1.19743	+	0.389068i
$714$		0			0
$715$	−21942.0	+	9566.11i	−1.14767	+	0.500353i
$716$		0			0
$717$	1013.27	−	3118.52i	0.0527772	−	0.162432i
$718$		0			0
$719$	−15122.5	+	20814.3i	−0.784387	+	1.07962i	0.210398	+	0.977616i	$0.432524\pi$
$719$	−15122.5	+	20814.3i	−0.784387	+	1.07962i	−0.994784	+	0.102000i	$0.967476\pi$
$720$		0			0
$721$	−10906.4	−	14421.1i	−0.563350	−	0.744894i
$722$		0			0
$723$	−1902.80	−	2618.98i	−0.0978783	−	0.134718i
$724$		0			0
$725$		−	10285.4i		−	0.526881i
$726$		0			0
$727$			13303.0i			0.678652i	0.940669	+	0.339326i	$0.110199\pi$
$727$			13303.0i			0.678652i	−0.940669	+	0.339326i	$0.889801\pi$
$728$		0			0
$729$	−13716.3	+	9965.44i	−0.696858	+	0.506297i
$730$		0			0
$731$	−3350.08	+	1088.51i	−0.169504	+	0.0550751i
$732$		0			0
$733$	−376.183	−	273.313i	−0.0189558	−	0.0137722i	0.578267	−	0.815848i	$-0.303729\pi$
$733$	−376.183	−	273.313i	−0.0189558	−	0.0137722i	−0.597223	+	0.802075i	$0.703729\pi$
$734$		0			0
$735$	1823.88	+	4957.40i	0.0915305	+	0.248784i
$736$		0			0
$737$	−8813.59	−	20216.0i	−0.440506	−	1.01040i
$738$		0			0
$739$	−22338.5	−	7258.22i	−1.11196	−	0.361296i	−0.305263	−	0.952268i	$-0.598744\pi$
$739$	−22338.5	−	7258.22i	−1.11196	−	0.361296i	−0.806692	+	0.590972i	$0.798744\pi$
$740$		0			0
$741$	−1090.43	+	1500.84i	−0.0540592	+	0.0744060i
$742$		0			0
$743$	−3208.99	+	1042.66i	−0.158447	+	0.0514827i	−0.387167	−	0.922010i	$-0.626546\pi$
$743$	−3208.99	+	1042.66i	−0.158447	+	0.0514827i	0.228719	+	0.973492i	$0.426546\pi$
$744$		0			0
$745$	−25526.9	+	18546.4i	−1.25535	+	0.912062i
$746$		0			0
$747$	−34289.9			−1.67952
$748$		0			0
$749$	−3058.06	+	1058.92i	−0.149184	+	0.0516584i
$750$		0			0
$751$	29361.4	−	21332.3i	1.42665	−	1.03652i	0.436022	−	0.899936i	$-0.356387\pi$
$751$	29361.4	−	21332.3i	1.42665	−	1.03652i	0.990628	−	0.136586i	$-0.0436129\pi$
$752$		0			0
$753$	−10.1646	−	31.2834i	−0.000491923	−	0.00151398i
$754$		0			0
$755$	−27348.0	−	19869.5i	−1.31827	−	0.957782i
$756$		0			0
$757$	−5411.44	+	16654.7i	−0.259818	+	0.799637i	0.733024	+	0.680203i	$0.238108\pi$
$757$	−5411.44	+	16654.7i	−0.259818	+	0.799637i	−0.992842	+	0.119435i	$0.961892\pi$
$758$		0			0
$759$	1396.70	−	2376.42i	0.0667946	−	0.113648i
$760$		0			0
$761$	−7225.25	+	22237.0i	−0.344172	+	1.05925i	0.617853	+	0.786294i	$0.288003\pi$
$761$	−7225.25	+	22237.0i	−0.344172	+	1.05925i	−0.962025	+	0.272960i	$0.911997\pi$
$762$		0			0
$763$	−33532.0	−	10188.1i	−1.59101	−	0.483399i
$764$		0			0
$765$	3213.31	−	1044.07i	0.151866	−	0.0493443i
$766$		0			0
$767$	−14338.5	−	19735.2i	−0.675009	−	0.929070i
$768$		0			0
$769$	37698.1			1.76779			0.883893	−	0.467689i	$-0.154913\pi$
$769$	37698.1			1.76779			0.883893	+	0.467689i	$0.154913\pi$
$770$		0			0
$771$	2947.89			0.137699
$772$		0			0
$773$	24131.7	+	33214.5i	1.12284	+	1.54546i	0.800996	+	0.598669i	$0.204304\pi$
$773$	24131.7	+	33214.5i	1.12284	+	1.54546i	0.321847	+	0.946792i	$0.395696\pi$
$774$		0			0
$775$	59624.3	−	19373.1i	2.76357	−	0.897939i
$776$		0			0
$777$	321.481	+	97.6761i	0.0148431	+	0.00450980i
$778$		0			0
$779$	−2127.70	+	6548.37i	−0.0978596	+	0.301181i
$780$		0			0
$781$	−775.765	+	687.688i	−0.0355430	+	0.0315076i
$782$		0			0
$783$	546.142	−	1680.85i	0.0249266	−	0.0767161i
$784$		0			0
$785$	44214.5	+	32123.7i	2.01030	+	1.46057i
$786$		0			0
$787$	7027.21	+	21627.5i	0.318289	+	0.979592i	0.974380	+	0.224910i	$0.0722087\pi$
$787$	7027.21	+	21627.5i	0.318289	+	0.979592i	−0.656091	+	0.754682i	$0.727791\pi$
$788$		0			0
$789$	−919.109	+	667.772i	−0.0414717	+	0.0301309i
$790$		0			0
$791$	11913.2	+	34404.1i	0.535505	+	1.54648i
$792$		0			0
$793$	18556.0			0.830949
$794$		0			0
$795$	−3336.60	+	2424.18i	−0.148851	+	0.108147i
$796$		0			0
$797$	−23214.4	+	7542.83i	−1.03174	+	0.335233i	−0.775478	−	0.631374i	$-0.782491\pi$
$797$	−23214.4	+	7542.83i	−1.03174	+	0.335233i	−0.256262	+	0.966607i	$0.582491\pi$
$798$		0			0
$799$	−1058.09	+	1456.34i	−0.0468494	+	0.0644827i
$800$		0			0
$801$	−28337.5	−	9207.41i	−1.25001	−	0.406152i
$802$		0			0
$803$	7839.97	−	35527.6i	0.344541	−	1.56132i
$804$		0			0
$805$	−649.902	−	33860.8i	−0.0284547	−	1.48253i
$806$		0			0
$807$	4267.36	+	3100.42i	0.186144	+	0.135241i
$808$		0			0
$809$	−6715.45	+	2181.98i	−0.291845	+	0.0948263i	−0.451281	−	0.892382i	$-0.649033\pi$
$809$	−6715.45	+	2181.98i	−0.291845	+	0.0948263i	0.159435	+	0.987208i	$0.449033\pi$
$810$		0			0
$811$	−5475.04	+	3977.85i	−0.237059	+	0.172233i	−0.699972	−	0.714170i	$-0.746804\pi$
$811$	−5475.04	+	3977.85i	−0.237059	+	0.172233i	0.462913	+	0.886404i	$0.346804\pi$
$812$		0			0
$813$		−	2796.66i		−	0.120643i
$814$		0			0
$815$			8544.76i			0.367251i
$816$		0			0
$817$	−21344.8	−	29378.6i	−0.914026	−	1.25805i
$818$		0			0
$819$	−13234.6	+	10009.1i	−0.564658	+	0.427040i
$820$		0			0
$821$	−20889.8	+	28752.3i	−0.888014	+	1.22225i	0.0861228	+	0.996285i	$0.472552\pi$
$821$	−20889.8	+	28752.3i	−0.888014	+	1.22225i	−0.974136	+	0.225961i	$0.927448\pi$
$822$		0			0
$823$	7444.70	−	22912.4i	0.315317	−	0.970446i	−0.660307	−	0.750996i	$-0.729574\pi$
$823$	7444.70	−	22912.4i	0.315317	−	0.970446i	0.975624	−	0.219450i	$-0.0704262\pi$
$824$		0			0
$825$	−697.976	−	7175.44i	−0.0294550	−	0.302808i
$826$		0			0
$827$	−5970.46	−	1939.92i	−0.251044	−	0.0815691i	0.180792	−	0.983521i	$-0.442134\pi$
$827$	−5970.46	−	1939.92i	−0.251044	−	0.0815691i	−0.431836	+	0.901952i	$0.642134\pi$
$828$		0			0
$829$	2929.76	−	4032.47i	0.122744	−	0.168943i	−0.743223	−	0.669044i	$-0.766704\pi$
$829$	2929.76	−	4032.47i	0.122744	−	0.168943i	0.865967	+	0.500101i	$0.166704\pi$
$830$		0			0
$831$	−472.694	−	1454.80i	−0.0197324	−	0.0607300i
$832$		0			0
$833$	−619.981	+	2190.84i	−0.0257876	+	0.0911262i
$834$		0			0
$835$			35517.6i			1.47202i
$836$		0			0
$837$	10772.6			0.444869
$838$		0			0
$839$	21540.5	+	29648.0i	0.886366	+	1.21998i	0.974617	+	0.223880i	$0.0718723\pi$
$839$	21540.5	+	29648.0i	0.886366	+	1.21998i	−0.0882509	+	0.996098i	$0.528128\pi$
$840$		0			0
$841$	7003.93	+	21555.9i	0.287176	+	0.883836i
$842$		0			0
$843$	1243.73	+	903.620i	0.0508140	+	0.0369185i
$844$		0			0
$845$	−19133.6	−	6216.88i	−0.778954	−	0.253097i
$846$		0			0
$847$	−12403.9	−	21302.3i	−0.503190	−	0.864176i
$848$		0			0
$849$	−1303.37	−	423.491i	−0.0526874	−	0.0171192i
$850$		0			0
$851$	−1742.78	−	1266.21i	−0.0702020	−	0.0510047i
$852$		0			0
$853$	1645.26	+	5063.58i	0.0660404	+	0.203252i	0.978632	−	0.205622i	$-0.0659217\pi$
$853$	1645.26	+	5063.58i	0.0660404	+	0.203252i	−0.912591	+	0.408874i	$0.865922\pi$
$854$		0			0
$855$	20473.4	+	28179.2i	0.818917	+	1.12714i
$856$		0			0
$857$	17099.3			0.681567			0.340783	−	0.940142i	$-0.389308\pi$
$857$	17099.3			0.681567			0.340783	+	0.940142i	$0.389308\pi$
$858$		0			0
$859$		−	35881.4i		−	1.42521i	−0.701563	−	0.712607i	$-0.747514\pi$
$859$		−	35881.4i		−	1.42521i	0.701563	−	0.712607i	$-0.252486\pi$
$860$		0			0
$861$	850.449	−	1219.07i	0.0336623	−	0.0482529i
$862$		0			0
$863$	14881.3	+	45799.9i	0.586981	+	1.80654i	0.591165	+	0.806550i	$0.298668\pi$
$863$	14881.3	+	45799.9i	0.586981	+	1.80654i	−0.00418458	+	0.999991i	$0.501332\pi$
$864$		0			0
$865$	−12135.9	+	16703.6i	−0.477032	+	0.656578i
$866$		0			0
$867$	3693.78	+	1200.18i	0.144691	+	0.0470131i
$868$		0			0
$869$	1089.14	+	11196.8i	0.0425163	+	0.437083i
$870$		0			0
$871$	−6348.23	+	19537.9i	−0.246960	+	0.760063i
$872$		0			0
$873$	15162.7	−	20869.7i	0.587837	−	0.809088i
$874$		0			0
$875$	−26469.5	−	34999.5i	−1.02267	−	1.35223i
$876$		0			0
$877$	−7545.53	−	10385.5i	−0.290529	−	0.399880i	0.638657	−	0.769492i	$-0.279490\pi$
$877$	−7545.53	−	10385.5i	−0.290529	−	0.399880i	−0.929186	+	0.369612i	$0.879490\pi$
$878$		0			0
$879$		−	614.471i		−	0.0235786i
$880$		0			0
$881$		−	18.2726i		−	0.000698775i	−1.00000		0.000349387i	$-0.999889\pi$
$881$		−	18.2726i		−	0.000698775i	1.00000		0.000349387i	$-0.000111213\pi$
$882$		0			0
$883$	6600.21	−	4795.33i	0.251546	−	0.182759i	−0.454866	−	0.890560i	$-0.650313\pi$
$883$	6600.21	−	4795.33i	0.251546	−	0.182759i	0.706412	+	0.707801i	$0.250313\pi$
$884$		0			0
$885$	10513.3	−	3415.97i	0.399322	−	0.129747i
$886$		0			0
$887$	−5831.39	−	4236.75i	−0.220743	−	0.160379i	0.471918	−	0.881642i	$-0.343562\pi$
$887$	−5831.39	−	4236.75i	−0.220743	−	0.160379i	−0.692661	+	0.721263i	$0.743562\pi$
$888$		0			0
$889$	−556.304	−	28984.2i	−0.0209874	−	1.09347i
$890$		0			0
$891$	−5329.11	+	24149.4i	−0.200373	+	0.908010i
$892$		0			0
$893$	−17649.6	−	5734.71i	−0.661391	−	0.214899i
$894$		0			0
$895$	23728.0	−	32658.8i	0.886190	−	1.21974i
$896$		0			0
$897$	−2442.03	+	793.463i	−0.0908996	+	0.0295351i
$898$		0			0
$899$	8500.55	−	6176.01i	0.315361	−	0.229123i
$900$		0			0
$901$	−1777.72			−0.0657321
$902$		0			0
$903$	2565.13	+	7407.84i	0.0945318	+	0.272998i
$904$		0			0
$905$	−23107.4	+	16788.5i	−0.848748	+	0.616651i
$906$		0			0
$907$	−10133.7	−	31188.4i	−0.370987	−	1.14178i	−0.946147	−	0.323739i	$-0.895060\pi$
$907$	−10133.7	−	31188.4i	−0.370987	−	1.14178i	0.575160	−	0.818041i	$-0.304940\pi$
$908$		0			0
$909$	−17452.8	−	12680.2i	−0.636825	−	0.462681i
$910$		0			0
$911$	−13935.3	+	42888.3i	−0.506801	+	1.55977i	0.290921	+	0.956747i	$0.406038\pi$
$911$	−13935.3	+	42888.3i	−0.506801	+	1.55977i	−0.797722	+	0.603025i	$0.793962\pi$
$912$		0			0
$913$	−35508.4	+	31476.9i	−1.28714	+	1.14100i
$914$		0			0
$915$	−2598.45	+	7997.20i	−0.0938820	+	0.288939i
$916$		0			0
$917$	8811.59	−	29001.6i	0.317322	−	1.04440i
$918$		0			0
$919$	−40347.8	+	13109.8i	−1.44826	+	0.470568i	−0.924462	−	0.381275i	$-0.875485\pi$
$919$	−40347.8	+	13109.8i	−1.44826	+	0.470568i	−0.523798	+	0.851843i	$0.675485\pi$
$920$		0			0
$921$	4041.03	+	5562.00i	0.144578	+	0.198995i
$922$		0			0
$923$	965.692			0.0344379
$924$		0			0
$925$	−5634.11			−0.200268
$926$		0			0
$927$	15128.5	+	20822.6i	0.536015	+	0.737761i
$928$		0			0
$929$	−20902.1	+	6791.50i	−0.738186	+	0.239851i	−0.653890	−	0.756589i	$-0.726864\pi$
$929$	−20902.1	+	6791.50i	−0.738186	+	0.239851i	−0.0842962	+	0.996441i	$0.526864\pi$
$930$		0			0
$931$	−23455.4	+	900.706i	−0.825692	+	0.0317073i
$932$		0			0
$933$	−1926.58	+	5929.40i	−0.0676028	+	0.208060i
$934$		0			0
$935$	2369.08	−	4030.87i	0.0828631	−	0.140988i
$936$		0			0
$937$	3094.66	−	9524.38i	0.107895	−	0.332068i	−0.882504	−	0.470306i	$-0.844144\pi$
$937$	3094.66	−	9524.38i	0.107895	−	0.332068i	0.990399	+	0.138237i	$0.0441437\pi$
$938$		0			0
$939$	6404.06	+	4652.82i	0.222565	+	0.161703i
$940$		0			0
$941$	13407.8	+	41265.0i	0.464487	+	1.42954i	0.859627	+	0.510923i	$0.170696\pi$
$941$	13407.8	+	41265.0i	0.464487	+	1.42954i	−0.395140	+	0.918621i	$0.629304\pi$
$942$		0			0
$943$	−7709.94	+	5601.60i	−0.266246	+	0.193439i
$944$		0			0
$945$	−4980.20	−	14382.3i	−0.171435	−	0.495086i
$946$		0			0
$947$	−32701.1			−1.12211			−0.561057	−	0.827777i	$-0.689605\pi$
$947$	−32701.1			−1.12211			−0.561057	+	0.827777i	$0.689605\pi$
$948$		0			0
$949$	−27418.2	+	19920.5i	−0.937863	+	0.681397i
$950$		0			0
$951$	5619.67	−	1825.94i	0.191620	−	0.0622610i
$952$		0			0
$953$	28773.9	−	39603.8i	0.978045	−	1.34616i	0.0401685	−	0.999193i	$-0.487211\pi$
$953$	28773.9	−	39603.8i	0.978045	−	1.34616i	0.937876	−	0.346970i	$-0.112789\pi$
$954$		0			0
$955$	932.670	+	303.043i	0.0316026	+	0.0102683i
$956$		0			0
$957$	−482.879	−	1107.59i	−0.0163106	−	0.0374121i
$958$		0			0
$959$	−23914.9	+	459.006i	−0.805268	+	0.0154558i
$960$		0			0
$961$	27712.2	+	20134.1i	0.930221	+	0.675845i
$962$		0			0
$963$	4381.29	−	1423.57i	0.146610	−	0.0476364i
$964$		0			0
$965$	−71917.5	+	52251.1i	−2.39907	+	1.74303i
$966$		0			0
$967$			10448.0i			0.347451i	0.984794	+	0.173725i	$0.0555805\pi$
$967$			10448.0i			0.347451i	−0.984794	+	0.173725i	$0.944420\pi$
$968$		0			0
$969$		−	362.363i		−	0.0120132i
$970$		0			0
$971$	−8958.15	−	12329.8i	−0.296067	−	0.407501i	0.634906	−	0.772589i	$-0.281039\pi$
$971$	−8958.15	−	12329.8i	−0.296067	−	0.407501i	−0.930973	+	0.365088i	$0.881039\pi$
$972$		0			0
$973$	13218.3	−	9996.75i	0.435518	−	0.329374i
$974$		0			0
$975$	−3947.31	+	5433.01i	−0.129657	+	0.178457i
$976$		0			0
$977$	10919.1	−	33605.7i	0.357558	−	1.10045i	−0.596953	−	0.802276i	$-0.703622\pi$
$977$	10919.1	−	33605.7i	0.357558	−	1.10045i	0.954511	−	0.298175i	$-0.0963778\pi$
$978$		0			0
$979$	−37796.5	+	16478.2i	−1.23389	+	0.537943i
$980$		0			0
$981$	47445.9	+	15416.1i	1.54417	+	0.501732i
$982$		0			0
$983$	6975.16	−	9600.48i	0.226320	−	0.311503i	−0.680723	−	0.732541i	$-0.738334\pi$
$983$	6975.16	−	9600.48i	0.226320	−	0.311503i	0.907043	+	0.421038i	$0.138334\pi$
$984$		0			0
$985$	21308.9	+	65582.1i	0.689298	+	2.12144i
$986$		0			0
$987$	3285.72	+	2292.19i	0.105963	+	0.0739221i
$988$		0			0
$989$		−	50261.9i		−	1.61601i
$990$		0			0
$991$	10399.1			0.333338			0.166669	−	0.986013i	$-0.446699\pi$
$991$	10399.1			0.333338			0.166669	+	0.986013i	$0.446699\pi$
$992$		0			0
$993$	1704.77	+	2346.42i	0.0544807	+	0.0749862i
$994$		0			0
$995$	24164.5	+	74370.7i	0.769916	+	2.36956i
$996$		0			0
$997$	−18668.2	−	13563.2i	−0.593005	−	0.430844i	0.250384	−	0.968147i	$-0.419443\pi$
$997$	−18668.2	−	13563.2i	−0.593005	−	0.430844i	−0.843389	+	0.537303i	$0.819443\pi$
$998$		0			0
$999$	−920.735	−	299.165i	−0.0291599	−	0.00947463i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.4.w.a.13.14	yes	96
7.6	odd	2	inner	308.4.w.a.13.11	✓	96
11.6	odd	10	inner	308.4.w.a.237.11	yes	96
77.6	even	10	inner	308.4.w.a.237.14	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.4.w.a.13.11	✓	96	7.6	odd	2	inner
308.4.w.a.13.14	yes	96	1.1	even	1	trivial
308.4.w.a.237.11	yes	96	11.6	odd	10	inner
308.4.w.a.237.14	yes	96	77.6	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	308.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.468867 + 0.645340i) q^{3} +(-18.3612 + 5.96593i) q^{5} +(-5.38402 + 17.7204i) q^{7} +(8.14683 - 25.0734i) q^{9} +(-14.5801 - 33.4428i) q^{11} +(-10.5017 + 32.3210i) q^{13} +(-12.4590 - 9.05201i) q^{15} +(-2.05129 - 6.31322i) q^{17} +(55.3638 - 40.2242i) q^{19} +(-13.9601 + 4.83398i) q^{21} +94.7185 q^{23} +(200.415 - 145.610i) q^{25} +(40.4840 - 13.1540i) q^{27} +(24.4042 - 33.5895i) q^{29} +(240.685 + 78.2034i) q^{31} +(14.7458 - 25.0893i) q^{33} +(-6.86141 - 357.489i) q^{35} +(-18.3996 - 13.3681i) q^{37} +(-25.7820 + 8.37706i) q^{39} +(-81.3985 + 59.1395i) q^{41} -530.645i q^{43} +508.981i q^{45} +(-159.397 - 219.391i) q^{47} +(-285.025 - 190.814i) q^{49} +(3.11239 - 4.28384i) q^{51} +(82.7565 - 254.698i) q^{53} +(467.226 + 527.067i) q^{55} +(51.9165 + 16.8687i) q^{57} +(-421.914 + 580.715i) q^{59} +(-168.728 - 519.292i) q^{61} +(400.447 + 279.360i) q^{63} -656.106i q^{65} +604.494 q^{67} +(44.4103 + 61.1256i) q^{69} +(-8.78097 - 27.0250i) q^{71} +(806.789 + 586.166i) q^{73} +(187.936 + 61.0642i) q^{75} +(671.119 - 78.3089i) q^{77} +(-293.262 - 95.2866i) q^{79} +(-548.404 - 398.439i) q^{81} +(-401.923 - 1236.99i) q^{83} +(75.3285 + 103.681i) q^{85} +33.1190 q^{87} -1130.18i q^{89} +(-516.200 - 360.112i) q^{91} +(62.3816 + 191.991i) q^{93} +(-776.574 + 1068.86i) q^{95} +(930.592 + 302.368i) q^{97} +(-957.305 + 93.1199i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 10 q^{7} + 168 q^{9} + 60 q^{11} - 192 q^{15} - 112 q^{23} + 548 q^{25} - 700 q^{29} - 940 q^{35} + 288 q^{37} + 460 q^{39} + 90 q^{49} - 1420 q^{51} - 2240 q^{53} + 560 q^{57} + 320 q^{63} + 4272 q^{67}+ \cdots - 10212 q^{99}+O(q^{100}) \) 96 * q - 10 * q^7 + 168 * q^9 + 60 * q^11 - 192 * q^15 - 112 * q^23 + 548 * q^25 - 700 * q^29 - 940 * q^35 + 288 * q^37 + 460 * q^39 + 90 * q^49 - 1420 * q^51 - 2240 * q^53 + 560 * q^57 + 320 * q^63 + 4272 * q^67 + 296 * q^71 + 430 * q^77 + 2100 * q^79 - 6088 * q^81 + 5900 * q^85 - 636 * q^91 - 2628 * q^93 + 780 * q^95 - 10212 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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