LMFDB - Embedded newform 1500.2.o.c.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(49,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1500.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.o (of order $10$, degree $4$, 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:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	1500.49
Dual form			1500.2.o.c.949.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{3} +1.04684i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{3} +1.04684i q^{7} +(0.809017 - 0.587785i) q^{9} +(-5.08783 - 3.69653i) q^{11} +(-0.591485 - 0.814109i) q^{13} +(-4.46202 - 1.44980i) q^{17} +(1.84654 - 5.68307i) q^{19} +(0.323490 + 0.995600i) q^{21} +(-4.73227 + 6.51341i) q^{23} +(0.587785 - 0.809017i) q^{27} +(-2.13691 - 6.57673i) q^{29} +(-2.94312 + 9.05799i) q^{31} +(-5.98110 - 1.94338i) q^{33} +(-4.52472 - 6.22774i) q^{37} +(-0.814109 - 0.591485i) q^{39} +(-1.26960 + 0.922421i) q^{41} -9.94897i q^{43} +(4.60938 - 1.49768i) q^{47} +5.90413 q^{49} -4.69165 q^{51} +(2.68802 - 0.873389i) q^{53} -5.97554i q^{57} +(3.30248 - 2.39939i) q^{59} +(-2.55692 - 1.85771i) q^{61} +(0.615315 + 0.846908i) q^{63} +(3.01519 + 0.979694i) q^{67} +(-2.48790 + 7.65697i) q^{69} +(2.01138 + 6.19039i) q^{71} +(0.216191 - 0.297561i) q^{73} +(3.86966 - 5.32612i) q^{77} +(1.02596 + 3.15759i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-13.1796 - 4.28231i) q^{83} +(-4.06465 - 5.59450i) q^{87} +(-2.02776 - 1.47326i) q^{89} +(0.852238 - 0.619187i) q^{91} +9.52414i q^{93} +(-0.173748 + 0.0564542i) q^{97} -6.28891 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{9}+O(q^{10}) $ 24 * q + 6 * q^9	$ 24 q + 6 q^{9} - 6 q^{11} - 10 q^{17} + 10 q^{19} - 4 q^{21} - 40 q^{23} + 4 q^{29} + 6 q^{31} - 10 q^{33} - 10 q^{41} + 40 q^{47} - 56 q^{49} + 16 q^{51} + 60 q^{53} - 36 q^{59} - 12 q^{61} + 10 q^{63} - 20 q^{67} + 4 q^{69} + 40 q^{71} - 60 q^{73} + 40 q^{77} + 8 q^{79} - 6 q^{81} + 50 q^{83} + 20 q^{87} - 30 q^{91} + 40 q^{97} - 4 q^{99}+O(q^{100}) $ 24 * q + 6 * q^9 - 6 * q^11 - 10 * q^17 + 10 * q^19 - 4 * q^21 - 40 * q^23 + 4 * q^29 + 6 * q^31 - 10 * q^33 - 10 * q^41 + 40 * q^47 - 56 * q^49 + 16 * q^51 + 60 * q^53 - 36 * q^59 - 12 * q^61 + 10 * q^63 - 20 * q^67 + 4 * q^69 + 40 * q^71 - 60 * q^73 + 40 * q^77 + 8 * q^79 - 6 * q^81 + 50 * q^83 + 20 * q^87 - 30 * q^91 + 40 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$	$1$

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
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			1.04684i			0.395667i	0.980236	+	0.197833i	$0.0633905\pi$
$7$			1.04684i			0.395667i	−0.980236	+	0.197833i	$0.936610\pi$
$8$		0			0
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$		0			0
$11$	−5.08783	−	3.69653i	−1.53404	−	1.11454i	−0.953940	−	0.299999i	$-0.903014\pi$
$11$	−5.08783	−	3.69653i	−1.53404	−	1.11454i	−0.580099	−	0.814546i	$-0.696986\pi$
$12$		0			0
$13$	−0.591485	−	0.814109i	−0.164048	−	0.225793i	0.719077	−	0.694931i	$-0.244565\pi$
$13$	−0.591485	−	0.814109i	−0.164048	−	0.225793i	−0.883125	+	0.469137i	$0.844565\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.46202	−	1.44980i	−1.08220	−	0.351628i	−0.286972	−	0.957939i	$-0.592649\pi$
$17$	−4.46202	−	1.44980i	−1.08220	−	0.351628i	−0.795228	+	0.606311i	$0.792649\pi$
$18$		0			0
$19$	1.84654	−	5.68307i	0.423626	−	1.30379i	−0.480678	−	0.876897i	$-0.659609\pi$
$19$	1.84654	−	5.68307i	0.423626	−	1.30379i	0.904304	−	0.426889i	$-0.140391\pi$
$20$		0			0
$21$	0.323490	+	0.995600i	0.0705913	+	0.217258i
$22$		0			0
$23$	−4.73227	+	6.51341i	−0.986746	+	1.35814i	−0.0536312	+	0.998561i	$0.517080\pi$
$23$	−4.73227	+	6.51341i	−0.986746	+	1.35814i	−0.933115	+	0.359579i	$0.882920\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$		0			0
$29$	−2.13691	−	6.57673i	−0.396814	−	1.22127i	−0.927540	−	0.373725i	$-0.878080\pi$
$29$	−2.13691	−	6.57673i	−0.396814	−	1.22127i	0.530725	−	0.847544i	$-0.321920\pi$
$30$		0			0
$31$	−2.94312	+	9.05799i	−0.528600	+	1.62686i	0.228485	+	0.973547i	$0.426623\pi$
$31$	−2.94312	+	9.05799i	−0.528600	+	1.62686i	−0.757085	+	0.653316i	$0.773377\pi$
$32$		0			0
$33$	−5.98110	−	1.94338i	−1.04118	−	0.338299i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.52472	−	6.22774i	−0.743859	−	1.02383i	−0.998387	−	0.0567693i	$-0.981920\pi$
$37$	−4.52472	−	6.22774i	−0.743859	−	1.02383i	0.254528	−	0.967065i	$-0.418080\pi$
$38$		0			0
$39$	−0.814109	−	0.591485i	−0.130362	−	0.0947133i
$40$		0			0
$41$	−1.26960	+	0.922421i	−0.198279	+	0.144058i	−0.682495	−	0.730891i	$-0.739105\pi$
$41$	−1.26960	+	0.922421i	−0.198279	+	0.144058i	0.484216	+	0.874949i	$0.339105\pi$
$42$		0			0
$43$		−	9.94897i		−	1.51720i	−0.651555	−	0.758602i	$-0.725883\pi$
$43$		−	9.94897i		−	1.51720i	0.651555	−	0.758602i	$-0.274117\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.60938	−	1.49768i	0.672347	−	0.218459i	0.0471053	−	0.998890i	$-0.485000\pi$
$47$	4.60938	−	1.49768i	0.672347	−	0.218459i	0.625242	+	0.780431i	$0.285000\pi$
$48$		0			0
$49$	5.90413			0.843448
$50$		0			0
$51$	−4.69165			−0.656962
$52$		0			0
$53$	2.68802	−	0.873389i	0.369227	−	0.119969i	−0.118525	−	0.992951i	$-0.537817\pi$
$53$	2.68802	−	0.873389i	0.369227	−	0.119969i	0.487753	+	0.872982i	$0.337817\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	5.97554i		−	0.791479i
$58$		0			0
$59$	3.30248	−	2.39939i	0.429946	−	0.312374i	−0.351681	−	0.936120i	$-0.614390\pi$
$59$	3.30248	−	2.39939i	0.429946	−	0.312374i	0.781627	+	0.623746i	$0.214390\pi$
$60$		0			0
$61$	−2.55692	−	1.85771i	−0.327381	−	0.237856i	0.411938	−	0.911212i	$-0.364852\pi$
$61$	−2.55692	−	1.85771i	−0.327381	−	0.237856i	−0.739318	+	0.673356i	$0.764852\pi$
$62$		0			0
$63$	0.615315	+	0.846908i	0.0775224	+	0.106700i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	3.01519	+	0.979694i	0.368364	+	0.119689i	0.487349	−	0.873207i	$-0.337964\pi$
$67$	3.01519	+	0.979694i	0.368364	+	0.119689i	−0.118985	+	0.992896i	$0.537964\pi$
$68$		0			0
$69$	−2.48790	+	7.65697i	−0.299508	+	0.921791i
$70$		0			0
$71$	2.01138	+	6.19039i	0.238707	+	0.734664i	0.996608	+	0.0822947i	$0.0262249\pi$
$71$	2.01138	+	6.19039i	0.238707	+	0.734664i	−0.757901	+	0.652369i	$0.773775\pi$
$72$		0			0
$73$	0.216191	−	0.297561i	0.0253032	−	0.0348269i	−0.796178	−	0.605063i	$-0.793148\pi$
$73$	0.216191	−	0.297561i	0.0253032	−	0.0348269i	0.821481	+	0.570236i	$0.193148\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.86966	−	5.32612i	0.440988	−	0.606968i
$78$		0			0
$79$	1.02596	+	3.15759i	0.115430	+	0.355257i	0.992036	−	0.125951i	$-0.0401982\pi$
$79$	1.02596	+	3.15759i	0.115430	+	0.355257i	−0.876607	+	0.481208i	$0.840198\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	−13.1796	−	4.28231i	−1.44665	−	0.470045i	−0.522686	−	0.852525i	$-0.675070\pi$
$83$	−13.1796	−	4.28231i	−1.44665	−	0.470045i	−0.923964	+	0.382480i	$0.875070\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−4.06465	−	5.59450i	−0.435776	−	0.599794i
$88$		0			0
$89$	−2.02776	−	1.47326i	−0.214942	−	0.156165i	0.475105	−	0.879929i	$-0.342410\pi$
$89$	−2.02776	−	1.47326i	−0.214942	−	0.156165i	−0.690047	+	0.723765i	$0.742410\pi$
$90$		0			0
$91$	0.852238	−	0.619187i	0.0893388	−	0.0649085i
$92$		0			0
$93$			9.52414i			0.987607i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.173748	+	0.0564542i	−0.0176414	+	0.00573205i	−0.317824	−	0.948150i	$-0.602952\pi$
$97$	−0.173748	+	0.0564542i	−0.0176414	+	0.00573205i	0.300183	+	0.953882i	$0.402952\pi$
$98$		0			0
$99$	−6.28891			−0.632059
$100$		0			0
$101$	−5.96970			−0.594008			−0.297004	−	0.954876i	$-0.595987\pi$
$101$	−5.96970			−0.594008			−0.297004	+	0.954876i	$0.595987\pi$
$102$		0			0
$103$	−8.52017	+	2.76837i	−0.839517	+	0.272776i	−0.697049	−	0.717024i	$-0.745504\pi$
$103$	−8.52017	+	2.76837i	−0.839517	+	0.272776i	−0.142468	+	0.989799i	$0.545504\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	2.69495i		−	0.260530i	−0.991479	−	0.130265i	$-0.958417\pi$
$107$		−	2.69495i		−	0.260530i	0.991479	−	0.130265i	$-0.0415829\pi$
$108$		0			0
$109$	8.33278	−	6.05412i	0.798135	−	0.579879i	−0.112231	−	0.993682i	$-0.535800\pi$
$109$	8.33278	−	6.05412i	0.798135	−	0.579879i	0.910366	+	0.413803i	$0.135800\pi$
$110$		0			0
$111$	−6.22774	−	4.52472i	−0.591111	−	0.429467i
$112$		0			0
$113$	−1.98712	−	2.73504i	−0.186933	−	0.257291i	0.705257	−	0.708952i	$-0.250832\pi$
$113$	−1.98712	−	2.73504i	−0.186933	−	0.257291i	−0.892190	+	0.451661i	$0.850832\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.957042	−	0.310962i	−0.0884786	−	0.0287484i
$118$		0			0
$119$	1.51770	−	4.67101i	0.139128	−	0.428191i
$120$		0			0
$121$	8.82254	+	27.1530i	0.802049	+	2.46845i
$122$		0			0
$123$	−0.922421	+	1.26960i	−0.0831719	+	0.114476i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−3.51155	+	4.83324i	−0.311600	+	0.428881i	−0.935879	−	0.352321i	$-0.885393\pi$
$127$	−3.51155	+	4.83324i	−0.311600	+	0.428881i	0.624279	+	0.781201i	$0.285393\pi$
$128$		0			0
$129$	−3.07440	−	9.46203i	−0.270686	−	0.833085i
$130$		0			0
$131$	1.91817	−	5.90352i	0.167591	−	0.515793i	−0.831627	−	0.555335i	$-0.812590\pi$
$131$	1.91817	−	5.90352i	0.167591	−	0.515793i	0.999218	+	0.0395422i	$0.0125900\pi$
$132$		0			0
$133$	5.94925	+	1.93303i	0.515865	+	0.167615i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.62811	−	10.4992i	−0.651714	−	0.897007i	0.347458	−	0.937695i	$-0.387045\pi$
$137$	−7.62811	−	10.4992i	−0.651714	−	0.897007i	−0.999172	+	0.0406885i	$0.987045\pi$
$138$		0			0
$139$	3.23564	+	2.35083i	0.274444	+	0.199395i	0.716490	−	0.697597i	$-0.245747\pi$
$139$	3.23564	+	2.35083i	0.274444	+	0.199395i	−0.442047	+	0.896992i	$0.645747\pi$
$140$		0			0
$141$	3.92097	−	2.84875i	0.330205	−	0.239908i
$142$		0			0
$143$			6.32849i			0.529215i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	5.61517	−	1.82448i	0.463131	−	0.150480i
$148$		0			0
$149$	−5.68762			−0.465948			−0.232974	−	0.972483i	$-0.574846\pi$
$149$	−5.68762			−0.465948			−0.232974	+	0.972483i	$0.574846\pi$
$150$		0			0
$151$	−5.51150			−0.448519			−0.224260	−	0.974529i	$-0.571996\pi$
$151$	−5.51150			−0.448519			−0.224260	+	0.974529i	$0.571996\pi$
$152$		0			0
$153$	−4.46202	+	1.44980i	−0.360733	+	0.117209i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			17.0217i			1.35848i	0.733915	+	0.679242i	$0.237691\pi$
$157$			17.0217i			1.35848i	−0.733915	+	0.679242i	$0.762309\pi$
$158$		0			0
$159$	2.28656	−	1.66129i	0.181336	−	0.131748i
$160$		0			0
$161$	−6.81847	−	4.95391i	−0.537371	−	0.390423i
$162$		0			0
$163$	7.22726	+	9.94747i	0.566083	+	0.779146i	0.992084	−	0.125576i	$-0.0400780\pi$
$163$	7.22726	+	9.94747i	0.566083	+	0.779146i	−0.426001	+	0.904723i	$0.640078\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.16289	−	1.67752i	−0.399516	−	0.129811i	0.102366	−	0.994747i	$-0.467359\pi$
$167$	−5.16289	−	1.67752i	−0.399516	−	0.129811i	−0.501882	+	0.864936i	$0.667359\pi$
$168$		0			0
$169$	3.70430	−	11.4007i	0.284946	−	0.876975i
$170$		0			0
$171$	−1.84654	−	5.68307i	−0.141209	−	0.434596i
$172$		0			0
$173$	−6.31611	+	8.69337i	−0.480205	+	0.660945i	−0.978544	−	0.206037i	$-0.933943\pi$
$173$	−6.31611	+	8.69337i	−0.480205	+	0.660945i	0.498340	+	0.866982i	$0.333943\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.39939	−	3.30248i	0.180349	−	0.248230i
$178$		0			0
$179$	5.96596	+	18.3613i	0.445917	+	1.37239i	0.881476	+	0.472230i	$0.156551\pi$
$179$	5.96596	+	18.3613i	0.445917	+	1.37239i	−0.435559	+	0.900160i	$0.643449\pi$
$180$		0			0
$181$	5.17642	−	15.9314i	0.384760	−	1.18417i	−0.551894	−	0.833914i	$-0.686095\pi$
$181$	5.17642	−	15.9314i	0.384760	−	1.18417i	0.936654	−	0.350255i	$-0.113905\pi$
$182$		0			0
$183$	−3.00585	−	0.976658i	−0.222198	−	0.0721967i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	17.3428	+	23.8703i	1.26823	+	1.74557i
$188$		0			0
$189$	0.846908	+	0.615315i	0.0616035	+	0.0447576i
$190$		0			0
$191$	9.66400	−	7.02131i	0.699263	−	0.508044i	−0.180429	−	0.983588i	$-0.557749\pi$
$191$	9.66400	−	7.02131i	0.699263	−	0.508044i	0.879692	+	0.475544i	$0.157749\pi$
$192$		0			0
$193$		−	26.4298i		−	1.90246i	−0.308485	−	0.951229i	$-0.599822\pi$
$193$		−	26.4298i		−	1.90246i	0.308485	−	0.951229i	$-0.400178\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	10.5299	−	3.42138i	0.750225	−	0.243763i	0.0911471	−	0.995837i	$-0.470947\pi$
$197$	10.5299	−	3.42138i	0.750225	−	0.243763i	0.659078	+	0.752074i	$0.270947\pi$
$198$		0			0
$199$	16.5548			1.17354			0.586768	−	0.809755i	$-0.300400\pi$
$199$	16.5548			1.17354			0.586768	+	0.809755i	$0.300400\pi$
$200$		0			0
$201$	3.17036			0.223620
$202$		0			0
$203$	6.88476	−	2.23699i	0.483215	−	0.157006i
$204$		0			0
$205$		0			0
$206$		0			0
$207$			8.05101i			0.559584i
$208$		0			0
$209$	−30.4025	+	22.0887i	−2.10299	+	1.52791i
$210$		0			0
$211$	3.32274	+	2.41411i	0.228747	+	0.166194i	0.696255	−	0.717794i	$-0.254848\pi$
$211$	3.32274	+	2.41411i	0.228747	+	0.166194i	−0.467508	+	0.883989i	$0.654848\pi$
$212$		0			0
$213$	3.82587	+	5.26586i	0.262144	+	0.360811i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−9.48223	−	3.08096i	−0.643696	−	0.209149i
$218$		0			0
$219$	0.113658	−	0.349804i	0.00768032	−	0.0236376i
$220$		0			0
$221$	1.45892	+	4.49011i	0.0981379	+	0.302037i
$222$		0			0
$223$	3.68040	−	5.06564i	0.246458	−	0.339220i	−0.667809	−	0.744333i	$-0.732768\pi$
$223$	3.68040	−	5.06564i	0.246458	−	0.339220i	0.914267	+	0.405113i	$0.132768\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.16101	+	8.47990i	−0.408921	+	0.562831i	−0.962955	−	0.269663i	$-0.913088\pi$
$227$	−6.16101	+	8.47990i	−0.408921	+	0.562831i	0.554034	+	0.832494i	$0.313088\pi$
$228$		0			0
$229$	−2.33827	−	7.19645i	−0.154517	−	0.475555i	0.843595	−	0.536981i	$-0.180435\pi$
$229$	−2.33827	−	7.19645i	−0.154517	−	0.475555i	−0.998112	+	0.0614260i	$0.980435\pi$
$230$		0			0
$231$	2.03440	−	6.26123i	0.133854	−	0.411959i
$232$		0			0
$233$	15.2009	+	4.93908i	0.995846	+	0.323570i	0.761204	−	0.648512i	$-0.224608\pi$
$233$	15.2009	+	4.93908i	0.995846	+	0.323570i	0.234642	+	0.972082i	$0.424608\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.95150	+	2.68601i	0.126763	+	0.174475i
$238$		0			0
$239$	−2.36231	−	1.71632i	−0.152805	−	0.111019i	0.508756	−	0.860911i	$-0.330106\pi$
$239$	−2.36231	−	1.71632i	−0.152805	−	0.111019i	−0.661561	+	0.749892i	$0.730106\pi$
$240$		0			0
$241$	18.6460	−	13.5471i	1.20109	−	0.872644i	0.206700	−	0.978404i	$-0.433728\pi$
$241$	18.6460	−	13.5471i	1.20109	−	0.872644i	0.994392	+	0.105760i	$0.0337277\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−5.71884	+	1.85816i	−0.363881	+	0.118232i
$248$		0			0
$249$	−13.8579			−0.878206
$250$		0			0
$251$	−9.79130			−0.618021			−0.309011	−	0.951059i	$-0.599998\pi$
$251$	−9.79130			−0.618021			−0.309011	+	0.951059i	$0.599998\pi$
$252$		0			0
$253$	48.1540	−	15.6462i	3.02741	−	0.983666i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	22.3147i		−	1.39195i	−0.718066	−	0.695975i	$-0.754973\pi$
$257$		−	22.3147i		−	1.39195i	0.718066	−	0.695975i	$-0.245027\pi$
$258$		0			0
$259$	6.51943	−	4.73664i	0.405097	−	0.294320i
$260$		0			0
$261$	−5.59450	−	4.06465i	−0.346291	−	0.251595i
$262$		0			0
$263$	0.428586	+	0.589898i	0.0264277	+	0.0363747i	0.822026	−	0.569449i	$-0.192844\pi$
$263$	0.428586	+	0.589898i	0.0264277	+	0.0363747i	−0.795599	+	0.605824i	$0.792844\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.38378	−	0.774536i	−0.145885	−	0.0474008i
$268$		0			0
$269$	0.574531	−	1.76822i	0.0350298	−	0.107811i	−0.932013	−	0.362425i	$-0.881949\pi$
$269$	0.574531	−	1.76822i	0.0350298	−	0.107811i	0.967043	+	0.254615i	$0.0819487\pi$
$270$		0			0
$271$	6.04232	+	18.5964i	0.367045	+	1.12965i	0.948691	+	0.316206i	$0.102409\pi$
$271$	6.04232	+	18.5964i	0.367045	+	1.12965i	−0.581646	+	0.813442i	$0.697591\pi$
$272$		0			0
$273$	0.619187	−	0.852238i	0.0374749	−	0.0515798i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−9.96956	+	13.7219i	−0.599013	+	0.824471i	−0.995618	−	0.0935189i	$-0.970188\pi$
$277$	−9.96956	+	13.7219i	−0.599013	+	0.824471i	0.396604	+	0.917990i	$0.370188\pi$
$278$		0			0
$279$	2.94312	+	9.05799i	0.176200	+	0.542288i
$280$		0			0
$281$	−8.06159	+	24.8110i	−0.480914	+	1.48010i	0.356898	+	0.934143i	$0.383834\pi$
$281$	−8.06159	+	24.8110i	−0.480914	+	1.48010i	−0.837812	+	0.545958i	$0.816166\pi$
$282$		0			0
$283$	−24.3559	−	7.91372i	−1.44781	−	0.470422i	−0.523487	−	0.852033i	$-0.675369\pi$
$283$	−24.3559	−	7.91372i	−1.44781	−	0.470422i	−0.924323	+	0.381611i	$0.875369\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.965624	−	1.32907i	−0.0569990	−	0.0784524i
$288$		0			0
$289$	4.05446	+	2.94573i	0.238497	+	0.173279i
$290$		0			0
$291$	−0.147799	+	0.107382i	−0.00866412	+	0.00629485i
$292$		0			0
$293$		−	27.7845i		−	1.62319i	−0.584220	−	0.811595i	$-0.698600\pi$
$293$		−	27.7845i		−	1.62319i	0.584220	−	0.811595i	$-0.301400\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−5.98110	+	1.94338i	−0.347059	+	0.112766i
$298$		0			0
$299$	8.10169			0.468533
$300$		0			0
$301$	10.4149			0.600307
$302$		0			0
$303$	−5.67753	+	1.84474i	−0.326165	+	0.105978i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			16.1422i			0.921283i	0.887586	+	0.460642i	$0.152381\pi$
$307$			16.1422i			0.921283i	−0.887586	+	0.460642i	$0.847619\pi$
$308$		0			0
$309$	−7.24769	+	5.26575i	−0.412307	+	0.299558i
$310$		0			0
$311$	−23.2496	−	16.8918i	−1.31837	−	0.957849i	−0.999951	−	0.00989736i	$-0.996850\pi$
$311$	−23.2496	−	16.8918i	−1.31837	−	0.957849i	−0.318415	−	0.947951i	$-0.603150\pi$
$312$		0			0
$313$	15.5683	+	21.4279i	0.879973	+	1.21118i	0.976428	+	0.215841i	$0.0692494\pi$
$313$	15.5683	+	21.4279i	0.879973	+	1.21118i	−0.0964557	+	0.995337i	$0.530751\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	25.0109	+	8.12654i	1.40475	+	0.456432i	0.910725	−	0.413014i	$-0.135524\pi$
$317$	25.0109	+	8.12654i	1.40475	+	0.456432i	0.494028	+	0.869446i	$0.335524\pi$
$318$		0			0
$319$	−13.4388	+	41.3605i	−0.752430	+	2.31574i
$320$		0			0
$321$	−0.832784	−	2.56305i	−0.0464815	−	0.143055i
$322$		0			0
$323$	−16.4786	+	22.6809i	−0.916896	+	1.26200i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	6.05412	−	8.33278i	0.334793	−	0.460804i
$328$		0			0
$329$	1.56782	+	4.82526i	0.0864369	+	0.266025i
$330$		0			0
$331$	−9.66091	+	29.7332i	−0.531012	+	1.63429i	0.221101	+	0.975251i	$0.429035\pi$
$331$	−9.66091	+	29.7332i	−0.531012	+	1.63429i	−0.752113	+	0.659035i	$0.770965\pi$
$332$		0			0
$333$	−7.32115	−	2.37879i	−0.401197	−	0.130357i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−5.23438	−	7.20451i	−0.285135	−	0.392455i	0.642291	−	0.766461i	$-0.277984\pi$
$337$	−5.23438	−	7.20451i	−0.285135	−	0.392455i	−0.927426	+	0.374006i	$0.877984\pi$
$338$		0			0
$339$	−2.73504	−	1.98712i	−0.148547	−	0.107926i
$340$		0			0
$341$	48.4572	−	35.2062i	2.62410	−	1.90652i
$342$		0			0
$343$			13.5085i			0.729391i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−20.4981	+	6.66023i	−1.10039	+	0.357540i	−0.802255	−	0.596982i	$-0.796366\pi$
$347$	−20.4981	+	6.66023i	−1.10039	+	0.357540i	−0.298140	+	0.954522i	$0.596366\pi$
$348$		0			0
$349$	−17.3958			−0.931178			−0.465589	−	0.885001i	$-0.654158\pi$
$349$	−17.3958			−0.931178			−0.465589	+	0.885001i	$0.654158\pi$
$350$		0			0
$351$	−1.00629			−0.0537120
$352$		0			0
$353$	16.9871	−	5.51945i	0.904133	−	0.293770i	0.180191	−	0.983632i	$-0.442328\pi$
$353$	16.9871	−	5.51945i	0.904133	−	0.293770i	0.723942	+	0.689861i	$0.242328\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	4.91139i		−	0.259938i
$358$		0			0
$359$	2.95995	−	2.15053i	0.156220	−	0.113501i	−0.506929	−	0.861988i	$-0.669219\pi$
$359$	2.95995	−	2.15053i	0.156220	−	0.113501i	0.663149	+	0.748487i	$0.269219\pi$
$360$		0			0
$361$	−13.5163	−	9.82016i	−0.711384	−	0.516851i
$362$		0			0
$363$	16.7815	+	23.0977i	0.880798	+	1.21232i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	24.7677	+	8.04751i	1.29286	+	0.420077i	0.873093	−	0.487554i	$-0.162111\pi$
$367$	24.7677	+	8.04751i	1.29286	+	0.420077i	0.419770	+	0.907631i	$0.362111\pi$
$368$		0			0
$369$	−0.484946	+	1.49251i	−0.0252453	+	0.0776969i
$370$		0			0
$371$	0.914295	+	2.81391i	0.0474678	+	0.146091i
$372$		0			0
$373$	17.1991	−	23.6726i	0.890538	−	1.22572i	−0.0828510	−	0.996562i	$-0.526403\pi$
$373$	17.1991	−	23.6726i	0.890538	−	1.22572i	0.973389	−	0.229159i	$-0.0735974\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.09023	+	5.62971i	−0.210657	+	0.289945i
$378$		0			0
$379$	3.17264	+	9.76437i	0.162967	+	0.501562i	0.998881	−	0.0472993i	$-0.0150614\pi$
$379$	3.17264	+	9.76437i	0.162967	+	0.501562i	−0.835913	+	0.548861i	$0.815061\pi$
$380$		0			0
$381$	−1.84613	+	5.68181i	−0.0945803	+	0.291088i
$382$		0			0
$383$	24.3926	+	7.92564i	1.24640	+	0.404981i	0.856631	−	0.515930i	$-0.172554\pi$
$383$	24.3926	+	7.92564i	1.24640	+	0.404981i	0.389773	+	0.920911i	$0.372554\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−5.84786	−	8.04888i	−0.297263	−	0.409148i
$388$		0			0
$389$	−7.75696	−	5.63576i	−0.393293	−	0.285744i	0.373510	−	0.927626i	$-0.378154\pi$
$389$	−7.75696	−	5.63576i	−0.393293	−	0.285744i	−0.766804	+	0.641882i	$0.778154\pi$
$390$		0			0
$391$	30.5586	−	22.2021i	1.54542	−	1.12281i
$392$		0			0
$393$		−	6.20733i		−	0.313118i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	11.7274	−	3.81045i	0.588580	−	0.191241i	0.000439093	−	1.00000i	$-0.499860\pi$
$397$	11.7274	−	3.81045i	0.588580	−	0.191241i	0.588140	+	0.808759i	$0.299860\pi$
$398$		0			0
$399$	6.25541			0.313162
$400$		0			0
$401$	18.9779			0.947709			0.473855	−	0.880603i	$-0.342862\pi$
$401$	18.9779			0.947709			0.473855	+	0.880603i	$0.342862\pi$
$402$		0			0
$403$	9.11500	−	2.96164i	0.454051	−	0.147530i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			48.4115i			2.39967i
$408$		0			0
$409$	15.7841	−	11.4678i	0.780474	−	0.567048i	−0.124647	−	0.992201i	$-0.539780\pi$
$409$	15.7841	−	11.4678i	0.780474	−	0.567048i	0.905121	+	0.425154i	$0.139780\pi$
$410$		0			0
$411$	−10.4992	−	7.62811i	−0.517887	−	0.376267i
$412$		0			0
$413$	2.51177	+	3.45715i	0.123596	+	0.170115i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	3.80373	+	1.23591i	0.186269	+	0.0605226i
$418$		0			0
$419$	−0.571420	+	1.75865i	−0.0279157	+	0.0859156i	−0.964044	−	0.265744i	$-0.914382\pi$
$419$	−0.571420	+	1.75865i	−0.0279157	+	0.0859156i	0.936128	+	0.351659i	$0.114382\pi$
$420$		0			0
$421$	−2.06347	−	6.35070i	−0.100567	−	0.309514i	0.888097	−	0.459656i	$-0.152027\pi$
$421$	−2.06347	−	6.35070i	−0.100567	−	0.309514i	−0.988665	+	0.150141i	$0.952027\pi$
$422$		0			0
$423$	2.84875	−	3.92097i	0.138511	−	0.190644i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.94472	−	2.67668i	0.0941117	−	0.129534i
$428$		0			0
$429$	1.95561	+	6.01875i	0.0944177	+	0.290588i
$430$		0			0
$431$	9.16108	−	28.1949i	0.441274	−	1.35810i	−0.445245	−	0.895409i	$-0.646884\pi$
$431$	9.16108	−	28.1949i	0.441274	−	1.35810i	0.886519	−	0.462692i	$-0.153116\pi$
$432$		0			0
$433$	−26.6465	−	8.65798i	−1.28055	−	0.416076i	−0.411776	−	0.911285i	$-0.635091\pi$
$433$	−26.6465	−	8.65798i	−1.28055	−	0.416076i	−0.868774	+	0.495209i	$0.835091\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	28.2778	+	38.9211i	1.35271	+	1.86185i
$438$		0			0
$439$	8.27205	+	6.01000i	0.394803	+	0.286842i	0.767421	−	0.641143i	$-0.221540\pi$
$439$	8.27205	+	6.01000i	0.394803	+	0.286842i	−0.372618	+	0.927985i	$0.621540\pi$
$440$		0			0
$441$	4.77655	−	3.47036i	0.227455	−	0.165255i
$442$		0			0
$443$		−	26.5115i		−	1.25960i	−0.776757	−	0.629800i	$-0.783137\pi$
$443$		−	26.5115i		−	1.25960i	0.776757	−	0.629800i	$-0.216863\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−5.40925	+	1.75757i	−0.255849	+	0.0831303i
$448$		0			0
$449$	6.39692			0.301889			0.150945	−	0.988542i	$-0.451768\pi$
$449$	6.39692			0.301889			0.150945	+	0.988542i	$0.451768\pi$
$450$		0			0
$451$	9.86929			0.464727
$452$		0			0
$453$	−5.24175	+	1.70315i	−0.246279	+	0.0800208i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	14.9784i		−	0.700661i	−0.936626	−	0.350330i	$-0.886069\pi$
$457$		−	14.9784i		−	0.700661i	0.936626	−	0.350330i	$-0.113931\pi$
$458$		0			0
$459$	−3.79562	+	2.75768i	−0.177165	+	0.128718i
$460$		0			0
$461$	9.85643	+	7.16112i	0.459060	+	0.333526i	0.793162	−	0.609010i	$-0.208433\pi$
$461$	9.85643	+	7.16112i	0.459060	+	0.333526i	−0.334103	+	0.942537i	$0.608433\pi$
$462$		0			0
$463$	4.89012	+	6.73067i	0.227263	+	0.312801i	0.907387	−	0.420297i	$-0.138074\pi$
$463$	4.89012	+	6.73067i	0.227263	+	0.312801i	−0.680124	+	0.733097i	$0.738074\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.89818	−	2.56627i	−0.365484	−	0.118753i	0.120517	−	0.992711i	$-0.461545\pi$
$467$	−7.89818	−	2.56627i	−0.365484	−	0.118753i	−0.486001	+	0.873958i	$0.661545\pi$
$468$		0			0
$469$	−1.02558	+	3.15641i	−0.0473568	+	0.145749i
$470$		0			0
$471$	5.26001	+	16.1886i	0.242368	+	0.745933i
$472$		0			0
$473$	−36.7766	+	50.6187i	−1.69099	+	2.32745i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.66129	−	2.28656i	0.0760650	−	0.104695i
$478$		0			0
$479$	0.944475	+	2.90680i	0.0431542	+	0.132815i	0.970312	−	0.241855i	$-0.0777559\pi$
$479$	0.944475	+	2.90680i	0.0431542	+	0.132815i	−0.927158	+	0.374670i	$0.877756\pi$
$480$		0			0
$481$	−2.39376	+	7.36723i	−0.109146	+	0.335917i
$482$		0			0
$483$	−8.01559	−	2.60442i	−0.364722	−	0.118505i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	6.88809	+	9.48064i	0.312129	+	0.429609i	0.936044	−	0.351884i	$-0.114459\pi$
$487$	6.88809	+	9.48064i	0.312129	+	0.429609i	−0.623915	+	0.781492i	$0.714459\pi$
$488$		0			0
$489$	9.94747	+	7.22726i	0.449840	+	0.326828i
$490$		0			0
$491$	−13.7147	+	9.96433i	−0.618937	+	0.449684i	−0.852550	−	0.522646i	$-0.824945\pi$
$491$	−13.7147	+	9.96433i	−0.618937	+	0.449684i	0.233613	+	0.972330i	$0.424945\pi$
$492$		0			0
$493$			32.4436i			1.46119i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.48032	+	2.10558i	−0.290682	+	0.0944484i
$498$		0			0
$499$	−14.0674			−0.629742			−0.314871	−	0.949135i	$-0.601961\pi$
$499$	−14.0674			−0.629742			−0.314871	+	0.949135i	$0.601961\pi$
$500$		0			0
$501$	−5.42858			−0.242531
$502$		0			0
$503$	5.33310	−	1.73283i	0.237791	−	0.0772630i	−0.187697	−	0.982227i	$-0.560102\pi$
$503$	5.33310	−	1.73283i	0.237791	−	0.0772630i	0.425488	+	0.904964i	$0.360102\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	11.9874i		−	0.532378i
$508$		0			0
$509$	−9.27535	+	6.73894i	−0.411123	+	0.298698i	−0.774056	−	0.633117i	$-0.781775\pi$
$509$	−9.27535	+	6.73894i	−0.411123	+	0.298698i	0.362933	+	0.931815i	$0.381775\pi$
$510$		0			0
$511$	0.311498	+	0.226317i	0.0137799	+	0.0100117i
$512$		0			0
$513$	−3.51233	−	4.83431i	−0.155073	−	0.213440i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−28.9880	−	9.41876i	−1.27489	−	0.414236i
$518$		0			0
$519$	−3.32057	+	10.2197i	−0.145757	+	0.448594i
$520$		0			0
$521$	5.53178	+	17.0251i	0.242352	+	0.745882i	0.996061	+	0.0886737i	$0.0282628\pi$
$521$	5.53178	+	17.0251i	0.242352	+	0.745882i	−0.753709	+	0.657208i	$0.771737\pi$
$522$		0			0
$523$	−0.791609	+	1.08956i	−0.0346146	+	0.0476430i	−0.825974	−	0.563709i	$-0.809374\pi$
$523$	−0.791609	+	1.08956i	−0.0346146	+	0.0476430i	0.791359	+	0.611352i	$0.209374\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	26.2646	−	36.1501i	1.14410	−	1.57472i
$528$		0			0
$529$	−12.9227	−	39.7721i	−0.561858	−	1.72922i
$530$		0			0
$531$	1.26144	−	3.88230i	0.0547416	−	0.168477i
$532$		0			0
$533$	1.50190	+	0.487998i	0.0650546	+	0.0211375i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	11.3479	+	15.6191i	0.489699	+	0.674013i
$538$		0			0
$539$	−30.0392	−	21.8248i	−1.29388	−	0.940060i
$540$		0			0
$541$	−9.14001	+	6.64061i	−0.392960	+	0.285502i	−0.766667	−	0.642045i	$-0.778086\pi$
$541$	−9.14001	+	6.64061i	−0.392960	+	0.285502i	0.373708	+	0.927547i	$0.378086\pi$
$542$		0			0
$543$		−	16.7512i		−	0.718864i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−24.5513	+	7.97719i	−1.04974	+	0.341080i	−0.782565	−	0.622569i	$-0.786089\pi$
$547$	−24.5513	+	7.97719i	−1.04974	+	0.341080i	−0.267171	+	0.963649i	$0.586089\pi$
$548$		0			0
$549$	−3.16053			−0.134888
$550$		0			0
$551$	−41.3220			−1.76037
$552$		0			0
$553$	−3.30548	+	1.07402i	−0.140563	+	0.0456718i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	35.3575i		−	1.49814i	−0.662489	−	0.749072i	$-0.730500\pi$
$557$		−	35.3575i		−	1.49814i	0.662489	−	0.749072i	$-0.269500\pi$
$558$		0			0
$559$	−8.09954	+	5.88466i	−0.342574	+	0.248895i
$560$		0			0
$561$	23.8703	+	17.3428i	1.00781	+	0.732214i
$562$		0			0
$563$	−2.67693	−	3.68448i	−0.112819	−	0.155282i	0.748873	−	0.662713i	$-0.230595\pi$
$563$	−2.67693	−	3.68448i	−0.112819	−	0.155282i	−0.861692	+	0.507431i	$0.830595\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.995600	+	0.323490i	0.0418113	+	0.0135853i
$568$		0			0
$569$	11.4772	−	35.3231i	0.481148	−	1.48082i	−0.356335	−	0.934358i	$-0.615974\pi$
$569$	11.4772	−	35.3231i	0.481148	−	1.48082i	0.837483	−	0.546463i	$-0.184026\pi$
$570$		0			0
$571$	−1.32882	−	4.08969i	−0.0556094	−	0.171148i	0.919394	−	0.393338i	$-0.128680\pi$
$571$	−1.32882	−	4.08969i	−0.0556094	−	0.171148i	−0.975003	+	0.222190i	$0.928680\pi$
$572$		0			0
$573$	7.02131	−	9.66400i	0.293319	−	0.403720i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	0.274601	−	0.377955i	0.0114318	−	0.0157345i	−0.803263	−	0.595625i	$-0.796905\pi$
$577$	0.274601	−	0.377955i	0.0114318	−	0.0157345i	0.814695	+	0.579890i	$0.196905\pi$
$578$		0			0
$579$	−8.16726	−	25.1362i	−0.339420	−	1.04463i
$580$		0			0
$581$	4.48288	−	13.7969i	0.185981	−	0.572391i
$582$		0			0
$583$	−16.9047	−	5.49266i	−0.700120	−	0.227483i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−19.3704	−	26.6610i	−0.799500	−	1.10042i	−0.992860	−	0.119289i	$-0.961938\pi$
$587$	−19.3704	−	26.6610i	−0.799500	−	1.10042i	0.193360	−	0.981128i	$-0.438062\pi$
$588$		0			0
$589$	46.0427	+	33.4519i	1.89715	+	1.37836i
$590$		0			0
$591$	8.95728	−	6.50784i	0.368453	−	0.267697i
$592$		0			0
$593$			15.5285i			0.637680i	0.947809	+	0.318840i	$0.103293\pi$
$593$			15.5285i			0.637680i	−0.947809	+	0.318840i	$0.896707\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	15.7445	−	5.11571i	0.644381	−	0.209372i
$598$		0			0
$599$	36.0116			1.47140			0.735698	−	0.677310i	$-0.236854\pi$
$599$	36.0116			1.47140			0.735698	+	0.677310i	$0.236854\pi$
$600$		0			0
$601$	−24.1503			−0.985112			−0.492556	−	0.870281i	$-0.663937\pi$
$601$	−24.1503			−0.985112			−0.492556	+	0.870281i	$0.663937\pi$
$602$		0			0
$603$	3.01519	−	0.979694i	0.122788	−	0.0398962i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	29.8098i		−	1.20994i	−0.796248	−	0.604970i	$-0.793185\pi$
$607$		−	29.8098i		−	1.20994i	0.796248	−	0.604970i	$-0.206815\pi$
$608$		0			0
$609$	5.85653	−	4.25502i	0.237318	−	0.172422i
$610$		0			0
$611$	−3.94565	−	2.86668i	−0.159624	−	0.115974i
$612$		0			0
$613$	−18.8873	−	25.9961i	−0.762850	−	1.04997i	−0.996972	−	0.0777657i	$-0.975221\pi$
$613$	−18.8873	−	25.9961i	−0.762850	−	1.04997i	0.234122	−	0.972207i	$-0.424779\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−16.4065	−	5.33081i	−0.660502	−	0.214610i	−0.0404631	−	0.999181i	$-0.512883\pi$
$617$	−16.4065	−	5.33081i	−0.660502	−	0.214610i	−0.620039	+	0.784571i	$0.712883\pi$
$618$		0			0
$619$	−2.18171	+	6.71462i	−0.0876904	+	0.269883i	−0.985280	−	0.170949i	$-0.945317\pi$
$619$	−2.18171	+	6.71462i	−0.0876904	+	0.269883i	0.897589	+	0.440832i	$0.145317\pi$
$620$		0			0
$621$	2.48790	+	7.65697i	0.0998360	+	0.307264i
$622$		0			0
$623$	1.54226	−	2.12273i	0.0617892	−	0.0850455i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−22.0887	+	30.4025i	−0.882139	+	1.21416i
$628$		0			0
$629$	11.1604	+	34.3483i	0.444996	+	1.36956i
$630$		0			0
$631$	−3.02377	+	9.30621i	−0.120374	+	0.370474i	−0.993030	−	0.117862i	$-0.962396\pi$
$631$	−3.02377	+	9.30621i	−0.120374	+	0.370474i	0.872656	+	0.488336i	$0.162396\pi$
$632$		0			0
$633$	3.90612	+	1.26917i	0.155254	+	0.0504452i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−3.49220	−	4.80661i	−0.138366	−	0.190445i
$638$		0			0
$639$	5.26586	+	3.82587i	0.208314	+	0.151349i
$640$		0			0
$641$	−12.6773	+	9.21063i	−0.500725	+	0.363798i	−0.809294	−	0.587404i	$-0.800150\pi$
$641$	−12.6773	+	9.21063i	−0.500725	+	0.363798i	0.308569	+	0.951202i	$0.400150\pi$
$642$		0			0
$643$		−	0.766747i		−	0.0302375i	−0.999886	−	0.0151188i	$-0.995187\pi$
$643$		−	0.766747i		−	0.0302375i	0.999886	−	0.0151188i	$-0.00481264\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	12.5281	−	4.07063i	0.492531	−	0.160033i	−0.0522121	−	0.998636i	$-0.516627\pi$
$647$	12.5281	−	4.07063i	0.492531	−	0.160033i	0.544743	+	0.838603i	$0.316627\pi$
$648$		0			0
$649$	−25.6719			−1.00771
$650$		0			0
$651$	−9.97021			−0.390763
$652$		0			0
$653$	12.4514	−	4.04569i	0.487259	−	0.158320i	−0.0550762	−	0.998482i	$-0.517540\pi$
$653$	12.4514	−	4.04569i	0.487259	−	0.158320i	0.542336	+	0.840162i	$0.317540\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	0.367806i		−	0.0143495i
$658$		0			0
$659$	−7.65921	+	5.56474i	−0.298361	+	0.216772i	−0.726886	−	0.686758i	$-0.759033\pi$
$659$	−7.65921	+	5.56474i	−0.298361	+	0.216772i	0.428526	+	0.903530i	$0.359033\pi$
$660$		0			0
$661$	−4.49719	−	3.26740i	−0.174921	−	0.127087i	0.496880	−	0.867819i	$-0.334479\pi$
$661$	−4.49719	−	3.26740i	−0.174921	−	0.127087i	−0.671801	+	0.740732i	$0.734479\pi$
$662$		0			0
$663$	2.77504	+	3.81951i	0.107774	+	0.148338i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	52.9494	+	17.2043i	2.05021	+	0.666153i
$668$		0			0
$669$	1.93490	−	5.95502i	0.0748076	−	0.230234i
$670$		0			0
$671$	6.14211	+	18.9035i	0.237114	+	0.729761i
$672$		0			0
$673$	0.178700	−	0.245960i	0.00688840	−	0.00948106i	−0.805559	−	0.592516i	$-0.798135\pi$
$673$	0.178700	−	0.245960i	0.00688840	−	0.00948106i	0.812447	+	0.583035i	$0.198135\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−23.2339	+	31.9787i	−0.892950	+	1.22904i	0.0797128	+	0.996818i	$0.474600\pi$
$677$	−23.2339	+	31.9787i	−0.892950	+	1.22904i	−0.972663	+	0.232222i	$0.925400\pi$
$678$		0			0
$679$	−0.0590982	−	0.181886i	−0.00226798	−	0.00698013i
$680$		0			0
$681$	−3.23904	+	9.96873i	−0.124120	+	0.382002i
$682$		0			0
$683$	30.0040	+	9.74888i	1.14807	+	0.373031i	0.820416	−	0.571767i	$-0.193742\pi$
$683$	30.0040	+	9.74888i	1.14807	+	0.373031i	0.327654	+	0.944798i	$0.393742\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−4.44765	−	6.12166i	−0.169688	−	0.233556i
$688$		0			0
$689$	−2.30095	−	1.67174i	−0.0876594	−	0.0636883i
$690$		0			0
$691$	−7.59169	+	5.51569i	−0.288802	+	0.209827i	−0.722747	−	0.691112i	$-0.757121\pi$
$691$	−7.59169	+	5.51569i	−0.288802	+	0.209827i	0.433946	+	0.900939i	$0.357121\pi$
$692$		0			0
$693$		−	6.58345i		−	0.250085i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	7.00233	−	2.27520i	0.265232	−	0.0861792i
$698$		0			0
$699$	15.9832			0.604540
$700$		0			0
$701$	−20.4347			−0.771809			−0.385904	−	0.922539i	$-0.626111\pi$
$701$	−20.4347			−0.771809			−0.385904	+	0.922539i	$0.626111\pi$
$702$		0			0
$703$	−43.7478	+	14.2145i	−1.64998	+	0.536111i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	6.24930i		−	0.235029i
$708$		0			0
$709$	−4.78774	+	3.47850i	−0.179808	+	0.130638i	−0.674048	−	0.738687i	$-0.735446\pi$
$709$	−4.78774	+	3.47850i	−0.179808	+	0.130638i	0.494241	+	0.869325i	$0.335446\pi$
$710$		0			0
$711$	2.68601	+	1.95150i	0.100733	+	0.0731869i
$712$		0			0
$713$	−45.0708	−	62.0346i	−1.68791	−	2.32321i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−2.77706	−	0.902322i	−0.103711	−	0.0336978i
$718$		0			0
$719$	2.47253	−	7.60966i	0.0922098	−	0.283793i	−0.894307	−	0.447455i	$-0.852331\pi$
$719$	2.47253	−	7.60966i	0.0922098	−	0.283793i	0.986516	+	0.163662i	$0.0523306\pi$
$720$		0			0
$721$	−2.89803	−	8.91922i	−0.107928	−	0.332169i
$722$		0			0
$723$	13.5471	−	18.6460i	0.503821	−	0.693450i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	23.6752	−	32.5861i	0.878065	−	1.20855i	−0.0988886	−	0.995099i	$-0.531529\pi$
$727$	23.6752	−	32.5861i	0.878065	−	1.20855i	0.976953	−	0.213454i	$-0.0684713\pi$
$728$		0			0
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$		0			0
$731$	−14.4240	+	44.3925i	−0.533491	+	1.64192i
$732$		0			0
$733$	10.0786	+	3.27474i	0.372262	+	0.120955i	0.489172	−	0.872187i	$-0.337299\pi$
$733$	10.0786	+	3.27474i	0.372262	+	0.120955i	−0.116910	+	0.993143i	$0.537299\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−11.7193	−	16.1302i	−0.431686	−	0.594165i
$738$		0			0
$739$	−36.8178	−	26.7497i	−1.35437	−	0.984005i	−0.998781	−	0.0493609i	$-0.984282\pi$
$739$	−36.8178	−	26.7497i	−1.35437	−	0.984005i	−0.355585	−	0.934644i	$-0.615718\pi$
$740$		0			0
$741$	−4.86474	+	3.53444i	−0.178711	+	0.129841i
$742$		0			0
$743$		−	8.64344i		−	0.317097i	−0.987351	−	0.158549i	$-0.949319\pi$
$743$		−	8.64344i		−	0.317097i	0.987351	−	0.158549i	$-0.0506814\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−13.1796	+	4.28231i	−0.482217	+	0.156682i
$748$		0			0
$749$	2.82117			0.103083
$750$		0			0
$751$	−54.4382			−1.98648			−0.993239	−	0.116086i	$-0.962965\pi$
$751$	−54.4382			−1.98648			−0.993239	+	0.116086i	$0.962965\pi$
$752$		0			0
$753$	−9.31208	+	3.02568i	−0.339351	+	0.110262i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	34.1378i		−	1.24076i	−0.784302	−	0.620380i	$-0.786978\pi$
$757$		−	34.1378i		−	1.24076i	0.784302	−	0.620380i	$-0.213022\pi$
$758$		0			0
$759$	40.9622	−	29.7608i	1.48683	−	1.08025i
$760$		0			0
$761$	−2.52798	−	1.83668i	−0.0916391	−	0.0665797i	0.541022	−	0.841008i	$-0.318037\pi$
$761$	−2.52798	−	1.83668i	−0.0916391	−	0.0665797i	−0.632661	+	0.774429i	$0.718037\pi$
$762$		0			0
$763$	6.33767	+	8.72305i	0.229439	+	0.315796i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.90673	−	1.26937i	−0.141064	−	0.0458344i
$768$		0			0
$769$	16.4999	−	50.7816i	0.595003	−	1.83123i	0.0402920	−	0.999188i	$-0.487171\pi$
$769$	16.4999	−	50.7816i	0.595003	−	1.83123i	0.554711	−	0.832043i	$-0.312829\pi$
$770$		0			0
$771$	−6.89561	−	21.2225i	−0.248339	−	0.764309i
$772$		0			0
$773$	0.468593	−	0.644963i	0.0168541	−	0.0231977i	−0.800507	−	0.599324i	$-0.795436\pi$
$773$	0.468593	−	0.644963i	0.0168541	−	0.0231977i	0.817361	+	0.576126i	$0.195436\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	4.73664	−	6.51943i	0.169926	−	0.233883i
$778$		0			0
$779$	2.89781	+	8.91855i	0.103825	+	0.319540i
$780$		0			0
$781$	12.6494	−	38.9308i	0.452630	−	1.39305i
$782$		0			0
$783$	−6.57673	−	2.13691i	−0.235033	−	0.0763669i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−24.5442	−	33.7822i	−0.874906	−	1.20420i	−0.977806	−	0.209513i	$-0.932812\pi$
$787$	−24.5442	−	33.7822i	−0.874906	−	1.20420i	0.102900	−	0.994692i	$-0.467188\pi$
$788$		0			0
$789$	0.589898	+	0.428586i	0.0210009	+	0.0152581i
$790$		0			0
$791$	2.86314	−	2.08019i	0.101802	−	0.0739631i
$792$		0			0
$793$			3.18042i			0.112940i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−26.2979	+	8.54471i	−0.931520	+	0.302669i	−0.735184	−	0.677868i	$-0.762904\pi$
$797$	−26.2979	+	8.54471i	−0.931520	+	0.302669i	−0.196336	+	0.980537i	$0.562904\pi$
$798$		0			0
$799$	−22.7385			−0.804430
$800$		0			0
$801$	−2.50645			−0.0885611
$802$		0			0
$803$	−2.19989	+	0.714787i	−0.0776323	+	0.0252243i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	1.85922i		−	0.0654477i
$808$		0			0
$809$	28.2998	−	20.5610i	0.994968	−	0.722887i	0.0339649	−	0.999423i	$-0.489187\pi$
$809$	28.2998	−	20.5610i	0.994968	−	0.722887i	0.961004	+	0.276536i	$0.0891866\pi$
$810$		0			0
$811$	−7.40374	−	5.37913i	−0.259980	−	0.188887i	0.450158	−	0.892949i	$-0.351368\pi$
$811$	−7.40374	−	5.37913i	−0.259980	−	0.188887i	−0.710138	+	0.704062i	$0.751368\pi$
$812$		0			0
$813$	11.4932	+	15.8190i	0.403083	+	0.554797i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−56.5407	−	18.3712i	−1.97811	−	0.642727i
$818$		0			0
$819$	0.325526	−	1.00187i	0.0113748	−	0.0350080i
$820$		0			0
$821$	−0.998901	−	3.07430i	−0.0348619	−	0.107294i	0.932111	−	0.362172i	$-0.117965\pi$
$821$	−0.998901	−	3.07430i	−0.0348619	−	0.107294i	−0.966973	+	0.254878i	$0.917965\pi$
$822$		0			0
$823$	−26.5706	+	36.5713i	−0.926193	+	1.27480i	0.0351334	+	0.999383i	$0.488814\pi$
$823$	−26.5706	+	36.5713i	−0.926193	+	1.27480i	−0.961326	+	0.275412i	$0.911186\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.9051	−	19.1388i	0.483529	−	0.665521i	−0.495649	−	0.868523i	$-0.665070\pi$
$827$	13.9051	−	19.1388i	0.483529	−	0.665521i	0.979178	+	0.203002i	$0.0650698\pi$
$828$		0			0
$829$	−3.94442	−	12.1397i	−0.136995	−	0.421628i	0.858900	−	0.512144i	$-0.171148\pi$
$829$	−3.94442	−	12.1397i	−0.136995	−	0.421628i	−0.995895	+	0.0905157i	$0.971148\pi$
$830$		0			0
$831$	−5.24131	+	16.1311i	−0.181819	+	0.559581i
$832$		0			0
$833$	−26.3444	−	8.55981i	−0.912779	−	0.296580i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	5.59815	+	7.70519i	0.193500	+	0.266330i
$838$		0			0
$839$	−42.0974	−	30.5855i	−1.45336	−	1.05593i	−0.985031	−	0.172378i	$-0.944855\pi$
$839$	−42.0974	−	30.5855i	−1.45336	−	1.05593i	−0.468333	−	0.883552i	$-0.655145\pi$
$840$		0			0
$841$	−15.2255	+	11.0620i	−0.525019	+	0.381449i
$842$		0			0
$843$			26.0879i			0.898513i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−28.4247	+	9.23575i	−0.976685	+	0.317344i
$848$		0			0
$849$	−25.6093			−0.878911
$850$		0			0
$851$	61.9760			2.12451
$852$		0			0
$853$	−33.8823	+	11.0090i	−1.16011	+	0.376942i	−0.824942	−	0.565217i	$-0.808792\pi$
$853$	−33.8823	+	11.0090i	−1.16011	+	0.376942i	−0.335166	+	0.942159i	$0.608792\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			24.6745i			0.842866i	0.906860	+	0.421433i	$0.138473\pi$
$857$			24.6745i			0.842866i	−0.906860	+	0.421433i	$0.861527\pi$
$858$		0			0
$859$	17.7355	−	12.8856i	0.605127	−	0.439650i	−0.242568	−	0.970134i	$-0.577990\pi$
$859$	17.7355	−	12.8856i	0.605127	−	0.439650i	0.847695	+	0.530484i	$0.177990\pi$
$860$		0			0
$861$	−1.32907	−	0.965624i	−0.0452945	−	0.0329084i
$862$		0			0
$863$	−16.2088	−	22.3095i	−0.551755	−	0.759426i	0.438494	−	0.898734i	$-0.355512\pi$
$863$	−16.2088	−	22.3095i	−0.551755	−	0.759426i	−0.990249	+	0.139308i	$0.955512\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	4.76630	+	1.54866i	0.161872	+	0.0525954i
$868$		0			0
$869$	6.45219	−	19.8578i	0.218876	−	0.673630i
$870$		0			0
$871$	−0.985860	−	3.03417i	−0.0334046	−	0.102809i
$872$		0			0
$873$	−0.107382	+	0.147799i	−0.00363434	+	0.00500223i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	12.1600	−	16.7368i	0.410615	−	0.565163i	−0.552754	−	0.833345i	$-0.686423\pi$
$877$	12.1600	−	16.7368i	0.410615	−	0.565163i	0.963368	+	0.268182i	$0.0864229\pi$
$878$		0			0
$879$	−8.58590	−	26.4247i	−0.289595	−	0.891282i
$880$		0			0
$881$	−11.7074	+	36.0318i	−0.394434	+	1.21394i	0.534968	+	0.844872i	$0.320324\pi$
$881$	−11.7074	+	36.0318i	−0.394434	+	1.21394i	−0.929402	+	0.369069i	$0.879676\pi$
$882$		0			0
$883$	−37.4188	−	12.1581i	−1.25924	−	0.409152i	−0.398017	−	0.917378i	$-0.630302\pi$
$883$	−37.4188	−	12.1581i	−1.25924	−	0.409152i	−0.861224	+	0.508226i	$0.830302\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.2693	+	19.6400i	0.479116	+	0.659446i	0.978335	−	0.207030i	$-0.0663796\pi$
$887$	14.2693	+	19.6400i	0.479116	+	0.659446i	−0.499219	+	0.866476i	$0.666380\pi$
$888$		0			0
$889$	−5.05961	−	3.67602i	−0.169694	−	0.123290i
$890$		0			0
$891$	−5.08783	+	3.69653i	−0.170449	+	0.123838i
$892$		0			0
$893$		−	28.9610i		−	0.969142i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	7.70516	−	2.50356i	0.257268	−	0.0835914i
$898$		0			0
$899$	65.8612			2.19659
$900$		0			0
$901$	−13.2602			−0.441762
$902$		0			0
$903$	9.90519	−	3.21839i	0.329624	−	0.107101i
$904$		0			0
$905$		0			0
$906$		0			0
$907$			13.1961i			0.438169i	0.975706	+	0.219085i	$0.0703071\pi$
$907$			13.1961i			0.438169i	−0.975706	+	0.219085i	$0.929693\pi$
$908$		0			0
$909$	−4.82959	+	3.50890i	−0.160187	+	0.116383i
$910$		0			0
$911$	22.3318	+	16.2250i	0.739884	+	0.537557i	0.892675	−	0.450701i	$-0.148826\pi$
$911$	22.3318	+	16.2250i	0.739884	+	0.537557i	−0.152791	+	0.988259i	$0.548826\pi$
$912$		0			0
$913$	51.2259	+	70.5064i	1.69533	+	2.33342i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	6.18002	+	2.00801i	0.204082	+	0.0663103i
$918$		0			0
$919$	−3.75430	+	11.5546i	−0.123843	+	0.381150i	−0.993689	−	0.112175i	$-0.964218\pi$
$919$	−3.75430	+	11.5546i	−0.123843	+	0.381150i	0.869845	+	0.493324i	$0.164218\pi$
$920$		0			0
$921$	4.98821	+	15.3521i	0.164367	+	0.505870i
$922$		0			0
$923$	3.84995	−	5.29900i	0.126723	−	0.174419i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−5.26575	+	7.24769i	−0.172950	+	0.238045i
$928$		0			0
$929$	−10.8881	−	33.5101i	−0.357227	−	1.09943i	−0.954707	−	0.297547i	$-0.903831\pi$
$929$	−10.8881	−	33.5101i	−0.357227	−	1.09943i	0.597481	−	0.801883i	$-0.296169\pi$
$930$		0			0
$931$	10.9022	−	33.5536i	0.357306	−	1.09968i
$932$		0			0
$933$	−27.3316	−	8.88057i	−0.894796	−	0.290737i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	4.00849	+	5.51721i	0.130952	+	0.180240i	0.869458	−	0.494007i	$-0.164468\pi$
$937$	4.00849	+	5.51721i	0.130952	+	0.180240i	−0.738506	+	0.674247i	$0.764468\pi$
$938$		0			0
$939$	21.4279	+	15.5683i	0.699274	+	0.508052i
$940$		0			0
$941$	−25.2441	+	18.3409i	−0.822934	+	0.597897i	−0.917551	−	0.397617i	$-0.869837\pi$
$941$	−25.2441	+	18.3409i	−0.822934	+	0.597897i	0.0946174	+	0.995514i	$0.469837\pi$
$942$		0			0
$943$		−	12.6346i		−	0.411439i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	27.0090	−	8.77576i	0.877675	−	0.285174i	0.164683	−	0.986347i	$-0.447340\pi$
$947$	27.0090	−	8.77576i	0.877675	−	0.285174i	0.712991	+	0.701173i	$0.247340\pi$
$948$		0			0
$949$	−0.370121			−0.0120146
$950$		0			0
$951$	26.2980			0.852772
$952$		0			0
$953$	11.1288	−	3.61597i	0.360497	−	0.117133i	−0.123168	−	0.992386i	$-0.539305\pi$
$953$	11.1288	−	3.61597i	0.360497	−	0.117133i	0.483665	+	0.875253i	$0.339305\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			43.4890i			1.40580i
$958$		0			0
$959$	10.9909	−	7.98538i	0.354916	−	0.257861i
$960$		0			0
$961$	−48.3058	−	35.0962i	−1.55825	−	1.13214i
$962$		0			0
$963$	−1.58405	−	2.18026i	−0.0510453	−	0.0702578i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−16.1031	−	5.23221i	−0.517840	−	0.168257i	0.0384246	−	0.999262i	$-0.487766\pi$
$967$	−16.1031	−	5.23221i	−0.517840	−	0.168257i	−0.556265	+	0.831005i	$0.687766\pi$
$968$		0			0
$969$	−8.66333	+	26.6630i	−0.278306	+	0.856539i
$970$		0			0
$971$	−3.80798	−	11.7198i	−0.122204	−	0.376105i	0.871177	−	0.490968i	$-0.163357\pi$
$971$	−3.80798	−	11.7198i	−0.122204	−	0.376105i	−0.993381	+	0.114864i	$0.963357\pi$
$972$		0			0
$973$	−2.46094	+	3.38719i	−0.0788940	+	0.108588i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2.44310	−	3.36263i	0.0781615	−	0.107580i	−0.768146	−	0.640275i	$-0.778821\pi$
$977$	2.44310	−	3.36263i	0.0781615	−	0.107580i	0.846308	+	0.532695i	$0.178821\pi$
$978$		0			0
$979$	4.87098	+	14.9913i	0.155677	+	0.479126i
$980$		0			0
$981$	3.18284	−	9.79577i	0.101620	−	0.312755i
$982$		0			0
$983$	13.0196	+	4.23033i	0.415261	+	0.134927i	0.509194	−	0.860652i	$-0.329944\pi$
$983$	13.0196	+	4.23033i	0.415261	+	0.134927i	−0.0939323	+	0.995579i	$0.529944\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	2.98218	+	4.10461i	0.0949237	+	0.130651i
$988$		0			0
$989$	64.8017	+	47.0812i	2.06057	+	1.49709i
$990$		0			0
$991$	6.19447	−	4.50055i	0.196774	−	0.142965i	−0.485036	−	0.874494i	$-0.661193\pi$
$991$	6.19447	−	4.50055i	0.196774	−	0.142965i	0.681809	+	0.731530i	$0.261193\pi$
$992$		0			0
$993$			31.2634i			0.992113i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	49.0006	−	15.9213i	1.55187	−	0.504232i	0.597245	−	0.802059i	$-0.296262\pi$
$997$	49.0006	−	15.9213i	1.55187	−	0.504232i	0.954620	+	0.297827i	$0.0962619\pi$
$998$		0			0
$999$	−7.69791			−0.243551

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.o.c.49.4		24
5.2	odd	4		1500.2.m.d.1201.3		24
5.3	odd	4		1500.2.m.c.1201.4		24
5.4	even	2		300.2.o.a.109.3	✓	24
15.14	odd	2		900.2.w.c.109.2		24
25.2	odd	20		1500.2.m.d.301.3		24
25.6	even	5		7500.2.d.g.1249.7		24
25.8	odd	20		7500.2.a.n.1.7		12
25.11	even	5		300.2.o.a.289.3	yes	24
25.14	even	10	inner	1500.2.o.c.949.4		24
25.17	odd	20		7500.2.a.m.1.6		12
25.19	even	10		7500.2.d.g.1249.18		24
25.23	odd	20		1500.2.m.c.301.4		24
75.11	odd	10		900.2.w.c.289.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.109.3	✓	24	5.4	even	2
300.2.o.a.289.3	yes	24	25.11	even	5
900.2.w.c.109.2		24	15.14	odd	2
900.2.w.c.289.2		24	75.11	odd	10
1500.2.m.c.301.4		24	25.23	odd	20
1500.2.m.c.1201.4		24	5.3	odd	4
1500.2.m.d.301.3		24	25.2	odd	20
1500.2.m.d.1201.3		24	5.2	odd	4
1500.2.o.c.49.4		24	1.1	even	1	trivial
1500.2.o.c.949.4		24	25.14	even	10	inner
7500.2.a.m.1.6		12	25.17	odd	20
7500.2.a.n.1.7		12	25.8	odd	20
7500.2.d.g.1249.7		24	25.6	even	5
7500.2.d.g.1249.18		24	25.19	even	10

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:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{3} +1.04684i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{3} +1.04684i q^{7} +(0.809017 - 0.587785i) q^{9} +(-5.08783 - 3.69653i) q^{11} +(-0.591485 - 0.814109i) q^{13} +(-4.46202 - 1.44980i) q^{17} +(1.84654 - 5.68307i) q^{19} +(0.323490 + 0.995600i) q^{21} +(-4.73227 + 6.51341i) q^{23} +(0.587785 - 0.809017i) q^{27} +(-2.13691 - 6.57673i) q^{29} +(-2.94312 + 9.05799i) q^{31} +(-5.98110 - 1.94338i) q^{33} +(-4.52472 - 6.22774i) q^{37} +(-0.814109 - 0.591485i) q^{39} +(-1.26960 + 0.922421i) q^{41} -9.94897i q^{43} +(4.60938 - 1.49768i) q^{47} +5.90413 q^{49} -4.69165 q^{51} +(2.68802 - 0.873389i) q^{53} -5.97554i q^{57} +(3.30248 - 2.39939i) q^{59} +(-2.55692 - 1.85771i) q^{61} +(0.615315 + 0.846908i) q^{63} +(3.01519 + 0.979694i) q^{67} +(-2.48790 + 7.65697i) q^{69} +(2.01138 + 6.19039i) q^{71} +(0.216191 - 0.297561i) q^{73} +(3.86966 - 5.32612i) q^{77} +(1.02596 + 3.15759i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-13.1796 - 4.28231i) q^{83} +(-4.06465 - 5.59450i) q^{87} +(-2.02776 - 1.47326i) q^{89} +(0.852238 - 0.619187i) q^{91} +9.52414i q^{93} +(-0.173748 + 0.0564542i) q^{97} -6.28891 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{9}+O(q^{10}) \) 24 * q + 6 * q^9	\( 24 q + 6 q^{9} - 6 q^{11} - 10 q^{17} + 10 q^{19} - 4 q^{21} - 40 q^{23} + 4 q^{29} + 6 q^{31} - 10 q^{33} - 10 q^{41} + 40 q^{47} - 56 q^{49} + 16 q^{51} + 60 q^{53} - 36 q^{59} - 12 q^{61} + 10 q^{63} - 20 q^{67} + 4 q^{69} + 40 q^{71} - 60 q^{73} + 40 q^{77} + 8 q^{79} - 6 q^{81} + 50 q^{83} + 20 q^{87} - 30 q^{91} + 40 q^{97} - 4 q^{99}+O(q^{100}) \) 24 * q + 6 * q^9 - 6 * q^11 - 10 * q^17 + 10 * q^19 - 4 * q^21 - 40 * q^23 + 4 * q^29 + 6 * q^31 - 10 * q^33 - 10 * q^41 + 40 * q^47 - 56 * q^49 + 16 * q^51 + 60 * q^53 - 36 * q^59 - 12 * q^61 + 10 * q^63 - 20 * q^67 + 4 * q^69 + 40 * q^71 - 60 * q^73 + 40 * q^77 + 8 * q^79 - 6 * q^81 + 50 * q^83 + 20 * q^87 - 30 * q^91 + 40 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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