LMFDB - Embedded newform 1500.2.o.b.49.1

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 5x^{14} + 6x^{12} - 20x^{10} - 79x^{8} - 80x^{6} + 96x^{4} + 320x^{2} + 256 $ x^16 + 5x^14 + 6x^12 - 20x^10 - 79x^8 - 80x^6 + 96x^4 + 320*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.1
Root			$0.720348 - 1.21700i$ of defining polynomial
Character	$\chi$	$=$	1500.49
Dual form			1500.2.o.b.949.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{3} -1.74037i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{3} -1.74037i q^{7} +(0.809017 - 0.587785i) q^{9} +(-1.87714 - 1.36382i) q^{11} +(2.90266 + 3.99517i) q^{13} +(3.55730 + 1.15584i) q^{17} +(0.523364 - 1.61075i) q^{19} +(0.537803 + 1.65519i) q^{21} +(-5.10120 + 7.02120i) q^{23} +(-0.587785 + 0.809017i) q^{27} +(-0.964854 - 2.96952i) q^{29} +(2.95471 - 9.09368i) q^{31} +(2.20671 + 0.717004i) q^{33} +(-3.15464 - 4.34199i) q^{37} +(-3.99517 - 2.90266i) q^{39} +(7.05900 - 5.12866i) q^{41} -2.86270i q^{43} +(8.04830 - 2.61505i) q^{47} +3.97112 q^{49} -3.74037 q^{51} +(-1.27868 + 0.415470i) q^{53} +1.69364i q^{57} +(3.54991 - 2.57916i) q^{59} +(12.4035 + 9.01166i) q^{61} +(-1.02296 - 1.40799i) q^{63} +(8.77897 + 2.85246i) q^{67} +(2.68186 - 8.25391i) q^{69} +(0.00728184 + 0.0224112i) q^{71} +(0.601018 - 0.827230i) q^{73} +(-2.37355 + 3.26691i) q^{77} +(0.246835 + 0.759681i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-2.25408 - 0.732396i) q^{83} +(1.83526 + 2.52602i) q^{87} +(-3.93348 - 2.85784i) q^{89} +(6.95307 - 5.05170i) q^{91} +9.56166i q^{93} +(3.29209 - 1.06966i) q^{97} -2.32027 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^9	$ 16 q + 4 q^{9} + 16 q^{11} - 10 q^{19} + 14 q^{21} + 6 q^{29} - 6 q^{31} + 20 q^{41} + 16 q^{49} - 16 q^{51} + 76 q^{59} + 92 q^{61} - 4 q^{69} - 50 q^{71} + 32 q^{79} - 4 q^{81} + 60 q^{89} + 50 q^{91} + 4 q^{99}+O(q^{100}) $ 16 * q + 4 * q^9 + 16 * q^11 - 10 * q^19 + 14 * q^21 + 6 * q^29 - 6 * q^31 + 20 * q^41 + 16 * q^49 - 16 * q^51 + 76 * q^59 + 92 * q^61 - 4 * q^69 - 50 * q^71 + 32 * q^79 - 4 * q^81 + 60 * q^89 + 50 * q^91 + 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
$7$		−	1.74037i		−	0.657797i	−0.944365	−	0.328899i	$-0.893323\pi$
$7$		−	1.74037i		−	0.657797i	0.944365	−	0.328899i	$-0.106677\pi$
$8$		0			0
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$		0			0
$11$	−1.87714	−	1.36382i	−0.565979	−	0.411208i	0.267663	−	0.963513i	$-0.413749\pi$
$11$	−1.87714	−	1.36382i	−0.565979	−	0.411208i	−0.833642	+	0.552305i	$0.813749\pi$
$12$		0			0
$13$	2.90266	+	3.99517i	0.805054	+	1.10806i	0.992068	+	0.125705i	$0.0401192\pi$
$13$	2.90266	+	3.99517i	0.805054	+	1.10806i	−0.187014	+	0.982357i	$0.559881\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.55730	+	1.15584i	0.862772	+	0.280332i	0.706786	−	0.707428i	$-0.250144\pi$
$17$	3.55730	+	1.15584i	0.862772	+	0.280332i	0.155986	+	0.987759i	$0.450144\pi$
$18$		0			0
$19$	0.523364	−	1.61075i	0.120068	−	0.369531i	−0.872902	−	0.487895i	$-0.837765\pi$
$19$	0.523364	−	1.61075i	0.120068	−	0.369531i	0.992970	+	0.118364i	$0.0377650\pi$
$20$		0			0
$21$	0.537803	+	1.65519i	0.117358	+	0.361192i
$22$		0			0
$23$	−5.10120	+	7.02120i	−1.06367	+	1.46402i	−0.187352	+	0.982293i	$0.559991\pi$
$23$	−5.10120	+	7.02120i	−1.06367	+	1.46402i	−0.876321	+	0.481728i	$0.840009\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$		0			0
$29$	−0.964854	−	2.96952i	−0.179169	−	0.551425i	0.820630	−	0.571459i	$-0.193623\pi$
$29$	−0.964854	−	2.96952i	−0.179169	−	0.551425i	−0.999799	+	0.0200341i	$0.993623\pi$
$30$		0			0
$31$	2.95471	−	9.09368i	0.530682	−	1.63327i	−0.222115	−	0.975020i	$-0.571296\pi$
$31$	2.95471	−	9.09368i	0.530682	−	1.63327i	0.752798	−	0.658252i	$-0.228704\pi$
$32$		0			0
$33$	2.20671	+	0.717004i	0.384139	+	0.124814i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.15464	−	4.34199i	−0.518620	−	0.713820i	0.466723	−	0.884404i	$-0.345435\pi$
$37$	−3.15464	−	4.34199i	−0.518620	−	0.713820i	−0.985343	+	0.170584i	$0.945435\pi$
$38$		0			0
$39$	−3.99517	−	2.90266i	−0.639740	−	0.464798i
$40$		0			0
$41$	7.05900	−	5.12866i	1.10243	−	0.800963i	0.120975	−	0.992656i	$-0.461398\pi$
$41$	7.05900	−	5.12866i	1.10243	−	0.800963i	0.981455	+	0.191693i	$0.0613978\pi$
$42$		0			0
$43$		−	2.86270i		−	0.436558i	−0.975886	−	0.218279i	$-0.929956\pi$
$43$		−	2.86270i		−	0.436558i	0.975886	−	0.218279i	$-0.0700442\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	8.04830	−	2.61505i	1.17397	−	0.381444i	0.343844	−	0.939027i	$-0.388271\pi$
$47$	8.04830	−	2.61505i	1.17397	−	0.381444i	0.830122	+	0.557582i	$0.188271\pi$
$48$		0			0
$49$	3.97112			0.567303
$50$		0			0
$51$	−3.74037			−0.523756
$52$		0			0
$53$	−1.27868	+	0.415470i	−0.175641	+	0.0570691i	−0.395517	−	0.918459i	$-0.629435\pi$
$53$	−1.27868	+	0.415470i	−0.175641	+	0.0570691i	0.219876	+	0.975528i	$0.429435\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			1.69364i			0.224328i
$58$		0			0
$59$	3.54991	−	2.57916i	0.462159	−	0.335778i	−0.332219	−	0.943202i	$-0.607797\pi$
$59$	3.54991	−	2.57916i	0.462159	−	0.335778i	0.794378	+	0.607424i	$0.207797\pi$
$60$		0			0
$61$	12.4035	+	9.01166i	1.58810	+	1.15382i	0.906584	+	0.422025i	$0.138681\pi$
$61$	12.4035	+	9.01166i	1.58810	+	1.15382i	0.681519	+	0.731800i	$0.261319\pi$
$62$		0			0
$63$	−1.02296	−	1.40799i	−0.128881	−	0.177390i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	8.77897	+	2.85246i	1.07252	+	0.348483i	0.791469	−	0.611209i	$-0.209317\pi$
$67$	8.77897	+	2.85246i	1.07252	+	0.348483i	0.281052	+	0.959692i	$0.409317\pi$
$68$		0			0
$69$	2.68186	−	8.25391i	0.322858	−	0.993654i
$70$		0			0
$71$	0.00728184	+	0.0224112i	0.000864195	+	0.00265972i	0.951488	−	0.307687i	$-0.0995549\pi$
$71$	0.00728184	+	0.0224112i	0.000864195	+	0.00265972i	−0.950623	+	0.310347i	$0.899555\pi$
$72$		0			0
$73$	0.601018	−	0.827230i	0.0703438	−	0.0968200i	−0.772395	−	0.635142i	$-0.780942\pi$
$73$	0.601018	−	0.827230i	0.0703438	−	0.0968200i	0.842739	+	0.538322i	$0.180942\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.37355	+	3.26691i	−0.270491	+	0.372299i
$78$		0			0
$79$	0.246835	+	0.759681i	0.0277711	+	0.0854708i	0.963981	−	0.265969i	$-0.0856920\pi$
$79$	0.246835	+	0.759681i	0.0277711	+	0.0854708i	−0.936210	+	0.351440i	$0.885692\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	−2.25408	−	0.732396i	−0.247418	−	0.0803909i	0.182683	−	0.983172i	$-0.441522\pi$
$83$	−2.25408	−	0.732396i	−0.247418	−	0.0803909i	−0.430100	+	0.902781i	$0.641522\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.83526	+	2.52602i	0.196761	+	0.270818i
$88$		0			0
$89$	−3.93348	−	2.85784i	−0.416948	−	0.302931i	0.359461	−	0.933160i	$-0.382961\pi$
$89$	−3.93348	−	2.85784i	−0.416948	−	0.302931i	−0.776409	+	0.630230i	$0.782961\pi$
$90$		0			0
$91$	6.95307	−	5.05170i	0.728880	−	0.529562i
$92$		0			0
$93$			9.56166i			0.991498i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.29209	−	1.06966i	0.334261	−	0.108608i	−0.137078	−	0.990560i	$-0.543771\pi$
$97$	3.29209	−	1.06966i	0.334261	−	0.108608i	0.471339	+	0.881952i	$0.343771\pi$
$98$		0			0
$99$	−2.32027			−0.233196
$100$		0			0
$101$	−7.58056			−0.754294			−0.377147	−	0.926154i	$-0.623095\pi$
$101$	−7.58056			−0.754294			−0.377147	+	0.926154i	$0.623095\pi$
$102$		0			0
$103$	10.2428	−	3.32808i	1.00925	−	0.327926i	0.242695	−	0.970103i	$-0.421969\pi$
$103$	10.2428	−	3.32808i	1.00925	−	0.327926i	0.766556	+	0.642177i	$0.221969\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	4.34344i		−	0.419896i	−0.977713	−	0.209948i	$-0.932671\pi$
$107$		−	4.34344i		−	0.419896i	0.977713	−	0.209948i	$-0.0673294\pi$
$108$		0			0
$109$	0.866675	−	0.629677i	0.0830125	−	0.0603121i	−0.545505	−	0.838108i	$-0.683662\pi$
$109$	0.866675	−	0.629677i	0.0830125	−	0.0603121i	0.628517	+	0.777796i	$0.283662\pi$
$110$		0			0
$111$	4.34199	+	3.15464i	0.412124	+	0.299426i
$112$		0			0
$113$	10.9103	+	15.0167i	1.02635	+	1.41265i	0.907653	+	0.419722i	$0.137872\pi$
$113$	10.9103	+	15.0167i	1.02635	+	1.41265i	0.118699	+	0.992930i	$0.462128\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	4.69661	+	1.52602i	0.434202	+	0.141081i
$118$		0			0
$119$	2.01158	−	6.19101i	0.184401	−	0.567529i
$120$		0			0
$121$	−1.73554	−	5.34145i	−0.157777	−	0.485586i
$122$		0			0
$123$	−5.12866	+	7.05900i	−0.462436	+	0.636488i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	11.1735	−	15.3791i	0.991492	−	1.36467i	0.0610897	−	0.998132i	$-0.480542\pi$
$127$	11.1735	−	15.3791i	0.991492	−	1.36467i	0.930402	−	0.366540i	$-0.119458\pi$
$128$		0			0
$129$	0.884623	+	2.72259i	0.0778867	+	0.239711i
$130$		0			0
$131$	−0.230228	+	0.708567i	−0.0201151	+	0.0619078i	−0.960610	−	0.277899i	$-0.910362\pi$
$131$	−0.230228	+	0.708567i	−0.0201151	+	0.0619078i	0.940495	+	0.339807i	$0.110362\pi$
$132$		0			0
$133$	−2.80329	−	0.910845i	−0.243076	−	0.0789803i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.54355	+	9.00643i	0.559054	+	0.769471i	0.991206	−	0.132329i	$-0.0422457\pi$
$137$	6.54355	+	9.00643i	0.559054	+	0.769471i	−0.432152	+	0.901801i	$0.642246\pi$
$138$		0			0
$139$	11.0746	+	8.04613i	0.939331	+	0.682464i	0.948260	−	0.317496i	$-0.102842\pi$
$139$	11.0746	+	8.04613i	0.939331	+	0.682464i	−0.00892821	+	0.999960i	$0.502842\pi$
$140$		0			0
$141$	−6.84629	+	4.97412i	−0.576562	+	0.418897i
$142$		0			0
$143$		−	11.4582i		−	0.958185i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−3.77676	+	1.22714i	−0.311502	+	0.101213i
$148$		0			0
$149$	10.6283			0.870701			0.435351	−	0.900261i	$-0.356624\pi$
$149$	10.6283			0.870701			0.435351	+	0.900261i	$0.356624\pi$
$150$		0			0
$151$	−10.4689			−0.851943			−0.425972	−	0.904737i	$-0.640068\pi$
$151$	−10.4689			−0.851943			−0.425972	+	0.904737i	$0.640068\pi$
$152$		0			0
$153$	3.55730	−	1.15584i	0.287591	−	0.0934439i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	17.2987i		−	1.38059i	−0.723528	−	0.690295i	$-0.757481\pi$
$157$		−	17.2987i		−	1.38059i	0.723528	−	0.690295i	$-0.242519\pi$
$158$		0			0
$159$	1.08771	−	0.790270i	0.0862613	−	0.0626725i
$160$		0			0
$161$	12.2195	+	8.87796i	0.963028	+	0.699681i
$162$		0			0
$163$	−3.61304	−	4.97293i	−0.282995	−	0.389510i	0.643728	−	0.765255i	$-0.277387\pi$
$163$	−3.61304	−	4.97293i	−0.282995	−	0.389510i	−0.926723	+	0.375745i	$0.877387\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.80718	−	0.587188i	−0.139844	−	0.0454379i	0.238259	−	0.971202i	$-0.423423\pi$
$167$	−1.80718	−	0.587188i	−0.139844	−	0.0454379i	−0.378103	+	0.925764i	$0.623423\pi$
$168$		0			0
$169$	−3.51874	+	10.8296i	−0.270672	+	0.833043i
$170$		0			0
$171$	−0.523364	−	1.61075i	−0.0400226	−	0.123177i
$172$		0			0
$173$	−6.81000	+	9.37317i	−0.517755	+	0.712629i	−0.985203	−	0.171392i	$-0.945174\pi$
$173$	−6.81000	+	9.37317i	−0.517755	+	0.712629i	0.467448	+	0.884021i	$0.345174\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2.57916	+	3.54991i	−0.193862	+	0.266828i
$178$		0			0
$179$	−6.81312	−	20.9686i	−0.509236	−	1.56727i	−0.793530	−	0.608531i	$-0.791759\pi$
$179$	−6.81312	−	20.9686i	−0.509236	−	1.56727i	0.284294	−	0.958737i	$-0.408241\pi$
$180$		0			0
$181$	6.38341	−	19.6461i	0.474475	−	1.46028i	−0.372190	−	0.928157i	$-0.621393\pi$
$181$	6.38341	−	19.6461i	0.474475	−	1.46028i	0.846665	−	0.532127i	$-0.178607\pi$
$182$		0			0
$183$	−14.5812	−	4.73771i	−1.07787	−	0.350222i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−5.10120	−	7.02120i	−0.373036	−	0.513441i
$188$		0			0
$189$	1.40799	+	1.02296i	0.102416	+	0.0744096i
$190$		0			0
$191$	−16.8535	+	12.2448i	−1.21948	+	0.886004i	−0.996057	−	0.0887181i	$-0.971723\pi$
$191$	−16.8535	+	12.2448i	−1.21948	+	0.886004i	−0.223423	+	0.974722i	$0.571723\pi$
$192$		0			0
$193$		−	4.78053i		−	0.344110i	−0.985087	−	0.172055i	$-0.944959\pi$
$193$		−	4.78053i		−	0.344110i	0.985087	−	0.172055i	$-0.0550406\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−16.5028	+	5.36207i	−1.17577	+	0.382032i	−0.830795	−	0.556579i	$-0.812114\pi$
$197$	−16.5028	+	5.36207i	−1.17577	+	0.382032i	−0.344978	+	0.938611i	$0.612114\pi$
$198$		0			0
$199$	−11.0756			−0.785129			−0.392564	−	0.919724i	$-0.628412\pi$
$199$	−11.0756			−0.785129			−0.392564	+	0.919724i	$0.628412\pi$
$200$		0			0
$201$	−9.23075			−0.651087
$202$		0			0
$203$	−5.16805	+	1.67920i	−0.362726	+	0.117857i
$204$		0			0
$205$		0			0
$206$		0			0
$207$			8.67867i			0.603210i
$208$		0			0
$209$	−3.17920	+	2.30982i	−0.219910	+	0.159774i
$210$		0			0
$211$	−4.58634	−	3.33217i	−0.315736	−	0.229396i	0.418618	−	0.908163i	$-0.362515\pi$
$211$	−4.58634	−	3.33217i	−0.315736	−	0.229396i	−0.734354	+	0.678767i	$0.762515\pi$
$212$		0			0
$213$	−0.0138509	−	0.0190641i	−0.000949047	−	0.00130625i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−15.8263	−	5.14229i	−1.07436	−	0.349081i
$218$		0			0
$219$	−0.315974	+	0.972467i	−0.0213515	+	0.0657132i
$220$		0			0
$221$	5.70788	+	17.5670i	0.383953	+	1.18169i
$222$		0			0
$223$	12.5671	−	17.2972i	0.841559	−	1.15831i	−0.144101	−	0.989563i	$-0.546029\pi$
$223$	12.5671	−	17.2972i	0.841559	−	1.15831i	0.985660	−	0.168743i	$-0.0539708\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−13.4970	+	18.5770i	−0.895827	+	1.23300i	0.0759536	+	0.997111i	$0.475800\pi$
$227$	−13.4970	+	18.5770i	−0.895827	+	1.23300i	−0.971780	+	0.235888i	$0.924200\pi$
$228$		0			0
$229$	8.68482	+	26.7291i	0.573909	+	1.76631i	0.639865	+	0.768487i	$0.278990\pi$
$229$	8.68482	+	26.7291i	0.573909	+	1.76631i	−0.0659560	+	0.997823i	$0.521010\pi$
$230$		0			0
$231$	1.24785	−	3.84049i	0.0821025	−	0.252686i
$232$		0			0
$233$	1.26676	+	0.411596i	0.0829885	+	0.0269646i	0.350217	−	0.936669i	$-0.386108\pi$
$233$	1.26676	+	0.411596i	0.0829885	+	0.0269646i	−0.267229	+	0.963633i	$0.586108\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.469509	−	0.646223i	−0.0304979	−	0.0419767i
$238$		0			0
$239$	2.78730	+	2.02509i	0.180295	+	0.130992i	0.674272	−	0.738483i	$-0.264457\pi$
$239$	2.78730	+	2.02509i	0.180295	+	0.130992i	−0.493977	+	0.869475i	$0.664457\pi$
$240$		0			0
$241$	19.4923	−	14.1620i	1.25561	−	0.912253i	0.257075	−	0.966392i	$-0.417241\pi$
$241$	19.4923	−	14.1620i	1.25561	−	0.912253i	0.998533	+	0.0541389i	$0.0172414\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	7.95437	−	2.58453i	0.506124	−	0.164450i
$248$		0			0
$249$	2.37008			0.150198
$250$		0			0
$251$	−30.1621			−1.90381			−0.951907	−	0.306387i	$-0.900880\pi$
$251$	−30.1621			−1.90381			−0.951907	+	0.306387i	$0.900880\pi$
$252$		0			0
$253$	19.1513	−	6.22264i	1.20403	−	0.391214i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			10.6862i			0.666588i	0.942823	+	0.333294i	$0.108160\pi$
$257$			10.6862i			0.666588i	−0.942823	+	0.333294i	$0.891840\pi$
$258$		0			0
$259$	−7.55667	+	5.49024i	−0.469548	+	0.341147i
$260$		0			0
$261$	−2.52602	−	1.83526i	−0.156357	−	0.113600i
$262$		0			0
$263$	5.42689	+	7.46948i	0.334637	+	0.460588i	0.942865	−	0.333174i	$-0.108120\pi$
$263$	5.42689	+	7.46948i	0.334637	+	0.460588i	−0.608229	+	0.793762i	$0.708120\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	4.62409	+	1.50246i	0.282989	+	0.0919488i
$268$		0			0
$269$	−8.26252	+	25.4294i	−0.503774	+	1.55046i	0.299047	+	0.954238i	$0.403331\pi$
$269$	−8.26252	+	25.4294i	−0.503774	+	1.55046i	−0.802821	+	0.596220i	$0.796669\pi$
$270$		0			0
$271$	7.47325	+	23.0003i	0.453968	+	1.39717i	0.872343	+	0.488895i	$0.162600\pi$
$271$	7.47325	+	23.0003i	0.453968	+	1.39717i	−0.418375	+	0.908274i	$0.637400\pi$
$272$		0			0
$273$	−5.05170	+	6.95307i	−0.305743	+	0.420819i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−18.5787	+	25.5713i	−1.11628	+	1.53643i	−0.304464	+	0.952524i	$0.598477\pi$
$277$	−18.5787	+	25.5713i	−1.11628	+	1.53643i	−0.811819	+	0.583909i	$0.801523\pi$
$278$		0			0
$279$	−2.95471	−	9.09368i	−0.176894	−	0.544424i
$280$		0			0
$281$	7.18851	−	22.1240i	0.428831	−	1.31981i	−0.470447	−	0.882428i	$-0.655907\pi$
$281$	7.18851	−	22.1240i	0.428831	−	1.31981i	0.899278	−	0.437377i	$-0.144093\pi$
$282$		0			0
$283$	−23.6167	−	7.67355i	−1.40387	−	0.456145i	−0.493430	−	0.869786i	$-0.664257\pi$
$283$	−23.6167	−	7.67355i	−1.40387	−	0.456145i	−0.910440	+	0.413641i	$0.864257\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.92576	−	12.2853i	−0.526871	−	0.725175i
$288$		0			0
$289$	−2.43486	−	1.76903i	−0.143227	−	0.104060i
$290$		0			0
$291$	−2.80042	+	2.03462i	−0.164163	+	0.119272i
$292$		0			0
$293$		−	29.2758i		−	1.71031i	−0.518371	−	0.855156i	$-0.673461\pi$
$293$		−	29.2758i		−	1.71031i	0.518371	−	0.855156i	$-0.326539\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2.20671	−	0.717004i	0.128046	−	0.0416048i
$298$		0			0
$299$	−42.8580			−2.47854
$300$		0			0
$301$	−4.98215			−0.287166
$302$		0			0
$303$	7.20954	−	2.34252i	0.414177	−	0.134574i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			8.73972i			0.498802i	0.968400	+	0.249401i	$0.0802337\pi$
$307$			8.73972i			0.498802i	−0.968400	+	0.249401i	$0.919766\pi$
$308$		0			0
$309$	−8.71303	+	6.33039i	−0.495667	+	0.360123i
$310$		0			0
$311$	12.5043	+	9.08488i	0.709052	+	0.515156i	0.882868	−	0.469622i	$-0.155610\pi$
$311$	12.5043	+	9.08488i	0.709052	+	0.515156i	−0.173816	+	0.984778i	$0.555610\pi$
$312$		0			0
$313$	−0.916343	−	1.26124i	−0.0517948	−	0.0712894i	0.782334	−	0.622859i	$-0.214029\pi$
$313$	−0.916343	−	1.26124i	−0.0517948	−	0.0712894i	−0.834129	+	0.551570i	$0.814029\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.19520	−	1.68802i	−0.291792	−	0.0948088i	0.159464	−	0.987204i	$-0.449024\pi$
$317$	−5.19520	−	1.68802i	−0.291792	−	0.0948088i	−0.451255	+	0.892395i	$0.649024\pi$
$318$		0			0
$319$	−2.23873	+	6.89009i	−0.125345	+	0.385771i
$320$		0			0
$321$	1.34220	+	4.13085i	0.0749140	+	0.230562i
$322$		0			0
$323$	3.72352	−	5.12499i	0.207182	−	0.285162i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−0.629677	+	0.866675i	−0.0348212	+	0.0479273i
$328$		0			0
$329$	−4.55115	−	14.0070i	−0.250913	−	0.772231i
$330$		0			0
$331$	0.264458	−	0.813918i	0.0145359	−	0.0447370i	−0.943525	−	0.331300i	$-0.892513\pi$
$331$	0.264458	−	0.813918i	0.0145359	−	0.0447370i	0.958061	+	0.286563i	$0.0925128\pi$
$332$		0			0
$333$	−5.10432	−	1.65849i	−0.279715	−	0.0908849i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−8.71367	−	11.9933i	−0.474664	−	0.653318i	0.502805	−	0.864400i	$-0.332301\pi$
$337$	−8.71367	−	11.9933i	−0.474664	−	0.653318i	−0.977468	+	0.211082i	$0.932301\pi$
$338$		0			0
$339$	−15.0167	−	10.9103i	−0.815595	−	0.592564i
$340$		0			0
$341$	−17.9486	+	13.0404i	−0.971970	+	0.706177i
$342$		0			0
$343$		−	19.0938i		−	1.03097i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.11339	−	0.361763i	0.0597700	−	0.0194204i	−0.278979	−	0.960297i	$-0.589996\pi$
$347$	1.11339	−	0.361763i	0.0597700	−	0.0194204i	0.338749	+	0.940877i	$0.389996\pi$
$348$		0			0
$349$	21.4346			1.14737			0.573683	−	0.819077i	$-0.305514\pi$
$349$	21.4346			1.14737			0.573683	+	0.819077i	$0.305514\pi$
$350$		0			0
$351$	−4.93831			−0.263587
$352$		0			0
$353$	−3.38834	+	1.10094i	−0.180343	+	0.0585970i	−0.397796	−	0.917474i	$-0.630225\pi$
$353$	−3.38834	+	1.10094i	−0.180343	+	0.0585970i	0.217453	+	0.976071i	$0.430225\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			6.50961i			0.344525i
$358$		0			0
$359$	10.8337	−	7.87116i	0.571782	−	0.415424i	−0.263970	−	0.964531i	$-0.585032\pi$
$359$	10.8337	−	7.87116i	0.571782	−	0.415424i	0.835752	+	0.549107i	$0.185032\pi$
$360$		0			0
$361$	13.0507	+	9.48191i	0.686880	+	0.499048i
$362$		0			0
$363$	3.30120	+	4.54371i	0.173268	+	0.238483i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−1.35464	−	0.440150i	−0.0707118	−	0.0229757i	0.273447	−	0.961887i	$-0.411836\pi$
$367$	−1.35464	−	0.440150i	−0.0707118	−	0.0229757i	−0.344159	+	0.938911i	$0.611836\pi$
$368$		0			0
$369$	2.69630	−	8.29835i	0.140364	−	0.431995i
$370$		0			0
$371$	0.723070	+	2.22538i	0.0375399	+	0.115536i
$372$		0			0
$373$	−15.0077	+	20.6564i	−0.777072	+	1.06955i	0.218527	+	0.975831i	$0.429875\pi$
$373$	−15.0077	+	20.6564i	−0.777072	+	1.06955i	−0.995599	+	0.0937165i	$0.970125\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	9.06309	−	12.4743i	0.466773	−	0.642457i
$378$		0			0
$379$	11.7671	+	36.2153i	0.604434	+	1.86026i	0.500634	+	0.865659i	$0.333100\pi$
$379$	11.7671	+	36.2153i	0.604434	+	1.86026i	0.103800	+	0.994598i	$0.466900\pi$
$380$		0			0
$381$	−5.87428	+	18.0792i	−0.300949	+	0.926225i
$382$		0			0
$383$	−12.9862	−	4.21946i	−0.663562	−	0.215604i	−0.0421775	−	0.999110i	$-0.513429\pi$
$383$	−12.9862	−	4.21946i	−0.663562	−	0.215604i	−0.621384	+	0.783506i	$0.713429\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.68265	−	2.31597i	−0.0855341	−	0.117728i
$388$		0			0
$389$	28.9546	+	21.0368i	1.46806	+	1.06661i	0.981171	+	0.193142i	$0.0618679\pi$
$389$	28.9546	+	21.0368i	1.46806	+	1.06661i	0.486888	+	0.873465i	$0.338132\pi$
$390$		0			0
$391$	−26.2619	+	19.0804i	−1.32812	+	0.964935i
$392$		0			0
$393$		−	0.745032i		−	0.0375819i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−23.3412	+	7.58400i	−1.17146	+	0.380630i	−0.829187	−	0.558971i	$-0.811196\pi$
$397$	−23.3412	+	7.58400i	−1.17146	+	0.380630i	−0.342272	+	0.939601i	$0.611196\pi$
$398$		0			0
$399$	2.94756			0.147562
$400$		0			0
$401$	−25.7068			−1.28373			−0.641867	−	0.766816i	$-0.721840\pi$
$401$	−25.7068			−1.28373			−0.641867	+	0.766816i	$0.721840\pi$
$402$		0			0
$403$	44.9074	−	14.5913i	2.23700	−	0.726844i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			12.4529i			0.617268i
$408$		0			0
$409$	−15.0121	+	10.9069i	−0.742299	+	0.539312i	−0.893430	−	0.449202i	$-0.851708\pi$
$409$	−15.0121	+	10.9069i	−0.742299	+	0.539312i	0.151131	+	0.988514i	$0.451708\pi$
$410$		0			0
$411$	−9.00643	−	6.54355i	−0.444254	−	0.322770i
$412$		0			0
$413$	−4.48869	−	6.17815i	−0.220874	−	0.304007i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−13.0189	−	4.23010i	−0.637539	−	0.207149i
$418$		0			0
$419$	−1.45029	+	4.46354i	−0.0708513	+	0.218058i	−0.980212	−	0.197951i	$-0.936571\pi$
$419$	−1.45029	+	4.46354i	−0.0708513	+	0.218058i	0.909361	+	0.416009i	$0.136571\pi$
$420$		0			0
$421$	2.84929	+	8.76921i	0.138866	+	0.427385i	0.996171	−	0.0874228i	$-0.0278631\pi$
$421$	2.84929	+	8.76921i	0.138866	+	0.427385i	−0.857305	+	0.514808i	$0.827863\pi$
$422$		0			0
$423$	4.97412	−	6.84629i	0.241850	−	0.332878i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	15.6836	−	21.5866i	0.758983	−	1.04465i
$428$		0			0
$429$	3.54079	+	10.8974i	0.170951	+	0.526132i
$430$		0			0
$431$	8.83198	−	27.1820i	0.425421	−	1.30931i	−0.477169	−	0.878812i	$-0.658337\pi$
$431$	8.83198	−	27.1820i	0.425421	−	1.30931i	0.902590	−	0.430501i	$-0.141663\pi$
$432$		0			0
$433$	−3.45581	−	1.12286i	−0.166075	−	0.0539612i	0.224799	−	0.974405i	$-0.427827\pi$
$433$	−3.45581	−	1.12286i	−0.166075	−	0.0539612i	−0.390875	+	0.920444i	$0.627827\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	8.63959	+	11.8914i	0.413288	+	0.568842i
$438$		0			0
$439$	−14.2446	−	10.3493i	−0.679859	−	0.493947i	0.193452	−	0.981110i	$-0.438032\pi$
$439$	−14.2446	−	10.3493i	−0.679859	−	0.493947i	−0.873311	+	0.487163i	$0.838032\pi$
$440$		0			0
$441$	3.21270	−	2.33417i	0.152986	−	0.111151i
$442$		0			0
$443$		−	7.11807i		−	0.338190i	−0.985600	−	0.169095i	$-0.945916\pi$
$443$		−	7.11807i		−	0.338190i	0.985600	−	0.169095i	$-0.0540844\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−10.1081	+	3.28431i	−0.478096	+	0.155343i
$448$		0			0
$449$	20.4121			0.963305			0.481653	−	0.876362i	$-0.340037\pi$
$449$	20.4121			0.963305			0.481653	+	0.876362i	$0.340037\pi$
$450$		0			0
$451$	−20.2453			−0.953315
$452$		0			0
$453$	9.95647	−	3.23505i	0.467796	−	0.151996i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	16.8375i		−	0.787624i	−0.919191	−	0.393812i	$-0.871156\pi$
$457$		−	16.8375i		−	0.787624i	0.919191	−	0.393812i	$-0.128844\pi$
$458$		0			0
$459$	−3.02602	+	2.19853i	−0.141243	+	0.102619i
$460$		0			0
$461$	−14.0162	−	10.1833i	−0.652798	−	0.474286i	0.211425	−	0.977394i	$-0.432190\pi$
$461$	−14.0162	−	10.1833i	−0.652798	−	0.474286i	−0.864223	+	0.503109i	$0.832190\pi$
$462$		0			0
$463$	5.05738	+	6.96088i	0.235036	+	0.323500i	0.910201	−	0.414168i	$-0.135927\pi$
$463$	5.05738	+	6.96088i	0.235036	+	0.323500i	−0.675164	+	0.737667i	$0.735927\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.794942	+	0.258292i	0.0367855	+	0.0119523i	0.327352	−	0.944902i	$-0.393844\pi$
$467$	0.794942	+	0.258292i	0.0367855	+	0.0119523i	−0.290566	+	0.956855i	$0.593844\pi$
$468$		0			0
$469$	4.96433	−	15.2786i	0.229231	−	0.705502i
$470$		0			0
$471$	5.34560	+	16.4521i	0.246312	+	0.758072i
$472$		0			0
$473$	−3.90422	+	5.37369i	−0.179516	+	0.247083i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.790270	+	1.08771i	−0.0361840	+	0.0498030i
$478$		0			0
$479$	10.3365	+	31.8123i	0.472285	+	1.45354i	0.849585	+	0.527452i	$0.176853\pi$
$479$	10.3365	+	31.8123i	0.472285	+	1.45354i	−0.377300	+	0.926091i	$0.623147\pi$
$480$		0			0
$481$	8.19015	−	25.2067i	0.373439	−	1.14933i
$482$		0			0
$483$	−14.3648	−	4.66742i	−0.653623	−	0.212375i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	14.3512	+	19.7528i	0.650316	+	0.895083i	0.999113	−	0.0421152i	$-0.0134097\pi$
$487$	14.3512	+	19.7528i	0.650316	+	0.895083i	−0.348797	+	0.937198i	$0.613410\pi$
$488$		0			0
$489$	4.97293	+	3.61304i	0.224884	+	0.163387i
$490$		0			0
$491$	11.8501	−	8.60958i	0.534786	−	0.388545i	−0.287359	−	0.957823i	$-0.592777\pi$
$491$	11.8501	−	8.60958i	0.534786	−	0.388545i	0.822145	+	0.569278i	$0.192777\pi$
$492$		0			0
$493$		−	11.6787i		−	0.525981i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.0390037	−	0.0126731i	0.00174956	−	0.000568465i
$498$		0			0
$499$	13.5655			0.607276			0.303638	−	0.952787i	$-0.401799\pi$
$499$	13.5655			0.607276			0.303638	+	0.952787i	$0.401799\pi$
$500$		0			0
$501$	1.90018			0.0848937
$502$		0			0
$503$	−38.9250	+	12.6475i	−1.73558	+	0.563924i	−0.994237	−	0.107202i	$-0.965811\pi$
$503$	−38.9250	+	12.6475i	−1.73558	+	0.563924i	−0.741343	+	0.671126i	$0.765811\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	11.3869i		−	0.505709i
$508$		0			0
$509$	9.82240	−	7.13639i	0.435370	−	0.316315i	−0.348422	−	0.937338i	$-0.613282\pi$
$509$	9.82240	−	7.13639i	0.435370	−	0.316315i	0.783793	+	0.621023i	$0.213282\pi$
$510$		0			0
$511$	−1.43968	−	1.04599i	−0.0636879	−	0.0462720i
$512$		0			0
$513$	0.995497	+	1.37018i	0.0439523	+	0.0604951i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−18.6743	−	6.06763i	−0.821293	−	0.266854i
$518$		0			0
$519$	3.58023	−	11.0188i	0.157155	−	0.483672i
$520$		0			0
$521$	8.10398	+	24.9415i	0.355042	+	1.09271i	0.955985	+	0.293415i	$0.0947918\pi$
$521$	8.10398	+	24.9415i	0.355042	+	1.09271i	−0.600943	+	0.799292i	$0.705208\pi$
$522$		0			0
$523$	−9.00754	+	12.3978i	−0.393872	+	0.542118i	−0.959193	−	0.282753i	$-0.908752\pi$
$523$	−9.00754	+	12.3978i	−0.393872	+	0.542118i	0.565321	+	0.824871i	$0.308752\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	21.0216	−	28.9338i	0.915716	−	1.26037i
$528$		0			0
$529$	−16.1676	−	49.7587i	−0.702938	−	2.16342i
$530$		0			0
$531$	1.35595	−	4.17317i	0.0588430	−	0.181100i
$532$		0			0
$533$	40.9798	+	13.3151i	1.77503	+	0.576743i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	12.9593	+	17.8370i	0.559236	+	0.769722i
$538$		0			0
$539$	−7.45435	−	5.41590i	−0.321082	−	0.233279i
$540$		0			0
$541$	−7.66742	+	5.57071i	−0.329648	+	0.239503i	−0.740281	−	0.672297i	$-0.765308\pi$
$541$	−7.66742	+	5.57071i	−0.329648	+	0.239503i	0.410633	+	0.911801i	$0.365308\pi$
$542$		0			0
$543$			20.6571i			0.886483i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.614321	+	0.199605i	−0.0262665	+	0.00853449i	−0.322121	−	0.946699i	$-0.604396\pi$
$547$	−0.614321	+	0.199605i	−0.0262665	+	0.00853449i	0.295854	+	0.955233i	$0.404396\pi$
$548$		0			0
$549$	15.3316			0.654335
$550$		0			0
$551$	−5.28811			−0.225281
$552$		0			0
$553$	1.32212	−	0.429584i	0.0562224	−	0.0182678i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	12.0297i		−	0.509716i	−0.966978	−	0.254858i	$-0.917971\pi$
$557$		−	12.0297i		−	0.509716i	0.966978	−	0.254858i	$-0.0820287\pi$
$558$		0			0
$559$	11.4370	−	8.30946i	0.483733	−	0.351453i
$560$		0			0
$561$	7.02120	+	5.10120i	0.296435	+	0.215373i
$562$		0			0
$563$	9.33593	+	12.8498i	0.393462	+	0.541555i	0.959088	−	0.283107i	$-0.0913653\pi$
$563$	9.33593	+	12.8498i	0.393462	+	0.541555i	−0.565626	+	0.824662i	$0.691365\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.65519	−	0.537803i	−0.0695114	−	0.0225856i
$568$		0			0
$569$	−6.77685	+	20.8570i	−0.284100	+	0.874371i	0.702566	+	0.711618i	$0.252037\pi$
$569$	−6.77685	+	20.8570i	−0.284100	+	0.874371i	−0.986667	+	0.162753i	$0.947963\pi$
$570$		0			0
$571$	−2.10390	−	6.47513i	−0.0880453	−	0.270976i	0.897334	−	0.441353i	$-0.145501\pi$
$571$	−2.10390	−	6.47513i	−0.0880453	−	0.270976i	−0.985379	+	0.170377i	$0.945501\pi$
$572$		0			0
$573$	12.2448	−	16.8535i	0.511534	−	0.704067i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	10.9488	−	15.0698i	0.455806	−	0.627364i	−0.517826	−	0.855486i	$-0.673259\pi$
$577$	10.9488	−	15.0698i	0.455806	−	0.627364i	0.973632	+	0.228122i	$0.0732586\pi$
$578$		0			0
$579$	1.47726	+	4.54655i	0.0613930	+	0.188948i
$580$		0			0
$581$	−1.27464	+	3.92293i	−0.0528809	+	0.162751i
$582$		0			0
$583$	2.96690	+	0.964003i	0.122876	+	0.0399249i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.35254	+	11.4963i	0.344746	+	0.474503i	0.945820	−	0.324691i	$-0.105260\pi$
$587$	8.35254	+	11.4963i	0.344746	+	0.474503i	−0.601074	+	0.799194i	$0.705260\pi$
$588$		0			0
$589$	−13.1012	−	9.51860i	−0.539827	−	0.392207i
$590$		0			0
$591$	14.0381	−	10.1993i	0.577450	−	0.419542i
$592$		0			0
$593$		−	40.7850i		−	1.67484i	−0.546559	−	0.837420i	$-0.684063\pi$
$593$		−	40.7850i		−	1.67484i	0.546559	−	0.837420i	$-0.315937\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	10.5335	−	3.42255i	0.431109	−	0.140076i
$598$		0			0
$599$	−34.8928			−1.42568			−0.712841	−	0.701326i	$-0.752592\pi$
$599$	−34.8928			−1.42568			−0.712841	+	0.701326i	$0.752592\pi$
$600$		0			0
$601$	10.6287			0.433552			0.216776	−	0.976221i	$-0.430446\pi$
$601$	10.6287			0.433552			0.216776	+	0.976221i	$0.430446\pi$
$602$		0			0
$603$	8.77897	−	2.85246i	0.357507	−	0.116161i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			30.5033i			1.23809i	0.785355	+	0.619045i	$0.212480\pi$
$607$			30.5033i			1.23809i	−0.785355	+	0.619045i	$0.787520\pi$
$608$		0			0
$609$	4.39620	−	3.19403i	0.178143	−	0.129429i
$610$		0			0
$611$	33.8091	+	24.5638i	1.36777	+	0.993743i
$612$		0			0
$613$	−7.50789	−	10.3337i	−0.303241	−	0.417375i	0.630018	−	0.776581i	$-0.283048\pi$
$613$	−7.50789	−	10.3337i	−0.303241	−	0.417375i	−0.933258	+	0.359206i	$0.883048\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−11.3486	−	3.68740i	−0.456879	−	0.148449i	0.0715308	−	0.997438i	$-0.477212\pi$
$617$	−11.3486	−	3.68740i	−0.456879	−	0.148449i	−0.528410	+	0.848989i	$0.677212\pi$
$618$		0			0
$619$	4.48215	−	13.7946i	0.180153	−	0.554454i	−0.819678	−	0.572824i	$-0.805848\pi$
$619$	4.48215	−	13.7946i	0.180153	−	0.554454i	0.999831	+	0.0183705i	$0.00584783\pi$
$620$		0			0
$621$	−2.68186	−	8.25391i	−0.107619	−	0.331218i
$622$		0			0
$623$	−4.97369	+	6.84570i	−0.199267	+	0.274267i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	2.30982	−	3.17920i	0.0922455	−	0.126965i
$628$		0			0
$629$	−6.20338	−	19.0920i	−0.247345	−	0.761249i
$630$		0			0
$631$	−1.13341	+	3.48828i	−0.0451204	+	0.138866i	−0.971079	−	0.238759i	$-0.923259\pi$
$631$	−1.13341	+	3.48828i	−0.0451204	+	0.138866i	0.925958	+	0.377626i	$0.123259\pi$
$632$		0			0
$633$	5.39156	+	1.75182i	0.214295	+	0.0696288i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	11.5268	+	15.8653i	0.456710	+	0.628607i
$638$		0			0
$639$	0.0190641	+	0.0138509i	0.000754164	+	0.000547932i
$640$		0			0
$641$	11.2064	−	8.14192i	0.442626	−	0.321587i	−0.344051	−	0.938951i	$-0.611799\pi$
$641$	11.2064	−	8.14192i	0.442626	−	0.321587i	0.786678	+	0.617364i	$0.211799\pi$
$642$		0			0
$643$			27.1641i			1.07125i	0.844456	+	0.535624i	$0.179924\pi$
$643$			27.1641i			1.07125i	−0.844456	+	0.535624i	$0.820076\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.89783	−	1.59140i	0.192553	−	0.0625644i	−0.211153	−	0.977453i	$-0.567722\pi$
$647$	4.89783	−	1.59140i	0.192553	−	0.0625644i	0.403706	+	0.914889i	$0.367722\pi$
$648$		0			0
$649$	−10.1812			−0.399647
$650$		0			0
$651$	16.6408			0.652204
$652$		0			0
$653$	−28.2210	+	9.16957i	−1.10437	+	0.358833i	−0.803785	−	0.594920i	$-0.797184\pi$
$653$	−28.2210	+	9.16957i	−1.10437	+	0.358833i	−0.300590	+	0.953753i	$0.597184\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	1.02251i		−	0.0398920i
$658$		0			0
$659$	12.7614	−	9.27170i	0.497114	−	0.361174i	−0.310800	−	0.950475i	$-0.600597\pi$
$659$	12.7614	−	9.27170i	0.497114	−	0.361174i	0.807913	+	0.589301i	$0.200597\pi$
$660$		0			0
$661$	19.4614	+	14.1396i	0.756962	+	0.549965i	0.897977	−	0.440042i	$-0.145037\pi$
$661$	19.4614	+	14.1396i	0.756962	+	0.549965i	−0.141015	+	0.990007i	$0.545037\pi$
$662$		0			0
$663$	−10.8570	−	14.9434i	−0.421652	−	0.580354i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	25.7715	+	8.37366i	0.997875	+	0.324229i
$668$		0			0
$669$	−6.60694	+	20.3341i	−0.255439	+	0.786161i
$670$		0			0
$671$	−10.9928	−	33.8323i	−0.424372	−	1.30608i
$672$		0			0
$673$	−18.8112	+	25.8914i	−0.725119	+	0.998040i	0.274220	+	0.961667i	$0.411580\pi$
$673$	−18.8112	+	25.8914i	−0.725119	+	0.998040i	−0.999338	+	0.0363731i	$0.988420\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−14.3307	+	19.7246i	−0.550775	+	0.758077i	−0.990117	−	0.140243i	$-0.955212\pi$
$677$	−14.3307	+	19.7246i	−0.550775	+	0.758077i	0.439342	+	0.898320i	$0.355212\pi$
$678$		0			0
$679$	−1.86161	−	5.72944i	−0.0714420	−	0.219876i
$680$		0			0
$681$	7.09579	−	21.8386i	0.271911	−	0.836856i
$682$		0			0
$683$	10.6070	+	3.44642i	0.405865	+	0.131873i	0.504833	−	0.863217i	$-0.331554\pi$
$683$	10.6070	+	3.44642i	0.405865	+	0.131873i	−0.0989680	+	0.995091i	$0.531554\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−16.5195	−	22.7371i	−0.630258	−	0.867476i
$688$		0			0
$689$	−5.37146	−	3.90260i	−0.204636	−	0.148677i
$690$		0			0
$691$	−8.76055	+	6.36491i	−0.333267	+	0.242133i	−0.741816	−	0.670604i	$-0.766035\pi$
$691$	−8.76055	+	6.36491i	−0.333267	+	0.242133i	0.408549	+	0.912737i	$0.366035\pi$
$692$		0			0
$693$			4.03813i			0.153396i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	31.0389	−	10.0851i	1.17568	−	0.382002i
$698$		0			0
$699$	−1.33195			−0.0503791
$700$		0			0
$701$	43.2512			1.63357			0.816787	−	0.576939i	$-0.195753\pi$
$701$	43.2512			1.63357			0.816787	+	0.576939i	$0.195753\pi$
$702$		0			0
$703$	−8.64488	+	2.80889i	−0.326048	+	0.105939i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			13.1930i			0.496172i
$708$		0			0
$709$	−36.0864	+	26.2183i	−1.35525	+	0.984649i	−0.356522	+	0.934287i	$0.616037\pi$
$709$	−36.0864	+	26.2183i	−1.35525	+	0.984649i	−0.998731	+	0.0503617i	$0.983963\pi$
$710$		0			0
$711$	0.646223	+	0.469509i	0.0242353	+	0.0176079i
$712$		0			0
$713$	48.7759	+	67.1343i	1.82667	+	2.51420i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−3.27666	−	1.06465i	−0.122369	−	0.0397602i
$718$		0			0
$719$	9.91537	−	30.5164i	0.369781	−	1.13807i	−0.577152	−	0.816637i	$-0.695836\pi$
$719$	9.91537	−	30.5164i	0.369781	−	1.13807i	0.946933	−	0.321432i	$-0.104164\pi$
$720$		0			0
$721$	−5.79208	−	17.8262i	−0.215708	−	0.663882i
$722$		0			0
$723$	−14.1620	+	19.4923i	−0.526689	+	0.724926i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−8.00656	+	11.0201i	−0.296947	+	0.408712i	−0.931255	−	0.364368i	$-0.881285\pi$
$727$	−8.00656	+	11.0201i	−0.296947	+	0.408712i	0.634308	+	0.773080i	$0.281285\pi$
$728$		0			0
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$		0			0
$731$	3.30882	−	10.1835i	0.122381	−	0.376650i
$732$		0			0
$733$	−27.0330	−	8.78355i	−0.998486	−	0.324428i	−0.236225	−	0.971698i	$-0.575910\pi$
$733$	−27.0330	−	8.78355i	−0.998486	−	0.324428i	−0.762260	+	0.647271i	$0.775910\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.5891	−	17.3274i	−0.463726	−	0.638264i
$738$		0			0
$739$	7.85925	+	5.71008i	0.289107	+	0.210049i	0.722880	−	0.690974i	$-0.242818\pi$
$739$	7.85925	+	5.71008i	0.289107	+	0.210049i	−0.433773	+	0.901022i	$0.642818\pi$
$740$		0			0
$741$	−6.76639	+	4.91607i	−0.248569	+	0.180596i
$742$		0			0
$743$		−	34.2029i		−	1.25478i	−0.778705	−	0.627390i	$-0.784123\pi$
$743$		−	34.2029i		−	1.25478i	0.778705	−	0.627390i	$-0.215877\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−2.25408	+	0.732396i	−0.0824726	+	0.0267970i
$748$		0			0
$749$	−7.55917			−0.276206
$750$		0			0
$751$	−12.7840			−0.466495			−0.233248	−	0.972417i	$-0.574935\pi$
$751$	−12.7840			−0.466495			−0.233248	+	0.972417i	$0.574935\pi$
$752$		0			0
$753$	28.6859	−	9.32060i	1.04537	−	0.339661i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			26.6200i			0.967520i	0.875201	+	0.483760i	$0.160729\pi$
$757$			26.6200i			0.967520i	−0.875201	+	0.483760i	$0.839271\pi$
$758$		0			0
$759$	−16.2911	+	11.8362i	−0.591329	+	0.429626i
$760$		0			0
$761$	−20.8028	−	15.1141i	−0.754102	−	0.547887i	0.142993	−	0.989724i	$-0.454327\pi$
$761$	−20.8028	−	15.1141i	−0.754102	−	0.547887i	−0.897096	+	0.441836i	$0.854327\pi$
$762$		0			0
$763$	−1.09587	−	1.50833i	−0.0396731	−	0.0546053i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	20.6084	+	6.69607i	0.744126	+	0.241781i
$768$		0			0
$769$	11.8575	−	36.4937i	0.427593	−	1.31600i	−0.472897	−	0.881118i	$-0.656792\pi$
$769$	11.8575	−	36.4937i	0.427593	−	1.31600i	0.900490	−	0.434877i	$-0.143208\pi$
$770$		0			0
$771$	−3.30222	−	10.1632i	−0.118927	−	0.366019i
$772$		0			0
$773$	0.822215	−	1.13168i	0.0295730	−	0.0407038i	−0.793974	−	0.607951i	$-0.791992\pi$
$773$	0.822215	−	1.13168i	0.0295730	−	0.0407038i	0.823547	+	0.567247i	$0.191992\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	5.49024	−	7.55667i	0.196961	−	0.271094i
$778$		0			0
$779$	−4.56656	−	14.0544i	−0.163614	−	0.503552i
$780$		0			0
$781$	0.0168959	−	0.0520001i	0.000604581	−	0.00186071i
$782$		0			0
$783$	2.96952	+	0.964854i	0.106122	+	0.0344811i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	2.47471	+	3.40614i	0.0882138	+	0.121416i	0.850843	−	0.525420i	$-0.176092\pi$
$787$	2.47471	+	3.40614i	0.0882138	+	0.121416i	−0.762629	+	0.646836i	$0.776092\pi$
$788$		0			0
$789$	−7.46948	−	5.42689i	−0.265920	−	0.193203i
$790$		0			0
$791$	26.1346	−	18.9879i	0.929238	−	0.675131i
$792$		0			0
$793$			75.7119i			2.68861i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	30.0720	−	9.77099i	1.06521	−	0.346106i	0.276587	−	0.960989i	$-0.410797\pi$
$797$	30.0720	−	9.77099i	1.06521	−	0.346106i	0.788619	+	0.614883i	$0.210797\pi$
$798$		0			0
$799$	31.6528			1.11980
$800$		0			0
$801$	−4.86205			−0.171792
$802$		0			0
$803$	−2.25639	+	0.733145i	−0.0796263	+	0.0258721i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	26.7381i		−	0.941224i
$808$		0			0
$809$	34.0676	−	24.7515i	1.19775	−	0.870218i	0.203691	−	0.979035i	$-0.434706\pi$
$809$	34.0676	−	24.7515i	1.19775	−	0.870218i	0.994062	+	0.108817i	$0.0347063\pi$
$810$		0			0
$811$	−12.2591	−	8.90674i	−0.430474	−	0.312758i	0.351364	−	0.936239i	$-0.385718\pi$
$811$	−12.2591	−	8.90674i	−0.430474	−	0.312758i	−0.781838	+	0.623481i	$0.785718\pi$
$812$		0			0
$813$	−14.2150	−	19.5652i	−0.498541	−	0.686183i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−4.61109	−	1.49823i	−0.161322	−	0.0524166i
$818$		0			0
$819$	2.65584	−	8.17383i	0.0928025	−	0.285617i
$820$		0			0
$821$	−0.124324	−	0.382629i	−0.00433893	−	0.0133538i	0.948864	−	0.315686i	$-0.102235\pi$
$821$	−0.124324	−	0.382629i	−0.00433893	−	0.0133538i	−0.953203	+	0.302332i	$0.902235\pi$
$822$		0			0
$823$	0.358173	−	0.492983i	0.0124851	−	0.0171843i	−0.802729	−	0.596344i	$-0.796619\pi$
$823$	0.358173	−	0.492983i	0.0124851	−	0.0171843i	0.815214	+	0.579160i	$0.196619\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	16.1448	−	22.2214i	0.561410	−	0.772715i	−0.430095	−	0.902784i	$-0.641520\pi$
$827$	16.1448	−	22.2214i	0.561410	−	0.772715i	0.991505	+	0.130069i	$0.0415199\pi$
$828$		0			0
$829$	−9.62722	−	29.6295i	−0.334367	−	1.02908i	−0.967033	−	0.254651i	$-0.918039\pi$
$829$	−9.62722	−	29.6295i	−0.334367	−	1.02908i	0.632666	−	0.774425i	$-0.281961\pi$
$830$		0			0
$831$	9.76738	−	30.0609i	0.338827	−	1.04280i
$832$		0			0
$833$	14.1265	+	4.58997i	0.489453	+	0.159033i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	5.62020	+	7.73554i	0.194263	+	0.267379i
$838$		0			0
$839$	31.6468	+	22.9927i	1.09257	+	0.793798i	0.979831	−	0.199827i	$-0.0640380\pi$
$839$	31.6468	+	22.9927i	1.09257	+	0.793798i	0.112738	+	0.993625i	$0.464038\pi$
$840$		0			0
$841$	15.5744	−	11.3155i	0.537049	−	0.390189i
$842$		0			0
$843$			23.2625i			0.801204i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−9.29608	+	3.02048i	−0.319417	+	0.103785i
$848$		0			0
$849$	24.8321			0.852236
$850$		0			0
$851$	46.5785			1.59669
$852$		0			0
$853$	−50.0025	+	16.2468i	−1.71205	+	0.556279i	−0.990673	−	0.136261i	$-0.956491\pi$
$853$	−50.0025	+	16.2468i	−1.71205	+	0.556279i	−0.721379	+	0.692541i	$0.756491\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	31.0291i		−	1.05993i	−0.848018	−	0.529967i	$-0.822204\pi$
$857$		−	31.0291i		−	1.05993i	0.848018	−	0.529967i	$-0.177796\pi$
$858$		0			0
$859$	31.4263	−	22.8325i	1.07225	−	0.779035i	0.0959345	−	0.995388i	$-0.469416\pi$
$859$	31.4263	−	22.8325i	1.07225	−	0.779035i	0.976315	+	0.216353i	$0.0694161\pi$
$860$		0			0
$861$	12.2853	+	8.92576i	0.418680	+	0.304189i
$862$		0			0
$863$	−2.11748	−	2.91445i	−0.0720797	−	0.0992092i	0.771455	−	0.636284i	$-0.219529\pi$
$863$	−2.11748	−	2.91445i	−0.0720797	−	0.0992092i	−0.843535	+	0.537075i	$0.819529\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	2.86235	+	0.930033i	0.0972104	+	0.0315856i
$868$		0			0
$869$	0.572725	−	1.76267i	0.0194284	−	0.0597944i
$870$		0			0
$871$	14.0863	+	43.3532i	0.477297	+	1.46897i
$872$		0			0
$873$	2.03462	−	2.80042i	0.0688615	−	0.0947798i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−18.5503	+	25.5323i	−0.626399	+	0.862165i	−0.997799	−	0.0663082i	$-0.978878\pi$
$877$	−18.5503	+	25.5323i	−0.626399	+	0.862165i	0.371400	+	0.928473i	$0.378878\pi$
$878$		0			0
$879$	9.04673	+	27.8430i	0.305139	+	0.939120i
$880$		0			0
$881$	1.86270	−	5.73280i	0.0627560	−	0.193143i	−0.914763	−	0.403991i	$-0.867623\pi$
$881$	1.86270	−	5.73280i	0.0627560	−	0.193143i	0.977519	+	0.210848i	$0.0676226\pi$
$882$		0			0
$883$	3.77171	+	1.22550i	0.126928	+	0.0412414i	0.371792	−	0.928316i	$-0.378743\pi$
$883$	3.77171	+	1.22550i	0.126928	+	0.0412414i	−0.244864	+	0.969557i	$0.578743\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−32.7485	−	45.0745i	−1.09959	−	1.51345i	−0.835930	−	0.548836i	$-0.815071\pi$
$887$	−32.7485	−	45.0745i	−1.09959	−	1.51345i	−0.263657	−	0.964616i	$-0.584929\pi$
$888$		0			0
$889$	−26.7652	−	19.4461i	−0.897677	−	0.652201i
$890$		0			0
$891$	−1.87714	+	1.36382i	−0.0628866	+	0.0456898i
$892$		0			0
$893$		−	14.3324i		−	0.479616i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	40.7603	−	13.2438i	1.36095	−	0.442199i
$898$		0			0
$899$	−29.8547			−0.995709
$900$		0			0
$901$	−5.02888			−0.167536
$902$		0			0
$903$	4.73831	−	1.53957i	0.157681	−	0.0512337i
$904$		0			0
$905$		0			0
$906$		0			0
$907$		−	21.4063i		−	0.710785i	−0.934717	−	0.355392i	$-0.884347\pi$
$907$		−	21.4063i		−	0.710785i	0.934717	−	0.355392i	$-0.115653\pi$
$908$		0			0
$909$	−6.13280	+	4.45574i	−0.203412	+	0.147788i
$910$		0			0
$911$	−25.5560	−	18.5676i	−0.846709	−	0.615170i	0.0775273	−	0.996990i	$-0.475298\pi$
$911$	−25.5560	−	18.5676i	−0.846709	−	0.615170i	−0.924237	+	0.381820i	$0.875298\pi$
$912$		0			0
$913$	3.23237	+	4.44898i	0.106976	+	0.147240i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.23317	+	0.400680i	0.0407228	+	0.0132316i
$918$		0			0
$919$	5.58626	−	17.1927i	0.184274	−	0.567136i	−0.815661	−	0.578530i	$-0.803627\pi$
$919$	5.58626	−	17.1927i	0.184274	−	0.567136i	0.999935	+	0.0113935i	$0.00362676\pi$
$920$		0			0
$921$	−2.70072	−	8.31197i	−0.0889918	−	0.273889i
$922$		0			0
$923$	−0.0683999	+	0.0941444i	−0.00225141	+	0.00309880i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	6.33039	−	8.71303i	0.207917	−	0.286173i
$928$		0			0
$929$	−2.75953	−	8.49296i	−0.0905373	−	0.278645i	0.895528	−	0.445006i	$-0.146798\pi$
$929$	−2.75953	−	8.49296i	−0.0905373	−	0.278645i	−0.986065	+	0.166361i	$0.946798\pi$
$930$		0			0
$931$	2.07834	−	6.39647i	0.0681149	−	0.209636i
$932$		0			0
$933$	−14.6996	−	4.77620i	−0.481245	−	0.156366i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	0.0356872	+	0.0491192i	0.00116585	+	0.00160466i	0.809600	−	0.586983i	$-0.199684\pi$
$937$	0.0356872	+	0.0491192i	0.00116585	+	0.00160466i	−0.808434	+	0.588587i	$0.799684\pi$
$938$		0			0
$939$	1.26124	+	0.916343i	0.0411589	+	0.0299037i
$940$		0			0
$941$	−16.7021	+	12.1348i	−0.544473	+	0.395583i	−0.825744	−	0.564046i	$-0.809244\pi$
$941$	−16.7021	+	12.1348i	−0.544473	+	0.395583i	0.281271	+	0.959628i	$0.409244\pi$
$942$		0			0
$943$			75.7249i			2.46594i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−48.8696	+	15.8787i	−1.58805	+	0.515988i	−0.964114	−	0.265489i	$-0.914466\pi$
$947$	−48.8696	+	15.8787i	−1.58805	+	0.515988i	−0.623934	+	0.781477i	$0.714466\pi$
$948$		0			0
$949$	5.04948			0.163913
$950$		0			0
$951$	5.46256			0.177136
$952$		0			0
$953$	23.3429	−	7.58457i	0.756151	−	0.245688i	0.0945251	−	0.995522i	$-0.469867\pi$
$953$	23.3429	−	7.58457i	0.756151	−	0.245688i	0.661626	+	0.749834i	$0.269867\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	7.24467i		−	0.234187i
$958$		0			0
$959$	15.6745	−	11.3882i	0.506156	−	0.367744i
$960$		0			0
$961$	−48.8851	−	35.5171i	−1.57694	−	1.14571i
$962$		0			0
$963$	−2.55301	−	3.51391i	−0.0822695	−	0.113234i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	36.3155	+	11.7996i	1.16783	+	0.379451i	0.827832	−	0.560976i	$-0.189574\pi$
$967$	36.3155	+	11.7996i	1.16783	+	0.379451i	0.339997	+	0.940427i	$0.389574\pi$
$968$		0			0
$969$	−1.95757	+	6.02479i	−0.0628863	+	0.193544i
$970$		0			0
$971$	7.97794	+	24.5536i	0.256024	+	0.787962i	0.993626	+	0.112726i	$0.0359582\pi$
$971$	7.97794	+	24.5536i	0.256024	+	0.787962i	−0.737602	+	0.675236i	$0.764042\pi$
$972$		0			0
$973$	14.0032	−	19.2738i	0.448923	−	0.617889i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	12.1236	−	16.6867i	0.387868	−	0.533855i	−0.569779	−	0.821798i	$-0.692971\pi$
$977$	12.1236	−	16.6867i	0.387868	−	0.533855i	0.957648	+	0.287943i	$0.0929713\pi$
$978$		0			0
$979$	3.48611	+	10.7291i	0.111417	+	0.342905i
$980$		0			0
$981$	0.331041	−	1.01884i	0.0105693	−	0.0325290i
$982$		0			0
$983$	21.0503	+	6.83966i	0.671401	+	0.218151i	0.624827	−	0.780763i	$-0.285170\pi$
$983$	21.0503	+	6.83966i	0.671401	+	0.218151i	0.0465741	+	0.998915i	$0.485170\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	8.65680	+	11.9151i	0.275549	+	0.379261i
$988$		0			0
$989$	20.0996	+	14.6032i	0.639130	+	0.464355i
$990$		0			0
$991$	1.34709	−	0.978715i	0.0427916	−	0.0310899i	−0.566184	−	0.824279i	$-0.691581\pi$
$991$	1.34709	−	0.978715i	0.0427916	−	0.0310899i	0.608975	+	0.793189i	$0.291581\pi$
$992$		0			0
$993$			0.855804i			0.0271581i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	22.3271	−	7.25453i	0.707108	−	0.229753i	0.0666831	−	0.997774i	$-0.478758\pi$
$997$	22.3271	−	7.25453i	0.707108	−	0.229753i	0.640425	+	0.768021i	$0.278758\pi$
$998$		0			0
$999$	5.36700			0.169804

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.o.b.49.1		16
5.2	odd	4		1500.2.m.a.1201.2		8
5.3	odd	4		300.2.m.b.241.1	yes	8
5.4	even	2	inner	1500.2.o.b.49.4		16
15.8	even	4		900.2.n.b.541.2		8
25.2	odd	20		1500.2.m.a.301.2		8
25.6	even	5		7500.2.d.c.1249.5		8
25.8	odd	20		7500.2.a.e.1.1		4
25.11	even	5	inner	1500.2.o.b.949.3		16
25.14	even	10	inner	1500.2.o.b.949.2		16
25.17	odd	20		7500.2.a.f.1.4		4
25.19	even	10		7500.2.d.c.1249.4		8
25.23	odd	20		300.2.m.b.61.1	✓	8
75.23	even	20		900.2.n.b.361.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.b.61.1	✓	8	25.23	odd	20
300.2.m.b.241.1	yes	8	5.3	odd	4
900.2.n.b.361.2		8	75.23	even	20
900.2.n.b.541.2		8	15.8	even	4
1500.2.m.a.301.2		8	25.2	odd	20
1500.2.m.a.1201.2		8	5.2	odd	4
1500.2.o.b.49.1		16	1.1	even	1	trivial
1500.2.o.b.49.4		16	5.4	even	2	inner
1500.2.o.b.949.2		16	25.14	even	10	inner
1500.2.o.b.949.3		16	25.11	even	5	inner
7500.2.a.e.1.1		4	25.8	odd	20
7500.2.a.f.1.4		4	25.17	odd	20
7500.2.d.c.1249.4		8	25.19	even	10
7500.2.d.c.1249.5		8	25.6	even	5

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)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{3} -1.74037i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{3} -1.74037i q^{7} +(0.809017 - 0.587785i) q^{9} +(-1.87714 - 1.36382i) q^{11} +(2.90266 + 3.99517i) q^{13} +(3.55730 + 1.15584i) q^{17} +(0.523364 - 1.61075i) q^{19} +(0.537803 + 1.65519i) q^{21} +(-5.10120 + 7.02120i) q^{23} +(-0.587785 + 0.809017i) q^{27} +(-0.964854 - 2.96952i) q^{29} +(2.95471 - 9.09368i) q^{31} +(2.20671 + 0.717004i) q^{33} +(-3.15464 - 4.34199i) q^{37} +(-3.99517 - 2.90266i) q^{39} +(7.05900 - 5.12866i) q^{41} -2.86270i q^{43} +(8.04830 - 2.61505i) q^{47} +3.97112 q^{49} -3.74037 q^{51} +(-1.27868 + 0.415470i) q^{53} +1.69364i q^{57} +(3.54991 - 2.57916i) q^{59} +(12.4035 + 9.01166i) q^{61} +(-1.02296 - 1.40799i) q^{63} +(8.77897 + 2.85246i) q^{67} +(2.68186 - 8.25391i) q^{69} +(0.00728184 + 0.0224112i) q^{71} +(0.601018 - 0.827230i) q^{73} +(-2.37355 + 3.26691i) q^{77} +(0.246835 + 0.759681i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-2.25408 - 0.732396i) q^{83} +(1.83526 + 2.52602i) q^{87} +(-3.93348 - 2.85784i) q^{89} +(6.95307 - 5.05170i) q^{91} +9.56166i q^{93} +(3.29209 - 1.06966i) q^{97} -2.32027 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^9	\( 16 q + 4 q^{9} + 16 q^{11} - 10 q^{19} + 14 q^{21} + 6 q^{29} - 6 q^{31} + 20 q^{41} + 16 q^{49} - 16 q^{51} + 76 q^{59} + 92 q^{61} - 4 q^{69} - 50 q^{71} + 32 q^{79} - 4 q^{81} + 60 q^{89} + 50 q^{91} + 4 q^{99}+O(q^{100}) \) 16 * q + 4 * q^9 + 16 * q^11 - 10 * q^19 + 14 * q^21 + 6 * q^29 - 6 * q^31 + 20 * q^41 + 16 * q^49 - 16 * q^51 + 76 * q^59 + 92 * q^61 - 4 * q^69 - 50 * q^71 + 32 * q^79 - 4 * q^81 + 60 * q^89 + 50 * q^91 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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