LMFDB - Embedded newform 1500.2.m.a.1201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(301,1500)]

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, 8]))

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

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

chi := DirichletCharacter("1500.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.m (of order $5$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.26265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 $ x^8 - 3x^7 + 2x^6 + x^4 + 8x^2 - 24x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1201.2
Root			$-1.21700 + 0.720348i$ of defining polynomial
Character	$\chi$	$=$	1500.1201
Dual form			1500.2.m.a.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{3} +1.74037 q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{3} +1.74037 q^{7} +(-0.809017 + 0.587785i) q^{9} +(-1.87714 - 1.36382i) q^{11} +(3.99517 - 2.90266i) q^{13} +(-1.15584 + 3.55730i) q^{17} +(-0.523364 + 1.61075i) q^{19} +(0.537803 + 1.65519i) q^{21} +(7.02120 + 5.10120i) q^{23} +(-0.809017 - 0.587785i) q^{27} +(0.964854 + 2.96952i) q^{29} +(2.95471 - 9.09368i) q^{31} +(0.717004 - 2.20671i) q^{33} +(4.34199 - 3.15464i) q^{37} +(3.99517 + 2.90266i) q^{39} +(7.05900 - 5.12866i) q^{41} -2.86270 q^{43} +(2.61505 + 8.04830i) q^{47} -3.97112 q^{49} -3.74037 q^{51} +(0.415470 + 1.27868i) q^{53} -1.69364 q^{57} +(-3.54991 + 2.57916i) q^{59} +(12.4035 + 9.01166i) q^{61} +(-1.40799 + 1.02296i) q^{63} +(-2.85246 + 8.77897i) q^{67} +(-2.68186 + 8.25391i) q^{69} +(0.00728184 + 0.0224112i) q^{71} +(-0.827230 - 0.601018i) q^{73} +(-3.26691 - 2.37355i) q^{77} +(-0.246835 - 0.759681i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-0.732396 + 2.25408i) q^{83} +(-2.52602 + 1.83526i) q^{87} +(3.93348 + 2.85784i) q^{89} +(6.95307 - 5.05170i) q^{91} +9.56166 q^{93} +(1.06966 + 3.29209i) q^{97} +2.32027 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 8 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 - 8 * q^7 - 2 * q^9	$ 8 q - 2 q^{3} - 8 q^{7} - 2 q^{9} + 8 q^{11} - 3 q^{17} + 5 q^{19} + 7 q^{21} + 7 q^{23} - 2 q^{27} - 3 q^{29} - 3 q^{31} - 7 q^{33} + q^{37} + 10 q^{41} + 12 q^{43} + 33 q^{47} - 8 q^{49} - 8 q^{51} + 19 q^{53} - 10 q^{57} - 38 q^{59} + 46 q^{61} - 3 q^{63} + 8 q^{67} + 2 q^{69} - 25 q^{71} + 26 q^{73} - 23 q^{77} - 16 q^{79} - 2 q^{81} - 8 q^{83} - 3 q^{87} - 30 q^{89} + 25 q^{91} + 22 q^{93} + 14 q^{97} - 2 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 - 8 * q^7 - 2 * q^9 + 8 * q^11 - 3 * q^17 + 5 * q^19 + 7 * q^21 + 7 * q^23 - 2 * q^27 - 3 * q^29 - 3 * q^31 - 7 * q^33 + q^37 + 10 * q^41 + 12 * q^43 + 33 * q^47 - 8 * q^49 - 8 * q^51 + 19 * q^53 - 10 * q^57 - 38 * q^59 + 46 * q^61 - 3 * q^63 + 8 * q^67 + 2 * q^69 - 25 * q^71 + 26 * q^73 - 23 * q^77 - 16 * q^79 - 2 * q^81 - 8 * q^83 - 3 * q^87 - 30 * q^89 + 25 * q^91 + 22 * q^93 + 14 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$

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
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.74037			0.657797			0.328899	−	0.944365i	$-0.393323\pi$
$7$	1.74037			0.657797			0.328899	+	0.944365i	$0.393323\pi$
$8$		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
$13$	3.99517	−	2.90266i	1.10806	−	0.805054i	0.125705	−	0.992068i	$-0.459881\pi$
$13$	3.99517	−	2.90266i	1.10806	−	0.805054i	0.982357	+	0.187014i	$0.0598808\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.15584	+	3.55730i	−0.280332	+	0.862772i	0.707428	+	0.706786i	$0.249856\pi$
$17$	−1.15584	+	3.55730i	−0.280332	+	0.862772i	−0.987759	+	0.155986i	$0.950144\pi$
$18$		0			0
$19$	−0.523364	+	1.61075i	−0.120068	+	0.369531i	−0.992970	−	0.118364i	$-0.962235\pi$
$19$	−0.523364	+	1.61075i	−0.120068	+	0.369531i	0.872902	+	0.487895i	$0.162235\pi$
$20$		0			0
$21$	0.537803	+	1.65519i	0.117358	+	0.361192i
$22$		0			0
$23$	7.02120	+	5.10120i	1.46402	+	1.06367i	0.982293	+	0.187352i	$0.0599905\pi$
$23$	7.02120	+	5.10120i	1.46402	+	1.06367i	0.481728	+	0.876321i	$0.340009\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$		0			0
$29$	0.964854	+	2.96952i	0.179169	+	0.551425i	0.999799	−	0.0200341i	$-0.00637749\pi$
$29$	0.964854	+	2.96952i	0.179169	+	0.551425i	−0.820630	+	0.571459i	$0.806377\pi$
$30$		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
$33$	0.717004	−	2.20671i	0.124814	−	0.384139i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.34199	−	3.15464i	0.713820	−	0.518620i	−0.170584	−	0.985343i	$-0.554565\pi$
$37$	4.34199	−	3.15464i	0.713820	−	0.518620i	0.884404	+	0.466723i	$0.154565\pi$
$38$		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
$43$	−2.86270			−0.436558			−0.218279	−	0.975886i	$-0.570044\pi$
$43$	−2.86270			−0.436558			−0.218279	+	0.975886i	$0.570044\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.61505	+	8.04830i	0.381444	+	1.17397i	0.939027	+	0.343844i	$0.111729\pi$
$47$	2.61505	+	8.04830i	0.381444	+	1.17397i	−0.557582	+	0.830122i	$0.688271\pi$
$48$		0			0
$49$	−3.97112			−0.567303
$50$		0			0
$51$	−3.74037			−0.523756
$52$		0			0
$53$	0.415470	+	1.27868i	0.0570691	+	0.175641i	0.975528	−	0.219876i	$-0.0705654\pi$
$53$	0.415470	+	1.27868i	0.0570691	+	0.175641i	−0.918459	+	0.395517i	$0.870565\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.69364			−0.224328
$58$		0			0
$59$	−3.54991	+	2.57916i	−0.462159	+	0.335778i	−0.794378	−	0.607424i	$-0.792203\pi$
$59$	−3.54991	+	2.57916i	−0.462159	+	0.335778i	0.332219	+	0.943202i	$0.392203\pi$
$60$		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
$63$	−1.40799	+	1.02296i	−0.177390	+	0.128881i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.85246	+	8.77897i	−0.348483	+	1.07252i	0.611209	+	0.791469i	$0.290683\pi$
$67$	−2.85246	+	8.77897i	−0.348483	+	1.07252i	−0.959692	+	0.281052i	$0.909317\pi$
$68$		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
$73$	−0.827230	−	0.601018i	−0.0968200	−	0.0703438i	0.538322	−	0.842739i	$-0.319058\pi$
$73$	−0.827230	−	0.601018i	−0.0968200	−	0.0703438i	−0.635142	+	0.772395i	$0.719058\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.26691	−	2.37355i	−0.372299	−	0.270491i
$78$		0			0
$79$	−0.246835	−	0.759681i	−0.0277711	−	0.0854708i	0.936210	−	0.351440i	$-0.114308\pi$
$79$	−0.246835	−	0.759681i	−0.0277711	−	0.0854708i	−0.963981	+	0.265969i	$0.914308\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	−0.732396	+	2.25408i	−0.0803909	+	0.247418i	−0.983172	−	0.182683i	$-0.941522\pi$
$83$	−0.732396	+	2.25408i	−0.0803909	+	0.247418i	0.902781	+	0.430100i	$0.141522\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.52602	+	1.83526i	−0.270818	+	0.196761i
$88$		0			0
$89$	3.93348	+	2.85784i	0.416948	+	0.302931i	0.776409	−	0.630230i	$-0.217039\pi$
$89$	3.93348	+	2.85784i	0.416948	+	0.302931i	−0.359461	+	0.933160i	$0.617039\pi$
$90$		0			0
$91$	6.95307	−	5.05170i	0.728880	−	0.529562i
$92$		0			0
$93$	9.56166			0.991498
$94$		0			0
$95$		0			0
$96$		0			0
$97$	1.06966	+	3.29209i	0.108608	+	0.334261i	0.990560	−	0.137078i	$-0.0437710\pi$
$97$	1.06966	+	3.29209i	0.108608	+	0.334261i	−0.881952	+	0.471339i	$0.843771\pi$
$98$		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
$103$	−3.32808	−	10.2428i	−0.327926	−	1.00925i	−0.970103	−	0.242695i	$-0.921969\pi$
$103$	−3.32808	−	10.2428i	−0.327926	−	1.00925i	0.642177	−	0.766556i	$-0.278031\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.34344			0.419896			0.209948	−	0.977713i	$-0.432671\pi$
$107$	4.34344			0.419896			0.209948	+	0.977713i	$0.432671\pi$
$108$		0			0
$109$	−0.866675	+	0.629677i	−0.0830125	+	0.0603121i	−0.628517	−	0.777796i	$-0.716338\pi$
$109$	−0.866675	+	0.629677i	−0.0830125	+	0.0603121i	0.545505	+	0.838108i	$0.316338\pi$
$110$		0			0
$111$	4.34199	+	3.15464i	0.412124	+	0.299426i
$112$		0			0
$113$	15.0167	−	10.9103i	1.41265	−	1.02635i	0.419722	−	0.907653i	$-0.362128\pi$
$113$	15.0167	−	10.9103i	1.41265	−	1.02635i	0.992930	−	0.118699i	$-0.0378723\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.52602	+	4.69661i	−0.141081	+	0.434202i
$118$		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
$123$	7.05900	+	5.12866i	0.636488	+	0.462436i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	15.3791	+	11.1735i	1.36467	+	0.991492i	0.998132	+	0.0610897i	$0.0194576\pi$
$127$	15.3791	+	11.1735i	1.36467	+	0.991492i	0.366540	+	0.930402i	$0.380542\pi$
$128$		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
$133$	−0.910845	+	2.80329i	−0.0789803	+	0.243076i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.00643	+	6.54355i	−0.769471	+	0.559054i	−0.901801	−	0.432152i	$-0.857754\pi$
$137$	−9.00643	+	6.54355i	−0.769471	+	0.559054i	0.132329	+	0.991206i	$0.457754\pi$
$138$		0			0
$139$	−11.0746	−	8.04613i	−0.939331	−	0.682464i	0.00892821	−	0.999960i	$-0.497158\pi$
$139$	−11.0746	−	8.04613i	−0.939331	−	0.682464i	−0.948260	+	0.317496i	$0.897158\pi$
$140$		0			0
$141$	−6.84629	+	4.97412i	−0.576562	+	0.418897i
$142$		0			0
$143$	−11.4582			−0.958185
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.22714	−	3.77676i	−0.101213	−	0.311502i
$148$		0			0
$149$	−10.6283			−0.870701			−0.435351	−	0.900261i	$-0.643376\pi$
$149$	−10.6283			−0.870701			−0.435351	+	0.900261i	$0.643376\pi$
$150$		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
$153$	−1.15584	−	3.55730i	−0.0934439	−	0.287591i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	17.2987			1.38059			0.690295	−	0.723528i	$-0.257481\pi$
$157$	17.2987			1.38059			0.690295	+	0.723528i	$0.257481\pi$
$158$		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
$163$	−4.97293	+	3.61304i	−0.389510	+	0.282995i	−0.765255	−	0.643728i	$-0.777387\pi$
$163$	−4.97293	+	3.61304i	−0.389510	+	0.282995i	0.375745	+	0.926723i	$0.377387\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.587188	−	1.80718i	0.0454379	−	0.139844i	−0.925764	−	0.378103i	$-0.876577\pi$
$167$	0.587188	−	1.80718i	0.0454379	−	0.139844i	0.971202	+	0.238259i	$0.0765767\pi$
$168$		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
$173$	9.37317	+	6.81000i	0.712629	+	0.517755i	0.884021	−	0.467448i	$-0.154826\pi$
$173$	9.37317	+	6.81000i	0.712629	+	0.517755i	−0.171392	+	0.985203i	$0.554826\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.54991	−	2.57916i	−0.266828	−	0.193862i
$178$		0			0
$179$	6.81312	+	20.9686i	0.509236	+	1.56727i	0.793530	+	0.608531i	$0.208241\pi$
$179$	6.81312	+	20.9686i	0.509236	+	1.56727i	−0.284294	+	0.958737i	$0.591759\pi$
$180$		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
$183$	−4.73771	+	14.5812i	−0.350222	+	1.07787i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	7.02120	−	5.10120i	0.513441	−	0.373036i
$188$		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
$193$	−4.78053			−0.344110			−0.172055	−	0.985087i	$-0.555041\pi$
$193$	−4.78053			−0.344110			−0.172055	+	0.985087i	$0.555041\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.36207	−	16.5028i	−0.382032	−	1.17577i	−0.938611	−	0.344978i	$-0.887886\pi$
$197$	−5.36207	−	16.5028i	−0.382032	−	1.17577i	0.556579	−	0.830795i	$-0.312114\pi$
$198$		0			0
$199$	11.0756			0.785129			0.392564	−	0.919724i	$-0.371588\pi$
$199$	11.0756			0.785129			0.392564	+	0.919724i	$0.371588\pi$
$200$		0			0
$201$	−9.23075			−0.651087
$202$		0			0
$203$	1.67920	+	5.16805i	0.117857	+	0.362726i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−8.67867			−0.603210
$208$		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
$213$	−0.0190641	+	0.0138509i	−0.00130625	+	0.000949047i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	5.14229	−	15.8263i	0.349081	−	1.07436i
$218$		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
$223$	−17.2972	−	12.5671i	−1.15831	−	0.841559i	−0.168743	−	0.985660i	$-0.553971\pi$
$223$	−17.2972	−	12.5671i	−1.15831	−	0.841559i	−0.989563	+	0.144101i	$0.953971\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−18.5770	−	13.4970i	−1.23300	−	0.895827i	−0.235888	−	0.971780i	$-0.575800\pi$
$227$	−18.5770	−	13.4970i	−1.23300	−	0.895827i	−0.997111	+	0.0759536i	$0.975800\pi$
$228$		0			0
$229$	−8.68482	−	26.7291i	−0.573909	−	1.76631i	−0.639865	−	0.768487i	$-0.721010\pi$
$229$	−8.68482	−	26.7291i	−0.573909	−	1.76631i	0.0659560	−	0.997823i	$-0.478990\pi$
$230$		0			0
$231$	1.24785	−	3.84049i	0.0821025	−	0.252686i
$232$		0			0
$233$	0.411596	−	1.26676i	0.0269646	−	0.0829885i	−0.936669	−	0.350217i	$-0.886108\pi$
$233$	0.411596	−	1.26676i	0.0269646	−	0.0829885i	0.963633	+	0.267229i	$0.0861079\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.646223	−	0.469509i	0.0419767	−	0.0304979i
$238$		0			0
$239$	−2.78730	−	2.02509i	−0.180295	−	0.130992i	0.493977	−	0.869475i	$-0.335543\pi$
$239$	−2.78730	−	2.02509i	−0.180295	−	0.130992i	−0.674272	+	0.738483i	$0.735543\pi$
$240$		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
$243$	1.00000			0.0641500
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.58453	+	7.95437i	0.164450	+	0.506124i
$248$		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
$253$	−6.22264	−	19.1513i	−0.391214	−	1.20403i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.6862			−0.666588			−0.333294	−	0.942823i	$-0.608160\pi$
$257$	−10.6862			−0.666588			−0.333294	+	0.942823i	$0.608160\pi$
$258$		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
$263$	7.46948	−	5.42689i	0.460588	−	0.334637i	−0.333174	−	0.942865i	$-0.608120\pi$
$263$	7.46948	−	5.42689i	0.460588	−	0.334637i	0.793762	+	0.608229i	$0.208120\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.50246	+	4.62409i	−0.0919488	+	0.282989i
$268$		0			0
$269$	8.26252	−	25.4294i	0.503774	−	1.55046i	−0.299047	−	0.954238i	$-0.596669\pi$
$269$	8.26252	−	25.4294i	0.503774	−	1.55046i	0.802821	−	0.596220i	$-0.203331\pi$
$270$		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
$273$	6.95307	+	5.05170i	0.420819	+	0.305743i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−25.5713	−	18.5787i	−1.53643	−	1.11628i	−0.952524	−	0.304464i	$-0.901523\pi$
$277$	−25.5713	−	18.5787i	−1.53643	−	1.11628i	−0.583909	−	0.811819i	$-0.698477\pi$
$278$		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
$283$	−7.67355	+	23.6167i	−0.456145	+	1.40387i	0.413641	+	0.910440i	$0.364257\pi$
$283$	−7.67355	+	23.6167i	−0.456145	+	1.40387i	−0.869786	+	0.493430i	$0.835743\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	12.2853	−	8.92576i	0.725175	−	0.526871i
$288$		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
$293$	−29.2758			−1.71031			−0.855156	−	0.518371i	$-0.826539\pi$
$293$	−29.2758			−1.71031			−0.855156	+	0.518371i	$0.826539\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.717004	+	2.20671i	0.0416048	+	0.128046i
$298$		0			0
$299$	42.8580			2.47854
$300$		0			0
$301$	−4.98215			−0.287166
$302$		0			0
$303$	−2.34252	−	7.20954i	−0.134574	−	0.414177i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−8.73972			−0.498802			−0.249401	−	0.968400i	$-0.580234\pi$
$307$	−8.73972			−0.498802			−0.249401	+	0.968400i	$0.580234\pi$
$308$		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
$313$	−1.26124	+	0.916343i	−0.0712894	+	0.0517948i	−0.622859	−	0.782334i	$-0.714029\pi$
$313$	−1.26124	+	0.916343i	−0.0712894	+	0.0517948i	0.551570	+	0.834129i	$0.314029\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.68802	−	5.19520i	0.0948088	−	0.291792i	−0.892395	−	0.451255i	$-0.850976\pi$
$317$	1.68802	−	5.19520i	0.0948088	−	0.291792i	0.987204	+	0.159464i	$0.0509764\pi$
$318$		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
$323$	−5.12499	−	3.72352i	−0.285162	−	0.207182i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−0.866675	−	0.629677i	−0.0479273	−	0.0348212i
$328$		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
$333$	−1.65849	+	5.10432i	−0.0908849	+	0.279715i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	11.9933	−	8.71367i	0.653318	−	0.474664i	−0.211082	−	0.977468i	$-0.567699\pi$
$337$	11.9933	−	8.71367i	0.653318	−	0.474664i	0.864400	+	0.502805i	$0.167699\pi$
$338$		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
$343$	−19.0938			−1.03097
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.361763	+	1.11339i	0.0194204	+	0.0597700i	0.960297	−	0.278979i	$-0.0899961\pi$
$347$	0.361763	+	1.11339i	0.0194204	+	0.0597700i	−0.940877	+	0.338749i	$0.889996\pi$
$348$		0			0
$349$	−21.4346			−1.14737			−0.573683	−	0.819077i	$-0.694486\pi$
$349$	−21.4346			−1.14737			−0.573683	+	0.819077i	$0.694486\pi$
$350$		0			0
$351$	−4.93831			−0.263587
$352$		0			0
$353$	1.10094	+	3.38834i	0.0585970	+	0.180343i	0.976071	−	0.217453i	$-0.0697750\pi$
$353$	1.10094	+	3.38834i	0.0585970	+	0.180343i	−0.917474	+	0.397796i	$0.869775\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−6.50961			−0.344525
$358$		0			0
$359$	−10.8337	+	7.87116i	−0.571782	+	0.415424i	−0.835752	−	0.549107i	$-0.814968\pi$
$359$	−10.8337	+	7.87116i	−0.571782	+	0.415424i	0.263970	+	0.964531i	$0.414968\pi$
$360$		0			0
$361$	13.0507	+	9.48191i	0.686880	+	0.499048i
$362$		0			0
$363$	4.54371	−	3.30120i	0.238483	−	0.173268i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.440150	−	1.35464i	0.0229757	−	0.0707118i	−0.938911	−	0.344159i	$-0.888164\pi$
$367$	0.440150	−	1.35464i	0.0229757	−	0.0707118i	0.961887	+	0.273447i	$0.0881640\pi$
$368$		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
$373$	20.6564	+	15.0077i	1.06955	+	0.777072i	0.975831	−	0.218527i	$-0.0701253\pi$
$373$	20.6564	+	15.0077i	1.06955	+	0.777072i	0.0937165	+	0.995599i	$0.470125\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	12.4743	+	9.06309i	0.642457	+	0.466773i
$378$		0			0
$379$	−11.7671	−	36.2153i	−0.604434	−	1.86026i	−0.500634	−	0.865659i	$-0.666900\pi$
$379$	−11.7671	−	36.2153i	−0.604434	−	1.86026i	−0.103800	−	0.994598i	$-0.533100\pi$
$380$		0			0
$381$	−5.87428	+	18.0792i	−0.300949	+	0.926225i
$382$		0			0
$383$	−4.21946	+	12.9862i	−0.215604	+	0.663562i	0.783506	+	0.621384i	$0.213429\pi$
$383$	−4.21946	+	12.9862i	−0.215604	+	0.663562i	−0.999110	+	0.0421775i	$0.986571\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.31597	−	1.68265i	0.117728	−	0.0855341i
$388$		0			0
$389$	−28.9546	−	21.0368i	−1.46806	−	1.06661i	−0.981171	−	0.193142i	$-0.938132\pi$
$389$	−28.9546	−	21.0368i	−1.46806	−	1.06661i	−0.486888	−	0.873465i	$-0.661868\pi$
$390$		0			0
$391$	−26.2619	+	19.0804i	−1.32812	+	0.964935i
$392$		0			0
$393$	−0.745032			−0.0375819
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−7.58400	−	23.3412i	−0.380630	−	1.17146i	−0.939601	−	0.342272i	$-0.888804\pi$
$397$	−7.58400	−	23.3412i	−0.380630	−	1.17146i	0.558971	−	0.829187i	$-0.311196\pi$
$398$		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
$403$	−14.5913	−	44.9074i	−0.726844	−	2.23700i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−12.4529			−0.617268
$408$		0			0
$409$	15.0121	−	10.9069i	0.742299	−	0.539312i	−0.151131	−	0.988514i	$-0.548292\pi$
$409$	15.0121	−	10.9069i	0.742299	−	0.539312i	0.893430	+	0.449202i	$0.148292\pi$
$410$		0			0
$411$	−9.00643	−	6.54355i	−0.444254	−	0.322770i
$412$		0			0
$413$	−6.17815	+	4.48869i	−0.304007	+	0.220874i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	4.23010	−	13.0189i	0.207149	−	0.637539i
$418$		0			0
$419$	1.45029	−	4.46354i	0.0708513	−	0.218058i	−0.909361	−	0.416009i	$-0.863429\pi$
$419$	1.45029	−	4.46354i	0.0708513	−	0.218058i	0.980212	+	0.197951i	$0.0634286\pi$
$420$		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
$423$	−6.84629	−	4.97412i	−0.332878	−	0.241850i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	21.5866	+	15.6836i	1.04465	+	0.758983i
$428$		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
$433$	−1.12286	+	3.45581i	−0.0539612	+	0.166075i	−0.974405	−	0.224799i	$-0.927827\pi$
$433$	−1.12286	+	3.45581i	−0.0539612	+	0.166075i	0.920444	+	0.390875i	$0.127827\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−11.8914	+	8.63959i	−0.568842	+	0.413288i
$438$		0			0
$439$	14.2446	+	10.3493i	0.679859	+	0.493947i	0.873311	−	0.487163i	$-0.161968\pi$
$439$	14.2446	+	10.3493i	0.679859	+	0.493947i	−0.193452	+	0.981110i	$0.561968\pi$
$440$		0			0
$441$	3.21270	−	2.33417i	0.152986	−	0.111151i
$442$		0			0
$443$	−7.11807			−0.338190			−0.169095	−	0.985600i	$-0.554084\pi$
$443$	−7.11807			−0.338190			−0.169095	+	0.985600i	$0.554084\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−3.28431	−	10.1081i	−0.155343	−	0.478096i
$448$		0			0
$449$	−20.4121			−0.963305			−0.481653	−	0.876362i	$-0.659963\pi$
$449$	−20.4121			−0.963305			−0.481653	+	0.876362i	$0.659963\pi$
$450$		0			0
$451$	−20.2453			−0.953315
$452$		0			0
$453$	−3.23505	−	9.95647i	−0.151996	−	0.467796i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	16.8375			0.787624			0.393812	−	0.919191i	$-0.371156\pi$
$457$	16.8375			0.787624			0.393812	+	0.919191i	$0.371156\pi$
$458$		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
$463$	6.96088	−	5.05738i	0.323500	−	0.235036i	−0.414168	−	0.910201i	$-0.635927\pi$
$463$	6.96088	−	5.05738i	0.323500	−	0.235036i	0.737667	+	0.675164i	$0.235927\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.258292	+	0.794942i	−0.0119523	+	0.0367855i	−0.956855	−	0.290566i	$-0.906156\pi$
$467$	−0.258292	+	0.794942i	−0.0119523	+	0.0367855i	0.944902	+	0.327352i	$0.106156\pi$
$468$		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
$473$	5.37369	+	3.90422i	0.247083	+	0.179516i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.08771	−	0.790270i	−0.0498030	−	0.0361840i
$478$		0			0
$479$	−10.3365	−	31.8123i	−0.472285	−	1.45354i	−0.849585	−	0.527452i	$-0.823147\pi$
$479$	−10.3365	−	31.8123i	−0.472285	−	1.45354i	0.377300	−	0.926091i	$-0.376853\pi$
$480$		0			0
$481$	8.19015	−	25.2067i	0.373439	−	1.14933i
$482$		0			0
$483$	−4.66742	+	14.3648i	−0.212375	+	0.653623i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−19.7528	+	14.3512i	−0.895083	+	0.650316i	−0.937198	−	0.348797i	$-0.886590\pi$
$487$	−19.7528	+	14.3512i	−0.895083	+	0.650316i	0.0421152	+	0.999113i	$0.486590\pi$
$488$		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
$493$	−11.6787			−0.525981
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.0126731	+	0.0390037i	0.000568465	+	0.00174956i
$498$		0			0
$499$	−13.5655			−0.607276			−0.303638	−	0.952787i	$-0.598201\pi$
$499$	−13.5655			−0.607276			−0.303638	+	0.952787i	$0.598201\pi$
$500$		0			0
$501$	1.90018			0.0848937
$502$		0			0
$503$	12.6475	+	38.9250i	0.563924	+	1.73558i	0.671126	+	0.741343i	$0.265811\pi$
$503$	12.6475	+	38.9250i	0.563924	+	1.73558i	−0.107202	+	0.994237i	$0.534189\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	11.3869			0.505709
$508$		0			0
$509$	−9.82240	+	7.13639i	−0.435370	+	0.316315i	−0.783793	−	0.621023i	$-0.786718\pi$
$509$	−9.82240	+	7.13639i	−0.435370	+	0.316315i	0.348422	+	0.937338i	$0.386718\pi$
$510$		0			0
$511$	−1.43968	−	1.04599i	−0.0636879	−	0.0462720i
$512$		0			0
$513$	1.37018	−	0.995497i	0.0604951	−	0.0439523i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	6.06763	−	18.6743i	0.266854	−	0.821293i
$518$		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
$523$	12.3978	+	9.00754i	0.542118	+	0.393872i	0.824871	−	0.565321i	$-0.191248\pi$
$523$	12.3978	+	9.00754i	0.542118	+	0.393872i	−0.282753	+	0.959193i	$0.591248\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	28.9338	+	21.0216i	1.26037	+	0.915716i
$528$		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
$533$	13.3151	−	40.9798i	0.576743	−	1.77503i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−17.8370	+	12.9593i	−0.769722	+	0.559236i
$538$		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
$543$	20.6571			0.886483
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.199605	−	0.614321i	−0.00853449	−	0.0262665i	0.946699	−	0.322121i	$-0.104396\pi$
$547$	−0.199605	−	0.614321i	−0.00853449	−	0.0262665i	−0.955233	+	0.295854i	$0.904396\pi$
$548$		0			0
$549$	−15.3316			−0.654335
$550$		0			0
$551$	−5.28811			−0.225281
$552$		0			0
$553$	−0.429584	−	1.32212i	−0.0182678	−	0.0562224i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	12.0297			0.509716			0.254858	−	0.966978i	$-0.417971\pi$
$557$	12.0297			0.509716			0.254858	+	0.966978i	$0.417971\pi$
$558$		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
$563$	12.8498	−	9.33593i	0.541555	−	0.393462i	−0.283107	−	0.959088i	$-0.591365\pi$
$563$	12.8498	−	9.33593i	0.541555	−	0.393462i	0.824662	+	0.565626i	$0.191365\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.537803	−	1.65519i	0.0225856	−	0.0695114i
$568$		0			0
$569$	6.77685	−	20.8570i	0.284100	−	0.874371i	−0.702566	−	0.711618i	$-0.747963\pi$
$569$	6.77685	−	20.8570i	0.284100	−	0.874371i	0.986667	−	0.162753i	$-0.0520374\pi$
$570$		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
$573$	−16.8535	−	12.2448i	−0.704067	−	0.511534i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	15.0698	+	10.9488i	0.627364	+	0.455806i	0.855486	−	0.517826i	$-0.173259\pi$
$577$	15.0698	+	10.9488i	0.627364	+	0.455806i	−0.228122	+	0.973632i	$0.573259\pi$
$578$		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
$583$	0.964003	−	2.96690i	0.0399249	−	0.122876i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.4963	+	8.35254i	−0.474503	+	0.344746i	−0.799194	−	0.601074i	$-0.794740\pi$
$587$	−11.4963	+	8.35254i	−0.474503	+	0.344746i	0.324691	+	0.945820i	$0.394740\pi$
$588$		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
$593$	−40.7850			−1.67484			−0.837420	−	0.546559i	$-0.815937\pi$
$593$	−40.7850			−1.67484			−0.837420	+	0.546559i	$0.815937\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.42255	+	10.5335i	0.140076	+	0.431109i
$598$		0			0
$599$	34.8928			1.42568			0.712841	−	0.701326i	$-0.247408\pi$
$599$	34.8928			1.42568			0.712841	+	0.701326i	$0.247408\pi$
$600$		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
$603$	−2.85246	−	8.77897i	−0.116161	−	0.357507i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−30.5033			−1.23809			−0.619045	−	0.785355i	$-0.712480\pi$
$607$	−30.5033			−1.23809			−0.619045	+	0.785355i	$0.712480\pi$
$608$		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
$613$	−10.3337	+	7.50789i	−0.417375	+	0.303241i	−0.776581	−	0.630018i	$-0.783048\pi$
$613$	−10.3337	+	7.50789i	−0.417375	+	0.303241i	0.359206	+	0.933258i	$0.383048\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.68740	−	11.3486i	0.148449	−	0.456879i	−0.848989	−	0.528410i	$-0.822788\pi$
$617$	3.68740	−	11.3486i	0.148449	−	0.456879i	0.997438	+	0.0715308i	$0.0227884\pi$
$618$		0			0
$619$	−4.48215	+	13.7946i	−0.180153	+	0.554454i	−0.999831	−	0.0183705i	$-0.994152\pi$
$619$	−4.48215	+	13.7946i	−0.180153	+	0.554454i	0.819678	+	0.572824i	$0.194152\pi$
$620$		0			0
$621$	−2.68186	−	8.25391i	−0.107619	−	0.331218i
$622$		0			0
$623$	6.84570	+	4.97369i	0.274267	+	0.199267i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	3.17920	+	2.30982i	0.126965	+	0.0922455i
$628$		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
$633$	1.75182	−	5.39156i	0.0696288	−	0.214295i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−15.8653	+	11.5268i	−0.628607	+	0.456710i
$638$		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
$643$	27.1641			1.07125			0.535624	−	0.844456i	$-0.320076\pi$
$643$	27.1641			1.07125			0.535624	+	0.844456i	$0.320076\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.59140	+	4.89783i	0.0625644	+	0.192553i	0.977453	−	0.211153i	$-0.0677218\pi$
$647$	1.59140	+	4.89783i	0.0625644	+	0.192553i	−0.914889	+	0.403706i	$0.867722\pi$
$648$		0			0
$649$	10.1812			0.399647
$650$		0			0
$651$	16.6408			0.652204
$652$		0			0
$653$	9.16957	+	28.2210i	0.358833	+	1.10437i	0.953753	+	0.300590i	$0.0971836\pi$
$653$	9.16957	+	28.2210i	0.358833	+	1.10437i	−0.594920	+	0.803785i	$0.702816\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	1.02251			0.0398920
$658$		0			0
$659$	−12.7614	+	9.27170i	−0.497114	+	0.361174i	−0.807913	−	0.589301i	$-0.799403\pi$
$659$	−12.7614	+	9.27170i	−0.497114	+	0.361174i	0.310800	+	0.950475i	$0.399403\pi$
$660$		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
$663$	−14.9434	+	10.8570i	−0.580354	+	0.421652i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−8.37366	+	25.7715i	−0.324229	+	0.997875i
$668$		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
$673$	25.8914	+	18.8112i	0.998040	+	0.725119i	0.961667	−	0.274220i	$-0.0884195\pi$
$673$	25.8914	+	18.8112i	0.998040	+	0.725119i	0.0363731	+	0.999338i	$0.488420\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−19.7246	−	14.3307i	−0.758077	−	0.550775i	0.140243	−	0.990117i	$-0.455212\pi$
$677$	−19.7246	−	14.3307i	−0.758077	−	0.550775i	−0.898320	+	0.439342i	$0.855212\pi$
$678$		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
$683$	3.44642	−	10.6070i	0.131873	−	0.405865i	−0.863217	−	0.504833i	$-0.831554\pi$
$683$	3.44642	−	10.6070i	0.131873	−	0.405865i	0.995091	+	0.0989680i	$0.0315541\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	22.7371	−	16.5195i	0.867476	−	0.630258i
$688$		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
$693$	4.03813			0.153396
$694$		0			0
$695$		0			0
$696$		0			0
$697$	10.0851	+	31.0389i	0.382002	+	1.17568i
$698$		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
$703$	2.80889	+	8.64488i	0.105939	+	0.326048i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−13.1930			−0.496172
$708$		0			0
$709$	36.0864	−	26.2183i	1.35525	−	0.984649i	0.356522	−	0.934287i	$-0.383963\pi$
$709$	36.0864	−	26.2183i	1.35525	−	0.984649i	0.998731	−	0.0503617i	$-0.0160374\pi$
$710$		0			0
$711$	0.646223	+	0.469509i	0.0242353	+	0.0176079i
$712$		0			0
$713$	67.1343	−	48.7759i	2.51420	−	1.82667i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.06465	−	3.27666i	0.0397602	−	0.122369i
$718$		0			0
$719$	−9.91537	+	30.5164i	−0.369781	+	1.13807i	0.577152	+	0.816637i	$0.304164\pi$
$719$	−9.91537	+	30.5164i	−0.369781	+	1.13807i	−0.946933	+	0.321432i	$0.895836\pi$
$720$		0			0
$721$	−5.79208	−	17.8262i	−0.215708	−	0.663882i
$722$		0			0
$723$	19.4923	+	14.1620i	0.724926	+	0.526689i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−11.0201	−	8.00656i	−0.408712	−	0.296947i	0.364368	−	0.931255i	$-0.381285\pi$
$727$	−11.0201	−	8.00656i	−0.408712	−	0.296947i	−0.773080	+	0.634308i	$0.781285\pi$
$728$		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
$733$	−8.78355	+	27.0330i	−0.324428	+	0.998486i	0.647271	+	0.762260i	$0.275910\pi$
$733$	−8.78355	+	27.0330i	−0.324428	+	0.998486i	−0.971698	+	0.236225i	$0.924090\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	17.3274	−	12.5891i	0.638264	−	0.463726i
$738$		0			0
$739$	−7.85925	−	5.71008i	−0.289107	−	0.210049i	0.433773	−	0.901022i	$-0.357182\pi$
$739$	−7.85925	−	5.71008i	−0.289107	−	0.210049i	−0.722880	+	0.690974i	$0.757182\pi$
$740$		0			0
$741$	−6.76639	+	4.91607i	−0.248569	+	0.180596i
$742$		0			0
$743$	−34.2029			−1.25478			−0.627390	−	0.778705i	$-0.715877\pi$
$743$	−34.2029			−1.25478			−0.627390	+	0.778705i	$0.715877\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.732396	−	2.25408i	−0.0267970	−	0.0824726i
$748$		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
$753$	−9.32060	−	28.6859i	−0.339661	−	1.04537i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−26.6200			−0.967520			−0.483760	−	0.875201i	$-0.660729\pi$
$757$	−26.6200			−0.967520			−0.483760	+	0.875201i	$0.660729\pi$
$758$		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
$763$	−1.50833	+	1.09587i	−0.0546053	+	0.0396731i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.69607	+	20.6084i	−0.241781	+	0.744126i
$768$		0			0
$769$	−11.8575	+	36.4937i	−0.427593	+	1.31600i	0.472897	+	0.881118i	$0.343208\pi$
$769$	−11.8575	+	36.4937i	−0.427593	+	1.31600i	−0.900490	+	0.434877i	$0.856792\pi$
$770$		0			0
$771$	−3.30222	−	10.1632i	−0.118927	−	0.366019i
$772$		0			0
$773$	−1.13168	−	0.822215i	−0.0407038	−	0.0295730i	0.567247	−	0.823547i	$-0.308008\pi$
$773$	−1.13168	−	0.822215i	−0.0407038	−	0.0295730i	−0.607951	+	0.793974i	$0.708008\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	7.55667	+	5.49024i	0.271094	+	0.196961i
$778$		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
$783$	0.964854	−	2.96952i	0.0344811	−	0.106122i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−3.40614	+	2.47471i	−0.121416	+	0.0882138i	−0.646836	−	0.762629i	$-0.723908\pi$
$787$	−3.40614	+	2.47471i	−0.121416	+	0.0882138i	0.525420	+	0.850843i	$0.323908\pi$
$788$		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
$793$	75.7119			2.68861
$794$		0			0
$795$		0			0
$796$		0			0
$797$	9.77099	+	30.0720i	0.346106	+	1.06521i	0.960989	+	0.276587i	$0.0892033\pi$
$797$	9.77099	+	30.0720i	0.346106	+	1.06521i	−0.614883	+	0.788619i	$0.710797\pi$
$798$		0			0
$799$	−31.6528			−1.11980
$800$		0			0
$801$	−4.86205			−0.171792
$802$		0			0
$803$	0.733145	+	2.25639i	0.0258721	+	0.0796263i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	26.7381			0.941224
$808$		0			0
$809$	−34.0676	+	24.7515i	−1.19775	+	0.870218i	−0.994062	−	0.108817i	$-0.965294\pi$
$809$	−34.0676	+	24.7515i	−1.19775	+	0.870218i	−0.203691	+	0.979035i	$0.565294\pi$
$810$		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
$813$	−19.5652	+	14.2150i	−0.686183	+	0.498541i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	1.49823	−	4.61109i	0.0524166	−	0.161322i
$818$		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
$823$	−0.492983	−	0.358173i	−0.0171843	−	0.0124851i	0.579160	−	0.815214i	$-0.303381\pi$
$823$	−0.492983	−	0.358173i	−0.0171843	−	0.0124851i	−0.596344	+	0.802729i	$0.703381\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	22.2214	+	16.1448i	0.772715	+	0.561410i	0.902784	−	0.430095i	$-0.141520\pi$
$827$	22.2214	+	16.1448i	0.772715	+	0.561410i	−0.130069	+	0.991505i	$0.541520\pi$
$828$		0			0
$829$	9.62722	+	29.6295i	0.334367	+	1.02908i	0.967033	+	0.254651i	$0.0819607\pi$
$829$	9.62722	+	29.6295i	0.334367	+	1.02908i	−0.632666	+	0.774425i	$0.718039\pi$
$830$		0			0
$831$	9.76738	−	30.0609i	0.338827	−	1.04280i
$832$		0			0
$833$	4.58997	−	14.1265i	0.159033	−	0.489453i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−7.73554	+	5.62020i	−0.267379	+	0.194263i
$838$		0			0
$839$	−31.6468	−	22.9927i	−1.09257	−	0.793798i	−0.112738	−	0.993625i	$-0.535962\pi$
$839$	−31.6468	−	22.9927i	−1.09257	−	0.793798i	−0.979831	+	0.199827i	$0.935962\pi$
$840$		0			0
$841$	15.5744	−	11.3155i	0.537049	−	0.390189i
$842$		0			0
$843$	23.2625			0.801204
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−3.02048	−	9.29608i	−0.103785	−	0.319417i
$848$		0			0
$849$	−24.8321			−0.852236
$850$		0			0
$851$	46.5785			1.59669
$852$		0			0
$853$	16.2468	+	50.0025i	0.556279	+	1.71205i	0.692541	+	0.721379i	$0.256491\pi$
$853$	16.2468	+	50.0025i	0.556279	+	1.71205i	−0.136261	+	0.990673i	$0.543509\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	31.0291			1.05993			0.529967	−	0.848018i	$-0.322204\pi$
$857$	31.0291			1.05993			0.529967	+	0.848018i	$0.322204\pi$
$858$		0			0
$859$	−31.4263	+	22.8325i	−1.07225	+	0.779035i	−0.976315	−	0.216353i	$-0.930584\pi$
$859$	−31.4263	+	22.8325i	−1.07225	+	0.779035i	−0.0959345	+	0.995388i	$0.530584\pi$
$860$		0			0
$861$	12.2853	+	8.92576i	0.418680	+	0.304189i
$862$		0			0
$863$	−2.91445	+	2.11748i	−0.0992092	+	0.0720797i	−0.636284	−	0.771455i	$-0.719529\pi$
$863$	−2.91445	+	2.11748i	−0.0992092	+	0.0720797i	0.537075	+	0.843535i	$0.319529\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−0.930033	+	2.86235i	−0.0315856	+	0.0972104i
$868$		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
$873$	−2.80042	−	2.03462i	−0.0947798	−	0.0688615i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−25.5323	−	18.5503i	−0.862165	−	0.626399i	0.0663082	−	0.997799i	$-0.478878\pi$
$877$	−25.5323	−	18.5503i	−0.862165	−	0.626399i	−0.928473	+	0.371400i	$0.878878\pi$
$878$		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
$883$	1.22550	−	3.77171i	0.0412414	−	0.126928i	−0.928316	−	0.371792i	$-0.878743\pi$
$883$	1.22550	−	3.77171i	0.0412414	−	0.126928i	0.969557	+	0.244864i	$0.0787434\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	45.0745	−	32.7485i	1.51345	−	1.09959i	0.548836	−	0.835930i	$-0.315071\pi$
$887$	45.0745	−	32.7485i	1.51345	−	1.09959i	0.964616	−	0.263657i	$-0.0849289\pi$
$888$		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
$893$	−14.3324			−0.479616
$894$		0			0
$895$		0			0
$896$		0			0
$897$	13.2438	+	40.7603i	0.442199	+	1.36095i
$898$		0			0
$899$	29.8547			0.995709
$900$		0			0
$901$	−5.02888			−0.167536
$902$		0			0
$903$	−1.53957	−	4.73831i	−0.0512337	−	0.157681i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	21.4063			0.710785			0.355392	−	0.934717i	$-0.384347\pi$
$907$	21.4063			0.710785			0.355392	+	0.934717i	$0.384347\pi$
$908$		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
$913$	4.44898	−	3.23237i	0.147240	−	0.106976i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.400680	+	1.23317i	−0.0132316	+	0.0407228i
$918$		0			0
$919$	−5.58626	+	17.1927i	−0.184274	+	0.567136i	−0.999935	−	0.0113935i	$-0.996373\pi$
$919$	−5.58626	+	17.1927i	−0.184274	+	0.567136i	0.815661	+	0.578530i	$0.196373\pi$
$920$		0			0
$921$	−2.70072	−	8.31197i	−0.0889918	−	0.273889i
$922$		0			0
$923$	0.0941444	+	0.0683999i	0.00309880	+	0.00225141i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	8.71303	+	6.33039i	0.286173	+	0.207917i
$928$		0			0
$929$	2.75953	+	8.49296i	0.0905373	+	0.278645i	0.986065	−	0.166361i	$-0.0532016\pi$
$929$	2.75953	+	8.49296i	0.0905373	+	0.278645i	−0.895528	+	0.445006i	$0.853202\pi$
$930$		0			0
$931$	2.07834	−	6.39647i	0.0681149	−	0.209636i
$932$		0			0
$933$	−4.77620	+	14.6996i	−0.156366	+	0.481245i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−0.0491192	+	0.0356872i	−0.00160466	+	0.00116585i	−0.588587	−	0.808434i	$-0.700316\pi$
$937$	−0.0491192	+	0.0356872i	−0.00160466	+	0.00116585i	0.586983	+	0.809600i	$0.300316\pi$
$938$		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
$943$	75.7249			2.46594
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15.8787	−	48.8696i	−0.515988	−	1.58805i	−0.781477	−	0.623934i	$-0.785534\pi$
$947$	−15.8787	−	48.8696i	−0.515988	−	1.58805i	0.265489	−	0.964114i	$-0.414466\pi$
$948$		0			0
$949$	−5.04948			−0.163913
$950$		0			0
$951$	5.46256			0.177136
$952$		0			0
$953$	−7.58457	−	23.3429i	−0.245688	−	0.756151i	−0.995522	−	0.0945251i	$-0.969867\pi$
$953$	−7.58457	−	23.3429i	−0.245688	−	0.756151i	0.749834	−	0.661626i	$-0.230133\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	7.24467			0.234187
$958$		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
$963$	−3.51391	+	2.55301i	−0.113234	+	0.0822695i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−11.7996	+	36.3155i	−0.379451	+	1.16783i	0.560976	+	0.827832i	$0.310426\pi$
$967$	−11.7996	+	36.3155i	−0.379451	+	1.16783i	−0.940427	+	0.339997i	$0.889574\pi$
$968$		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
$973$	−19.2738	−	14.0032i	−0.617889	−	0.448923i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	16.6867	+	12.1236i	0.533855	+	0.387868i	0.821798	−	0.569779i	$-0.192971\pi$
$977$	16.6867	+	12.1236i	0.533855	+	0.387868i	−0.287943	+	0.957648i	$0.592971\pi$
$978$		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
$983$	6.83966	−	21.0503i	0.218151	−	0.671401i	−0.780763	−	0.624827i	$-0.785170\pi$
$983$	6.83966	−	21.0503i	0.218151	−	0.671401i	0.998915	−	0.0465741i	$-0.0148304\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−11.9151	+	8.65680i	−0.379261	+	0.275549i
$988$		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
$993$	0.855804			0.0271581
$994$		0			0
$995$		0			0
$996$		0			0
$997$	7.25453	+	22.3271i	0.229753	+	0.707108i	0.997774	+	0.0666831i	$0.0212416\pi$
$997$	7.25453	+	22.3271i	0.229753	+	0.707108i	−0.768021	+	0.640425i	$0.778758\pi$
$998$		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.m.a.1201.2		8
5.2	odd	4		1500.2.o.b.49.4		16
5.3	odd	4		1500.2.o.b.49.1		16
5.4	even	2		300.2.m.b.241.1	yes	8
15.14	odd	2		900.2.n.b.541.2		8
25.2	odd	20		1500.2.o.b.949.2		16
25.6	even	5		7500.2.a.f.1.4		4
25.8	odd	20		7500.2.d.c.1249.5		8
25.11	even	5	inner	1500.2.m.a.301.2		8
25.14	even	10		300.2.m.b.61.1	✓	8
25.17	odd	20		7500.2.d.c.1249.4		8
25.19	even	10		7500.2.a.e.1.1		4
25.23	odd	20		1500.2.o.b.949.3		16
75.14	odd	10		900.2.n.b.361.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.b.61.1	✓	8	25.14	even	10
300.2.m.b.241.1	yes	8	5.4	even	2
900.2.n.b.361.2		8	75.14	odd	10
900.2.n.b.541.2		8	15.14	odd	2
1500.2.m.a.301.2		8	25.11	even	5	inner
1500.2.m.a.1201.2		8	1.1	even	1	trivial
1500.2.o.b.49.1		16	5.3	odd	4
1500.2.o.b.49.4		16	5.2	odd	4
1500.2.o.b.949.2		16	25.2	odd	20
1500.2.o.b.949.3		16	25.23	odd	20
7500.2.a.e.1.1		4	25.19	even	10
7500.2.a.f.1.4		4	25.6	even	5
7500.2.d.c.1249.4		8	25.17	odd	20
7500.2.d.c.1249.5		8	25.8	odd	20

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.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{3} +1.74037 q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{3} +1.74037 q^{7} +(-0.809017 + 0.587785i) q^{9} +(-1.87714 - 1.36382i) q^{11} +(3.99517 - 2.90266i) q^{13} +(-1.15584 + 3.55730i) q^{17} +(-0.523364 + 1.61075i) q^{19} +(0.537803 + 1.65519i) q^{21} +(7.02120 + 5.10120i) q^{23} +(-0.809017 - 0.587785i) q^{27} +(0.964854 + 2.96952i) q^{29} +(2.95471 - 9.09368i) q^{31} +(0.717004 - 2.20671i) q^{33} +(4.34199 - 3.15464i) q^{37} +(3.99517 + 2.90266i) q^{39} +(7.05900 - 5.12866i) q^{41} -2.86270 q^{43} +(2.61505 + 8.04830i) q^{47} -3.97112 q^{49} -3.74037 q^{51} +(0.415470 + 1.27868i) q^{53} -1.69364 q^{57} +(-3.54991 + 2.57916i) q^{59} +(12.4035 + 9.01166i) q^{61} +(-1.40799 + 1.02296i) q^{63} +(-2.85246 + 8.77897i) q^{67} +(-2.68186 + 8.25391i) q^{69} +(0.00728184 + 0.0224112i) q^{71} +(-0.827230 - 0.601018i) q^{73} +(-3.26691 - 2.37355i) q^{77} +(-0.246835 - 0.759681i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-0.732396 + 2.25408i) q^{83} +(-2.52602 + 1.83526i) q^{87} +(3.93348 + 2.85784i) q^{89} +(6.95307 - 5.05170i) q^{91} +9.56166 q^{93} +(1.06966 + 3.29209i) q^{97} +2.32027 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 8 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 - 8 * q^7 - 2 * q^9	\( 8 q - 2 q^{3} - 8 q^{7} - 2 q^{9} + 8 q^{11} - 3 q^{17} + 5 q^{19} + 7 q^{21} + 7 q^{23} - 2 q^{27} - 3 q^{29} - 3 q^{31} - 7 q^{33} + q^{37} + 10 q^{41} + 12 q^{43} + 33 q^{47} - 8 q^{49} - 8 q^{51} + 19 q^{53} - 10 q^{57} - 38 q^{59} + 46 q^{61} - 3 q^{63} + 8 q^{67} + 2 q^{69} - 25 q^{71} + 26 q^{73} - 23 q^{77} - 16 q^{79} - 2 q^{81} - 8 q^{83} - 3 q^{87} - 30 q^{89} + 25 q^{91} + 22 q^{93} + 14 q^{97} - 2 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 - 8 * q^7 - 2 * q^9 + 8 * q^11 - 3 * q^17 + 5 * q^19 + 7 * q^21 + 7 * q^23 - 2 * q^27 - 3 * q^29 - 3 * q^31 - 7 * q^33 + q^37 + 10 * q^41 + 12 * q^43 + 33 * q^47 - 8 * q^49 - 8 * q^51 + 19 * q^53 - 10 * q^57 - 38 * q^59 + 46 * q^61 - 3 * q^63 + 8 * q^67 + 2 * q^69 - 25 * q^71 + 26 * q^73 - 23 * q^77 - 16 * q^79 - 2 * q^81 - 8 * q^83 - 3 * q^87 - 30 * q^89 + 25 * q^91 + 22 * q^93 + 14 * q^97 - 2 * q^99

Introduction

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