LMFDB - Embedded newform 300.2.m.b.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(61,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, 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("300.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.m (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.39551206064$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			61.1
Root			$1.40799 - 0.132563i$ of defining polynomial
Character	$\chi$	$=$	300.61
Dual form			300.2.m.b.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{3} +(-1.96485 + 1.06740i) q^{5} -1.74037 q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{3} +(-1.96485 + 1.06740i) q^{5} -1.74037 q^{7} +(-0.809017 - 0.587785i) q^{9} +(-1.87714 + 1.36382i) q^{11} +(-3.99517 - 2.90266i) q^{13} +(-0.407987 - 2.19853i) q^{15} +(1.15584 + 3.55730i) q^{17} +(-0.523364 - 1.61075i) q^{19} +(0.537803 - 1.65519i) q^{21} +(-7.02120 + 5.10120i) q^{23} +(2.72130 - 4.19458i) q^{25} +(0.809017 - 0.587785i) q^{27} +(0.964854 - 2.96952i) q^{29} +(2.95471 + 9.09368i) q^{31} +(-0.717004 - 2.20671i) q^{33} +(3.41957 - 1.85767i) q^{35} +(-4.34199 - 3.15464i) q^{37} +(3.99517 - 2.90266i) q^{39} +(7.05900 + 5.12866i) q^{41} +2.86270 q^{43} +(2.21700 + 0.291365i) q^{45} +(-2.61505 + 8.04830i) q^{47} -3.97112 q^{49} -3.74037 q^{51} +(-0.415470 + 1.27868i) q^{53} +(2.23256 - 4.68338i) q^{55} +1.69364 q^{57} +(-3.54991 - 2.57916i) q^{59} +(12.4035 - 9.01166i) q^{61} +(1.40799 + 1.02296i) q^{63} +(10.9482 + 1.43885i) q^{65} +(2.85246 + 8.77897i) q^{67} +(-2.68186 - 8.25391i) q^{69} +(0.00728184 - 0.0224112i) q^{71} +(0.827230 - 0.601018i) q^{73} +(3.14835 + 3.88431i) q^{75} +(3.26691 - 2.37355i) q^{77} +(-0.246835 + 0.759681i) q^{79} +(0.309017 + 0.951057i) q^{81} +(0.732396 + 2.25408i) q^{83} +(-6.06812 - 5.75583i) q^{85} +(2.52602 + 1.83526i) q^{87} +(3.93348 - 2.85784i) q^{89} +(6.95307 + 5.05170i) q^{91} -9.56166 q^{93} +(2.74765 + 2.60624i) q^{95} +(-1.06966 + 3.29209i) q^{97} +2.32027 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 5 q^{5} + 8 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 - 5 * q^5 + 8 * q^7 - 2 * q^9	$ 8 q + 2 q^{3} - 5 q^{5} + 8 q^{7} - 2 q^{9} + 8 q^{11} + 5 q^{15} + 3 q^{17} + 5 q^{19} + 7 q^{21} - 7 q^{23} + 5 q^{25} + 2 q^{27} - 3 q^{29} - 3 q^{31} + 7 q^{33} - 10 q^{35} - q^{37} + 10 q^{41} - 12 q^{43} + 5 q^{45} - 33 q^{47} - 8 q^{49} - 8 q^{51} - 19 q^{53} - 15 q^{55} + 10 q^{57} - 38 q^{59} + 46 q^{61} + 3 q^{63} + 25 q^{65} - 8 q^{67} + 2 q^{69} - 25 q^{71} - 26 q^{73} - 5 q^{75} + 23 q^{77} - 16 q^{79} - 2 q^{81} + 8 q^{83} - 30 q^{85} + 3 q^{87} - 30 q^{89} + 25 q^{91} - 22 q^{93} - 25 q^{95} - 14 q^{97} - 2 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 - 5 * q^5 + 8 * q^7 - 2 * q^9 + 8 * q^11 + 5 * q^15 + 3 * q^17 + 5 * q^19 + 7 * q^21 - 7 * q^23 + 5 * q^25 + 2 * q^27 - 3 * q^29 - 3 * q^31 + 7 * q^33 - 10 * q^35 - q^37 + 10 * q^41 - 12 * q^43 + 5 * q^45 - 33 * q^47 - 8 * q^49 - 8 * q^51 - 19 * q^53 - 15 * q^55 + 10 * q^57 - 38 * q^59 + 46 * q^61 + 3 * q^63 + 25 * q^65 - 8 * q^67 + 2 * q^69 - 25 * q^71 - 26 * q^73 - 5 * q^75 + 23 * q^77 - 16 * q^79 - 2 * q^81 + 8 * q^83 - 30 * q^85 + 3 * q^87 - 30 * q^89 + 25 * q^91 - 22 * q^93 - 25 * q^95 - 14 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$5$	−1.96485	+	1.06740i	−0.878709	+	0.477357i
$5$	−1.96485	+	1.06740i	−0.878709	+	0.477357i
$6$		0			0
$7$	−1.74037			−0.657797			−0.328899	−	0.944365i	$-0.606677\pi$
$7$	−1.74037			−0.657797			−0.328899	+	0.944365i	$0.606677\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	−1.87714	+	1.36382i	−0.565979	+	0.411208i	−0.833642	−	0.552305i	$-0.813749\pi$
$11$	−1.87714	+	1.36382i	−0.565979	+	0.411208i	0.267663	+	0.963513i	$0.413749\pi$
$12$		0			0
$13$	−3.99517	−	2.90266i	−1.10806	−	0.805054i	−0.125705	−	0.992068i	$-0.540119\pi$
$13$	−3.99517	−	2.90266i	−1.10806	−	0.805054i	−0.982357	+	0.187014i	$0.940119\pi$
$14$		0			0
$15$	−0.407987	−	2.19853i	−0.105342	−	0.567659i
$16$		0			0
$17$	1.15584	+	3.55730i	0.280332	+	0.862772i	0.987759	+	0.155986i	$0.0498556\pi$
$17$	1.15584	+	3.55730i	0.280332	+	0.862772i	−0.707428	+	0.706786i	$0.750144\pi$
$18$		0			0
$19$	−0.523364	−	1.61075i	−0.120068	−	0.369531i	0.872902	−	0.487895i	$-0.162235\pi$
$19$	−0.523364	−	1.61075i	−0.120068	−	0.369531i	−0.992970	+	0.118364i	$0.962235\pi$
$20$		0			0
$21$	0.537803	−	1.65519i	0.117358	−	0.361192i
$22$		0			0
$23$	−7.02120	+	5.10120i	−1.46402	+	1.06367i	−0.481728	+	0.876321i	$0.659991\pi$
$23$	−7.02120	+	5.10120i	−1.46402	+	1.06367i	−0.982293	+	0.187352i	$0.940009\pi$
$24$		0			0
$25$	2.72130	−	4.19458i	0.544261	−	0.838916i
$26$		0			0
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$		0			0
$29$	0.964854	−	2.96952i	0.179169	−	0.551425i	−0.820630	−	0.571459i	$-0.806377\pi$
$29$	0.964854	−	2.96952i	0.179169	−	0.551425i	0.999799	+	0.0200341i	$0.00637749\pi$
$30$		0			0
$31$	2.95471	+	9.09368i	0.530682	+	1.63327i	0.752798	+	0.658252i	$0.228704\pi$
$31$	2.95471	+	9.09368i	0.530682	+	1.63327i	−0.222115	+	0.975020i	$0.571296\pi$
$32$		0			0
$33$	−0.717004	−	2.20671i	−0.124814	−	0.384139i
$34$		0			0
$35$	3.41957	−	1.85767i	0.578013	−	0.314004i
$36$		0			0
$37$	−4.34199	−	3.15464i	−0.713820	−	0.518620i	0.170584	−	0.985343i	$-0.445435\pi$
$37$	−4.34199	−	3.15464i	−0.713820	−	0.518620i	−0.884404	+	0.466723i	$0.845435\pi$
$38$		0			0
$39$	3.99517	−	2.90266i	0.639740	−	0.464798i
$40$		0			0
$41$	7.05900	+	5.12866i	1.10243	+	0.800963i	0.981455	−	0.191693i	$-0.0613978\pi$
$41$	7.05900	+	5.12866i	1.10243	+	0.800963i	0.120975	+	0.992656i	$0.461398\pi$
$42$		0			0
$43$	2.86270			0.436558			0.218279	−	0.975886i	$-0.429956\pi$
$43$	2.86270			0.436558			0.218279	+	0.975886i	$0.429956\pi$
$44$		0			0
$45$	2.21700	+	0.291365i	0.330491	+	0.0434342i
$46$		0			0
$47$	−2.61505	+	8.04830i	−0.381444	+	1.17397i	0.557582	+	0.830122i	$0.311729\pi$
$47$	−2.61505	+	8.04830i	−0.381444	+	1.17397i	−0.939027	+	0.343844i	$0.888271\pi$
$48$		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	$-0.929435\pi$
$53$	−0.415470	+	1.27868i	−0.0570691	+	0.175641i	0.918459	+	0.395517i	$0.129435\pi$
$54$		0			0
$55$	2.23256	−	4.68338i	0.301038	−	0.631506i
$56$		0			0
$57$	1.69364			0.224328
$58$		0			0
$59$	−3.54991	−	2.57916i	−0.462159	−	0.335778i	0.332219	−	0.943202i	$-0.392203\pi$
$59$	−3.54991	−	2.57916i	−0.462159	−	0.335778i	−0.794378	+	0.607424i	$0.792203\pi$
$60$		0			0
$61$	12.4035	−	9.01166i	1.58810	−	1.15382i	0.681519	−	0.731800i	$-0.261319\pi$
$61$	12.4035	−	9.01166i	1.58810	−	1.15382i	0.906584	−	0.422025i	$-0.138681\pi$
$62$		0			0
$63$	1.40799	+	1.02296i	0.177390	+	0.128881i
$64$		0			0
$65$	10.9482	+	1.43885i	1.35796	+	0.178468i
$66$		0			0
$67$	2.85246	+	8.77897i	0.348483	+	1.07252i	0.959692	+	0.281052i	$0.0906835\pi$
$67$	2.85246	+	8.77897i	0.348483	+	1.07252i	−0.611209	+	0.791469i	$0.709317\pi$
$68$		0			0
$69$	−2.68186	−	8.25391i	−0.322858	−	0.993654i
$70$		0			0
$71$	0.00728184	−	0.0224112i	0.000864195	−	0.00265972i	−0.950623	−	0.310347i	$-0.899555\pi$
$71$	0.00728184	−	0.0224112i	0.000864195	−	0.00265972i	0.951488	+	0.307687i	$0.0995549\pi$
$72$		0			0
$73$	0.827230	−	0.601018i	0.0968200	−	0.0703438i	−0.538322	−	0.842739i	$-0.680942\pi$
$73$	0.827230	−	0.601018i	0.0968200	−	0.0703438i	0.635142	+	0.772395i	$0.280942\pi$
$74$		0			0
$75$	3.14835	+	3.88431i	0.363541	+	0.448521i
$76$		0			0
$77$	3.26691	−	2.37355i	0.372299	−	0.270491i
$78$		0			0
$79$	−0.246835	+	0.759681i	−0.0277711	+	0.0854708i	−0.963981	−	0.265969i	$-0.914308\pi$
$79$	−0.246835	+	0.759681i	−0.0277711	+	0.0854708i	0.936210	+	0.351440i	$0.114308\pi$
$80$		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	$-0.0584781\pi$
$83$	0.732396	+	2.25408i	0.0803909	+	0.247418i	−0.902781	+	0.430100i	$0.858478\pi$
$84$		0			0
$85$	−6.06812	−	5.75583i	−0.658180	−	0.624308i
$86$		0			0
$87$	2.52602	+	1.83526i	0.270818	+	0.196761i
$88$		0			0
$89$	3.93348	−	2.85784i	0.416948	−	0.302931i	−0.359461	−	0.933160i	$-0.617039\pi$
$89$	3.93348	−	2.85784i	0.416948	−	0.302931i	0.776409	+	0.630230i	$0.217039\pi$
$90$		0			0
$91$	6.95307	+	5.05170i	0.728880	+	0.529562i
$92$		0			0
$93$	−9.56166			−0.991498
$94$		0			0
$95$	2.74765	+	2.60624i	0.281903	+	0.267395i
$96$		0			0
$97$	−1.06966	+	3.29209i	−0.108608	+	0.334261i	−0.990560	−	0.137078i	$-0.956229\pi$
$97$	−1.06966	+	3.29209i	−0.108608	+	0.334261i	0.881952	+	0.471339i	$0.156229\pi$
$98$		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	−0.642177	−	0.766556i	$-0.721969\pi$
$103$	3.32808	−	10.2428i	0.327926	−	1.00925i	0.970103	−	0.242695i	$-0.0780314\pi$
$104$		0			0
$105$	0.710047	+	3.82626i	0.0692935	+	0.373404i
$106$		0			0
$107$	−4.34344			−0.419896			−0.209948	−	0.977713i	$-0.567329\pi$
$107$	−4.34344			−0.419896			−0.209948	+	0.977713i	$0.567329\pi$
$108$		0			0
$109$	−0.866675	−	0.629677i	−0.0830125	−	0.0603121i	0.545505	−	0.838108i	$-0.316338\pi$
$109$	−0.866675	−	0.629677i	−0.0830125	−	0.0603121i	−0.628517	+	0.777796i	$0.716338\pi$
$110$		0			0
$111$	4.34199	−	3.15464i	0.412124	−	0.299426i
$112$		0			0
$113$	−15.0167	−	10.9103i	−1.41265	−	1.02635i	−0.992930	−	0.118699i	$-0.962128\pi$
$113$	−15.0167	−	10.9103i	−1.41265	−	1.02635i	−0.419722	−	0.907653i	$-0.637872\pi$
$114$		0			0
$115$	8.35059	−	17.5176i	0.778697	−	1.63352i
$116$		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
$125$	−0.869658	+	11.1465i	−0.0777846	+	0.996970i
$126$		0			0
$127$	−15.3791	+	11.1735i	−1.36467	+	0.991492i	−0.366540	+	0.930402i	$0.619458\pi$
$127$	−15.3791	+	11.1735i	−1.36467	+	0.991492i	−0.998132	+	0.0610897i	$0.980542\pi$
$128$		0			0
$129$	−0.884623	+	2.72259i	−0.0778867	+	0.239711i
$130$		0			0
$131$	−0.230228	−	0.708567i	−0.0201151	−	0.0619078i	0.940495	−	0.339807i	$-0.110362\pi$
$131$	−0.230228	−	0.708567i	−0.0201151	−	0.0619078i	−0.960610	+	0.277899i	$0.910362\pi$
$132$		0			0
$133$	0.910845	+	2.80329i	0.0789803	+	0.243076i
$134$		0			0
$135$	−0.962197	+	2.01846i	−0.0828127	+	0.173721i
$136$		0			0
$137$	9.00643	+	6.54355i	0.769471	+	0.559054i	0.901801	−	0.432152i	$-0.142246\pi$
$137$	9.00643	+	6.54355i	0.769471	+	0.559054i	−0.132329	+	0.991206i	$0.542246\pi$
$138$		0			0
$139$	−11.0746	+	8.04613i	−0.939331	+	0.682464i	−0.948260	−	0.317496i	$-0.897158\pi$
$139$	−11.0746	+	8.04613i	−0.939331	+	0.682464i	0.00892821	+	0.999960i	$0.497158\pi$
$140$		0			0
$141$	−6.84629	−	4.97412i	−0.576562	−	0.418897i
$142$		0			0
$143$	11.4582			0.958185
$144$		0			0
$145$	1.27387	+	6.86455i	0.105789	+	0.570070i
$146$		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
$155$	−15.5122	−	14.7139i	−1.24597	−	1.18185i
$156$		0			0
$157$	−17.2987			−1.38059			−0.690295	−	0.723528i	$-0.742519\pi$
$157$	−17.2987			−1.38059			−0.690295	+	0.723528i	$0.742519\pi$
$158$		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	$-0.222613\pi$
$163$	4.97293	+	3.61304i	0.389510	+	0.282995i	−0.375745	+	0.926723i	$0.622613\pi$
$164$		0			0
$165$	3.76426	+	3.57053i	0.293047	+	0.277966i
$166$		0			0
$167$	−0.587188	−	1.80718i	−0.0454379	−	0.139844i	0.925764	−	0.378103i	$-0.123423\pi$
$167$	−0.587188	−	1.80718i	−0.0454379	−	0.139844i	−0.971202	+	0.238259i	$0.923423\pi$
$168$		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	$-0.845174\pi$
$173$	−9.37317	+	6.81000i	−0.712629	+	0.517755i	0.171392	+	0.985203i	$0.445174\pi$
$174$		0			0
$175$	−4.73607	+	7.30011i	−0.358013	+	0.551837i
$176$		0			0
$177$	3.54991	−	2.57916i	0.266828	−	0.193862i
$178$		0			0
$179$	6.81312	−	20.9686i	0.509236	−	1.56727i	−0.284294	−	0.958737i	$-0.591759\pi$
$179$	6.81312	−	20.9686i	0.509236	−	1.56727i	0.793530	−	0.608531i	$-0.208241\pi$
$180$		0			0
$181$	6.38341	+	19.6461i	0.474475	+	1.46028i	0.846665	+	0.532127i	$0.178607\pi$
$181$	6.38341	+	19.6461i	0.474475	+	1.46028i	−0.372190	+	0.928157i	$0.621393\pi$
$182$		0			0
$183$	4.73771	+	14.5812i	0.350222	+	1.07787i
$184$		0			0
$185$	11.8987	+	1.56376i	0.874807	+	0.114970i
$186$		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	−0.223423	−	0.974722i	$-0.571723\pi$
$191$	−16.8535	−	12.2448i	−1.21948	−	0.886004i	−0.996057	+	0.0887181i	$0.971723\pi$
$192$		0			0
$193$	4.78053			0.344110			0.172055	−	0.985087i	$-0.444959\pi$
$193$	4.78053			0.344110			0.172055	+	0.985087i	$0.444959\pi$
$194$		0			0
$195$	−4.75162	+	9.96777i	−0.340271	+	0.713807i
$196$		0			0
$197$	5.36207	−	16.5028i	0.382032	−	1.17577i	−0.556579	−	0.830795i	$-0.687886\pi$
$197$	5.36207	−	16.5028i	0.382032	−	1.17577i	0.938611	−	0.344978i	$-0.112114\pi$
$198$		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
$205$	−19.3443	−	2.54228i	−1.35106	−	0.177561i
$206$		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	−0.734354	−	0.678767i	$-0.762515\pi$
$211$	−4.58634	+	3.33217i	−0.315736	+	0.229396i	0.418618	+	0.908163i	$0.362515\pi$
$212$		0			0
$213$	0.0190641	+	0.0138509i	0.00130625	+	0.000949047i
$214$		0			0
$215$	−5.62479	+	3.05565i	−0.383607	+	0.208394i
$216$		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	$-0.446029\pi$
$223$	17.2972	−	12.5671i	1.15831	−	0.841559i	0.989563	+	0.144101i	$0.0460292\pi$
$224$		0			0
$225$	−4.66709	+	1.79395i	−0.311140	+	0.119596i
$226$		0			0
$227$	18.5770	−	13.4970i	1.23300	−	0.895827i	0.235888	−	0.971780i	$-0.424200\pi$
$227$	18.5770	−	13.4970i	1.23300	−	0.895827i	0.997111	+	0.0759536i	$0.0242001\pi$
$228$		0			0
$229$	−8.68482	+	26.7291i	−0.573909	+	1.76631i	0.0659560	+	0.997823i	$0.478990\pi$
$229$	−8.68482	+	26.7291i	−0.573909	+	1.76631i	−0.639865	+	0.768487i	$0.721010\pi$
$230$		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	$-0.113892\pi$
$233$	−0.411596	−	1.26676i	−0.0269646	−	0.0829885i	−0.963633	+	0.267229i	$0.913892\pi$
$234$		0			0
$235$	−3.45258	−	18.6051i	−0.225222	−	1.21366i
$236$		0			0
$237$	−0.646223	−	0.469509i	−0.0419767	−	0.0304979i
$238$		0			0
$239$	−2.78730	+	2.02509i	−0.180295	+	0.130992i	−0.674272	−	0.738483i	$-0.735543\pi$
$239$	−2.78730	+	2.02509i	−0.180295	+	0.130992i	0.493977	+	0.869475i	$0.335543\pi$
$240$		0			0
$241$	19.4923	+	14.1620i	1.25561	+	0.912253i	0.998533	−	0.0541389i	$-0.0172414\pi$
$241$	19.4923	+	14.1620i	1.25561	+	0.912253i	0.257075	+	0.966392i	$0.417241\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	7.80267	−	4.23878i	0.498495	−	0.270806i
$246$		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
$255$	7.34928	−	3.99248i	0.460230	−	0.250019i
$256$		0			0
$257$	10.6862			0.666588			0.333294	−	0.942823i	$-0.391840\pi$
$257$	10.6862			0.666588			0.333294	+	0.942823i	$0.391840\pi$
$258$		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	$-0.391880\pi$
$263$	−7.46948	−	5.42689i	−0.460588	−	0.334637i	−0.793762	+	0.608229i	$0.791880\pi$
$264$		0			0
$265$	−0.548533	−	2.95590i	−0.0336961	−	0.181580i
$266$		0			0
$267$	1.50246	+	4.62409i	0.0919488	+	0.282989i
$268$		0			0
$269$	8.26252	+	25.4294i	0.503774	+	1.55046i	0.802821	+	0.596220i	$0.203331\pi$
$269$	8.26252	+	25.4294i	0.503774	+	1.55046i	−0.299047	+	0.954238i	$0.596669\pi$
$270$		0			0
$271$	7.47325	−	23.0003i	0.453968	−	1.39717i	−0.418375	−	0.908274i	$-0.637400\pi$
$271$	7.47325	−	23.0003i	0.453968	−	1.39717i	0.872343	−	0.488895i	$-0.162600\pi$
$272$		0			0
$273$	−6.95307	+	5.05170i	−0.420819	+	0.305743i
$274$		0			0
$275$	0.612394	+	11.5852i	0.0369288	+	0.698613i
$276$		0			0
$277$	25.5713	−	18.5787i	1.53643	−	1.11628i	0.583909	−	0.811819i	$-0.301523\pi$
$277$	25.5713	−	18.5787i	1.53643	−	1.11628i	0.952524	−	0.304464i	$-0.0984775\pi$
$278$		0			0
$279$	2.95471	−	9.09368i	0.176894	−	0.544424i
$280$		0			0
$281$	7.18851	+	22.1240i	0.428831	+	1.31981i	0.899278	+	0.437377i	$0.144093\pi$
$281$	7.18851	+	22.1240i	0.428831	+	1.31981i	−0.470447	+	0.882428i	$0.655907\pi$
$282$		0			0
$283$	7.67355	+	23.6167i	0.456145	+	1.40387i	0.869786	+	0.493430i	$0.164257\pi$
$283$	7.67355	+	23.6167i	0.456145	+	1.40387i	−0.413641	+	0.910440i	$0.635743\pi$
$284$		0			0
$285$	−3.32776	+	1.80780i	−0.197119	+	0.107085i
$286$		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	$-0.173461\pi$
$293$	29.2758			1.71031			0.855156	+	0.518371i	$0.173461\pi$
$294$		0			0
$295$	9.72806	+	1.27849i	0.566390	+	0.0744366i
$296$		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
$305$	−14.7520	+	30.9461i	−0.844695	+	1.77197i
$306$		0			0
$307$	8.73972			0.498802			0.249401	−	0.968400i	$-0.419766\pi$
$307$	8.73972			0.498802			0.249401	+	0.968400i	$0.419766\pi$
$308$		0			0
$309$	8.71303	+	6.33039i	0.495667	+	0.360123i
$310$		0			0
$311$	12.5043	−	9.08488i	0.709052	−	0.515156i	−0.173816	−	0.984778i	$-0.555610\pi$
$311$	12.5043	−	9.08488i	0.709052	−	0.515156i	0.882868	+	0.469622i	$0.155610\pi$
$312$		0			0
$313$	1.26124	+	0.916343i	0.0712894	+	0.0517948i	0.622859	−	0.782334i	$-0.285971\pi$
$313$	1.26124	+	0.916343i	0.0712894	+	0.0517948i	−0.551570	+	0.834129i	$0.685971\pi$
$314$		0			0
$315$	−3.85840	−	0.507083i	−0.217396	−	0.0285709i
$316$		0			0
$317$	−1.68802	−	5.19520i	−0.0948088	−	0.291792i	0.892395	−	0.451255i	$-0.149024\pi$
$317$	−1.68802	−	5.19520i	−0.0948088	−	0.291792i	−0.987204	+	0.159464i	$0.949024\pi$
$318$		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
$325$	−23.0475	+	8.85905i	−1.27845	+	0.491412i
$326$		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	0.958061	−	0.286563i	$-0.0925128\pi$
$331$	0.264458	+	0.813918i	0.0145359	+	0.0447370i	−0.943525	+	0.331300i	$0.892513\pi$
$332$		0			0
$333$	1.65849	+	5.10432i	0.0908849	+	0.279715i
$334$		0			0
$335$	−14.9754	−	14.2047i	−0.818191	−	0.776084i
$336$		0			0
$337$	−11.9933	−	8.71367i	−0.653318	−	0.474664i	0.211082	−	0.977468i	$-0.432301\pi$
$337$	−11.9933	−	8.71367i	−0.653318	−	0.474664i	−0.864400	+	0.502805i	$0.832301\pi$
$338$		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
$345$	14.0797	+	13.3551i	0.758026	+	0.719015i
$346$		0			0
$347$	−0.361763	+	1.11339i	−0.0194204	+	0.0597700i	−0.960297	−	0.278979i	$-0.910004\pi$
$347$	−0.361763	+	1.11339i	−0.0194204	+	0.0597700i	0.940877	+	0.338749i	$0.110004\pi$
$348$		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	$-0.930225\pi$
$353$	−1.10094	+	3.38834i	−0.0585970	+	0.180343i	0.917474	+	0.397796i	$0.130225\pi$
$354$		0			0
$355$	0.00961402	+	0.0518074i	0.000510259	+	0.00274965i
$356$		0			0
$357$	6.50961			0.344525
$358$		0			0
$359$	−10.8337	−	7.87116i	−0.571782	−	0.415424i	0.263970	−	0.964531i	$-0.414968\pi$
$359$	−10.8337	−	7.87116i	−0.571782	−	0.415424i	−0.835752	+	0.549107i	$0.814968\pi$
$360$		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
$365$	−0.983858	+	2.06390i	−0.0514975	+	0.108029i
$366$		0			0
$367$	−0.440150	−	1.35464i	−0.0229757	−	0.0707118i	0.938911	−	0.344159i	$-0.111836\pi$
$367$	−0.440150	−	1.35464i	−0.0229757	−	0.0707118i	−0.961887	+	0.273447i	$0.911836\pi$
$368$		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	$-0.929875\pi$
$373$	−20.6564	+	15.0077i	−1.06955	+	0.777072i	−0.0937165	+	0.995599i	$0.529875\pi$
$374$		0			0
$375$	−10.3322	−	4.27154i	−0.533551	−	0.220581i
$376$		0			0
$377$	−12.4743	+	9.06309i	−0.642457	+	0.466773i
$378$		0			0
$379$	−11.7671	+	36.2153i	−0.604434	+	1.86026i	−0.103800	+	0.994598i	$0.533100\pi$
$379$	−11.7671	+	36.2153i	−0.604434	+	1.86026i	−0.500634	+	0.865659i	$0.666900\pi$
$380$		0			0
$381$	−5.87428	−	18.0792i	−0.300949	−	0.926225i
$382$		0			0
$383$	4.21946	+	12.9862i	0.215604	+	0.663562i	0.999110	+	0.0421775i	$0.0134295\pi$
$383$	4.21946	+	12.9862i	0.215604	+	0.663562i	−0.783506	+	0.621384i	$0.786571\pi$
$384$		0			0
$385$	−3.88547	+	8.15080i	−0.198022	+	0.415403i
$386$		0			0
$387$	−2.31597	−	1.68265i	−0.117728	−	0.0855341i
$388$		0			0
$389$	−28.9546	+	21.0368i	−1.46806	+	1.06661i	−0.486888	+	0.873465i	$0.661868\pi$
$389$	−28.9546	+	21.0368i	−1.46806	+	1.06661i	−0.981171	+	0.193142i	$0.938132\pi$
$390$		0			0
$391$	−26.2619	−	19.0804i	−1.32812	−	0.964935i
$392$		0			0
$393$	0.745032			0.0375819
$394$		0			0
$395$	−0.325890	−	1.75613i	−0.0163973	−	0.0883607i
$396$		0			0
$397$	7.58400	−	23.3412i	0.380630	−	1.17146i	−0.558971	−	0.829187i	$-0.688804\pi$
$397$	7.58400	−	23.3412i	0.380630	−	1.17146i	0.939601	−	0.342272i	$-0.111196\pi$
$398$		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
$405$	−1.62233	−	1.53884i	−0.0806144	−	0.0764657i
$406$		0			0
$407$	12.4529			0.617268
$408$		0			0
$409$	15.0121	+	10.9069i	0.742299	+	0.539312i	0.893430	−	0.449202i	$-0.148292\pi$
$409$	15.0121	+	10.9069i	0.742299	+	0.539312i	−0.151131	+	0.988514i	$0.548292\pi$
$410$		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
$415$	−3.84506	−	3.64718i	−0.188747	−	0.179033i
$416$		0			0
$417$	−4.23010	−	13.0189i	−0.207149	−	0.637539i
$418$		0			0
$419$	1.45029	+	4.46354i	0.0708513	+	0.218058i	0.980212	−	0.197951i	$-0.0634286\pi$
$419$	1.45029	+	4.46354i	0.0708513	+	0.218058i	−0.909361	+	0.416009i	$0.863429\pi$
$420$		0			0
$421$	2.84929	−	8.76921i	0.138866	−	0.427385i	−0.857305	−	0.514808i	$-0.827863\pi$
$421$	2.84929	−	8.76921i	0.138866	−	0.427385i	0.996171	+	0.0874228i	$0.0278631\pi$
$422$		0			0
$423$	6.84629	−	4.97412i	0.332878	−	0.241850i
$424$		0			0
$425$	18.0668	+	4.83224i	0.876367	+	0.234398i
$426$		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	0.902590	+	0.430501i	$0.141663\pi$
$431$	8.83198	+	27.1820i	0.425421	+	1.30931i	−0.477169	+	0.878812i	$0.658337\pi$
$432$		0			0
$433$	1.12286	+	3.45581i	0.0539612	+	0.166075i	0.974405	−	0.224799i	$-0.0721726\pi$
$433$	1.12286	+	3.45581i	0.0539612	+	0.166075i	−0.920444	+	0.390875i	$0.872173\pi$
$434$		0			0
$435$	−6.92223	−	0.909740i	−0.331895	−	0.0436187i
$436$		0			0
$437$	11.8914	+	8.63959i	0.568842	+	0.413288i
$438$		0			0
$439$	14.2446	−	10.3493i	0.679859	−	0.493947i	−0.193452	−	0.981110i	$-0.561968\pi$
$439$	14.2446	−	10.3493i	0.679859	−	0.493947i	0.873311	+	0.487163i	$0.161968\pi$
$440$		0			0
$441$	3.21270	+	2.33417i	0.152986	+	0.111151i
$442$		0			0
$443$	7.11807			0.338190			0.169095	−	0.985600i	$-0.445916\pi$
$443$	7.11807			0.338190			0.169095	+	0.985600i	$0.445916\pi$
$444$		0			0
$445$	−4.67825	+	9.81385i	−0.221770	+	0.465221i
$446$		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
$455$	−19.0540	−	2.50413i	−0.893264	−	0.117395i
$456$		0			0
$457$	−16.8375			−0.787624			−0.393812	−	0.919191i	$-0.628844\pi$
$457$	−16.8375			−0.787624			−0.393812	+	0.919191i	$0.628844\pi$
$458$		0			0
$459$	3.02602	+	2.19853i	0.141243	+	0.102619i
$460$		0			0
$461$	−14.0162	+	10.1833i	−0.652798	+	0.474286i	−0.864223	−	0.503109i	$-0.832190\pi$
$461$	−14.0162	+	10.1833i	−0.652798	+	0.474286i	0.211425	+	0.977394i	$0.432190\pi$
$462$		0			0
$463$	−6.96088	−	5.05738i	−0.323500	−	0.235036i	0.414168	−	0.910201i	$-0.364073\pi$
$463$	−6.96088	−	5.05738i	−0.323500	−	0.235036i	−0.737667	+	0.675164i	$0.764073\pi$
$464$		0			0
$465$	18.7873	−	10.2061i	0.871238	−	0.473298i
$466$		0			0
$467$	0.258292	+	0.794942i	0.0119523	+	0.0367855i	0.956855	−	0.290566i	$-0.0938437\pi$
$467$	0.258292	+	0.794942i	0.0119523	+	0.0367855i	−0.944902	+	0.327352i	$0.893844\pi$
$468$		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
$475$	−8.18064	−	2.18804i	−0.375354	−	0.100394i
$476$		0			0
$477$	1.08771	−	0.790270i	0.0498030	−	0.0361840i
$478$		0			0
$479$	−10.3365	+	31.8123i	−0.472285	+	1.45354i	0.377300	+	0.926091i	$0.376853\pi$
$479$	−10.3365	+	31.8123i	−0.472285	+	1.45354i	−0.849585	+	0.527452i	$0.823147\pi$
$480$		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
$485$	−1.41225	−	7.61024i	−0.0641269	−	0.345563i
$486$		0			0
$487$	19.7528	+	14.3512i	0.895083	+	0.650316i	0.937198	−	0.348797i	$-0.113410\pi$
$487$	19.7528	+	14.3512i	0.895083	+	0.650316i	−0.0421152	+	0.999113i	$0.513410\pi$
$488$		0			0
$489$	−4.97293	+	3.61304i	−0.224884	+	0.163387i
$490$		0			0
$491$	11.8501	+	8.60958i	0.534786	+	0.388545i	0.822145	−	0.569278i	$-0.192777\pi$
$491$	11.8501	+	8.60958i	0.534786	+	0.388545i	−0.287359	+	0.957823i	$0.592777\pi$
$492$		0			0
$493$	11.6787			0.525981
$494$		0			0
$495$	−4.55900	+	2.47667i	−0.204912	+	0.111318i
$496$		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	0.107202	+	0.994237i	$0.465811\pi$
$503$	−12.6475	+	38.9250i	−0.563924	+	1.73558i	−0.671126	+	0.741343i	$0.734189\pi$
$504$		0			0
$505$	14.8947	−	8.09151i	0.662805	−	0.360067i
$506$		0			0
$507$	−11.3869			−0.505709
$508$		0			0
$509$	−9.82240	−	7.13639i	−0.435370	−	0.316315i	0.348422	−	0.937338i	$-0.386718\pi$
$509$	−9.82240	−	7.13639i	−0.435370	−	0.316315i	−0.783793	+	0.621023i	$0.786718\pi$
$510$		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
$515$	4.39398	+	23.6780i	0.193622	+	1.04338i
$516$		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	−0.600943	−	0.799292i	$-0.705208\pi$
$521$	8.10398	−	24.9415i	0.355042	−	1.09271i	0.955985	−	0.293415i	$-0.0947918\pi$
$522$		0			0
$523$	−12.3978	+	9.00754i	−0.542118	+	0.393872i	−0.824871	−	0.565321i	$-0.808752\pi$
$523$	−12.3978	+	9.00754i	−0.542118	+	0.393872i	0.282753	+	0.959193i	$0.408752\pi$
$524$		0			0
$525$	−5.47929	−	6.76013i	−0.239136	−	0.295036i
$526$		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
$535$	8.53422	−	4.63619i	0.368966	−	0.200440i
$536$		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	0.410633	−	0.911801i	$-0.365308\pi$
$541$	−7.66742	−	5.57071i	−0.329648	−	0.239503i	−0.740281	+	0.672297i	$0.765308\pi$
$542$		0			0
$543$	−20.6571			−0.886483
$544$		0			0
$545$	2.37501	+	0.312131i	0.101734	+	0.0133702i
$546$		0			0
$547$	0.199605	−	0.614321i	0.00853449	−	0.0262665i	−0.946699	−	0.322121i	$-0.895604\pi$
$547$	0.199605	−	0.614321i	0.00853449	−	0.0262665i	0.955233	+	0.295854i	$0.0956043\pi$
$548$		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
$555$	−5.16411	+	10.8331i	−0.219204	+	0.459838i
$556$		0			0
$557$	−12.0297			−0.509716			−0.254858	−	0.966978i	$-0.582029\pi$
$557$	−12.0297			−0.509716			−0.254858	+	0.966978i	$0.582029\pi$
$558$		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	$-0.408635\pi$
$563$	−12.8498	−	9.33593i	−0.541555	−	0.393462i	−0.824662	+	0.565626i	$0.808635\pi$
$564$		0			0
$565$	41.1513	+	5.40822i	1.73125	+	0.227526i
$566$		0			0
$567$	−0.537803	−	1.65519i	−0.0225856	−	0.0695114i
$568$		0			0
$569$	6.77685	+	20.8570i	0.284100	+	0.874371i	0.986667	+	0.162753i	$0.0520374\pi$
$569$	6.77685	+	20.8570i	0.284100	+	0.874371i	−0.702566	+	0.711618i	$0.747963\pi$
$570$		0			0
$571$	−2.10390	+	6.47513i	−0.0880453	+	0.270976i	−0.985379	−	0.170377i	$-0.945501\pi$
$571$	−2.10390	+	6.47513i	−0.0880453	+	0.270976i	0.897334	+	0.441353i	$0.145501\pi$
$572$		0			0
$573$	16.8535	−	12.2448i	0.704067	−	0.511534i
$574$		0			0
$575$	2.29058	+	43.3329i	0.0955238	+	1.80711i
$576$		0			0
$577$	−15.0698	+	10.9488i	−0.627364	+	0.455806i	−0.855486	−	0.517826i	$-0.826741\pi$
$577$	−15.0698	+	10.9488i	−0.627364	+	0.455806i	0.228122	+	0.973632i	$0.426741\pi$
$578$		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
$585$	−8.01158	−	7.59927i	−0.331238	−	0.314191i
$586$		0			0
$587$	11.4963	+	8.35254i	0.474503	+	0.344746i	0.799194	−	0.601074i	$-0.205260\pi$
$587$	11.4963	+	8.35254i	0.474503	+	0.344746i	−0.324691	+	0.945820i	$0.605260\pi$
$588$		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	$-0.184063\pi$
$593$	40.7850			1.67484			0.837420	+	0.546559i	$0.184063\pi$
$594$		0			0
$595$	10.5608	+	10.0173i	0.432949	+	0.410668i
$596$		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
$605$	−2.29139	−	12.3477i	−0.0931582	−	0.502005i
$606$		0			0
$607$	30.5033			1.23809			0.619045	−	0.785355i	$-0.287520\pi$
$607$	30.5033			1.23809			0.619045	+	0.785355i	$0.287520\pi$
$608$		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	$-0.216952\pi$
$613$	10.3337	+	7.50789i	0.417375	+	0.303241i	−0.359206	+	0.933258i	$0.616952\pi$
$614$		0			0
$615$	8.39555	−	17.6119i	0.338541	−	0.710179i
$616$		0			0
$617$	−3.68740	−	11.3486i	−0.148449	−	0.456879i	0.848989	−	0.528410i	$-0.177212\pi$
$617$	−3.68740	−	11.3486i	−0.148449	−	0.456879i	−0.997438	+	0.0715308i	$0.977212\pi$
$618$		0			0
$619$	−4.48215	−	13.7946i	−0.180153	−	0.554454i	0.819678	−	0.572824i	$-0.194152\pi$
$619$	−4.48215	−	13.7946i	−0.180153	−	0.554454i	−0.999831	+	0.0183705i	$0.994152\pi$
$620$		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
$625$	−10.1890	−	22.8295i	−0.407561	−	0.913178i
$626$		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	0.925958	−	0.377626i	$-0.123259\pi$
$631$	−1.13341	−	3.48828i	−0.0451204	−	0.138866i	−0.971079	+	0.238759i	$0.923259\pi$
$632$		0			0
$633$	−1.75182	−	5.39156i	−0.0696288	−	0.214295i
$634$		0			0
$635$	18.2910	−	38.3701i	0.725854	−	1.52267i
$636$		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	0.786678	−	0.617364i	$-0.211799\pi$
$641$	11.2064	+	8.14192i	0.442626	+	0.321587i	−0.344051	+	0.938951i	$0.611799\pi$
$642$		0			0
$643$	−27.1641			−1.07125			−0.535624	−	0.844456i	$-0.679924\pi$
$643$	−27.1641			−1.07125			−0.535624	+	0.844456i	$0.679924\pi$
$644$		0			0
$645$	−1.16794	−	6.29374i	−0.0459878	−	0.247816i
$646$		0			0
$647$	−1.59140	+	4.89783i	−0.0625644	+	0.192553i	−0.977453	−	0.211153i	$-0.932278\pi$
$647$	−1.59140	+	4.89783i	−0.0625644	+	0.192553i	0.914889	+	0.403706i	$0.132278\pi$
$648$		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	0.594920	+	0.803785i	$0.297184\pi$
$653$	−9.16957	+	28.2210i	−0.358833	+	1.10437i	−0.953753	+	0.300590i	$0.902816\pi$
$654$		0			0
$655$	1.20869	+	1.14649i	0.0472274	+	0.0447969i
$656$		0			0
$657$	−1.02251			−0.0398920
$658$		0			0
$659$	−12.7614	−	9.27170i	−0.497114	−	0.361174i	0.310800	−	0.950475i	$-0.399403\pi$
$659$	−12.7614	−	9.27170i	−0.497114	−	0.361174i	−0.807913	+	0.589301i	$0.799403\pi$
$660$		0			0
$661$	19.4614	−	14.1396i	0.756962	−	0.549965i	−0.141015	−	0.990007i	$-0.545037\pi$
$661$	19.4614	−	14.1396i	0.756962	−	0.549965i	0.897977	+	0.440042i	$0.145037\pi$
$662$		0			0
$663$	14.9434	+	10.8570i	0.580354	+	0.421652i
$664$		0			0
$665$	−4.78192	−	4.53582i	−0.185435	−	0.175892i
$666$		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	$-0.911580\pi$
$673$	−25.8914	+	18.8112i	−0.998040	+	0.725119i	−0.0363731	+	0.999338i	$0.511580\pi$
$674$		0			0
$675$	−0.263932	−	4.99303i	−0.0101587	−	0.192182i
$676$		0			0
$677$	19.7246	−	14.3307i	0.758077	−	0.550775i	−0.140243	−	0.990117i	$-0.544788\pi$
$677$	19.7246	−	14.3307i	0.758077	−	0.550775i	0.898320	+	0.439342i	$0.144788\pi$
$678$		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	$-0.168446\pi$
$683$	−3.44642	−	10.6070i	−0.131873	−	0.405865i	−0.995091	+	0.0989680i	$0.968446\pi$
$684$		0			0
$685$	−24.6809	−	3.24364i	−0.943010	−	0.123933i
$686$		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	0.408549	−	0.912737i	$-0.366035\pi$
$691$	−8.76055	−	6.36491i	−0.333267	−	0.242133i	−0.741816	+	0.670604i	$0.766035\pi$
$692$		0			0
$693$	−4.03813			−0.153396
$694$		0			0
$695$	13.1714	−	27.6305i	0.499620	−	1.04808i
$696$		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
$705$	18.7614	+	2.46568i	0.706594	+	0.0928627i
$706$		0			0
$707$	13.1930			0.496172
$708$		0			0
$709$	36.0864	+	26.2183i	1.35525	+	0.984649i	0.998731	+	0.0503617i	$0.0160374\pi$
$709$	36.0864	+	26.2183i	1.35525	+	0.984649i	0.356522	+	0.934287i	$0.383963\pi$
$710$		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
$715$	−22.5137	+	12.2305i	−0.841966	+	0.457396i
$716$		0			0
$717$	−1.06465	−	3.27666i	−0.0397602	−	0.122369i
$718$		0			0
$719$	−9.91537	−	30.5164i	−0.369781	−	1.13807i	−0.946933	−	0.321432i	$-0.895836\pi$
$719$	−9.91537	−	30.5164i	−0.369781	−	1.13807i	0.577152	−	0.816637i	$-0.304164\pi$
$720$		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
$725$	−9.83021	−	12.1281i	−0.365085	−	0.450427i
$726$		0			0
$727$	11.0201	−	8.00656i	0.408712	−	0.296947i	−0.364368	−	0.931255i	$-0.618715\pi$
$727$	11.0201	−	8.00656i	0.408712	−	0.296947i	0.773080	+	0.634308i	$0.218715\pi$
$728$		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	0.971698	+	0.236225i	$0.0759104\pi$
$733$	8.78355	+	27.0330i	0.324428	+	0.998486i	−0.647271	+	0.762260i	$0.724090\pi$
$734$		0			0
$735$	1.62017	+	8.73064i	0.0597607	+	0.322035i
$736$		0			0
$737$	−17.3274	−	12.5891i	−0.638264	−	0.463726i
$738$		0			0
$739$	−7.85925	+	5.71008i	−0.289107	+	0.210049i	−0.722880	−	0.690974i	$-0.757182\pi$
$739$	−7.85925	+	5.71008i	−0.289107	+	0.210049i	0.433773	+	0.901022i	$0.357182\pi$
$740$		0			0
$741$	−6.76639	−	4.91607i	−0.248569	−	0.180596i
$742$		0			0
$743$	34.2029			1.25478			0.627390	−	0.778705i	$-0.284123\pi$
$743$	34.2029			1.25478			0.627390	+	0.778705i	$0.284123\pi$
$744$		0			0
$745$	20.8830	−	11.3446i	0.765093	−	0.415635i
$746$		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
$755$	20.5698	−	11.1745i	0.748610	−	0.406681i
$756$		0			0
$757$	26.6200			0.967520			0.483760	−	0.875201i	$-0.339271\pi$
$757$	26.6200			0.967520			0.483760	+	0.875201i	$0.339271\pi$
$758$		0			0
$759$	16.2911	+	11.8362i	0.591329	+	0.429626i
$760$		0			0
$761$	−20.8028	+	15.1141i	−0.754102	+	0.547887i	−0.897096	−	0.441836i	$-0.854327\pi$
$761$	−20.8028	+	15.1141i	−0.754102	+	0.547887i	0.142993	+	0.989724i	$0.454327\pi$
$762$		0			0
$763$	1.50833	+	1.09587i	0.0546053	+	0.0396731i
$764$		0			0
$765$	1.52602	+	8.22332i	0.0551734	+	0.297315i
$766$		0			0
$767$	6.69607	+	20.6084i	0.241781	+	0.744126i
$768$		0			0
$769$	−11.8575	−	36.4937i	−0.427593	−	1.31600i	−0.900490	−	0.434877i	$-0.856792\pi$
$769$	−11.8575	−	36.4937i	−0.427593	−	1.31600i	0.472897	−	0.881118i	$-0.343208\pi$
$770$		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	$-0.691992\pi$
$773$	1.13168	−	0.822215i	0.0407038	−	0.0295730i	0.607951	+	0.793974i	$0.291992\pi$
$774$		0			0
$775$	46.1848	+	12.3529i	1.65901	+	0.443728i
$776$		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
$785$	33.9895	−	18.4647i	1.21314	−	0.659034i
$786$		0			0
$787$	3.40614	+	2.47471i	0.121416	+	0.0882138i	0.646836	−	0.762629i	$-0.276092\pi$
$787$	3.40614	+	2.47471i	0.121416	+	0.0882138i	−0.525420	+	0.850843i	$0.676092\pi$
$788$		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
$795$	2.98073	+	0.391737i	0.105716	+	0.0138935i
$796$		0			0
$797$	−9.77099	+	30.0720i	−0.346106	+	1.06521i	0.614883	+	0.788619i	$0.289203\pi$
$797$	−9.77099	+	30.0720i	−0.346106	+	1.06521i	−0.960989	+	0.276587i	$0.910797\pi$
$798$		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
$805$	−14.5331	+	30.4870i	−0.512225	+	1.07452i
$806$		0			0
$807$	−26.7381			−0.941224
$808$		0			0
$809$	−34.0676	−	24.7515i	−1.19775	−	0.870218i	−0.203691	−	0.979035i	$-0.565294\pi$
$809$	−34.0676	−	24.7515i	−1.19775	−	0.870218i	−0.994062	+	0.108817i	$0.965294\pi$
$810$		0			0
$811$	−12.2591	+	8.90674i	−0.430474	+	0.312758i	−0.781838	−	0.623481i	$-0.785718\pi$
$811$	−12.2591	+	8.90674i	−0.430474	+	0.312758i	0.351364	+	0.936239i	$0.385718\pi$
$812$		0			0
$813$	19.5652	+	14.2150i	0.686183	+	0.498541i
$814$		0			0
$815$	−13.6276	−	1.79099i	−0.477356	−	0.0627355i
$816$		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	−0.953203	−	0.302332i	$-0.902235\pi$
$821$	−0.124324	+	0.382629i	−0.00433893	+	0.0133538i	0.948864	+	0.315686i	$0.102235\pi$
$822$		0			0
$823$	0.492983	−	0.358173i	0.0171843	−	0.0124851i	−0.579160	−	0.815214i	$-0.696619\pi$
$823$	0.492983	−	0.358173i	0.0171843	−	0.0124851i	0.596344	+	0.802729i	$0.296619\pi$
$824$		0			0
$825$	−11.2074	−	2.99760i	−0.390192	−	0.104363i
$826$		0			0
$827$	−22.2214	+	16.1448i	−0.772715	+	0.561410i	−0.902784	−	0.430095i	$-0.858480\pi$
$827$	−22.2214	+	16.1448i	−0.772715	+	0.561410i	0.130069	+	0.991505i	$0.458480\pi$
$828$		0			0
$829$	9.62722	−	29.6295i	0.334367	−	1.02908i	−0.632666	−	0.774425i	$-0.718039\pi$
$829$	9.62722	−	29.6295i	0.334367	−	1.02908i	0.967033	−	0.254651i	$-0.0819607\pi$
$830$		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
$835$	3.08272	+	2.92407i	0.106682	+	0.101192i
$836$		0			0
$837$	7.73554	+	5.62020i	0.267379	+	0.194263i
$838$		0			0
$839$	−31.6468	+	22.9927i	−1.09257	+	0.793798i	−0.979831	−	0.199827i	$-0.935962\pi$
$839$	−31.6468	+	22.9927i	−1.09257	+	0.793798i	−0.112738	+	0.993625i	$0.535962\pi$
$840$		0			0
$841$	15.5744	+	11.3155i	0.537049	+	0.390189i
$842$		0			0
$843$	−23.2625			−0.801204
$844$		0			0
$845$	−18.4733	−	17.5226i	−0.635501	−	0.602796i
$846$		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	0.136261	+	0.990673i	$0.456491\pi$
$853$	−16.2468	+	50.0025i	−0.556279	+	1.71205i	−0.692541	+	0.721379i	$0.743509\pi$
$854$		0			0
$855$	−0.690983	−	3.72352i	−0.0236311	−	0.127342i
$856$		0			0
$857$	−31.0291			−1.05993			−0.529967	−	0.848018i	$-0.677796\pi$
$857$	−31.0291			−1.05993			−0.529967	+	0.848018i	$0.677796\pi$
$858$		0			0
$859$	−31.4263	−	22.8325i	−1.07225	−	0.779035i	−0.0959345	−	0.995388i	$-0.530584\pi$
$859$	−31.4263	−	22.8325i	−1.07225	−	0.779035i	−0.976315	+	0.216353i	$0.930584\pi$
$860$		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	$-0.280471\pi$
$863$	2.91445	+	2.11748i	0.0992092	+	0.0720797i	−0.537075	+	0.843535i	$0.680471\pi$
$864$		0			0
$865$	11.1479	−	23.3856i	0.379040	−	0.795134i
$866$		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
$875$	1.51352	−	19.3989i	0.0511665	−	0.655804i
$876$		0			0
$877$	25.5323	−	18.5503i	0.862165	−	0.626399i	−0.0663082	−	0.997799i	$-0.521122\pi$
$877$	25.5323	−	18.5503i	0.862165	−	0.626399i	0.928473	+	0.371400i	$0.121122\pi$
$878$		0			0
$879$	−9.04673	+	27.8430i	−0.305139	+	0.939120i
$880$		0			0
$881$	1.86270	+	5.73280i	0.0627560	+	0.193143i	0.977519	−	0.210848i	$-0.0676226\pi$
$881$	1.86270	+	5.73280i	0.0627560	+	0.193143i	−0.914763	+	0.403991i	$0.867623\pi$
$882$		0			0
$883$	−1.22550	−	3.77171i	−0.0412414	−	0.126928i	0.928316	−	0.371792i	$-0.121257\pi$
$883$	−1.22550	−	3.77171i	−0.0412414	−	0.126928i	−0.969557	+	0.244864i	$0.921257\pi$
$884$		0			0
$885$	−4.22205	+	8.85686i	−0.141923	+	0.297720i
$886$		0			0
$887$	−45.0745	−	32.7485i	−1.51345	−	1.09959i	−0.964616	−	0.263657i	$-0.915071\pi$
$887$	−45.0745	−	32.7485i	−1.51345	−	1.09959i	−0.548836	−	0.835930i	$-0.684929\pi$
$888$		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
$895$	8.99517	+	48.4726i	0.300676	+	1.62026i
$896$		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
$905$	−33.5128	−	31.7881i	−1.11400	−	1.05667i
$906$		0			0
$907$	−21.4063			−0.710785			−0.355392	−	0.934717i	$-0.615653\pi$
$907$	−21.4063			−0.710785			−0.355392	+	0.934717i	$0.615653\pi$
$908$		0			0
$909$	6.13280	+	4.45574i	0.203412	+	0.147788i
$910$		0			0
$911$	−25.5560	+	18.5676i	−0.846709	+	0.615170i	−0.924237	−	0.381820i	$-0.875298\pi$
$911$	−25.5560	+	18.5676i	−0.846709	+	0.615170i	0.0775273	+	0.996990i	$0.475298\pi$
$912$		0			0
$913$	−4.44898	−	3.23237i	−0.147240	−	0.106976i
$914$		0			0
$915$	−24.8729	−	23.5928i	−0.822272	−	0.779955i
$916$		0			0
$917$	0.400680	+	1.23317i	0.0132316	+	0.0407228i
$918$		0			0
$919$	−5.58626	−	17.1927i	−0.184274	−	0.567136i	0.815661	−	0.578530i	$-0.196373\pi$
$919$	−5.58626	−	17.1927i	−0.184274	−	0.567136i	−0.999935	+	0.0113935i	$0.996373\pi$
$920$		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
$925$	−25.0483	+	9.62810i	−0.823583	+	0.316570i
$926$		0			0
$927$	−8.71303	+	6.33039i	−0.286173	+	0.207917i
$928$		0			0
$929$	2.75953	−	8.49296i	0.0905373	−	0.278645i	−0.895528	−	0.445006i	$-0.853202\pi$
$929$	2.75953	−	8.49296i	0.0905373	−	0.278645i	0.986065	+	0.166361i	$0.0532016\pi$
$930$		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
$935$	19.2407	+	2.52867i	0.629237	+	0.0826962i
$936$		0			0
$937$	0.0491192	+	0.0356872i	0.00160466	+	0.00116585i	0.588587	−	0.808434i	$-0.299684\pi$
$937$	0.0491192	+	0.0356872i	0.00160466	+	0.00116585i	−0.586983	+	0.809600i	$0.699684\pi$
$938$		0			0
$939$	−1.26124	+	0.916343i	−0.0411589	+	0.0299037i
$940$		0			0
$941$	−16.7021	−	12.1348i	−0.544473	−	0.395583i	0.281271	−	0.959628i	$-0.409244\pi$
$941$	−16.7021	−	12.1348i	−0.544473	−	0.395583i	−0.825744	+	0.564046i	$0.809244\pi$
$942$		0			0
$943$	−75.7249			−2.46594
$944$		0			0
$945$	1.67458	−	3.51286i	0.0544740	−	0.114273i
$946$		0			0
$947$	15.8787	−	48.8696i	0.515988	−	1.58805i	−0.265489	−	0.964114i	$-0.585534\pi$
$947$	15.8787	−	48.8696i	0.515988	−	1.58805i	0.781477	−	0.623934i	$-0.214466\pi$
$948$		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	−0.749834	−	0.661626i	$-0.769867\pi$
$953$	7.58457	−	23.3429i	0.245688	−	0.756151i	0.995522	−	0.0945251i	$-0.0301333\pi$
$954$		0			0
$955$	46.1849	+	6.06976i	1.49451	+	0.196413i
$956$		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
$965$	−9.39304	+	5.10275i	−0.302373	+	0.164263i
$966$		0			0
$967$	11.7996	+	36.3155i	0.379451	+	1.16783i	0.940427	+	0.339997i	$0.110426\pi$
$967$	11.7996	+	36.3155i	0.379451	+	1.16783i	−0.560976	+	0.827832i	$0.689574\pi$
$968$		0			0
$969$	1.95757	+	6.02479i	0.0628863	+	0.193544i
$970$		0			0
$971$	7.97794	−	24.5536i	0.256024	−	0.787962i	−0.737602	−	0.675236i	$-0.764042\pi$
$971$	7.97794	−	24.5536i	0.256024	−	0.787962i	0.993626	−	0.112726i	$-0.0359582\pi$
$972$		0			0
$973$	19.2738	−	14.0032i	0.617889	−	0.448923i
$974$		0			0
$975$	−1.30338	−	24.6571i	−0.0417415	−	0.789660i
$976$		0			0
$977$	−16.6867	+	12.1236i	−0.533855	+	0.387868i	−0.821798	−	0.569779i	$-0.807029\pi$
$977$	−16.6867	+	12.1236i	−0.533855	+	0.387868i	0.287943	+	0.957648i	$0.407029\pi$
$978$		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	−0.998915	−	0.0465741i	$-0.985170\pi$
$983$	−6.83966	−	21.0503i	−0.218151	−	0.671401i	0.780763	−	0.624827i	$-0.214830\pi$
$984$		0			0
$985$	7.07940	+	38.1490i	0.225569	+	1.21553i
$986$		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	0.608975	−	0.793189i	$-0.291581\pi$
$991$	1.34709	+	0.978715i	0.0427916	+	0.0310899i	−0.566184	+	0.824279i	$0.691581\pi$
$992$		0			0
$993$	−0.855804			−0.0271581
$994$		0			0
$995$	−21.7620	+	11.8221i	−0.689900	+	0.374787i
$996$		0			0
$997$	−7.25453	+	22.3271i	−0.229753	+	0.707108i	0.768021	+	0.640425i	$0.221242\pi$
$997$	−7.25453	+	22.3271i	−0.229753	+	0.707108i	−0.997774	+	0.0666831i	$0.978758\pi$
$998$		0			0
$999$	−5.36700			−0.169804

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.m.b.61.1	✓	8
3.2	odd	2		900.2.n.b.361.2		8
5.2	odd	4		1500.2.o.b.949.3		16
5.3	odd	4		1500.2.o.b.949.2		16
5.4	even	2		1500.2.m.a.301.2		8
25.3	odd	20		7500.2.d.c.1249.4		8
25.4	even	10		7500.2.a.f.1.4		4
25.9	even	10		1500.2.m.a.1201.2		8
25.12	odd	20		1500.2.o.b.49.1		16
25.13	odd	20		1500.2.o.b.49.4		16
25.16	even	5	inner	300.2.m.b.241.1	yes	8
25.21	even	5		7500.2.a.e.1.1		4
25.22	odd	20		7500.2.d.c.1249.5		8
75.41	odd	10		900.2.n.b.541.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.b.61.1	✓	8	1.1	even	1	trivial
300.2.m.b.241.1	yes	8	25.16	even	5	inner
900.2.n.b.361.2		8	3.2	odd	2
900.2.n.b.541.2		8	75.41	odd	10
1500.2.m.a.301.2		8	5.4	even	2
1500.2.m.a.1201.2		8	25.9	even	10
1500.2.o.b.49.1		16	25.12	odd	20
1500.2.o.b.49.4		16	25.13	odd	20
1500.2.o.b.949.2		16	5.3	odd	4
1500.2.o.b.949.3		16	5.2	odd	4
7500.2.a.e.1.1		4	25.21	even	5
7500.2.a.f.1.4		4	25.4	even	10
7500.2.d.c.1249.4		8	25.3	odd	20
7500.2.d.c.1249.5		8	25.22	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{3} +(-1.96485 + 1.06740i) q^{5} -1.74037 q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{3} +(-1.96485 + 1.06740i) q^{5} -1.74037 q^{7} +(-0.809017 - 0.587785i) q^{9} +(-1.87714 + 1.36382i) q^{11} +(-3.99517 - 2.90266i) q^{13} +(-0.407987 - 2.19853i) q^{15} +(1.15584 + 3.55730i) q^{17} +(-0.523364 - 1.61075i) q^{19} +(0.537803 - 1.65519i) q^{21} +(-7.02120 + 5.10120i) q^{23} +(2.72130 - 4.19458i) q^{25} +(0.809017 - 0.587785i) q^{27} +(0.964854 - 2.96952i) q^{29} +(2.95471 + 9.09368i) q^{31} +(-0.717004 - 2.20671i) q^{33} +(3.41957 - 1.85767i) q^{35} +(-4.34199 - 3.15464i) q^{37} +(3.99517 - 2.90266i) q^{39} +(7.05900 + 5.12866i) q^{41} +2.86270 q^{43} +(2.21700 + 0.291365i) q^{45} +(-2.61505 + 8.04830i) q^{47} -3.97112 q^{49} -3.74037 q^{51} +(-0.415470 + 1.27868i) q^{53} +(2.23256 - 4.68338i) q^{55} +1.69364 q^{57} +(-3.54991 - 2.57916i) q^{59} +(12.4035 - 9.01166i) q^{61} +(1.40799 + 1.02296i) q^{63} +(10.9482 + 1.43885i) q^{65} +(2.85246 + 8.77897i) q^{67} +(-2.68186 - 8.25391i) q^{69} +(0.00728184 - 0.0224112i) q^{71} +(0.827230 - 0.601018i) q^{73} +(3.14835 + 3.88431i) q^{75} +(3.26691 - 2.37355i) q^{77} +(-0.246835 + 0.759681i) q^{79} +(0.309017 + 0.951057i) q^{81} +(0.732396 + 2.25408i) q^{83} +(-6.06812 - 5.75583i) q^{85} +(2.52602 + 1.83526i) q^{87} +(3.93348 - 2.85784i) q^{89} +(6.95307 + 5.05170i) q^{91} -9.56166 q^{93} +(2.74765 + 2.60624i) q^{95} +(-1.06966 + 3.29209i) q^{97} +2.32027 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 5 q^{5} + 8 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 - 5 * q^5 + 8 * q^7 - 2 * q^9	\( 8 q + 2 q^{3} - 5 q^{5} + 8 q^{7} - 2 q^{9} + 8 q^{11} + 5 q^{15} + 3 q^{17} + 5 q^{19} + 7 q^{21} - 7 q^{23} + 5 q^{25} + 2 q^{27} - 3 q^{29} - 3 q^{31} + 7 q^{33} - 10 q^{35} - q^{37} + 10 q^{41} - 12 q^{43} + 5 q^{45} - 33 q^{47} - 8 q^{49} - 8 q^{51} - 19 q^{53} - 15 q^{55} + 10 q^{57} - 38 q^{59} + 46 q^{61} + 3 q^{63} + 25 q^{65} - 8 q^{67} + 2 q^{69} - 25 q^{71} - 26 q^{73} - 5 q^{75} + 23 q^{77} - 16 q^{79} - 2 q^{81} + 8 q^{83} - 30 q^{85} + 3 q^{87} - 30 q^{89} + 25 q^{91} - 22 q^{93} - 25 q^{95} - 14 q^{97} - 2 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 - 5 * q^5 + 8 * q^7 - 2 * q^9 + 8 * q^11 + 5 * q^15 + 3 * q^17 + 5 * q^19 + 7 * q^21 - 7 * q^23 + 5 * q^25 + 2 * q^27 - 3 * q^29 - 3 * q^31 + 7 * q^33 - 10 * q^35 - q^37 + 10 * q^41 - 12 * q^43 + 5 * q^45 - 33 * q^47 - 8 * q^49 - 8 * q^51 - 19 * q^53 - 15 * q^55 + 10 * q^57 - 38 * q^59 + 46 * q^61 + 3 * q^63 + 25 * q^65 - 8 * q^67 + 2 * q^69 - 25 * q^71 - 26 * q^73 - 5 * q^75 + 23 * q^77 - 16 * q^79 - 2 * q^81 + 8 * q^83 - 30 * q^85 + 3 * q^87 - 30 * q^89 + 25 * q^91 - 22 * q^93 - 25 * q^95 - 14 * q^97 - 2 * q^99

Introduction

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