LMFDB - Embedded newform 630.2.m.a.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(197,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("630.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.m (of order $4$, degree $2$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	630.323
Dual form			630.2.m.a.197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.707107 + 2.12132i) q^{10} +0.585786i q^{11} +(4.00000 + 4.00000i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(0.585786 + 0.585786i) q^{17} -2.82843i q^{19} +(1.00000 - 2.00000i) q^{20} +(0.414214 - 0.414214i) q^{22} +(4.82843 - 4.82843i) q^{23} +(3.00000 + 4.00000i) q^{25} -5.65685i q^{26} +(-0.707107 - 0.707107i) q^{28} +0.828427 q^{29} +1.75736 q^{31} +(0.707107 + 0.707107i) q^{32} -0.828427i q^{34} +(2.12132 - 0.707107i) q^{35} +(6.24264 - 6.24264i) q^{37} +(-2.00000 + 2.00000i) q^{38} +(-2.12132 + 0.707107i) q^{40} -3.17157i q^{41} +(6.07107 + 6.07107i) q^{43} -0.585786 q^{44} -6.82843 q^{46} +(9.24264 + 9.24264i) q^{47} -1.00000i q^{49} +(0.707107 - 4.94975i) q^{50} +(-4.00000 + 4.00000i) q^{52} +(-2.58579 + 2.58579i) q^{53} +(0.585786 - 1.17157i) q^{55} +1.00000i q^{56} +(-0.585786 - 0.585786i) q^{58} +2.82843 q^{59} -9.89949 q^{61} +(-1.24264 - 1.24264i) q^{62} -1.00000i q^{64} +(-4.00000 - 12.0000i) q^{65} +(8.41421 - 8.41421i) q^{67} +(-0.585786 + 0.585786i) q^{68} +(-2.00000 - 1.00000i) q^{70} +1.17157i q^{71} +(7.07107 + 7.07107i) q^{73} -8.82843 q^{74} +2.82843 q^{76} +(-0.414214 - 0.414214i) q^{77} -5.65685i q^{79} +(2.00000 + 1.00000i) q^{80} +(-2.24264 + 2.24264i) q^{82} +(-0.828427 + 0.828427i) q^{83} +(-0.585786 - 1.75736i) q^{85} -8.58579i q^{86} +(0.414214 + 0.414214i) q^{88} +3.17157 q^{89} -5.65685 q^{91} +(4.82843 + 4.82843i) q^{92} -13.0711i q^{94} +(-2.82843 + 5.65685i) q^{95} +(-4.58579 + 4.58579i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{5}+O(q^{10}) $ 4 * q - 8 * q^5	$ 4 q - 8 q^{5} + 16 q^{13} + 4 q^{14} - 4 q^{16} + 8 q^{17} + 4 q^{20} - 4 q^{22} + 8 q^{23} + 12 q^{25} - 8 q^{29} + 24 q^{31} + 8 q^{37} - 8 q^{38} - 4 q^{43} - 8 q^{44} - 16 q^{46} + 20 q^{47} - 16 q^{52} - 16 q^{53} + 8 q^{55} - 8 q^{58} + 12 q^{62} - 16 q^{65} + 28 q^{67} - 8 q^{68} - 8 q^{70} - 24 q^{74} + 4 q^{77} + 8 q^{80} + 8 q^{82} + 8 q^{83} - 8 q^{85} - 4 q^{88} + 24 q^{89} + 8 q^{92} - 24 q^{97}+O(q^{100}) $ 4 * q - 8 * q^5 + 16 * q^13 + 4 * q^14 - 4 * q^16 + 8 * q^17 + 4 * q^20 - 4 * q^22 + 8 * q^23 + 12 * q^25 - 8 * q^29 + 24 * q^31 + 8 * q^37 - 8 * q^38 - 4 * q^43 - 8 * q^44 - 16 * q^46 + 20 * q^47 - 16 * q^52 - 16 * q^53 + 8 * q^55 - 8 * q^58 + 12 * q^62 - 16 * q^65 + 28 * q^67 - 8 * q^68 - 8 * q^70 - 24 * q^74 + 4 * q^77 + 8 * q^80 + 8 * q^82 + 8 * q^83 - 8 * q^85 - 4 * q^88 + 24 * q^89 + 8 * q^92 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	0.707107	+	2.12132i	0.223607	+	0.670820i
$11$			0.585786i			0.176621i	0.996093	+	0.0883106i	$0.0281468\pi$
$11$			0.585786i			0.176621i	−0.996093	+	0.0883106i	$0.971853\pi$
$12$		0			0
$13$	4.00000	+	4.00000i	1.10940	+	1.10940i	0.993229	+	0.116171i	$0.0370621\pi$
$13$	4.00000	+	4.00000i	1.10940	+	1.10940i	0.116171	+	0.993229i	$0.462938\pi$
$14$	1.00000			0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	0.585786	+	0.585786i	0.142074	+	0.142074i	0.774567	−	0.632492i	$-0.217968\pi$
$17$	0.585786	+	0.585786i	0.142074	+	0.142074i	−0.632492	+	0.774567i	$0.717968\pi$
$18$		0			0
$19$		−	2.82843i		−	0.648886i	−0.945905	−	0.324443i	$-0.894823\pi$
$19$		−	2.82843i		−	0.648886i	0.945905	−	0.324443i	$-0.105177\pi$
$20$	1.00000	−	2.00000i	0.223607	−	0.447214i
$21$		0			0
$22$	0.414214	−	0.414214i	0.0883106	−	0.0883106i
$23$	4.82843	−	4.82843i	1.00680	−	1.00680i	0.00681991	−	0.999977i	$-0.497829\pi$
$23$	4.82843	−	4.82843i	1.00680	−	1.00680i	0.999977	−	0.00681991i	$-0.00217086\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$		−	5.65685i		−	1.10940i
$27$		0			0
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$	0.828427			0.153835			0.0769175	−	0.997037i	$-0.475492\pi$
$29$	0.828427			0.153835			0.0769175	+	0.997037i	$0.475492\pi$
$30$		0			0
$31$	1.75736			0.315631			0.157816	−	0.987469i	$-0.449555\pi$
$31$	1.75736			0.315631			0.157816	+	0.987469i	$0.449555\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$		−	0.828427i		−	0.142074i
$35$	2.12132	−	0.707107i	0.358569	−	0.119523i
$36$		0			0
$37$	6.24264	−	6.24264i	1.02628	−	1.02628i	0.0266387	−	0.999645i	$-0.491520\pi$
$37$	6.24264	−	6.24264i	1.02628	−	1.02628i	0.999645	−	0.0266387i	$-0.00848036\pi$
$38$	−2.00000	+	2.00000i	−0.324443	+	0.324443i
$39$		0			0
$40$	−2.12132	+	0.707107i	−0.335410	+	0.111803i
$41$		−	3.17157i		−	0.495316i	−0.968847	−	0.247658i	$-0.920339\pi$
$41$		−	3.17157i		−	0.495316i	0.968847	−	0.247658i	$-0.0796610\pi$
$42$		0			0
$43$	6.07107	+	6.07107i	0.925829	+	0.925829i	0.997433	−	0.0716040i	$-0.0228118\pi$
$43$	6.07107	+	6.07107i	0.925829	+	0.925829i	−0.0716040	+	0.997433i	$0.522812\pi$
$44$	−0.585786			−0.0883106
$45$		0			0
$46$	−6.82843			−1.00680
$47$	9.24264	+	9.24264i	1.34818	+	1.34818i	0.887640	+	0.460537i	$0.152343\pi$
$47$	9.24264	+	9.24264i	1.34818	+	1.34818i	0.460537	+	0.887640i	$0.347657\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	0.707107	−	4.94975i	0.100000	−	0.700000i
$51$		0			0
$52$	−4.00000	+	4.00000i	−0.554700	+	0.554700i
$53$	−2.58579	+	2.58579i	−0.355185	+	0.355185i	−0.862035	−	0.506849i	$-0.830810\pi$
$53$	−2.58579	+	2.58579i	−0.355185	+	0.355185i	0.506849	+	0.862035i	$0.330810\pi$
$54$		0			0
$55$	0.585786	−	1.17157i	0.0789874	−	0.157975i
$56$			1.00000i			0.133631i
$57$		0			0
$58$	−0.585786	−	0.585786i	−0.0769175	−	0.0769175i
$59$	2.82843			0.368230			0.184115	−	0.982905i	$-0.441058\pi$
$59$	2.82843			0.368230			0.184115	+	0.982905i	$0.441058\pi$
$60$		0			0
$61$	−9.89949			−1.26750			−0.633750	−	0.773538i	$-0.718485\pi$
$61$	−9.89949			−1.26750			−0.633750	+	0.773538i	$0.718485\pi$
$62$	−1.24264	−	1.24264i	−0.157816	−	0.157816i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−4.00000	−	12.0000i	−0.496139	−	1.48842i
$66$		0			0
$67$	8.41421	−	8.41421i	1.02796	−	1.02796i	0.0283621	−	0.999598i	$-0.490971\pi$
$67$	8.41421	−	8.41421i	1.02796	−	1.02796i	0.999598	−	0.0283621i	$-0.00902914\pi$
$68$	−0.585786	+	0.585786i	−0.0710370	+	0.0710370i
$69$		0			0
$70$	−2.00000	−	1.00000i	−0.239046	−	0.119523i
$71$			1.17157i			0.139040i	0.997581	+	0.0695201i	$0.0221468\pi$
$71$			1.17157i			0.139040i	−0.997581	+	0.0695201i	$0.977853\pi$
$72$		0			0
$73$	7.07107	+	7.07107i	0.827606	+	0.827606i	0.987185	−	0.159579i	$-0.0510137\pi$
$73$	7.07107	+	7.07107i	0.827606	+	0.827606i	−0.159579	+	0.987185i	$0.551014\pi$
$74$	−8.82843			−1.02628
$75$		0			0
$76$	2.82843			0.324443
$77$	−0.414214	−	0.414214i	−0.0472040	−	0.0472040i
$78$		0			0
$79$		−	5.65685i		−	0.636446i	−0.948016	−	0.318223i	$-0.896914\pi$
$79$		−	5.65685i		−	0.636446i	0.948016	−	0.318223i	$-0.103086\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$		0			0
$82$	−2.24264	+	2.24264i	−0.247658	+	0.247658i
$83$	−0.828427	+	0.828427i	−0.0909317	+	0.0909317i	−0.751109	−	0.660178i	$-0.770481\pi$
$83$	−0.828427	+	0.828427i	−0.0909317	+	0.0909317i	0.660178	+	0.751109i	$0.270481\pi$
$84$		0			0
$85$	−0.585786	−	1.75736i	−0.0635375	−	0.190612i
$86$		−	8.58579i		−	0.925829i
$87$		0			0
$88$	0.414214	+	0.414214i	0.0441553	+	0.0441553i
$89$	3.17157			0.336186			0.168093	−	0.985771i	$-0.446239\pi$
$89$	3.17157			0.336186			0.168093	+	0.985771i	$0.446239\pi$
$90$		0			0
$91$	−5.65685			−0.592999
$92$	4.82843	+	4.82843i	0.503398	+	0.503398i
$93$		0			0
$94$		−	13.0711i		−	1.34818i
$95$	−2.82843	+	5.65685i	−0.290191	+	0.580381i
$96$		0			0
$97$	−4.58579	+	4.58579i	−0.465616	+	0.465616i	−0.900491	−	0.434875i	$-0.856793\pi$
$97$	−4.58579	+	4.58579i	−0.465616	+	0.465616i	0.434875	+	0.900491i	$0.356793\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$		0			0
$100$	−4.00000	+	3.00000i	−0.400000	+	0.300000i
$101$			17.6569i			1.75692i	0.477813	+	0.878461i	$0.341429\pi$
$101$			17.6569i			1.75692i	−0.477813	+	0.878461i	$0.658571\pi$
$102$		0			0
$103$	−7.41421	−	7.41421i	−0.730544	−	0.730544i	0.240183	−	0.970728i	$-0.422792\pi$
$103$	−7.41421	−	7.41421i	−0.730544	−	0.730544i	−0.970728	+	0.240183i	$0.922792\pi$
$104$	5.65685			0.554700
$105$		0			0
$106$	3.65685			0.355185
$107$	−5.17157	−	5.17157i	−0.499955	−	0.499955i	0.411469	−	0.911424i	$-0.365016\pi$
$107$	−5.17157	−	5.17157i	−0.499955	−	0.499955i	−0.911424	+	0.411469i	$0.865016\pi$
$108$		0			0
$109$		−	9.31371i		−	0.892091i	−0.895010	−	0.446046i	$-0.852832\pi$
$109$		−	9.31371i		−	0.892091i	0.895010	−	0.446046i	$-0.147168\pi$
$110$	−1.24264	+	0.414214i	−0.118481	+	0.0394937i
$111$		0			0
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$	−11.3137	+	11.3137i	−1.06430	+	1.06430i	−0.0665190	+	0.997785i	$0.521189\pi$
$113$	−11.3137	+	11.3137i	−1.06430	+	1.06430i	−0.997785	+	0.0665190i	$0.978811\pi$
$114$		0			0
$115$	−14.4853	+	4.82843i	−1.35076	+	0.450253i
$116$			0.828427i			0.0769175i
$117$		0			0
$118$	−2.00000	−	2.00000i	−0.184115	−	0.184115i
$119$	−0.828427			−0.0759418
$120$		0			0
$121$	10.6569			0.968805
$122$	7.00000	+	7.00000i	0.633750	+	0.633750i
$123$		0			0
$124$			1.75736i			0.157816i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$	7.65685	−	7.65685i	0.679436	−	0.679436i	−0.280437	−	0.959873i	$-0.590479\pi$
$127$	7.65685	−	7.65685i	0.679436	−	0.679436i	0.959873	+	0.280437i	$0.0904792\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−5.65685	+	11.3137i	−0.496139	+	0.992278i
$131$			16.4853i			1.44033i	0.693805	+	0.720163i	$0.255933\pi$
$131$			16.4853i			1.44033i	−0.693805	+	0.720163i	$0.744067\pi$
$132$		0			0
$133$	2.00000	+	2.00000i	0.173422	+	0.173422i
$134$	−11.8995			−1.02796
$135$		0			0
$136$	0.828427			0.0710370
$137$	12.0000	+	12.0000i	1.02523	+	1.02523i	0.999673	+	0.0255558i	$0.00813555\pi$
$137$	12.0000	+	12.0000i	1.02523	+	1.02523i	0.0255558	+	0.999673i	$0.491864\pi$
$138$		0			0
$139$		−	17.6569i		−	1.49763i	−0.662776	−	0.748817i	$-0.730622\pi$
$139$		−	17.6569i		−	1.49763i	0.662776	−	0.748817i	$-0.269378\pi$
$140$	0.707107	+	2.12132i	0.0597614	+	0.179284i
$141$		0			0
$142$	0.828427	−	0.828427i	0.0695201	−	0.0695201i
$143$	−2.34315	+	2.34315i	−0.195944	+	0.195944i
$144$		0			0
$145$	−1.65685	−	0.828427i	−0.137594	−	0.0687971i
$146$		−	10.0000i		−	0.827606i
$147$		0			0
$148$	6.24264	+	6.24264i	0.513142	+	0.513142i
$149$	−8.14214			−0.667030			−0.333515	−	0.942745i	$-0.608235\pi$
$149$	−8.14214			−0.667030			−0.333515	+	0.942745i	$0.608235\pi$
$150$		0			0
$151$	−18.8284			−1.53224			−0.766118	−	0.642700i	$-0.777814\pi$
$151$	−18.8284			−1.53224			−0.766118	+	0.642700i	$0.777814\pi$
$152$	−2.00000	−	2.00000i	−0.162221	−	0.162221i
$153$		0			0
$154$			0.585786i			0.0472040i
$155$	−3.51472	−	1.75736i	−0.282309	−	0.141154i
$156$		0			0
$157$	−9.65685	+	9.65685i	−0.770701	+	0.770701i	−0.978229	−	0.207528i	$-0.933458\pi$
$157$	−9.65685	+	9.65685i	−0.770701	+	0.770701i	0.207528	+	0.978229i	$0.433458\pi$
$158$	−4.00000	+	4.00000i	−0.318223	+	0.318223i
$159$		0			0
$160$	−0.707107	−	2.12132i	−0.0559017	−	0.167705i
$161$			6.82843i			0.538155i
$162$		0			0
$163$	11.7279	+	11.7279i	0.918602	+	0.918602i	0.996928	−	0.0783260i	$-0.0249575\pi$
$163$	11.7279	+	11.7279i	0.918602	+	0.918602i	−0.0783260	+	0.996928i	$0.524958\pi$
$164$	3.17157			0.247658
$165$		0			0
$166$	1.17157			0.0909317
$167$	−7.58579	−	7.58579i	−0.587006	−	0.587006i	0.349814	−	0.936819i	$-0.386245\pi$
$167$	−7.58579	−	7.58579i	−0.587006	−	0.587006i	−0.936819	+	0.349814i	$0.886245\pi$
$168$		0			0
$169$			19.0000i			1.46154i
$170$	−0.828427	+	1.65685i	−0.0635375	+	0.127075i
$171$		0			0
$172$	−6.07107	+	6.07107i	−0.462915	+	0.462915i
$173$	−11.4853	+	11.4853i	−0.873210	+	0.873210i	−0.992821	−	0.119611i	$-0.961835\pi$
$173$	−11.4853	+	11.4853i	−0.873210	+	0.873210i	0.119611	+	0.992821i	$0.461835\pi$
$174$		0			0
$175$	−4.94975	−	0.707107i	−0.374166	−	0.0534522i
$176$		−	0.585786i		−	0.0441553i
$177$		0			0
$178$	−2.24264	−	2.24264i	−0.168093	−	0.168093i
$179$	16.5858			1.23968			0.619840	−	0.784728i	$-0.287198\pi$
$179$	16.5858			1.23968			0.619840	+	0.784728i	$0.287198\pi$
$180$		0			0
$181$	−19.0711			−1.41754			−0.708771	−	0.705439i	$-0.750750\pi$
$181$	−19.0711			−1.41754			−0.708771	+	0.705439i	$0.750750\pi$
$182$	4.00000	+	4.00000i	0.296500	+	0.296500i
$183$		0			0
$184$		−	6.82843i		−	0.503398i
$185$	−18.7279	+	6.24264i	−1.37690	+	0.458968i
$186$		0			0
$187$	−0.343146	+	0.343146i	−0.0250933	+	0.0250933i
$188$	−9.24264	+	9.24264i	−0.674089	+	0.674089i
$189$		0			0
$190$	6.00000	−	2.00000i	0.435286	−	0.145095i
$191$		−	14.3431i		−	1.03783i	−0.854825	−	0.518917i	$-0.826335\pi$
$191$		−	14.3431i		−	1.03783i	0.854825	−	0.518917i	$-0.173665\pi$
$192$		0			0
$193$	13.4853	+	13.4853i	0.970692	+	0.970692i	0.999583	−	0.0288908i	$-0.00919750\pi$
$193$	13.4853	+	13.4853i	0.970692	+	0.970692i	−0.0288908	+	0.999583i	$0.509198\pi$
$194$	6.48528			0.465616
$195$		0			0
$196$	1.00000			0.0714286
$197$	−10.2426	−	10.2426i	−0.729758	−	0.729758i	0.240813	−	0.970571i	$-0.422586\pi$
$197$	−10.2426	−	10.2426i	−0.729758	−	0.729758i	−0.970571	+	0.240813i	$0.922586\pi$
$198$		0			0
$199$		−	4.10051i		−	0.290677i	−0.989382	−	0.145339i	$-0.953573\pi$
$199$		−	4.10051i		−	0.290677i	0.989382	−	0.145339i	$-0.0464271\pi$
$200$	4.94975	+	0.707107i	0.350000	+	0.0500000i
$201$		0			0
$202$	12.4853	−	12.4853i	0.878461	−	0.878461i
$203$	−0.585786	+	0.585786i	−0.0411141	+	0.0411141i
$204$		0			0
$205$	−3.17157	+	6.34315i	−0.221512	+	0.443025i
$206$			10.4853i			0.730544i
$207$		0			0
$208$	−4.00000	−	4.00000i	−0.277350	−	0.277350i
$209$	1.65685			0.114607
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	−2.58579	−	2.58579i	−0.177593	−	0.177593i
$213$		0			0
$214$			7.31371i			0.499955i
$215$	−6.07107	−	18.2132i	−0.414043	−	1.24213i
$216$		0			0
$217$	−1.24264	+	1.24264i	−0.0843559	+	0.0843559i
$218$	−6.58579	+	6.58579i	−0.446046	+	0.446046i
$219$		0			0
$220$	1.17157	+	0.585786i	0.0789874	+	0.0394937i
$221$			4.68629i			0.315234i
$222$		0			0
$223$	7.31371	+	7.31371i	0.489762	+	0.489762i	0.908231	−	0.418469i	$-0.137433\pi$
$223$	7.31371	+	7.31371i	0.489762	+	0.489762i	−0.418469	+	0.908231i	$0.637433\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	16.0000			1.06430
$227$	1.17157	+	1.17157i	0.0777600	+	0.0777600i	0.744917	−	0.667157i	$-0.232489\pi$
$227$	1.17157	+	1.17157i	0.0777600	+	0.0777600i	−0.667157	+	0.744917i	$0.732489\pi$
$228$		0			0
$229$			8.24264i			0.544689i	0.962200	+	0.272345i	$0.0877990\pi$
$229$			8.24264i			0.544689i	−0.962200	+	0.272345i	$0.912201\pi$
$230$	13.6569	+	6.82843i	0.900506	+	0.450253i
$231$		0			0
$232$	0.585786	−	0.585786i	0.0384588	−	0.0384588i
$233$	14.8284	−	14.8284i	0.971443	−	0.971443i	−0.0281608	−	0.999603i	$-0.508965\pi$
$233$	14.8284	−	14.8284i	0.971443	−	0.971443i	0.999603	+	0.0281608i	$0.00896506\pi$
$234$		0			0
$235$	−9.24264	−	27.7279i	−0.602923	−	1.80877i
$236$			2.82843i			0.184115i
$237$		0			0
$238$	0.585786	+	0.585786i	0.0379709	+	0.0379709i
$239$	13.6569			0.883388			0.441694	−	0.897166i	$-0.354378\pi$
$239$	13.6569			0.883388			0.441694	+	0.897166i	$0.354378\pi$
$240$		0			0
$241$	−4.14214			−0.266818			−0.133409	−	0.991061i	$-0.542592\pi$
$241$	−4.14214			−0.266818			−0.133409	+	0.991061i	$0.542592\pi$
$242$	−7.53553	−	7.53553i	−0.484402	−	0.484402i
$243$		0			0
$244$		−	9.89949i		−	0.633750i
$245$	−1.00000	+	2.00000i	−0.0638877	+	0.127775i
$246$		0			0
$247$	11.3137	−	11.3137i	0.719874	−	0.719874i
$248$	1.24264	−	1.24264i	0.0789078	−	0.0789078i
$249$		0			0
$250$	−6.36396	+	9.19239i	−0.402492	+	0.581378i
$251$		−	26.6274i		−	1.68071i	−0.542038	−	0.840354i	$-0.682347\pi$
$251$		−	26.6274i		−	1.68071i	0.542038	−	0.840354i	$-0.317653\pi$
$252$		0			0
$253$	2.82843	+	2.82843i	0.177822	+	0.177822i
$254$	−10.8284			−0.679436
$255$		0			0
$256$	1.00000			0.0625000
$257$	8.58579	+	8.58579i	0.535567	+	0.535567i	0.922224	−	0.386657i	$-0.126370\pi$
$257$	8.58579	+	8.58579i	0.535567	+	0.535567i	−0.386657	+	0.922224i	$0.626370\pi$
$258$		0			0
$259$			8.82843i			0.548572i
$260$	12.0000	−	4.00000i	0.744208	−	0.248069i
$261$		0			0
$262$	11.6569	−	11.6569i	0.720163	−	0.720163i
$263$	7.65685	−	7.65685i	0.472142	−	0.472142i	−0.430465	−	0.902607i	$-0.641651\pi$
$263$	7.65685	−	7.65685i	0.472142	−	0.472142i	0.902607	+	0.430465i	$0.141651\pi$
$264$		0			0
$265$	7.75736	−	2.58579i	0.476531	−	0.158844i
$266$		−	2.82843i		−	0.173422i
$267$		0			0
$268$	8.41421	+	8.41421i	0.513980	+	0.513980i
$269$	5.65685			0.344904			0.172452	−	0.985018i	$-0.444831\pi$
$269$	5.65685			0.344904			0.172452	+	0.985018i	$0.444831\pi$
$270$		0			0
$271$	4.10051			0.249088			0.124544	−	0.992214i	$-0.460253\pi$
$271$	4.10051			0.249088			0.124544	+	0.992214i	$0.460253\pi$
$272$	−0.585786	−	0.585786i	−0.0355185	−	0.0355185i
$273$		0			0
$274$		−	16.9706i		−	1.02523i
$275$	−2.34315	+	1.75736i	−0.141297	+	0.105973i
$276$		0			0
$277$	−2.10051	+	2.10051i	−0.126207	+	0.126207i	−0.767389	−	0.641182i	$-0.778444\pi$
$277$	−2.10051	+	2.10051i	−0.126207	+	0.126207i	0.641182	+	0.767389i	$0.278444\pi$
$278$	−12.4853	+	12.4853i	−0.748817	+	0.748817i
$279$		0			0
$280$	1.00000	−	2.00000i	0.0597614	−	0.119523i
$281$		−	19.0711i		−	1.13768i	−0.822447	−	0.568842i	$-0.807391\pi$
$281$		−	19.0711i		−	1.13768i	0.822447	−	0.568842i	$-0.192609\pi$
$282$		0			0
$283$	−21.3137	−	21.3137i	−1.26697	−	1.26697i	−0.947646	−	0.319322i	$-0.896545\pi$
$283$	−21.3137	−	21.3137i	−1.26697	−	1.26697i	−0.319322	−	0.947646i	$-0.603455\pi$
$284$	−1.17157			−0.0695201
$285$		0			0
$286$	3.31371			0.195944
$287$	2.24264	+	2.24264i	0.132379	+	0.132379i
$288$		0			0
$289$		−	16.3137i		−	0.959630i
$290$	0.585786	+	1.75736i	0.0343986	+	0.103196i
$291$		0			0
$292$	−7.07107	+	7.07107i	−0.413803	+	0.413803i
$293$	8.65685	−	8.65685i	0.505739	−	0.505739i	−0.407477	−	0.913216i	$-0.633591\pi$
$293$	8.65685	−	8.65685i	0.505739	−	0.505739i	0.913216	+	0.407477i	$0.133591\pi$
$294$		0			0
$295$	−5.65685	−	2.82843i	−0.329355	−	0.164677i
$296$		−	8.82843i		−	0.513142i
$297$		0			0
$298$	5.75736	+	5.75736i	0.333515	+	0.333515i
$299$	38.6274			2.23388
$300$		0			0
$301$	−8.58579			−0.494877
$302$	13.3137	+	13.3137i	0.766118	+	0.766118i
$303$		0			0
$304$			2.82843i			0.162221i
$305$	19.7990	+	9.89949i	1.13369	+	0.566843i
$306$		0			0
$307$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$307$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$308$	0.414214	−	0.414214i	0.0236020	−	0.0236020i
$309$		0			0
$310$	1.24264	+	3.72792i	0.0705772	+	0.211732i
$311$		−	4.82843i		−	0.273795i	−0.990585	−	0.136897i	$-0.956287\pi$
$311$		−	4.82843i		−	0.273795i	0.990585	−	0.136897i	$-0.0437131\pi$
$312$		0			0
$313$	2.24264	+	2.24264i	0.126762	+	0.126762i	0.767641	−	0.640880i	$-0.221430\pi$
$313$	2.24264	+	2.24264i	0.126762	+	0.126762i	−0.640880	+	0.767641i	$0.721430\pi$
$314$	13.6569			0.770701
$315$		0			0
$316$	5.65685			0.318223
$317$	−24.7279	−	24.7279i	−1.38886	−	1.38886i	−0.827726	−	0.561132i	$-0.810366\pi$
$317$	−24.7279	−	24.7279i	−1.38886	−	1.38886i	−0.561132	−	0.827726i	$-0.689634\pi$
$318$		0			0
$319$			0.485281i			0.0271705i
$320$	−1.00000	+	2.00000i	−0.0559017	+	0.111803i
$321$		0			0
$322$	4.82843	−	4.82843i	0.269078	−	0.269078i
$323$	1.65685	−	1.65685i	0.0921898	−	0.0921898i
$324$		0			0
$325$	−4.00000	+	28.0000i	−0.221880	+	1.55316i
$326$		−	16.5858i		−	0.918602i
$327$		0			0
$328$	−2.24264	−	2.24264i	−0.123829	−	0.123829i
$329$	−13.0711			−0.720631
$330$		0			0
$331$	18.6274			1.02386			0.511928	−	0.859029i	$-0.328932\pi$
$331$	18.6274			1.02386			0.511928	+	0.859029i	$0.328932\pi$
$332$	−0.828427	−	0.828427i	−0.0454658	−	0.0454658i
$333$		0			0
$334$			10.7279i			0.587006i
$335$	−25.2426	+	8.41421i	−1.37915	+	0.459718i
$336$		0			0
$337$	10.1716	−	10.1716i	0.554081	−	0.554081i	−0.373535	−	0.927616i	$-0.621854\pi$
$337$	10.1716	−	10.1716i	0.554081	−	0.554081i	0.927616	+	0.373535i	$0.121854\pi$
$338$	13.4350	−	13.4350i	0.730769	−	0.730769i
$339$		0			0
$340$	1.75736	−	0.585786i	0.0953062	−	0.0317687i
$341$			1.02944i			0.0557472i
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	8.58579			0.462915
$345$		0			0
$346$	16.2426			0.873210
$347$	−8.48528	−	8.48528i	−0.455514	−	0.455514i	0.441666	−	0.897180i	$-0.354388\pi$
$347$	−8.48528	−	8.48528i	−0.455514	−	0.455514i	−0.897180	+	0.441666i	$0.854388\pi$
$348$		0			0
$349$			32.7279i			1.75189i	0.482415	+	0.875943i	$0.339760\pi$
$349$			32.7279i			1.75189i	−0.482415	+	0.875943i	$0.660240\pi$
$350$	3.00000	+	4.00000i	0.160357	+	0.213809i
$351$		0			0
$352$	−0.414214	+	0.414214i	−0.0220777	+	0.0220777i
$353$	18.3848	−	18.3848i	0.978523	−	0.978523i	−0.0212513	−	0.999774i	$-0.506765\pi$
$353$	18.3848	−	18.3848i	0.978523	−	0.978523i	0.999774	+	0.0212513i	$0.00676499\pi$
$354$		0			0
$355$	1.17157	−	2.34315i	0.0621806	−	0.124361i
$356$			3.17157i			0.168093i
$357$		0			0
$358$	−11.7279	−	11.7279i	−0.619840	−	0.619840i
$359$	23.7990			1.25606			0.628031	−	0.778188i	$-0.283861\pi$
$359$	23.7990			1.25606			0.628031	+	0.778188i	$0.283861\pi$
$360$		0			0
$361$	11.0000			0.578947
$362$	13.4853	+	13.4853i	0.708771	+	0.708771i
$363$		0			0
$364$		−	5.65685i		−	0.296500i
$365$	−7.07107	−	21.2132i	−0.370117	−	1.11035i
$366$		0			0
$367$	−10.2426	+	10.2426i	−0.534661	+	0.534661i	−0.921956	−	0.387295i	$-0.873410\pi$
$367$	−10.2426	+	10.2426i	−0.534661	+	0.534661i	0.387295	+	0.921956i	$0.373410\pi$
$368$	−4.82843	+	4.82843i	−0.251699	+	0.251699i
$369$		0			0
$370$	17.6569	+	8.82843i	0.917936	+	0.458968i
$371$		−	3.65685i		−	0.189854i
$372$		0			0
$373$	−11.0711	−	11.0711i	−0.573238	−	0.573238i	0.359794	−	0.933032i	$-0.382847\pi$
$373$	−11.0711	−	11.0711i	−0.573238	−	0.573238i	−0.933032	+	0.359794i	$0.882847\pi$
$374$	0.485281			0.0250933
$375$		0			0
$376$	13.0711			0.674089
$377$	3.31371	+	3.31371i	0.170665	+	0.170665i
$378$		0			0
$379$			25.7990i			1.32521i	0.748971	+	0.662603i	$0.230548\pi$
$379$			25.7990i			1.32521i	−0.748971	+	0.662603i	$0.769452\pi$
$380$	−5.65685	−	2.82843i	−0.290191	−	0.145095i
$381$		0			0
$382$	−10.1421	+	10.1421i	−0.518917	+	0.518917i
$383$	4.41421	−	4.41421i	0.225556	−	0.225556i	−0.585277	−	0.810833i	$-0.699014\pi$
$383$	4.41421	−	4.41421i	0.225556	−	0.225556i	0.810833	+	0.585277i	$0.199014\pi$
$384$		0			0
$385$	0.414214	+	1.24264i	0.0211103	+	0.0633308i
$386$		−	19.0711i		−	0.970692i
$387$		0			0
$388$	−4.58579	−	4.58579i	−0.232808	−	0.232808i
$389$	−9.79899			−0.496829			−0.248414	−	0.968654i	$-0.579909\pi$
$389$	−9.79899			−0.496829			−0.248414	+	0.968654i	$0.579909\pi$
$390$		0			0
$391$	5.65685			0.286079
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$		0			0
$394$			14.4853i			0.729758i
$395$	−5.65685	+	11.3137i	−0.284627	+	0.569254i
$396$		0			0
$397$	−0.928932	+	0.928932i	−0.0466218	+	0.0466218i	−0.730033	−	0.683412i	$-0.760495\pi$
$397$	−0.928932	+	0.928932i	−0.0466218	+	0.0466218i	0.683412	+	0.730033i	$0.260495\pi$
$398$	−2.89949	+	2.89949i	−0.145339	+	0.145339i
$399$		0			0
$400$	−3.00000	−	4.00000i	−0.150000	−	0.200000i
$401$			26.8701i			1.34183i	0.741536	+	0.670913i	$0.234098\pi$
$401$			26.8701i			1.34183i	−0.741536	+	0.670913i	$0.765902\pi$
$402$		0			0
$403$	7.02944	+	7.02944i	0.350161	+	0.350161i
$404$	−17.6569			−0.878461
$405$		0			0
$406$	0.828427			0.0411141
$407$	3.65685	+	3.65685i	0.181264	+	0.181264i
$408$		0			0
$409$		−	10.0000i		−	0.494468i	−0.968956	−	0.247234i	$-0.920478\pi$
$409$		−	10.0000i		−	0.494468i	0.968956	−	0.247234i	$-0.0795217\pi$
$410$	6.72792	−	2.24264i	0.332268	−	0.110756i
$411$		0			0
$412$	7.41421	−	7.41421i	0.365272	−	0.365272i
$413$	−2.00000	+	2.00000i	−0.0984136	+	0.0984136i
$414$		0			0
$415$	2.48528	−	0.828427i	0.121998	−	0.0406659i
$416$			5.65685i			0.277350i
$417$		0			0
$418$	−1.17157	−	1.17157i	−0.0573035	−	0.0573035i
$419$	−18.6274			−0.910009			−0.455004	−	0.890489i	$-0.650362\pi$
$419$	−18.6274			−0.910009			−0.455004	+	0.890489i	$0.650362\pi$
$420$		0			0
$421$	−40.6274			−1.98006			−0.990030	−	0.140860i	$-0.955013\pi$
$421$	−40.6274			−1.98006			−0.990030	+	0.140860i	$0.955013\pi$
$422$	2.82843	+	2.82843i	0.137686	+	0.137686i
$423$		0			0
$424$			3.65685i			0.177593i
$425$	−0.585786	+	4.10051i	−0.0284148	+	0.198904i
$426$		0			0
$427$	7.00000	−	7.00000i	0.338754	−	0.338754i
$428$	5.17157	−	5.17157i	0.249977	−	0.249977i
$429$		0			0
$430$	−8.58579	+	17.1716i	−0.414043	+	0.828087i
$431$			26.1421i			1.25922i	0.776910	+	0.629611i	$0.216786\pi$
$431$			26.1421i			1.25922i	−0.776910	+	0.629611i	$0.783214\pi$
$432$		0			0
$433$	18.2426	+	18.2426i	0.876685	+	0.876685i	0.993190	−	0.116505i	$-0.0371690\pi$
$433$	18.2426	+	18.2426i	0.876685	+	0.876685i	−0.116505	+	0.993190i	$0.537169\pi$
$434$	1.75736			0.0843559
$435$		0			0
$436$	9.31371			0.446046
$437$	−13.6569	−	13.6569i	−0.653296	−	0.653296i
$438$		0			0
$439$		−	3.89949i		−	0.186113i	−0.995661	−	0.0930564i	$-0.970336\pi$
$439$		−	3.89949i		−	0.186113i	0.995661	−	0.0930564i	$-0.0296637\pi$
$440$	−0.414214	−	1.24264i	−0.0197469	−	0.0592406i
$441$		0			0
$442$	3.31371	−	3.31371i	0.157617	−	0.157617i
$443$	−3.51472	+	3.51472i	−0.166989	+	0.166989i	−0.785655	−	0.618665i	$-0.787674\pi$
$443$	−3.51472	+	3.51472i	−0.166989	+	0.166989i	0.618665	+	0.785655i	$0.287674\pi$
$444$		0			0
$445$	−6.34315	−	3.17157i	−0.300694	−	0.150347i
$446$		−	10.3431i		−	0.489762i
$447$		0			0
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$	−16.7279			−0.789439			−0.394720	−	0.918802i	$-0.629158\pi$
$449$	−16.7279			−0.789439			−0.394720	+	0.918802i	$0.629158\pi$
$450$		0			0
$451$	1.85786			0.0874834
$452$	−11.3137	−	11.3137i	−0.532152	−	0.532152i
$453$		0			0
$454$		−	1.65685i		−	0.0777600i
$455$	11.3137	+	5.65685i	0.530395	+	0.265197i
$456$		0			0
$457$	2.17157	−	2.17157i	0.101582	−	0.101582i	−0.654489	−	0.756071i	$-0.727116\pi$
$457$	2.17157	−	2.17157i	0.101582	−	0.101582i	0.756071	+	0.654489i	$0.227116\pi$
$458$	5.82843	−	5.82843i	0.272345	−	0.272345i
$459$		0			0
$460$	−4.82843	−	14.4853i	−0.225127	−	0.675380i
$461$		−	5.31371i		−	0.247484i	−0.992314	−	0.123742i	$-0.960510\pi$
$461$		−	5.31371i		−	0.247484i	0.992314	−	0.123742i	$-0.0394895\pi$
$462$		0			0
$463$	−19.7990	−	19.7990i	−0.920137	−	0.920137i	0.0769016	−	0.997039i	$-0.475497\pi$
$463$	−19.7990	−	19.7990i	−0.920137	−	0.920137i	−0.997039	+	0.0769016i	$0.975497\pi$
$464$	−0.828427			−0.0384588
$465$		0			0
$466$	−20.9706			−0.971443
$467$	−14.0000	−	14.0000i	−0.647843	−	0.647843i	0.304629	−	0.952471i	$-0.401468\pi$
$467$	−14.0000	−	14.0000i	−0.647843	−	0.647843i	−0.952471	+	0.304629i	$0.901468\pi$
$468$		0			0
$469$			11.8995i			0.549468i
$470$	−13.0711	+	26.1421i	−0.602923	+	1.20585i
$471$		0			0
$472$	2.00000	−	2.00000i	0.0920575	−	0.0920575i
$473$	−3.55635	+	3.55635i	−0.163521	+	0.163521i
$474$		0			0
$475$	11.3137	−	8.48528i	0.519109	−	0.389331i
$476$		−	0.828427i		−	0.0379709i
$477$		0			0
$478$	−9.65685	−	9.65685i	−0.441694	−	0.441694i
$479$	19.1716			0.875972			0.437986	−	0.898982i	$-0.355692\pi$
$479$	19.1716			0.875972			0.437986	+	0.898982i	$0.355692\pi$
$480$		0			0
$481$	49.9411			2.27712
$482$	2.92893	+	2.92893i	0.133409	+	0.133409i
$483$		0			0
$484$			10.6569i			0.484402i
$485$	13.7574	−	4.58579i	0.624690	−	0.208230i
$486$		0			0
$487$	18.9706	−	18.9706i	0.859638	−	0.859638i	−0.131657	−	0.991295i	$-0.542030\pi$
$487$	18.9706	−	18.9706i	0.859638	−	0.859638i	0.991295	+	0.131657i	$0.0420298\pi$
$488$	−7.00000	+	7.00000i	−0.316875	+	0.316875i
$489$		0			0
$490$	2.12132	−	0.707107i	0.0958315	−	0.0319438i
$491$		−	26.7279i		−	1.20621i	−0.797660	−	0.603107i	$-0.793929\pi$
$491$		−	26.7279i		−	1.20621i	0.797660	−	0.603107i	$-0.206071\pi$
$492$		0			0
$493$	0.485281	+	0.485281i	0.0218560	+	0.0218560i
$494$	−16.0000			−0.719874
$495$		0			0
$496$	−1.75736			−0.0789078
$497$	−0.828427	−	0.828427i	−0.0371600	−	0.0371600i
$498$		0			0
$499$			23.4558i			1.05003i	0.851094	+	0.525014i	$0.175940\pi$
$499$			23.4558i			1.05003i	−0.851094	+	0.525014i	$0.824060\pi$
$500$	11.0000	−	2.00000i	0.491935	−	0.0894427i
$501$		0			0
$502$	−18.8284	+	18.8284i	−0.840354	+	0.840354i
$503$	−16.5563	+	16.5563i	−0.738211	+	0.738211i	−0.972232	−	0.234021i	$-0.924812\pi$
$503$	−16.5563	+	16.5563i	−0.738211	+	0.738211i	0.234021	+	0.972232i	$0.424812\pi$
$504$		0			0
$505$	17.6569	−	35.3137i	0.785720	−	1.57144i
$506$		−	4.00000i		−	0.177822i
$507$		0			0
$508$	7.65685	+	7.65685i	0.339718	+	0.339718i
$509$	−18.3431			−0.813046			−0.406523	−	0.913641i	$-0.633259\pi$
$509$	−18.3431			−0.813046			−0.406523	+	0.913641i	$0.633259\pi$
$510$		0			0
$511$	−10.0000			−0.442374
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	12.1421i		−	0.535567i
$515$	7.41421	+	22.2426i	0.326709	+	0.980128i
$516$		0			0
$517$	−5.41421	+	5.41421i	−0.238117	+	0.238117i
$518$	6.24264	−	6.24264i	0.274286	−	0.274286i
$519$		0			0
$520$	−11.3137	−	5.65685i	−0.496139	−	0.248069i
$521$			42.7696i			1.87377i	0.349640	+	0.936884i	$0.386304\pi$
$521$			42.7696i			1.87377i	−0.349640	+	0.936884i	$0.613696\pi$
$522$		0			0
$523$	−25.3137	−	25.3137i	−1.10689	−	1.10689i	−0.993557	−	0.113334i	$-0.963847\pi$
$523$	−25.3137	−	25.3137i	−1.10689	−	1.10689i	−0.113334	−	0.993557i	$-0.536153\pi$
$524$	−16.4853			−0.720163
$525$		0			0
$526$	−10.8284			−0.472142
$527$	1.02944	+	1.02944i	0.0448430	+	0.0448430i
$528$		0			0
$529$		−	23.6274i		−	1.02728i
$530$	−7.31371	−	3.65685i	−0.317687	−	0.158844i
$531$		0			0
$532$	−2.00000	+	2.00000i	−0.0867110	+	0.0867110i
$533$	12.6863	−	12.6863i	0.549504	−	0.549504i
$534$		0			0
$535$	5.17157	+	15.5147i	0.223587	+	0.670760i
$536$		−	11.8995i		−	0.513980i
$537$		0			0
$538$	−4.00000	−	4.00000i	−0.172452	−	0.172452i
$539$	0.585786			0.0252316
$540$		0			0
$541$	−29.1127			−1.25165			−0.625826	−	0.779962i	$-0.715238\pi$
$541$	−29.1127			−1.25165			−0.625826	+	0.779962i	$0.715238\pi$
$542$	−2.89949	−	2.89949i	−0.124544	−	0.124544i
$543$		0			0
$544$			0.828427i			0.0355185i
$545$	−9.31371	+	18.6274i	−0.398955	+	0.797911i
$546$		0			0
$547$	−12.5563	+	12.5563i	−0.536871	+	0.536871i	−0.922608	−	0.385738i	$-0.873947\pi$
$547$	−12.5563	+	12.5563i	−0.536871	+	0.536871i	0.385738	+	0.922608i	$0.373947\pi$
$548$	−12.0000	+	12.0000i	−0.512615	+	0.512615i
$549$		0			0
$550$	2.89949	+	0.414214i	0.123635	+	0.0176621i
$551$		−	2.34315i		−	0.0998214i
$552$		0			0
$553$	4.00000	+	4.00000i	0.170097	+	0.170097i
$554$	2.97056			0.126207
$555$		0			0
$556$	17.6569			0.748817
$557$	7.55635	+	7.55635i	0.320173	+	0.320173i	0.848833	−	0.528661i	$-0.177306\pi$
$557$	7.55635	+	7.55635i	0.320173	+	0.320173i	−0.528661	+	0.848833i	$0.677306\pi$
$558$		0			0
$559$			48.5685i			2.05423i
$560$	−2.12132	+	0.707107i	−0.0896421	+	0.0298807i
$561$		0			0
$562$	−13.4853	+	13.4853i	−0.568842	+	0.568842i
$563$	6.68629	−	6.68629i	0.281794	−	0.281794i	−0.552030	−	0.833824i	$-0.686147\pi$
$563$	6.68629	−	6.68629i	0.281794	−	0.281794i	0.833824	+	0.552030i	$0.186147\pi$
$564$		0			0
$565$	33.9411	−	11.3137i	1.42791	−	0.475971i
$566$			30.1421i			1.26697i
$567$		0			0
$568$	0.828427	+	0.828427i	0.0347600	+	0.0347600i
$569$	−14.1005			−0.591124			−0.295562	−	0.955324i	$-0.595507\pi$
$569$	−14.1005			−0.591124			−0.295562	+	0.955324i	$0.595507\pi$
$570$		0			0
$571$	−11.0294			−0.461568			−0.230784	−	0.973005i	$-0.574129\pi$
$571$	−11.0294			−0.461568			−0.230784	+	0.973005i	$0.574129\pi$
$572$	−2.34315	−	2.34315i	−0.0979718	−	0.0979718i
$573$		0			0
$574$		−	3.17157i		−	0.132379i
$575$	33.7990	+	4.82843i	1.40952	+	0.201359i
$576$		0			0
$577$	−10.7279	+	10.7279i	−0.446609	+	0.446609i	−0.894226	−	0.447616i	$-0.852273\pi$
$577$	−10.7279	+	10.7279i	−0.446609	+	0.446609i	0.447616	+	0.894226i	$0.352273\pi$
$578$	−11.5355	+	11.5355i	−0.479815	+	0.479815i
$579$		0			0
$580$	0.828427	−	1.65685i	0.0343986	−	0.0687971i
$581$		−	1.17157i		−	0.0486050i
$582$		0			0
$583$	−1.51472	−	1.51472i	−0.0627332	−	0.0627332i
$584$	10.0000			0.413803
$585$		0			0
$586$	−12.2426			−0.505739
$587$	17.7990	+	17.7990i	0.734643	+	0.734643i	0.971536	−	0.236893i	$-0.0761290\pi$
$587$	17.7990	+	17.7990i	0.734643	+	0.734643i	−0.236893	+	0.971536i	$0.576129\pi$
$588$		0			0
$589$		−	4.97056i		−	0.204808i
$590$	2.00000	+	6.00000i	0.0823387	+	0.247016i
$591$		0			0
$592$	−6.24264	+	6.24264i	−0.256571	+	0.256571i
$593$	−16.3848	+	16.3848i	−0.672842	+	0.672842i	−0.958370	−	0.285528i	$-0.907831\pi$
$593$	−16.3848	+	16.3848i	−0.672842	+	0.672842i	0.285528	+	0.958370i	$0.407831\pi$
$594$		0			0
$595$	1.65685	+	0.828427i	0.0679244	+	0.0339622i
$596$		−	8.14214i		−	0.333515i
$597$		0			0
$598$	−27.3137	−	27.3137i	−1.11694	−	1.11694i
$599$	−15.3137			−0.625701			−0.312851	−	0.949802i	$-0.601284\pi$
$599$	−15.3137			−0.625701			−0.312851	+	0.949802i	$0.601284\pi$
$600$		0			0
$601$	−4.14214			−0.168961			−0.0844806	−	0.996425i	$-0.526923\pi$
$601$	−4.14214			−0.168961			−0.0844806	+	0.996425i	$0.526923\pi$
$602$	6.07107	+	6.07107i	0.247438	+	0.247438i
$603$		0			0
$604$		−	18.8284i		−	0.766118i
$605$	−21.3137	−	10.6569i	−0.866525	−	0.433263i
$606$		0			0
$607$	−7.31371	+	7.31371i	−0.296854	+	0.296854i	−0.839780	−	0.542926i	$-0.817316\pi$
$607$	−7.31371	+	7.31371i	−0.296854	+	0.296854i	0.542926	+	0.839780i	$0.317316\pi$
$608$	2.00000	−	2.00000i	0.0811107	−	0.0811107i
$609$		0			0
$610$	−7.00000	−	21.0000i	−0.283422	−	0.850265i
$611$			73.9411i			2.99134i
$612$		0			0
$613$	−9.07107	−	9.07107i	−0.366377	−	0.366377i	0.499777	−	0.866154i	$-0.333415\pi$
$613$	−9.07107	−	9.07107i	−0.366377	−	0.366377i	−0.866154	+	0.499777i	$0.833415\pi$
$614$		0			0
$615$		0			0
$616$	−0.585786			−0.0236020
$617$	24.0416	+	24.0416i	0.967880	+	0.967880i	0.999500	−	0.0316203i	$-0.0100667\pi$
$617$	24.0416	+	24.0416i	0.967880	+	0.967880i	−0.0316203	+	0.999500i	$0.510067\pi$
$618$		0			0
$619$		−	17.8579i		−	0.717768i	−0.933382	−	0.358884i	$-0.883157\pi$
$619$		−	17.8579i		−	0.717768i	0.933382	−	0.358884i	$-0.116843\pi$
$620$	1.75736	−	3.51472i	0.0705772	−	0.141154i
$621$		0			0
$622$	−3.41421	+	3.41421i	−0.136897	+	0.136897i
$623$	−2.24264	+	2.24264i	−0.0898495	+	0.0898495i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		−	3.17157i		−	0.126762i
$627$		0			0
$628$	−9.65685	−	9.65685i	−0.385350	−	0.385350i
$629$	7.31371			0.291617
$630$		0			0
$631$	−0.201010			−0.00800209			−0.00400104	−	0.999992i	$-0.501274\pi$
$631$	−0.201010			−0.00800209			−0.00400104	+	0.999992i	$0.501274\pi$
$632$	−4.00000	−	4.00000i	−0.159111	−	0.159111i
$633$		0			0
$634$			34.9706i			1.38886i
$635$	−22.9706	+	7.65685i	−0.911559	+	0.303853i
$636$		0			0
$637$	4.00000	−	4.00000i	0.158486	−	0.158486i
$638$	0.343146	−	0.343146i	0.0135853	−	0.0135853i
$639$		0			0
$640$	2.12132	−	0.707107i	0.0838525	−	0.0279508i
$641$		−	21.2132i		−	0.837871i	−0.908016	−	0.418936i	$-0.862403\pi$
$641$		−	21.2132i		−	0.837871i	0.908016	−	0.418936i	$-0.137597\pi$
$642$		0			0
$643$	−10.9706	−	10.9706i	−0.432637	−	0.432637i	0.456888	−	0.889524i	$-0.348964\pi$
$643$	−10.9706	−	10.9706i	−0.432637	−	0.432637i	−0.889524	+	0.456888i	$0.848964\pi$
$644$	−6.82843			−0.269078
$645$		0			0
$646$	−2.34315			−0.0921898
$647$	−33.2426	−	33.2426i	−1.30690	−	1.30690i	−0.923639	−	0.383264i	$-0.874800\pi$
$647$	−33.2426	−	33.2426i	−1.30690	−	1.30690i	−0.383264	−	0.923639i	$-0.625200\pi$
$648$		0			0
$649$			1.65685i			0.0650372i
$650$	22.6274	−	16.9706i	0.887520	−	0.665640i
$651$		0			0
$652$	−11.7279	+	11.7279i	−0.459301	+	0.459301i
$653$	14.2426	−	14.2426i	0.557358	−	0.557358i	−0.371197	−	0.928554i	$-0.621052\pi$
$653$	14.2426	−	14.2426i	0.557358	−	0.557358i	0.928554	+	0.371197i	$0.121052\pi$
$654$		0			0
$655$	16.4853	−	32.9706i	0.644133	−	1.28827i
$656$			3.17157i			0.123829i
$657$		0			0
$658$	9.24264	+	9.24264i	0.360316	+	0.360316i
$659$	−26.7279			−1.04117			−0.520586	−	0.853809i	$-0.674286\pi$
$659$	−26.7279			−1.04117			−0.520586	+	0.853809i	$0.674286\pi$
$660$		0			0
$661$	40.0416			1.55744			0.778719	−	0.627372i	$-0.215870\pi$
$661$	40.0416			1.55744			0.778719	+	0.627372i	$0.215870\pi$
$662$	−13.1716	−	13.1716i	−0.511928	−	0.511928i
$663$		0			0
$664$			1.17157i			0.0454658i
$665$	−2.00000	−	6.00000i	−0.0775567	−	0.232670i
$666$		0			0
$667$	4.00000	−	4.00000i	0.154881	−	0.154881i
$668$	7.58579	−	7.58579i	0.293503	−	0.293503i
$669$		0			0
$670$	23.7990	+	11.8995i	0.919435	+	0.459718i
$671$		−	5.79899i		−	0.223868i
$672$		0			0
$673$	3.34315	+	3.34315i	0.128869	+	0.128869i	0.768599	−	0.639731i	$-0.220954\pi$
$673$	3.34315	+	3.34315i	0.128869	+	0.128869i	−0.639731	+	0.768599i	$0.720954\pi$
$674$	−14.3848			−0.554081
$675$		0			0
$676$	−19.0000			−0.730769
$677$	15.8284	+	15.8284i	0.608336	+	0.608336i	0.942511	−	0.334175i	$-0.108458\pi$
$677$	15.8284	+	15.8284i	0.608336	+	0.608336i	−0.334175	+	0.942511i	$0.608458\pi$
$678$		0			0
$679$		−	6.48528i		−	0.248882i
$680$	−1.65685	−	0.828427i	−0.0635375	−	0.0317687i
$681$		0			0
$682$	0.727922	−	0.727922i	0.0278736	−	0.0278736i
$683$	24.3848	−	24.3848i	0.933058	−	0.933058i	−0.0648383	−	0.997896i	$-0.520653\pi$
$683$	24.3848	−	24.3848i	0.933058	−	0.933058i	0.997896	+	0.0648383i	$0.0206531\pi$
$684$		0			0
$685$	−12.0000	−	36.0000i	−0.458496	−	1.37549i
$686$		−	1.00000i		−	0.0381802i
$687$		0			0
$688$	−6.07107	−	6.07107i	−0.231457	−	0.231457i
$689$	−20.6863			−0.788085
$690$		0			0
$691$		0			0			−	1.00000i	$-0.5\pi$
$691$		0			0				1.00000i	$0.5\pi$
$692$	−11.4853	−	11.4853i	−0.436605	−	0.436605i
$693$		0			0
$694$			12.0000i			0.455514i
$695$	−17.6569	+	35.3137i	−0.669763	+	1.33953i
$696$		0			0
$697$	1.85786	−	1.85786i	0.0703716	−	0.0703716i
$698$	23.1421	−	23.1421i	0.875943	−	0.875943i
$699$		0			0
$700$	0.707107	−	4.94975i	0.0267261	−	0.187083i
$701$			40.8284i			1.54207i	0.636794	+	0.771034i	$0.280260\pi$
$701$			40.8284i			1.54207i	−0.636794	+	0.771034i	$0.719740\pi$
$702$		0			0
$703$	−17.6569	−	17.6569i	−0.665941	−	0.665941i
$704$	0.585786			0.0220777
$705$		0			0
$706$	−26.0000			−0.978523
$707$	−12.4853	−	12.4853i	−0.469557	−	0.469557i
$708$		0			0
$709$		−	40.8284i		−	1.53334i	−0.642039	−	0.766672i	$-0.721911\pi$
$709$		−	40.8284i		−	1.53334i	0.642039	−	0.766672i	$-0.278089\pi$
$710$	−2.48528	+	0.828427i	−0.0932709	+	0.0310903i
$711$		0			0
$712$	2.24264	−	2.24264i	0.0840465	−	0.0840465i
$713$	8.48528	−	8.48528i	0.317776	−	0.317776i
$714$		0			0
$715$	7.02944	−	2.34315i	0.262886	−	0.0876287i
$716$			16.5858i			0.619840i
$717$		0			0
$718$	−16.8284	−	16.8284i	−0.628031	−	0.628031i
$719$	38.6274			1.44056			0.720280	−	0.693684i	$-0.244013\pi$
$719$	38.6274			1.44056			0.720280	+	0.693684i	$0.244013\pi$
$720$		0			0
$721$	10.4853			0.390492
$722$	−7.77817	−	7.77817i	−0.289474	−	0.289474i
$723$		0			0
$724$		−	19.0711i		−	0.708771i
$725$	2.48528	+	3.31371i	0.0923010	+	0.123068i
$726$		0			0
$727$	−22.6274	+	22.6274i	−0.839204	+	0.839204i	−0.988754	−	0.149550i	$-0.952218\pi$
$727$	−22.6274	+	22.6274i	−0.839204	+	0.839204i	0.149550	+	0.988754i	$0.452218\pi$
$728$	−4.00000	+	4.00000i	−0.148250	+	0.148250i
$729$		0			0
$730$	−10.0000	+	20.0000i	−0.370117	+	0.740233i
$731$			7.11270i			0.263073i
$732$		0			0
$733$	−0.443651	−	0.443651i	−0.0163866	−	0.0163866i	0.698866	−	0.715253i	$-0.253688\pi$
$733$	−0.443651	−	0.443651i	−0.0163866	−	0.0163866i	−0.715253	+	0.698866i	$0.753688\pi$
$734$	14.4853			0.534661
$735$		0			0
$736$	6.82843			0.251699
$737$	4.92893	+	4.92893i	0.181560	+	0.181560i
$738$		0			0
$739$		−	7.45584i		−	0.274268i	−0.990553	−	0.137134i	$-0.956211\pi$
$739$		−	7.45584i		−	0.274268i	0.990553	−	0.137134i	$-0.0437890\pi$
$740$	−6.24264	−	18.7279i	−0.229484	−	0.688452i
$741$		0			0
$742$	−2.58579	+	2.58579i	−0.0949272	+	0.0949272i
$743$	−31.1127	+	31.1127i	−1.14141	+	1.14141i	−0.153222	+	0.988192i	$0.548965\pi$
$743$	−31.1127	+	31.1127i	−1.14141	+	1.14141i	−0.988192	+	0.153222i	$0.951035\pi$
$744$		0			0
$745$	16.2843	+	8.14214i	0.596610	+	0.298305i
$746$			15.6569i			0.573238i
$747$		0			0
$748$	−0.343146	−	0.343146i	−0.0125467	−	0.0125467i
$749$	7.31371			0.267237
$750$		0			0
$751$	48.4853			1.76925			0.884627	−	0.466300i	$-0.154413\pi$
$751$	48.4853			1.76925			0.884627	+	0.466300i	$0.154413\pi$
$752$	−9.24264	−	9.24264i	−0.337044	−	0.337044i
$753$		0			0
$754$		−	4.68629i		−	0.170665i
$755$	37.6569	+	18.8284i	1.37047	+	0.685237i
$756$		0			0
$757$	−23.5563	+	23.5563i	−0.856170	+	0.856170i	−0.990884	−	0.134714i	$-0.956988\pi$
$757$	−23.5563	+	23.5563i	−0.856170	+	0.856170i	0.134714	+	0.990884i	$0.456988\pi$
$758$	18.2426	−	18.2426i	0.662603	−	0.662603i
$759$		0			0
$760$	2.00000	+	6.00000i	0.0725476	+	0.217643i
$761$			18.9706i			0.687682i	0.939028	+	0.343841i	$0.111728\pi$
$761$			18.9706i			0.687682i	−0.939028	+	0.343841i	$0.888272\pi$
$762$		0			0
$763$	6.58579	+	6.58579i	0.238421	+	0.238421i
$764$	14.3431			0.518917
$765$		0			0
$766$	−6.24264			−0.225556
$767$	11.3137	+	11.3137i	0.408514	+	0.408514i
$768$		0			0
$769$		−	41.5980i		−	1.50006i	−0.661403	−	0.750031i	$-0.730039\pi$
$769$		−	41.5980i		−	1.50006i	0.661403	−	0.750031i	$-0.269961\pi$
$770$	0.585786	−	1.17157i	0.0211103	−	0.0422206i
$771$		0			0
$772$	−13.4853	+	13.4853i	−0.485346	+	0.485346i
$773$	34.9411	−	34.9411i	1.25674	−	1.25674i	0.304107	−	0.952638i	$-0.401642\pi$
$773$	34.9411	−	34.9411i	1.25674	−	1.25674i	0.952638	−	0.304107i	$-0.0983581\pi$
$774$		0			0
$775$	5.27208	+	7.02944i	0.189379	+	0.252505i
$776$			6.48528i			0.232808i
$777$		0			0
$778$	6.92893	+	6.92893i	0.248414	+	0.248414i
$779$	−8.97056			−0.321404
$780$		0			0
$781$	−0.686292			−0.0245574
$782$	−4.00000	−	4.00000i	−0.143040	−	0.143040i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$	28.9706	−	9.65685i	1.03400	−	0.344668i
$786$		0			0
$787$	−15.5147	+	15.5147i	−0.553040	+	0.553040i	−0.927317	−	0.374277i	$-0.877891\pi$
$787$	−15.5147	+	15.5147i	−0.553040	+	0.553040i	0.374277	+	0.927317i	$0.377891\pi$
$788$	10.2426	−	10.2426i	0.364879	−	0.364879i
$789$		0			0
$790$	12.0000	−	4.00000i	0.426941	−	0.142314i
$791$		−	16.0000i		−	0.568895i
$792$		0			0
$793$	−39.5980	−	39.5980i	−1.40617	−	1.40617i
$794$	1.31371			0.0466218
$795$		0			0
$796$	4.10051			0.145339
$797$	20.1716	+	20.1716i	0.714514	+	0.714514i	0.967476	−	0.252962i	$-0.0814049\pi$
$797$	20.1716	+	20.1716i	0.714514	+	0.714514i	−0.252962	+	0.967476i	$0.581405\pi$
$798$		0			0
$799$			10.8284i			0.383082i
$800$	−0.707107	+	4.94975i	−0.0250000	+	0.175000i
$801$		0			0
$802$	19.0000	−	19.0000i	0.670913	−	0.670913i
$803$	−4.14214	+	4.14214i	−0.146173	+	0.146173i
$804$		0			0
$805$	6.82843	−	13.6569i	0.240670	−	0.481341i
$806$		−	9.94113i		−	0.350161i
$807$		0			0
$808$	12.4853	+	12.4853i	0.439231	+	0.439231i
$809$	−46.3848			−1.63080			−0.815401	−	0.578897i	$-0.803483\pi$
$809$	−46.3848			−1.63080			−0.815401	+	0.578897i	$0.803483\pi$
$810$		0			0
$811$	28.9706			1.01729			0.508647	−	0.860975i	$-0.330146\pi$
$811$	28.9706			1.01729			0.508647	+	0.860975i	$0.330146\pi$
$812$	−0.585786	−	0.585786i	−0.0205571	−	0.0205571i
$813$		0			0
$814$		−	5.17157i		−	0.181264i
$815$	−11.7279	−	35.1838i	−0.410811	−	1.23243i
$816$		0			0
$817$	17.1716	−	17.1716i	0.600757	−	0.600757i
$818$	−7.07107	+	7.07107i	−0.247234	+	0.247234i
$819$		0			0
$820$	−6.34315	−	3.17157i	−0.221512	−	0.110756i
$821$		−	9.79899i		−	0.341987i	−0.985272	−	0.170994i	$-0.945302\pi$
$821$		−	9.79899i		−	0.341987i	0.985272	−	0.170994i	$-0.0546977\pi$
$822$		0			0
$823$	28.4853	+	28.4853i	0.992934	+	0.992934i	0.999975	−	0.00704072i	$-0.00224115\pi$
$823$	28.4853	+	28.4853i	0.992934	+	0.992934i	−0.00704072	+	0.999975i	$0.502241\pi$
$824$	−10.4853			−0.365272
$825$		0			0
$826$	2.82843			0.0984136
$827$	−14.2426	−	14.2426i	−0.495265	−	0.495265i	0.414695	−	0.909960i	$-0.363888\pi$
$827$	−14.2426	−	14.2426i	−0.495265	−	0.495265i	−0.909960	+	0.414695i	$0.863888\pi$
$828$		0			0
$829$		−	11.7574i		−	0.408350i	−0.978934	−	0.204175i	$-0.934549\pi$
$829$		−	11.7574i		−	0.408350i	0.978934	−	0.204175i	$-0.0654512\pi$
$830$	−2.34315	−	1.17157i	−0.0813318	−	0.0406659i
$831$		0			0
$832$	4.00000	−	4.00000i	0.138675	−	0.138675i
$833$	0.585786	−	0.585786i	0.0202963	−	0.0202963i
$834$		0			0
$835$	7.58579	+	22.7574i	0.262517	+	0.787551i
$836$			1.65685i			0.0573035i
$837$		0			0
$838$	13.1716	+	13.1716i	0.455004	+	0.455004i
$839$	−30.4853			−1.05247			−0.526234	−	0.850340i	$-0.676397\pi$
$839$	−30.4853			−1.05247			−0.526234	+	0.850340i	$0.676397\pi$
$840$		0			0
$841$	−28.3137			−0.976335
$842$	28.7279	+	28.7279i	0.990030	+	0.990030i
$843$		0			0
$844$		−	4.00000i		−	0.137686i
$845$	19.0000	−	38.0000i	0.653620	−	1.30724i
$846$		0			0
$847$	−7.53553	+	7.53553i	−0.258924	+	0.258924i
$848$	2.58579	−	2.58579i	0.0887963	−	0.0887963i
$849$		0			0
$850$	3.31371	−	2.48528i	0.113659	−	0.0852444i
$851$		−	60.2843i		−	2.06652i
$852$		0			0
$853$	−15.0711	−	15.0711i	−0.516024	−	0.516024i	0.400342	−	0.916366i	$-0.368891\pi$
$853$	−15.0711	−	15.0711i	−0.516024	−	0.516024i	−0.916366	+	0.400342i	$0.868891\pi$
$854$	−9.89949			−0.338754
$855$		0			0
$856$	−7.31371			−0.249977
$857$	6.44365	+	6.44365i	0.220111	+	0.220111i	0.808545	−	0.588434i	$-0.200255\pi$
$857$	6.44365	+	6.44365i	0.220111	+	0.220111i	−0.588434	+	0.808545i	$0.700255\pi$
$858$		0			0
$859$			40.0000i			1.36478i	0.730987	+	0.682391i	$0.239060\pi$
$859$			40.0000i			1.36478i	−0.730987	+	0.682391i	$0.760940\pi$
$860$	18.2132	−	6.07107i	0.621065	−	0.207022i
$861$		0			0
$862$	18.4853	−	18.4853i	0.629611	−	0.629611i
$863$	−21.1716	+	21.1716i	−0.720689	+	0.720689i	−0.968745	−	0.248057i	$-0.920208\pi$
$863$	−21.1716	+	21.1716i	−0.720689	+	0.720689i	0.248057	+	0.968745i	$0.420208\pi$
$864$		0			0
$865$	34.4558	−	11.4853i	1.17153	−	0.390511i
$866$		−	25.7990i		−	0.876685i
$867$		0			0
$868$	−1.24264	−	1.24264i	−0.0421780	−	0.0421780i
$869$	3.31371			0.112410
$870$		0			0
$871$	67.3137			2.28084
$872$	−6.58579	−	6.58579i	−0.223023	−	0.223023i
$873$		0			0
$874$			19.3137i			0.653296i
$875$	9.19239	+	6.36396i	0.310759	+	0.215141i
$876$		0			0
$877$	−37.6985	+	37.6985i	−1.27299	+	1.27299i	−0.328475	+	0.944513i	$0.606535\pi$
$877$	−37.6985	+	37.6985i	−1.27299	+	1.27299i	−0.944513	+	0.328475i	$0.893465\pi$
$878$	−2.75736	+	2.75736i	−0.0930564	+	0.0930564i
$879$		0			0
$880$	−0.585786	+	1.17157i	−0.0197469	+	0.0394937i
$881$		−	8.62742i		−	0.290665i	−0.989383	−	0.145333i	$-0.953575\pi$
$881$		−	8.62742i		−	0.290665i	0.989383	−	0.145333i	$-0.0464252\pi$
$882$		0			0
$883$	37.3848	+	37.3848i	1.25810	+	1.25810i	0.952000	+	0.306098i	$0.0990235\pi$
$883$	37.3848	+	37.3848i	1.25810	+	1.25810i	0.306098	+	0.952000i	$0.400977\pi$
$884$	−4.68629			−0.157617
$885$		0			0
$886$	4.97056			0.166989
$887$	−39.7279	−	39.7279i	−1.33393	−	1.33393i	−0.901819	−	0.432114i	$-0.857768\pi$
$887$	−39.7279	−	39.7279i	−1.33393	−	1.33393i	−0.432114	−	0.901819i	$-0.642232\pi$
$888$		0			0
$889$			10.8284i			0.363174i
$890$	2.24264	+	6.72792i	0.0751735	+	0.225520i
$891$		0			0
$892$	−7.31371	+	7.31371i	−0.244881	+	0.244881i
$893$	26.1421	−	26.1421i	0.874813	−	0.874813i
$894$		0			0
$895$	−33.1716	−	16.5858i	−1.10880	−	0.554402i
$896$		−	1.00000i		−	0.0334077i
$897$		0			0
$898$	11.8284	+	11.8284i	0.394720	+	0.394720i
$899$	1.45584			0.0485551
$900$		0			0
$901$	−3.02944			−0.100925
$902$	−1.31371	−	1.31371i	−0.0437417	−	0.0437417i
$903$		0			0
$904$			16.0000i			0.532152i
$905$	38.1421	+	19.0711i	1.26789	+	0.633944i
$906$		0			0
$907$	19.5858	−	19.5858i	0.650335	−	0.650335i	−0.302738	−	0.953074i	$-0.597901\pi$
$907$	19.5858	−	19.5858i	0.650335	−	0.650335i	0.953074	+	0.302738i	$0.0979008\pi$
$908$	−1.17157	+	1.17157i	−0.0388800	+	0.0388800i
$909$		0			0
$910$	−4.00000	−	12.0000i	−0.132599	−	0.397796i
$911$			4.00000i			0.132526i	0.997802	+	0.0662630i	$0.0211076\pi$
$911$			4.00000i			0.132526i	−0.997802	+	0.0662630i	$0.978892\pi$
$912$		0			0
$913$	−0.485281	−	0.485281i	−0.0160605	−	0.0160605i
$914$	−3.07107			−0.101582
$915$		0			0
$916$	−8.24264			−0.272345
$917$	−11.6569	−	11.6569i	−0.384943	−	0.384943i
$918$		0			0
$919$			55.7990i			1.84064i	0.391168	+	0.920319i	$0.372071\pi$
$919$			55.7990i			1.84064i	−0.391168	+	0.920319i	$0.627929\pi$
$920$	−6.82843	+	13.6569i	−0.225127	+	0.450253i
$921$		0			0
$922$	−3.75736	+	3.75736i	−0.123742	+	0.123742i
$923$	−4.68629	+	4.68629i	−0.154251	+	0.154251i
$924$		0			0
$925$	43.6985	+	6.24264i	1.43680	+	0.205257i
$926$			28.0000i			0.920137i
$927$		0			0
$928$	0.585786	+	0.585786i	0.0192294	+	0.0192294i
$929$	−13.0294			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$929$	−13.0294			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$930$		0			0
$931$	−2.82843			−0.0926980
$932$	14.8284	+	14.8284i	0.485721	+	0.485721i
$933$		0			0
$934$			19.7990i			0.647843i
$935$	1.02944	−	0.343146i	0.0336662	−	0.0112221i
$936$		0			0
$937$	−29.2132	+	29.2132i	−0.954354	+	0.954354i	−0.999003	−	0.0446490i	$-0.985783\pi$
$937$	−29.2132	+	29.2132i	−0.954354	+	0.954354i	0.0446490	+	0.999003i	$0.485783\pi$
$938$	8.41421	−	8.41421i	0.274734	−	0.274734i
$939$		0			0
$940$	27.7279	−	9.24264i	0.904385	−	0.301462i
$941$			10.2843i			0.335258i	0.985850	+	0.167629i	$0.0536110\pi$
$941$			10.2843i			0.335258i	−0.985850	+	0.167629i	$0.946389\pi$
$942$		0			0
$943$	−15.3137	−	15.3137i	−0.498683	−	0.498683i
$944$	−2.82843			−0.0920575
$945$		0			0
$946$	5.02944			0.163521
$947$	9.75736	+	9.75736i	0.317072	+	0.317072i	0.847641	−	0.530570i	$-0.178022\pi$
$947$	9.75736	+	9.75736i	0.317072	+	0.317072i	−0.530570	+	0.847641i	$0.678022\pi$
$948$		0			0
$949$			56.5685i			1.83629i
$950$	−14.0000	−	2.00000i	−0.454220	−	0.0648886i
$951$		0			0
$952$	−0.585786	+	0.585786i	−0.0189854	+	0.0189854i
$953$	−27.7574	+	27.7574i	−0.899149	+	0.899149i	−0.995361	−	0.0962118i	$-0.969327\pi$
$953$	−27.7574	+	27.7574i	−0.899149	+	0.899149i	0.0962118	+	0.995361i	$0.469327\pi$
$954$		0			0
$955$	−14.3431	+	28.6863i	−0.464133	+	0.928267i
$956$			13.6569i			0.441694i
$957$		0			0
$958$	−13.5563	−	13.5563i	−0.437986	−	0.437986i
$959$	−16.9706			−0.548008
$960$		0			0
$961$	−27.9117			−0.900377
$962$	−35.3137	−	35.3137i	−1.13856	−	1.13856i
$963$		0			0
$964$		−	4.14214i		−	0.133409i
$965$	−13.4853	−	40.4558i	−0.434107	−	1.30232i
$966$		0			0
$967$	20.2843	−	20.2843i	0.652298	−	0.652298i	−0.301248	−	0.953546i	$-0.597403\pi$
$967$	20.2843	−	20.2843i	0.652298	−	0.652298i	0.953546	+	0.301248i	$0.0974031\pi$
$968$	7.53553	−	7.53553i	0.242201	−	0.242201i
$969$		0			0
$970$	−12.9706	−	6.48528i	−0.416460	−	0.208230i
$971$		−	36.0000i		−	1.15529i	−0.816286	−	0.577647i	$-0.803971\pi$
$971$		−	36.0000i		−	1.15529i	0.816286	−	0.577647i	$-0.196029\pi$
$972$		0			0
$973$	12.4853	+	12.4853i	0.400260	+	0.400260i
$974$	−26.8284			−0.859638
$975$		0			0
$976$	9.89949			0.316875
$977$	32.9706	+	32.9706i	1.05482	+	1.05482i	0.998407	+	0.0564143i	$0.0179668\pi$
$977$	32.9706	+	32.9706i	1.05482	+	1.05482i	0.0564143	+	0.998407i	$0.482033\pi$
$978$		0			0
$979$			1.85786i			0.0593776i
$980$	−2.00000	−	1.00000i	−0.0638877	−	0.0319438i
$981$		0			0
$982$	−18.8995	+	18.8995i	−0.603107	+	0.603107i
$983$	40.5563	−	40.5563i	1.29355	−	1.29355i	0.360969	−	0.932578i	$-0.382446\pi$
$983$	40.5563	−	40.5563i	1.29355	−	1.29355i	0.932578	−	0.360969i	$-0.117554\pi$
$984$		0			0
$985$	10.2426	+	30.7279i	0.326358	+	0.979073i
$986$		−	0.686292i		−	0.0218560i
$987$		0			0
$988$	11.3137	+	11.3137i	0.359937	+	0.359937i
$989$	58.6274			1.86424
$990$		0			0
$991$	−30.1421			−0.957496			−0.478748	−	0.877952i	$-0.658909\pi$
$991$	−30.1421			−0.957496			−0.478748	+	0.877952i	$0.658909\pi$
$992$	1.24264	+	1.24264i	0.0394539	+	0.0394539i
$993$		0			0
$994$			1.17157i			0.0371600i
$995$	−4.10051	+	8.20101i	−0.129995	+	0.259989i
$996$		0			0
$997$	1.89949	−	1.89949i	0.0601576	−	0.0601576i	−0.676388	−	0.736546i	$-0.736456\pi$
$997$	1.89949	−	1.89949i	0.0601576	−	0.0601576i	0.736546	+	0.676388i	$0.236456\pi$
$998$	16.5858	−	16.5858i	0.525014	−	0.525014i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.m.a.323.1	yes	4
3.2	odd	2		630.2.m.b.323.2	yes	4
5.2	odd	4		630.2.m.b.197.2	yes	4
5.3	odd	4		3150.2.m.a.1457.1		4
5.4	even	2		3150.2.m.b.2843.2		4
15.2	even	4	inner	630.2.m.a.197.1	✓	4
15.8	even	4		3150.2.m.b.1457.2		4
15.14	odd	2		3150.2.m.a.2843.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.m.a.197.1	✓	4	15.2	even	4	inner
630.2.m.a.323.1	yes	4	1.1	even	1	trivial
630.2.m.b.197.2	yes	4	5.2	odd	4
630.2.m.b.323.2	yes	4	3.2	odd	2
3150.2.m.a.1457.1		4	5.3	odd	4
3150.2.m.a.2843.1		4	15.14	odd	2
3150.2.m.b.1457.2		4	15.8	even	4
3150.2.m.b.2843.2		4	5.4	even	2

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.707107 + 2.12132i) q^{10} +0.585786i q^{11} +(4.00000 + 4.00000i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(0.585786 + 0.585786i) q^{17} -2.82843i q^{19} +(1.00000 - 2.00000i) q^{20} +(0.414214 - 0.414214i) q^{22} +(4.82843 - 4.82843i) q^{23} +(3.00000 + 4.00000i) q^{25} -5.65685i q^{26} +(-0.707107 - 0.707107i) q^{28} +0.828427 q^{29} +1.75736 q^{31} +(0.707107 + 0.707107i) q^{32} -0.828427i q^{34} +(2.12132 - 0.707107i) q^{35} +(6.24264 - 6.24264i) q^{37} +(-2.00000 + 2.00000i) q^{38} +(-2.12132 + 0.707107i) q^{40} -3.17157i q^{41} +(6.07107 + 6.07107i) q^{43} -0.585786 q^{44} -6.82843 q^{46} +(9.24264 + 9.24264i) q^{47} -1.00000i q^{49} +(0.707107 - 4.94975i) q^{50} +(-4.00000 + 4.00000i) q^{52} +(-2.58579 + 2.58579i) q^{53} +(0.585786 - 1.17157i) q^{55} +1.00000i q^{56} +(-0.585786 - 0.585786i) q^{58} +2.82843 q^{59} -9.89949 q^{61} +(-1.24264 - 1.24264i) q^{62} -1.00000i q^{64} +(-4.00000 - 12.0000i) q^{65} +(8.41421 - 8.41421i) q^{67} +(-0.585786 + 0.585786i) q^{68} +(-2.00000 - 1.00000i) q^{70} +1.17157i q^{71} +(7.07107 + 7.07107i) q^{73} -8.82843 q^{74} +2.82843 q^{76} +(-0.414214 - 0.414214i) q^{77} -5.65685i q^{79} +(2.00000 + 1.00000i) q^{80} +(-2.24264 + 2.24264i) q^{82} +(-0.828427 + 0.828427i) q^{83} +(-0.585786 - 1.75736i) q^{85} -8.58579i q^{86} +(0.414214 + 0.414214i) q^{88} +3.17157 q^{89} -5.65685 q^{91} +(4.82843 + 4.82843i) q^{92} -13.0711i q^{94} +(-2.82843 + 5.65685i) q^{95} +(-4.58579 + 4.58579i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{5}+O(q^{10}) \) 4 * q - 8 * q^5	\( 4 q - 8 q^{5} + 16 q^{13} + 4 q^{14} - 4 q^{16} + 8 q^{17} + 4 q^{20} - 4 q^{22} + 8 q^{23} + 12 q^{25} - 8 q^{29} + 24 q^{31} + 8 q^{37} - 8 q^{38} - 4 q^{43} - 8 q^{44} - 16 q^{46} + 20 q^{47} - 16 q^{52} - 16 q^{53} + 8 q^{55} - 8 q^{58} + 12 q^{62} - 16 q^{65} + 28 q^{67} - 8 q^{68} - 8 q^{70} - 24 q^{74} + 4 q^{77} + 8 q^{80} + 8 q^{82} + 8 q^{83} - 8 q^{85} - 4 q^{88} + 24 q^{89} + 8 q^{92} - 24 q^{97}+O(q^{100}) \) 4 * q - 8 * q^5 + 16 * q^13 + 4 * q^14 - 4 * q^16 + 8 * q^17 + 4 * q^20 - 4 * q^22 + 8 * q^23 + 12 * q^25 - 8 * q^29 + 24 * q^31 + 8 * q^37 - 8 * q^38 - 4 * q^43 - 8 * q^44 - 16 * q^46 + 20 * q^47 - 16 * q^52 - 16 * q^53 + 8 * q^55 - 8 * q^58 + 12 * q^62 - 16 * q^65 + 28 * q^67 - 8 * q^68 - 8 * q^70 - 24 * q^74 + 4 * q^77 + 8 * q^80 + 8 * q^82 + 8 * q^83 - 8 * q^85 - 4 * q^88 + 24 * q^89 + 8 * q^92 - 24 * q^97

Introduction

L-functions

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Database

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