LMFDB - Embedded newform 630.2.m.d.197.4

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:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.4
Root			$1.69230i$ of defining polynomial
Character	$\chi$	$=$	630.197
Dual form			630.2.m.d.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.489528 - 2.18183i) q^{5} +(0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.489528 - 2.18183i) q^{5} +(0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.19663 - 1.88893i) q^{10} -1.77786i q^{11} +(0.692297 - 0.692297i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(2.39327 - 2.39327i) q^{17} +(-2.18183 - 0.489528i) q^{20} +(-1.25714 - 1.25714i) q^{22} +(-3.38459 - 3.38459i) q^{23} +(-4.52072 - 2.13613i) q^{25} -0.979056i q^{26} +(0.707107 - 0.707107i) q^{28} +4.42289 q^{29} -5.77786 q^{31} +(-0.707107 + 0.707107i) q^{32} -3.38459i q^{34} +(1.88893 - 1.19663i) q^{35} +(5.91399 + 5.91399i) q^{37} +(-1.88893 + 1.19663i) q^{40} +0.807922i q^{41} +(-4.64173 + 4.64173i) q^{43} -1.77786 q^{44} -4.78654 q^{46} +(7.47016 - 7.47016i) q^{47} +1.00000i q^{49} +(-4.70711 + 1.68616i) q^{50} +(-0.692297 - 0.692297i) q^{52} +(-3.56484 - 3.56484i) q^{53} +(-3.87899 - 0.870315i) q^{55} -1.00000i q^{56} +(3.12745 - 3.12745i) q^{58} +5.89887 q^{59} +2.39327 q^{61} +(-4.08557 + 4.08557i) q^{62} +1.00000i q^{64} +(-1.17157 - 1.84937i) q^{65} +(-0.641735 - 0.641735i) q^{67} +(-2.39327 - 2.39327i) q^{68} +(0.489528 - 2.18183i) q^{70} +10.6854i q^{71} +(5.70097 - 5.70097i) q^{73} +8.36365 q^{74} +(1.25714 - 1.25714i) q^{77} +16.3423i q^{79} +(-0.489528 + 2.18183i) q^{80} +(0.571287 + 0.571287i) q^{82} +(0.171134 + 0.171134i) q^{83} +(-4.05012 - 6.39327i) q^{85} +6.56440i q^{86} +(-1.25714 + 1.25714i) q^{88} +13.2340 q^{89} +0.979056 q^{91} +(-3.38459 + 3.38459i) q^{92} -10.5644i q^{94} +(12.6413 + 12.6413i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 4 q^{13} + 8 q^{14} - 8 q^{16} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 4 q^{25} + 24 q^{29} - 8 q^{31} - 4 q^{35} - 4 q^{37} + 4 q^{40} - 12 q^{43} + 24 q^{44} + 12 q^{47} - 32 q^{50} + 4 q^{52} - 32 q^{53} - 24 q^{55} + 12 q^{58} + 16 q^{59} - 4 q^{62} - 32 q^{65} + 20 q^{67} + 36 q^{73} + 40 q^{74} + 4 q^{77} - 12 q^{82} - 56 q^{83} + 32 q^{85} - 4 q^{88} + 72 q^{89} - 8 q^{92} - 4 q^{97}+O(q^{100}) $ 8 * q - 4 * q^13 + 8 * q^14 - 8 * q^16 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 4 * q^25 + 24 * q^29 - 8 * q^31 - 4 * q^35 - 4 * q^37 + 4 * q^40 - 12 * q^43 + 24 * q^44 + 12 * q^47 - 32 * q^50 + 4 * q^52 - 32 * q^53 - 24 * q^55 + 12 * q^58 + 16 * q^59 - 4 * q^62 - 32 * q^65 + 20 * q^67 + 36 * q^73 + 40 * q^74 + 4 * q^77 - 12 * q^82 - 56 * q^83 + 32 * q^85 - 4 * q^88 + 72 * q^89 - 8 * q^92 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	0.489528	−	2.18183i	0.218924	−	0.975742i
$5$	0.489528	−	2.18183i	0.218924	−	0.975742i
$6$		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
$10$	−1.19663	−	1.88893i	−0.378409	−	0.597333i
$11$		−	1.77786i		−	0.536046i	−0.963412	−	0.268023i	$-0.913630\pi$
$11$		−	1.77786i		−	0.536046i	0.963412	−	0.268023i	$-0.0863704\pi$
$12$		0			0
$13$	0.692297	−	0.692297i	0.192009	−	0.192009i	−0.604555	−	0.796564i	$-0.706649\pi$
$13$	0.692297	−	0.692297i	0.192009	−	0.192009i	0.796564	+	0.604555i	$0.206649\pi$
$14$	1.00000			0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	2.39327	−	2.39327i	0.580453	−	0.580453i	−0.354575	−	0.935028i	$-0.615374\pi$
$17$	2.39327	−	2.39327i	0.580453	−	0.580453i	0.935028	+	0.354575i	$0.115374\pi$
$18$		0			0
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	−2.18183	−	0.489528i	−0.487871	−	0.109462i
$21$		0			0
$22$	−1.25714	−	1.25714i	−0.268023	−	0.268023i
$23$	−3.38459	−	3.38459i	−0.705737	−	0.705737i	0.259899	−	0.965636i	$-0.416311\pi$
$23$	−3.38459	−	3.38459i	−0.705737	−	0.705737i	−0.965636	+	0.259899i	$0.916311\pi$
$24$		0			0
$25$	−4.52072	−	2.13613i	−0.904145	−	0.427226i
$26$		−	0.979056i		−	0.192009i
$27$		0			0
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$	4.42289			0.821310			0.410655	−	0.911791i	$-0.365300\pi$
$29$	4.42289			0.821310			0.410655	+	0.911791i	$0.365300\pi$
$30$		0			0
$31$	−5.77786			−1.03774			−0.518868	−	0.854855i	$-0.673646\pi$
$31$	−5.77786			−1.03774			−0.518868	+	0.854855i	$0.673646\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	3.38459i		−	0.580453i
$35$	1.88893	−	1.19663i	0.319288	−	0.202268i
$36$		0			0
$37$	5.91399	+	5.91399i	0.972255	+	0.972255i	0.999625	−	0.0273707i	$-0.00871345\pi$
$37$	5.91399	+	5.91399i	0.972255	+	0.972255i	−0.0273707	+	0.999625i	$0.508713\pi$
$38$		0			0
$39$		0			0
$40$	−1.88893	+	1.19663i	−0.298666	+	0.189205i
$41$			0.807922i			0.126176i	0.998008	+	0.0630881i	$0.0200949\pi$
$41$			0.807922i			0.126176i	−0.998008	+	0.0630881i	$0.979905\pi$
$42$		0			0
$43$	−4.64173	+	4.64173i	−0.707858	+	0.707858i	−0.966084	−	0.258227i	$-0.916862\pi$
$43$	−4.64173	+	4.64173i	−0.707858	+	0.707858i	0.258227	+	0.966084i	$0.416862\pi$
$44$	−1.77786			−0.268023
$45$		0			0
$46$	−4.78654			−0.705737
$47$	7.47016	−	7.47016i	1.08964	−	1.08964i	0.0940694	−	0.995566i	$-0.470012\pi$
$47$	7.47016	−	7.47016i	1.08964	−	1.08964i	0.995566	−	0.0940694i	$-0.0299876\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$	−4.70711	+	1.68616i	−0.665685	+	0.238459i
$51$		0			0
$52$	−0.692297	−	0.692297i	−0.0960044	−	0.0960044i
$53$	−3.56484	−	3.56484i	−0.489669	−	0.489669i	0.418533	−	0.908202i	$-0.362544\pi$
$53$	−3.56484	−	3.56484i	−0.489669	−	0.489669i	−0.908202	+	0.418533i	$0.862544\pi$
$54$		0			0
$55$	−3.87899	−	0.870315i	−0.523043	−	0.117353i
$56$		−	1.00000i		−	0.133631i
$57$		0			0
$58$	3.12745	−	3.12745i	0.410655	−	0.410655i
$59$	5.89887			0.767968			0.383984	−	0.923340i	$-0.374552\pi$
$59$	5.89887			0.767968			0.383984	+	0.923340i	$0.374552\pi$
$60$		0			0
$61$	2.39327			0.306427			0.153213	−	0.988193i	$-0.451038\pi$
$61$	2.39327			0.306427			0.153213	+	0.988193i	$0.451038\pi$
$62$	−4.08557	+	4.08557i	−0.518868	+	0.518868i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−1.17157	−	1.84937i	−0.145316	−	0.229386i
$66$		0			0
$67$	−0.641735	−	0.641735i	−0.0784004	−	0.0784004i	0.666819	−	0.745220i	$-0.267655\pi$
$67$	−0.641735	−	0.641735i	−0.0784004	−	0.0784004i	−0.745220	+	0.666819i	$0.767655\pi$
$68$	−2.39327	−	2.39327i	−0.290227	−	0.290227i
$69$		0			0
$70$	0.489528	−	2.18183i	0.0585098	−	0.260778i
$71$			10.6854i			1.26813i	0.773282	+	0.634063i	$0.218614\pi$
$71$			10.6854i			1.26813i	−0.773282	+	0.634063i	$0.781386\pi$
$72$		0			0
$73$	5.70097	−	5.70097i	0.667248	−	0.667248i	−0.289830	−	0.957078i	$-0.593599\pi$
$73$	5.70097	−	5.70097i	0.667248	−	0.667248i	0.957078	+	0.289830i	$0.0935987\pi$
$74$	8.36365			0.972255
$75$		0			0
$76$		0			0
$77$	1.25714	−	1.25714i	0.143264	−	0.143264i
$78$		0			0
$79$			16.3423i			1.83865i	0.393500	+	0.919324i	$0.371264\pi$
$79$			16.3423i			1.83865i	−0.393500	+	0.919324i	$0.628736\pi$
$80$	−0.489528	+	2.18183i	−0.0547309	+	0.243935i
$81$		0			0
$82$	0.571287	+	0.571287i	0.0630881	+	0.0630881i
$83$	0.171134	+	0.171134i	0.0187844	+	0.0187844i	0.716437	−	0.697652i	$-0.245772\pi$
$83$	0.171134	+	0.171134i	0.0187844	+	0.0187844i	−0.697652	+	0.716437i	$0.745772\pi$
$84$		0			0
$85$	−4.05012	−	6.39327i	−0.439298	−	0.693447i
$86$			6.56440i			0.707858i
$87$		0			0
$88$	−1.25714	+	1.25714i	−0.134012	+	0.134012i
$89$	13.2340			1.40280			0.701399	−	0.712769i	$-0.252559\pi$
$89$	13.2340			1.40280			0.701399	+	0.712769i	$0.252559\pi$
$90$		0			0
$91$	0.979056			0.102633
$92$	−3.38459	+	3.38459i	−0.352868	+	0.352868i
$93$		0			0
$94$		−	10.5644i		−	1.08964i
$95$		0			0
$96$		0			0
$97$	12.6413	+	12.6413i	1.28353	+	1.28353i	0.938645	+	0.344884i	$0.112082\pi$
$97$	12.6413	+	12.6413i	1.28353	+	1.28353i	0.344884	+	0.938645i	$0.387918\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$		0			0
$100$	−2.13613	+	4.52072i	−0.213613	+	0.452072i
$101$			12.6778i			1.26149i	0.775991	+	0.630744i	$0.217250\pi$
$101$			12.6778i			1.26149i	−0.775991	+	0.630744i	$0.782750\pi$
$102$		0			0
$103$	7.43472	−	7.43472i	0.732565	−	0.732565i	−0.238563	−	0.971127i	$-0.576676\pi$
$103$	7.43472	−	7.43472i	0.732565	−	0.732565i	0.971127	+	0.238563i	$0.0766762\pi$
$104$	−0.979056			−0.0960044
$105$		0			0
$106$	−5.04145			−0.489669
$107$	−13.5138	+	13.5138i	−1.30643	+	1.30643i	−0.382461	+	0.923972i	$0.624923\pi$
$107$	−13.5138	+	13.5138i	−1.30643	+	1.30643i	−0.923972	+	0.382461i	$0.875077\pi$
$108$		0			0
$109$		−	3.30082i		−	0.316161i	−0.987426	−	0.158081i	$-0.949469\pi$
$109$		−	3.30082i		−	0.316161i	0.987426	−	0.158081i	$-0.0505306\pi$
$110$	−3.35827	+	2.12745i	−0.320198	+	0.202845i
$111$		0			0
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	−5.84937	−	5.84937i	−0.550263	−	0.550263i	0.376254	−	0.926517i	$-0.377212\pi$
$113$	−5.84937	−	5.84937i	−0.550263	−	0.550263i	−0.926517	+	0.376254i	$0.877212\pi$
$114$		0			0
$115$	−9.04145	+	5.72774i	−0.843119	+	0.534115i
$116$		−	4.42289i		−	0.410655i
$117$		0			0
$118$	4.17113	−	4.17113i	0.383984	−	0.383984i
$119$	3.38459			0.310265
$120$		0			0
$121$	7.83920			0.712654
$122$	1.69230	−	1.69230i	0.153213	−	0.153213i
$123$		0			0
$124$			5.77786i			0.518868i
$125$	−6.87368	+	8.81774i	−0.614801	+	0.788682i
$126$		0			0
$127$	−0.615405	−	0.615405i	−0.0546084	−	0.0546084i	0.679275	−	0.733884i	$-0.262294\pi$
$127$	−0.615405	−	0.615405i	−0.0546084	−	0.0546084i	−0.733884	+	0.679275i	$0.762294\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−2.13613	−	0.479276i	−0.187351	−	0.0420352i
$131$			6.52717i			0.570281i	0.958486	+	0.285141i	$0.0920403\pi$
$131$			6.52717i			0.570281i	−0.958486	+	0.285141i	$0.907960\pi$
$132$		0			0
$133$		0			0
$134$	−0.907550			−0.0784004
$135$		0			0
$136$	−3.38459			−0.290227
$137$	0.192517	−	0.192517i	0.0164478	−	0.0164478i	−0.698835	−	0.715283i	$-0.746298\pi$
$137$	0.192517	−	0.192517i	0.0164478	−	0.0164478i	0.715283	+	0.698835i	$0.246298\pi$
$138$		0			0
$139$			14.8694i			1.26121i	0.776104	+	0.630605i	$0.217193\pi$
$139$			14.8694i			1.26121i	−0.776104	+	0.630605i	$0.782807\pi$
$140$	−1.19663	−	1.88893i	−0.101134	−	0.159644i
$141$		0			0
$142$	7.55573	+	7.55573i	0.634063	+	0.634063i
$143$	−1.23081	−	1.23081i	−0.102926	−	0.102926i
$144$		0			0
$145$	2.16513	−	9.64997i	0.179804	−	0.801386i
$146$		−	8.06239i		−	0.667248i
$147$		0			0
$148$	5.91399	−	5.91399i	0.486127	−	0.486127i
$149$	−20.6467			−1.69144			−0.845721	−	0.533625i	$-0.820829\pi$
$149$	−20.6467			−1.69144			−0.845721	+	0.533625i	$0.820829\pi$
$150$		0			0
$151$	6.01735			0.489685			0.244843	−	0.969563i	$-0.421264\pi$
$151$	6.01735			0.489685			0.244843	+	0.969563i	$0.421264\pi$
$152$		0			0
$153$		0			0
$154$		−	1.77786i		−	0.143264i
$155$	−2.82843	+	12.6063i	−0.227185	+	1.01256i
$156$		0			0
$157$	−0.608522	−	0.608522i	−0.0485654	−	0.0485654i	0.682407	−	0.730972i	$-0.260933\pi$
$157$	−0.608522	−	0.608522i	−0.0485654	−	0.0485654i	−0.730972	+	0.682407i	$0.760933\pi$
$158$	11.5557	+	11.5557i	0.919324	+	0.919324i
$159$		0			0
$160$	1.19663	+	1.88893i	0.0946023	+	0.149333i
$161$		−	4.78654i		−	0.377232i
$162$		0			0
$163$	6.12745	−	6.12745i	0.479939	−	0.479939i	−0.425173	−	0.905112i	$-0.639787\pi$
$163$	6.12745	−	6.12745i	0.479939	−	0.479939i	0.905112	+	0.425173i	$0.139787\pi$
$164$	0.807922			0.0630881
$165$		0			0
$166$	0.242020			0.0187844
$167$	6.18669	−	6.18669i	0.478741	−	0.478741i	−0.425988	−	0.904729i	$-0.640073\pi$
$167$	6.18669	−	6.18669i	0.478741	−	0.478741i	0.904729	+	0.425988i	$0.140073\pi$
$168$		0			0
$169$			12.0414i			0.926265i
$170$	−7.38459	−	1.65685i	−0.566373	−	0.127075i
$171$		0			0
$172$	4.64173	+	4.64173i	0.353929	+	0.353929i
$173$	−15.7720	−	15.7720i	−1.19913	−	1.19913i	−0.974429	−	0.224697i	$-0.927861\pi$
$173$	−15.7720	−	15.7720i	−1.19913	−	1.19913i	−0.224697	−	0.974429i	$-0.572139\pi$
$174$		0			0
$175$	−1.68616	−	4.70711i	−0.127462	−	0.355824i
$176$			1.77786i			0.134012i
$177$		0			0
$178$	9.35783	−	9.35783i	0.701399	−	0.701399i
$179$	−3.87899			−0.289929			−0.144965	−	0.989437i	$-0.546307\pi$
$179$	−3.87899			−0.289929			−0.144965	+	0.989437i	$0.546307\pi$
$180$		0			0
$181$	23.6896			1.76084			0.880418	−	0.474198i	$-0.157262\pi$
$181$	23.6896			1.76084			0.880418	+	0.474198i	$0.157262\pi$
$182$	0.692297	−	0.692297i	0.0513165	−	0.0513165i
$183$		0			0
$184$			4.78654i			0.352868i
$185$	15.7984	−	10.0082i	1.16152	−	0.735820i
$186$		0			0
$187$	−4.25491	−	4.25491i	−0.311150	−	0.311150i
$188$	−7.47016	−	7.47016i	−0.544818	−	0.544818i
$189$		0			0
$190$		0			0
$191$			23.4720i			1.69837i	0.528095	+	0.849185i	$0.322907\pi$
$191$			23.4720i			1.69837i	−0.528095	+	0.849185i	$0.677093\pi$
$192$		0			0
$193$	18.1288	−	18.1288i	1.30494	−	1.30494i	0.379921	−	0.925019i	$-0.375951\pi$
$193$	18.1288	−	18.1288i	1.30494	−	1.30494i	0.925019	−	0.379921i	$-0.124049\pi$
$194$	17.8775			1.28353
$195$		0			0
$196$	1.00000			0.0714286
$197$	−9.58535	+	9.58535i	−0.682928	+	0.682928i	−0.960659	−	0.277731i	$-0.910418\pi$
$197$	−9.58535	+	9.58535i	−0.682928	+	0.682928i	0.277731	+	0.960659i	$0.410418\pi$
$198$		0			0
$199$		−	2.46416i		−	0.174679i	−0.996179	−	0.0873397i	$-0.972163\pi$
$199$		−	2.46416i		−	0.174679i	0.996179	−	0.0873397i	$-0.0278366\pi$
$200$	1.68616	+	4.70711i	0.119230	+	0.332843i
$201$		0			0
$202$	8.96456	+	8.96456i	0.630744	+	0.630744i
$203$	3.12745	+	3.12745i	0.219504	+	0.219504i
$204$		0			0
$205$	1.76274	+	0.395501i	0.123115	+	0.0276230i
$206$		−	10.5143i		−	0.732565i
$207$		0			0
$208$	−0.692297	+	0.692297i	−0.0480022	+	0.0480022i
$209$		0			0
$210$		0			0
$211$	−5.57308			−0.383667			−0.191833	−	0.981428i	$-0.561443\pi$
$211$	−5.57308			−0.383667			−0.191833	+	0.981428i	$0.561443\pi$
$212$	−3.56484	+	3.56484i	−0.244834	+	0.244834i
$213$		0			0
$214$			19.1115i			1.30643i
$215$	7.85519	+	12.3997i	0.535720	+	0.845653i
$216$		0			0
$217$	−4.08557	−	4.08557i	−0.277346	−	0.277346i
$218$	−2.33403	−	2.33403i	−0.158081	−	0.158081i
$219$		0			0
$220$	−0.870315	+	3.87899i	−0.0586766	+	0.261521i
$221$		−	3.31371i		−	0.222904i
$222$		0			0
$223$	−14.6854	+	14.6854i	−0.983408	+	0.983408i	−0.999865	−	0.0164565i	$-0.994761\pi$
$223$	−14.6854	+	14.6854i	−0.983408	+	0.983408i	0.0164565	+	0.999865i	$0.494761\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	−8.27226			−0.550263
$227$	19.5557	−	19.5557i	1.29796	−	1.29796i	0.368221	−	0.929738i	$-0.379967\pi$
$227$	19.5557	−	19.5557i	1.29796	−	1.29796i	0.929738	−	0.368221i	$-0.120033\pi$
$228$		0			0
$229$		−	24.3622i		−	1.60990i	−0.593345	−	0.804948i	$-0.702193\pi$
$229$		−	24.3622i		−	1.60990i	0.593345	−	0.804948i	$-0.297807\pi$
$230$	−2.34315	+	10.4434i	−0.154502	+	0.688617i
$231$		0			0
$232$	−3.12745	−	3.12745i	−0.205327	−	0.205327i
$233$	−14.7692	−	14.7692i	−0.967562	−	0.967562i	0.0319284	−	0.999490i	$-0.489835\pi$
$233$	−14.7692	−	14.7692i	−0.967562	−	0.967562i	−0.999490	+	0.0319284i	$0.989835\pi$
$234$		0			0
$235$	−12.6417	−	19.9554i	−0.824656	−	1.30175i
$236$		−	5.89887i		−	0.383984i
$237$		0			0
$238$	2.39327	−	2.39327i	0.155133	−	0.155133i
$239$	−1.47283			−0.0952695			−0.0476348	−	0.998865i	$-0.515168\pi$
$239$	−1.47283			−0.0952695			−0.0476348	+	0.998865i	$0.515168\pi$
$240$		0			0
$241$	−21.5557			−1.38853			−0.694263	−	0.719721i	$-0.744270\pi$
$241$	−21.5557			−1.38853			−0.694263	+	0.719721i	$0.744270\pi$
$242$	5.54315	−	5.54315i	0.356327	−	0.356327i
$243$		0			0
$244$		−	2.39327i		−	0.153213i
$245$	2.18183	+	0.489528i	0.139392	+	0.0312748i
$246$		0			0
$247$		0			0
$248$	4.08557	+	4.08557i	0.259434	+	0.259434i
$249$		0			0
$250$	1.37465	+	11.0955i	0.0869406	+	0.701742i
$251$			2.68541i			0.169502i	0.996402	+	0.0847509i	$0.0270095\pi$
$251$			2.68541i			0.169502i	−0.996402	+	0.0847509i	$0.972991\pi$
$252$		0			0
$253$	−6.01735	+	6.01735i	−0.378308	+	0.378308i
$254$	−0.870315			−0.0546084
$255$		0			0
$256$	1.00000			0.0625000
$257$	10.9873	−	10.9873i	0.685368	−	0.685368i	−0.275836	−	0.961205i	$-0.588955\pi$
$257$	10.9873	−	10.9873i	0.685368	−	0.685368i	0.961205	+	0.275836i	$0.0889547\pi$
$258$		0			0
$259$			8.36365i			0.519692i
$260$	−1.84937	+	1.17157i	−0.114693	+	0.0726579i
$261$		0			0
$262$	4.61541	+	4.61541i	0.285141	+	0.285141i
$263$	7.92911	+	7.92911i	0.488930	+	0.488930i	0.907969	−	0.419038i	$-0.137633\pi$
$263$	7.92911	+	7.92911i	0.488930	+	0.488930i	−0.419038	+	0.907969i	$0.637633\pi$
$264$		0			0
$265$	−9.52296	+	6.03277i	−0.584990	+	0.370590i
$266$		0			0
$267$		0			0
$268$	−0.641735	+	0.641735i	−0.0392002	+	0.0392002i
$269$	−7.26420			−0.442906			−0.221453	−	0.975171i	$-0.571080\pi$
$269$	−7.26420			−0.442906			−0.221453	+	0.975171i	$0.571080\pi$
$270$		0			0
$271$	−17.5756			−1.06764			−0.533821	−	0.845597i	$-0.679244\pi$
$271$	−17.5756			−1.06764			−0.533821	+	0.845597i	$0.679244\pi$
$272$	−2.39327	+	2.39327i	−0.145113	+	0.145113i
$273$		0			0
$274$		−	0.272260i		−	0.0164478i
$275$	−3.79775	+	8.03724i	−0.229013	+	0.484664i
$276$		0			0
$277$	−9.81287	−	9.81287i	−0.589598	−	0.589598i	0.347924	−	0.937523i	$-0.386887\pi$
$277$	−9.81287	−	9.81287i	−0.589598	−	0.589598i	−0.937523	+	0.347924i	$0.886887\pi$
$278$	10.5143	+	10.5143i	0.630605	+	0.630605i
$279$		0			0
$280$	−2.18183	−	0.489528i	−0.130389	−	0.0292549i
$281$		−	12.5849i		−	0.750753i	−0.926872	−	0.375376i	$-0.877513\pi$
$281$		−	12.5849i		−	0.750753i	0.926872	−	0.375376i	$-0.122487\pi$
$282$		0			0
$283$	4.69918	−	4.69918i	0.279337	−	0.279337i	−0.553507	−	0.832844i	$-0.686711\pi$
$283$	4.69918	−	4.69918i	0.279337	−	0.279337i	0.832844	+	0.553507i	$0.186711\pi$
$284$	10.6854			0.634063
$285$		0			0
$286$	−1.74063			−0.102926
$287$	−0.571287	+	0.571287i	−0.0337220	+	0.0337220i
$288$		0			0
$289$			5.54452i			0.326148i
$290$	−5.29258	−	8.35454i	−0.310791	−	0.490595i
$291$		0			0
$292$	−5.70097	−	5.70097i	−0.333624	−	0.333624i
$293$	−3.39866	−	3.39866i	−0.198552	−	0.198552i	0.600827	−	0.799379i	$-0.294838\pi$
$293$	−3.39866	−	3.39866i	−0.198552	−	0.198552i	−0.799379	+	0.600827i	$0.794838\pi$
$294$		0			0
$295$	2.88767	−	12.8703i	0.168126	−	0.749339i
$296$		−	8.36365i		−	0.486127i
$297$		0			0
$298$	−14.5994	+	14.5994i	−0.845721	+	0.845721i
$299$	−4.68629			−0.271015
$300$		0			0
$301$	−6.56440			−0.378366
$302$	4.25491	−	4.25491i	0.244843	−	0.244843i
$303$		0			0
$304$		0			0
$305$	1.17157	−	5.22170i	0.0670841	−	0.298993i
$306$		0			0
$307$	−15.5557	−	15.5557i	−0.887812	−	0.887812i	0.106500	−	0.994313i	$-0.466035\pi$
$307$	−15.5557	−	15.5557i	−0.887812	−	0.887812i	−0.994313	+	0.106500i	$0.966035\pi$
$308$	−1.25714	−	1.25714i	−0.0716322	−	0.0716322i
$309$		0			0
$310$	6.91399	+	10.9140i	0.392688	+	0.619873i
$311$		−	0.773651i		−	0.0438697i	−0.999759	−	0.0219349i	$-0.993017\pi$
$311$		−	0.773651i		−	0.0438697i	0.999759	−	0.0219349i	$-0.00698264\pi$
$312$		0			0
$313$	−11.8548	+	11.8548i	−0.670070	+	0.670070i	−0.957732	−	0.287662i	$-0.907122\pi$
$313$	−11.8548	+	11.8548i	−0.670070	+	0.670070i	0.287662	+	0.957732i	$0.407122\pi$
$314$	−0.860580			−0.0485654
$315$		0			0
$316$	16.3423			0.919324
$317$	0.00911383	−	0.00911383i	0.000511884	−	0.000511884i	−0.706851	−	0.707363i	$-0.749885\pi$
$317$	0.00911383	−	0.00911383i	0.000511884	−	0.000511884i	0.707363	+	0.706851i	$0.249885\pi$
$318$		0			0
$319$		−	7.86330i		−	0.440260i
$320$	2.18183	+	0.489528i	0.121968	+	0.0273655i
$321$		0			0
$322$	−3.38459	−	3.38459i	−0.188616	−	0.188616i
$323$		0			0
$324$		0			0
$325$	−4.60852	+	1.65085i	−0.255635	+	0.0915726i
$326$		−	8.66553i		−	0.479939i
$327$		0			0
$328$	0.571287	−	0.571287i	0.0315441	−	0.0315441i
$329$	10.5644			0.582434
$330$		0			0
$331$	−23.7977			−1.30804			−0.654021	−	0.756476i	$-0.726919\pi$
$331$	−23.7977			−1.30804			−0.654021	+	0.756476i	$0.726919\pi$
$332$	0.171134	−	0.171134i	0.00939221	−	0.00939221i
$333$		0			0
$334$		−	8.74930i		−	0.478741i
$335$	−1.71430	+	1.08601i	−0.0936622	+	0.0593348i
$336$		0			0
$337$	−0.828866	−	0.828866i	−0.0451512	−	0.0451512i	0.684171	−	0.729322i	$-0.260164\pi$
$337$	−0.828866	−	0.828866i	−0.0451512	−	0.0451512i	−0.729322	+	0.684171i	$0.760164\pi$
$338$	8.51459	+	8.51459i	0.463133	+	0.463133i
$339$		0			0
$340$	−6.39327	+	4.05012i	−0.346724	+	0.219649i
$341$			10.2723i			0.556274i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	6.56440			0.353929
$345$		0			0
$346$	−22.3050			−1.19913
$347$	5.17157	−	5.17157i	0.277625	−	0.277625i	−0.554535	−	0.832160i	$-0.687104\pi$
$347$	5.17157	−	5.17157i	0.277625	−	0.277625i	0.832160	+	0.554535i	$0.187104\pi$
$348$		0			0
$349$			4.20837i			0.225269i	0.993636	+	0.112634i	$0.0359289\pi$
$349$			4.20837i			0.225269i	−0.993636	+	0.112634i	$0.964071\pi$
$350$	−4.52072	−	2.13613i	−0.241643	−	0.114181i
$351$		0			0
$352$	1.25714	+	1.25714i	0.0670058	+	0.0670058i
$353$	2.22214	+	2.22214i	0.118272	+	0.118272i	0.763766	−	0.645493i	$-0.223348\pi$
$353$	2.22214	+	2.22214i	0.118272	+	0.118272i	−0.645493	+	0.763766i	$0.723348\pi$
$354$		0			0
$355$	23.3137	+	5.23081i	1.23736	+	0.277623i
$356$		−	13.2340i		−	0.701399i
$357$		0			0
$358$	−2.74286	+	2.74286i	−0.144965	+	0.144965i
$359$	−22.7692			−1.20171			−0.600856	−	0.799357i	$-0.705173\pi$
$359$	−22.7692			−1.20171			−0.600856	+	0.799357i	$0.705173\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$	16.7511	−	16.7511i	0.880418	−	0.880418i
$363$		0			0
$364$		−	0.979056i		−	0.0513165i
$365$	−9.64774	−	15.2293i	−0.504986	−	0.797139i
$366$		0			0
$367$	2.13836	+	2.13836i	0.111622	+	0.111622i	0.760712	−	0.649090i	$-0.224850\pi$
$367$	2.13836	+	2.13836i	0.111622	+	0.111622i	−0.649090	+	0.760712i	$0.724850\pi$
$368$	3.38459	+	3.38459i	0.176434	+	0.176434i
$369$		0			0
$370$	4.09424	−	18.2480i	0.212850	−	0.948670i
$371$		−	5.04145i		−	0.261739i
$372$		0			0
$373$	13.0263	−	13.0263i	0.674478	−	0.674478i	−0.284267	−	0.958745i	$-0.591750\pi$
$373$	13.0263	−	13.0263i	0.674478	−	0.674478i	0.958745	+	0.284267i	$0.0917503\pi$
$374$	−6.01735			−0.311150
$375$		0			0
$376$	−10.5644			−0.544818
$377$	3.06195	−	3.06195i	0.157699	−	0.157699i
$378$		0			0
$379$			27.4011i			1.40750i	0.710449	+	0.703749i	$0.248492\pi$
$379$			27.4011i			1.40750i	−0.710449	+	0.703749i	$0.751508\pi$
$380$		0			0
$381$		0			0
$382$	16.5972	+	16.5972i	0.849185	+	0.849185i
$383$	−17.6715	−	17.6715i	−0.902973	−	0.902973i	0.0927190	−	0.995692i	$-0.470444\pi$
$383$	−17.6715	−	17.6715i	−0.902973	−	0.902973i	−0.995692	+	0.0927190i	$0.970444\pi$
$384$		0			0
$385$	−2.12745	−	3.35827i	−0.108425	−	0.171153i
$386$		−	25.6380i		−	1.30494i
$387$		0			0
$388$	12.6413	−	12.6413i	0.641765	−	0.641765i
$389$	−15.8356			−0.802897			−0.401449	−	0.915882i	$-0.631493\pi$
$389$	−15.8356			−0.802897			−0.401449	+	0.915882i	$0.631493\pi$
$390$		0			0
$391$	−16.2005			−0.819294
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$		0			0
$394$			13.5557i			0.682928i
$395$	35.6560	+	8.00000i	1.79405	+	0.402524i
$396$		0			0
$397$	−14.5575	−	14.5575i	−0.730621	−	0.730621i	0.240122	−	0.970743i	$-0.422813\pi$
$397$	−14.5575	−	14.5575i	−0.730621	−	0.730621i	−0.970743	+	0.240122i	$0.922813\pi$
$398$	−1.74242	−	1.74242i	−0.0873397	−	0.0873397i
$399$		0			0
$400$	4.52072	+	2.13613i	0.226036	+	0.106806i
$401$		−	9.78102i		−	0.488441i	−0.969720	−	0.244220i	$-0.921468\pi$
$401$		−	9.78102i		−	0.488441i	0.969720	−	0.244220i	$-0.0785320\pi$
$402$		0			0
$403$	−4.00000	+	4.00000i	−0.199254	+	0.199254i
$404$	12.6778			0.630744
$405$		0			0
$406$	4.42289			0.219504
$407$	10.5143	−	10.5143i	0.521174	−	0.521174i
$408$		0			0
$409$		−	10.3907i		−	0.513789i	−0.966439	−	0.256894i	$-0.917301\pi$
$409$		−	10.3907i		−	0.513789i	0.966439	−	0.256894i	$-0.0826993\pi$
$410$	1.52611	−	0.966788i	0.0753692	−	0.0477462i
$411$		0			0
$412$	−7.43472	−	7.43472i	−0.366282	−	0.366282i
$413$	4.17113	+	4.17113i	0.205248	+	0.205248i
$414$		0			0
$415$	0.457160	−	0.289610i	0.0224411	−	0.0142164i
$416$			0.979056i			0.0480022i
$417$		0			0
$418$		0			0
$419$	−32.8521			−1.60493			−0.802465	−	0.596700i	$-0.796478\pi$
$419$	−32.8521			−1.60493			−0.802465	+	0.596700i	$0.796478\pi$
$420$		0			0
$421$	33.6560			1.64029			0.820146	−	0.572154i	$-0.193892\pi$
$421$	33.6560			1.64029			0.820146	+	0.572154i	$0.193892\pi$
$422$	−3.94076	+	3.94076i	−0.191833	+	0.191833i
$423$		0			0
$424$			5.04145i			0.244834i
$425$	−15.9316	+	5.70698i	−0.772798	+	0.276829i
$426$		0			0
$427$	1.69230	+	1.69230i	0.0818960	+	0.0818960i
$428$	13.5138	+	13.5138i	0.653216	+	0.653216i
$429$		0			0
$430$	14.3224	+	3.21346i	0.690687	+	0.154967i
$431$		−	28.4260i		−	1.36923i	−0.728903	−	0.684617i	$-0.759969\pi$
$431$		−	28.4260i		−	1.36923i	0.728903	−	0.684617i	$-0.240031\pi$
$432$		0			0
$433$	−8.84355	+	8.84355i	−0.424994	+	0.424994i	−0.886919	−	0.461925i	$-0.847159\pi$
$433$	−8.84355	+	8.84355i	−0.424994	+	0.424994i	0.461925	+	0.886919i	$0.347159\pi$
$434$	−5.77786			−0.277346
$435$		0			0
$436$	−3.30082			−0.158081
$437$		0			0
$438$		0			0
$439$		−	0.481506i		−	0.0229810i	−0.999934	−	0.0114905i	$-0.996342\pi$
$439$		−	0.481506i		−	0.0229810i	0.999934	−	0.0114905i	$-0.00365763\pi$
$440$	2.12745	+	3.35827i	0.101422	+	0.160099i
$441$		0			0
$442$	−2.34315	−	2.34315i	−0.111452	−	0.111452i
$443$	15.8570	+	15.8570i	0.753388	+	0.753388i	0.975110	−	0.221722i	$-0.0711677\pi$
$443$	15.8570	+	15.8570i	0.753388	+	0.753388i	−0.221722	+	0.975110i	$0.571168\pi$
$444$		0			0
$445$	6.47840	−	28.8742i	0.307106	−	1.36877i
$446$			20.7683i			0.983408i
$447$		0			0
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$	31.8986			1.50539			0.752694	−	0.658370i	$-0.228754\pi$
$449$	31.8986			1.50539			0.752694	+	0.658370i	$0.228754\pi$
$450$		0			0
$451$	1.43638			0.0676363
$452$	−5.84937	+	5.84937i	−0.275131	+	0.275131i
$453$		0			0
$454$		−	27.6560i		−	1.29796i
$455$	0.479276	−	2.13613i	0.0224688	−	0.100143i
$456$		0			0
$457$	20.5557	+	20.5557i	0.961556	+	0.961556i	0.999288	−	0.0377315i	$-0.0120132\pi$
$457$	20.5557	+	20.5557i	0.961556	+	0.961556i	−0.0377315	+	0.999288i	$0.512013\pi$
$458$	−17.2266	−	17.2266i	−0.804948	−	0.804948i
$459$		0			0
$460$	5.72774	+	9.04145i	0.267057	+	0.421560i
$461$			35.9849i			1.67599i	0.545682	+	0.837993i	$0.316271\pi$
$461$			35.9849i			1.67599i	−0.545682	+	0.837993i	$0.683729\pi$
$462$		0			0
$463$	−12.8703	+	12.8703i	−0.598134	+	0.598134i	−0.939816	−	0.341682i	$-0.889004\pi$
$463$	−12.8703	+	12.8703i	−0.598134	+	0.598134i	0.341682	+	0.939816i	$0.389004\pi$
$464$	−4.42289			−0.205327
$465$		0			0
$466$	−20.8868			−0.967562
$467$	−0.531630	+	0.531630i	−0.0246009	+	0.0246009i	−0.719300	−	0.694699i	$-0.755537\pi$
$467$	−0.531630	+	0.531630i	−0.0246009	+	0.0246009i	0.694699	+	0.719300i	$0.255537\pi$
$468$		0			0
$469$		−	0.907550i		−	0.0419068i
$470$	−23.0497	−	5.17157i	−1.06320	−	0.238547i
$471$		0			0
$472$	−4.17113	−	4.17113i	−0.191992	−	0.191992i
$473$	8.25237	+	8.25237i	0.379445	+	0.379445i
$474$		0			0
$475$		0			0
$476$		−	3.38459i		−	0.155133i
$477$		0			0
$478$	−1.04145	+	1.04145i	−0.0476348	+	0.0476348i
$479$	−23.0588			−1.05358			−0.526792	−	0.849994i	$-0.676605\pi$
$479$	−23.0588			−1.05358			−0.526792	+	0.849994i	$0.676605\pi$
$480$		0			0
$481$	8.18848			0.373363
$482$	−15.2422	+	15.2422i	−0.694263	+	0.694263i
$483$		0			0
$484$		−	7.83920i		−	0.356327i
$485$	33.7694	−	21.3928i	1.53339	−	0.971398i
$486$		0			0
$487$	−15.9291	−	15.9291i	−0.721817	−	0.721817i	0.247158	−	0.968975i	$-0.420503\pi$
$487$	−15.9291	−	15.9291i	−0.721817	−	0.721817i	−0.968975	+	0.247158i	$0.920503\pi$
$488$	−1.69230	−	1.69230i	−0.0766067	−	0.0766067i
$489$		0			0
$490$	1.88893	−	1.19663i	0.0853333	−	0.0540585i
$491$		−	11.3509i		−	0.512261i	−0.966642	−	0.256130i	$-0.917552\pi$
$491$		−	11.3509i		−	0.512261i	0.966642	−	0.256130i	$-0.0824477\pi$
$492$		0			0
$493$	10.5852	−	10.5852i	0.476732	−	0.476732i
$494$		0			0
$495$		0			0
$496$	5.77786			0.259434
$497$	−7.55573	+	7.55573i	−0.338921	+	0.338921i
$498$		0			0
$499$		−	20.6319i		−	0.923610i	−0.886982	−	0.461805i	$-0.847202\pi$
$499$		−	20.6319i		−	0.923610i	0.886982	−	0.461805i	$-0.152798\pi$
$500$	8.81774	+	6.87368i	0.394341	+	0.307400i
$501$		0			0
$502$	1.89887	+	1.89887i	0.0847509	+	0.0847509i
$503$	21.2982	+	21.2982i	0.949638	+	0.949638i	0.998791	−	0.0491536i	$-0.0156524\pi$
$503$	21.2982	+	21.2982i	0.949638	+	0.949638i	−0.0491536	+	0.998791i	$0.515652\pi$
$504$		0			0
$505$	27.6607	+	6.20614i	1.23089	+	0.276170i
$506$			8.50982i			0.378308i
$507$		0			0
$508$	−0.615405	+	0.615405i	−0.0273042	+	0.0273042i
$509$	−8.13328			−0.360501			−0.180251	−	0.983621i	$-0.557691\pi$
$509$	−8.13328			−0.360501			−0.180251	+	0.983621i	$0.557691\pi$
$510$		0			0
$511$	8.06239			0.356659
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	15.5384i		−	0.685368i
$515$	−12.5818	−	19.8608i	−0.554418	−	0.875170i
$516$		0			0
$517$	−13.2809	−	13.2809i	−0.584095	−	0.584095i
$518$	5.91399	+	5.91399i	0.259846	+	0.259846i
$519$		0			0
$520$	−0.479276	+	2.13613i	−0.0210176	+	0.0936755i
$521$			19.2331i			0.842617i	0.906917	+	0.421308i	$0.138429\pi$
$521$			19.2331i			0.842617i	−0.906917	+	0.421308i	$0.861571\pi$
$522$		0			0
$523$	−3.22635	+	3.22635i	−0.141078	+	0.141078i	−0.774119	−	0.633040i	$-0.781807\pi$
$523$	−3.22635	+	3.22635i	−0.141078	+	0.141078i	0.633040	+	0.774119i	$0.281807\pi$
$524$	6.52717			0.285141
$525$		0			0
$526$	11.2135			0.488930
$527$	−13.8280	+	13.8280i	−0.602357	+	0.602357i
$528$		0			0
$529$		−	0.0890385i		−	0.00387124i
$530$	−2.46793	+	10.9996i	−0.107200	+	0.477790i
$531$		0			0
$532$		0			0
$533$	0.559322	+	0.559322i	0.0242269	+	0.0242269i
$534$		0			0
$535$	22.8694	+	36.1002i	0.988732	+	1.56075i
$536$			0.907550i			0.0392002i
$537$		0			0
$538$	−5.13657	+	5.13657i	−0.221453	+	0.221453i
$539$	1.77786			0.0765780
$540$		0			0
$541$	−12.9412			−0.556386			−0.278193	−	0.960525i	$-0.589735\pi$
$541$	−12.9412			−0.556386			−0.278193	+	0.960525i	$0.589735\pi$
$542$	−12.4278	+	12.4278i	−0.533821	+	0.533821i
$543$		0			0
$544$			3.38459i			0.145113i
$545$	−7.20181	−	1.61584i	−0.308492	−	0.0692152i
$546$		0			0
$547$	7.15601	+	7.15601i	0.305969	+	0.305969i	0.843344	−	0.537375i	$-0.180584\pi$
$547$	7.15601	+	7.15601i	0.305969	+	0.305969i	−0.537375	+	0.843344i	$0.680584\pi$
$548$	−0.192517	−	0.192517i	−0.00822390	−	0.00822390i
$549$		0			0
$550$	2.99777	+	8.36860i	0.127825	+	0.356838i
$551$		0			0
$552$		0			0
$553$	−11.5557	+	11.5557i	−0.491400	+	0.491400i
$554$	−13.8775			−0.589598
$555$		0			0
$556$	14.8694			0.630605
$557$	−19.5648	+	19.5648i	−0.828989	+	0.828989i	−0.987377	−	0.158388i	$-0.949370\pi$
$557$	−19.5648	+	19.5648i	−0.828989	+	0.828989i	0.158388	+	0.987377i	$0.449370\pi$
$558$		0			0
$559$			6.42692i			0.271830i
$560$	−1.88893	+	1.19663i	−0.0798220	+	0.0505671i
$561$		0			0
$562$	−8.89887	−	8.89887i	−0.375376	−	0.375376i
$563$	0.0708861	+	0.0708861i	0.00298749	+	0.00298749i	0.708599	−	0.705611i	$-0.249328\pi$
$563$	0.0708861	+	0.0708861i	0.00298749	+	0.00298749i	−0.705611	+	0.708599i	$0.749328\pi$
$564$		0			0
$565$	−15.6257	+	9.89887i	−0.657380	+	0.416449i
$566$		−	6.64564i		−	0.279337i
$567$		0			0
$568$	7.55573	−	7.55573i	0.317031	−	0.317031i
$569$	20.2232			0.847799			0.423900	−	0.905709i	$-0.360661\pi$
$569$	20.2232			0.847799			0.423900	+	0.905709i	$0.360661\pi$
$570$		0			0
$571$	34.9439			1.46236			0.731179	−	0.682186i	$-0.238971\pi$
$571$	34.9439			1.46236			0.731179	+	0.682186i	$0.238971\pi$
$572$	−1.23081	+	1.23081i	−0.0514628	+	0.0514628i
$573$		0			0
$574$			0.807922i			0.0337220i
$575$	8.07089	+	22.5308i	0.336579	+	0.939597i
$576$		0			0
$577$	32.2853	+	32.2853i	1.34405	+	1.34405i	0.891982	+	0.452071i	$0.149315\pi$
$577$	32.2853	+	32.2853i	1.34405	+	1.34405i	0.452071	+	0.891982i	$0.350685\pi$
$578$	3.92057	+	3.92057i	0.163074	+	0.163074i
$579$		0			0
$580$	−9.64997	−	2.16513i	−0.400693	−	0.0899021i
$581$			0.242020i			0.0100407i
$582$		0			0
$583$	−6.33781	+	6.33781i	−0.262485	+	0.262485i
$584$	−8.06239			−0.333624
$585$		0			0
$586$	−4.80642			−0.198552
$587$	9.40194	−	9.40194i	0.388060	−	0.388060i	−0.485935	−	0.873995i	$-0.661521\pi$
$587$	9.40194	−	9.40194i	0.388060	−	0.388060i	0.873995	+	0.485935i	$0.161521\pi$
$588$		0			0
$589$		0			0
$590$	−7.05880	−	11.1426i	−0.290606	−	0.458733i
$591$		0			0
$592$	−5.91399	−	5.91399i	−0.243064	−	0.243064i
$593$	−0.326416	−	0.326416i	−0.0134043	−	0.0134043i	0.700373	−	0.713777i	$-0.253017\pi$
$593$	−0.326416	−	0.326416i	−0.0134043	−	0.0134043i	−0.713777	+	0.700373i	$0.753017\pi$
$594$		0			0
$595$	1.65685	−	7.38459i	0.0679244	−	0.302739i
$596$			20.6467i			0.845721i
$597$		0			0
$598$	−3.31371	+	3.31371i	−0.135508	+	0.135508i
$599$	−29.1288			−1.19017			−0.595085	−	0.803662i	$-0.702882\pi$
$599$	−29.1288			−1.19017			−0.595085	+	0.803662i	$0.702882\pi$
$600$		0			0
$601$	45.0579			1.83795			0.918975	−	0.394315i	$-0.129018\pi$
$601$	45.0579			1.83795			0.918975	+	0.394315i	$0.129018\pi$
$602$	−4.64173	+	4.64173i	−0.189183	+	0.189183i
$603$		0			0
$604$		−	6.01735i		−	0.244843i
$605$	3.83751	−	17.1038i	0.156017	−	0.695367i
$606$		0			0
$607$	6.68541	+	6.68541i	0.271353	+	0.271353i	0.829645	−	0.558292i	$-0.188543\pi$
$607$	6.68541	+	6.68541i	0.271353	+	0.271353i	−0.558292	+	0.829645i	$0.688543\pi$
$608$		0			0
$609$		0			0
$610$	−2.86387	−	4.52072i	−0.115955	−	0.183039i
$611$		−	10.3431i		−	0.418439i
$612$		0			0
$613$	−20.5112	+	20.5112i	−0.828438	+	0.828438i	−0.987301	−	0.158862i	$-0.949217\pi$
$613$	−20.5112	+	20.5112i	−0.828438	+	0.828438i	0.158862	+	0.987301i	$0.449217\pi$
$614$	−21.9991			−0.887812
$615$		0			0
$616$	−1.77786			−0.0716322
$617$	4.29214	−	4.29214i	0.172795	−	0.172795i	−0.615411	−	0.788206i	$-0.711010\pi$
$617$	4.29214	−	4.29214i	0.172795	−	0.172795i	0.788206	+	0.615411i	$0.211010\pi$
$618$		0			0
$619$		−	8.16755i		−	0.328282i	−0.986437	−	0.164141i	$-0.947515\pi$
$619$		−	8.16755i		−	0.328282i	0.986437	−	0.164141i	$-0.0524851\pi$
$620$	12.6063	+	2.82843i	0.506281	+	0.113592i
$621$		0			0
$622$	−0.547054	−	0.547054i	−0.0219349	−	0.0219349i
$623$	9.35783	+	9.35783i	0.374913	+	0.374913i
$624$		0			0
$625$	15.8739	+	19.3137i	0.634956	+	0.772548i
$626$			16.7652i			0.670070i
$627$		0			0
$628$	−0.608522	+	0.608522i	−0.0242827	+	0.0242827i
$629$	28.3076			1.12870
$630$		0			0
$631$	38.8694			1.54737			0.773684	−	0.633572i	$-0.218412\pi$
$631$	38.8694			1.54737			0.773684	+	0.633572i	$0.218412\pi$
$632$	11.5557	−	11.5557i	0.459662	−	0.459662i
$633$		0			0
$634$		−	0.0128889i		−	0.000511884i
$635$	−1.64397	+	1.04145i	−0.0652388	+	0.0413286i
$636$		0			0
$637$	0.692297	+	0.692297i	0.0274298	+	0.0274298i
$638$	−5.56019	−	5.56019i	−0.220130	−	0.220130i
$639$		0			0
$640$	1.88893	−	1.19663i	0.0746666	−	0.0473011i
$641$			20.0751i			0.792918i	0.918052	+	0.396459i	$0.129761\pi$
$641$			20.0751i			0.792918i	−0.918052	+	0.396459i	$0.870239\pi$
$642$		0			0
$643$	−13.6257	+	13.6257i	−0.537347	+	0.537347i	−0.922749	−	0.385402i	$-0.874063\pi$
$643$	−13.6257	+	13.6257i	−0.537347	+	0.537347i	0.385402	+	0.922749i	$0.374063\pi$
$644$	−4.78654			−0.188616
$645$		0			0
$646$		0			0
$647$	−1.47104	+	1.47104i	−0.0578325	+	0.0578325i	−0.735432	−	0.677599i	$-0.763021\pi$
$647$	−1.47104	+	1.47104i	−0.0578325	+	0.0578325i	0.677599	+	0.735432i	$0.263021\pi$
$648$		0			0
$649$		−	10.4874i		−	0.411666i
$650$	−2.09139	+	4.42604i	−0.0820311	+	0.173604i
$651$		0			0
$652$	−6.12745	−	6.12745i	−0.239970	−	0.239970i
$653$	−4.09647	−	4.09647i	−0.160307	−	0.160307i	0.622396	−	0.782703i	$-0.286160\pi$
$653$	−4.09647	−	4.09647i	−0.160307	−	0.160307i	−0.782703	+	0.622396i	$0.786160\pi$
$654$		0			0
$655$	14.2411	+	3.19523i	0.556448	+	0.124848i
$656$		−	0.807922i		−	0.0315441i
$657$		0			0
$658$	7.47016	−	7.47016i	0.291217	−	0.291217i
$659$	−0.683757			−0.0266354			−0.0133177	−	0.999911i	$-0.504239\pi$
$659$	−0.683757			−0.0266354			−0.0133177	+	0.999911i	$0.504239\pi$
$660$		0			0
$661$	−42.9776			−1.67163			−0.835817	−	0.549009i	$-0.815005\pi$
$661$	−42.9776			−1.67163			−0.835817	+	0.549009i	$0.815005\pi$
$662$	−16.8275	+	16.8275i	−0.654021	+	0.654021i
$663$		0			0
$664$		−	0.242020i		−	0.00939221i
$665$		0			0
$666$		0			0
$667$	−14.9697	−	14.9697i	−0.579629	−	0.579629i
$668$	−6.18669	−	6.18669i	−0.239370	−	0.239370i
$669$		0			0
$670$	−0.444271	+	1.98012i	−0.0171637	+	0.0764985i
$671$		−	4.25491i		−	0.164259i
$672$		0			0
$673$	−24.6569	+	24.6569i	−0.950452	+	0.950452i	−0.998829	−	0.0483773i	$-0.984595\pi$
$673$	−24.6569	+	24.6569i	−0.950452	+	0.950452i	0.0483773	+	0.998829i	$0.484595\pi$
$674$	−1.17219			−0.0451512
$675$		0			0
$676$	12.0414			0.463133
$677$	−31.2343	+	31.2343i	−1.20043	+	1.20043i	−0.226394	+	0.974036i	$0.572694\pi$
$677$	−31.2343	+	31.2343i	−1.20043	+	1.20043i	−0.974036	+	0.226394i	$0.927306\pi$
$678$		0			0
$679$			17.8775i			0.686075i
$680$	−1.65685	+	7.38459i	−0.0635375	+	0.283186i
$681$		0			0
$682$	7.26358	+	7.26358i	0.278137	+	0.278137i
$683$	7.92000	+	7.92000i	0.303050	+	0.303050i	0.842206	−	0.539156i	$-0.181257\pi$
$683$	7.92000	+	7.92000i	0.303050	+	0.303050i	−0.539156	+	0.842206i	$0.681257\pi$
$684$		0			0
$685$	−0.325795	−	0.514280i	−0.0124480	−	0.0196496i
$686$			1.00000i			0.0381802i
$687$		0			0
$688$	4.64173	−	4.64173i	0.176964	−	0.176964i
$689$	−4.93586			−0.188041
$690$		0			0
$691$	22.1227			0.841586			0.420793	−	0.907157i	$-0.361752\pi$
$691$	22.1227			0.841586			0.420793	+	0.907157i	$0.361752\pi$
$692$	−15.7720	+	15.7720i	−0.599563	+	0.599563i
$693$		0			0
$694$		−	7.31371i		−	0.277625i
$695$	32.4425	+	7.27901i	1.23061	+	0.276109i
$696$		0			0
$697$	1.93358	+	1.93358i	0.0732394	+	0.0732394i
$698$	2.97577	+	2.97577i	0.112634	+	0.112634i
$699$		0			0
$700$	−4.70711	+	1.68616i	−0.177912	+	0.0637310i
$701$		−	6.16352i		−	0.232793i	−0.993203	−	0.116396i	$-0.962866\pi$
$701$		−	6.16352i		−	0.232793i	0.993203	−	0.116396i	$-0.0371343\pi$
$702$		0			0
$703$		0			0
$704$	1.77786			0.0670058
$705$		0			0
$706$	3.14257			0.118272
$707$	−8.96456	+	8.96456i	−0.337147	+	0.337147i
$708$		0			0
$709$		−	49.7215i		−	1.86733i	−0.358146	−	0.933666i	$-0.616591\pi$
$709$		−	49.7215i		−	1.86733i	0.358146	−	0.933666i	$-0.383409\pi$
$710$	20.1840	−	12.7865i	0.757493	−	0.479870i
$711$		0			0
$712$	−9.35783	−	9.35783i	−0.350699	−	0.350699i
$713$	19.5557	+	19.5557i	0.732368	+	0.732368i
$714$		0			0
$715$	−3.28793	+	2.08290i	−0.122962	+	0.0778960i
$716$			3.87899i			0.144965i
$717$		0			0
$718$	−16.1002	+	16.1002i	−0.600856	+	0.600856i
$719$	16.9706			0.632895			0.316448	−	0.948610i	$-0.397510\pi$
$719$	16.9706			0.632895			0.316448	+	0.948610i	$0.397510\pi$
$720$		0			0
$721$	10.5143			0.391572
$722$	13.4350	−	13.4350i	0.500000	−	0.500000i
$723$		0			0
$724$		−	23.6896i		−	0.880418i
$725$	−19.9947	−	9.44786i	−0.742583	−	0.350885i
$726$		0			0
$727$	−15.9162	−	15.9162i	−0.590300	−	0.590300i	0.347412	−	0.937712i	$-0.387060\pi$
$727$	−15.9162	−	15.9162i	−0.590300	−	0.590300i	−0.937712	+	0.347412i	$0.887060\pi$
$728$	−0.692297	−	0.692297i	−0.0256582	−	0.0256582i
$729$		0			0
$730$	−17.5907	−	3.94677i	−0.651062	−	0.146076i
$731$			22.2178i			0.821757i
$732$		0			0
$733$	−15.3578	+	15.3578i	−0.567254	+	0.567254i	−0.931358	−	0.364104i	$-0.881375\pi$
$733$	−15.3578	+	15.3578i	−0.567254	+	0.567254i	0.364104	+	0.931358i	$0.381375\pi$
$734$	3.02410			0.111622
$735$		0			0
$736$	4.78654			0.176434
$737$	−1.14092	+	1.14092i	−0.0420262	+	0.0420262i
$738$		0			0
$739$			45.6515i			1.67932i	0.543114	+	0.839659i	$0.317245\pi$
$739$			45.6515i			1.67932i	−0.543114	+	0.839659i	$0.682755\pi$
$740$	−10.0082	−	15.7984i	−0.367910	−	0.580760i
$741$		0			0
$742$	−3.56484	−	3.56484i	−0.130869	−	0.130869i
$743$	5.67508	+	5.67508i	0.208199	+	0.208199i	0.803501	−	0.595303i	$-0.202968\pi$
$743$	5.67508	+	5.67508i	0.208199	+	0.208199i	−0.595303	+	0.803501i	$0.702968\pi$
$744$		0			0
$745$	−10.1071	+	45.0475i	−0.370297	+	1.65041i
$746$		−	18.4220i		−	0.674478i
$747$		0			0
$748$	−4.25491	+	4.25491i	−0.155575	+	0.155575i
$749$	−19.1115			−0.698317
$750$		0			0
$751$	−41.4364			−1.51203			−0.756017	−	0.654552i	$-0.772857\pi$
$751$	−41.4364			−1.51203			−0.756017	+	0.654552i	$0.772857\pi$
$752$	−7.47016	+	7.47016i	−0.272409	+	0.272409i
$753$		0			0
$754$		−	4.33026i		−	0.157699i
$755$	2.94566	−	13.1288i	0.107204	−	0.477806i
$756$		0			0
$757$	−22.4109	−	22.4109i	−0.814539	−	0.814539i	0.170772	−	0.985311i	$-0.445374\pi$
$757$	−22.4109	−	22.4109i	−0.814539	−	0.814539i	−0.985311	+	0.170772i	$0.945374\pi$
$758$	19.3755	+	19.3755i	0.703749	+	0.703749i
$759$		0			0
$760$		0			0
$761$			15.1675i			0.549823i	0.961470	+	0.274911i	$0.0886485\pi$
$761$			15.1675i			0.549823i	−0.961470	+	0.274911i	$0.911351\pi$
$762$		0			0
$763$	2.33403	−	2.33403i	0.0844976	−	0.0844976i
$764$	23.4720			0.849185
$765$		0			0
$766$	−24.9913			−0.902973
$767$	4.08378	−	4.08378i	0.147457	−	0.147457i
$768$		0			0
$769$			19.8686i			0.716481i	0.933629	+	0.358241i	$0.116623\pi$
$769$			19.8686i			0.716481i	−0.933629	+	0.358241i	$0.883377\pi$
$770$	−3.87899	−	0.870315i	−0.139789	−	0.0313640i
$771$		0			0
$772$	−18.1288	−	18.1288i	−0.652470	−	0.652470i
$773$	0.293937	+	0.293937i	0.0105722	+	0.0105722i	0.712373	−	0.701801i	$-0.247620\pi$
$773$	0.293937	+	0.293937i	0.0105722	+	0.0105722i	−0.701801	+	0.712373i	$0.747620\pi$
$774$		0			0
$775$	26.1201	+	12.3423i	0.938263	+	0.443347i
$776$		−	17.8775i		−	0.641765i
$777$		0			0
$778$	−11.1975	+	11.1975i	−0.401449	+	0.401449i
$779$		0			0
$780$		0			0
$781$	18.9972			0.679774
$782$	−11.4555	+	11.4555i	−0.409647	+	0.409647i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$	−1.62558	+	1.02980i	−0.0580194	+	0.0367552i
$786$		0			0
$787$	16.3076	+	16.3076i	0.581302	+	0.581302i	0.935261	−	0.353959i	$-0.115165\pi$
$787$	16.3076	+	16.3076i	0.581302	+	0.581302i	−0.353959	+	0.935261i	$0.615165\pi$
$788$	9.58535	+	9.58535i	0.341464	+	0.341464i
$789$		0			0
$790$	30.8694	−	19.5557i	1.09829	−	0.695762i
$791$		−	8.27226i		−	0.294128i
$792$		0			0
$793$	1.65685	−	1.65685i	0.0588366	−	0.0588366i
$794$	−20.5874			−0.730621
$795$		0			0
$796$	−2.46416			−0.0873397
$797$	22.1562	−	22.1562i	0.784813	−	0.784813i	−0.195826	−	0.980639i	$-0.562739\pi$
$797$	22.1562	−	22.1562i	0.784813	−	0.784813i	0.980639	+	0.195826i	$0.0627388\pi$
$798$		0			0
$799$		−	35.7562i		−	1.26496i
$800$	4.70711	−	1.68616i	0.166421	−	0.0596149i
$801$		0			0
$802$	−6.91622	−	6.91622i	−0.244220	−	0.244220i
$803$	−10.1356	−	10.1356i	−0.357676	−	0.357676i
$804$		0			0
$805$	−10.4434	−	2.34315i	−0.368081	−	0.0825850i
$806$			5.65685i			0.199254i
$807$		0			0
$808$	8.96456	−	8.96456i	0.315372	−	0.315372i
$809$	17.0046			0.597851			0.298926	−	0.954276i	$-0.403372\pi$
$809$	17.0046			0.597851			0.298926	+	0.954276i	$0.403372\pi$
$810$		0			0
$811$	19.7927			0.695015			0.347508	−	0.937677i	$-0.387028\pi$
$811$	19.7927			0.695015			0.347508	+	0.937677i	$0.387028\pi$
$812$	3.12745	−	3.12745i	0.109752	−	0.109752i
$813$		0			0
$814$		−	14.8694i		−	0.521174i
$815$	−10.3695	−	16.3686i	−0.363227	−	0.573367i
$816$		0			0
$817$		0			0
$818$	−7.34736	−	7.34736i	−0.256894	−	0.256894i
$819$		0			0
$820$	0.395501	−	1.76274i	0.0138115	−	0.0615577i
$821$		−	8.89887i		−	0.310573i	−0.987870	−	0.155286i	$-0.950370\pi$
$821$		−	8.89887i		−	0.310573i	0.987870	−	0.155286i	$-0.0496300\pi$
$822$		0			0
$823$	31.0932	−	31.0932i	1.08384	−	1.08384i	0.0876944	−	0.996147i	$-0.472050\pi$
$823$	31.0932	−	31.0932i	1.08384	−	1.08384i	0.996147	−	0.0876944i	$-0.0279499\pi$
$824$	−10.5143			−0.366282
$825$		0			0
$826$	5.89887			0.205248
$827$	−25.5604	+	25.5604i	−0.888822	+	0.888822i	−0.994410	−	0.105588i	$-0.966327\pi$
$827$	−25.5604	+	25.5604i	−0.888822	+	0.888822i	0.105588	+	0.994410i	$0.466327\pi$
$828$		0			0
$829$		−	13.6067i		−	0.472581i	−0.971682	−	0.236291i	$-0.924068\pi$
$829$		−	13.6067i		−	0.472581i	0.971682	−	0.236291i	$-0.0759317\pi$
$830$	0.118476	−	0.528046i	0.00411235	−	0.0183288i
$831$		0			0
$832$	0.692297	+	0.692297i	0.0240011	+	0.0240011i
$833$	2.39327	+	2.39327i	0.0829219	+	0.0829219i
$834$		0			0
$835$	−10.4697	−	16.5268i	−0.362320	−	0.571935i
$836$		0			0
$837$		0			0
$838$	−23.2299	+	23.2299i	−0.802465	+	0.802465i
$839$	45.4002			1.56739			0.783694	−	0.621147i	$-0.213333\pi$
$839$	45.4002			1.56739			0.783694	+	0.621147i	$0.213333\pi$
$840$		0			0
$841$	−9.43806			−0.325450
$842$	23.7984	−	23.7984i	0.820146	−	0.820146i
$843$		0			0
$844$			5.57308i			0.191833i
$845$	26.2723	+	5.89463i	0.903796	+	0.202781i
$846$		0			0
$847$	5.54315	+	5.54315i	0.190465	+	0.190465i
$848$	3.56484	+	3.56484i	0.122417	+	0.122417i
$849$		0			0
$850$	−7.22993	+	15.3008i	−0.247985	+	0.524814i
$851$		−	40.0329i		−	1.37231i
$852$		0			0
$853$	4.62841	−	4.62841i	0.158474	−	0.158474i	−0.623416	−	0.781890i	$-0.714256\pi$
$853$	4.62841	−	4.62841i	0.158474	−	0.158474i	0.781890	+	0.623416i	$0.214256\pi$
$854$	2.39327			0.0818960
$855$		0			0
$856$	19.1115			0.653216
$857$	−23.4218	+	23.4218i	−0.800074	+	0.800074i	−0.983107	−	0.183032i	$-0.941409\pi$
$857$	−23.4218	+	23.4218i	−0.800074	+	0.800074i	0.183032	+	0.983107i	$0.441409\pi$
$858$		0			0
$859$		−	29.8062i		−	1.01697i	−0.861070	−	0.508487i	$-0.830205\pi$
$859$		−	29.8062i		−	1.01697i	0.861070	−	0.508487i	$-0.169795\pi$
$860$	12.3997	−	7.85519i	0.422827	−	0.267860i
$861$		0			0
$862$	−20.1002	−	20.1002i	−0.684617	−	0.684617i
$863$	−12.8868	−	12.8868i	−0.438671	−	0.438671i	0.452893	−	0.891565i	$-0.350392\pi$
$863$	−12.8868	−	12.8868i	−0.438671	−	0.438671i	−0.891565	+	0.452893i	$0.850392\pi$
$864$		0			0
$865$	−42.1327	+	26.6910i	−1.43255	+	0.907521i
$866$			12.5067i			0.424994i
$867$		0			0
$868$	−4.08557	+	4.08557i	−0.138673	+	0.138673i
$869$	29.0543			0.985601
$870$		0			0
$871$	−0.888542			−0.0301071
$872$	−2.33403	+	2.33403i	−0.0790403	+	0.0790403i
$873$		0			0
$874$		0			0
$875$	−11.0955	+	1.37465i	−0.375097	+	0.0464717i
$876$		0			0
$877$	10.6479	+	10.6479i	0.359553	+	0.359553i	0.863648	−	0.504095i	$-0.168174\pi$
$877$	10.6479	+	10.6479i	0.359553	+	0.359553i	−0.504095	+	0.863648i	$0.668174\pi$
$878$	−0.340476	−	0.340476i	−0.0114905	−	0.0114905i
$879$		0			0
$880$	3.87899	+	0.870315i	0.130761	+	0.0293383i
$881$		−	59.0706i		−	1.99014i	−0.0991785	−	0.995070i	$-0.531621\pi$
$881$		−	59.0706i		−	1.99014i	0.0991785	−	0.995070i	$-0.468379\pi$
$882$		0			0
$883$	−14.9269	+	14.9269i	−0.502330	+	0.502330i	−0.912161	−	0.409832i	$-0.865587\pi$
$883$	−14.9269	+	14.9269i	−0.502330	+	0.502330i	0.409832	+	0.912161i	$0.365587\pi$
$884$	−3.31371			−0.111452
$885$		0			0
$886$	22.4252			0.753388
$887$	7.58864	−	7.58864i	0.254802	−	0.254802i	−0.568134	−	0.822936i	$-0.692335\pi$
$887$	7.58864	−	7.58864i	0.254802	−	0.254802i	0.822936	+	0.568134i	$0.192335\pi$
$888$		0			0
$889$		−	0.870315i		−	0.0291894i
$890$	−15.8362	−	24.9981i	−0.530831	−	0.837937i
$891$		0			0
$892$	14.6854	+	14.6854i	0.491704	+	0.491704i
$893$		0			0
$894$		0			0
$895$	−1.89887	+	8.46328i	−0.0634724	+	0.282896i
$896$			1.00000i			0.0334077i
$897$		0			0
$898$	22.5557	−	22.5557i	0.752694	−	0.752694i
$899$	−25.5549			−0.852302
$900$		0			0
$901$	−17.0633			−0.568460
$902$	1.01567	−	1.01567i	0.0338181	−	0.0338181i
$903$		0			0
$904$			8.27226i			0.275131i
$905$	11.5967	−	51.6866i	0.385489	−	1.71812i
$906$		0			0
$907$	7.95544	+	7.95544i	0.264156	+	0.264156i	0.826740	−	0.562584i	$-0.190193\pi$
$907$	7.95544	+	7.95544i	0.264156	+	0.264156i	−0.562584	+	0.826740i	$0.690193\pi$
$908$	−19.5557	−	19.5557i	−0.648980	−	0.648980i
$909$		0			0
$910$	−1.17157	−	1.84937i	−0.0388373	−	0.0613060i
$911$		−	53.4969i		−	1.77243i	−0.463274	−	0.886215i	$-0.653326\pi$
$911$		−	53.4969i		−	1.77243i	0.463274	−	0.886215i	$-0.346674\pi$
$912$		0			0
$913$	0.304253	−	0.304253i	0.0100693	−	0.0100693i
$914$	29.0702			0.961556
$915$		0			0
$916$	−24.3622			−0.804948
$917$	−4.61541	+	4.61541i	−0.152414	+	0.152414i
$918$		0			0
$919$		−	43.3882i		−	1.43124i	−0.698488	−	0.715622i	$-0.746143\pi$
$919$		−	43.3882i		−	1.43124i	0.698488	−	0.715622i	$-0.253857\pi$
$920$	10.4434	+	2.34315i	0.344308	+	0.0772512i
$921$		0			0
$922$	25.4452	+	25.4452i	0.837993	+	0.837993i
$923$	7.39748	+	7.39748i	0.243491	+	0.243491i
$924$		0			0
$925$	−14.1025	−	39.3686i	−0.463687	−	1.29443i
$926$			18.2014i			0.598134i
$927$		0			0
$928$	−3.12745	+	3.12745i	−0.102664	+	0.102664i
$929$	−12.2024			−0.400348			−0.200174	−	0.979760i	$-0.564151\pi$
$929$	−12.2024			−0.400348			−0.200174	+	0.979760i	$0.564151\pi$
$930$		0			0
$931$		0			0
$932$	−14.7692	+	14.7692i	−0.483781	+	0.483781i
$933$		0			0
$934$			0.751839i			0.0246009i
$935$	−11.3664	+	7.20057i	−0.371720	+	0.235484i
$936$		0			0
$937$	2.82978	+	2.82978i	0.0924449	+	0.0924449i	0.751817	−	0.659372i	$-0.229178\pi$
$937$	2.82978	+	2.82978i	0.0924449	+	0.0924449i	−0.659372	+	0.751817i	$0.729178\pi$
$938$	−0.641735	−	0.641735i	−0.0209534	−	0.0209534i
$939$		0			0
$940$	−19.9554	+	12.6417i	−0.650875	+	0.412328i
$941$			42.7478i			1.39354i	0.717295	+	0.696769i	$0.245380\pi$
$941$			42.7478i			1.39354i	−0.717295	+	0.696769i	$0.754620\pi$
$942$		0			0
$943$	2.73449	−	2.73449i	0.0890472	−	0.0890472i
$944$	−5.89887			−0.191992
$945$		0			0
$946$	11.6706			0.379445
$947$	35.5502	−	35.5502i	1.15523	−	1.15523i	0.169737	−	0.985489i	$-0.445708\pi$
$947$	35.5502	−	35.5502i	1.15523	−	1.15523i	0.985489	−	0.169737i	$-0.0542918\pi$
$948$		0			0
$949$		−	7.89354i		−	0.256235i
$950$		0			0
$951$		0			0
$952$	−2.39327	−	2.39327i	−0.0775663	−	0.0775663i
$953$	−1.05372	−	1.05372i	−0.0341333	−	0.0341333i	0.689834	−	0.723967i	$-0.257683\pi$
$953$	−1.05372	−	1.05372i	−0.0341333	−	0.0341333i	−0.723967	+	0.689834i	$0.757683\pi$
$954$		0			0
$955$	51.2117	+	11.4902i	1.65717	+	0.371814i
$956$			1.47283i			0.0476348i
$957$		0			0
$958$	−16.3050	+	16.3050i	−0.526792	+	0.526792i
$959$	0.272260			0.00879172
$960$		0			0
$961$	2.38372			0.0768941
$962$	5.79013	−	5.79013i	0.186681	−	0.186681i
$963$		0			0
$964$			21.5557i			0.694263i
$965$	−30.6793	−	48.4285i	−0.987603	−	1.55897i
$966$		0			0
$967$	−26.3414	−	26.3414i	−0.847082	−	0.847082i	0.142686	−	0.989768i	$-0.454426\pi$
$967$	−26.3414	−	26.3414i	−0.847082	−	0.847082i	−0.989768	+	0.142686i	$0.954426\pi$
$968$	−5.54315	−	5.54315i	−0.178164	−	0.178164i
$969$		0			0
$970$	8.75154	−	39.0056i	0.280995	−	1.25239i
$971$		−	30.7692i		−	0.987430i	−0.869624	−	0.493715i	$-0.835639\pi$
$971$		−	30.7692i		−	0.987430i	0.869624	−	0.493715i	$-0.164361\pi$
$972$		0			0
$973$	−10.5143	+	10.5143i	−0.337072	+	0.337072i
$974$	−22.5272			−0.721817
$975$		0			0
$976$	−2.39327			−0.0766067
$977$	−5.55661	+	5.55661i	−0.177772	+	0.177772i	−0.790384	−	0.612612i	$-0.790119\pi$
$977$	−5.55661	+	5.55661i	−0.177772	+	0.177772i	0.612612	+	0.790384i	$0.290119\pi$
$978$		0			0
$979$		−	23.5282i		−	0.751964i
$980$	0.489528	−	2.18183i	0.0156374	−	0.0696959i
$981$		0			0
$982$	−8.02633	−	8.02633i	−0.256130	−	0.256130i
$983$	−40.8357	−	40.8357i	−1.30246	−	1.30246i	−0.926732	−	0.375723i	$-0.877394\pi$
$983$	−40.8357	−	40.8357i	−1.30246	−	1.30246i	−0.375723	−	0.926732i	$-0.622606\pi$
$984$		0			0
$985$	16.2213	+	25.6059i	0.516852	+	0.815870i
$986$		−	14.9697i		−	0.476732i
$987$		0			0
$988$		0			0
$989$	31.4208			0.999123
$990$		0			0
$991$	−9.67333			−0.307283			−0.153642	−	0.988127i	$-0.549100\pi$
$991$	−9.67333			−0.307283			−0.153642	+	0.988127i	$0.549100\pi$
$992$	4.08557	−	4.08557i	0.129717	−	0.129717i
$993$		0			0
$994$			10.6854i			0.338921i
$995$	−5.37636	−	1.20627i	−0.170442	−	0.0382414i
$996$		0			0
$997$	−28.1841	−	28.1841i	−0.892601	−	0.892601i	0.102167	−	0.994767i	$-0.467422\pi$
$997$	−28.1841	−	28.1841i	−0.892601	−	0.892601i	−0.994767	+	0.102167i	$0.967422\pi$
$998$	−14.5889	−	14.5889i	−0.461805	−	0.461805i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.m.d.197.4	yes	8
3.2	odd	2		630.2.m.c.197.1	✓	8
5.2	odd	4		3150.2.m.i.2843.3		8
5.3	odd	4		630.2.m.c.323.1	yes	8
5.4	even	2		3150.2.m.j.1457.1		8
15.2	even	4		3150.2.m.j.2843.2		8
15.8	even	4	inner	630.2.m.d.323.4	yes	8
15.14	odd	2		3150.2.m.i.1457.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.m.c.197.1	✓	8	3.2	odd	2
630.2.m.c.323.1	yes	8	5.3	odd	4
630.2.m.d.197.4	yes	8	1.1	even	1	trivial
630.2.m.d.323.4	yes	8	15.8	even	4	inner
3150.2.m.i.1457.4		8	15.14	odd	2
3150.2.m.i.2843.3		8	5.2	odd	4
3150.2.m.j.1457.1		8	5.4	even	2
3150.2.m.j.2843.2		8	15.2	even	4

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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.489528 - 2.18183i) q^{5} +(0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.489528 - 2.18183i) q^{5} +(0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.19663 - 1.88893i) q^{10} -1.77786i q^{11} +(0.692297 - 0.692297i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(2.39327 - 2.39327i) q^{17} +(-2.18183 - 0.489528i) q^{20} +(-1.25714 - 1.25714i) q^{22} +(-3.38459 - 3.38459i) q^{23} +(-4.52072 - 2.13613i) q^{25} -0.979056i q^{26} +(0.707107 - 0.707107i) q^{28} +4.42289 q^{29} -5.77786 q^{31} +(-0.707107 + 0.707107i) q^{32} -3.38459i q^{34} +(1.88893 - 1.19663i) q^{35} +(5.91399 + 5.91399i) q^{37} +(-1.88893 + 1.19663i) q^{40} +0.807922i q^{41} +(-4.64173 + 4.64173i) q^{43} -1.77786 q^{44} -4.78654 q^{46} +(7.47016 - 7.47016i) q^{47} +1.00000i q^{49} +(-4.70711 + 1.68616i) q^{50} +(-0.692297 - 0.692297i) q^{52} +(-3.56484 - 3.56484i) q^{53} +(-3.87899 - 0.870315i) q^{55} -1.00000i q^{56} +(3.12745 - 3.12745i) q^{58} +5.89887 q^{59} +2.39327 q^{61} +(-4.08557 + 4.08557i) q^{62} +1.00000i q^{64} +(-1.17157 - 1.84937i) q^{65} +(-0.641735 - 0.641735i) q^{67} +(-2.39327 - 2.39327i) q^{68} +(0.489528 - 2.18183i) q^{70} +10.6854i q^{71} +(5.70097 - 5.70097i) q^{73} +8.36365 q^{74} +(1.25714 - 1.25714i) q^{77} +16.3423i q^{79} +(-0.489528 + 2.18183i) q^{80} +(0.571287 + 0.571287i) q^{82} +(0.171134 + 0.171134i) q^{83} +(-4.05012 - 6.39327i) q^{85} +6.56440i q^{86} +(-1.25714 + 1.25714i) q^{88} +13.2340 q^{89} +0.979056 q^{91} +(-3.38459 + 3.38459i) q^{92} -10.5644i q^{94} +(12.6413 + 12.6413i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 4 q^{13} + 8 q^{14} - 8 q^{16} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 4 q^{25} + 24 q^{29} - 8 q^{31} - 4 q^{35} - 4 q^{37} + 4 q^{40} - 12 q^{43} + 24 q^{44} + 12 q^{47} - 32 q^{50} + 4 q^{52} - 32 q^{53} - 24 q^{55} + 12 q^{58} + 16 q^{59} - 4 q^{62} - 32 q^{65} + 20 q^{67} + 36 q^{73} + 40 q^{74} + 4 q^{77} - 12 q^{82} - 56 q^{83} + 32 q^{85} - 4 q^{88} + 72 q^{89} - 8 q^{92} - 4 q^{97}+O(q^{100}) \) 8 * q - 4 * q^13 + 8 * q^14 - 8 * q^16 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 4 * q^25 + 24 * q^29 - 8 * q^31 - 4 * q^35 - 4 * q^37 + 4 * q^40 - 12 * q^43 + 24 * q^44 + 12 * q^47 - 32 * q^50 + 4 * q^52 - 32 * q^53 - 24 * q^55 + 12 * q^58 + 16 * q^59 - 4 * q^62 - 32 * q^65 + 20 * q^67 + 36 * q^73 + 40 * q^74 + 4 * q^77 - 12 * q^82 - 56 * q^83 + 32 * q^85 - 4 * q^88 + 72 * q^89 - 8 * q^92 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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