LMFDB - Embedded newform 912.2.bn.i.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(65,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("912.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bn (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.2
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	912.65
Dual form			912.2.bn.i.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 1.65831i) q^{3} +(-0.686141 - 0.396143i) q^{5} +2.37228 q^{7} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 1.65831i) q^{3} +(-0.686141 - 0.396143i) q^{5} +2.37228 q^{7} +(-2.50000 - 1.65831i) q^{9} +3.46410i q^{11} +(-2.87228 + 1.65831i) q^{13} +(1.00000 - 0.939764i) q^{15} +(-0.686141 - 0.396143i) q^{17} +(4.00000 + 1.73205i) q^{19} +(-1.18614 + 3.93398i) q^{21} +(-6.43070 + 3.71277i) q^{23} +(-2.18614 - 3.78651i) q^{25} +(4.00000 - 3.31662i) q^{27} +(2.68614 + 4.65253i) q^{29} +4.40387i q^{31} +(-5.74456 - 1.73205i) q^{33} +(-1.62772 - 0.939764i) q^{35} +7.86797i q^{37} +(-1.31386 - 5.59230i) q^{39} +(0.313859 - 0.543620i) q^{41} +(0.127719 - 0.221215i) q^{43} +(1.05842 + 2.12819i) q^{45} +(-3.68614 + 2.12819i) q^{47} -1.37228 q^{49} +(1.00000 - 0.939764i) q^{51} +(-5.68614 - 9.84868i) q^{53} +(1.37228 - 2.37686i) q^{55} +(-4.87228 + 5.76722i) q^{57} +(-3.68614 + 6.38458i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-5.93070 - 3.93398i) q^{63} +2.62772 q^{65} +(-10.2446 + 5.91470i) q^{67} +(-2.94158 - 12.5205i) q^{69} +(-3.31386 + 5.73977i) q^{71} +(2.87228 - 4.97494i) q^{73} +(7.37228 - 1.73205i) q^{75} +8.21782i q^{77} +(-9.98913 - 5.76722i) q^{79} +(3.50000 + 8.29156i) q^{81} -3.46410i q^{83} +(0.313859 + 0.543620i) q^{85} +(-9.05842 + 2.12819i) q^{87} +(-3.68614 - 6.38458i) q^{89} +(-6.81386 + 3.93398i) q^{91} +(-7.30298 - 2.20193i) q^{93} +(-2.05842 - 2.77300i) q^{95} +(11.0584 + 6.38458i) q^{97} +(5.74456 - 8.66025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 3 q^{5} - 2 q^{7} - 10 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 3 * q^5 - 2 * q^7 - 10 * q^9	$ 4 q - 2 q^{3} + 3 q^{5} - 2 q^{7} - 10 q^{9} + 4 q^{15} + 3 q^{17} + 16 q^{19} + q^{21} + 3 q^{23} - 3 q^{25} + 16 q^{27} + 5 q^{29} - 18 q^{35} - 11 q^{39} + 7 q^{41} + 12 q^{43} - 13 q^{45} - 9 q^{47} + 6 q^{49} + 4 q^{51} - 17 q^{53} - 6 q^{55} - 8 q^{57} - 9 q^{59} + 2 q^{61} + 5 q^{63} + 22 q^{65} - 18 q^{67} - 29 q^{69} - 19 q^{71} + 18 q^{75} + 6 q^{79} + 14 q^{81} + 7 q^{85} - 19 q^{87} - 9 q^{89} - 33 q^{91} + 11 q^{93} + 9 q^{95} + 27 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 3 * q^5 - 2 * q^7 - 10 * q^9 + 4 * q^15 + 3 * q^17 + 16 * q^19 + q^21 + 3 * q^23 - 3 * q^25 + 16 * q^27 + 5 * q^29 - 18 * q^35 - 11 * q^39 + 7 * q^41 + 12 * q^43 - 13 * q^45 - 9 * q^47 + 6 * q^49 + 4 * q^51 - 17 * q^53 - 6 * q^55 - 8 * q^57 - 9 * q^59 + 2 * q^61 + 5 * q^63 + 22 * q^65 - 18 * q^67 - 29 * q^69 - 19 * q^71 + 18 * q^75 + 6 * q^79 + 14 * q^81 + 7 * q^85 - 19 * q^87 - 9 * q^89 - 33 * q^91 + 11 * q^93 + 9 * q^95 + 27 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

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			0
$2$		0			0
$3$	−0.500000	+	1.65831i	−0.288675	+	0.957427i
$3$	−0.500000	+	1.65831i	−0.288675	+	0.957427i
$4$		0			0
$5$	−0.686141	−	0.396143i	−0.306851	−	0.177161i	0.338665	−	0.940907i	$-0.390025\pi$
$5$	−0.686141	−	0.396143i	−0.306851	−	0.177161i	−0.645517	+	0.763746i	$0.723358\pi$
$6$		0			0
$7$	2.37228			0.896638			0.448319	−	0.893874i	$-0.352023\pi$
$7$	2.37228			0.896638			0.448319	+	0.893874i	$0.352023\pi$
$8$		0			0
$9$	−2.50000	−	1.65831i	−0.833333	−	0.552771i
$10$		0			0
$11$			3.46410i			1.04447i	0.852803	+	0.522233i	$0.174901\pi$
$11$			3.46410i			1.04447i	−0.852803	+	0.522233i	$0.825099\pi$
$12$		0			0
$13$	−2.87228	+	1.65831i	−0.796628	+	0.459933i	−0.842291	−	0.539024i	$-0.818793\pi$
$13$	−2.87228	+	1.65831i	−0.796628	+	0.459933i	0.0456630	+	0.998957i	$0.485460\pi$
$14$		0			0
$15$	1.00000	−	0.939764i	0.258199	−	0.242646i
$16$		0			0
$17$	−0.686141	−	0.396143i	−0.166414	−	0.0960789i	0.414480	−	0.910058i	$-0.363963\pi$
$17$	−0.686141	−	0.396143i	−0.166414	−	0.0960789i	−0.580894	+	0.813979i	$0.697297\pi$
$18$		0			0
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$20$		0			0
$21$	−1.18614	+	3.93398i	−0.258837	+	0.858466i
$22$		0			0
$23$	−6.43070	+	3.71277i	−1.34089	+	0.774166i	−0.986939	−	0.161096i	$-0.948497\pi$
$23$	−6.43070	+	3.71277i	−1.34089	+	0.774166i	−0.353956	+	0.935262i	$0.615164\pi$
$24$		0			0
$25$	−2.18614	−	3.78651i	−0.437228	−	0.757301i
$26$		0			0
$27$	4.00000	−	3.31662i	0.769800	−	0.638285i
$28$		0			0
$29$	2.68614	+	4.65253i	0.498804	+	0.863954i	0.999999	−	0.00138070i	$-0.000439492\pi$
$29$	2.68614	+	4.65253i	0.498804	+	0.863954i	−0.501195	+	0.865334i	$0.667106\pi$
$30$		0			0
$31$			4.40387i			0.790958i	0.918475	+	0.395479i	$0.129421\pi$
$31$			4.40387i			0.790958i	−0.918475	+	0.395479i	$0.870579\pi$
$32$		0			0
$33$	−5.74456	−	1.73205i	−1.00000	−	0.301511i
$34$		0			0
$35$	−1.62772	−	0.939764i	−0.275135	−	0.158849i
$36$		0			0
$37$			7.86797i			1.29349i	0.762708	+	0.646743i	$0.223869\pi$
$37$			7.86797i			1.29349i	−0.762708	+	0.646743i	$0.776131\pi$
$38$		0			0
$39$	−1.31386	−	5.59230i	−0.210386	−	0.895484i
$40$		0			0
$41$	0.313859	−	0.543620i	0.0490166	−	0.0848992i	−0.840476	−	0.541849i	$-0.817725\pi$
$41$	0.313859	−	0.543620i	0.0490166	−	0.0848992i	0.889493	+	0.456949i	$0.151058\pi$
$42$		0			0
$43$	0.127719	−	0.221215i	0.0194769	−	0.0337350i	−0.856123	−	0.516773i	$-0.827133\pi$
$43$	0.127719	−	0.221215i	0.0194769	−	0.0337350i	0.875600	+	0.483038i	$0.160467\pi$
$44$		0			0
$45$	1.05842	+	2.12819i	0.157780	+	0.317252i
$46$		0			0
$47$	−3.68614	+	2.12819i	−0.537679	+	0.310429i	−0.744138	−	0.668026i	$-0.767139\pi$
$47$	−3.68614	+	2.12819i	−0.537679	+	0.310429i	0.206459	+	0.978455i	$0.433806\pi$
$48$		0			0
$49$	−1.37228			−0.196040
$50$		0			0
$51$	1.00000	−	0.939764i	0.140028	−	0.131593i
$52$		0			0
$53$	−5.68614	−	9.84868i	−0.781051	−	1.35282i	−0.931330	−	0.364177i	$-0.881350\pi$
$53$	−5.68614	−	9.84868i	−0.781051	−	1.35282i	0.150278	−	0.988644i	$-0.451983\pi$
$54$		0			0
$55$	1.37228	−	2.37686i	0.185038	−	0.320496i
$56$		0			0
$57$	−4.87228	+	5.76722i	−0.645349	+	0.763888i
$58$		0			0
$59$	−3.68614	+	6.38458i	−0.479895	+	0.831202i	−0.999734	−	0.0230621i	$-0.992658\pi$
$59$	−3.68614	+	6.38458i	−0.479895	+	0.831202i	0.519839	+	0.854264i	$0.325992\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$		0			0
$63$	−5.93070	−	3.93398i	−0.747198	−	0.495635i
$64$		0			0
$65$	2.62772			0.325928
$66$		0			0
$67$	−10.2446	+	5.91470i	−1.25157	+	0.722596i	−0.971422	−	0.237360i	$-0.923718\pi$
$67$	−10.2446	+	5.91470i	−1.25157	+	0.722596i	−0.280151	+	0.959956i	$0.590384\pi$
$68$		0			0
$69$	−2.94158	−	12.5205i	−0.354124	−	1.50729i
$70$		0			0
$71$	−3.31386	+	5.73977i	−0.393283	+	0.681186i	−0.992880	−	0.119116i	$-0.961994\pi$
$71$	−3.31386	+	5.73977i	−0.393283	+	0.681186i	0.599598	+	0.800302i	$0.295327\pi$
$72$		0			0
$73$	2.87228	−	4.97494i	0.336175	−	0.582272i	−0.647535	−	0.762036i	$-0.724200\pi$
$73$	2.87228	−	4.97494i	0.336175	−	0.582272i	0.983710	+	0.179764i	$0.0575333\pi$
$74$		0			0
$75$	7.37228	−	1.73205i	0.851278	−	0.200000i
$76$		0			0
$77$			8.21782i			0.936508i
$78$		0			0
$79$	−9.98913	−	5.76722i	−1.12386	−	0.648863i	−0.181480	−	0.983395i	$-0.558089\pi$
$79$	−9.98913	−	5.76722i	−1.12386	−	0.648863i	−0.942385	+	0.334531i	$0.891422\pi$
$80$		0			0
$81$	3.50000	+	8.29156i	0.388889	+	0.921285i
$82$		0			0
$83$		−	3.46410i		−	0.380235i	−0.981761	−	0.190117i	$-0.939113\pi$
$83$		−	3.46410i		−	0.380235i	0.981761	−	0.190117i	$-0.0608868\pi$
$84$		0			0
$85$	0.313859	+	0.543620i	0.0340428	+	0.0589639i
$86$		0			0
$87$	−9.05842	+	2.12819i	−0.971165	+	0.228166i
$88$		0			0
$89$	−3.68614	−	6.38458i	−0.390730	−	0.676764i	0.601816	−	0.798635i	$-0.294444\pi$
$89$	−3.68614	−	6.38458i	−0.390730	−	0.676764i	−0.992546	+	0.121870i	$0.961111\pi$
$90$		0			0
$91$	−6.81386	+	3.93398i	−0.714287	+	0.412394i
$92$		0			0
$93$	−7.30298	−	2.20193i	−0.757284	−	0.228330i
$94$		0			0
$95$	−2.05842	−	2.77300i	−0.211190	−	0.284504i
$96$		0			0
$97$	11.0584	+	6.38458i	1.12281	+	0.648256i	0.942117	−	0.335283i	$-0.108832\pi$
$97$	11.0584	+	6.38458i	1.12281	+	0.648256i	0.180695	+	0.983539i	$0.442165\pi$
$98$		0			0
$99$	5.74456	−	8.66025i	0.577350	−	0.870388i
$100$		0			0
$101$	−0.686141	+	0.396143i	−0.0682735	+	0.0394178i	−0.533748	−	0.845643i	$-0.679217\pi$
$101$	−0.686141	+	0.396143i	−0.0682735	+	0.0394178i	0.465475	+	0.885061i	$0.345884\pi$
$102$		0			0
$103$		−	0.644810i		−	0.0635350i	−0.999495	−	0.0317675i	$-0.989886\pi$
$103$		−	0.644810i		−	0.0635350i	0.999495	−	0.0317675i	$-0.0101136\pi$
$104$		0			0
$105$	2.37228	−	2.22938i	0.231511	−	0.217566i
$106$		0			0
$107$	16.7446			1.61876			0.809379	−	0.587287i	$-0.199804\pi$
$107$	16.7446			1.61876			0.809379	+	0.587287i	$0.199804\pi$
$108$		0			0
$109$	5.05842	+	2.92048i	0.484509	+	0.279731i	0.722294	−	0.691587i	$-0.243088\pi$
$109$	5.05842	+	2.92048i	0.484509	+	0.279731i	−0.237785	+	0.971318i	$0.576421\pi$
$110$		0			0
$111$	−13.0475	−	3.93398i	−1.23842	−	0.373397i
$112$		0			0
$113$	14.7446			1.38705			0.693526	−	0.720432i	$-0.256056\pi$
$113$	14.7446			1.38705			0.693526	+	0.720432i	$0.256056\pi$
$114$		0			0
$115$	5.88316			0.548607
$116$		0			0
$117$	9.93070	+	0.617359i	0.918094	+	0.0570748i
$118$		0			0
$119$	−1.62772	−	0.939764i	−0.149213	−	0.0861480i
$120$		0			0
$121$	−1.00000			−0.0909091
$122$		0			0
$123$	0.744563	+	0.792287i	0.0671350	+	0.0714381i
$124$		0			0
$125$			7.42554i			0.664160i
$126$		0			0
$127$	16.8030	−	9.70121i	1.49102	−	0.860843i	0.491077	−	0.871116i	$-0.336604\pi$
$127$	16.8030	−	9.70121i	1.49102	−	0.860843i	0.999947	+	0.0102734i	$0.00327020\pi$
$128$		0			0
$129$	0.302985	+	0.322405i	0.0266763	+	0.0283862i
$130$		0			0
$131$	4.80298	+	2.77300i	0.419639	+	0.242279i	0.694923	−	0.719084i	$-0.255439\pi$
$131$	4.80298	+	2.77300i	0.419639	+	0.242279i	−0.275284	+	0.961363i	$0.588772\pi$
$132$		0			0
$133$	9.48913	+	4.10891i	0.822812	+	0.356288i
$134$		0			0
$135$	−4.05842	+	0.691097i	−0.349293	+	0.0594802i
$136$		0			0
$137$	11.3139	−	6.53206i	0.966608	−	0.558072i	0.0684077	−	0.997657i	$-0.478208\pi$
$137$	11.3139	−	6.53206i	0.966608	−	0.558072i	0.898201	+	0.439586i	$0.144875\pi$
$138$		0			0
$139$	8.24456	+	14.2800i	0.699295	+	1.21121i	0.968711	+	0.248190i	$0.0798358\pi$
$139$	8.24456	+	14.2800i	0.699295	+	1.21121i	−0.269417	+	0.963024i	$0.586831\pi$
$140$		0			0
$141$	−1.68614	−	7.17687i	−0.141999	−	0.604401i
$142$		0			0
$143$	−5.74456	−	9.94987i	−0.480384	−	0.832050i
$144$		0			0
$145$		−	4.25639i		−	0.353474i
$146$		0			0
$147$	0.686141	−	2.27567i	0.0565919	−	0.187694i
$148$		0			0
$149$	2.05842	+	1.18843i	0.168632	+	0.0973600i	0.581941	−	0.813231i	$-0.302294\pi$
$149$	2.05842	+	1.18843i	0.168632	+	0.0973600i	−0.413308	+	0.910591i	$0.635627\pi$
$150$		0			0
$151$			13.5615i			1.10362i	0.833971	+	0.551808i	$0.186062\pi$
$151$			13.5615i			1.10362i	−0.833971	+	0.551808i	$0.813938\pi$
$152$		0			0
$153$	1.05842	+	2.12819i	0.0855683	+	0.172054i
$154$		0			0
$155$	1.74456	−	3.02167i	0.140127	−	0.242706i
$156$		0			0
$157$	−10.2446	+	17.7441i	−0.817605	+	1.41613i	0.0898370	+	0.995956i	$0.471365\pi$
$157$	−10.2446	+	17.7441i	−0.817605	+	1.41613i	−0.907442	+	0.420177i	$0.861968\pi$
$158$		0			0
$159$	19.1753	−	4.50506i	1.52070	−	0.357274i
$160$		0			0
$161$	−15.2554	+	8.80773i	−1.20230	+	0.694146i
$162$		0			0
$163$	−9.62772			−0.754101			−0.377051	−	0.926193i	$-0.623062\pi$
$163$	−9.62772			−0.754101			−0.377051	+	0.926193i	$0.623062\pi$
$164$		0			0
$165$	3.25544	+	3.46410i	0.253435	+	0.269680i
$166$		0			0
$167$	−9.05842	−	15.6896i	−0.700962	−	1.21410i	−0.968129	−	0.250451i	$-0.919421\pi$
$167$	−9.05842	−	15.6896i	−0.700962	−	1.21410i	0.267167	−	0.963650i	$-0.413912\pi$
$168$		0			0
$169$	−1.00000	+	1.73205i	−0.0769231	+	0.133235i
$170$		0			0
$171$	−7.12772	−	10.9634i	−0.545070	−	0.838390i
$172$		0			0
$173$	7.43070	−	12.8704i	0.564946	−	0.978515i	−0.432109	−	0.901821i	$-0.642230\pi$
$173$	7.43070	−	12.8704i	0.564946	−	0.978515i	0.997055	−	0.0766935i	$-0.0244363\pi$
$174$		0			0
$175$	−5.18614	−	8.98266i	−0.392035	−	0.679025i
$176$		0			0
$177$	−8.74456	−	9.30506i	−0.657282	−	0.699411i
$178$		0			0
$179$	21.4891			1.60617			0.803086	−	0.595863i	$-0.203190\pi$
$179$	21.4891			1.60617			0.803086	+	0.595863i	$0.203190\pi$
$180$		0			0
$181$	1.80298	−	1.04095i	0.134015	−	0.0773735i	−0.431494	−	0.902116i	$-0.642013\pi$
$181$	1.80298	−	1.04095i	0.134015	−	0.0773735i	0.565508	+	0.824742i	$0.308680\pi$
$182$		0			0
$183$	−1.68614	+	0.396143i	−0.124643	+	0.0292838i
$184$		0			0
$185$	3.11684	−	5.39853i	0.229155	−	0.396908i
$186$		0			0
$187$	1.37228	−	2.37686i	0.100351	−	0.173813i
$188$		0			0
$189$	9.48913	−	7.86797i	0.690232	−	0.572310i
$190$		0			0
$191$			6.63325i			0.479965i	0.970777	+	0.239983i	$0.0771417\pi$
$191$			6.63325i			0.479965i	−0.970777	+	0.239983i	$0.922858\pi$
$192$		0			0
$193$	13.5000	+	7.79423i	0.971751	+	0.561041i	0.899770	−	0.436365i	$-0.143734\pi$
$193$	13.5000	+	7.79423i	0.971751	+	0.561041i	0.0719816	+	0.997406i	$0.477068\pi$
$194$		0			0
$195$	−1.31386	+	4.35758i	−0.0940874	+	0.312053i
$196$		0			0
$197$		−	16.4356i		−	1.17099i	−0.810676	−	0.585496i	$-0.800900\pi$
$197$		−	16.4356i		−	1.17099i	0.810676	−	0.585496i	$-0.199100\pi$
$198$		0			0
$199$	10.2446	+	17.7441i	0.726218	+	1.25785i	0.958471	+	0.285191i	$0.0920569\pi$
$199$	10.2446	+	17.7441i	0.726218	+	1.25785i	−0.232253	+	0.972655i	$0.574610\pi$
$200$		0			0
$201$	−4.68614	−	19.9460i	−0.330535	−	1.40688i
$202$		0			0
$203$	6.37228	+	11.0371i	0.447246	+	0.774654i
$204$		0			0
$205$	−0.430703	+	0.248667i	−0.0300816	+	0.0173676i
$206$		0			0
$207$	22.2337	+	1.38219i	1.54535	+	0.0960691i
$208$		0			0
$209$	−6.00000	+	13.8564i	−0.415029	+	0.958468i
$210$		0			0
$211$	12.9891	+	7.49927i	0.894208	+	0.516271i	0.875317	−	0.483550i	$-0.160653\pi$
$211$	12.9891	+	7.49927i	0.894208	+	0.516271i	0.0188916	+	0.999822i	$0.493986\pi$
$212$		0			0
$213$	−7.86141	−	8.36530i	−0.538655	−	0.573181i
$214$		0			0
$215$	−0.175266	+	0.101190i	−0.0119530	+	0.00690109i
$216$		0			0
$217$			10.4472i			0.709203i
$218$		0			0
$219$	6.81386	+	7.25061i	0.460438	+	0.489951i
$220$		0			0
$221$	2.62772			0.176759
$222$		0			0
$223$	15.7337	+	9.08385i	1.05361	+	0.608300i	0.923657	−	0.383221i	$-0.125185\pi$
$223$	15.7337	+	9.08385i	1.05361	+	0.608300i	0.129949	+	0.991521i	$0.458519\pi$
$224$		0			0
$225$	−0.813859	+	13.0916i	−0.0542573	+	0.872771i
$226$		0			0
$227$	−7.25544			−0.481560			−0.240780	−	0.970580i	$-0.577403\pi$
$227$	−7.25544			−0.481560			−0.240780	+	0.970580i	$0.577403\pi$
$228$		0			0
$229$	−21.1168			−1.39544			−0.697720	−	0.716370i	$-0.745802\pi$
$229$	−21.1168			−1.39544			−0.697720	+	0.716370i	$0.745802\pi$
$230$		0			0
$231$	−13.6277	−	4.10891i	−0.896638	−	0.270347i
$232$		0			0
$233$	−3.94158	−	2.27567i	−0.258221	−	0.149084i	0.365302	−	0.930889i	$-0.380966\pi$
$233$	−3.94158	−	2.27567i	−0.258221	−	0.149084i	−0.623523	+	0.781805i	$0.714299\pi$
$234$		0			0
$235$	3.37228			0.219983
$236$		0			0
$237$	14.5584	−	13.6815i	0.945671	−	0.888708i
$238$		0			0
$239$		−	10.3923i		−	0.672222i	−0.941822	−	0.336111i	$-0.890888\pi$
$239$		−	10.3923i		−	0.672222i	0.941822	−	0.336111i	$-0.109112\pi$
$240$		0			0
$241$	0.383156	−	0.221215i	0.0246812	−	0.0142497i	−0.487609	−	0.873062i	$-0.662131\pi$
$241$	0.383156	−	0.221215i	0.0246812	−	0.0142497i	0.512290	+	0.858813i	$0.328797\pi$
$242$		0			0
$243$	−15.5000	+	1.65831i	−0.994325	+	0.106381i
$244$		0			0
$245$	0.941578	+	0.543620i	0.0601552	+	0.0347306i
$246$		0			0
$247$	−14.3614	+	1.65831i	−0.913794	+	0.105516i
$248$		0			0
$249$	5.74456	+	1.73205i	0.364047	+	0.109764i
$250$		0			0
$251$	5.56930	−	3.21543i	0.351531	−	0.202956i	−0.313828	−	0.949480i	$-0.601612\pi$
$251$	5.56930	−	3.21543i	0.351531	−	0.202956i	0.665359	+	0.746523i	$0.268278\pi$
$252$		0			0
$253$	−12.8614	−	22.2766i	−0.808590	−	1.40052i
$254$		0			0
$255$	−1.05842	+	0.248667i	−0.0662810	+	0.0155721i
$256$		0			0
$257$	−0.941578	−	1.63086i	−0.0587340	−	0.101730i	0.835163	−	0.550002i	$-0.185373\pi$
$257$	−0.941578	−	1.63086i	−0.0587340	−	0.101730i	−0.893897	+	0.448272i	$0.852040\pi$
$258$		0			0
$259$			18.6650i			1.15979i
$260$		0			0
$261$	1.00000	−	16.0858i	0.0618984	−	0.995685i
$262$		0			0
$263$	−3.43070	−	1.98072i	−0.211546	−	0.122136i	0.390484	−	0.920610i	$-0.372308\pi$
$263$	−3.43070	−	1.98072i	−0.211546	−	0.122136i	−0.602030	+	0.798474i	$0.705641\pi$
$264$		0			0
$265$			9.01011i			0.553487i
$266$		0			0
$267$	12.4307	−	2.92048i	0.760747	−	0.178731i
$268$		0			0
$269$	−6.43070	+	11.1383i	−0.392087	+	0.679114i	−0.992725	−	0.120407i	$-0.961580\pi$
$269$	−6.43070	+	11.1383i	−0.392087	+	0.679114i	0.600638	+	0.799521i	$0.294913\pi$
$270$		0			0
$271$	4.43070	−	7.67420i	0.269146	−	0.466175i	−0.699495	−	0.714637i	$-0.746592\pi$
$271$	4.43070	−	7.67420i	0.269146	−	0.466175i	0.968642	+	0.248462i	$0.0799252\pi$
$272$		0			0
$273$	−3.11684	−	13.2665i	−0.188640	−	0.802925i
$274$		0			0
$275$	13.1168	−	7.57301i	0.790975	−	0.456670i
$276$		0			0
$277$	3.48913			0.209641			0.104821	−	0.994491i	$-0.466573\pi$
$277$	3.48913			0.209641			0.104821	+	0.994491i	$0.466573\pi$
$278$		0			0
$279$	7.30298	−	11.0097i	0.437218	−	0.659131i
$280$		0			0
$281$	−12.8030	−	22.1754i	−0.763762	−	1.32287i	−0.940899	−	0.338688i	$-0.890017\pi$
$281$	−12.8030	−	22.1754i	−0.763762	−	1.32287i	0.177137	−	0.984186i	$-0.443317\pi$
$282$		0			0
$283$	14.4307	−	24.9947i	0.857816	−	1.48578i	−0.0161912	−	0.999869i	$-0.505154\pi$
$283$	14.4307	−	24.9947i	0.857816	−	1.48578i	0.874007	−	0.485912i	$-0.161513\pi$
$284$		0			0
$285$	5.62772	−	2.02700i	0.333357	−	0.120069i
$286$		0			0
$287$	0.744563	−	1.28962i	0.0439501	−	0.0761239i
$288$		0			0
$289$	−8.18614	−	14.1788i	−0.481538	−	0.834048i
$290$		0			0
$291$	−16.1168	+	15.1460i	−0.944786	+	0.887876i
$292$		0			0
$293$	9.25544			0.540708			0.270354	−	0.962761i	$-0.412859\pi$
$293$	9.25544			0.540708			0.270354	+	0.962761i	$0.412859\pi$
$294$		0			0
$295$	5.05842	−	2.92048i	0.294513	−	0.170037i
$296$		0			0
$297$	11.4891	+	13.8564i	0.666667	+	0.804030i
$298$		0			0
$299$	12.3139	−	21.3282i	0.712129	−	1.23344i
$300$		0			0
$301$	0.302985	−	0.524785i	0.0174637	−	0.0302481i
$302$		0			0
$303$	−0.313859	−	1.33591i	−0.0180307	−	0.0767459i
$304$		0			0
$305$		−	0.792287i		−	0.0453662i
$306$		0			0
$307$	−16.2921	−	9.40625i	−0.929840	−	0.536843i	−0.0430789	−	0.999072i	$-0.513717\pi$
$307$	−16.2921	−	9.40625i	−0.929840	−	0.536843i	−0.886761	+	0.462228i	$0.847050\pi$
$308$		0			0
$309$	1.06930	+	0.322405i	0.0608302	+	0.0183410i
$310$		0			0
$311$		−	12.2718i		−	0.695872i	−0.937518	−	0.347936i	$-0.886883\pi$
$311$		−	12.2718i		−	0.695872i	0.937518	−	0.347936i	$-0.113117\pi$
$312$		0			0
$313$	−16.1753	−	28.0164i	−0.914280	−	1.58358i	−0.807952	−	0.589248i	$-0.799424\pi$
$313$	−16.1753	−	28.0164i	−0.914280	−	1.58358i	−0.106328	−	0.994331i	$-0.533909\pi$
$314$		0			0
$315$	2.51087	+	5.04868i	0.141472	+	0.284461i
$316$		0			0
$317$	10.6861	+	18.5089i	0.600193	+	1.03957i	0.992791	+	0.119855i	$0.0382431\pi$
$317$	10.6861	+	18.5089i	0.600193	+	1.03957i	−0.392598	+	0.919710i	$0.628424\pi$
$318$		0			0
$319$	−16.1168	+	9.30506i	−0.902370	+	0.520984i
$320$		0			0
$321$	−8.37228	+	27.7677i	−0.467295	+	1.54984i
$322$		0			0
$323$	−2.05842	−	2.77300i	−0.114534	−	0.154294i
$324$		0			0
$325$	12.5584	+	7.25061i	0.696616	+	0.402191i
$326$		0			0
$327$	−7.37228	+	6.92820i	−0.407688	+	0.383131i
$328$		0			0
$329$	−8.74456	+	5.04868i	−0.482103	+	0.278342i
$330$		0			0
$331$		−	19.5499i		−	1.07456i	−0.843404	−	0.537280i	$-0.819452\pi$
$331$		−	19.5499i		−	1.07456i	0.843404	−	0.537280i	$-0.180548\pi$
$332$		0			0
$333$	13.0475	−	19.6699i	0.715001	−	1.07790i
$334$		0			0
$335$	9.37228			0.512062
$336$		0			0
$337$	9.73369	+	5.61975i	0.530228	+	0.306127i	0.741109	−	0.671385i	$-0.234300\pi$
$337$	9.73369	+	5.61975i	0.530228	+	0.306127i	−0.210881	+	0.977512i	$0.567633\pi$
$338$		0			0
$339$	−7.37228	+	24.4511i	−0.400407	+	1.32800i
$340$		0			0
$341$	−15.2554			−0.826128
$342$		0			0
$343$	−19.8614			−1.07242
$344$		0			0
$345$	−2.94158	+	9.75611i	−0.158369	+	0.525251i
$346$		0			0
$347$	7.54755	+	4.35758i	0.405174	+	0.233927i	0.688714	−	0.725033i	$-0.258176\pi$
$347$	7.54755	+	4.35758i	0.405174	+	0.233927i	−0.283540	+	0.958960i	$0.591509\pi$
$348$		0			0
$349$	−30.6060			−1.63830			−0.819150	−	0.573579i	$-0.805554\pi$
$349$	−30.6060			−1.63830			−0.819150	+	0.573579i	$0.805554\pi$
$350$		0			0
$351$	−5.98913	+	16.1595i	−0.319676	+	0.862532i
$352$		0			0
$353$			35.3407i			1.88100i	0.339798	+	0.940499i	$0.389641\pi$
$353$			35.3407i			1.88100i	−0.339798	+	0.940499i	$0.610359\pi$
$354$		0			0
$355$	4.54755	−	2.62553i	0.241359	−	0.139349i
$356$		0			0
$357$	2.37228	−	2.22938i	0.125554	−	0.117992i
$358$		0			0
$359$	−1.80298	−	1.04095i	−0.0951579	−	0.0549394i	0.451666	−	0.892187i	$-0.350830\pi$
$359$	−1.80298	−	1.04095i	−0.0951579	−	0.0549394i	−0.546824	+	0.837248i	$0.684163\pi$
$360$		0			0
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$		0			0
$363$	0.500000	−	1.65831i	0.0262432	−	0.0870388i
$364$		0			0
$365$	−3.94158	+	2.27567i	−0.206312	+	0.119114i
$366$		0			0
$367$	−9.61684	−	16.6569i	−0.501995	−	0.869481i	−0.999997	−	0.00230536i	$-0.999266\pi$
$367$	−9.61684	−	16.6569i	−0.501995	−	0.869481i	0.498002	−	0.867176i	$-0.334067\pi$
$368$		0			0
$369$	−1.68614	+	0.838574i	−0.0877770	+	0.0436544i
$370$		0			0
$371$	−13.4891	−	23.3639i	−0.700320	−	1.21299i
$372$		0			0
$373$		−	6.92820i		−	0.358729i	−0.983783	−	0.179364i	$-0.942596\pi$
$373$		−	6.92820i		−	0.358729i	0.983783	−	0.179364i	$-0.0574041\pi$
$374$		0			0
$375$	−12.3139	−	3.71277i	−0.635885	−	0.191727i
$376$		0			0
$377$	−15.4307	−	8.90892i	−0.794722	−	0.458833i
$378$		0			0
$379$			10.7422i			0.551788i	0.961188	+	0.275894i	$0.0889738\pi$
$379$			10.7422i			0.551788i	−0.961188	+	0.275894i	$0.911026\pi$
$380$		0			0
$381$	7.68614	+	32.7152i	0.393773	+	1.67605i
$382$		0			0
$383$	−4.80298	+	8.31901i	−0.245421	+	0.425082i	−0.962250	−	0.272167i	$-0.912260\pi$
$383$	−4.80298	+	8.31901i	−0.245421	+	0.425082i	0.716829	+	0.697249i	$0.245593\pi$
$384$		0			0
$385$	3.25544	−	5.63858i	0.165912	−	0.287369i
$386$		0			0
$387$	−0.686141	+	0.341241i	−0.0348785	+	0.0173462i
$388$		0			0
$389$	26.6644	−	15.3947i	1.35194	−	0.780542i	0.363417	−	0.931626i	$-0.381610\pi$
$389$	26.6644	−	15.3947i	1.35194	−	0.780542i	0.988521	+	0.151084i	$0.0482765\pi$
$390$		0			0
$391$	5.88316			0.297524
$392$		0			0
$393$	−7.00000	+	6.57835i	−0.353103	+	0.331834i
$394$		0			0
$395$	4.56930	+	7.91425i	0.229906	+	0.398209i
$396$		0			0
$397$	−4.61684	+	7.99661i	−0.231713	+	0.401338i	−0.958312	−	0.285723i	$-0.907766\pi$
$397$	−4.61684	+	7.99661i	−0.231713	+	0.401338i	0.726599	+	0.687061i	$0.241100\pi$
$398$		0			0
$399$	−11.5584	+	13.6815i	−0.578645	+	0.684931i
$400$		0			0
$401$	−9.17527	+	15.8920i	−0.458191	+	0.793610i	−0.998865	−	0.0476219i	$-0.984836\pi$
$401$	−9.17527	+	15.8920i	−0.458191	+	0.793610i	0.540675	+	0.841232i	$0.318169\pi$
$402$		0			0
$403$	−7.30298	−	12.6491i	−0.363788	−	0.630099i
$404$		0			0
$405$	0.883156	−	7.07568i	0.0438844	−	0.351593i
$406$		0			0
$407$	−27.2554			−1.35100
$408$		0			0
$409$	31.2921	−	18.0665i	1.54730	−	0.893331i	0.548948	−	0.835856i	$-0.315028\pi$
$409$	31.2921	−	18.0665i	1.54730	−	0.893331i	0.998347	−	0.0574750i	$-0.0183050\pi$
$410$		0			0
$411$	5.17527	+	22.0279i	0.255277	+	1.08656i
$412$		0			0
$413$	−8.74456	+	15.1460i	−0.430292	+	0.745287i
$414$		0			0
$415$	−1.37228	+	2.37686i	−0.0673626	+	0.116676i
$416$		0			0
$417$	−27.8030	+	6.53206i	−1.36152	+	0.319876i
$418$		0			0
$419$			37.5152i			1.83274i	0.400335	+	0.916369i	$0.368894\pi$
$419$			37.5152i			1.83274i	−0.400335	+	0.916369i	$0.631106\pi$
$420$		0			0
$421$	25.2921	+	14.6024i	1.23266	+	0.711678i	0.967584	−	0.252549i	$-0.0812690\pi$
$421$	25.2921	+	14.6024i	1.23266	+	0.711678i	0.265078	+	0.964227i	$0.414602\pi$
$422$		0			0
$423$	12.7446	+	0.792287i	0.619662	+	0.0385223i
$424$		0			0
$425$			3.46410i			0.168034i
$426$		0			0
$427$	1.18614	+	2.05446i	0.0574014	+	0.0994221i
$428$		0			0
$429$	19.3723	−	4.55134i	0.935303	−	0.219741i
$430$		0			0
$431$	18.4307	+	31.9229i	0.887776	+	1.53767i	0.842499	+	0.538698i	$0.181084\pi$
$431$	18.4307	+	31.9229i	0.887776	+	1.53767i	0.0452769	+	0.998974i	$0.485583\pi$
$432$		0			0
$433$	3.73369	−	2.15565i	0.179430	−	0.103594i	−0.407595	−	0.913163i	$-0.633632\pi$
$433$	3.73369	−	2.15565i	0.179430	−	0.103594i	0.587025	+	0.809569i	$0.300299\pi$
$434$		0			0
$435$	7.05842	+	2.12819i	0.338425	+	0.102039i
$436$		0			0
$437$	−32.1535	+	3.71277i	−1.53811	+	0.177606i
$438$		0			0
$439$	−4.50000	−	2.59808i	−0.214773	−	0.123999i	0.388755	−	0.921341i	$-0.372905\pi$
$439$	−4.50000	−	2.59808i	−0.214773	−	0.123999i	−0.603528	+	0.797342i	$0.706239\pi$
$440$		0			0
$441$	3.43070	+	2.27567i	0.163367	+	0.108365i
$442$		0			0
$443$	−31.0367	+	17.9190i	−1.47460	+	0.851359i	−0.999590	−	0.0286234i	$-0.990888\pi$
$443$	−31.0367	+	17.9190i	−1.47460	+	0.851359i	−0.475007	+	0.879982i	$0.657554\pi$
$444$		0			0
$445$			5.84096i			0.276888i
$446$		0			0
$447$	−3.00000	+	2.81929i	−0.141895	+	0.133348i
$448$		0			0
$449$	38.4674			1.81539			0.907694	−	0.419633i	$-0.137841\pi$
$449$	38.4674			1.81539			0.907694	+	0.419633i	$0.137841\pi$
$450$		0			0
$451$	1.88316	+	1.08724i	0.0886744	+	0.0511962i
$452$		0			0
$453$	−22.4891	−	6.78073i	−1.05663	−	0.318586i
$454$		0			0
$455$	6.23369			0.292240
$456$		0			0
$457$	36.3723			1.70142			0.850712	−	0.525632i	$-0.176171\pi$
$457$	36.3723			1.70142			0.850712	+	0.525632i	$0.176171\pi$
$458$		0			0
$459$	−4.05842	+	0.691097i	−0.189431	+	0.0322577i
$460$		0			0
$461$	−11.5693	−	6.67954i	−0.538836	−	0.311097i	0.205771	−	0.978600i	$-0.434030\pi$
$461$	−11.5693	−	6.67954i	−0.538836	−	0.311097i	−0.744607	+	0.667503i	$0.767363\pi$
$462$		0			0
$463$	−17.6277			−0.819230			−0.409615	−	0.912259i	$-0.634337\pi$
$463$	−17.6277			−0.819230			−0.409615	+	0.912259i	$0.634337\pi$
$464$		0			0
$465$	4.13859	+	4.40387i	0.191923	+	0.204224i
$466$		0			0
$467$			4.16381i			0.192678i	0.995349	+	0.0963392i	$0.0307133\pi$
$467$			4.16381i			0.192678i	−0.995349	+	0.0963392i	$0.969287\pi$
$468$		0			0
$469$	−24.3030	+	14.0313i	−1.12221	+	0.647907i
$470$		0			0
$471$	−24.3030	−	25.8607i	−1.11982	−	1.19160i
$472$		0			0
$473$	0.766312	+	0.442430i	0.0352351	+	0.0203430i
$474$		0			0
$475$	−2.18614	−	18.9325i	−0.100307	−	0.868684i
$476$		0			0
$477$	−2.11684	+	34.0511i	−0.0969236	+	1.55909i
$478$		0			0
$479$	−8.56930	+	4.94749i	−0.391541	+	0.226056i	−0.682828	−	0.730579i	$-0.739250\pi$
$479$	−8.56930	+	4.94749i	−0.391541	+	0.226056i	0.291287	+	0.956636i	$0.405917\pi$
$480$		0			0
$481$	−13.0475	−	22.5990i	−0.594917	−	1.03043i
$482$		0			0
$483$	−6.97825	−	29.7021i	−0.317521	−	1.35149i
$484$		0			0
$485$	−5.05842	−	8.76144i	−0.229691	−	0.397837i
$486$		0			0
$487$		−	0.294954i		−	0.0133656i	−0.999978	−	0.00668281i	$-0.997873\pi$
$487$		−	0.294954i		−	0.0133656i	0.999978	−	0.00668281i	$-0.00212722\pi$
$488$		0			0
$489$	4.81386	−	15.9658i	0.217690	−	0.721997i
$490$		0			0
$491$	−18.1753	−	10.4935i	−0.820238	−	0.473565i	0.0302604	−	0.999542i	$-0.490366\pi$
$491$	−18.1753	−	10.4935i	−0.820238	−	0.473565i	−0.850499	+	0.525977i	$0.823700\pi$
$492$		0			0
$493$		−	4.25639i		−	0.191698i
$494$		0			0
$495$	−7.37228	+	3.66648i	−0.331359	+	0.164796i
$496$		0			0
$497$	−7.86141	+	13.6164i	−0.352632	+	0.610777i
$498$		0			0
$499$	−11.8723	+	20.5634i	−0.531476	+	0.920544i	0.467849	+	0.883809i	$0.345029\pi$
$499$	−11.8723	+	20.5634i	−0.531476	+	0.920544i	−0.999325	+	0.0367354i	$0.988304\pi$
$500$		0			0
$501$	30.5475	−	7.17687i	1.36476	−	0.320639i
$502$		0			0
$503$	36.6861	−	21.1808i	1.63575	−	0.944403i	0.653482	−	0.756942i	$-0.273307\pi$
$503$	36.6861	−	21.1808i	1.63575	−	0.944403i	0.982272	−	0.187461i	$-0.0600259\pi$
$504$		0			0
$505$	0.627719			0.0279331
$506$		0			0
$507$	−2.37228	−	2.52434i	−0.105357	−	0.112110i
$508$		0			0
$509$	5.05842	+	8.76144i	0.224211	+	0.388344i	0.956082	−	0.293098i	$-0.0946863\pi$
$509$	5.05842	+	8.76144i	0.224211	+	0.388344i	−0.731872	+	0.681442i	$0.761353\pi$
$510$		0			0
$511$	6.81386	−	11.8020i	0.301427	−	0.522088i
$512$		0			0
$513$	21.7446	−	6.33830i	0.960046	−	0.279843i
$514$		0			0
$515$	−0.255437	+	0.442430i	−0.0112559	+	0.0194958i
$516$		0			0
$517$	−7.37228	−	12.7692i	−0.324233	−	0.561587i
$518$		0			0
$519$	17.6277	+	18.7576i	0.773771	+	0.823367i
$520$		0			0
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		0			0
$523$	−10.2446	+	5.91470i	−0.447963	+	0.258632i	−0.706970	−	0.707244i	$-0.749938\pi$
$523$	−10.2446	+	5.91470i	−0.447963	+	0.258632i	0.259006	+	0.965876i	$0.416605\pi$
$524$		0			0
$525$	17.4891	−	4.10891i	0.763288	−	0.179328i
$526$		0			0
$527$	1.74456	−	3.02167i	0.0759943	−	0.131626i
$528$		0			0
$529$	16.0693	−	27.8328i	0.698665	−	1.21012i
$530$		0			0
$531$	19.8030	−	9.84868i	0.859376	−	0.427397i
$532$		0			0
$533$			2.08191i			0.0901774i
$534$		0			0
$535$	−11.4891	−	6.63325i	−0.496718	−	0.286780i
$536$		0			0
$537$	−10.7446	+	35.6357i	−0.463662	+	1.53779i
$538$		0			0
$539$		−	4.75372i		−	0.204757i
$540$		0			0
$541$	7.98913	+	13.8376i	0.343479	+	0.594924i	0.985076	−	0.172118i	$-0.0550611\pi$
$541$	7.98913	+	13.8376i	0.343479	+	0.594924i	−0.641597	+	0.767042i	$0.721728\pi$
$542$		0			0
$543$	0.824734	+	3.51039i	0.0353927	+	0.150645i
$544$		0			0
$545$	−2.31386	−	4.00772i	−0.0991148	−	0.171672i
$546$		0			0
$547$	35.6168	−	20.5634i	1.52287	−	0.879227i	0.523232	−	0.852190i	$-0.324726\pi$
$547$	35.6168	−	20.5634i	1.52287	−	0.879227i	0.999634	−	0.0270369i	$-0.00860716\pi$
$548$		0			0
$549$	0.186141	−	2.99422i	0.00794429	−	0.127790i
$550$		0			0
$551$	2.68614	+	23.2627i	0.114433	+	0.991023i
$552$		0			0
$553$	−23.6970	−	13.6815i	−1.00770	−	0.581796i
$554$		0			0
$555$	7.39403	+	7.86797i	0.313859	+	0.333977i
$556$		0			0
$557$	−27.4307	+	15.8371i	−1.16228	+	0.671040i	−0.951848	−	0.306569i	$-0.900819\pi$
$557$	−27.4307	+	15.8371i	−1.16228	+	0.671040i	−0.210428	+	0.977609i	$0.567486\pi$
$558$		0			0
$559$			0.847190i			0.0358323i
$560$		0			0
$561$	3.25544	+	3.46410i	0.137445	+	0.146254i
$562$		0			0
$563$	−43.7228			−1.84270			−0.921348	−	0.388738i	$-0.872911\pi$
$563$	−43.7228			−1.84270			−0.921348	+	0.388738i	$0.872911\pi$
$564$		0			0
$565$	−10.1168	−	5.84096i	−0.425619	−	0.245731i
$566$		0			0
$567$	8.30298	+	19.6699i	0.348693	+	0.826059i
$568$		0			0
$569$	38.7446			1.62426			0.812128	−	0.583479i	$-0.198309\pi$
$569$	38.7446			1.62426			0.812128	+	0.583479i	$0.198309\pi$
$570$		0			0
$571$	−9.62772			−0.402907			−0.201454	−	0.979498i	$-0.564567\pi$
$571$	−9.62772			−0.402907			−0.201454	+	0.979498i	$0.564567\pi$
$572$		0			0
$573$	−11.0000	−	3.31662i	−0.459532	−	0.138554i
$574$		0			0
$575$	28.1168	+	16.2333i	1.17255	+	0.676974i
$576$		0			0
$577$	−27.4891			−1.14439			−0.572194	−	0.820119i	$-0.693907\pi$
$577$	−27.4891			−1.14439			−0.572194	+	0.820119i	$0.693907\pi$
$578$		0			0
$579$	−19.6753	+	18.4901i	−0.817676	+	0.768422i
$580$		0			0
$581$		−	8.21782i		−	0.340933i
$582$		0			0
$583$	34.1168	−	19.6974i	1.41298	−	0.815782i
$584$		0			0
$585$	−6.56930	−	4.35758i	−0.271607	−	0.180164i
$586$		0			0
$587$	−38.3139	−	22.1205i	−1.58138	−	0.913011i	−0.994658	−	0.103225i	$-0.967084\pi$
$587$	−38.3139	−	22.1205i	−1.58138	−	0.913011i	−0.586724	−	0.809787i	$-0.699583\pi$
$588$		0			0
$589$	−7.62772	+	17.6155i	−0.314295	+	0.725832i
$590$		0			0
$591$	27.2554	+	8.21782i	1.12114	+	0.338036i
$592$		0			0
$593$	−4.54755	+	2.62553i	−0.186745	+	0.107817i	−0.590458	−	0.807068i	$-0.701053\pi$
$593$	−4.54755	+	2.62553i	−0.186745	+	0.107817i	0.403713	+	0.914886i	$0.367720\pi$
$594$		0			0
$595$	0.744563	+	1.28962i	0.0305241	+	0.0528693i
$596$		0			0
$597$	−34.5475	+	8.11663i	−1.41394	+	0.332192i
$598$		0			0
$599$	0.0584220	+	0.101190i	0.00238706	+	0.00413451i	0.867216	−	0.497931i	$-0.165907\pi$
$599$	0.0584220	+	0.101190i	0.00238706	+	0.00413451i	−0.864829	+	0.502066i	$0.832574\pi$
$600$		0			0
$601$		−	27.4728i		−	1.12064i	−0.828277	−	0.560319i	$-0.810679\pi$
$601$		−	27.4728i		−	1.12064i	0.828277	−	0.560319i	$-0.189321\pi$
$602$		0			0
$603$	35.4198	+	2.20193i	1.44241	+	0.0896696i
$604$		0			0
$605$	0.686141	+	0.396143i	0.0278956	+	0.0161055i
$606$		0			0
$607$		−	2.52434i		−	0.102460i	−0.998687	−	0.0512299i	$-0.983686\pi$
$607$		−	2.52434i		−	0.102460i	0.998687	−	0.0512299i	$-0.0163141\pi$
$608$		0			0
$609$	−21.4891	+	5.04868i	−0.870783	+	0.204583i
$610$		0			0
$611$	7.05842	−	12.2255i	0.285553	−	0.494593i
$612$		0			0
$613$	−3.94158	+	6.82701i	−0.159199	+	0.275740i	−0.934580	−	0.355753i	$-0.884224\pi$
$613$	−3.94158	+	6.82701i	−0.159199	+	0.275740i	0.775381	+	0.631494i	$0.217558\pi$
$614$		0			0
$615$	−0.197015	−	0.838574i	−0.00794443	−	0.0338146i
$616$		0			0
$617$	−3.94158	+	2.27567i	−0.158682	+	0.0916151i	−0.577238	−	0.816576i	$-0.695870\pi$
$617$	−3.94158	+	2.27567i	−0.158682	+	0.0916151i	0.418556	+	0.908191i	$0.362536\pi$
$618$		0			0
$619$	−31.8614			−1.28062			−0.640309	−	0.768117i	$-0.721194\pi$
$619$	−31.8614			−1.28062			−0.640309	+	0.768117i	$0.721194\pi$
$620$		0			0
$621$	−13.4090	+	36.1793i	−0.538083	+	1.45183i
$622$		0			0
$623$	−8.74456	−	15.1460i	−0.350344	−	0.606813i
$624$		0			0
$625$	−7.98913	+	13.8376i	−0.319565	+	0.553503i
$626$		0			0
$627$	−19.9783	−	16.8781i	−0.797854	−	0.674045i
$628$		0			0
$629$	3.11684	−	5.39853i	0.124277	−	0.215254i
$630$		0			0
$631$	4.61684	+	7.99661i	0.183794	+	0.318340i	0.943169	−	0.332312i	$-0.107829\pi$
$631$	4.61684	+	7.99661i	0.183794	+	0.318340i	−0.759376	+	0.650652i	$0.774496\pi$
$632$		0			0
$633$	−18.9307	+	17.7904i	−0.752428	+	0.707105i
$634$		0			0
$635$	−15.3723			−0.610030
$636$		0			0
$637$	3.94158	−	2.27567i	0.156171	−	0.0901654i
$638$		0			0
$639$	17.8030	−	8.85402i	0.704275	−	0.350260i
$640$		0			0
$641$	10.3139	−	17.8641i	0.407373	−	0.705591i	−0.587222	−	0.809426i	$-0.699778\pi$
$641$	10.3139	−	17.8641i	0.407373	−	0.705591i	0.994594	+	0.103836i	$0.0331116\pi$
$642$		0			0
$643$	−1.50000	+	2.59808i	−0.0591542	+	0.102458i	−0.894086	−	0.447895i	$-0.852174\pi$
$643$	−1.50000	+	2.59808i	−0.0591542	+	0.102458i	0.834932	+	0.550353i	$0.185507\pi$
$644$		0			0
$645$	−0.0801714	−	0.341241i	−0.00315675	−	0.0134363i
$646$		0			0
$647$			44.4434i			1.74725i	0.486599	+	0.873625i	$0.338237\pi$
$647$			44.4434i			1.74725i	−0.486599	+	0.873625i	$0.661763\pi$
$648$		0			0
$649$	−22.1168	−	12.7692i	−0.868162	−	0.501234i
$650$		0			0
$651$	−17.3247	−	5.22360i	−0.679010	−	0.204729i
$652$		0			0
$653$		−	22.0742i		−	0.863831i	−0.901914	−	0.431916i	$-0.857838\pi$
$653$		−	22.0742i		−	0.863831i	0.901914	−	0.431916i	$-0.142162\pi$
$654$		0			0
$655$	−2.19702	−	3.80534i	−0.0858445	−	0.148687i
$656$		0			0
$657$	−15.4307	+	7.67420i	−0.602009	+	0.299399i
$658$		0			0
$659$	19.5475	+	33.8573i	0.761464	+	1.31889i	0.942096	+	0.335344i	$0.108853\pi$
$659$	19.5475	+	33.8573i	0.761464	+	1.31889i	−0.180631	+	0.983551i	$0.557814\pi$
$660$		0			0
$661$	−4.19702	+	2.42315i	−0.163245	+	0.0942495i	−0.579397	−	0.815046i	$-0.696712\pi$
$661$	−4.19702	+	2.42315i	−0.163245	+	0.0942495i	0.416152	+	0.909295i	$0.363378\pi$
$662$		0			0
$663$	−1.31386	+	4.35758i	−0.0510261	+	0.169234i
$664$		0			0
$665$	−4.88316	−	6.57835i	−0.189361	−	0.255097i
$666$		0			0
$667$	−34.5475	−	19.9460i	−1.33769	−	0.772314i
$668$		0			0
$669$	−22.9307	+	21.5494i	−0.886552	+	0.833150i
$670$		0			0
$671$	−3.00000	+	1.73205i	−0.115814	+	0.0668651i
$672$		0			0
$673$		−	21.1345i		−	0.814674i	−0.913278	−	0.407337i	$-0.866457\pi$
$673$		−	21.1345i		−	0.814674i	0.913278	−	0.407337i	$-0.133543\pi$
$674$		0			0
$675$	−21.3030	−	7.89542i	−0.819952	−	0.303895i
$676$		0			0
$677$	26.7446			1.02788			0.513939	−	0.857827i	$-0.328186\pi$
$677$	26.7446			1.02788			0.513939	+	0.857827i	$0.328186\pi$
$678$		0			0
$679$	26.2337	+	15.1460i	1.00676	+	0.581251i
$680$		0			0
$681$	3.62772	−	12.0318i	0.139014	−	0.461059i
$682$		0			0
$683$	−4.74456			−0.181546			−0.0907728	−	0.995872i	$-0.528934\pi$
$683$	−4.74456			−0.181546			−0.0907728	+	0.995872i	$0.528934\pi$
$684$		0			0
$685$	−10.3505			−0.395473
$686$		0			0
$687$	10.5584	−	35.0183i	0.402829	−	1.33603i
$688$		0			0
$689$	32.6644	+	18.8588i	1.24441	+	0.718463i
$690$		0			0
$691$	41.9565			1.59610			0.798050	−	0.602591i	$-0.205865\pi$
$691$	41.9565			1.59610			0.798050	+	0.602591i	$0.205865\pi$
$692$		0			0
$693$	13.6277	−	20.5446i	0.517674	−	0.780423i
$694$		0			0
$695$		−	13.0641i		−	0.495550i
$696$		0			0
$697$	−0.430703	+	0.248667i	−0.0163141	+	0.00941892i
$698$		0			0
$699$	5.74456	−	5.39853i	0.217279	−	0.204191i
$700$		0			0
$701$	14.0584	+	8.11663i	0.530979	+	0.306561i	0.741415	−	0.671047i	$-0.234155\pi$
$701$	14.0584	+	8.11663i	0.530979	+	0.306561i	−0.210436	+	0.977608i	$0.567488\pi$
$702$		0			0
$703$	−13.6277	+	31.4719i	−0.513979	+	1.18698i
$704$		0			0
$705$	−1.68614	+	5.59230i	−0.0635037	+	0.210618i
$706$		0			0
$707$	−1.62772	+	0.939764i	−0.0612167	+	0.0353435i
$708$		0			0
$709$	−0.244563	−	0.423595i	−0.00918474	−	0.0159084i	0.861397	−	0.507933i	$-0.169590\pi$
$709$	−0.244563	−	0.423595i	−0.00918474	−	0.0159084i	−0.870581	+	0.492025i	$0.836257\pi$
$710$		0			0
$711$	15.4090	+	30.9832i	0.577881	+	1.16196i
$712$		0			0
$713$	−16.3505	−	28.3200i	−0.612332	−	1.06059i
$714$		0			0
$715$			9.10268i			0.340421i
$716$		0			0
$717$	17.2337	+	5.19615i	0.643604	+	0.194054i
$718$		0			0
$719$	3.68614	+	2.12819i	0.137470	+	0.0793683i	0.567158	−	0.823609i	$-0.308043\pi$
$719$	3.68614	+	2.12819i	0.137470	+	0.0793683i	−0.429688	+	0.902978i	$0.641376\pi$
$720$		0			0
$721$		−	1.52967i		−	0.0569679i
$722$		0			0
$723$	0.175266	+	0.746000i	0.00651821	+	0.0277440i
$724$		0			0
$725$	11.7446	−	20.3422i	0.436182	−	0.755490i
$726$		0			0
$727$	16.8723	−	29.2236i	0.625758	−	1.08385i	−0.362635	−	0.931931i	$-0.618123\pi$
$727$	16.8723	−	29.2236i	0.625758	−	1.08385i	0.988394	−	0.151914i	$-0.0485437\pi$
$728$		0			0
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$		0			0
$731$	−0.175266	+	0.101190i	−0.00648245	+	0.00374264i
$732$		0			0
$733$	−24.9783			−0.922593			−0.461296	−	0.887246i	$-0.652616\pi$
$733$	−24.9783			−0.922593			−0.461296	+	0.887246i	$0.652616\pi$
$734$		0			0
$735$	−1.37228	+	1.28962i	−0.0506174	+	0.0475684i
$736$		0			0
$737$	−20.4891	−	35.4882i	−0.754727	−	1.30722i
$738$		0			0
$739$	15.2446	−	26.4044i	0.560780	−	0.971300i	−0.436648	−	0.899632i	$-0.643835\pi$
$739$	15.2446	−	26.4044i	0.560780	−	0.971300i	0.997429	−	0.0716677i	$-0.0228321\pi$
$740$		0			0
$741$	4.43070	−	24.6449i	0.162766	−	0.905351i
$742$		0			0
$743$	−5.31386	+	9.20387i	−0.194947	+	0.337657i	−0.946883	−	0.321578i	$-0.895787\pi$
$743$	−5.31386	+	9.20387i	−0.194947	+	0.337657i	0.751936	+	0.659236i	$0.229120\pi$
$744$		0			0
$745$	−0.941578	−	1.63086i	−0.0344967	−	0.0597501i
$746$		0			0
$747$	−5.74456	+	8.66025i	−0.210183	+	0.316862i
$748$		0			0
$749$	39.7228			1.45144
$750$		0			0
$751$	−24.9891	+	14.4275i	−0.911866	+	0.526466i	−0.881031	−	0.473058i	$-0.843150\pi$
$751$	−24.9891	+	14.4275i	−0.911866	+	0.526466i	−0.0308350	+	0.999524i	$0.509817\pi$
$752$		0			0
$753$	2.54755	+	10.8434i	0.0928378	+	0.395154i
$754$		0			0
$755$	5.37228	−	9.30506i	0.195517	−	0.338646i
$756$		0			0
$757$	12.8723	−	22.2954i	0.467851	−	0.810342i	−0.531474	−	0.847075i	$-0.678362\pi$
$757$	12.8723	−	22.2954i	0.467851	−	0.810342i	0.999325	+	0.0367328i	$0.0116950\pi$
$758$		0			0
$759$	43.3723	−	10.1899i	1.57431	−	0.369871i
$760$		0			0
$761$		−	33.4612i		−	1.21297i	−0.795096	−	0.606484i	$-0.792579\pi$
$761$		−	33.4612i		−	1.21297i	0.795096	−	0.606484i	$-0.207421\pi$
$762$		0			0
$763$	12.0000	+	6.92820i	0.434429	+	0.250818i
$764$		0			0
$765$	0.116844	−	1.87953i	0.00422450	−	0.0679545i
$766$		0			0
$767$		−	24.4511i		−	0.882878i
$768$		0			0
$769$	10.1277	+	17.5417i	0.365215	+	0.632571i	0.988811	−	0.149176i	$-0.0476622\pi$
$769$	10.1277	+	17.5417i	0.365215	+	0.632571i	−0.623596	+	0.781747i	$0.714329\pi$
$770$		0			0
$771$	3.17527	−	0.746000i	0.114354	−	0.0268665i
$772$		0			0
$773$	−21.6861	−	37.5615i	−0.779996	−	1.35099i	−0.931943	−	0.362604i	$-0.881888\pi$
$773$	−21.6861	−	37.5615i	−0.779996	−	1.35099i	0.151947	−	0.988389i	$-0.451446\pi$
$774$		0			0
$775$	16.6753	−	9.62747i	0.598993	−	0.345829i
$776$		0			0
$777$	−30.9525	−	9.33252i	−1.11041	−	0.334802i
$778$		0			0
$779$	2.19702	−	1.63086i	0.0787162	−	0.0584317i
$780$		0			0
$781$	−19.8832	−	11.4795i	−0.711475	−	0.410770i
$782$		0			0
$783$	26.1753	+	9.70121i	0.935428	+	0.346693i
$784$		0			0
$785$	14.0584	−	8.11663i	0.501767	−	0.289695i
$786$		0			0
$787$		−	7.57301i		−	0.269949i	−0.990849	−	0.134974i	$-0.956905\pi$
$787$		−	7.57301i		−	0.269949i	0.990849	−	0.134974i	$-0.0430952\pi$
$788$		0			0
$789$	5.00000	−	4.69882i	0.178005	−	0.167282i
$790$		0			0
$791$	34.9783			1.24368
$792$		0			0
$793$	−2.87228	−	1.65831i	−0.101998	−	0.0588884i
$794$		0			0
$795$	−14.9416	−	4.50506i	−0.529923	−	0.159778i
$796$		0			0
$797$	47.4891			1.68215			0.841076	−	0.540918i	$-0.181923\pi$
$797$	47.4891			1.68215			0.841076	+	0.540918i	$0.181923\pi$
$798$		0			0
$799$	3.37228			0.119303
$800$		0			0
$801$	−1.37228	+	22.0742i	−0.0484872	+	0.779955i
$802$		0			0
$803$	17.2337	+	9.94987i	0.608164	+	0.351123i
$804$		0			0
$805$	13.9565			0.491902
$806$		0			0
$807$	−15.2554	−	16.2333i	−0.537017	−	0.571438i
$808$		0			0
$809$			5.04868i			0.177502i	0.996054	+	0.0887510i	$0.0282875\pi$
$809$			5.04868i			0.177502i	−0.996054	+	0.0887510i	$0.971712\pi$
$810$		0			0
$811$	−24.1753	+	13.9576i	−0.848908	+	0.490117i	−0.860282	−	0.509818i	$-0.829713\pi$
$811$	−24.1753	+	13.9576i	−0.848908	+	0.490117i	0.0113740	+	0.999935i	$0.496379\pi$
$812$		0			0
$813$	10.5109	+	11.1846i	0.368632	+	0.392261i
$814$		0			0
$815$	6.60597	+	3.81396i	0.231397	+	0.133597i
$816$		0			0
$817$	0.894031	−	0.663646i	0.0312782	−	0.0232180i
$818$		0			0
$819$	23.5584	+	1.46455i	0.823198	+	0.0511755i
$820$		0			0
$821$	−44.4090	+	25.6395i	−1.54988	+	0.894825i	−0.551734	+	0.834020i	$0.686033\pi$
$821$	−44.4090	+	25.6395i	−1.54988	+	0.894825i	−0.998150	+	0.0608050i	$0.980633\pi$
$822$		0			0
$823$	3.56930	+	6.18220i	0.124418	+	0.215498i	0.921505	−	0.388366i	$-0.126960\pi$
$823$	3.56930	+	6.18220i	0.124418	+	0.215498i	−0.797087	+	0.603864i	$0.793627\pi$
$824$		0			0
$825$	6.00000	+	25.5383i	0.208893	+	0.889131i
$826$		0			0
$827$	2.56930	+	4.45015i	0.0893432	+	0.154747i	0.907234	−	0.420627i	$-0.138190\pi$
$827$	2.56930	+	4.45015i	0.0893432	+	0.154747i	−0.817890	+	0.575374i	$0.804857\pi$
$828$		0			0
$829$			31.2318i			1.08473i	0.840144	+	0.542363i	$0.182470\pi$
$829$			31.2318i			1.08473i	−0.840144	+	0.542363i	$0.817530\pi$
$830$		0			0
$831$	−1.74456	+	5.78606i	−0.0605182	+	0.200716i
$832$		0			0
$833$	0.941578	+	0.543620i	0.0326237	+	0.0188353i
$834$		0			0
$835$			14.3537i			0.496732i
$836$		0			0
$837$	14.6060	+	17.6155i	0.504856	+	0.608879i
$838$		0			0
$839$	−1.31386	+	2.27567i	−0.0453595	+	0.0785649i	−0.887814	−	0.460203i	$-0.847777\pi$
$839$	−1.31386	+	2.27567i	−0.0453595	+	0.0785649i	0.842454	+	0.538768i	$0.181110\pi$
$840$		0			0
$841$	0.0692967	−	0.120025i	0.00238954	−	0.00413881i
$842$		0			0
$843$	43.1753	−	10.1436i	1.48704	−	0.349365i
$844$		0			0
$845$	1.37228	−	0.792287i	0.0472079	−	0.0272555i
$846$		0			0
$847$	−2.37228			−0.0815126
$848$		0			0
$849$	34.2337	+	36.4280i	1.17490	+	1.25020i
$850$		0			0
$851$	−29.2119	−	50.5966i	−1.00137	−	1.73443i
$852$		0			0
$853$	4.87228	−	8.43904i	0.166824	−	0.288947i	−0.770478	−	0.637467i	$-0.779982\pi$
$853$	4.87228	−	8.43904i	0.166824	−	0.288947i	0.937301	+	0.348520i	$0.113316\pi$
$854$		0			0
$855$	0.547547	+	10.3460i	0.0187257	+	0.353826i
$856$		0			0
$857$	2.31386	−	4.00772i	0.0790399	−	0.136901i	−0.823796	−	0.566886i	$-0.808148\pi$
$857$	2.31386	−	4.00772i	0.0790399	−	0.136901i	0.902836	+	0.429985i	$0.141481\pi$
$858$		0			0
$859$	−3.38316	−	5.85980i	−0.115432	−	0.199934i	0.802520	−	0.596625i	$-0.203492\pi$
$859$	−3.38316	−	5.85980i	−0.115432	−	0.199934i	−0.917952	+	0.396691i	$0.870159\pi$
$860$		0			0
$861$	1.76631	+	1.87953i	0.0601958	+	0.0640541i
$862$		0			0
$863$	−10.5109			−0.357794			−0.178897	−	0.983868i	$-0.557253\pi$
$863$	−10.5109			−0.357794			−0.178897	+	0.983868i	$0.557253\pi$
$864$		0			0
$865$	−10.1970	+	5.88725i	−0.346709	+	0.200172i
$866$		0			0
$867$	27.6060	−	6.48577i	0.937548	−	0.220268i
$868$		0			0
$869$	19.9783	−	34.6033i	0.677716	−	1.17384i
$870$		0			0
$871$	19.6168	−	33.9774i	0.664691	−	1.15128i
$872$		0			0
$873$	−17.0584	−	34.2998i	−0.577340	−	1.16087i
$874$		0			0
$875$			17.6155i			0.595511i
$876$		0			0
$877$	17.3614	+	10.0236i	0.586253	+	0.338473i	0.763615	−	0.645672i	$-0.223423\pi$
$877$	17.3614	+	10.0236i	0.586253	+	0.338473i	−0.177361	+	0.984146i	$0.556756\pi$
$878$		0			0
$879$	−4.62772	+	15.3484i	−0.156089	+	0.517689i
$880$		0			0
$881$			8.80773i			0.296740i	0.988932	+	0.148370i	$0.0474027\pi$
$881$			8.80773i			0.296740i	−0.988932	+	0.148370i	$0.952597\pi$
$882$		0			0
$883$	9.87228	+	17.0993i	0.332229	+	0.575437i	0.982949	−	0.183881i	$-0.0588661\pi$
$883$	9.87228	+	17.0993i	0.332229	+	0.575437i	−0.650720	+	0.759318i	$0.725533\pi$
$884$		0			0
$885$	2.31386	+	9.84868i	0.0777795	+	0.331060i
$886$		0			0
$887$	−1.80298	−	3.12286i	−0.0605383	−	0.104855i	0.834168	−	0.551511i	$-0.185948\pi$
$887$	−1.80298	−	3.12286i	−0.0605383	−	0.104855i	−0.894706	+	0.446655i	$0.852615\pi$
$888$		0			0
$889$	39.8614	−	23.0140i	1.33691	−	0.771865i
$890$		0			0
$891$	−28.7228	+	12.1244i	−0.962250	+	0.406181i
$892$		0			0
$893$	−18.4307	+	2.12819i	−0.616760	+	0.0712173i
$894$		0			0
$895$	−14.7446	−	8.51278i	−0.492856	−	0.284551i
$896$		0			0
$897$	29.2119	+	31.0843i	0.975358	+	1.03788i
$898$		0			0
$899$	−20.4891	+	11.8294i	−0.683351	+	0.394533i
$900$		0			0
$901$			9.01011i			0.300170i
$902$		0			0
$903$	0.718765	+	0.764836i	0.0239190	+	0.0254521i
$904$		0			0
$905$	−1.64947			−0.0548302
$906$		0			0
$907$	−26.0584	−	15.0448i	−0.865256	−	0.499556i	0.000513060	−	1.00000i	$-0.499837\pi$
$907$	−26.0584	−	15.0448i	−0.865256	−	0.499556i	−0.865769	+	0.500444i	$0.833170\pi$
$908$		0			0
$909$	2.37228	+	0.147477i	0.0786836	+	0.00489150i
$910$		0			0
$911$	9.48913			0.314389			0.157194	−	0.987568i	$-0.449755\pi$
$911$	9.48913			0.314389			0.157194	+	0.987568i	$0.449755\pi$
$912$		0			0
$913$	12.0000			0.397142
$914$		0			0
$915$	1.31386	+	0.396143i	0.0434348	+	0.0130961i
$916$		0			0
$917$	11.3940	+	6.57835i	0.376264	+	0.217236i
$918$		0			0
$919$	−19.8614			−0.655167			−0.327584	−	0.944822i	$-0.606234\pi$
$919$	−19.8614			−0.655167			−0.327584	+	0.944822i	$0.606234\pi$
$920$		0			0
$921$	23.7446	−	22.3143i	0.782410	−	0.735281i
$922$		0			0
$923$		−	21.9817i		−	0.723535i
$924$		0			0
$925$	29.7921	−	17.2005i	0.979559	−	0.565548i
$926$		0			0
$927$	−1.06930	+	1.61203i	−0.0351203	+	0.0529459i
$928$		0			0
$929$	17.3139	+	9.99616i	0.568049	+	0.327963i	0.756370	−	0.654144i	$-0.226971\pi$
$929$	17.3139	+	9.99616i	0.568049	+	0.327963i	−0.188321	+	0.982108i	$0.560304\pi$
$930$		0			0
$931$	−5.48913	−	2.37686i	−0.179899	−	0.0778985i
$932$		0			0
$933$	20.3505	+	6.13592i	0.666247	+	0.200881i
$934$		0			0
$935$	−1.88316	+	1.08724i	−0.0615858	+	0.0355566i
$936$		0			0
$937$	5.98913	+	10.3735i	0.195656	+	0.338886i	0.947115	−	0.320893i	$-0.103983\pi$
$937$	5.98913	+	10.3735i	0.195656	+	0.338886i	−0.751459	+	0.659780i	$0.770650\pi$
$938$		0			0
$939$	54.5475	−	12.8155i	1.78009	−	0.418216i
$940$		0			0
$941$	27.8030	+	48.1562i	0.906351	+	1.56985i	0.819093	+	0.573661i	$0.194477\pi$
$941$	27.8030	+	48.1562i	0.906351	+	1.56985i	0.0872585	+	0.996186i	$0.472189\pi$
$942$		0			0
$943$			4.66115i			0.151788i
$944$		0			0
$945$	−9.62772	+	1.63948i	−0.313190	+	0.0533322i
$946$		0			0
$947$	−6.68614	−	3.86025i	−0.217270	−	0.125441i	0.387415	−	0.921905i	$-0.373368\pi$
$947$	−6.68614	−	3.86025i	−0.217270	−	0.125441i	−0.604686	+	0.796464i	$0.706701\pi$
$948$		0			0
$949$			19.0526i			0.618472i
$950$		0			0
$951$	−36.0367	+	8.46649i	−1.16857	+	0.274545i
$952$		0			0
$953$	−24.8030	+	42.9600i	−0.803447	+	1.39161i	0.113887	+	0.993494i	$0.463670\pi$
$953$	−24.8030	+	42.9600i	−0.803447	+	1.39161i	−0.917334	+	0.398118i	$0.869663\pi$
$954$		0			0
$955$	2.62772	−	4.55134i	0.0850310	−	0.147278i
$956$		0			0
$957$	−7.37228	−	31.3793i	−0.238312	−	1.01435i
$958$		0			0
$959$	26.8397	−	15.4959i	0.866698	−	0.500388i
$960$		0			0
$961$	11.6060			0.374386
$962$		0			0
$963$	−41.8614	−	27.7677i	−1.34896	−	0.894802i
$964$		0			0
$965$	−6.17527	−	10.6959i	−0.198789	−	0.344312i
$966$		0			0
$967$	−1.87228	+	3.24289i	−0.0602085	+	0.104284i	−0.894559	−	0.446951i	$-0.852510\pi$
$967$	−1.87228	+	3.24289i	−0.0602085	+	0.104284i	0.834350	+	0.551235i	$0.185843\pi$
$968$		0			0
$969$	5.62772	−	2.02700i	0.180788	−	0.0651168i
$970$		0			0
$971$	−0.430703	+	0.746000i	−0.0138219	+	0.0239403i	−0.872854	−	0.487982i	$-0.837733\pi$
$971$	−0.430703	+	0.746000i	−0.0138219	+	0.0239403i	0.859032	+	0.511922i	$0.171066\pi$
$972$		0			0
$973$	19.5584	+	33.8762i	0.627014	+	1.08602i
$974$		0			0
$975$	−18.3030	+	17.2005i	−0.586165	+	0.550856i
$976$		0			0
$977$	43.2119			1.38247			0.691236	−	0.722629i	$-0.257066\pi$
$977$	43.2119			1.38247			0.691236	+	0.722629i	$0.257066\pi$
$978$		0			0
$979$	22.1168	−	12.7692i	0.706857	−	0.408104i
$980$		0			0
$981$	−7.80298	−	15.6896i	−0.249130	−	0.500932i
$982$		0			0
$983$	1.43070	−	2.47805i	0.0456323	−	0.0790375i	−0.842307	−	0.538998i	$-0.818803\pi$
$983$	1.43070	−	2.47805i	0.0456323	−	0.0790375i	0.887939	+	0.459960i	$0.152136\pi$
$984$		0			0
$985$	−6.51087	+	11.2772i	−0.207454	+	0.359320i
$986$		0			0
$987$	−4.00000	−	17.0256i	−0.127321	−	0.541929i
$988$		0			0
$989$			1.89676i			0.0603134i
$990$		0			0
$991$	−14.8723	−	8.58652i	−0.472434	−	0.272760i	0.244824	−	0.969567i	$-0.421270\pi$
$991$	−14.8723	−	8.58652i	−0.472434	−	0.272760i	−0.717258	+	0.696808i	$0.754603\pi$
$992$		0			0
$993$	32.4198	+	9.77495i	1.02881	+	0.310199i
$994$		0			0
$995$		−	16.2333i		−	0.514629i
$996$		0			0
$997$	−6.75544	−	11.7008i	−0.213947	−	0.370567i	0.738999	−	0.673706i	$-0.235299\pi$
$997$	−6.75544	−	11.7008i	−0.213947	−	0.370567i	−0.952946	+	0.303139i	$0.901965\pi$
$998$		0			0
$999$	26.0951	+	31.4719i	0.825612	+	0.995726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bn.i.65.2		4
3.2	odd	2		912.2.bn.j.65.2		4
4.3	odd	2		456.2.bf.b.65.1	yes	4
12.11	even	2		456.2.bf.a.65.1	✓	4
19.12	odd	6		912.2.bn.j.449.2		4
57.50	even	6	inner	912.2.bn.i.449.1		4
76.31	even	6		456.2.bf.a.449.1	yes	4
228.107	odd	6		456.2.bf.b.449.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bf.a.65.1	✓	4	12.11	even	2
456.2.bf.a.449.1	yes	4	76.31	even	6
456.2.bf.b.65.1	yes	4	4.3	odd	2
456.2.bf.b.449.2	yes	4	228.107	odd	6
912.2.bn.i.65.2		4	1.1	even	1	trivial
912.2.bn.i.449.1		4	57.50	even	6	inner
912.2.bn.j.65.2		4	3.2	odd	2
912.2.bn.j.449.2		4	19.12	odd	6

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 1.65831i) q^{3} +(-0.686141 - 0.396143i) q^{5} +2.37228 q^{7} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 1.65831i) q^{3} +(-0.686141 - 0.396143i) q^{5} +2.37228 q^{7} +(-2.50000 - 1.65831i) q^{9} +3.46410i q^{11} +(-2.87228 + 1.65831i) q^{13} +(1.00000 - 0.939764i) q^{15} +(-0.686141 - 0.396143i) q^{17} +(4.00000 + 1.73205i) q^{19} +(-1.18614 + 3.93398i) q^{21} +(-6.43070 + 3.71277i) q^{23} +(-2.18614 - 3.78651i) q^{25} +(4.00000 - 3.31662i) q^{27} +(2.68614 + 4.65253i) q^{29} +4.40387i q^{31} +(-5.74456 - 1.73205i) q^{33} +(-1.62772 - 0.939764i) q^{35} +7.86797i q^{37} +(-1.31386 - 5.59230i) q^{39} +(0.313859 - 0.543620i) q^{41} +(0.127719 - 0.221215i) q^{43} +(1.05842 + 2.12819i) q^{45} +(-3.68614 + 2.12819i) q^{47} -1.37228 q^{49} +(1.00000 - 0.939764i) q^{51} +(-5.68614 - 9.84868i) q^{53} +(1.37228 - 2.37686i) q^{55} +(-4.87228 + 5.76722i) q^{57} +(-3.68614 + 6.38458i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-5.93070 - 3.93398i) q^{63} +2.62772 q^{65} +(-10.2446 + 5.91470i) q^{67} +(-2.94158 - 12.5205i) q^{69} +(-3.31386 + 5.73977i) q^{71} +(2.87228 - 4.97494i) q^{73} +(7.37228 - 1.73205i) q^{75} +8.21782i q^{77} +(-9.98913 - 5.76722i) q^{79} +(3.50000 + 8.29156i) q^{81} -3.46410i q^{83} +(0.313859 + 0.543620i) q^{85} +(-9.05842 + 2.12819i) q^{87} +(-3.68614 - 6.38458i) q^{89} +(-6.81386 + 3.93398i) q^{91} +(-7.30298 - 2.20193i) q^{93} +(-2.05842 - 2.77300i) q^{95} +(11.0584 + 6.38458i) q^{97} +(5.74456 - 8.66025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 3 q^{5} - 2 q^{7} - 10 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 3 * q^5 - 2 * q^7 - 10 * q^9	\( 4 q - 2 q^{3} + 3 q^{5} - 2 q^{7} - 10 q^{9} + 4 q^{15} + 3 q^{17} + 16 q^{19} + q^{21} + 3 q^{23} - 3 q^{25} + 16 q^{27} + 5 q^{29} - 18 q^{35} - 11 q^{39} + 7 q^{41} + 12 q^{43} - 13 q^{45} - 9 q^{47} + 6 q^{49} + 4 q^{51} - 17 q^{53} - 6 q^{55} - 8 q^{57} - 9 q^{59} + 2 q^{61} + 5 q^{63} + 22 q^{65} - 18 q^{67} - 29 q^{69} - 19 q^{71} + 18 q^{75} + 6 q^{79} + 14 q^{81} + 7 q^{85} - 19 q^{87} - 9 q^{89} - 33 q^{91} + 11 q^{93} + 9 q^{95} + 27 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 3 * q^5 - 2 * q^7 - 10 * q^9 + 4 * q^15 + 3 * q^17 + 16 * q^19 + q^21 + 3 * q^23 - 3 * q^25 + 16 * q^27 + 5 * q^29 - 18 * q^35 - 11 * q^39 + 7 * q^41 + 12 * q^43 - 13 * q^45 - 9 * q^47 + 6 * q^49 + 4 * q^51 - 17 * q^53 - 6 * q^55 - 8 * q^57 - 9 * q^59 + 2 * q^61 + 5 * q^63 + 22 * q^65 - 18 * q^67 - 29 * q^69 - 19 * q^71 + 18 * q^75 + 6 * q^79 + 14 * q^81 + 7 * q^85 - 19 * q^87 - 9 * q^89 - 33 * q^91 + 11 * q^93 + 9 * q^95 + 27 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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