LMFDB - Embedded newform 456.2.bf.b.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(65,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, 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("456.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bf (of order $6$, 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:	$3.64117833217$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.1
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	456.65
Dual form			456.2.bf.b.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 1.65831i) q^{3} +(-0.686141 - 0.396143i) q^{5} -2.37228 q^{7} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})$	\(q+(0.500000 - 1.65831i) q^{3} +(-0.686141 - 0.396143i) q^{5} -2.37228 q^{7} +(-2.50000 - 1.65831i) q^{9} -3.46410i q^{11} +(-2.87228 + 1.65831i) q^{13} +(-1.00000 + 0.939764i) q^{15} +(-0.686141 - 0.396143i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(-1.18614 + 3.93398i) q^{21} +(6.43070 - 3.71277i) q^{23} +(-2.18614 - 3.78651i) q^{25} +(-4.00000 + 3.31662i) q^{27} +(2.68614 + 4.65253i) q^{29} -4.40387i q^{31} +(-5.74456 - 1.73205i) q^{33} +(1.62772 + 0.939764i) q^{35} +7.86797i q^{37} +(1.31386 + 5.59230i) q^{39} +(0.313859 - 0.543620i) q^{41} +(-0.127719 + 0.221215i) q^{43} +(1.05842 + 2.12819i) q^{45} +(3.68614 - 2.12819i) q^{47} -1.37228 q^{49} +(-1.00000 + 0.939764i) q^{51} +(-5.68614 - 9.84868i) q^{53} +(-1.37228 + 2.37686i) q^{55} +(-4.87228 + 5.76722i) q^{57} +(3.68614 - 6.38458i) q^{59} +(0.500000 + 0.866025i) q^{61} +(5.93070 + 3.93398i) q^{63} +2.62772 q^{65} +(10.2446 - 5.91470i) q^{67} +(-2.94158 - 12.5205i) q^{69} +(3.31386 - 5.73977i) q^{71} +(2.87228 - 4.97494i) q^{73} +(-7.37228 + 1.73205i) q^{75} +8.21782i q^{77} +(9.98913 + 5.76722i) q^{79} +(3.50000 + 8.29156i) q^{81} +3.46410i q^{83} +(0.313859 + 0.543620i) q^{85} +(9.05842 - 2.12819i) q^{87} +(-3.68614 - 6.38458i) q^{89} +(6.81386 - 3.93398i) q^{91} +(-7.30298 - 2.20193i) q^{93} +(2.05842 + 2.77300i) q^{95} +(11.0584 + 6.38458i) q^{97} +(-5.74456 + 8.66025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

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	$-0.647977\pi$
$7$	−2.37228			−0.896638			−0.448319	+	0.893874i	$0.647977\pi$
$8$		0			0
$9$	−2.50000	−	1.65831i	−0.833333	−	0.552771i
$10$		0			0
$11$		−	3.46410i		−	1.04447i	−0.852803	−	0.522233i	$-0.825099\pi$
$11$		−	3.46410i		−	1.04447i	0.852803	−	0.522233i	$-0.174901\pi$
$12$		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	0.353956	−	0.935262i	$-0.384836\pi$
$23$	6.43070	−	3.71277i	1.34089	−	0.774166i	0.986939	+	0.161096i	$0.0515030\pi$
$24$		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	$-0.870579\pi$
$31$		−	4.40387i		−	0.790958i	0.918475	−	0.395479i	$-0.129421\pi$
$32$		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	−0.875600	−	0.483038i	$-0.839533\pi$
$43$	−0.127719	+	0.221215i	−0.0194769	+	0.0337350i	0.856123	+	0.516773i	$0.172867\pi$
$44$		0			0
$45$	1.05842	+	2.12819i	0.157780	+	0.317252i
$46$		0			0
$47$	3.68614	−	2.12819i	0.537679	−	0.310429i	−0.206459	−	0.978455i	$-0.566194\pi$
$47$	3.68614	−	2.12819i	0.537679	−	0.310429i	0.744138	+	0.668026i	$0.232861\pi$
$48$		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	−0.519839	−	0.854264i	$-0.674008\pi$
$59$	3.68614	−	6.38458i	0.479895	−	0.831202i	0.999734	+	0.0230621i	$0.00734155\pi$
$60$		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	0.280151	−	0.959956i	$-0.409616\pi$
$67$	10.2446	−	5.91470i	1.25157	−	0.722596i	0.971422	+	0.237360i	$0.0762822\pi$
$68$		0			0
$69$	−2.94158	−	12.5205i	−0.354124	−	1.50729i
$70$		0			0
$71$	3.31386	−	5.73977i	0.393283	−	0.681186i	−0.599598	−	0.800302i	$-0.704673\pi$
$71$	3.31386	−	5.73977i	0.393283	−	0.681186i	0.992880	+	0.119116i	$0.0380060\pi$
$72$		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	0.942385	−	0.334531i	$-0.108578\pi$
$79$	9.98913	+	5.76722i	1.12386	+	0.648863i	0.181480	+	0.983395i	$0.441911\pi$
$80$		0			0
$81$	3.50000	+	8.29156i	0.388889	+	0.921285i
$82$		0			0
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$		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	$0.0101136\pi$
$103$			0.644810i			0.0635350i	−0.999495	+	0.0317675i	$0.989886\pi$
$104$		0			0
$105$	2.37228	−	2.22938i	0.231511	−	0.217566i
$106$		0			0
$107$	−16.7446			−1.61876			−0.809379	−	0.587287i	$-0.800196\pi$
$107$	−16.7446			−1.61876			−0.809379	+	0.587287i	$0.800196\pi$
$108$		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	−0.999947	−	0.0102734i	$-0.996730\pi$
$127$	−16.8030	+	9.70121i	−1.49102	+	0.860843i	−0.491077	+	0.871116i	$0.663396\pi$
$128$		0			0
$129$	0.302985	+	0.322405i	0.0266763	+	0.0283862i
$130$		0			0
$131$	−4.80298	−	2.77300i	−0.419639	−	0.242279i	0.275284	−	0.961363i	$-0.411228\pi$
$131$	−4.80298	−	2.77300i	−0.419639	−	0.242279i	−0.694923	+	0.719084i	$0.744561\pi$
$132$		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	$-0.920164\pi$
$139$	−8.24456	−	14.2800i	−0.699295	−	1.21121i	0.269417	−	0.963024i	$-0.413169\pi$
$140$		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	$-0.813938\pi$
$151$		−	13.5615i		−	1.10362i	0.833971	−	0.551808i	$-0.186062\pi$
$152$		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	$-0.376938\pi$
$163$	9.62772			0.754101			0.377051	+	0.926193i	$0.376938\pi$
$164$		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	$0.0805790\pi$
$167$	9.05842	+	15.6896i	0.700962	+	1.21410i	−0.267167	+	0.963650i	$0.586088\pi$
$168$		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	$-0.796810\pi$
$179$	−21.4891			−1.60617			−0.803086	+	0.595863i	$0.796810\pi$
$180$		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	$-0.922858\pi$
$191$		−	6.63325i		−	0.479965i	0.970777	−	0.239983i	$-0.0771417\pi$
$192$		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	$-0.907943\pi$
$199$	−10.2446	−	17.7441i	−0.726218	−	1.25785i	0.232253	−	0.972655i	$-0.425390\pi$
$200$		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	−0.0188916	−	0.999822i	$-0.506014\pi$
$211$	−12.9891	−	7.49927i	−0.894208	−	0.516271i	−0.875317	+	0.483550i	$0.839347\pi$
$212$		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	−0.129949	−	0.991521i	$-0.541481\pi$
$223$	−15.7337	−	9.08385i	−1.05361	−	0.608300i	−0.923657	+	0.383221i	$0.874815\pi$
$224$		0			0
$225$	−0.813859	+	13.0916i	−0.0542573	+	0.872771i
$226$		0			0
$227$	7.25544			0.481560			0.240780	−	0.970580i	$-0.422597\pi$
$227$	7.25544			0.481560			0.240780	+	0.970580i	$0.422597\pi$
$228$		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	$0.109112\pi$
$239$			10.3923i			0.672222i	−0.941822	+	0.336111i	$0.890888\pi$
$240$		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	−0.665359	−	0.746523i	$-0.731722\pi$
$251$	−5.56930	+	3.21543i	−0.351531	+	0.202956i	0.313828	+	0.949480i	$0.398388\pi$
$252$		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	0.602030	−	0.798474i	$-0.294359\pi$
$263$	3.43070	+	1.98072i	0.211546	+	0.122136i	−0.390484	+	0.920610i	$0.627692\pi$
$264$		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	−0.968642	−	0.248462i	$-0.920075\pi$
$271$	−4.43070	+	7.67420i	−0.269146	+	0.466175i	0.699495	+	0.714637i	$0.253408\pi$
$272$		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	$0.494846\pi$
$283$	−14.4307	+	24.9947i	−0.857816	+	1.48578i	−0.874007	+	0.485912i	$0.838487\pi$
$284$		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	0.886761	−	0.462228i	$-0.152950\pi$
$307$	16.2921	+	9.40625i	0.929840	+	0.536843i	0.0430789	+	0.999072i	$0.486283\pi$
$308$		0			0
$309$	1.06930	+	0.322405i	0.0608302	+	0.0183410i
$310$		0			0
$311$			12.2718i			0.695872i	0.937518	+	0.347936i	$0.113117\pi$
$311$			12.2718i			0.695872i	−0.937518	+	0.347936i	$0.886883\pi$
$312$		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	$0.180548\pi$
$331$			19.5499i			1.07456i	−0.843404	+	0.537280i	$0.819452\pi$
$332$		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	0.283540	−	0.958960i	$-0.408491\pi$
$347$	−7.54755	−	4.35758i	−0.405174	−	0.233927i	−0.688714	+	0.725033i	$0.741824\pi$
$348$		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	0.546824	−	0.837248i	$-0.315837\pi$
$359$	1.80298	+	1.04095i	0.0951579	+	0.0549394i	−0.451666	+	0.892187i	$0.649170\pi$
$360$		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	$0.000733819\pi$
$367$	9.61684	+	16.6569i	0.501995	+	0.869481i	−0.498002	+	0.867176i	$0.665933\pi$
$368$		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	$-0.911026\pi$
$379$		−	10.7422i		−	0.551788i	0.961188	−	0.275894i	$-0.0889738\pi$
$380$		0			0
$381$	7.68614	+	32.7152i	0.393773	+	1.67605i
$382$		0			0
$383$	4.80298	−	8.31901i	0.245421	−	0.425082i	−0.716829	−	0.697249i	$-0.754407\pi$
$383$	4.80298	−	8.31901i	0.245421	−	0.425082i	0.962250	+	0.272167i	$0.0877405\pi$
$384$		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	$-0.631106\pi$
$419$		−	37.5152i		−	1.83274i	0.400335	−	0.916369i	$-0.368894\pi$
$420$		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	$-0.818916\pi$
$431$	−18.4307	−	31.9229i	−0.887776	−	1.53767i	−0.0452769	−	0.998974i	$-0.514417\pi$
$432$		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	0.603528	−	0.797342i	$-0.293761\pi$
$439$	4.50000	+	2.59808i	0.214773	+	0.123999i	−0.388755	+	0.921341i	$0.627095\pi$
$440$		0			0
$441$	3.43070	+	2.27567i	0.163367	+	0.108365i
$442$		0			0
$443$	31.0367	−	17.9190i	1.47460	−	0.851359i	0.475007	−	0.879982i	$-0.342446\pi$
$443$	31.0367	−	17.9190i	1.47460	−	0.851359i	0.999590	+	0.0286234i	$0.00911235\pi$
$444$		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	$-0.365663\pi$
$463$	17.6277			0.819230			0.409615	+	0.912259i	$0.365663\pi$
$464$		0			0
$465$	4.13859	+	4.40387i	0.191923	+	0.204224i
$466$		0			0
$467$		−	4.16381i		−	0.192678i	−0.995349	−	0.0963392i	$-0.969287\pi$
$467$		−	4.16381i		−	0.192678i	0.995349	−	0.0963392i	$-0.0307133\pi$
$468$		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	−0.291287	−	0.956636i	$-0.594083\pi$
$479$	8.56930	−	4.94749i	0.391541	−	0.226056i	0.682828	+	0.730579i	$0.260750\pi$
$480$		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	$0.00212722\pi$
$487$			0.294954i			0.0133656i	−0.999978	+	0.00668281i	$0.997873\pi$
$488$		0			0
$489$	4.81386	−	15.9658i	0.217690	−	0.721997i
$490$		0			0
$491$	18.1753	+	10.4935i	0.820238	+	0.473565i	0.850499	−	0.525977i	$-0.176300\pi$
$491$	18.1753	+	10.4935i	0.820238	+	0.473565i	−0.0302604	+	0.999542i	$0.509634\pi$
$492$		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	$-0.654971\pi$
$499$	11.8723	−	20.5634i	0.531476	−	0.920544i	0.999325	−	0.0367354i	$-0.0116959\pi$
$500$		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	$0.726693\pi$
$503$	−36.6861	+	21.1808i	−1.63575	+	0.944403i	−0.982272	+	0.187461i	$0.939974\pi$
$504$		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	−0.259006	−	0.965876i	$-0.583395\pi$
$523$	10.2446	−	5.91470i	0.447963	−	0.258632i	0.706970	+	0.707244i	$0.250062\pi$
$524$		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	$0.675274\pi$
$547$	−35.6168	+	20.5634i	−1.52287	+	0.879227i	−0.999634	+	0.0270369i	$0.991393\pi$
$548$		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	$-0.127089\pi$
$563$	43.7228			1.84270			0.921348	+	0.388738i	$0.127089\pi$
$564$		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	$-0.435433\pi$
$571$	9.62772			0.402907			0.201454	+	0.979498i	$0.435433\pi$
$572$		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	$0.0329160\pi$
$587$	38.3139	+	22.1205i	1.58138	+	0.913011i	0.586724	+	0.809787i	$0.300417\pi$
$588$		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	0.864829	−	0.502066i	$-0.167426\pi$
$599$	−0.0584220	−	0.101190i	−0.00238706	−	0.00413451i	−0.867216	+	0.497931i	$0.834093\pi$
$600$		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	$0.0163141\pi$
$607$			2.52434i			0.102460i	−0.998687	+	0.0512299i	$0.983686\pi$
$608$		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	$-0.278806\pi$
$619$	31.8614			1.28062			0.640309	+	0.768117i	$0.278806\pi$
$620$		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	0.759376	−	0.650652i	$-0.225504\pi$
$631$	−4.61684	−	7.99661i	−0.183794	−	0.318340i	−0.943169	+	0.332312i	$0.892171\pi$
$632$		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	−0.834932	−	0.550353i	$-0.814493\pi$
$643$	1.50000	−	2.59808i	0.0591542	−	0.102458i	0.894086	+	0.447895i	$0.147826\pi$
$644$		0			0
$645$	−0.0801714	−	0.341241i	−0.00315675	−	0.0134363i
$646$		0			0
$647$		−	44.4434i		−	1.74725i	−0.486599	−	0.873625i	$-0.661763\pi$
$647$		−	44.4434i		−	1.74725i	0.486599	−	0.873625i	$-0.338237\pi$
$648$		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	$-0.891147\pi$
$659$	−19.5475	−	33.8573i	−0.761464	−	1.31889i	0.180631	−	0.983551i	$-0.442186\pi$
$660$		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	$-0.471066\pi$
$683$	4.74456			0.181546			0.0907728	+	0.995872i	$0.471066\pi$
$684$		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	$-0.794135\pi$
$691$	−41.9565			−1.59610			−0.798050	+	0.602591i	$0.794135\pi$
$692$		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	0.429688	−	0.902978i	$-0.358624\pi$
$719$	−3.68614	−	2.12819i	−0.137470	−	0.0793683i	−0.567158	+	0.823609i	$0.691957\pi$
$720$		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	$0.381877\pi$
$727$	−16.8723	+	29.2236i	−0.625758	+	1.08385i	−0.988394	+	0.151914i	$0.951456\pi$
$728$		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	$0.356165\pi$
$739$	−15.2446	+	26.4044i	−0.560780	+	0.971300i	−0.997429	+	0.0716677i	$0.977168\pi$
$740$		0			0
$741$	4.43070	−	24.6449i	0.162766	−	0.905351i
$742$		0			0
$743$	5.31386	−	9.20387i	0.194947	−	0.337657i	−0.751936	−	0.659236i	$-0.770880\pi$
$743$	5.31386	−	9.20387i	0.194947	−	0.337657i	0.946883	+	0.321578i	$0.104213\pi$
$744$		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	0.0308350	−	0.999524i	$-0.490183\pi$
$751$	24.9891	−	14.4275i	0.911866	−	0.526466i	0.881031	+	0.473058i	$0.156850\pi$
$752$		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	$0.0430952\pi$
$787$			7.57301i			0.269949i	−0.990849	+	0.134974i	$0.956905\pi$
$788$		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	−0.0113740	−	0.999935i	$-0.503621\pi$
$811$	24.1753	−	13.9576i	0.848908	−	0.490117i	0.860282	+	0.509818i	$0.170287\pi$
$812$		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	0.797087	−	0.603864i	$-0.206373\pi$
$823$	−3.56930	−	6.18220i	−0.124418	−	0.215498i	−0.921505	+	0.388366i	$0.873040\pi$
$824$		0			0
$825$	6.00000	+	25.5383i	0.208893	+	0.889131i
$826$		0			0
$827$	−2.56930	−	4.45015i	−0.0893432	−	0.154747i	0.817890	−	0.575374i	$-0.195143\pi$
$827$	−2.56930	−	4.45015i	−0.0893432	−	0.154747i	−0.907234	+	0.420627i	$0.861810\pi$
$828$		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	−0.842454	−	0.538768i	$-0.818890\pi$
$839$	1.31386	−	2.27567i	0.0453595	−	0.0785649i	0.887814	+	0.460203i	$0.152223\pi$
$840$		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	0.917952	−	0.396691i	$-0.129841\pi$
$859$	3.38316	+	5.85980i	0.115432	+	0.199934i	−0.802520	+	0.596625i	$0.796508\pi$
$860$		0			0
$861$	1.76631	+	1.87953i	0.0601958	+	0.0640541i
$862$		0			0
$863$	10.5109			0.357794			0.178897	−	0.983868i	$-0.442747\pi$
$863$	10.5109			0.357794			0.178897	+	0.983868i	$0.442747\pi$
$864$		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	0.650720	−	0.759318i	$-0.274467\pi$
$883$	−9.87228	−	17.0993i	−0.332229	−	0.575437i	−0.982949	+	0.183881i	$0.941134\pi$
$884$		0			0
$885$	2.31386	+	9.84868i	0.0777795	+	0.331060i
$886$		0			0
$887$	1.80298	+	3.12286i	0.0605383	+	0.104855i	0.894706	−	0.446655i	$-0.147385\pi$
$887$	1.80298	+	3.12286i	0.0605383	+	0.104855i	−0.834168	+	0.551511i	$0.814052\pi$
$888$		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	0.865769	−	0.500444i	$-0.166830\pi$
$907$	26.0584	+	15.0448i	0.865256	+	0.499556i	−0.000513060		1.00000i	$0.500163\pi$
$908$		0			0
$909$	2.37228	+	0.147477i	0.0786836	+	0.00489150i
$910$		0			0
$911$	−9.48913			−0.314389			−0.157194	−	0.987568i	$-0.550245\pi$
$911$	−9.48913			−0.314389			−0.157194	+	0.987568i	$0.550245\pi$
$912$		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	$-0.393766\pi$
$919$	19.8614			0.655167			0.327584	+	0.944822i	$0.393766\pi$
$920$		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	0.604686	−	0.796464i	$-0.293299\pi$
$947$	6.68614	+	3.86025i	0.217270	+	0.125441i	−0.387415	+	0.921905i	$0.626632\pi$
$948$		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	−0.834350	−	0.551235i	$-0.814157\pi$
$967$	1.87228	−	3.24289i	0.0602085	−	0.104284i	0.894559	+	0.446951i	$0.147490\pi$
$968$		0			0
$969$	5.62772	−	2.02700i	0.180788	−	0.0651168i
$970$		0			0
$971$	0.430703	−	0.746000i	0.0138219	−	0.0239403i	−0.859032	−	0.511922i	$-0.828934\pi$
$971$	0.430703	−	0.746000i	0.0138219	−	0.0239403i	0.872854	+	0.487982i	$0.162267\pi$
$972$		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	−0.887939	−	0.459960i	$-0.847864\pi$
$983$	−1.43070	+	2.47805i	−0.0456323	+	0.0790375i	0.842307	+	0.538998i	$0.181197\pi$
$984$		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	0.717258	−	0.696808i	$-0.245397\pi$
$991$	14.8723	+	8.58652i	0.472434	+	0.272760i	−0.244824	+	0.969567i	$0.578730\pi$
$992$		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	456.2.bf.b.65.1	yes	4
3.2	odd	2		456.2.bf.a.65.1	✓	4
4.3	odd	2		912.2.bn.i.65.2		4
12.11	even	2		912.2.bn.j.65.2		4
19.12	odd	6		456.2.bf.a.449.1	yes	4
57.50	even	6	inner	456.2.bf.b.449.2	yes	4
76.31	even	6		912.2.bn.j.449.2		4
228.107	odd	6		912.2.bn.i.449.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bf.a.65.1	✓	4	3.2	odd	2
456.2.bf.a.449.1	yes	4	19.12	odd	6
456.2.bf.b.65.1	yes	4	1.1	even	1	trivial
456.2.bf.b.449.2	yes	4	57.50	even	6	inner
912.2.bn.i.65.2		4	4.3	odd	2
912.2.bn.i.449.1		4	228.107	odd	6
912.2.bn.j.65.2		4	12.11	even	2
912.2.bn.j.449.2		4	76.31	even	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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bf (of order \(6\), degree \(2\), 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

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Representations

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Database

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