LMFDB - Embedded newform 456.2.bf.a.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			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	456.65
Dual form			456.2.bf.a.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18614 + 1.26217i) q^{3} +(0.686141 + 0.396143i) q^{5} -2.37228 q^{7} +(-0.186141 - 2.99422i) q^{9} +O(q^{10})$	\(q+(-1.18614 + 1.26217i) q^{3} +(0.686141 + 0.396143i) q^{5} -2.37228 q^{7} +(-0.186141 - 2.99422i) q^{9} +3.46410i q^{11} +(-2.87228 + 1.65831i) q^{13} +(-1.31386 + 0.396143i) q^{15} +(0.686141 + 0.396143i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(2.81386 - 2.99422i) q^{21} +(-6.43070 + 3.71277i) q^{23} +(-2.18614 - 3.78651i) q^{25} +(4.00000 + 3.31662i) q^{27} +(-2.68614 - 4.65253i) q^{29} -4.40387i q^{31} +(-4.37228 - 4.10891i) q^{33} +(-1.62772 - 0.939764i) q^{35} +7.86797i q^{37} +(1.31386 - 5.59230i) q^{39} +(-0.313859 + 0.543620i) q^{41} +(-0.127719 + 0.221215i) q^{43} +(1.05842 - 2.12819i) q^{45} +(-3.68614 + 2.12819i) q^{47} -1.37228 q^{49} +(-1.31386 + 0.396143i) q^{51} +(5.68614 + 9.84868i) q^{53} +(-1.37228 + 2.37686i) q^{55} +(6.93070 - 2.99422i) q^{57} +(-3.68614 + 6.38458i) q^{59} +(0.500000 + 0.866025i) q^{61} +(0.441578 + 7.10313i) q^{63} -2.62772 q^{65} +(10.2446 - 5.91470i) q^{67} +(2.94158 - 12.5205i) q^{69} +(-3.31386 + 5.73977i) q^{71} +(2.87228 - 4.97494i) q^{73} +(7.37228 + 1.73205i) q^{75} -8.21782i q^{77} +(9.98913 + 5.76722i) q^{79} +(-8.93070 + 1.11469i) q^{81} -3.46410i q^{83} +(0.313859 + 0.543620i) q^{85} +(9.05842 + 2.12819i) q^{87} +(3.68614 + 6.38458i) q^{89} +(6.81386 - 3.93398i) q^{91} +(5.55842 + 5.22360i) q^{93} +(-2.05842 - 2.77300i) q^{95} +(11.0584 + 6.38458i) q^{97} +(10.3723 - 0.644810i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - 3 q^{5} + 2 q^{7} + 5 q^{9}+O(q^{10}) $ 4 * q + q^3 - 3 * q^5 + 2 * q^7 + 5 * q^9	$ 4 q + q^{3} - 3 q^{5} + 2 q^{7} + 5 q^{9} - 11 q^{15} - 3 q^{17} - 16 q^{19} + 17 q^{21} + 3 q^{23} - 3 q^{25} + 16 q^{27} - 5 q^{29} - 6 q^{33} - 18 q^{35} + 11 q^{39} - 7 q^{41} - 12 q^{43} - 13 q^{45} - 9 q^{47} + 6 q^{49} - 11 q^{51} + 17 q^{53} + 6 q^{55} - q^{57} - 9 q^{59} + 2 q^{61} + 19 q^{63} - 22 q^{65} + 18 q^{67} + 29 q^{69} - 19 q^{71} + 18 q^{75} - 6 q^{79} - 7 q^{81} + 7 q^{85} + 19 q^{87} + 9 q^{89} + 33 q^{91} + 5 q^{93} + 9 q^{95} + 27 q^{97} + 30 q^{99}+O(q^{100}) $ 4 * q + q^3 - 3 * q^5 + 2 * q^7 + 5 * q^9 - 11 * q^15 - 3 * q^17 - 16 * q^19 + 17 * q^21 + 3 * q^23 - 3 * q^25 + 16 * q^27 - 5 * q^29 - 6 * q^33 - 18 * q^35 + 11 * q^39 - 7 * q^41 - 12 * q^43 - 13 * q^45 - 9 * q^47 + 6 * q^49 - 11 * q^51 + 17 * q^53 + 6 * q^55 - q^57 - 9 * q^59 + 2 * q^61 + 19 * q^63 - 22 * q^65 + 18 * q^67 + 29 * q^69 - 19 * q^71 + 18 * q^75 - 6 * q^79 - 7 * q^81 + 7 * q^85 + 19 * q^87 + 9 * q^89 + 33 * q^91 + 5 * q^93 + 9 * q^95 + 27 * q^97 + 30 * q^99

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
$3$	−1.18614	+	1.26217i	−0.684819	+	0.728714i
$3$	−1.18614	+	1.26217i	−0.684819	+	0.728714i
$4$		0			0
$5$	0.686141	+	0.396143i	0.306851	+	0.177161i	0.645517	−	0.763746i	$-0.276642\pi$
$5$	0.686141	+	0.396143i	0.306851	+	0.177161i	−0.338665	+	0.940907i	$0.609975\pi$
$6$		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
$9$	−0.186141	−	2.99422i	−0.0620469	−	0.998073i
$10$		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
$15$	−1.31386	+	0.396143i	−0.339237	+	0.102284i
$16$		0			0
$17$	0.686141	+	0.396143i	0.166414	+	0.0960789i	0.580894	−	0.813979i	$-0.302703\pi$
$17$	0.686141	+	0.396143i	0.166414	+	0.0960789i	−0.414480	+	0.910058i	$0.636037\pi$
$18$		0			0
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$20$		0			0
$21$	2.81386	−	2.99422i	0.614034	−	0.653392i
$22$		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	0.501195	−	0.865334i	$-0.332894\pi$
$29$	−2.68614	−	4.65253i	−0.498804	−	0.863954i	−0.999999	+	0.00138070i	$0.999561\pi$
$30$		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
$33$	−4.37228	−	4.10891i	−0.761116	−	0.715270i
$34$		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	−0.889493	−	0.456949i	$-0.848942\pi$
$41$	−0.313859	+	0.543620i	−0.0490166	+	0.0848992i	0.840476	+	0.541849i	$0.182275\pi$
$42$		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	−0.744138	−	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
$51$	−1.31386	+	0.396143i	−0.183977	+	0.0554712i
$52$		0			0
$53$	5.68614	+	9.84868i	0.781051	+	1.35282i	0.931330	+	0.364177i	$0.118650\pi$
$53$	5.68614	+	9.84868i	0.781051	+	1.35282i	−0.150278	+	0.988644i	$0.548017\pi$
$54$		0			0
$55$	−1.37228	+	2.37686i	−0.185038	+	0.320496i
$56$		0			0
$57$	6.93070	−	2.99422i	0.917994	−	0.396594i
$58$		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
$63$	0.441578	+	7.10313i	0.0556336	+	0.894910i
$64$		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	−0.992880	−	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	0.942385	−	0.334531i	$-0.108578\pi$
$79$	9.98913	+	5.76722i	1.12386	+	0.648863i	0.181480	+	0.983395i	$0.441911\pi$
$80$		0			0
$81$	−8.93070	+	1.11469i	−0.992300	+	0.123855i
$82$		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	0.992546	−	0.121870i	$-0.0388892\pi$
$89$	3.68614	+	6.38458i	0.390730	+	0.676764i	−0.601816	+	0.798635i	$0.705556\pi$
$90$		0			0
$91$	6.81386	−	3.93398i	0.714287	−	0.412394i
$92$		0			0
$93$	5.55842	+	5.22360i	0.576382	+	0.541662i
$94$		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
$99$	10.3723	−	0.644810i	1.04245	−	0.0648059i
$100$		0			0
$101$	0.686141	−	0.396143i	0.0682735	−	0.0394178i	−0.465475	−	0.885061i	$-0.654116\pi$
$101$	0.686141	−	0.396143i	0.0682735	−	0.0394178i	0.533748	+	0.845643i	$0.320783\pi$
$102$		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
$105$	3.11684	−	0.939764i	0.304173	−	0.0917116i
$106$		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
$111$	−9.93070	−	9.33252i	−0.942581	−	0.885803i
$112$		0			0
$113$	−14.7446			−1.38705			−0.693526	−	0.720432i	$-0.743944\pi$
$113$	−14.7446			−1.38705			−0.693526	+	0.720432i	$0.743944\pi$
$114$		0			0
$115$	−5.88316			−0.548607
$116$		0			0
$117$	5.50000	+	8.29156i	0.508475	+	0.766555i
$118$		0			0
$119$	−1.62772	−	0.939764i	−0.149213	−	0.0861480i
$120$		0			0
$121$	−1.00000			−0.0909091
$122$		0			0
$123$	−0.313859	−	1.04095i	−0.0282997	−	0.0938596i
$124$		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
$129$	−0.127719	−	0.423595i	−0.0112450	−	0.0372955i
$130$		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
$135$	1.43070	+	3.86025i	0.123135	+	0.332237i
$136$		0			0
$137$	−11.3139	+	6.53206i	−0.966608	+	0.558072i	−0.898201	−	0.439586i	$-0.855125\pi$
$137$	−11.3139	+	6.53206i	−0.966608	+	0.558072i	−0.0684077	+	0.997657i	$0.521792\pi$
$138$		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
$147$	1.62772	−	1.73205i	0.134252	−	0.142857i
$148$		0			0
$149$	−2.05842	−	1.18843i	−0.168632	−	0.0973600i	0.413308	−	0.910591i	$-0.364373\pi$
$149$	−2.05842	−	1.18843i	−0.168632	−	0.0973600i	−0.581941	+	0.813231i	$0.697706\pi$
$150$		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
$165$	−1.37228	−	4.55134i	−0.106832	−	0.354322i
$166$		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
$171$	−4.44158	+	12.2993i	−0.339656	+	0.940550i
$172$		0			0
$173$	−7.43070	+	12.8704i	−0.564946	+	0.978515i	0.432109	+	0.901821i	$0.357770\pi$
$173$	−7.43070	+	12.8704i	−0.564946	+	0.978515i	−0.997055	+	0.0766935i	$0.975564\pi$
$174$		0			0
$175$	5.18614	+	8.98266i	0.392035	+	0.679025i
$176$		0			0
$177$	−3.68614	−	12.2255i	−0.277067	−	0.918928i
$178$		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
$195$	3.11684	−	3.31662i	0.223202	−	0.237508i
$196$		0			0
$197$			16.4356i			1.17099i	0.810676	+	0.585496i	$0.199100\pi$
$197$			16.4356i			1.17099i	−0.810676	+	0.585496i	$0.800900\pi$
$198$		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
$207$	12.3139	+	18.5638i	0.855872	+	1.29028i
$208$		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
$213$	−3.31386	−	10.9908i	−0.227062	−	0.753079i
$214$		0			0
$215$	−0.175266	+	0.101190i	−0.0119530	+	0.00690109i
$216$		0			0
$217$			10.4472i			0.709203i
$218$		0			0
$219$	2.87228	+	9.52628i	0.194091	+	0.643726i
$220$		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
$225$	−10.9307	+	7.25061i	−0.728714	+	0.483374i
$226$		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
$231$	10.3723	+	9.74749i	0.682446	+	0.641338i
$232$		0			0
$233$	3.94158	+	2.27567i	0.258221	+	0.149084i	0.623523	−	0.781805i	$-0.285701\pi$
$233$	3.94158	+	2.27567i	0.258221	+	0.149084i	−0.365302	+	0.930889i	$0.619034\pi$
$234$		0			0
$235$	−3.37228			−0.219983
$236$		0			0
$237$	−19.1277	+	5.76722i	−1.24248	+	0.374621i
$238$		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
$243$	9.18614	−	12.5942i	0.589291	−	0.807921i
$244$		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
$249$	4.37228	+	4.10891i	0.277082	+	0.260392i
$250$		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	0.893897	−	0.448272i	$-0.147960\pi$
$257$	0.941578	+	1.63086i	0.0587340	+	0.101730i	−0.835163	+	0.550002i	$0.814627\pi$
$258$		0			0
$259$		−	18.6650i		−	1.15979i
$260$		0			0
$261$	−13.4307	+	8.90892i	−0.831340	+	0.551448i
$262$		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	−0.600638	−	0.799521i	$-0.705087\pi$
$269$	6.43070	−	11.1383i	0.392087	−	0.679114i	0.992725	+	0.120407i	$0.0384199\pi$
$270$		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
$279$	−13.1861	+	0.819738i	−0.789434	+	0.0490765i
$280$		0			0
$281$	12.8030	+	22.1754i	0.763762	+	1.32287i	0.940899	+	0.338688i	$0.109983\pi$
$281$	12.8030	+	22.1754i	0.763762	+	1.32287i	−0.177137	+	0.984186i	$0.556683\pi$
$282$		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
$285$	5.94158	+	0.691097i	0.351949	+	0.0409371i
$286$		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
$291$	−21.1753	+	6.38458i	−1.24132	+	0.374271i
$292$		0			0
$293$	−9.25544			−0.540708			−0.270354	−	0.962761i	$-0.587141\pi$
$293$	−9.25544			−0.540708			−0.270354	+	0.962761i	$0.587141\pi$
$294$		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
$309$	−0.813859	−	0.764836i	−0.0462988	−	0.0435100i
$310$		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	$-0.961757\pi$
$317$	−10.6861	−	18.5089i	−0.600193	−	1.03957i	0.392598	−	0.919710i	$-0.371576\pi$
$318$		0			0
$319$	16.1168	−	9.30506i	0.902370	−	0.520984i
$320$		0			0
$321$	−19.8614	+	21.1345i	−1.10856	+	1.17961i
$322$		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
$327$	−9.68614	+	2.92048i	−0.535645	+	0.161503i
$328$		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
$333$	23.5584	−	1.46455i	1.29099	−	0.0802568i
$334$		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
$339$	17.4891	−	18.6101i	0.949879	−	1.01076i
$340$		0			0
$341$	15.2554			0.826128
$342$		0			0
$343$	19.8614			1.07242
$344$		0			0
$345$	6.97825	−	7.42554i	0.375696	−	0.399777i
$346$		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
$351$	−16.9891	−	2.89303i	−0.906812	−	0.154419i
$352$		0			0
$353$		−	35.3407i		−	1.88100i	−0.339798	−	0.940499i	$-0.610359\pi$
$353$		−	35.3407i		−	1.88100i	0.339798	−	0.940499i	$-0.389641\pi$
$354$		0			0
$355$	−4.54755	+	2.62553i	−0.241359	+	0.139349i
$356$		0			0
$357$	3.11684	−	0.939764i	0.164961	−	0.0497376i
$358$		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
$363$	1.18614	−	1.26217i	0.0622562	−	0.0662467i
$364$		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
$375$	9.37228	+	8.80773i	0.483983	+	0.454829i
$376$		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	−0.962250	−	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	−0.988521	−	0.151084i	$-0.951723\pi$
$389$	−26.6644	+	15.3947i	−1.35194	+	0.780542i	−0.363417	+	0.931626i	$0.618390\pi$
$390$		0			0
$391$	−5.88316			−0.297524
$392$		0			0
$393$	−9.19702	+	2.77300i	−0.463928	+	0.139880i
$394$		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
$399$	−16.4416	+	7.10313i	−0.823108	+	0.355601i
$400$		0			0
$401$	9.17527	−	15.8920i	0.458191	−	0.793610i	−0.540675	−	0.841232i	$-0.681831\pi$
$401$	9.17527	−	15.8920i	0.458191	−	0.793610i	0.998865	+	0.0476219i	$0.0151643\pi$
$402$		0			0
$403$	7.30298	+	12.6491i	0.363788	+	0.630099i
$404$		0			0
$405$	−6.56930	−	2.77300i	−0.326431	−	0.137792i
$406$		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
$423$	7.05842	+	10.6410i	0.343192	+	0.517382i
$424$		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
$435$	5.37228	+	5.04868i	0.257581	+	0.242065i
$436$		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
$441$	0.255437	+	4.10891i	0.0121637	+	0.195662i
$442$		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
$447$	3.94158	−	1.18843i	0.186430	−	0.0562108i
$448$		0			0
$449$	−38.4674			−1.81539			−0.907694	−	0.419633i	$-0.862159\pi$
$449$	−38.4674			−1.81539			−0.907694	+	0.419633i	$0.862159\pi$
$450$		0			0
$451$	−1.88316	−	1.08724i	−0.0886744	−	0.0511962i
$452$		0			0
$453$	17.1168	+	16.0858i	0.804219	+	0.755776i
$454$		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
$459$	1.43070	+	3.86025i	0.0667795	+	0.180181i
$460$		0			0
$461$	11.5693	+	6.67954i	0.538836	+	0.311097i	0.744607	−	0.667503i	$-0.232637\pi$
$461$	11.5693	+	6.67954i	0.538836	+	0.311097i	−0.205771	+	0.978600i	$0.565970\pi$
$462$		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
$465$	1.74456	+	5.78606i	0.0809022	+	0.268322i
$466$		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
$471$	−10.2446	−	33.9774i	−0.472045	−	1.56559i
$472$		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
$477$	28.4307	−	18.8588i	1.30175	−	0.863485i
$478$		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	$0.00212722\pi$
$487$			0.294954i			0.0133656i	−0.999978	+	0.00668281i	$0.997873\pi$
$488$		0			0
$489$	−11.4198	+	12.1518i	−0.516423	+	0.549524i
$490$		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	$-0.654971\pi$
$499$	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	$-0.273307\pi$
$503$	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
$507$	−1.00000	−	3.31662i	−0.0444116	−	0.147296i
$508$		0			0
$509$	−5.05842	−	8.76144i	−0.224211	−	0.388344i	0.731872	−	0.681442i	$-0.238647\pi$
$509$	−5.05842	−	8.76144i	−0.224211	−	0.388344i	−0.956082	+	0.293098i	$0.905314\pi$
$510$		0			0
$511$	−6.81386	+	11.8020i	−0.301427	+	0.522088i
$512$		0			0
$513$	−10.2554	−	20.1947i	−0.452789	−	0.891618i
$514$		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
$519$	−7.43070	−	24.6449i	−0.326172	−	1.08179i
$520$		0			0
$521$	10.0000			0.438108			0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000			0.438108			0.219054	+	0.975713i	$0.429703\pi$
$522$		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
$537$	−25.4891	+	27.1229i	−1.09994	+	1.17044i
$538$		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
$549$	2.50000	−	1.65831i	0.106697	−	0.0707750i
$550$		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
$555$	−3.11684	−	10.3374i	−0.132303	−	0.438798i
$556$		0			0
$557$	27.4307	−	15.8371i	1.16228	−	0.671040i	0.210428	−	0.977609i	$-0.432514\pi$
$557$	27.4307	−	15.8371i	1.16228	−	0.671040i	0.951848	+	0.306569i	$0.0991810\pi$
$558$		0			0
$559$		−	0.847190i		−	0.0358323i
$560$		0			0
$561$	−1.37228	−	4.55134i	−0.0579378	−	0.192158i
$562$		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
$567$	21.1861	−	2.64436i	0.889734	−	0.111053i
$568$		0			0
$569$	−38.7446			−1.62426			−0.812128	−	0.583479i	$-0.801691\pi$
$569$	−38.7446			−1.62426			−0.812128	+	0.583479i	$0.801691\pi$
$570$		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
$573$	−8.37228	−	7.86797i	−0.349757	−	0.328689i
$574$		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
$579$	−25.8505	+	7.79423i	−1.07431	+	0.323917i
$580$		0			0
$581$			8.21782i			0.340933i
$582$		0			0
$583$	−34.1168	+	19.6974i	−1.41298	+	0.815782i
$584$		0			0
$585$	0.489125	+	7.86797i	0.0202228	+	0.325300i
$586$		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
$591$	−20.7446	−	19.4950i	−0.853317	−	0.801917i
$592$		0			0
$593$	4.54755	−	2.62553i	0.186745	−	0.107817i	−0.403713	−	0.914886i	$-0.632280\pi$
$593$	4.54755	−	2.62553i	0.186745	−	0.107817i	0.590458	+	0.807068i	$0.298947\pi$
$594$		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
$603$	−19.6168	−	29.5735i	−0.798860	−	1.20433i
$604$		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	−0.418556	−	0.908191i	$-0.637464\pi$
$617$	3.94158	−	2.27567i	0.158682	−	0.0916151i	0.577238	+	0.816576i	$0.304130\pi$
$618$		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
$621$	−38.0367	−	6.47716i	−1.52636	−	0.259919i
$622$		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
$627$	10.3723	+	24.0087i	0.414229	+	0.958814i
$628$		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
$633$	24.8723	−	7.49927i	0.988584	−	0.298069i
$634$		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	−0.994594	−	0.103836i	$-0.966888\pi$
$641$	−10.3139	+	17.8641i	−0.407373	+	0.705591i	0.587222	+	0.809426i	$0.300222\pi$
$642$		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	$0.338237\pi$
$647$			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
$651$	−13.1861	−	12.3919i	−0.516806	−	0.485675i
$652$		0			0
$653$			22.0742i			0.863831i	0.901914	+	0.431916i	$0.142162\pi$
$653$			22.0742i			0.863831i	−0.901914	+	0.431916i	$0.857838\pi$
$654$		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
$663$	3.11684	−	3.31662i	0.121048	−	0.128807i
$664$		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
$669$	30.1277	−	9.08385i	1.16480	−	0.351202i
$670$		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
$675$	3.81386	−	22.3966i	0.146796	−	0.862047i
$676$		0			0
$677$	−26.7446			−1.02788			−0.513939	−	0.857827i	$-0.671814\pi$
$677$	−26.7446			−1.02788			−0.513939	+	0.857827i	$0.671814\pi$
$678$		0			0
$679$	−26.2337	−	15.1460i	−1.00676	−	0.581251i
$680$		0			0
$681$	8.60597	−	9.15759i	0.329781	−	0.350920i
$682$		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
$687$	25.0475	−	26.6530i	0.955624	−	1.01688i
$688$		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
$693$	−24.6060	+	1.52967i	−0.934703	+	0.0581074i
$694$		0			0
$695$		−	13.0641i		−	0.495550i
$696$		0			0
$697$	−0.430703	+	0.248667i	−0.0163141	+	0.00941892i
$698$		0			0
$699$	−7.54755	+	2.27567i	−0.285474	+	0.0860738i
$700$		0			0
$701$	−14.0584	−	8.11663i	−0.530979	−	0.306561i	0.210436	−	0.977608i	$-0.432512\pi$
$701$	−14.0584	−	8.11663i	−0.530979	−	0.306561i	−0.741415	+	0.671047i	$0.765845\pi$
$702$		0			0
$703$	13.6277	−	31.4719i	0.513979	−	1.18698i
$704$		0			0
$705$	4.00000	−	4.25639i	0.150649	−	0.160305i
$706$		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
$717$	13.1168	+	12.3267i	0.489858	+	0.460350i
$718$		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	$0.381877\pi$
$727$	−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
$735$	1.80298	−	0.543620i	0.0665041	−	0.0200517i
$736$		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
$741$	−14.9416	+	20.0935i	−0.548893	+	0.738154i
$742$		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
$747$	−10.3723	+	0.644810i	−0.379502	+	0.0235924i
$748$		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	$0.207421\pi$
$761$			33.4612i			1.21297i	−0.795096	+	0.606484i	$0.792579\pi$
$762$		0			0
$763$	−12.0000	−	6.92820i	−0.434429	−	0.250818i
$764$		0			0
$765$	1.56930	−	1.04095i	0.0567380	−	0.0376358i
$766$		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	$0.118112\pi$
$773$	21.6861	+	37.5615i	0.779996	+	1.35099i	−0.151947	+	0.988389i	$0.548554\pi$
$774$		0			0
$775$	−16.6753	+	9.62747i	−0.598993	+	0.345829i
$776$		0			0
$777$	23.5584	+	22.1394i	0.845154	+	0.794245i
$778$		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
$783$	4.68614	−	27.5190i	0.167469	−	0.983451i
$784$		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
$789$	6.56930	−	1.98072i	0.233873	−	0.0705154i
$790$		0			0
$791$	34.9783			1.24368
$792$		0			0
$793$	−2.87228	−	1.65831i	−0.101998	−	0.0588884i
$794$		0			0
$795$	−11.3723	−	10.6873i	−0.403333	−	0.379038i
$796$		0			0
$797$	−47.4891			−1.68215			−0.841076	−	0.540918i	$-0.818077\pi$
$797$	−47.4891			−1.68215			−0.841076	+	0.540918i	$0.818077\pi$
$798$		0			0
$799$	−3.37228			−0.119303
$800$		0			0
$801$	18.4307	−	12.2255i	0.651217	−	0.431968i
$802$		0			0
$803$	17.2337	+	9.94987i	0.608164	+	0.351123i
$804$		0			0
$805$	13.9565			0.491902
$806$		0			0
$807$	6.43070	+	21.3282i	0.226371	+	0.750789i
$808$		0			0
$809$		−	5.04868i		−	0.177502i	−0.996054	−	0.0887510i	$-0.971712\pi$
$809$		−	5.04868i		−	0.177502i	0.996054	−	0.0887510i	$-0.0282875\pi$
$810$		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
$813$	−4.43070	−	14.6950i	−0.155392	−	0.515375i
$814$		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
$819$	−13.0475	−	19.6699i	−0.455918	−	0.687323i
$820$		0			0
$821$	44.4090	−	25.6395i	1.54988	−	0.894825i	0.551734	−	0.834020i	$-0.313967\pi$
$821$	44.4090	−	25.6395i	1.54988	−	0.894825i	0.998150	−	0.0608050i	$-0.0193668\pi$
$822$		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	0.907234	−	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
$831$	−4.13859	+	4.40387i	−0.143566	+	0.152768i
$832$		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
$849$	−14.4307	−	47.8612i	−0.495260	−	1.64259i
$850$		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
$855$	−7.91983	+	6.67954i	−0.270852	+	0.228435i
$856$		0			0
$857$	−2.31386	+	4.00772i	−0.0790399	+	0.136901i	−0.902836	−	0.429985i	$-0.858519\pi$
$857$	−2.31386	+	4.00772i	−0.0790399	+	0.136901i	0.823796	+	0.566886i	$0.191852\pi$
$858$		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
$861$	0.744563	+	2.46943i	0.0253746	+	0.0841581i
$862$		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
$879$	10.9783	−	11.6819i	0.370287	−	0.394022i
$880$		0			0
$881$		−	8.80773i		−	0.296740i	−0.988932	−	0.148370i	$-0.952597\pi$
$881$		−	8.80773i		−	0.296740i	0.988932	−	0.148370i	$-0.0474027\pi$
$882$		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	0.834168	−	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
$891$	−3.86141	−	30.9369i	−0.129362	−	1.03642i
$892$		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
$897$	12.3139	+	40.8405i	0.411148	+	1.36362i
$898$		0			0
$899$	−20.4891	+	11.8294i	−0.683351	+	0.394533i
$900$		0			0
$901$			9.01011i			0.300170i
$902$		0			0
$903$	0.302985	+	1.00489i	0.0100827	+	0.0334405i
$904$		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
$909$	−1.31386	−	1.98072i	−0.0435780	−	0.0656963i
$910$		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
$915$	−1.00000	−	0.939764i	−0.0330590	−	0.0310676i
$916$		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
$921$	−31.1970	+	9.40625i	−1.02798	+	0.309947i
$922$		0			0
$923$		−	21.9817i		−	0.723535i
$924$		0			0
$925$	29.7921	−	17.2005i	0.979559	−	0.565548i
$926$		0			0
$927$	1.93070	−	0.120025i	0.0634126	−	0.00394215i
$928$		0			0
$929$	−17.3139	−	9.99616i	−0.568049	−	0.327963i	0.188321	−	0.982108i	$-0.439696\pi$
$929$	−17.3139	−	9.99616i	−0.568049	−	0.327963i	−0.756370	+	0.654144i	$0.773029\pi$
$930$		0			0
$931$	5.48913	+	2.37686i	0.179899	+	0.0778985i
$932$		0			0
$933$	15.4891	+	14.5561i	0.507091	+	0.476546i
$934$		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	$-0.805523\pi$
$941$	−27.8030	−	48.1562i	−0.906351	−	1.56985i	−0.0872585	−	0.996186i	$-0.527811\pi$
$942$		0			0
$943$		−	4.66115i		−	0.151788i
$944$		0			0
$945$	−3.39403	−	9.15759i	−0.110408	−	0.297896i
$946$		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	$-0.536330\pi$
$953$	24.8030	−	42.9600i	0.803447	−	1.39161i	0.917334	−	0.398118i	$-0.130337\pi$
$954$		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
$963$	−3.11684	−	50.1369i	−0.100439	−	1.61564i
$964$		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
$969$	5.94158	+	0.691097i	0.190871	+	0.0222012i
$970$		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
$975$	−24.0475	+	7.25061i	−0.770138	+	0.232205i
$976$		0			0
$977$	−43.2119			−1.38247			−0.691236	−	0.722629i	$-0.742934\pi$
$977$	−43.2119			−1.38247			−0.691236	+	0.722629i	$0.742934\pi$
$978$		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	0.717258	−	0.696808i	$-0.245397\pi$
$991$	14.8723	+	8.58652i	0.472434	+	0.272760i	−0.244824	+	0.969567i	$0.578730\pi$
$992$		0			0
$993$	−24.6753	−	23.1889i	−0.783046	−	0.735878i
$994$		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.a.65.1	✓	4
3.2	odd	2		456.2.bf.b.65.1	yes	4
4.3	odd	2		912.2.bn.j.65.2		4
12.11	even	2		912.2.bn.i.65.2		4
19.12	odd	6		456.2.bf.b.449.2	yes	4
57.50	even	6	inner	456.2.bf.a.449.1	yes	4
76.31	even	6		912.2.bn.i.449.1		4
228.107	odd	6		912.2.bn.j.449.2		4

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

\(f(q)\)	\(=\)	\(q+(-1.18614 + 1.26217i) q^{3} +(0.686141 + 0.396143i) q^{5} -2.37228 q^{7} +(-0.186141 - 2.99422i) q^{9} +O(q^{10})\)	\(q+(-1.18614 + 1.26217i) q^{3} +(0.686141 + 0.396143i) q^{5} -2.37228 q^{7} +(-0.186141 - 2.99422i) q^{9} +3.46410i q^{11} +(-2.87228 + 1.65831i) q^{13} +(-1.31386 + 0.396143i) q^{15} +(0.686141 + 0.396143i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(2.81386 - 2.99422i) q^{21} +(-6.43070 + 3.71277i) q^{23} +(-2.18614 - 3.78651i) q^{25} +(4.00000 + 3.31662i) q^{27} +(-2.68614 - 4.65253i) q^{29} -4.40387i q^{31} +(-4.37228 - 4.10891i) q^{33} +(-1.62772 - 0.939764i) q^{35} +7.86797i q^{37} +(1.31386 - 5.59230i) q^{39} +(-0.313859 + 0.543620i) q^{41} +(-0.127719 + 0.221215i) q^{43} +(1.05842 - 2.12819i) q^{45} +(-3.68614 + 2.12819i) q^{47} -1.37228 q^{49} +(-1.31386 + 0.396143i) q^{51} +(5.68614 + 9.84868i) q^{53} +(-1.37228 + 2.37686i) q^{55} +(6.93070 - 2.99422i) q^{57} +(-3.68614 + 6.38458i) q^{59} +(0.500000 + 0.866025i) q^{61} +(0.441578 + 7.10313i) q^{63} -2.62772 q^{65} +(10.2446 - 5.91470i) q^{67} +(2.94158 - 12.5205i) q^{69} +(-3.31386 + 5.73977i) q^{71} +(2.87228 - 4.97494i) q^{73} +(7.37228 + 1.73205i) q^{75} -8.21782i q^{77} +(9.98913 + 5.76722i) q^{79} +(-8.93070 + 1.11469i) q^{81} -3.46410i q^{83} +(0.313859 + 0.543620i) q^{85} +(9.05842 + 2.12819i) q^{87} +(3.68614 + 6.38458i) q^{89} +(6.81386 - 3.93398i) q^{91} +(5.55842 + 5.22360i) q^{93} +(-2.05842 - 2.77300i) q^{95} +(11.0584 + 6.38458i) q^{97} +(10.3723 - 0.644810i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 3 q^{5} + 2 q^{7} + 5 q^{9}+O(q^{10}) \) 4 * q + q^3 - 3 * q^5 + 2 * q^7 + 5 * q^9	\( 4 q + q^{3} - 3 q^{5} + 2 q^{7} + 5 q^{9} - 11 q^{15} - 3 q^{17} - 16 q^{19} + 17 q^{21} + 3 q^{23} - 3 q^{25} + 16 q^{27} - 5 q^{29} - 6 q^{33} - 18 q^{35} + 11 q^{39} - 7 q^{41} - 12 q^{43} - 13 q^{45} - 9 q^{47} + 6 q^{49} - 11 q^{51} + 17 q^{53} + 6 q^{55} - q^{57} - 9 q^{59} + 2 q^{61} + 19 q^{63} - 22 q^{65} + 18 q^{67} + 29 q^{69} - 19 q^{71} + 18 q^{75} - 6 q^{79} - 7 q^{81} + 7 q^{85} + 19 q^{87} + 9 q^{89} + 33 q^{91} + 5 q^{93} + 9 q^{95} + 27 q^{97} + 30 q^{99}+O(q^{100}) \) 4 * q + q^3 - 3 * q^5 + 2 * q^7 + 5 * q^9 - 11 * q^15 - 3 * q^17 - 16 * q^19 + 17 * q^21 + 3 * q^23 - 3 * q^25 + 16 * q^27 - 5 * q^29 - 6 * q^33 - 18 * q^35 + 11 * q^39 - 7 * q^41 - 12 * q^43 - 13 * q^45 - 9 * q^47 + 6 * q^49 - 11 * q^51 + 17 * q^53 + 6 * q^55 - q^57 - 9 * q^59 + 2 * q^61 + 19 * q^63 - 22 * q^65 + 18 * q^67 + 29 * q^69 - 19 * q^71 + 18 * q^75 - 6 * q^79 - 7 * q^81 + 7 * q^85 + 19 * q^87 + 9 * q^89 + 33 * q^91 + 5 * q^93 + 9 * q^95 + 27 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more