LMFDB - Embedded newform 637.2.q.i.491.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(491,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.6
Root			$1.32725 - 0.488273i$ of defining polynomial
Character	$\chi$	$=$	637.491
Dual form			637.2.q.i.589.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.24179 - 1.29430i) q^{2} +(0.259233 + 0.449005i) q^{3} +(2.35043 - 4.07106i) q^{4} -1.61205i q^{5} +(1.16229 + 0.671051i) q^{6} -6.99143i q^{8} +(1.36560 - 2.36528i) q^{9} +O(q^{10})$	\(q+(2.24179 - 1.29430i) q^{2} +(0.259233 + 0.449005i) q^{3} +(2.35043 - 4.07106i) q^{4} -1.61205i q^{5} +(1.16229 + 0.671051i) q^{6} -6.99143i q^{8} +(1.36560 - 2.36528i) q^{9} +(-2.08648 - 3.61389i) q^{10} +(-2.34256 + 1.35248i) q^{11} +2.43723 q^{12} +(-2.36840 + 2.71858i) q^{13} +(0.723819 - 0.417897i) q^{15} +(-4.34816 - 7.53123i) q^{16} +(-1.56330 + 2.70772i) q^{17} -7.06997i q^{18} +(3.18828 + 1.84075i) q^{19} +(-6.56276 - 3.78901i) q^{20} +(-3.50103 + 6.06396i) q^{22} +(0.993019 + 1.71996i) q^{23} +(3.13918 - 1.81241i) q^{24} +2.40128 q^{25} +(-1.79081 + 9.15992i) q^{26} +2.97143 q^{27} +(2.68636 + 4.65290i) q^{29} +(1.08177 - 1.87368i) q^{30} -10.4780i q^{31} +(-7.38583 - 4.26421i) q^{32} +(-1.21454 - 0.701214i) q^{33} +8.09354i q^{34} +(-6.41947 - 11.1188i) q^{36} +(-5.15585 + 2.97673i) q^{37} +9.52994 q^{38} +(-1.83462 - 0.358678i) q^{39} -11.2706 q^{40} +(6.66970 - 3.85075i) q^{41} +(-1.67800 + 2.90638i) q^{43} +12.7156i q^{44} +(-3.81296 - 2.20141i) q^{45} +(4.45229 + 2.57053i) q^{46} +1.05508i q^{47} +(2.25437 - 3.90469i) q^{48} +(5.38318 - 3.10798i) q^{50} -1.62104 q^{51} +(5.50074 + 16.0317i) q^{52} +7.26568 q^{53} +(6.66133 - 3.84592i) q^{54} +(2.18027 + 3.77633i) q^{55} +1.90873i q^{57} +(12.0445 + 6.95390i) q^{58} +(-9.89352 - 5.71203i) q^{59} -3.92895i q^{60} +(-1.46254 + 2.53319i) q^{61} +(-13.5617 - 23.4896i) q^{62} -4.68406 q^{64} +(4.38250 + 3.81799i) q^{65} -3.63033 q^{66} +(-11.7622 + 6.79091i) q^{67} +(7.34886 + 12.7286i) q^{68} +(-0.514846 + 0.891740i) q^{69} +(1.17009 + 0.675554i) q^{71} +(-16.5367 - 9.54747i) q^{72} +9.10335i q^{73} +(-7.70557 + 13.3464i) q^{74} +(0.622492 + 1.07819i) q^{75} +(14.9876 - 8.65311i) q^{76} +(-4.57708 + 1.57047i) q^{78} -6.20578 q^{79} +(-12.1407 + 7.00946i) q^{80} +(-3.32650 - 5.76166i) q^{81} +(9.96806 - 17.2652i) q^{82} +2.69672i q^{83} +(4.36499 + 2.52013i) q^{85} +8.68734i q^{86} +(-1.39278 + 2.41237i) q^{87} +(9.45576 + 16.3779i) q^{88} +(1.52410 - 0.879938i) q^{89} -11.3972 q^{90} +9.33607 q^{92} +(4.70469 - 2.71625i) q^{93} +(1.36560 + 2.36528i) q^{94} +(2.96739 - 5.13967i) q^{95} -4.42170i q^{96} +(13.4078 + 7.74102i) q^{97} +7.38776i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} + 4 q^{4} + 9 q^{6} - q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 + 4 * q^4 + 9 * q^6 - q^9	$ 12 q + 3 q^{3} + 4 q^{4} + 9 q^{6} - q^{9} - 12 q^{10} - 12 q^{11} - 2 q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 3 q^{23} + 15 q^{24} + 10 q^{25} - 15 q^{26} - 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{32} - 6 q^{33} - 13 q^{36} - 15 q^{37} + 38 q^{38} + 5 q^{39} - 2 q^{40} + 6 q^{41} + 11 q^{43} - 9 q^{45} + 30 q^{46} - 19 q^{48} + 18 q^{50} - 8 q^{51} + 40 q^{52} + 16 q^{53} + 6 q^{54} + 15 q^{55} + 24 q^{58} + 27 q^{59} - 5 q^{61} - 41 q^{62} + 2 q^{64} - 18 q^{65} - 68 q^{66} - 15 q^{67} + 11 q^{68} - 7 q^{69} + 30 q^{71} - 57 q^{72} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} + 70 q^{79} - 63 q^{80} + 14 q^{81} - 5 q^{82} - 21 q^{85} - 10 q^{87} - 14 q^{88} + 48 q^{89} - 66 q^{92} + 81 q^{93} - q^{94} + 2 q^{95} + 3 q^{97}+O(q^{100}) $ 12 * q + 3 * q^3 + 4 * q^4 + 9 * q^6 - q^9 - 12 * q^10 - 12 * q^11 - 2 * q^12 + 2 * q^13 - 12 * q^15 - 8 * q^16 - 17 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 3 * q^23 + 15 * q^24 + 10 * q^25 - 15 * q^26 - 12 * q^27 - q^29 + 11 * q^30 - 18 * q^32 - 6 * q^33 - 13 * q^36 - 15 * q^37 + 38 * q^38 + 5 * q^39 - 2 * q^40 + 6 * q^41 + 11 * q^43 - 9 * q^45 + 30 * q^46 - 19 * q^48 + 18 * q^50 - 8 * q^51 + 40 * q^52 + 16 * q^53 + 6 * q^54 + 15 * q^55 + 24 * q^58 + 27 * q^59 - 5 * q^61 - 41 * q^62 + 2 * q^64 - 18 * q^65 - 68 * q^66 - 15 * q^67 + 11 * q^68 - 7 * q^69 + 30 * q^71 - 57 * q^72 - 33 * q^74 - q^75 + 45 * q^76 + 44 * q^78 + 70 * q^79 - 63 * q^80 + 14 * q^81 - 5 * q^82 - 21 * q^85 - 10 * q^87 - 14 * q^88 + 48 * q^89 - 66 * q^92 + 81 * q^93 - q^94 + 2 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	2.24179	−	1.29430i	1.58519	−	0.915209i	0.591104	−	0.806596i	$-0.298692\pi$
$2$	2.24179	−	1.29430i	1.58519	−	0.915209i	0.994084	−	0.108613i	$-0.0346409\pi$
$3$	0.259233	+	0.449005i	0.149668	+	0.259233i	0.931105	−	0.364752i	$-0.118846\pi$
$3$	0.259233	+	0.449005i	0.149668	+	0.259233i	−0.781437	+	0.623985i	$0.785513\pi$
$4$	2.35043	−	4.07106i	1.17521	−	2.03553i
$5$		−	1.61205i		−	0.720932i	−0.932772	−	0.360466i	$-0.882618\pi$
$5$		−	1.61205i		−	0.720932i	0.932772	−	0.360466i	$-0.117382\pi$
$6$	1.16229	+	0.671051i	0.474504	+	0.273955i
$7$		0			0
$7$		0			0
$8$		−	6.99143i		−	2.47184i
$9$	1.36560	−	2.36528i	0.455199	−	0.788428i
$10$	−2.08648	−	3.61389i	−0.659803	−	1.14281i
$11$	−2.34256	+	1.35248i	−0.706309	+	0.407788i	−0.809693	−	0.586854i	$-0.800366\pi$
$11$	−2.34256	+	1.35248i	−0.706309	+	0.407788i	0.103384	+	0.994642i	$0.467033\pi$
$12$	2.43723			0.703568
$13$	−2.36840	+	2.71858i	−0.656876	+	0.753998i
$13$	−2.36840	+	2.71858i	−0.656876	+	0.753998i
$14$		0			0
$15$	0.723819	−	0.417897i	0.186889	−	0.107901i
$16$	−4.34816	−	7.53123i	−1.08704	−	1.88281i
$17$	−1.56330	+	2.70772i	−0.379157	+	0.656719i	−0.990940	−	0.134307i	$-0.957119\pi$
$17$	−1.56330	+	2.70772i	−0.379157	+	0.656719i	0.611783	+	0.791026i	$0.290453\pi$
$18$		−	7.06997i		−	1.66641i
$19$	3.18828	+	1.84075i	0.731441	+	0.422297i	0.818949	−	0.573866i	$-0.194557\pi$
$19$	3.18828	+	1.84075i	0.731441	+	0.422297i	−0.0875083	+	0.996164i	$0.527890\pi$
$20$	−6.56276	−	3.78901i	−1.46748	−	0.847249i
$21$		0			0
$22$	−3.50103	+	6.06396i	−0.746421	+	1.29284i
$23$	0.993019	+	1.71996i	0.207059	+	0.358636i	0.950787	−	0.309846i	$-0.100278\pi$
$23$	0.993019	+	1.71996i	0.207059	+	0.358636i	−0.743728	+	0.668482i	$0.766944\pi$
$24$	3.13918	−	1.81241i	0.640783	−	0.369956i
$25$	2.40128			0.480257
$26$	−1.79081	+	9.15992i	−0.351206	+	1.79641i
$27$	2.97143			0.571852
$28$		0			0
$29$	2.68636	+	4.65290i	0.498844	+	0.864023i	0.999999	−	0.00133469i	$-0.000424845\pi$
$29$	2.68636	+	4.65290i	0.498844	+	0.864023i	−0.501155	+	0.865357i	$0.667092\pi$
$30$	1.08177	−	1.87368i	0.197503	−	0.342086i
$31$		−	10.4780i		−	1.88191i	−0.338529	−	0.940956i	$-0.609929\pi$
$31$		−	10.4780i		−	1.88191i	0.338529	−	0.940956i	$-0.390071\pi$
$32$	−7.38583	−	4.26421i	−1.30564	−	0.753813i
$33$	−1.21454	−	0.701214i	−0.211424	−	0.122066i
$34$			8.09354i			1.38803i
$35$		0			0
$36$	−6.41947	−	11.1188i	−1.06991	−	1.85314i
$37$	−5.15585	+	2.97673i	−0.847616	+	0.489371i	−0.859846	−	0.510554i	$-0.829440\pi$
$37$	−5.15585	+	2.97673i	−0.847616	+	0.489371i	0.0122297	+	0.999925i	$0.496107\pi$
$38$	9.52994			1.54596
$39$	−1.83462	−	0.358678i	−0.293775	−	0.0574344i
$40$	−11.2706			−1.78203
$41$	6.66970	−	3.85075i	1.04163	−	0.601386i	0.121337	−	0.992611i	$-0.461282\pi$
$41$	6.66970	−	3.85075i	1.04163	−	0.601386i	0.920295	+	0.391225i	$0.127949\pi$
$42$		0			0
$43$	−1.67800	+	2.90638i	−0.255892	+	0.443219i	−0.965138	−	0.261743i	$-0.915703\pi$
$43$	−1.67800	+	2.90638i	−0.255892	+	0.443219i	0.709245	+	0.704962i	$0.249036\pi$
$44$			12.7156i			1.91695i
$45$	−3.81296	−	2.20141i	−0.568403	−	0.328168i
$46$	4.45229	+	2.57053i	0.656454	+	0.379004i
$47$			1.05508i			0.153900i	0.997035	+	0.0769500i	$0.0245182\pi$
$47$			1.05508i			0.153900i	−0.997035	+	0.0769500i	$0.975482\pi$
$48$	2.25437	−	3.90469i	0.325390	−	0.563593i
$49$		0			0
$50$	5.38318	−	3.10798i	0.761297	−	0.439535i
$51$	−1.62104			−0.226991
$52$	5.50074	+	16.0317i	0.762816	+	2.22320i
$53$	7.26568			0.998017			0.499009	−	0.866597i	$-0.333698\pi$
$53$	7.26568			0.998017			0.499009	+	0.866597i	$0.333698\pi$
$54$	6.66133	−	3.84592i	0.906492	−	0.523363i
$55$	2.18027	+	3.77633i	0.293987	+	0.509201i
$56$		0			0
$57$			1.90873i			0.252818i
$58$	12.0445	+	6.95390i	1.58152	+	0.913092i
$59$	−9.89352	−	5.71203i	−1.28803	−	0.743643i	−0.309725	−	0.950826i	$-0.600237\pi$
$59$	−9.89352	−	5.71203i	−1.28803	−	0.743643i	−0.978302	+	0.207183i	$0.933570\pi$
$60$		−	3.92895i		−	0.507225i
$61$	−1.46254	+	2.53319i	−0.187259	+	0.324341i	−0.944335	−	0.328985i	$-0.893294\pi$
$61$	−1.46254	+	2.53319i	−0.187259	+	0.324341i	0.757077	+	0.653326i	$0.226627\pi$
$62$	−13.5617	−	23.4896i	−1.72234	−	2.98318i
$63$		0			0
$64$	−4.68406			−0.585507
$65$	4.38250	+	3.81799i	0.543582	+	0.473563i
$66$	−3.63033			−0.446862
$67$	−11.7622	+	6.79091i	−1.43698	+	0.829642i	−0.997639	−	0.0686778i	$-0.978122\pi$
$67$	−11.7622	+	6.79091i	−1.43698	+	0.829642i	−0.439343	+	0.898320i	$0.644789\pi$
$68$	7.34886	+	12.7286i	0.891180	+	1.54357i
$69$	−0.514846	+	0.891740i	−0.0619802	+	0.107353i
$70$		0			0
$71$	1.17009	+	0.675554i	0.138865	+	0.0801736i	0.567823	−	0.823151i	$-0.307786\pi$
$71$	1.17009	+	0.675554i	0.138865	+	0.0801736i	−0.428958	+	0.903324i	$0.641119\pi$
$72$	−16.5367	−	9.54747i	−1.94887	−	1.12518i
$73$			9.10335i			1.06547i	0.846283	+	0.532733i	$0.178835\pi$
$73$			9.10335i			1.06547i	−0.846283	+	0.532733i	$0.821165\pi$
$74$	−7.70557	+	13.3464i	−0.895754	+	1.55149i
$75$	0.622492	+	1.07819i	0.0718791	+	0.124498i
$76$	14.9876	−	8.65311i	1.71920	−	0.992579i
$77$		0			0
$78$	−4.57708	+	1.57047i	−0.518252	+	0.177821i
$79$	−6.20578			−0.698205			−0.349102	−	0.937085i	$-0.613513\pi$
$79$	−6.20578			−0.698205			−0.349102	+	0.937085i	$0.613513\pi$
$80$	−12.1407	+	7.00946i	−1.35738	+	0.783682i
$81$	−3.32650	−	5.76166i	−0.369611	−	0.640185i
$82$	9.96806	−	17.2652i	1.10079	−	1.90662i
$83$			2.69672i			0.296003i	0.988987	+	0.148002i	$0.0472841\pi$
$83$			2.69672i			0.296003i	−0.988987	+	0.148002i	$0.952716\pi$
$84$		0			0
$85$	4.36499	+	2.52013i	0.473450	+	0.273346i
$86$			8.68734i			0.936780i
$87$	−1.39278	+	2.41237i	−0.149322	+	0.258633i
$88$	9.45576	+	16.3779i	1.00799	+	1.74589i
$89$	1.52410	−	0.879938i	0.161554	−	0.0932732i	−0.417043	−	0.908887i	$-0.636934\pi$
$89$	1.52410	−	0.879938i	0.161554	−	0.0932732i	0.578597	+	0.815613i	$0.303600\pi$
$90$	−11.3972			−1.20137
$91$		0			0
$92$	9.33607			0.973353
$93$	4.70469	−	2.71625i	0.487853	−	0.281662i
$94$	1.36560	+	2.36528i	0.140851	+	0.243960i
$95$	2.96739	−	5.13967i	0.304448	−	0.527319i
$96$		−	4.42170i		−	0.451288i
$97$	13.4078	+	7.74102i	1.36136	+	0.785981i	0.989805	−	0.142430i	$-0.0454915\pi$
$97$	13.4078	+	7.74102i	1.36136	+	0.785981i	0.371555	+	0.928411i	$0.378825\pi$
$98$		0			0
$99$			7.38776i			0.742498i
$100$	5.64404	−	9.77576i	0.564404	−	0.977576i
$101$	0.639651	+	1.10791i	0.0636477	+	0.110241i	0.896093	−	0.443866i	$-0.146393\pi$
$101$	0.639651	+	1.10791i	0.0636477	+	0.110241i	−0.832446	+	0.554107i	$0.813060\pi$
$102$	−3.63404	+	2.09811i	−0.359823	+	0.207744i
$103$	−11.4673			−1.12991			−0.564956	−	0.825121i	$-0.691107\pi$
$103$	−11.4673			−1.12991			−0.564956	+	0.825121i	$0.691107\pi$
$104$	19.0068	+	16.5585i	1.86377	+	1.62370i
$105$		0			0
$106$	16.2881	−	9.40397i	1.58204	−	0.913394i
$107$	2.56763	+	4.44726i	0.248222	+	0.429933i	0.963033	−	0.269385i	$-0.0868205\pi$
$107$	2.56763	+	4.44726i	0.248222	+	0.429933i	−0.714811	+	0.699318i	$0.753487\pi$
$108$	6.98412	−	12.0969i	0.672048	−	1.16402i
$109$			1.72783i			0.165496i	0.996570	+	0.0827481i	$0.0263697\pi$
$109$			1.72783i			0.165496i	−0.996570	+	0.0827481i	$0.973630\pi$
$110$	9.77542	+	5.64384i	0.932050	+	0.538119i
$111$	−2.67313	−	1.54333i	−0.253722	−	0.146487i
$112$		0			0
$113$	4.29556	−	7.44014i	0.404093	−	0.699909i	−0.590123	−	0.807314i	$-0.700921\pi$
$113$	4.29556	−	7.44014i	0.404093	−	0.699909i	0.994215	+	0.107404i	$0.0342540\pi$
$114$	2.47048	+	4.27899i	0.231381	+	0.400764i
$115$	2.77267	−	1.60080i	0.258552	−	0.149275i
$116$	25.2563			2.34499
$117$	3.19593	+	9.31442i	0.295464	+	0.861119i
$118$	−29.5723			−2.72235
$119$		0			0
$120$	−2.92170	−	5.06053i	−0.266714	−	0.461961i
$121$	−1.84160	+	3.18975i	−0.167419	+	0.289977i
$122$			7.57184i			0.685522i
$123$	3.45801	+	1.99648i	0.311798	+	0.180017i
$124$	−42.6567	−	24.6279i	−3.83069	−	2.21165i
$125$		−	11.9313i		−	1.06716i
$126$		0			0
$127$	−1.56206	−	2.70556i	−0.138610	−	0.240080i	0.788361	−	0.615214i	$-0.210930\pi$
$127$	−1.56206	−	2.70556i	−0.138610	−	0.240080i	−0.926971	+	0.375133i	$0.877597\pi$
$128$	4.27097	−	2.46585i	0.377504	−	0.217952i
$129$	−1.73997			−0.153196
$130$	14.7663	+	2.88688i	1.29509	+	0.253196i
$131$	−10.2092			−0.891982			−0.445991	−	0.895038i	$-0.647149\pi$
$131$	−10.2092			−0.891982			−0.445991	+	0.895038i	$0.647149\pi$
$132$	−5.70937	+	3.29630i	−0.496936	+	0.286906i
$133$		0			0
$134$	−17.5790	+	30.4476i	−1.51859	+	2.63028i
$135$		−	4.79010i		−	0.412266i
$136$	18.9308	+	10.9297i	1.62331	+	0.937216i
$137$	−8.65385	−	4.99630i	−0.739348	−	0.426863i	0.0824839	−	0.996592i	$-0.473715\pi$
$137$	−8.65385	−	4.99630i	−0.739348	−	0.426863i	−0.821832	+	0.569729i	$0.807048\pi$
$138$			2.66546i			0.226899i
$139$	−0.832100	+	1.44124i	−0.0705778	+	0.122244i	−0.899155	−	0.437631i	$-0.855818\pi$
$139$	−0.832100	+	1.44124i	−0.0705778	+	0.122244i	0.828577	+	0.559875i	$0.189151\pi$
$140$		0			0
$141$	−0.473738	+	0.273513i	−0.0398959	+	0.0230339i
$142$	3.49748			0.293502
$143$	1.87130	−	9.57165i	0.156486	−	0.800422i
$144$	−23.7513			−1.97928
$145$	7.50073	−	4.33055i	0.622902	−	0.359633i
$146$	11.7825	+	20.4078i	0.975124	+	1.68897i
$147$		0			0
$148$			27.9863i			2.30046i
$149$	−17.1456	−	9.89902i	−1.40462	−	0.810959i	−0.409760	−	0.912193i	$-0.634387\pi$
$149$	−17.1456	−	9.89902i	−1.40462	−	0.810959i	−0.994863	+	0.101234i	$0.967721\pi$
$150$	2.79100	+	1.61138i	0.227884	+	0.131569i
$151$		−	7.53493i		−	0.613184i	−0.951841	−	0.306592i	$-0.900811\pi$
$151$		−	7.53493i		−	0.613184i	0.951841	−	0.306592i	$-0.0991886\pi$
$152$	12.8695	−	22.2906i	1.04385	−	1.80801i
$153$	4.26968	+	7.39531i	0.345183	+	0.597875i
$154$		0			0
$155$	−16.8912			−1.35673
$156$	−5.77234	+	6.62581i	−0.462157	+	0.530489i
$157$	−14.0045			−1.11768			−0.558839	−	0.829276i	$-0.688753\pi$
$157$	−14.0045			−1.11768			−0.558839	+	0.829276i	$0.688753\pi$
$158$	−13.9121	+	8.03214i	−1.10679	+	0.639003i
$159$	1.88350	+	3.26232i	0.149371	+	0.258719i
$160$	−6.87414	+	11.9064i	−0.543448	+	0.941280i
$161$		0			0
$162$	−14.9146	−	8.61097i	−1.17181	−	0.676542i
$163$	−6.20936	−	3.58498i	−0.486355	−	0.280797i	0.236706	−	0.971581i	$-0.423932\pi$
$163$	−6.20936	−	3.58498i	−0.486355	−	0.280797i	−0.723061	+	0.690784i	$0.757265\pi$
$164$		−	36.2036i		−	2.82703i
$165$	−1.13039	+	1.95790i	−0.0880011	+	0.152422i
$166$	3.49036	+	6.04548i	0.270904	+	0.469220i
$167$	−15.5716	+	8.99027i	−1.20497	+	0.695688i	−0.961656	−	0.274260i	$-0.911567\pi$
$167$	−15.5716	+	8.99027i	−1.20497	+	0.695688i	−0.243312	+	0.969948i	$0.578234\pi$
$168$		0			0
$169$	−1.78135	−	12.8774i	−0.137027	−	0.990567i
$170$	13.0472			1.00068
$171$	8.70780	−	5.02745i	0.665902	−	0.384459i
$172$	7.88803	+	13.6625i	0.601456	+	1.04175i
$173$	6.40579	−	11.0952i	0.487023	−	0.843549i	−0.512865	−	0.858469i	$-0.671416\pi$
$173$	6.40579	−	11.0952i	0.487023	−	0.843549i	0.999889	+	0.0149198i	$0.00474930\pi$
$174$			7.21072i			0.546643i
$175$		0			0
$176$	20.3717	+	11.7616i	1.53557	+	0.886562i
$177$		−	5.92298i		−	0.445199i
$178$	2.27781	−	3.94528i	0.170729	−	0.295711i
$179$	0.920110	+	1.59368i	0.0687723	+	0.119117i	0.898361	−	0.439258i	$-0.144758\pi$
$179$	0.920110	+	1.59368i	0.0687723	+	0.119117i	−0.829589	+	0.558375i	$0.811425\pi$
$180$	−17.9242	+	10.3485i	−1.33599	+	0.771334i
$181$	3.29928			0.245234			0.122617	−	0.992454i	$-0.460871\pi$
$181$	3.29928			0.245234			0.122617	+	0.992454i	$0.460871\pi$
$182$		0			0
$183$	−1.51655			−0.112107
$184$	12.0250	−	6.94262i	0.886493	−	0.511817i
$185$	4.79865	+	8.31150i	0.352804	+	0.611074i
$186$	7.03129	−	12.1786i	0.515560	−	0.892975i
$187$		−	8.45734i		−	0.618462i
$188$	4.29531	+	2.47990i	0.313268	+	0.180865i
$189$		0			0
$190$		−	15.3628i		−	1.11453i
$191$	−2.44807	+	4.24018i	−0.177136	+	0.306809i	−0.940898	−	0.338689i	$-0.890017\pi$
$191$	−2.44807	+	4.24018i	−0.177136	+	0.306809i	0.763762	+	0.645498i	$0.223350\pi$
$192$	−1.21426	−	2.10316i	−0.0876318	−	0.151783i
$193$	−2.61462	+	1.50955i	−0.188204	+	0.108660i	−0.591142	−	0.806568i	$-0.701323\pi$
$193$	−2.61462	+	1.50955i	−0.188204	+	0.108660i	0.402937	+	0.915228i	$0.367989\pi$
$194$	40.0768			2.87735
$195$	−0.578207	+	2.95751i	−0.0414063	+	0.211792i
$196$		0			0
$197$	4.02694	−	2.32496i	0.286908	−	0.165646i	−0.349639	−	0.936885i	$-0.613696\pi$
$197$	4.02694	−	2.32496i	0.286908	−	0.165646i	0.636546	+	0.771238i	$0.280362\pi$
$198$	9.56198	+	16.5618i	0.679540	+	1.17700i
$199$	−0.205360	+	0.355694i	−0.0145576	+	0.0252145i	−0.873212	−	0.487340i	$-0.837967\pi$
$199$	−0.205360	+	0.355694i	−0.0145576	+	0.0252145i	0.858655	+	0.512554i	$0.171301\pi$
$200$		−	16.7884i		−	1.18712i
$201$	−6.09830	−	3.52085i	−0.430141	−	0.248342i
$202$	2.86793	+	1.65580i	0.201787	+	0.116502i
$203$		0			0
$204$	−3.81013	+	6.59934i	−0.266763	+	0.462047i
$205$	−6.20762	−	10.7519i	−0.433559	−	0.750946i
$206$	−25.7074	+	14.8422i	−1.79112	+	1.03410i
$207$	5.42425			0.377012
$208$	30.7724	+	6.01616i	2.13368	+	0.417146i
$209$	−9.95831			−0.688831
$210$		0			0
$211$	3.75800	+	6.50905i	0.258711	+	0.448101i	0.965897	−	0.258927i	$-0.0833688\pi$
$211$	3.75800	+	6.50905i	0.258711	+	0.448101i	−0.707186	+	0.707028i	$0.750035\pi$
$212$	17.0774	−	29.5790i	1.17288	−	2.03149i
$213$			0.700504i			0.0479977i
$214$	11.5122	+	6.64656i	0.786956	+	0.454349i
$215$	4.68524	+	2.70502i	0.319531	+	0.184481i
$216$		−	20.7745i		−	1.41353i
$217$		0			0
$218$	2.23633	+	3.87344i	0.151464	+	0.262343i
$219$	−4.08745	+	2.35989i	−0.276204	+	0.159467i
$220$	20.4982			1.38199
$221$	−3.65863	−	10.6629i	−0.246106	−	0.717267i
$222$	−7.99014			−0.536263
$223$	19.5544	−	11.2897i	1.30946	−	0.756016i	0.327452	−	0.944868i	$-0.393810\pi$
$223$	19.5544	−	11.2897i	1.30946	−	0.756016i	0.982006	+	0.188852i	$0.0604766\pi$
$224$		0			0
$225$	3.27918	−	5.67971i	0.218612	−	0.378648i
$226$		−	22.2390i		−	1.47932i
$227$	11.8401	+	6.83586i	0.785853	+	0.453712i	0.838500	−	0.544901i	$-0.183433\pi$
$227$	11.8401	+	6.83586i	0.785853	+	0.453712i	−0.0526478	+	0.998613i	$0.516766\pi$
$228$	7.77057	+	4.48634i	0.514618	+	0.297115i
$229$			7.93086i			0.524086i	0.965056	+	0.262043i	$0.0843962\pi$
$229$			7.93086i			0.524086i	−0.965056	+	0.262043i	$0.915604\pi$
$230$	4.14383	−	7.17733i	0.273236	−	0.473259i
$231$		0			0
$232$	32.5305	−	18.7815i	2.13573	−	1.23306i
$233$	6.57171			0.430527			0.215263	−	0.976556i	$-0.430939\pi$
$233$	6.57171			0.430527			0.215263	+	0.976556i	$0.430939\pi$
$234$	19.2203	+	16.7445i	1.25647	+	1.09462i
$235$	1.70085			0.110951
$236$	−46.5080	+	26.8514i	−3.02741	+	1.74788i
$237$	−1.60874	−	2.78642i	−0.104499	−	0.180998i
$238$		0			0
$239$		−	9.39284i		−	0.607572i	−0.952740	−	0.303786i	$-0.901749\pi$
$239$		−	9.39284i		−	0.607572i	0.952740	−	0.303786i	$-0.0982508\pi$
$240$	−6.29456	−	3.63417i	−0.406312	−	0.234584i
$241$	8.73460	+	5.04292i	0.562645	+	0.324843i	0.754206	−	0.656637i	$-0.228022\pi$
$241$	8.73460	+	5.04292i	0.562645	+	0.324843i	−0.191562	+	0.981481i	$0.561355\pi$
$242$			9.53435i			0.612891i
$243$	6.18182	−	10.7072i	0.396564	−	0.686869i
$244$	6.87517	+	11.9081i	0.440137	+	0.762340i
$245$		0			0
$246$	10.3362			0.659012
$247$	−12.5553	+	4.30794i	−0.798878	+	0.274108i
$248$	−73.2565			−4.65179
$249$	−1.21084	+	0.699078i	−0.0767337	+	0.0443022i
$250$	−15.4426	−	26.7474i	−0.976678	−	1.69166i
$251$	5.17427	−	8.96209i	0.326597	−	0.565682i	−0.655237	−	0.755423i	$-0.727431\pi$
$251$	5.17427	−	8.96209i	0.326597	−	0.565682i	0.981834	+	0.189741i	$0.0607648\pi$
$252$		0			0
$253$	−4.65242	−	2.68607i	−0.292495	−	0.168872i
$254$	−7.00363	−	4.04355i	−0.439447	−	0.253715i
$255$			2.61320i			0.163645i
$256$	11.0672	−	19.1689i	0.691697	−	1.19805i
$257$	−3.99329	−	6.91658i	−0.249095	−	0.431445i	0.714180	−	0.699962i	$-0.246800\pi$
$257$	−3.99329	−	6.91658i	−0.249095	−	0.431445i	−0.963275	+	0.268517i	$0.913466\pi$
$258$	−3.90065	+	2.25204i	−0.242844	+	0.140206i
$259$		0			0
$260$	25.8440	−	8.86749i	1.60278	−	0.549939i
$261$	14.6739			0.908292
$262$	−22.8869	+	13.2138i	−1.41396	+	0.816349i
$263$	−2.52967	−	4.38152i	−0.155986	−	0.270176i	0.777431	−	0.628968i	$-0.216522\pi$
$263$	−2.52967	−	4.38152i	−0.155986	−	0.270176i	−0.933418	+	0.358792i	$0.883189\pi$
$264$	−4.90249	+	8.49136i	−0.301727	+	0.522607i
$265$		−	11.7127i		−	0.719503i
$266$		0			0
$267$	0.790192	+	0.456218i	0.0483590	+	0.0279201i
$268$			63.8461i			3.90002i
$269$	6.94512	−	12.0293i	0.423451	−	0.733439i	−0.572823	−	0.819679i	$-0.694152\pi$
$269$	6.94512	−	12.0293i	0.423451	−	0.733439i	0.996274	+	0.0862400i	$0.0274852\pi$
$270$	−6.19983	−	10.7384i	−0.377310	−	0.653519i
$271$	−7.21158	+	4.16361i	−0.438072	+	0.252921i	−0.702780	−	0.711408i	$-0.748058\pi$
$271$	−7.21158	+	4.16361i	−0.438072	+	0.252921i	0.264707	+	0.964329i	$0.414725\pi$
$272$	27.1900			1.64863
$273$		0			0
$274$	−25.8669			−1.56267
$275$	−5.62515	+	3.24768i	−0.339210	+	0.195843i
$276$	2.42022	+	4.19194i	0.145680	+	0.252325i
$277$	−11.6058	+	20.1018i	−0.697325	+	1.20780i	0.272066	+	0.962279i	$0.412293\pi$
$277$	−11.6058	+	20.1018i	−0.697325	+	1.20780i	−0.969391	+	0.245523i	$0.921040\pi$
$278$			4.30795i			0.258374i
$279$	−24.7835	−	14.3088i	−1.48375	−	0.856644i
$280$		0			0
$281$		−	27.1595i		−	1.62020i	−0.586292	−	0.810100i	$-0.699413\pi$
$281$		−	27.1595i		−	1.62020i	0.586292	−	0.810100i	$-0.300587\pi$
$282$	−0.708015	+	1.22632i	−0.0421617	+	0.0730262i
$283$	8.07563	+	13.9874i	0.480046	+	0.831464i	0.999738	−	0.0228894i	$-0.00728654\pi$
$283$	8.07563	+	13.9874i	0.480046	+	0.831464i	−0.519692	+	0.854354i	$0.673953\pi$
$284$	5.50044	−	3.17568i	0.326391	−	0.188442i
$285$	3.07698			0.182265
$286$	−8.19351	−	23.8797i	−0.484493	−	1.41204i
$287$		0			0
$288$	−20.1721	+	11.6464i	−1.18865	+	0.686270i
$289$	3.61216	+	6.25645i	0.212480	+	0.368027i
$290$	11.2101	−	19.4164i	0.658278	−	1.14017i
$291$			8.02691i			0.470546i
$292$	37.0603	+	21.3968i	2.16879	+	1.25215i
$293$	12.6831	+	7.32260i	0.740956	+	0.427791i	0.822417	−	0.568885i	$-0.192625\pi$
$293$	12.6831	+	7.32260i	0.740956	+	0.427791i	−0.0814609	+	0.996677i	$0.525959\pi$
$294$		0			0
$295$	−9.20810	+	15.9489i	−0.536116	+	0.928580i
$296$	20.8116	+	36.0468i	1.20965	+	2.09517i
$297$	−6.96075	+	4.01879i	−0.403904	+	0.233194i
$298$	−51.2492			−2.96879
$299$	−7.02771	−	1.37395i	−0.406423	−	0.0794577i
$300$	5.85248			0.337893
$301$		0			0
$302$	−9.75246	−	16.8918i	−0.561191	−	0.972011i
$303$	−0.331637	+	0.574412i	−0.0190521	+	0.0329991i
$304$		−	32.0155i		−	1.83622i
$305$	4.08363	+	2.35769i	0.233828	+	0.135001i
$306$	19.1435	+	11.0525i	1.09436	+	0.631830i
$307$		−	8.97844i		−	0.512427i	−0.966620	−	0.256213i	$-0.917525\pi$
$307$		−	8.97844i		−	0.512427i	0.966620	−	0.256213i	$-0.0824750\pi$
$308$		0			0
$309$	−2.97271	−	5.14889i	−0.169112	−	0.292910i
$310$	−37.8665	+	21.8622i	−2.15067	+	1.24169i
$311$	12.1816			0.690755			0.345378	−	0.938464i	$-0.387751\pi$
$311$	12.1816			0.690755			0.345378	+	0.938464i	$0.387751\pi$
$312$	−2.50767	+	12.8266i	−0.141969	+	0.726165i
$313$	−13.1240			−0.741810			−0.370905	−	0.928671i	$-0.620953\pi$
$313$	−13.1240			−0.741810			−0.370905	+	0.928671i	$0.620953\pi$
$314$	−31.3951	+	18.1260i	−1.77173	+	1.02291i
$315$		0			0
$316$	−14.5862	+	25.2641i	−0.820540	+	1.42122i
$317$		−	16.7155i		−	0.938836i	−0.882976	−	0.469418i	$-0.844464\pi$
$317$		−	16.7155i		−	0.938836i	0.882976	−	0.469418i	$-0.155536\pi$
$318$	8.44485	+	4.87563i	0.473564	+	0.273412i
$319$	−12.5859	−	7.26648i	−0.704675	−	0.406845i
$320$			7.55095i			0.422111i
$321$	−1.33123	+	2.30575i	−0.0743018	+	0.128695i
$322$		0			0
$323$	−9.96849	+	5.75531i	−0.554661	+	0.320234i
$324$	−31.2748			−1.73749
$325$	−5.68720	+	6.52808i	−0.315469	+	0.362113i
$326$	−18.5601			−1.02795
$327$	−0.775804	+	0.447911i	−0.0429021	+	0.0247695i
$328$	−26.9223	−	46.6307i	−1.48653	−	2.57475i
$329$		0			0
$330$			5.85228i			0.322157i
$331$	3.43522	+	1.98332i	0.188817	+	0.109013i	0.591428	−	0.806357i	$-0.298564\pi$
$331$	3.43522	+	1.98332i	0.188817	+	0.109013i	−0.402612	+	0.915371i	$0.631898\pi$
$332$	10.9785	+	6.33843i	0.602523	+	0.347867i
$333$			16.2600i			0.891045i
$334$	−23.2722	+	40.3087i	−1.27340	+	2.20559i
$335$	10.9473	+	18.9613i	0.598116	+	1.03597i
$336$		0			0
$337$	−13.7032			−0.746461			−0.373230	−	0.927739i	$-0.621750\pi$
$337$	−13.7032			−0.746461			−0.373230	+	0.927739i	$0.621750\pi$
$338$	−20.6606	−	26.5628i	−1.12379	−	1.44483i
$339$	4.45421			0.241919
$340$	20.5192	−	11.8468i	1.11281	−	0.642481i
$341$	14.1713	+	24.5455i	0.767420	+	1.32921i
$342$	13.0141	−	22.5410i	0.703720	−	1.21888i
$343$		0			0
$344$	20.3197	+	11.7316i	1.09557	+	0.632526i
$345$	1.43753	+	0.829960i	0.0773942	+	0.0446835i
$346$		−	33.1641i		−	1.78291i
$347$	13.1989	−	22.8612i	0.708556	−	1.22725i	−0.256837	−	0.966455i	$-0.582680\pi$
$347$	13.1989	−	22.8612i	0.708556	−	1.22725i	0.965393	−	0.260800i	$-0.0839863\pi$
$348$	6.54727	+	11.3402i	0.350971	+	0.607899i
$349$	4.23507	−	2.44512i	0.226698	−	0.130884i	−0.382350	−	0.924018i	$-0.624885\pi$
$349$	4.23507	−	2.44512i	0.226698	−	0.130884i	0.609048	+	0.793133i	$0.291552\pi$
$350$		0			0
$351$	−7.03753	+	8.07806i	−0.375636	+	0.431175i
$352$	23.0690			1.22958
$353$	−11.7413	+	6.77886i	−0.624928	+	0.360802i	−0.778785	−	0.627291i	$-0.784164\pi$
$353$	−11.7413	+	6.77886i	−0.624928	+	0.360802i	0.153857	+	0.988093i	$0.450830\pi$
$354$	−7.66612	−	13.2781i	−0.407450	−	0.705724i
$355$	1.08903	−	1.88626i	0.0577997	−	0.100112i
$356$		−	8.27291i		−	0.438464i
$357$		0			0
$358$	4.12540	+	2.38180i	0.218034	+	0.125882i
$359$		−	8.58568i		−	0.453135i	−0.973996	−	0.226567i	$-0.927250\pi$
$359$		−	8.58568i		−	0.453135i	0.973996	−	0.226567i	$-0.0727503\pi$
$360$	−15.3910	+	26.6581i	−0.811179	+	1.40500i
$361$	−2.72326	−	4.71683i	−0.143330	−	0.248254i
$362$	7.39632	−	4.27026i	0.388742	−	0.224440i
$363$	−1.90962			−0.100229
$364$		0			0
$365$	14.6751			0.768130
$366$	−3.39979	+	1.96287i	−0.177710	+	0.102601i
$367$	−0.831612	−	1.44039i	−0.0434098	−	0.0751880i	0.843504	−	0.537123i	$-0.180489\pi$
$367$	−0.831612	−	1.44039i	−0.0434098	−	0.0751880i	−0.886914	+	0.461935i	$0.847155\pi$
$368$	8.63560	−	14.9573i	0.450162	−	0.779703i
$369$		−	21.0343i		−	1.09500i
$370$	21.5152	+	12.4218i	1.11852	+	0.645778i
$371$		0			0
$372$		−	25.5374i		−	1.32405i
$373$	−6.98174	+	12.0927i	−0.361501	+	0.626138i	−0.988208	−	0.153117i	$-0.951069\pi$
$373$	−6.98174	+	12.0927i	−0.361501	+	0.626138i	0.626707	+	0.779255i	$0.284402\pi$
$374$	−10.9463	−	18.9596i	−0.566022	−	0.980378i
$375$	5.35719	−	3.09298i	0.276644	−	0.159721i
$376$	7.37655			0.380417
$377$	−19.0117	−	3.71687i	−0.979150	−	0.191429i
$378$		0			0
$379$	−27.3454	+	15.7879i	−1.40464	+	0.810969i	−0.994864	−	0.101218i	$-0.967726\pi$
$379$	−27.3454	+	15.7879i	−1.40464	+	0.810969i	−0.409775	+	0.912187i	$0.634393\pi$
$380$	−13.9493	−	24.1608i	−0.715582	−	1.23943i
$381$	0.809874	−	1.40274i	0.0414911	−	0.0718647i
$382$			12.6741i			0.648466i
$383$	−27.6333	−	15.9541i	−1.41200	−	0.815217i	−0.416420	−	0.909172i	$-0.636716\pi$
$383$	−27.6333	−	15.9541i	−1.41200	−	0.815217i	−0.995576	+	0.0939554i	$0.970049\pi$
$384$	2.21435	+	1.27846i	0.113001	+	0.0652410i
$385$		0			0
$386$	−3.90762	+	6.76820i	−0.198893	+	0.344492i
$387$	4.58294	+	7.93788i	0.232964	+	0.403505i
$388$	63.0283	−	36.3894i	3.19978	−	1.84739i
$389$	25.4150			1.28859			0.644296	−	0.764776i	$-0.277150\pi$
$389$	25.4150			1.28859			0.644296	+	0.764776i	$0.277150\pi$
$390$	2.53168	+	7.37850i	0.128197	+	0.373625i
$391$	−6.20956			−0.314031
$392$		0			0
$393$	−2.64656	−	4.58398i	−0.133501	−	0.231231i
$394$	6.01838	−	10.4241i	0.303202	−	0.525161i
$395$			10.0041i			0.503358i
$396$	30.0760	+	17.3644i	1.51138	+	0.872593i
$397$	−3.60178	−	2.07949i	−0.180768	−	0.104366i	0.406885	−	0.913479i	$-0.366615\pi$
$397$	−3.60178	−	2.07949i	−0.180768	−	0.104366i	−0.587653	+	0.809113i	$0.699948\pi$
$398$			1.06319i			0.0532930i
$399$		0			0
$400$	−10.4412	−	18.0846i	−0.522058	−	0.904231i
$401$	16.9753	−	9.80067i	0.847704	−	0.489422i	−0.0121716	−	0.999926i	$-0.503874\pi$
$401$	16.9753	−	9.80067i	0.847704	−	0.489422i	0.859875	+	0.510504i	$0.170541\pi$
$402$	−18.2282			−0.909139
$403$	28.4854	+	24.8162i	1.41896	+	1.23618i
$404$	6.01381			0.299198
$405$	−9.28811	+	5.36249i	−0.461530	+	0.266464i
$406$		0			0
$407$	8.05193	−	13.9463i	0.399119	−	0.691295i
$408$			11.3334i			0.561086i
$409$	−15.2712	−	8.81685i	−0.755114	−	0.435965i	0.0724249	−	0.997374i	$-0.476926\pi$
$409$	−15.2712	−	8.81685i	−0.755114	−	0.435965i	−0.827539	+	0.561409i	$0.810260\pi$
$410$	−27.8324	−	16.0690i	−1.37454	−	0.793594i
$411$		−	5.18083i		−	0.255551i
$412$	−26.9532	+	46.6842i	−1.32789	+	2.29997i
$413$		0			0
$414$	12.1601	−	7.02061i	0.597634	−	0.345044i
$415$	4.34725			0.213398
$416$	29.0852	−	9.97961i	1.42602	−	0.489291i
$417$	−0.862831			−0.0422530
$418$	−22.3245	+	12.8890i	−1.09193	+	0.630424i
$419$	14.9455	+	25.8864i	0.730137	+	1.26463i	0.956824	+	0.290666i	$0.0938770\pi$
$419$	14.9455	+	25.8864i	0.730137	+	1.26463i	−0.226688	+	0.973968i	$0.572790\pi$
$420$		0			0
$421$		−	12.8528i		−	0.626407i	−0.949686	−	0.313203i	$-0.898598\pi$
$421$		−	12.8528i		−	0.626407i	0.949686	−	0.313203i	$-0.101402\pi$
$422$	16.8493	+	9.72796i	0.820212	+	0.473550i
$423$	2.49557	+	1.44082i	0.121339	+	0.0700551i
$424$		−	50.7975i		−	2.46694i
$425$	−3.75393	+	6.50200i	−0.182093	+	0.315394i
$426$	0.906662	+	1.57038i	0.0439279	+	0.0760854i
$427$		0			0
$428$	24.1401			1.16685
$429$	4.78282	−	1.64106i	0.230917	−	0.0792313i
$430$	14.0045			0.675355
$431$	−7.76876	+	4.48530i	−0.374208	+	0.216049i	−0.675295	−	0.737547i	$-0.735984\pi$
$431$	−7.76876	+	4.48530i	−0.374208	+	0.216049i	0.301087	+	0.953597i	$0.402650\pi$
$432$	−12.9202	−	22.3785i	−0.621625	−	1.07669i
$433$	1.72531	−	2.98833i	0.0829132	−	0.143610i	−0.821587	−	0.570083i	$-0.806911\pi$
$433$	1.72531	−	2.98833i	0.0829132	−	0.143610i	0.904500	+	0.426473i	$0.140244\pi$
$434$		0			0
$435$	3.88887	+	2.24524i	0.186457	+	0.107651i
$436$	7.03410	+	4.06114i	0.336872	+	0.194493i
$437$			7.31161i			0.349762i
$438$	−6.10881	+	10.5808i	−0.291890	+	0.505569i
$439$	19.2572	+	33.3544i	0.919096	+	1.59192i	0.800792	+	0.598943i	$0.204412\pi$
$439$	19.2572	+	33.3544i	0.919096	+	1.59192i	0.118304	+	0.992977i	$0.462254\pi$
$440$	26.4020	−	15.2432i	1.25867	−	0.726691i
$441$		0			0
$442$	−22.0029	−	19.1687i	−1.04657	−	0.911764i
$443$	−15.0399			−0.714569			−0.357284	−	0.933996i	$-0.616297\pi$
$443$	−15.0399			−0.714569			−0.357284	+	0.933996i	$0.616297\pi$
$444$	−12.5660	+	7.25498i	−0.596356	+	0.344306i
$445$	−1.41851	−	2.45693i	−0.0672437	−	0.116469i
$446$	29.2246	−	50.6185i	1.38382	−	2.39685i
$447$		−	10.2646i		−	0.485499i
$448$		0			0
$449$	33.7087	+	19.4617i	1.59081	+	0.918456i	0.993168	+	0.116696i	$0.0372304\pi$
$449$	33.7087	+	19.4617i	1.59081	+	0.918456i	0.597646	+	0.801760i	$0.296103\pi$
$450$		−	16.9770i		−	0.800303i
$451$	−10.4161	+	18.0412i	−0.490476	+	0.849529i
$452$	−20.1928	−	34.9750i	−0.949790	−	1.64509i
$453$	3.38322	−	1.95330i	0.158957	−	0.0917741i
$454$	35.3906			1.66097
$455$		0			0
$456$	13.3448			0.624927
$457$	12.0721	−	6.96982i	0.564708	−	0.326034i	−0.190325	−	0.981721i	$-0.560954\pi$
$457$	12.0721	−	6.96982i	0.564708	−	0.326034i	0.755033	+	0.655687i	$0.227621\pi$
$458$	10.2649	+	17.7793i	0.479648	+	0.830774i
$459$	−4.64524	+	8.04580i	−0.216821	+	0.375546i
$460$		−	15.0502i		−	0.701721i
$461$	−32.4443	−	18.7317i	−1.51108	−	0.872424i	−0.999916	−	0.0129430i	$-0.995880\pi$
$461$	−32.4443	−	18.7317i	−1.51108	−	0.872424i	−0.511167	−	0.859481i	$-0.670787\pi$
$462$		0			0
$463$			6.75275i			0.313827i	0.987612	+	0.156913i	$0.0501544\pi$
$463$			6.75275i			0.313827i	−0.987612	+	0.156913i	$0.949846\pi$
$464$	23.3614	−	40.4631i	1.08453	−	1.87845i
$465$	−4.37875	−	7.58421i	−0.203059	−	0.351709i
$466$	14.7324	−	8.50576i	0.682466	−	0.394022i
$467$	5.05032			0.233701			0.116851	−	0.993150i	$-0.462720\pi$
$467$	5.05032			0.233701			0.116851	+	0.993150i	$0.462720\pi$
$468$	45.4314	+	8.88205i	2.10006	+	0.410573i
$469$		0			0
$470$	3.81296	−	2.20141i	0.175879	−	0.101544i
$471$	−3.63042	−	6.28807i	−0.167281	−	0.289739i
$472$	−39.9353	+	69.1699i	−1.83817	+	3.18380i
$473$		−	9.07783i		−	0.417399i
$474$	−7.21294	−	4.16439i	−0.331301	−	0.191277i
$475$	7.65595	+	4.42017i	0.351279	+	0.202811i
$476$		0			0
$477$	9.92198	−	17.1854i	0.454296	−	0.786864i
$478$	−12.1572	−	21.0568i	−0.556055	−	0.963116i
$479$	8.18670	−	4.72659i	0.374060	−	0.215964i	−0.301171	−	0.953570i	$-0.597377\pi$
$479$	8.18670	−	4.72659i	0.374060	−	0.215964i	0.675231	+	0.737607i	$0.264044\pi$
$480$	−7.12801			−0.325348
$481$	4.11864	−	21.0667i	0.187794	−	0.960558i
$482$	26.1082			1.18920
$483$		0			0
$484$	8.65711	+	14.9946i	0.393505	+	0.681571i
$485$	12.4789	−	21.6142i	0.566639	−	0.981448i
$486$		−	32.0045i		−	1.45175i
$487$	−34.6407	−	19.9998i	−1.56972	−	0.906277i	−0.996201	−	0.0870831i	$-0.972245\pi$
$487$	−34.6407	−	19.9998i	−1.56972	−	0.906277i	−0.573517	−	0.819194i	$-0.694421\pi$
$488$	17.7106	+	10.2252i	0.801721	+	0.462874i
$489$		−	3.71737i		−	0.168105i
$490$		0			0
$491$	−3.38049	−	5.85517i	−0.152559	−	0.264240i	0.779608	−	0.626267i	$-0.215418\pi$
$491$	−3.38049	−	5.85517i	−0.152559	−	0.264240i	−0.932168	+	0.362027i	$0.882085\pi$
$492$	16.2556	−	9.38518i	0.732859	−	0.423116i
$493$	−16.7984			−0.756560
$494$	−22.5707	+	25.9079i	−1.01551	+	1.16565i
$495$	11.9095			0.535291
$496$	−78.9125	+	45.5602i	−3.54328	+	2.04571i
$497$		0			0
$498$	−1.80963	+	3.13438i	−0.0810916	+	0.140455i
$499$			11.3575i			0.508433i	0.967147	+	0.254217i	$0.0818176\pi$
$499$			11.3575i			0.508433i	−0.967147	+	0.254217i	$0.918182\pi$
$500$	−48.5729	−	28.0436i	−2.17225	−	1.25415i
$501$	−8.07335	−	4.66115i	−0.360691	−	0.208245i
$502$		−	26.7882i		−	1.19562i
$503$	−6.96423	+	12.0624i	−0.310520	+	0.537836i	−0.978475	−	0.206365i	$-0.933836\pi$
$503$	−6.96423	+	12.0624i	−0.310520	+	0.537836i	0.667955	+	0.744202i	$0.267170\pi$
$504$		0			0
$505$	1.78601	−	1.03115i	0.0794763	−	0.0458857i
$506$	−13.9063			−0.618212
$507$	5.32022	−	4.13807i	0.236279	−	0.183778i
$508$	−14.6860			−0.651587
$509$	17.1602	−	9.90746i	0.760614	−	0.439141i	−0.0689022	−	0.997623i	$-0.521950\pi$
$509$	17.1602	−	9.90746i	0.760614	−	0.439141i	0.829516	+	0.558483i	$0.188616\pi$
$510$	3.38227	+	5.85826i	0.149769	+	0.259408i
$511$		0			0
$512$		−	47.4335i		−	2.09628i
$513$	9.47373	+	5.46966i	0.418276	+	0.241491i
$514$	−17.9043	−	10.3370i	−0.789724	−	0.455947i
$515$			18.4860i			0.814590i
$516$	−4.08967	+	7.08352i	−0.180038	+	0.311835i
$517$	−1.42698	−	2.47160i	−0.0627585	−	0.108701i
$518$		0			0
$519$	6.64237			0.291568
$520$	26.6932	−	30.6399i	1.17057	−	1.34365i
$521$	31.0951			1.36230			0.681151	−	0.732143i	$-0.261480\pi$
$521$	31.0951			1.36230			0.681151	+	0.732143i	$0.261480\pi$
$522$	32.8959	−	18.9924i	1.43981	−	0.831277i
$523$	11.3601	+	19.6763i	0.496742	+	0.860383i	0.999993	−	0.00375758i	$-0.00119608\pi$
$523$	11.3601	+	19.6763i	0.496742	+	0.860383i	−0.503251	+	0.864140i	$0.667863\pi$
$524$	−23.9960	+	41.5622i	−1.04827	+	1.81565i
$525$		0			0
$526$	−11.3420	−	6.54831i	−0.494535	−	0.285520i
$527$	28.3716	+	16.3804i	1.23589	+	0.713540i
$528$			12.1960i			0.530761i
$529$	9.52783	−	16.5027i	0.414253	−	0.717508i
$530$	−15.1597	−	26.2574i	−0.658495	−	1.14055i
$531$	−27.0211	+	15.6007i	−1.17262	+	0.677011i
$532$		0			0
$533$	−5.32794	+	27.2522i	−0.230779	+	1.18043i
$534$	2.36193			0.102211
$535$	7.16922	−	4.13915i	0.309952	−	0.178951i
$536$	47.4782	+	82.2346i	2.05074	+	3.55199i
$537$	−0.477046	+	0.826267i	−0.0205860	+	0.0356561i
$538$		−	35.9563i		−	1.55018i
$539$		0			0
$540$	−19.5008	−	11.2588i	−0.839180	−	0.484501i
$541$		−	2.09872i		−	0.0902310i	−0.998982	−	0.0451155i	$-0.985634\pi$
$541$		−	2.09872i		−	0.0902310i	0.998982	−	0.0451155i	$-0.0143656\pi$
$542$	−10.7779	+	18.6679i	−0.462951	+	0.801855i
$543$	0.855283	+	1.48139i	0.0367037	+	0.0635727i
$544$	23.0926	−	13.3325i	0.990087	−	0.571627i
$545$	2.78536			0.119312
$546$		0			0
$547$	25.3770			1.08504			0.542521	−	0.840042i	$-0.317470\pi$
$547$	25.3770			1.08504			0.542521	+	0.840042i	$0.317470\pi$
$548$	−40.6805	+	23.4869i	−1.73778	+	1.00331i
$549$	3.99447	+	6.91862i	0.170480	+	0.295280i
$550$	−8.40696	+	14.5613i	−0.358474	+	0.620895i
$551$			19.7797i			0.842642i
$552$	6.23454	+	3.59951i	0.265360	+	0.153205i
$553$		0			0
$554$			60.0855i			2.55279i
$555$	−2.48794	+	4.30923i	−0.105607	+	0.182917i
$556$	3.91158	+	6.77506i	0.165888	+	0.287327i
$557$	38.3219	−	22.1252i	1.62375	−	0.937473i	0.637846	−	0.770164i	$-0.279826\pi$
$557$	38.3219	−	22.1252i	1.62375	−	0.937473i	0.985904	−	0.167309i	$-0.0535078\pi$
$558$	−74.0794			−3.13603
$559$	−3.92705	−	11.4452i	−0.166097	−	0.484082i
$560$		0			0
$561$	3.79738	−	2.19242i	0.160326	−	0.0925641i
$562$	−35.1526	−	60.8860i	−1.48282	−	2.56832i
$563$	19.4453	−	33.6803i	0.819523	−	1.41946i	−0.0865108	−	0.996251i	$-0.527572\pi$
$563$	19.4453	−	33.6803i	0.819523	−	1.41946i	0.906034	−	0.423205i	$-0.139095\pi$
$564$			2.57149i			0.108279i
$565$	−11.9939	−	6.92468i	−0.504587	−	0.291324i
$566$	36.2078	+	20.9046i	1.52193	+	0.878685i
$567$		0			0
$568$	4.72309	−	8.18063i	0.198177	−	0.343252i
$569$	23.0789	+	39.9739i	0.967520	+	1.67579i	0.702687	+	0.711499i	$0.251983\pi$
$569$	23.0789	+	39.9739i	0.967520	+	1.67579i	0.264832	+	0.964294i	$0.414683\pi$
$570$	6.89796	−	3.98254i	0.288924	−	0.166810i
$571$	−21.1368			−0.884548			−0.442274	−	0.896880i	$-0.645828\pi$
$571$	−21.1368			−0.884548			−0.442274	+	0.896880i	$0.645828\pi$
$572$	−34.5684	−	30.1157i	−1.44538	−	1.25920i
$573$	−2.53848			−0.106047
$574$		0			0
$575$	2.38452	+	4.13011i	0.0994413	+	0.172237i
$576$	−6.39653	+	11.0791i	−0.266522	+	0.461630i
$577$		−	25.3304i		−	1.05452i	−0.849705	−	0.527259i	$-0.823220\pi$
$577$		−	25.3304i		−	1.05452i	0.849705	−	0.527259i	$-0.176780\pi$
$578$	16.1955	+	9.35045i	0.673642	+	0.388927i
$579$	−1.35559	−	0.782650i	−0.0563364	−	0.0325258i
$580$		−	40.7146i		−	1.69058i
$581$		0			0
$582$	10.3892	+	17.9947i	0.430647	+	0.745903i
$583$	−17.0203	+	9.82667i	−0.704908	+	0.406979i
$584$	63.6455			2.63367
$585$	15.0153	−	5.15201i	0.620808	−	0.213009i
$586$	37.9106			1.56607
$587$	−3.08554	+	1.78144i	−0.127354	+	0.0735278i	−0.562324	−	0.826917i	$-0.690092\pi$
$587$	−3.08554	+	1.78144i	−0.127354	+	0.0735278i	0.434970	+	0.900445i	$0.356759\pi$
$588$		0			0
$589$	19.2875	−	33.4069i	0.794727	−	1.37651i
$590$			47.6722i			1.96263i
$591$	2.08783	+	1.20541i	0.0858819	+	0.0495839i
$592$	44.8369	+	25.8866i	1.84278	+	1.06393i
$593$			25.3536i			1.04115i	0.853817	+	0.520573i	$0.174282\pi$
$593$			25.3536i			1.04115i	−0.853817	+	0.520573i	$0.825718\pi$
$594$	−10.4030	+	18.0186i	−0.426842	+	0.739312i
$595$		0			0
$596$	−80.5990	+	46.5338i	−3.30146	+	1.90610i
$597$	−0.212945			−0.00871524
$598$	−17.5330	+	6.01585i	−0.716977	+	0.246007i
$599$	10.9216			0.446243			0.223122	−	0.974791i	$-0.428375\pi$
$599$	10.9216			0.446243			0.223122	+	0.974791i	$0.428375\pi$
$600$	7.53807	−	4.35211i	0.307740	−	0.177674i
$601$	12.1282	+	21.0067i	0.494720	+	0.856880i	0.999981	−	0.00608649i	$-0.00193740\pi$
$601$	12.1282	+	21.0067i	0.494720	+	0.856880i	−0.505262	+	0.862966i	$0.668604\pi$
$602$		0			0
$603$			37.0946i			1.51061i
$604$	−30.6751	−	17.7103i	−1.24815	−	0.720621i
$605$	5.14205	+	2.96876i	0.209054	+	0.120697i
$606$			1.71695i			0.0697464i
$607$	−4.92724	+	8.53422i	−0.199990	+	0.346393i	−0.948525	−	0.316702i	$-0.897424\pi$
$607$	−4.92724	+	8.53422i	−0.199990	+	0.346393i	0.748535	+	0.663096i	$0.230758\pi$
$608$	−15.6987	−	27.1910i	−0.636667	−	1.10274i
$609$		0			0
$610$	12.2062			0.494215
$611$	−2.86833	−	2.49886i	−0.116040	−	0.101093i
$612$	40.1423			1.62266
$613$	3.18428	−	1.83844i	0.128612	−	0.0742540i	−0.434314	−	0.900762i	$-0.643009\pi$
$613$	3.18428	−	1.83844i	0.128612	−	0.0742540i	0.562926	+	0.826508i	$0.309676\pi$
$614$	−11.6208	−	20.1278i	−0.468977	−	0.812293i
$615$	3.21844	−	5.57450i	0.129780	−	0.224785i
$616$		0			0
$617$	16.2352	+	9.37341i	0.653605	+	0.377359i	0.789836	−	0.613318i	$-0.210166\pi$
$617$	16.2352	+	9.37341i	0.653605	+	0.377359i	−0.136231	+	0.990677i	$0.543499\pi$
$618$	−13.3284	−	7.69517i	−0.536148	−	0.309545i
$619$		−	15.8945i		−	0.638854i	−0.947611	−	0.319427i	$-0.896510\pi$
$619$		−	15.8945i		−	0.638854i	0.947611	−	0.319427i	$-0.103490\pi$
$620$	−39.7014	+	68.7649i	−1.59445	+	2.76167i
$621$	2.95068	+	5.11073i	0.118407	+	0.205087i
$622$	27.3086	−	15.7667i	1.09498	−	0.632185i
$623$		0			0
$624$	5.27594	+	15.3765i	0.211207	+	0.615555i
$625$	−7.22743			−0.289097
$626$	−29.4212	+	16.9864i	−1.17591	+	0.678911i
$627$	−2.58152	−	4.47133i	−0.103096	−	0.178568i
$628$	−32.9165	+	57.0130i	−1.31351	+	2.27507i
$629$		−	18.6141i		−	0.742194i
$630$		0			0
$631$	−17.0998	−	9.87255i	−0.680731	−	0.393020i	0.119400	−	0.992846i	$-0.461903\pi$
$631$	−17.0998	−	9.87255i	−0.680731	−	0.393020i	−0.800130	+	0.599826i	$0.795236\pi$
$632$			43.3873i			1.72585i
$633$	−1.94839	+	3.37472i	−0.0774417	+	0.134133i
$634$	−21.6349	−	37.4727i	−0.859231	−	1.48823i
$635$	−4.36151	+	2.51812i	−0.173081	+	0.0999286i
$636$	17.7081			0.702173
$637$		0			0
$638$	−37.6200			−1.48939
$639$	3.19575	−	1.84507i	0.126422	−	0.0729898i
$640$	−3.97508	−	6.88504i	−0.157129	−	0.272155i
$641$	−14.8893	+	25.7890i	−0.588092	+	1.01860i	0.406390	+	0.913699i	$0.366787\pi$
$641$	−14.8893	+	25.7890i	−0.588092	+	1.01860i	−0.994482	+	0.104905i	$0.966546\pi$
$642$			6.89203i			0.272007i
$643$	−10.0220	−	5.78623i	−0.395231	−	0.228187i	0.289193	−	0.957271i	$-0.406613\pi$
$643$	−10.0220	−	5.78623i	−0.395231	−	0.228187i	−0.684424	+	0.729084i	$0.739946\pi$
$644$		0			0
$645$			2.80493i			0.110444i
$646$	−14.8982	+	25.8044i	−0.586162	+	1.01526i
$647$	−12.7533	−	22.0893i	−0.501382	−	0.868420i	−0.999999	−	0.00159698i	$-0.999492\pi$
$647$	−12.7533	−	22.0893i	−0.501382	−	0.868420i	0.498616	−	0.866823i	$-0.333842\pi$
$648$	−40.2823	+	23.2570i	−1.58244	+	0.913620i
$649$	30.9016			1.21299
$650$	−4.30024	+	21.9956i	−0.168669	+	0.862737i
$651$		0			0
$652$	−29.1893	+	16.8524i	−1.14314	+	0.659993i
$653$	22.4146	+	38.8233i	0.877152	+	1.51927i	0.854452	+	0.519530i	$0.173893\pi$
$653$	22.4146	+	38.8233i	0.877152	+	1.51927i	0.0227004	+	0.999742i	$0.492774\pi$
$654$	−1.15946	+	2.00825i	−0.0453386	+	0.0785287i
$655$			16.4578i			0.643058i
$656$	−58.0018	−	33.4874i	−2.26459	−	1.30746i
$657$	21.5320	+	12.4315i	0.840043	+	0.484999i
$658$		0			0
$659$	−20.5867	+	35.6572i	−0.801944	+	1.38901i	0.116390	+	0.993204i	$0.462868\pi$
$659$	−20.5867	+	35.6572i	−0.801944	+	1.38901i	−0.918335	+	0.395805i	$0.870466\pi$
$660$	5.31382	+	9.20380i	0.206840	+	0.358258i
$661$	−18.9606	+	10.9469i	−0.737481	+	0.425785i	−0.821153	−	0.570709i	$-0.806669\pi$
$661$	−18.9606	+	10.9469i	−0.737481	+	0.425785i	0.0836719	+	0.996493i	$0.473335\pi$
$662$	10.2681			0.399080
$663$	3.83927	−	4.40692i	0.149105	−	0.171151i
$664$	18.8539			0.731673
$665$		0			0
$666$	21.0454	+	36.4517i	0.815492	+	1.41247i
$667$	−5.33520	+	9.24084i	−0.206580	+	0.357807i
$668$			84.5239i			3.27033i
$669$	10.1383	+	5.85334i	0.391968	+	0.226303i
$670$	49.0832	+	28.3382i	1.89625	+	1.09480i
$671$		−	7.91219i		−	0.305447i
$672$		0			0
$673$	17.8344	+	30.8901i	0.687466	+	1.19073i	0.972655	+	0.232254i	$0.0746102\pi$
$673$	17.8344	+	30.8901i	0.687466	+	1.19073i	−0.285189	+	0.958471i	$0.592056\pi$
$674$	−30.7197	+	17.7361i	−1.18328	+	0.683167i
$675$	7.13524			0.274635
$676$	−56.6115	−	23.0153i	−2.17736	−	0.885205i
$677$	−2.55532			−0.0982089			−0.0491044	−	0.998794i	$-0.515637\pi$
$677$	−2.55532			−0.0982089			−0.0491044	+	0.998794i	$0.515637\pi$
$678$	9.98541	−	5.76508i	0.383488	−	0.221407i
$679$		0			0
$680$	17.6193	−	30.5175i	0.675670	−	1.17029i
$681$			7.08832i			0.271625i
$682$	63.5384	+	36.6839i	2.43301	+	1.40470i
$683$	30.9517	+	17.8700i	1.18433	+	0.683775i	0.957013	−	0.290045i	$-0.0936704\pi$
$683$	30.9517	+	17.8700i	1.18433	+	0.683775i	0.227320	+	0.973820i	$0.427004\pi$
$684$		−	47.2666i		−	1.80728i
$685$	−8.05431	+	13.9505i	−0.307739	+	0.533020i
$686$		0			0
$687$	−3.56099	+	2.05594i	−0.135860	+	0.0784390i
$688$	29.1848			1.11266
$689$	−17.2080	+	19.7523i	−0.655574	+	0.752503i
$690$	4.29687			0.163579
$691$	22.5419	−	13.0146i	0.857536	−	0.495099i	−0.00565028	−	0.999984i	$-0.501799\pi$
$691$	22.5419	−	13.0146i	0.857536	−	0.495099i	0.863186	+	0.504885i	$0.168465\pi$
$692$	−30.1127	−	52.1567i	−1.14471	−	1.98270i
$693$		0			0
$694$		−	68.3335i		−	2.59391i
$695$	2.32336	+	1.34139i	0.0881299	+	0.0508818i
$696$	16.8659	+	9.73755i	0.639301	+	0.369101i
$697$			24.0796i			0.912079i
$698$	6.32944	−	10.9629i	0.239573	−	0.414952i
$699$	1.70360	+	2.95073i	0.0644362	+	0.111607i
$700$		0			0
$701$	−1.12731			−0.0425779			−0.0212890	−	0.999773i	$-0.506777\pi$
$701$	−1.12731			−0.0425779			−0.0212890	+	0.999773i	$0.506777\pi$
$702$	−5.32126	+	27.2180i	−0.200838	+	1.02728i
$703$	−21.9177			−0.826641
$704$	10.9727	−	6.33509i	0.413549	−	0.238763i
$705$	0.440917	+	0.763691i	0.0166059	+	0.0287623i
$706$	−17.5478	+	30.3936i	−0.660419	+	1.14388i
$707$		0			0
$708$	−24.1128	−	13.9215i	−0.906215	−	0.523203i
$709$	5.23972	+	3.02515i	0.196782	+	0.113612i	0.595153	−	0.803612i	$-0.297091\pi$
$709$	5.23972	+	3.02515i	0.196782	+	0.113612i	−0.398372	+	0.917224i	$0.630425\pi$
$710$		−	5.63813i		−	0.211595i
$711$	−8.47459	+	14.6784i	−0.317822	+	0.550484i
$712$	−6.15202	−	10.6556i	−0.230557	−	0.399336i
$713$	18.0218	−	10.4049i	0.674922	−	0.389666i
$714$		0			0
$715$	−15.4300	−	3.01664i	−0.577050	−	0.112816i
$716$	8.65061			0.323288
$717$	4.21743	−	2.43493i	0.157503	−	0.0909342i
$718$	−11.1124	−	19.2473i	−0.414713	−	0.718304i
$719$	−23.5589	+	40.8052i	−0.878597	+	1.52178i	−0.0257170	+	0.999669i	$0.508187\pi$
$719$	−23.5589	+	40.8052i	−0.878597	+	1.52178i	−0.852880	+	0.522106i	$0.825146\pi$
$720$			38.2884i			1.42692i
$721$		0			0
$722$	−12.2100	−	7.04944i	−0.454409	−	0.262353i
$723$			5.22916i			0.194475i
$724$	7.75473	−	13.4316i	0.288202	−	0.499181i
$725$	6.45070	+	11.1729i	0.239573	+	0.414953i
$726$	−4.28097	+	2.47162i	−0.158882	+	0.0917303i
$727$	−17.9215			−0.664671			−0.332335	−	0.943161i	$-0.607837\pi$
$727$	−17.9215			−0.664671			−0.332335	+	0.943161i	$0.607837\pi$
$728$		0			0
$729$	−13.5489			−0.501810
$730$	32.8985	−	18.9940i	1.21763	−	0.702999i
$731$	−5.24644	−	9.08711i	−0.194047	−	0.336099i
$732$	−3.56454	+	6.17396i	−0.131749	+	0.228196i
$733$		−	45.2685i		−	1.67203i	−0.548705	−	0.836016i	$-0.684879\pi$
$733$		−	45.2685i		−	1.67203i	0.548705	−	0.836016i	$-0.315121\pi$
$734$	−3.72861	−	2.15271i	−0.137625	−	0.0794581i
$735$		0			0
$736$		−	16.9378i		−	0.624335i
$737$	18.3691	−	31.8163i	0.676635	−	1.17197i
$738$	−27.2247	−	47.1546i	−1.00215	−	1.73578i
$739$	−16.6808	+	9.63066i	−0.613613	+	0.354270i	−0.774378	−	0.632723i	$-0.781937\pi$
$739$	−16.6808	+	9.63066i	−0.613613	+	0.354270i	0.160765	+	0.986993i	$0.448604\pi$
$740$	45.1155			1.65848
$741$	−5.18905	−	4.52065i	−0.190624	−	0.166070i
$742$		0			0
$743$	30.2115	−	17.4426i	1.10835	−	0.639908i	0.169951	−	0.985453i	$-0.445639\pi$
$743$	30.2115	−	17.4426i	1.10835	−	0.639908i	0.938402	+	0.345545i	$0.112306\pi$
$744$	−18.9905	−	32.8925i	−0.696225	−	1.20590i
$745$	−15.9577	+	27.6396i	−0.584647	+	1.01264i
$746$			36.1459i			1.32339i
$747$	6.37850	+	3.68263i	0.233377	+	0.134740i
$748$	−34.4303	−	19.8784i	−1.25890	−	0.726825i
$749$		0			0
$750$	8.00648	−	13.8676i	0.292355	−	0.506374i
$751$	−12.4834	−	21.6219i	−0.455526	−	0.788993i	0.543193	−	0.839608i	$-0.317215\pi$
$751$	−12.4834	−	21.6219i	−0.455526	−	0.788993i	−0.998718	+	0.0506146i	$0.983882\pi$
$752$	7.94609	−	4.58767i	0.289764	−	0.167295i
$753$	5.36536			0.195525
$754$	−47.4310	+	16.2743i	−1.72733	+	0.592676i
$755$	−12.1467			−0.442064
$756$		0			0
$757$	5.30243	+	9.18408i	0.192720	+	0.333801i	0.946151	−	0.323726i	$-0.104936\pi$
$757$	5.30243	+	9.18408i	0.192720	+	0.333801i	−0.753431	+	0.657527i	$0.771602\pi$
$758$	−40.8685	+	70.7863i	−1.48441	+	2.57108i
$759$		−	2.78527i		−	0.101099i
$760$	−35.9337	−	20.7463i	−1.30345	−	0.752548i
$761$	28.2660	+	16.3194i	1.02464	+	0.591578i	0.915446	−	0.402442i	$-0.131838\pi$
$761$	28.2660	+	16.3194i	1.02464	+	0.591578i	0.109198	+	0.994020i	$0.465172\pi$
$762$		−	4.19288i		−	0.151892i
$763$		0			0
$764$	11.5080	+	19.9325i	0.416345	+	0.721131i
$765$	11.9216	−	6.88296i	0.431028	−	0.248854i
$766$	−82.5976			−2.98437
$767$	38.9604	−	13.3680i	1.40678	−	0.482689i
$768$	11.4759			0.414100
$769$	45.1851	−	26.0876i	1.62942	−	0.940744i	0.645148	−	0.764057i	$-0.276796\pi$
$769$	45.1851	−	26.0876i	1.62942	−	0.940744i	0.984267	−	0.176686i	$-0.0565378\pi$
$770$		0			0
$771$	2.07039	−	3.58601i	0.0745631	−	0.129147i
$772$			14.1924i			0.510794i
$773$	−30.9221	−	17.8529i	−1.11219	−	0.642123i	−0.172794	−	0.984958i	$-0.555279\pi$
$773$	−30.9221	−	17.8529i	−1.11219	−	0.642123i	−0.939396	+	0.342835i	$0.888613\pi$
$774$	20.5480	+	11.8634i	0.738583	+	0.426421i
$775$		−	25.1607i		−	0.903800i
$776$	54.1208	−	93.7400i	1.94282	−	3.36507i
$777$		0			0
$778$	56.9752	−	32.8947i	2.04266	−	1.17933i
$779$	28.3531			1.01586
$780$	10.6812	+	9.30533i	0.382447	+	0.333184i
$781$	−3.65469			−0.130775
$782$	−13.9206	+	8.03703i	−0.497798	+	0.287404i
$783$	7.98231	+	13.8258i	0.285265	+	0.494093i
$784$		0			0
$785$			22.5760i			0.805770i
$786$	−11.8661	−	6.85089i	−0.423249	−	0.244363i
$787$	5.28813	+	3.05310i	0.188501	+	0.108831i	0.591281	−	0.806466i	$-0.298622\pi$
$787$	5.28813	+	3.05310i	0.188501	+	0.108831i	−0.402779	+	0.915297i	$0.631956\pi$
$788$		−	21.8586i		−	0.778679i
$789$	1.31155	−	2.27167i	0.0466923	−	0.0808735i
$790$	12.9482	+	22.4270i	0.460678	+	0.797918i
$791$		0			0
$792$	51.6510			1.83534
$793$	−3.42280	−	9.97562i	−0.121547	−	0.354245i
$794$	−10.7659			−0.382068
$795$	5.25904	−	3.03631i	0.186519	−	0.107687i
$796$	0.965369	+	1.67207i	0.0342166	+	0.0592649i
$797$	23.1149	−	40.0363i	0.818773	−	1.41816i	−0.0878129	−	0.996137i	$-0.527988\pi$
$797$	23.1149	−	40.0363i	0.818773	−	1.41816i	0.906586	−	0.422020i	$-0.138679\pi$
$798$		0			0
$799$	−2.85688	−	1.64942i	−0.101069	−	0.0583522i
$800$	−17.7355	−	10.2396i	−0.627044	−	0.362024i
$801$		−	4.80656i		−	0.169831i
$802$	25.3700	−	43.9422i	0.895847	−	1.55165i
$803$	−12.3121	−	21.3252i	−0.434484	−	0.752549i
$804$	−28.6672	+	16.5510i	−1.01101	+	0.583710i
$805$		0			0
$806$	95.9780	+	18.7642i	3.38068	+	0.660939i
$807$	7.20161			0.253509
$808$	7.74586	−	4.47208i	0.272498	−	0.157327i
$809$	−19.6439	−	34.0243i	−0.690644	−	1.19623i	−0.971627	−	0.236518i	$-0.923994\pi$
$809$	−19.6439	−	34.0243i	−0.690644	−	1.19623i	0.280983	−	0.959713i	$-0.409339\pi$
$810$	−13.8814	+	24.0432i	−0.487741	+	0.844792i
$811$			6.90664i			0.242525i	0.992620	+	0.121262i	$0.0386943\pi$
$811$			6.90664i			0.242525i	−0.992620	+	0.121262i	$0.961306\pi$
$812$		0			0
$813$	−3.73896	−	2.15869i	−0.131131	−	0.0757085i
$814$		−	41.6864i		−	1.46111i
$815$	−5.77917	+	10.0098i	−0.202436	+	0.350629i
$816$	7.04853	+	12.2084i	0.246748	+	0.427380i
$817$	−10.6998	+	6.17756i	−0.374340	+	0.216125i
$818$	−45.6466			−1.59600
$819$		0			0
$820$	−58.3622			−2.03810
$821$	1.65453	−	0.955244i	0.0577435	−	0.0333382i	−0.470850	−	0.882213i	$-0.656053\pi$
$821$	1.65453	−	0.955244i	0.0577435	−	0.0333382i	0.528594	+	0.848875i	$0.322719\pi$
$822$	−6.70554	−	11.6143i	−0.233883	−	0.405097i
$823$	0.789844	−	1.36805i	0.0275322	−	0.0476872i	−0.851931	−	0.523654i	$-0.824568\pi$
$823$	0.789844	−	1.36805i	0.0275322	−	0.0476872i	0.879463	+	0.475967i	$0.157902\pi$
$824$			80.1732i			2.79296i
$825$	−2.91645	−	1.68381i	−0.101538	−	0.0586228i
$826$		0			0
$827$		−	32.5050i		−	1.13031i	−0.824985	−	0.565155i	$-0.808816\pi$
$827$		−	32.5050i		−	1.13031i	0.824985	−	0.565155i	$-0.191184\pi$
$828$	12.7493	−	22.0824i	0.443069	−	0.767418i
$829$	17.5269	+	30.3575i	0.608735	+	1.05436i	0.991449	+	0.130493i	$0.0416561\pi$
$829$	17.5269	+	30.3575i	0.608735	+	1.05436i	−0.382714	+	0.923867i	$0.625011\pi$
$830$	9.74564	−	5.62665i	0.338276	−	0.195304i
$831$	−12.0344			−0.417469
$832$	11.0937	−	12.7340i	0.384606	−	0.441472i
$833$		0			0
$834$	−1.93429	+	1.11676i	−0.0669790	+	0.0386703i
$835$	14.4928	+	25.1023i	0.501544	+	0.868700i
$836$	−23.4063	+	40.5409i	−0.809523	+	1.40214i
$837$		−	31.1347i		−	1.07617i
$838$	67.0096	+	38.6880i	2.31481	+	1.33645i
$839$	−4.63746	−	2.67744i	−0.160103	−	0.0924354i	0.417808	−	0.908535i	$-0.362798\pi$
$839$	−4.63746	−	2.67744i	−0.160103	−	0.0924354i	−0.577911	+	0.816100i	$0.696132\pi$
$840$		0			0
$841$	0.0669890	−	0.116028i	0.00230997	−	0.00400098i
$842$	−16.6354	−	28.8133i	−0.573293	−	0.992973i
$843$	12.1947	−	7.04064i	0.420009	−	0.242492i
$844$	35.3316			1.21616
$845$	−20.7590	+	2.87164i	−0.714132	+	0.0987873i
$846$	7.45942			0.256460
$847$		0			0
$848$	−31.5923	−	54.7195i	−1.08488	−	1.87907i
$849$	−4.18694	+	7.25199i	−0.143695	+	0.248888i
$850$			19.4349i			0.666611i
$851$	−10.2397	−	5.91190i	−0.351013	−	0.202657i
$852$	2.85179	+	1.64648i	0.0977008	+	0.0564076i
$853$			49.6270i			1.69920i	0.527431	+	0.849598i	$0.323155\pi$
$853$			49.6270i			1.69920i	−0.527431	+	0.849598i	$0.676845\pi$
$854$		0			0
$855$	−8.10452	−	14.0374i	−0.277169	−	0.480070i
$856$	31.0927	−	17.9514i	1.06273	−	0.613566i
$857$	5.88392			0.200991			0.100496	−	0.994938i	$-0.467957\pi$
$857$	5.88392			0.200991			0.100496	+	0.994938i	$0.467957\pi$
$858$	8.59807	−	9.86933i	0.293533	−	0.336933i
$859$	−43.3862			−1.48032			−0.740159	−	0.672432i	$-0.765250\pi$
$859$	−43.3862			−1.48032			−0.740159	+	0.672432i	$0.765250\pi$
$860$	22.0246	−	12.7159i	0.751033	−	0.433609i
$861$		0			0
$862$	−11.6106	+	20.1102i	−0.395460	+	0.684957i
$863$		−	31.1272i		−	1.05958i	−0.848128	−	0.529792i	$-0.822270\pi$
$863$		−	31.1272i		−	1.05958i	0.848128	−	0.529792i	$-0.177730\pi$
$864$	−21.9465	−	12.6708i	−0.746634	−	0.431069i
$865$	−17.8860	−	10.3265i	−0.608142	−	0.351111i
$866$		−	8.93228i		−	0.303531i
$867$	−1.87278	+	3.24376i	−0.0636031	+	0.110164i
$868$		0			0
$869$	14.5374	−	8.39318i	0.493148	−	0.284719i
$870$	11.6241			0.394093
$871$	9.39598	−	48.0601i	0.318371	−	1.62845i
$872$	12.0800			0.409081
$873$	36.6194	−	21.1422i	1.23938	−	0.715556i
$874$	9.46341	+	16.3911i	0.320105	+	0.554438i
$875$		0			0
$876$			22.1870i			0.749629i
$877$	−25.9033	−	14.9553i	−0.874693	−	0.505004i	−0.00578807	−	0.999983i	$-0.501842\pi$
$877$	−25.9033	−	14.9553i	−0.874693	−	0.505004i	−0.868905	+	0.494979i	$0.835176\pi$
$878$	86.3413	+	49.8492i	2.91388	+	1.68233i
$879$			7.59304i			0.256107i
$880$	18.9603	−	32.8402i	0.639152	−	1.10704i
$881$	−7.28477	−	12.6176i	−0.245430	−	0.425097i	0.716822	−	0.697256i	$-0.245596\pi$
$881$	−7.28477	−	12.6176i	−0.245430	−	0.425097i	−0.962252	+	0.272159i	$0.912262\pi$
$882$		0			0
$883$	48.9296			1.64661			0.823307	−	0.567597i	$-0.192127\pi$
$883$	48.9296			1.64661			0.823307	+	0.567597i	$0.192127\pi$
$884$	−52.0088	−	10.1680i	−1.74924	−	0.341986i
$885$	−9.54817			−0.320958
$886$	−33.7164	+	19.4662i	−1.13273	+	0.653980i
$887$	27.2951	+	47.2765i	0.916480	+	1.58739i	0.804719	+	0.593655i	$0.202316\pi$
$887$	27.2951	+	47.2765i	0.916480	+	1.58739i	0.111761	+	0.993735i	$0.464351\pi$
$888$	−10.7901	+	18.6890i	−0.362092	+	0.627162i
$889$		0			0
$890$	−6.36000	−	3.67195i	−0.213188	−	0.123084i
$891$	15.5851	+	8.99803i	0.522119	+	0.301445i
$892$		−	106.143i		−	3.55392i
$893$	−1.94215	+	3.36390i	−0.0649916	+	0.112569i
$894$	−13.2855	−	23.0111i	−0.444333	−	0.769607i
$895$	2.56909	−	1.48327i	0.0858753	−	0.0495801i
$896$		0			0
$897$	−1.20490	−	3.51165i	−0.0402306	−	0.117251i
$898$	100.757			3.36232
$899$	48.7533	−	28.1477i	1.62601	−	0.938780i
$900$	−15.4150	−	26.6995i	−0.513832	−	0.889983i
$901$	−11.3585	+	19.6734i	−0.378405	+	0.655417i
$902$			53.9263i			1.79555i
$903$		0			0
$904$	−52.0172	−	30.0321i	−1.73007	−	0.998854i
$905$		−	5.31862i		−	0.176797i
$906$	5.05632	−	8.75780i	0.167985	−	0.290958i
$907$	11.3628	+	19.6809i	0.377295	+	0.653494i	0.990668	−	0.136300i	$-0.0435211\pi$
$907$	11.3628	+	19.6809i	0.377295	+	0.653494i	−0.613373	+	0.789793i	$0.710188\pi$
$908$	55.6584	−	32.1344i	1.84709	−	1.06642i
$909$	3.49402			0.115889
$910$		0			0
$911$	−42.2359			−1.39934			−0.699669	−	0.714467i	$-0.746669\pi$
$911$	−42.2359			−1.39934			−0.699669	+	0.714467i	$0.746669\pi$
$912$	14.3751	−	8.29948i	0.476008	−	0.274823i
$913$	−3.64725	−	6.31722i	−0.120706	−	0.209070i
$914$	18.0421	−	31.2498i	0.596779	−	1.03365i
$915$			2.44476i			0.0808213i
$916$	32.2870	+	18.6409i	1.06679	+	0.615912i
$917$		0			0
$918$			24.0494i			0.793747i
$919$	−15.3470	+	26.5818i	−0.506251	+	0.876853i	0.493722	+	0.869620i	$0.335636\pi$
$919$	−15.3470	+	26.5818i	−0.506251	+	0.876853i	−0.999974	+	0.00723365i	$0.997697\pi$
$920$	−11.1919	−	19.3849i	−0.368985	−	0.639101i
$921$	4.03136	−	2.32751i	0.132838	−	0.0766940i
$922$	−96.9780			−3.19380
$923$	−4.60780	+	1.58101i	−0.151668	+	0.0520396i
$924$		0			0
$925$	−12.3806	+	7.14797i	−0.407073	+	0.235024i
$926$	8.74009	+	15.1383i	0.287217	+	0.497474i
$927$	−15.6598	+	27.1235i	−0.514334	+	0.890853i
$928$		−	45.8208i		−	1.50414i
$929$	−32.4110	−	18.7125i	−1.06337	−	0.613936i	−0.137007	−	0.990570i	$-0.543748\pi$
$929$	−32.4110	−	18.7125i	−1.06337	−	0.613936i	−0.926362	+	0.376634i	$0.877082\pi$
$930$	−19.6325	−	11.3348i	−0.643775	−	0.371684i
$931$		0			0
$932$	15.4463	−	26.7538i	0.505961	−	0.876350i
$933$	3.15787	+	5.46960i	0.103384	+	0.179067i
$934$	11.3218	−	6.53663i	0.370460	−	0.213885i
$935$	−13.6337			−0.445869
$936$	65.1211	−	22.3441i	2.12855	−	0.730340i
$937$	−44.3386			−1.44848			−0.724239	−	0.689549i	$-0.757809\pi$
$937$	−44.3386			−1.44848			−0.724239	+	0.689549i	$0.757809\pi$
$938$		0			0
$939$	−3.40216	−	5.89272i	−0.111025	−	0.192302i
$940$	3.99773	−	6.92427i	0.130392	−	0.225845i
$941$			27.5052i			0.896646i	0.893872	+	0.448323i	$0.147978\pi$
$941$			27.5052i			0.896646i	−0.893872	+	0.448323i	$0.852022\pi$
$942$	−16.2773	−	9.39771i	−0.530343	−	0.306194i
$943$	13.2463	+	7.64774i	0.431358	+	0.249045i
$944$			99.3472i			3.23348i
$945$		0			0
$946$	−11.7494	−	20.3506i	−0.382007	−	0.661656i
$947$	−4.40226	+	2.54165i	−0.143054	+	0.0825925i	−0.569819	−	0.821770i	$-0.692987\pi$
$947$	−4.40226	+	2.54165i	−0.143054	+	0.0825925i	0.426765	+	0.904363i	$0.359653\pi$
$948$	−15.1249			−0.491235
$949$	−24.7482	−	21.5604i	−0.803360	−	0.699880i
$950$	22.8841			0.742458
$951$	7.50534	−	4.33321i	0.243377	−	0.140514i
$952$		0			0
$953$	4.90718	−	8.49949i	0.158959	−	0.275326i	−0.775534	−	0.631305i	$-0.782519\pi$
$953$	4.90718	−	8.49949i	0.158959	−	0.275326i	0.934494	+	0.355980i	$0.115853\pi$
$954$		−	51.3681i		−	1.66310i
$955$	6.83540	+	3.94642i	0.221188	+	0.127703i
$956$	−38.2388	−	22.0772i	−1.23673	−	0.714027i
$957$		−	7.53484i		−	0.243567i
$958$	12.2353	−	21.1921i	0.395303	−	0.684685i
$959$		0			0
$960$	−3.39041	+	1.95746i	−0.109425	+	0.0631766i
$961$	−78.7893			−2.54159
$962$	−18.0335	−	52.5579i	−0.581422	−	1.69453i
$963$	14.0254			0.451961
$964$	41.0601	−	23.7060i	1.32246	−	0.763520i
$965$	2.43348	+	4.21490i	0.0783364	+	0.135683i
$966$		0			0
$967$		−	2.69619i		−	0.0867036i	−0.999060	−	0.0433518i	$-0.986196\pi$
$967$		−	2.69619i		−	0.0867036i	0.999060	−	0.0433518i	$-0.0138036\pi$
$968$	22.3009	+	12.8754i	0.716779	+	0.413832i
$969$	−5.16832	−	2.98393i	−0.166030	−	0.0958577i
$970$		−	64.6060i		−	2.07437i
$971$	12.4620	−	21.5848i	0.399925	−	0.692691i	−0.593791	−	0.804619i	$-0.702369\pi$
$971$	12.4620	−	21.5848i	0.399925	−	0.692691i	0.993716	+	0.111929i	$0.0357028\pi$
$972$	−29.0598	−	50.3331i	−0.932094	−	1.61443i
$973$		0			0
$974$	−103.543			−3.31773
$975$	−4.40545	−	0.861286i	−0.141087	−	0.0275832i
$976$	25.4373			0.814230
$977$	−24.5197	+	14.1565i	−0.784456	+	0.452906i	−0.838007	−	0.545659i	$-0.816279\pi$
$977$	−24.5197	+	14.1565i	−0.784456	+	0.452906i	0.0535514	+	0.998565i	$0.482946\pi$
$978$	−4.81140	−	8.33359i	−0.153852	−	0.266479i
$979$	−2.38019	+	4.12262i	−0.0760713	+	0.131759i
$980$		0			0
$981$	4.08681	+	2.35952i	0.130482	+	0.0753337i
$982$	−15.1567	−	8.75073i	−0.483670	−	0.279247i
$983$			37.8517i			1.20728i	0.797256	+	0.603641i	$0.206284\pi$
$983$			37.8517i			1.20728i	−0.797256	+	0.603641i	$0.793716\pi$
$984$	13.9583	−	24.1764i	0.444974	−	0.770717i
$985$	−3.74795	−	6.49165i	−0.119420	−	0.206841i
$986$	−37.6585	+	21.7421i	−1.19929	+	0.692410i
$987$		0			0
$988$	−11.9725	+	61.2391i	−0.380897	+	1.94827i
$989$	−6.66514			−0.211939
$990$	26.6986	−	15.4144i	0.848536	−	0.489903i
$991$	−29.2079	−	50.5896i	−0.927820	−	1.60703i	−0.786962	−	0.617001i	$-0.788347\pi$
$991$	−29.2079	−	50.5896i	−0.927820	−	1.60703i	−0.140858	−	0.990030i	$-0.544986\pi$
$992$	−44.6806	+	77.3891i	−1.41861	+	2.45711i
$993$			2.05657i			0.0652633i
$994$		0			0
$995$	0.573399	+	0.331052i	0.0181780	+	0.0104950i
$996$			6.57252i			0.208258i
$997$	14.0294	−	24.2997i	0.444316	−	0.769578i	−0.553688	−	0.832724i	$-0.686780\pi$
$997$	14.0294	−	24.2997i	0.444316	−	0.769578i	0.998004	+	0.0631462i	$0.0201134\pi$
$998$	14.7001	+	25.4613i	0.465322	+	0.805962i
$999$	−15.3202	+	8.84514i	−0.484711	+	0.279848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.i.491.6		12
7.2	even	3		637.2.u.g.361.1		12
7.3	odd	6		91.2.k.b.23.6	yes	12
7.4	even	3		637.2.k.i.569.6		12
7.5	odd	6		91.2.u.b.88.1	yes	12
7.6	odd	2		637.2.q.g.491.6		12
13.2	odd	12		8281.2.a.co.1.12		12
13.4	even	6	inner	637.2.q.i.589.6		12
13.11	odd	12		8281.2.a.co.1.1		12
21.5	even	6		819.2.do.e.361.6		12
21.17	even	6		819.2.bm.f.478.1		12
91.4	even	6		637.2.u.g.30.1		12
91.17	odd	6		91.2.u.b.30.1	yes	12
91.24	even	12		1183.2.e.j.170.12		24
91.30	even	6		637.2.k.i.459.1		12
91.41	even	12		8281.2.a.cp.1.12		12
91.54	even	12		1183.2.e.j.508.1		24
91.69	odd	6		637.2.q.g.589.6		12
91.76	even	12		8281.2.a.cp.1.1		12
91.80	even	12		1183.2.e.j.170.1		24
91.82	odd	6		91.2.k.b.4.1	✓	12
91.89	even	12		1183.2.e.j.508.12		24
273.17	even	6		819.2.do.e.667.6		12
273.173	even	6		819.2.bm.f.550.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.1	✓	12	91.82	odd	6
91.2.k.b.23.6	yes	12	7.3	odd	6
91.2.u.b.30.1	yes	12	91.17	odd	6
91.2.u.b.88.1	yes	12	7.5	odd	6
637.2.k.i.459.1		12	91.30	even	6
637.2.k.i.569.6		12	7.4	even	3
637.2.q.g.491.6		12	7.6	odd	2
637.2.q.g.589.6		12	91.69	odd	6
637.2.q.i.491.6		12	1.1	even	1	trivial
637.2.q.i.589.6		12	13.4	even	6	inner
637.2.u.g.30.1		12	91.4	even	6
637.2.u.g.361.1		12	7.2	even	3
819.2.bm.f.478.1		12	21.17	even	6
819.2.bm.f.550.6		12	273.173	even	6
819.2.do.e.361.6		12	21.5	even	6
819.2.do.e.667.6		12	273.17	even	6
1183.2.e.j.170.1		24	91.80	even	12
1183.2.e.j.170.12		24	91.24	even	12
1183.2.e.j.508.1		24	91.54	even	12
1183.2.e.j.508.12		24	91.89	even	12
8281.2.a.co.1.1		12	13.11	odd	12
8281.2.a.co.1.12		12	13.2	odd	12
8281.2.a.cp.1.1		12	91.76	even	12
8281.2.a.cp.1.12		12	91.41	even	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.24179 - 1.29430i) q^{2} +(0.259233 + 0.449005i) q^{3} +(2.35043 - 4.07106i) q^{4} -1.61205i q^{5} +(1.16229 + 0.671051i) q^{6} -6.99143i q^{8} +(1.36560 - 2.36528i) q^{9} +O(q^{10})\)	\(q+(2.24179 - 1.29430i) q^{2} +(0.259233 + 0.449005i) q^{3} +(2.35043 - 4.07106i) q^{4} -1.61205i q^{5} +(1.16229 + 0.671051i) q^{6} -6.99143i q^{8} +(1.36560 - 2.36528i) q^{9} +(-2.08648 - 3.61389i) q^{10} +(-2.34256 + 1.35248i) q^{11} +2.43723 q^{12} +(-2.36840 + 2.71858i) q^{13} +(0.723819 - 0.417897i) q^{15} +(-4.34816 - 7.53123i) q^{16} +(-1.56330 + 2.70772i) q^{17} -7.06997i q^{18} +(3.18828 + 1.84075i) q^{19} +(-6.56276 - 3.78901i) q^{20} +(-3.50103 + 6.06396i) q^{22} +(0.993019 + 1.71996i) q^{23} +(3.13918 - 1.81241i) q^{24} +2.40128 q^{25} +(-1.79081 + 9.15992i) q^{26} +2.97143 q^{27} +(2.68636 + 4.65290i) q^{29} +(1.08177 - 1.87368i) q^{30} -10.4780i q^{31} +(-7.38583 - 4.26421i) q^{32} +(-1.21454 - 0.701214i) q^{33} +8.09354i q^{34} +(-6.41947 - 11.1188i) q^{36} +(-5.15585 + 2.97673i) q^{37} +9.52994 q^{38} +(-1.83462 - 0.358678i) q^{39} -11.2706 q^{40} +(6.66970 - 3.85075i) q^{41} +(-1.67800 + 2.90638i) q^{43} +12.7156i q^{44} +(-3.81296 - 2.20141i) q^{45} +(4.45229 + 2.57053i) q^{46} +1.05508i q^{47} +(2.25437 - 3.90469i) q^{48} +(5.38318 - 3.10798i) q^{50} -1.62104 q^{51} +(5.50074 + 16.0317i) q^{52} +7.26568 q^{53} +(6.66133 - 3.84592i) q^{54} +(2.18027 + 3.77633i) q^{55} +1.90873i q^{57} +(12.0445 + 6.95390i) q^{58} +(-9.89352 - 5.71203i) q^{59} -3.92895i q^{60} +(-1.46254 + 2.53319i) q^{61} +(-13.5617 - 23.4896i) q^{62} -4.68406 q^{64} +(4.38250 + 3.81799i) q^{65} -3.63033 q^{66} +(-11.7622 + 6.79091i) q^{67} +(7.34886 + 12.7286i) q^{68} +(-0.514846 + 0.891740i) q^{69} +(1.17009 + 0.675554i) q^{71} +(-16.5367 - 9.54747i) q^{72} +9.10335i q^{73} +(-7.70557 + 13.3464i) q^{74} +(0.622492 + 1.07819i) q^{75} +(14.9876 - 8.65311i) q^{76} +(-4.57708 + 1.57047i) q^{78} -6.20578 q^{79} +(-12.1407 + 7.00946i) q^{80} +(-3.32650 - 5.76166i) q^{81} +(9.96806 - 17.2652i) q^{82} +2.69672i q^{83} +(4.36499 + 2.52013i) q^{85} +8.68734i q^{86} +(-1.39278 + 2.41237i) q^{87} +(9.45576 + 16.3779i) q^{88} +(1.52410 - 0.879938i) q^{89} -11.3972 q^{90} +9.33607 q^{92} +(4.70469 - 2.71625i) q^{93} +(1.36560 + 2.36528i) q^{94} +(2.96739 - 5.13967i) q^{95} -4.42170i q^{96} +(13.4078 + 7.74102i) q^{97} +7.38776i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} + 4 q^{4} + 9 q^{6} - q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 + 4 * q^4 + 9 * q^6 - q^9	\( 12 q + 3 q^{3} + 4 q^{4} + 9 q^{6} - q^{9} - 12 q^{10} - 12 q^{11} - 2 q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 3 q^{23} + 15 q^{24} + 10 q^{25} - 15 q^{26} - 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{32} - 6 q^{33} - 13 q^{36} - 15 q^{37} + 38 q^{38} + 5 q^{39} - 2 q^{40} + 6 q^{41} + 11 q^{43} - 9 q^{45} + 30 q^{46} - 19 q^{48} + 18 q^{50} - 8 q^{51} + 40 q^{52} + 16 q^{53} + 6 q^{54} + 15 q^{55} + 24 q^{58} + 27 q^{59} - 5 q^{61} - 41 q^{62} + 2 q^{64} - 18 q^{65} - 68 q^{66} - 15 q^{67} + 11 q^{68} - 7 q^{69} + 30 q^{71} - 57 q^{72} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} + 70 q^{79} - 63 q^{80} + 14 q^{81} - 5 q^{82} - 21 q^{85} - 10 q^{87} - 14 q^{88} + 48 q^{89} - 66 q^{92} + 81 q^{93} - q^{94} + 2 q^{95} + 3 q^{97}+O(q^{100}) \) 12 * q + 3 * q^3 + 4 * q^4 + 9 * q^6 - q^9 - 12 * q^10 - 12 * q^11 - 2 * q^12 + 2 * q^13 - 12 * q^15 - 8 * q^16 - 17 * q^17 + 9 * q^19 + 3 * q^20 - 15 * q^22 + 3 * q^23 + 15 * q^24 + 10 * q^25 - 15 * q^26 - 12 * q^27 - q^29 + 11 * q^30 - 18 * q^32 - 6 * q^33 - 13 * q^36 - 15 * q^37 + 38 * q^38 + 5 * q^39 - 2 * q^40 + 6 * q^41 + 11 * q^43 - 9 * q^45 + 30 * q^46 - 19 * q^48 + 18 * q^50 - 8 * q^51 + 40 * q^52 + 16 * q^53 + 6 * q^54 + 15 * q^55 + 24 * q^58 + 27 * q^59 - 5 * q^61 - 41 * q^62 + 2 * q^64 - 18 * q^65 - 68 * q^66 - 15 * q^67 + 11 * q^68 - 7 * q^69 + 30 * q^71 - 57 * q^72 - 33 * q^74 - q^75 + 45 * q^76 + 44 * q^78 + 70 * q^79 - 63 * q^80 + 14 * q^81 - 5 * q^82 - 21 * q^85 - 10 * q^87 - 14 * q^88 + 48 * q^89 - 66 * q^92 + 81 * q^93 - q^94 + 2 * q^95 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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