LMFDB - Embedded newform 234.2.f.c.133.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(133,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("234.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.f (of order $3$, 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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 4 x^{10} - 6 x^{9} + 22 x^{8} - 45 x^{7} + 75 x^{6} - 135 x^{5} + 198 x^{4} + \cdots + 729 $ x^12 - 3x^11 + 4x^10 - 6x^9 + 22x^8 - 45x^7 + 75x^6 - 135x^5 + 198x^4 - 162x^3 + 324x^2 - 729*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.4
Root			$-1.29053 - 1.15522i$ of defining polynomial
Character	$\chi$	$=$	234.133
Dual form			234.2.f.c.139.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.355184 + 1.69524i) q^{3} +1.00000 q^{4} +(-2.14571 - 3.71649i) q^{5} +(-0.355184 - 1.69524i) q^{6} +(-0.751135 - 1.30100i) q^{7} -1.00000 q^{8} +(-2.74769 + 1.20424i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.355184 + 1.69524i) q^{3} +1.00000 q^{4} +(-2.14571 - 3.71649i) q^{5} +(-0.355184 - 1.69524i) q^{6} +(-0.751135 - 1.30100i) q^{7} -1.00000 q^{8} +(-2.74769 + 1.20424i) q^{9} +(2.14571 + 3.71649i) q^{10} -4.24294 q^{11} +(0.355184 + 1.69524i) q^{12} +(-3.60531 - 0.0419947i) q^{13} +(0.751135 + 1.30100i) q^{14} +(5.53822 - 4.95754i) q^{15} +1.00000 q^{16} +(0.0242456 - 0.0419947i) q^{17} +(2.74769 - 1.20424i) q^{18} +(2.87736 - 4.98373i) q^{19} +(-2.14571 - 3.71649i) q^{20} +(1.93873 - 1.73545i) q^{21} +4.24294 q^{22} +(3.41675 - 5.91799i) q^{23} +(-0.355184 - 1.69524i) q^{24} +(-6.70818 + 11.6189i) q^{25} +(3.60531 + 0.0419947i) q^{26} +(-3.01742 - 4.23027i) q^{27} +(-0.751135 - 1.30100i) q^{28} +2.21264 q^{29} +(-5.53822 + 4.95754i) q^{30} +(3.74769 + 6.49119i) q^{31} -1.00000 q^{32} +(-1.50702 - 7.19280i) q^{33} +(-0.0242456 + 0.0419947i) q^{34} +(-3.22344 + 5.58317i) q^{35} +(-2.74769 + 1.20424i) q^{36} +(-1.35174 - 2.34128i) q^{37} +(-2.87736 + 4.98373i) q^{38} +(-1.20936 - 6.12678i) q^{39} +(2.14571 + 3.71649i) q^{40} +(-3.68986 + 6.39103i) q^{41} +(-1.93873 + 1.73545i) q^{42} +(-2.89251 - 5.00997i) q^{43} -4.24294 q^{44} +(10.3713 + 7.62778i) q^{45} +(-3.41675 + 5.91799i) q^{46} +(-1.67341 + 2.89842i) q^{47} +(0.355184 + 1.69524i) q^{48} +(2.37159 - 4.10772i) q^{49} +(6.70818 - 11.6189i) q^{50} +(0.0798028 + 0.0261864i) q^{51} +(-3.60531 - 0.0419947i) q^{52} +1.82220 q^{53} +(3.01742 + 4.23027i) q^{54} +(9.10413 + 15.7688i) q^{55} +(0.751135 + 1.30100i) q^{56} +(9.47061 + 3.10767i) q^{57} -2.21264 q^{58} -1.88614 q^{59} +(5.53822 - 4.95754i) q^{60} +(-0.877519 - 1.51991i) q^{61} +(-3.74769 - 6.49119i) q^{62} +(3.63061 + 2.67021i) q^{63} +1.00000 q^{64} +(7.57989 + 13.4892i) q^{65} +(1.50702 + 7.19280i) q^{66} +(1.73270 - 3.00113i) q^{67} +(0.0242456 - 0.0419947i) q^{68} +(11.2460 + 3.69025i) q^{69} +(3.22344 - 5.58317i) q^{70} +(0.645714 - 1.11841i) q^{71} +(2.74769 - 1.20424i) q^{72} -12.9836 q^{73} +(1.35174 + 2.34128i) q^{74} +(-22.0795 - 7.24514i) q^{75} +(2.87736 - 4.98373i) q^{76} +(3.18702 + 5.52008i) q^{77} +(1.20936 + 6.12678i) q^{78} +(4.24521 - 7.35292i) q^{79} +(-2.14571 - 3.71649i) q^{80} +(6.09959 - 6.61778i) q^{81} +(3.68986 - 6.39103i) q^{82} +(-0.370694 + 0.642060i) q^{83} +(1.93873 - 1.73545i) q^{84} -0.208097 q^{85} +(2.89251 + 5.00997i) q^{86} +(0.785893 + 3.75096i) q^{87} +4.24294 q^{88} +(0.288865 + 0.500328i) q^{89} +(-10.3713 - 7.62778i) q^{90} +(2.65344 + 4.72206i) q^{91} +(3.41675 - 5.91799i) q^{92} +(-9.67301 + 8.65880i) q^{93} +(1.67341 - 2.89842i) q^{94} -24.6959 q^{95} +(-0.355184 - 1.69524i) q^{96} +(-2.59585 - 4.49614i) q^{97} +(-2.37159 + 4.10772i) q^{98} +(11.6583 - 5.10953i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 12 q^{4} - 3 q^{5} + q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 12 * q^4 - 3 * q^5 + q^7 - 12 * q^8 + 4 * q^9	\( 12 q - 12 q^{2} + 12 q^{4} - 3 q^{5} + q^{7} - 12 q^{8} + 4 q^{9} + 3 q^{10} - 8 q^{11} - 5 q^{13} - q^{14} + 11 q^{15} + 12 q^{16} - q^{17} - 4 q^{18} + 9 q^{19} - 3 q^{20} + 8 q^{21} + 8 q^{22} + 7 q^{23} - q^{25} + 5 q^{26} - 9 q^{27} + q^{28} - 2 q^{29} - 11 q^{30} + 8 q^{31} - 12 q^{32} - 4 q^{33} + q^{34} - 3 q^{35} + 4 q^{36} + 15 q^{37} - 9 q^{38} + 18 q^{39} + 3 q^{40} - 19 q^{41} - 8 q^{42} - 2 q^{43} - 8 q^{44} - 5 q^{45} - 7 q^{46} - 23 q^{47} - 27 q^{49} + q^{50} + 8 q^{51} - 5 q^{52} - 4 q^{53} + 9 q^{54} + 24 q^{55} - q^{56} - 16 q^{57} + 2 q^{58} + 8 q^{59} + 11 q^{60} - 8 q^{61} - 8 q^{62} + 12 q^{64} + 7 q^{65} + 4 q^{66} + 14 q^{67} - q^{68} - 6 q^{69} + 3 q^{70} - 15 q^{71} - 4 q^{72} - 90 q^{73} - 15 q^{74} - 56 q^{75} + 9 q^{76} + 4 q^{77} - 18 q^{78} - 12 q^{79} - 3 q^{80} + 28 q^{81} + 19 q^{82} + 24 q^{83} + 8 q^{84} - 14 q^{85} + 2 q^{86} + 36 q^{87} + 8 q^{88} + 23 q^{89} + 5 q^{90} + 8 q^{91} + 7 q^{92} + 6 q^{93} + 23 q^{94} + 14 q^{95} - 4 q^{97} + 27 q^{98} + 31 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^4 - 3 * q^5 + q^7 - 12 * q^8 + 4 * q^9 + 3 * q^10 - 8 * q^11 - 5 * q^13 - q^14 + 11 * q^15 + 12 * q^16 - q^17 - 4 * q^18 + 9 * q^19 - 3 * q^20 + 8 * q^21 + 8 * q^22 + 7 * q^23 - q^25 + 5 * q^26 - 9 * q^27 + q^28 - 2 * q^29 - 11 * q^30 + 8 * q^31 - 12 * q^32 - 4 * q^33 + q^34 - 3 * q^35 + 4 * q^36 + 15 * q^37 - 9 * q^38 + 18 * q^39 + 3 * q^40 - 19 * q^41 - 8 * q^42 - 2 * q^43 - 8 * q^44 - 5 * q^45 - 7 * q^46 - 23 * q^47 - 27 * q^49 + q^50 + 8 * q^51 - 5 * q^52 - 4 * q^53 + 9 * q^54 + 24 * q^55 - q^56 - 16 * q^57 + 2 * q^58 + 8 * q^59 + 11 * q^60 - 8 * q^61 - 8 * q^62 + 12 * q^64 + 7 * q^65 + 4 * q^66 + 14 * q^67 - q^68 - 6 * q^69 + 3 * q^70 - 15 * q^71 - 4 * q^72 - 90 * q^73 - 15 * q^74 - 56 * q^75 + 9 * q^76 + 4 * q^77 - 18 * q^78 - 12 * q^79 - 3 * q^80 + 28 * q^81 + 19 * q^82 + 24 * q^83 + 8 * q^84 - 14 * q^85 + 2 * q^86 + 36 * q^87 + 8 * q^88 + 23 * q^89 + 5 * q^90 + 8 * q^91 + 7 * q^92 + 6 * q^93 + 23 * q^94 + 14 * q^95 - 4 * q^97 + 27 * q^98 + 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.355184	+	1.69524i	0.205065	+	0.978748i
$3$	0.355184	+	1.69524i	0.205065	+	0.978748i
$4$	1.00000			0.500000
$5$	−2.14571	−	3.71649i	−0.959593	−	1.66206i	−0.723490	−	0.690335i	$-0.757463\pi$
$5$	−2.14571	−	3.71649i	−0.959593	−	1.66206i	−0.236103	−	0.971728i	$-0.575870\pi$
$6$	−0.355184	−	1.69524i	−0.145003	−	0.692080i
$7$	−0.751135	−	1.30100i	−0.283902	−	0.491733i	0.688440	−	0.725293i	$-0.258296\pi$
$7$	−0.751135	−	1.30100i	−0.283902	−	0.491733i	−0.972342	+	0.233560i	$0.924963\pi$
$8$	−1.00000			−0.353553
$9$	−2.74769	+	1.20424i	−0.915896	+	0.401415i
$10$	2.14571	+	3.71649i	0.678534	+	1.17526i
$11$	−4.24294			−1.27929			−0.639647	−	0.768669i	$-0.720919\pi$
$11$	−4.24294			−1.27929			−0.639647	+	0.768669i	$0.720919\pi$
$12$	0.355184	+	1.69524i	0.102533	+	0.489374i
$13$	−3.60531	−	0.0419947i	−0.999932	−	0.0116472i
$13$	−3.60531	−	0.0419947i	−0.999932	−	0.0116472i
$14$	0.751135	+	1.30100i	0.200749	+	0.347708i
$15$	5.53822	−	4.95754i	1.42996	−	1.28003i
$16$	1.00000			0.250000
$17$	0.0242456	−	0.0419947i	0.00588043	−	0.0101852i	−0.863070	−	0.505084i	$-0.831462\pi$
$17$	0.0242456	−	0.0419947i	0.00588043	−	0.0101852i	0.868951	+	0.494899i	$0.164795\pi$
$18$	2.74769	−	1.20424i	0.647637	−	0.283843i
$19$	2.87736	−	4.98373i	0.660111	−	1.14335i	−0.320476	−	0.947257i	$-0.603843\pi$
$19$	2.87736	−	4.98373i	0.660111	−	1.14335i	0.980586	−	0.196088i	$-0.0628240\pi$
$20$	−2.14571	−	3.71649i	−0.479796	−	0.831032i
$21$	1.93873	−	1.73545i	0.423065	−	0.378707i
$22$	4.24294			0.904597
$23$	3.41675	−	5.91799i	0.712442	−	1.23399i	−0.251496	−	0.967858i	$-0.580923\pi$
$23$	3.41675	−	5.91799i	0.712442	−	1.23399i	0.963938	−	0.266127i	$-0.0857441\pi$
$24$	−0.355184	−	1.69524i	−0.0725016	−	0.346040i
$25$	−6.70818	+	11.6189i	−1.34164	+	2.32378i
$26$	3.60531	+	0.0419947i	0.707059	+	0.00823584i
$27$	−3.01742	−	4.23027i	−0.580703	−	0.814116i
$28$	−0.751135	−	1.30100i	−0.141951	−	0.245867i
$29$	2.21264			0.410877			0.205438	−	0.978670i	$-0.434138\pi$
$29$	2.21264			0.410877			0.205438	+	0.978670i	$0.434138\pi$
$30$	−5.53822	+	4.95754i	−1.01114	+	0.905119i
$31$	3.74769	+	6.49119i	0.673105	+	1.16585i	0.977019	+	0.213152i	$0.0683731\pi$
$31$	3.74769	+	6.49119i	0.673105	+	1.16585i	−0.303914	+	0.952699i	$0.598294\pi$
$32$	−1.00000			−0.176777
$33$	−1.50702	−	7.19280i	−0.262339	−	1.25211i
$34$	−0.0242456	+	0.0419947i	−0.00415809	+	0.00720203i
$35$	−3.22344	+	5.58317i	−0.544861	+	0.943728i
$36$	−2.74769	+	1.20424i	−0.457948	+	0.200707i
$37$	−1.35174	−	2.34128i	−0.222224	−	0.384904i	0.733259	−	0.679950i	$-0.237998\pi$
$37$	−1.35174	−	2.34128i	−0.222224	−	0.384904i	−0.955483	+	0.295046i	$0.904665\pi$
$38$	−2.87736	+	4.98373i	−0.466769	+	0.808467i
$39$	−1.20936	−	6.12678i	−0.193652	−	0.981070i
$40$	2.14571	+	3.71649i	0.339267	+	0.587628i
$41$	−3.68986	+	6.39103i	−0.576260	+	0.998111i	0.419644	+	0.907689i	$0.362155\pi$
$41$	−3.68986	+	6.39103i	−0.576260	+	0.998111i	−0.995904	+	0.0904220i	$0.971178\pi$
$42$	−1.93873	+	1.73545i	−0.299152	+	0.267786i
$43$	−2.89251	−	5.00997i	−0.441103	−	0.764013i	0.556669	−	0.830735i	$-0.312079\pi$
$43$	−2.89251	−	5.00997i	−0.441103	−	0.764013i	−0.997772	+	0.0667219i	$0.978746\pi$
$44$	−4.24294			−0.639647
$45$	10.3713	+	7.62778i	1.54606	+	1.13708i
$46$	−3.41675	+	5.91799i	−0.503772	+	0.872559i
$47$	−1.67341	+	2.89842i	−0.244091	+	0.422779i	−0.961876	−	0.273487i	$-0.911823\pi$
$47$	−1.67341	+	2.89842i	−0.244091	+	0.422779i	0.717784	+	0.696265i	$0.245156\pi$
$48$	0.355184	+	1.69524i	0.0512664	+	0.244687i
$49$	2.37159	−	4.10772i	0.338799	−	0.586817i
$50$	6.70818	−	11.6189i	0.948680	−	1.64316i
$51$	0.0798028	+	0.0261864i	0.0111746	+	0.00366683i
$52$	−3.60531	−	0.0419947i	−0.499966	−	0.00582362i
$53$	1.82220			0.250299			0.125149	−	0.992138i	$-0.460059\pi$
$53$	1.82220			0.250299			0.125149	+	0.992138i	$0.460059\pi$
$54$	3.01742	+	4.23027i	0.410619	+	0.575667i
$55$	9.10413	+	15.7688i	1.22760	+	2.12627i
$56$	0.751135	+	1.30100i	0.100375	+	0.173854i
$57$	9.47061	+	3.10767i	1.25441	+	0.411622i
$58$	−2.21264			−0.290534
$59$	−1.88614			−0.245555			−0.122777	−	0.992434i	$-0.539180\pi$
$59$	−1.88614			−0.245555			−0.122777	+	0.992434i	$0.539180\pi$
$60$	5.53822	−	4.95754i	0.714981	−	0.640016i
$61$	−0.877519	−	1.51991i	−0.112355	−	0.194604i	0.804364	−	0.594136i	$-0.202506\pi$
$61$	−0.877519	−	1.51991i	−0.112355	−	0.194604i	−0.916719	+	0.399532i	$0.869173\pi$
$62$	−3.74769	−	6.49119i	−0.475957	−	0.824382i
$63$	3.63061	+	2.67021i	0.457414	+	0.336414i
$64$	1.00000			0.125000
$65$	7.57989	+	13.4892i	0.940169	+	1.67313i
$66$	1.50702	+	7.19280i	0.185502	+	0.885373i
$67$	1.73270	−	3.00113i	0.211683	−	0.366646i	−0.740558	−	0.671992i	$-0.765439\pi$
$67$	1.73270	−	3.00113i	0.211683	−	0.366646i	0.952241	+	0.305346i	$0.0987721\pi$
$68$	0.0242456	−	0.0419947i	0.00294022	−	0.00509260i
$69$	11.2460	+	3.69025i	1.35386	+	0.444253i
$70$	3.22344	−	5.58317i	0.385275	−	0.667316i
$71$	0.645714	−	1.11841i	0.0766322	−	0.132731i	−0.825163	−	0.564895i	$-0.808917\pi$
$71$	0.645714	−	1.11841i	0.0766322	−	0.132731i	0.901795	+	0.432164i	$0.142250\pi$
$72$	2.74769	−	1.20424i	0.323818	−	0.141922i
$73$	−12.9836			−1.51962			−0.759808	−	0.650148i	$-0.774707\pi$
$73$	−12.9836			−1.51962			−0.759808	+	0.650148i	$0.774707\pi$
$74$	1.35174	+	2.34128i	0.157136	+	0.272168i
$75$	−22.0795	−	7.24514i	−2.54952	−	0.836597i
$76$	2.87736	−	4.98373i	0.330055	−	0.571673i
$77$	3.18702	+	5.52008i	0.363195	+	0.629072i
$78$	1.20936	+	6.12678i	0.136933	+	0.693721i
$79$	4.24521	−	7.35292i	0.477623	−	0.827268i	−0.522048	−	0.852916i	$-0.674832\pi$
$79$	4.24521	−	7.35292i	0.477623	−	0.827268i	0.999671	+	0.0256486i	$0.00816509\pi$
$80$	−2.14571	−	3.71649i	−0.239898	−	0.415516i
$81$	6.09959	−	6.61778i	0.677732	−	0.735309i
$82$	3.68986	−	6.39103i	0.407477	−	0.705771i
$83$	−0.370694	+	0.642060i	−0.0406889	+	0.0704753i	−0.885653	−	0.464348i	$-0.846289\pi$
$83$	−0.370694	+	0.642060i	−0.0406889	+	0.0704753i	0.844964	+	0.534824i	$0.179622\pi$
$84$	1.93873	−	1.73545i	0.211532	−	0.189353i
$85$	−0.208097			−0.0225713
$86$	2.89251	+	5.00997i	0.311907	+	0.540239i
$87$	0.785893	+	3.75096i	0.0842566	+	0.402145i
$88$	4.24294			0.452299
$89$	0.288865	+	0.500328i	0.0306196	+	0.0530347i	0.880929	−	0.473248i	$-0.156919\pi$
$89$	0.288865	+	0.500328i	0.0306196	+	0.0530347i	−0.850310	+	0.526283i	$0.823585\pi$
$90$	−10.3713	−	7.62778i	−1.09323	−	0.804039i
$91$	2.65344	+	4.72206i	0.278156	+	0.495007i
$92$	3.41675	−	5.91799i	0.356221	−	0.616993i
$93$	−9.67301	+	8.65880i	−1.00304	+	0.897876i
$94$	1.67341	−	2.89842i	0.172599	−	0.298950i
$95$	−24.6959			−2.53375
$96$	−0.355184	−	1.69524i	−0.0362508	−	0.173020i
$97$	−2.59585	−	4.49614i	−0.263569	−	0.456514i	0.703619	−	0.710577i	$-0.251566\pi$
$97$	−2.59585	−	4.49614i	−0.263569	−	0.456514i	−0.967188	+	0.254063i	$0.918233\pi$
$98$	−2.37159	+	4.10772i	−0.239567	+	0.414942i
$99$	11.6583	−	5.10953i	1.17170	−	0.513528i
$100$	−6.70818	+	11.6189i	−0.670818	+	1.16189i
$101$	−0.165943			−0.0165119			−0.00825596	−	0.999966i	$-0.502628\pi$
$101$	−0.165943			−0.0165119			−0.00825596	+	0.999966i	$0.502628\pi$
$102$	−0.0798028	−	0.0261864i	−0.00790166	−	0.00259284i
$103$	−5.53079	−	9.57962i	−0.544965	−	0.943908i	−0.998609	−	0.0527245i	$-0.983209\pi$
$103$	−5.53079	−	9.57962i	−0.544965	−	0.943908i	0.453644	−	0.891183i	$-0.350124\pi$
$104$	3.60531	+	0.0419947i	0.353529	+	0.00411792i
$105$	−10.6097	−	3.48147i	−1.03540	−	0.339756i
$106$	−1.82220			−0.176988
$107$	−4.39210	−	7.60734i	−0.424600	−	0.735429i	0.571783	−	0.820405i	$-0.306252\pi$
$107$	−4.39210	−	7.60734i	−0.424600	−	0.735429i	−0.996383	+	0.0849760i	$0.972919\pi$
$108$	−3.01742	−	4.23027i	−0.290351	−	0.407058i
$109$	8.91409			0.853815			0.426907	−	0.904295i	$-0.359603\pi$
$109$	8.91409			0.853815			0.426907	+	0.904295i	$0.359603\pi$
$110$	−9.10413	−	15.7688i	−0.868045	−	1.50350i
$111$	3.48892	−	3.12311i	0.331153	−	0.296432i
$112$	−0.751135	−	1.30100i	−0.0709756	−	0.122933i
$113$	−3.72239			−0.350173			−0.175086	−	0.984553i	$-0.556020\pi$
$113$	−3.72239			−0.350173			−0.175086	+	0.984553i	$0.556020\pi$
$114$	−9.47061	−	3.10767i	−0.887004	−	0.291060i
$115$	−29.3255			−2.73462
$116$	2.21264			0.205438
$117$	9.95683	−	4.22628i	0.920510	−	0.390720i
$118$	1.88614			0.173633
$119$	−0.0728470			−0.00667788
$120$	−5.53822	+	4.95754i	−0.505568	+	0.452559i
$121$	7.00252			0.636592
$122$	0.877519	+	1.51991i	0.0794468	+	0.137606i
$123$	−12.1449	−	3.98522i	−1.09507	−	0.359335i
$124$	3.74769	+	6.49119i	0.336552	+	0.582926i
$125$	36.1182			3.23051
$126$	−3.63061	−	2.67021i	−0.323441	−	0.237881i
$127$	1.13354	+	1.96334i	0.100585	+	0.174218i	0.911926	−	0.410355i	$-0.134595\pi$
$127$	1.13354	+	1.96334i	0.100585	+	0.174218i	−0.811341	+	0.584573i	$0.801262\pi$
$128$	−1.00000			−0.0883883
$129$	7.46573	−	6.68295i	0.657321	−	0.588401i
$130$	−7.57989	−	13.4892i	−0.664800	−	1.18308i
$131$	5.37112	+	9.30305i	0.469277	+	0.812811i	0.999383	−	0.0351201i	$-0.0111814\pi$
$131$	5.37112	+	9.30305i	0.469277	+	0.812811i	−0.530106	+	0.847931i	$0.677848\pi$
$132$	−1.50702	−	7.19280i	−0.131169	−	0.626053i
$133$	−8.64513			−0.749628
$134$	−1.73270	+	3.00113i	−0.149683	+	0.259258i
$135$	−9.24721	+	20.2911i	−0.795874	+	1.74638i
$136$	−0.0242456	+	0.0419947i	−0.00207905	+	0.00360102i
$137$	5.95858	+	10.3206i	0.509076	+	0.881745i	0.999945	+	0.0105118i	$0.00334607\pi$
$137$	5.95858	+	10.3206i	0.509076	+	0.881745i	−0.490869	+	0.871233i	$0.663321\pi$
$138$	−11.2460	−	3.69025i	−0.957322	−	0.314135i
$139$	−0.333976			−0.0283275			−0.0141638	−	0.999900i	$-0.504509\pi$
$139$	−0.333976			−0.0283275			−0.0141638	+	0.999900i	$0.504509\pi$
$140$	−3.22344	+	5.58317i	−0.272431	+	0.471864i
$141$	−5.50790	−	1.80735i	−0.463849	−	0.152207i
$142$	−0.645714	+	1.11841i	−0.0541871	+	0.0938549i
$143$	15.2971	+	0.178181i	1.27921	+	0.0149002i
$144$	−2.74769	+	1.20424i	−0.228974	+	0.100354i
$145$	−4.74769	−	8.22324i	−0.394274	−	0.682903i
$146$	12.9836			1.07453
$147$	7.80592	+	2.56143i	0.643822	+	0.211263i
$148$	−1.35174	−	2.34128i	−0.111112	−	0.192452i
$149$	13.3045			1.08995			0.544975	−	0.838453i	$-0.316539\pi$
$149$	13.3045			1.08995			0.544975	+	0.838453i	$0.316539\pi$
$150$	22.0795	+	7.24514i	1.80278	+	0.591563i
$151$	6.07725	−	10.5261i	0.494560	−	0.856603i	−0.505420	−	0.862873i	$-0.668663\pi$
$151$	6.07725	−	10.5261i	0.494560	−	0.856603i	0.999980	+	0.00627026i	$0.00199590\pi$
$152$	−2.87736	+	4.98373i	−0.233384	+	0.404234i
$153$	−0.0160476	+	0.144586i	−0.00129737	+	0.0116891i
$154$	−3.18702	−	5.52008i	−0.256817	−	0.444821i
$155$	16.0829	−	27.8565i	1.29181	−	2.23749i
$156$	−1.20936	−	6.12678i	−0.0968259	−	0.490535i
$157$	−4.11819	−	7.13291i	−0.328667	−	0.569268i	0.653581	−	0.756857i	$-0.273266\pi$
$157$	−4.11819	−	7.13291i	−0.328667	−	0.569268i	−0.982248	+	0.187589i	$0.939933\pi$
$158$	−4.24521	+	7.35292i	−0.337731	+	0.584967i
$159$	0.647217	+	3.08907i	0.0513276	+	0.244979i
$160$	2.14571	+	3.71649i	0.169634	+	0.293814i
$161$	−10.2658			−0.809056
$162$	−6.09959	+	6.61778i	−0.479229	+	0.519942i
$163$	−1.74521	+	3.02279i	−0.136695	+	0.236763i	−0.926244	−	0.376925i	$-0.876981\pi$
$163$	−1.74521	+	3.02279i	−0.136695	+	0.236763i	0.789549	+	0.613688i	$0.210315\pi$
$164$	−3.68986	+	6.39103i	−0.288130	+	0.499055i
$165$	−23.4983	+	21.0345i	−1.82934	+	1.63754i
$166$	0.370694	−	0.642060i	0.0287714	−	0.0498335i
$167$	10.2219	−	17.7049i	0.790995	−	1.37004i	−0.134356	−	0.990933i	$-0.542897\pi$
$167$	10.2219	−	17.7049i	0.790995	−	1.37004i	0.925351	−	0.379111i	$-0.123770\pi$
$168$	−1.93873	+	1.73545i	−0.149576	+	0.133893i
$169$	12.9965	+	0.302807i	0.999729	+	0.0232929i
$170$	0.208097			0.0159603
$171$	−1.90445	+	17.1588i	−0.145637	+	1.31216i
$172$	−2.89251	−	5.00997i	−0.220551	−	0.382006i
$173$	−5.88402	−	10.1914i	−0.447354	−	0.774839i	0.550859	−	0.834598i	$-0.314300\pi$
$173$	−5.88402	−	10.1914i	−0.447354	−	0.774839i	−0.998213	+	0.0597590i	$0.980967\pi$
$174$	−0.785893	−	3.75096i	−0.0595784	−	0.284359i
$175$	20.1550			1.52357
$176$	−4.24294			−0.319823
$177$	−0.669926	−	3.19746i	−0.0503548	−	0.240336i
$178$	−0.288865	−	0.500328i	−0.0216513	−	0.0375012i
$179$	−0.270676	−	0.468825i	−0.0202313	−	0.0350416i	0.855732	−	0.517418i	$-0.173107\pi$
$179$	−0.270676	−	0.468825i	−0.0202313	−	0.0350416i	−0.875964	+	0.482377i	$0.839774\pi$
$180$	10.3713	+	7.62778i	0.773032	+	0.568541i
$181$	−22.8671			−1.69970			−0.849848	−	0.527028i	$-0.823306\pi$
$181$	−22.8671			−1.69970			−0.849848	+	0.527028i	$0.823306\pi$
$182$	−2.65344	−	4.72206i	−0.196686	−	0.350023i
$183$	2.26493	−	2.02745i	0.167428	−	0.149874i
$184$	−3.41675	+	5.91799i	−0.251886	+	0.436280i
$185$	−5.80088	+	10.0474i	−0.426490	+	0.738702i
$186$	9.67301	−	8.65880i	0.709260	−	0.634894i
$187$	−0.102873	+	0.178181i	−0.00752280	+	0.0130299i
$188$	−1.67341	+	2.89842i	−0.122046	+	0.211389i
$189$	−3.23711	+	7.10318i	−0.235465	+	0.516680i
$190$	24.6959			1.79163
$191$	3.02741	+	5.24364i	0.219056	+	0.379416i	0.954520	−	0.298148i	$-0.0963689\pi$
$191$	3.02741	+	5.24364i	0.219056	+	0.379416i	−0.735464	+	0.677564i	$0.763036\pi$
$192$	0.355184	+	1.69524i	0.0256332	+	0.122344i
$193$	−0.837352	+	1.45034i	−0.0602739	+	0.104397i	−0.894588	−	0.446892i	$-0.852531\pi$
$193$	−0.837352	+	1.45034i	−0.0602739	+	0.104397i	0.834314	+	0.551290i	$0.185864\pi$
$194$	2.59585	+	4.49614i	0.186371	+	0.322804i
$195$	−20.1752	+	17.6409i	−1.44477	+	1.26329i
$196$	2.37159	−	4.10772i	0.169399	−	0.293408i
$197$	−6.37148	−	11.0357i	−0.453949	−	0.786263i	0.544678	−	0.838645i	$-0.316652\pi$
$197$	−6.37148	−	11.0357i	−0.453949	−	0.786263i	−0.998627	+	0.0523825i	$0.983318\pi$
$198$	−11.6583	+	5.10953i	−0.828517	+	0.363119i
$199$	−4.54939	+	7.87977i	−0.322498	+	0.558582i	−0.981003	−	0.193994i	$-0.937856\pi$
$199$	−4.54939	+	7.87977i	−0.322498	+	0.558582i	0.658505	+	0.752576i	$0.271189\pi$
$200$	6.70818	−	11.6189i	0.474340	−	0.821581i
$201$	5.70307	+	1.87140i	0.402263	+	0.131998i
$202$	0.165943			0.0116757
$203$	−1.66199	−	2.87865i	−0.116649	−	0.202042i
$204$	0.0798028	+	0.0261864i	0.00558731	+	0.00183341i
$205$	31.6696			2.21190
$206$	5.53079	+	9.57962i	0.385349	+	0.667443i
$207$	−2.26147	+	20.3754i	−0.157183	+	1.41619i
$208$	−3.60531	−	0.0419947i	−0.249983	−	0.00291181i
$209$	−12.2084	+	21.1456i	−0.844475	+	1.46267i
$210$	10.6097	+	3.48147i	0.732141	+	0.240244i
$211$	9.79869	−	16.9718i	0.674570	−	1.16839i	−0.302025	−	0.953300i	$-0.597663\pi$
$211$	9.79869	−	16.9718i	0.674570	−	1.16839i	0.976594	−	0.215089i	$-0.0690041\pi$
$212$	1.82220			0.125149
$213$	2.12532	+	0.697401i	0.145625	+	0.0477851i
$214$	4.39210	+	7.60734i	0.300238	+	0.520027i
$215$	−12.4130	+	21.4999i	−0.846558	+	1.46628i
$216$	3.01742	+	4.23027i	0.205309	+	0.287833i
$217$	5.63004	−	9.75152i	0.382192	−	0.661976i
$218$	−8.91409			−0.603738
$219$	−4.61157	−	22.0103i	−0.311621	−	1.48732i
$220$	9.10413	+	15.7688i	0.613800	+	1.06313i
$221$	−0.0891765	+	0.150386i	−0.00599866	+	0.0101160i
$222$	−3.48892	+	3.12311i	−0.234161	+	0.209609i
$223$	4.52761			0.303191			0.151596	−	0.988443i	$-0.451559\pi$
$223$	4.52761			0.303191			0.151596	+	0.988443i	$0.451559\pi$
$224$	0.751135	+	1.30100i	0.0501873	+	0.0869270i
$225$	4.43998	−	40.0034i	0.295999	−	2.66690i
$226$	3.72239			0.247610
$227$	−4.95437	−	8.58121i	−0.328833	−	0.569555i	0.653448	−	0.756972i	$-0.273322\pi$
$227$	−4.95437	−	8.58121i	−0.328833	−	0.569555i	−0.982281	+	0.187416i	$0.939989\pi$
$228$	9.47061	+	3.10767i	0.627207	+	0.205811i
$229$	0.0362267	+	0.0627465i	0.00239393	+	0.00414640i	0.867220	−	0.497925i	$-0.165905\pi$
$229$	0.0362267	+	0.0627465i	0.00239393	+	0.00414640i	−0.864826	+	0.502072i	$0.832571\pi$
$230$	29.3255			1.93367
$231$	−8.22589	+	7.36341i	−0.541224	+	0.484477i
$232$	−2.21264			−0.145267
$233$	−23.4584			−1.53681			−0.768404	−	0.639965i	$-0.778949\pi$
$233$	−23.4584			−1.53681			−0.768404	+	0.639965i	$0.778949\pi$
$234$	−9.95683	+	4.22628i	−0.650899	+	0.276281i
$235$	14.3626			0.936913
$236$	−1.88614			−0.122777
$237$	13.9728	+	4.58502i	0.907631	+	0.297829i
$238$	0.0728470			0.00472197
$239$	1.52229	+	2.63668i	0.0984685	+	0.170552i	0.911051	−	0.412294i	$-0.135272\pi$
$239$	1.52229	+	2.63668i	0.0984685	+	0.170552i	−0.812582	+	0.582846i	$0.801939\pi$
$240$	5.53822	−	4.95754i	0.357491	−	0.320008i
$241$	−1.99311	−	3.45216i	−0.128387	−	0.222373i	0.794665	−	0.607049i	$-0.207647\pi$
$241$	−1.99311	−	3.45216i	−0.128387	−	0.222373i	−0.923052	+	0.384675i	$0.874313\pi$
$242$	−7.00252			−0.450139
$243$	13.3852	+	7.98975i	0.858662	+	0.512543i
$244$	−0.877519	−	1.51991i	−0.0561774	−	0.0973021i
$245$	−20.3550			−1.30044
$246$	12.1449	+	3.98522i	0.774331	+	0.254088i
$247$	−10.5830	+	17.8470i	−0.673383	+	1.13558i
$248$	−3.74769	−	6.49119i	−0.237978	−	0.412191i
$249$	−1.22011	−	0.400366i	−0.0773214	−	0.0253722i
$250$	−36.1182			−2.28432
$251$	7.25721	−	12.5699i	0.458071	−	0.793402i	−0.540788	−	0.841159i	$-0.681874\pi$
$251$	7.25721	−	12.5699i	0.458071	−	0.793402i	0.998859	+	0.0477567i	$0.0152072\pi$
$252$	3.63061	+	2.67021i	0.228707	+	0.168207i
$253$	−14.4971	+	25.1096i	−0.911422	+	1.57863i
$254$	−1.13354	−	1.96334i	−0.0711244	−	0.123191i
$255$	−0.0739126	−	0.352775i	−0.00462859	−	0.0220916i
$256$	1.00000			0.0625000
$257$	−13.3068	+	23.0481i	−0.830057	+	1.43770i	0.0679355	+	0.997690i	$0.478359\pi$
$257$	−13.3068	+	23.0481i	−0.830057	+	1.43770i	−0.897992	+	0.440011i	$0.854975\pi$
$258$	−7.46573	+	6.68295i	−0.464796	+	0.416063i
$259$	−2.03068	+	3.51723i	−0.126180	+	0.218550i
$260$	7.57989	+	13.4892i	0.470085	+	0.836563i
$261$	−6.07964	+	2.66456i	−0.376320	+	0.164932i
$262$	−5.37112	−	9.30305i	−0.331829	−	0.574744i
$263$	13.4095			0.826863			0.413432	−	0.910535i	$-0.364330\pi$
$263$	13.4095			0.826863			0.413432	+	0.910535i	$0.364330\pi$
$264$	1.50702	+	7.19280i	0.0927508	+	0.442687i
$265$	−3.90993	−	6.77219i	−0.240185	−	0.416012i
$266$	8.64513			0.530067
$267$	−0.745578	+	0.667404i	−0.0456286	+	0.0408445i
$268$	1.73270	−	3.00113i	0.105842	−	0.183323i
$269$	10.6794	−	18.4972i	0.651133	−	1.12780i	−0.331715	−	0.943380i	$-0.607627\pi$
$269$	10.6794	−	18.4972i	0.651133	−	1.12780i	0.982848	−	0.184416i	$-0.0590394\pi$
$270$	9.24721	−	20.2911i	0.562768	−	1.23488i
$271$	−3.34991	−	5.80222i	−0.203493	−	0.352460i	0.746159	−	0.665768i	$-0.231896\pi$
$271$	−3.34991	−	5.80222i	−0.203493	−	0.352460i	−0.949651	+	0.313308i	$0.898563\pi$
$272$	0.0242456	−	0.0419947i	0.00147011	−	0.00254630i
$273$	−7.06258	+	6.17542i	−0.427447	+	0.373753i
$274$	−5.95858	−	10.3206i	−0.359971	−	0.623488i
$275$	28.4624	−	49.2983i	1.71635	−	2.97280i
$276$	11.2460	+	3.69025i	0.676929	+	0.222127i
$277$	5.13691	+	8.89739i	0.308647	+	0.534592i	0.978067	−	0.208292i	$-0.0667905\pi$
$277$	5.13691	+	8.89739i	0.308647	+	0.534592i	−0.669420	+	0.742885i	$0.733457\pi$
$278$	0.333976			0.0200306
$279$	−18.1145	−	13.3226i	−1.08448	−	0.797605i
$280$	3.22344	−	5.58317i	0.192638	−	0.333658i
$281$	0.675072	−	1.16926i	0.0402714	−	0.0697521i	−0.845187	−	0.534470i	$-0.820511\pi$
$281$	0.675072	−	1.16926i	0.0402714	−	0.0697521i	0.885459	+	0.464718i	$0.153844\pi$
$282$	5.50790	+	1.80735i	0.327990	+	0.107626i
$283$	3.63466	−	6.29542i	0.216058	−	0.374224i	−0.737541	−	0.675302i	$-0.764013\pi$
$283$	3.63466	−	6.29542i	0.216058	−	0.374224i	0.953599	+	0.301078i	$0.0973465\pi$
$284$	0.645714	−	1.11841i	0.0383161	−	0.0663654i
$285$	−8.77159	−	41.8656i	−0.519584	−	2.47990i
$286$	−15.2971	−	0.178181i	−0.904536	−	0.0105361i
$287$	11.0863			0.654406
$288$	2.74769	−	1.20424i	0.161909	−	0.0709608i
$289$	8.49882	+	14.7204i	0.499931	+	0.865906i
$290$	4.74769	+	8.22324i	0.278794	+	0.482885i
$291$	6.70005	−	5.99755i	0.392764	−	0.351583i
$292$	−12.9836			−0.759808
$293$	−31.3528			−1.83165			−0.915826	−	0.401574i	$-0.868463\pi$
$293$	−31.3528			−1.83165			−0.915826	+	0.401574i	$0.868463\pi$
$294$	−7.80592	−	2.56143i	−0.455251	−	0.149385i
$295$	4.04712	+	7.00982i	0.235632	+	0.408127i
$296$	1.35174	+	2.34128i	0.0785681	+	0.136084i
$297$	12.8027	+	17.9488i	0.742889	+	1.04149i
$298$	−13.3045			−0.770710
$299$	−12.5670	+	21.1927i	−0.726766	+	1.22560i
$300$	−22.0795	−	7.24514i	−1.27476	−	0.418298i
$301$	−4.34533	+	7.52632i	−0.250460	+	0.433810i
$302$	−6.07725	+	10.5261i	−0.349707	+	0.605710i
$303$	−0.0589402	−	0.281313i	−0.00338602	−	0.0161610i
$304$	2.87736	−	4.98373i	0.165028	−	0.285836i
$305$	−3.76581	+	6.52257i	−0.215630	+	0.373482i
$306$	0.0160476	−	0.144586i	0.000917381	−	0.00826543i
$307$	9.56515			0.545912			0.272956	−	0.962027i	$-0.411999\pi$
$307$	9.56515			0.545912			0.272956	+	0.962027i	$0.411999\pi$
$308$	3.18702	+	5.52008i	0.181597	+	0.314536i
$309$	14.2753	−	12.7786i	0.812094	−	0.726947i
$310$	−16.0829	+	27.8565i	−0.913450	+	1.58214i
$311$	−0.316125	−	0.547545i	−0.0179258	−	0.0310484i	0.856923	−	0.515444i	$-0.172373\pi$
$311$	−0.316125	−	0.547545i	−0.0179258	−	0.0310484i	−0.874849	+	0.484395i	$0.839040\pi$
$312$	1.20936	+	6.12678i	0.0684663	+	0.346861i
$313$	−5.25048	+	9.09409i	−0.296775	+	0.514029i	−0.975396	−	0.220459i	$-0.929244\pi$
$313$	−5.25048	+	9.09409i	−0.296775	+	0.514029i	0.678622	+	0.734488i	$0.262578\pi$
$314$	4.11819	+	7.13291i	0.232403	+	0.402533i
$315$	2.13352	−	19.2226i	0.120210	−	1.08307i
$316$	4.24521	−	7.35292i	0.238812	−	0.413634i
$317$	9.36121	−	16.2141i	0.525778	−	0.910674i	−0.473771	−	0.880648i	$-0.657108\pi$
$317$	9.36121	−	16.2141i	0.525778	−	0.910674i	0.999549	−	0.0300261i	$-0.00955904\pi$
$318$	−0.647217	−	3.08907i	−0.0362941	−	0.173227i
$319$	−9.38808			−0.525632
$320$	−2.14571	−	3.71649i	−0.119949	−	0.207758i
$321$	11.3363	−	10.1477i	0.632729	−	0.566388i
$322$	10.2658			0.572089
$323$	−0.139527	−	0.241667i	−0.00776347	−	0.0134467i
$324$	6.09959	−	6.61778i	0.338866	−	0.367654i
$325$	24.6730	−	41.6080i	1.36861	−	2.30800i
$326$	1.74521	−	3.02279i	0.0966581	−	0.167417i
$327$	3.16614	+	15.1115i	0.175088	+	0.835670i
$328$	3.68986	−	6.39103i	0.203739	−	0.352885i
$329$	5.02782			0.277193
$330$	23.4983	−	21.0345i	1.29354	−	1.15791i
$331$	11.4289	+	19.7955i	0.628192	+	1.08806i	0.987914	+	0.155001i	$0.0495379\pi$
$331$	11.4289	+	19.7955i	0.628192	+	1.08806i	−0.359723	+	0.933059i	$0.617129\pi$
$332$	−0.370694	+	0.642060i	−0.0203445	+	0.0352376i
$333$	6.53363	+	4.80528i	0.358040	+	0.263328i
$334$	−10.2219	+	17.7049i	−0.559318	+	0.968767i
$335$	−14.8715			−0.812519
$336$	1.93873	−	1.73545i	0.105766	−	0.0946766i
$337$	17.2502	+	29.8782i	0.939679	+	1.62757i	0.766071	+	0.642756i	$0.222209\pi$
$337$	17.2502	+	29.8782i	0.939679	+	1.62757i	0.173608	+	0.984815i	$0.444458\pi$
$338$	−12.9965	−	0.302807i	−0.706915	−	0.0164706i
$339$	−1.32213	−	6.31035i	−0.0718083	−	0.342731i
$340$	−0.208097			−0.0112856
$341$	−15.9012	−	27.5417i	−0.861099	−	1.49147i
$342$	1.90445	−	17.1588i	0.102981	−	0.927840i
$343$	−17.6414			−0.952548
$344$	2.89251	+	5.00997i	0.155953	+	0.270119i
$345$	−10.4159	−	49.7138i	−0.560775	−	2.67650i
$346$	5.88402	+	10.1914i	0.316327	+	0.547894i
$347$	−22.3954			−1.20225			−0.601125	−	0.799155i	$-0.705280\pi$
$347$	−22.3954			−1.20225			−0.601125	+	0.799155i	$0.705280\pi$
$348$	0.785893	+	3.75096i	0.0421283	+	0.201072i
$349$	−27.8257			−1.48948			−0.744739	−	0.667356i	$-0.767426\pi$
$349$	−27.8257			−1.48948			−0.744739	+	0.667356i	$0.767426\pi$
$350$	−20.1550			−1.07733
$351$	10.7011	+	15.3781i	0.571181	+	0.820824i
$352$	4.24294			0.226149
$353$	37.0443			1.97167			0.985834	−	0.167725i	$-0.0536420\pi$
$353$	37.0443			1.97167			0.985834	+	0.167725i	$0.0536420\pi$
$354$	0.669926	+	3.19746i	0.0356062	+	0.169943i
$355$	−5.54207			−0.294143
$356$	0.288865	+	0.500328i	0.0153098	+	0.0265174i
$357$	−0.0258741	−	0.123493i	−0.00136940	−	0.00653596i
$358$	0.270676	+	0.468825i	0.0143057	+	0.0247782i
$359$	−15.9020			−0.839276			−0.419638	−	0.907692i	$-0.637843\pi$
$359$	−15.9020			−0.839276			−0.419638	+	0.907692i	$0.637843\pi$
$360$	−10.3713	−	7.62778i	−0.546616	−	0.402019i
$361$	−7.05835	−	12.2254i	−0.371492	−	0.643443i
$362$	22.8671			1.20187
$363$	2.48718	+	11.8710i	0.130543	+	0.623064i
$364$	2.65344	+	4.72206i	0.139078	+	0.247503i
$365$	27.8591	+	48.2534i	1.45821	+	2.52570i
$366$	−2.26493	+	2.02745i	−0.118390	+	0.105977i
$367$	25.4758			1.32983			0.664914	−	0.746920i	$-0.268468\pi$
$367$	25.4758			1.32983			0.664914	+	0.746920i	$0.268468\pi$
$368$	3.41675	−	5.91799i	0.178110	−	0.308496i
$369$	2.44223	−	22.0041i	0.127137	−	1.14549i
$370$	5.80088	−	10.0474i	0.301574	−	0.522341i
$371$	−1.36872	−	2.37069i	−0.0710604	−	0.123080i
$372$	−9.67301	+	8.65880i	−0.501522	+	0.448938i
$373$	−29.4233			−1.52348			−0.761740	−	0.647883i	$-0.775654\pi$
$373$	−29.4233			−1.52348			−0.761740	+	0.647883i	$0.775654\pi$
$374$	0.102873	−	0.178181i	0.00531942	−	0.00921351i
$375$	12.8286	+	61.2291i	0.662466	+	3.16186i
$376$	1.67341	−	2.89842i	0.0862993	−	0.149475i
$377$	−7.97724	−	0.0929191i	−0.410849	−	0.00478557i
$378$	3.23711	−	7.10318i	0.166499	−	0.365348i
$379$	15.6605	+	27.1247i	0.804424	+	1.39330i	0.916679	+	0.399624i	$0.130859\pi$
$379$	15.6605	+	27.1247i	0.804424	+	1.39330i	−0.112255	+	0.993679i	$0.535807\pi$
$380$	−24.6959			−1.26687
$381$	−2.92573	+	2.61897i	−0.149890	+	0.134174i
$382$	−3.02741	−	5.24364i	−0.154896	−	0.268288i
$383$	−9.84210			−0.502908			−0.251454	−	0.967869i	$-0.580909\pi$
$383$	−9.84210			−0.502908			−0.251454	+	0.967869i	$0.580909\pi$
$384$	−0.355184	−	1.69524i	−0.0181254	−	0.0865099i
$385$	13.6769	−	23.6890i	0.697038	−	1.20730i
$386$	0.837352	−	1.45034i	0.0426201	−	0.0738202i
$387$	13.9809	+	10.2825i	0.710691	+	0.522691i
$388$	−2.59585	−	4.49614i	−0.131784	−	0.228257i
$389$	−8.42401	+	14.5908i	−0.427114	+	0.739784i	−0.996615	−	0.0822068i	$-0.973803\pi$
$389$	−8.42401	+	14.5908i	−0.427114	+	0.739784i	0.569501	+	0.821991i	$0.307137\pi$
$390$	20.1752	−	17.6409i	1.02161	−	0.893280i
$391$	−0.165683	−	0.286971i	−0.00837893	−	0.0145127i
$392$	−2.37159	+	4.10772i	−0.119783	+	0.207471i
$393$	−13.8632	+	12.4096i	−0.699305	+	0.625983i
$394$	6.37148	+	11.0357i	0.320990	+	0.555972i
$395$	−36.4360			−1.83329
$396$	11.6583	−	5.10953i	0.585850	−	0.256764i
$397$	10.0323	−	17.3764i	0.503506	−	0.872097i	−0.496486	−	0.868045i	$-0.665377\pi$
$397$	10.0323	−	17.3764i	0.503506	−	0.872097i	0.999992	−	0.00405255i	$-0.00128997\pi$
$398$	4.54939	−	7.87977i	0.228040	−	0.394977i
$399$	−3.07061	−	14.6556i	−0.153723	−	0.733697i
$400$	−6.70818	+	11.6189i	−0.335409	+	0.580945i
$401$	9.57225	−	16.5796i	0.478015	−	0.827947i	−0.521667	−	0.853149i	$-0.674690\pi$
$401$	9.57225	−	16.5796i	0.478015	−	0.827947i	0.999682	+	0.0252024i	$0.00802302\pi$
$402$	−5.70307	−	1.87140i	−0.284443	−	0.0933368i
$403$	−13.2390	−	23.5601i	−0.659480	−	1.17361i
$404$	−0.165943			−0.00825596
$405$	−37.6829	−	8.46918i	−1.87248	−	0.420837i
$406$	1.66199	+	2.87865i	0.0824832	+	0.142865i
$407$	5.73534	+	9.93390i	0.284290	+	0.492405i
$408$	−0.0798028	−	0.0261864i	−0.00395083	−	0.00129642i
$409$	−25.6832			−1.26995			−0.634976	−	0.772532i	$-0.718990\pi$
$409$	−25.6832			−1.26995			−0.634976	+	0.772532i	$0.718990\pi$
$410$	−31.6696			−1.56405
$411$	−15.3795	+	13.7669i	−0.758613	+	0.679073i
$412$	−5.53079	−	9.57962i	−0.272483	−	0.471954i
$413$	1.41675	+	2.45388i	0.0697135	+	0.120747i
$414$	2.26147	−	20.3754i	0.111145	−	1.00140i
$415$	3.18161			0.156179
$416$	3.60531	+	0.0419947i	0.176765	+	0.00205896i
$417$	−0.118623	−	0.566171i	−0.00580899	−	0.0277255i
$418$	12.2084	−	21.1456i	0.597134	−	1.03427i
$419$	5.95225	−	10.3096i	0.290786	−	0.503657i	−0.683210	−	0.730222i	$-0.739416\pi$
$419$	5.95225	−	10.3096i	0.290786	−	0.503657i	0.973996	+	0.226566i	$0.0727498\pi$
$420$	−10.6097	−	3.48147i	−0.517702	−	0.169878i
$421$	−7.55605	+	13.0875i	−0.368259	+	0.637844i	−0.989293	−	0.145940i	$-0.953379\pi$
$421$	−7.55605	+	13.0875i	−0.368259	+	0.637844i	0.621034	+	0.783783i	$0.286713\pi$
$422$	−9.79869	+	16.9718i	−0.476993	+	0.826176i
$423$	1.10759	−	9.97916i	0.0538528	−	0.485203i
$424$	−1.82220			−0.0884940
$425$	0.325288	+	0.563416i	0.0157788	+	0.0273297i
$426$	−2.12532	−	0.697401i	−0.102972	−	0.0337892i
$427$	−1.31827	+	2.28331i	−0.0637956	+	0.110497i
$428$	−4.39210	−	7.60734i	−0.212300	−	0.367714i
$429$	5.13122	+	25.9956i	0.247738	+	1.25508i
$430$	12.4130	−	21.4999i	0.598607	−	1.03682i
$431$	−14.0198	−	24.2830i	−0.675310	−	1.16967i	−0.976378	−	0.216069i	$-0.930677\pi$
$431$	−14.0198	−	24.2830i	−0.675310	−	1.16967i	0.301068	−	0.953603i	$-0.402657\pi$
$432$	−3.01742	−	4.23027i	−0.145176	−	0.203529i
$433$	−13.1577	+	22.7899i	−0.632321	+	1.09521i	0.354755	+	0.934959i	$0.384564\pi$
$433$	−13.1577	+	22.7899i	−0.632321	+	1.09521i	−0.987076	+	0.160253i	$0.948769\pi$
$434$	−5.63004	+	9.75152i	−0.270251	+	0.468088i
$435$	12.2541	−	10.9692i	0.587538	−	0.525935i
$436$	8.91409			0.426907
$437$	−19.6624	−	34.0563i	−0.940581	−	1.62913i
$438$	4.61157	+	22.0103i	0.220349	+	1.05170i
$439$	−7.98913			−0.381301			−0.190650	−	0.981658i	$-0.561060\pi$
$439$	−7.98913			−0.381301			−0.190650	+	0.981658i	$0.561060\pi$
$440$	−9.10413	−	15.7688i	−0.434022	−	0.751749i
$441$	−1.56970	+	14.1427i	−0.0747476	+	0.673462i
$442$	0.0891765	−	0.150386i	0.00424170	−	0.00715311i
$443$	0.708370	−	1.22693i	0.0336557	−	0.0582934i	−0.848707	−	0.528863i	$-0.822618\pi$
$443$	0.708370	−	1.22693i	0.0336557	−	0.0582934i	0.882363	+	0.470570i	$0.155952\pi$
$444$	3.48892	−	3.12311i	0.165577	−	0.148216i
$445$	1.23964	−	2.14712i	0.0587647	−	0.101783i
$446$	−4.52761			−0.214388
$447$	4.72555	+	22.5544i	0.223511	+	1.06679i
$448$	−0.751135	−	1.30100i	−0.0354878	−	0.0614667i
$449$	15.3503	−	26.5875i	0.724426	−	1.25474i	−0.234784	−	0.972048i	$-0.575438\pi$
$449$	15.3503	−	26.5875i	0.724426	−	1.25474i	0.959210	−	0.282695i	$-0.0912283\pi$
$450$	−4.43998	+	40.0034i	−0.209303	+	1.88578i
$451$	15.6558	−	27.1167i	0.737205	−	1.27688i
$452$	−3.72239			−0.175086
$453$	20.0028	+	6.56371i	0.939816	+	0.308390i
$454$	4.95437	+	8.58121i	0.232520	+	0.402736i
$455$	11.8560	−	19.9937i	0.555816	−	0.937317i
$456$	−9.47061	−	3.10767i	−0.443502	−	0.145530i
$457$	9.15912			0.428445			0.214223	−	0.976785i	$-0.431278\pi$
$457$	9.15912			0.428445			0.214223	+	0.976785i	$0.431278\pi$
$458$	−0.0362267	−	0.0627465i	−0.00169276	−	0.00293195i
$459$	−0.250808	+	0.0241500i	−0.0117067	+	0.00112723i
$460$	−29.3255			−1.36731
$461$	0.921259	+	1.59567i	0.0429073	+	0.0743176i	0.886681	−	0.462381i	$-0.153005\pi$
$461$	0.921259	+	1.59567i	0.0429073	+	0.0743176i	−0.843774	+	0.536698i	$0.819671\pi$
$462$	8.22589	−	7.36341i	0.382703	−	0.342577i
$463$	16.5132	+	28.6016i	0.767432	+	1.32923i	0.938951	+	0.344050i	$0.111799\pi$
$463$	16.5132	+	28.6016i	0.767432	+	1.32923i	−0.171520	+	0.985181i	$0.554868\pi$
$464$	2.21264			0.102719
$465$	52.9358	+	17.3703i	2.45484	+	0.805529i
$466$	23.4584			1.08669
$467$	39.8056			1.84198			0.920992	−	0.389581i	$-0.127380\pi$
$467$	39.8056			1.84198			0.920992	+	0.389581i	$0.127380\pi$
$468$	9.95683	−	4.22628i	0.460255	−	0.195360i
$469$	−5.20598			−0.240390
$470$	−14.3626			−0.662498
$471$	10.6293	−	9.51481i	0.489772	−	0.438419i
$472$	1.88614			0.0868167
$473$	12.2727	+	21.2570i	0.564300	+	0.977397i
$474$	−13.9728	−	4.58502i	−0.641792	−	0.210597i
$475$	38.6036	+	66.8635i	1.77126	+	3.06791i
$476$	−0.0728470			−0.00333894
$477$	−5.00685	+	2.19438i	−0.229248	+	0.100474i
$478$	−1.52229	−	2.63668i	−0.0696278	−	0.120599i
$479$	1.22167			0.0558197			0.0279098	−	0.999610i	$-0.491115\pi$
$479$	1.22167			0.0558197			0.0279098	+	0.999610i	$0.491115\pi$
$480$	−5.53822	+	4.95754i	−0.252784	+	0.226280i
$481$	4.77511	+	8.49779i	0.217726	+	0.387466i
$482$	1.99311	+	3.45216i	0.0907836	+	0.157242i
$483$	−3.64623	−	17.4030i	−0.165909	−	0.791862i
$484$	7.00252			0.318296
$485$	−11.1399	+	19.2949i	−0.505837	+	0.876136i
$486$	−13.3852	−	7.98975i	−0.607165	−	0.362422i
$487$	18.6227	−	32.2555i	0.843877	−	1.46164i	−0.0427162	−	0.999087i	$-0.513601\pi$
$487$	18.6227	−	32.2555i	0.843877	−	1.46164i	0.886593	−	0.462550i	$-0.153066\pi$
$488$	0.877519	+	1.51991i	0.0397234	+	0.0688030i
$489$	−5.74423	−	1.88490i	−0.259763	−	0.0852383i
$490$	20.3550			0.919547
$491$	−14.9729	+	25.9338i	−0.675717	+	1.17038i	0.300542	+	0.953769i	$0.402832\pi$
$491$	−14.9729	+	25.9338i	−0.675717	+	1.17038i	−0.976259	+	0.216607i	$0.930501\pi$
$492$	−12.1449	−	3.98522i	−0.547535	−	0.179667i
$493$	0.0536468	−	0.0929191i	0.00241613	−	0.00418486i
$494$	10.5830	−	17.8470i	0.476153	−	0.802976i
$495$	−44.0048	−	32.3642i	−1.97787	−	1.45466i
$496$	3.74769	+	6.49119i	0.168276	+	0.291463i
$497$	−1.94008			−0.0870243
$498$	1.22011	+	0.400366i	0.0546745	+	0.0179408i
$499$	15.3917	+	26.6592i	0.689027	+	1.19343i	0.972153	+	0.234348i	$0.0752954\pi$
$499$	15.3917	+	26.6592i	0.689027	+	1.19343i	−0.283125	+	0.959083i	$0.591371\pi$
$500$	36.1182			1.61526
$501$	33.6447	+	11.0401i	1.50313	+	0.493236i
$502$	−7.25721	+	12.5699i	−0.323905	+	0.561020i
$503$	9.77265	−	16.9267i	0.435741	−	0.754726i	−0.561615	−	0.827399i	$-0.689820\pi$
$503$	9.77265	−	16.9267i	0.435741	−	0.754726i	0.997356	+	0.0726733i	$0.0231530\pi$
$504$	−3.63061	−	2.67021i	−0.161720	−	0.118940i
$505$	0.356066	+	0.616724i	0.0158447	+	0.0274439i
$506$	14.4971	−	25.1096i	0.644473	−	1.11626i
$507$	4.10280	+	22.1397i	0.182212	+	0.983259i
$508$	1.13354	+	1.96334i	0.0502925	+	0.0871092i
$509$	−8.53574	+	14.7843i	−0.378340	+	0.655304i	−0.990821	−	0.135181i	$-0.956838\pi$
$509$	−8.53574	+	14.7843i	−0.378340	+	0.655304i	0.612481	+	0.790485i	$0.290172\pi$
$510$	0.0739126	+	0.352775i	0.00327291	+	0.0156211i
$511$	9.75244	+	16.8917i	0.431423	+	0.747246i
$512$	−1.00000			−0.0441942
$513$	−29.7647	+	2.86601i	−1.31414	+	0.126537i
$514$	13.3068	−	23.0481i	0.586939	−	1.01661i
$515$	−23.7350	+	41.1102i	−1.04589	+	1.81153i
$516$	7.46573	−	6.68295i	0.328661	−	0.294201i
$517$	7.10016	−	12.2978i	0.312265	−	0.540858i
$518$	2.03068	−	3.51723i	0.0892228	−	0.154538i
$519$	15.1870	−	13.5947i	0.666636	−	0.596739i
$520$	−7.57989	−	13.4892i	−0.332400	−	0.591540i
$521$	26.0051			1.13930			0.569651	−	0.821887i	$-0.307078\pi$
$521$	26.0051			1.13930			0.569651	+	0.821887i	$0.307078\pi$
$522$	6.07964	−	2.66456i	0.266099	−	0.116625i
$523$	−16.6348	−	28.8123i	−0.727388	−	1.25987i	−0.957984	−	0.286823i	$-0.907401\pi$
$523$	−16.6348	−	28.8123i	−0.727388	−	1.25987i	0.230596	−	0.973050i	$-0.425933\pi$
$524$	5.37112	+	9.30305i	0.234638	+	0.406406i
$525$	7.15873	+	34.1676i	0.312433	+	1.49120i
$526$	−13.4095			−0.584681
$527$	0.363461			0.0158326
$528$	−1.50702	−	7.19280i	−0.0655847	−	0.313027i
$529$	−11.8484	−	20.5220i	−0.515147	−	0.892260i
$530$	3.90993	+	6.77219i	0.169836	+	0.294165i
$531$	5.18253	−	2.27137i	0.224903	−	0.0985693i
$532$	−8.64513			−0.374814
$533$	13.5715	−	22.8867i	0.587846	−	0.991331i
$534$	0.745578	−	0.667404i	0.0322643	−	0.0288814i
$535$	−18.8484	+	32.6463i	−0.814886	+	1.41142i
$536$	−1.73270	+	3.00113i	−0.0748414	+	0.129629i
$537$	0.698632	−	0.625381i	0.0301482	−	0.0269872i
$538$	−10.6794	+	18.4972i	−0.460421	+	0.797472i
$539$	−10.0625	+	17.4288i	−0.433423	+	0.750711i
$540$	−9.24721	+	20.2911i	−0.397937	+	0.873192i
$541$	−31.6760			−1.36186			−0.680928	−	0.732351i	$-0.738423\pi$
$541$	−31.6760			−1.36186			−0.680928	+	0.732351i	$0.738423\pi$
$542$	3.34991	+	5.80222i	0.143891	+	0.249227i
$543$	−8.12201	−	38.7652i	−0.348549	−	1.66357i
$544$	−0.0242456	+	0.0419947i	−0.00103952	+	0.00180051i
$545$	−19.1271	−	33.1291i	−0.819314	−	1.41909i
$546$	7.06258	−	6.17542i	0.302251	−	0.264284i
$547$	5.57763	−	9.66074i	0.238482	−	0.413063i	−0.721797	−	0.692105i	$-0.756683\pi$
$547$	5.57763	−	9.66074i	0.238482	−	0.413063i	0.960279	+	0.279042i	$0.0900168\pi$
$548$	5.95858	+	10.3206i	0.254538	+	0.440873i
$549$	4.24149	+	3.11949i	0.181022	+	0.133136i
$550$	−28.4624	+	49.2983i	−1.21364	+	2.10209i
$551$	6.36655	−	11.0272i	0.271224	−	0.469774i
$552$	−11.2460	−	3.69025i	−0.478661	−	0.157067i
$553$	−12.7549			−0.542394
$554$	−5.13691	−	8.89739i	−0.218246	−	0.378014i
$555$	−19.0932	−	6.26522i	−0.810461	−	0.265944i
$556$	−0.333976			−0.0141638
$557$	18.8367	+	32.6261i	0.798137	+	1.38241i	0.920828	+	0.389969i	$0.127514\pi$
$557$	18.8367	+	32.6261i	0.798137	+	1.38241i	−0.122691	+	0.992445i	$0.539153\pi$
$558$	18.1145	+	13.3226i	0.766846	+	0.563992i
$559$	10.2180	+	18.1839i	0.432174	+	0.769098i
$560$	−3.22344	+	5.58317i	−0.136215	+	0.235932i
$561$	−0.338598	−	0.111107i	−0.0142956	−	0.00469095i
$562$	−0.675072	+	1.16926i	−0.0284762	+	0.0493222i
$563$	14.7622			0.622152			0.311076	−	0.950385i	$-0.399311\pi$
$563$	14.7622			0.622152			0.311076	+	0.950385i	$0.399311\pi$
$564$	−5.50790	−	1.80735i	−0.231924	−	0.0761034i
$565$	7.98718	+	13.8342i	0.336023	+	0.582009i
$566$	−3.63466	+	6.29542i	−0.152776	+	0.264616i
$567$	−13.1914	−	2.96475i	−0.553986	−	0.124508i
$568$	−0.645714	+	1.11841i	−0.0270936	+	0.0469274i
$569$	−7.50302			−0.314543			−0.157272	−	0.987555i	$-0.550270\pi$
$569$	−7.50302			−0.314543			−0.157272	+	0.987555i	$0.550270\pi$
$570$	8.77159	+	41.8656i	0.367402	+	1.75356i
$571$	−9.01702	−	15.6179i	−0.377351	−	0.653591i	0.613325	−	0.789830i	$-0.289832\pi$
$571$	−9.01702	−	15.6179i	−0.377351	−	0.653591i	−0.990676	+	0.136240i	$0.956498\pi$
$572$	15.2971	+	0.178181i	0.639603	+	0.00745012i
$573$	−7.81394	+	6.99465i	−0.326432	+	0.292206i
$574$	−11.0863			−0.462735
$575$	45.8404	+	79.3978i	1.91168	+	3.31112i
$576$	−2.74769	+	1.20424i	−0.114487	+	0.0501769i
$577$	−34.2209			−1.42463			−0.712317	−	0.701858i	$-0.752354\pi$
$577$	−34.2209			−1.42463			−0.712317	+	0.701858i	$0.752354\pi$
$578$	−8.49882	−	14.7204i	−0.353504	−	0.612288i
$579$	−2.75608	−	0.904378i	−0.114539	−	0.0375847i
$580$	−4.74769	−	8.22324i	−0.197137	−	0.341451i
$581$	1.11376			0.0462067
$582$	−6.70005	+	5.99755i	−0.277726	+	0.248607i
$583$	−7.73149			−0.320206
$584$	12.9836			0.537265
$585$	−37.0714	−	27.9360i	−1.53272	−	1.15501i
$586$	31.3528			1.29517
$587$	−44.1578			−1.82259			−0.911293	−	0.411758i	$-0.864915\pi$
$587$	−44.1578			−1.82259			−0.911293	+	0.411758i	$0.864915\pi$
$588$	7.80592	+	2.56143i	0.321911	+	0.105631i
$589$	43.1337			1.77729
$590$	−4.04712	−	7.00982i	−0.166617	−	0.288590i
$591$	16.4452	−	14.7209i	0.676464	−	0.605537i
$592$	−1.35174	−	2.34128i	−0.0555561	−	0.0962259i
$593$	11.4553			0.470412			0.235206	−	0.971946i	$-0.424424\pi$
$593$	11.4553			0.470412			0.235206	+	0.971946i	$0.424424\pi$
$594$	−12.8027	−	17.9488i	−0.525302	−	0.736447i
$595$	0.156309	+	0.270735i	0.00640804	+	0.0110991i
$596$	13.3045			0.544975
$597$	−14.9740	−	4.91355i	−0.612845	−	0.201098i
$598$	12.5670	−	21.1927i	0.513901	−	0.866633i
$599$	12.8270	+	22.2171i	0.524099	+	0.907766i	0.999606	+	0.0280543i	$0.00893113\pi$
$599$	12.8270	+	22.2171i	0.524099	+	0.907766i	−0.475507	+	0.879712i	$0.657736\pi$
$600$	22.0795	+	7.24514i	0.901392	+	0.295782i
$601$	1.35828			0.0554053			0.0277026	−	0.999616i	$-0.491181\pi$
$601$	1.35828			0.0554053			0.0277026	+	0.999616i	$0.491181\pi$
$602$	4.34533	−	7.52632i	0.177102	−	0.306750i
$603$	−1.14683	+	10.3328i	−0.0467027	+	0.420783i
$604$	6.07725	−	10.5261i	0.247280	−	0.428301i
$605$	−15.0254	−	26.0248i	−0.610869	−	1.05806i
$606$	0.0589402	+	0.281313i	0.00239428	+	0.0114276i
$607$	4.77195			0.193688			0.0968438	−	0.995300i	$-0.469125\pi$
$607$	4.77195			0.193688			0.0968438	+	0.995300i	$0.469125\pi$
$608$	−2.87736	+	4.98373i	−0.116692	+	0.202117i
$609$	4.28970	−	3.83993i	0.173827	−	0.155602i
$610$	3.76581	−	6.52257i	0.152473	−	0.264091i
$611$	6.15486	−	10.3794i	0.248999	−	0.419907i
$612$	−0.0160476	+	0.144586i	−0.000648686	+	0.00584454i
$613$	7.76439	+	13.4483i	0.313601	+	0.543172i	0.979139	−	0.203191i	$-0.0651313\pi$
$613$	7.76439	+	13.4483i	0.313601	+	0.543172i	−0.665538	+	0.746364i	$0.731798\pi$
$614$	−9.56515			−0.386018
$615$	11.2485	+	53.6875i	0.453584	+	2.16489i
$616$	−3.18702	−	5.52008i	−0.128409	−	0.222410i
$617$	−1.04258			−0.0419727			−0.0209863	−	0.999780i	$-0.506681\pi$
$617$	−1.04258			−0.0419727			−0.0209863	+	0.999780i	$0.506681\pi$
$618$	−14.2753	+	12.7786i	−0.574237	+	0.514029i
$619$	16.1897	−	28.0413i	0.650718	−	1.12708i	−0.332231	−	0.943198i	$-0.607801\pi$
$619$	16.1897	−	28.0413i	0.650718	−	1.12708i	0.982949	−	0.183878i	$-0.0588652\pi$
$620$	16.0829	−	27.8565i	0.645906	−	1.11874i
$621$	−35.3444	+	3.40328i	−1.41832	+	0.136569i
$622$	0.316125	+	0.547545i	0.0126755	+	0.0219546i
$623$	0.433953	−	0.751629i	0.0173860	−	0.0301134i
$624$	−1.20936	−	6.12678i	−0.0484130	−	0.245268i
$625$	−43.9584	−	76.1383i	−1.75834	−	3.04553i
$626$	5.25048	−	9.09409i	0.209851	−	0.363473i
$627$	−40.1832	−	13.1857i	−1.60476	−	0.526585i
$628$	−4.11819	−	7.13291i	−0.164334	−	0.284634i
$629$	−0.131095			−0.00522710
$630$	−2.13352	+	19.2226i	−0.0850015	+	0.765848i
$631$	0.440036	−	0.762164i	0.0175175	−	0.0303413i	−0.857134	−	0.515094i	$-0.827757\pi$
$631$	0.440036	−	0.762164i	0.0175175	−	0.0303413i	0.874651	+	0.484753i	$0.161090\pi$
$632$	−4.24521	+	7.35292i	−0.168865	+	0.292483i
$633$	32.2517	+	10.5830i	1.28189	+	0.420638i
$634$	−9.36121	+	16.2141i	−0.371781	+	0.643944i
$635$	4.86449	−	8.42554i	0.193041	−	0.334358i
$636$	0.647217	+	3.08907i	0.0256638	+	0.122490i
$637$	−8.72282	+	14.7100i	−0.345611	+	0.582831i
$638$	9.38808			0.371678
$639$	−0.427383	+	3.85064i	−0.0169070	+	0.152329i
$640$	2.14571	+	3.71649i	0.0848168	+	0.146907i
$641$	−2.55527	−	4.42586i	−0.100927	−	0.174811i	0.811140	−	0.584852i	$-0.198848\pi$
$641$	−2.55527	−	4.42586i	−0.100927	−	0.174811i	−0.912067	+	0.410041i	$0.865514\pi$
$642$	−11.3363	+	10.1477i	−0.447407	+	0.400497i
$643$	−22.5308			−0.888528			−0.444264	−	0.895896i	$-0.646535\pi$
$643$	−22.5308			−0.888528			−0.444264	+	0.895896i	$0.646535\pi$
$644$	−10.2658			−0.404528
$645$	−40.8564	−	13.4066i	−1.60872	−	0.527884i
$646$	0.139527	+	0.241667i	0.00548960	+	0.00950827i
$647$	−2.31086	−	4.00252i	−0.0908492	−	0.157355i	0.817020	−	0.576610i	$-0.195625\pi$
$647$	−2.31086	−	4.00252i	−0.0908492	−	0.157355i	−0.907869	+	0.419255i	$0.862291\pi$
$648$	−6.09959	+	6.61778i	−0.239615	+	0.259971i
$649$	8.00278			0.314136
$650$	−24.6730	+	41.6080i	−0.967754	+	1.63200i
$651$	18.5309	+	6.08070i	0.726283	+	0.238322i
$652$	−1.74521	+	3.02279i	−0.0683476	+	0.118382i
$653$	18.3289	−	31.7465i	0.717264	−	1.24234i	−0.244815	−	0.969570i	$-0.578727\pi$
$653$	18.3289	−	31.7465i	0.717264	−	1.24234i	0.962080	−	0.272769i	$-0.0879393\pi$
$654$	−3.16614	−	15.1115i	−0.123806	−	0.590908i
$655$	23.0498	−	39.9234i	0.900629	−	1.55993i
$656$	−3.68986	+	6.39103i	−0.144065	+	0.249528i
$657$	35.6749	−	15.6354i	1.39181	−	0.609996i
$658$	−5.02782			−0.196005
$659$	−15.1961	−	26.3204i	−0.591957	−	1.02530i	−0.993969	−	0.109665i	$-0.965022\pi$
$659$	−15.1961	−	26.3204i	−0.591957	−	1.02530i	0.402012	−	0.915634i	$-0.368311\pi$
$660$	−23.4983	+	21.0345i	−0.914671	+	0.818768i
$661$	14.7804	−	25.6004i	0.574890	−	0.995739i	−0.421164	−	0.906985i	$-0.638378\pi$
$661$	14.7804	−	25.6004i	0.574890	−	0.995739i	0.996054	−	0.0887539i	$-0.0282885\pi$
$662$	−11.4289	−	19.7955i	−0.444199	−	0.769374i
$663$	−0.286614	−	0.0977613i	−0.0111312	−	0.00379673i
$664$	0.370694	−	0.642060i	0.0143857	−	0.0249168i
$665$	18.5500	+	32.1295i	0.719338	+	1.24593i
$666$	−6.53363	−	4.80528i	−0.253173	−	0.186201i
$667$	7.56003	−	13.0944i	0.292726	−	0.507016i
$668$	10.2219	−	17.7049i	0.395498	−	0.685022i
$669$	1.60813	+	7.67539i	0.0621740	+	0.296748i
$670$	14.8715			0.574538
$671$	3.72326	+	6.44887i	0.143735	+	0.248956i
$672$	−1.93873	+	1.73545i	−0.0747880	+	0.0669465i
$673$	4.77045			0.183887			0.0919437	−	0.995764i	$-0.470692\pi$
$673$	4.77045			0.183887			0.0919437	+	0.995764i	$0.470692\pi$
$674$	−17.2502	−	29.8782i	−0.664453	−	1.15087i
$675$	69.3925	−	6.68172i	2.67092	−	0.257180i
$676$	12.9965	+	0.302807i	0.499864	+	0.0116464i
$677$	13.6686	−	23.6747i	0.525327	−	0.909893i	−0.474238	−	0.880397i	$-0.657276\pi$
$677$	13.6686	−	23.6747i	0.525327	−	0.909893i	0.999565	−	0.0294965i	$-0.00939039\pi$
$678$	1.32213	+	6.31035i	0.0507762	+	0.242347i
$679$	−3.89967	+	6.75443i	−0.149656	+	0.259211i
$680$	0.208097			0.00798015
$681$	12.7875	−	11.4468i	0.490019	−	0.438641i
$682$	15.9012	+	27.5417i	0.608889	+	1.05463i
$683$	−0.345146	+	0.597811i	−0.0132066	+	0.0228746i	−0.872553	−	0.488519i	$-0.837537\pi$
$683$	−0.345146	+	0.597811i	−0.0132066	+	0.0228746i	0.859347	+	0.511394i	$0.170871\pi$
$684$	−1.90445	+	17.1588i	−0.0728186	+	0.656082i
$685$	25.5708	−	44.2900i	0.977011	−	1.69223i
$686$	17.6414			0.673553
$687$	−0.0935033	+	0.0836995i	−0.00356737	+	0.00319334i
$688$	−2.89251	−	5.00997i	−0.110276	−	0.191003i
$689$	−6.56960	−	0.0765228i	−0.250282	−	0.00291529i
$690$	10.4159	+	49.7138i	0.396528	+	1.89257i
$691$	−36.0393			−1.37100			−0.685501	−	0.728072i	$-0.740417\pi$
$691$	−36.0393			−1.37100			−0.685501	+	0.728072i	$0.740417\pi$
$692$	−5.88402	−	10.1914i	−0.223677	−	0.387420i
$693$	−15.4045	−	11.3295i	−0.585167	−	0.430373i
$694$	22.3954			0.850119
$695$	0.716618	+	1.24122i	0.0271829	+	0.0470821i
$696$	−0.785893	−	3.75096i	−0.0297892	−	0.142180i
$697$	0.178926	+	0.309909i	0.00677731	+	0.0117386i
$698$	27.8257			1.05322
$699$	−8.33203	−	39.7676i	−0.315146	−	1.50415i
$700$	20.1550			0.761787
$701$	−25.5695			−0.965748			−0.482874	−	0.875690i	$-0.660407\pi$
$701$	−25.5695			−0.965748			−0.482874	+	0.875690i	$0.660407\pi$
$702$	−10.7011	−	15.3781i	−0.403886	−	0.580410i
$703$	−15.5577			−0.586770
$704$	−4.24294			−0.159912
$705$	5.10136	+	24.3481i	0.192128	+	0.917002i
$706$	−37.0443			−1.39418
$707$	0.124645	+	0.215892i	0.00468778	+	0.00811947i
$708$	−0.669926	−	3.19746i	−0.0251774	−	0.120168i
$709$	2.04951	+	3.54985i	0.0769708	+	0.133317i	0.901942	−	0.431858i	$-0.142142\pi$
$709$	2.04951	+	3.54985i	0.0769708	+	0.133317i	−0.824971	+	0.565175i	$0.808809\pi$
$710$	5.54207			0.207990
$711$	−2.80980	+	25.3158i	−0.105376	+	0.949416i
$712$	−0.288865	−	0.500328i	−0.0108257	−	0.0187506i
$713$	51.2197			1.91819
$714$	0.0258741	+	0.123493i	0.000968313	+	0.00462162i
$715$	−32.1610	−	57.2337i	−1.20275	−	2.14042i
$716$	−0.270676	−	0.468825i	−0.0101157	−	0.0175208i
$717$	−3.92911	+	3.51715i	−0.146735	+	0.131350i
$718$	15.9020			0.593457
$719$	−20.6867	+	35.8304i	−0.771483	+	1.33625i	0.165268	+	0.986249i	$0.447151\pi$
$719$	−20.6867	+	35.8304i	−0.771483	+	1.33625i	−0.936750	+	0.349998i	$0.886182\pi$
$720$	10.3713	+	7.62778i	0.386516	+	0.284271i
$721$	−8.30875	+	14.3912i	−0.309434	+	0.535955i
$722$	7.05835	+	12.2254i	0.262685	+	0.454983i
$723$	5.14433	−	4.60495i	0.191320	−	0.171260i
$724$	−22.8671			−0.849848
$725$	−14.8428	+	25.7084i	−0.551247	+	0.954787i
$726$	−2.48718	−	11.8710i	−0.0923079	−	0.440573i
$727$	20.7179	−	35.8844i	0.768383	−	1.33088i	−0.170056	−	0.985434i	$-0.554395\pi$
$727$	20.7179	−	35.8844i	0.768383	−	1.33088i	0.938439	−	0.345445i	$-0.112272\pi$
$728$	−2.65344	−	4.72206i	−0.0983429	−	0.175011i
$729$	−8.79035	+	25.5290i	−0.325569	+	0.945518i
$730$	−27.8591	−	48.2534i	−1.03111	−	1.78594i
$731$	−0.280523			−0.0103755
$732$	2.26493	−	2.02745i	0.0837142	−	0.0749368i
$733$	12.8351	+	22.2310i	0.474074	+	0.821121i	0.999559	−	0.0296822i	$-0.00944952\pi$
$733$	12.8351	+	22.2310i	0.474074	+	0.821121i	−0.525485	+	0.850803i	$0.676116\pi$
$734$	−25.4758			−0.940330
$735$	−7.22978	−	34.5067i	−0.266674	−	1.27280i
$736$	−3.41675	+	5.91799i	−0.125943	+	0.218140i
$737$	−7.35175	+	12.7336i	−0.270805	+	0.469048i
$738$	−2.44223	+	22.0041i	−0.0898998	+	0.809980i
$739$	8.08326	+	14.0006i	0.297348	+	0.515021i	0.975528	−	0.219874i	$-0.0705646\pi$
$739$	8.08326	+	14.0006i	0.297348	+	0.515021i	−0.678181	+	0.734895i	$0.737231\pi$
$740$	−5.80088	+	10.0474i	−0.213245	+	0.369351i
$741$	−34.0140	−	11.6018i	−1.24953	−	0.426204i
$742$	1.36872	+	2.37069i	0.0502473	+	0.0870309i
$743$	6.93550	−	12.0126i	0.254439	−	0.440701i	−0.710304	−	0.703895i	$-0.751443\pi$
$743$	6.93550	−	12.0126i	0.254439	−	0.440701i	0.964743	+	0.263194i	$0.0847759\pi$
$744$	9.67301	−	8.65880i	0.354630	−	0.317447i
$745$	−28.5477	−	49.4461i	−1.04591	−	1.81156i
$746$	29.4233			1.07726
$747$	0.245353	−	2.21059i	0.00897701	−	0.0808812i
$748$	−0.102873	+	0.178181i	−0.00376140	+	0.00651494i
$749$	−6.59812	+	11.4283i	−0.241090	+	0.417580i
$750$	−12.8286	−	61.2291i	−0.468434	−	2.23577i
$751$	−5.85703	+	10.1447i	−0.213726	+	0.370184i	−0.952878	−	0.303355i	$-0.901893\pi$
$751$	−5.85703	+	10.1447i	−0.213726	+	0.370184i	0.739152	+	0.673539i	$0.235227\pi$
$752$	−1.67341	+	2.89842i	−0.0610228	+	0.105695i
$753$	23.8866	+	7.83811i	0.870475	+	0.285637i
$754$	7.97724	+	0.0929191i	0.290514	+	0.00338391i
$755$	−52.1602			−1.89830
$756$	−3.23711	+	7.10318i	−0.117732	+	0.258340i
$757$	1.02202	+	1.77019i	0.0371459	+	0.0643386i	0.884001	−	0.467486i	$-0.154840\pi$
$757$	1.02202	+	1.77019i	0.0371459	+	0.0643386i	−0.846855	+	0.531824i	$0.821507\pi$
$758$	−15.6605	−	27.1247i	−0.568814	−	0.985215i
$759$	−47.7160	−	15.6575i	−1.73198	−	0.568331i
$760$	24.6959			0.895816
$761$	22.6436			0.820831			0.410415	−	0.911899i	$-0.365384\pi$
$761$	22.6436			0.820831			0.410415	+	0.911899i	$0.365384\pi$
$762$	2.92573	−	2.61897i	0.105988	−	0.0948751i
$763$	−6.69569	−	11.5973i	−0.242400	−	0.419849i
$764$	3.02741	+	5.24364i	0.109528	+	0.189708i
$765$	0.571786	−	0.250600i	0.0206730	−	0.00906045i
$766$	9.84210			0.355610
$767$	6.80012	+	0.0792079i	0.245538	+	0.00286003i

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.355184 + 1.69524i) q^{3} +1.00000 q^{4} +(-2.14571 - 3.71649i) q^{5} +(-0.355184 - 1.69524i) q^{6} +(-0.751135 - 1.30100i) q^{7} -1.00000 q^{8} +(-2.74769 + 1.20424i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.355184 + 1.69524i) q^{3} +1.00000 q^{4} +(-2.14571 - 3.71649i) q^{5} +(-0.355184 - 1.69524i) q^{6} +(-0.751135 - 1.30100i) q^{7} -1.00000 q^{8} +(-2.74769 + 1.20424i) q^{9} +(2.14571 + 3.71649i) q^{10} -4.24294 q^{11} +(0.355184 + 1.69524i) q^{12} +(-3.60531 - 0.0419947i) q^{13} +(0.751135 + 1.30100i) q^{14} +(5.53822 - 4.95754i) q^{15} +1.00000 q^{16} +(0.0242456 - 0.0419947i) q^{17} +(2.74769 - 1.20424i) q^{18} +(2.87736 - 4.98373i) q^{19} +(-2.14571 - 3.71649i) q^{20} +(1.93873 - 1.73545i) q^{21} +4.24294 q^{22} +(3.41675 - 5.91799i) q^{23} +(-0.355184 - 1.69524i) q^{24} +(-6.70818 + 11.6189i) q^{25} +(3.60531 + 0.0419947i) q^{26} +(-3.01742 - 4.23027i) q^{27} +(-0.751135 - 1.30100i) q^{28} +2.21264 q^{29} +(-5.53822 + 4.95754i) q^{30} +(3.74769 + 6.49119i) q^{31} -1.00000 q^{32} +(-1.50702 - 7.19280i) q^{33} +(-0.0242456 + 0.0419947i) q^{34} +(-3.22344 + 5.58317i) q^{35} +(-2.74769 + 1.20424i) q^{36} +(-1.35174 - 2.34128i) q^{37} +(-2.87736 + 4.98373i) q^{38} +(-1.20936 - 6.12678i) q^{39} +(2.14571 + 3.71649i) q^{40} +(-3.68986 + 6.39103i) q^{41} +(-1.93873 + 1.73545i) q^{42} +(-2.89251 - 5.00997i) q^{43} -4.24294 q^{44} +(10.3713 + 7.62778i) q^{45} +(-3.41675 + 5.91799i) q^{46} +(-1.67341 + 2.89842i) q^{47} +(0.355184 + 1.69524i) q^{48} +(2.37159 - 4.10772i) q^{49} +(6.70818 - 11.6189i) q^{50} +(0.0798028 + 0.0261864i) q^{51} +(-3.60531 - 0.0419947i) q^{52} +1.82220 q^{53} +(3.01742 + 4.23027i) q^{54} +(9.10413 + 15.7688i) q^{55} +(0.751135 + 1.30100i) q^{56} +(9.47061 + 3.10767i) q^{57} -2.21264 q^{58} -1.88614 q^{59} +(5.53822 - 4.95754i) q^{60} +(-0.877519 - 1.51991i) q^{61} +(-3.74769 - 6.49119i) q^{62} +(3.63061 + 2.67021i) q^{63} +1.00000 q^{64} +(7.57989 + 13.4892i) q^{65} +(1.50702 + 7.19280i) q^{66} +(1.73270 - 3.00113i) q^{67} +(0.0242456 - 0.0419947i) q^{68} +(11.2460 + 3.69025i) q^{69} +(3.22344 - 5.58317i) q^{70} +(0.645714 - 1.11841i) q^{71} +(2.74769 - 1.20424i) q^{72} -12.9836 q^{73} +(1.35174 + 2.34128i) q^{74} +(-22.0795 - 7.24514i) q^{75} +(2.87736 - 4.98373i) q^{76} +(3.18702 + 5.52008i) q^{77} +(1.20936 + 6.12678i) q^{78} +(4.24521 - 7.35292i) q^{79} +(-2.14571 - 3.71649i) q^{80} +(6.09959 - 6.61778i) q^{81} +(3.68986 - 6.39103i) q^{82} +(-0.370694 + 0.642060i) q^{83} +(1.93873 - 1.73545i) q^{84} -0.208097 q^{85} +(2.89251 + 5.00997i) q^{86} +(0.785893 + 3.75096i) q^{87} +4.24294 q^{88} +(0.288865 + 0.500328i) q^{89} +(-10.3713 - 7.62778i) q^{90} +(2.65344 + 4.72206i) q^{91} +(3.41675 - 5.91799i) q^{92} +(-9.67301 + 8.65880i) q^{93} +(1.67341 - 2.89842i) q^{94} -24.6959 q^{95} +(-0.355184 - 1.69524i) q^{96} +(-2.59585 - 4.49614i) q^{97} +(-2.37159 + 4.10772i) q^{98} +(11.6583 - 5.10953i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{4} - 3 q^{5} + q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 12 * q^4 - 3 * q^5 + q^7 - 12 * q^8 + 4 * q^9	\( 12 q - 12 q^{2} + 12 q^{4} - 3 q^{5} + q^{7} - 12 q^{8} + 4 q^{9} + 3 q^{10} - 8 q^{11} - 5 q^{13} - q^{14} + 11 q^{15} + 12 q^{16} - q^{17} - 4 q^{18} + 9 q^{19} - 3 q^{20} + 8 q^{21} + 8 q^{22} + 7 q^{23} - q^{25} + 5 q^{26} - 9 q^{27} + q^{28} - 2 q^{29} - 11 q^{30} + 8 q^{31} - 12 q^{32} - 4 q^{33} + q^{34} - 3 q^{35} + 4 q^{36} + 15 q^{37} - 9 q^{38} + 18 q^{39} + 3 q^{40} - 19 q^{41} - 8 q^{42} - 2 q^{43} - 8 q^{44} - 5 q^{45} - 7 q^{46} - 23 q^{47} - 27 q^{49} + q^{50} + 8 q^{51} - 5 q^{52} - 4 q^{53} + 9 q^{54} + 24 q^{55} - q^{56} - 16 q^{57} + 2 q^{58} + 8 q^{59} + 11 q^{60} - 8 q^{61} - 8 q^{62} + 12 q^{64} + 7 q^{65} + 4 q^{66} + 14 q^{67} - q^{68} - 6 q^{69} + 3 q^{70} - 15 q^{71} - 4 q^{72} - 90 q^{73} - 15 q^{74} - 56 q^{75} + 9 q^{76} + 4 q^{77} - 18 q^{78} - 12 q^{79} - 3 q^{80} + 28 q^{81} + 19 q^{82} + 24 q^{83} + 8 q^{84} - 14 q^{85} + 2 q^{86} + 36 q^{87} + 8 q^{88} + 23 q^{89} + 5 q^{90} + 8 q^{91} + 7 q^{92} + 6 q^{93} + 23 q^{94} + 14 q^{95} - 4 q^{97} + 27 q^{98} + 31 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^4 - 3 * q^5 + q^7 - 12 * q^8 + 4 * q^9 + 3 * q^10 - 8 * q^11 - 5 * q^13 - q^14 + 11 * q^15 + 12 * q^16 - q^17 - 4 * q^18 + 9 * q^19 - 3 * q^20 + 8 * q^21 + 8 * q^22 + 7 * q^23 - q^25 + 5 * q^26 - 9 * q^27 + q^28 - 2 * q^29 - 11 * q^30 + 8 * q^31 - 12 * q^32 - 4 * q^33 + q^34 - 3 * q^35 + 4 * q^36 + 15 * q^37 - 9 * q^38 + 18 * q^39 + 3 * q^40 - 19 * q^41 - 8 * q^42 - 2 * q^43 - 8 * q^44 - 5 * q^45 - 7 * q^46 - 23 * q^47 - 27 * q^49 + q^50 + 8 * q^51 - 5 * q^52 - 4 * q^53 + 9 * q^54 + 24 * q^55 - q^56 - 16 * q^57 + 2 * q^58 + 8 * q^59 + 11 * q^60 - 8 * q^61 - 8 * q^62 + 12 * q^64 + 7 * q^65 + 4 * q^66 + 14 * q^67 - q^68 - 6 * q^69 + 3 * q^70 - 15 * q^71 - 4 * q^72 - 90 * q^73 - 15 * q^74 - 56 * q^75 + 9 * q^76 + 4 * q^77 - 18 * q^78 - 12 * q^79 - 3 * q^80 + 28 * q^81 + 19 * q^82 + 24 * q^83 + 8 * q^84 - 14 * q^85 + 2 * q^86 + 36 * q^87 + 8 * q^88 + 23 * q^89 + 5 * q^90 + 8 * q^91 + 7 * q^92 + 6 * q^93 + 23 * q^94 + 14 * q^95 - 4 * q^97 + 27 * q^98 + 31 * q^99

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