LMFDB - Embedded newform 234.2.y.a.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(11,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 7]))

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

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

chi := DirichletCharacter("234.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (of order $12$, degree $4$, 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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	234.11
Dual form			234.2.y.a.149.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.04323 + 1.38263i) q^{3} -1.00000i q^{4} +(1.62665 + 0.435860i) q^{5} +(1.71534 + 0.239994i) q^{6} +(0.290365 + 0.0778030i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.823344 + 2.88481i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.04323 + 1.38263i) q^{3} -1.00000i q^{4} +(1.62665 + 0.435860i) q^{5} +(1.71534 + 0.239994i) q^{6} +(0.290365 + 0.0778030i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.823344 + 2.88481i) q^{9} +(1.45842 - 0.842018i) q^{10} +(-1.12392 - 1.12392i) q^{11} +(1.38263 - 1.04323i) q^{12} +(-3.56563 + 0.535061i) q^{13} +(0.260334 - 0.150304i) q^{14} +(1.09434 + 2.70377i) q^{15} -1.00000 q^{16} +(1.26545 - 2.19182i) q^{17} +(1.45767 + 2.62206i) q^{18} +(4.16702 - 1.11655i) q^{19} +(0.435860 - 1.62665i) q^{20} +(0.195344 + 0.482634i) q^{21} -1.58947 q^{22} +(0.660949 - 1.14480i) q^{23} +(0.239994 - 1.71534i) q^{24} +(-1.87410 - 1.08201i) q^{25} +(-2.14293 + 2.89963i) q^{26} +(-4.84756 + 1.87113i) q^{27} +(0.0778030 - 0.290365i) q^{28} -7.48368i q^{29} +(2.68566 + 1.13804i) q^{30} +(-2.78151 + 10.3807i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.381463 - 2.72648i) q^{33} +(-0.655045 - 2.44466i) q^{34} +(0.438411 + 0.253117i) q^{35} +(2.88481 + 0.823344i) q^{36} +(-2.37887 - 0.637416i) q^{37} +(2.15701 - 3.73605i) q^{38} +(-4.45956 - 4.37176i) q^{39} +(-0.842018 - 1.45842i) q^{40} +(-0.974309 - 3.63617i) q^{41} +(0.479403 + 0.203145i) q^{42} +(-6.42917 + 3.71188i) q^{43} +(-1.12392 + 1.12392i) q^{44} +(-2.59667 + 4.33371i) q^{45} +(-0.342133 - 1.27686i) q^{46} +(3.46610 - 0.928739i) q^{47} +(-1.04323 - 1.38263i) q^{48} +(-5.98392 - 3.45482i) q^{49} +(-2.09029 + 0.560091i) q^{50} +(4.35064 - 0.536923i) q^{51} +(0.535061 + 3.56563i) q^{52} -3.63112i q^{53} +(-2.10465 + 4.75083i) q^{54} +(-1.33836 - 2.31811i) q^{55} +(-0.150304 - 0.260334i) q^{56} +(5.89093 + 4.59664i) q^{57} +(-5.29176 - 5.29176i) q^{58} +(-0.512425 - 0.512425i) q^{59} +(2.70377 - 1.09434i) q^{60} +(5.62852 + 9.74888i) q^{61} +(5.37346 + 9.30710i) q^{62} +(-0.463517 + 0.773587i) q^{63} +1.00000i q^{64} +(-6.03325 - 0.683757i) q^{65} +(-1.65818 - 2.19765i) q^{66} +(0.943886 - 0.252913i) q^{67} +(-2.19182 - 1.26545i) q^{68} +(2.27236 - 0.280437i) q^{69} +(0.488984 - 0.131023i) q^{70} +(1.84126 + 6.87167i) q^{71} +(2.62206 - 1.45767i) q^{72} +(3.38109 - 3.38109i) q^{73} +(-2.13284 + 1.23139i) q^{74} +(-0.459092 - 3.71998i) q^{75} +(-1.11655 - 4.16702i) q^{76} +(-0.238903 - 0.413792i) q^{77} +(-6.24469 + 0.0620844i) q^{78} +(-3.69530 + 6.40045i) q^{79} +(-1.62665 - 0.435860i) q^{80} +(-7.64421 - 4.75038i) q^{81} +(-3.26010 - 1.88222i) q^{82} +(3.18219 + 11.8761i) q^{83} +(0.482634 - 0.195344i) q^{84} +(3.01378 - 3.01378i) q^{85} +(-1.92141 + 7.17081i) q^{86} +(10.3472 - 7.80720i) q^{87} +1.58947i q^{88} +(0.512119 - 1.91125i) q^{89} +(1.22828 + 4.90052i) q^{90} +(-1.07696 - 0.122054i) q^{91} +(-1.14480 - 0.660949i) q^{92} +(-17.2545 + 6.98367i) q^{93} +(1.79419 - 3.10762i) q^{94} +7.26495 q^{95} +(-1.71534 - 0.239994i) q^{96} +(1.61645 - 6.03268i) q^{97} +(-6.67419 + 1.78835i) q^{98} +(4.16768 - 2.31693i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7}+O(q^{10}) $ 56 * q + 4 * q^7	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.04323	+	1.38263i	0.602309	+	0.798263i
$3$	1.04323	+	1.38263i	0.602309	+	0.798263i
$4$		−	1.00000i		−	0.500000i
$5$	1.62665	+	0.435860i	0.727461	+	0.194923i	0.603498	−	0.797364i	$-0.293773\pi$
$5$	1.62665	+	0.435860i	0.727461	+	0.194923i	0.123963	+	0.992287i	$0.460440\pi$
$6$	1.71534	+	0.239994i	0.700286	+	0.0979772i
$7$	0.290365	+	0.0778030i	0.109748	+	0.0294068i	0.313275	−	0.949663i	$-0.398574\pi$
$7$	0.290365	+	0.0778030i	0.109748	+	0.0294068i	−0.203527	+	0.979069i	$0.565241\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−0.823344	+	2.88481i	−0.274448	+	0.961602i
$10$	1.45842	−	0.842018i	0.461192	−	0.266269i
$11$	−1.12392	−	1.12392i	−0.338876	−	0.338876i	0.517068	−	0.855944i	$-0.327023\pi$
$11$	−1.12392	−	1.12392i	−0.338876	−	0.338876i	−0.855944	+	0.517068i	$0.827023\pi$
$12$	1.38263	−	1.04323i	0.399132	−	0.301154i
$13$	−3.56563	+	0.535061i	−0.988928	+	0.148399i
$13$	−3.56563	+	0.535061i	−0.988928	+	0.148399i
$14$	0.260334	−	0.150304i	0.0695771	−	0.0401704i
$15$	1.09434	+	2.70377i	0.282557	+	0.698109i
$16$	−1.00000			−0.250000
$17$	1.26545	−	2.19182i	0.306917	−	0.531595i	−0.670770	−	0.741666i	$-0.734036\pi$
$17$	1.26545	−	2.19182i	0.306917	−	0.531595i	0.977686	+	0.210071i	$0.0673694\pi$
$18$	1.45767	+	2.62206i	0.343577	+	0.618025i
$19$	4.16702	−	1.11655i	0.955980	−	0.256154i	0.253082	−	0.967445i	$-0.418556\pi$
$19$	4.16702	−	1.11655i	0.955980	−	0.256154i	0.702898	+	0.711291i	$0.251889\pi$
$20$	0.435860	−	1.62665i	0.0974613	−	0.363731i
$21$	0.195344	+	0.482634i	0.0426276	+	0.105319i
$22$	−1.58947			−0.338876
$23$	0.660949	−	1.14480i	0.137817	−	0.238707i	−0.788853	−	0.614582i	$-0.789325\pi$
$23$	0.660949	−	1.14480i	0.137817	−	0.238707i	0.926670	+	0.375875i	$0.122658\pi$
$24$	0.239994	−	1.71534i	0.0489886	−	0.350143i
$25$	−1.87410	−	1.08201i	−0.374820	−	0.216403i
$26$	−2.14293	+	2.89963i	−0.420264	+	0.568663i
$27$	−4.84756	+	1.87113i	−0.932914	+	0.360099i
$28$	0.0778030	−	0.290365i	0.0147034	−	0.0548738i
$29$		−	7.48368i		−	1.38969i	−0.719162	−	0.694843i	$-0.755474\pi$
$29$		−	7.48368i		−	1.38969i	0.719162	−	0.694843i	$-0.244526\pi$
$30$	2.68566	+	1.13804i	0.490333	+	0.207776i
$31$	−2.78151	+	10.3807i	−0.499573	+	1.86443i	0.00316697	+	0.999995i	$0.498992\pi$
$31$	−2.78151	+	10.3807i	−0.499573	+	1.86443i	−0.502740	+	0.864438i	$0.667675\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.381463	−	2.72648i	0.0664042	−	0.474620i
$34$	−0.655045	−	2.44466i	−0.112339	−	0.419256i
$35$	0.438411	+	0.253117i	0.0741050	+	0.0427846i
$36$	2.88481	+	0.823344i	0.480801	+	0.137224i
$37$	−2.37887	−	0.637416i	−0.391084	−	0.104791i	0.0579183	−	0.998321i	$-0.481554\pi$
$37$	−2.37887	−	0.637416i	−0.391084	−	0.104791i	−0.449002	+	0.893531i	$0.648220\pi$
$38$	2.15701	−	3.73605i	0.349913	−	0.606067i
$39$	−4.45956	−	4.37176i	−0.714102	−	0.700042i
$40$	−0.842018	−	1.45842i	−0.133135	−	0.230596i
$41$	−0.974309	−	3.63617i	−0.152161	−	0.567874i	−0.999332	−	0.0365529i	$-0.988362\pi$
$41$	−0.974309	−	3.63617i	−0.152161	−	0.567874i	0.847170	−	0.531322i	$-0.178304\pi$
$42$	0.479403	+	0.203145i	0.0739735	+	0.0313459i
$43$	−6.42917	+	3.71188i	−0.980439	+	0.566057i	−0.902403	−	0.430894i	$-0.858198\pi$
$43$	−6.42917	+	3.71188i	−0.980439	+	0.566057i	−0.0780366	+	0.996950i	$0.524865\pi$
$44$	−1.12392	+	1.12392i	−0.169438	+	0.169438i
$45$	−2.59667	+	4.33371i	−0.387088	+	0.646032i
$46$	−0.342133	−	1.27686i	−0.0504447	−	0.188262i
$47$	3.46610	−	0.928739i	0.505583	−	0.135470i	0.00299296	−	0.999996i	$-0.499047\pi$
$47$	3.46610	−	0.928739i	0.505583	−	0.135470i	0.502590	+	0.864525i	$0.332381\pi$
$48$	−1.04323	−	1.38263i	−0.150577	−	0.199566i
$49$	−5.98392	−	3.45482i	−0.854846	−	0.493545i
$50$	−2.09029	+	0.560091i	−0.295611	+	0.0792088i
$51$	4.35064	−	0.536923i	0.609212	−	0.0751843i
$52$	0.535061	+	3.56563i	0.0741997	+	0.494464i
$53$		−	3.63112i		−	0.498772i	−0.968404	−	0.249386i	$-0.919771\pi$
$53$		−	3.63112i		−	0.498772i	0.968404	−	0.249386i	$-0.0802288\pi$
$54$	−2.10465	+	4.75083i	−0.286407	+	0.646507i
$55$	−1.33836	−	2.31811i	−0.180464	−	0.312574i
$56$	−0.150304	−	0.260334i	−0.0200852	−	0.0347886i
$57$	5.89093	+	4.59664i	0.780273	+	0.608840i
$58$	−5.29176	−	5.29176i	−0.694843	−	0.694843i
$59$	−0.512425	−	0.512425i	−0.0667121	−	0.0667121i	0.672964	−	0.739676i	$-0.265021\pi$
$59$	−0.512425	−	0.512425i	−0.0667121	−	0.0667121i	−0.739676	+	0.672964i	$0.765021\pi$
$60$	2.70377	−	1.09434i	0.349055	−	0.141278i
$61$	5.62852	+	9.74888i	0.720658	+	1.24822i	0.960736	+	0.277463i	$0.0894935\pi$
$61$	5.62852	+	9.74888i	0.720658	+	1.24822i	−0.240078	+	0.970754i	$0.577173\pi$
$62$	5.37346	+	9.30710i	0.682430	+	1.18200i
$63$	−0.463517	+	0.773587i	−0.0583976	+	0.0974628i
$64$			1.00000i			0.125000i
$65$	−6.03325	−	0.683757i	−0.748333	−	0.0848096i
$66$	−1.65818	−	2.19765i	−0.204108	−	0.270512i
$67$	0.943886	−	0.252913i	0.115314	−	0.0308983i	−0.200701	−	0.979653i	$-0.564322\pi$
$67$	0.943886	−	0.252913i	0.115314	−	0.0308983i	0.316015	+	0.948754i	$0.397655\pi$
$68$	−2.19182	−	1.26545i	−0.265798	−	0.153458i
$69$	2.27236	−	0.280437i	0.273560	−	0.0337606i
$70$	0.488984	−	0.131023i	0.0584448	−	0.0156602i
$71$	1.84126	+	6.87167i	0.218517	+	0.815518i	0.984899	+	0.173132i	$0.0553887\pi$
$71$	1.84126	+	6.87167i	0.218517	+	0.815518i	−0.766381	+	0.642386i	$0.777945\pi$
$72$	2.62206	−	1.45767i	0.309013	−	0.171788i
$73$	3.38109	−	3.38109i	0.395727	−	0.395727i	−0.480996	−	0.876723i	$-0.659725\pi$
$73$	3.38109	−	3.38109i	0.395727	−	0.395727i	0.876723	+	0.480996i	$0.159725\pi$
$74$	−2.13284	+	1.23139i	−0.247937	+	0.143147i
$75$	−0.459092	−	3.71998i	−0.0530113	−	0.429546i
$76$	−1.11655	−	4.16702i	−0.128077	−	0.477990i
$77$	−0.238903	−	0.413792i	−0.0272255	−	0.0471560i
$78$	−6.24469	+	0.0620844i	−0.707072	+	0.00702967i
$79$	−3.69530	+	6.40045i	−0.415754	+	0.720107i	−0.995507	−	0.0946854i	$-0.969815\pi$
$79$	−3.69530	+	6.40045i	−0.415754	+	0.720107i	0.579754	+	0.814792i	$0.303149\pi$
$80$	−1.62665	−	0.435860i	−0.181865	−	0.0487307i
$81$	−7.64421	−	4.75038i	−0.849356	−	0.527820i
$82$	−3.26010	−	1.88222i	−0.360018	−	0.207856i
$83$	3.18219	+	11.8761i	0.349291	+	1.30357i	0.887518	+	0.460773i	$0.152428\pi$
$83$	3.18219	+	11.8761i	0.349291	+	1.30357i	−0.538227	+	0.842800i	$0.680906\pi$
$84$	0.482634	−	0.195344i	0.0526597	−	0.0213138i
$85$	3.01378	−	3.01378i	0.326890	−	0.326890i
$86$	−1.92141	+	7.17081i	−0.207191	+	0.773248i
$87$	10.3472	−	7.80720i	1.10933	−	0.837020i
$88$			1.58947i			0.169438i
$89$	0.512119	−	1.91125i	0.0542845	−	0.202592i	−0.933457	−	0.358688i	$-0.883224\pi$
$89$	0.512119	−	1.91125i	0.0542845	−	0.202592i	0.987742	+	0.156096i	$0.0498908\pi$
$90$	1.22828	+	4.90052i	0.129472	+	0.516560i
$91$	−1.07696	−	0.122054i	−0.112896	−	0.0127947i
$92$	−1.14480	−	0.660949i	−0.119353	−	0.0689087i
$93$	−17.2545	+	6.98367i	−1.78921	+	0.724173i
$94$	1.79419	−	3.10762i	0.185056	−	0.320527i
$95$	7.26495			0.745368
$96$	−1.71534	−	0.239994i	−0.175071	−	0.0244943i
$97$	1.61645	−	6.03268i	0.164126	−	0.612526i	−0.834024	−	0.551728i	$-0.813969\pi$
$97$	1.61645	−	6.03268i	0.164126	−	0.612526i	0.998150	−	0.0607982i	$-0.0193646\pi$
$98$	−6.67419	+	1.78835i	−0.674196	+	0.180650i
$99$	4.16768	−	2.31693i	0.418868	−	0.232860i
$100$	−1.08201	+	1.87410i	−0.108201	+	0.187410i
$101$	8.59259			0.854995			0.427498	−	0.904017i	$-0.359395\pi$
$101$	8.59259			0.854995			0.427498	+	0.904017i	$0.359395\pi$
$102$	2.69671	−	3.45603i	0.267014	−	0.342198i
$103$	0.228107	−	0.131698i	0.0224761	−	0.0129766i	−0.488720	−	0.872441i	$-0.662536\pi$
$103$	0.228107	−	0.131698i	0.0224761	−	0.0129766i	0.511196	+	0.859464i	$0.329203\pi$
$104$	2.89963	+	2.14293i	0.284332	+	0.210132i
$105$	0.107396	+	0.870221i	0.0104808	+	0.0849248i
$106$	−2.56759	−	2.56759i	−0.249386	−	0.249386i
$107$	11.4443	−	6.60737i	1.10636	−	0.638759i	0.168478	−	0.985705i	$-0.446115\pi$
$107$	11.4443	−	6.60737i	1.10636	−	0.638759i	0.937885	+	0.346947i	$0.112782\pi$
$108$	1.87113	+	4.84756i	0.180050	+	0.466457i
$109$	11.1164	+	11.1164i	1.06475	+	1.06475i	0.997753	+	0.0670011i	$0.0213431\pi$
$109$	11.1164	+	11.1164i	1.06475	+	1.06475i	0.0670011	+	0.997753i	$0.478657\pi$
$110$	−2.58551	−	0.692786i	−0.246519	−	0.0660546i
$111$	−1.60039	−	3.95407i	−0.151903	−	0.375304i
$112$	−0.290365	−	0.0778030i	−0.0274369	−	0.00735169i
$113$		−	9.74067i		−	0.916325i	−0.888868	−	0.458163i	$-0.848508\pi$
$113$		−	9.74067i		−	0.916325i	0.888868	−	0.458163i	$-0.151492\pi$
$114$	7.41583	−	0.915206i	0.694556	−	0.0857169i
$115$	1.57411	−	1.57411i	0.146786	−	0.146786i
$116$	−7.48368			−0.694843
$117$	1.39219	−	10.7267i	0.128708	−	0.991683i
$118$	−0.724678			−0.0667121
$119$	0.537972	−	0.537972i	0.0493158	−	0.0493158i
$120$	1.13804	−	2.68566i	0.103888	−	0.245166i
$121$		−	8.47359i		−	0.770326i
$122$	10.8735	+	2.91354i	0.984437	+	0.263779i
$123$	4.01106	−	5.14047i	0.361665	−	0.463501i
$124$	10.3807	+	2.78151i	0.932216	+	0.249787i
$125$	−8.53087	−	8.53087i	−0.763024	−	0.763024i
$126$	0.219253	+	0.874764i	0.0195326	+	0.0779302i
$127$	15.1666	−	8.75644i	1.34582	−	0.777009i	0.358164	−	0.933659i	$-0.383403\pi$
$127$	15.1666	−	8.75644i	1.34582	−	0.777009i	0.987654	+	0.156650i	$0.0500694\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−11.8393	−	5.01683i	−1.04239	−	0.441708i
$130$	−4.74964	+	3.78266i	−0.416571	+	0.331762i
$131$	13.4168	−	7.74619i	1.17223	−	0.676788i	0.218027	−	0.975943i	$-0.430038\pi$
$131$	13.4168	−	7.74619i	1.17223	−	0.676788i	0.954205	+	0.299155i	$0.0967047\pi$
$132$	−2.72648	−	0.381463i	−0.237310	−	0.0332021i
$133$	1.29683			0.112449
$134$	0.488591	−	0.846265i	0.0422079	−	0.0731062i
$135$	−8.70085	+	0.930822i	−0.748850	+	0.0801124i
$136$	−2.44466	+	0.655045i	−0.209628	+	0.0561697i
$137$	−5.53629	+	20.6617i	−0.472997	+	1.76525i	0.155913	+	0.987771i	$0.450168\pi$
$137$	−5.53629	+	20.6617i	−0.472997	+	1.76525i	−0.628910	+	0.777478i	$0.716499\pi$
$138$	1.40850	−	1.80510i	0.119899	−	0.153660i
$139$	9.22919			0.782810			0.391405	−	0.920219i	$-0.371989\pi$
$139$	9.22919			0.782810			0.391405	+	0.920219i	$0.371989\pi$
$140$	0.253117	−	0.438411i	0.0213923	−	0.0370525i
$141$	4.90004	+	3.82345i	0.412658	+	0.321993i
$142$	6.16098	+	3.55704i	0.517018	+	0.298500i
$143$	4.60886	+	3.40613i	0.385413	+	0.284835i
$144$	0.823344	−	2.88481i	0.0686120	−	0.240400i
$145$	3.26184	−	12.1734i	0.270881	−	1.01094i
$146$		−	4.78159i		−	0.395727i
$147$	−1.46586	−	11.8777i	−0.120902	−	0.979659i
$148$	−0.637416	+	2.37887i	−0.0523953	+	0.195542i
$149$	−15.7059	+	15.7059i	−1.28668	+	1.28668i	−0.349891	+	0.936790i	$0.613781\pi$
$149$	−15.7059	+	15.7059i	−1.28668	+	1.28668i	−0.936790	+	0.349891i	$0.886219\pi$
$150$	−2.95505	−	2.30580i	−0.241279	−	0.188268i
$151$	4.46564	+	16.6660i	0.363409	+	1.35626i	0.869565	+	0.493818i	$0.164399\pi$
$151$	4.46564	+	16.6660i	0.363409	+	1.35626i	−0.506157	+	0.862441i	$0.668934\pi$
$152$	−3.73605	−	2.15701i	−0.303033	−	0.174956i
$153$	5.28108	+	5.45520i	0.426950	+	0.441027i
$154$	−0.461525	−	0.123665i	−0.0371908	−	0.00996524i
$155$	−9.04909	+	15.6735i	−0.726840	+	1.25892i
$156$	−4.37176	+	4.45956i	−0.350021	+	0.357051i
$157$	0.300573	+	0.520608i	0.0239884	+	0.0415490i	0.877770	−	0.479082i	$-0.159030\pi$
$157$	0.300573	+	0.520608i	0.0239884	+	0.0415490i	−0.853782	+	0.520631i	$0.825697\pi$
$158$	1.91283	+	7.13877i	0.152176	+	0.567930i
$159$	5.02050	−	3.78809i	0.398151	−	0.300415i
$160$	−1.45842	+	0.842018i	−0.115298	+	0.0665673i
$161$	0.280985	−	0.280985i	0.0221447	−	0.0221447i
$162$	−8.76430	+	2.04625i	−0.688588	+	0.160768i
$163$	0.929908	+	3.47046i	0.0728360	+	0.271828i	0.992734	−	0.120330i	$-0.0383953\pi$
$163$	0.929908	+	3.47046i	0.0728360	+	0.271828i	−0.919898	+	0.392158i	$0.871729\pi$
$164$	−3.63617	+	0.974309i	−0.283937	+	0.0760807i
$165$	1.80887	−	4.26878i	0.140821	−	0.332324i
$166$	10.6478	+	6.14753i	0.826432	+	0.477141i
$167$	−8.72138	+	2.33689i	−0.674881	+	0.180834i	−0.579952	−	0.814650i	$-0.696929\pi$
$167$	−8.72138	+	2.33689i	−0.674881	+	0.180834i	−0.0949283	+	0.995484i	$0.530262\pi$
$168$	0.203145	−	0.479403i	0.0156729	−	0.0369867i
$169$	12.4274	−	3.81566i	0.955955	−	0.293512i
$170$		−	4.26212i		−	0.326890i
$171$	−0.209864	+	12.9403i	−0.0160487	+	0.989573i
$172$	3.71188	+	6.42917i	0.283028	+	0.490220i
$173$	−7.86600	−	13.6243i	−0.598041	−	1.03584i	−0.993110	−	0.117186i	$-0.962613\pi$
$173$	−7.86600	−	13.6243i	−0.598041	−	1.03584i	0.395069	−	0.918651i	$-0.370721\pi$
$174$	1.79604	−	12.8371i	0.136157	−	0.973177i
$175$	−0.459989	−	0.459989i	−0.0347719	−	0.0347719i
$176$	1.12392	+	1.12392i	0.0847190	+	0.0847190i
$177$	0.173919	−	1.24307i	0.0130725	−	0.0934350i
$178$	−0.989338	−	1.71358i	−0.0741540	−	0.128438i
$179$	3.29562	+	5.70819i	0.246326	+	0.426650i	0.962504	−	0.271268i	$-0.0874431\pi$
$179$	3.29562	+	5.70819i	0.246326	+	0.426650i	−0.716177	+	0.697918i	$0.754110\pi$
$180$	4.33371	+	2.59667i	0.323016	+	0.193544i
$181$			11.2750i			0.838063i	0.907972	+	0.419031i	$0.137630\pi$
$181$			11.2750i			0.838063i	−0.907972	+	0.419031i	$0.862370\pi$
$182$	−0.847832	+	0.675222i	−0.0628455	+	0.0500508i
$183$	−7.60728	+	17.9525i	−0.562346	+	1.32709i
$184$	−1.27686	+	0.342133i	−0.0941311	+	0.0252223i
$185$	−3.59177	−	2.07371i	−0.264072	−	0.152462i
$186$	−7.26255	+	17.1390i	−0.532516	+	1.25669i
$187$	−3.88571	+	1.04117i	−0.284151	+	0.0761382i
$188$	−0.928739	−	3.46610i	−0.0677352	−	0.252791i
$189$	−1.55314	+	0.166156i	−0.112974	+	0.0120860i
$190$	5.13710	−	5.13710i	0.372684	−	0.372684i
$191$	−9.49618	+	5.48262i	−0.687120	+	0.396709i	−0.802532	−	0.596609i	$-0.796514\pi$
$191$	−9.49618	+	5.48262i	−0.687120	+	0.396709i	0.115412	+	0.993318i	$0.463181\pi$
$192$	−1.38263	+	1.04323i	−0.0997829	+	0.0752886i
$193$	−3.61591	−	13.4948i	−0.260279	−	0.971374i	−0.965077	−	0.261966i	$-0.915629\pi$
$193$	−3.61591	−	13.4948i	−0.260279	−	0.971374i	0.704798	−	0.709408i	$-0.251038\pi$
$194$	−3.12275	−	5.40876i	−0.224200	−	0.388326i
$195$	−5.34868	−	9.05509i	−0.383027	−	0.648448i
$196$	−3.45482	+	5.98392i	−0.246773	+	0.427423i
$197$	4.59113	+	1.23019i	0.327105	+	0.0876474i	0.418634	−	0.908155i	$-0.362509\pi$
$197$	4.59113	+	1.23019i	0.327105	+	0.0876474i	−0.0915295	+	0.995802i	$0.529176\pi$
$198$	1.30868	−	4.58531i	0.0930039	−	0.325864i
$199$	−20.1187	−	11.6155i	−1.42618	−	0.823403i	−0.429359	−	0.903134i	$-0.641260\pi$
$199$	−20.1187	−	11.6155i	−1.42618	−	0.823403i	−0.996816	+	0.0797315i	$0.974594\pi$
$200$	0.560091	+	2.09029i	0.0396044	+	0.147806i
$201$	1.33438	+	1.04120i	0.0941196	+	0.0734406i
$202$	6.07588	−	6.07588i	0.427498	−	0.427498i
$203$	0.582253	−	2.17300i	0.0408661	−	0.152514i
$204$	−0.536923	−	4.35064i	−0.0375921	−	0.304606i
$205$		−	6.33945i		−	0.442766i
$206$	0.0681718	−	0.254421i	0.00474975	−	0.0177263i
$207$	2.75833	+	2.84927i	0.191717	+	0.198038i
$208$	3.56563	−	0.535061i	0.247232	−	0.0370998i
$209$	−5.93833	−	3.42850i	−0.410763	−	0.237154i
$210$	0.691279	+	0.539398i	0.0477028	+	0.0372220i
$211$	1.02671	−	1.77832i	0.0706817	−	0.122424i	−0.828519	−	0.559962i	$-0.810816\pi$
$211$	1.02671	−	1.77832i	0.0706817	−	0.122424i	0.899200	+	0.437537i	$0.144149\pi$
$212$	−3.63112			−0.249386
$213$	−7.58014	+	9.71452i	−0.519383	+	0.665628i
$214$	3.42023	−	12.7645i	0.233802	−	0.872560i
$215$	−12.0759	+	3.23573i	−0.823569	+	0.220675i
$216$	4.75083	+	2.10465i	0.323253	+	0.143204i
$217$	−1.61530	+	2.79778i	−0.109654	+	0.189926i
$218$	15.7209			1.06475
$219$	8.20206	+	1.14755i	0.554244	+	0.0775444i
$220$	−2.31811	+	1.33836i	−0.156287	+	0.0902322i
$221$	−3.33936	+	8.49232i	−0.224630	+	0.571255i
$222$	−3.92760	−	1.66430i	−0.263603	−	0.111701i
$223$	−0.420741	−	0.420741i	−0.0281749	−	0.0281749i	0.692879	−	0.721054i	$-0.256342\pi$
$223$	−0.420741	−	0.420741i	−0.0281749	−	0.0281749i	−0.721054	+	0.692879i	$0.756342\pi$
$224$	−0.260334	+	0.150304i	−0.0173943	+	0.0100426i
$225$	4.66443	−	4.51555i	0.310962	−	0.301037i
$226$	−6.88769	−	6.88769i	−0.458163	−	0.458163i
$227$	17.6264	+	4.72299i	1.16991	+	0.313476i	0.790916	−	0.611924i	$-0.209604\pi$
$227$	17.6264	+	4.72299i	1.16991	+	0.313476i	0.378992	+	0.925400i	$0.376271\pi$
$228$	4.59664	−	5.89093i	0.304420	−	0.390137i
$229$	9.93612	+	2.66237i	0.656597	+	0.175935i	0.571710	−	0.820456i	$-0.306280\pi$
$229$	9.93612	+	2.66237i	0.656597	+	0.175935i	0.0848872	+	0.996391i	$0.472947\pi$
$230$		−	2.22612i		−	0.146786i
$231$	0.322892	−	0.761996i	0.0212447	−	0.0501356i
$232$	−5.29176	+	5.29176i	−0.347421	+	0.347421i
$233$	−21.7770			−1.42666			−0.713328	−	0.700830i	$-0.752813\pi$
$233$	−21.7770			−1.42666			−0.713328	+	0.700830i	$0.752813\pi$
$234$	−6.60048	−	8.56934i	−0.431487	−	0.560195i
$235$	6.04294			0.394198
$236$	−0.512425	+	0.512425i	−0.0333560	+	0.0333560i
$237$	−12.7045	+	1.56789i	−0.825247	+	0.101846i
$238$		−	0.760808i		−	0.0493158i
$239$	−18.0937	−	4.84819i	−1.17038	−	0.313603i	−0.379278	−	0.925283i	$-0.623828\pi$
$239$	−18.0937	−	4.84819i	−1.17038	−	0.313603i	−0.791106	+	0.611679i	$0.790494\pi$
$240$	−1.09434	−	2.70377i	−0.0706392	−	0.174527i
$241$	4.27560	+	1.14564i	0.275416	+	0.0737974i	0.393883	−	0.919160i	$-0.371131\pi$
$241$	4.27560	+	1.14564i	0.275416	+	0.0737974i	−0.118467	+	0.992958i	$0.537798\pi$
$242$	−5.99173	−	5.99173i	−0.385163	−	0.385163i
$243$	−1.40664	−	15.5249i	−0.0902358	−	0.995920i
$244$	9.74888	−	5.62852i	0.624108	−	0.360329i
$245$	−8.22794	−	8.22794i	−0.525664	−	0.525664i
$246$	−0.798615	−	6.47111i	−0.0509178	−	0.412583i
$247$	−14.2606	+	6.21081i	−0.907381	+	0.395184i
$248$	9.30710	−	5.37346i	0.591001	−	0.341215i
$249$	−13.1005	+	16.7893i	−0.830213	+	1.06398i
$250$	−12.0645			−0.763024
$251$	14.8094	−	25.6507i	0.934763	−	1.61906i	0.159706	−	0.987165i	$-0.448945\pi$
$251$	14.8094	−	25.6507i	0.934763	−	1.61906i	0.775057	−	0.631892i	$-0.217721\pi$
$252$	0.773587	+	0.463517i	0.0487314	+	0.0291988i
$253$	−2.02952	+	0.543809i	−0.127595	+	0.0341890i
$254$	4.53267	−	16.9162i	0.284405	−	1.06141i
$255$	7.31101	+	1.02288i	0.457833	+	0.0640555i
$256$	1.00000			0.0625000
$257$	−8.32426	+	14.4180i	−0.519253	+	0.899373i	0.480496	+	0.876997i	$0.340457\pi$
$257$	−8.32426	+	14.4180i	−0.519253	+	0.899373i	−0.999750	+	0.0223764i	$0.992877\pi$
$258$	−11.9191	+	4.82419i	−0.742049	+	0.300341i
$259$	−0.641147	−	0.370166i	−0.0398389	−	0.0230010i
$260$	−0.683757	+	6.03325i	−0.0424048	+	0.374166i
$261$	21.5890	+	6.16165i	1.33632	+	0.381397i
$262$	4.00972	−	14.9645i	0.247722	−	0.924510i
$263$			28.0711i			1.73094i	0.500963	+	0.865469i	$0.332979\pi$
$263$			28.0711i			1.73094i	−0.500963	+	0.865469i	$0.667021\pi$
$264$	−2.19765	+	1.65818i	−0.135256	+	0.102054i
$265$	1.58266	−	5.90657i	0.0972220	−	0.362838i
$266$	0.916994	−	0.916994i	0.0562245	−	0.0562245i
$267$	3.17682	−	1.28580i	0.194418	−	0.0786899i
$268$	−0.252913	−	0.943886i	−0.0154491	−	0.0576570i
$269$	16.1655	+	9.33318i	0.985631	+	0.569054i	0.903965	−	0.427606i	$-0.140643\pi$
$269$	16.1655	+	9.33318i	0.985631	+	0.569054i	0.0816654	+	0.996660i	$0.473976\pi$
$270$	−5.49424	+	6.81062i	−0.334369	+	0.414481i
$271$	−24.6548	−	6.60622i	−1.49767	−	0.401299i	−0.585351	−	0.810780i	$-0.699043\pi$
$271$	−24.6548	−	6.60622i	−1.49767	−	0.401299i	−0.912319	+	0.409481i	$0.865710\pi$
$272$	−1.26545	+	2.19182i	−0.0767292	+	0.132899i
$273$	−0.954763	−	1.61637i	−0.0577849	−	0.0978273i
$274$	10.6953	+	18.5248i	0.646126	+	1.11912i
$275$	0.890247	+	3.32245i	0.0536839	+	0.200351i
$276$	−0.280437	−	2.27236i	−0.0168803	−	0.136780i
$277$	−13.6852	+	7.90117i	−0.822265	+	0.474735i	−0.851197	−	0.524846i	$-0.824123\pi$
$277$	−13.6852	+	7.90117i	−0.822265	+	0.474735i	0.0289317	+	0.999581i	$0.490789\pi$
$278$	6.52602	−	6.52602i	0.391405	−	0.391405i
$279$	−27.6562	−	16.5710i	−1.65573	−	0.992081i
$280$	−0.131023	−	0.488984i	−0.00783012	−	0.0292224i
$281$	26.0117	−	6.96981i	1.55173	−	0.415784i	0.621694	−	0.783261i	$-0.286445\pi$
$281$	26.0117	−	6.96981i	1.55173	−	0.415784i	0.930033	+	0.367477i	$0.119778\pi$
$282$	6.16844	−	0.761262i	0.367325	−	0.0453325i
$283$	−20.1578	−	11.6381i	−1.19826	−	0.691813i	−0.238089	−	0.971243i	$-0.576521\pi$
$283$	−20.1578	−	11.6381i	−1.19826	−	0.691813i	−0.960166	+	0.279430i	$0.909854\pi$
$284$	6.87167	−	1.84126i	0.407759	−	0.109259i
$285$	7.57901	+	10.0448i	0.448942	+	0.595000i
$286$	5.66746	−	0.850463i	0.335124	−	0.0502890i
$287$		−	1.13162i		−	0.0667974i
$288$	−1.45767	−	2.62206i	−0.0858942	−	0.154506i
$289$	5.29727	+	9.17515i	0.311604	+	0.539714i
$290$	−6.30139	−	10.9143i	−0.370031	−	0.640912i
$291$	10.0273	−	4.05851i	0.587811	−	0.237914i
$292$	−3.38109	−	3.38109i	−0.197864	−	0.197864i
$293$	−16.5979	−	16.5979i	−0.969662	−	0.969662i	0.0298907	−	0.999553i	$-0.490484\pi$
$293$	−16.5979	−	16.5979i	−0.969662	−	0.969662i	−0.999553	+	0.0298907i	$0.990484\pi$
$294$	−9.43534	−	7.36230i	−0.550280	−	0.429378i
$295$	−0.610192	−	1.05688i	−0.0355267	−	0.0615341i
$296$	1.23139	+	2.13284i	0.0715733	+	0.123969i
$297$	7.55130	+	3.34528i	0.438171	+	0.194113i
$298$			22.2116i			1.28668i
$299$	−1.74416	+	4.43557i	−0.100868	+	0.256516i
$300$	−3.71998	+	0.459092i	−0.214773	+	0.0265057i
$301$	−2.15560	+	0.577591i	−0.124247	+	0.0332918i
$302$	14.9423	+	8.62695i	0.859834	+	0.496425i
$303$	8.96405	+	11.8804i	0.514971	+	0.682511i
$304$	−4.16702	+	1.11655i	−0.238995	+	0.0640385i
$305$	4.90650	+	18.3113i	0.280945	+	1.04850i
$306$	7.59170	+	0.123121i	0.433989	+	0.00703834i
$307$	−15.1916	+	15.1916i	−0.867028	+	0.867028i	−0.992142	−	0.125115i	$-0.960070\pi$
$307$	−15.1916	+	15.1916i	−0.867028	+	0.867028i	0.125115	+	0.992142i	$0.460070\pi$
$308$	−0.413792	+	0.238903i	−0.0235780	+	0.0136128i
$309$	0.420058	+	0.177997i	0.0238962	+	0.0101259i
$310$	4.68415	+	17.4815i	0.266042	+	0.992882i
$311$	5.02062	+	8.69597i	0.284693	+	0.493103i	0.972535	−	0.232758i	$-0.0747749\pi$
$311$	5.02062	+	8.69597i	0.284693	+	0.493103i	−0.687841	+	0.725861i	$0.741442\pi$
$312$	0.0620844	+	6.24469i	0.00351484	+	0.353536i
$313$	−3.93637	+	6.81799i	−0.222497	+	0.385376i	−0.955565	−	0.294779i	$-0.904754\pi$
$313$	−3.93637	+	6.81799i	−0.222497	+	0.385376i	0.733069	+	0.680154i	$0.238087\pi$
$314$	0.580663	+	0.155588i	0.0327687	+	0.00878035i
$315$	−1.09116	+	1.05633i	−0.0614797	+	0.0595174i
$316$	6.40045	+	3.69530i	0.360053	+	0.207877i
$317$	−2.84693	−	10.6249i	−0.159900	−	0.596753i	−0.998636	−	0.0522155i	$-0.983372\pi$
$317$	−2.84693	−	10.6249i	−0.159900	−	0.596753i	0.838736	−	0.544538i	$-0.183295\pi$
$318$	0.871446	−	6.22861i	0.0488683	−	0.349283i
$319$	−8.41109	+	8.41109i	−0.470931	+	0.470931i
$320$	−0.435860	+	1.62665i	−0.0243653	+	0.0909327i
$321$	21.0746	+	8.93026i	1.17627	+	0.498438i
$322$		−	0.397373i		−	0.0221447i
$323$	2.82587	−	10.5463i	0.157236	−	0.586812i
$324$	−4.75038	+	7.64421i	−0.263910	+	0.424678i
$325$	7.26129	+	2.85530i	0.402784	+	0.158383i
$326$	3.11153	+	1.79644i	0.172332	+	0.0994958i
$327$	−3.77292	+	26.9667i	−0.208643	+	1.49126i
$328$	−1.88222	+	3.26010i	−0.103928	+	0.180009i
$329$	1.07869			0.0594702
$330$	−1.73942	−	4.29755i	−0.0957517	−	0.236572i
$331$	5.82719	−	21.7474i	0.320292	−	1.19534i	−0.598669	−	0.800996i	$-0.704304\pi$
$331$	5.82719	−	21.7474i	0.320292	−	1.19534i	0.918961	−	0.394348i	$-0.129030\pi$
$332$	11.8761	−	3.18219i	0.651786	−	0.174646i
$333$	3.79745	−	6.33776i	0.208099	−	0.347307i
$334$	−4.51452	+	7.81938i	−0.247023	+	0.427857i
$335$	1.64561			0.0899093
$336$	−0.195344	−	0.482634i	−0.0106569	−	0.0263298i
$337$	12.2213	−	7.05595i	0.665734	−	0.384362i	−0.128724	−	0.991680i	$-0.541088\pi$
$337$	12.2213	−	7.05595i	0.665734	−	0.384362i	0.794458	+	0.607318i	$0.207755\pi$
$338$	6.08943	−	11.4856i	0.331221	−	0.624734i
$339$	13.4678	−	10.1618i	0.731469	−	0.551911i
$340$	−3.01378	−	3.01378i	−0.163445	−	0.163445i
$341$	14.7933	−	8.54094i	0.801105	−	0.462518i
$342$	9.00181	+	9.29860i	0.486762	+	0.502811i
$343$	−2.95666	−	2.95666i	−0.159644	−	0.159644i
$344$	7.17081	+	1.92141i	0.386624	+	0.103596i
$345$	3.81857	+	0.534256i	0.205585	+	0.0287634i
$346$	−15.1959	−	4.07174i	−0.816939	−	0.218898i
$347$		−	24.6130i		−	1.32130i	−0.750696	−	0.660648i	$-0.770282\pi$
$347$		−	24.6130i		−	1.32130i	0.750696	−	0.660648i	$-0.229718\pi$
$348$	−7.80720	−	10.3472i	−0.418510	−	0.554667i
$349$	15.8417	−	15.8417i	0.847984	−	0.847984i	−0.141897	−	0.989881i	$-0.545320\pi$
$349$	15.8417	−	15.8417i	0.847984	−	0.847984i	0.989881	+	0.141897i	$0.0453203\pi$
$350$	−0.650523			−0.0347719
$351$	16.2834	−	9.26551i	0.869146	−	0.494556i
$352$	1.58947			0.0847190
$353$	12.5669	−	12.5669i	0.668870	−	0.668870i	−0.288584	−	0.957455i	$-0.593184\pi$
$353$	12.5669	−	12.5669i	0.668870	−	0.668870i	0.957455	+	0.288584i	$0.0931845\pi$
$354$	−0.756006	−	1.00196i	−0.0401813	−	0.0532538i
$355$			11.9804i			0.635852i
$356$	−1.91125	−	0.512119i	−0.101296	−	0.0271422i
$357$	1.30505	+	0.182589i	0.0690704	+	0.00966365i
$358$	6.36666	+	1.70594i	0.336488	+	0.0901618i
$359$	9.00574	+	9.00574i	0.475305	+	0.475305i	0.903626	−	0.428322i	$-0.140895\pi$
$359$	9.00574	+	9.00574i	0.475305	+	0.475305i	−0.428322	+	0.903626i	$0.640895\pi$
$360$	4.90052	−	1.22828i	0.258280	−	0.0647359i
$361$	−0.337122	+	0.194638i	−0.0177433	+	0.0102441i
$362$	7.97262	+	7.97262i	0.419031	+	0.419031i
$363$	11.7159	−	8.83990i	0.614923	−	0.463974i
$364$	−0.122054	+	1.07696i	−0.00639735	+	0.0564481i
$365$	6.97355	−	4.02618i	0.365012	−	0.210740i
$366$	7.31517	+	18.0735i	0.382370	+	0.944716i
$367$	−35.7209			−1.86462			−0.932308	−	0.361667i	$-0.882208\pi$
$367$	−35.7209			−1.86462			−0.932308	+	0.361667i	$0.882208\pi$
$368$	−0.660949	+	1.14480i	−0.0344544	+	0.0596767i
$369$	11.2918	+	0.183129i	0.587830	+	0.00953330i
$370$	−4.00610	+	1.07343i	−0.208267	+	0.0558050i
$371$	0.282512	−	1.05435i	0.0146673	−	0.0547390i
$372$	6.98367	+	17.2545i	0.362087	+	0.894603i
$373$	−10.8592			−0.562267			−0.281134	−	0.959669i	$-0.590710\pi$
$373$	−10.8592			−0.562267			−0.281134	+	0.959669i	$0.590710\pi$
$374$	−2.01139	+	3.48384i	−0.104007	+	0.180145i
$375$	2.89540	−	20.6947i	0.149518	−	1.06867i
$376$	−3.10762	−	1.79419i	−0.160263	−	0.0925281i
$377$	4.00423	+	26.6840i	0.206228	+	1.37430i
$378$	−0.980746	+	1.21573i	−0.0504441	+	0.0625302i
$379$	3.41411	−	12.7416i	0.175371	−	0.654494i	−0.821117	−	0.570760i	$-0.806649\pi$
$379$	3.41411	−	12.7416i	0.175371	−	0.654494i	0.996488	−	0.0837342i	$-0.0266847\pi$
$380$		−	7.26495i		−	0.372684i
$381$	27.9292	+	11.8349i	1.43086	+	0.606318i
$382$	−2.83802	+	10.5916i	−0.145206	+	0.541914i
$383$	9.74254	−	9.74254i	0.497820	−	0.497820i	−0.412938	−	0.910759i	$-0.635498\pi$
$383$	9.74254	−	9.74254i	0.497820	−	0.497820i	0.910759	+	0.412938i	$0.135498\pi$
$384$	−0.239994	+	1.71534i	−0.0122471	+	0.0875357i
$385$	−0.208257	−	0.777225i	−0.0106138	−	0.0396111i
$386$	−12.0991	−	6.98540i	−0.615826	−	0.355548i
$387$	−5.41464	−	21.6031i	−0.275242	−	1.09815i
$388$	−6.03268	−	1.61645i	−0.306263	−	0.0820629i
$389$	10.3218	−	17.8779i	0.523336	−	0.906445i	−0.476295	−	0.879286i	$-0.658020\pi$
$389$	10.3218	−	17.8779i	0.523336	−	0.906445i	0.999631	−	0.0271595i	$-0.00864621\pi$
$390$	−10.1850	−	2.62082i	−0.515738	−	0.132711i
$391$	−1.67280	−	2.89737i	−0.0845970	−	0.146526i
$392$	1.78835	+	6.67419i	0.0903251	+	0.337098i
$393$	24.7069	+	10.4694i	1.24630	+	0.528114i
$394$	4.11630	−	2.37655i	0.207376	−	0.119729i
$395$	−8.80067	+	8.80067i	−0.442810	+	0.442810i
$396$	−2.31693	−	4.16768i	−0.116430	−	0.209434i
$397$	2.46047	+	9.18259i	0.123487	+	0.460861i	0.999781	−	0.0209159i	$-0.00665821\pi$
$397$	2.46047	+	9.18259i	0.123487	+	0.460861i	−0.876294	+	0.481777i	$0.839992\pi$
$398$	−22.4395	+	6.01264i	−1.12479	+	0.301386i
$399$	1.35289	+	1.79303i	0.0677290	+	0.0897639i
$400$	1.87410	+	1.08201i	0.0937051	+	0.0541006i
$401$	−11.4410	+	3.06561i	−0.571337	+	0.153089i	−0.532910	−	0.846172i	$-0.678901\pi$
$401$	−11.4410	+	3.06561i	−0.571337	+	0.153089i	−0.0384272	+	0.999261i	$0.512235\pi$
$402$	1.67979	−	0.207306i	0.0837801	−	0.0103395i
$403$	4.36349	−	38.5021i	0.217361	−	1.91792i
$404$		−	8.59259i		−	0.427498i
$405$	−10.3640	−	11.0590i	−0.514990	−	0.549527i
$406$	−1.12483	−	1.94826i	−0.0558242	−	0.0966903i
$407$	1.95726	+	3.39008i	0.0970178	+	0.168040i
$408$	−3.45603	−	2.69671i	−0.171099	−	0.133507i
$409$	27.1747	+	27.1747i	1.34370	+	1.34370i	0.892340	+	0.451364i	$0.149062\pi$
$409$	27.1747	+	27.1747i	1.34370	+	1.34370i	0.451364	+	0.892340i	$0.350938\pi$
$410$	−4.48267	−	4.48267i	−0.221383	−	0.221383i
$411$	−34.3432	+	13.9003i	−1.69402	+	0.685649i
$412$	−0.131698	−	0.228107i	−0.00648828	−	0.0112380i
$413$	−0.108922	−	0.188658i	−0.00535970	−	0.00928327i
$414$	3.96517	+	0.0643064i	0.194878	+	0.00316049i
$415$			20.7053i			1.01638i
$416$	2.14293	−	2.89963i	0.105066	−	0.142166i
$417$	9.62816	+	12.7606i	0.471493	+	0.624888i
$418$	−6.62335	+	1.77472i	−0.323958	+	0.0868044i
$419$	−18.2166	−	10.5173i	−0.889937	−	0.513805i	−0.0160151	−	0.999872i	$-0.505098\pi$
$419$	−18.2166	−	10.5173i	−0.889937	−	0.513805i	−0.873922	+	0.486066i	$0.838431\pi$
$420$	0.870221	−	0.107396i	0.0424624	−	0.00524039i
$421$	25.7609	−	6.90262i	1.25551	−	0.336413i	0.431048	−	0.902329i	$-0.358144\pi$
$421$	25.7609	−	6.90262i	1.25551	−	0.336413i	0.824463	+	0.565916i	$0.191477\pi$
$422$	−0.531465	−	1.98345i	−0.0258713	−	0.0965530i
$423$	−0.174564	+	10.7637i	−0.00848757	+	0.523349i
$424$	−2.56759	+	2.56759i	−0.124693	+	0.124693i
$425$	−4.74316	+	2.73847i	−0.230077	+	0.132835i
$426$	1.50923	+	12.2292i	0.0731225	+	0.592505i
$427$	0.875831	+	3.26865i	0.0423844	+	0.158181i
$428$	−6.60737	−	11.4443i	−0.319379	−	0.553181i
$429$	0.0986812	+	9.92574i	0.00476437	+	0.479219i
$430$	−6.25094	+	10.8269i	−0.301447	+	0.522122i
$431$	30.6200	+	8.20459i	1.47491	+	0.395201i	0.904612	−	0.426236i	$-0.140161\pi$
$431$	30.6200	+	8.20459i	1.47491	+	0.395201i	0.570299	+	0.821437i	$0.306827\pi$
$432$	4.84756	−	1.87113i	0.233228	−	0.0900249i
$433$	−32.6337	−	18.8411i	−1.56827	−	0.905444i	−0.996370	−	0.0851235i	$-0.972872\pi$
$433$	−32.6337	−	18.8411i	−1.56827	−	0.905444i	−0.571904	−	0.820320i	$-0.693795\pi$
$434$	0.836142	+	3.12052i	0.0401361	+	0.149790i
$435$	20.2341	−	8.18968i	0.970152	−	0.392665i
$436$	11.1164	−	11.1164i	0.532377	−	0.532377i
$437$	1.47596	−	5.50838i	0.0706050	−	0.263501i
$438$	6.61118	−	4.98829i	0.315894	−	0.238350i
$439$			2.96173i			0.141356i	0.997499	+	0.0706779i	$0.0225162\pi$
$439$			2.96173i			0.141356i	−0.997499	+	0.0706779i	$0.977484\pi$
$440$	−0.692786	+	2.58551i	−0.0330273	+	0.123260i
$441$	14.8933	−	14.4179i	0.709205	−	0.686569i
$442$	3.64369	+	8.36627i	0.173313	+	0.397943i
$443$	−23.4384	−	13.5322i	−1.11359	−	0.642933i	−0.173835	−	0.984775i	$-0.555616\pi$
$443$	−23.4384	−	13.5322i	−1.11359	−	0.642933i	−0.939757	+	0.341842i	$0.888949\pi$
$444$	−3.95407	+	1.60039i	−0.187652	+	0.0759514i
$445$	1.66608	−	2.88573i	0.0789797	−	0.136797i
$446$	−0.595018			−0.0281749
$447$	−38.1005	−	5.33064i	−1.80209	−	0.252131i
$448$	−0.0778030	+	0.290365i	−0.00367584	+	0.0137184i
$449$	−38.6090	+	10.3453i	−1.82207	+	0.488223i	−0.997041	−	0.0768655i	$-0.975509\pi$
$449$	−38.6090	+	10.3453i	−1.82207	+	0.488223i	−0.825030	+	0.565088i	$0.808842\pi$
$450$	0.105273	−	6.49122i	0.00496263	−	0.305999i
$451$	−2.99173	+	5.18183i	−0.140875	+	0.244003i
$452$	−9.74067			−0.458163
$453$	−18.3843	+	23.5608i	−0.863767	+	1.10698i
$454$	15.8034	−	9.12412i	0.741692	−	0.428216i
$455$	−1.69864	−	0.667944i	−0.0796337	−	0.0313137i
$456$	−0.915206	−	7.41583i	−0.0428584	−	0.347278i
$457$	−22.8591	−	22.8591i	−1.06930	−	1.06930i	−0.997413	−	0.0718891i	$-0.977097\pi$
$457$	−22.8591	−	22.8591i	−1.06930	−	1.06930i	−0.0718891	−	0.997413i	$-0.522903\pi$
$458$	8.90848	−	5.14331i	0.416266	−	0.240331i
$459$	−2.03316	+	12.9928i	−0.0948997	+	0.606453i
$460$	−1.57411	−	1.57411i	−0.0733931	−	0.0733931i
$461$	10.0612	+	2.69590i	0.468598	+	0.125560i	0.485389	−	0.874299i	$-0.338678\pi$
$461$	10.0612	+	2.69590i	0.468598	+	0.125560i	−0.0167904	+	0.999859i	$0.505345\pi$
$462$	−0.310493	−	0.767131i	−0.0144455	−	0.0356902i
$463$	12.6632	+	3.39310i	0.588509	+	0.157691i	0.540772	−	0.841169i	$-0.318132\pi$
$463$	12.6632	+	3.39310i	0.588509	+	0.157691i	0.0477376	+	0.998860i	$0.484799\pi$
$464$			7.48368i			0.347421i
$465$	−31.1109	+	3.83948i	−1.44274	+	0.178051i
$466$	−15.3986	+	15.3986i	−0.713328	+	0.713328i
$467$	1.37176			0.0634775			0.0317388	−	0.999496i	$-0.489896\pi$
$467$	1.37176			0.0634775			0.0317388	+	0.999496i	$0.489896\pi$
$468$	−10.7267	−	1.39219i	−0.495841	−	0.0643541i
$469$	0.293749			0.0135640
$470$	4.27301	−	4.27301i	0.197099	−	0.197099i
$471$	−0.406243	+	0.958696i	−0.0187187	+	0.0441744i
$472$			0.724678i			0.0333560i
$473$	11.3978	+	3.05402i	0.524070	+	0.140424i
$474$	−7.87478	+	10.0921i	−0.361700	+	0.463546i
$475$	−9.01754	−	2.41624i	−0.413753	−	0.110865i
$476$	−0.537972	−	0.537972i	−0.0246579	−	0.0246579i
$477$	10.4751	+	2.98966i	0.479620	+	0.136887i
$478$	−16.2224	+	9.36599i	−0.741994	+	0.428390i
$479$	−6.56789	−	6.56789i	−0.300094	−	0.300094i	0.540956	−	0.841051i	$-0.318062\pi$
$479$	−6.56789	−	6.56789i	−0.300094	−	0.300094i	−0.841051	+	0.540956i	$0.818062\pi$
$480$	−2.68566	−	1.13804i	−0.122583	−	0.0519441i
$481$	8.82322	+	0.999948i	0.402304	+	0.0455937i
$482$	3.83340	−	2.21322i	0.174607	−	0.100809i
$483$	0.681631	+	0.0953671i	0.0310153	+	0.00433935i
$484$	−8.47359			−0.385163
$485$	5.25881	−	9.10853i	0.238790	−	0.413597i
$486$	−11.9724	−	9.98309i	−0.543078	−	0.452842i
$487$	−11.7546	+	3.14965i	−0.532654	+	0.142724i	−0.515113	−	0.857122i	$-0.672250\pi$
$487$	−11.7546	+	3.14965i	−0.532654	+	0.142724i	−0.0175402	+	0.999846i	$0.505584\pi$
$488$	2.91354	−	10.8735i	0.131890	−	0.492219i
$489$	−3.82827	+	4.90621i	−0.173120	+	0.221866i
$490$	−11.6361			−0.525664
$491$	−3.72316	+	6.44870i	−0.168024	+	0.291026i	−0.937725	−	0.347378i	$-0.887072\pi$
$491$	−3.72316	+	6.44870i	−0.168024	+	0.291026i	0.769701	+	0.638404i	$0.220405\pi$
$492$	−5.14047	−	4.01106i	−0.231750	−	0.180833i
$493$	−16.4029	−	9.47023i	−0.738750	−	0.426518i
$494$	−5.69207	+	14.4755i	−0.256098	+	0.651283i
$495$	7.78922	−	1.95231i	0.350100	−	0.0877497i
$496$	2.78151	−	10.3807i	0.124893	−	0.466108i
$497$			2.13855i			0.0959269i
$498$	2.60836	+	21.1353i	0.116883	+	0.947096i
$499$	−1.27227	+	4.74819i	−0.0569548	+	0.212558i	−0.988539	−	0.150968i	$-0.951761\pi$
$499$	−1.27227	+	4.74819i	−0.0569548	+	0.212558i	0.931584	+	0.363527i	$0.118427\pi$
$500$	−8.53087	+	8.53087i	−0.381512	+	0.381512i
$501$	−12.3295	−	9.62055i	−0.550840	−	0.429815i
$502$	−7.66592	−	28.6096i	−0.342147	−	1.27691i
$503$	−24.0111	−	13.8628i	−1.07060	−	0.618112i	−0.142255	−	0.989830i	$-0.545435\pi$
$503$	−24.0111	−	13.8628i	−1.07060	−	0.618112i	−0.928346	+	0.371718i	$0.878769\pi$
$504$	0.874764	−	0.219253i	0.0389651	−	0.00976630i
$505$	13.9772	+	3.74517i	0.621976	+	0.166658i
$506$	−1.05056	+	1.81962i	−0.0467030	+	0.0808920i
$507$	18.2403	+	13.2019i	0.810080	+	0.586319i
$508$	−8.75644	−	15.1666i	−0.388504	−	0.672909i
$509$	−2.37610	−	8.86772i	−0.105319	−	0.393055i	0.893062	−	0.449933i	$-0.148552\pi$
$509$	−2.37610	−	8.86772i	−0.105319	−	0.393055i	−0.998381	+	0.0568780i	$0.981885\pi$
$510$	5.89295	−	4.44637i	0.260944	−	0.196889i
$511$	1.24481	−	0.718691i	0.0550671	−	0.0317930i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−18.1107	+	13.2096i	−0.799606	+	0.583217i
$514$	4.30896	+	16.0812i	0.190060	+	0.709313i
$515$	0.428453	−	0.114804i	0.0188799	−	0.00505885i
$516$	−5.01683	+	11.8393i	−0.220854	+	0.521195i
$517$	−4.93947	−	2.85180i	−0.217237	−	0.125422i
$518$	−0.715106	+	0.191612i	−0.0314200	+	0.00841895i
$519$	10.6314	−	25.0891i	0.466665	−	1.10129i
$520$	3.78266	+	4.74964i	0.165881	+	0.208286i
$521$		−	29.1318i		−	1.27629i	−0.769918	−	0.638143i	$-0.779703\pi$
$521$		−	29.1318i		−	1.27629i	0.769918	−	0.638143i	$-0.220297\pi$
$522$	19.6227	−	10.9088i	0.858860	−	0.477464i
$523$	1.29854	+	2.24913i	0.0567811	+	0.0983478i	0.893019	−	0.450019i	$-0.148583\pi$
$523$	1.29854	+	2.24913i	0.0567811	+	0.0983478i	−0.836238	+	0.548367i	$0.815250\pi$
$524$	−7.74619	−	13.4168i	−0.338394	−	0.586116i
$525$	0.156122	−	1.11587i	0.00681370	−	0.0487005i
$526$	19.8493	+	19.8493i	0.865469	+	0.865469i
$527$	19.2329	+	19.2329i	0.837796	+	0.837796i
$528$	−0.381463	+	2.72648i	−0.0166010	+	0.118655i
$529$	10.6263	+	18.4053i	0.462013	+	0.800229i
$530$	−3.05746	−	5.29568i	−0.132808	−	0.230030i
$531$	1.90015	−	1.05634i	0.0824594	−	0.0458414i
$532$		−	1.29683i		−	0.0562245i
$533$	5.41960	+	12.4439i	0.234749	+	0.539006i
$534$	1.33715	−	3.15555i	0.0578641	−	0.136554i
$535$	21.4958	−	5.75978i	0.929344	−	0.249017i
$536$	−0.846265	−	0.488591i	−0.0365531	−	0.0211039i
$537$	−4.45423	+	10.5116i	−0.192214	+	0.453608i
$538$	18.0303	−	4.83121i	0.777343	−	0.208288i
$539$	2.84252	+	10.6084i	0.122436	+	0.456937i
$540$	0.930822	+	8.70085i	0.0400562	+	0.374425i
$541$	−4.52095	+	4.52095i	−0.194371	+	0.194371i	−0.797582	−	0.603211i	$-0.793888\pi$
$541$	−4.52095	+	4.52095i	−0.194371	+	0.194371i	0.603211	+	0.797582i	$0.293888\pi$
$542$	−22.1049	+	12.7622i	−0.949485	+	0.548185i
$543$	−15.5892	+	11.7624i	−0.668995	+	0.504773i
$544$	0.655045	+	2.44466i	0.0280848	+	0.104814i
$545$	13.2373	+	22.9276i	0.567023	+	0.982112i
$546$	−1.81807	−	0.467828i	−0.0778061	−	0.0200212i
$547$	−7.08272	+	12.2676i	−0.302835	+	0.524526i	−0.976777	−	0.214259i	$-0.931267\pi$
$547$	−7.08272	+	12.2676i	−0.302835	+	0.524526i	0.673942	+	0.738784i	$0.264600\pi$
$548$	20.6617	+	5.53629i	0.882624	+	0.236498i
$549$	−32.7578	+	8.21050i	−1.39807	+	0.350415i
$550$	2.97883	+	1.71983i	0.127018	+	0.0733336i
$551$	−8.35590	−	31.1846i	−0.355973	−	1.32851i
$552$	−1.80510	−	1.40850i	−0.0768300	−	0.0599497i
$553$	−1.57096	+	1.57096i	−0.0668039	+	0.0668039i
$554$	−4.08995	+	15.2639i	−0.173765	+	0.648500i
$555$	−0.879863	−	7.12945i	−0.0373481	−	0.302628i
$556$		−	9.22919i		−	0.391405i
$557$	−2.54976	+	9.51584i	−0.108037	+	0.403199i	−0.998672	−	0.0515195i	$-0.983594\pi$
$557$	−2.54976	+	9.51584i	−0.108037	+	0.403199i	0.890635	+	0.454719i	$0.150260\pi$
$558$	−31.2734	+	7.83843i	−1.32391	+	0.331827i
$559$	20.9380	−	16.6752i	0.885581	−	0.705286i
$560$	−0.438411	−	0.253117i	−0.0185263	−	0.0106961i
$561$	−5.49325	−	4.28633i	−0.231925	−	0.180969i
$562$	13.4646	−	23.3214i	0.567971	−	0.983755i
$563$	33.4682			1.41051			0.705257	−	0.708951i	$-0.250831\pi$
$563$	33.4682			1.41051			0.705257	+	0.708951i	$0.250831\pi$
$564$	3.82345	−	4.90004i	0.160996	−	0.206329i
$565$	4.24557	−	15.8447i	0.178613	−	0.666591i
$566$	−22.4831	+	6.02432i	−0.945034	+	0.253221i
$567$	−1.85001	−	1.97408i	−0.0776933	−	0.0829037i
$568$	3.55704	−	6.16098i	0.149250	−	0.258509i
$569$	−10.6707			−0.447337			−0.223669	−	0.974665i	$-0.571803\pi$
$569$	−10.6707			−0.447337			−0.223669	+	0.974665i	$0.571803\pi$
$570$	12.4619	+	1.74355i	0.521971	+	0.0730291i
$571$	31.5424	−	18.2110i	1.32001	−	0.762107i	0.336279	−	0.941763i	$-0.390832\pi$
$571$	31.5424	−	18.2110i	1.32001	−	0.762107i	0.983730	+	0.179656i	$0.0574983\pi$
$572$	3.40613	−	4.60886i	0.142417	−	0.192706i
$573$	−17.4872	−	7.41010i	−0.730536	−	0.309561i
$574$	−0.800176	−	0.800176i	−0.0333987	−	0.0333987i
$575$	−2.47737	+	1.43031i	−0.103314	+	0.0596481i
$576$	−2.88481	−	0.823344i	−0.120200	−	0.0343060i
$577$	−17.7894	−	17.7894i	−0.740581	−	0.740581i	0.232109	−	0.972690i	$-0.425437\pi$
$577$	−17.7894	−	17.7894i	−0.740581	−	0.740581i	−0.972690	+	0.232109i	$0.925437\pi$
$578$	10.2335	+	2.74207i	0.425659	+	0.114055i
$579$	14.8861	−	19.0776i	0.618644	−	0.792838i
$580$	−12.1734	−	3.26184i	−0.505471	−	0.135441i
$581$			3.69599i			0.153335i
$582$	4.22058	−	9.96018i	0.174949	−	0.412863i
$583$	−4.08110	+	4.08110i	−0.169022	+	0.169022i
$584$	−4.78159			−0.197864
$585$	6.93995	−	16.8418i	0.286932	−	0.696323i
$586$	−23.4730			−0.969662
$587$	−14.6657	+	14.6657i	−0.605317	+	0.605317i	−0.941719	−	0.336401i	$-0.890790\pi$
$587$	−14.6657	+	14.6657i	−0.605317	+	0.605317i	0.336401	+	0.941719i	$0.390790\pi$
$588$	−11.8777	+	1.46586i	−0.489829	+	0.0604510i
$589$			46.3623i			1.91033i
$590$	−1.17880	−	0.315859i	−0.0485304	−	0.0130037i
$591$	3.08870	+	7.63122i	0.127052	+	0.313906i
$592$	2.37887	+	0.637416i	0.0977709	+	0.0261976i
$593$	−25.1984	−	25.1984i	−1.03477	−	1.03477i	−0.999373	−	0.0353990i	$-0.988730\pi$
$593$	−25.1984	−	25.1984i	−1.03477	−	1.03477i	−0.0353990	−	0.999373i	$-0.511270\pi$
$594$	7.70505	−	2.97411i	0.316142	−	0.122029i
$595$	1.10958	−	0.640613i	0.0454881	−	0.0262626i
$596$	15.7059	+	15.7059i	0.643341	+	0.643341i
$597$	−4.92840	−	39.9344i	−0.201706	−	1.63441i
$598$	1.90311	+	4.36973i	0.0778241	+	0.178692i
$599$	−27.2170	+	15.7138i	−1.11206	+	0.642047i	−0.939362	−	0.342928i	$-0.888581\pi$
$599$	−27.2170	+	15.7138i	−1.11206	+	0.642047i	−0.172697	+	0.984975i	$0.555248\pi$
$600$	−2.30580	+	2.95505i	−0.0941338	+	0.120639i
$601$	25.4826			1.03946			0.519728	−	0.854332i	$-0.326033\pi$
$601$	25.4826			1.03946			0.519728	+	0.854332i	$0.326033\pi$
$602$	−1.11582	+	1.93266i	−0.0454774	+	0.0787692i
$603$	−0.0475370	+	2.93116i	−0.00193586	+	0.119366i
$604$	16.6660	−	4.46564i	0.678130	−	0.181704i
$605$	3.69330	−	13.7836i	0.150154	−	0.560383i
$606$	14.7392	+	2.06217i	0.598741	+	0.0837700i
$607$	14.5125			0.589045			0.294522	−	0.955645i	$-0.404839\pi$
$607$	14.5125			0.589045			0.294522	+	0.955645i	$0.404839\pi$
$608$	−2.15701	+	3.73605i	−0.0874782	+	0.151517i
$609$	3.61188	−	1.46189i	0.146361	−	0.0592389i
$610$	16.4175	+	9.47862i	0.664723	+	0.383778i
$611$	−11.8619	+	5.16611i	−0.479881	+	0.208999i
$612$	5.45520	−	5.28108i	0.220514	−	0.213475i
$613$	1.08903	−	4.06431i	0.0439855	−	0.164156i	−0.940440	−	0.339961i	$-0.889586\pi$
$613$	1.08903	−	4.06431i	0.0439855	−	0.164156i	0.984425	+	0.175805i	$0.0562528\pi$
$614$			21.4841i			0.867028i
$615$	8.76513	−	6.61350i	0.353444	−	0.266682i
$616$	−0.123665	+	0.461525i	−0.00498262	+	0.0185954i
$617$	1.56048	−	1.56048i	0.0628225	−	0.0628225i	−0.674997	−	0.737820i	$-0.735855\pi$
$617$	1.56048	−	1.56048i	0.0628225	−	0.0628225i	0.737820	+	0.674997i	$0.235855\pi$
$618$	0.422889	−	0.171162i	0.0170111	−	0.00688516i
$619$	6.37151	+	23.7788i	0.256092	+	0.955750i	0.967479	+	0.252950i	$0.0814007\pi$
$619$	6.37151	+	23.7788i	0.256092	+	0.955750i	−0.711387	+	0.702800i	$0.751933\pi$
$620$	15.6735	+	9.04909i	0.629462	+	0.363420i
$621$	−1.06193	+	6.78620i	−0.0426136	+	0.272321i
$622$	9.69909	+	2.59886i	0.388898	+	0.104205i
$623$	0.297402	−	0.515116i	0.0119152	−	0.0206377i
$624$	4.45956	+	4.37176i	0.178525	+	0.175011i
$625$	−4.74843	−	8.22452i	−0.189937	−	0.328981i
$626$	2.03761	+	7.60448i	0.0814394	+	0.303936i
$627$	−1.45469	−	11.7872i	−0.0580948	−	0.470737i
$628$	0.520608	−	0.300573i	0.0207745	−	0.0119942i
$629$	−4.40744	+	4.40744i	−0.175736	+	0.175736i
$630$	−0.0246268	+	1.51850i	−0.000981153	+	0.0604985i
$631$	9.44199	+	35.2380i	0.375880	+	1.40280i	0.852055	+	0.523452i	$0.175356\pi$
$631$	9.44199	+	35.2380i	0.375880	+	1.40280i	−0.476176	+	0.879350i	$0.657977\pi$
$632$	7.13877	−	1.91283i	0.283965	−	0.0760882i
$633$	3.52985	−	0.435627i	0.140299	−	0.0173146i
$634$	−9.52602	−	5.49985i	−0.378326	−	0.218427i
$635$	28.4874	−	7.63317i	1.13049	−	0.302913i
$636$	−3.78809	−	5.02050i	−0.150207	−	0.199076i
$637$	23.1850	+	9.11683i	0.918622	+	0.361222i
$638$			11.8951i			0.470931i
$639$	−21.3394	−	0.346079i	−0.844175	−	0.0136907i
$640$	0.842018	+	1.45842i	0.0332837	+	0.0576490i
$641$	10.4318	+	18.0685i	0.412033	+	0.713663i	0.995112	−	0.0987531i	$-0.0314854\pi$
$641$	10.4318	+	18.0685i	0.412033	+	0.713663i	−0.583079	+	0.812416i	$0.698152\pi$
$642$	21.2166	−	8.58734i	0.837354	−	0.338915i
$643$	0.982746	+	0.982746i	0.0387557	+	0.0387557i	0.726219	−	0.687463i	$-0.241276\pi$
$643$	0.982746	+	0.982746i	0.0387557	+	0.0387557i	−0.687463	+	0.726219i	$0.741276\pi$
$644$	−0.280985	−	0.280985i	−0.0110724	−	0.0110724i
$645$	−17.0717	−	13.3209i	−0.672199	−	0.524511i
$646$	−5.45917	−	9.45556i	−0.214788	−	0.372024i
$647$	−5.20265	−	9.01126i	−0.204537	−	0.354269i	0.745448	−	0.666564i	$-0.232236\pi$
$647$	−5.20265	−	9.01126i	−0.204537	−	0.354269i	−0.949985	+	0.312295i	$0.898902\pi$
$648$	2.04625	+	8.76430i	0.0803842	+	0.344294i
$649$			1.15185i			0.0452142i
$650$	7.15351	−	3.11551i	0.280584	−	0.122200i
$651$	−5.55344	+	0.685363i	−0.217656	+	0.0268615i
$652$	3.47046	−	0.929908i	0.135914	−	0.0364180i
$653$	23.5364	+	13.5887i	0.921050	+	0.531769i	0.883970	−	0.467544i	$-0.154861\pi$
$653$	23.5364	+	13.5887i	0.921050	+	0.531769i	0.0370803	+	0.999312i	$0.488194\pi$
$654$	16.4005	+	21.7362i	0.641311	+	0.849954i
$655$	25.2007	−	6.75252i	0.984674	−	0.263843i
$656$	0.974309	+	3.63617i	0.0380404	+	0.141969i
$657$	6.96999	+	12.5376i	0.271925	+	0.489138i
$658$	0.762750	−	0.762750i	0.0297351	−	0.0297351i
$659$	−20.1845	+	11.6535i	−0.786277	+	0.453957i	−0.838650	−	0.544670i	$-0.816655\pi$
$659$	−20.1845	+	11.6535i	−0.786277	+	0.453957i	0.0523733	+	0.998628i	$0.483321\pi$
$660$	−4.26878	−	1.80887i	−0.166162	−	0.0704103i
$661$	0.131680	+	0.491436i	0.00512175	+	0.0191146i	0.968439	−	0.249249i	$-0.0801838\pi$
$661$	0.131680	+	0.491436i	0.00512175	+	0.0191146i	−0.963318	+	0.268364i	$0.913517\pi$
$662$	−11.2573	−	19.4982i	−0.437526	−	0.757818i
$663$	−15.2255	+	4.24233i	−0.591309	+	0.164758i
$664$	6.14753	−	10.6478i	0.238570	−	0.413216i
$665$	2.10949	+	0.565235i	0.0818023	+	0.0219189i
$666$	−1.79627	−	7.16668i	−0.0696041	−	0.277703i
$667$	−8.56730	−	4.94634i	−0.331727	−	0.191523i
$668$	2.33689	+	8.72138i	0.0904169	+	0.337440i
$669$	0.142801	−	1.02066i	0.00552099	−	0.0394610i
$670$	1.16362	−	1.16362i	0.0449546	−	0.0449546i
$671$	4.63097	−	17.2830i	0.178777	−	0.667204i
$672$	−0.479403	−	0.203145i	−0.0184934	−	0.00783647i
$673$			8.41494i			0.324372i	0.986760	+	0.162186i	$0.0518545\pi$
$673$			8.41494i			0.324372i	−0.986760	+	0.162186i	$0.948146\pi$
$674$	3.65243	−	13.6310i	0.140686	−	0.525048i
$675$	11.1094	+	1.73844i	0.427602	+	0.0669124i
$676$	−3.81566	−	12.4274i	−0.146756	−	0.477978i
$677$	−17.7008	−	10.2196i	−0.680297	−	0.392770i	0.119670	−	0.992814i	$-0.461816\pi$
$677$	−17.7008	−	10.2196i	−0.680297	−	0.392770i	−0.799967	+	0.600044i	$0.795150\pi$
$678$	2.33770	−	16.7086i	0.0897789	−	0.641690i
$679$	0.938721	−	1.62591i	0.0360248	−	0.0623968i
$680$	−4.26212			−0.163445
$681$	11.8583	+	29.2981i	0.454410	+	1.12270i
$682$	4.42112	−	16.4998i	0.169293	−	0.631811i
$683$	16.8568	−	4.51677i	0.645008	−	0.172829i	0.0785371	−	0.996911i	$-0.474975\pi$
$683$	16.8568	−	4.51677i	0.645008	−	0.172829i	0.566471	+	0.824082i	$0.308308\pi$
$684$	12.9403	+	0.209864i	0.494786	+	0.00802435i
$685$	−18.0112	+	31.1964i	−0.688174	+	1.19195i
$686$	−4.18134			−0.159644
$687$	6.68456	+	16.5155i	0.255032	+	0.630104i
$688$	6.42917	−	3.71188i	0.245110	−	0.141514i
$689$	1.94287	+	12.9472i	0.0740175	+	0.493250i
$690$	3.07791	−	2.32236i	0.117174	−	0.0884106i
$691$	5.28654	+	5.28654i	0.201110	+	0.201110i	0.800475	−	0.599366i	$-0.204580\pi$
$691$	5.28654	+	5.28654i	0.201110	+	0.201110i	−0.599366	+	0.800475i	$0.704580\pi$
$692$	−13.6243	+	7.86600i	−0.517919	+	0.299020i
$693$	1.39041	−	0.348496i	0.0528173	−	0.0132383i
$694$	−17.4040	−	17.4040i	−0.660648	−	0.660648i
$695$	15.0127	+	4.02264i	0.569464	+	0.152587i
$696$	−12.8371	−	1.79604i	−0.486589	−	0.0680787i
$697$	−9.20278	−	2.46588i	−0.348580	−	0.0934018i
$698$		−	22.4035i		−	0.847984i
$699$	−22.7184	−	30.1095i	−0.859288	−	1.13885i
$700$	−0.459989	+	0.459989i	−0.0173859	+	0.0173859i
$701$	−31.1840			−1.17780			−0.588901	−	0.808205i	$-0.700439\pi$
$701$	−31.1840			−1.17780			−0.588901	+	0.808205i	$0.700439\pi$
$702$	4.96243	−	18.0658i	0.187295	−	0.681851i
$703$	−10.6245			−0.400711
$704$	1.12392	−	1.12392i	0.0423595	−	0.0423595i
$705$	6.30418	+	8.35517i	0.237429	+	0.314674i
$706$		−	17.7723i		−	0.668870i
$707$	2.49499	+	0.668529i	0.0938336	+	0.0251426i
$708$	−1.24307	−	0.173919i	−0.0467175	−	0.00653626i
$709$	−8.04984	−	2.15695i	−0.302318	−	0.0810059i	0.104471	−	0.994528i	$-0.466685\pi$
$709$	−8.04984	−	2.15695i	−0.302318	−	0.0810059i	−0.406789	+	0.913522i	$0.633352\pi$
$710$	8.47140	+	8.47140i	0.317926	+	0.317926i
$711$	−15.4215	−	15.9300i	−0.578353	−	0.597421i
$712$	−1.71358	+	0.989338i	−0.0642192	+	0.0370770i
$713$	10.0454	+	10.0454i	0.376203	+	0.376203i
$714$	1.05192	−	0.793697i	0.0393670	−	0.0297034i
$715$	6.01243	+	7.54941i	0.224852	+	0.282332i
$716$	5.70819	−	3.29562i	0.213325	−	0.123163i
$717$	−12.1726	−	30.0747i	−0.454595	−	1.12316i
$718$	12.7360			0.475305
$719$	−5.63051	+	9.75233i	−0.209983	+	0.363701i	−0.951709	−	0.307002i	$-0.900674\pi$
$719$	−5.63051	+	9.75233i	−0.209983	+	0.363701i	0.741726	+	0.670703i	$0.234007\pi$
$720$	2.59667	−	4.33371i	0.0967721	−	0.161508i
$721$	0.0764807	−	0.0204930i	0.00284829	−	0.000763197i
$722$	−0.100752	+	0.376011i	−0.00374959	+	0.0139937i
$723$	2.87643	+	7.10676i	0.106976	+	0.264303i
$724$	11.2750			0.419031
$725$	−8.09744	+	14.0252i	−0.300731	+	0.520882i
$726$	2.03361	−	14.5351i	0.0754744	−	0.539449i
$727$	5.52426	+	3.18943i	0.204883	+	0.118290i	0.598931	−	0.800800i	$-0.295592\pi$
$727$	5.52426	+	3.18943i	0.204883	+	0.118290i	−0.394048	+	0.919090i	$0.628926\pi$
$728$	0.675222	+	0.847832i	0.0250254	+	0.0314227i
$729$	19.9977	−	18.1409i	0.740657	−	0.671884i
$730$	2.08410	−	7.77798i	0.0771362	−	0.287876i
$731$			18.7888i			0.694929i
$732$	17.9525	+	7.60728i	0.663543	+	0.281173i
$733$	6.48221	−	24.1919i	0.239426	−	0.893550i	−0.736678	−	0.676244i	$-0.763606\pi$
$733$	6.48221	−	24.1919i	0.239426	−	0.893550i	0.976104	−	0.217306i	$-0.0697268\pi$
$734$	−25.2585	+	25.2585i	−0.932308	+	0.932308i
$735$	2.79259	−	19.9599i	0.103006	−	0.736230i
$736$	0.342133	+	1.27686i	0.0126112	+	0.0470655i
$737$	−1.34511	−	0.776601i	−0.0495478	−	0.0286065i
$738$	8.11403	−	7.85504i	0.298681	−	0.289148i
$739$	42.5336	+	11.3968i	1.56462	+	0.419240i	0.934124	−	0.356950i	$-0.116183\pi$
$739$	42.5336	+	11.3968i	1.56462	+	0.419240i	0.630500	+	0.776189i	$0.282850\pi$
$740$	−2.07371	+	3.59177i	−0.0762311	+	0.132036i
$741$	−23.4644	−	13.2379i	−0.861985	−	0.486306i
$742$	−0.545771	−	0.945302i	−0.0200359	−	0.0347031i
$743$	−1.38387	−	5.16468i	−0.0507693	−	0.189474i	0.935884	−	0.352308i	$-0.114603\pi$
$743$	−1.38387	−	5.16468i	−0.0507693	−	0.189474i	−0.986653	+	0.162834i	$0.947936\pi$
$744$	17.1390	+	7.26255i	0.628345	+	0.266258i
$745$	−32.3937	+	18.7025i	−1.18681	+	0.685208i
$746$	−7.67860	+	7.67860i	−0.281134	+	0.281134i
$747$	−36.8803	−	0.598118i	−1.34938	−	0.0218840i
$748$	1.04117	+	3.88571i	0.0380691	+	0.142076i
$749$	3.83709	−	1.02815i	0.140204	−	0.0375676i
$750$	−12.5860	−	16.6807i	−0.459576	−	0.609094i
$751$	−16.4494	−	9.49704i	−0.600246	−	0.346552i	0.168892	−	0.985634i	$-0.445981\pi$
$751$	−16.4494	−	9.49704i	−0.600246	−	0.346552i	−0.769138	+	0.639082i	$0.779314\pi$
$752$	−3.46610	+	0.928739i	−0.126396	+	0.0338676i
$753$	50.9151	−	6.28355i	1.85545	−	0.228985i
$754$	21.6999	+	16.0370i	0.790263	+	0.584035i
$755$			29.0562i			1.05746i
$756$	0.166156	+	1.55314i	0.00604302	+	0.0564872i
$757$	16.5655	+	28.6922i	0.602082	+	1.04284i	0.992505	+	0.122202i	$0.0389954\pi$
$757$	16.5655	+	28.6922i	0.602082	+	1.04284i	−0.390423	+	0.920636i	$0.627671\pi$
$758$	−6.59556	−	11.4238i	−0.239562	−	0.414933i
$759$	−2.86915	−	2.23877i	−0.104143	−	0.0812621i
$760$	−5.13710	−	5.13710i	−0.186342	−	0.186342i
$761$	31.7060	+	31.7060i	1.14934	+	1.14934i	0.986683	+	0.162658i	$0.0520067\pi$
$761$	31.7060	+	31.7060i	1.14934	+	1.14934i	0.162658	+	0.986683i	$0.447993\pi$
$762$	28.1174	−	11.3804i	1.01859	−	0.412269i
$763$	2.36291	+	4.09268i	0.0855431	+	0.148165i
$764$	5.48262	+	9.49618i	0.198354	+	0.343560i
$765$	6.21278	+	11.1755i	0.224624	+	0.404052i
$766$		−	13.7780i		−	0.497820i
$767$	2.10130	+	1.55294i	0.0758734	+	0.0560734i
$768$	1.04323	+	1.38263i	0.0376443	+	0.0498914i
$769$	−7.46852	+	2.00118i	−0.269322

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.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.04323 + 1.38263i) q^{3} -1.00000i q^{4} +(1.62665 + 0.435860i) q^{5} +(1.71534 + 0.239994i) q^{6} +(0.290365 + 0.0778030i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.823344 + 2.88481i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.04323 + 1.38263i) q^{3} -1.00000i q^{4} +(1.62665 + 0.435860i) q^{5} +(1.71534 + 0.239994i) q^{6} +(0.290365 + 0.0778030i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.823344 + 2.88481i) q^{9} +(1.45842 - 0.842018i) q^{10} +(-1.12392 - 1.12392i) q^{11} +(1.38263 - 1.04323i) q^{12} +(-3.56563 + 0.535061i) q^{13} +(0.260334 - 0.150304i) q^{14} +(1.09434 + 2.70377i) q^{15} -1.00000 q^{16} +(1.26545 - 2.19182i) q^{17} +(1.45767 + 2.62206i) q^{18} +(4.16702 - 1.11655i) q^{19} +(0.435860 - 1.62665i) q^{20} +(0.195344 + 0.482634i) q^{21} -1.58947 q^{22} +(0.660949 - 1.14480i) q^{23} +(0.239994 - 1.71534i) q^{24} +(-1.87410 - 1.08201i) q^{25} +(-2.14293 + 2.89963i) q^{26} +(-4.84756 + 1.87113i) q^{27} +(0.0778030 - 0.290365i) q^{28} -7.48368i q^{29} +(2.68566 + 1.13804i) q^{30} +(-2.78151 + 10.3807i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.381463 - 2.72648i) q^{33} +(-0.655045 - 2.44466i) q^{34} +(0.438411 + 0.253117i) q^{35} +(2.88481 + 0.823344i) q^{36} +(-2.37887 - 0.637416i) q^{37} +(2.15701 - 3.73605i) q^{38} +(-4.45956 - 4.37176i) q^{39} +(-0.842018 - 1.45842i) q^{40} +(-0.974309 - 3.63617i) q^{41} +(0.479403 + 0.203145i) q^{42} +(-6.42917 + 3.71188i) q^{43} +(-1.12392 + 1.12392i) q^{44} +(-2.59667 + 4.33371i) q^{45} +(-0.342133 - 1.27686i) q^{46} +(3.46610 - 0.928739i) q^{47} +(-1.04323 - 1.38263i) q^{48} +(-5.98392 - 3.45482i) q^{49} +(-2.09029 + 0.560091i) q^{50} +(4.35064 - 0.536923i) q^{51} +(0.535061 + 3.56563i) q^{52} -3.63112i q^{53} +(-2.10465 + 4.75083i) q^{54} +(-1.33836 - 2.31811i) q^{55} +(-0.150304 - 0.260334i) q^{56} +(5.89093 + 4.59664i) q^{57} +(-5.29176 - 5.29176i) q^{58} +(-0.512425 - 0.512425i) q^{59} +(2.70377 - 1.09434i) q^{60} +(5.62852 + 9.74888i) q^{61} +(5.37346 + 9.30710i) q^{62} +(-0.463517 + 0.773587i) q^{63} +1.00000i q^{64} +(-6.03325 - 0.683757i) q^{65} +(-1.65818 - 2.19765i) q^{66} +(0.943886 - 0.252913i) q^{67} +(-2.19182 - 1.26545i) q^{68} +(2.27236 - 0.280437i) q^{69} +(0.488984 - 0.131023i) q^{70} +(1.84126 + 6.87167i) q^{71} +(2.62206 - 1.45767i) q^{72} +(3.38109 - 3.38109i) q^{73} +(-2.13284 + 1.23139i) q^{74} +(-0.459092 - 3.71998i) q^{75} +(-1.11655 - 4.16702i) q^{76} +(-0.238903 - 0.413792i) q^{77} +(-6.24469 + 0.0620844i) q^{78} +(-3.69530 + 6.40045i) q^{79} +(-1.62665 - 0.435860i) q^{80} +(-7.64421 - 4.75038i) q^{81} +(-3.26010 - 1.88222i) q^{82} +(3.18219 + 11.8761i) q^{83} +(0.482634 - 0.195344i) q^{84} +(3.01378 - 3.01378i) q^{85} +(-1.92141 + 7.17081i) q^{86} +(10.3472 - 7.80720i) q^{87} +1.58947i q^{88} +(0.512119 - 1.91125i) q^{89} +(1.22828 + 4.90052i) q^{90} +(-1.07696 - 0.122054i) q^{91} +(-1.14480 - 0.660949i) q^{92} +(-17.2545 + 6.98367i) q^{93} +(1.79419 - 3.10762i) q^{94} +7.26495 q^{95} +(-1.71534 - 0.239994i) q^{96} +(1.61645 - 6.03268i) q^{97} +(-6.67419 + 1.78835i) q^{98} +(4.16768 - 2.31693i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 56 * q + 4 * q^7	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

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