LMFDB - Embedded newform 234.3.bb.d.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,3,Mod(19,234)]

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([0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("234.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	234.bb (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:	$6.37603818603$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 82x^{5} + 5053x^{4} - 6736x^{3} + 6728x^{2} + 275384x + 5635876 $ x^8 - 2x^7 + 2x^6 + 82x^5 + 5053x^4 - 6736x^3 + 6728x^2 + 275384*x + 5635876
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.1
Root			$5.41254 + 5.41254i$ of defining polynomial
Character	$\chi$	$=$	234.19
Dual form			234.3.bb.d.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-4.41254 + 4.41254i) q^{5} +(2.11510 - 7.89367i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-4.41254 + 4.41254i) q^{5} +(2.11510 - 7.89367i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-7.64274 - 4.41254i) q^{10} +(-18.5194 + 4.96225i) q^{11} +(-12.9213 + 1.42820i) q^{13} +11.5571 q^{14} +(2.00000 - 3.46410i) q^{16} +(19.9936 - 11.5433i) q^{17} +(0.417587 + 0.111892i) q^{19} +(3.23020 - 12.0553i) q^{20} +(-13.5571 - 23.4816i) q^{22} +(-36.4688 - 21.0553i) q^{23} -13.9410i q^{25} +(-6.68049 - 17.1281i) q^{26} +(4.23020 + 15.7873i) q^{28} +(3.25785 - 5.64275i) q^{29} +(-17.8476 + 17.8476i) q^{31} +(5.46410 + 1.46410i) q^{32} +(23.0866 + 23.0866i) q^{34} +(25.4982 + 44.1641i) q^{35} +(-1.37988 + 0.369738i) q^{37} +0.611390i q^{38} +17.6502 q^{40} +(10.8187 + 40.3758i) q^{41} +(-51.1299 + 29.5199i) q^{43} +(27.1143 - 27.1143i) q^{44} +(15.4135 - 57.5241i) q^{46} +(-15.0543 - 15.0543i) q^{47} +(-15.4011 - 8.89182i) q^{49} +(19.0438 - 5.10277i) q^{50} +(20.9522 - 15.3950i) q^{52} -8.90794 q^{53} +(59.8214 - 103.614i) q^{55} +(-20.0175 + 11.5571i) q^{56} +(8.90060 + 2.38491i) q^{58} +(-11.4200 + 42.6199i) q^{59} +(44.8027 + 77.6005i) q^{61} +(-30.9130 - 17.8476i) q^{62} +8.00000i q^{64} +(50.7138 - 63.3178i) q^{65} +(10.2563 + 38.2772i) q^{67} +(-23.0866 + 39.9872i) q^{68} +(-50.9963 + 50.9963i) q^{70} +(-8.56730 - 2.29560i) q^{71} +(-5.92683 - 5.92683i) q^{73} +(-1.01014 - 1.74962i) q^{74} +(-0.835174 + 0.223784i) q^{76} +156.682i q^{77} +115.826 q^{79} +(6.46041 + 24.1106i) q^{80} +(-51.1945 + 29.5572i) q^{82} +(34.2340 - 34.2340i) q^{83} +(-37.2872 + 139.158i) q^{85} +(-59.0397 - 59.0397i) q^{86} +(46.9633 + 27.1143i) q^{88} +(-58.0728 + 15.5606i) q^{89} +(-16.0561 + 105.017i) q^{91} +84.2211 q^{92} +(15.0543 - 26.0747i) q^{94} +(-2.33635 + 1.34889i) q^{95} +(-129.142 - 34.6035i) q^{97} +(6.50926 - 24.2929i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 6 q^{5} + 10 q^{7} - 16 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 + 6 * q^5 + 10 * q^7 - 16 * q^8	$ 8 q - 4 q^{2} + 6 q^{5} + 10 q^{7} - 16 q^{8} - 6 q^{10} - 24 q^{11} - 4 q^{14} + 16 q^{16} + 84 q^{17} + 10 q^{19} + 12 q^{20} - 12 q^{22} + 12 q^{23} - 26 q^{26} + 20 q^{28} - 36 q^{29} - 94 q^{31} + 16 q^{32} + 60 q^{34} + 204 q^{35} + 140 q^{37} - 24 q^{40} - 72 q^{41} - 222 q^{43} + 24 q^{44} - 84 q^{46} - 300 q^{47} + 42 q^{49} + 62 q^{50} + 44 q^{52} - 84 q^{53} + 396 q^{55} - 36 q^{56} - 66 q^{58} + 60 q^{59} - 90 q^{61} - 198 q^{62} + 108 q^{65} + 304 q^{67} - 60 q^{68} - 408 q^{70} + 192 q^{71} + 16 q^{73} + 46 q^{74} - 20 q^{76} - 96 q^{79} + 24 q^{80} + 114 q^{82} - 390 q^{85} - 168 q^{86} + 72 q^{88} - 354 q^{89} - 218 q^{91} + 288 q^{92} + 300 q^{94} + 576 q^{95} - 460 q^{97} - 58 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 6 * q^5 + 10 * q^7 - 16 * q^8 - 6 * q^10 - 24 * q^11 - 4 * q^14 + 16 * q^16 + 84 * q^17 + 10 * q^19 + 12 * q^20 - 12 * q^22 + 12 * q^23 - 26 * q^26 + 20 * q^28 - 36 * q^29 - 94 * q^31 + 16 * q^32 + 60 * q^34 + 204 * q^35 + 140 * q^37 - 24 * q^40 - 72 * q^41 - 222 * q^43 + 24 * q^44 - 84 * q^46 - 300 * q^47 + 42 * q^49 + 62 * q^50 + 44 * q^52 - 84 * q^53 + 396 * q^55 - 36 * q^56 - 66 * q^58 + 60 * q^59 - 90 * q^61 - 198 * q^62 + 108 * q^65 + 304 * q^67 - 60 * q^68 - 408 * q^70 + 192 * q^71 + 16 * q^73 + 46 * q^74 - 20 * q^76 - 96 * q^79 + 24 * q^80 + 114 * q^82 - 390 * q^85 - 168 * q^86 + 72 * q^88 - 354 * q^89 - 218 * q^91 + 288 * q^92 + 300 * q^94 + 576 * q^95 - 460 * q^97 - 58 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.366025	+	1.36603i	0.183013	+	0.683013i
$2$	0.366025	+	1.36603i	0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$	−4.41254	+	4.41254i	−0.882508	+	0.882508i	−0.993789	−	0.111281i	$-0.964505\pi$
$5$	−4.41254	+	4.41254i	−0.882508	+	0.882508i	0.111281	+	0.993789i	$0.464505\pi$
$6$		0			0
$7$	2.11510	−	7.89367i	0.302157	−	1.12767i	−0.633207	−	0.773982i	$-0.718262\pi$
$7$	2.11510	−	7.89367i	0.302157	−	1.12767i	0.935365	−	0.353685i	$-0.115071\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$		0			0
$10$	−7.64274	−	4.41254i	−0.764274	−	0.441254i
$11$	−18.5194	+	4.96225i	−1.68358	+	0.451114i	−0.968721	−	0.248154i	$-0.920176\pi$
$11$	−18.5194	+	4.96225i	−1.68358	+	0.451114i	−0.714860	+	0.699268i	$0.753510\pi$
$12$		0			0
$13$	−12.9213	+	1.42820i	−0.993947	+	0.109862i
$13$	−12.9213	+	1.42820i	−0.993947	+	0.109862i
$14$	11.5571			0.825509
$15$		0			0
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	19.9936	−	11.5433i	1.17609	−	0.679018i	0.220986	−	0.975277i	$-0.429073\pi$
$17$	19.9936	−	11.5433i	1.17609	−	0.679018i	0.955108	+	0.296259i	$0.0957392\pi$
$18$		0			0
$19$	0.417587	+	0.111892i	0.0219783	+	0.00588906i	0.269791	−	0.962919i	$-0.413045\pi$
$19$	0.417587	+	0.111892i	0.0219783	+	0.00588906i	−0.247813	+	0.968808i	$0.579712\pi$
$20$	3.23020	−	12.0553i	0.161510	−	0.602764i
$21$		0			0
$22$	−13.5571	−	23.4816i	−0.616233	−	1.06735i
$23$	−36.4688	−	21.0553i	−1.58560	−	0.915447i	−0.994020	−	0.109202i	$-0.965171\pi$
$23$	−36.4688	−	21.0553i	−1.58560	−	0.915447i	−0.591581	−	0.806245i	$-0.701496\pi$
$24$		0			0
$25$		−	13.9410i		−	0.557641i
$26$	−6.68049	−	17.1281i	−0.256942	−	0.658772i
$27$		0			0
$28$	4.23020	+	15.7873i	0.151079	+	0.563833i
$29$	3.25785	−	5.64275i	0.112340	−	0.194578i	−0.804374	−	0.594124i	$-0.797499\pi$
$29$	3.25785	−	5.64275i	0.112340	−	0.194578i	0.916713	+	0.399546i	$0.130832\pi$
$30$		0			0
$31$	−17.8476	+	17.8476i	−0.575730	+	0.575730i	−0.933724	−	0.357994i	$-0.883461\pi$
$31$	−17.8476	+	17.8476i	−0.575730	+	0.575730i	0.357994	+	0.933724i	$0.383461\pi$
$32$	5.46410	+	1.46410i	0.170753	+	0.0457532i
$33$		0			0
$34$	23.0866	+	23.0866i	0.679018	+	0.679018i
$35$	25.4982	+	44.1641i	0.728519	+	1.26183i
$36$		0			0
$37$	−1.37988	+	0.369738i	−0.0372940	+	0.00999291i	−0.277418	−	0.960749i	$-0.589479\pi$
$37$	−1.37988	+	0.369738i	−0.0372940	+	0.00999291i	0.240124	+	0.970742i	$0.422812\pi$
$38$			0.611390i			0.0160892i
$39$		0			0
$40$	17.6502			0.441254
$41$	10.8187	+	40.3758i	0.263870	+	0.984776i	0.962938	+	0.269721i	$0.0869316\pi$
$41$	10.8187	+	40.3758i	0.263870	+	0.984776i	−0.699068	+	0.715055i	$0.746402\pi$
$42$		0			0
$43$	−51.1299	+	29.5199i	−1.18907	+	0.686509i	−0.958095	−	0.286452i	$-0.907524\pi$
$43$	−51.1299	+	29.5199i	−1.18907	+	0.686509i	−0.230973	+	0.972960i	$0.574191\pi$
$44$	27.1143	−	27.1143i	0.616233	−	0.616233i
$45$		0			0
$46$	15.4135	−	57.5241i	0.335077	−	1.25052i
$47$	−15.0543	−	15.0543i	−0.320303	−	0.320303i	0.528580	−	0.848883i	$-0.322725\pi$
$47$	−15.0543	−	15.0543i	−0.320303	−	0.320303i	−0.848883	+	0.528580i	$0.822725\pi$
$48$		0			0
$49$	−15.4011	−	8.89182i	−0.314308	−	0.181466i
$50$	19.0438	−	5.10277i	0.380876	−	0.102055i
$51$		0			0
$52$	20.9522	−	15.3950i	0.402926	−	0.296058i
$53$	−8.90794			−0.168074			−0.0840372	−	0.996463i	$-0.526781\pi$
$53$	−8.90794			−0.168074			−0.0840372	+	0.996463i	$0.526781\pi$
$54$		0			0
$55$	59.8214	−	103.614i	1.08766	−	1.88389i
$56$	−20.0175	+	11.5571i	−0.357456	+	0.206377i
$57$		0			0
$58$	8.90060	+	2.38491i	0.153459	+	0.0411191i
$59$	−11.4200	+	42.6199i	−0.193559	+	0.722371i	0.799077	+	0.601229i	$0.205322\pi$
$59$	−11.4200	+	42.6199i	−0.193559	+	0.722371i	−0.992635	+	0.121141i	$0.961345\pi$
$60$		0			0
$61$	44.8027	+	77.6005i	0.734470	+	1.27214i	0.954955	+	0.296749i	$0.0959025\pi$
$61$	44.8027	+	77.6005i	0.734470	+	1.27214i	−0.220485	+	0.975390i	$0.570764\pi$
$62$	−30.9130	−	17.8476i	−0.498597	−	0.287865i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	50.7138	−	63.3178i	0.780212	−	0.974120i
$66$		0			0
$67$	10.2563	+	38.2772i	0.153080	+	0.571302i	0.999262	+	0.0384081i	$0.0122287\pi$
$67$	10.2563	+	38.2772i	0.153080	+	0.571302i	−0.846182	+	0.532893i	$0.821105\pi$
$68$	−23.0866	+	39.9872i	−0.339509	+	0.588047i
$69$		0			0
$70$	−50.9963	+	50.9963i	−0.728519	+	0.728519i
$71$	−8.56730	−	2.29560i	−0.120666	−	0.0323324i	0.197981	−	0.980206i	$-0.436562\pi$
$71$	−8.56730	−	2.29560i	−0.120666	−	0.0323324i	−0.318647	+	0.947874i	$0.603228\pi$
$72$		0			0
$73$	−5.92683	−	5.92683i	−0.0811895	−	0.0811895i	0.665346	−	0.746535i	$-0.268284\pi$
$73$	−5.92683	−	5.92683i	−0.0811895	−	0.0811895i	−0.746535	+	0.665346i	$0.768284\pi$
$74$	−1.01014	−	1.74962i	−0.0136506	−	0.0236435i
$75$		0			0
$76$	−0.835174	+	0.223784i	−0.0109891	+	0.00294453i
$77$			156.682i			2.03483i
$78$		0			0
$79$	115.826			1.46616			0.733078	−	0.680144i	$-0.238083\pi$
$79$	115.826			1.46616			0.733078	+	0.680144i	$0.238083\pi$
$80$	6.46041	+	24.1106i	0.0807551	+	0.301382i
$81$		0			0
$82$	−51.1945	+	29.5572i	−0.624323	+	0.360453i
$83$	34.2340	−	34.2340i	0.412458	−	0.412458i	−0.470136	−	0.882594i	$-0.655795\pi$
$83$	34.2340	−	34.2340i	0.412458	−	0.412458i	0.882594	+	0.470136i	$0.155795\pi$
$84$		0			0
$85$	−37.2872	+	139.158i	−0.438673	+	1.63715i
$86$	−59.0397	−	59.0397i	−0.686509	−	0.686509i
$87$		0			0
$88$	46.9633	+	27.1143i	0.533674	+	0.308117i
$89$	−58.0728	+	15.5606i	−0.652503	+	0.174838i	−0.569860	−	0.821741i	$-0.693003\pi$
$89$	−58.0728	+	15.5606i	−0.652503	+	0.174838i	−0.0826429	+	0.996579i	$0.526336\pi$
$90$		0			0
$91$	−16.0561	+	105.017i	−0.176441	+	1.15404i
$92$	84.2211			0.915447
$93$		0			0
$94$	15.0543	−	26.0747i	0.160152	−	0.277391i
$95$	−2.33635	+	1.34889i	−0.0245931	+	0.0141988i
$96$		0			0
$97$	−129.142	−	34.6035i	−1.33136	−	0.356737i	−0.478139	−	0.878284i	$-0.658688\pi$
$97$	−129.142	−	34.6035i	−1.33136	−	0.356737i	−0.853223	+	0.521547i	$0.825355\pi$
$98$	6.50926	−	24.2929i	0.0664211	−	0.247887i
$99$		0			0
$100$	13.9410	+	24.1466i	0.139410	+	0.241466i
$101$	−33.1291	−	19.1271i	−0.328010	−	0.189377i	0.326947	−	0.945043i	$-0.393980\pi$
$101$	−33.1291	−	19.1271i	−0.328010	−	0.189377i	−0.654957	+	0.755666i	$0.727313\pi$
$102$		0			0
$103$		−	65.9827i		−	0.640609i	−0.947315	−	0.320304i	$-0.896215\pi$
$103$		−	65.9827i		−	0.640609i	0.947315	−	0.320304i	$-0.103785\pi$
$104$	28.6990	+	22.9862i	0.275952	+	0.221021i
$105$		0			0
$106$	−3.26053	−	12.1685i	−0.0307597	−	0.114797i
$107$	47.2413	−	81.8244i	0.441508	−	0.764714i	−0.556294	−	0.830986i	$-0.687777\pi$
$107$	47.2413	−	81.8244i	0.441508	−	0.764714i	0.997802	+	0.0662716i	$0.0211104\pi$
$108$		0			0
$109$	−100.935	+	100.935i	−0.926011	+	0.926011i	−0.997445	−	0.0714342i	$-0.977242\pi$
$109$	−100.935	+	100.935i	−0.926011	+	0.926011i	0.0714342	+	0.997445i	$0.477242\pi$
$110$	163.435	+	43.7923i	1.48577	+	0.398112i
$111$		0			0
$112$	−23.1143	−	23.1143i	−0.206377	−	0.206377i
$113$	15.3509	+	26.5885i	0.135849	+	0.235297i	0.925921	−	0.377716i	$-0.123291\pi$
$113$	15.3509	+	26.5885i	0.135849	+	0.235297i	−0.790073	+	0.613013i	$0.789957\pi$
$114$		0			0
$115$	253.827	−	68.0129i	2.20720	−	0.591416i
$116$			13.0314i			0.112340i
$117$		0			0
$118$	−62.3998			−0.528812
$119$	−48.8305	−	182.238i	−0.410341	−	1.53141i
$120$		0			0
$121$	213.555	−	123.296i	1.76491	−	1.01897i
$122$	−89.6053	+	89.6053i	−0.734470	+	0.734470i
$123$		0			0
$124$	13.0654	−	48.7607i	0.105366	−	0.393231i
$125$	−48.7982	−	48.7982i	−0.390385	−	0.390385i
$126$		0			0
$127$	−137.861	−	79.5940i	−1.08552	−	0.626725i	−0.153139	−	0.988205i	$-0.548938\pi$
$127$	−137.861	−	79.5940i	−1.08552	−	0.626725i	−0.932380	+	0.361480i	$0.882272\pi$
$128$	−10.9282	+	2.92820i	−0.0853766	+	0.0228766i
$129$		0			0
$130$	105.056	+	46.1004i	0.808125	+	0.354619i
$131$	−88.8918			−0.678563			−0.339282	−	0.940685i	$-0.610184\pi$
$131$	−88.8918			−0.678563			−0.339282	+	0.940685i	$0.610184\pi$
$132$		0			0
$133$	1.76648	−	3.05963i	0.0132818	−	0.0230047i
$134$	−48.5335	+	28.0209i	−0.362191	+	0.209111i
$135$		0			0
$136$	−63.0738	−	16.9006i	−0.463778	−	0.124269i
$137$	−28.4831	+	106.300i	−0.207906	+	0.775915i	0.780638	+	0.624983i	$0.214894\pi$
$137$	−28.4831	+	106.300i	−0.207906	+	0.775915i	−0.988544	+	0.150932i	$0.951773\pi$
$138$		0			0
$139$	−124.068	−	214.891i	−0.892573	−	1.54598i	−0.836780	−	0.547539i	$-0.815565\pi$
$139$	−124.068	−	214.891i	−0.892573	−	1.54598i	−0.0557926	−	0.998442i	$-0.517769\pi$
$140$	−88.3282	−	50.9963i	−0.630916	−	0.364259i
$141$		0			0
$142$		−	12.5434i		−	0.0883338i
$143$	232.208	−	90.5683i	1.62383	−	0.633345i
$144$		0			0
$145$	10.5235	+	39.2743i	0.0725759	+	0.270857i
$146$	5.92683	−	10.2656i	0.0405947	−	0.0703121i
$147$		0			0
$148$	2.02028	−	2.02028i	0.0136506	−	0.0136506i
$149$	133.409	+	35.7469i	0.895363	+	0.239912i	0.677024	−	0.735961i	$-0.263269\pi$
$149$	133.409	+	35.7469i	0.895363	+	0.239912i	0.218339	+	0.975873i	$0.429936\pi$
$150$		0			0
$151$	−19.6390	−	19.6390i	−0.130060	−	0.130060i	0.639080	−	0.769140i	$-0.279315\pi$
$151$	−19.6390	−	19.6390i	−0.130060	−	0.130060i	−0.769140	+	0.639080i	$0.779315\pi$
$152$	−0.611390	−	1.05896i	−0.00402230	−	0.00696683i
$153$		0			0
$154$	−214.031	+	57.3494i	−1.38981	+	0.372399i
$155$		−	157.507i		−	1.01617i
$156$		0			0
$157$	−121.293			−0.772569			−0.386285	−	0.922380i	$-0.626242\pi$
$157$	−121.293			−0.772569			−0.386285	+	0.922380i	$0.626242\pi$
$158$	42.3954	+	158.222i	0.268325	+	1.00140i
$159$		0			0
$160$	−30.5710	+	17.6502i	−0.191069	+	0.110314i
$161$	−243.339	+	243.339i	−1.51142	+	1.51142i
$162$		0			0
$163$	48.9961	−	182.856i	0.300590	−	1.12182i	−0.636086	−	0.771618i	$-0.719448\pi$
$163$	48.9961	−	182.856i	0.300590	−	1.12182i	0.936676	−	0.350198i	$-0.113886\pi$
$164$	−59.1143	−	59.1143i	−0.360453	−	0.360453i
$165$		0			0
$166$	59.2950	+	34.2340i	0.357199	+	0.206229i
$167$	54.7719	−	14.6761i	0.327976	−	0.0878808i	−0.0910740	−	0.995844i	$-0.529030\pi$
$167$	54.7719	−	14.6761i	0.327976	−	0.0878808i	0.419050	+	0.907963i	$0.362363\pi$
$168$		0			0
$169$	164.920	−	36.9085i	0.975861	−	0.218394i
$170$	−203.741			−1.19848
$171$		0			0
$172$	59.0397	−	102.260i	0.343254	−	0.594534i
$173$	281.887	−	162.747i	1.62940	−	0.940736i	0.645130	−	0.764072i	$-0.276803\pi$
$173$	281.887	−	162.747i	1.62940	−	0.940736i	0.984271	−	0.176663i	$-0.0565303\pi$
$174$		0			0
$175$	−110.046	−	29.4867i	−0.628833	−	0.168495i
$176$	−19.8490	+	74.0775i	−0.112779	+	0.420895i
$177$		0			0
$178$	−42.5122	−	73.6334i	−0.238833	−	0.413671i
$179$	122.019	+	70.4476i	0.681670	+	0.393562i	0.800484	−	0.599354i	$-0.204576\pi$
$179$	122.019	+	70.4476i	0.681670	+	0.393562i	−0.118814	+	0.992917i	$0.537909\pi$
$180$		0			0
$181$		−	56.0814i		−	0.309842i	−0.987927	−	0.154921i	$-0.950488\pi$
$181$		−	56.0814i		−	0.309842i	0.987927	−	0.154921i	$-0.0495123\pi$
$182$	−149.333	+	16.5059i	−0.820512	+	0.0906919i
$183$		0			0
$184$	30.8271	+	115.048i	0.167538	+	0.625262i
$185$	4.45729	−	7.72026i	0.0240935	−	0.0417311i
$186$		0			0
$187$	−312.988	+	312.988i	−1.67373	+	1.67373i
$188$	41.1290	+	11.0205i	0.218771	+	0.0586196i
$189$		0			0
$190$	−2.69778	−	2.69778i	−0.0141988	−	0.0141988i
$191$	−80.6165	−	139.632i	−0.422076	−	0.731057i	0.574067	−	0.818809i	$-0.305365\pi$
$191$	−80.6165	−	139.632i	−0.422076	−	0.731057i	−0.996142	+	0.0877520i	$0.972032\pi$
$192$		0			0
$193$	162.089	−	43.4316i	0.839838	−	0.225034i	0.186837	−	0.982391i	$-0.440176\pi$
$193$	162.089	−	43.4316i	0.839838	−	0.225034i	0.653001	+	0.757357i	$0.273510\pi$
$194$		−	189.077i		−	0.974624i
$195$		0			0
$196$	35.5673			0.181466
$197$	−52.3324	−	195.307i	−0.265647	−	0.991407i	−0.961853	−	0.273565i	$-0.911797\pi$
$197$	−52.3324	−	195.307i	−0.265647	−	0.991407i	0.696207	−	0.717841i	$-0.254870\pi$
$198$		0			0
$199$	80.8275	−	46.6658i	0.406168	−	0.234501i	−0.282974	−	0.959128i	$-0.591321\pi$
$199$	80.8275	−	46.6658i	0.406168	−	0.234501i	0.689142	+	0.724626i	$0.257988\pi$
$200$	−27.8820	+	27.8820i	−0.139410	+	0.139410i
$201$		0			0
$202$	14.0020	−	52.2561i	0.0693168	−	0.258694i
$203$	−37.6513	−	37.6513i	−0.185475	−	0.185475i
$204$		0			0
$205$	−225.898	−	130.422i	−1.10194	−	0.636206i
$206$	90.1341	−	24.1514i	0.437544	−	0.117240i
$207$		0			0
$208$	−20.8952	+	47.6171i	−0.100458	+	0.228929i
$209$	−8.28869			−0.0396588
$210$		0			0
$211$	−158.226	+	274.055i	−0.749885	+	1.29884i	0.197993	+	0.980203i	$0.436558\pi$
$211$	−158.226	+	274.055i	−0.749885	+	1.29884i	−0.947877	+	0.318635i	$0.896776\pi$
$212$	15.4290	−	8.90794i	0.0727783	−	0.0420186i
$213$		0			0
$214$	129.066	+	34.5831i	0.603111	+	0.161603i
$215$	95.3552	−	355.870i	0.443513	−	1.65521i
$216$		0			0
$217$	103.134	+	178.633i	0.475271	+	0.823193i
$218$	−174.825	−	100.935i	−0.801949	−	0.463006i
$219$		0			0
$220$			239.286i			1.08766i
$221$	−241.857	+	177.710i	−1.09438	+	0.804116i
$222$		0			0
$223$	17.6758	+	65.9671i	0.0792638	+	0.295817i	0.994166	−	0.107858i	$-0.0343993\pi$
$223$	17.6758	+	65.9671i	0.0792638	+	0.295817i	−0.914902	+	0.403675i	$0.867733\pi$
$224$	23.1143	−	40.0351i	0.103189	−	0.178728i
$225$		0			0
$226$	−30.7018	+	30.7018i	−0.135849	+	0.135849i
$227$	−24.3066	−	6.51292i	−0.107077	−	0.0286913i	0.204882	−	0.978787i	$-0.434319\pi$
$227$	−24.3066	−	6.51292i	−0.107077	−	0.0286913i	−0.311960	+	0.950095i	$0.600985\pi$
$228$		0			0
$229$	−274.910	−	274.910i	−1.20048	−	1.20048i	−0.974020	−	0.226461i	$-0.927284\pi$
$229$	−274.910	−	274.910i	−1.20048	−	1.20048i	−0.226461	−	0.974020i	$-0.572716\pi$
$230$	185.815	+	321.840i	0.807889	+	1.39931i
$231$		0			0
$232$	−17.8012	+	4.76982i	−0.0767293	+	0.0205596i
$233$			401.576i			1.72350i	0.507333	+	0.861750i	$0.330631\pi$
$233$			401.576i			1.72350i	−0.507333	+	0.861750i	$0.669369\pi$
$234$		0			0
$235$	132.855			0.565341
$236$	−22.8399	−	85.2397i	−0.0967793	−	0.361185i
$237$		0			0
$238$	231.069	−	133.407i	0.970876	−	0.560536i
$239$	−305.397	+	305.397i	−1.27781	+	1.27781i	−0.335919	+	0.941891i	$0.609047\pi$
$239$	−305.397	+	305.397i	−1.27781	+	1.27781i	−0.941891	+	0.335919i	$0.890953\pi$
$240$		0			0
$241$	−28.8074	+	107.511i	−0.119533	+	0.446102i	−0.999586	−	0.0287729i	$-0.990840\pi$
$241$	−28.8074	+	107.511i	−0.119533	+	0.446102i	0.880053	+	0.474875i	$0.157507\pi$
$242$	246.592	+	246.592i	1.01897	+	1.01897i
$243$		0			0
$244$	−155.201	−	89.6053i	−0.636070	−	0.367235i
$245$	107.193	−	28.7224i	0.437524	−	0.117234i
$246$		0			0
$247$	−5.55557	−	0.849393i	−0.0224922	−	0.00343884i
$248$	71.3905			0.287865
$249$		0			0
$250$	48.7982	−	84.5209i	0.195193	−	0.338084i
$251$	−75.9010	+	43.8214i	−0.302394	+	0.174587i	−0.643518	−	0.765431i	$-0.722526\pi$
$251$	−75.9010	+	43.8214i	−0.302394	+	0.174587i	0.341124	+	0.940018i	$0.389192\pi$
$252$		0			0
$253$	779.862	+	208.963i	3.08246	+	0.825942i
$254$	58.2669	−	217.455i	0.229397	−	0.856122i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	151.909	+	87.7045i	0.591084	+	0.341263i	0.765526	−	0.643405i	$-0.222479\pi$
$257$	151.909	+	87.7045i	0.591084	+	0.341263i	−0.174442	+	0.984667i	$0.555812\pi$
$258$		0			0
$259$			11.6743i			0.0450747i
$260$	−24.5211	+	160.383i	−0.0943118	+	0.616859i
$261$		0			0
$262$	−32.5366	−	121.428i	−0.124186	−	0.463467i
$263$	−63.6818	+	110.300i	−0.242136	+	0.419392i	−0.961323	−	0.275425i	$-0.911181\pi$
$263$	−63.6818	+	110.300i	−0.242136	+	0.419392i	0.719186	+	0.694817i	$0.244515\pi$
$264$		0			0
$265$	39.3066	−	39.3066i	0.148327	−	0.148327i
$266$	4.82611	+	1.29315i	0.0181433	+	0.00486147i
$267$		0			0
$268$	−56.0417	−	56.0417i	−0.209111	−	0.209111i
$269$	−104.127	−	180.352i	−0.387087	−	0.670455i	0.604969	−	0.796249i	$-0.293186\pi$
$269$	−104.127	−	180.352i	−0.387087	−	0.670455i	−0.992056	+	0.125794i	$0.959852\pi$
$270$		0			0
$271$	3.66031	−	0.980776i	0.0135067	−	0.00361910i	−0.252059	−	0.967712i	$-0.581108\pi$
$271$	3.66031	−	0.980776i	0.0135067	−	0.00361910i	0.265566	+	0.964093i	$0.414441\pi$
$272$		−	92.3464i		−	0.339509i
$273$		0			0
$274$	−155.634			−0.568009
$275$	69.1789	+	258.179i	0.251560	+	0.938833i
$276$		0			0
$277$	59.5357	−	34.3730i	0.214930	−	0.124090i	−0.388670	−	0.921377i	$-0.627065\pi$
$277$	59.5357	−	34.3730i	0.214930	−	0.124090i	0.603601	+	0.797287i	$0.293732\pi$
$278$	248.135	−	248.135i	0.892573	−	0.892573i
$279$		0			0
$280$	37.3319	−	139.324i	0.133328	−	0.497587i
$281$	19.5583	+	19.5583i	0.0696025	+	0.0696025i	0.741051	−	0.671449i	$-0.234328\pi$
$281$	19.5583	+	19.5583i	0.0696025	+	0.0696025i	−0.671449	+	0.741051i	$0.734328\pi$
$282$		0			0
$283$	−109.532	−	63.2384i	−0.387039	−	0.223457i	0.293837	−	0.955855i	$-0.405068\pi$
$283$	−109.532	−	63.2384i	−0.387039	−	0.223457i	−0.680876	+	0.732398i	$0.738401\pi$
$284$	17.1346	−	4.59120i	0.0603331	−	0.0161662i
$285$		0			0
$286$	208.712	+	284.051i	0.729764	+	0.993186i
$287$	341.596			1.19023
$288$		0			0
$289$	121.996	−	211.303i	0.422131	−	0.731152i
$290$	−49.7978	+	28.7507i	−0.171716	+	0.0991405i
$291$		0			0
$292$	16.1924	+	4.33874i	0.0554534	+	0.0148587i
$293$	−96.4402	+	359.920i	−0.329148	+	1.22840i	0.580929	+	0.813954i	$0.302689\pi$
$293$	−96.4402	+	359.920i	−0.329148	+	1.22840i	−0.910076	+	0.414441i	$0.863977\pi$
$294$		0			0
$295$	−137.671	−	238.453i	−0.466681	−	0.808315i
$296$	3.49923	+	2.02028i	0.0118217	+	0.00682528i
$297$		0			0
$298$			195.325i			0.655452i
$299$	501.296	+	219.977i	1.67658	+	0.735709i
$300$		0			0
$301$	124.875	+	466.040i	0.414867	+	1.54831i
$302$	19.6390	−	34.0158i	0.0650299	−	0.112635i
$303$		0			0
$304$	1.22278	−	1.22278i	0.00402230	−	0.00402230i
$305$	−540.109	−	144.722i	−1.77085	−	0.474498i
$306$		0			0
$307$	259.830	+	259.830i	0.846352	+	0.846352i	0.989676	−	0.143324i	$-0.0457792\pi$
$307$	259.830	+	259.830i	0.846352	+	0.846352i	−0.143324	+	0.989676i	$0.545779\pi$
$308$	−156.682	−	271.380i	−0.508706	−	0.881105i
$309$		0			0
$310$	215.158	−	57.6515i	0.694059	−	0.185973i
$311$		−	356.838i		−	1.14739i	−0.819069	−	0.573695i	$-0.805509\pi$
$311$		−	356.838i		−	1.14739i	0.819069	−	0.573695i	$-0.194491\pi$
$312$		0			0
$313$	−19.6152			−0.0626683			−0.0313342	−	0.999509i	$-0.509976\pi$
$313$	−19.6152			−0.0626683			−0.0313342	+	0.999509i	$0.509976\pi$
$314$	−44.3965	−	165.690i	−0.141390	−	0.527675i
$315$		0			0
$316$	−200.617	+	115.826i	−0.634865	+	0.366539i
$317$	139.801	−	139.801i	0.441011	−	0.441011i	−0.451341	−	0.892352i	$-0.649054\pi$
$317$	139.801	−	139.801i	0.441011	−	0.441011i	0.892352	+	0.451341i	$0.149054\pi$
$318$		0			0
$319$	−32.3325	+	120.667i	−0.101356	+	0.378265i
$320$	−35.3003	−	35.3003i	−0.110314	−	0.110314i
$321$		0			0
$322$	−421.475	−	243.339i	−1.30893	−	0.755710i
$323$	9.64066	−	2.58321i	0.0298473	−	0.00799755i
$324$		0			0
$325$	19.9106	+	180.136i	0.0612634	+	0.554265i
$326$	267.720			0.821226
$327$		0			0
$328$	59.1143	−	102.389i	0.180227	−	0.312162i
$329$	−150.675	+	86.9920i	−0.457978	+	0.264413i
$330$		0			0
$331$	265.737	+	71.2040i	0.802830	+	0.215118i	0.636826	−	0.771007i	$-0.280247\pi$
$331$	265.737	+	71.2040i	0.802830	+	0.215118i	0.166004	+	0.986125i	$0.446914\pi$
$332$	−25.0610	+	93.5290i	−0.0754850	+	0.281714i
$333$		0			0
$334$	40.0958	+	69.4480i	0.120047	+	0.207928i
$335$	−214.156	−	123.643i	−0.639272	−	0.369084i
$336$		0			0
$337$			625.952i			1.85743i	0.370800	+	0.928713i	$0.379084\pi$
$337$			625.952i			1.85743i	−0.370800	+	0.928713i	$0.620916\pi$
$338$	110.783	+	211.776i	0.327760	+	0.626557i
$339$		0			0
$340$	−74.5745	−	278.316i	−0.219337	−	0.818575i
$341$	241.963	−	419.092i	0.709568	−	1.22901i
$342$		0			0
$343$	180.386	−	180.386i	0.525906	−	0.525906i
$344$	161.300	+	43.2201i	0.468894	+	0.125640i
$345$		0			0
$346$	325.495	+	325.495i	0.940736	+	0.940736i
$347$	−52.8438	−	91.5282i	−0.152288	−	0.263770i	0.779780	−	0.626053i	$-0.215331\pi$
$347$	−52.8438	−	91.5282i	−0.152288	−	0.263770i	−0.932068	+	0.362283i	$0.881997\pi$
$348$		0			0
$349$	−418.494	+	112.135i	−1.19912	+	0.321304i	−0.802485	−	0.596672i	$-0.796489\pi$
$349$	−418.494	+	112.135i	−1.19912	+	0.321304i	−0.396637	+	0.917976i	$0.629823\pi$
$350$		−	161.118i		−	0.460338i
$351$		0			0
$352$	−108.457			−0.308117
$353$	152.231	+	568.133i	0.431248	+	1.60944i	0.749888	+	0.661565i	$0.230108\pi$
$353$	152.231	+	568.133i	0.431248	+	1.60944i	−0.318639	+	0.947876i	$0.603226\pi$
$354$		0			0
$355$	47.9330	−	27.6741i	0.135023	−	0.0779553i
$356$	85.0245	−	85.0245i	0.238833	−	0.238833i
$357$		0			0
$358$	−51.5712	+	192.466i	−0.144054	+	0.537616i
$359$	−172.896	−	172.896i	−0.481604	−	0.481604i	0.424040	−	0.905644i	$-0.360612\pi$
$359$	−172.896	−	172.896i	−0.481604	−	0.481604i	−0.905644	+	0.424040i	$0.860612\pi$
$360$		0			0
$361$	−312.473	−	180.407i	−0.865577	−	0.499741i
$362$	76.6086	−	20.5272i	0.211626	−	0.0567050i
$363$		0			0
$364$	−77.2073	−	197.951i	−0.212108	−	0.543823i
$365$	52.3048			0.143301
$366$		0			0
$367$	172.613	−	298.974i	0.470335	−	0.814644i	−0.529090	−	0.848566i	$-0.677467\pi$
$367$	172.613	−	298.974i	0.470335	−	0.814644i	0.999424	+	0.0339223i	$0.0107999\pi$
$368$	−145.875	+	84.2211i	−0.396400	+	0.228862i
$369$		0			0
$370$	12.1775	+	3.26296i	0.0329123	+	0.00881882i
$371$	−18.8412	+	70.3163i	−0.0507849	+	0.189532i
$372$		0			0
$373$	−223.291	−	386.751i	−0.598635	−	1.03687i	−0.993023	−	0.117922i	$-0.962377\pi$
$373$	−223.291	−	386.751i	−0.598635	−	1.03687i	0.394388	−	0.918944i	$-0.370957\pi$
$374$	−542.111	−	312.988i	−1.44950	−	0.836867i
$375$		0			0
$376$			60.2170i			0.160152i
$377$	−34.0366	+	77.5646i	−0.0902828	+	0.205742i
$378$		0			0
$379$	58.0212	+	216.538i	0.153090	+	0.571340i	0.999261	+	0.0384290i	$0.0122353\pi$
$379$	58.0212	+	216.538i	0.153090	+	0.571340i	−0.846171	+	0.532911i	$0.821098\pi$
$380$	2.69778	−	4.67269i	0.00709942	−	0.0122966i
$381$		0			0
$382$	161.233	−	161.233i	0.422076	−	0.422076i
$383$	−275.080	−	73.7074i	−0.718224	−	0.192448i	−0.118845	−	0.992913i	$-0.537919\pi$
$383$	−275.080	−	73.7074i	−0.718224	−	0.192448i	−0.599379	+	0.800465i	$0.704586\pi$
$384$		0			0
$385$	−691.364	−	691.364i	−1.79575	−	1.79575i
$386$	118.657	+	205.520i	0.307402	+	0.532436i
$387$		0			0
$388$	258.284	−	69.2070i	0.665681	−	0.178369i
$389$		−	55.5965i		−	0.142922i	−0.997443	−	0.0714608i	$-0.977234\pi$
$389$		−	55.5965i		−	0.142922i	0.997443	−	0.0714608i	$-0.0227661\pi$
$390$		0			0
$391$	−972.190			−2.48642
$392$	13.0185	+	48.5858i	0.0332105	+	0.123943i
$393$		0			0
$394$	247.640	−	142.975i	0.628527	−	0.362880i
$395$	−511.089	+	511.089i	−1.29390	+	1.29390i
$396$		0			0
$397$	−60.5246	+	225.881i	−0.152455	+	0.568969i	0.846855	+	0.531824i	$0.178493\pi$
$397$	−60.5246	+	225.881i	−0.152455	+	0.568969i	−0.999310	+	0.0371454i	$0.988174\pi$
$398$	93.3316	+	93.3316i	0.234501	+	0.234501i
$399$		0			0
$400$	−48.2931	−	27.8820i	−0.120733	−	0.0697051i
$401$	139.942	−	37.4974i	0.348983	−	0.0935096i	−0.0800696	−	0.996789i	$-0.525514\pi$
$401$	139.942	−	37.4974i	0.348983	−	0.0935096i	0.429052	+	0.903280i	$0.358848\pi$
$402$		0			0
$403$	205.125	−	256.105i	0.508995	−	0.635496i
$404$	76.5083			0.189377
$405$		0			0
$406$	37.6513	−	65.2140i	0.0927373	−	0.160626i
$407$	23.7198	−	13.6946i	0.0582796	−	0.0336477i
$408$		0			0
$409$	−666.035	−	178.463i	−1.62845	−	0.436341i	−0.674979	−	0.737837i	$-0.735847\pi$
$409$	−666.035	−	178.463i	−1.62845	−	0.436341i	−0.953468	+	0.301496i	$0.902514\pi$
$410$	95.4756	−	356.320i	0.232867	−	0.869073i
$411$		0			0
$412$	65.9827	+	114.285i	0.160152	+	0.277392i
$413$	312.273	+	180.291i	0.756108	+	0.436539i
$414$		0			0
$415$			302.118i			0.727994i
$416$	−72.6944	−	11.1143i	−0.174746	−	0.0267170i
$417$		0			0
$418$	−3.03387	−	11.3226i	−0.00725806	−	0.0270875i
$419$	−35.3241	+	61.1831i	−0.0843056	+	0.146022i	−0.905095	−	0.425209i	$-0.860201\pi$
$419$	−35.3241	+	61.1831i	−0.0843056	+	0.146022i	0.820789	+	0.571231i	$0.193534\pi$
$420$		0			0
$421$	−269.923	+	269.923i	−0.641148	+	0.641148i	−0.950838	−	0.309690i	$-0.899775\pi$
$421$	−269.923	+	269.923i	−0.641148	+	0.641148i	0.309690	+	0.950838i	$0.399775\pi$
$422$	−432.281	−	115.829i	−1.02436	−	0.274477i
$423$		0			0
$424$	17.8159	+	17.8159i	0.0420186	+	0.0420186i
$425$	−160.925	−	278.731i	−0.378648	−	0.655838i
$426$		0			0
$427$	707.315	−	189.524i	1.65647	−	0.443851i
$428$			188.965i			0.441508i
$429$		0			0
$430$	521.030			1.21170
$431$	167.809	+	626.272i	0.389348	+	1.45307i	0.831197	+	0.555978i	$0.187656\pi$
$431$	167.809	+	626.272i	0.389348	+	1.45307i	−0.441848	+	0.897090i	$0.645677\pi$
$432$		0			0
$433$	330.115	−	190.592i	0.762391	−	0.440166i	−0.0677628	−	0.997701i	$-0.521586\pi$
$433$	330.115	−	190.592i	0.762391	−	0.440166i	0.830153	+	0.557535i	$0.188253\pi$
$434$	−206.267	+	206.267i	−0.475271	+	0.475271i
$435$		0			0
$436$	73.8897	−	275.760i	0.169472	−	0.632477i
$437$	−12.8730	−	12.8730i	−0.0294576	−	0.0294576i
$438$		0			0
$439$	96.4945	+	55.7111i	0.219805	+	0.126905i	0.605860	−	0.795571i	$-0.292829\pi$
$439$	96.4945	+	55.7111i	0.219805	+	0.126905i	−0.386055	+	0.922476i	$0.626162\pi$
$440$	−326.870	+	87.5846i	−0.742887	+	0.199056i
$441$		0			0
$442$	−331.282	−	265.337i	−0.749506	−	0.600310i
$443$	−480.157			−1.08388			−0.541938	−	0.840418i	$-0.682309\pi$
$443$	−480.157			−1.08388			−0.541938	+	0.840418i	$0.682309\pi$
$444$		0			0
$445$	187.587	−	324.910i	0.421544	−	0.730135i
$446$	−83.6430	+	48.2913i	−0.187540	+	0.108276i
$447$		0			0
$448$	63.1493	+	16.9208i	0.140958	+	0.0377697i
$449$	105.379	−	393.279i	0.234697	−	0.875900i	−0.743589	−	0.668637i	$-0.766878\pi$
$449$	105.379	−	393.279i	0.234697	−	0.875900i	0.978285	−	0.207263i	$-0.0664555\pi$
$450$		0			0
$451$	−400.710	−	694.051i	−0.888493	−	1.53891i
$452$	−53.1771	−	30.7018i	−0.117648	−	0.0679243i
$453$		0			0
$454$		−	35.5873i		−	0.0783861i
$455$	−392.545	−	534.241i	−0.862736	−	1.17416i
$456$		0			0
$457$	−5.25408	−	19.6085i	−0.0114969	−	0.0429069i	0.959939	−	0.280209i	$-0.0904037\pi$
$457$	−5.25408	−	19.6085i	−0.0114969	−	0.0429069i	−0.971436	+	0.237302i	$0.923737\pi$
$458$	274.910	−	476.159i	0.600241	−	1.03965i
$459$		0			0
$460$	−371.629	+	371.629i	−0.807889	+	0.807889i
$461$	−457.719	−	122.645i	−0.992882	−	0.266042i	−0.274421	−	0.961610i	$-0.588486\pi$
$461$	−457.719	−	122.645i	−0.992882	−	0.266042i	−0.718461	+	0.695568i	$0.755153\pi$
$462$		0			0
$463$	266.154	+	266.154i	0.574846	+	0.574846i	0.933479	−	0.358633i	$-0.116757\pi$
$463$	266.154	+	266.154i	0.574846	+	0.574846i	−0.358633	+	0.933479i	$0.616757\pi$
$464$	−13.0314	−	22.5710i	−0.0280849	−	0.0486444i
$465$		0			0
$466$	−548.562	+	146.987i	−1.17717	+	0.315422i
$467$			231.396i			0.495494i	0.968825	+	0.247747i	$0.0796901\pi$
$467$			231.396i			0.495494i	−0.968825	+	0.247747i	$0.920310\pi$
$468$		0			0
$469$	323.841			0.690492
$470$	48.6283	+	181.483i	0.103465	+	0.386135i
$471$		0			0
$472$	108.080	−	62.3998i	0.228982	−	0.132203i
$473$	800.410	−	800.410i	1.69220	−	1.69220i
$474$		0			0
$475$	1.55989	−	5.82159i	0.00328398	−	0.0122560i
$476$	266.815	+	266.815i	0.560536	+	0.560536i
$477$		0			0
$478$	−528.962	−	305.397i	−1.10662	−	0.638905i
$479$	81.0183	−	21.7088i	0.169140	−	0.0453210i	−0.173255	−	0.984877i	$-0.555428\pi$
$479$	81.0183	−	21.7088i	0.169140	−	0.0453210i	0.342395	+	0.939556i	$0.388762\pi$
$480$		0			0
$481$	17.3018	−	6.74824i	0.0359705	−	0.0140296i
$482$	−157.406			−0.326569
$483$		0			0
$484$	−246.592	+	427.109i	−0.509487	+	0.882457i
$485$	722.534	−	417.155i	1.48976	−	0.860114i
$486$		0			0
$487$	−51.6346	−	13.8354i	−0.106026	−	0.0284095i	0.205416	−	0.978675i	$-0.434145\pi$
$487$	−51.6346	−	13.8354i	−0.106026	−	0.0284095i	−0.311442	+	0.950265i	$0.600812\pi$
$488$	65.5957	−	244.806i	0.134417	−	0.501652i
$489$		0			0
$490$	78.4710	+	135.916i	0.160145	+	0.277379i
$491$	755.689	+	436.297i	1.53908	+	0.888589i	0.998893	+	0.0470443i	$0.0149802\pi$
$491$	755.689	+	436.297i	1.53908	+	0.888589i	0.540188	+	0.841544i	$0.318353\pi$
$492$		0			0
$493$		−	150.425i		−	0.305122i
$494$	−0.873189	−	7.89995i	−0.00176759	−	0.0159918i
$495$		0			0
$496$	26.1308	+	97.5213i	0.0526830	+	0.196616i
$497$	−36.2414	+	62.7720i	−0.0729204	+	0.126302i
$498$		0			0
$499$	178.607	−	178.607i	0.357929	−	0.357929i	−0.505120	−	0.863049i	$-0.668552\pi$
$499$	178.607	−	178.607i	0.357929	−	0.357929i	0.863049	+	0.505120i	$0.168552\pi$
$500$	133.319	+	35.7228i	0.266638	+	0.0714455i
$501$		0			0
$502$	−87.6429	−	87.6429i	−0.174587	−	0.174587i
$503$	−290.935	−	503.915i	−0.578401	−	1.00182i	−0.995663	−	0.0930331i	$-0.970344\pi$
$503$	−290.935	−	503.915i	−0.578401	−	1.00182i	0.417262	−	0.908786i	$-0.362990\pi$
$504$		0			0
$505$	230.582	−	61.7843i	0.456599	−	0.122345i
$506$			1141.80i			2.25652i
$507$		0			0
$508$	318.376			0.626725
$509$	80.3135	+	299.734i	0.157787	+	0.588868i	0.998851	+	0.0479323i	$0.0152632\pi$
$509$	80.3135	+	299.734i	0.157787	+	0.588868i	−0.841064	+	0.540936i	$0.818070\pi$
$510$		0			0
$511$	−59.3203	+	34.2486i	−0.116087	+	0.0670227i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−64.2041	+	239.613i	−0.124911	+	0.466173i
$515$	291.151	+	291.151i	0.565343	+	0.565343i
$516$		0			0
$517$	353.499	+	204.093i	0.683750	+	0.394763i
$518$	−15.9474	+	4.27311i	−0.0307866	+	0.00824924i
$519$		0			0
$520$	−228.063	+	25.2080i	−0.438583	+	0.0484770i
$521$	−400.878			−0.769440			−0.384720	−	0.923033i	$-0.625702\pi$
$521$	−400.878			−0.769440			−0.384720	+	0.923033i	$0.625702\pi$
$522$		0			0
$523$	−255.340	+	442.262i	−0.488222	+	0.845626i	−0.999908	−	0.0135467i	$-0.995688\pi$
$523$	−255.340	+	442.262i	−0.488222	+	0.845626i	0.511686	+	0.859173i	$0.329021\pi$
$524$	153.965	−	88.8918i	0.293826	−	0.169641i
$525$		0			0
$526$	−173.982	−	46.6183i	−0.330764	−	0.0886279i
$527$	−150.818	+	562.859i	−0.286181	+	1.06804i
$528$		0			0
$529$	622.150	+	1077.60i	1.17609	+	2.03704i
$530$	68.0811	+	39.3066i	0.128455	+	0.0741635i
$531$		0			0
$532$			7.06591i			0.0132818i
$533$	−197.456	−	506.257i	−0.370462	−	0.949826i
$534$		0			0
$535$	152.599	+	569.508i	0.285232	+	1.06450i
$536$	56.0417	−	97.0671i	0.104555	−	0.181095i
$537$		0			0
$538$	208.253	−	208.253i	0.387087	−	0.387087i
$539$	329.342	+	88.2469i	0.611024	+	0.163723i
$540$		0			0
$541$	75.0411	+	75.0411i	0.138708	+	0.138708i	0.773051	−	0.634343i	$-0.218729\pi$
$541$	75.0411	+	75.0411i	0.138708	+	0.138708i	−0.634343	+	0.773051i	$0.718729\pi$
$542$	2.67953	+	4.64108i	0.00494378	+	0.00856288i
$543$		0			0
$544$	126.148	−	33.8011i	0.231889	−	0.0621345i
$545$		−	890.761i		−	1.63442i
$546$		0			0
$547$	−328.719			−0.600950			−0.300475	−	0.953790i	$-0.597145\pi$
$547$	−328.719			−0.600950			−0.300475	+	0.953790i	$0.597145\pi$
$548$	−56.9662	−	212.601i	−0.103953	−	0.387957i
$549$		0			0
$550$	−327.358	+	189.000i	−0.595196	+	0.343637i
$551$	1.99181	−	1.99181i	0.00361491	−	0.00361491i
$552$		0			0
$553$	244.985	−	914.295i	0.443010	−	1.65334i
$554$	68.7460	+	68.7460i	0.124090	+	0.124090i
$555$		0			0
$556$	429.783	+	248.135i	0.772991	+	0.446286i
$557$	331.165	−	88.7354i	0.594551	−	0.159309i	0.0510186	−	0.998698i	$-0.483753\pi$
$557$	331.165	−	88.7354i	0.594551	−	0.159309i	0.543532	+	0.839388i	$0.317087\pi$
$558$		0			0
$559$	618.505	−	454.459i	1.10645	−	0.812986i
$560$	203.985			0.364259
$561$		0			0
$562$	−19.5583	+	33.8760i	−0.0348013	+	0.0602776i
$563$	314.882	−	181.797i	0.559293	−	0.322908i	−0.193569	−	0.981087i	$-0.562006\pi$
$563$	314.882	−	181.797i	0.559293	−	0.322908i	0.752862	+	0.658179i	$0.228673\pi$
$564$		0			0
$565$	−185.059	−	49.5865i	−0.327539	−	0.0877637i
$566$	46.2937	−	172.770i	0.0817910	−	0.305248i
$567$		0			0
$568$	12.5434	+	21.7258i	0.0220835	+	0.0382497i
$569$	−548.662	−	316.770i	−0.964256	−	0.556714i	−0.0667758	−	0.997768i	$-0.521271\pi$
$569$	−548.662	−	316.770i	−0.964256	−	0.556714i	−0.897480	+	0.441054i	$0.854605\pi$
$570$		0			0
$571$			54.2364i			0.0949849i	0.998872	+	0.0474925i	$0.0151230\pi$
$571$			54.2364i			0.0949849i	−0.998872	+	0.0474925i	$0.984877\pi$
$572$	−311.627	+	389.076i	−0.544803	+	0.680204i
$573$		0			0
$574$	125.033	+	466.629i	0.217827	+	0.812942i
$575$	−293.532	+	508.413i	−0.510491	+	0.884196i
$576$		0			0
$577$	−704.420	+	704.420i	−1.22083	+	1.22083i	−0.253495	+	0.967337i	$0.581580\pi$
$577$	−704.420	+	704.420i	−1.22083	+	1.22083i	−0.967337	+	0.253495i	$0.918420\pi$
$578$	333.299	+	89.3071i	0.576641	+	0.154511i
$579$		0			0
$580$	−57.5015	−	57.5015i	−0.0991405	−	0.0991405i
$581$	−197.823	−	342.640i	−0.340488	−	0.589742i
$582$		0			0
$583$	164.970	−	44.2035i	0.282967	−	0.0758207i
$584$			23.7073i			0.0405947i
$585$		0			0
$586$	−526.959			−0.899248
$587$	−243.773	−	909.773i	−0.415286	−	1.54987i	−0.784262	−	0.620430i	$-0.786958\pi$
$587$	−243.773	−	909.773i	−0.415286	−	1.54987i	0.368975	−	0.929439i	$-0.379709\pi$
$588$		0			0
$589$	−9.44995	+	5.45593i	−0.0160441	+	0.00926304i
$590$	275.342	−	275.342i	0.466681	−	0.466681i
$591$		0			0
$592$	−1.47895	+	5.51952i	−0.00249823	+	0.00932351i
$593$	457.589	+	457.589i	0.771650	+	0.771650i	0.978395	−	0.206745i	$-0.0662870\pi$
$593$	457.589	+	457.589i	0.771650	+	0.771650i	−0.206745	+	0.978395i	$0.566287\pi$
$594$		0			0
$595$	1019.60	+	588.666i	1.71361	+	0.989354i
$596$	−266.818	+	71.4937i	−0.447682	+	0.119956i
$597$		0			0
$598$	−117.007	+	765.300i	−0.195664	+	1.27977i
$599$	78.9882			0.131867			0.0659334	−	0.997824i	$-0.478998\pi$
$599$	78.9882			0.131867			0.0659334	+	0.997824i	$0.478998\pi$
$600$		0			0
$601$	182.344	−	315.829i	0.303401	−	0.525506i	−0.673503	−	0.739185i	$-0.735211\pi$
$601$	182.344	−	315.829i	0.303401	−	0.525506i	0.976904	+	0.213678i	$0.0685445\pi$
$602$	−590.915	+	341.165i	−0.981587	+	0.566719i
$603$		0			0
$604$	53.6549	+	14.3768i	0.0888325	+	0.0238026i
$605$	−398.271	+	1486.37i	−0.658298	+	2.45680i
$606$		0			0
$607$	−295.511	−	511.839i	−0.486838	−	0.843228i	0.513048	−	0.858360i	$-0.328516\pi$
$607$	−295.511	−	511.839i	−0.486838	−	0.843228i	−0.999886	+	0.0151322i	$0.995183\pi$
$608$	2.11792	+	1.22278i	0.00348341	+	0.00201115i
$609$		0			0
$610$		−	790.774i		−	1.29635i
$611$	216.021	+	173.020i	0.353554	+	0.283175i
$612$		0			0
$613$	−112.817	−	421.040i	−0.184041	−	0.686852i	−0.994834	−	0.101518i	$-0.967630\pi$
$613$	−112.817	−	421.040i	−0.184041	−	0.686852i	0.810792	−	0.585334i	$-0.199037\pi$
$614$	−259.830	+	450.039i	−0.423176	+	0.732962i
$615$		0			0
$616$	313.363	−	313.363i	0.508706	−	0.508706i
$617$	288.834	+	77.3930i	0.468127	+	0.125434i	0.485169	−	0.874420i	$-0.338758\pi$
$617$	288.834	+	77.3930i	0.468127	+	0.125434i	−0.0170417	+	0.999855i	$0.505425\pi$
$618$		0			0
$619$	84.5481	+	84.5481i	0.136588	+	0.136588i	0.772095	−	0.635507i	$-0.219209\pi$
$619$	84.5481	+	84.5481i	0.136588	+	0.136588i	−0.635507	+	0.772095i	$0.719209\pi$
$620$	157.507	+	272.810i	0.254043	+	0.440016i
$621$		0			0
$622$	487.450	−	130.612i	0.783682	−	0.209987i
$623$			491.319i			0.788635i
$624$		0			0
$625$	779.173			1.24668
$626$	−7.17966	−	26.7948i	−0.0114691	−	0.0428033i
$627$		0			0
$628$	210.086	−	121.293i	0.334532	−	0.193142i
$629$	−23.3208	+	23.3208i	−0.0370759	+	0.0370759i
$630$		0			0
$631$	−195.299	+	728.867i	−0.309508	+	1.15510i	0.619488	+	0.785006i	$0.287340\pi$
$631$	−195.299	+	728.867i	−0.309508	+	1.15510i	−0.928995	+	0.370092i	$0.879326\pi$
$632$	−231.653	−	231.653i	−0.366539	−	0.366539i
$633$		0			0
$634$	242.142	+	139.801i	0.381927	+	0.220506i
$635$	959.529	−	257.105i	1.51107	−	0.404890i
$636$		0			0
$637$	211.702	+	92.8981i	0.332341	+	0.145837i
$638$	−176.668			−0.276909
$639$		0			0
$640$	35.3003	−	61.1420i	0.0551568	−	0.0955343i
$641$	−326.603	+	188.565i	−0.509522	+	0.294172i	−0.732637	−	0.680620i	$-0.761711\pi$
$641$	−326.603	+	188.565i	−0.509522	+	0.294172i	0.223115	+	0.974792i	$0.428377\pi$
$642$		0			0
$643$	−1166.74	−	312.627i	−1.81452	−	0.486200i	−0.818438	−	0.574595i	$-0.805160\pi$
$643$	−1166.74	−	312.627i	−1.81452	−	0.486200i	−0.996086	+	0.0883945i	$0.971826\pi$
$644$	178.136	−	664.814i	0.276609	−	1.03232i
$645$		0			0
$646$	7.05746	+	12.2239i	0.0109249	+	0.0189224i
$647$	−219.028	−	126.456i	−0.338529	−	0.195450i	0.321093	−	0.947048i	$-0.395950\pi$
$647$	−219.028	−	126.456i	−0.338529	−	0.195450i	−0.659621	+	0.751598i	$0.729283\pi$
$648$		0			0
$649$		−	845.962i		−	1.30349i
$650$	−238.783	+	93.1328i	−0.367358	+	0.143281i
$651$		0			0
$652$	97.9922	+	365.712i	0.150295	+	0.560908i
$653$	216.293	−	374.631i	0.331230	−	0.573707i	−0.651523	−	0.758629i	$-0.725870\pi$
$653$	216.293	−	374.631i	0.331230	−	0.573707i	0.982753	+	0.184921i	$0.0592031\pi$
$654$		0			0
$655$	392.239	−	392.239i	0.598837	−	0.598837i
$656$	161.503	+	43.2747i	0.246194	+	0.0659675i
$657$		0			0
$658$	−173.984	−	173.984i	−0.264413	−	0.264413i
$659$	604.428	+	1046.90i	0.917190	+	1.58862i	0.803663	+	0.595085i	$0.202882\pi$
$659$	604.428	+	1046.90i	0.917190	+	1.58862i	0.113527	+	0.993535i	$0.463785\pi$
$660$		0			0
$661$	−1018.51	+	272.908i	−1.54086	+	0.412872i	−0.926543	−	0.376188i	$-0.877235\pi$
$661$	−1018.51	+	272.908i	−1.54086	+	0.412872i	−0.614316	+	0.789060i	$0.710568\pi$
$662$			389.066i			0.587713i
$663$		0			0
$664$	−136.936			−0.206229
$665$	5.70608	+	21.2954i	0.00858057	+	0.0320231i
$666$		0			0
$667$	−237.620	+	137.190i	−0.356251	+	0.205682i
$668$	−80.1917	+	80.1917i	−0.120047	+	0.120047i
$669$		0			0
$670$	90.5131	−	337.799i	0.135094	−	0.504178i
$671$	−1214.79	−	1214.79i	−1.81042	−	1.81042i
$672$		0			0
$673$	688.514	+	397.514i	1.02305	+	0.590659i	0.914986	−	0.403484i	$-0.132201\pi$
$673$	688.514	+	397.514i	1.02305	+	0.590659i	0.108065	+	0.994144i	$0.465534\pi$
$674$	−855.067	+	229.114i	−1.26865	+	0.339932i
$675$		0			0
$676$	−248.742	+	228.848i	−0.367962	+	0.338532i
$677$	−642.236			−0.948649			−0.474325	−	0.880350i	$-0.657308\pi$
$677$	−642.236			−0.948649			−0.474325	+	0.880350i	$0.657308\pi$
$678$		0			0
$679$	−546.297	+	946.214i	−0.804561	+	1.39354i
$680$	352.890	−	203.741i	0.518956	−	0.299619i
$681$		0			0
$682$	661.055	+	177.129i	0.969288	+	0.259720i
$683$	−168.964	+	630.582i	−0.247385	+	0.923253i	0.724785	+	0.688975i	$0.241939\pi$
$683$	−168.964	+	630.582i	−0.247385	+	0.923253i	−0.972170	+	0.234277i	$0.924728\pi$
$684$		0			0
$685$	−343.372	−	594.737i	−0.501272	−	0.868229i
$686$	312.437	+	180.386i	0.455448	+	0.262953i
$687$		0			0
$688$			236.159i			0.343254i
$689$	115.102	−	12.7223i	0.167057	−	0.0184649i
$690$		0			0
$691$	−199.113	−	743.100i	−0.288152	−	1.07540i	−0.946505	−	0.322689i	$-0.895413\pi$
$691$	−199.113	−	743.100i	−0.288152	−	1.07540i	0.658353	−	0.752709i	$-0.271253\pi$
$692$	−325.495	+	563.773i	−0.470368	+	0.814701i
$693$		0			0
$694$	105.688	−	105.688i	0.152288	−	0.152288i
$695$	1495.67	+	400.764i	2.15204	+	0.576638i
$696$		0			0
$697$	682.375	+	682.375i	0.979017	+	0.979017i
$698$	−306.359	−	530.629i	−0.438909	−	0.760213i
$699$		0			0
$700$	220.092	−	58.9734i	0.314417	−	0.0842477i
$701$			415.401i			0.592584i	0.955097	+	0.296292i	$0.0957502\pi$
$701$			415.401i			0.592584i	−0.955097	+	0.296292i	$0.904250\pi$
$702$		0			0
$703$	−0.617590			−0.000878507
$704$	−39.6980	−	148.155i	−0.0563893	−	0.210448i
$705$		0			0
$706$	−720.363	+	415.902i	−1.02034	+	0.589096i
$707$	−221.054	+	221.054i	−0.312665	+	0.312665i
$708$		0			0
$709$	81.1586	−	302.888i	0.114469	−	0.427204i	−0.884778	−	0.466014i	$-0.845690\pi$
$709$	81.1586	−	302.888i	0.114469	−	0.427204i	0.999247	+	0.0388092i	$0.0123565\pi$
$710$	55.3483	+	55.3483i	0.0779553	+	0.0779553i
$711$		0			0
$712$	147.267	+	85.0245i	0.206835	+	0.119416i
$713$	1026.67	−	275.095i	1.43993	−	0.385828i
$714$		0			0
$715$	−624.989	+	1424.26i	−0.874111	+	1.99197i
$716$	−281.790			−0.393562
$717$		0			0
$718$	172.896	−	299.464i	0.240802	−	0.417081i
$719$	−205.104	+	118.417i	−0.285263	+	0.164697i	−0.635804	−	0.771851i	$-0.719331\pi$
$719$	−205.104	+	118.417i	−0.285263	+	0.164697i	0.350541	+	0.936547i	$0.385998\pi$
$720$		0			0
$721$	−520.846	−	139.560i	−0.722393	−	0.193565i
$722$	132.067	−	492.880i	0.182918	−	0.682659i
$723$		0			0
$724$	56.0814	+	97.1359i	0.0774605	+	0.134166i
$725$	−78.6658	−	45.4177i	−0.108504	−	0.0626451i
$726$		0			0
$727$			919.030i			1.26414i	0.774911	+	0.632070i	$0.217794\pi$
$727$			919.030i			1.26414i	−0.774911	+	0.632070i	$0.782206\pi$
$728$	242.147	−	177.922i	0.332619	−	0.244399i
$729$		0			0
$730$	19.1449	+	71.4496i	0.0262258	+	0.0978762i
$731$	−681.514	+	1180.42i	−0.932303	+	1.61480i
$732$		0			0
$733$	709.566	−	709.566i	0.968030	−	0.968030i	−0.0314750	−	0.999505i	$-0.510020\pi$
$733$	709.566	−	709.566i	0.968030	−	0.968030i	0.999505	+	0.0314750i	$0.0100205\pi$
$734$	471.587	+	126.361i	0.642489	+	0.172154i
$735$		0			0
$736$	−168.442	−	168.442i	−0.228862	−	0.228862i
$737$	−379.882	−	657.976i	−0.515444	−	0.892776i
$738$		0			0
$739$	118.782	−	31.8276i	0.160734	−	0.0430685i	−0.177555	−	0.984111i	$-0.556819\pi$
$739$	118.782	−	31.8276i	0.160734	−	0.0430685i	0.338289	+	0.941042i	$0.390152\pi$
$740$			17.8292i			0.0240935i
$741$		0			0
$742$	−102.950			−0.138747
$743$	−344.461	−	1285.55i	−0.463609	−	1.73021i	−0.661461	−	0.749980i	$-0.730063\pi$
$743$	−344.461	−	1285.55i	−0.463609	−	1.73021i	0.197852	−	0.980232i	$-0.436604\pi$
$744$		0			0
$745$	−746.408	+	430.939i	−1.00189	+	0.578441i
$746$	446.582	−	446.582i	0.598635	−	0.598635i
$747$		0			0
$748$	229.123	−	855.100i	0.306315	−	1.14318i
$749$	−545.974	−	545.974i	−0.728938	−	0.728938i
$750$		0			0
$751$	−1177.85	−	680.031i	−1.56837	−	0.905501i	−0.996359	−	0.0852568i	$-0.972829\pi$
$751$	−1177.85	−	680.031i	−1.56837	−	0.905501i	−0.572014	−	0.820244i	$-0.693838\pi$
$752$	−82.2580	+	22.0410i	−0.109386	+	0.0293098i
$753$		0			0
$754$	−118.414	−	18.1043i	−0.157047	−	0.0240110i
$755$	173.316			0.229558
$756$		0			0
$757$	541.869	−	938.545i	0.715812	−	1.23982i	−0.246834	−	0.969058i	$-0.579390\pi$
$757$	541.869	−	938.545i	0.715812	−	1.23982i	0.962646	−	0.270764i	$-0.0872764\pi$
$758$	−274.559	+	158.517i	−0.362215	+	0.209125i
$759$		0			0
$760$	7.37047	+	1.97491i	0.00969799	+	0.00259857i
$761$	301.591	−	1125.55i	0.396309	−	1.47905i	−0.423229	−	0.906023i	$-0.639103\pi$
$761$	301.591	−	1125.55i	0.396309	−	1.47905i	0.819538	−	0.573024i	$-0.194230\pi$
$762$		0			0
$763$	583.261	+	1010.24i	0.764431	+	1.32403i
$764$	279.264	+	161.233i	0.365528	+	0.211038i
$765$		0			0
$766$		−	402.745i		−	0.525776i
$767$	86.6910	−	567.014i	0.113026	−	0.739263i
$768$		0			0
$769$	−238.002	−	888.237i	−0.309496	−	1.15505i	−0.929006	−	0.370065i	$-0.879335\pi$
$769$	−238.002	−	888.237i	−0.309496	−	1.15505i	0.619510	−	0.784989i	$-0.287331\pi$
$770$	691.364	−	1197.48i	0.897875	−	1.55516i
$771$		0			0
$772$	−237.314	+	237.314i	−0.307402	+	0.307402i
$773$	−1181.38	−	316.550i	−1.52830	−	0.409508i	−0.605839	−	0.795587i	$-0.707163\pi$
$773$	−1181.38	−	316.550i	−1.52830	−	0.409508i	−0.922466	+	0.386079i	$0.873829\pi$
$774$		0			0
$775$	248.814	+	248.814i	0.321051	+	0.321051i
$776$	189.077	+	327.491i	0.243656	+	0.422025i
$777$		0			0

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	234.bb (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-4.41254 + 4.41254i) q^{5} +(2.11510 - 7.89367i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-4.41254 + 4.41254i) q^{5} +(2.11510 - 7.89367i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-7.64274 - 4.41254i) q^{10} +(-18.5194 + 4.96225i) q^{11} +(-12.9213 + 1.42820i) q^{13} +11.5571 q^{14} +(2.00000 - 3.46410i) q^{16} +(19.9936 - 11.5433i) q^{17} +(0.417587 + 0.111892i) q^{19} +(3.23020 - 12.0553i) q^{20} +(-13.5571 - 23.4816i) q^{22} +(-36.4688 - 21.0553i) q^{23} -13.9410i q^{25} +(-6.68049 - 17.1281i) q^{26} +(4.23020 + 15.7873i) q^{28} +(3.25785 - 5.64275i) q^{29} +(-17.8476 + 17.8476i) q^{31} +(5.46410 + 1.46410i) q^{32} +(23.0866 + 23.0866i) q^{34} +(25.4982 + 44.1641i) q^{35} +(-1.37988 + 0.369738i) q^{37} +0.611390i q^{38} +17.6502 q^{40} +(10.8187 + 40.3758i) q^{41} +(-51.1299 + 29.5199i) q^{43} +(27.1143 - 27.1143i) q^{44} +(15.4135 - 57.5241i) q^{46} +(-15.0543 - 15.0543i) q^{47} +(-15.4011 - 8.89182i) q^{49} +(19.0438 - 5.10277i) q^{50} +(20.9522 - 15.3950i) q^{52} -8.90794 q^{53} +(59.8214 - 103.614i) q^{55} +(-20.0175 + 11.5571i) q^{56} +(8.90060 + 2.38491i) q^{58} +(-11.4200 + 42.6199i) q^{59} +(44.8027 + 77.6005i) q^{61} +(-30.9130 - 17.8476i) q^{62} +8.00000i q^{64} +(50.7138 - 63.3178i) q^{65} +(10.2563 + 38.2772i) q^{67} +(-23.0866 + 39.9872i) q^{68} +(-50.9963 + 50.9963i) q^{70} +(-8.56730 - 2.29560i) q^{71} +(-5.92683 - 5.92683i) q^{73} +(-1.01014 - 1.74962i) q^{74} +(-0.835174 + 0.223784i) q^{76} +156.682i q^{77} +115.826 q^{79} +(6.46041 + 24.1106i) q^{80} +(-51.1945 + 29.5572i) q^{82} +(34.2340 - 34.2340i) q^{83} +(-37.2872 + 139.158i) q^{85} +(-59.0397 - 59.0397i) q^{86} +(46.9633 + 27.1143i) q^{88} +(-58.0728 + 15.5606i) q^{89} +(-16.0561 + 105.017i) q^{91} +84.2211 q^{92} +(15.0543 - 26.0747i) q^{94} +(-2.33635 + 1.34889i) q^{95} +(-129.142 - 34.6035i) q^{97} +(6.50926 - 24.2929i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 6 q^{5} + 10 q^{7} - 16 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 + 6 * q^5 + 10 * q^7 - 16 * q^8	\( 8 q - 4 q^{2} + 6 q^{5} + 10 q^{7} - 16 q^{8} - 6 q^{10} - 24 q^{11} - 4 q^{14} + 16 q^{16} + 84 q^{17} + 10 q^{19} + 12 q^{20} - 12 q^{22} + 12 q^{23} - 26 q^{26} + 20 q^{28} - 36 q^{29} - 94 q^{31} + 16 q^{32} + 60 q^{34} + 204 q^{35} + 140 q^{37} - 24 q^{40} - 72 q^{41} - 222 q^{43} + 24 q^{44} - 84 q^{46} - 300 q^{47} + 42 q^{49} + 62 q^{50} + 44 q^{52} - 84 q^{53} + 396 q^{55} - 36 q^{56} - 66 q^{58} + 60 q^{59} - 90 q^{61} - 198 q^{62} + 108 q^{65} + 304 q^{67} - 60 q^{68} - 408 q^{70} + 192 q^{71} + 16 q^{73} + 46 q^{74} - 20 q^{76} - 96 q^{79} + 24 q^{80} + 114 q^{82} - 390 q^{85} - 168 q^{86} + 72 q^{88} - 354 q^{89} - 218 q^{91} + 288 q^{92} + 300 q^{94} + 576 q^{95} - 460 q^{97} - 58 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 6 * q^5 + 10 * q^7 - 16 * q^8 - 6 * q^10 - 24 * q^11 - 4 * q^14 + 16 * q^16 + 84 * q^17 + 10 * q^19 + 12 * q^20 - 12 * q^22 + 12 * q^23 - 26 * q^26 + 20 * q^28 - 36 * q^29 - 94 * q^31 + 16 * q^32 + 60 * q^34 + 204 * q^35 + 140 * q^37 - 24 * q^40 - 72 * q^41 - 222 * q^43 + 24 * q^44 - 84 * q^46 - 300 * q^47 + 42 * q^49 + 62 * q^50 + 44 * q^52 - 84 * q^53 + 396 * q^55 - 36 * q^56 - 66 * q^58 + 60 * q^59 - 90 * q^61 - 198 * q^62 + 108 * q^65 + 304 * q^67 - 60 * q^68 - 408 * q^70 + 192 * q^71 + 16 * q^73 + 46 * q^74 - 20 * q^76 - 96 * q^79 + 24 * q^80 + 114 * q^82 - 390 * q^85 - 168 * q^86 + 72 * q^88 - 354 * q^89 - 218 * q^91 + 288 * q^92 + 300 * q^94 + 576 * q^95 - 460 * q^97 - 58 * q^98

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