LMFDB - Embedded newform 342.2.u.c.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(55,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("342.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.u (of order $9$, degree $6$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	342.73
Dual form			342.2.u.c.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.347296 + 1.96962i) q^{5} +(-1.34730 - 2.33359i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.347296 + 1.96962i) q^{5} +(-1.34730 - 2.33359i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.53209 - 1.28558i) q^{10} +(1.59240 - 2.75811i) q^{11} +(5.41147 + 1.96962i) q^{13} +(-0.467911 + 2.65366i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(4.99273 + 4.18939i) q^{17} +(2.82635 + 3.31839i) q^{19} -2.00000 q^{20} +(-2.99273 + 1.08926i) q^{22} +(0.120615 + 0.684040i) q^{23} +(0.939693 + 0.342020i) q^{25} +(-2.87939 - 4.98724i) q^{26} +(2.06418 - 1.73205i) q^{28} +(2.16250 - 1.81456i) q^{29} +(-1.22668 - 2.12467i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-1.13176 - 6.41852i) q^{34} +(5.06418 - 1.84321i) q^{35} -4.36959 q^{37} +(-0.0320889 - 4.35878i) q^{38} +(1.53209 + 1.28558i) q^{40} +(-0.326352 + 0.118782i) q^{41} +(1.05303 - 5.97205i) q^{43} +(2.99273 + 1.08926i) q^{44} +(0.347296 - 0.601535i) q^{46} +(-6.04189 + 5.06975i) q^{47} +(-0.130415 + 0.225885i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-1.00000 + 5.67128i) q^{52} +(-1.42602 - 8.08737i) q^{53} +(4.87939 + 4.09429i) q^{55} -2.69459 q^{56} -2.82295 q^{58} +(-0.439693 - 0.368946i) q^{59} +(0.509800 + 2.89122i) q^{61} +(-0.426022 + 2.41609i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-5.75877 + 9.97448i) q^{65} +(-3.79813 + 3.18701i) q^{67} +(-3.25877 + 5.64436i) q^{68} +(-5.06418 - 1.84321i) q^{70} +(1.46791 - 8.32494i) q^{71} +(-14.8157 + 5.39246i) q^{73} +(3.34730 + 2.80872i) q^{74} +(-2.77719 + 3.35965i) q^{76} -8.58172 q^{77} +(8.51754 - 3.10013i) q^{79} +(-0.347296 - 1.96962i) q^{80} +(0.326352 + 0.118782i) q^{82} +(4.23783 + 7.34013i) q^{83} +(-9.98545 + 8.37879i) q^{85} +(-4.64543 + 3.89798i) q^{86} +(-1.59240 - 2.75811i) q^{88} +(7.27244 + 2.64695i) q^{89} +(-2.69459 - 15.2818i) q^{91} +(-0.652704 + 0.237565i) q^{92} +7.88713 q^{94} +(-7.51754 + 4.41436i) q^{95} +(-0.266044 - 0.223238i) q^{97} +(0.245100 - 0.0892091i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 6 * q^7 + 3 * q^8	$ 6 q - 6 q^{7} + 3 q^{8} + 6 q^{11} + 12 q^{13} - 12 q^{14} + 12 q^{17} + 18 q^{19} - 12 q^{20} + 12 q^{23} - 6 q^{26} - 6 q^{28} + 18 q^{29} + 6 q^{31} - 12 q^{34} + 12 q^{35} - 12 q^{37} + 9 q^{38} - 3 q^{41} - 6 q^{43} - 30 q^{47} - 15 q^{49} - 3 q^{50} - 6 q^{52} - 24 q^{53} + 18 q^{55} - 12 q^{56} + 24 q^{58} + 3 q^{59} + 6 q^{61} - 18 q^{62} - 3 q^{64} - 12 q^{65} - 9 q^{67} + 3 q^{68} - 12 q^{70} + 18 q^{71} - 30 q^{73} + 18 q^{74} - 6 q^{76} + 12 q^{77} + 6 q^{79} + 3 q^{82} + 6 q^{83} - 24 q^{85} - 12 q^{86} - 6 q^{88} - 12 q^{91} - 6 q^{92} - 12 q^{94} + 3 q^{97}+O(q^{100}) $ 6 * q - 6 * q^7 + 3 * q^8 + 6 * q^11 + 12 * q^13 - 12 * q^14 + 12 * q^17 + 18 * q^19 - 12 * q^20 + 12 * q^23 - 6 * q^26 - 6 * q^28 + 18 * q^29 + 6 * q^31 - 12 * q^34 + 12 * q^35 - 12 * q^37 + 9 * q^38 - 3 * q^41 - 6 * q^43 - 30 * q^47 - 15 * q^49 - 3 * q^50 - 6 * q^52 - 24 * q^53 + 18 * q^55 - 12 * q^56 + 24 * q^58 + 3 * q^59 + 6 * q^61 - 18 * q^62 - 3 * q^64 - 12 * q^65 - 9 * q^67 + 3 * q^68 - 12 * q^70 + 18 * q^71 - 30 * q^73 + 18 * q^74 - 6 * q^76 + 12 * q^77 + 6 * q^79 + 3 * q^82 + 6 * q^83 - 24 * q^85 - 12 * q^86 - 6 * q^88 - 12 * q^91 - 6 * q^92 - 12 * q^94 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$		0			0
$3$		0			0
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.347296	+	1.96962i	−0.155316	+	0.880839i	0.803181	+	0.595735i	$0.203139\pi$
$5$	−0.347296	+	1.96962i	−0.155316	+	0.880839i	−0.958497	+	0.285104i	$0.907972\pi$
$6$		0			0
$7$	−1.34730	−	2.33359i	−0.509230	−	0.882013i	−0.999943	−	0.0106911i	$-0.996597\pi$
$7$	−1.34730	−	2.33359i	−0.509230	−	0.882013i	0.490713	−	0.871321i	$-0.336736\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$		0			0
$10$	1.53209	−	1.28558i	0.484489	−	0.406535i
$11$	1.59240	−	2.75811i	0.480126	−	0.831602i	−0.519615	−	0.854401i	$-0.673924\pi$
$11$	1.59240	−	2.75811i	0.480126	−	0.831602i	0.999740	+	0.0227990i	$0.00725777\pi$
$12$		0			0
$13$	5.41147	+	1.96962i	1.50087	+	0.546273i	0.956286	−	0.292432i	$-0.0944644\pi$
$13$	5.41147	+	1.96962i	1.50087	+	0.546273i	0.544586	+	0.838705i	$0.316687\pi$
$14$	−0.467911	+	2.65366i	−0.125055	+	0.709219i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	4.99273	+	4.18939i	1.21091	+	1.01608i	0.999250	+	0.0387350i	$0.0123328\pi$
$17$	4.99273	+	4.18939i	1.21091	+	1.01608i	0.211664	+	0.977342i	$0.432112\pi$
$18$		0			0
$19$	2.82635	+	3.31839i	0.648410	+	0.761292i
$19$	2.82635	+	3.31839i	0.648410	+	0.761292i
$20$	−2.00000			−0.447214
$21$		0			0
$22$	−2.99273	+	1.08926i	−0.638051	+	0.232232i
$23$	0.120615	+	0.684040i	0.0251499	+	0.142632i	0.994797	−	0.101876i	$-0.0324845\pi$
$23$	0.120615	+	0.684040i	0.0251499	+	0.142632i	−0.969647	+	0.244508i	$0.921373\pi$
$24$		0			0
$25$	0.939693	+	0.342020i	0.187939	+	0.0684040i
$26$	−2.87939	−	4.98724i	−0.564694	−	0.978079i
$27$		0			0
$28$	2.06418	−	1.73205i	0.390093	−	0.327327i
$29$	2.16250	−	1.81456i	0.401567	−	0.336955i	−0.419532	−	0.907741i	$-0.637806\pi$
$29$	2.16250	−	1.81456i	0.401567	−	0.336955i	0.821099	+	0.570786i	$0.193361\pi$
$30$		0			0
$31$	−1.22668	−	2.12467i	−0.220319	−	0.381603i	0.734586	−	0.678515i	$-0.237376\pi$
$31$	−1.22668	−	2.12467i	−0.220319	−	0.381603i	−0.954905	+	0.296913i	$0.904043\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$		0			0
$34$	−1.13176	−	6.41852i	−0.194095	−	1.10077i
$35$	5.06418	−	1.84321i	0.856002	−	0.311559i
$36$		0			0
$37$	−4.36959			−0.718355			−0.359178	−	0.933269i	$-0.616943\pi$
$37$	−4.36959			−0.718355			−0.359178	+	0.933269i	$0.616943\pi$
$38$	−0.0320889	−	4.35878i	−0.00520550	−	0.707088i
$39$		0			0
$40$	1.53209	+	1.28558i	0.242245	+	0.203267i
$41$	−0.326352	+	0.118782i	−0.0509676	+	0.0185507i	−0.367378	−	0.930072i	$-0.619745\pi$
$41$	−0.326352	+	0.118782i	−0.0509676	+	0.0185507i	0.316411	+	0.948622i	$0.397522\pi$
$42$		0			0
$43$	1.05303	−	5.97205i	0.160586	−	0.910729i	−0.792913	−	0.609334i	$-0.791437\pi$
$43$	1.05303	−	5.97205i	0.160586	−	0.910729i	0.953499	−	0.301395i	$-0.0974522\pi$
$44$	2.99273	+	1.08926i	0.451170	+	0.164213i
$45$		0			0
$46$	0.347296	−	0.601535i	0.0512061	−	0.0886915i
$47$	−6.04189	+	5.06975i	−0.881300	+	0.739499i	−0.966446	−	0.256870i	$-0.917309\pi$
$47$	−6.04189	+	5.06975i	−0.881300	+	0.739499i	0.0851459	+	0.996368i	$0.472864\pi$
$48$		0			0
$49$	−0.130415	+	0.225885i	−0.0186307	+	0.0322693i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$		0			0
$52$	−1.00000	+	5.67128i	−0.138675	+	0.786465i
$53$	−1.42602	−	8.08737i	−0.195879	−	1.11089i	−0.911161	−	0.412050i	$-0.864813\pi$
$53$	−1.42602	−	8.08737i	−0.195879	−	1.11089i	0.715282	−	0.698836i	$-0.246298\pi$
$54$		0			0
$55$	4.87939	+	4.09429i	0.657936	+	0.552074i
$56$	−2.69459			−0.360080
$57$		0			0
$58$	−2.82295			−0.370671
$59$	−0.439693	−	0.368946i	−0.0572431	−	0.0480327i	0.613717	−	0.789526i	$-0.289673\pi$
$59$	−0.439693	−	0.368946i	−0.0572431	−	0.0480327i	−0.670960	+	0.741493i	$0.734118\pi$
$60$		0			0
$61$	0.509800	+	2.89122i	0.0652732	+	0.370183i	0.999894	+	0.0145378i	$0.00462769\pi$
$61$	0.509800	+	2.89122i	0.0652732	+	0.370183i	−0.934621	+	0.355645i	$0.884261\pi$
$62$	−0.426022	+	2.41609i	−0.0541049	+	0.306844i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−5.75877	+	9.97448i	−0.714288	+	1.23718i
$66$		0			0
$67$	−3.79813	+	3.18701i	−0.464016	+	0.389356i	−0.844606	−	0.535388i	$-0.820165\pi$
$67$	−3.79813	+	3.18701i	−0.464016	+	0.389356i	0.380590	+	0.924744i	$0.375721\pi$
$68$	−3.25877	+	5.64436i	−0.395184	+	0.684479i
$69$		0			0
$70$	−5.06418	−	1.84321i	−0.605285	−	0.220306i
$71$	1.46791	−	8.32494i	0.174209	−	0.987988i	−0.764844	−	0.644216i	$-0.777184\pi$
$71$	1.46791	−	8.32494i	0.174209	−	0.987988i	0.939053	−	0.343773i	$-0.111705\pi$
$72$		0			0
$73$	−14.8157	+	5.39246i	−1.73404	+	0.631140i	−0.998905	−	0.0467771i	$-0.985105\pi$
$73$	−14.8157	+	5.39246i	−1.73404	+	0.631140i	−0.735138	+	0.677917i	$0.762883\pi$
$74$	3.34730	+	2.80872i	0.389115	+	0.326507i
$75$		0			0
$76$	−2.77719	+	3.35965i	−0.318565	+	0.385378i
$77$	−8.58172			−0.977978
$78$		0			0
$79$	8.51754	−	3.10013i	0.958298	−	0.348792i	0.184932	−	0.982751i	$-0.440794\pi$
$79$	8.51754	−	3.10013i	0.958298	−	0.348792i	0.773366	+	0.633959i	$0.218571\pi$
$80$	−0.347296	−	1.96962i	−0.0388289	−	0.220210i
$81$		0			0
$82$	0.326352	+	0.118782i	0.0360395	+	0.0131173i
$83$	4.23783	+	7.34013i	0.465162	+	0.805684i	0.999209	−	0.0397709i	$-0.0126628\pi$
$83$	4.23783	+	7.34013i	0.465162	+	0.805684i	−0.534047	+	0.845455i	$0.679329\pi$
$84$		0			0
$85$	−9.98545	+	8.37879i	−1.08307	+	0.908807i
$86$	−4.64543	+	3.89798i	−0.500930	+	0.420330i
$87$		0			0
$88$	−1.59240	−	2.75811i	−0.169750	−	0.294016i
$89$	7.27244	+	2.64695i	0.770877	+	0.280576i	0.697363	−	0.716718i	$-0.254356\pi$
$89$	7.27244	+	2.64695i	0.770877	+	0.280576i	0.0735139	+	0.997294i	$0.476579\pi$
$90$		0			0
$91$	−2.69459	−	15.2818i	−0.282470	−	1.60197i
$92$	−0.652704	+	0.237565i	−0.0680491	+	0.0247678i
$93$		0			0
$94$	7.88713			0.813495
$95$	−7.51754	+	4.41436i	−0.771283	+	0.452904i
$96$		0			0
$97$	−0.266044	−	0.223238i	−0.0270127	−	0.0226664i	0.629181	−	0.777259i	$-0.283390\pi$
$97$	−0.266044	−	0.223238i	−0.0270127	−	0.0226664i	−0.656194	+	0.754592i	$0.727835\pi$
$98$	0.245100	−	0.0892091i	0.0247588	−	0.00901148i
$99$		0			0
$100$	−0.173648	+	0.984808i	−0.0173648	+	0.0984808i
$101$	−0.347296	−	0.126406i	−0.0345573	−	0.0125778i	0.324684	−	0.945823i	$-0.394742\pi$
$101$	−0.347296	−	0.126406i	−0.0345573	−	0.0125778i	−0.359241	+	0.933245i	$0.616964\pi$
$102$		0			0
$103$	−4.29086	+	7.43199i	−0.422791	+	0.732295i	−0.996211	−	0.0869659i	$-0.972283\pi$
$103$	−4.29086	+	7.43199i	−0.422791	+	0.732295i	0.573420	+	0.819261i	$0.305616\pi$
$104$	4.41147	−	3.70167i	0.432581	−	0.362978i
$105$		0			0
$106$	−4.10607	+	7.11192i	−0.398816	+	0.690770i
$107$	−5.72668	−	9.91890i	−0.553619	−	0.958897i	−0.998010	−	0.0630633i	$-0.979913\pi$
$107$	−5.72668	−	9.91890i	−0.553619	−	0.958897i	0.444390	−	0.895833i	$-0.353420\pi$
$108$		0			0
$109$	1.50980	−	8.56250i	0.144613	−	0.820139i	−0.823065	−	0.567948i	$-0.807738\pi$
$109$	1.50980	−	8.56250i	0.144613	−	0.820139i	0.967677	−	0.252191i	$-0.0811513\pi$
$110$	−1.10607	−	6.27282i	−0.105459	−	0.598090i
$111$		0			0
$112$	2.06418	+	1.73205i	0.195046	+	0.163663i
$113$	−2.85978			−0.269026			−0.134513	−	0.990912i	$-0.542947\pi$
$113$	−2.85978			−0.269026			−0.134513	+	0.990912i	$0.542947\pi$
$114$		0			0
$115$	−1.38919			−0.129542
$116$	2.16250	+	1.81456i	0.200783	+	0.168477i
$117$		0			0
$118$	0.0996702	+	0.565258i	0.00917539	+	0.0520362i
$119$	3.04963	−	17.2953i	0.279559	−	1.58546i
$120$		0			0
$121$	0.428548	+	0.742267i	0.0389589	+	0.0674789i
$122$	1.46791	−	2.54250i	0.132898	−	0.230187i
$123$		0			0
$124$	1.87939	−	1.57699i	0.168774	−	0.141618i
$125$	−6.00000	+	10.3923i	−0.536656	+	0.929516i
$126$		0			0
$127$	−9.14290	−	3.32774i	−0.811301	−	0.295290i	−0.0971401	−	0.995271i	$-0.530970\pi$
$127$	−9.14290	−	3.32774i	−0.811301	−	0.295290i	−0.714161	+	0.699981i	$0.753192\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$		0			0
$130$	10.8229	−	3.93923i	0.949235	−	0.345493i
$131$	4.95471	+	4.15749i	0.432895	+	0.363242i	0.833043	−	0.553209i	$-0.186597\pi$
$131$	4.95471	+	4.15749i	0.432895	+	0.363242i	−0.400148	+	0.916451i	$0.631041\pi$
$132$		0			0
$133$	3.93582	−	11.0664i	0.341279	−	0.959578i
$134$	4.95811			0.428316
$135$		0			0
$136$	6.12449	−	2.22913i	0.525170	−	0.191146i
$137$	2.02481	+	11.4833i	0.172992	+	0.981084i	0.940437	+	0.339969i	$0.110417\pi$
$137$	2.02481	+	11.4833i	0.172992	+	0.981084i	−0.767445	+	0.641115i	$0.778472\pi$
$138$		0			0
$139$	7.76517	+	2.82629i	0.658633	+	0.239723i	0.649646	−	0.760237i	$-0.274917\pi$
$139$	7.76517	+	2.82629i	0.658633	+	0.239723i	0.00898688	+	0.999960i	$0.497139\pi$
$140$	2.69459	+	4.66717i	0.227735	+	0.394448i
$141$		0			0
$142$	−6.47565	+	5.43372i	−0.543425	+	0.455987i
$143$	14.0496	−	11.7890i	1.17489	−	0.985849i
$144$		0			0
$145$	2.82295	+	4.88949i	0.234433	+	0.406050i
$146$	14.8157	+	5.39246i	1.22615	+	0.446284i
$147$		0			0
$148$	−0.758770	−	4.30320i	−0.0623705	−	0.353721i
$149$	−15.4611	+	5.62738i	−1.26662	+	0.461013i	−0.885986	−	0.463712i	$-0.846517\pi$
$149$	−15.4611	+	5.62738i	−1.26662	+	0.461013i	−0.380637	+	0.924725i	$0.624295\pi$
$150$		0			0
$151$	4.65539			0.378850			0.189425	−	0.981895i	$-0.439338\pi$
$151$	4.65539			0.378850			0.189425	+	0.981895i	$0.439338\pi$
$152$	4.28699	−	0.788496i	0.347721	−	0.0639554i
$153$		0			0
$154$	6.57398	+	5.51622i	0.529746	+	0.444510i
$155$	4.61081	−	1.67820i	0.370350	−	0.134796i
$156$		0			0
$157$	1.46791	−	8.32494i	0.117152	−	0.664402i	−0.868510	−	0.495671i	$-0.834922\pi$
$157$	1.46791	−	8.32494i	0.117152	−	0.664402i	0.985662	−	0.168731i	$-0.0539669\pi$
$158$	−8.51754	−	3.10013i	−0.677619	−	0.246633i
$159$		0			0
$160$	−1.00000	+	1.73205i	−0.0790569	+	0.136931i
$161$	1.43376	−	1.20307i	0.112996	−	0.0948152i
$162$		0			0
$163$	−8.52481	+	14.7654i	−0.667715	+	1.15652i	0.310826	+	0.950467i	$0.399394\pi$
$163$	−8.52481	+	14.7654i	−0.667715	+	1.15652i	−0.978542	+	0.206050i	$0.933939\pi$
$164$	−0.173648	−	0.300767i	−0.0135596	−	0.0234860i
$165$		0			0
$166$	1.47178	−	8.34689i	0.114232	−	0.647844i
$167$	0.554378	+	3.14403i	0.0428990	+	0.243292i	0.998715	−	0.0506721i	$-0.0161363\pi$
$167$	0.554378	+	3.14403i	0.0428990	+	0.243292i	−0.955816	+	0.293965i	$0.905025\pi$
$168$		0			0
$169$	15.4461	+	12.9608i	1.18816	+	0.996985i
$170$	13.0351			0.999745
$171$		0			0
$172$	6.06418			0.462389
$173$	−7.37733	−	6.19031i	−0.560888	−	0.470641i	0.317720	−	0.948185i	$-0.397083\pi$
$173$	−7.37733	−	6.19031i	−0.560888	−	0.470641i	−0.878608	+	0.477544i	$0.841527\pi$
$174$		0			0
$175$	−0.467911	−	2.65366i	−0.0353708	−	0.200598i
$176$	−0.553033	+	3.13641i	−0.0416865	+	0.236416i
$177$		0			0
$178$	−3.86959	−	6.70232i	−0.290038	−	0.502360i
$179$	9.40807	−	16.2953i	0.703192	−	1.21796i	−0.264148	−	0.964482i	$-0.585091\pi$
$179$	9.40807	−	16.2953i	0.703192	−	1.21796i	0.967340	−	0.253482i	$-0.0815760\pi$
$180$		0			0
$181$	2.12836	−	1.78590i	0.158199	−	0.132745i	−0.560252	−	0.828322i	$-0.689296\pi$
$181$	2.12836	−	1.78590i	0.158199	−	0.132745i	0.718451	+	0.695577i	$0.244851\pi$
$182$	−7.75877	+	13.4386i	−0.575118	+	0.996134i
$183$		0			0
$184$	0.652704	+	0.237565i	0.0481180	+	0.0175135i
$185$	1.51754	−	8.60640i	0.111572	−	0.632755i
$186$		0			0
$187$	19.5052	−	7.09932i	1.42636	−	0.519154i
$188$	−6.04189	−	5.06975i	−0.440650	−	0.369749i
$189$		0			0
$190$	8.59627	+	1.45059i	0.623639	+	0.105237i
$191$	−9.56212			−0.691891			−0.345945	−	0.938255i	$-0.612442\pi$
$191$	−9.56212			−0.691891			−0.345945	+	0.938255i	$0.612442\pi$
$192$		0			0
$193$	22.2528	−	8.09937i	1.60179	−	0.583006i	0.622001	−	0.783017i	$-0.286320\pi$
$193$	22.2528	−	8.09937i	1.60179	−	0.583006i	0.979794	+	0.200011i	$0.0640978\pi$
$194$	0.0603074	+	0.342020i	0.00432982	+	0.0245556i
$195$		0			0
$196$	−0.245100	−	0.0892091i	−0.0175071	−	0.00637208i
$197$	−11.4611	−	19.8512i	−0.816570	−	1.41434i	−0.908195	−	0.418547i	$-0.862540\pi$
$197$	−11.4611	−	19.8512i	−0.816570	−	1.41434i	0.0916253	−	0.995794i	$-0.470794\pi$
$198$		0			0
$199$	7.72462	−	6.48173i	0.547584	−	0.459477i	−0.326538	−	0.945184i	$-0.605882\pi$
$199$	7.72462	−	6.48173i	0.547584	−	0.459477i	0.874122	+	0.485707i	$0.161438\pi$
$200$	0.766044	−	0.642788i	0.0541675	−	0.0454519i
$201$		0			0
$202$	0.184793	+	0.320070i	0.0130020	+	0.0225201i
$203$	−7.14796	−	2.60164i	−0.501688	−	0.182600i
$204$		0			0
$205$	−0.120615	−	0.684040i	−0.00842410	−	0.0477754i
$206$	8.06418	−	2.93512i	0.561858	−	0.204500i
$207$		0			0
$208$	−5.75877			−0.399299
$209$	13.6532	−	2.51120i	0.944410	−	0.173703i
$210$		0			0
$211$	−17.1288	−	14.3728i	−1.17920	−	0.989464i	−0.999984	−	0.00565322i	$-0.998201\pi$
$211$	−17.1288	−	14.3728i	−1.17920	−	0.989464i	−0.179213	−	0.983810i	$-0.557355\pi$
$212$	7.71688	−	2.80872i	0.529998	−	0.192903i
$213$		0			0
$214$	−1.98886	+	11.2794i	−0.135955	+	0.771041i
$215$	11.3969	+	4.14814i	0.777264	+	0.282901i
$216$		0			0
$217$	−3.30541	+	5.72513i	−0.224386	+	0.388647i
$218$	−6.66044	+	5.58878i	−0.451102	+	0.378520i
$219$		0			0
$220$	−3.18479	+	5.51622i	−0.214719	+	0.371904i
$221$	18.7665	+	32.5046i	1.26237	+	2.18649i
$222$		0			0
$223$	−1.61081	+	9.13538i	−0.107868	+	0.611751i	0.882168	+	0.470935i	$0.156083\pi$
$223$	−1.61081	+	9.13538i	−0.107868	+	0.611751i	−0.990036	+	0.140815i	$0.955028\pi$
$224$	−0.467911	−	2.65366i	−0.0312636	−	0.177305i
$225$		0			0
$226$	2.19072	+	1.83823i	0.145725	+	0.122278i
$227$	−7.73648			−0.513488			−0.256744	−	0.966479i	$-0.582650\pi$
$227$	−7.73648			−0.513488			−0.256744	+	0.966479i	$0.582650\pi$
$228$		0			0
$229$	−23.0351			−1.52220			−0.761101	−	0.648634i	$-0.775341\pi$
$229$	−23.0351			−1.52220			−0.761101	+	0.648634i	$0.775341\pi$
$230$	1.06418	+	0.892951i	0.0701698	+	0.0588795i
$231$		0			0
$232$	−0.490200	−	2.78006i	−0.0321832	−	0.182520i
$233$	−1.45858	+	8.27201i	−0.0955546	+	0.541917i	0.899021	+	0.437905i	$0.144279\pi$
$233$	−1.45858	+	8.27201i	−0.0955546	+	0.541917i	−0.994576	+	0.104012i	$0.966832\pi$
$234$		0			0
$235$	−7.88713	−	13.6609i	−0.514499	−	0.891139i
$236$	0.286989	−	0.497079i	0.0186814	−	0.0323571i
$237$		0			0
$238$	−13.4534	+	11.2887i	−0.872052	+	0.731739i
$239$	−7.86484	+	13.6223i	−0.508734	+	0.881153i	0.491215	+	0.871038i	$0.336553\pi$
$239$	−7.86484	+	13.6223i	−0.508734	+	0.881153i	−0.999949	+	0.0101147i	$0.996780\pi$
$240$		0			0
$241$	−16.4474	−	5.98638i	−1.05947	−	0.385616i	−0.247242	−	0.968954i	$-0.579524\pi$
$241$	−16.4474	−	5.98638i	−1.05947	−	0.385616i	−0.812230	+	0.583337i	$0.801747\pi$
$242$	0.148833	−	0.844075i	0.00956736	−	0.0542592i
$243$		0			0
$244$	−2.75877	+	1.00411i	−0.176612	+	0.0642816i
$245$	−0.399615	−	0.335316i	−0.0255304	−	0.0214226i
$246$		0			0
$247$	8.75877	+	23.5242i	0.557307	+	1.49681i
$248$	−2.45336			−0.155789
$249$		0			0
$250$	11.2763	−	4.10424i	0.713177	−	0.259575i
$251$	−1.48767	−	8.43702i	−0.0939011	−	0.532540i	−0.995079	−	0.0990893i	$-0.968407\pi$
$251$	−1.48767	−	8.43702i	−0.0939011	−	0.532540i	0.901177	−	0.433450i	$-0.142704\pi$
$252$		0			0
$253$	2.07873	+	0.756594i	0.130688	+	0.0475667i
$254$	4.86484	+	8.42615i	0.305247	+	0.528703i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	6.14724	−	5.15815i	0.383454	−	0.321756i	−0.430602	−	0.902542i	$-0.641699\pi$
$257$	6.14724	−	5.15815i	0.383454	−	0.321756i	0.814057	+	0.580785i	$0.197254\pi$
$258$		0			0
$259$	5.88713	+	10.1968i	0.365808	+	0.633598i
$260$	−10.8229	−	3.93923i	−0.671211	−	0.244301i
$261$		0			0
$262$	−1.12314	−	6.36965i	−0.0693879	−	0.393518i
$263$	−5.60132	+	2.03871i	−0.345392	+	0.125712i	−0.508891	−	0.860831i	$-0.669944\pi$
$263$	−5.60132	+	2.03871i	−0.345392	+	0.125712i	0.163499	+	0.986544i	$0.447722\pi$
$264$		0			0
$265$	16.4243			1.00893
$266$	−10.1284	+	5.94745i	−0.621009	+	0.364662i
$267$		0			0
$268$	−3.79813	−	3.18701i	−0.232008	−	0.194678i
$269$	−1.07873	+	0.392624i	−0.0657711	+	0.0239387i	−0.374696	−	0.927148i	$-0.622253\pi$
$269$	−1.07873	+	0.392624i	−0.0657711	+	0.0239387i	0.308925	+	0.951086i	$0.400031\pi$
$270$		0			0
$271$	3.48246	−	19.7500i	0.211544	−	1.19973i	−0.675259	−	0.737581i	$-0.735968\pi$
$271$	3.48246	−	19.7500i	0.211544	−	1.19973i	0.886803	−	0.462147i	$-0.152921\pi$
$272$	−6.12449	−	2.22913i	−0.371351	−	0.135161i
$273$		0			0
$274$	5.83022	−	10.0982i	0.352217	−	0.610057i
$275$	2.43969	−	2.04715i	0.147119	−	0.123447i
$276$		0			0
$277$	−8.68004	+	15.0343i	−0.521533	+	0.903322i	0.478153	+	0.878277i	$0.341306\pi$
$277$	−8.68004	+	15.0343i	−0.521533	+	0.903322i	−0.999686	+	0.0250457i	$0.992027\pi$
$278$	−4.13176	−	7.15642i	−0.247806	−	0.429213i
$279$		0			0
$280$	0.935822	−	5.30731i	0.0559261	−	0.317173i
$281$	−0.507274	−	2.87689i	−0.0302614	−	0.171621i	0.965931	−	0.258798i	$-0.0833265\pi$
$281$	−0.507274	−	2.87689i	−0.0302614	−	0.171621i	−0.996193	+	0.0871772i	$0.972215\pi$
$282$		0			0
$283$	−7.26264	−	6.09408i	−0.431719	−	0.362255i	0.400881	−	0.916130i	$-0.368704\pi$
$283$	−7.26264	−	6.09408i	−0.431719	−	0.362255i	−0.832600	+	0.553875i	$0.813149\pi$
$284$	8.45336			0.501615
$285$		0			0
$286$	−18.3405			−1.08450
$287$	0.716881	+	0.601535i	0.0423162	+	0.0355075i
$288$		0			0
$289$	4.42427	+	25.0913i	0.260251	+	1.47596i
$290$	0.980400	−	5.56012i	0.0575710	−	0.326502i
$291$		0			0
$292$	−7.88326	−	13.6542i	−0.461333	−	0.799052i
$293$	−13.6459	+	23.6354i	−0.797202	+	1.38079i	0.124230	+	0.992253i	$0.460354\pi$
$293$	−13.6459	+	23.6354i	−0.797202	+	1.38079i	−0.921432	+	0.388541i	$0.872979\pi$
$294$		0			0
$295$	0.879385	−	0.737892i	0.0511998	−	0.0429617i
$296$	−2.18479	+	3.78417i	−0.126988	+	0.219951i
$297$		0			0
$298$	15.4611	+	5.62738i	0.895638	+	0.325985i
$299$	−0.694593	+	3.93923i	−0.0401693	+	0.227812i
$300$		0			0
$301$	−15.3550	+	5.58878i	−0.885050	+	0.322132i
$302$	−3.56624	−	2.99243i	−0.205214	−	0.172195i
$303$		0			0
$304$	−3.79086	−	2.15160i	−0.217421	−	0.123403i
$305$	−5.87164			−0.336209
$306$		0			0
$307$	−20.0424	+	7.29482i	−1.14388	+	0.416337i	−0.843312	−	0.537424i	$-0.819398\pi$
$307$	−20.0424	+	7.29482i	−1.14388	+	0.416337i	−0.300565	+	0.953761i	$0.597175\pi$
$308$	−1.49020	−	8.45134i	−0.0849120	−	0.481560i
$309$		0			0
$310$	−4.61081	−	1.67820i	−0.261877	−	0.0953153i
$311$	−14.6459	−	25.3674i	−0.830493	−	1.43846i	−0.897648	−	0.440713i	$-0.854726\pi$
$311$	−14.6459	−	25.3674i	−0.830493	−	1.43846i	0.0671555	−	0.997743i	$-0.478608\pi$
$312$		0			0
$313$	4.26011	−	3.57466i	0.240796	−	0.202052i	−0.514401	−	0.857550i	$-0.671986\pi$
$313$	4.26011	−	3.57466i	0.240796	−	0.202052i	0.755197	+	0.655498i	$0.227541\pi$
$314$	−6.47565	+	5.43372i	−0.365442	+	0.306642i
$315$		0			0
$316$	4.53209	+	7.84981i	0.254950	+	0.441586i
$317$	3.57398	+	1.30082i	0.200735	+	0.0730614i	0.440431	−	0.897786i	$-0.354826\pi$
$317$	3.57398	+	1.30082i	0.200735	+	0.0730614i	−0.239696	+	0.970848i	$0.577048\pi$
$318$		0			0
$319$	−1.56118	−	8.85392i	−0.0874096	−	0.495724i
$320$	1.87939	−	0.684040i	0.105061	−	0.0382390i
$321$		0			0
$322$	−1.87164			−0.104303
$323$	0.209141	+	28.4085i	0.0116369	+	1.58069i
$324$		0			0
$325$	4.41147	+	3.70167i	0.244705	+	0.205332i
$326$	16.0214	−	5.83132i	0.887344	−	0.322967i
$327$		0			0
$328$	−0.0603074	+	0.342020i	−0.00332992	+	0.0188849i
$329$	19.9709	+	7.26881i	1.10103	+	0.400743i
$330$		0			0
$331$	−10.2110	+	17.6859i	−0.561245	+	0.972104i	0.436144	+	0.899877i	$0.356344\pi$
$331$	−10.2110	+	17.6859i	−0.561245	+	0.972104i	−0.997388	+	0.0722272i	$0.976989\pi$
$332$	−6.49273	+	5.44804i	−0.356335	+	0.299000i
$333$		0			0
$334$	1.59627	−	2.76481i	0.0873438	−	0.151284i
$335$	−4.95811	−	8.58770i	−0.270891	−	0.469196i
$336$		0			0
$337$	3.52687	−	20.0019i	0.192121	−	1.08957i	−0.724338	−	0.689445i	$-0.757855\pi$
$337$	3.52687	−	20.0019i	0.192121	−	1.08957i	0.916459	−	0.400128i	$-0.131034\pi$
$338$	−3.50134	−	19.8571i	−0.190448	−	1.08008i
$339$		0			0
$340$	−9.98545	−	8.37879i	−0.541537	−	0.454404i
$341$	−7.81345			−0.423122
$342$		0			0
$343$	−18.1593			−0.980511
$344$	−4.64543	−	3.89798i	−0.250465	−	0.210165i
$345$		0			0
$346$	1.67230	+	9.48411i	0.0899036	+	0.509869i
$347$	−0.905544	+	5.13560i	−0.0486122	+	0.275693i	−0.999419	−	0.0340920i	$-0.989146\pi$
$347$	−0.905544	+	5.13560i	−0.0486122	+	0.275693i	0.950807	+	0.309785i	$0.100257\pi$
$348$		0			0
$349$	−7.17024	−	12.4192i	−0.383814	−	0.664786i	0.607790	−	0.794098i	$-0.292056\pi$
$349$	−7.17024	−	12.4192i	−0.383814	−	0.664786i	−0.991604	+	0.129312i	$0.958723\pi$
$350$	−1.34730	+	2.33359i	−0.0720160	+	0.124735i
$351$		0			0
$352$	2.43969	−	2.04715i	0.130036	−	0.109113i
$353$	13.1250	−	22.7331i	0.698571	−	1.20996i	−0.270391	−	0.962750i	$-0.587153\pi$
$353$	13.1250	−	22.7331i	0.698571	−	1.20996i	0.968962	−	0.247209i	$-0.0795136\pi$
$354$		0			0
$355$	15.8871	+	5.78244i	0.843201	+	0.306900i
$356$	−1.34389	+	7.62159i	−0.0712262	+	0.403944i
$357$		0			0
$358$	−17.6814	+	6.43550i	−0.934490	+	0.340127i
$359$	25.8084	+	21.6558i	1.36212	+	1.14295i	0.975323	+	0.220784i	$0.0708615\pi$
$359$	25.8084	+	21.6558i	1.36212	+	1.14295i	0.386792	+	0.922167i	$0.373583\pi$
$360$		0			0
$361$	−3.02347	+	18.7579i	−0.159130	+	0.987258i
$362$	−2.77837			−0.146028
$363$		0			0
$364$	14.5817	−	5.30731i	0.764290	−	0.278179i
$365$	−5.47565	−	31.0540i	−0.286609	−	1.62544i
$366$		0			0
$367$	9.83750	+	3.58056i	0.513513	+	0.186903i	0.585762	−	0.810483i	$-0.300795\pi$
$367$	9.83750	+	3.58056i	0.513513	+	0.186903i	−0.0722488	+	0.997387i	$0.523018\pi$
$368$	−0.347296	−	0.601535i	−0.0181041	−	0.0313572i
$369$		0			0
$370$	−6.69459	+	5.61743i	−0.348035	+	0.292036i
$371$	−16.9513	+	14.2238i	−0.880068	+	0.738465i
$372$		0			0
$373$	−11.9513	−	20.7003i	−0.618815	−	1.07182i	−0.989702	−	0.143141i	$-0.954280\pi$
$373$	−11.9513	−	20.7003i	−0.618815	−	1.07182i	0.370887	−	0.928678i	$-0.379054\pi$
$374$	−19.5052	−	7.09932i	−1.00859	−	0.367097i
$375$		0			0
$376$	1.36959	+	7.76730i	0.0706310	+	0.400568i
$377$	15.2763	−	5.56012i	0.786770	−	0.286361i
$378$		0			0
$379$	17.8135			0.915016			0.457508	−	0.889206i	$-0.348742\pi$
$379$	17.8135			0.915016			0.457508	+	0.889206i	$0.348742\pi$
$380$	−5.65270	−	6.63679i	−0.289978	−	0.340460i
$381$		0			0
$382$	7.32501	+	6.14641i	0.374780	+	0.314478i
$383$	23.5672	−	8.57775i	1.20423	−	0.438302i	0.339529	−	0.940596i	$-0.389732\pi$
$383$	23.5672	−	8.57775i	1.20423	−	0.438302i	0.864697	+	0.502293i	$0.167510\pi$
$384$		0			0
$385$	2.98040	−	16.9027i	0.151895	−	0.861441i
$386$	−22.2528	−	8.09937i	−1.13264	−	0.412247i
$387$		0			0
$388$	0.173648	−	0.300767i	0.00881565	−	0.0152692i
$389$	7.21482	−	6.05395i	0.365806	−	0.306948i	−0.441294	−	0.897363i	$-0.645480\pi$
$389$	7.21482	−	6.05395i	0.365806	−	0.306948i	0.807100	+	0.590415i	$0.201036\pi$
$390$		0			0
$391$	−2.26352	+	3.92053i	−0.114471	+	0.198270i
$392$	0.130415	+	0.225885i	0.00658695	+	0.0114089i
$393$		0			0
$394$	−3.98040	+	22.5740i	−0.200530	+	1.13726i
$395$	3.14796	+	17.8529i	0.158391	+	0.898279i
$396$		0			0
$397$	5.24897	+	4.40441i	0.263438	+	0.221051i	0.764933	−	0.644110i	$-0.222772\pi$
$397$	5.24897	+	4.40441i	0.263438	+	0.221051i	−0.501495	+	0.865161i	$0.667216\pi$
$398$	−10.0838			−0.505454
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−3.63634	−	3.05126i	−0.181590	−	0.152372i	0.547461	−	0.836831i	$-0.315594\pi$
$401$	−3.63634	−	3.05126i	−0.181590	−	0.152372i	−0.729052	+	0.684458i	$0.760039\pi$
$402$		0			0
$403$	−2.45336	−	13.9137i	−0.122211	−	0.693091i
$404$	0.0641778	−	0.363970i	0.00319296	−	0.0181082i
$405$		0			0
$406$	3.80335	+	6.58759i	0.188757	+	0.326937i
$407$	−6.95811	+	12.0518i	−0.344901	+	0.597386i
$408$		0			0
$409$	24.2781	−	20.3718i	1.20048	−	1.00732i	0.200860	−	0.979620i	$-0.435627\pi$
$409$	24.2781	−	20.3718i	1.20048	−	1.00732i	0.999616	−	0.0276988i	$-0.00881794\pi$
$410$	−0.347296	+	0.601535i	−0.0171517	+	0.0297077i
$411$		0			0
$412$	−8.06418	−	2.93512i	−0.397294	−	0.144603i
$413$	−0.268571	+	1.52314i	−0.0132155	+	0.0749488i
$414$		0			0
$415$	−15.9290	+	5.79769i	−0.781925	+	0.284597i
$416$	4.41147	+	3.70167i	0.216290	+	0.181489i
$417$		0			0
$418$	−12.0731	−	6.85240i	−0.590515	−	0.335162i
$419$	11.0101			0.537879			0.268939	−	0.963157i	$-0.413327\pi$
$419$	11.0101			0.537879			0.268939	+	0.963157i	$0.413327\pi$
$420$		0			0
$421$	8.14290	−	2.96377i	0.396861	−	0.144446i	−0.135877	−	0.990726i	$-0.543385\pi$
$421$	8.14290	−	2.96377i	0.396861	−	0.144446i	0.532738	+	0.846280i	$0.321163\pi$
$422$	3.88279	+	22.0204i	0.189011	+	1.07194i
$423$		0			0
$424$	−7.71688	−	2.80872i	−0.374765	−	0.136403i
$425$	3.25877	+	5.64436i	0.158074	+	0.273791i
$426$		0			0
$427$	6.06006	−	5.08499i	0.293267	−	0.246080i
$428$	8.77379	−	7.36208i	0.424097	−	0.355860i
$429$		0			0
$430$	−6.06418	−	10.5035i	−0.292441	−	0.506522i
$431$	−28.0847	−	10.2220i	−1.35279	−	0.492376i	−0.438975	−	0.898499i	$-0.644658\pi$
$431$	−28.0847	−	10.2220i	−1.35279	−	0.492376i	−0.913818	+	0.406123i	$0.866880\pi$
$432$		0			0
$433$	1.60813	+	9.12014i	0.0772816	+	0.438286i	0.998757	+	0.0498486i	$0.0158739\pi$
$433$	1.60813	+	9.12014i	0.0772816	+	0.438286i	−0.921475	+	0.388437i	$0.873015\pi$
$434$	6.21213	−	2.26103i	0.298192	−	0.108533i
$435$		0			0
$436$	8.69459			0.416395
$437$	−1.92902	+	2.33359i	−0.0922773	+	0.111631i
$438$		0			0
$439$	15.9813	+	13.4099i	0.762747	+	0.640021i	0.938840	−	0.344352i	$-0.111902\pi$
$439$	15.9813	+	13.4099i	0.762747	+	0.640021i	−0.176093	+	0.984374i	$0.556346\pi$
$440$	5.98545	−	2.17853i	0.285345	−	0.103857i
$441$		0			0
$442$	6.51754	−	36.9628i	0.310008	−	1.75814i
$443$	22.3910	+	8.14966i	1.06383	+	0.387202i	0.813865	−	0.581054i	$-0.197359\pi$
$443$	22.3910	+	8.14966i	1.06383	+	0.387202i	0.249963	+	0.968255i	$0.419582\pi$
$444$		0			0
$445$	−7.73917	+	13.4046i	−0.366872	+	0.635441i
$446$	7.10607	−	5.96270i	0.336482	−	0.282342i
$447$		0			0
$448$	−1.34730	+	2.33359i	−0.0636538	+	0.110252i
$449$	−1.09105	−	1.88976i	−0.0514899	−	0.0891832i	0.839132	−	0.543928i	$-0.183064\pi$
$449$	−1.09105	−	1.88976i	−0.0514899	−	0.0891832i	−0.890622	+	0.454745i	$0.849730\pi$
$450$		0			0
$451$	−0.192066	+	1.08926i	−0.00904406	+	0.0512914i
$452$	−0.496596	−	2.81634i	−0.0233579	−	0.132469i
$453$		0			0
$454$	5.92649	+	4.97291i	0.278144	+	0.233390i
$455$	31.0351			1.45495
$456$		0			0
$457$	1.78106			0.0833144			0.0416572	−	0.999132i	$-0.486736\pi$
$457$	1.78106			0.0833144			0.0416572	+	0.999132i	$0.486736\pi$
$458$	17.6459	+	14.8067i	0.824539	+	0.691870i
$459$		0			0
$460$	−0.241230	−	1.36808i	−0.0112474	−	0.0637871i
$461$	2.68954	−	15.2531i	0.125264	−	0.710410i	−0.855886	−	0.517164i	$-0.826988\pi$
$461$	2.68954	−	15.2531i	0.125264	−	0.710410i	0.981150	−	0.193245i	$-0.0619013\pi$
$462$		0			0
$463$	1.35504	+	2.34699i	0.0629739	+	0.109074i	0.895793	−	0.444471i	$-0.146608\pi$
$463$	1.35504	+	2.34699i	0.0629739	+	0.109074i	−0.832820	+	0.553545i	$0.813275\pi$
$464$	−1.41147	+	2.44474i	−0.0655260	+	0.113494i
$465$		0			0
$466$	6.43448	−	5.39917i	0.298071	−	0.250112i
$467$	6.45677	−	11.1834i	0.298784	−	0.517508i	−0.677074	−	0.735915i	$-0.736752\pi$
$467$	6.45677	−	11.1834i	0.298784	−	0.517508i	0.975858	+	0.218406i	$0.0700858\pi$
$468$		0			0
$469$	12.5544	+	4.56942i	0.579707	+	0.210996i
$470$	−2.73917	+	15.5346i	−0.126348	+	0.716558i
$471$		0			0
$472$	−0.539363	+	0.196312i	−0.0248262	+	0.00903599i
$473$	−14.7947	−	12.4143i	−0.680262	−	0.570808i
$474$		0			0
$475$	1.52094	+	4.08494i	0.0697857	+	0.187430i
$476$	17.5621			0.804958
$477$		0			0
$478$	14.7811	−	5.37987i	0.676070	−	0.246069i
$479$	3.22163	+	18.2708i	0.147200	+	0.834813i	0.965574	+	0.260127i	$0.0837645\pi$
$479$	3.22163	+	18.2708i	0.147200	+	0.834813i	−0.818374	+	0.574685i	$0.805124\pi$
$480$		0			0
$481$	−23.6459	−	8.60640i	−1.07816	−	0.392418i
$482$	8.75150	+	15.1580i	0.398620	+	0.690430i
$483$		0			0
$484$	−0.656574	+	0.550931i	−0.0298443	+	0.0250423i
$485$	0.532089	−	0.446476i	0.0241609	−	0.0202734i
$486$		0			0
$487$	−20.5868	−	35.6573i	−0.932876	−	1.61579i	−0.778379	−	0.627795i	$-0.783958\pi$
$487$	−20.5868	−	35.6573i	−0.932876	−	1.61579i	−0.154497	−	0.987993i	$-0.549376\pi$
$488$	2.75877	+	1.00411i	0.124884	+	0.0454539i
$489$		0			0
$490$	0.0905853	+	0.513735i	0.00409223	+	0.0232082i
$491$	−21.2160	+	7.72199i	−0.957465	+	0.348489i	−0.773040	−	0.634358i	$-0.781265\pi$
$491$	−21.2160	+	7.72199i	−0.957465	+	0.348489i	−0.184425	+	0.982847i	$0.559042\pi$
$492$		0			0
$493$	18.3987			0.828635
$494$	8.41147	−	23.6506i	0.378450	−	1.06409i
$495$		0			0
$496$	1.87939	+	1.57699i	0.0843869	+	0.0708090i
$497$	−21.4047	+	7.79066i	−0.960131	+	0.349459i
$498$		0			0
$499$	−5.09286	+	28.8831i	−0.227988	+	1.29298i	0.628902	+	0.777484i	$0.283505\pi$
$499$	−5.09286	+	28.8831i	−0.227988	+	1.29298i	−0.856890	+	0.515499i	$0.827607\pi$
$500$	−11.2763	−	4.10424i	−0.504292	−	0.183547i
$501$		0			0
$502$	−4.28359	+	7.41939i	−0.191186	+	0.331143i
$503$	−25.7520	+	21.6085i	−1.14822	+	0.963474i	−0.999677	−	0.0254316i	$-0.991904\pi$
$503$	−25.7520	+	21.6085i	−1.14822	+	0.963474i	−0.148547	+	0.988905i	$0.547460\pi$
$504$		0			0
$505$	0.369585	−	0.640140i	0.0164463	−	0.0284859i
$506$	−1.10607	−	1.91576i	−0.0491707	−	0.0851661i
$507$		0			0
$508$	1.68954	−	9.58186i	0.0749612	−	0.425126i
$509$	−0.699645	−	3.96788i	−0.0310112	−	0.175873i	0.965368	−	0.260891i	$-0.0840164\pi$
$509$	−0.699645	−	3.96788i	−0.0310112	−	0.175873i	−0.996379	+	0.0850178i	$0.972905\pi$
$510$		0			0
$511$	32.5449	+	27.3084i	1.43970	+	1.20805i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−8.02465			−0.353952
$515$	−13.1480	−	11.0324i	−0.579368	−	0.486148i
$516$		0			0
$517$	4.36184	+	24.7372i	0.191834	+	1.08794i
$518$	2.04458	−	11.5954i	0.0898336	−	0.509472i
$519$		0			0
$520$	5.75877	+	9.97448i	0.252539	+	0.437410i
$521$	2.49479	−	4.32110i	0.109299	−	0.189311i	−0.806188	−	0.591660i	$-0.798473\pi$
$521$	2.49479	−	4.32110i	0.109299	−	0.189311i	0.915486	+	0.402349i	$0.131806\pi$
$522$		0			0
$523$	−20.3405	+	17.0677i	−0.889427	+	0.746318i	−0.968095	−	0.250583i	$-0.919378\pi$
$523$	−20.3405	+	17.0677i	−0.889427	+	0.746318i	0.0786677	+	0.996901i	$0.474933\pi$
$524$	−3.23396	+	5.60138i	−0.141276	+	0.244697i
$525$		0			0
$526$	5.60132	+	2.03871i	0.244229	+	0.0888921i
$527$	2.77662	−	15.7470i	0.120951	−	0.685949i
$528$		0			0
$529$	21.1596	−	7.70145i	0.919981	−	0.334846i
$530$	−12.5817	−	10.5573i	−0.546515	−	0.458580i
$531$		0			0
$532$	11.5817	+	1.95437i	0.502131	+	0.0847326i
$533$	−2.00000			−0.0866296
$534$		0			0
$535$	21.5253	−	7.83456i	0.930619	−	0.338718i
$536$	0.860967	+	4.88279i	0.0371881	+	0.210904i
$537$		0			0
$538$	1.07873	+	0.392624i	0.0465072	+	0.0169272i
$539$	0.415345	+	0.719398i	0.0178902	+	0.0309867i
$540$		0			0
$541$	−9.17024	+	7.69475i	−0.394260	+	0.330823i	−0.818270	−	0.574834i	$-0.805067\pi$
$541$	−9.17024	+	7.69475i	−0.394260	+	0.330823i	0.424010	+	0.905657i	$0.360622\pi$
$542$	−15.3628	+	12.8909i	−0.659888	+	0.553712i
$543$		0			0
$544$	3.25877	+	5.64436i	0.139719	+	0.242000i
$545$	16.3405	+	5.94745i	0.699950	+	0.254761i
$546$		0			0
$547$	0.555093	+	3.14809i	0.0237341	+	0.134603i	0.994372	−	0.105941i	$-0.0337855\pi$
$547$	0.555093	+	3.14809i	0.0237341	+	0.134603i	−0.970638	+	0.240543i	$0.922674\pi$
$548$	−10.9572	+	3.98811i	−0.468070	+	0.170363i
$549$		0			0
$550$	−3.18479			−0.135800
$551$	12.1334	+	2.04746i	0.516901	+	0.0872249i
$552$		0			0
$553$	−18.7101	−	15.6996i	−0.795633	−	0.667616i
$554$	16.3131	−	5.93750i	0.693079	−	0.252260i
$555$		0			0
$556$	−1.43494	+	8.13798i	−0.0608552	+	0.345127i
$557$	−22.5303	−	8.20037i	−0.954641	−	0.347461i	−0.182710	−	0.983167i	$-0.558487\pi$
$557$	−22.5303	−	8.20037i	−0.954641	−	0.347461i	−0.771931	+	0.635706i	$0.780709\pi$
$558$		0			0
$559$	17.4611	−	30.2435i	0.738526	−	1.27916i
$560$	−4.12836	+	3.46410i	−0.174455	+	0.146385i
$561$		0			0
$562$	−1.46064	+	2.52990i	−0.0616133	+	0.106717i
$563$	−4.37851	−	7.58380i	−0.184532	−	0.319619i	0.758887	−	0.651223i	$-0.225744\pi$
$563$	−4.37851	−	7.58380i	−0.184532	−	0.319619i	−0.943419	+	0.331604i	$0.892410\pi$
$564$		0			0
$565$	0.993193	−	5.63268i	0.0417839	−	0.236968i
$566$	1.64631	+	9.33667i	0.0691994	+	0.392450i
$567$		0			0
$568$	−6.47565	−	5.43372i	−0.271712	−	0.227994i
$569$	36.4201			1.52681			0.763406	−	0.645919i	$-0.223526\pi$
$569$	36.4201			1.52681			0.763406	+	0.645919i	$0.223526\pi$
$570$		0			0
$571$	34.2131			1.43177			0.715886	−	0.698217i	$-0.246023\pi$
$571$	34.2131			1.43177			0.715886	+	0.698217i	$0.246023\pi$
$572$	14.0496	+	11.7890i	0.587445	+	0.492924i
$573$		0			0
$574$	−0.162504	−	0.921605i	−0.00678278	−	0.0384670i
$575$	−0.120615	+	0.684040i	−0.00502998	+	0.0285265i
$576$		0			0
$577$	−7.75490	−	13.4319i	−0.322841	−	0.559177i	0.658232	−	0.752815i	$-0.271304\pi$
$577$	−7.75490	−	13.4319i	−0.322841	−	0.559177i	−0.981073	+	0.193638i	$0.937971\pi$
$578$	12.7392	−	22.0649i	0.529880	−	0.917778i
$579$		0			0
$580$	−4.32501	+	3.62911i	−0.179586	+	0.150691i
$581$	11.4192	−	19.7787i	0.473749	−	0.820557i
$582$		0			0
$583$	−24.5767	−	8.94517i	−1.01786	−	0.370471i
$584$	−2.73783	+	15.5270i	−0.113292	+	0.642511i
$585$		0			0
$586$	25.6459	−	9.33434i	1.05942	−	0.385598i
$587$	8.87211	+	7.44459i	0.366191	+	0.307271i	0.807253	−	0.590206i	$-0.200953\pi$
$587$	8.87211	+	7.44459i	0.366191	+	0.307271i	−0.441061	+	0.897477i	$0.645398\pi$
$588$		0			0
$589$	3.58347	−	10.0757i	0.147654	−	0.415162i
$590$	−1.14796			−0.0472606
$591$		0			0
$592$	4.10607	−	1.49449i	0.168758	−	0.0614230i
$593$	8.05603	+	45.6880i	0.330821	+	1.87618i	0.465131	+	0.885242i	$0.346007\pi$
$593$	8.05603	+	45.6880i	0.330821	+	1.87618i	−0.134310	+	0.990939i	$0.542882\pi$
$594$		0			0
$595$	33.0060	+	12.0132i	1.35311	+	0.492493i
$596$	−8.22668	−	14.2490i	−0.336978	−	0.583663i
$597$		0			0
$598$	3.06418	−	2.57115i	0.125304	−	0.105142i
$599$	−19.6355	+	16.4761i	−0.802283	+	0.673196i	−0.948753	−	0.316019i	$-0.897654\pi$
$599$	−19.6355	+	16.4761i	−0.802283	+	0.673196i	0.146469	+	0.989215i	$0.453209\pi$
$600$		0			0
$601$	−3.99613	−	6.92150i	−0.163006	−	0.282334i	0.772940	−	0.634480i	$-0.218786\pi$
$601$	−3.99613	−	6.92150i	−0.163006	−	0.282334i	−0.935945	+	0.352146i	$0.885452\pi$
$602$	15.3550	+	5.58878i	0.625825	+	0.227782i
$603$		0			0
$604$	0.808400	+	4.58467i	0.0328933	+	0.186547i
$605$	−1.61081	+	0.586289i	−0.0654889	+	0.0238360i
$606$		0			0
$607$	−26.9905			−1.09551			−0.547755	−	0.836639i	$-0.684518\pi$
$607$	−26.9905			−1.09551			−0.547755	+	0.836639i	$0.684518\pi$
$608$	1.52094	+	4.08494i	0.0616824	+	0.165666i
$609$		0			0
$610$	4.49794	+	3.77422i	0.182116	+	0.152814i
$611$	−42.6810	+	15.5346i	−1.72669	+	0.628463i
$612$		0			0
$613$	−2.47472	+	14.0348i	−0.0999529	+	0.566861i	0.893164	+	0.449732i	$0.148480\pi$
$613$	−2.47472	+	14.0348i	−0.0999529	+	0.566861i	−0.993117	+	0.117130i	$0.962631\pi$
$614$	20.0424	+	7.29482i	0.808844	+	0.294395i
$615$		0			0
$616$	−4.29086	+	7.43199i	−0.172884	+	0.299443i
$617$	23.4106	−	19.6438i	0.942475	−	0.790831i	−0.0355392	−	0.999368i	$-0.511315\pi$
$617$	23.4106	−	19.6438i	0.942475	−	0.790831i	0.978014	+	0.208538i	$0.0668704\pi$
$618$		0			0
$619$	14.3375	−	24.8333i	0.576273	−	0.998133i	−0.419629	−	0.907695i	$-0.637840\pi$
$619$	14.3375	−	24.8333i	0.576273	−	0.998133i	0.995902	−	0.0904380i	$-0.0288267\pi$
$620$	2.45336	+	4.24935i	0.0985294	+	0.170658i
$621$		0			0
$622$	−5.08647	+	28.8468i	−0.203949	+	1.15665i
$623$	−3.62124	−	20.5371i	−0.145082	−	0.822801i
$624$		0			0
$625$	−14.5548	−	12.2130i	−0.582194	−	0.488519i
$626$	−5.56118			−0.222270
$627$		0			0
$628$	8.45336			0.337326
$629$	−21.8161	−	18.3059i	−0.869867	−	0.729905i
$630$		0			0
$631$	−0.781059	−	4.42961i	−0.0310935	−	0.176340i	0.965306	−	0.261121i	$-0.0840921\pi$
$631$	−0.781059	−	4.42961i	−0.0310935	−	0.176340i	−0.996400	+	0.0847809i	$0.972981\pi$
$632$	1.57398	−	8.92647i	0.0626095	−	0.355076i
$633$		0			0
$634$	−1.90167	−	3.29380i	−0.0755251	−	0.130813i
$635$	9.72967	−	16.8523i	0.386110	−	0.668763i
$636$		0			0
$637$	−1.15064	+	0.965505i	−0.0455902	+	0.0382547i
$638$	−4.49525	+	7.78601i	−0.177969	+	0.308251i
$639$		0			0
$640$	−1.87939	−	0.684040i	−0.0742892	−	0.0270391i
$641$	2.01573	−	11.4318i	0.0796165	−	0.451528i	−0.918772	−	0.394788i	$-0.870818\pi$
$641$	2.01573	−	11.4318i	0.0796165	−	0.451528i	0.998389	−	0.0567403i	$-0.0180707\pi$
$642$		0			0
$643$	−24.4748	+	8.90809i	−0.965191	+	0.351301i	−0.776066	−	0.630652i	$-0.782787\pi$
$643$	−24.4748	+	8.90809i	−0.965191	+	0.351301i	−0.189125	+	0.981953i	$0.560565\pi$
$644$	1.43376	+	1.20307i	0.0564982	+	0.0474076i
$645$		0			0
$646$	18.1004	−	21.8966i	0.712152	−	0.861511i
$647$	2.31490			0.0910082			0.0455041	−	0.998964i	$-0.485511\pi$
$647$	2.31490			0.0910082			0.0455041	+	0.998964i	$0.485511\pi$
$648$		0			0
$649$	−1.71776	+	0.625213i	−0.0674279	+	0.0245418i
$650$	−1.00000	−	5.67128i	−0.0392232	−	0.222446i
$651$		0			0
$652$	−16.0214	−	5.83132i	−0.627447	−	0.228372i
$653$	1.65270	+	2.86257i	0.0646753	+	0.112021i	0.896550	−	0.442943i	$-0.146066\pi$
$653$	1.65270	+	2.86257i	0.0646753	+	0.112021i	−0.831875	+	0.554964i	$0.812732\pi$
$654$		0			0
$655$	−9.90941	+	8.31499i	−0.387193	+	0.324893i
$656$	0.266044	−	0.223238i	0.0103873	−	0.00871597i
$657$		0			0
$658$	−10.6263	−	18.4053i	−0.414256	−	0.717513i
$659$	−12.9201	−	4.70253i	−0.503295	−	0.183185i	0.0778802	−	0.996963i	$-0.475185\pi$
$659$	−12.9201	−	4.70253i	−0.503295	−	0.183185i	−0.581176	+	0.813778i	$0.697407\pi$
$660$		0			0
$661$	−0.579030	−	3.28384i	−0.0225217	−	0.127727i	0.971474	−	0.237146i	$-0.0762120\pi$
$661$	−0.579030	−	3.28384i	−0.0225217	−	0.127727i	−0.993996	+	0.109419i	$0.965101\pi$
$662$	19.1903	−	6.98470i	0.745853	−	0.271468i
$663$		0			0
$664$	8.47565			0.328919
$665$	20.4296	+	11.5954i	0.792228	+	0.449649i
$666$		0			0
$667$	1.50206	+	1.26038i	0.0581600	+	0.0488020i
$668$	−3.00000	+	1.09191i	−0.116073	+	0.0422473i
$669$		0			0
$670$	−1.72193	+	9.76557i	−0.0665241	+	0.377277i
$671$	8.78611	+	3.19788i	0.339184	+	0.123453i
$672$		0			0
$673$	−19.4905	+	33.7585i	−0.751304	+	1.30130i	0.195887	+	0.980626i	$0.437241\pi$
$673$	−19.4905	+	33.7585i	−0.751304	+	1.30130i	−0.947191	+	0.320670i	$0.896092\pi$
$674$	−15.5587	+	13.0553i	−0.599299	+	0.502872i
$675$		0			0
$676$	−10.0817	+	17.4620i	−0.387758	+	0.671617i
$677$	−21.7939	−	37.7481i	−0.837606	−	1.45078i	−0.891891	−	0.452250i	$-0.850621\pi$
$677$	−21.7939	−	37.7481i	−0.837606	−	1.45078i	0.0542853	−	0.998525i	$-0.482712\pi$
$678$		0			0
$679$	−0.162504	+	0.921605i	−0.00623632	+	0.0353680i
$680$	2.26352	+	12.8370i	0.0868020	+	0.492278i
$681$		0			0
$682$	5.98545	+	5.02239i	0.229195	+	0.192317i
$683$	−32.9317			−1.26010			−0.630048	−	0.776556i	$-0.716965\pi$
$683$	−32.9317			−1.26010			−0.630048	+	0.776556i	$0.716965\pi$
$684$		0			0
$685$	−23.3209			−0.891045
$686$	13.9108	+	11.6726i	0.531119	+	0.445661i
$687$		0			0
$688$	1.05303	+	5.97205i	0.0401465	+	0.227682i
$689$	8.21213	−	46.5733i	0.312857	−	1.77430i
$690$		0			0
$691$	−17.1604	−	29.7228i	−0.652814	−	1.13071i	−0.982437	−	0.186594i	$-0.940255\pi$
$691$	−17.1604	−	29.7228i	−0.652814	−	1.13071i	0.329623	−	0.944113i	$-0.393078\pi$
$692$	4.81521	−	8.34018i	0.183047	−	0.317046i
$693$		0			0
$694$	3.99479	−	3.35202i	0.151640	−	0.127241i
$695$	−8.26352	+	14.3128i	−0.313453	+	0.542917i
$696$		0			0
$697$	−2.12701	−	0.774169i	−0.0805663	−	0.0293237i
$698$	−2.49020	+	14.1226i	−0.0942555	+	0.534549i
$699$		0			0
$700$	2.53209	−	0.921605i	0.0957040	−	0.0348334i
$701$	−4.94356	−	4.14814i	−0.186716	−	0.156673i	0.544638	−	0.838671i	$-0.316667\pi$
$701$	−4.94356	−	4.14814i	−0.186716	−	0.156673i	−0.731354	+	0.681998i	$0.761111\pi$
$702$		0			0
$703$	−12.3500	−	14.5000i	−0.465788	−	0.546878i
$704$	−3.18479			−0.120031
$705$		0			0
$706$	−24.6668	+	8.97800i	−0.928349	+	0.337891i
$707$	0.172933	+	0.980752i	0.00650381	+	0.0368850i
$708$		0			0
$709$	3.17530	+	1.15571i	0.119251	+	0.0434037i	0.400956	−	0.916097i	$-0.368678\pi$
$709$	3.17530	+	1.15571i	0.119251	+	0.0434037i	−0.281706	+	0.959501i	$0.590900\pi$
$710$	−8.45336	−	14.6417i	−0.317249	−	0.549492i
$711$		0			0
$712$	5.92855	−	4.97464i	0.222182	−	0.186433i
$713$	1.30541	−	1.09537i	0.0488879	−	0.0410218i
$714$		0			0
$715$	18.3405	+	31.7667i	0.685895	+	1.18801i
$716$	17.6814	+	6.43550i	0.660785	+	0.240506i
$717$		0			0
$718$	−5.85029	−	33.1786i	−0.218331	−	1.23822i
$719$	−29.3209	+	10.6719i	−1.09348	+	0.397996i	−0.824911	−	0.565263i	$-0.808775\pi$
$719$	−29.3209	+	10.6719i	−1.09348	+	0.397996i	−0.268574	+	0.963259i	$0.586552\pi$
$720$		0			0
$721$	23.1242			0.861192
$722$	14.3735	−	12.4259i	0.534925	−	0.462445i
$723$		0			0
$724$	2.12836	+	1.78590i	0.0790997	+	0.0663725i
$725$	2.65270	−	0.965505i	0.0985189	−	0.0358580i
$726$		0			0
$727$	−4.45605	+	25.2715i	−0.165266	+	0.937269i	0.783524	+	0.621361i	$0.213420\pi$
$727$	−4.45605	+	25.2715i	−0.165266	+	0.937269i	−0.948790	+	0.315908i	$0.897691\pi$
$728$	−14.5817	−	5.30731i	−0.540434	−	0.196702i
$729$		0			0
$730$	−15.7665	+	27.3084i	−0.583545	+	1.01073i
$731$	30.2768	−	25.4052i	1.11983	−	0.939647i
$732$		0			0
$733$	11.9368	−	20.6751i	0.440894	−	0.763651i	−0.556862	−	0.830605i	$-0.687995\pi$
$733$	11.9368	−	20.6751i	0.440894	−	0.763651i	0.997756	+	0.0669540i	$0.0213281\pi$
$734$	−5.23442	−	9.06629i	−0.193206	−	0.334643i
$735$		0			0
$736$	−0.120615	+	0.684040i	−0.00444592	+	0.0252141i
$737$	2.74200	+	15.5507i	0.101003	+	0.572816i
$738$		0			0
$739$	−35.1924	−	29.5299i	−1.29457	−	1.08628i	−0.991056	−	0.133449i	$-0.957395\pi$
$739$	−35.1924	−	29.5299i	−1.29457	−	1.08628i	−0.303517	−	0.952826i	$-0.598161\pi$
$740$	8.73917			0.321258
$741$		0			0
$742$	22.1284			0.812357
$743$	39.0770	+	32.7895i	1.43360	+	1.20293i	0.943549	+	0.331232i	$0.107464\pi$
$743$	39.0770	+	32.7895i	1.43360	+	1.20293i	0.490046	+	0.871697i	$0.336980\pi$
$744$		0			0
$745$	−5.71419	−	32.4068i	−0.209352	−	1.18729i
$746$	−4.15064	+	23.5395i	−0.151966	+	0.861841i
$747$		0			0
$748$	10.3785	+	17.9761i	0.379476	+	0.657271i
$749$	−15.4311	+	26.7274i	−0.563839	+	0.976598i
$750$		0			0
$751$	−27.8607	+	23.3779i	−1.01665	+	0.853072i	−0.989203	−	0.146551i	$-0.953183\pi$
$751$	−27.8607	+	23.3779i	−1.01665	+	0.853072i	−0.0274489	+	0.999623i	$0.508738\pi$
$752$	3.94356	−	6.83045i	0.143807	−	0.249081i
$753$		0			0
$754$	−15.2763	−	5.56012i	−0.556330	−	0.202488i
$755$	−1.61680	+	9.16933i	−0.0588414	+	0.333706i
$756$		0			0
$757$	5.45336	−	1.98486i	0.198206	−	0.0721410i	−0.241010	−	0.970523i	$-0.577479\pi$
$757$	5.45336	−	1.98486i	0.198206	−	0.0721410i	0.439216	+	0.898382i	$0.355256\pi$
$758$	−13.6459	−	11.4503i	−0.495641	−	0.415892i
$759$		0			0
$760$	0.0641778	+	8.71756i	0.00232797	+	0.316219i
$761$	−22.6355			−0.820535			−0.410268	−	0.911965i	$-0.634565\pi$
$761$	−22.6355			−0.820535			−0.410268	+	0.911965i	$0.634565\pi$
$762$		0			0
$763$	−22.0155	+	8.01298i	−0.797014	+	0.290089i
$764$	−1.66044	−	9.41685i	−0.0600728	−	0.340690i
$765$		0			0
$766$	−23.5672	−	8.57775i	−0.851516	−	0.309927i
$767$	−1.65270	−	2.86257i	−0.0596757	−	0.103361i
$768$		0			0
$769$	8.35188	−	7.00806i	0.301177	−	0.252717i	−0.479657	−	0.877456i	$-0.659239\pi$
$769$	8.35188	−	7.00806i	0.301177	−	0.252717i	0.780834	+	0.624739i	$0.214795\pi$
$770$	−13.1480	+	11.0324i	−0.473819	+	0.397582i
$771$		0			0
$772$	11.8405	+	20.5083i	0.426149	+	0.738111i
$773$	−4.93407	−	1.79585i	−0.177466	−	0.0645924i	0.251759	−	0.967790i	$-0.418991\pi$
$773$	−4.93407	−	1.79585i	−0.177466	−	0.0645924i	−0.429225	+	0.903198i	$0.641213\pi$
$774$		0			0
$775$	−0.426022	−	2.41609i	−0.0153032	−	0.0867886i
$776$	−0.326352	+	0.118782i	−0.0117153	+	0.00426404i
$777$		0			0
$778$	−9.41828			−0.337662
$779$	−1.31655	−	0.747243i	−0.0471704	−	0.0267728i
$780$		0			0
$781$	−20.6236	−	17.3053i	−0.737971	−	0.619231i
$782$	4.25402	−	1.54834i	0.152124	−	0.0553684i
$783$		0			0
$784$	0.0452926	−	0.256867i	0.00161759	−	0.00917383i
$785$	15.8871	+	5.78244i	0.567036	+	0.206384i
$786$		0			0
$787$	1.19372	−	2.06758i	0.0425514	−	0.0737011i	−0.843965	−	0.536398i	$-0.819785\pi$
$787$	1.19372	−	2.06758i	0.0425514	−	0.0737011i	0.886517	+	0.462697i	$0.153118\pi$
$788$	17.5594	−	14.7341i	0.625529	−	0.524881i
$789$		0			0
$790$	9.06418	−	15.6996i	0.322489	−	0.558567i
$791$	3.85298	+	6.67355i	0.136996	+	0.237284i
$792$		0			0
$793$	−2.93582	+	16.6499i	−0.104254	+	0.591254i
$794$	−1.18984	−	6.74795i	−0.0422260	−	0.239476i
$795$		0			0
$796$	7.72462	+	6.48173i	0.273792	+	0.229739i
$797$	−31.0951			−1.10145			−0.550723	−	0.834688i	$-0.685648\pi$
$797$	−31.0951			−1.10145			−0.550723	+	0.834688i	$0.685648\pi$
$798$		0			0
$799$	−51.4047			−1.81857
$800$	0.766044	+	0.642788i	0.0270838	+	0.0227260i
$801$		0			0
$802$	0.824292	+	4.67479i	0.0291068	+	0.165073i
$803$	−8.71941	+	49.4502i	−0.307701	+	1.74506i
$804$		0			0
$805$	1.87164	+	3.24178i	0.0659668	+	0.114258i
$806$	−7.06418	+	12.2355i	−0.248825	+	0.430978i
$807$		0			0
$808$	−0.283119	+	0.237565i	−0.00996008	+	0.00835750i
$809$	11.1518	−	19.3155i	0.392077	−	0.679098i	−0.600646	−	0.799515i	$-0.705090\pi$
$809$	11.1518	−	19.3155i	0.392077	−	0.679098i	0.992723	+	0.120417i	$0.0384232\pi$
$810$		0			0
$811$	−3.11886	−	1.13517i	−0.109518	−	0.0398613i	0.286680	−	0.958026i	$-0.407448\pi$
$811$	−3.11886	−	1.13517i	−0.109518	−	0.0398613i	−0.396198	+	0.918165i	$0.629671\pi$
$812$	1.32089	−	7.49113i	0.0463541	−	0.262887i
$813$		0			0
$814$	13.0770	−	4.75963i	0.458348	−	0.166825i
$815$	−26.1215	−	21.9186i	−0.914998	−	0.767774i
$816$		0			0
$817$	22.7939	−	13.3847i	0.797456	−	0.468273i
$818$	−31.6928			−1.10811
$819$		0			0
$820$	0.652704	−	0.237565i	0.0227934	−	0.00829612i
$821$	0.318201	+	1.80460i	0.0111053	+	0.0629811i	0.989857	−	0.142069i	$-0.0453754\pi$
$821$	0.318201	+	1.80460i	0.0111053	+	0.0629811i	−0.978752	+	0.205050i	$0.934264\pi$
$822$		0			0
$823$	32.1729	+	11.7100i	1.12148	+	0.408185i	0.835191	−	0.549959i	$-0.185357\pi$
$823$	32.1729	+	11.7100i	1.12148	+	0.408185i	0.286287	+	0.958144i	$0.407579\pi$
$824$	4.29086	+	7.43199i	0.149479	+	0.258906i
$825$		0			0
$826$	1.18479	−	0.994159i	0.0412242	−	0.0345912i
$827$	15.2181	−	12.7695i	0.529184	−	0.444038i	−0.338636	−	0.940918i	$-0.609965\pi$
$827$	15.2181	−	12.7695i	0.529184	−	0.444038i	0.867820	+	0.496880i	$0.165521\pi$
$828$		0			0
$829$	17.8675	+	30.9475i	0.620565	+	1.07485i	0.989381	+	0.145347i	$0.0464300\pi$
$829$	17.8675	+	30.9475i	0.620565	+	1.07485i	−0.368816	+	0.929502i	$0.620237\pi$
$830$	15.9290	+	5.79769i	0.552904	+	0.201241i
$831$		0			0
$832$	−1.00000	−	5.67128i	−0.0346688	−	0.196616i
$833$	−1.59745	+	0.581424i	−0.0553483	+	0.0201451i
$834$		0			0
$835$	−6.38507			−0.220964
$836$	4.84389	+	13.0097i	0.167530	+	0.449949i
$837$		0			0
$838$	−8.43423	−	7.07716i	−0.291356	−	0.244476i
$839$	−51.1147	+	18.6042i	−1.76468	+	0.642290i	−0.999998	−	0.00212143i	$-0.999325\pi$
$839$	−51.1147	+	18.6042i	−1.76468	+	0.642290i	−0.764679	+	0.644411i	$0.777103\pi$
$840$		0			0
$841$	−3.65199	+	20.7115i	−0.125931	+	0.714188i
$842$	−8.14290	−	2.96377i	−0.280623	−	0.102138i
$843$		0			0
$844$	11.1800	−	19.3644i	0.384833	−	0.666550i
$845$	−30.8922	+	25.9216i	−1.06272	+	0.891731i
$846$		0			0
$847$	1.15476	−	2.00011i	0.0396781	−	0.0687245i
$848$	4.10607	+	7.11192i	0.141003	+	0.244224i
$849$		0			0
$850$	1.13176	−	6.41852i	0.0388190	−	0.220154i
$851$	−0.527036	−	2.98897i	−0.0180666	−	0.102461i
$852$		0			0
$853$	12.2385	+	10.2694i	0.419040	+	0.351616i	0.827798	−	0.561027i	$-0.189594\pi$
$853$	12.2385	+	10.2694i	0.419040	+	0.351616i	−0.408758	+	0.912643i	$0.634038\pi$
$854$	−7.91085			−0.270704
$855$		0			0
$856$	−11.4534			−0.391468
$857$	19.9283	+	16.7218i	0.680738	+	0.571207i	0.916222	−	0.400671i	$-0.131223\pi$
$857$	19.9283	+	16.7218i	0.680738	+	0.571207i	−0.235484	+	0.971878i	$0.575668\pi$
$858$		0			0
$859$	9.25031	+	52.4611i	0.315617	+	1.78995i	0.568740	+	0.822517i	$0.307431\pi$
$859$	9.25031	+	52.4611i	0.315617	+	1.78995i	−0.253124	+	0.967434i	$0.581458\pi$
$860$	−2.10607	+	11.9441i	−0.0718163	+	0.407290i
$861$		0			0
$862$	14.9436	+	25.8830i	0.508980	+	0.881579i
$863$	1.61587	−	2.79876i	0.0550048	−	0.0952710i	−0.837212	−	0.546879i	$-0.815816\pi$
$863$	1.61587	−	2.79876i	0.0550048	−	0.0952710i	0.892217	+	0.451608i	$0.149149\pi$
$864$		0			0
$865$	14.7547	−	12.3806i	0.501673	−	0.420954i
$866$	4.63041	−	8.02011i	0.157348	−	0.272535i
$867$		0			0
$868$	−6.21213	−	2.26103i	−0.210854	−	0.0767444i
$869$	5.01279	−	28.4290i	0.170047	−	0.964387i
$870$		0			0
$871$	−26.8307	+	9.76557i	−0.909123	+	0.330894i
$872$	−6.66044	−	5.58878i	−0.225551	−	0.189260i
$873$		0			0
$874$	2.97771	−	0.547683i	0.100723	−	0.0185257i
$875$	32.3351			1.09313
$876$		0			0
$877$	−11.0172	+	4.00995i	−0.372026	+	0.135406i	−0.521265	−	0.853395i	$-0.674540\pi$
$877$	−11.0172	+	4.00995i	−0.372026	+	0.135406i	0.149239	+	0.988801i	$0.452317\pi$
$878$	−3.62267	−	20.5452i	−0.122259	−	0.693367i
$879$		0			0
$880$	−5.98545	−	2.17853i	−0.201770	−	0.0734381i
$881$	13.5236	+	23.4236i	0.455623	+	0.789162i	0.998724	−	0.0505056i	$-0.0160833\pi$
$881$	13.5236	+	23.4236i	0.455623	+	0.789162i	−0.543101	+	0.839667i	$0.682750\pi$
$882$		0			0
$883$	11.0931	−	9.30823i	0.373313	−	0.313247i	−0.436758	−	0.899579i	$-0.643873\pi$
$883$	11.0931	−	9.30823i	0.373313	−	0.313247i	0.810070	+	0.586333i	$0.199429\pi$
$884$	−28.7520	+	24.1258i	−0.967033	+	0.811437i
$885$		0			0
$886$	−11.9140	−	20.6357i	−0.400259	−	0.693268i
$887$	−10.8922	−	3.96443i	−0.365724	−	0.133112i	0.152620	−	0.988285i	$-0.451229\pi$
$887$	−10.8922	−	3.96443i	−0.365724	−	0.133112i	−0.518344	+	0.855172i	$0.673451\pi$
$888$		0			0
$889$	4.55262	+	25.8192i	0.152690	+	0.865948i
$890$	14.5449	−	5.29390i	0.487546	−	0.177452i
$891$		0			0
$892$	−9.27631			−0.310594
$893$	−33.8999	−	5.72048i	−1.13442	−	0.191428i
$894$		0			0
$895$	28.8280	+	24.1896i	0.963614	+	0.808568i
$896$	2.53209	−	0.921605i	0.0845912	−	0.0307887i
$897$		0			0
$898$	−0.378918	+	2.14895i	−0.0126447	+	0.0717115i
$899$	−6.50805	−	2.36873i	−0.217055	−	0.0790017i
$900$		0			0
$901$	26.7615	−	46.3522i	0.891553	−	1.54422i
$902$	0.847296	−	0.710966i	0.0282119	−	0.0236726i
$903$		0			0
$904$	−1.42989	+	2.47665i	−0.0475575	+	0.0823720i
$905$	2.77837	+	4.81228i	0.0923562	+	0.159966i
$906$		0			0
$907$	7.28952	−	41.3409i	0.242044	−	1.37270i	−0.585213	−	0.810879i	$-0.698989\pi$
$907$	7.28952	−	41.3409i	0.242044	−	1.37270i	0.827258	−	0.561823i	$-0.189900\pi$
$908$	−1.34343	−	7.61895i	−0.0445832	−	0.252844i
$909$		0			0
$910$	−23.7743	−	19.9490i	−0.788109	−	0.661302i
$911$	44.8675			1.48653			0.743264	−	0.668999i	$-0.233277\pi$
$911$	44.8675			1.48653			0.743264	+	0.668999i	$0.233277\pi$
$912$		0			0
$913$	26.9932			0.893344
$914$	−1.36437	−	1.14484i	−0.0451294	−	0.0378680i
$915$		0			0
$916$	−4.00000	−	22.6851i	−0.132164	−	0.749538i
$917$	3.02641	−	17.1636i	0.0999408	−	0.566792i
$918$		0			0
$919$	16.2635	+	28.1692i	0.536484	+	0.929217i	0.999090	+	0.0426535i	$0.0135811\pi$
$919$	16.2635	+	28.1692i	0.536484	+	0.929217i	−0.462606	+	0.886564i	$0.653086\pi$
$920$	−0.694593	+	1.20307i	−0.0229000	+	0.0396640i
$921$		0			0
$922$	−11.8648	+	9.95578i	−0.390748	+	0.327876i
$923$	24.3405	−	42.1590i	0.801177	−	1.38768i
$924$		0			0
$925$	−4.10607	−	1.49449i	−0.135007	−	0.0491384i
$926$	0.470599	−	2.66890i	0.0154649	−	0.0877056i
$927$		0			0
$928$	2.65270	−	0.965505i	0.0870793	−	0.0316943i
$929$	−9.07011	−	7.61072i	−0.297581	−	0.249700i	0.481756	−	0.876305i	$-0.339999\pi$
$929$	−9.07011	−	7.61072i	−0.297581	−	0.249700i	−0.779336	+	0.626606i	$0.784444\pi$
$930$		0			0
$931$	−1.11817	+	0.205663i	−0.0366467	+	0.00674034i
$932$	−8.39961			−0.275139
$933$		0			0
$934$	−12.1348	+	4.41669i	−0.397061	+	0.144518i
$935$	7.20884	+	40.8833i	0.235754	+	1.33703i
$936$		0			0
$937$	0.717759	+	0.261243i	0.0234482	+	0.00853443i	0.353718	−	0.935352i	$-0.384917\pi$
$937$	0.717759	+	0.261243i	0.0234482	+	0.00853443i	−0.330269	+	0.943887i	$0.607140\pi$
$938$	−6.68004	−	11.5702i	−0.218111	−	0.377780i
$939$		0			0
$940$	12.0838	−	10.1395i	0.394129	−	0.330714i
$941$	16.4652	−	13.8160i	0.536751	−	0.450388i	−0.333674	−	0.942688i	$-0.608289\pi$
$941$	16.4652	−	13.8160i	0.536751	−	0.450388i	0.870425	+	0.492301i	$0.163844\pi$
$942$		0			0
$943$	−0.120615	−	0.208911i	−0.00392776	−	0.00680307i
$944$	0.539363	+	0.196312i	0.0175548	+	0.00638941i
$945$		0			0
$946$	3.35369	+	19.0197i	0.109038	+	0.618385i
$947$	29.7743	−	10.8369i	0.967533	−	0.352153i	0.190552	−	0.981677i	$-0.438972\pi$
$947$	29.7743	−	10.8369i	0.967533	−	0.352153i	0.776981	+	0.629524i	$0.216750\pi$
$948$		0			0
$949$	−90.7957			−2.94735
$950$	1.46064	−	4.10689i	0.0473893	−	0.133245i
$951$		0			0
$952$	−13.4534	−	11.2887i	−0.436026	−	0.365869i
$953$	52.5017	−	19.1091i	1.70070	−	0.619003i	0.704792	−	0.709414i	$-0.251040\pi$
$953$	52.5017	−	19.1091i	1.70070	−	0.619003i	0.995905	+	0.0904104i	$0.0288179\pi$
$954$		0			0
$955$	3.32089	−	18.8337i	0.107461	−	0.609444i
$956$	−14.7811	−	5.37987i	−0.478054	−	0.173997i
$957$		0			0
$958$	9.27631	−	16.0670i	0.299704	−	0.519103i
$959$	24.0692	−	20.1965i	0.777236	−	0.652178i
$960$		0			0
$961$	12.4905	−	21.6342i	0.402920	−	0.697877i
$962$	12.5817	+	21.7922i	0.405651	+	0.702608i
$963$		0			0
$964$	3.03936	−	17.2371i	0.0978913	−	0.555169i
$965$	8.22432	+	46.6424i	0.264750	+	1.50147i
$966$		0			0
$967$	16.5134	+	13.8564i	0.531036	+	0.445592i	0.868459	−	0.495761i	$-0.165111\pi$
$967$	16.5134	+	13.8564i	0.531036	+	0.445592i	−0.337423	+	0.941353i	$0.609555\pi$
$968$	0.857097			0.0275481
$969$		0			0
$970$	−0.694593			−0.0223020
$971$	−37.2729	−	31.2757i	−1.19614	−	1.00368i	−0.999732	−	0.0231632i	$-0.992626\pi$
$971$	−37.2729	−	31.2757i	−1.19614	−	1.00368i	−0.196413	−	0.980521i	$-0.562929\pi$
$972$		0			0
$973$	−3.86659	−	21.9285i	−0.123957	−	0.702996i
$974$	−7.14971	+	40.5480i	−0.229092	+	1.29924i
$975$		0			0
$976$	−1.46791	−	2.54250i	−0.0469867	−	0.0813833i
$977$	−25.2741	+	43.7760i	−0.808590	+	1.40052i	0.105251	+	0.994446i	$0.466435\pi$
$977$	−25.2741	+	43.7760i	−0.808590	+	1.40052i	−0.913841	+	0.406073i	$0.866898\pi$
$978$		0			0
$979$	18.8812	−	15.8432i	0.603446	−	0.506351i
$980$	0.260830	−	0.451771i	0.00833190	−	0.0144313i
$981$		0			0
$982$	21.2160	+	7.72199i	0.677030	+	0.246419i
$983$	5.21987	−	29.6034i	0.166488	−	0.944201i	−0.781029	−	0.624495i	$-0.785305\pi$
$983$	5.21987	−	29.6034i	0.166488	−	0.944201i	0.947517	−	0.319706i	$-0.103584\pi$
$984$		0			0
$985$	43.0797	−	15.6797i	1.37263	−	0.499597i
$986$	−14.0942	−	11.8264i	−0.448851	−	0.376631i
$987$		0			0
$988$	−21.6459	+	12.7106i	−0.688648	+	0.404379i
$989$	4.21213			0.133938
$990$		0			0
$991$	−2.58677	+	0.941508i	−0.0821715	+	0.0299080i	−0.382779	−	0.923840i	$-0.625033\pi$
$991$	−2.58677	+	0.941508i	−0.0821715	+	0.0299080i	0.300607	+	0.953748i	$0.402811\pi$
$992$	−0.426022	−	2.41609i	−0.0135262	−	0.0767110i
$993$		0			0
$994$	21.4047	+	7.79066i	0.678915	+	0.247105i
$995$	10.0838	+	17.4656i	0.319677	+	0.553697i
$996$		0			0
$997$	6.66819	−	5.59527i	0.211184	−	0.177204i	−0.531060	−	0.847334i	$-0.678206\pi$
$997$	6.66819	−	5.59527i	0.211184	−	0.177204i	0.742244	+	0.670130i	$0.233762\pi$
$998$	22.4670	−	18.8521i	0.711182	−	0.596752i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.u.c.73.1		6
3.2	odd	2		38.2.e.a.35.1	yes	6
12.11	even	2		304.2.u.c.225.1		6
15.2	even	4		950.2.u.b.149.1		12
15.8	even	4		950.2.u.b.149.2		12
15.14	odd	2		950.2.l.d.301.1		6
19.5	even	9		6498.2.a.bl.1.2		3
19.6	even	9	inner	342.2.u.c.253.1		6
19.14	odd	18		6498.2.a.bq.1.2		3
57.2	even	18		722.2.c.l.653.3		6
57.5	odd	18		722.2.a.l.1.3		3
57.8	even	6		722.2.e.a.245.1		6
57.11	odd	6		722.2.e.m.245.1		6
57.14	even	18		722.2.a.k.1.1		3
57.17	odd	18		722.2.c.k.653.1		6
57.23	odd	18		722.2.e.m.389.1		6
57.26	odd	6		722.2.e.b.423.1		6
57.29	even	18		722.2.e.l.99.1		6
57.32	even	18		722.2.e.k.595.1		6
57.35	odd	18		722.2.c.k.429.1		6
57.41	even	18		722.2.c.l.429.3		6
57.44	odd	18		38.2.e.a.25.1	✓	6
57.47	odd	18		722.2.e.b.99.1		6
57.50	even	6		722.2.e.l.423.1		6
57.53	even	18		722.2.e.a.389.1		6
57.56	even	2		722.2.e.k.415.1		6
228.71	odd	18		5776.2.a.bo.1.3		3
228.119	even	18		5776.2.a.bn.1.1		3
228.215	even	18		304.2.u.c.177.1		6
285.44	odd	18		950.2.l.d.101.1		6
285.158	even	36		950.2.u.b.899.1		12
285.272	even	36		950.2.u.b.899.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.25.1	✓	6	57.44	odd	18
38.2.e.a.35.1	yes	6	3.2	odd	2
304.2.u.c.177.1		6	228.215	even	18
304.2.u.c.225.1		6	12.11	even	2
342.2.u.c.73.1		6	1.1	even	1	trivial
342.2.u.c.253.1		6	19.6	even	9	inner
722.2.a.k.1.1		3	57.14	even	18
722.2.a.l.1.3		3	57.5	odd	18
722.2.c.k.429.1		6	57.35	odd	18
722.2.c.k.653.1		6	57.17	odd	18
722.2.c.l.429.3		6	57.41	even	18
722.2.c.l.653.3		6	57.2	even	18
722.2.e.a.245.1		6	57.8	even	6
722.2.e.a.389.1		6	57.53	even	18
722.2.e.b.99.1		6	57.47	odd	18
722.2.e.b.423.1		6	57.26	odd	6
722.2.e.k.415.1		6	57.56	even	2
722.2.e.k.595.1		6	57.32	even	18
722.2.e.l.99.1		6	57.29	even	18
722.2.e.l.423.1		6	57.50	even	6
722.2.e.m.245.1		6	57.11	odd	6
722.2.e.m.389.1		6	57.23	odd	18
950.2.l.d.101.1		6	285.44	odd	18
950.2.l.d.301.1		6	15.14	odd	2
950.2.u.b.149.1		12	15.2	even	4
950.2.u.b.149.2		12	15.8	even	4
950.2.u.b.899.1		12	285.158	even	36
950.2.u.b.899.2		12	285.272	even	36
5776.2.a.bn.1.1		3	228.119	even	18
5776.2.a.bo.1.3		3	228.71	odd	18
6498.2.a.bl.1.2		3	19.5	even	9
6498.2.a.bq.1.2		3	19.14	odd	18

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.347296 + 1.96962i) q^{5} +(-1.34730 - 2.33359i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.347296 + 1.96962i) q^{5} +(-1.34730 - 2.33359i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.53209 - 1.28558i) q^{10} +(1.59240 - 2.75811i) q^{11} +(5.41147 + 1.96962i) q^{13} +(-0.467911 + 2.65366i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(4.99273 + 4.18939i) q^{17} +(2.82635 + 3.31839i) q^{19} -2.00000 q^{20} +(-2.99273 + 1.08926i) q^{22} +(0.120615 + 0.684040i) q^{23} +(0.939693 + 0.342020i) q^{25} +(-2.87939 - 4.98724i) q^{26} +(2.06418 - 1.73205i) q^{28} +(2.16250 - 1.81456i) q^{29} +(-1.22668 - 2.12467i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-1.13176 - 6.41852i) q^{34} +(5.06418 - 1.84321i) q^{35} -4.36959 q^{37} +(-0.0320889 - 4.35878i) q^{38} +(1.53209 + 1.28558i) q^{40} +(-0.326352 + 0.118782i) q^{41} +(1.05303 - 5.97205i) q^{43} +(2.99273 + 1.08926i) q^{44} +(0.347296 - 0.601535i) q^{46} +(-6.04189 + 5.06975i) q^{47} +(-0.130415 + 0.225885i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-1.00000 + 5.67128i) q^{52} +(-1.42602 - 8.08737i) q^{53} +(4.87939 + 4.09429i) q^{55} -2.69459 q^{56} -2.82295 q^{58} +(-0.439693 - 0.368946i) q^{59} +(0.509800 + 2.89122i) q^{61} +(-0.426022 + 2.41609i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-5.75877 + 9.97448i) q^{65} +(-3.79813 + 3.18701i) q^{67} +(-3.25877 + 5.64436i) q^{68} +(-5.06418 - 1.84321i) q^{70} +(1.46791 - 8.32494i) q^{71} +(-14.8157 + 5.39246i) q^{73} +(3.34730 + 2.80872i) q^{74} +(-2.77719 + 3.35965i) q^{76} -8.58172 q^{77} +(8.51754 - 3.10013i) q^{79} +(-0.347296 - 1.96962i) q^{80} +(0.326352 + 0.118782i) q^{82} +(4.23783 + 7.34013i) q^{83} +(-9.98545 + 8.37879i) q^{85} +(-4.64543 + 3.89798i) q^{86} +(-1.59240 - 2.75811i) q^{88} +(7.27244 + 2.64695i) q^{89} +(-2.69459 - 15.2818i) q^{91} +(-0.652704 + 0.237565i) q^{92} +7.88713 q^{94} +(-7.51754 + 4.41436i) q^{95} +(-0.266044 - 0.223238i) q^{97} +(0.245100 - 0.0892091i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 6 * q^7 + 3 * q^8	\( 6 q - 6 q^{7} + 3 q^{8} + 6 q^{11} + 12 q^{13} - 12 q^{14} + 12 q^{17} + 18 q^{19} - 12 q^{20} + 12 q^{23} - 6 q^{26} - 6 q^{28} + 18 q^{29} + 6 q^{31} - 12 q^{34} + 12 q^{35} - 12 q^{37} + 9 q^{38} - 3 q^{41} - 6 q^{43} - 30 q^{47} - 15 q^{49} - 3 q^{50} - 6 q^{52} - 24 q^{53} + 18 q^{55} - 12 q^{56} + 24 q^{58} + 3 q^{59} + 6 q^{61} - 18 q^{62} - 3 q^{64} - 12 q^{65} - 9 q^{67} + 3 q^{68} - 12 q^{70} + 18 q^{71} - 30 q^{73} + 18 q^{74} - 6 q^{76} + 12 q^{77} + 6 q^{79} + 3 q^{82} + 6 q^{83} - 24 q^{85} - 12 q^{86} - 6 q^{88} - 12 q^{91} - 6 q^{92} - 12 q^{94} + 3 q^{97}+O(q^{100}) \) 6 * q - 6 * q^7 + 3 * q^8 + 6 * q^11 + 12 * q^13 - 12 * q^14 + 12 * q^17 + 18 * q^19 - 12 * q^20 + 12 * q^23 - 6 * q^26 - 6 * q^28 + 18 * q^29 + 6 * q^31 - 12 * q^34 + 12 * q^35 - 12 * q^37 + 9 * q^38 - 3 * q^41 - 6 * q^43 - 30 * q^47 - 15 * q^49 - 3 * q^50 - 6 * q^52 - 24 * q^53 + 18 * q^55 - 12 * q^56 + 24 * q^58 + 3 * q^59 + 6 * q^61 - 18 * q^62 - 3 * q^64 - 12 * q^65 - 9 * q^67 + 3 * q^68 - 12 * q^70 + 18 * q^71 - 30 * q^73 + 18 * q^74 - 6 * q^76 + 12 * q^77 + 6 * q^79 + 3 * q^82 + 6 * q^83 - 24 * q^85 - 12 * q^86 - 6 * q^88 - 12 * q^91 - 6 * q^92 - 12 * q^94 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more