LMFDB - Embedded newform 770.2.bv.a.157.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			157.7
Character	$\chi$	$=$	770.157
Dual form			770.2.bv.a.103.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.358368 - 0.933580i) q^{2} +(-0.907018 - 1.39668i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(1.00738 + 1.99629i) q^{5} +(-0.978872 + 1.34730i) q^{6} +(2.13291 + 1.56547i) q^{7} +(0.891007 + 0.453990i) q^{8} +(0.0921626 - 0.207001i) q^{9} +O(q^{10})$	\(q+(-0.358368 - 0.933580i) q^{2} +(-0.907018 - 1.39668i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(1.00738 + 1.99629i) q^{5} +(-0.978872 + 1.34730i) q^{6} +(2.13291 + 1.56547i) q^{7} +(0.891007 + 0.453990i) q^{8} +(0.0921626 - 0.207001i) q^{9} +(1.50269 - 1.65588i) q^{10} +(-3.26107 + 0.604526i) q^{11} +(1.60861 + 0.431026i) q^{12} +(-2.67775 - 0.424114i) q^{13} +(0.697128 - 2.55226i) q^{14} +(1.87448 - 3.21766i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-2.59774 + 6.76735i) q^{17} +(-0.226280 - 0.0118588i) q^{18} +(-3.60549 + 4.00431i) q^{19} +(-2.08441 - 0.809467i) q^{20} +(0.251886 - 4.39891i) q^{21} +(1.73303 + 2.82782i) q^{22} +(0.670055 + 0.179541i) q^{23} +(-0.174077 - 1.65623i) q^{24} +(-2.97038 + 4.02205i) q^{25} +(0.563676 + 2.65189i) q^{26} +(-5.30726 + 0.840588i) q^{27} +(-2.63256 + 0.263822i) q^{28} +(4.04700 + 1.31495i) q^{29} +(-3.67570 - 0.596872i) q^{30} +(-4.35187 + 0.457400i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(3.80218 + 4.00637i) q^{33} +7.24882 q^{34} +(-0.976495 + 5.83493i) q^{35} +(0.0700203 + 0.215500i) q^{36} +(-5.55132 - 3.60507i) q^{37} +(5.03043 + 1.93100i) q^{38} +(1.83642 + 4.12466i) q^{39} +(-0.00871699 + 2.23605i) q^{40} +(6.92798 - 2.25104i) q^{41} +(-4.19701 + 1.34127i) q^{42} +(-5.74428 + 5.74428i) q^{43} +(2.01894 - 2.63133i) q^{44} +(0.506076 - 0.0245444i) q^{45} +(-0.0725106 - 0.689892i) q^{46} +(-0.266774 - 5.09035i) q^{47} +(-1.48384 + 0.756056i) q^{48} +(2.09859 + 6.67802i) q^{49} +(4.81939 + 1.33171i) q^{50} +(11.8081 - 2.50988i) q^{51} +(2.27375 - 1.47659i) q^{52} +(1.11175 + 0.900278i) q^{53} +(2.68671 + 4.65352i) q^{54} +(-4.49194 - 5.90106i) q^{55} +(1.18973 + 2.36317i) q^{56} +(8.86300 + 1.40376i) q^{57} +(-0.222703 - 4.24944i) q^{58} +(0.117426 + 0.130415i) q^{59} +(0.760026 + 3.64546i) q^{60} +(12.0193 + 1.26328i) q^{61} +(1.98659 + 3.89890i) q^{62} +(0.520628 - 0.297235i) q^{63} +(0.587785 + 0.809017i) q^{64} +(-1.85086 - 5.77282i) q^{65} +(2.37769 - 4.98539i) q^{66} +(2.98794 - 0.800616i) q^{67} +(-2.59774 - 6.76735i) q^{68} +(-0.356990 - 1.09870i) q^{69} +(5.79732 - 1.17942i) q^{70} +(6.84431 + 4.97268i) q^{71} +(0.176094 - 0.142598i) q^{72} +(-0.808400 + 15.4252i) q^{73} +(-1.37621 + 6.47454i) q^{74} +(8.31172 + 0.500609i) q^{75} -5.38832i q^{76} +(-7.90192 - 3.81571i) q^{77} +(3.19259 - 3.19259i) q^{78} +(3.52302 - 7.91282i) q^{79} +(2.09066 - 0.793191i) q^{80} +(5.53296 + 6.14498i) q^{81} +(-4.58429 - 5.66113i) q^{82} +(-2.65409 - 16.7573i) q^{83} +(2.75626 + 3.43757i) q^{84} +(-16.1265 + 1.63143i) q^{85} +(7.42132 + 3.30418i) q^{86} +(-1.83413 - 6.84507i) q^{87} +(-3.18008 - 0.941856i) q^{88} +(0.366866 + 0.635431i) q^{89} +(-0.204276 - 0.463667i) q^{90} +(-5.04746 - 5.09654i) q^{91} +(-0.618084 + 0.314930i) q^{92} +(4.58606 + 5.66332i) q^{93} +(-4.65665 + 2.07328i) q^{94} +(-11.6259 - 3.16377i) q^{95} +(1.23760 + 1.11434i) q^{96} +(-2.14514 + 13.5439i) q^{97} +(5.48240 - 4.35239i) q^{98} +(-0.175411 + 0.730757i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.358368	−	0.933580i	−0.253404	−	0.660141i
$2$	−0.358368	−	0.933580i	−0.253404	−	0.660141i
$3$	−0.907018	−	1.39668i	−0.523667	−	0.806376i	0.473563	−	0.880760i	$-0.342968\pi$
$3$	−0.907018	−	1.39668i	−0.523667	−	0.806376i	−0.997230	+	0.0743837i	$0.976301\pi$
$4$	−0.743145	+	0.669131i	−0.371572	+	0.334565i
$5$	1.00738	+	1.99629i	0.450514	+	0.892770i
$5$	1.00738	+	1.99629i	0.450514	+	0.892770i
$6$	−0.978872	+	1.34730i	−0.399623	+	0.550033i
$7$	2.13291	+	1.56547i	0.806164	+	0.591693i
$7$	2.13291	+	1.56547i	0.806164	+	0.591693i
$8$	0.891007	+	0.453990i	0.315018	+	0.160510i
$9$	0.0921626	−	0.207001i	0.0307209	−	0.0690002i
$10$	1.50269	−	1.65588i	0.475192	−	0.523634i
$11$	−3.26107	+	0.604526i	−0.983248	+	0.182271i
$11$	−3.26107	+	0.604526i	−0.983248	+	0.182271i
$12$	1.60861	+	0.431026i	0.464366	+	0.124426i
$13$	−2.67775	−	0.424114i	−0.742675	−	0.117628i	−0.226380	−	0.974039i	$-0.572689\pi$
$13$	−2.67775	−	0.424114i	−0.742675	−	0.117628i	−0.516295	+	0.856411i	$0.672689\pi$
$14$	0.697128	−	2.55226i	0.186315	−	0.682119i
$15$	1.87448	−	3.21766i	0.483989	−	0.830797i
$16$	0.104528	−	0.994522i	0.0261321	−	0.248630i
$17$	−2.59774	+	6.76735i	−0.630046	+	1.64132i	0.130046	+	0.991508i	$0.458488\pi$
$17$	−2.59774	+	6.76735i	−0.630046	+	1.64132i	−0.760091	+	0.649817i	$0.774846\pi$
$18$	−0.226280	−	0.0118588i	−0.0533347	−	0.00279515i
$19$	−3.60549	+	4.00431i	−0.827157	+	0.918651i	−0.997774	−	0.0666868i	$-0.978757\pi$
$19$	−3.60549	+	4.00431i	−0.827157	+	0.918651i	0.170617	+	0.985337i	$0.445424\pi$
$20$	−2.08441	−	0.809467i	−0.466088	−	0.181002i
$21$	0.251886	−	4.39891i	0.0549659	−	0.959921i
$22$	1.73303	+	2.82782i	0.369484	+	0.602894i
$23$	0.670055	+	0.179541i	0.139716	+	0.0374368i	0.327999	−	0.944678i	$-0.393626\pi$
$23$	0.670055	+	0.179541i	0.139716	+	0.0374368i	−0.188283	+	0.982115i	$0.560292\pi$
$24$	−0.174077	−	1.65623i	−0.0355333	−	0.338077i
$25$	−2.97038	+	4.02205i	−0.594075	+	0.804410i
$26$	0.563676	+	2.65189i	0.110546	+	0.520078i
$27$	−5.30726	+	0.840588i	−1.02138	+	0.161771i
$28$	−2.63256	+	0.263822i	−0.497508	+	0.0498576i
$29$	4.04700	+	1.31495i	0.751509	+	0.244180i	0.659630	−	0.751590i	$-0.270713\pi$
$29$	4.04700	+	1.31495i	0.751509	+	0.244180i	0.0918786	+	0.995770i	$0.470713\pi$
$30$	−3.67570	−	0.596872i	−0.671088	−	0.108973i
$31$	−4.35187	+	0.457400i	−0.781618	+	0.0821514i	−0.486929	−	0.873442i	$-0.661883\pi$
$31$	−4.35187	+	0.457400i	−0.781618	+	0.0821514i	−0.294689	+	0.955593i	$0.595216\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	3.80218	+	4.00637i	0.661874	+	0.697419i
$34$	7.24882			1.24316
$35$	−0.976495	+	5.83493i	−0.165058	+	0.986284i
$36$	0.0700203	+	0.215500i	0.0116700	+	0.0359167i
$37$	−5.55132	−	3.60507i	−0.912631	−	0.592670i	0.000649914	−	1.00000i	$-0.499793\pi$
$37$	−5.55132	−	3.60507i	−0.912631	−	0.592670i	−0.913281	+	0.407330i	$0.866460\pi$
$38$	5.03043	+	1.93100i	0.816044	+	0.313250i
$39$	1.83642	+	4.12466i	0.294062	+	0.660474i
$40$	−0.00871699	+	2.23605i	−0.00137828	+	0.353551i
$41$	6.92798	−	2.25104i	1.08197	−	0.351553i	0.286830	−	0.957981i	$-0.407398\pi$
$41$	6.92798	−	2.25104i	1.08197	−	0.351553i	0.795138	+	0.606428i	$0.207398\pi$
$42$	−4.19701	+	1.34127i	−0.647612	+	0.206963i
$43$	−5.74428	+	5.74428i	−0.875995	+	0.875995i	−0.993117	−	0.117123i	$-0.962633\pi$
$43$	−5.74428	+	5.74428i	−0.875995	+	0.875995i	0.117123	+	0.993117i	$0.462633\pi$
$44$	2.01894	−	2.63133i	0.304366	−	0.396688i
$45$	0.506076	−	0.0245444i	0.0754414	−	0.00365887i
$46$	−0.0725106	−	0.689892i	−0.0106911	−	0.101719i
$47$	−0.266774	−	5.09035i	−0.0389130	−	0.742505i	−0.946512	−	0.322667i	$-0.895420\pi$
$47$	−0.266774	−	5.09035i	−0.0389130	−	0.742505i	0.907599	−	0.419837i	$-0.137913\pi$
$48$	−1.48384	+	0.756056i	−0.214174	+	0.109127i
$49$	2.09859	+	6.67802i	0.299799	+	0.954002i
$50$	4.81939	+	1.33171i	0.681565	+	0.188332i
$51$	11.8081	−	2.50988i	1.65346	−	0.351454i
$52$	2.27375	−	1.47659i	0.315312	−	0.204766i
$53$	1.11175	+	0.900278i	0.152711	+	0.123663i	0.702631	−	0.711554i	$-0.252009\pi$
$53$	1.11175	+	0.900278i	0.152711	+	0.123663i	−0.549920	+	0.835217i	$0.685342\pi$
$54$	2.68671	+	4.65352i	0.365615	+	0.633264i
$55$	−4.49194	−	5.90106i	−0.605693	−	0.795698i
$56$	1.18973	+	2.36317i	0.158984	+	0.315791i
$57$	8.86300	+	1.40376i	1.17393	+	0.185933i
$58$	−0.222703	−	4.24944i	−0.0292424	−	0.557978i
$59$	0.117426	+	0.130415i	0.0152876	+	0.0169785i	0.750740	−	0.660598i	$-0.229697\pi$
$59$	0.117426	+	0.130415i	0.0152876	+	0.0169785i	−0.735453	+	0.677576i	$0.763030\pi$
$60$	0.760026	+	3.64546i	0.0981189	+	0.470627i
$61$	12.0193	+	1.26328i	1.53891	+	0.161746i	0.835681	−	0.549215i	$-0.185073\pi$
$61$	12.0193	+	1.26328i	1.53891	+	0.161746i	0.703231	+	0.710961i	$0.251740\pi$
$62$	1.98659	+	3.89890i	0.252297	+	0.495161i
$63$	0.520628	−	0.297235i	0.0655929	−	0.0374481i
$64$	0.587785	+	0.809017i	0.0734732	+	0.101127i
$65$	−1.85086	−	5.77282i	−0.229570	−	0.716031i
$66$	2.37769	−	4.98539i	0.292673	−	0.613659i
$67$	2.98794	−	0.800616i	0.365035	−	0.0978108i	−0.0716391	−	0.997431i	$-0.522823\pi$
$67$	2.98794	−	0.800616i	0.365035	−	0.0978108i	0.436674	+	0.899620i	$0.356156\pi$
$68$	−2.59774	−	6.76735i	−0.315023	−	0.820662i
$69$	−0.356990	−	1.09870i	−0.0429765	−	0.132268i
$70$	5.79732	−	1.17942i	0.692913	−	0.140967i
$71$	6.84431	+	4.97268i	0.812270	+	0.590149i	0.914488	−	0.404613i	$-0.132594\pi$
$71$	6.84431	+	4.97268i	0.812270	+	0.590149i	−0.102218	+	0.994762i	$0.532594\pi$
$72$	0.176094	−	0.142598i	0.0207528	−	0.0168053i
$73$	−0.808400	+	15.4252i	−0.0946161	+	1.80538i	0.379786	+	0.925074i	$0.375998\pi$
$73$	−0.808400	+	15.4252i	−0.0946161	+	1.80538i	−0.474402	+	0.880308i	$0.657336\pi$
$74$	−1.37621	+	6.47454i	−0.159981	+	0.752650i
$75$	8.31172	+	0.500609i	0.959754	+	0.0578053i
$76$		−	5.38832i		−	0.618083i
$77$	−7.90192	−	3.81571i	−0.900508	−	0.434840i
$78$	3.19259	−	3.19259i	0.361489	−	0.361489i
$79$	3.52302	−	7.91282i	0.396370	−	0.890262i	−0.599576	−	0.800317i	$-0.704664\pi$
$79$	3.52302	−	7.91282i	0.396370	−	0.890262i	0.995947	−	0.0899447i	$-0.0286690\pi$
$80$	2.09066	−	0.793191i	0.233743	−	0.0886814i
$81$	5.53296	+	6.14498i	0.614774	+	0.682776i
$82$	−4.58429	−	5.66113i	−0.506250	−	0.625167i
$83$	−2.65409	−	16.7573i	−0.291324	−	1.83935i	−0.505838	−	0.862629i	$-0.668816\pi$
$83$	−2.65409	−	16.7573i	−0.291324	−	1.83935i	0.214513	−	0.976721i	$-0.431184\pi$
$84$	2.75626	+	3.43757i	0.300732	+	0.375070i
$85$	−16.1265	+	1.63143i	−1.74917	+	0.176954i
$86$	7.42132	+	3.30418i	0.800261	+	0.356299i
$87$	−1.83413	−	6.84507i	−0.196639	−	0.733868i
$88$	−3.18008	−	0.941856i	−0.338998	−	0.100402i
$89$	0.366866	+	0.635431i	0.0388877	+	0.0673555i	0.884814	−	0.465944i	$-0.154285\pi$
$89$	0.366866	+	0.635431i	0.0388877	+	0.0673555i	−0.845926	+	0.533300i	$0.820952\pi$
$90$	−0.204276	−	0.463667i	−0.0215326	−	0.0488748i
$91$	−5.04746	−	5.09654i	−0.529118	−	0.534263i
$92$	−0.618084	+	0.314930i	−0.0644397	+	0.0328337i
$93$	4.58606	+	5.66332i	0.475553	+	0.587258i
$94$	−4.65665	+	2.07328i	−0.480297	+	0.213842i
$95$	−11.6259	−	3.16377i	−1.19279	−	0.324596i
$96$	1.23760	+	1.11434i	0.126312	+	0.113732i
$97$	−2.14514	+	13.5439i	−0.217806	+	1.37517i	0.600149	+	0.799888i	$0.295108\pi$
$97$	−2.14514	+	13.5439i	−0.217806	+	1.37517i	−0.817954	+	0.575283i	$0.804892\pi$
$98$	5.48240	−	4.35239i	0.553806	−	0.439658i
$99$	−0.175411	+	0.730757i	−0.0176295	+	0.0734438i
$100$	−0.483857	−	4.97653i	−0.0483857	−	0.497653i
$101$	2.01523	−	0.211809i	0.200522	−	0.0210758i	−0.00373470	−	0.999993i	$-0.501189\pi$
$101$	2.01523	−	0.211809i	0.200522	−	0.0210758i	0.204257	+	0.978917i	$0.434522\pi$
$102$	−6.57481	−	10.1243i	−0.651003	−	1.00246i
$103$	9.73886	+	6.32449i	0.959599	+	0.623171i	0.926505	−	0.376282i	$-0.122797\pi$
$103$	9.73886	+	6.32449i	0.959599	+	0.623171i	0.0330933	+	0.999452i	$0.489464\pi$
$104$	−2.19335	−	1.59356i	−0.215076	−	0.156262i
$105$	9.03526	−	3.92853i	0.881751	−	0.383386i
$106$	0.442066	−	1.36054i	0.0429373	−	0.132147i
$107$	−10.1389	+	0.531357i	−0.980165	+	0.0513682i	−0.535682	−	0.844419i	$-0.679946\pi$
$107$	−10.1389	+	0.531357i	−0.980165	+	0.0513682i	−0.444482	+	0.895788i	$0.646612\pi$
$108$	3.38160	−	4.17593i	0.325395	−	0.401829i
$109$	−3.99177	−	2.30465i	−0.382343	−	0.220746i	0.296494	−	0.955035i	$-0.404182\pi$
$109$	−3.99177	−	2.30465i	−0.382343	−	0.220746i	−0.678837	+	0.734289i	$0.737516\pi$
$110$	−3.89934	+	6.30834i	−0.371788	+	0.601476i
$111$			11.0233i			1.04629i
$112$	1.77985	−	1.95759i	0.168180	−	0.184975i
$113$	−1.36948	−	0.697783i	−0.128830	−	0.0656419i	0.388388	−	0.921496i	$-0.373032\pi$
$113$	−1.36948	−	0.697783i	−0.128830	−	0.0656419i	−0.517217	+	0.855854i	$0.673032\pi$
$114$	−1.86569	−	8.77738i	−0.174738	−	0.822077i
$115$	0.316583	+	1.51849i	0.0295216	+	0.141600i
$116$	−3.88738	+	1.73077i	−0.360934	+	0.160698i
$117$	−0.334581	+	0.515209i	−0.0309320	+	0.0476311i
$118$	0.0796709	−	0.156363i	0.00733430	−	0.0143944i
$119$	−16.1349	+	10.3675i	−1.47908	+	0.950383i
$120$	3.13096	−	2.01596i	0.285817	−	0.184031i
$121$	10.2691	−	3.94280i	0.933554	−	0.358436i
$122$	−3.12796	−	11.6737i	−0.283192	−	1.05689i
$123$	−9.42779	−	7.63447i	−0.850075	−	0.688377i
$124$	2.92801	−	3.25188i	0.262943	−	0.292027i
$125$	−11.0215	−	1.87801i	−0.985791	−	0.167975i
$126$	−0.464069	−	0.379528i	−0.0413426	−	0.0338111i
$127$	−2.33032	−	14.7130i	−0.206782	−	1.30557i	−0.844606	−	0.535389i	$-0.820165\pi$
$127$	−2.33032	−	14.7130i	−0.206782	−	1.30557i	0.637823	−	0.770183i	$-0.279835\pi$
$128$	0.544639	−	0.838671i	0.0481397	−	0.0741287i
$129$	13.2331	+	2.81279i	1.16511	+	0.247652i
$130$	−4.72611	+	3.79672i	−0.414507	+	0.332994i
$131$	2.97921	−	1.72005i	0.260295	−	0.150281i	−0.364174	−	0.931331i	$-0.618649\pi$
$131$	2.97921	−	1.72005i	0.260295	−	0.150281i	0.624469	+	0.781050i	$0.285315\pi$
$132$	−5.50635	−	0.433157i	−0.479266	−	0.0377015i
$133$	−13.9588	+	2.89652i	−1.21038	+	0.251160i
$134$	−1.81822	−	2.50257i	−0.157070	−	0.216189i
$135$	−7.02449	−	9.74807i	−0.604572	−	0.838980i
$136$	−5.38692	+	4.85041i	−0.461925	+	0.415919i
$137$	−3.72227	−	1.42885i	−0.318015	−	0.122075i	0.194124	−	0.980977i	$-0.437813\pi$
$137$	−3.72227	−	1.42885i	−0.318015	−	0.122075i	−0.512139	+	0.858902i	$0.671147\pi$
$138$	−0.897793	+	0.727019i	−0.0764252	+	0.0618879i
$139$	−6.25818	+	19.2607i	−0.530812	+	1.63367i	0.221716	+	0.975111i	$0.428834\pi$
$139$	−6.25818	+	19.2607i	−0.530812	+	1.63367i	−0.752528	+	0.658560i	$0.771166\pi$
$140$	−3.17866	−	4.98960i	−0.268645	−	0.421698i
$141$	−6.86765	+	4.98964i	−0.578361	+	0.420204i
$142$	2.18962	−	8.17176i	0.183749	−	0.685759i
$143$	8.98872	−	0.235706i	0.751674	−	0.0197107i
$144$	−0.196233	−	0.113295i	−0.0163527	−	0.00944126i
$145$	1.45184	+	9.40365i	0.120568	+	0.780931i
$146$	14.6904	−	4.77319i	1.21578	−	0.395032i
$147$	7.42362	−	8.98815i	0.612290	−	0.741330i
$148$	6.53769	−	1.03547i	0.537395	−	0.0851150i
$149$	10.4446	+	1.09778i	0.855658	+	0.0899333i	0.522191	−	0.852828i	$-0.325115\pi$
$149$	10.4446	+	1.09778i	0.855658	+	0.0899333i	0.333467	+	0.942762i	$0.391781\pi$
$150$	−2.51129	−	7.93906i	−0.205046	−	0.648221i
$151$	1.96244	+	0.417129i	0.159701	+	0.0339455i	0.287068	−	0.957910i	$-0.407319\pi$
$151$	1.96244	+	0.417129i	0.159701	+	0.0339455i	−0.127367	+	0.991856i	$0.540653\pi$
$152$	−5.03043	+	1.93100i	−0.408022	+	0.156625i
$153$	1.16143	+	1.16143i	0.0938962	+	0.0938962i
$154$	−0.730476	+	8.74451i	−0.0588634	+	0.704652i
$155$	−5.29708	−	8.22683i	−0.425472	−	0.660795i
$156$	−4.12466	−	1.83642i	−0.330237	−	0.147031i
$157$	−19.5579	+	12.7011i	−1.56089	+	1.01366i	−0.581056	+	0.813864i	$0.697360\pi$
$157$	−19.5579	+	12.7011i	−1.56089	+	1.01366i	−0.979838	+	0.199793i	$0.935973\pi$
$158$	−8.64979	−	0.453316i	−0.688141	−	0.0360639i
$159$	0.249027	−	2.36933i	0.0197491	−	0.187900i
$160$	−1.48973	−	1.66754i	−0.117774	−	0.131831i
$161$	1.14810	+	1.43190i	0.0904830	+	0.112849i
$162$	3.75400	−	7.36763i	0.294942	−	0.578856i
$163$	−8.44168	+	3.24046i	−0.661203	+	0.253812i	−0.665747	−	0.746178i	$-0.731887\pi$
$163$	−8.44168	+	3.24046i	−0.661203	+	0.253812i	0.00454385	+	0.999990i	$0.498554\pi$
$164$	−3.64225	+	6.30857i	−0.284412	+	0.492616i
$165$	−4.16765	+	11.6262i	−0.324451	+	0.905097i
$166$	−14.6931	+	8.48308i	−1.14041	+	0.658415i
$167$	−2.74280	+	17.3174i	−0.212244	+	1.34006i	0.619543	+	0.784963i	$0.287318\pi$
$167$	−2.74280	+	17.3174i	−0.212244	+	1.34006i	−0.831787	+	0.555095i	$0.812682\pi$
$168$	2.22150	−	3.80511i	0.171392	−	0.293570i
$169$	−5.37325	−	1.74587i	−0.413327	−	0.134298i
$170$	7.30231	+	14.4708i	0.560061	+	1.10986i
$171$	0.496602	+	1.11539i	0.0379761	+	0.0852957i
$172$	0.425159	−	8.11251i	0.0324180	−	0.618573i
$173$	22.2213	−	1.16457i	1.68946	−	0.0885407i	0.816815	−	0.576900i	$-0.195738\pi$
$173$	22.2213	−	1.16457i	1.68946	−	0.0885407i	0.872643	+	0.488359i	$0.162404\pi$
$174$	−5.73313	+	4.16536i	−0.434627	+	0.315775i
$175$	−12.6319	+	3.92862i	−0.954885	+	0.296976i
$176$	0.260340	+	3.30639i	0.0196239	+	0.249229i
$177$	0.0756408	−	0.282295i	0.00568551	−	0.0212186i
$178$	0.461753	−	0.570217i	0.0346098	−	0.0427396i
$179$	5.40400	−	25.4238i	0.403914	−	1.90027i	−0.0304645	−	0.999536i	$-0.509699\pi$
$179$	5.40400	−	25.4238i	0.403914	−	1.90027i	0.434379	−	0.900730i	$-0.356968\pi$
$180$	−0.359665	+	0.356871i	−0.0268078	+	0.0265996i
$181$	1.41883	−	1.95286i	0.105461	−	0.145155i	−0.753024	−	0.657993i	$-0.771406\pi$
$181$	1.41883	−	1.95286i	0.105461	−	0.145155i	0.858486	+	0.512838i	$0.171406\pi$
$182$	−2.94919	+	6.53865i	−0.218608	+	0.484677i
$183$	−9.13730	−	17.9330i	−0.675449	−	1.32564i
$184$	0.515514	+	0.464171i	0.0380042	+	0.0342191i
$185$	1.60449	−	14.7137i	0.117965	−	1.08177i
$186$	3.64366	−	6.31101i	0.267166	−	0.462746i
$187$	4.38037	−	23.6392i	0.320325	−	1.72867i
$188$	3.60436	+	3.60436i	0.262875	+	0.262875i
$189$	−12.6358	−	6.51548i	−0.919121	−	0.473931i
$190$	1.21271	+	11.9875i	0.0879789	+	0.869663i
$191$	−12.6607	+	2.69112i	−0.916099	+	0.194723i	−0.641756	−	0.766909i	$-0.721794\pi$
$191$	−12.6607	+	2.69112i	−0.916099	+	0.194723i	−0.274343	+	0.961632i	$0.588461\pi$
$192$	0.596810	−	1.55474i	0.0430711	−	0.112204i
$193$	3.68449	−	9.59843i	0.265215	−	0.690910i	−0.734706	−	0.678386i	$-0.762680\pi$
$193$	3.68449	−	9.59843i	0.265215	−	0.690910i	0.999922	−	0.0125243i	$-0.00398672\pi$
$194$	13.4130	−	2.85103i	0.963000	−	0.204692i
$195$	−6.38406	+	7.82112i	−0.457172	+	0.560082i
$196$	−6.02802	−	3.55850i	−0.430573	−	0.254179i
$197$	−1.34381	−	1.34381i	−0.0957425	−	0.0957425i	0.657613	−	0.753356i	$-0.271566\pi$
$197$	−1.34381	−	1.34381i	−0.0957425	−	0.0957425i	−0.753356	+	0.657613i	$0.771566\pi$
$198$	0.745082	−	0.0981196i	0.0529507	−	0.00697305i
$199$	3.84664	−	6.66258i	0.272681	−	0.472298i	−0.696866	−	0.717201i	$-0.745423\pi$
$199$	3.84664	−	6.66258i	0.272681	−	0.472298i	0.969548	+	0.244903i	$0.0787562\pi$
$200$	−4.47260	+	2.23515i	−0.316260	+	0.158049i
$201$	−3.82832	−	3.44704i	−0.270029	−	0.243135i
$202$	−0.919933	−	1.80547i	−0.0647262	−	0.127032i
$203$	6.57336	+	9.14013i	0.461359	+	0.641511i
$204$	−7.09566	+	9.76634i	−0.496796	+	0.683781i
$205$	11.4728	+	11.5626i	0.801297	+	0.807569i
$206$	2.41433	−	11.3585i	0.168214	−	0.791385i
$207$	0.0989190	−	0.122155i	0.00687535	−	0.00849035i
$208$	−0.701692	+	2.61875i	−0.0486536	+	0.181578i
$209$	9.33704	−	15.2379i	0.645857	−	1.05403i
$210$	−6.90555	−	7.02728i	−0.476528	−	0.484929i
$211$	4.49025	−	3.26236i	0.309122	−	0.224590i	−0.422398	−	0.906411i	$-0.638811\pi$
$211$	4.49025	−	3.26236i	0.309122	−	0.224590i	0.731520	+	0.681820i	$0.238811\pi$
$212$	−1.42860	+	0.0748696i	−0.0981164	+	0.00514206i
$213$	0.737359	−	14.0697i	0.0505230	−	0.964037i
$214$	4.12952	+	9.27506i	0.282288	+	0.634030i
$215$	−17.2539	−	5.68060i	−1.17671	−	0.387414i
$216$	−5.11043	−	1.66048i	−0.347720	−	0.112981i
$217$	−9.99818	−	5.83713i	−0.678720	−	0.396250i
$218$	−0.721054	+	4.55255i	−0.0488359	+	0.308338i
$219$	22.2774	−	12.8618i	1.50537	−	0.869123i
$220$	7.28674	+	1.37965i	0.491272	+	0.0930157i
$221$	9.82625	−	17.0196i	0.660985	−	1.14486i
$222$	10.2911	−	3.95040i	0.690696	−	0.265133i
$223$	−2.59950	+	5.10181i	−0.174076	+	0.341643i	−0.961516	−	0.274748i	$-0.911406\pi$
$223$	−2.59950	+	5.10181i	−0.174076	+	0.341643i	0.787441	+	0.616390i	$0.211406\pi$
$224$	−2.46541	−	0.960093i	−0.164727	−	0.0641489i
$225$	0.558809	+	0.985552i	0.0372539	+	0.0657034i
$226$	−0.160660	+	1.52858i	−0.0106870	+	0.101680i
$227$	−5.78894	−	0.303385i	−0.384225	−	0.0201364i	−0.140754	−	0.990045i	$-0.544953\pi$
$227$	−5.78894	−	0.303385i	−0.384225	−	0.0201364i	−0.243471	+	0.969908i	$0.578286\pi$
$228$	−7.52579	+	4.88731i	−0.498408	+	0.323670i
$229$	12.8387	+	5.71616i	0.848406	+	0.377735i	0.784431	−	0.620217i	$-0.212955\pi$
$229$	12.8387	+	5.71616i	0.848406	+	0.377735i	0.0639756	+	0.997951i	$0.479622\pi$
$230$	1.30418	−	0.839735i	0.0859952	−	0.0553705i
$231$	1.83784	+	14.4974i	0.120921	+	0.953860i
$232$	3.00893	+	3.00893i	0.197546	+	0.197546i
$233$	27.3743	−	10.5080i	1.79335	−	0.688403i	0.796910	−	0.604098i	$-0.206466\pi$
$233$	27.3743	−	10.5080i	1.79335	−	0.688403i	0.996440	−	0.0843048i	$-0.0268669\pi$
$234$	0.600892	+	0.127724i	0.0392815	+	0.00834955i
$235$	9.89310	−	5.66048i	0.645355	−	0.369249i
$236$	−0.174529	−	0.0183437i	−0.0113609	−	0.00119407i
$237$	−14.2472	+	2.25653i	−0.925452	+	0.146577i
$238$	15.4611	+	11.3478i	1.00219	+	0.735570i
$239$	8.93813	−	2.90418i	0.578160	−	0.187856i	−0.00531622	−	0.999986i	$-0.501692\pi$
$239$	8.93813	−	2.90418i	0.578160	−	0.187856i	0.583476	+	0.812130i	$0.301692\pi$
$240$	−3.00410	−	2.20055i	−0.193914	−	0.142045i
$241$	−4.60001	−	2.65582i	−0.296313	−	0.171076i	0.344473	−	0.938796i	$-0.388058\pi$
$241$	−4.60001	−	2.65582i	−0.296313	−	0.171076i	−0.640785	+	0.767720i	$0.721391\pi$
$242$	−7.36103	−	8.17406i	−0.473185	−	0.525448i
$243$	−0.608128	+	2.26956i	−0.0390114	+	0.145593i
$244$	−9.77737	+	7.10367i	−0.625932	+	0.454766i
$245$	−11.2172	+	10.9167i	−0.716641	+	0.697443i
$246$	−3.74878	+	11.5375i	−0.239013	+	0.735607i
$247$	11.3529	−	9.19340i	0.722368	−	0.584962i
$248$	−4.08520	−	1.56816i	−0.259410	−	0.0995782i
$249$	−20.9973	+	18.9061i	−1.33065	+	1.19812i
$250$	2.19647	+	10.9625i	0.138917	+	0.693327i
$251$	−5.46268	−	7.51874i	−0.344802	−	0.474579i	0.601035	−	0.799223i	$-0.294755\pi$
$251$	−5.46268	−	7.51874i	−0.344802	−	0.474579i	−0.945836	+	0.324644i	$0.894755\pi$
$252$	−0.188013	+	0.569257i	−0.0118437	+	0.0358598i
$253$	−2.29363	−	0.180429i	−0.144199	−	0.0113434i
$254$	−12.9007	+	7.44822i	−0.809462	+	0.467343i
$255$	16.9057	+	21.0440i	1.05867	+	1.31782i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	3.15346	−	4.85590i	0.196707	−	0.302903i	−0.726529	−	0.687136i	$-0.758868\pi$
$257$	3.15346	−	4.85590i	0.196707	−	0.302903i	0.923236	+	0.384234i	$0.125534\pi$
$258$	−2.11636	−	13.3622i	−0.131759	−	0.831894i
$259$	−6.19682	−	16.3797i	−0.385052	−	1.01779i
$260$	5.23823	+	3.05158i	0.324861	+	0.189251i
$261$	0.645177	−	0.716542i	0.0399355	−	0.0443528i
$262$	−2.67346	−	2.16492i	−0.165167	−	0.133749i
$263$	4.58799	+	17.1226i	0.282907	+	1.05582i	0.950355	+	0.311168i	$0.100720\pi$
$263$	4.58799	+	17.1226i	0.282907	+	1.05582i	−0.667448	+	0.744657i	$0.732613\pi$
$264$	1.56891	+	5.29585i	0.0965599	+	0.325937i
$265$	−0.677265	+	3.12630i	−0.0416041	+	0.192047i
$266$	7.70652	+	11.9937i	0.472517	+	0.735378i
$267$	0.554742	−	1.08874i	0.0339497	−	0.0666300i
$268$	−1.68476	+	2.59430i	−0.102913	+	0.158472i
$269$	−16.6392	+	7.40825i	−1.01451	+	0.451689i	−0.845528	−	0.533931i	$-0.820714\pi$
$269$	−16.6392	+	7.40825i	−1.01451	+	0.451689i	−0.168981	+	0.985619i	$0.554048\pi$
$270$	−6.58325	+	10.0513i	−0.400644	+	0.611704i
$271$	−1.22648	−	5.77012i	−0.0745032	−	0.350510i	0.925068	−	0.379802i	$-0.124008\pi$
$271$	−1.22648	−	5.77012i	−0.0745032	−	0.350510i	−0.999571	+	0.0292923i	$0.990675\pi$
$272$	6.45874	+	3.29089i	0.391619	+	0.199540i
$273$	−2.54013	+	11.6724i	−0.153736	+	0.706444i
$274$			3.98709i			0.240869i
$275$	7.25516	−	14.9118i	0.437502	−	0.899217i
$276$	1.00047	+	0.577622i	0.0602213	+	0.0347688i
$277$	−10.8066	+	13.3451i	−0.649306	+	0.801827i	−0.990404	−	0.138201i	$-0.955868\pi$
$277$	−10.8066	+	13.3451i	−0.649306	+	0.801827i	0.341098	+	0.940028i	$0.389201\pi$
$278$	20.2242	−	1.05990i	1.21296	−	0.0635687i
$279$	−0.306397	+	0.942994i	−0.0183435	+	0.0564556i
$280$	−3.51907	+	4.75565i	−0.210305	+	0.284204i
$281$	4.89302	+	3.55499i	0.291893	+	0.212073i	0.724088	−	0.689707i	$-0.242261\pi$
$281$	4.89302	+	3.55499i	0.291893	+	0.212073i	−0.432195	+	0.901780i	$0.642261\pi$
$282$	7.11938	+	4.62338i	0.423953	+	0.275318i
$283$	−3.40909	−	5.24954i	−0.202650	−	0.312053i	0.722704	−	0.691157i	$-0.242899\pi$
$283$	−3.40909	−	5.24954i	−0.202650	−	0.312053i	−0.925354	+	0.379104i	$0.876232\pi$
$284$	−8.41369	+	0.884314i	−0.499260	+	0.0524744i
$285$	6.12608	+	19.1073i	0.362878	+	1.13182i
$286$	−3.44132	−	8.30722i	−0.203489	−	0.491216i
$287$	18.3007	+	6.04430i	1.08025	+	0.356784i
$288$	−0.0354465	+	0.223801i	−0.00208871	+	0.0131876i
$289$	−26.4154	−	23.7845i	−1.55384	−	1.39909i
$290$	8.25877	−	4.72537i	0.484972	−	0.277483i
$291$	20.8622	−	9.28845i	1.22296	−	0.544498i
$292$	−9.72071	−	12.0041i	−0.568862	−	0.702486i
$293$	14.3406	−	7.30690i	0.837787	−	0.426874i	0.0182041	−	0.999834i	$-0.494205\pi$
$293$	14.3406	−	7.30690i	0.837787	−	0.426874i	0.819583	+	0.572960i	$0.194205\pi$
$294$	−11.0516	−	3.70948i	−0.644540	−	0.216341i
$295$	−0.142054	+	0.365794i	−0.00827068	+	0.0212973i
$296$	−3.30959	−	5.73238i	−0.192366	−	0.333188i
$297$	16.7992	−	5.94959i	0.974787	−	0.345230i
$298$	−2.71816	−	10.1443i	−0.157459	−	0.587645i
$299$	−1.71810	−	0.764946i	−0.0993601	−	0.0442380i
$300$	−6.51178	+	5.18960i	−0.375958	+	0.299622i
$301$	−21.2445	+	3.25951i	−1.22451	+	0.187875i
$302$	−0.313851	−	1.98158i	−0.0180601	−	0.114027i
$303$	−2.12368	−	2.62252i	−0.122002	−	0.150660i
$304$	3.60549	+	4.00431i	0.206789	+	0.229663i
$305$	9.58610	+	25.2666i	0.548899	+	1.44676i
$306$	0.668070	−	1.50051i	0.0381910	−	0.0857784i
$307$	17.4447	−	17.4447i	0.995620	−	0.995620i	−0.00437072	−	0.999990i	$-0.501391\pi$
$307$	17.4447	−	17.4447i	0.995620	−	0.995620i	0.999990	+	0.00437072i	$0.00139125\pi$
$308$	8.42548	−	2.45179i	0.480086	−	0.139704i
$309$		−	19.3385i		−	1.10013i
$310$	−5.78210	+	7.89348i	−0.328401	+	0.448320i
$311$	2.92600	−	13.7658i	0.165919	−	0.780585i	−0.813949	−	0.580936i	$-0.802687\pi$
$311$	2.92600	−	13.7658i	0.165919	−	0.780585i	0.979868	−	0.199649i	$-0.0639802\pi$
$312$	−0.236297	+	4.50881i	−0.0133777	+	0.255261i
$313$	−1.56250	+	1.26529i	−0.0883175	+	0.0715181i	−0.672462	−	0.740131i	$-0.734763\pi$
$313$	−1.56250	+	1.26529i	−0.0883175	+	0.0715181i	0.584145	+	0.811649i	$0.301430\pi$
$314$	18.8664	+	13.7073i	1.06469	+	0.773545i
$315$	1.11784	+	0.739898i	0.0629831	+	0.0416885i
$316$	2.67660	+	8.23773i	0.150571	+	0.463409i
$317$	−0.827198	−	2.15492i	−0.0464601	−	0.121033i	0.908387	−	0.418131i	$-0.137315\pi$
$317$	−0.827198	−	2.15492i	−0.0464601	−	0.121033i	−0.954847	+	0.297098i	$0.903981\pi$
$318$	−2.30121	+	0.616607i	−0.129045	+	0.0345776i
$319$	−13.9925	−	1.84162i	−0.783427	−	0.103111i
$320$	−1.02291	+	1.98838i	−0.0571826	+	0.111154i
$321$	9.93830	+	13.6789i	0.554702	+	0.763482i
$322$	0.925348	−	1.58499i	0.0515676	−	0.0883280i
$323$	−17.7324	−	34.8018i	−0.986657	−	1.93642i
$324$	−8.22359	−	0.864334i	−0.456866	−	0.0480186i
$325$	9.65974	−	9.51027i	0.535826	−	0.527535i
$326$	6.05045	+	6.71971i	0.335104	+	0.372170i
$327$	0.401738	+	7.66561i	0.0222161	+	0.423909i
$328$	7.19482	+	1.13955i	0.397268	+	0.0629210i
$329$	7.39980	−	11.2749i	0.407964	−	0.621605i
$330$	12.3475	−	0.275618i	0.679709	−	0.0151723i
$331$	−4.07846	−	7.06410i	−0.224172	−	0.388278i	0.731898	−	0.681414i	$-0.238635\pi$
$331$	−4.07846	−	7.06410i	−0.224172	−	0.388278i	−0.956071	+	0.293136i	$0.905301\pi$
$332$	13.1852	+	10.6771i	0.723631	+	0.585985i
$333$	−1.25787	+	0.816873i	−0.0689311	+	0.0447644i
$334$	17.1501	−	3.64536i	0.938411	−	0.199465i
$335$	4.60825	+	5.15828i	0.251776	+	0.281827i
$336$	−4.34848	−	0.710317i	−0.237229	−	0.0387510i
$337$	−8.75268	+	4.45971i	−0.476789	+	0.242936i	−0.675834	−	0.737054i	$-0.736216\pi$
$337$	−8.75268	+	4.45971i	−0.476789	+	0.242936i	0.199044	+	0.979990i	$0.436216\pi$
$338$	0.295686	+	5.64202i	0.0160832	+	0.306886i
$339$	0.267556	+	2.54563i	0.0145317	+	0.138260i
$340$	10.8927	−	12.0032i	0.590740	−	0.650962i
$341$	13.9152	−	4.12242i	0.753551	−	0.223242i
$342$	0.863336	−	0.863336i	0.0466839	−	0.0466839i
$343$	−5.97814	+	17.5289i	−0.322789	+	0.946471i
$344$	−7.72604	+	2.51034i	−0.416560	+	0.135349i
$345$	1.83371	−	1.81947i	0.0987235	−	0.0979568i
$346$	−9.05064	−	20.3281i	−0.486565	−	1.09284i
$347$	11.4762	+	4.40529i	0.616073	+	0.236488i	0.646335	−	0.763054i	$-0.276301\pi$
$347$	11.4762	+	4.40529i	0.616073	+	0.236488i	−0.0302618	+	0.999542i	$0.509634\pi$
$348$	5.94327	+	3.85960i	0.318593	+	0.206896i
$349$	10.4808	+	32.2565i	0.561022	+	1.72665i	0.679484	+	0.733690i	$0.262204\pi$
$349$	10.4808	+	32.2565i	0.561022	+	1.72665i	−0.118462	+	0.992959i	$0.537796\pi$
$350$	8.19457	+	10.3850i	0.438018	+	0.555104i
$351$	14.5681			0.777585
$352$	2.99348	−	1.42795i	0.159553	−	0.0761101i
$353$	10.3398	−	2.77055i	0.550334	−	0.147461i	0.0270719	−	0.999633i	$-0.491382\pi$
$353$	10.3398	−	2.77055i	0.550334	−	0.147461i	0.523262	+	0.852172i	$0.324715\pi$
$354$	−0.290653	+	0.0305488i	−0.0154480	+	0.00162365i
$355$	−3.03212	+	18.6726i	−0.160928	+	0.991040i
$356$	−0.697821	−	0.226736i	−0.0369844	−	0.0120170i
$357$	29.1147	+	13.1318i	1.54091	+	0.695011i
$358$	−25.6718	+	4.06602i	−1.35680	+	0.214896i
$359$	−3.26992	−	15.3838i	−0.172580	−	0.811923i	−0.976216	−	0.216802i	$-0.930437\pi$
$359$	−3.26992	−	15.3838i	−0.172580	−	0.811923i	0.803636	−	0.595121i	$-0.202896\pi$
$360$	0.462060	+	0.207885i	0.0243527	+	0.0109565i
$361$	−1.04884	−	9.97907i	−0.0552022	−	0.525214i
$362$	−2.33162	−	0.624754i	−0.122547	−	0.0328364i
$363$	−14.8211	−	10.7665i	−0.777906	−	0.565095i
$364$	7.16125	+	0.410059i	0.375351	+	0.0214930i
$365$	−31.6076	+	13.9252i	−1.65442	+	0.728879i
$366$	−13.4674	+	14.9570i	−0.703950	+	0.781815i
$367$	−18.7750	−	0.983959i	−0.980049	−	0.0513622i	−0.444423	−	0.895817i	$-0.646591\pi$
$367$	−18.7750	−	0.983959i	−0.980049	−	0.0513622i	−0.535627	+	0.844455i	$0.679925\pi$
$368$	0.248597	−	0.647617i	0.0129590	−	0.0337594i
$369$	0.172535	−	1.64156i	0.00898179	−	0.0854560i
$370$	−14.3114	+	3.77501i	−0.744017	+	0.196253i
$371$	0.961903	+	3.66063i	0.0499395	+	0.190050i
$372$	−7.19761	−	1.13999i	−0.373178	−	0.0591057i
$373$	1.41310	+	0.378638i	0.0731673	+	0.0196051i	0.295217	−	0.955430i	$-0.404608\pi$
$373$	1.41310	+	0.378638i	0.0731673	+	0.0196051i	−0.222050	+	0.975035i	$0.571275\pi$
$374$	−23.6389	+	4.38210i	−1.22234	+	0.226593i
$375$	7.37369	+	17.0969i	0.380776	+	0.882882i
$376$	2.07328	−	4.65665i	0.106921	−	0.240148i
$377$	−10.2792	−	5.23750i	−0.529405	−	0.269745i
$378$	−1.55445	+	14.1315i	−0.0799521	+	0.726846i
$379$	−8.35920	+	11.5054i	−0.429383	+	0.590995i	−0.967812	−	0.251676i	$-0.919018\pi$
$379$	−8.35920	+	11.5054i	−0.429383	+	0.590995i	0.538428	+	0.842671i	$0.319018\pi$
$380$	10.7567	−	5.42808i	0.551806	−	0.278455i
$381$	−18.4358	+	16.5997i	−0.944497	+	0.850429i
$382$	7.04959	+	10.8554i	0.360688	+	0.555411i
$383$	−4.11774	−	10.7271i	−0.210407	−	0.548128i	0.787244	−	0.616642i	$-0.211507\pi$
$383$	−4.11774	−	10.7271i	−0.210407	−	0.548128i	−0.997650	+	0.0685143i	$0.978174\pi$
$384$	−1.66536			−0.0849848
$385$	−0.342955	−	19.6184i	−0.0174786	−	0.999847i
$386$	−10.2813			−0.523305
$387$	0.659662	+	1.71848i	0.0335325	+	0.0873551i
$388$	−7.46847	−	11.5004i	−0.379154	−	0.583846i
$389$	−4.52653	+	4.07570i	−0.229504	+	0.206646i	−0.775857	−	0.630909i	$-0.782682\pi$
$389$	−4.52653	+	4.07570i	−0.229504	+	0.206646i	0.546353	+	0.837555i	$0.316016\pi$
$390$	9.58948	+	3.15719i	0.485582	+	0.159871i
$391$	−2.95565	+	4.06810i	−0.149474	+	0.205733i
$392$	−1.16189	+	6.90290i	−0.0586845	+	0.348649i
$393$	−5.10456	−	2.60090i	−0.257491	−	0.131198i
$394$	−0.772976	+	1.73613i	−0.0389420	+	0.0874651i
$395$	19.3453	−	0.938239i	0.973369	−	0.0472079i
$396$	−0.358616	−	0.660431i	−0.0180211	−	0.0331879i
$397$	−21.9926	−	5.89289i	−1.10377	−	0.295756i	−0.339474	−	0.940615i	$-0.610249\pi$
$397$	−21.9926	−	5.89289i	−1.10377	−	0.295756i	−0.764301	+	0.644860i	$0.776916\pi$
$398$	−7.59857	−	1.20350i	−0.380882	−	0.0603258i
$399$	16.7064	+	16.8689i	0.836367	+	0.844500i
$400$	3.68953	+	3.37452i	0.184476	+	0.168726i
$401$	−0.965777	+	9.18876i	−0.0482286	+	0.458865i	0.943581	+	0.331141i	$0.107434\pi$
$401$	−0.965777	+	9.18876i	−0.0482286	+	0.458865i	−0.991810	+	0.127723i	$0.959233\pi$
$402$	−1.84614	+	4.80936i	−0.0920770	+	0.239869i
$403$	11.8472	+	0.620886i	0.590152	+	0.0309285i
$404$	−1.35588	+	1.50585i	−0.0674574	+	0.0749190i
$405$	−6.69339	+	17.2357i	−0.332597	+	0.856451i
$406$	6.17737	−	9.41229i	0.306578	−	0.467124i
$407$	20.2826	+	8.40045i	1.00537	+	0.416395i
$408$	11.6605	+	3.12443i	0.577282	+	0.154682i
$409$	2.29122	+	21.7995i	0.113293	+	1.07791i	0.892469	+	0.451109i	$0.148971\pi$
$409$	2.29122	+	21.7995i	0.113293	+	1.07791i	−0.779176	+	0.626806i	$0.784362\pi$
$410$	6.68315	−	14.8545i	0.330057	−	0.733611i
$411$	1.38052	+	6.49483i	0.0680959	+	0.320366i
$412$	−11.4693	+	1.81656i	−0.565052	+	0.0894954i
$413$	0.0462981	+	0.461989i	0.00227818	+	0.0227330i
$414$	−0.149491	−	0.0485725i	−0.00734707	−	0.00238721i
$415$	30.7788	−	22.1793i	1.51087	−	1.08874i
$416$	2.69628	−	0.283390i	0.132196	−	0.0138944i
$417$	32.5774	−	8.72909i	1.59532	−	0.427466i
$418$	−17.5719	−	3.25610i	−0.859470	−	0.159261i
$419$	7.53267			0.367995			0.183998	−	0.982927i	$-0.441096\pi$
$419$	7.53267			0.367995			0.183998	+	0.982927i	$0.441096\pi$
$420$	−4.08581	+	8.96524i	−0.199367	+	0.437459i
$421$	−5.77790	−	17.7825i	−0.281597	−	0.866668i	−0.987398	−	0.158257i	$-0.949413\pi$
$421$	−5.77790	−	17.7825i	−0.281597	−	0.866668i	0.705801	−	0.708411i	$-0.250587\pi$
$422$	−4.65484	−	3.02289i	−0.226594	−	0.147152i
$423$	−1.07829	−	0.413918i	−0.0524284	−	0.0201254i
$424$	0.581860	+	1.30688i	0.0282576	+	0.0634676i
$425$	−19.5024	−	30.5498i	−0.946003	−	1.48188i
$426$	−13.3994	+	4.35373i	−0.649203	+	0.210939i
$427$	23.6584	+	21.5103i	1.14491	+	1.04096i
$428$	7.17912	−	7.17912i	0.347016	−	0.347016i
$429$	−8.48213	−	12.3406i	−0.409521	−	0.595810i
$430$	0.879960	+	18.1437i	0.0424354	+	0.874966i
$431$	0.856543	+	8.14946i	0.0412582	+	0.392546i	0.995591	+	0.0938002i	$0.0299015\pi$
$431$	0.856543	+	8.14946i	0.0412582	+	0.392546i	−0.954333	+	0.298745i	$0.903432\pi$
$432$	0.281223	+	5.36606i	0.0135304	+	0.258175i
$433$	15.2187	−	7.75429i	0.731362	−	0.372647i	−0.0483129	−	0.998832i	$-0.515384\pi$
$433$	15.2187	−	7.75429i	0.731362	−	0.372647i	0.779675	+	0.626185i	$0.215384\pi$
$434$	−1.86641	+	11.4259i	−0.0895904	+	0.548463i
$435$	11.8171	−	10.5570i	0.566586	−	0.506171i
$436$	4.50858	−	0.958328i	0.215922	−	0.0458956i
$437$	−3.13481	+	2.03577i	−0.149958	+	0.0973842i
$438$	−19.9911	−	16.1884i	−0.955210	−	0.773514i
$439$	20.2480	+	35.0705i	0.966384	+	1.67383i	0.705850	+	0.708361i	$0.250565\pi$
$439$	20.2480	+	35.0705i	0.966384	+	1.67383i	0.260533	+	0.965465i	$0.416102\pi$
$440$	−1.32332	−	7.29718i	−0.0630870	−	0.347879i
$441$	1.57576	+	0.181053i	0.0750364	+	0.00862157i
$442$	−19.4105	−	3.07433i	−0.923266	−	0.146231i
$443$	1.83687	+	35.0496i	0.0872725	+	1.66526i	0.594989	+	0.803734i	$0.297157\pi$
$443$	1.83687	+	35.0496i	0.0872725	+	1.66526i	−0.507716	+	0.861524i	$0.669510\pi$
$444$	−7.37603	−	8.19191i	−0.350051	−	0.388771i
$445$	−0.898933	+	1.37249i	−0.0426135	+	0.0650624i
$446$	5.69453	+	0.598520i	0.269644	+	0.0283407i
$447$	−7.94023	−	15.5836i	−0.375560	−	0.737078i
$448$	−0.0128015	+	2.64572i	−0.000604816	+	0.124999i
$449$	7.78106	+	10.7097i	0.367211	+	0.505422i	0.952140	−	0.305662i	$-0.0988778\pi$
$449$	7.78106	+	10.7097i	0.367211	+	0.505422i	−0.584929	+	0.811084i	$0.698878\pi$
$450$	0.719833	−	0.874883i	0.0339332	−	0.0412424i
$451$	−21.2318	+	11.5289i	−0.999766	+	0.542876i
$452$	1.48463	−	0.397805i	0.0698310	−	0.0187112i
$453$	−1.19737	−	3.11925i	−0.0562573	−	0.146555i
$454$	1.79134	+	5.51316i	0.0840715	+	0.258746i
$455$	5.08949	−	15.2104i	0.238599	−	0.713073i
$456$	7.25969	+	5.27448i	0.339966	+	0.247000i
$457$	−29.7652	+	24.1034i	−1.39236	+	1.12751i	−0.416488	+	0.909141i	$0.636739\pi$
$457$	−29.7652	+	24.1034i	−1.39236	+	1.12751i	−0.975867	+	0.218366i	$0.929927\pi$
$458$	0.735515	−	14.0345i	0.0343684	−	0.655787i
$459$	8.09836	−	38.0998i	0.377999	−	1.77835i
$460$	−1.25134	−	0.916624i	−0.0583439	−	0.0427378i
$461$		−	5.72987i		−	0.266867i	−0.991058	−	0.133433i	$-0.957400\pi$
$461$		−	5.72987i		−	0.266867i	0.991058	−	0.133433i	$-0.0426002\pi$
$462$	12.8759	−	6.91118i	0.599040	−	0.321537i
$463$	5.42629	−	5.42629i	0.252181	−	0.252181i	−0.569683	−	0.821864i	$-0.692934\pi$
$463$	5.42629	−	5.42629i	0.252181	−	0.252181i	0.821864	+	0.569683i	$0.192934\pi$
$464$	1.73077	−	3.88738i	0.0803491	−	0.180467i
$465$	−6.68574	+	14.8602i	−0.310044	+	0.689127i
$466$	−19.6201	−	21.7904i	−0.908886	−	1.00942i
$467$	21.9029	+	27.0478i	1.01354	+	1.25162i	0.967550	+	0.252681i	$0.0813124\pi$
$467$	21.9029	+	27.0478i	1.01354	+	1.25162i	0.0459947	+	0.998942i	$0.485354\pi$
$468$	−0.0961002	−	0.606753i	−0.00444223	−	0.0280472i
$469$	7.62634	+	2.96990i	0.352152	+	0.137137i
$470$	−8.82988	−	7.20747i	−0.407292	−	0.332456i
$471$	35.4788	+	15.7962i	1.63478	+	0.727850i
$472$	0.0454202	+	0.169511i	0.00209064	+	0.00780236i
$473$	15.2599	−	22.2050i	0.701652	−	1.02099i
$474$	7.21238	+	12.4922i	0.331275	+	0.573786i
$475$	−5.39584	−	26.3958i	−0.247578	−	1.21112i
$476$	5.05336	−	18.5008i	0.231620	−	0.847985i
$477$	0.288820	−	0.147161i	0.0132242	−	0.00673805i
$478$	−5.91442	−	7.30370i	−0.270519	−	0.334064i
$479$	24.2647	−	10.8033i	1.10868	−	0.493617i	0.231045	−	0.972943i	$-0.425785\pi$
$479$	24.2647	−	10.8033i	1.10868	−	0.493617i	0.877637	+	0.479326i	$0.159119\pi$
$480$	−0.977818	+	3.59318i	−0.0446311	+	0.164005i
$481$	13.3361	+	12.0079i	0.608074	+	0.547512i
$482$	−0.830923	+	5.24624i	−0.0378475	+	0.238960i
$483$	0.958561	−	2.90229i	0.0436160	−	0.132059i
$484$	−4.99318	+	9.80144i	−0.226963	+	0.445520i
$485$	−29.1985	+	9.36148i	−1.32584	+	0.425083i
$486$	2.33675	−	0.245603i	0.105997	−	0.0111408i
$487$	0.673395	+	1.03694i	0.0305145	+	0.0469881i	0.853599	−	0.520931i	$-0.174415\pi$
$487$	0.673395	+	1.03694i	0.0305145	+	0.0469881i	−0.823084	+	0.567919i	$0.807749\pi$
$488$	10.1357	+	6.58223i	0.458824	+	0.297964i
$489$	12.1826	+	8.85121i	0.550918	+	0.400266i
$490$	14.2115	+	6.55996i	0.642010	+	0.296349i
$491$	6.92200	−	21.3037i	0.312386	−	0.961424i	−0.664432	−	0.747349i	$-0.731326\pi$
$491$	6.92200	−	21.3037i	0.312386	−	0.961424i	0.976817	−	0.214075i	$-0.0686737\pi$
$492$	12.1147	−	0.634903i	0.546172	−	0.0286236i
$493$	−19.4118	+	23.9716i	−0.874264	+	1.07963i
$494$	−12.6513	−	7.30423i	−0.569209	−	0.328633i
$495$	−1.63551	+	0.385977i	−0.0735107	+	0.0173484i
$496$			4.37584i			0.196481i
$497$	6.81369	+	21.3208i	0.305636	+	0.956371i
$498$	25.1751	+	12.8274i	1.12812	+	0.574808i
$499$	1.57993	+	7.43301i	0.0707276	+	0.332747i	0.999258	−	0.0385085i	$-0.0122607\pi$
$499$	1.57993	+	7.43301i	0.0707276	+	0.332747i	−0.928531	+	0.371256i	$0.878927\pi$
$500$	9.44719	−	5.97918i	0.422491	−	0.267397i
$501$	26.6747	−	11.8763i	1.19174	−	0.530595i
$502$	−5.06170	+	7.79433i	−0.225915	+	0.347878i
$503$	−12.7080	+	24.9408i	−0.566620	+	1.11205i	0.412913	+	0.910771i	$0.364511\pi$
$503$	−12.7080	+	24.9408i	−0.566620	+	1.11205i	−0.979533	+	0.201284i	$0.935489\pi$
$504$	0.598825	−	0.0284784i	0.0266738	−	0.00126853i
$505$	2.45293	+	3.80961i	0.109154	+	0.169525i
$506$	0.653519	+	2.20595i	0.0290525	+	0.0980664i
$507$	2.43519	+	9.08827i	0.108151	+	0.403624i
$508$	11.5767	+	9.37464i	0.513633	+	0.415932i
$509$	5.56748	−	6.18331i	0.246774	−	0.274070i	−0.607014	−	0.794691i	$-0.707633\pi$
$509$	5.56748	−	6.18331i	0.246774	−	0.274070i	0.853788	+	0.520621i	$0.174299\pi$
$510$	13.5878	−	23.3243i	0.601677	−	1.03282i
$511$	−25.8720	+	31.6350i	−1.14451	+	1.39945i
$512$	0.156434	+	0.987688i	0.00691349	+	0.0436501i
$513$	15.7693	−	24.2826i	0.696233	−	1.07210i
$514$	−5.66347	−	1.20381i	−0.249805	−	0.0530977i
$515$	−2.81481	+	25.8128i	−0.124036	+	1.13745i
$516$	−11.7162	+	6.76438i	−0.515779	+	0.297785i
$517$	3.94722	+	16.4387i	0.173598	+	0.722974i
$518$	−13.0710	+	11.6552i	−0.574308	+	0.512100i
$519$	−21.7817	−	29.9799i	−0.956110	−	1.31597i
$520$	0.971683	−	5.98390i	0.0426111	−	0.262411i
$521$	−13.4218	+	12.0851i	−0.588022	+	0.529457i	−0.908547	−	0.417783i	$-0.862807\pi$
$521$	−13.4218	+	12.0851i	−0.588022	+	0.529457i	0.320525	+	0.947240i	$0.396141\pi$
$522$	−0.900160	−	0.345539i	−0.0393989	−	0.0151238i
$523$	−27.2345	+	22.0541i	−1.19088	+	0.964358i	−0.999852	−	0.0172257i	$-0.994517\pi$
$523$	−27.2345	+	22.0541i	−1.19088	+	0.964358i	−0.191032	+	0.981584i	$0.561183\pi$
$524$	−1.06305	+	3.27172i	−0.0464395	+	0.142926i
$525$	16.9444	+	14.0795i	0.739516	+	0.614480i
$526$	14.3411	−	10.4194i	0.625303	−	0.454309i
$527$	8.20965	−	30.6388i	0.357618	−	1.33465i
$528$	4.38185	−	3.36257i	0.190696	−	0.146337i
$529$	−19.5018	−	11.2594i	−0.847906	−	0.489539i
$530$	3.16137	−	0.488086i	0.137321	−	0.0212011i
$531$	0.0378182	−	0.0122879i	0.00164117	−	0.000533248i
$532$	8.43527	−	11.4928i	0.365715	−	0.498276i
$533$	−19.5061	+	3.08947i	−0.844904	+	0.133820i
$534$	−1.21523	−	0.127726i	−0.0525882	−	0.00552724i
$535$	−11.2745	−	19.7049i	−0.487437	−	0.851919i
$536$	3.02575	+	0.643142i	0.130692	+	0.0277795i
$537$	−40.4106	+	15.5122i	−1.74385	+	0.669400i
$538$	12.8791	+	12.8791i	0.555259	+	0.555259i
$539$	−10.8807	−	20.5088i	−0.468664	−	0.883376i
$540$	11.7429	+	2.54393i	0.505336	+	0.109473i
$541$	9.98647	+	4.44626i	0.429352	+	0.191160i	0.610023	−	0.792384i	$-0.291160\pi$
$541$	9.98647	+	4.44626i	0.429352	+	0.191160i	−0.180671	+	0.983544i	$0.557827\pi$
$542$	−4.94734	+	3.21284i	−0.212507	+	0.138003i
$543$	−4.01444	−	0.210388i	−0.172276	−	0.00902860i
$544$	0.757708	−	7.20911i	0.0324865	−	0.309088i
$545$	0.579532	−	10.2904i	0.0248244	−	0.440793i
$546$	11.8074	−	1.81159i	0.505310	−	0.0775288i
$547$	9.48799	−	18.6212i	0.405677	−	0.796186i	−0.594290	−	0.804251i	$-0.702567\pi$
$547$	9.48799	−	18.6212i	0.405677	−	0.796186i	0.999967	+	0.00806428i	$0.00256697\pi$
$548$	3.72227	−	1.42885i	0.159007	−	0.0610373i
$549$	1.36923	−	2.37157i	0.0584372	−	0.101216i
$550$	−16.5214	−	1.42935i	−0.704475	−	0.0609477i
$551$	−19.8569	+	11.4644i	−0.845932	+	0.488399i
$552$	0.180720	−	1.14102i	0.00769195	−	0.0485651i
$553$	19.9016	−	11.3621i	0.846301	−	0.483167i
$554$	16.3314	+	5.30640i	0.693856	+	0.225447i
$555$	−22.0057	+	11.1046i	−0.934092	+	0.471366i
$556$	−8.23719	−	18.5010i	−0.349335	−	0.784619i
$557$	1.46693	−	27.9907i	0.0621559	−	1.18601i	−0.772420	−	0.635112i	$-0.780954\pi$
$557$	1.46693	−	27.9907i	0.0621559	−	1.18601i	0.834576	−	0.550893i	$-0.185713\pi$
$558$	0.990163	−	0.0518923i	0.0419170	−	0.00219677i
$559$	17.8180	−	12.9455i	0.753621	−	0.547538i
$560$	5.70090	+	1.58106i	0.240907	+	0.0668121i
$561$	−36.9896	+	15.3232i	−1.56170	+	0.646944i
$562$	1.56537	−	5.84202i	0.0660309	−	0.246431i
$563$	−20.2880	+	25.0536i	−0.855036	+	1.05588i	0.142775	+	0.989755i	$0.454397\pi$
$563$	−20.2880	+	25.0536i	−0.855036	+	1.05588i	−0.997811	+	0.0661263i	$0.978936\pi$
$564$	1.76494	−	8.30338i	0.0743173	−	0.349635i
$565$	0.0133980	−	3.43681i	0.000563659	−	0.144588i
$566$	−3.67916	+	5.06393i	−0.154647	+	0.212853i
$567$	2.18151	+	21.7684i	0.0916149	+	0.914186i
$568$	3.84077	+	7.53794i	0.161155	+	0.316285i
$569$	9.49523	+	8.54954i	0.398061	+	0.358416i	0.843717	−	0.536789i	$-0.180363\pi$
$569$	9.49523	+	8.54954i	0.398061	+	0.358416i	−0.445656	+	0.895204i	$0.647029\pi$
$570$	15.6428	−	12.5666i	0.655204	−	0.526358i
$571$	−17.1917	+	29.7768i	−0.719449	+	1.24612i	0.241770	+	0.970334i	$0.422272\pi$
$571$	−17.1917	+	29.7768i	−0.719449	+	1.24612i	−0.961218	+	0.275788i	$0.911061\pi$
$572$	−6.52220	+	6.18979i	−0.272707	+	0.258808i
$573$	15.2422	+	15.2422i	0.636751	+	0.636751i
$574$	−0.915534	−	19.2512i	−0.0382136	−	0.803531i
$575$	−2.71244	+	2.16169i	−0.113116	+	0.0901487i
$576$	0.221639	−	0.0471108i	0.00923495	−	0.00196295i
$577$	14.7439	−	38.4093i	0.613798	−	1.59900i	−0.175151	−	0.984542i	$-0.556041\pi$
$577$	14.7439	−	38.4093i	0.613798	−	1.59900i	0.788949	−	0.614458i	$-0.210625\pi$
$578$	−12.7383	+	33.1845i	−0.529844	+	1.38029i
$579$	−16.7479	+	3.55987i	−0.696018	+	0.147943i
$580$	−7.37120	−	6.01681i	−0.306072	−	0.249834i
$581$	20.5721	−	39.8966i	0.853475	−	1.65519i
$582$	−16.1479	−	16.1479i	−0.669350	−	0.669350i
$583$	−4.16974	−	2.26378i	−0.172693	−	0.0937564i
$584$	−7.72318	+	13.3769i	−0.319588	+	0.553542i
$585$	−1.36556	−	0.148910i	−0.0564589	−	0.00615669i
$586$	−11.9608	−	10.7695i	−0.494096	−	0.444886i
$587$	6.27740	+	12.3201i	0.259096	+	0.508504i	0.983508	−	0.180862i	$-0.0578889\pi$
$587$	6.27740	+	12.3201i	0.259096	+	0.508504i	−0.724413	+	0.689367i	$0.757889\pi$
$588$	0.497423	+	11.6469i	0.0205134	+	0.480309i
$589$	13.8591	−	19.0753i	0.571052	−	0.785986i
$590$	0.392405	+	0.00152975i	0.0161551	+	6.29787e-5i
$591$	−0.658019	+	3.09574i	−0.0270673	+	0.127342i
$592$	−4.16559	+	5.14407i	−0.171205	+	0.211420i
$593$	0.623178	−	2.32573i	0.0255908	−	0.0955063i	−0.951949	−	0.306256i	$-0.900924\pi$
$593$	0.623178	−	2.32573i	0.0255908	−	0.0955063i	0.977540	+	0.210749i	$0.0675904\pi$
$594$	−11.5747	−	13.5512i	−0.474916	−	0.556014i
$595$	−36.9504	−	21.7660i	−1.51482	−	0.892317i
$596$	−8.49644	+	6.17302i	−0.348028	+	0.252857i
$597$	−12.7945	+	0.670531i	−0.523644	+	0.0274430i
$598$	−0.0984277	+	1.87811i	−0.00402501	+	0.0768018i
$599$	−1.54366	−	3.46712i	−0.0630724	−	0.141663i	0.879259	−	0.476344i	$-0.158038\pi$
$599$	−1.54366	−	3.46712i	−0.0630724	−	0.141663i	−0.942332	+	0.334681i	$0.891372\pi$
$600$	7.17852	+	4.21949i	0.293062	+	0.172260i
$601$	6.97654	+	2.26682i	0.284579	+	0.0924653i	0.447828	−	0.894120i	$-0.352198\pi$
$601$	6.97654	+	2.26682i	0.284579	+	0.0924653i	−0.163249	+	0.986585i	$0.552198\pi$
$602$	10.6564	+	18.6654i	0.434322	+	0.760744i
$603$	0.109648	−	0.692292i	0.00446522	−	0.0281923i
$604$	−1.73749	+	1.00314i	−0.0706975	+	0.0408172i
$605$	18.2159	+	16.5282i	0.740580	+	0.671969i
$606$	−1.68728	+	2.92245i	−0.0685409	+	0.118716i
$607$	4.04677	−	1.55341i	0.164253	−	0.0630509i	−0.274852	−	0.961487i	$-0.588629\pi$
$607$	4.04677	−	1.55341i	0.164253	−	0.0630509i	0.439105	+	0.898436i	$0.355296\pi$
$608$	2.44625	−	4.80103i	0.0992085	−	0.194708i
$609$	6.80373	−	17.4712i	0.275701	−	0.707968i
$610$	20.1531	−	18.0041i	0.815974	−	0.728967i
$611$	−1.44454	+	13.7439i	−0.0584397	+	0.556017i
$612$	−1.64026	−	0.0859624i	−0.0663036	−	0.00347483i
$613$	3.40571	−	2.21169i	0.137555	−	0.0893294i	−0.474027	−	0.880510i	$-0.657200\pi$
$613$	3.40571	−	2.21169i	0.137555	−	0.0893294i	0.611582	+	0.791181i	$0.290533\pi$
$614$	−22.5376	−	10.0344i	−0.909544	−	0.404955i
$615$	5.74329	−	26.5114i	0.231592	−	1.06904i
$616$	−5.30837	−	6.98722i	−0.213880	−	0.281523i
$617$	25.7194	+	25.7194i	1.03542	+	1.03542i	0.999349	+	0.0360736i	$0.0114851\pi$
$617$	25.7194	+	25.7194i	1.03542	+	1.03542i	0.0360736	+	0.999349i	$0.488515\pi$
$618$	−18.0541	+	6.93032i	−0.726242	+	0.278778i
$619$	8.50917	+	1.80868i	0.342013	+	0.0726970i	0.375716	−	0.926735i	$-0.377397\pi$
$619$	8.50917	+	1.80868i	0.342013	+	0.0726970i	−0.0337034	+	0.999432i	$0.510730\pi$
$620$	9.44132	+	2.56928i	0.379173	+	0.103185i
$621$	−3.70708	−	0.389630i	−0.148760	−	0.0156353i
$622$	−13.9000	+	2.20155i	−0.557341	+	0.0882741i
$623$	−0.212257	+	1.92963i	−0.00850391	+	0.0773092i
$624$	4.29402	−	1.39521i	0.171898	−	0.0558532i
$625$	−7.35374	−	23.8940i	−0.294150	−	0.955759i
$626$	1.74119	+	1.00528i	0.0695921	+	0.0401790i
$627$	−29.7514	+	0.780154i	−1.18816	+	0.0311563i
$628$	6.03571	−	22.5256i	0.240851	−	0.898868i
$629$	38.8177	−	28.2027i	1.54776	−	1.12452i
$630$	0.290156	−	1.30875i	0.0115601	−	0.0521417i
$631$	1.22732	−	3.77729i	0.0488587	−	0.150371i	−0.923651	−	0.383236i	$-0.874810\pi$
$631$	1.22732	−	3.77729i	0.0488587	−	0.150371i	0.972509	+	0.232864i	$0.0748097\pi$
$632$	6.73138	−	5.45096i	0.267760	−	0.216828i
$633$	−8.62923	−	3.31245i	−0.342981	−	0.131658i
$634$	−1.71535	+	1.54451i	−0.0681254	+	0.0613404i
$635$	27.0240	−	19.4736i	1.07242	−	0.772787i
$636$	1.40033	+	1.92739i	0.0555267	+	0.0764260i
$637$	−2.78727	−	18.7721i	−0.110436	−	0.743779i
$638$	3.29514	+	13.7231i	0.130456	+	0.543301i
$639$	1.66014	−	0.958481i	0.0656740	−	0.0379169i
$640$	2.22289	+	0.242400i	0.0878675	+	0.00958171i
$641$	−23.0300	−	4.89518i	−0.909630	−	0.193348i	−0.270746	−	0.962651i	$-0.587270\pi$
$641$	−23.0300	−	4.89518i	−0.909630	−	0.193348i	−0.638884	+	0.769303i	$0.720604\pi$
$642$	9.20878	−	14.1803i	0.363442	−	0.559651i
$643$	−5.57033	−	35.1697i	−0.219673	−	1.38696i	−0.813125	−	0.582089i	$-0.802236\pi$
$643$	−5.57033	−	35.1697i	−0.219673	−	1.38696i	0.593453	−	0.804869i	$-0.297764\pi$
$644$	−1.81133	−	0.295878i	−0.0713764	−	0.0116592i
$645$	7.71562	+	29.2507i	0.303802	+	1.15175i
$646$	−26.1356	+	29.0265i	−1.02829	+	1.14203i
$647$	−5.01282	−	4.05930i	−0.197074	−	0.159588i	0.525704	−	0.850668i	$-0.323802\pi$
$647$	−5.01282	−	4.05930i	−0.197074	−	0.159588i	−0.722778	+	0.691080i	$0.757135\pi$
$648$	2.14015	+	7.98713i	0.0840728	+	0.313764i
$649$	−0.461773	−	0.354304i	−0.0181262	−	0.0139076i
$650$	−12.3403	−	5.60997i	−0.484028	−	0.220041i
$651$	0.915888	+	19.2587i	0.0358965	+	0.754807i
$652$	4.10510	−	8.05671i	0.160768	−	0.315525i
$653$	−24.0548	+	37.0412i	−0.941339	+	1.44953i	−0.0486733	+	0.998815i	$0.515499\pi$
$653$	−24.0548	+	37.0412i	−0.941339	+	1.44953i	−0.892665	+	0.450720i	$0.851167\pi$
$654$	7.01249	−	3.12216i	0.274210	−	0.122086i
$655$	6.43491	+	4.21464i	0.251433	+	0.164679i
$656$	−1.51453	−	7.12532i	−0.0591326	−	0.278197i
$657$	3.11852	+	1.58897i	0.121665	+	0.0619914i
$658$	−13.1779	−	2.86775i	−0.513727	−	0.111797i
$659$			23.9051i			0.931212i	0.884992	+	0.465606i	$0.154164\pi$
$659$			23.9051i			0.931212i	−0.884992	+	0.465606i	$0.845836\pi$
$660$	−4.68227	−	11.4286i	−0.182257	−	0.444859i
$661$	33.3740	+	19.2685i	1.29810	+	0.749457i	0.980075	−	0.198626i	$-0.0636478\pi$
$661$	33.3740	+	19.2685i	1.29810	+	0.749457i	0.318023	+	0.948083i	$0.396981\pi$
$662$	−5.13331	+	6.33911i	−0.199512	+	0.246377i
$663$	−32.6836	+	1.71287i	−1.26932	+	0.0665224i
$664$	5.24283	−	16.1358i	0.203461	−	0.626189i
$665$	−19.8441	−	24.9480i	−0.769522	−	0.967442i
$666$	1.21340	+	0.881586i	0.0470183	+	0.0341608i
$667$	2.47563	+	1.60769i	0.0958566	+	0.0622500i
$668$	−9.54928	−	14.7046i	−0.369473	−	0.568938i
$669$	9.48342	−	0.996748i	0.366650	−	0.0385365i
$670$	3.16422	−	6.15074i	0.122245	−	0.237624i
$671$	−39.9594	+	3.14634i	−1.54261	+	0.121463i
$672$	0.895219	+	4.31421i	0.0345338	+	0.166424i
$673$	7.33570	−	46.3158i	0.282771	−	1.78534i	−0.281303	−	0.959619i	$-0.590767\pi$
$673$	7.33570	−	46.3158i	0.282771	−	1.78534i	0.564074	−	0.825724i	$-0.309233\pi$
$674$	7.30018	+	6.57311i	0.281193	+	0.253187i
$675$	12.3837	−	23.8429i	0.476648	−	0.917715i
$676$	5.16132	−	2.29797i	0.198512	−	0.0883833i
$677$	−16.8201	−	20.7711i	−0.646448	−	0.798297i	0.343586	−	0.939121i	$-0.388358\pi$
$677$	−16.8201	−	20.7711i	−0.646448	−	0.798297i	−0.990035	+	0.140824i	$0.955025\pi$
$678$	2.28067	−	1.16206i	0.0875885	−	0.0446285i
$679$	−25.7779	+	25.5297i	−0.989266	+	0.979739i
$680$	−15.1095	−	5.86768i	−0.579423	−	0.225015i
$681$	4.82694	+	8.36050i	0.184969	+	0.320375i
$682$	−8.83538	−	11.5136i	−0.338324	−	0.440879i
$683$	−1.83982	−	6.86629i	−0.0703987	−	0.262731i	0.921752	−	0.387780i	$-0.126758\pi$
$683$	−1.83982	−	6.86629i	−0.0703987	−	0.262731i	−0.992151	+	0.125049i	$0.960091\pi$
$684$	−1.11539	−	0.496602i	−0.0426478	−	0.0189880i
$685$	−0.897342	−	8.87013i	−0.0342857	−	0.338910i
$686$	18.5070	−	0.700718i	0.706600	−	0.0267535i
$687$	−3.66126	−	23.1163i	−0.139686	−	0.881942i
$688$	5.11237	+	6.31326i	0.194907	+	0.240691i
$689$	−2.59517	−	2.88223i	−0.0988683	−	0.109804i
$690$	−2.35576	−	1.05988i	−0.0896823	−	0.0403488i
$691$	−5.02352	+	11.2830i	−0.191104	+	0.429226i	−0.983531	−	0.180741i	$-0.942151\pi$
$691$	−5.02352	+	11.2830i	−0.191104	+	0.429226i	0.792427	+	0.609967i	$0.208817\pi$
$692$	−15.7344	+	15.7344i	−0.598133	+	0.598133i
$693$	−1.51812	+	1.28404i	−0.0576684	+	0.0487765i
$694$		−	12.2926i		−	0.466623i
$695$	−44.7544	+	6.90966i	−1.69763	+	0.262098i
$696$	1.47337	−	6.93168i	0.0558481	−	0.262744i
$697$	−2.76355	+	52.7317i	−0.104677	+	1.99736i
$698$	26.3580	−	21.3443i	0.997666	−	0.807894i
$699$	−39.5054	−	28.7023i	−1.49423	−	1.08562i
$700$	6.75860	−	11.3720i	0.255451	−	0.429819i
$701$	2.77017	+	8.52572i	0.104628	+	0.322012i	0.989643	−	0.143551i	$-0.0458520\pi$
$701$	2.77017	+	8.52572i	0.104628	+	0.322012i	−0.885015	+	0.465563i	$0.845852\pi$
$702$	−5.22072	−	13.6004i	−0.197043	−	0.513316i
$703$	34.4510	−	9.23112i	1.29935	−	0.348158i
$704$	−2.40588	−	2.28293i	−0.0906749	−	0.0860410i
$705$	−16.8791	−	8.68339i	−0.635704	−	0.327035i
$706$	−6.29199	−	8.66019i	−0.236802	−	0.325930i
$707$	4.62987	+	2.70301i	0.174124	+	0.101657i
$708$	0.132680	+	0.260400i	0.00498644	+	0.00978643i
$709$	−25.3497	−	2.66436i	−0.952029	−	0.100062i	−0.384237	−	0.923234i	$-0.625536\pi$
$709$	−25.3497	−	2.66436i	−0.952029	−	0.100062i	−0.567792	+	0.823172i	$0.692202\pi$
$710$	18.5190	−	3.86094i	0.695006	−	0.144899i
$711$	−1.31327	−	1.45853i	−0.0492514	−	0.0546992i
$712$	0.0384006	+	0.732727i	0.00143912	+	0.0274601i
$713$	−2.99811	−	0.474854i	−0.112280	−	0.0177834i
$714$	1.82587	−	31.8869i	0.0683316	−	1.19334i
$715$	9.52558	+	17.7067i	0.356237	+	0.662192i
$716$	12.9959	+	22.5096i	0.485680	+	0.841222i
$717$	−12.1633	−	9.84962i	−0.454245	−	0.367841i
$718$	−13.1901	+	8.56578i	−0.492252	+	0.319672i
$719$	6.85845	−	1.45781i	0.255777	−	0.0543670i	−0.0782385	−	0.996935i	$-0.524930\pi$
$719$	6.85845	−	1.45781i	0.255777	−	0.0543670i	0.334015	+	0.942568i	$0.391596\pi$
$720$	0.0284894	−	0.505870i	0.00106174	−	0.0188527i
$721$	10.8713	+	28.7355i	0.404868	+	1.07017i
$722$	−8.94039	+	4.55536i	−0.332727	+	0.169533i
$723$	0.462951	+	8.83364i	0.0172173	+	0.328527i
$724$	0.252318	+	2.40064i	0.00937731	+	0.0892192i
$725$	−17.3099	+	12.3713i	−0.642873	+	0.459460i
$726$	−4.73999	+	17.6951i	−0.175918	+	0.656725i
$727$	17.6537	−	17.6537i	0.654740	−	0.654740i	−0.299391	−	0.954131i	$-0.596783\pi$
$727$	17.6537	−	17.6537i	0.654740	−	0.654740i	0.954131	+	0.299391i	$0.0967834\pi$
$728$	−2.18354	−	6.83255i	−0.0809273	−	0.253231i
$729$	27.3140	−	8.87485i	1.01163	−	0.328698i
$730$	24.3275	+	24.5179i	0.900400	+	0.907447i
$731$	−23.9514	−	53.7958i	−0.885875	−	1.98971i
$732$	18.7898	+	7.21274i	0.694492	+	0.266591i
$733$	−15.1267	−	9.82337i	−0.558716	−	0.362834i	0.234178	−	0.972194i	$-0.424760\pi$
$733$	−15.1267	−	9.82337i	−0.558716	−	0.362834i	−0.792894	+	0.609359i	$0.791427\pi$
$734$	5.80977	+	17.8806i	0.214443	+	0.659986i
$735$	25.4214	+	5.76525i	0.937682	+	0.212654i
$736$	−0.693692			−0.0255698
$737$	−9.25988	+	4.41715i	−0.341092	+	0.162708i
$738$	−1.59436	+	0.427206i	−0.0586891	+	0.0157257i
$739$	−31.4141	+	3.30175i	−1.15559	+	0.121457i	−0.662871	−	0.748734i	$-0.730662\pi$
$739$	−31.4141	+	3.30175i	−1.15559	+	0.121457i	−0.492715	+	0.870191i	$0.663996\pi$
$740$	8.65304	+	12.0080i	0.318092	+	0.441425i
$741$	−23.1376	−	7.51785i	−0.849980	−	0.276175i
$742$	3.07277	−	2.20986i	0.112805	−	0.0811267i
$743$	−0.935777	+	0.148212i	−0.0343303	+	0.00543739i	−0.173576	−	0.984820i	$-0.555532\pi$
$743$	−0.935777	+	0.148212i	−0.0343303	+	0.00543739i	0.139246	+	0.990258i	$0.455532\pi$
$744$	1.51512	+	7.12808i	0.0555470	+	0.261328i
$745$	8.33023	+	21.9564i	0.305196	+	0.804422i
$746$	−0.152919	−	1.45493i	−0.00559878	−	0.0532688i
$747$	−3.71337	−	0.994995i	−0.135865	−	0.0364050i
$748$	12.5625	+	20.4984i	0.459329	+	0.749495i
$749$	−22.4572	−	14.7388i	−0.820567	−	0.538545i
$750$	13.3189	−	13.0109i	0.486336	−	0.475092i
$751$	29.7961	−	33.0919i	1.08727	−	1.20754i	0.110363	−	0.993891i	$-0.464799\pi$
$751$	29.7961	−	33.0919i	1.08727	−	1.20754i	0.976911	−	0.213648i	$-0.0685347\pi$
$752$	−5.09035	−	0.266774i	−0.185626	−	0.00972825i
$753$	−5.54656	+	14.4493i	−0.202128	+	0.526561i
$754$	−1.20590	+	11.4734i	−0.0439164	+	0.417836i
$755$	1.14421	+	4.33781i	0.0416420	+	0.157869i
$756$	13.7500	−	3.61307i	0.500081	−	0.131406i
$757$	19.8886	+	3.15005i	0.722864	+	0.114490i	0.507016	−	0.861937i	$-0.330748\pi$
$757$	19.8886	+	3.15005i	0.722864	+	0.114490i	0.215848	+	0.976427i	$0.430748\pi$
$758$	13.7369	+	3.68080i	0.498948	+	0.133693i
$759$	1.82836	+	3.36713i	0.0663653	+	0.122219i
$760$	−8.92240	−	8.09697i	−0.323650	−	0.293708i
$761$	−0.442409	+	0.993667i	−0.0160373	+	0.0360204i	−0.921387	−	0.388647i	$-0.872942\pi$
$761$	−0.442409	+	0.993667i	−0.0160373	+	0.0360204i	0.905349	+	0.424668i	$0.139609\pi$
$762$	22.1040	+	11.2625i	0.800743	+	0.407999i
$763$	−4.90622	−	11.1646i	−0.177617	−	0.404186i
$764$	7.60805	−	10.4716i	0.275250	−	0.378849i
$765$	−1.14856	+	3.48856i	−0.0415261	+	0.126129i
$766$	−8.53892	+	7.68848i	−0.308524	+	0.277796i
$767$	−0.259127	−	0.399020i	−0.00935653	−	0.0144078i
$768$	0.596810	+	1.55474i	0.0215355	+	0.0561020i
$769$	36.9221			1.33145			0.665723	−	0.746199i	$-0.268123\pi$
$769$	36.9221			1.33145			0.665723	+	0.746199i	$0.268123\pi$
$770$	−18.1925	+	7.35079i	−0.655611	+	0.264904i
$771$	−9.64240			−0.347263
$772$	3.68449	+	9.59843i	0.132608	+	0.345455i
$773$	2.00423	+	3.08625i	0.0720873	+	0.111005i	0.872876	−	0.487943i	$-0.162253\pi$
$773$	2.00423	+	3.08625i	0.0720873	+	0.111005i	−0.800788	+	0.598947i	$0.795586\pi$
$774$	1.36794	−	1.23169i	0.0491694	−	0.0442723i
$775$	11.0870	−	18.8621i	0.398256	−	0.677545i
$776$	−8.06012	+	11.0938i	−0.289341	+	0.398244i
$777$	−17.2567	+	23.5117i	−0.619080	+	0.843477i
$778$	5.42716	+	2.76527i	0.194573	+	0.0991399i
$779$	−15.9649	+	35.8578i	−0.572003	+	1.28474i
$780$	−0.489068	−	10.0840i	−0.0175115	−	0.361065i
$781$	−25.3259	−	12.0787i	−0.906230	−	0.432209i
$782$	4.85711	+	1.30146i	0.173690	+	0.0465400i
$783$	−22.5838	−	3.57693i	−0.807080	−	0.127829i
$784$	6.86080	−	1.38906i	0.245028	−	0.0496091i
$785$	−45.0573	−	26.2486i	−1.60817	−	0.936853i
$786$	−0.598842	+	5.69760i	−0.0213600	+	0.203227i
$787$	−15.1199	+	39.3888i	−0.538967	+	1.40406i	0.345925	+	0.938262i	$0.387565\pi$
$787$	−15.1199	+	39.3888i	−0.538967	+	1.40406i	−0.884892	+	0.465795i	$0.845768\pi$
$788$	1.89783	+	0.0994610i	0.0676074	+	0.00354315i
$789$	19.7535	−	21.9385i	0.703243	−	0.781030i
$790$	−7.80867	−	17.7242i	−0.277820	−	0.630598i
$791$	−1.82861	−	3.63219i	−0.0650178	−	0.129146i
$792$	−0.488049	+	0.571474i	−0.0173421	+	0.0203065i
$793$	−31.6489	−	8.48030i	−1.12389	−	0.301144i
$794$	2.37994	+	22.6436i	0.0844610	+	0.803593i
$795$	4.98075	−	1.88969i	0.176649	−	0.0670203i
$796$	1.59952	+	7.52517i	0.0566936	+	0.266723i
$797$	12.7877	−	2.02537i	0.452963	−	0.0717424i	0.0742155	−	0.997242i	$-0.476355\pi$
$797$	12.7877	−	2.02537i	0.452963	−	0.0717424i	0.378748	+	0.925500i	$0.376355\pi$
$798$	9.76140	−	21.6420i	0.345550	−	0.766120i
$799$	35.1412	+	11.4181i	1.24321	+	0.403943i
$800$	1.82818	−	4.65379i	0.0646359	−	0.164536i
$801$	0.165346	−	0.0173785i	0.00584221	−	0.000614041i
$802$	8.92455	−	2.39133i	0.315137	−	0.0844406i
$803$	−6.68868	−	50.7913i	−0.236038	−	1.79239i
$804$	5.15152			0.181680
$805$	−1.70191	+	3.73441i	−0.0599846	+	0.131621i
$806$	−3.66601	−	11.2828i	−0.129130	−	0.397421i
$807$	25.4390	+	16.5203i	0.895496	+	0.581542i
$808$	1.89174	+	0.726170i	0.0665511	+	0.0255466i
$809$	8.48796	+	19.0643i	0.298421	+	0.670264i	0.999064	−	0.0432476i	$-0.0137704\pi$
$809$	8.48796	+	19.0643i	0.298421	+	0.670264i	−0.700644	+	0.713511i	$0.747104\pi$
$810$	18.4897	+	0.0720798i	0.649660	+	0.00253263i
$811$	34.7635	−	11.2954i	1.22071	−	0.396633i	0.373371	−	0.927682i	$-0.378202\pi$
$811$	34.7635	−	11.2954i	1.22071	−	0.396633i	0.847341	+	0.531049i	$0.178202\pi$
$812$	−11.0009	−	2.39400i	−0.386056	−	0.0840131i
$813$	−6.94661	+	6.94661i	−0.243628	+	0.243628i
$814$	0.573872	−	21.9459i	0.0201142	−	0.769202i
$815$	−14.9729	−	13.5877i	−0.524477	−	0.475956i
$816$	−1.26185	−	12.0057i	−0.0441737	−	0.420285i
$817$	−2.29089	−	43.7128i	−0.0801482	−	1.52932i
$818$	19.5305	−	9.95127i	0.682866	−	0.347938i
$819$	−1.52017	+	0.575117i	−0.0531192	+	0.0200962i
$820$	−16.2629	−	0.915888i	−0.567925	−	0.0319842i
$821$	31.1099	−	6.61261i	1.08574	−	0.230782i	0.369920	−	0.929064i	$-0.379385\pi$
$821$	31.1099	−	6.61261i	1.08574	−	0.230782i	0.715823	+	0.698282i	$0.246052\pi$
$822$	5.56871	−	3.61636i	0.194231	−	0.126135i
$823$	27.5332	+	22.2959i	0.959747	+	0.777188i	0.974888	−	0.222698i	$-0.0714863\pi$
$823$	27.5332	+	22.2959i	0.959747	+	0.777188i	−0.0151406	+	0.999885i	$0.504820\pi$
$824$	5.80613	+	10.0565i	0.202266	+	0.350335i
$825$	−27.4077	+	3.39213i	−0.954213	+	0.118099i
$826$	0.414713	−	0.208785i	0.0144297	−	0.00726457i
$827$	−0.136413	−	0.0216057i	−0.00474355	−	0.000751304i	0.154062	−	0.988061i	$-0.450764\pi$
$827$	−0.136413	−	0.0216057i	−0.00474355	−	0.000751304i	−0.158806	+	0.987310i	$0.550764\pi$
$828$	0.00822637	+	0.156968i	0.000285886	+	0.00545503i
$829$	15.6611	+	17.3935i	0.543934	+	0.604100i	0.950959	−	0.309317i	$-0.100100\pi$
$829$	15.6611	+	17.3935i	0.543934	+	0.604100i	−0.407025	+	0.913417i	$0.633434\pi$
$830$	−31.7363	−	20.7861i	−1.10158	−	0.721496i
$831$	28.4406	+	2.98923i	0.986594	+	0.103695i
$832$	−1.23083	−	2.41564i	−0.0426713	−	0.0837471i
$833$	−50.6441	−	3.14584i	−1.75471	−	0.108997i
$834$	−19.8240	−	27.2854i	−0.686449	−	0.944817i
$835$	−37.3336	+	11.9697i	−1.29198	+	0.414229i
$836$	3.25738	+	17.5717i	0.112659	+	0.607729i
$837$	22.7120	−	6.08567i	0.785042	−	0.210351i
$838$	−2.69947	−	7.03236i	−0.0932516	−	0.242929i
$839$	5.07481	+	15.6186i	0.175202	+	0.539216i	0.999643	−	0.0267325i	$-0.00851024\pi$
$839$	5.07481	+	15.6186i	0.175202	+	0.539216i	−0.824441	+	0.565948i	$0.808510\pi$
$840$	9.83399	+	0.601574i	0.339305	+	0.0207563i
$841$	−8.81238	−	6.40257i	−0.303875	−	0.220778i
$842$	−14.5308	+	11.7668i	−0.500765	+	0.405511i
$843$	0.527141	−	10.0584i	0.0181557	−	0.346431i
$844$	−1.15396	+	5.42897i	−0.0397211	+	0.186873i
$845$	−1.92762	−	12.4853i	−0.0663121	−	0.429508i
$846$			1.15501i			0.0397100i
$847$	28.0754	+	7.66636i	0.964681	+	0.263419i
$848$	1.01156	−	1.01156i	0.0347370	−	0.0347370i
$849$	−4.23985	+	9.52286i	−0.145511	+	0.326824i
$850$	−21.5317	+	29.1551i	−0.738532	+	1.00001i
$851$	−3.07243	−	3.41228i	−0.105322	−	0.116972i
$852$	8.86647	+	10.9492i	0.303760	+	0.375113i
$853$	−4.43445	−	27.9980i	−0.151833	−	0.958635i	−0.939504	−	0.342538i	$-0.888713\pi$
$853$	−4.43445	−	27.9980i	−0.151833	−	0.958635i	0.787671	−	0.616096i	$-0.211287\pi$
$854$	11.6032	−	29.7956i	0.397053	−	1.01959i
$855$	−1.72637	+	2.11498i	−0.0590407	+	0.0723308i
$856$	−9.27506	−	4.12952i	−0.317015	−	0.141144i
$857$	9.64137	+	35.9821i	0.329343	+	1.22912i	0.909873	+	0.414886i	$0.136178\pi$
$857$	9.64137	+	35.9821i	0.329343	+	1.22912i	−0.580531	+	0.814238i	$0.697155\pi$
$858$	−8.48123	+	12.3412i	−0.289544	+	0.421323i
$859$	−21.8642	−	37.8700i	−0.745998	−	1.29211i	−0.949727	−	0.313079i	$-0.898640\pi$
$859$	−21.8642	−	37.8700i	−0.745998	−	1.29211i	0.203729	−	0.979027i	$-0.434694\pi$
$860$	16.6232	−	7.32363i	0.566848	−	0.249734i
$861$	−8.15705	−	31.0426i	−0.277992	−	1.05793i
$862$	7.30122	−	3.72016i	0.248681	−	0.126709i
$863$	20.5915	+	25.4284i	0.700942	+	0.865592i	0.995951	−	0.0899030i	$-0.0286557\pi$
$863$	20.5915	+	25.4284i	0.700942	+	0.865592i	−0.295008	+	0.955495i	$0.595322\pi$
$864$	4.90886	−	2.18557i	0.167003	−	0.0743545i
$865$	24.7101	+	43.1872i	0.840170	+	1.46841i
$866$	−12.6931	−	11.4289i	−0.431330	−	0.388371i
$867$	−9.26024	+	58.4669i	−0.314494	+	1.98564i
$868$	11.3359	−	2.35225i	0.384765	−	0.0798406i
$869$	−6.70528	+	27.9340i	−0.227461	+	0.947596i
$870$	−14.0907	−	7.24891i	−0.477720	−	0.245761i
$871$	−8.34052	+	0.876624i	−0.282608	+	0.0297033i
$872$	−2.51041	−	3.86569i	−0.0850131	−	0.130909i
$873$	2.60589	+	1.69228i	0.0881959	+	0.0572751i
$874$	3.02397	+	2.19705i	0.102287	+	0.0743162i
$875$	−20.5678	−	21.2595i	−0.695320	−	0.718701i
$876$	−7.94906	+	24.4647i	−0.268574	+	0.826585i
$877$	45.7495	−	2.39763i	1.54485	−	0.0809621i	0.739253	−	0.673427i	$-0.235179\pi$
$877$	45.7495	−	2.39763i	1.54485	−	0.0809621i	0.805596	+	0.592465i	$0.201845\pi$
$878$	25.4849	−	31.4713i	0.860075	−	1.06210i
$879$	−23.2126	−	13.4018i	−0.782942	−	0.452032i
$880$	−6.33827	+	3.85050i	−0.213663	+	0.129800i
$881$		−	1.24914i		−	0.0420847i	−0.999779	−	0.0210423i	$-0.993302\pi$
$881$		−	1.24914i		−	0.0420847i	0.999779	−	0.0210423i	$-0.00669848\pi$
$882$	−0.395676	−	1.53599i	−0.0133231	−	0.0517194i
$883$	10.6651	+	5.43416i	0.358910	+	0.182874i	0.624142	−	0.781311i	$-0.285449\pi$
$883$	10.6651	+	5.43416i	0.358910	+	0.182874i	−0.265232	+	0.964185i	$0.585449\pi$
$884$	4.08598	+	19.2230i	0.137427	+	0.646541i
$885$	0.639743	−	0.133377i	0.0215047	−	0.00448342i
$886$	32.0634	−	14.2755i	1.07719	−	0.479596i
$887$	−24.8811	+	38.3135i	−0.835425	+	1.28644i	0.120465	+	0.992718i	$0.461562\pi$
$887$	−24.8811	+	38.3135i	−0.835425	+	1.28644i	−0.955890	+	0.293725i	$0.905105\pi$
$888$	−5.00447	+	9.82183i	−0.167939	+	0.329599i
$889$	18.0625	−	35.0296i	0.605797	−	1.17486i
$890$	1.60348	+	0.347369i	0.0537488	+	0.0116438i
$891$	−21.7582	−	16.6944i	−0.728926	−	0.559282i
$892$	−1.48197	−	5.53079i	−0.0496201	−	0.185185i
$893$	21.3452	+	17.2850i	0.714289	+	0.578420i
$894$	−11.7030	+	12.9975i	−0.391407	+	0.434701i
$895$	56.1973	−	14.8235i	1.87847	−	0.495494i
$896$	2.47458	−	0.936190i	0.0826699	−	0.0312759i
$897$	0.489956	+	3.09346i	0.0163591	+	0.103288i
$898$	7.20989	−	11.1023i	0.240597	−	0.370487i
$899$	−18.2135	−	3.87139i	−0.607453	−	0.129118i
$900$	−1.07474	−	0.358492i	−0.0358246	−	0.0119497i
$901$	−8.98055	+	5.18492i	−0.299185	+	0.172735i
$902$	18.3720	+	15.6900i	0.611720	+	0.522419i
$903$	23.8217	+	26.7155i	0.792736	+	0.889036i
$904$	−0.903426	−	1.24346i	−0.0300475	−	0.0413568i
$905$	5.32778	+	0.865142i	0.177101	+	0.0287583i
$906$	−2.48297	+	2.23568i	−0.0824913	+	0.0742755i
$907$	−22.3084	−	8.56339i	−0.740738	−	0.284343i	−0.0414087	−	0.999142i	$-0.513185\pi$
$907$	−22.3084	−	8.56339i	−0.740738	−	0.284343i	−0.699329	+	0.714800i	$0.746518\pi$
$908$	4.50502	−	3.64810i	0.149504	−	0.121066i
$909$	0.141884	−	0.436674i	0.00470599	−	0.0144836i
$910$	−16.0240	+	0.699459i	−0.531191	+	0.0231868i
$911$	−34.9432	+	25.3877i	−1.15772	+	0.841133i	−0.989488	−	0.144614i	$-0.953806\pi$
$911$	−34.9432	+	25.3877i	−1.15772	+	0.841133i	−0.168233	+	0.985747i	$0.553806\pi$
$912$	2.32251	−	8.66771i	0.0769059	−	0.287017i
$913$	18.7854	+	53.0421i	0.621705	+	1.75544i
$914$	33.1693	+	19.1503i	1.09714	+	0.633436i
$915$	26.5947	−	36.3060i	0.879195	−	1.20024i
$916$	−13.3659	+	4.34284i	−0.441621	+	0.143491i
$917$	9.04707	+	0.995166i	0.298760	+	0.0328633i
$918$	−38.4714	+	6.09327i	−1.26975	+	0.201108i
$919$	55.6682	+	5.85096i	1.83632	+	0.193005i	0.958329	−	0.285665i	$-0.0922145\pi$
$919$	55.6682	+	5.85096i	1.83632	+	0.193005i	0.877995	+	0.478671i	$0.158881\pi$
$920$	−0.407303	+	1.49671i	−0.0134284	+	0.0493451i
$921$	−40.1873	−	8.54208i	−1.32422	−	0.281471i
$922$	−5.34930	+	2.05340i	−0.176170	+	0.0676252i
$923$	−16.2184	−	16.2184i	−0.533835	−	0.533835i
$924$	−11.0664	−	9.54392i	−0.364059	−	0.313972i
$925$	30.9893	−	11.6193i	1.01892	−	0.382039i
$926$	−7.01049	−	3.12127i	−0.230379	−	0.102571i
$927$	2.20673	−	1.43307i	0.0724786	−	0.0470681i
$928$	−4.24944	−	0.222703i	−0.139495	−	0.00731060i
$929$	−2.52964	+	24.0679i	−0.0829948	+	0.789643i	0.871295	+	0.490760i	$0.163281\pi$
$929$	−2.52964	+	24.0679i	−0.0829948	+	0.789643i	−0.954290	+	0.298883i	$0.903386\pi$
$930$	16.2692	+	0.916242i	0.533487	+	0.0300448i
$931$	−34.3073	−	15.6741i	−1.12438	−	0.513699i
$932$	−13.3118	+	26.1260i	−0.436044	+	0.855784i
$933$	−21.8804	+	8.39909i	−0.716332	+	0.274974i
$934$	17.4020	−	30.1412i	0.569411	−	0.986249i
$935$	51.6035	−	15.0691i	1.68761	−	0.492813i
$936$	−0.532013	+	0.307158i	−0.0173894	+	0.0100398i
$937$	4.13462	−	26.1050i	0.135072	−	0.852812i	−0.823366	−	0.567511i	$-0.807907\pi$
$937$	4.13462	−	26.1050i	0.135072	−	0.852812i	0.958438	−	0.285301i	$-0.0920935\pi$
$938$	0.0395995	−	8.18412i	0.00129297	−	0.267221i
$939$	3.18442	+	1.03468i	0.103920	+	0.0337655i
$940$	−3.56441	+	10.8263i	−0.116258	+	0.353116i
$941$	−20.5587	−	46.1755i	−0.670193	−	1.50528i	−0.852880	−	0.522108i	$-0.825146\pi$
$941$	−20.5587	−	46.1755i	−0.670193	−	1.50528i	0.182686	−	0.983171i	$-0.441521\pi$
$942$	2.03254	−	38.7832i	0.0662237	−	1.26362i
$943$	5.04628	−	0.264464i	0.164329	−	0.00861214i
$944$	0.141975	−	0.103151i	0.00462088	−	0.00335727i
$945$	0.277739	−	31.7884i	0.00903486	−	1.03408i
$946$	−26.1989	−	6.28878i	−0.851798	−	0.204466i
$947$	5.86545	−	21.8901i	0.190601	−	0.711334i	−0.802760	−	0.596302i	$-0.796636\pi$
$947$	5.86545	−	21.8901i	0.190601	−	0.711334i	0.993362	−	0.115032i	$-0.0366972\pi$
$948$	9.07779	−	11.2101i	0.294833	−	0.364088i
$949$	8.70675	−	40.9620i	0.282633	−	1.32968i
$950$	−22.7089	+	14.4968i	−0.736773	+	0.470340i
$951$	−2.25947	+	3.10989i	−0.0732682	+	0.100845i
$952$	−19.0830	+	1.91240i	−0.618483	+	0.0619811i
$953$	8.21636	+	16.1255i	0.266154	+	0.522357i	0.984945	−	0.172870i	$-0.0553040\pi$
$953$	8.21636	+	16.1255i	0.266154	+	0.522357i	−0.718791	+	0.695227i	$0.755304\pi$
$954$	−0.240891	−	0.216899i	−0.00779912	−	0.00702236i
$955$	−18.1264	−	22.5636i	−0.586558	−	0.730140i
$956$	−4.69905	+	8.13900i	−0.151978	+	0.263234i
$957$	10.1192	+	21.2134i	0.327108	+	0.685733i
$958$	−18.7815	−	18.7815i	−0.606802	−	0.606802i
$959$	−5.70244	−	8.87471i	−0.184141	−	0.286579i
$960$	3.70494	−	0.374808i	0.119576	−	0.0120969i
$961$	−11.5931	+	2.46418i	−0.373970	+	0.0794897i
$962$	6.43109	−	16.7536i	0.207347	−	0.540156i
$963$	−0.824436	+	2.14773i	−0.0265671	+	0.0692096i
$964$	5.19556	−	1.10435i	0.167338	−	0.0355687i
$965$	22.8730	−	2.31393i	0.736306	−	0.0744880i
$966$	−3.05304	+	0.145194i	−0.0982299	+	0.00467153i
$967$	18.8577	+	18.8577i	0.606424	+	0.606424i	0.942010	−	0.335586i	$-0.108934\pi$
$967$	18.8577	+	18.8577i	0.606424	+	0.606424i	−0.335586	+	0.942010i	$0.608934\pi$
$968$	10.9398	+	1.14902i	0.351619	+	0.0369308i
$969$	−32.5235	+	56.3324i	−1.04481	+	1.80966i
$970$	19.2035	+	23.9043i	0.616587	+	0.767521i
$971$	9.95001	+	8.95903i	0.319311	+	0.287509i	0.813162	−	0.582038i	$-0.197744\pi$
$971$	9.95001	+	8.95903i	0.319311	+	0.287509i	−0.493851	+	0.869547i	$0.664411\pi$
$972$	−1.06671	−	2.09353i	−0.0342147	−	0.0671501i
$973$	−43.5002	+	31.2843i	−1.39455	+	1.00293i
$974$	0.726742	−	1.00027i	0.0232863	−	0.0320508i
$975$	−22.0444	−	4.86563i	−0.705986	−	0.155825i
$976$	2.51272	−	11.8214i	0.0804301	−	0.378394i
$977$	36.9436	−	45.6216i	1.18193	−	1.45956i	0.323807	−	0.946123i	$-0.395037\pi$
$977$	36.9436	−	45.6216i	1.18193	−	1.45956i	0.858125	−	0.513442i	$-0.171630\pi$
$978$	3.89745	−	14.5455i	0.124627	−	0.465113i
$979$	−1.58051	−	1.85040i	−0.0505133	−	0.0591391i
$980$	1.03130	−	15.6185i	0.0329438	−	0.498914i
$981$	−0.844956	+	0.613897i	−0.0269774	+	0.0196002i
$982$	−22.3694	+	1.17233i	−0.713835	+	0.0374105i
$983$	−0.640708	+	12.2254i	−0.0204354	+	0.389931i	0.969195	+	0.246294i	$0.0792130\pi$
$983$	−0.640708	+	12.2254i	−0.0204354	+	0.389931i	−0.989630	+	0.143637i	$0.954120\pi$
$984$	−4.93424	−	11.0825i	−0.157298	−	0.353297i
$985$	1.32891	−	4.03636i	0.0423427	−	0.128609i
$986$	29.3360	+	9.53183i	0.934247	+	0.303555i
$987$	−22.4592	−	0.108671i	−0.714885	−	0.00345903i
$988$	−2.28527	+	14.4286i	−0.0727040	+	0.459035i
$989$	−4.88032	+	2.81765i	−0.155185	+	0.0895961i
$990$	0.946456	+	1.38856i	0.0300803	+	0.0441313i
$991$	−2.02284	+	3.50366i	−0.0642577	+	0.111298i	−0.896364	−	0.443318i	$-0.853801\pi$
$991$	−2.02284	+	3.50366i	−0.0642577	+	0.111298i	0.832107	+	0.554615i	$0.187135\pi$
$992$	4.08520	−	1.56816i	0.129705	−	0.0497891i
$993$	−6.16708	+	12.1036i	−0.195706	+	0.384096i
$994$	17.4629	−	14.0018i	0.553890	−	0.444111i
$995$	17.1755	+	0.967284i	0.544500	+	0.0306650i
$996$	2.95342	−	28.0999i	0.0935827	−	0.890380i
$997$	−27.5587	−	1.44429i	−0.872794	−	0.0457412i	−0.389323	−	0.921101i	$-0.627291\pi$
$997$	−27.5587	−	1.44429i	−0.872794	−	0.0457412i	−0.483471	+	0.875360i	$0.660624\pi$
$998$	6.37311	−	4.13875i	0.201737	−	0.131010i
$999$	32.4927	+	14.4667i	1.02802	+	0.457705i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.157.7	yes	768
5.3	odd	4	inner	770.2.bv.a.3.18	✓	768
7.5	odd	6	inner	770.2.bv.a.47.7	yes	768
11.4	even	5	inner	770.2.bv.a.367.31	yes	768
35.33	even	12	inner	770.2.bv.a.663.31	yes	768
55.48	odd	20	inner	770.2.bv.a.213.7	yes	768
77.26	odd	30	inner	770.2.bv.a.257.18	yes	768
385.103	even	60	inner	770.2.bv.a.103.7	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.3.18	✓	768	5.3	odd	4	inner
770.2.bv.a.47.7	yes	768	7.5	odd	6	inner
770.2.bv.a.103.7	yes	768	385.103	even	60	inner
770.2.bv.a.157.7	yes	768	1.1	even	1	trivial
770.2.bv.a.213.7	yes	768	55.48	odd	20	inner
770.2.bv.a.257.18	yes	768	77.26	odd	30	inner
770.2.bv.a.367.31	yes	768	11.4	even	5	inner
770.2.bv.a.663.31	yes	768	35.33	even	12	inner

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.358368 - 0.933580i) q^{2} +(-0.907018 - 1.39668i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(1.00738 + 1.99629i) q^{5} +(-0.978872 + 1.34730i) q^{6} +(2.13291 + 1.56547i) q^{7} +(0.891007 + 0.453990i) q^{8} +(0.0921626 - 0.207001i) q^{9} +O(q^{10})\)	\(q+(-0.358368 - 0.933580i) q^{2} +(-0.907018 - 1.39668i) q^{3} +(-0.743145 + 0.669131i) q^{4} +(1.00738 + 1.99629i) q^{5} +(-0.978872 + 1.34730i) q^{6} +(2.13291 + 1.56547i) q^{7} +(0.891007 + 0.453990i) q^{8} +(0.0921626 - 0.207001i) q^{9} +(1.50269 - 1.65588i) q^{10} +(-3.26107 + 0.604526i) q^{11} +(1.60861 + 0.431026i) q^{12} +(-2.67775 - 0.424114i) q^{13} +(0.697128 - 2.55226i) q^{14} +(1.87448 - 3.21766i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-2.59774 + 6.76735i) q^{17} +(-0.226280 - 0.0118588i) q^{18} +(-3.60549 + 4.00431i) q^{19} +(-2.08441 - 0.809467i) q^{20} +(0.251886 - 4.39891i) q^{21} +(1.73303 + 2.82782i) q^{22} +(0.670055 + 0.179541i) q^{23} +(-0.174077 - 1.65623i) q^{24} +(-2.97038 + 4.02205i) q^{25} +(0.563676 + 2.65189i) q^{26} +(-5.30726 + 0.840588i) q^{27} +(-2.63256 + 0.263822i) q^{28} +(4.04700 + 1.31495i) q^{29} +(-3.67570 - 0.596872i) q^{30} +(-4.35187 + 0.457400i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(3.80218 + 4.00637i) q^{33} +7.24882 q^{34} +(-0.976495 + 5.83493i) q^{35} +(0.0700203 + 0.215500i) q^{36} +(-5.55132 - 3.60507i) q^{37} +(5.03043 + 1.93100i) q^{38} +(1.83642 + 4.12466i) q^{39} +(-0.00871699 + 2.23605i) q^{40} +(6.92798 - 2.25104i) q^{41} +(-4.19701 + 1.34127i) q^{42} +(-5.74428 + 5.74428i) q^{43} +(2.01894 - 2.63133i) q^{44} +(0.506076 - 0.0245444i) q^{45} +(-0.0725106 - 0.689892i) q^{46} +(-0.266774 - 5.09035i) q^{47} +(-1.48384 + 0.756056i) q^{48} +(2.09859 + 6.67802i) q^{49} +(4.81939 + 1.33171i) q^{50} +(11.8081 - 2.50988i) q^{51} +(2.27375 - 1.47659i) q^{52} +(1.11175 + 0.900278i) q^{53} +(2.68671 + 4.65352i) q^{54} +(-4.49194 - 5.90106i) q^{55} +(1.18973 + 2.36317i) q^{56} +(8.86300 + 1.40376i) q^{57} +(-0.222703 - 4.24944i) q^{58} +(0.117426 + 0.130415i) q^{59} +(0.760026 + 3.64546i) q^{60} +(12.0193 + 1.26328i) q^{61} +(1.98659 + 3.89890i) q^{62} +(0.520628 - 0.297235i) q^{63} +(0.587785 + 0.809017i) q^{64} +(-1.85086 - 5.77282i) q^{65} +(2.37769 - 4.98539i) q^{66} +(2.98794 - 0.800616i) q^{67} +(-2.59774 - 6.76735i) q^{68} +(-0.356990 - 1.09870i) q^{69} +(5.79732 - 1.17942i) q^{70} +(6.84431 + 4.97268i) q^{71} +(0.176094 - 0.142598i) q^{72} +(-0.808400 + 15.4252i) q^{73} +(-1.37621 + 6.47454i) q^{74} +(8.31172 + 0.500609i) q^{75} -5.38832i q^{76} +(-7.90192 - 3.81571i) q^{77} +(3.19259 - 3.19259i) q^{78} +(3.52302 - 7.91282i) q^{79} +(2.09066 - 0.793191i) q^{80} +(5.53296 + 6.14498i) q^{81} +(-4.58429 - 5.66113i) q^{82} +(-2.65409 - 16.7573i) q^{83} +(2.75626 + 3.43757i) q^{84} +(-16.1265 + 1.63143i) q^{85} +(7.42132 + 3.30418i) q^{86} +(-1.83413 - 6.84507i) q^{87} +(-3.18008 - 0.941856i) q^{88} +(0.366866 + 0.635431i) q^{89} +(-0.204276 - 0.463667i) q^{90} +(-5.04746 - 5.09654i) q^{91} +(-0.618084 + 0.314930i) q^{92} +(4.58606 + 5.66332i) q^{93} +(-4.65665 + 2.07328i) q^{94} +(-11.6259 - 3.16377i) q^{95} +(1.23760 + 1.11434i) q^{96} +(-2.14514 + 13.5439i) q^{97} +(5.48240 - 4.35239i) q^{98} +(-0.175411 + 0.730757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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