LMFDB - Embedded newform 324.2.p.a.263.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			263.40
Character	$\chi$	$=$	324.263
Dual form			324.2.p.a.239.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08140 + 0.911358i) q^{2} +(-1.15333 + 1.29222i) q^{3} +(0.338851 + 1.97109i) q^{4} +(-0.676824 + 1.34767i) q^{5} +(-2.42489 + 0.346312i) q^{6} +(-1.90225 + 0.569497i) q^{7} +(-1.42993 + 2.44035i) q^{8} +(-0.339668 - 2.98071i) q^{9} +O(q^{10})$	\(q+(1.08140 + 0.911358i) q^{2} +(-1.15333 + 1.29222i) q^{3} +(0.338851 + 1.97109i) q^{4} +(-0.676824 + 1.34767i) q^{5} +(-2.42489 + 0.346312i) q^{6} +(-1.90225 + 0.569497i) q^{7} +(-1.42993 + 2.44035i) q^{8} +(-0.339668 - 2.98071i) q^{9} +(-1.96013 + 0.840538i) q^{10} +(0.0271329 - 0.465854i) q^{11} +(-2.93788 - 1.83544i) q^{12} +(2.08519 - 2.80089i) q^{13} +(-2.57611 - 1.11778i) q^{14} +(-0.960884 - 2.42891i) q^{15} +(-3.77036 + 1.33581i) q^{16} +(1.49530 + 1.78202i) q^{17} +(2.34918 - 3.53290i) q^{18} +(-1.70596 + 2.03308i) q^{19} +(-2.88571 - 0.877420i) q^{20} +(1.45801 - 3.11495i) q^{21} +(0.453902 - 0.479047i) q^{22} +(-1.76005 + 5.87896i) q^{23} +(-1.50429 - 4.66231i) q^{24} +(1.62768 + 2.18635i) q^{25} +(4.80754 - 1.12853i) q^{26} +(4.24348 + 2.99881i) q^{27} +(-1.76711 - 3.55653i) q^{28} +(4.45451 + 1.92149i) q^{29} +(1.17451 - 3.50233i) q^{30} +(-2.49716 + 2.35595i) q^{31} +(-5.29467 - 1.99160i) q^{32} +(0.570693 + 0.572345i) q^{33} +(-0.00705013 + 3.28983i) q^{34} +(0.519998 - 2.94905i) q^{35} +(5.76014 - 1.67953i) q^{36} +(-0.895186 - 5.07685i) q^{37} +(-3.69769 + 0.643835i) q^{38} +(1.21447 + 5.92487i) q^{39} +(-2.32096 - 3.57876i) q^{40} +(-1.31257 + 11.2298i) q^{41} +(4.41552 - 2.03974i) q^{42} +(4.58576 - 6.97231i) q^{43} +(0.927433 - 0.104374i) q^{44} +(4.24690 + 1.55966i) q^{45} +(-7.26115 + 4.75347i) q^{46} +(4.87340 - 5.16550i) q^{47} +(2.62230 - 6.41276i) q^{48} +(-2.55418 + 1.67991i) q^{49} +(-0.232378 + 3.84771i) q^{50} +(-4.02733 - 0.123007i) q^{51} +(6.22737 + 3.16100i) q^{52} +(1.98674 - 1.14705i) q^{53} +(1.85591 + 7.11025i) q^{54} +(0.609453 + 0.351868i) q^{55} +(1.33032 - 5.45650i) q^{56} +(-0.659660 - 4.54928i) q^{57} +(3.06594 + 6.13756i) q^{58} +(0.428899 + 7.36391i) q^{59} +(4.46199 - 2.71702i) q^{60} +(-3.25713 - 0.771953i) q^{61} +(-4.84753 + 0.271915i) q^{62} +(2.34364 + 5.47662i) q^{63} +(-3.91059 - 6.97906i) q^{64} +(2.36337 + 4.70586i) q^{65} +(0.0955366 + 1.13904i) q^{66} +(9.27305 - 4.00000i) q^{67} +(-3.00584 + 3.55120i) q^{68} +(-5.56700 - 9.05474i) q^{69} +(3.24997 - 2.71520i) q^{70} +(12.9381 + 4.70907i) q^{71} +(7.75967 + 3.43330i) q^{72} +(10.3071 - 3.75146i) q^{73} +(3.65878 - 6.30594i) q^{74} +(-4.70249 - 0.418260i) q^{75} +(-4.58544 - 2.67368i) q^{76} +(0.213689 + 0.901625i) q^{77} +(-4.08636 + 7.51397i) q^{78} +(-1.24779 - 10.6755i) q^{79} +(0.751642 - 5.98530i) q^{80} +(-8.76925 + 2.02490i) q^{81} +(-11.6538 + 10.9476i) q^{82} +(6.60241 - 0.771711i) q^{83} +(6.63387 + 1.81835i) q^{84} +(-3.41363 + 0.809045i) q^{85} +(11.3133 - 3.36059i) q^{86} +(-7.62050 + 3.54011i) q^{87} +(1.09805 + 0.732354i) q^{88} +(-1.79425 - 4.92967i) q^{89} +(3.17119 + 5.55706i) q^{90} +(-2.37145 + 6.51552i) q^{91} +(-12.1843 - 1.47711i) q^{92} +(-0.164361 - 5.94405i) q^{93} +(9.97771 - 1.14456i) q^{94} +(-1.58528 - 3.67510i) q^{95} +(8.68008 - 4.54491i) q^{96} +(-11.6762 + 5.86401i) q^{97} +(-4.29309 - 0.511118i) q^{98} +(-1.39779 + 0.0773606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{25}{54}\right)$

Coefficient data

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

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

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

$2$	1.08140	+	0.911358i	0.764665	+	0.644428i
$2$	1.08140	+	0.911358i	0.764665	+	0.644428i
$3$	−1.15333	+	1.29222i	−0.665874	+	0.746064i
$3$	−1.15333	+	1.29222i	−0.665874	+	0.746064i
$4$	0.338851	+	1.97109i	0.169426	+	0.985543i
$5$	−0.676824	+	1.34767i	−0.302685	+	0.602695i	−0.992632	−	0.121164i	$-0.961337\pi$
$5$	−0.676824	+	1.34767i	−0.302685	+	0.602695i	0.689948	+	0.723859i	$0.257634\pi$
$6$	−2.42489	+	0.346312i	−0.989955	+	0.141381i
$7$	−1.90225	+	0.569497i	−0.718984	+	0.215250i	−0.625336	−	0.780356i	$-0.715038\pi$
$7$	−1.90225	+	0.569497i	−0.718984	+	0.215250i	−0.0936479	+	0.995605i	$0.529853\pi$
$8$	−1.42993	+	2.44035i	−0.505557	+	0.862793i
$9$	−0.339668	−	2.98071i	−0.113223	−	0.993570i
$10$	−1.96013	+	0.840538i	−0.619846	+	0.265802i
$11$	0.0271329	−	0.465854i	0.00818089	−	0.140460i	−0.991744	−	0.128231i	$-0.959070\pi$
$11$	0.0271329	−	0.465854i	0.00818089	−	0.140460i	0.999925	−	0.0122294i	$-0.00389284\pi$
$12$	−2.93788	−	1.83544i	−0.848094	−	0.529845i
$13$	2.08519	−	2.80089i	0.578327	−	0.776828i	−0.412645	−	0.910892i	$-0.635395\pi$
$13$	2.08519	−	2.80089i	0.578327	−	0.776828i	0.990973	+	0.134063i	$0.0428025\pi$
$14$	−2.57611	−	1.11778i	−0.688495	−	0.298739i
$15$	−0.960884	−	2.42891i	−0.248099	−	0.627142i
$16$	−3.77036	+	1.33581i	−0.942590	+	0.333953i
$17$	1.49530	+	1.78202i	0.362662	+	0.432204i	0.916262	−	0.400578i	$-0.131191\pi$
$17$	1.49530	+	1.78202i	0.362662	+	0.432204i	−0.553600	+	0.832783i	$0.686746\pi$
$18$	2.34918	−	3.53290i	0.553706	−	0.832712i
$19$	−1.70596	+	2.03308i	−0.391374	+	0.466421i	−0.925370	−	0.379066i	$-0.876245\pi$
$19$	−1.70596	+	2.03308i	−0.391374	+	0.466421i	0.533996	+	0.845487i	$0.320690\pi$
$20$	−2.88571	−	0.877420i	−0.645265	−	0.196197i
$21$	1.45801	−	3.11495i	0.318163	−	0.679737i
$22$	0.453902	−	0.479047i	0.0967722	−	0.102133i
$23$	−1.76005	+	5.87896i	−0.366995	+	1.22585i	0.552755	+	0.833344i	$0.313576\pi$
$23$	−1.76005	+	5.87896i	−0.366995	+	1.22585i	−0.919750	+	0.392504i	$0.871609\pi$
$24$	−1.50429	−	4.66231i	−0.307061	−	0.951690i
$25$	1.62768	+	2.18635i	0.325535	+	0.437270i
$26$	4.80754	−	1.12853i	0.942837	−	0.221323i
$27$	4.24348	+	2.99881i	0.816659	+	0.577121i
$28$	−1.76711	−	3.55653i	−0.333952	−	0.672120i
$29$	4.45451	+	1.92149i	0.827182	+	0.356812i	0.767216	−	0.641389i	$-0.221641\pi$
$29$	4.45451	+	1.92149i	0.827182	+	0.356812i	0.0599662	+	0.998200i	$0.480901\pi$
$30$	1.17451	−	3.50233i	0.214435	−	0.639435i
$31$	−2.49716	+	2.35595i	−0.448502	+	0.423140i	−0.877065	−	0.480372i	$-0.840502\pi$
$31$	−2.49716	+	2.35595i	−0.448502	+	0.423140i	0.428562	+	0.903512i	$0.359020\pi$
$32$	−5.29467	−	1.99160i	−0.935974	−	0.352069i
$33$	0.570693	+	0.572345i	0.0993450	+	0.0996324i
$34$	−0.00705013	+	3.28983i	−0.00120909	+	0.564201i
$35$	0.519998	−	2.94905i	0.0878956	−	0.498481i
$36$	5.76014	−	1.67953i	0.960023	−	0.279922i
$37$	−0.895186	−	5.07685i	−0.147168	−	0.834629i	−0.965601	−	0.260028i	$-0.916268\pi$
$37$	−0.895186	−	5.07685i	−0.147168	−	0.834629i	0.818433	−	0.574601i	$-0.194843\pi$
$38$	−3.69769	+	0.643835i	−0.599844	+	0.104444i
$39$	1.21447	+	5.92487i	0.194470	+	0.948739i
$40$	−2.32096	−	3.57876i	−0.366977	−	0.565852i
$41$	−1.31257	+	11.2298i	−0.204989	+	1.75379i	0.363953	+	0.931417i	$0.381427\pi$
$41$	−1.31257	+	11.2298i	−0.204989	+	1.75379i	−0.568942	+	0.822377i	$0.692647\pi$
$42$	4.41552	−	2.03974i	0.681329	−	0.314738i
$43$	4.58576	−	6.97231i	0.699322	−	1.06327i	−0.294858	−	0.955541i	$-0.595272\pi$
$43$	4.58576	−	6.97231i	0.699322	−	1.06327i	0.994181	−	0.107727i	$-0.0343572\pi$
$44$	0.927433	−	0.104374i	0.139816	−	0.0157350i
$45$	4.24690	+	1.55966i	0.633091	+	0.232500i
$46$	−7.26115	+	4.75347i	−1.07060	+	0.700862i
$47$	4.87340	−	5.16550i	0.710858	−	0.753466i	−0.266780	−	0.963757i	$-0.585960\pi$
$47$	4.87340	−	5.16550i	0.710858	−	0.753466i	0.977639	+	0.210292i	$0.0674414\pi$
$48$	2.62230	−	6.41276i	0.378496	−	0.925603i
$49$	−2.55418	+	1.67991i	−0.364883	+	0.239987i
$50$	−0.232378	+	3.84771i	−0.0328633	+	0.544149i
$51$	−4.02733	−	0.123007i	−0.563940	−	0.0172244i
$52$	6.22737	+	3.16100i	0.863581	+	0.438352i
$53$	1.98674	−	1.14705i	0.272900	−	0.157559i	−0.357305	−	0.933988i	$-0.616304\pi$
$53$	1.98674	−	1.14705i	0.272900	−	0.157559i	0.630205	+	0.776429i	$0.282971\pi$
$54$	1.85591	+	7.11025i	0.252558	+	0.967582i
$55$	0.609453	+	0.351868i	0.0821786	+	0.0474458i
$56$	1.33032	−	5.45650i	0.177772	−	0.729155i
$57$	−0.659660	−	4.54928i	−0.0873742	−	0.602567i
$58$	3.06594	+	6.13756i	0.402578	+	0.805901i
$59$	0.428899	+	7.36391i	0.0558379	+	0.958699i	0.903615	+	0.428346i	$0.140904\pi$
$59$	0.428899	+	7.36391i	0.0558379	+	0.958699i	−0.847777	+	0.530353i	$0.822059\pi$
$60$	4.46199	−	2.71702i	0.576041	−	0.350766i
$61$	−3.25713	−	0.771953i	−0.417032	−	0.0988385i	0.0167424	−	0.999860i	$-0.494670\pi$
$61$	−3.25713	−	0.771953i	−0.417032	−	0.0988385i	−0.433775	+	0.901021i	$0.642819\pi$
$62$	−4.84753	+	0.271915i	−0.615638	+	0.0345332i
$63$	2.34364	+	5.47662i	0.295271	+	0.689989i
$64$	−3.91059	−	6.97906i	−0.488824	−	0.872383i
$65$	2.36337	+	4.70586i	0.293140	+	0.583690i
$66$	0.0955366	+	1.13904i	0.0117597	+	0.140206i
$67$	9.27305	−	4.00000i	1.13288	−	0.488678i	0.254708	−	0.967018i	$-0.418020\pi$
$67$	9.27305	−	4.00000i	1.13288	−	0.488678i	0.878175	+	0.478340i	$0.158761\pi$
$68$	−3.00584	+	3.55120i	−0.364511	+	0.430646i
$69$	−5.56700	−	9.05474i	−0.670189	−	1.09006i
$70$	3.24997	−	2.71520i	0.388446	−	0.324529i
$71$	12.9381	+	4.70907i	1.53547	+	0.558864i	0.964953	−	0.262423i	$-0.0845216\pi$
$71$	12.9381	+	4.70907i	1.53547	+	0.558864i	0.570514	+	0.821288i	$0.306744\pi$
$72$	7.75967	+	3.43330i	0.914486	+	0.404619i
$73$	10.3071	−	3.75146i	1.20635	−	0.439075i	0.340914	−	0.940095i	$-0.389264\pi$
$73$	10.3071	−	3.75146i	1.20635	−	0.439075i	0.865436	+	0.501019i	$0.167041\pi$
$74$	3.65878	−	6.30594i	0.425324	−	0.733051i
$75$	−4.70249	−	0.418260i	−0.542996	−	0.0482966i
$76$	−4.58544	−	2.67368i	−0.525987	−	0.306692i
$77$	0.213689	+	0.901625i	0.0243521	+	0.102750i
$78$	−4.08636	+	7.51397i	−0.462689	+	0.850790i
$79$	−1.24779	−	10.6755i	−0.140387	−	1.20109i	−0.861313	−	0.508075i	$-0.830357\pi$
$79$	−1.24779	−	10.6755i	−0.140387	−	1.20109i	0.720926	−	0.693012i	$-0.243717\pi$
$80$	0.751642	−	5.98530i	0.0840361	−	0.669177i
$81$	−8.76925	+	2.02490i	−0.974361	+	0.224989i
$82$	−11.6538	+	10.9476i	−1.28694	+	1.20897i
$83$	6.60241	−	0.771711i	0.724708	−	0.0847062i	0.254263	−	0.967135i	$-0.418167\pi$
$83$	6.60241	−	0.771711i	0.724708	−	0.0847062i	0.470446	+	0.882429i	$0.344093\pi$
$84$	6.63387	+	1.81835i	0.723815	+	0.198398i
$85$	−3.41363	+	0.809045i	−0.370260	+	0.0877532i
$86$	11.3133	−	3.36059i	1.21995	−	0.362381i
$87$	−7.62050	+	3.54011i	−0.817004	+	0.379539i
$88$	1.09805	+	0.732354i	0.117052	+	0.0780692i
$89$	−1.79425	−	4.92967i	−0.190190	−	0.522544i	0.807545	−	0.589806i	$-0.200796\pi$
$89$	−1.79425	−	4.92967i	−0.190190	−	0.522544i	−0.997735	+	0.0672621i	$0.978574\pi$
$90$	3.17119	+	5.55706i	0.334273	+	0.585766i
$91$	−2.37145	+	6.51552i	−0.248596	+	0.683012i
$92$	−12.1843	−	1.47711i	−1.27030	−	0.153999i
$93$	−0.164361	−	5.94405i	−0.0170434	−	0.616370i
$94$	9.97771	−	1.14456i	1.02912	−	0.118052i
$95$	−1.58528	−	3.67510i	−0.162647	−	0.377058i
$96$	8.68008	−	4.54491i	0.885907	−	0.463863i
$97$	−11.6762	+	5.86401i	−1.18554	+	0.595400i	−0.928620	−	0.371033i	$-0.879004\pi$
$97$	−11.6762	+	5.86401i	−1.18554	+	0.595400i	−0.256920	+	0.966433i	$0.582708\pi$
$98$	−4.29309	−	0.511118i	−0.433668	−	0.0516307i
$99$	−1.39779	+	0.0773606i	−0.140483	+	0.00777503i
$100$	−3.75794	+	3.94914i	−0.375794	+	0.394914i
$101$	−1.15267	+	4.86349i	−0.114695	+	0.483935i	0.885132	+	0.465339i	$0.154068\pi$
$101$	−1.15267	+	4.86349i	−0.114695	+	0.483935i	−0.999827	+	0.0185957i	$0.994080\pi$
$102$	−4.24306	−	3.80336i	−0.420125	−	0.376589i
$103$	−5.69117	+	0.331473i	−0.560767	+	0.0326610i	−0.336188	−	0.941795i	$-0.609138\pi$
$103$	−5.69117	+	0.331473i	−0.560767	+	0.0326610i	−0.224579	+	0.974456i	$0.572101\pi$
$104$	3.85348	+	9.09367i	0.377865	+	0.891708i
$105$	3.21110	+	4.07318i	0.313371	+	0.397501i
$106$	3.19383	+	0.570219i	0.310212	+	0.0553845i
$107$	6.12540	−	10.6095i	0.592165	−	1.02566i	−0.401776	−	0.915738i	$-0.631607\pi$
$107$	6.12540	−	10.6095i	0.592165	−	1.02566i	0.993940	−	0.109921i	$-0.0350599\pi$
$108$	−4.47300	+	9.38042i	−0.430415	+	0.902631i
$109$	−6.31120	−	10.9313i	−0.604503	−	1.04703i	−0.992130	−	0.125214i	$-0.960038\pi$
$109$	−6.31120	−	10.9313i	−0.604503	−	1.04703i	0.387626	−	0.921817i	$-0.373295\pi$
$110$	0.338385	+	0.935940i	0.0322637	+	0.0892383i
$111$	7.59286	+	4.69850i	0.720682	+	0.445962i
$112$	6.41143	−	4.68826i	0.605824	−	0.442999i
$113$	4.27744	+	6.50352i	0.402387	+	0.611800i	0.978667	−	0.205452i	$-0.0658666\pi$
$113$	4.27744	+	6.50352i	0.402387	+	0.611800i	−0.576280	+	0.817252i	$0.695496\pi$
$114$	3.43267	−	5.52078i	0.321499	−	0.517069i
$115$	−6.73164	−	6.35098i	−0.627729	−	0.592232i
$116$	−2.27800	+	9.43133i	−0.211507	+	0.875677i
$117$	−9.05692	−	5.26397i	−0.837313	−	0.486654i
$118$	−6.24735	+	8.35421i	−0.575115	+	0.769067i
$119$	−3.85929	−	2.53829i	−0.353780	−	0.232685i
$120$	7.30138	+	1.12829i	0.666522	+	0.102998i
$121$	10.7093	+	1.25174i	0.973576	+	0.113795i
$122$	−2.81873	−	3.80320i	−0.255196	−	0.344326i
$123$	−12.9975	−	14.6477i	−1.17195	−	1.32074i
$124$	−5.48994	−	4.12379i	−0.493011	−	0.370328i
$125$	−11.4740	+	2.02317i	−1.02626	+	0.180958i
$126$	−2.45675	+	8.05831i	−0.218865	+	0.717891i
$127$	−12.5975	−	2.22128i	−1.11785	−	0.197107i	−0.415953	−	0.909386i	$-0.636552\pi$
$127$	−12.5975	−	2.22128i	−1.11785	−	0.197107i	−0.701896	+	0.712279i	$0.747663\pi$
$128$	2.13152	−	11.1111i	0.188401	−	0.982092i
$129$	3.72088	+	13.9672i	0.327605	+	1.22974i
$130$	−1.73297	+	7.24279i	−0.151992	+	0.635235i
$131$	0.963269	+	1.02101i	0.0841612	+	0.0892057i	0.768085	−	0.640347i	$-0.221210\pi$
$131$	0.963269	+	1.02101i	0.0841612	+	0.0892057i	−0.683924	+	0.729553i	$0.739728\pi$
$132$	−0.934760	+	1.31883i	−0.0813604	+	0.114789i
$133$	2.08733	−	4.83897i	0.180994	−	0.419592i
$134$	13.6733	+	4.12547i	1.18119	+	0.356386i
$135$	−6.91349	+	3.68914i	−0.595019	+	0.317510i
$136$	−6.48693	+	1.10087i	−0.556249	+	0.0943986i
$137$	10.4411	−	7.77308i	0.892040	−	0.664099i	−0.0503079	−	0.998734i	$-0.516020\pi$
$137$	10.4411	−	7.77308i	0.892040	−	0.664099i	0.942348	+	0.334635i	$0.108613\pi$
$138$	2.23195	−	14.8653i	0.189997	−	1.26542i
$139$	−5.91529	−	1.77092i	−0.501728	−	0.150208i	0.0259311	−	0.999664i	$-0.491745\pi$
$139$	−5.91529	−	1.77092i	−0.501728	−	0.150208i	−0.527659	+	0.849456i	$0.676930\pi$
$140$	5.98904	+	0.0256692i	0.506166	+	0.00216944i
$141$	1.05434	+	12.2550i	0.0887913	+	1.03206i
$142$	9.69958	+	16.8836i	0.813971	+	1.41684i
$143$	−1.24823	−	1.04739i	−0.104382	−	0.0875872i
$144$	5.26233	+	10.7846i	0.438528	+	0.898718i
$145$	−5.60445	+	4.70269i	−0.465424	+	0.390537i
$146$	14.5650	+	5.33659i	1.20541	+	0.441660i
$147$	0.774992	−	5.23805i	0.0639203	−	0.432027i
$148$	9.70358	−	3.48479i	0.797629	−	0.286448i
$149$	−10.2199	−	7.60841i	−0.837244	−	0.623305i	0.0907608	−	0.995873i	$-0.471070\pi$
$149$	−10.2199	−	7.60841i	−0.837244	−	0.623305i	−0.928005	+	0.372567i	$0.878478\pi$
$150$	−4.70408	−	4.73796i	−0.384087	−	0.386853i
$151$	3.05204	+	0.177761i	0.248372	+	0.0144660i	0.181879	−	0.983321i	$-0.441782\pi$
$151$	3.05204	+	0.177761i	0.248372	+	0.0144660i	0.0664926	+	0.997787i	$0.478819\pi$
$152$	−2.52202	−	7.07030i	−0.204563	−	0.573477i
$153$	4.80379	−	5.06234i	0.388363	−	0.409266i
$154$	−0.590620	+	1.16976i	−0.0475935	+	0.0942623i
$155$	−1.48490	−	4.95990i	−0.119270	−	0.398389i
$156$	−11.2669	+	4.40147i	−0.902075	+	0.352400i
$157$	18.5012	+	9.29165i	1.47656	+	0.741554i	0.991152	−	0.132735i	$-0.0423759\pi$
$157$	18.5012	+	9.29165i	1.47656	+	0.741554i	0.485405	+	0.874290i	$0.338672\pi$
$158$	8.37985	−	12.6817i	0.666665	−	1.00890i
$159$	−0.809129	+	3.89023i	−0.0641681	+	0.308515i
$160$	6.26758	−	5.78749i	0.495496	−	0.457541i
$161$		−	12.1856i		−	0.960360i
$162$	−11.3285	−	5.80220i	−0.890050	−	0.455864i
$163$		−	11.2973i		−	0.884870i	−0.896801	−	0.442435i	$-0.854115\pi$
$163$		−	11.2973i		−	0.884870i	0.896801	−	0.442435i	$-0.145885\pi$
$164$	−22.5796	+	1.21803i	−1.76317	+	0.0951122i
$165$	−1.15759	+	0.381728i	−0.0901182	+	0.0297175i
$166$	7.84315	+	5.18263i	0.608746	+	0.402250i
$167$	−3.54406	−	1.77989i	−0.274247	−	0.137732i	0.306360	−	0.951916i	$-0.400889\pi$
$167$	−3.54406	−	1.77989i	−0.274247	−	0.137732i	−0.580608	+	0.814183i	$0.697185\pi$
$168$	5.51670	+	8.01220i	0.425623	+	0.618155i
$169$	0.231443	+	0.773074i	0.0178033	+	0.0594673i
$170$	−4.42883	−	2.23614i	−0.339676	−	0.171504i
$171$	6.63948	+	4.39439i	0.507734	+	0.336047i
$172$	15.2969	+	6.67636i	1.16638	+	0.509067i
$173$	−16.2940	−	0.949015i	−1.23881	−	0.0721522i	−0.573803	−	0.818993i	$-0.694533\pi$
$173$	−16.2940	−	0.949015i	−1.23881	−	0.0721522i	−0.665003	+	0.746841i	$0.731570\pi$
$174$	−11.4671	−	3.11674i	−0.869320	−	0.236279i
$175$	−4.34137	−	3.23203i	−0.328176	−	0.244318i
$176$	0.519992	+	1.79268i	0.0391959	+	0.135129i
$177$	−10.0105	−	7.93877i	−0.752432	−	0.596714i
$178$	2.55239	−	6.96615i	0.191310	−	0.522135i
$179$	9.59631	−	8.05226i	0.717262	−	0.601854i	−0.209365	−	0.977838i	$-0.567140\pi$
$179$	9.59631	−	8.05226i	0.717262	−	0.601854i	0.926626	+	0.375984i	$0.122695\pi$
$180$	−1.63515	+	8.89950i	−0.121877	+	0.663329i
$181$	7.79507	+	6.54084i	0.579403	+	0.486177i	0.884751	−	0.466064i	$-0.154328\pi$
$181$	7.79507	+	6.54084i	0.579403	+	0.486177i	−0.305348	+	0.952241i	$0.598773\pi$
$182$	−8.50246	+	4.88463i	−0.630244	+	0.362073i
$183$	4.75407	−	3.31861i	0.351431	−	0.245319i
$184$	−11.8300	−	12.7016i	−0.872116	−	0.936377i
$185$	7.44780	+	2.22972i	0.547573	+	0.163933i
$186$	5.23943	−	6.57769i	0.384173	−	0.482300i
$187$	0.870735	−	0.648238i	0.0636745	−	0.0474039i
$188$	11.8330	+	7.85555i	0.863010	+	0.572925i
$189$	−9.77998	−	3.28784i	−0.711389	−	0.239155i
$190$	1.63501	−	5.41902i	0.118616	−	0.393137i
$191$	−5.23026	+	12.1251i	−0.378448	+	0.877341i	0.617429	+	0.786627i	$0.288174\pi$
$191$	−5.23026	+	12.1251i	−0.378448	+	0.877341i	−0.995877	+	0.0907147i	$0.971085\pi$
$192$	13.5287	+	2.99580i	0.976348	+	0.216204i
$193$	9.65351	+	10.2321i	0.694875	+	0.736524i	0.974698	−	0.223528i	$-0.0717573\pi$
$193$	9.65351	+	10.2321i	0.694875	+	0.736524i	−0.279823	+	0.960052i	$0.590276\pi$
$194$	−17.9709	−	4.29987i	−1.29023	−	0.308713i
$195$	−8.80674	−	2.37340i	−0.630664	−	0.169963i
$196$	−4.17673	−	4.46527i	−0.298338	−	0.318948i
$197$	−14.4303	−	2.54445i	−1.02811	−	0.181284i	−0.365943	−	0.930637i	$-0.619254\pi$
$197$	−14.4303	−	2.54445i	−1.02811	−	0.181284i	−0.662171	+	0.749353i	$0.730365\pi$
$198$	−1.58208	−	1.19023i	−0.112433	−	0.0845861i
$199$	2.40532	−	0.424122i	0.170508	−	0.0300652i	−0.0877421	−	0.996143i	$-0.527965\pi$
$199$	2.40532	−	0.424122i	0.170508	−	0.0300652i	0.258250	+	0.966078i	$0.416854\pi$
$200$	−7.66291	+	0.845765i	−0.541850	+	0.0598046i
$201$	−5.52598	+	16.5961i	−0.389773	+	1.17060i
$202$	−5.67887	+	4.20888i	−0.399564	+	0.296136i
$203$	−9.56789	−	1.11833i	−0.671534	−	0.0784911i
$204$	−1.12221	−	7.97990i	−0.0785705	−	0.558705i
$205$	−14.2456	−	9.36949i	−0.994957	−	0.654393i
$206$	−6.45652	−	4.82824i	−0.449847	−	0.336399i
$207$	18.1213	+	3.24929i	1.25952	+	0.225841i
$208$	−4.12045	+	13.3458i	−0.285702	+	0.925365i
$209$	0.900832	+	0.849891i	0.0623119	+	0.0587882i
$210$	−0.239643	+	7.33120i	−0.0165369	+	0.505901i
$211$	10.2040	+	15.5144i	0.702472	+	1.06806i	0.993773	+	0.111426i	$0.0355418\pi$
$211$	10.2040	+	15.5144i	0.702472	+	1.06806i	−0.291300	+	0.956632i	$0.594088\pi$
$212$	2.93414	+	3.52736i	0.201517	+	0.242260i
$213$	−21.0070	+	11.2877i	−1.43938	+	0.773423i
$214$	16.2931	−	5.89068i	1.11377	−	0.402679i
$215$	6.29261	+	10.8991i	0.429152	+	0.743314i
$216$	−13.3860	+	6.06748i	−0.910804	+	0.412840i
$217$	3.40852	−	5.90372i	0.231385	−	0.400771i
$218$	3.13742	−	17.5729i	0.212493	−	1.19019i
$219$	−7.03970	+	17.6457i	−0.475699	+	1.19238i
$220$	−0.487048	+	1.32051i	−0.0328367	+	0.0890291i
$221$	8.10923	−	0.472309i	0.545486	−	0.0317709i
$222$	3.92890	+	12.0008i	0.263690	+	0.805439i
$223$	5.73624	−	24.2031i	0.384127	−	1.62076i	−0.346547	−	0.938032i	$-0.612646\pi$
$223$	5.73624	−	24.2031i	0.384127	−	1.62076i	0.730674	−	0.682726i	$-0.239206\pi$
$224$	11.2060	+	0.773235i	0.748733	+	0.0516639i
$225$	5.96400	−	5.59426i	0.397600	−	0.372951i
$226$	−1.30142	+	10.9312i	−0.0865694	+	0.727132i
$227$	−11.9598	+	6.00643i	−0.793798	+	0.398661i	−0.799004	−	0.601326i	$-0.794639\pi$
$227$	−11.9598	+	6.00643i	−0.793798	+	0.398661i	0.00520547	+	0.999986i	$0.498343\pi$
$228$	8.74350	−	2.84178i	0.579053	−	0.188201i
$229$	−4.04364	−	9.37421i	−0.267211	−	0.619465i	0.730794	−	0.682598i	$-0.239150\pi$
$229$	−4.04364	−	9.37421i	−0.267211	−	0.619465i	−0.998005	+	0.0631328i	$0.979891\pi$
$230$	−1.49158	−	13.0029i	−0.0983519	−	0.857385i
$231$	−1.41155	−	0.763736i	−0.0928733	−	0.0502501i
$232$	−11.0588	+	8.12296i	−0.726043	+	0.533298i
$233$	−6.56753	+	18.0441i	−0.430253	+	1.18211i	0.515405	+	0.856947i	$0.327642\pi$
$233$	−6.56753	+	18.0441i	−0.430253	+	1.18211i	−0.945658	+	0.325164i	$0.894581\pi$
$234$	−4.99680	−	13.9466i	−0.326651	−	0.911715i
$235$	3.66294	+	10.0639i	0.238944	+	0.656494i
$236$	−14.3696	+	3.34067i	−0.935379	+	0.217459i
$237$	15.2342	+	10.6999i	0.989568	+	0.695036i
$238$	−1.86014	−	6.26210i	−0.120575	−	0.405912i
$239$	−22.7956	+	5.40267i	−1.47453	+	0.349470i	−0.887768	−	0.460291i	$-0.847745\pi$
$239$	−22.7956	+	5.40267i	−1.47453	+	0.349470i	−0.586760	+	0.809761i	$0.699597\pi$
$240$	6.86744	+	7.87430i	0.443291	+	0.508284i
$241$	12.7902	−	1.49496i	0.823889	−	0.0962988i	0.306307	−	0.951933i	$-0.400907\pi$
$241$	12.7902	−	1.49496i	0.823889	−	0.0962988i	0.517581	+	0.855634i	$0.326832\pi$
$242$	10.4403	+	11.1137i	0.671127	+	0.714414i
$243$	7.49720	−	13.6672i	0.480946	−	0.876750i
$244$	0.417904	−	6.68165i	0.0267536	−	0.427749i
$245$	−0.535230	−	4.57919i	−0.0341946	−	0.292554i
$246$	−0.706166	−	27.6855i	−0.0450235	−	1.76516i
$247$	2.13720	+	9.01757i	0.135987	+	0.573774i
$248$	−2.17856	−	9.46277i	−0.138339	−	0.600886i
$249$	−6.61752	+	9.42180i	−0.419368	+	0.597082i
$250$	−14.2518	−	8.26903i	−0.901361	−	0.522980i
$251$	−1.77821	+	0.647214i	−0.112239	+	0.0408518i	−0.397529	−	0.917589i	$-0.630132\pi$
$251$	−1.77821	+	0.647214i	−0.112239	+	0.0408518i	0.285290	+	0.958441i	$0.407910\pi$
$252$	−10.0007	+	6.47527i	−0.629987	+	0.407904i
$253$	2.69098	+	0.979438i	0.169181	+	0.0615768i
$254$	−11.5986	−	13.8830i	−0.727759	−	0.871094i
$255$	2.89157	−	5.34425i	0.181077	−	0.334670i
$256$	12.4312	−	10.0730i	0.776951	−	0.629561i
$257$	−20.8401	+	8.98954i	−1.29997	+	0.560752i	−0.929750	−	0.368192i	$-0.879977\pi$
$257$	−20.8401	+	8.98954i	−1.29997	+	0.560752i	−0.370220	+	0.928944i	$0.620718\pi$
$258$	−8.70536	+	18.4952i	−0.541972	+	1.15146i
$259$	4.59412	+	9.14765i	0.285465	+	0.568407i
$260$	−8.47481	+	6.25299i	−0.525586	+	0.387794i
$261$	4.21434	−	13.9303i	0.260861	−	0.862262i
$262$	0.111177	+	1.98200i	0.00686854	+	0.122448i
$263$	8.58873	+	2.03557i	0.529604	+	0.125518i	0.486714	−	0.873561i	$-0.338195\pi$
$263$	8.58873	+	2.03557i	0.529604	+	0.125518i	0.0428899	+	0.999080i	$0.486344\pi$
$264$	−2.21277	+	0.574276i	−0.136187	+	0.0353443i
$265$	0.201162	+	3.45382i	0.0123573	+	0.212166i
$266$	6.66727	−	3.33056i	0.408797	−	0.204210i
$267$	8.43958	+	3.36696i	0.516494	+	0.206054i
$268$	11.0265	+	16.9226i	0.673553	+	1.03371i
$269$	−1.13559	−	0.655633i	−0.0692381	−	0.0399746i	0.464981	−	0.885321i	$-0.346061\pi$
$269$	−1.13559	−	0.655633i	−0.0692381	−	0.0399746i	−0.534219	+	0.845346i	$0.679394\pi$
$270$	−10.8384	−	2.31123i	−0.659602	−	0.140657i
$271$	6.28461	−	3.62842i	0.381763	−	0.220411i	−0.296822	−	0.954933i	$-0.595927\pi$
$271$	6.28461	−	3.62842i	0.381763	−	0.220411i	0.678585	+	0.734522i	$0.262594\pi$
$272$	−8.01825	−	4.72144i	−0.486178	−	0.286279i
$273$	−5.68442	−	10.5790i	−0.344037	−	0.640268i
$274$	18.3750	+	1.10974i	1.11008	+	0.0670418i
$275$	1.06268	−	0.698938i	0.0640822	−	0.0421475i
$276$	15.9613	−	14.0413i	0.960756	−	0.845184i
$277$	12.7974	−	13.5644i	0.768920	−	0.815008i	−0.218046	−	0.975939i	$-0.569968\pi$
$277$	12.7974	−	13.5644i	0.768920	−	0.815008i	0.986966	+	0.160931i	$0.0514497\pi$
$278$	−4.78285	−	7.30602i	−0.286856	−	0.438186i
$279$	7.87059	+	6.64306i	0.471200	+	0.397709i
$280$	6.45315	+	5.48592i	0.385650	+	0.327846i
$281$	15.7127	−	23.8900i	0.937339	−	1.42516i	0.0324665	−	0.999473i	$-0.489664\pi$
$281$	15.7127	−	23.8900i	0.937339	−	1.42516i	0.904873	−	0.425682i	$-0.139966\pi$
$282$	−10.0286	+	14.2135i	−0.597192	+	0.846399i
$283$	−2.68781	+	22.9957i	−0.159774	+	1.36695i	0.640795	+	0.767712i	$0.278605\pi$
$283$	−2.68781	+	22.9957i	−0.159774	+	1.36695i	−0.800569	+	0.599241i	$0.795469\pi$
$284$	−4.89791	+	27.0977i	−0.290637	+	1.60795i
$285$	6.57740	+	2.19006i	0.389611	+	0.129728i
$286$	−0.395289	−	2.27024i	−0.0233739	−	0.134242i
$287$	−3.89847	−	22.1093i	−0.230120	−	1.30507i
$288$	−4.13796	+	16.4583i	−0.243832	+	0.969818i
$289$	2.01232	−	11.4124i	0.118372	−	0.671319i
$290$	−10.3465	−	0.0221726i	−0.607567	−	0.00130202i
$291$	5.88890	−	21.8514i	0.345214	−	1.28095i
$292$	10.8870	+	19.0449i	0.637114	+	1.11452i
$293$	24.7365	−	23.3377i	1.44512	−	1.36340i	0.643748	−	0.765238i	$-0.277378\pi$
$293$	24.7365	−	23.3377i	1.44512	−	1.36340i	0.801373	−	0.598164i	$-0.204103\pi$
$294$	5.61182	−	4.95813i	0.327288	−	0.289164i
$295$	−10.2144	−	4.40606i	−0.594705	−	0.256531i
$296$	13.6693	+	5.07499i	0.794514	+	0.294978i
$297$	1.51215	−	1.89548i	0.0877436	−	0.109987i
$298$	−4.11778	−	17.5417i	−0.238536	−	1.01616i
$299$	12.7963	+	17.1884i	0.740030	+	0.994033i
$300$	−0.769017	−	9.41073i	−0.0443992	−	0.543329i
$301$	−4.75257	+	15.8747i	−0.273933	+	0.915001i
$302$	3.13847	+	2.97374i	0.180599	+	0.171119i
$303$	−4.95529	−	7.09870i	−0.284674	−	0.407809i
$304$	3.71626	−	9.94428i	0.213142	−	0.570344i
$305$	3.24484	−	3.86705i	0.185799	−	0.221427i
$306$	9.80842	−	1.09644i	0.560710	−	0.0626791i
$307$	19.8843	+	23.6972i	1.13486	+	1.35247i	0.927332	+	0.374240i	$0.122096\pi$
$307$	19.8843	+	23.6972i	1.13486	+	1.35247i	0.207525	+	0.978230i	$0.433459\pi$
$308$	−1.70477	+	0.726716i	−0.0971383	+	0.0414085i
$309$	6.13545	−	7.73654i	0.349033	−	0.440116i
$310$	2.91448	−	6.71691i	0.165531	−	0.381495i
$311$	−10.0621	+	13.5158i	−0.570572	+	0.766411i	−0.989953	−	0.141399i	$-0.954840\pi$
$311$	−10.0621	+	13.5158i	−0.570572	+	0.766411i	0.419381	+	0.907810i	$0.362247\pi$
$312$	−16.1954	−	5.50845i	−0.916882	−	0.311854i
$313$	−1.66329	+	28.5576i	−0.0940147	+	1.61417i	0.540558	+	0.841307i	$0.318213\pi$
$313$	−1.66329	+	28.5576i	−0.0940147	+	1.61417i	−0.634573	+	0.772863i	$0.718824\pi$
$314$	11.5392	+	26.9092i	0.651193	+	1.51857i
$315$	−8.96689	−	0.548262i	−0.505227	−	0.0308911i
$316$	20.6195	−	6.07690i	1.15994	−	0.341853i
$317$	26.4076	−	7.90592i	1.48320	−	0.444040i	0.560042	−	0.828464i	$-0.310785\pi$
$317$	26.4076	−	7.90592i	1.48320	−	0.444040i	0.923157	+	0.384424i	$0.125600\pi$
$318$	−4.42039	+	3.46949i	−0.247883	+	0.194559i
$319$	1.01600	−	2.02302i	0.0568850	−	0.113267i
$320$	12.0522	−	0.546577i	0.673741	−	0.0305546i
$321$	6.64522	+	20.1516i	0.370900	+	1.12475i
$322$	11.1055	−	13.1775i	0.618883	−	0.734354i
$323$	−6.17391			−0.343526
$324$	−6.96273	−	16.5988i	−0.386819	−	0.922156i
$325$	9.51774			0.527949
$326$	10.2959	−	12.2169i	0.570235	−	0.676629i
$327$	21.4046	+	4.45194i	1.18368	+	0.246193i
$328$	−25.5276	−	19.2609i	−1.40953	−	1.06351i
$329$	−6.32869	+	12.6015i	−0.348912	+	0.694741i
$330$	−1.59971	−	0.642178i	−0.0880611	−	0.0353507i
$331$	−13.1168	+	3.92690i	−0.720963	+	0.215842i	−0.626205	−	0.779658i	$-0.715393\pi$
$331$	−13.1168	+	3.92690i	−0.720963	+	0.215842i	−0.0947578	+	0.995500i	$0.530208\pi$
$332$	3.75834	+	12.7524i	0.206266	+	0.699880i
$333$	−14.8286	+	4.39274i	−0.812600	+	0.240720i
$334$	−2.21042	−	5.15468i	−0.120949	−	0.282052i
$335$	−0.885549	+	15.2043i	−0.0483827	+	0.830699i
$336$	−1.33623	+	13.6921i	−0.0728971	+	0.746964i
$337$	13.1317	−	17.6389i	0.715327	−	0.960850i	−0.284671	−	0.958625i	$-0.591884\pi$
$337$	13.1317	−	17.6389i	0.715327	−	0.960850i	0.999998	−	0.00222505i	$-0.000708255\pi$
$338$	−0.454265	+	1.04693i	−0.0247088	+	0.0569455i
$339$	−13.3373	−	1.97331i	−0.724381	−	0.107175i
$340$	−2.75141	−	6.45441i	−0.149216	−	0.350039i
$341$	1.02977	+	1.22723i	0.0557653	+	0.0664585i
$342$	3.17507	+	10.8030i	0.171688	+	0.584162i
$343$	12.8365	−	15.2980i	0.693108	−	0.826014i
$344$	10.4575	+	21.1608i	0.563833	+	1.14091i
$345$	15.9707	−	1.37401i	0.859832	−	0.0739740i
$346$	−16.7554	−	15.8759i	−0.900775	−	0.853493i
$347$	9.75921	−	32.5980i	0.523902	−	1.74995i	−0.128124	−	0.991758i	$-0.540896\pi$
$347$	9.75921	−	32.5980i	0.523902	−	1.74995i	0.652026	−	0.758197i	$-0.273919\pi$
$348$	−9.56007	−	13.8211i	−0.512474	−	0.740889i
$349$	−13.6411	−	18.3232i	−0.730194	−	0.980820i	−0.999840	−	0.0178612i	$-0.994314\pi$
$349$	−13.6411	−	18.3232i	−0.730194	−	0.980820i	0.269647	−	0.962959i	$-0.413093\pi$
$350$	−1.74922	−	7.45166i	−0.0934996	−	0.398308i
$351$	17.2478	−	5.63246i	0.920620	−	0.300639i
$352$	−1.07146	+	2.41251i	−0.0571089	+	0.128587i
$353$	−1.60883	−	0.693980i	−0.0856292	−	0.0369368i	0.352834	−	0.935686i	$-0.385218\pi$
$353$	−1.60883	−	0.693980i	−0.0856292	−	0.0369368i	−0.438464	+	0.898749i	$0.644477\pi$
$354$	−3.59024	−	17.7081i	−0.190819	−	0.941175i
$355$	−15.1031	+	14.2490i	−0.801588	+	0.756259i
$356$	9.10882	−	5.20705i	0.482766	−	0.275973i
$357$	7.73106	−	2.05956i	0.409171	−	0.109004i
$358$	17.7159	+	0.0379654i	0.936316	+	0.00200653i
$359$	3.09472	−	17.5510i	0.163333	−	0.926307i	−0.787434	−	0.616399i	$-0.788591\pi$
$359$	3.09472	−	17.5510i	0.163333	−	0.926307i	0.950767	−	0.309908i	$-0.100298\pi$
$360$	−9.87888	+	8.13371i	−0.520663	+	0.428684i
$361$	2.07619	+	11.7746i	0.109273	+	0.619718i
$362$	2.46854	+	14.1774i	0.129743	+	0.745146i
$363$	−13.9689	+	12.3952i	−0.733178	+	0.650577i
$364$	−13.6462	−	2.46655i	−0.715256	−	0.129282i
$365$	−1.92034	+	16.4296i	−0.100515	+	0.859963i
$366$	8.16550	+	0.743917i	0.426817	+	0.0388851i
$367$	7.57101	−	11.5112i	0.395203	−	0.600877i	−0.581999	−	0.813190i	$-0.697729\pi$
$367$	7.57101	−	11.5112i	0.395203	−	0.600877i	0.977202	+	0.212312i	$0.0680994\pi$
$368$	−1.21717	−	24.5169i	−0.0634496	−	1.27803i
$369$	33.9185	+	0.0979982i	1.76573	+	0.00510158i
$370$	6.02197	+	9.19883i	0.313067	+	0.478225i
$371$	−3.12604	+	3.31341i	−0.162296	+	0.172024i
$372$	11.6605	−	2.33812i	0.604571	−	0.121226i
$373$	−23.9505	+	15.7525i	−1.24011	+	0.815632i	−0.988356	−	0.152160i	$-0.951377\pi$
$373$	−23.9505	+	15.7525i	−1.24011	+	0.815632i	−0.251752	+	0.967792i	$0.581007\pi$
$374$	1.53239	+	0.0925471i	0.0792380	+	0.00478549i
$375$	10.6189	−	17.1603i	0.548355	−	0.886152i
$376$	5.63699	+	19.2791i	0.290705	+	0.994244i
$377$	14.6704	−	8.46995i	0.755563	−	0.436225i
$378$	−7.57967	−	12.4685i	−0.389856	−	0.641313i
$379$	21.5558	+	12.4453i	1.10725	+	0.639270i	0.938115	−	0.346324i	$-0.112570\pi$
$379$	21.5558	+	12.4453i	1.10725	+	0.639270i	0.169133	+	0.985593i	$0.445903\pi$
$380$	6.70677	−	4.37005i	0.344050	−	0.224179i
$381$	17.3995	−	13.7169i	0.891402	−	0.702739i
$382$	−16.7063	+	8.34544i	−0.854769	+	0.426990i
$383$	−0.621308	−	10.6674i	−0.0317473	−	0.545081i	−0.976259	−	0.216604i	$-0.930502\pi$
$383$	−0.621308	−	10.6674i	−0.0317473	−	0.545081i	0.944512	−	0.328477i	$-0.106535\pi$
$384$	11.8997	+	15.5691i	0.607252	+	0.794509i
$385$	−1.35972	−	0.322260i	−0.0692978	−	0.0164239i
$386$	1.11417	+	19.8628i	0.0567099	+	1.01099i
$387$	−22.3401	−	11.3006i	−1.13561	−	0.574439i
$388$	−15.5150	−	21.0278i	−0.787653	−	1.06752i
$389$	−6.12641	−	12.1987i	−0.310622	−	0.618498i	0.683107	−	0.730318i	$-0.260628\pi$
$389$	−6.12641	−	12.1987i	−0.310622	−	0.618498i	−0.993728	+	0.111820i	$0.964332\pi$
$390$	−7.36059	−	10.5927i	−0.372718	−	0.536382i
$391$	−13.1082	+	5.65434i	−0.662912	+	0.285952i
$392$	−0.447261	−	8.63524i	−0.0225901	−	0.436146i
$393$	−2.43033	+	0.0672017i	−0.122594	+	0.00338988i
$394$	−13.2860	−	15.9027i	−0.669338	−	0.801167i
$395$	15.2316	+	5.54384i	0.766383	+	0.278941i
$396$	−0.626128	−	2.72896i	−0.0314641	−	0.137135i
$397$	4.97404	−	1.81040i	0.249640	−	0.0908614i	−0.214170	−	0.976797i	$-0.568705\pi$
$397$	4.97404	−	1.81040i	0.249640	−	0.0908614i	0.463809	+	0.885935i	$0.346482\pi$
$398$	2.98764	+	1.73346i	0.149757	+	0.0868905i
$399$	3.84564	+	8.27821i	0.192523	+	0.414429i
$400$	−9.05747	−	6.06905i	−0.452873	−	0.303453i
$401$	2.56100	+	10.8057i	0.127890	+	0.539611i	0.998836	+	0.0482325i	$0.0153588\pi$
$401$	2.56100	+	10.8057i	0.127890	+	0.539611i	−0.870946	+	0.491379i	$0.836493\pi$
$402$	−21.1008	+	12.9109i	−1.05241	+	0.643938i
$403$	1.39171	+	11.9069i	0.0693261	+	0.593123i
$404$	−9.97693	−	0.624007i	−0.496371	−	0.0310455i
$405$	3.20634	−	13.1885i	0.159324	−	0.655344i
$406$	−9.32752	−	9.92913i	−0.462917	−	0.492775i
$407$	−2.38936	+	0.279277i	−0.118436	+	0.0138432i
$408$	6.05899	−	9.65220i	0.299965	−	0.477855i
$409$	−31.9830	+	7.58011i	−1.58146	+	0.374812i	−0.925126	−	0.379660i	$-0.876041\pi$
$409$	−31.9830	+	7.58011i	−1.58146	+	0.374812i	−0.656332	+	0.754472i	$0.727893\pi$
$410$	−6.86624	−	23.1150i	−0.339100	−	1.14157i
$411$	−1.99743	+	22.4571i	−0.0985261	+	1.10773i
$412$	−2.58182	−	11.1055i	−0.127197	−	0.547127i
$413$	−5.00960	−	13.7638i	−0.246506	−	0.677270i
$414$	16.6351	+	20.0288i	0.817571	+	0.984361i
$415$	−3.42866	+	9.42016i	−0.168306	+	0.462418i
$416$	−16.6187	+	10.6769i	−0.814797	+	0.523480i
$417$	9.11069	−	5.60140i	0.446152	−	0.274302i
$418$	0.199604	+	1.74005i	0.00976296	+	0.0851088i
$419$	7.57392	+	17.5583i	0.370010	+	0.857780i	0.996901	+	0.0786725i	$0.0250681\pi$
$419$	7.57392	+	17.5583i	0.370010	+	0.857780i	−0.626890	+	0.779107i	$0.715673\pi$
$420$	−6.94050	+	7.70955i	−0.338662	+	0.376188i
$421$	−30.5115	+	15.3234i	−1.48704	+	0.746819i	−0.992489	−	0.122331i	$-0.960963\pi$
$421$	−30.5115	+	15.3234i	−1.48704	+	0.746819i	−0.494549	+	0.869150i	$0.664667\pi$
$422$	−3.10460	+	26.0768i	−0.151130	+	1.26940i
$423$	−17.0522	−	12.7716i	−0.829106	−	0.620978i
$424$	−0.0417154	+	6.48854i	−0.00202588	+	0.315111i
$425$	−1.46227	+	6.16979i	−0.0709304	+	0.299279i
$426$	−33.0042	−	6.93836i	−1.59906	−	0.336165i
$427$	6.63550	−	0.386474i	0.321114	−	0.0187028i
$428$	22.9878	+	8.47864i	1.11116	+	0.409831i
$429$	2.79308	−	0.405006i	0.134851	−	0.0195539i
$430$	−3.12818	+	17.5211i	−0.150854	+	0.844944i
$431$	−10.3997	+	18.0128i	−0.500937	+	0.867648i	0.499063	+	0.866566i	$0.333678\pi$
$431$	−10.3997	+	18.0128i	−0.500937	+	0.867648i	−0.999999	+	0.00108219i	$0.999656\pi$
$432$	−20.0053	−	5.63810i	−0.962505	−	0.271263i
$433$	−8.69284	−	15.0564i	−0.417751	−	0.723566i	0.577962	−	0.816064i	$-0.303848\pi$
$433$	−8.69284	−	15.0564i	−0.417751	−	0.723566i	−0.995713	+	0.0924977i	$0.970515\pi$
$434$	9.06638	−	3.27791i	0.435200	−	0.157345i
$435$	0.386855	−	12.6659i	0.0185483	−	0.607285i
$436$	19.4080	−	16.1440i	0.929475	−	0.773158i
$437$	−8.94984	−	13.6076i	−0.428129	−	0.650939i
$438$	−23.6943	+	12.6663i	−1.13216	+	0.605220i
$439$	15.0205	+	14.1711i	0.716888	+	0.676349i	0.955575	−	0.294748i	$-0.0952356\pi$
$439$	15.0205	+	14.1711i	0.716888	+	0.676349i	−0.238687	+	0.971096i	$0.576717\pi$
$440$	−1.73016	+	0.984129i	−0.0824819	+	0.0469165i
$441$	5.87490	+	7.04265i	0.279757	+	0.335364i
$442$	9.19977	+	6.87966i	0.437588	+	0.327232i
$443$	−13.8638	−	9.11834i	−0.658688	−	0.433226i	0.175670	−	0.984449i	$-0.443791\pi$
$443$	−13.8638	−	9.11834i	−0.658688	−	0.433226i	−0.834358	+	0.551223i	$0.814161\pi$
$444$	−6.68830	+	16.5583i	−0.317412	+	0.785821i
$445$	7.85795	+	0.918463i	0.372503	+	0.0435393i
$446$	28.2609	−	20.9454i	1.33819	−	0.991796i
$447$	21.6186	−	4.43133i	1.02253	−	0.209595i
$448$	11.4135	+	11.0489i	0.539236	+	0.522010i
$449$	−14.1839	+	2.50101i	−0.669382	+	0.118030i	−0.498003	−	0.867175i	$-0.665933\pi$
$449$	−14.1839	+	2.50101i	−0.669382	+	0.118030i	−0.171379	+	0.985205i	$0.554822\pi$
$450$	11.5478	−	0.614293i	0.544370	−	0.0289581i
$451$	5.19582	+	0.916164i	0.244662	+	0.0431405i
$452$	−11.3696	+	10.6349i	−0.534781	+	0.500225i
$453$	−3.74971	+	3.73889i	−0.176177	+	0.175669i
$454$	−18.4073	−	4.40430i	−0.863898	−	0.206704i
$455$	−7.17569	−	7.60579i	−0.336402	−	0.356565i
$456$	12.0451	+	4.89537i	0.564064	+	0.229247i
$457$	−7.04053	+	16.3218i	−0.329342	+	0.763501i	0.670426	+	0.741976i	$0.266111\pi$
$457$	−7.04053	+	16.3218i	−0.329342	+	0.763501i	−0.999768	+	0.0215244i	$0.993148\pi$
$458$	4.17048	−	13.8225i	0.194874	−	0.645882i
$459$	1.00131	+	12.0461i	0.0467372	+	0.562263i
$460$	10.2373	−	15.4207i	0.477316	−	0.718993i
$461$	6.14504	−	4.57481i	0.286203	−	0.213070i	−0.444477	−	0.895790i	$-0.646610\pi$
$461$	6.14504	−	4.57481i	0.286203	−	0.213070i	0.730680	+	0.682720i	$0.239203\pi$
$462$	−0.830414	−	2.11233i	−0.0386344	−	0.0982746i
$463$	−7.16996	−	2.14655i	−0.333216	−	0.0997584i	0.115824	−	0.993270i	$-0.463049\pi$
$463$	−7.16996	−	2.14655i	−0.333216	−	0.0997584i	−0.449041	+	0.893511i	$0.648234\pi$
$464$	−19.3619	−	1.29432i	−0.898852	−	0.0600873i
$465$	8.12185	+	3.80158i	0.376642	+	0.176294i
$466$	−23.5468	+	13.5276i	−1.09078	+	0.626652i
$467$	−2.71528	−	2.27839i	−0.125648	−	0.105431i	0.577798	−	0.816180i	$-0.303912\pi$
$467$	−2.71528	−	2.27839i	−0.125648	−	0.105431i	−0.703446	+	0.710748i	$0.748356\pi$
$468$	7.30678	−	19.6357i	0.337756	−	0.907660i
$469$	−15.3617	+	12.8900i	−0.709337	+	0.595204i
$470$	−5.21067	+	14.2213i	−0.240350	+	0.655980i
$471$	−33.3448	+	13.1913i	−1.53645	+	0.607823i
$472$	−18.5838	−	9.48323i	−0.855388	−	0.436501i
$473$	−3.12366	−	2.32548i	−0.143626	−	0.106926i
$474$	6.72279	+	25.4547i	0.308788	+	1.16918i
$475$	−7.22177	−	0.420620i	−0.331357	−	0.0192994i
$476$	3.69547	−	8.46709i	0.169381	−	0.388088i
$477$	−4.09384	−	5.53228i	−0.187444	−	0.253306i
$478$	−29.5750	−	14.9326i	−1.35273	−	0.683000i
$479$	0.295203	+	0.986048i	0.0134882	+	0.0450537i	0.964469	−	0.264197i	$-0.0851069\pi$
$479$	0.295203	+	0.986048i	0.0134882	+	0.0450537i	−0.950981	+	0.309251i	$0.899922\pi$
$480$	0.250135	+	14.7740i	0.0114171	+	0.674336i
$481$	−16.0864	−	8.07888i	−0.733475	−	0.368365i
$482$	15.1938	+	10.0398i	0.692056	+	0.457300i
$483$	15.7465	+	14.0540i	0.716490	+	0.639479i
$484$	1.16158	+	21.5332i	0.0527992	+	0.978781i
$485$		−	19.7046i		−	0.894738i
$486$	20.5632	−	7.94706i	0.932765	−	0.360486i
$487$		−	9.54118i		−	0.432352i	−0.976354	−	0.216176i	$-0.930641\pi$
$487$		−	9.54118i		−	0.432352i	0.976354	−	0.216176i	$-0.0693585\pi$
$488$	6.54130	−	6.84468i	0.296111	−	0.309844i
$489$	14.5986	+	13.0294i	0.660169	+	0.589212i
$490$	3.59448	−	5.43972i	0.162382	−	0.245742i
$491$	−3.03795	−	1.52572i	−0.137101	−	0.0688547i	0.378926	−	0.925427i	$-0.376293\pi$
$491$	−3.03795	−	1.52572i	−0.137101	−	0.0688547i	−0.516027	+	0.856572i	$0.672590\pi$
$492$	24.4677	−	30.5826i	1.10309	−	1.37877i
$493$	3.23667	+	10.8112i	0.145772	+	0.486914i
$494$	−5.90707	+	11.6994i	−0.265771	+	0.526379i
$495$	0.841803	−	1.93612i	0.0378363	−	0.0870221i
$496$	6.26808	−	12.2185i	0.281445	−	0.548626i
$497$	−27.2933	−	1.58965i	−1.22427	−	0.0713057i
$498$	−15.7428	+	4.15780i	−0.705453	+	0.186315i
$499$	−28.9331	−	21.5399i	−1.29522	−	0.964258i	−0.999961	−	0.00884241i	$-0.997185\pi$
$499$	−28.9331	−	21.5399i	−1.29522	−	0.964258i	−0.295263	−	0.955416i	$-0.595407\pi$
$500$	−7.87580	−	21.9306i	−0.352217	−	0.980766i
$501$	6.38748	−	2.52690i	0.285371	−	0.112894i
$502$	−2.51280	−	0.920686i	−0.112152	−	0.0410922i
$503$	−27.1420	+	22.7748i	−1.21020	+	1.01548i	−0.210922	+	0.977503i	$0.567647\pi$
$503$	−27.1420	+	22.7748i	−1.21020	+	1.01548i	−0.999279	+	0.0379763i	$0.987909\pi$
$504$	−16.7161	−	2.11190i	−0.744594	−	0.0940715i
$505$	−5.77421	−	4.84514i	−0.256949	−	0.215606i
$506$	2.01741	+	3.51162i	0.0896849	+	0.156110i
$507$	−1.26591	−	0.592533i	−0.0562212	−	0.0263153i
$508$	0.109652	−	25.5835i	0.00486501	−	1.13508i
$509$	4.42384	+	1.32441i	0.196083	+	0.0587035i	0.383339	−	0.923608i	$-0.374774\pi$
$509$	4.42384	+	1.32441i	0.196083	+	0.0587035i	−0.187256	+	0.982311i	$0.559959\pi$
$510$	7.99747	−	3.14402i	0.354134	−	0.139220i
$511$	−17.4702	+	13.0061i	−0.772835	+	0.575354i
$512$	22.6232	+	0.436389i	0.999814	+	0.0192858i
$513$	−13.3360	+	3.51150i	−0.588800	+	0.155037i
$514$	−30.7292	−	9.27151i	−1.35541	−	0.408949i
$515$	3.40521	−	7.89415i	0.150051	−	0.347858i
$516$	−26.2697	+	12.0670i	−1.15646	+	0.531219i
$517$	−2.27414	−	2.41045i	−0.100017	−	0.106011i
$518$	−3.36870	+	14.0792i	−0.148012	+	0.618603i
$519$	20.0186	−	19.9609i	0.878719	−	0.876184i
$520$	−14.8634	−	0.961611i	−0.651802	−	0.0421695i
$521$	25.0561	+	4.41807i	1.09773	+	0.193559i	0.693043	−	0.720896i	$-0.256270\pi$
$521$	25.0561	+	4.41807i	1.09773	+	0.193559i	0.404686	+	0.914456i	$0.367381\pi$
$522$	17.2529	−	11.2234i	0.755137	−	0.491236i
$523$	8.49643	−	1.49815i	0.371523	−	0.0655095i	0.0152305	−	0.999884i	$-0.495152\pi$
$523$	8.49643	−	1.49815i	0.371523	−	0.0655095i	0.356292	+	0.934375i	$0.384041\pi$
$524$	−1.68608	+	2.24466i	−0.0736569	+	0.0980582i
$525$	9.18351	−	1.88241i	0.400801	−	0.0821553i
$526$	7.43272	+	10.0287i	0.324082	+	0.437271i
$527$	−7.93234	−	0.927157i	−0.345538	−	0.0403876i
$528$	−2.91626	−	1.39561i	−0.126914	−	0.0607360i
$529$	−12.2482	−	8.05577i	−0.532530	−	0.350251i
$530$	−2.93013	+	3.91829i	−0.127277	+	0.170200i
$531$	21.8040	−	3.77971i	0.946212	−	0.164025i
$532$	10.2453	+	2.47461i	0.444191	+	0.107288i
$533$	28.7164	+	27.0926i	1.24385	+	1.17351i
$534$	6.05806	+	11.3325i	0.262158	+	0.490406i
$535$	10.1523	+	15.4358i	0.438921	+	0.667347i
$536$	−3.49843	+	28.3492i	−0.151109	+	1.22450i
$537$	−0.662398	+	21.6874i	−0.0285846	+	0.935882i
$538$	−0.630510	−	1.74393i	−0.0271832	−	0.0751862i
$539$	0.713291	+	1.23546i	0.0307236	+	0.0532149i
$540$	−9.61425	−	12.3770i	−0.413732	−	0.532622i
$541$	−8.76107	+	15.1746i	−0.376668	+	0.652407i	−0.990575	−	0.136971i	$-0.956263\pi$
$541$	−8.76107	+	15.1746i	−0.376668	+	0.652407i	0.613908	+	0.789378i	$0.289597\pi$
$542$	10.1030	+	1.80376i	0.433959	+	0.0774780i
$543$	−17.4425	+	2.52922i	−0.748529	+	0.108539i
$544$	−4.36801	−	12.4133i	−0.187277	−	0.532214i
$545$	19.0034	−	1.10682i	0.814015	−	0.0474110i
$546$	3.49410	−	16.6206i	0.149534	−	0.711298i
$547$	3.22916	−	13.6249i	0.138069	−	0.582559i	−0.859390	−	0.511320i	$-0.829157\pi$
$547$	3.22916	−	13.6249i	0.138069	−	0.582559i	0.997459	−	0.0712389i	$-0.0226953\pi$
$548$	18.8594	+	17.9463i	0.805633	+	0.766628i
$549$	−1.19463	+	9.97076i	−0.0509854	+	0.425541i
$550$	1.78617	+	0.212654i	0.0761625	+	0.00906760i
$551$	−11.5058	+	5.77841i	−0.490162	+	0.246168i
$552$	30.0571	−	0.637764i	1.27932	−	0.0271450i
$553$	8.45327	+	19.5969i	0.359470	+	0.833344i
$554$	26.2011	−	3.00557i	1.11318	−	0.127695i
$555$	−11.4710	+	7.05259i	−0.486919	+	0.299366i
$556$	1.48623	−	12.2596i	0.0630303	−	0.519924i
$557$	−9.54600	+	26.2274i	−0.404477	+	1.11129i	0.555574	+	0.831467i	$0.312499\pi$
$557$	−9.54600	+	26.2274i	−0.404477	+	1.11129i	−0.960051	+	0.279825i	$0.909724\pi$
$558$	2.45705	+	14.3567i	0.104015	+	0.607769i
$559$	−9.96654	−	27.3828i	−0.421540	−	1.15817i
$560$	1.97880	+	11.8136i	0.0836195	+	0.499216i
$561$	−0.166577	+	1.87281i	−0.00703287	+	0.0790703i
$562$	38.7640	−	11.5147i	1.63516	−	0.485719i
$563$	−5.30749	+	1.25790i	−0.223684	+	0.0530141i	−0.340929	−	0.940089i	$-0.610742\pi$
$563$	−5.30749	+	1.25790i	−0.223684	+	0.0530141i	0.117245	+	0.993103i	$0.462594\pi$
$564$	−23.7984	+	6.23082i	−1.00210	+	0.262365i
$565$	−11.6597	+	1.36282i	−0.490526	+	0.0573342i
$566$	−23.8639	+	22.4180i	−1.00308	+	0.942298i
$567$	15.5281	−	8.84594i	0.652121	−	0.371495i
$568$	−29.9923	+	24.8397i	−1.25845	+	1.04225i
$569$	0.506249	+	4.33124i	0.0212231	+	0.181575i	0.999692	−	0.0248195i	$-0.00790109\pi$
$569$	0.506249	+	4.33124i	0.0212231	+	0.181575i	−0.978469	+	0.206394i	$0.933827\pi$
$570$	5.11687	+	8.36270i	0.214322	+	0.350275i
$571$	3.43969	+	14.5132i	0.143946	+	0.607358i	0.996417	+	0.0845817i	$0.0269554\pi$
$571$	3.43969	+	14.5132i	0.143946	+	0.607358i	−0.852470	+	0.522776i	$0.824896\pi$
$572$	1.64153	−	2.81528i	0.0686359	−	0.117713i
$573$	−9.63610	−	20.7429i	−0.402554	−	0.866546i
$574$	15.9337	−	27.4620i	0.665061	−	1.14624i
$575$	−15.7182	+	5.72097i	−0.655496	+	0.238581i
$576$	−19.4742	+	14.0269i	−0.811427	+	0.584454i
$577$	−29.5490	−	10.7549i	−1.23014	−	0.447734i	−0.356495	−	0.934297i	$-0.616028\pi$
$577$	−29.5490	−	10.7549i	−1.23014	−	0.447734i	−0.873645	+	0.486563i	$0.838250\pi$
$578$	12.5769	−	10.5075i	0.523132	−	0.437052i
$579$	−24.3558	+	0.673469i	−1.01219	+	0.0279884i
$580$	−11.1685	−	9.45334i	−0.463746	−	0.392529i
$581$	−12.1200	+	5.22804i	−0.502820	+	0.216896i
$582$	26.2827	−	18.2632i	1.08945	−	0.757033i
$583$	−0.480450	−	0.956655i	−0.0198982	−	0.0396206i
$584$	−5.58352	+	30.5171i	−0.231048	+	1.26281i
$585$	13.2240	−	8.64295i	0.546746	−	0.357342i
$586$	48.0190	−	2.69355i	1.98365	−	0.111269i
$587$	16.3446	+	3.87375i	0.674615	+	0.159887i	0.553624	−	0.832767i	$-0.313245\pi$
$587$	16.3446	+	3.87375i	0.674615	+	0.159887i	0.120991	+	0.992654i	$0.461393\pi$
$588$	10.5873	−	0.247344i	0.436611	−	0.0102003i
$589$	−0.529785	−	9.09607i	−0.0218294	−	0.374797i
$590$	−7.03034	−	14.0737i	−0.289435	−	0.579404i
$591$	19.9308	−	15.7125i	0.819844	−	0.646326i
$592$	10.1569	+	17.9458i	0.417445	+	0.737566i
$593$	−21.8253	−	12.6008i	−0.896257	−	0.517454i	−0.0202734	−	0.999794i	$-0.506454\pi$
$593$	−21.8253	−	12.6008i	−0.896257	−	0.517454i	−0.875984	+	0.482340i	$0.839787\pi$
$594$	3.36270	−	0.671663i	0.137973	−	0.0275587i
$595$	6.03283	−	3.48306i	0.247322	−	0.142791i
$596$	11.5338	−	22.7224i	0.472443	−	0.930744i
$597$	−2.22606	+	3.59735i	−0.0911066	+	0.147230i
$598$	−1.82689	+	30.2496i	−0.0747072	+	1.23700i
$599$	11.7456	−	7.72518i	0.479911	−	0.315642i	−0.286402	−	0.958109i	$-0.592459\pi$
$599$	11.7456	−	7.72518i	0.479911	−	0.315642i	0.766313	+	0.642467i	$0.222089\pi$
$600$	7.74494	−	10.8776i	0.316186	−	0.444077i
$601$	26.7367	−	28.3392i	1.09061	−	1.15598i	0.103717	−	0.994607i	$-0.466926\pi$
$601$	26.7367	−	28.3392i	1.09061	−	1.15598i	0.986893	−	0.161373i	$-0.0515923\pi$
$602$	−19.6069	+	12.8356i	−0.799119	+	0.523139i
$603$	−15.0726	−	26.2816i	−0.613804	−	1.07027i
$604$	0.683806	+	6.07607i	0.0278237	+	0.247232i
$605$	−8.93527	+	13.5854i	−0.363270	+	0.552326i
$606$	1.11080	−	12.1926i	0.0451233	−	0.495290i
$607$	5.06814	−	43.3607i	0.205709	−	1.75996i	−0.357754	−	0.933816i	$-0.616457\pi$
$607$	5.06814	−	43.3607i	0.205709	−	1.75996i	0.563464	−	0.826141i	$-0.309468\pi$
$608$	13.0816	−	7.36690i	0.530528	−	0.298767i
$609$	12.4800	−	11.0740i	0.505717	−	0.448742i
$610$	7.03324	−	1.22461i	0.284767	−	0.0495832i
$611$	−4.30607	−	24.4209i	−0.174205	−	0.987965i
$612$	11.6061	+	7.75330i	0.469148	+	0.313409i
$613$	5.68895	−	32.2636i	0.229774	−	1.30312i	−0.623570	−	0.781768i	$-0.714318\pi$
$613$	5.68895	−	32.2636i	0.229774	−	1.30312i	0.853344	−	0.521348i	$-0.174571\pi$
$614$	−0.0937520	+	43.7479i	−0.00378352	+	1.76552i
$615$	28.5373	−	7.60238i	1.15074	−	0.306558i
$616$	−2.50584	−	0.767787i	−0.100963	−	0.0309350i
$617$	−12.4195	+	11.7172i	−0.499990	+	0.471716i	−0.894432	−	0.447205i	$-0.852419\pi$
$617$	−12.4195	+	11.7172i	−0.499990	+	0.471716i	0.394442	+	0.918921i	$0.370938\pi$
$618$	13.6856	−	2.77470i	0.550517	−	0.111615i
$619$	8.15835	+	3.51917i	0.327912	+	0.141447i	0.553670	−	0.832736i	$-0.313227\pi$
$619$	8.15835	+	3.51917i	0.327912	+	0.141447i	−0.225759	+	0.974183i	$0.572486\pi$
$620$	9.27323	−	4.60753i	0.372422	−	0.185043i
$621$	−25.0986	+	19.6692i	−1.00717	+	0.789299i
$622$	−23.1990	+	5.44577i	−0.930193	+	0.218356i
$623$	6.22055	+	8.35565i	0.249221	+	0.334762i
$624$	−12.4935	−	20.7166i	−0.500140	−	0.829328i
$625$	1.13059	−	3.77645i	0.0452238	−	0.151058i
$626$	−27.8249	+	29.3663i	−1.11211	+	1.17371i
$627$	−2.13720	+	0.183870i	−0.0853517	+	0.00734307i
$628$	−12.0455	+	39.6159i	−0.480667	+	1.58085i
$629$	7.70850	−	9.18664i	0.307358	−	0.366295i
$630$	−9.19714	−	8.76495i	−0.366423	−	0.349204i
$631$	8.35166	+	9.95312i	0.332474	+	0.396227i	0.906220	−	0.422806i	$-0.138955\pi$
$631$	8.35166	+	9.95312i	0.332474	+	0.396227i	−0.573746	+	0.819033i	$0.694510\pi$
$632$	27.8362	+	12.2202i	1.10726	+	0.486094i
$633$	−31.8166	−	4.70741i	−1.26460	−	0.187103i
$634$	35.7623	+	15.5173i	1.42030	+	0.616272i
$635$	11.5199	−	15.4739i	0.457152	−	0.614061i
$636$	−7.94215	−	0.276653i	−0.314927	−	0.0109700i
$637$	−0.620695	+	10.6569i	−0.0245928	+	0.422242i
$638$	2.94240	−	1.26175i	0.116491	−	0.0499533i
$639$	9.64173	−	40.1642i	0.381421	−	1.58887i
$640$	13.5314	+	10.3928i	0.534876	+	0.410813i
$641$	19.5704	−	5.85900i	0.772986	−	0.231417i	0.124066	−	0.992274i	$-0.460406\pi$
$641$	19.5704	−	5.85900i	0.772986	−	0.231417i	0.648919	+	0.760857i	$0.275221\pi$
$642$	−11.1792	+	27.8481i	−0.441208	+	1.09908i
$643$	19.2987	−	38.4269i	0.761068	−	1.51541i	−0.0932405	−	0.995644i	$-0.529723\pi$
$643$	19.2987	−	38.4269i	0.761068	−	1.51541i	0.854308	−	0.519767i	$-0.173981\pi$
$644$	24.0189	−	4.12911i	0.946476	−	0.162710i
$645$	−21.3415	−	4.43882i	−0.840321	−	0.174778i
$646$	−6.67647	−	5.62665i	−0.262682	−	0.221377i
$647$	−46.9927			−1.84747			−0.923737	−	0.383028i	$-0.874881\pi$
$647$	−46.9927			−1.84747			−0.923737	+	0.383028i	$0.874881\pi$
$648$	7.59796	−	24.2955i	0.298476	−	0.954417i
$649$	3.44215			0.135116
$650$	10.2925	+	8.67407i	0.403704	+	0.340225i
$651$	3.69778	+	11.2135i	0.144927	+	0.439491i
$652$	22.2679	−	3.82809i	0.872077	−	0.149920i
$653$	5.40440	−	10.7611i	0.211491	−	0.421113i	−0.762728	−	0.646720i	$-0.776140\pi$
$653$	5.40440	−	10.7611i	0.211491	−	0.421113i	0.974218	+	0.225607i	$0.0724366\pi$
$654$	19.0896	+	24.3216i	0.746462	+	0.951048i
$655$	−2.02794	+	0.607125i	−0.0792382	+	0.0237224i
$656$	−10.0520	−	44.0936i	−0.392464	−	1.72157i
$657$	−14.6830	−	29.4481i	−0.572838	−	1.14888i
$658$	−18.3283	+	7.85952i	−0.714512	+	0.306396i
$659$	0.667333	−	11.4577i	0.0259956	−	0.446327i	−0.960047	−	0.279837i	$-0.909720\pi$
$659$	0.667333	−	11.4577i	0.0259956	−	0.446327i	0.986043	−	0.166490i	$-0.0532434\pi$
$660$	−1.14467	−	2.15236i	−0.0445562	−	0.0837805i
$661$	20.4283	−	27.4400i	0.794570	−	1.06729i	−0.201566	−	0.979475i	$-0.564603\pi$
$661$	20.4283	−	27.4400i	0.794570	−	1.06729i	0.996137	−	0.0878182i	$-0.0279894\pi$
$662$	−17.7633	−	7.70753i	−0.690390	−	0.299562i
$663$	−8.74228	+	11.0236i	−0.339522	+	0.428123i
$664$	−7.55775	+	17.2157i	−0.293298	+	0.668097i
$665$	5.10857	+	6.08816i	0.198102	+	0.236089i
$666$	−20.0390	−	8.76383i	−0.776494	−	0.339591i
$667$	−19.1365	+	22.8060i	−0.740968	+	0.883052i
$668$	2.30741	−	7.58876i	0.0892765	−	0.293618i
$669$	24.6600	+	35.3266i	0.953409	+	1.36580i
$670$	−14.8142	+	15.6349i	−0.572322	+	0.604028i
$671$	−0.447993	+	1.49640i	−0.0172946	+	0.0577679i
$672$	−13.9234	+	13.5888i	−0.537107	+	0.524201i
$673$	5.21677	+	7.00734i	0.201092	+	0.270113i	0.891217	−	0.453577i	$-0.149852\pi$
$673$	5.21677	+	7.00734i	0.201092	+	0.270113i	−0.690126	+	0.723690i	$0.742445\pi$
$674$	30.2759	−	7.10703i	1.16618	−	0.273752i
$675$	0.350573	+	14.1588i	0.0134936	+	0.544973i
$676$	−1.44537	+	0.718152i	−0.0555912	+	0.0276212i
$677$	−27.9058	−	12.0374i	−1.07251	−	0.462634i	−0.214739	−	0.976671i	$-0.568890\pi$
$677$	−27.9058	−	12.0374i	−1.07251	−	0.462634i	−0.857768	+	0.514037i	$0.828149\pi$
$678$	−12.6245	−	14.2890i	−0.484842	−	0.548765i
$679$	18.8716	−	17.8044i	0.724224	−	0.683270i
$680$	2.90691	−	9.48732i	0.111475	−	0.363822i
$681$	6.03192	−	22.3821i	0.231144	−	0.857682i
$682$	−0.00485525	+	2.26562i	−0.000185917	+	0.0867552i
$683$	6.13939	−	34.8182i	0.234917	−	1.33228i	−0.607870	−	0.794036i	$-0.707976\pi$
$683$	6.13939	−	34.8182i	0.234917	−	1.33228i	0.842788	−	0.538246i	$-0.180913\pi$
$684$	−6.41192	+	14.5760i	−0.245166	+	0.557329i
$685$	3.40877	+	19.3321i	0.130242	+	0.738641i
$686$	27.8234	−	4.84456i	1.06230	−	0.184966i
$687$	16.7772	+	5.58627i	0.640090	+	0.213129i
$688$	−7.97629	+	32.4138i	−0.304093	+	1.23577i
$689$	0.929977	−	7.95646i	0.0354293	−	0.303117i
$690$	18.5229	+	13.0691i	0.705154	+	0.497534i
$691$	−19.8509	+	30.1818i	−0.755164	+	1.14817i	0.229432	+	0.973325i	$0.426313\pi$
$691$	−19.8509	+	30.1818i	−0.755164	+	1.14817i	−0.984596	+	0.174847i	$0.944057\pi$
$692$	−3.65064	−	32.4384i	−0.138776	−	1.23312i
$693$	2.61490	−	0.943198i	0.0993317	−	0.0358291i
$694$	40.2621	−	26.3574i	1.52833	−	1.00051i
$695$	6.39022	−	6.77324i	0.242395	−	0.256924i
$696$	2.25771	−	23.6588i	0.0855785	−	0.896784i
$697$	−21.9744	+	14.4528i	−0.832339	+	0.547438i
$698$	1.94751	−	32.2467i	0.0737142	−	1.22056i
$699$	−15.7425	−	29.2975i	−0.595435	−	1.10813i
$700$	4.89953	−	9.65238i	0.185185	−	0.364826i
$701$	−2.68333	+	1.54922i	−0.101348	+	0.0585132i	−0.549817	−	0.835285i	$-0.685303\pi$
$701$	−2.68333	+	1.54922i	−0.101348	+	0.0585132i	0.448469	+	0.893798i	$0.351969\pi$
$702$	23.7850	+	9.62799i	0.897706	+	0.363385i
$703$	11.8488	+	6.84091i	0.446886	+	0.258010i
$704$	−3.35733	+	1.63240i	−0.126534	+	0.0615235i
$705$	−17.2293	−	6.87360i	−0.648893	−	0.258875i
$706$	−1.10732	−	2.21669i	−0.0416745	−	0.0834261i
$707$	−0.577076	−	9.90802i	−0.0217032	−	0.372629i
$708$	12.2559	−	22.4215i	0.460606	−	0.842653i
$709$	−23.3242	−	5.52794i	−0.875959	−	0.207606i	−0.232046	−	0.972705i	$-0.574542\pi$
$709$	−23.3242	−	5.52794i	−0.875959	−	0.207606i	−0.643913	+	0.765099i	$0.722690\pi$
$710$	−29.3184	+	1.64457i	−1.10030	+	0.0617196i
$711$	−31.3967	+	7.34542i	−1.17747	+	0.275475i
$712$	14.5958	+	2.67049i	0.546999	+	0.100081i
$713$	−9.45540	−	18.8273i	−0.354108	−	0.705086i
$714$	10.2374	+	4.81855i	0.383124	+	0.180330i
$715$	2.25637	−	0.973302i	0.0843834	−	0.0363994i
$716$	19.1234	+	16.1866i	0.714676	+	0.604923i
$717$	19.3094	−	35.6881i	0.721124	−	1.33279i
$718$	19.3419	−	16.1593i	0.721833	−	0.603059i
$719$	45.0315	+	16.3901i	1.67939	+	0.611248i	0.993226	−	0.116199i	$-0.0370710\pi$
$719$	45.0315	+	16.3901i	1.67939	+	0.611248i	0.686164	+	0.727447i	$0.259293\pi$
$720$	−18.0957	−	0.207409i	−0.674389	−	0.00772966i
$721$	10.6373	−	3.87165i	0.396152	−	0.144188i
$722$	−8.48573	+	14.6252i	−0.315806	+	0.544295i
$723$	−12.8195	+	18.2519i	−0.476761	+	0.678796i
$724$	−10.2512	+	17.5811i	−0.380983	+	0.653398i
$725$	3.04946	+	12.8667i	0.113254	+	0.477856i
$726$	−26.4024	+	0.673439i	−0.979885	+	0.0249937i
$727$	5.12090	+	43.8121i	0.189924	+	1.62490i	0.666318	+	0.745668i	$0.267869\pi$
$727$	5.12090	+	43.8121i	0.189924	+	1.62490i	−0.476394	+	0.879232i	$0.658056\pi$
$728$	−12.5091	−	15.1039i	−0.463618	−	0.559788i
$729$	9.01429	+	25.4508i	0.333862	+	0.942622i
$730$	−17.0499	+	16.0168i	−0.631044	+	0.592809i
$731$	19.2819	−	2.25373i	0.713167	−	0.0833573i
$732$	8.15219	+	8.24616i	0.301314	+	0.304787i
$733$	34.2320	−	8.11314i	1.26439	−	0.299666i	0.456884	−	0.889526i	$-0.348965\pi$
$733$	34.2320	−	8.11314i	1.26439	−	0.299666i	0.807505	+	0.589861i	$0.200817\pi$
$734$	18.6781	−	5.54826i	0.689420	−	0.204790i
$735$	6.53462	+	4.58967i	0.241033	+	0.169293i
$736$	21.0274	−	27.6218i	0.775081	−	1.01815i
$737$	−1.61181	−	4.42842i	−0.0593719	−	0.163123i
$738$	36.5902	+	31.0179i	1.34690	+	1.14178i
$739$	2.96935	−	8.15821i	0.109229	−	0.300105i	−0.873020	−	0.487684i	$-0.837842\pi$
$739$	2.96935	−	8.15821i	0.109229	−	0.300105i	0.982250	+	0.187579i	$0.0600641\pi$
$740$	−1.87128	+	15.4358i	−0.0687896	+	0.567431i
$741$	−14.1176	−	7.63848i	−0.518622	−	0.280606i
$742$	−6.40021	+	0.734178i	−0.234959	+	0.0269525i
$743$	14.4505	+	33.5000i	0.530136	+	1.22899i	0.947354	+	0.320188i	$0.103746\pi$
$743$	14.4505	+	33.5000i	0.530136	+	1.22899i	−0.417218	+	0.908807i	$0.636995\pi$
$744$	14.7406	+	8.09850i	0.540416	+	0.296905i
$745$	17.1707	−	8.62343i	0.629085	−	0.315938i
$746$	−40.2562	−	4.79274i	−1.47388	−	0.175475i
$747$	−4.54287	−	19.4177i	−0.166215	−	0.710457i
$748$	1.57278	+	1.49664i	0.0575067	+	0.0547225i
$749$	−5.60997	+	23.6703i	−0.204984	+	0.864896i
$750$	27.1224	−	8.87952i	0.990369	−	0.324234i
$751$	−26.7127	+	1.55584i	−0.974762	+	0.0567734i	−0.538126	−	0.842865i	$-0.680867\pi$
$751$	−26.7127	+	1.55584i	−0.974762	+	0.0567734i	−0.436636	+	0.899638i	$0.643830\pi$
$752$	−11.4743	+	25.9857i	−0.418426	+	0.947602i
$753$	1.21451	−	3.04429i	0.0442593	−	0.110940i
$754$	23.5837	+	4.21058i	0.858868	+	0.153340i
$755$	−2.30526	+	3.99283i	−0.0838970	+	0.145314i
$756$	3.16665	−	20.3913i	0.115170	−	0.741624i
$757$	18.4444	+	31.9466i	0.670373	+	1.16112i	0.977798	+	0.209547i	$0.0671991\pi$
$757$	18.4444	+	31.9466i	0.670373	+	1.16112i	−0.307426	+	0.951572i	$0.599468\pi$
$758$	11.9684	+	33.1034i	0.434711	+	1.20237i
$759$	−4.36924	+	2.34773i	−0.158593	+	0.0852173i
$760$	11.2354	+	1.38650i	0.407550	+	0.0502937i
$761$	−0.437919	−	0.665823i	−0.0158746	−	0.0241361i	0.827463	−	0.561520i	$-0.189783\pi$
$761$	−0.437919	−	0.665823i	−0.0158746	−	0.0241361i	−0.843338	+	0.537384i	$0.819413\pi$
$762$	31.3168	+	1.02369i	1.13449	+	0.0370842i
$763$	18.2308	+	17.1999i	0.660001	+	0.622679i
$764$	−25.6719	−	6.20068i	−0.928777	−	0.224333i
$765$	3.57103	+	9.90022i	0.129111	+	0.357943i
$766$	9.04998	−	12.1020i	0.326989	−	0.437263i
$767$	21.5199	+	14.1538i	0.777037	+	0.511065i
$768$	−1.32078	+	27.6813i	−0.0476594	+	0.998864i
$769$	−1.75285	−	0.204878i	−0.0632093	−	0.00738810i	0.0844295	−	0.996429i	$-0.473093\pi$
$769$	−1.75285	−	0.204878i	−0.0632093	−	0.00738810i	−0.147639	+	0.989041i	$0.547167\pi$
$770$	−1.17671	−	1.58768i	−0.0424056	−	0.0572162i
$771$	12.4190	−	37.2979i	0.447259	−	1.34325i
$772$	−16.8973	+	22.4951i	−0.608146	+	0.809615i
$773$	1.76661	−	0.311501i	0.0635405	−	0.0112039i	−0.141788	−	0.989897i	$-0.545285\pi$
$773$	1.76661	−	0.311501i	0.0635405	−	0.0112039i	0.205328	+	0.978693i	$0.434174\pi$
$774$	−13.8597	−	32.5802i	−0.498177	−	1.17107i
$775$	−9.21547	−	1.62494i	−0.331030	−	0.0583695i
$776$	2.38596	−	36.8791i	0.0856509	−	1.32388i
$777$	−17.1193	−	4.61362i	−0.614152	−	0.165513i
$778$	4.49228	−	18.7750i	0.161056	−	0.673117i
$779$	−20.5918	−	21.8261i	−0.737779	−	0.782000i
$780$	1.69400	−	18.1631i	0.0606549	−	0.650343i
$781$	2.54479	−	5.89949i	0.0910598	−	0.211100i
$782$	−19.3284	−	5.83170i	−0.691181	−	0.208541i
$783$	13.1405	+	21.5120i	0.469602	+	0.768778i
$784$	7.38613	−	9.74576i	0.263790	−	0.348063i
$785$	−25.0441	+	18.6447i	−0.893863	+	0.665456i
$786$	−2.68940	−	2.14223i	−0.0959278	−	0.0764108i
$787$	−10.1881	−	3.05011i	−0.363165	−	0.108725i	0.100021	−	0.994985i	$-0.468109\pi$
$787$	−10.1881	−	3.05011i	−0.363165	−	0.108725i	−0.463187	+	0.886261i	$0.653294\pi$
$788$	0.125604	−	29.3055i	0.00447447	−	1.04396i
$789$	−12.5360	+	8.75086i	−0.446294	+	0.311539i
$790$	11.4190	+	19.8765i	0.406269	+	0.707175i
$791$	−11.8405	−	9.93536i	−0.421000	−	0.353261i
$792$	1.80996	−	3.52172i	0.0643142	−	0.125139i
$793$	−8.95388	+	7.51320i	−0.317962	+	0.266802i
$794$	7.02885	+	2.57536i	0.249444	+	0.0913962i
$795$	−4.69510	−	3.72344i	−0.166518	−	0.132057i
$796$	1.65103	+	4.59737i	0.0585191	+	0.162950i
$797$	−3.48217	−	2.59238i	−0.123345	−	0.0918269i	0.533718	−	0.845662i	$-0.320794\pi$
$797$	−3.48217	−	2.59238i	−0.123345	−	0.0918269i	−0.657063	+	0.753835i	$0.728202\pi$
$798$	−3.38574	+	12.4568i	−0.119854	+	0.440966i
$799$	16.4922	+	0.960562i	0.583453	+	0.0339822i
$800$	−4.26366	−	14.8177i	−0.150743	−	0.523884i
$801$	−14.0845	+	7.02260i	−0.497650	+	0.248131i
$802$	−7.07841	+	14.0193i	−0.249947	+	0.495038i
$803$	−1.46797	−	4.90338i	−0.0518037	−	0.173036i
$804$	−34.5849	−	5.26856i	−1.21972	−	0.185808i
$805$	16.4221	+	8.24751i	0.578805	+	0.290687i
$806$	−9.34642	+	14.1444i	−0.329214	+	0.498216i
$807$	2.15693	−	0.711272i	0.0759275	−	0.0250380i
$808$	−10.2204	−	9.76736i	−0.359551	−	0.343615i
$809$			27.5020i			0.966918i	0.875367	+	0.483459i	$0.160620\pi$
$809$			27.5020i			0.966918i	−0.875367	+	0.483459i	$0.839380\pi$
$810$	15.4868	−	11.3400i	0.544152	−	0.398446i
$811$			2.07002i			0.0726881i	0.999339	+	0.0363441i	$0.0115712\pi$
$811$			2.07002i			0.0726881i	−0.999339	+	0.0363441i	$0.988429\pi$
$812$	−1.03778	−	19.2381i	−0.0364188	−	0.675124i
$813$	−2.55950	+	12.3059i	−0.0897654	+	0.431585i
$814$	−2.83838	−	1.87556i	−0.0994851	−	0.0657382i
$815$	15.2250	+	7.64626i	0.533307	+	0.267837i
$816$	15.3488	−	4.91598i	0.537316	−	0.172094i
$817$	6.35216	+	21.2177i	0.222234	+	0.742314i
$818$	−41.4946	−	20.9509i	−1.45083	−	0.732529i
$819$	20.2264	+	4.85550i	0.706766	+	0.169665i
$820$	13.6409	−	31.2542i	0.476362	−	1.09144i
$821$	22.7676	+	1.32606i	0.794596	+	0.0462800i	0.450640	−	0.892706i	$-0.351196\pi$
$821$	22.7676	+	1.32606i	0.794596	+	0.0462800i	0.343956	+	0.938986i	$0.388233\pi$
$822$	−22.6265	+	22.4647i	−0.789189	+	0.783546i
$823$	−23.4681	−	17.4713i	−0.818045	−	0.609012i	0.104665	−	0.994508i	$-0.466623\pi$
$823$	−23.4681	−	17.4713i	−0.818045	−	0.609012i	−0.922710	+	0.385496i	$0.874030\pi$
$824$	7.32907	−	14.3624i	0.255320	−	0.500338i
$825$	−0.322441	+	2.17933i	−0.0112259	+	0.0758744i
$826$	7.12633	−	19.4497i	0.247957	−	0.676740i
$827$	−14.6764	+	12.3150i	−0.510349	+	0.428234i	−0.861252	−	0.508178i	$-0.830319\pi$
$827$	−14.6764	+	12.3150i	−0.510349	+	0.428234i	0.350903	+	0.936412i	$0.385875\pi$
$828$	−0.264194	+	36.8197i	−0.00918137	+	1.27957i
$829$	3.12979	+	2.62621i	0.108702	+	0.0912119i	0.695519	−	0.718508i	$-0.255175\pi$
$829$	3.12979	+	2.62621i	0.108702	+	0.0912119i	−0.586817	+	0.809720i	$0.699619\pi$
$830$	−12.2929	+	7.06222i	−0.426693	+	0.245133i
$831$	2.76866	+	32.1813i	0.0960437	+	1.11636i
$832$	−27.7019	−	3.59951i	−0.960392	−	0.124791i
$833$	−6.81289	−	2.03965i	−0.236053	−	0.0706695i
$834$	14.9572	+	2.24575i	0.517925	+	0.0777638i
$835$	4.79741	−	3.57154i	0.166021	−	0.123598i
$836$	−1.36996	+	2.06360i	−0.0473811	+	0.0713713i
$837$	−17.6617	+	2.50892i	−0.610477	+	0.0867209i
$838$	−7.81149	+	25.8901i	−0.269843	+	0.894359i
$839$	−5.04804	+	11.7027i	−0.174278	+	0.404021i	−0.982858	−	0.184365i	$-0.940977\pi$
$839$	−5.04804	+	11.7027i	−0.174278	+	0.404021i	0.808580	+	0.588386i	$0.200236\pi$
$840$	−14.5316	+	2.01183i	−0.501389	+	0.0694147i
$841$	−3.75044	−	3.97524i	−0.129326	−	0.137077i
$842$	−46.9603	−	11.2361i	−1.61836	−	0.387223i
$843$	12.7492	+	47.8572i	0.439107	+	1.64829i
$844$	−27.1226	+	25.3701i	−0.933600	+	0.873273i
$845$	−1.19849	−	0.211327i	−0.0412294	−	0.00726986i
$846$	−6.80071	−	29.3519i	−0.233813	−	1.00914i
$847$	−21.0847	+	3.71781i	−0.724480	+	0.127745i
$848$	−5.95849	+	6.97869i	−0.204616	+	0.239649i
$849$	−26.6156	−	29.9948i	−0.913445	−	1.02942i
$850$	−7.20419	+	5.33936i	−0.247102	+	0.183139i
$851$	31.4222	+	3.67273i	1.07714	+	0.125899i
$852$	−29.3674	−	37.5818i	−1.00611	−	1.28753i
$853$	10.7848	+	7.09325i	0.369263	+	0.242868i	0.720555	−	0.693398i	$-0.243887\pi$
$853$	10.7848	+	7.09325i	0.369263	+	0.242868i	−0.351292	+	0.936266i	$0.614257\pi$
$854$	7.52785	+	5.62939i	0.257598	+	0.192634i
$855$	−10.4159	+	5.97359i	−0.356218	+	0.204292i
$856$	17.1320	+	30.1190i	0.585559	+	1.02945i
$857$	1.05203	+	0.992535i	0.0359365	+	0.0339043i	0.704000	−	0.710200i	$-0.251395\pi$
$857$	1.05203	+	0.992535i	0.0359365	+	0.0339043i	−0.668064	+	0.744104i	$0.732877\pi$
$858$	3.38954	+	2.10753i	0.115717	+	0.0719497i
$859$	6.49742	+	9.87885i	0.221689	+	0.337062i	0.929158	−	0.369682i	$-0.120534\pi$
$859$	6.49742	+	9.87885i	0.221689	+	0.337062i	−0.707469	+	0.706744i	$0.750163\pi$
$860$	−19.3508	+	16.0965i	−0.659858	+	0.548884i
$861$	33.0664	+	20.4616i	1.12690	+	0.697331i
$862$	−27.6624	+	10.0012i	−0.942186	+	0.340643i
$863$	10.5646	+	18.2985i	0.359624	+	0.622887i	0.987898	−	0.155105i	$-0.0495716\pi$
$863$	10.5646	+	18.2985i	0.359624	+	0.622887i	−0.628274	+	0.777992i	$0.716238\pi$
$864$	−16.4954	−	24.3290i	−0.561185	−	0.827691i
$865$	12.3071	−	21.3165i	0.418454	−	0.724783i
$866$	4.32138	−	24.2043i	0.146846	−	0.822496i
$867$	12.4265	+	15.7626i	0.422026	+	0.535327i
$868$	12.7917	+	4.71799i	0.434180	+	0.160139i
$869$	−5.00709	+	0.291630i	−0.169854	+	0.00989285i
$870$	11.9616	−	13.3444i	0.405535	−	0.452417i
$871$	8.13247	−	34.3136i	0.275558	−	1.16267i
$872$	35.7008	+	0.229524i	1.20898	+	0.00777266i
$873$	21.4450	+	32.8116i	0.725802	+	1.11050i
$874$	2.72302	−	22.8717i	0.0921075	−	0.773648i
$875$	20.6742	−	10.3830i	0.698914	−	0.351008i
$876$	−37.1665	−	7.89660i	−1.25574	−	0.266801i
$877$	14.7765	+	34.2557i	0.498966	+	1.15673i	0.962654	+	0.270735i	$0.0872667\pi$
$877$	14.7765	+	34.2557i	0.498966	+	1.15673i	−0.463688	+	0.885999i	$0.653474\pi$
$878$	3.32820	+	29.0136i	0.112321	+	0.979163i
$879$	1.62813	+	58.8810i	0.0549156	+	1.98601i
$880$	−2.76788	−	0.512554i	−0.0933054	−	0.0172782i
$881$	9.65292	−	26.5212i	0.325215	−	0.893521i	−0.664089	−	0.747654i	$-0.731180\pi$
$881$	9.65292	−	26.5212i	0.325215	−	0.893521i	0.989304	−	0.145868i	$-0.0465974\pi$
$882$	−0.0652688	+	12.9701i	−0.00219771	+	0.436725i
$883$	−6.68345	−	18.3626i	−0.224916	−	0.617951i	0.774986	−	0.631979i	$-0.217757\pi$
$883$	−6.68345	−	18.3626i	−0.224916	−	0.617951i	−0.999902	+	0.0140275i	$0.995535\pi$
$884$	3.67879	+	15.8240i	0.123731	+	0.532217i
$885$	17.4741	−	8.11761i	0.587387	−	0.272871i
$886$	−6.68220	−	22.4954i	−0.224493	−	0.755749i
$887$	−7.87230	+	1.86577i	−0.264326	+	0.0626464i	−0.360642	−	0.932704i	$-0.617442\pi$
$887$	−7.87230	+	1.86577i	−0.264326	+	0.0626464i	0.0963157	+	0.995351i	$0.469294\pi$
$888$	−22.3232	+	11.8107i	−0.749119	+	0.396340i
$889$	25.2287	−	2.94881i	0.846143	−	0.0988999i
$890$	7.66054	+	8.15464i	0.256782	+	0.273344i
$891$	0.705375	+	4.14014i	0.0236310	+	0.138700i
$892$	49.6501	+	3.10537i	1.66241	+	0.103975i
$893$	2.18807	+	18.7201i	0.0732210	+	0.626446i
$894$	27.4169	+	14.9103i	0.916958	+	0.498674i
$895$	4.35676	+	18.3826i	0.145630	+	0.614462i
$896$	2.27306	+	22.3500i	0.0759375	+	0.746661i
$897$	−36.9696	−	3.28825i	−1.23438	−	0.109791i
$898$	−17.6178	−	10.2221i	−0.587915	−	0.341115i
$899$	−15.6505	+	5.69633i	−0.521975	+	0.189983i
$900$	13.0477	+	9.85993i	0.434922	+	0.328664i
$901$	5.01483	+	1.82525i	0.167068	+	0.0608078i
$902$	4.78381	+	5.72600i	0.159283	+	0.190655i
$903$	−15.0323	−	24.4501i	−0.500244	−	0.813648i
$904$	−21.9873	+	1.13883i	−0.731287	+	0.0378769i
$905$	−14.0908	+	6.07817i	−0.468393	+	0.202045i
$906$	−7.46241	+	0.625908i	−0.247922	+	0.0207944i
$907$	22.3068	+	44.4164i	0.740684	+	1.47482i	0.875122	+	0.483902i	$0.160781\pi$
$907$	22.3068	+	44.4164i	0.740684	+	1.47482i	−0.134438	+	0.990922i	$0.542923\pi$
$908$	−15.8918	−	21.5385i	−0.527387	−	0.714779i
$909$	14.8882	+	1.78379i	0.493809	+	0.0591647i
$910$	−0.828192	−	14.7645i	−0.0274543	−	0.489439i
$911$	−34.7673	−	8.24001i	−1.15189	−	0.273004i	−0.390068	−	0.920786i	$-0.627548\pi$
$911$	−34.7673	−	8.24001i	−1.15189	−	0.273004i	−0.761825	+	0.647783i	$0.775697\pi$
$912$	8.56414	+	16.2713i	0.283587	+	0.538795i
$913$	−0.180362	−	3.09670i	−0.00596912	−	0.102486i
$914$	−22.4886	+	11.2339i	−0.743857	+	0.371585i
$915$	1.25472	+	8.65302i	0.0414796	+	0.286060i
$916$	17.1072	−	11.1468i	0.565237	−	0.368302i
$917$	−2.41384	−	1.39363i	−0.0797120	−	0.0460217i
$918$	−9.89549	+	13.9392i	−0.326600	+	0.460062i
$919$	15.0835	−	8.70845i	0.497558	−	0.287265i	−0.230147	−	0.973156i	$-0.573921\pi$
$919$	15.0835	−	8.70845i	0.497558	−	0.287265i	0.727704	+	0.685891i	$0.240587\pi$
$920$	25.1244	−	7.34608i	0.828327	−	0.242193i
$921$	−53.5551	−	1.63573i	−1.76470	−	0.0538991i
$922$	10.8145	+	0.653133i	0.356158	+	0.0215098i
$923$	40.1680	−	26.4189i	1.32214	−	0.869588i
$924$	1.02708	−	3.04108i	0.0337885	−	0.100044i
$925$	9.64269	−	10.2207i	0.317050	−	0.336053i
$926$	−5.79732	−	8.85568i	−0.190512	−	0.291016i
$927$	2.92113	+	16.8511i	0.0959426	+	0.553464i
$928$	−19.7583	−	19.0453i	−0.648599	−	0.625192i
$929$	5.66525	−	8.61359i	0.185871	−	0.282603i	−0.730517	−	0.682894i	$-0.760721\pi$
$929$	5.66525	−	8.61359i	0.185871	−	0.282603i	0.916388	+	0.400292i	$0.131091\pi$
$930$	5.31837	+	11.5129i	0.174396	+	0.377524i
$931$	0.941928	−	8.05871i	0.0308704	−	0.264114i
$932$	−37.7920	−	6.83088i	−1.23792	−	0.223753i
$933$	−5.86045	−	28.5907i	−0.191863	−	0.936017i
$934$	−0.859873	−	4.93844i	−0.0281359	−	0.161591i
$935$	0.284275	+	1.61221i	0.00929680	+	0.0527248i
$936$	25.7967	−	14.5749i	0.843191	−	0.476396i
$937$	6.51141	−	36.9281i	0.212719	−	1.20639i	−0.672103	−	0.740458i	$-0.734609\pi$
$937$	6.51141	−	36.9281i	0.212719	−	1.20639i	0.884822	−	0.465930i	$-0.154280\pi$
$938$	−28.3595	−	0.0607747i	−0.925971	−	0.00198436i
$939$	−34.9844	−	35.0856i	−1.14167	−	1.14498i
$940$	−18.5955	+	10.6301i	−0.606519	+	0.346717i
$941$	31.2202	−	29.4548i	1.01775	−	0.960198i	0.0185358	−	0.999828i	$-0.494100\pi$
$941$	31.2202	−	29.4548i	1.01775	−	0.960198i	0.999214	+	0.0396304i	$0.0126181\pi$
$942$	−48.0811	−	16.1240i	−1.56657	−	0.525348i
$943$	−63.7092	−	27.4815i	−2.07466	−	0.894919i
$944$	−11.4539	−	27.1917i	−0.372792	−	0.885013i
$945$	11.0502	−	10.9549i	0.359465	−	0.356362i
$946$	−1.25858	−	5.36154i	−0.0409200	−	0.174319i
$947$	7.01481	+	9.42253i	0.227951	+	0.306191i	0.901353	−	0.433085i	$-0.142575\pi$
$947$	7.01481	+	9.42253i	0.227951	+	0.306191i	−0.673402	+	0.739276i	$0.735168\pi$
$948$	−15.9284	+	33.6536i	−0.517329	+	1.09302i
$949$	10.9847	−	36.6915i	0.356579	−	1.19106i
$950$	−7.42628	−	7.03648i	−0.240940	−	0.228294i
$951$	−20.2404	+	43.2426i	−0.656341	+	1.40224i
$952$	11.7128	−	5.78841i	0.379615	−	0.187603i
$953$	21.6215	−	25.7674i	0.700388	−	0.834689i	−0.292183	−	0.956363i	$-0.594382\pi$
$953$	21.6215	−	25.7674i	0.700388	−	0.834689i	0.992570	+	0.121673i	$0.0388260\pi$
$954$	0.614812	−	9.71357i	0.0199053	−	0.314488i
$955$	−12.8006	−	15.2552i	−0.414219	−	0.493647i
$956$	−18.3735	−	43.1015i	−0.594240	−	1.39400i
$957$	1.44241	+	3.64610i	0.0466264	+	0.117862i
$958$	−0.579410	+	1.33535i	−0.0187199	+	0.0431431i
$959$	−15.4348	+	20.7325i	−0.498415	+	0.669488i
$960$	−13.1939	+	16.2045i	−0.425831	+	0.522999i
$961$	−1.11718	+	19.1812i	−0.0360380	+	0.618749i
$962$	−10.0330	−	23.3969i	−0.323478	−	0.754348i
$963$	−33.7044	−	14.6543i	−1.08611	−	0.472229i
$964$	7.28067	+	24.7040i	0.234494	+	0.795662i
$965$	−20.3232	+	6.08437i	−0.654228	+	0.195863i
$966$	4.22002	+	29.5487i	0.135777	+	0.950714i
$967$	17.4959	−	34.8373i	0.562631	−	1.12029i	−0.414972	−	0.909834i	$-0.636209\pi$
$967$	17.4959	−	34.8373i	0.562631	−	1.12029i	0.977603	−	0.210457i	$-0.0674952\pi$
$968$	−18.3683	+	24.3446i	−0.590380	+	0.782465i
$969$	7.12054	−	7.97805i	0.228745	−	0.256292i
$970$	17.9579	−	21.3085i	0.576594	−	0.684175i
$971$	−13.3054			−0.426990			−0.213495	−	0.976944i	$-0.568485\pi$
$971$	−13.3054			−0.426990			−0.213495	+	0.976944i	$0.568485\pi$
$972$	29.4796	+	10.1465i	0.945560	+	0.325449i
$973$	12.2609			0.393066
$974$	8.69544	−	10.3178i	0.278620	−	0.330605i
$975$	−10.9771	+	12.2990i	−0.351548	+	0.393884i
$976$	13.3117	−	1.44036i	0.426098	−	0.0461049i
$977$	6.86810	−	13.6755i	0.219730	−	0.437518i	−0.756578	−	0.653903i	$-0.773130\pi$
$977$	6.86810	−	13.6755i	0.219730	−	0.437518i	0.976308	+	0.216385i	$0.0694266\pi$
$978$	3.91237	+	27.3946i	0.125104	+	0.875981i
$979$	−2.34519	+	0.702104i	−0.0749527	+	0.0224394i
$980$	8.84461	−	2.60665i	0.282531	−	0.0832664i
$981$	−30.4394	+	22.5249i	−0.971854	+	0.719164i
$982$	−1.89477	−	4.41857i	−0.0604644	−	0.141002i
$983$	−1.39925	+	24.0242i	−0.0446292	+	0.766254i	0.899549	+	0.436820i	$0.143895\pi$
$983$	−1.39925	+	24.0242i	−0.0446292	+	0.766254i	−0.944178	+	0.329435i	$0.893142\pi$
$984$	54.3311	−	10.7732i	1.73201	−	0.343436i
$985$	13.1958	−	17.7251i	0.420454	−	0.564768i
$986$	−6.35278	+	14.6410i	−0.202314	+	0.466266i
$987$	−8.98481	−	22.7117i	−0.285990	−	0.722921i
$988$	−17.0502	+	7.26823i	−0.542439	+	0.231233i
$989$	32.9188	+	39.2311i	1.04676	+	1.24748i
$990$	2.67483	−	1.32653i	0.0850115	−	0.0421600i
$991$	−3.26738	+	3.89391i	−0.103792	+	0.123694i	−0.815440	−	0.578842i	$-0.803505\pi$
$991$	−3.26738	+	3.89391i	−0.103792	+	0.123694i	0.711648	+	0.702536i	$0.247949\pi$
$992$	17.9137	−	7.50060i	0.568761	−	0.238144i
$993$	10.0535	−	21.4788i	0.319039	−	0.681608i
$994$	−28.0662	−	26.5930i	−0.890206	−	0.843479i
$995$	−1.05640	+	3.52862i	−0.0334902	+	0.111865i
$996$	−20.8135	−	9.85111i	−0.659502	−	0.312144i
$997$	−16.2771	−	21.8639i	−0.515499	−	0.692436i	0.465807	−	0.884886i	$-0.345764\pi$
$997$	−16.2771	−	21.8639i	−0.515499	−	0.692436i	−0.981307	+	0.192450i	$0.938357\pi$
$998$	−11.6577	−	49.6617i	−0.369018	−	1.57201i
$999$	11.4258	−	24.2280i	0.361497	−	0.766541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.263.40	yes	936
3.2	odd	2		972.2.p.a.467.13		936
4.3	odd	2	inner	324.2.p.a.263.17	yes	936
12.11	even	2		972.2.p.a.467.36		936
81.4	even	27		972.2.p.a.179.36		936
81.77	odd	54	inner	324.2.p.a.239.17	✓	936
324.239	even	54	inner	324.2.p.a.239.40	yes	936
324.247	odd	54		972.2.p.a.179.13		936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.239.17	✓	936	81.77	odd	54	inner
324.2.p.a.239.40	yes	936	324.239	even	54	inner
324.2.p.a.263.17	yes	936	4.3	odd	2	inner
324.2.p.a.263.40	yes	936	1.1	even	1	trivial
972.2.p.a.179.13		936	324.247	odd	54
972.2.p.a.179.36		936	81.4	even	27
972.2.p.a.467.13		936	3.2	odd	2
972.2.p.a.467.36		936	12.11	even	2

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(1.08140 + 0.911358i) q^{2} +(-1.15333 + 1.29222i) q^{3} +(0.338851 + 1.97109i) q^{4} +(-0.676824 + 1.34767i) q^{5} +(-2.42489 + 0.346312i) q^{6} +(-1.90225 + 0.569497i) q^{7} +(-1.42993 + 2.44035i) q^{8} +(-0.339668 - 2.98071i) q^{9} +O(q^{10})\)	\(q+(1.08140 + 0.911358i) q^{2} +(-1.15333 + 1.29222i) q^{3} +(0.338851 + 1.97109i) q^{4} +(-0.676824 + 1.34767i) q^{5} +(-2.42489 + 0.346312i) q^{6} +(-1.90225 + 0.569497i) q^{7} +(-1.42993 + 2.44035i) q^{8} +(-0.339668 - 2.98071i) q^{9} +(-1.96013 + 0.840538i) q^{10} +(0.0271329 - 0.465854i) q^{11} +(-2.93788 - 1.83544i) q^{12} +(2.08519 - 2.80089i) q^{13} +(-2.57611 - 1.11778i) q^{14} +(-0.960884 - 2.42891i) q^{15} +(-3.77036 + 1.33581i) q^{16} +(1.49530 + 1.78202i) q^{17} +(2.34918 - 3.53290i) q^{18} +(-1.70596 + 2.03308i) q^{19} +(-2.88571 - 0.877420i) q^{20} +(1.45801 - 3.11495i) q^{21} +(0.453902 - 0.479047i) q^{22} +(-1.76005 + 5.87896i) q^{23} +(-1.50429 - 4.66231i) q^{24} +(1.62768 + 2.18635i) q^{25} +(4.80754 - 1.12853i) q^{26} +(4.24348 + 2.99881i) q^{27} +(-1.76711 - 3.55653i) q^{28} +(4.45451 + 1.92149i) q^{29} +(1.17451 - 3.50233i) q^{30} +(-2.49716 + 2.35595i) q^{31} +(-5.29467 - 1.99160i) q^{32} +(0.570693 + 0.572345i) q^{33} +(-0.00705013 + 3.28983i) q^{34} +(0.519998 - 2.94905i) q^{35} +(5.76014 - 1.67953i) q^{36} +(-0.895186 - 5.07685i) q^{37} +(-3.69769 + 0.643835i) q^{38} +(1.21447 + 5.92487i) q^{39} +(-2.32096 - 3.57876i) q^{40} +(-1.31257 + 11.2298i) q^{41} +(4.41552 - 2.03974i) q^{42} +(4.58576 - 6.97231i) q^{43} +(0.927433 - 0.104374i) q^{44} +(4.24690 + 1.55966i) q^{45} +(-7.26115 + 4.75347i) q^{46} +(4.87340 - 5.16550i) q^{47} +(2.62230 - 6.41276i) q^{48} +(-2.55418 + 1.67991i) q^{49} +(-0.232378 + 3.84771i) q^{50} +(-4.02733 - 0.123007i) q^{51} +(6.22737 + 3.16100i) q^{52} +(1.98674 - 1.14705i) q^{53} +(1.85591 + 7.11025i) q^{54} +(0.609453 + 0.351868i) q^{55} +(1.33032 - 5.45650i) q^{56} +(-0.659660 - 4.54928i) q^{57} +(3.06594 + 6.13756i) q^{58} +(0.428899 + 7.36391i) q^{59} +(4.46199 - 2.71702i) q^{60} +(-3.25713 - 0.771953i) q^{61} +(-4.84753 + 0.271915i) q^{62} +(2.34364 + 5.47662i) q^{63} +(-3.91059 - 6.97906i) q^{64} +(2.36337 + 4.70586i) q^{65} +(0.0955366 + 1.13904i) q^{66} +(9.27305 - 4.00000i) q^{67} +(-3.00584 + 3.55120i) q^{68} +(-5.56700 - 9.05474i) q^{69} +(3.24997 - 2.71520i) q^{70} +(12.9381 + 4.70907i) q^{71} +(7.75967 + 3.43330i) q^{72} +(10.3071 - 3.75146i) q^{73} +(3.65878 - 6.30594i) q^{74} +(-4.70249 - 0.418260i) q^{75} +(-4.58544 - 2.67368i) q^{76} +(0.213689 + 0.901625i) q^{77} +(-4.08636 + 7.51397i) q^{78} +(-1.24779 - 10.6755i) q^{79} +(0.751642 - 5.98530i) q^{80} +(-8.76925 + 2.02490i) q^{81} +(-11.6538 + 10.9476i) q^{82} +(6.60241 - 0.771711i) q^{83} +(6.63387 + 1.81835i) q^{84} +(-3.41363 + 0.809045i) q^{85} +(11.3133 - 3.36059i) q^{86} +(-7.62050 + 3.54011i) q^{87} +(1.09805 + 0.732354i) q^{88} +(-1.79425 - 4.92967i) q^{89} +(3.17119 + 5.55706i) q^{90} +(-2.37145 + 6.51552i) q^{91} +(-12.1843 - 1.47711i) q^{92} +(-0.164361 - 5.94405i) q^{93} +(9.97771 - 1.14456i) q^{94} +(-1.58528 - 3.67510i) q^{95} +(8.68008 - 4.54491i) q^{96} +(-11.6762 + 5.86401i) q^{97} +(-4.29309 - 0.511118i) q^{98} +(-1.39779 + 0.0773606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

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