LMFDB - Embedded newform 378.2.w.b.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(25,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("378.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.w (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	378.25
Dual form			378.2.w.b.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(-1.37994 - 1.04679i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.829059 + 0.301753i) q^{5} +(-1.65474 - 0.511691i) q^{6} +(1.89032 + 1.85113i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.808471 + 2.88901i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(-1.37994 - 1.04679i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.829059 + 0.301753i) q^{5} +(-1.65474 - 0.511691i) q^{6} +(1.89032 + 1.85113i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.808471 + 2.88901i) q^{9} +0.882266 q^{10} +(4.19158 - 1.52561i) q^{11} +(-1.72996 + 0.0851228i) q^{12} +(-1.01265 - 5.74304i) q^{13} +(2.40944 + 1.09297i) q^{14} +(-0.828181 - 1.28425i) q^{15} +(0.173648 - 0.984808i) q^{16} -0.275531 q^{17} +(1.74781 + 2.43827i) q^{18} -0.827783 q^{19} +(0.829059 - 0.301753i) q^{20} +(-0.670787 - 4.53322i) q^{21} +(3.41700 - 2.86721i) q^{22} +(0.121171 + 0.687193i) q^{23} +(-1.59651 + 0.671670i) q^{24} +(-3.23394 - 2.71360i) q^{25} +(-2.91582 - 5.05034i) q^{26} +(1.90854 - 4.83296i) q^{27} +(2.63795 + 0.202975i) q^{28} +(-0.781152 + 4.43013i) q^{29} +(-1.21747 - 0.923545i) q^{30} +(-2.26209 + 1.89812i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-7.38111 - 2.28244i) q^{33} +(-0.258914 + 0.0942371i) q^{34} +(1.00860 + 2.10511i) q^{35} +(2.47634 + 1.69343i) q^{36} +(2.25391 - 3.90388i) q^{37} +(-0.777861 + 0.283118i) q^{38} +(-4.61434 + 8.98508i) q^{39} +(0.675855 - 0.567110i) q^{40} +(0.487212 + 2.76311i) q^{41} +(-2.18078 - 4.03041i) q^{42} +(8.27783 + 6.94593i) q^{43} +(2.23029 - 3.86298i) q^{44} +(-0.201496 + 2.63912i) q^{45} +(0.348897 + 0.604307i) q^{46} +(5.10365 + 4.28247i) q^{47} +(-1.27051 + 1.17720i) q^{48} +(0.146620 + 6.99846i) q^{49} +(-3.96701 - 1.44387i) q^{50} +(0.380216 + 0.288422i) q^{51} +(-4.46729 - 3.74850i) q^{52} +(-1.99907 + 3.46249i) q^{53} +(0.140468 - 5.19425i) q^{54} +3.93542 q^{55} +(2.54829 - 0.711499i) q^{56} +(1.14229 + 0.866513i) q^{57} +(0.781152 + 4.43013i) q^{58} +(0.834847 + 4.73465i) q^{59} +(-1.45992 - 0.451448i) q^{60} +(-10.1867 - 8.54764i) q^{61} +(-1.47648 + 2.55733i) q^{62} +(-3.81967 + 6.95774i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.893429 - 5.06689i) q^{65} +(-7.71662 + 0.379697i) q^{66} +(-4.42677 - 1.61121i) q^{67} +(-0.211069 + 0.177108i) q^{68} +(0.552137 - 1.07513i) q^{69} +(1.66777 + 1.63319i) q^{70} +(4.51335 + 7.81735i) q^{71} +(2.90619 + 0.744348i) q^{72} +(-2.86709 - 4.96595i) q^{73} +(0.782774 - 4.43933i) q^{74} +(1.62208 + 7.12985i) q^{75} +(-0.634118 + 0.532088i) q^{76} +(10.7475 + 4.87527i) q^{77} +(-1.26298 + 10.0214i) q^{78} +(-12.7430 + 4.63807i) q^{79} +(0.441133 - 0.764065i) q^{80} +(-7.69275 + 4.67136i) q^{81} +(1.40287 + 2.42984i) q^{82} +(-1.62387 + 9.20943i) q^{83} +(-3.42775 - 3.04147i) q^{84} +(-0.228431 - 0.0831422i) q^{85} +(10.1543 + 3.69585i) q^{86} +(5.71535 - 5.29562i) q^{87} +(0.774572 - 4.39282i) q^{88} -17.4000 q^{89} +(0.713287 + 2.54887i) q^{90} +(8.71688 - 12.7307i) q^{91} +(0.534541 + 0.448533i) q^{92} +(5.10848 - 0.251364i) q^{93} +(6.26055 + 2.27866i) q^{94} +(-0.686281 - 0.249786i) q^{95} +(-0.791260 + 1.54075i) q^{96} +(-5.48553 - 4.60290i) q^{97} +(2.53139 + 6.52626i) q^{98} +(7.79627 + 10.8761i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} + 9 q^{35} - 3 q^{36} + 51 q^{39} - 6 q^{41} - 27 q^{42} - 24 q^{43} + 18 q^{45} + 27 q^{47} + 6 q^{48} - 69 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{52} - 15 q^{53} + 45 q^{54} - 72 q^{55} + 6 q^{56} + 57 q^{57} - 3 q^{58} + 15 q^{59} - 33 q^{60} - 18 q^{61} - 24 q^{62} - 12 q^{63} - 36 q^{64} - 90 q^{65} - 36 q^{66} - 66 q^{67} - 18 q^{68} - 39 q^{69} - 12 q^{70} + 12 q^{71} + 30 q^{73} + 9 q^{74} - 21 q^{75} - 87 q^{77} + 6 q^{78} - 45 q^{79} - 6 q^{80} - 24 q^{81} + 33 q^{82} + 18 q^{83} + 6 q^{84} + 51 q^{85} - 12 q^{86} - 18 q^{87} - 12 q^{88} + 72 q^{89} - 69 q^{90} - 30 q^{91} + 12 q^{92} - 48 q^{93} + 21 q^{95} + 48 q^{97} + 6 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	−1.37994	−	1.04679i	−0.796709	−	0.604363i
$3$	−1.37994	−	1.04679i	−0.796709	−	0.604363i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	0.829059	+	0.301753i	0.370766	+	0.134948i	0.520682	−	0.853751i	$-0.325678\pi$
$5$	0.829059	+	0.301753i	0.370766	+	0.134948i	−0.149915	+	0.988699i	$0.547900\pi$
$6$	−1.65474	−	0.511691i	−0.675546	−	0.208897i
$7$	1.89032	+	1.85113i	0.714474	+	0.699662i
$7$	1.89032	+	1.85113i	0.714474	+	0.699662i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.808471	+	2.88901i	0.269490	+	0.963003i
$10$	0.882266			0.278997
$11$	4.19158	−	1.52561i	1.26381	−	0.459988i	0.378763	−	0.925494i	$-0.376350\pi$
$11$	4.19158	−	1.52561i	1.26381	−	0.459988i	0.885045	+	0.465505i	$0.154127\pi$
$12$	−1.72996	+	0.0851228i	−0.499396	+	0.0245728i
$13$	−1.01265	−	5.74304i	−0.280859	−	1.59283i	−0.719712	−	0.694273i	$-0.755726\pi$
$13$	−1.01265	−	5.74304i	−0.280859	−	1.59283i	0.438853	−	0.898559i	$-0.355385\pi$
$14$	2.40944	+	1.09297i	0.643951	+	0.292108i
$15$	−0.828181	−	1.28425i	−0.213835	−	0.331592i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−0.275531			−0.0668260			−0.0334130	−	0.999442i	$-0.510638\pi$
$17$	−0.275531			−0.0668260			−0.0334130	+	0.999442i	$0.510638\pi$
$18$	1.74781	+	2.43827i	0.411964	+	0.574705i
$19$	−0.827783			−0.189906			−0.0949532	−	0.995482i	$-0.530270\pi$
$19$	−0.827783			−0.189906			−0.0949532	+	0.995482i	$0.530270\pi$
$20$	0.829059	−	0.301753i	0.185383	−	0.0674740i
$21$	−0.670787	−	4.53322i	−0.146378	−	0.989229i
$22$	3.41700	−	2.86721i	0.728508	−	0.611291i
$23$	0.121171	+	0.687193i	0.0252658	+	0.143290i	0.994831	−	0.101543i	$-0.0323780\pi$
$23$	0.121171	+	0.687193i	0.0252658	+	0.143290i	−0.969565	+	0.244833i	$0.921267\pi$
$24$	−1.59651	+	0.671670i	−0.325887	+	0.137104i
$25$	−3.23394	−	2.71360i	−0.646788	−	0.542719i
$26$	−2.91582	−	5.05034i	−0.571839	−	0.990454i
$27$	1.90854	−	4.83296i	0.367298	−	0.930103i
$28$	2.63795	+	0.202975i	0.498526	+	0.0383587i
$29$	−0.781152	+	4.43013i	−0.145056	+	0.822655i	0.822266	+	0.569104i	$0.192710\pi$
$29$	−0.781152	+	4.43013i	−0.145056	+	0.822655i	−0.967322	+	0.253551i	$0.918401\pi$
$30$	−1.21747	−	0.923545i	−0.222279	−	0.168616i
$31$	−2.26209	+	1.89812i	−0.406284	+	0.340912i	−0.822916	−	0.568162i	$-0.807655\pi$
$31$	−2.26209	+	1.89812i	−0.406284	+	0.340912i	0.416633	+	0.909075i	$0.363210\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	−7.38111	−	2.28244i	−1.28489	−	0.397322i
$34$	−0.258914	+	0.0942371i	−0.0444034	+	0.0161615i
$35$	1.00860	+	2.10511i	0.170485	+	0.355828i
$36$	2.47634	+	1.69343i	0.412724	+	0.282239i
$37$	2.25391	−	3.90388i	0.370540	−	0.641794i	−0.619109	−	0.785305i	$-0.712506\pi$
$37$	2.25391	−	3.90388i	0.370540	−	0.641794i	0.989649	+	0.143511i	$0.0458392\pi$
$38$	−0.777861	+	0.283118i	−0.126186	+	0.0459279i
$39$	−4.61434	+	8.98508i	−0.738886	+	1.43876i
$40$	0.675855	−	0.567110i	0.106862	−	0.0896679i
$41$	0.487212	+	2.76311i	0.0760897	+	0.431526i	0.998926	+	0.0463337i	$0.0147537\pi$
$41$	0.487212	+	2.76311i	0.0760897	+	0.431526i	−0.922836	+	0.385192i	$0.874135\pi$
$42$	−2.18078	−	4.03041i	−0.336502	−	0.621905i
$43$	8.27783	+	6.94593i	1.26236	+	1.05924i	0.995427	+	0.0955283i	$0.0304540\pi$
$43$	8.27783	+	6.94593i	1.26236	+	1.05924i	0.266931	+	0.963716i	$0.413990\pi$
$44$	2.23029	−	3.86298i	0.336229	−	0.582366i
$45$	−0.201496	+	2.63912i	−0.0300373	+	0.393416i
$46$	0.348897	+	0.604307i	0.0514421	+	0.0891003i
$47$	5.10365	+	4.28247i	0.744444	+	0.624663i	0.934027	−	0.357202i	$-0.116269\pi$
$47$	5.10365	+	4.28247i	0.744444	+	0.624663i	−0.189583	+	0.981865i	$0.560714\pi$
$48$	−1.27051	+	1.17720i	−0.183382	+	0.169915i
$49$	0.146620	+	6.99846i	0.0209457	+	0.999781i
$50$	−3.96701	−	1.44387i	−0.561020	−	0.204195i
$51$	0.380216	+	0.288422i	0.0532409	+	0.0403872i
$52$	−4.46729	−	3.74850i	−0.619502	−	0.519824i
$53$	−1.99907	+	3.46249i	−0.274593	+	0.475609i	−0.970032	−	0.242976i	$-0.921876\pi$
$53$	−1.99907	+	3.46249i	−0.274593	+	0.475609i	0.695439	+	0.718585i	$0.255210\pi$
$54$	0.140468	−	5.19425i	0.0191153	−	0.706848i
$55$	3.93542			0.530652
$56$	2.54829	−	0.711499i	0.340529	−	0.0950781i
$57$	1.14229	+	0.866513i	0.151300	+	0.114772i
$58$	0.781152	+	4.43013i	0.102570	+	0.581705i
$59$	0.834847	+	4.73465i	0.108688	+	0.616399i	0.989683	+	0.143274i	$0.0457631\pi$
$59$	0.834847	+	4.73465i	0.108688	+	0.616399i	−0.880995	+	0.473125i	$0.843126\pi$
$60$	−1.45992	−	0.451448i	−0.188475	−	0.0582816i
$61$	−10.1867	−	8.54764i	−1.30427	−	1.09441i	−0.989390	−	0.145281i	$-0.953591\pi$
$61$	−10.1867	−	8.54764i	−1.30427	−	1.09441i	−0.314880	−	0.949132i	$-0.601964\pi$
$62$	−1.47648	+	2.55733i	−0.187513	+	0.324781i
$63$	−3.81967	+	6.95774i	−0.481233	+	0.876593i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.893429	−	5.06689i	0.110816	−	0.628470i
$66$	−7.71662	+	0.379697i	−0.949850	+	0.0467375i
$67$	−4.42677	−	1.61121i	−0.540816	−	0.196841i	0.0571451	−	0.998366i	$-0.481800\pi$
$67$	−4.42677	−	1.61121i	−0.540816	−	0.196841i	−0.597962	+	0.801525i	$0.704022\pi$
$68$	−0.211069	+	0.177108i	−0.0255959	+	0.0214775i
$69$	0.552137	−	1.07513i	0.0664695	−	0.129430i
$70$	1.66777	+	1.63319i	0.199336	+	0.195204i
$71$	4.51335	+	7.81735i	0.535636	+	0.927748i	0.999132	+	0.0416496i	$0.0132613\pi$
$71$	4.51335	+	7.81735i	0.535636	+	0.927748i	−0.463496	+	0.886099i	$0.653405\pi$
$72$	2.90619	+	0.744348i	0.342498	+	0.0877222i
$73$	−2.86709	−	4.96595i	−0.335568	−	0.581220i	0.648026	−	0.761618i	$-0.275595\pi$
$73$	−2.86709	−	4.96595i	−0.335568	−	0.581220i	−0.983594	+	0.180398i	$0.942261\pi$
$74$	0.782774	−	4.43933i	0.0909956	−	0.516062i
$75$	1.62208	+	7.12985i	0.187302	+	0.823284i
$76$	−0.634118	+	0.532088i	−0.0727384	+	0.0610347i
$77$	10.7475	+	4.87527i	1.22479	+	0.555589i
$78$	−1.26298	+	10.0214i	−0.143005	+	1.13470i
$79$	−12.7430	+	4.63807i	−1.43370	+	0.521823i	−0.937989	−	0.346665i	$-0.887314\pi$
$79$	−12.7430	+	4.63807i	−1.43370	+	0.521823i	−0.495709	+	0.868489i	$0.665092\pi$
$80$	0.441133	−	0.764065i	0.0493202	−	0.0854250i
$81$	−7.69275	+	4.67136i	−0.854750	+	0.519040i
$82$	1.40287	+	2.42984i	0.154921	+	0.268331i
$83$	−1.62387	+	9.20943i	−0.178243	+	1.01087i	0.756091	+	0.654467i	$0.227107\pi$
$83$	−1.62387	+	9.20943i	−0.178243	+	1.01087i	−0.934334	+	0.356399i	$0.884004\pi$
$84$	−3.42775	−	3.04147i	−0.373998	−	0.331852i
$85$	−0.228431	−	0.0831422i	−0.0247768	−	0.00901804i
$86$	10.1543	+	3.69585i	1.09496	+	0.398534i
$87$	5.71535	−	5.29562i	0.612750	−	0.567750i
$88$	0.774572	−	4.39282i	0.0825697	−	0.468276i
$89$	−17.4000			−1.84439			−0.922196	−	0.386723i	$-0.873607\pi$
$89$	−17.4000			−1.84439			−0.922196	+	0.386723i	$0.873607\pi$
$90$	0.713287	+	2.54887i	0.0751870	+	0.268675i
$91$	8.71688	−	12.7307i	0.913778	−	1.33454i
$92$	0.534541	+	0.448533i	0.0557298	+	0.0467628i
$93$	5.10848	−	0.251364i	0.529725	−	0.0260652i
$94$	6.26055	+	2.27866i	0.645727	+	0.235025i
$95$	−0.686281	−	0.249786i	−0.0704109	−	0.0256275i
$96$	−0.791260	+	1.54075i	−0.0807577	+	0.157252i
$97$	−5.48553	−	4.60290i	−0.556971	−	0.467354i	0.320322	−	0.947309i	$-0.396209\pi$
$97$	−5.48553	−	4.60290i	−0.556971	−	0.467354i	−0.877293	+	0.479954i	$0.840653\pi$
$98$	2.53139	+	6.52626i	0.255709	+	0.659252i
$99$	7.79627	+	10.8761i	0.783554	+	1.09309i
$100$	−4.22161			−0.422161
$101$	0.0632787	−	0.358872i	0.00629647	−	0.0357091i	−0.981498	−	0.191474i	$-0.938673\pi$
$101$	0.0632787	−	0.358872i	0.00629647	−	0.0357091i	0.987794	+	0.155765i	$0.0497843\pi$
$102$	0.455932	+	0.140987i	0.0451440	+	0.0139598i
$103$	−7.65402	−	2.78584i	−0.754173	−	0.274497i	−0.0638126	−	0.997962i	$-0.520326\pi$
$103$	−7.65402	−	2.78584i	−0.754173	−	0.274497i	−0.690361	+	0.723465i	$0.742548\pi$
$104$	−5.47994	−	1.99454i	−0.537353	−	0.195580i
$105$	0.811788	−	3.96071i	0.0792224	−	0.386526i
$106$	−0.694269	+	3.93739i	−0.0674333	+	0.382433i
$107$	−6.69049	−	11.5883i	−0.646794	−	1.12028i	−0.983884	−	0.178808i	$-0.942776\pi$
$107$	−6.69049	−	11.5883i	−0.646794	−	1.12028i	0.337090	−	0.941473i	$-0.390557\pi$
$108$	−1.64454	−	4.92904i	−0.158246	−	0.474298i
$109$	2.48589	−	4.30569i	0.238105	−	0.412411i	−0.722065	−	0.691825i	$-0.756807\pi$
$109$	2.48589	−	4.30569i	0.238105	−	0.412411i	0.960171	+	0.279414i	$0.0901403\pi$
$110$	3.69809	−	1.34599i	0.352599	−	0.128335i
$111$	−7.19680	+	3.02776i	−0.683090	+	0.287383i
$112$	2.15126	−	1.54016i	0.203275	−	0.145531i
$113$	0.948298	−	0.795717i	0.0892084	−	0.0748547i	−0.597093	−	0.802172i	$-0.703678\pi$
$113$	0.948298	−	0.795717i	0.0892084	−	0.0748547i	0.686301	+	0.727317i	$0.259233\pi$
$114$	1.36977	+	0.423569i	0.128290	+	0.0396709i
$115$	−0.106905	+	0.606287i	−0.00996892	+	0.0565366i
$116$	2.24924	+	3.89579i	0.208836	+	0.361715i
$117$	15.7730	−	7.56864i	1.45821	−	0.699721i
$118$	2.40385	+	4.16358i	0.221292	+	0.383289i
$119$	−0.520841	−	0.510044i	−0.0477455	−	0.0467556i
$120$	−1.52628	+	0.0751010i	−0.139330	+	0.00685575i
$121$	6.81534	−	5.71875i	0.619576	−	0.519886i
$122$	−12.4958	−	4.54810i	−1.13132	−	0.411766i
$123$	2.22007	−	4.32294i	0.200177	−	0.389786i
$124$	−0.512775	+	2.90809i	−0.0460485	+	0.261154i
$125$	−4.06796	−	7.04591i	−0.363849	−	0.630205i
$126$	−1.20963	+	7.84454i	−0.107762	+	0.698847i
$127$	2.60913	−	4.51914i	0.231523	−	0.401009i	−0.726734	−	0.686919i	$-0.758963\pi$
$127$	2.60913	−	4.51914i	0.231523	−	0.401009i	0.958256	+	0.285910i	$0.0922959\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	−4.15201	−	18.2501i	−0.365564	−	1.60683i
$130$	−0.893429	−	5.06689i	−0.0783589	−	0.444395i
$131$	3.54284	+	20.0924i	0.309539	+	1.75548i	0.601329	+	0.799002i	$0.294638\pi$
$131$	3.54284	+	20.0924i	0.309539	+	1.75548i	−0.291789	+	0.956483i	$0.594251\pi$
$132$	−7.12139	+	2.99604i	−0.619837	+	0.260772i
$133$	−1.56477	−	1.53233i	−0.135683	−	0.132870i
$134$	−4.71087			−0.406958
$135$	3.04065	−	3.43090i	0.261697	−	0.295285i
$136$	−0.137765	+	0.238617i	−0.0118133	+	0.0204612i
$137$	14.3239	+	12.0192i	1.22377	+	1.02687i	0.998619	+	0.0525430i	$0.0167327\pi$
$137$	14.3239	+	12.0192i	1.22377	+	1.02687i	0.225153	+	0.974323i	$0.427712\pi$
$138$	0.151124	−	1.19913i	0.0128646	−	0.102077i
$139$	14.9591	+	5.44467i	1.26881	+	0.461811i	0.886717	−	0.462312i	$-0.152980\pi$
$139$	14.9591	+	5.44467i	1.26881	+	0.461811i	0.382097	+	0.924122i	$0.375202\pi$
$140$	2.12577	+	0.964288i	0.179660	+	0.0814972i
$141$	−2.55990	−	11.2520i	−0.215582	−	0.947589i
$142$	6.91485	+	5.80225i	0.580281	+	0.486914i
$143$	−13.0062	−	22.5275i	−1.08764	−	1.88384i
$144$	2.98551	−	0.294518i	0.248792	−	0.0245431i
$145$	−1.98442	+	3.43712i	−0.164798	+	0.285438i
$146$	−4.39264	−	3.68586i	−0.363537	−	0.305044i
$147$	7.12358	−	9.81094i	0.587543	−	0.809193i
$148$	−0.782774	−	4.43933i	−0.0643436	−	0.364911i
$149$	1.31207	−	1.10096i	0.107489	−	0.0901942i	−0.587459	−	0.809254i	$-0.699872\pi$
$149$	1.31207	−	1.10096i	0.107489	−	0.0901942i	0.694948	+	0.719060i	$0.255427\pi$
$150$	3.96281	+	6.14508i	0.323562	+	0.501744i
$151$	−0.0716901	+	0.0260931i	−0.00583406	+	0.00212342i	−0.344936	−	0.938626i	$-0.612099\pi$
$151$	−0.0716901	+	0.0260931i	−0.00583406	+	0.00212342i	0.339101	+	0.940750i	$0.389877\pi$
$152$	−0.413891	+	0.716881i	−0.0335710	+	0.0581467i
$153$	−0.222759	−	0.796011i	−0.0180090	−	0.0643537i
$154$	11.7668	+	0.905387i	0.948197	+	0.0729582i
$155$	−2.44817	+	0.891061i	−0.196642	+	0.0715717i
$156$	2.24071	+	9.84901i	0.179400	+	0.788552i
$157$	4.01165	+	22.7512i	0.320165	+	1.81575i	0.541676	+	0.840587i	$0.317790\pi$
$157$	4.01165	+	22.7512i	0.320165	+	1.81575i	−0.221511	+	0.975158i	$0.571099\pi$
$158$	−10.3882	+	8.71672i	−0.826439	+	0.693465i
$159$	6.38308	−	2.68543i	0.506211	−	0.212968i
$160$	0.153204	−	0.868862i	0.0121118	−	0.0686896i
$161$	−1.04303	+	1.52332i	−0.0822026	+	0.120054i
$162$	−5.63112	+	7.02072i	−0.442422	+	0.551600i
$163$	−9.47704	−	16.4147i	−0.742299	−	1.28570i	−0.951446	−	0.307815i	$-0.900402\pi$
$163$	−9.47704	−	16.4147i	−0.742299	−	1.28570i	0.209147	−	0.977884i	$-0.432931\pi$
$164$	2.14932	+	1.80349i	0.167834	+	0.140829i
$165$	−5.43065	−	4.11955i	−0.422775	−	0.320706i
$166$	1.62387	+	9.20943i	0.126037	+	0.714790i
$167$	9.60067	−	8.05592i	0.742922	−	0.623385i	−0.190699	−	0.981649i	$-0.561075\pi$
$167$	9.60067	−	8.05592i	0.742922	−	0.623385i	0.933621	+	0.358263i	$0.116631\pi$
$168$	−4.26127	−	1.68569i	−0.328764	−	0.130054i
$169$	−19.7410	+	7.18514i	−1.51854	+	0.552703i
$170$	−0.243091			−0.0186443
$171$	−0.669239	−	2.39147i	−0.0511780	−	0.182880i
$172$	10.8059			0.823945
$173$	−1.50214	+	8.51908i	−0.114206	+	0.647694i	0.872934	+	0.487837i	$0.162214\pi$
$173$	−1.50214	+	8.51908i	−0.114206	+	0.647694i	−0.987140	+	0.159856i	$0.948897\pi$
$174$	3.55946	−	6.93102i	0.269842	−	0.525439i
$175$	−1.08995	−	11.1160i	−0.0823927	−	0.840292i
$176$	−0.774572	−	4.39282i	−0.0583856	−	0.331121i
$177$	3.80414	−	7.40745i	0.285936	−	0.556778i
$178$	−16.3506	+	5.95114i	−1.22553	+	0.446057i
$179$	−11.1486			−0.833282			−0.416641	−	0.909071i	$-0.636793\pi$
$179$	−11.1486			−0.833282			−0.416641	+	0.909071i	$0.636793\pi$
$180$	1.54204	+	2.15120i	0.114937	+	0.160341i
$181$	6.77495	−	11.7346i	0.503578	−	0.872223i	−0.496413	−	0.868086i	$-0.665350\pi$
$181$	6.77495	−	11.7346i	0.503578	−	0.872223i	0.999991	−	0.00413682i	$-0.00131679\pi$
$182$	3.83702	−	14.9443i	0.284419	−	1.10775i
$183$	5.10945	+	22.4585i	0.377701	+	1.66018i
$184$	0.655712	+	0.238660i	0.0483397	+	0.0175942i
$185$	3.04663	−	2.55643i	0.223993	−	0.187952i
$186$	4.71443	−	1.98341i	0.345679	−	0.145431i
$187$	−1.15491	+	0.420352i	−0.0844553	+	0.0307392i
$188$	6.66234			0.485901
$189$	12.5542	−	5.60289i	0.913183	−	0.407550i
$190$	−0.730324			−0.0529833
$191$	21.4361	−	7.80211i	1.55106	−	0.564541i	0.582396	−	0.812905i	$-0.302115\pi$
$191$	21.4361	−	7.80211i	1.55106	−	0.564541i	0.968667	+	0.248364i	$0.0798930\pi$
$192$	−0.216574	+	1.71846i	−0.0156299	+	0.124019i
$193$	−18.2205	+	15.2888i	−1.31154	+	1.10051i	−0.323513	+	0.946224i	$0.604864\pi$
$193$	−18.2205	+	15.2888i	−1.31154	+	1.10051i	−0.988026	+	0.154288i	$0.950692\pi$
$194$	−6.72900	−	2.44915i	−0.483114	−	0.175839i
$195$	−6.53683	+	6.05677i	−0.468112	+	0.433734i
$196$	4.61084	+	5.26689i	0.329346	+	0.376206i
$197$	0.0332154	−	0.0575308i	0.00236650	−	0.00409890i	−0.864840	−	0.502048i	$-0.832580\pi$
$197$	0.0332154	−	0.0575308i	0.00236650	−	0.00409890i	0.867206	+	0.497949i	$0.165913\pi$
$198$	11.0459	+	7.55370i	0.785001	+	0.536818i
$199$	3.73740			0.264937			0.132468	−	0.991187i	$-0.457710\pi$
$199$	3.73740			0.264937			0.132468	+	0.991187i	$0.457710\pi$
$200$	−3.96701	+	1.44387i	−0.280510	+	0.102097i
$201$	4.42209	+	6.85727i	0.311910	+	0.483675i
$202$	−0.0632787	−	0.358872i	−0.00445228	−	0.0252501i
$203$	−9.67738	+	6.92835i	−0.679219	+	0.486275i
$204$	0.476657	−	0.0234540i	0.0333726	−	0.00164211i
$205$	−0.429850	+	2.43780i	−0.0300220	+	0.170263i
$206$	−8.14524			−0.567506
$207$	−1.88734	+	0.905639i	−0.131179	+	0.0629463i
$208$	−5.83163			−0.404351
$209$	−3.46971	+	1.26287i	−0.240005	+	0.0873547i
$210$	−0.591813	−	3.99950i	−0.0408390	−	0.275992i
$211$	−15.0979	+	12.6686i	−1.03938	+	0.872143i	−0.991937	−	0.126731i	$-0.959552\pi$
$211$	−15.0979	+	12.6686i	−1.03938	+	0.872143i	−0.0474425	+	0.998874i	$0.515107\pi$
$212$	0.694269	+	3.93739i	0.0476826	+	0.270421i
$213$	1.95495	−	15.5120i	0.133951	−	1.06286i
$214$	−10.2504	−	8.60113i	−0.700705	−	0.587961i
$215$	4.76686	+	8.25644i	0.325097	+	0.563085i
$216$	−3.23120	−	4.06932i	−0.219855	−	0.276882i
$217$	−7.78975	−	0.599376i	−0.528803	−	0.0406883i
$218$	0.863341	−	4.89625i	0.0584729	−	0.331616i
$219$	−1.24188	+	9.85395i	−0.0839183	+	0.665868i
$220$	3.01471	−	2.52964i	0.203252	−	0.170548i
$221$	0.279017	+	1.58238i	0.0187687	+	0.106443i
$222$	−5.72722	+	5.30662i	−0.384386	+	0.356157i
$223$	14.0745	−	5.12270i	0.942498	−	0.343041i	0.175346	−	0.984507i	$-0.443896\pi$
$223$	14.0745	−	5.12270i	0.942498	−	0.343041i	0.767152	+	0.641466i	$0.221673\pi$
$224$	1.49476	−	2.18305i	0.0998728	−	0.145861i
$225$	5.22506	−	11.5367i	0.348337	−	0.769116i
$226$	0.618958	−	1.07207i	0.0411724	−	0.0713128i
$227$	−14.5679	+	5.30229i	−0.966906	+	0.351925i	−0.776736	−	0.629826i	$-0.783126\pi$
$227$	−14.5679	+	5.30229i	−0.966906	+	0.351925i	−0.190170	+	0.981751i	$0.560904\pi$
$228$	1.43203	−	0.0704632i	0.0948384	−	0.00466654i
$229$	10.0070	−	8.39683i	0.661278	−	0.554878i	−0.249192	−	0.968454i	$-0.580165\pi$
$229$	10.0070	−	8.39683i	0.661278	−	0.554878i	0.910470	+	0.413576i	$0.135720\pi$
$230$	0.106905	+	0.606287i	0.00704909	+	0.0399774i
$231$	−9.72757	−	17.9780i	−0.640027	−	1.18286i
$232$	3.44603	+	2.89156i	0.226243	+	0.189840i
$233$	14.4428	−	25.0156i	0.946177	−	1.63883i	0.192799	−	0.981238i	$-0.438243\pi$
$233$	14.4428	−	25.0156i	0.946177	−	1.63883i	0.753378	−	0.657588i	$-0.228423\pi$
$234$	12.2331	−	12.5069i	0.799705	−	0.817600i
$235$	2.93898	+	5.09046i	0.191718	+	0.332065i
$236$	3.68291	+	3.09033i	0.239737	+	0.201163i
$237$	22.4396	+	6.93894i	1.45761	+	0.450733i
$238$	−0.663876	−	0.301146i	−0.0430327	−	0.0195204i
$239$	−20.1559	−	7.33614i	−1.30378	−	0.474535i	−0.405551	−	0.914072i	$-0.632920\pi$
$239$	−20.1559	−	7.33614i	−1.30378	−	0.474535i	−0.898224	+	0.439537i	$0.855143\pi$
$240$	−1.40855	+	0.592591i	−0.0909216	+	0.0382516i
$241$	18.1603	+	15.2383i	1.16981	+	0.981588i	0.999992	−	0.00388777i	$-0.00123752\pi$
$241$	18.1603	+	15.2383i	1.16981	+	0.981588i	0.169818	+	0.985475i	$0.445682\pi$
$242$	4.44840	−	7.70485i	0.285954	−	0.495287i
$243$	15.5055	+	1.60647i	0.994676	+	0.103055i
$244$	−13.2978			−0.851302
$245$	−1.99025	+	5.84638i	−0.127152	+	0.373512i
$246$	0.607651	−	4.82154i	0.0387424	−	0.307410i
$247$	0.838256	+	4.75399i	0.0533370	+	0.302489i
$248$	0.512775	+	2.90809i	0.0325612	+	0.184664i
$249$	11.8812	−	11.0086i	0.752938	−	0.697643i
$250$	−6.23247	−	5.22966i	−0.394176	−	0.330753i
$251$	4.00465	−	6.93625i	0.252771	−	0.437813i	−0.711517	−	0.702669i	$-0.751991\pi$
$251$	4.00465	−	6.93625i	0.252771	−	0.437813i	0.964288	+	0.264857i	$0.0853247\pi$
$252$	1.54631	+	7.78517i	0.0974086	+	0.490420i
$253$	1.55628	+	2.69556i	0.0978428	+	0.169469i
$254$	0.906141	−	5.13898i	0.0568563	−	0.322448i
$255$	0.228189	+	0.353850i	0.0142898	+	0.0221590i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	14.3773	−	12.0640i	0.896832	−	0.752532i	−0.0727363	−	0.997351i	$-0.523173\pi$
$257$	14.3773	−	12.0640i	0.896832	−	0.752532i	0.969569	+	0.244819i	$0.0787287\pi$
$258$	−10.1435	−	15.7294i	−0.631507	−	0.979270i
$259$	11.4872	−	3.20731i	0.713781	−	0.199292i
$260$	−2.57253	−	4.45575i	−0.159541	−	0.276334i
$261$	−13.4302	+	1.32488i	−0.831310	+	0.0820080i
$262$	10.2012	+	17.6690i	0.630232	+	1.09159i
$263$	4.22513	−	23.9619i	0.260533	−	1.47755i	−0.520928	−	0.853600i	$-0.674414\pi$
$263$	4.22513	−	23.9619i	0.260533	−	1.47755i	0.781461	−	0.623954i	$-0.214475\pi$
$264$	−5.66721	+	5.25101i	−0.348793	+	0.323177i
$265$	−2.70216	+	2.26738i	−0.165992	+	0.139284i
$266$	−1.99450	−	0.904740i	−0.122290	−	0.0554731i
$267$	24.0109	+	18.2141i	1.46944	+	1.11468i
$268$	−4.42677	+	1.61121i	−0.270408	+	0.0984205i
$269$	4.24620	−	7.35464i	0.258895	−	0.448420i	−0.707051	−	0.707163i	$-0.749975\pi$
$269$	4.24620	−	7.35464i	0.258895	−	0.448420i	0.965946	+	0.258743i	$0.0833082\pi$
$270$	1.68384	−	4.26396i	0.102475	−	0.259496i
$271$	−0.505870	−	0.876192i	−0.0307294	−	0.0532249i	0.850252	−	0.526376i	$-0.176450\pi$
$271$	−0.505870	−	0.876192i	−0.0307294	−	0.0532249i	−0.880981	+	0.473151i	$0.843116\pi$
$272$	−0.0478454	+	0.271345i	−0.00290105	+	0.0164527i
$273$	−25.3552	+	8.44293i	−1.53456	+	0.510989i
$274$	17.5708	+	6.39526i	1.06149	+	0.386352i
$275$	−17.6952	−	6.44052i	−1.06706	−	0.388378i
$276$	−0.268116	−	1.17850i	−0.0161387	−	0.0709374i
$277$	3.65923	−	20.7525i	0.219862	−	1.24690i	−0.652406	−	0.757870i	$-0.726240\pi$
$277$	3.65923	−	20.7525i	0.219862	−	1.24690i	0.872268	−	0.489029i	$-0.162649\pi$
$278$	15.9191			0.954767
$279$	−7.31252	−	5.00063i	−0.437789	−	0.299380i
$280$	2.32738	+	0.179078i	0.139087	+	0.0107020i
$281$	−14.1454	−	11.8694i	−0.843844	−	0.708069i	0.114581	−	0.993414i	$-0.463448\pi$
$281$	−14.1454	−	11.8694i	−0.843844	−	0.708069i	−0.958425	+	0.285345i	$0.907892\pi$
$282$	−6.25392	−	9.69788i	−0.372416	−	0.577500i
$283$	13.4938	+	4.91136i	0.802125	+	0.291950i	0.710367	−	0.703832i	$-0.248529\pi$
$283$	13.4938	+	4.91136i	0.802125	+	0.291950i	0.0917585	+	0.995781i	$0.470751\pi$
$284$	8.48232	+	3.08731i	0.503333	+	0.183198i
$285$	0.685554	+	1.06308i	0.0406087	+	0.0629714i
$286$	−19.9267	−	16.7205i	−1.17829	−	0.988704i
$287$	−4.19390	+	6.12506i	−0.247558	+	0.361551i
$288$	2.70473	−	1.29786i	0.159378	−	0.0764771i
$289$	−16.9241			−0.995534
$290$	−0.689184	+	3.90855i	−0.0404703	+	0.229518i
$291$	2.75144	+	12.0939i	0.161292	+	0.708958i
$292$	−5.38837	−	1.96121i	−0.315331	−	0.114771i
$293$	2.56953	+	0.935233i	0.150114	+	0.0546369i	0.415984	−	0.909372i	$-0.363437\pi$
$293$	2.56953	+	0.935233i	0.150114	+	0.0546369i	−0.265871	+	0.964009i	$0.585659\pi$
$294$	3.33843	−	11.6557i	0.194701	−	0.679773i
$295$	−0.736557	+	4.17722i	−0.0428840	+	0.243207i
$296$	−2.25391	−	3.90388i	−0.131006	−	0.226909i
$297$	0.626571	−	23.1694i	0.0363574	−	1.34442i
$298$	0.856396	−	1.48332i	0.0496097	−	0.0859265i
$299$	3.82387	−	1.39178i	0.221140	−	0.0804885i
$300$	5.82557	+	4.41913i	0.336339	+	0.255138i
$301$	2.78993	+	28.4534i	0.160809	+	1.64003i
$302$	−0.0584423	+	0.0490389i	−0.00336298	+	0.00282187i
$303$	−0.462983	+	0.428982i	−0.0265977	+	0.0246444i
$304$	−0.143743	+	0.815207i	−0.00824422	+	0.0467553i
$305$	−5.86608	−	10.1604i	−0.335891	−	0.581780i
$306$	−0.481577	−	0.671818i	−0.0275299	−	0.0384053i
$307$	−0.543824	−	0.941930i	−0.0310377	−	0.0537588i	0.850089	−	0.526639i	$-0.176548\pi$
$307$	−0.543824	−	0.941930i	−0.0310377	−	0.0537588i	−0.881127	+	0.472880i	$0.843215\pi$
$308$	11.3668	−	3.17370i	0.647686	−	0.180838i
$309$	7.64592	+	11.8564i	0.434961	+	0.674489i
$310$	−1.99577	+	1.67465i	−0.113352	+	0.0951136i
$311$	−27.0824	−	9.85720i	−1.53570	−	0.558951i	−0.570694	−	0.821163i	$-0.693326\pi$
$311$	−27.0824	−	9.85720i	−1.53570	−	0.558951i	−0.965010	+	0.262212i	$0.915548\pi$
$312$	5.47414	+	8.48868i	0.309912	+	0.480577i
$313$	−3.74236	+	21.2240i	−0.211531	+	1.19965i	0.675295	+	0.737547i	$0.264016\pi$
$313$	−3.74236	+	21.2240i	−0.211531	+	1.19965i	−0.886826	+	0.462103i	$0.847095\pi$
$314$	11.5511	+	20.0071i	0.651866	+	1.12907i
$315$	−5.26625	+	4.61578i	−0.296719	+	0.260070i
$316$	−6.78040	+	11.7440i	−0.381427	+	0.660652i
$317$	1.97246	+	1.65509i	0.110785	+	0.0929593i	0.696497	−	0.717559i	$-0.254741\pi$
$317$	1.97246	+	1.65509i	0.110785	+	0.0929593i	−0.585713	+	0.810519i	$0.699185\pi$
$318$	5.07966	−	4.70662i	0.284853	−	0.263934i
$319$	3.48439	+	19.7610i	0.195088	+	1.10640i
$320$	−0.153204	−	0.868862i	−0.00856436	−	0.0485709i
$321$	−2.89798	+	22.9947i	−0.161749	+	1.28344i
$322$	−0.459126	+	1.78819i	−0.0255861	+	0.0996519i
$323$	0.228080			0.0126907
$324$	−2.89029	+	8.52327i	−0.160572	+	0.473515i
$325$	−12.3094	+	21.3206i	−0.682804	+	1.18265i
$326$	−14.5197	−	12.1834i	−0.804170	−	0.674779i
$327$	−7.93753	+	3.33940i	−0.438946	+	0.184669i
$328$	2.63653	+	0.959619i	0.145578	+	0.0529861i
$329$	1.72011	+	17.5428i	0.0948329	+	0.967164i
$330$	−6.51211	−	2.01372i	−0.358480	−	0.110852i
$331$	16.8386	+	14.1293i	0.925535	+	0.776616i	0.975010	−	0.222160i	$-0.0713106\pi$
$331$	16.8386	+	14.1293i	0.925535	+	0.776616i	−0.0494758	+	0.998775i	$0.515755\pi$
$332$	4.67575	+	8.09864i	0.256615	+	0.444470i
$333$	13.1006	+	3.35538i	0.717907	+	0.183874i
$334$	6.26639	−	10.8537i	0.342882	−	0.593888i
$335$	−3.18387	−	2.67158i	−0.173953	−	0.145964i
$336$	−4.58083	−	0.126588i	−0.249905	−	0.00690596i
$337$	−1.49240	−	8.46384i	−0.0812963	−	0.461054i	−0.998095	−	0.0617036i	$-0.980347\pi$
$337$	−1.49240	−	8.46384i	−0.0812963	−	0.461054i	0.916798	−	0.399351i	$-0.130764\pi$
$338$	−16.0930	+	13.5036i	−0.875345	+	0.734502i
$339$	−2.14154	+	0.105375i	−0.116313	+	0.00572317i
$340$	−0.228431	+	0.0831422i	−0.0123884	+	0.00450902i
$341$	−6.58594	+	11.4072i	−0.356649	+	0.617734i
$342$	−1.44681	−	2.01836i	−0.0782345	−	0.109140i
$343$	−12.6779	+	13.5008i	−0.684543	+	0.728972i
$344$	10.1543	−	3.69585i	0.547481	−	0.199267i
$345$	0.782176	−	0.724734i	0.0421109	−	0.0390183i
$346$	1.50214	+	8.51908i	0.0807557	+	0.457989i
$347$	18.3532	−	15.4001i	0.985249	−	0.826722i	0.000376119	−	1.00000i	$-0.499880\pi$
$347$	18.3532	−	15.4001i	0.985249	−	0.826722i	0.984873	+	0.173278i	$0.0554358\pi$
$348$	0.974254	−	7.73043i	0.0522255	−	0.414395i
$349$	1.60274	−	9.08960i	0.0857928	−	0.486555i	−0.911390	−	0.411544i	$-0.864990\pi$
$349$	1.60274	−	9.08960i	0.0857928	−	0.486555i	0.997183	−	0.0750112i	$-0.0238993\pi$
$350$	−4.82612	−	10.0728i	−0.257967	−	0.538416i
$351$	−29.6885	−	6.06669i	−1.58466	−	0.323816i
$352$	−2.23029	−	3.86298i	−0.118875	−	0.205897i
$353$	10.2920	+	8.63601i	0.547787	+	0.459648i	0.874191	−	0.485582i	$-0.161392\pi$
$353$	10.2920	+	8.63601i	0.547787	+	0.459648i	−0.326404	+	0.945231i	$0.605837\pi$
$354$	1.04122	−	8.26181i	0.0553404	−	0.439110i
$355$	1.38292	+	7.84296i	0.0733980	+	0.416261i
$356$	−13.3291	+	11.1845i	−0.706443	+	0.592776i
$357$	0.184823	+	1.24904i	0.00978184	+	0.0661062i
$358$	−10.4762	+	3.81303i	−0.553685	+	0.201525i
$359$	−5.32117			−0.280841			−0.140420	−	0.990092i	$-0.544845\pi$
$359$	−5.32117			−0.280841			−0.140420	+	0.990092i	$0.544845\pi$
$360$	2.18479	+	1.49406i	0.115149	+	0.0787438i
$361$	−18.3148			−0.963936
$362$	2.35292	−	13.3441i	0.123667	−	0.701348i
$363$	−15.3911	+	0.757320i	−0.807822	+	0.0397490i
$364$	−1.50564	−	15.3554i	−0.0789168	−	0.804842i
$365$	−0.878499	−	4.98222i	−0.0459828	−	0.260781i
$366$	12.4826	+	19.3566i	0.652475	+	1.01178i
$367$	4.11204	−	1.49666i	0.214647	−	0.0781250i	−0.232459	−	0.972606i	$-0.574677\pi$
$367$	4.11204	−	1.49666i	0.214647	−	0.0781250i	0.447105	+	0.894481i	$0.352455\pi$
$368$	0.697794			0.0363750
$369$	−7.58877	+	3.64146i	−0.395055	+	0.189567i
$370$	1.98855	−	3.44426i	0.103380	−	0.179059i
$371$	−10.1884	+	2.84467i	−0.528955	+	0.147688i
$372$	3.75175	−	3.47622i	0.194519	−	0.180234i
$373$	−11.6856	−	4.25323i	−0.605060	−	0.220224i	0.0212806	−	0.999774i	$-0.493226\pi$
$373$	−11.6856	−	4.25323i	−0.605060	−	0.220224i	−0.626340	+	0.779550i	$0.715448\pi$
$374$	−0.941490	+	0.790004i	−0.0486833	+	0.0408501i
$375$	−1.76203	+	13.9812i	−0.0909908	+	0.721987i
$376$	6.26055	−	2.27866i	0.322863	−	0.117513i
$377$	26.2334			1.35109
$378$	9.88078	−	9.55878i	0.508212	−	0.491650i
$379$	26.4250			1.35736			0.678681	−	0.734434i	$-0.262552\pi$
$379$	26.4250			1.35736			0.678681	+	0.734434i	$0.262552\pi$
$380$	−0.686281	+	0.249786i	−0.0352054	+	0.0128137i
$381$	−8.33102	+	3.50494i	−0.426811	+	0.179564i
$382$	17.4749	−	14.6632i	0.894093	−	0.750233i
$383$	−13.5746	−	4.94075i	−0.693629	−	0.252460i	−0.0289407	−	0.999581i	$-0.509213\pi$
$383$	−13.5746	−	4.94075i	−0.693629	−	0.252460i	−0.664688	+	0.747121i	$0.731436\pi$
$384$	0.384234	+	1.68889i	0.0196078	+	0.0861860i
$385$	7.43920	+	7.28498i	0.379137	+	0.371277i
$386$	−11.8926	+	20.5985i	−0.605316	+	1.04844i
$387$	−13.3745	+	29.5303i	−0.679862	+	1.50111i
$388$	−7.16085			−0.363537
$389$	−14.7347	+	5.36299i	−0.747078	+	0.271914i	−0.687376	−	0.726302i	$-0.741237\pi$
$389$	−14.7347	+	5.36299i	−0.747078	+	0.271914i	−0.0597025	+	0.998216i	$0.519015\pi$
$390$	−4.07108	+	7.92723i	−0.206147	+	0.401411i
$391$	−0.0333863	−	0.189343i	−0.00168842	−	0.00957548i
$392$	6.13416	+	3.37226i	0.309822	+	0.170325i
$393$	16.1436	−	31.4350i	0.814337	−	1.58568i
$394$	0.0115356	−	0.0654217i	0.000581155	−	0.00329590i
$395$	−11.9642			−0.601986
$396$	12.9633	+	3.32022i	0.651431	+	0.166848i
$397$	−1.77652			−0.0891612			−0.0445806	−	0.999006i	$-0.514195\pi$
$397$	−1.77652			−0.0891612			−0.0445806	+	0.999006i	$0.514195\pi$
$398$	3.51200	−	1.27826i	0.176041	−	0.0640736i
$399$	0.555266	+	3.75252i	0.0277981	+	0.187861i
$400$	−3.23394	+	2.71360i	−0.161697	+	0.135680i
$401$	5.14943	+	29.2039i	0.257150	+	1.45837i	0.790493	+	0.612472i	$0.209825\pi$
$401$	5.14943	+	29.2039i	0.257150	+	1.45837i	−0.533342	+	0.845899i	$0.679064\pi$
$402$	6.50073	+	4.93128i	0.324227	+	0.245950i
$403$	13.1917	+	11.0691i	0.657125	+	0.551393i
$404$	−0.182204	−	0.315586i	−0.00906498	−	0.0157010i
$405$	−7.78734	+	1.55153i	−0.386956	+	0.0770960i
$406$	−6.72413	+	9.82038i	−0.333713	+	0.487377i
$407$	3.49163	−	19.8020i	0.173074	−	0.981549i
$408$	0.439889	−	0.185066i	0.0217778	−	0.00916212i
$409$	5.21976	−	4.37989i	0.258100	−	0.216572i	−0.504551	−	0.863382i	$-0.668342\pi$
$409$	5.21976	−	4.37989i	0.258100	−	0.216572i	0.762651	+	0.646810i	$0.223897\pi$
$410$	0.429850	+	2.43780i	0.0212288	+	0.120394i
$411$	−7.18459	−	31.5798i	−0.354390	−	1.55772i
$412$	−7.65402	+	2.78584i	−0.377087	+	0.137248i
$413$	−7.18634	+	10.4954i	−0.353617	+	0.516446i
$414$	−1.46378	+	1.49653i	−0.0719407	+	0.0735505i
$415$	−4.12526	+	7.14515i	−0.202501	+	0.350742i
$416$	−5.47994	+	1.99454i	−0.268676	+	0.0977902i
$417$	−14.9433	−	23.1723i	−0.731774	−	1.13475i
$418$	−2.82854	+	2.37342i	−0.138348	+	0.116088i
$419$	4.70505	+	26.6837i	0.229857	+	1.30358i	0.853180	+	0.521617i	$0.174671\pi$
$419$	4.70505	+	26.6837i	0.229857	+	1.30358i	−0.623323	+	0.781964i	$0.714218\pi$
$420$	−1.92403	−	3.55589i	−0.0938832	−	0.173510i
$421$	−21.5456	−	18.0789i	−1.05007	−	0.881113i	−0.0569682	−	0.998376i	$-0.518143\pi$
$421$	−21.5456	−	18.0789i	−1.05007	−	0.881113i	−0.993101	+	0.117263i	$0.962588\pi$
$422$	−9.85443	+	17.0684i	−0.479706	+	0.830875i
$423$	−8.24594	+	18.2067i	−0.400931	+	0.885242i
$424$	1.99907	+	3.46249i	0.0970833	+	0.168153i
$425$	0.891050	+	0.747679i	0.0432223	+	0.0362678i
$426$	−3.46836	−	15.2451i	−0.168043	−	0.738629i
$427$	−3.43327	−	35.0146i	−0.166148	−	1.69448i
$428$	−12.5740	−	4.57657i	−0.607788	−	0.221217i
$429$	−5.63364	+	44.7013i	−0.271995	+	2.15820i
$430$	7.30325	+	6.12816i	0.352194	+	0.295526i
$431$	−20.4365	+	35.3970i	−0.984390	+	1.70501i	−0.339772	+	0.940508i	$0.610350\pi$
$431$	−20.4365	+	35.3970i	−0.984390	+	1.70501i	−0.644618	+	0.764505i	$0.722983\pi$
$432$	−4.42812	−	2.71878i	−0.213048	−	0.130807i
$433$	18.9809			0.912166			0.456083	−	0.889937i	$-0.349252\pi$
$433$	18.9809			0.912166			0.456083	+	0.889937i	$0.349252\pi$
$434$	−7.52497	+	2.10102i	−0.361210	+	0.100852i
$435$	6.33633	−	2.66576i	0.303804	−	0.127813i
$436$	−0.863341	−	4.89625i	−0.0413466	−	0.234488i
$437$	−0.100303	−	0.568846i	−0.00479814	−	0.0272116i
$438$	2.20327	+	9.68443i	0.105276	+	0.462740i
$439$	−9.69371	−	8.13399i	−0.462655	−	0.388214i	0.381452	−	0.924389i	$-0.375424\pi$
$439$	−9.69371	−	8.13399i	−0.462655	−	0.388214i	−0.844107	+	0.536175i	$0.819869\pi$
$440$	1.96771	−	3.40817i	0.0938069	−	0.162478i
$441$	−20.1001	+	6.08165i	−0.957147	+	0.289602i
$442$	0.803397	+	1.39152i	0.0382137	+	0.0661881i
$443$	7.06749	−	40.0817i	0.335786	−	1.90434i	−0.0835418	−	0.996504i	$-0.526623\pi$
$443$	7.06749	−	40.0817i	0.335786	−	1.90434i	0.419328	−	0.907835i	$-0.362266\pi$
$444$	−3.56686	+	6.94541i	−0.169276	+	0.329615i
$445$	−14.4256	−	5.25049i	−0.683839	−	0.248897i
$446$	11.4736	−	9.62752i	0.543292	−	0.455876i
$447$	−2.96306	+	0.145798i	−0.140148	+	0.00689599i
$448$	0.657967	−	2.56263i	0.0310860	−	0.121073i
$449$	−4.21584	−	7.30204i	−0.198958	−	0.344605i	0.749233	−	0.662306i	$-0.230422\pi$
$449$	−4.21584	−	7.30204i	−0.198958	−	0.344605i	−0.948191	+	0.317702i	$0.897089\pi$
$450$	0.964150	−	12.6281i	0.0454505	−	0.595293i
$451$	6.25762	+	10.8385i	0.294660	+	0.510365i
$452$	0.214962	−	1.21911i	0.0101109	−	0.0573420i
$453$	0.126242	+	0.0390375i	0.00593137	+	0.00183414i
$454$	−11.8759	+	9.96504i	−0.557362	+	0.467683i
$455$	11.0683	−	7.92418i	0.518892	−	0.371491i
$456$	1.32157	−	0.555996i	0.0618881	−	0.0260369i
$457$	5.27686	−	1.92062i	0.246841	−	0.0898428i	−0.215637	−	0.976474i	$-0.569183\pi$
$457$	5.27686	−	1.92062i	0.246841	−	0.0898428i	0.462478	+	0.886631i	$0.346960\pi$
$458$	6.53157	−	11.3130i	0.305200	−	0.528623i
$459$	−0.525861	+	1.33163i	−0.0245451	+	0.0621551i
$460$	0.307820	+	0.533160i	0.0143522	+	0.0248587i
$461$	−4.56772	+	25.9048i	−0.212740	+	1.20651i	0.672046	+	0.740510i	$0.265416\pi$
$461$	−4.56772	+	25.9048i	−0.212740	+	1.20651i	−0.884786	+	0.465998i	$0.845695\pi$
$462$	−15.2898	−	13.5667i	−0.711344	−	0.631182i
$463$	12.3467	+	4.49381i	0.573798	+	0.208845i	0.612588	−	0.790402i	$-0.290128\pi$
$463$	12.3467	+	4.49381i	0.573798	+	0.208845i	−0.0387907	+	0.999247i	$0.512351\pi$
$464$	4.22718	+	1.53857i	0.196242	+	0.0714262i
$465$	4.31108	+	1.33310i	0.199922	+	0.0618212i
$466$	5.01592	−	28.4467i	0.232358	−	1.31777i
$467$	26.8464			1.24230			0.621151	−	0.783691i	$-0.286665\pi$
$467$	26.8464			1.24230			0.621151	+	0.783691i	$0.286665\pi$
$468$	7.21778	−	15.9366i	0.333642	−	0.736670i
$469$	−5.38545	−	11.2403i	−0.248677	−	0.519027i
$470$	4.50278	+	3.77828i	0.207698	+	0.174279i
$471$	18.2799	−	35.5947i	0.842291	−	1.64012i
$472$	4.51775	+	1.64433i	0.207946	+	0.0756863i
$473$	45.2939	+	16.4856i	2.08262	+	0.758011i
$474$	23.4596	−	1.15433i	1.07754	−	0.0530203i
$475$	2.67700	+	2.24627i	0.122829	+	0.103066i
$476$	−0.726838	−	0.0559259i	−0.0333145	−	0.00256336i
$477$	−11.6193	−	2.97600i	−0.532013	−	0.136262i
$478$	−21.4494			−0.981074
$479$	−5.22184	+	29.6145i	−0.238592	+	1.35312i	0.596324	+	0.802744i	$0.296628\pi$
$479$	−5.22184	+	29.6145i	−0.238592	+	1.35312i	−0.834915	+	0.550378i	$0.814484\pi$
$480$	−1.12093	+	1.03861i	−0.0511631	+	0.0474057i
$481$	−24.7026	−	8.99100i	−1.12634	−	0.409954i
$482$	22.2770	+	8.10815i	1.01469	+	0.369316i
$483$	3.03391	−	1.01025i	0.138048	−	0.0459681i
$484$	1.54491	−	8.76163i	0.0702233	−	0.398256i
$485$	−3.15889	−	5.47135i	−0.143438	−	0.248441i
$486$	15.1198	−	3.79359i	0.685849	−	0.172081i
$487$	6.71776	−	11.6355i	0.304411	−	0.527255i	−0.672719	−	0.739898i	$-0.734874\pi$
$487$	6.71776	−	11.6355i	0.304411	−	0.527255i	0.977130	+	0.212643i	$0.0682071\pi$
$488$	−12.4958	+	4.54810i	−0.565659	+	0.205883i
$489$	−4.10497	+	32.5718i	−0.185633	+	1.47295i
$490$	0.129358	+	6.17451i	0.00584379	+	0.278936i
$491$	21.1654	−	17.7599i	0.955183	−	0.801493i	−0.0249800	−	0.999688i	$-0.507952\pi$
$491$	21.1654	−	17.7599i	0.955183	−	0.801493i	0.980163	+	0.198194i	$0.0635078\pi$
$492$	−1.07806	−	4.73860i	−0.0486027	−	0.213632i
$493$	0.215231	−	1.22064i	0.00969353	−	0.0549748i
$494$	2.41366	+	4.18059i	0.108596	+	0.188093i
$495$	3.18168	+	11.3695i	0.143006	+	0.511019i
$496$	1.47648	+	2.55733i	0.0662957	+	0.114828i
$497$	−5.93927	+	23.1321i	−0.266413	+	1.03762i
$498$	7.39947	−	14.4083i	0.331578	−	0.645652i
$499$	7.47586	−	6.27299i	0.334665	−	0.280818i	−0.459932	−	0.887954i	$-0.652126\pi$
$499$	7.47586	−	6.27299i	0.334665	−	0.280818i	0.794598	+	0.607136i	$0.207682\pi$
$500$	−7.64525	−	2.78265i	−0.341906	−	0.124444i
$501$	−21.6812	+	1.06683i	−0.968644	+	0.0476622i
$502$	1.39080	−	7.88762i	0.0620744	−	0.352042i
$503$	−5.74261	−	9.94650i	−0.256051	−	0.443493i	0.709130	−	0.705078i	$-0.249088\pi$
$503$	−5.74261	−	9.94650i	−0.256051	−	0.443493i	−0.965180	+	0.261585i	$0.915755\pi$
$504$	4.11575	+	6.78680i	0.183330	+	0.302308i
$505$	0.160752	−	0.278431i	0.00715338	−	0.0123900i
$506$	2.38437	+	2.00072i	0.105998	+	0.0889429i
$507$	34.7627	+	10.7496i	1.54387	+	0.477406i
$508$	−0.906141	−	5.13898i	−0.0402035	−	0.228005i
$509$	−7.18131	−	40.7272i	−0.318306	−	1.80520i	−0.553052	−	0.833147i	$-0.686537\pi$
$509$	−7.18131	−	40.7272i	−0.318306	−	1.80520i	0.234746	−	0.972057i	$-0.424574\pi$
$510$	0.335452	+	0.254465i	0.0148541	+	0.0112679i
$511$	3.77291	−	14.6946i	0.166904	−	0.650051i
$512$	−1.00000			−0.0441942
$513$	−1.57985	+	4.00064i	−0.0697522	+	0.176633i
$514$	9.38413	−	16.2538i	0.413916	−	0.716924i
$515$	−5.50500	−	4.61925i	−0.242579	−	0.203548i
$516$	−14.9116	−	11.3115i	−0.656445	−	0.497962i
$517$	27.9257	+	10.1641i	1.22817	+	0.447018i
$518$	9.69748	−	6.94274i	0.426083	−	0.305047i
$519$	10.9905	−	10.1834i	0.482431	−	0.447002i
$520$	−3.94134	−	3.30718i	−0.172839	−	0.145029i
$521$	−1.42023	−	2.45991i	−0.0622215	−	0.107771i	0.833237	−	0.552917i	$-0.186485\pi$
$521$	−1.42023	−	2.45991i	−0.0622215	−	0.107771i	−0.895458	+	0.445146i	$0.853152\pi$
$522$	−12.1672	+	5.83839i	−0.532542	+	0.255539i
$523$	1.52494	−	2.64128i	0.0666812	−	0.115495i	−0.830757	−	0.556635i	$-0.812092\pi$
$523$	1.52494	−	2.64128i	0.0666812	−	0.115495i	0.897439	+	0.441140i	$0.145426\pi$
$524$	15.6291	+	13.1144i	0.682762	+	0.572906i
$525$	−10.1320	+	16.4804i	−0.442198	+	0.719263i
$526$	−4.22513	−	23.9619i	−0.184224	−	1.04479i
$527$	0.623276	−	0.522991i	0.0271503	−	0.0227818i
$528$	−3.52948	+	6.87264i	−0.153601	+	0.299093i
$529$	21.1554	−	7.69993i	0.919799	−	0.334779i
$530$	−1.76371	+	3.05483i	−0.0766106	+	0.132693i
$531$	−13.0035	+	6.23971i	−0.564304	+	0.270780i
$532$	−2.18365	−	0.168019i	−0.0946733	−	0.00728456i
$533$	15.3753	−	5.59615i	0.665978	−	0.242396i
$534$	28.7925	+	8.90341i	1.24597	+	0.385288i
$535$	−2.05002	−	11.6262i	−0.0886300	−	0.502646i
$536$	−3.60874	+	3.02809i	−0.155874	+	0.130794i
$537$	15.3843	+	11.6702i	0.663883	+	0.503605i
$538$	1.47469	−	8.36338i	0.0635784	−	0.360571i
$539$	11.2915	+	29.1109i	0.486359	+	1.25390i
$540$	0.123931	−	4.58271i	0.00533312	−	0.197209i
$541$	−9.49589	−	16.4474i	−0.408260	−	0.707128i	0.586435	−	0.809997i	$-0.300531\pi$
$541$	−9.49589	−	16.4474i	−0.408260	−	0.707128i	−0.994695	+	0.102869i	$0.967198\pi$
$542$	−0.775037	−	0.650333i	−0.0332907	−	0.0279342i
$543$	−21.6326	+	9.10106i	−0.928345	+	0.390564i
$544$	0.0478454	+	0.271345i	0.00205136	+	0.0116338i
$545$	3.36021	−	2.81955i	0.143935	−	0.120776i
$546$	−20.9384	+	16.6057i	−0.896081	+	0.710660i
$547$	8.71723	−	3.17281i	0.372722	−	0.135660i	−0.148866	−	0.988857i	$-0.547562\pi$
$547$	8.71723	−	3.17281i	0.372722	−	0.135660i	0.521588	+	0.853198i	$0.325340\pi$
$548$	18.6985			0.798760
$549$	16.4586	−	36.3399i	0.702434	−	1.55095i
$550$	−18.8308			−0.802949
$551$	0.646624	−	3.66719i	0.0275471	−	0.156227i
$552$	−0.655018	−	1.01573i	−0.0278794	−	0.0432322i
$553$	−32.6740	−	14.8215i	−1.38944	−	0.630275i
$554$	−3.65923	−	20.7525i	−0.155466	−	0.881690i
$555$	−6.88020	+	0.338541i	−0.292048	+	0.0143703i
$556$	14.9591	−	5.44467i	0.634407	−	0.230905i
$557$	27.4082			1.16132			0.580661	−	0.814146i	$-0.302794\pi$
$557$	27.4082			1.16132			0.580661	+	0.814146i	$0.302794\pi$
$558$	−8.58184	−	2.19802i	−0.363298	−	0.0930497i
$559$	31.5082	−	54.5737i	1.33265	−	2.30822i
$560$	2.24827	−	0.627732i	0.0950066	−	0.0265265i
$561$	2.03372	+	0.628883i	0.0858639	+	0.0265514i
$562$	−17.3519	−	6.31558i	−0.731946	−	0.266407i
$563$	12.0378	−	10.1009i	0.507333	−	0.425703i	−0.352856	−	0.935677i	$-0.614790\pi$
$563$	12.0378	−	10.1009i	0.507333	−	0.425703i	0.860190	+	0.509974i	$0.170345\pi$
$564$	−9.19364	−	6.97406i	−0.387122	−	0.293661i
$565$	1.02630	−	0.373544i	0.0431770	−	0.0157151i
$566$	14.3598			0.603589
$567$	−23.1891	−	5.40992i	−0.973849	−	0.227195i
$568$	9.02669			0.378752
$569$	0.441083	−	0.160541i	0.0184912	−	0.00673023i	−0.332758	−	0.943012i	$-0.607979\pi$
$569$	0.441083	−	0.160541i	0.0184912	−	0.00673023i	0.351249	+	0.936282i	$0.385757\pi$
$570$	1.00780	+	0.764495i	0.0422123	+	0.0320212i
$571$	7.33017	−	6.15074i	0.306758	−	0.257401i	−0.476392	−	0.879233i	$-0.658056\pi$
$571$	7.33017	−	6.15074i	0.306758	−	0.257401i	0.783151	+	0.621832i	$0.213611\pi$
$572$	−24.4437	−	8.89679i	−1.02204	−	0.371994i
$573$	−37.7477	−	11.6726i	−1.57693	−	0.487631i
$574$	−1.84609	+	7.19008i	−0.0770541	+	0.300108i
$575$	1.47291	−	2.55115i	0.0614244	−	0.106390i
$576$	2.09772	−	2.14466i	0.0874050	−	0.0893609i
$577$	−13.6657			−0.568909			−0.284455	−	0.958689i	$-0.591813\pi$
$577$	−13.6657			−0.568909			−0.284455	+	0.958689i	$0.591813\pi$
$578$	−15.9034	+	5.78838i	−0.661496	+	0.240765i
$579$	41.1473	−	2.02466i	1.71002	−	0.0841419i
$580$	0.689184	+	3.90855i	0.0286168	+	0.162294i
$581$	−20.1175	+	14.4028i	−0.834615	+	0.597528i
$582$	6.72187	+	10.4235i	0.278630	+	0.432069i
$583$	−3.09684	+	17.5631i	−0.128258	+	0.727388i
$584$	−5.73418			−0.237282
$585$	15.3606	−	1.51531i	0.635082	−	0.0626503i
$586$	2.73444			0.112959
$587$	−18.3159	+	6.66645i	−0.755979	+	0.275154i	−0.691120	−	0.722740i	$-0.742882\pi$
$587$	−18.3159	+	6.66645i	−0.755979	+	0.275154i	−0.0648598	+	0.997894i	$0.520660\pi$
$588$	−0.849376	−	12.0946i	−0.0350277	−	0.498772i
$589$	1.87252	−	1.57123i	0.0771558	−	0.0647414i
$590$	0.736557	+	4.17722i	0.0303236	+	0.171974i
$591$	−0.106058	+	0.0446196i	−0.00436264	+	0.00183541i
$592$	−3.45319	−	2.89757i	−0.141925	−	0.119089i
$593$	−0.0251136	−	0.0434980i	−0.00103129	−	0.00178625i	0.865509	−	0.500893i	$-0.166995\pi$
$593$	−0.0251136	−	0.0434980i	−0.00103129	−	0.00178625i	−0.866541	+	0.499107i	$0.833662\pi$
$594$	−7.33562	−	21.9864i	−0.300984	−	0.902113i
$595$	−0.277901	−	0.580022i	−0.0113928	−	0.0237786i
$596$	0.297423	−	1.68677i	0.0121829	−	0.0690928i
$597$	−5.15738	−	3.91226i	−0.211078	−	0.160118i
$598$	3.11725	−	2.61568i	0.127474	−	0.106963i
$599$	−0.522182	−	2.96144i	−0.0213358	−	0.121001i	0.972280	−	0.233821i	$-0.0751229\pi$
$599$	−0.522182	−	2.96144i	−0.0213358	−	0.121001i	−0.993615	+	0.112820i	$0.964012\pi$
$600$	6.98567	+	2.16016i	0.285189	+	0.0881881i
$601$	14.2762	−	5.19610i	0.582337	−	0.211953i	−0.0340188	−	0.999421i	$-0.510831\pi$
$601$	14.2762	−	5.19610i	0.582337	−	0.211953i	0.616356	+	0.787468i	$0.288608\pi$
$602$	12.3533	+	25.7832i	0.503483	+	1.05085i
$603$	1.07589	−	14.0916i	0.0438137	−	0.573855i
$604$	−0.0381455	+	0.0660700i	−0.00155212	+	0.00268835i
$605$	7.37597	−	2.68463i	0.299876	−	0.109146i
$606$	−0.288341	+	0.561461i	−0.0117131	+	0.0228078i
$607$	4.51413	−	3.78780i	0.183223	−	0.153742i	−0.546563	−	0.837418i	$-0.684064\pi$
$607$	4.51413	−	3.78780i	0.183223	−	0.153742i	0.729786	+	0.683676i	$0.239620\pi$
$608$	0.143743	+	0.815207i	0.00582955	+	0.0330610i
$609$	20.6067	+	0.569454i	0.835027	+	0.0230754i
$610$	−8.98736	−	7.54129i	−0.363887	−	0.305338i
$611$	19.4262	−	33.6471i	0.785899	−	1.36122i
$612$	−0.682309	−	0.466593i	−0.0275807	−	0.0188609i
$613$	8.70886	+	15.0842i	0.351748	+	0.609245i	0.986556	−	0.163425i	$-0.0522542\pi$
$613$	8.70886	+	15.0842i	0.351748	+	0.609245i	−0.634808	+	0.772670i	$0.718921\pi$
$614$	−0.833186	−	0.699126i	−0.0336247	−	0.0282144i
$615$	3.14503	−	2.91406i	0.126820	−	0.117506i
$616$	9.59587	−	6.86999i	0.386629	−	0.276800i
$617$	1.34658	+	0.490114i	0.0542112	+	0.0197312i	0.368983	−	0.929436i	$-0.379706\pi$
$617$	1.34658	+	0.490114i	0.0542112	+	0.0197312i	−0.314772	+	0.949167i	$0.601928\pi$
$618$	11.2400	+	8.52634i	0.452137	+	0.342980i
$619$	−17.4409	−	14.6346i	−0.701007	−	0.588215i	0.221053	−	0.975262i	$-0.429051\pi$
$619$	−17.4409	−	14.6346i	−0.701007	−	0.588215i	−0.922060	+	0.387047i	$0.873495\pi$
$620$	−1.30264	+	2.25625i	−0.0523154	+	0.0906130i
$621$	3.55243	+	0.725920i	0.142554	+	0.0291302i
$622$	−28.8205			−1.15560
$623$	−32.8915	−	32.2096i	−1.31777	−	1.29045i
$624$	8.04731	+	6.10448i	0.322150	+	0.244375i
$625$	2.41892	+	13.7184i	0.0967567	+	0.548735i
$626$	3.74236	+	21.2240i	0.149575	+	0.848281i
$627$	6.10996	+	1.88936i	0.244008	+	0.0754540i
$628$	17.6973	+	14.8498i	0.706200	+	0.592572i
$629$	−0.621021	+	1.07564i	−0.0247617	+	0.0428886i
$630$	−3.36996	+	6.13858i	−0.134263	+	0.244567i
$631$	5.98954	+	10.3742i	0.238440	+	0.412990i	0.960267	−	0.279084i	$-0.0900308\pi$
$631$	5.98954	+	10.3742i	0.238440	+	0.412990i	−0.721827	+	0.692073i	$0.756697\pi$
$632$	−2.35481	+	13.3548i	−0.0936693	+	0.531225i
$633$	34.0955	−	1.67767i	1.35517	−	0.0666815i
$634$	2.41958	+	0.880656i	0.0960939	+	0.0349753i
$635$	3.52678	−	2.95932i	0.139956	−	0.117437i
$636$	3.16356	−	6.16012i	0.125443	−	0.244265i
$637$	40.0440	−	7.92906i	1.58660	−	0.314161i
$638$	10.0329	+	17.3775i	0.397207	+	0.687982i
$639$	−18.9355	+	19.3592i	−0.749076	+	0.765838i
$640$	−0.441133	−	0.764065i	−0.0174373	−	0.0302023i
$641$	−0.379580	+	2.15270i	−0.0149925	+	0.0850267i	−0.991386	−	0.130973i	$-0.958190\pi$
$641$	−0.379580	+	2.15270i	−0.0149925	+	0.0850267i	0.976393	+	0.216000i	$0.0693010\pi$
$642$	5.14142	+	22.5991i	0.202916	+	0.891914i
$643$	−23.2444	+	19.5044i	−0.916671	+	0.769178i	−0.973376	−	0.229213i	$-0.926385\pi$
$643$	−23.2444	+	19.5044i	−0.916671	+	0.769178i	0.0567052	+	0.998391i	$0.481940\pi$
$644$	0.180160	+	1.83738i	0.00709928	+	0.0724029i
$645$	2.06476	−	16.3833i	0.0812998	−	0.645091i
$646$	0.214325	−	0.0780078i	0.00843249	−	0.00306918i
$647$	−12.9853	+	22.4913i	−0.510507	+	0.884223i	0.489419	+	0.872049i	$0.337209\pi$
$647$	−12.9853	+	22.4913i	−0.510507	+	0.884223i	−0.999926	+	0.0121748i	$0.996125\pi$
$648$	0.199145	+	8.99780i	0.00782315	+	0.353467i
$649$	10.7226	+	18.5720i	0.420897	+	0.729015i
$650$	−4.27502	+	24.2448i	−0.167680	+	0.950961i
$651$	10.1220	+	8.98131i	0.396711	+	0.352005i
$652$	−17.8110	−	6.48268i	−0.697533	−	0.253881i
$653$	−13.7988	−	5.02236i	−0.539990	−	0.196540i	0.0576035	−	0.998340i	$-0.481654\pi$
$653$	−13.7988	−	5.02236i	−0.539990	−	0.196540i	−0.597593	+	0.801799i	$0.703876\pi$
$654$	−6.31670	+	5.85280i	−0.247002	+	0.228863i
$655$	−3.12573	+	17.7269i	−0.122132	+	0.692646i
$656$	2.80574			0.109546
$657$	12.0287	−	12.2979i	0.469285	−	0.479786i
$658$	7.61636	+	15.8965i	0.296917	+	0.619710i
$659$	26.4156	+	22.1653i	1.02901	+	0.863438i	0.990732	−	0.135829i	$-0.0433699\pi$
$659$	26.4156	+	22.1653i	1.02901	+	0.863438i	0.0382730	+	0.999267i	$0.487814\pi$
$660$	−6.80811	+	0.334994i	−0.265005	+	0.0130396i
$661$	33.0675	+	12.0356i	1.28618	+	0.468130i	0.892470	−	0.451107i	$-0.148971\pi$
$661$	33.0675	+	12.0356i	1.28618	+	0.468130i	0.393706	+	0.919237i	$0.371193\pi$
$662$	20.6556	+	7.51803i	0.802804	+	0.292197i
$663$	1.27139	−	2.47567i	0.0493768	−	0.0961469i
$664$	7.16367	+	6.01103i	0.278004	+	0.233273i
$665$	−0.834904	−	1.74257i	−0.0323762	−	0.0675740i
$666$	13.4581	−	1.32763i	0.521492	−	0.0514447i
$667$	−3.13901			−0.121543
$668$	2.17629	−	12.3424i	0.0842034	−	0.477541i
$669$	−24.7843	−	7.66399i	−0.958218	−	0.296307i
$670$	−3.90559	−	1.42152i	−0.150886	−	0.0549181i
$671$	−55.7386	−	20.2872i	−2.15176	−	0.783178i
$672$	−4.34787	+	1.44778i	−0.167723	+	0.0558494i
$673$	−1.28861	+	7.30805i	−0.0496721	+	0.281705i	−0.999519	−	0.0310105i	$-0.990127\pi$
$673$	−1.28861	+	7.30805i	−0.0496721	+	0.281705i	0.949847	+	0.312715i	$0.101239\pi$
$674$	−4.29720	−	7.44297i	−0.165522	−	0.286693i
$675$	−19.2868	+	10.4505i	−0.742349	+	0.402240i
$676$	−10.5040	+	18.1934i	−0.403999	+	0.699747i
$677$	−23.9772	+	8.72700i	−0.921521	+	0.335406i	−0.758843	−	0.651273i	$-0.774235\pi$
$677$	−23.9772	+	8.72700i	−0.921521	+	0.335406i	−0.162677	+	0.986679i	$0.552013\pi$
$678$	−1.97635	+	0.831470i	−0.0759013	+	0.0319324i
$679$	−1.84882	−	18.8554i	−0.0709512	−	0.723604i
$680$	−0.186219	+	0.156256i	−0.00714117	+	0.00599215i
$681$	25.6532	+	7.93267i	0.983034	+	0.303981i
$682$	−2.28727	+	12.9718i	−0.0875842	+	0.496715i
$683$	11.0979	+	19.2221i	0.424649	+	0.735514i	0.996388	−	0.0849220i	$-0.0270641\pi$
$683$	11.0979	+	19.2221i	0.424649	+	0.735514i	−0.571738	+	0.820436i	$0.693731\pi$
$684$	−2.04987	−	1.40180i	−0.0783789	−	0.0535990i
$685$	8.24853	+	14.2869i	0.315160	+	0.545873i
$686$	−7.29582	+	17.0227i	−0.278556	+	0.649928i
$687$	−22.5987	+	1.11197i	−0.862194	+	0.0424244i
$688$	8.27783	−	6.94593i	0.315589	−	0.264811i
$689$	21.9095	+	7.97442i	0.834687	+	0.303801i
$690$	0.487132	−	0.948547i	0.0185448	−	0.0361106i
$691$	3.33004	−	18.8856i	0.126681	−	0.718443i	−0.853614	−	0.520905i	$-0.825594\pi$
$691$	3.33004	−	18.8856i	0.126681	−	0.718443i	0.980295	−	0.197538i	$-0.0632944\pi$
$692$	4.32525	+	7.49155i	0.164421	+	0.284786i
$693$	−5.39564	+	34.9912i	−0.204963	+	1.32921i
$694$	11.9792	−	20.7485i	0.454723	−	0.787604i
$695$	10.7590	+	9.02790i	0.408113	+	0.342448i
$696$	−1.72846	−	7.59745i	−0.0655173	−	0.287980i
$697$	−0.134242	−	0.761323i	−0.00508477	−	0.0288372i
$698$	−1.60274	−	9.08960i	−0.0606647	−	0.344047i
$699$	−46.1162	+	19.4015i	−1.74427	+	0.733833i
$700$	−7.98019	−	7.81475i	−0.301623	−	0.295370i
$701$	9.73401			0.367648			0.183824	−	0.982959i	$-0.441152\pi$
$701$	9.73401			0.367648			0.183824	+	0.982959i	$0.441152\pi$
$702$	−29.9730	+	4.45326i	−1.13126	+	0.168077i
$703$	−1.86575	+	3.23157i	−0.0703679	+	0.121881i
$704$	−3.41700	−	2.86721i	−0.128783	−	0.108062i
$705$	1.27302	−	10.1010i	0.0479445	−	0.380426i
$706$	12.6250	+	4.59512i	0.475148	+	0.172940i
$707$	0.783936	−	0.561245i	0.0294829	−	0.0211078i
$708$	−1.84728	−	8.11969i	−0.0694249	−	0.305156i
$709$	11.1328	+	9.34153i	0.418101	+	0.350828i	0.827440	−	0.561554i	$-0.189796\pi$
$709$	11.1328	+	9.34153i	0.418101	+	0.350828i	−0.409339	+	0.912382i	$0.634241\pi$
$710$	3.98197	+	6.89698i	0.149441	+	0.258839i
$711$	−23.7018	−	33.0649i	−0.888885	−	1.24003i
$712$	−8.69998	+	15.0688i	−0.326046	+	0.564727i
$713$	−1.57847	−	1.32450i	−0.0591143	−	0.0496028i
$714$	0.600873	+	1.11050i	0.0224871	+	0.0415595i
$715$	−3.98521	−	22.6013i	−0.149039	−	0.845240i
$716$	−8.54029	+	7.16615i	−0.319166	+	0.267812i
$717$	20.1345	+	31.2224i	0.751938	+	1.16602i
$718$	−5.00027	+	1.81995i	−0.186608	+	0.0679199i
$719$	12.0520	−	20.8746i	0.449463	−	0.778492i	−0.548888	−	0.835896i	$-0.684949\pi$
$719$	12.0520	−	20.8746i	0.449463	−	0.778492i	0.998351	+	0.0574034i	$0.0182821\pi$
$720$	2.56403	+	0.656713i	0.0955559	+	0.0244742i
$721$	−9.31160	−	19.4347i	−0.346782	−	0.723787i
$722$	−17.2103	+	6.26402i	−0.640500	+	0.233123i
$723$	−9.10889	−	40.0380i	−0.338763	−	1.48903i
$724$	−2.35292	−	13.3441i	−0.0874455	−	0.495928i
$725$	14.5478	−	12.2070i	0.540291	−	0.453358i
$726$	−14.2039	+	5.97571i	−0.527155	+	0.221779i
$727$	0.656915	−	3.72555i	0.0243636	−	0.138173i	−0.970200	−	0.242307i	$-0.922096\pi$
$727$	0.656915	−	3.72555i	0.0243636	−	0.138173i	0.994563	+	0.104134i	$0.0332070\pi$
$728$	−6.66670	−	13.9144i	−0.247084	−	0.515702i
$729$	−19.7150	−	18.4478i	−0.730184	−	0.683250i
$730$	−2.52954	−	4.38129i	−0.0936224	−	0.162159i
$731$	−2.28080	−	1.91382i	−0.0843584	−	0.0707851i
$732$	18.3501	+	13.9199i	0.678240	+	0.514495i
$733$	−5.01688	−	28.4521i	−0.185303	−	1.05090i	−0.925566	−	0.378586i	$-0.876410\pi$
$733$	−5.01688	−	28.4521i	−0.185303	−	1.05090i	0.740263	−	0.672317i	$-0.234701\pi$
$734$	3.35216	−	2.81280i	0.123731	−	0.103822i
$735$	8.86635	−	5.98429i	0.327040	−	0.220734i
$736$	0.655712	−	0.238660i	0.0241699	−	0.00879711i
$737$	−21.0132			−0.774033
$738$	−5.88565	+	6.01736i	−0.216654	+	0.221502i
$739$	−25.0955			−0.923151			−0.461576	−	0.887101i	$-0.652716\pi$
$739$	−25.0955			−0.923151			−0.461576	+	0.887101i	$0.652716\pi$
$740$	0.690615	−	3.91667i	0.0253875	−	0.143980i
$741$	3.81967	−	7.43769i	0.140319	−	0.273231i
$742$	−8.60102	+	6.15775i	−0.315754	+	0.226058i
$743$	−2.23097	−	12.6525i	−0.0818463	−	0.464174i	−0.997993	−	0.0633296i	$-0.979828\pi$
$743$	−2.23097	−	12.6525i	−0.0818463	−	0.464174i	0.916146	−	0.400844i	$-0.131283\pi$
$744$	2.33655	−	4.54976i	0.0856622	−	0.166802i
$745$	1.42000	−	0.516839i	0.0520250	−	0.0189355i
$746$	−12.4356			−0.455300
$747$	−27.9190	+	2.75418i	−1.02150	+	0.100770i
$748$	−0.614514	+	1.06437i	−0.0224689	+	0.0389172i
$749$	8.80425	−	34.2905i	0.321700	−	1.25295i
$750$	3.12609	+	13.7407i	0.114149	+	0.501739i
$751$	−39.2236	−	14.2762i	−1.43129	−	0.520946i	−0.493988	−	0.869469i	$-0.664461\pi$
$751$	−39.2236	−	14.2762i	−1.43129	−	0.520946i	−0.937300	+	0.348522i	$0.886684\pi$
$752$	5.10365	−	4.28247i	0.186111	−	0.156166i
$753$	−12.7870	+	5.37960i	−0.465983	+	0.196044i
$754$	24.6514	−	8.97237i	0.897750	−	0.326754i
$755$	−0.0673090			−0.00244963
$756$	6.01560	−	12.3617i	0.218785	−	0.449592i
$757$	−33.0272			−1.20039			−0.600197	−	0.799852i	$-0.704911\pi$
$757$	−33.0272			−1.20039			−0.600197	+	0.799852i	$0.704911\pi$
$758$	24.8314	−	9.03788i	0.901916	−	0.328271i
$759$	0.674103	−	5.34882i	0.0244684	−	0.194150i
$760$	−0.559461	+	0.469444i	−0.0202938	+	0.0170285i
$761$	38.7648	+	14.1092i	1.40522	+	0.511460i	0.929724	−	0.368256i	$-0.120045\pi$
$761$	38.7648	+	14.1092i	1.40522	+	0.511460i	0.475500	+	0.879716i	$0.342267\pi$
$762$	−6.62984	+	6.14295i	−0.240174	+	0.222536i
$763$	12.6695	−	3.53742i	0.458668	−	0.128063i
$764$	11.4059	−	19.7556i	0.412652	−	0.714734i
$765$	0.0555184	−	0.727158i	0.00200727	−	0.0262905i
$766$	−14.4458			−0.521947
$767$	26.3459	−	9.58912i	0.951295	−	0.346243i
$768$	0.938697	+	1.45563i	0.0338723	+	0.0525254i
$769$	−0.00824195	−	0.0467424i	−0.000297212	−	0.00168557i	0.984659	−	0.174491i	$-0.0558280\pi$
$769$	−0.00824195	−	0.0467424i	−0.000297212	−	0.00168557i	−0.984956	+	0.172805i	$0.944717\pi$
$770$	9.48218	+	4.30129i	0.341714	+	0.155008i
$771$	−32.4683	+	1.59761i	−1.16932	+	0.0575364i
$772$	−4.13025	+	23.4238i	−0.148651	+	0.843041i
$773$	26.4099			0.949897			0.474949	−	0.880014i	$-0.342467\pi$
$773$	26.4099			0.949897			0.474949	+	0.880014i	$0.342467\pi$
$774$	−2.46791	+	32.3238i	−0.0887073	+	1.16185i
$775$	12.4662			0.447799
$776$	−6.72900	+	2.44915i	−0.241557	+	0.0879195i
$777$	−19.2090	−	7.59878i	−0.689120	−	0.272605i
$778$	−12.0118	+	10.0791i	−0.430645	+	0.361354i
$779$	−0.403305	−	2.28726i	−0.0144499	−	0.0819495i
$780$	−1.11429	+	8.84155i	−0.0398979	+	0.316578i
$781$	30.8443	+	25.8814i	1.10369	+	0.926109i
$782$	−0.0961319	−	0.166505i	−0.00343767	−	0.00595422i
$783$	19.9198	+	12.2303i	0.711875	+	0.437077i
$784$	6.91760	+	1.07088i	0.247057	+	0.0382456i
$785$	−3.53935	+	20.0726i	−0.126325	+	0.716423i
$786$	4.41864	−	35.0606i	0.157608	−	1.25057i
$787$	25.3395	−	21.2624i	0.903256	−	0.757922i	−0.0675678	−	0.997715i	$-0.521524\pi$
$787$	25.3395	−	21.2624i	0.903256	−	0.757922i	0.970824	+	0.239793i	$0.0770795\pi$
$788$	−0.0115356	−	0.0654217i	−0.000410939	−	0.00233055i
$789$	−30.9135	+	28.6432i	−1.10055	+	1.01972i
$790$	−11.2427	+	4.09201i	−0.399997	+	0.145587i
$791$	3.26556	+	0.251266i	0.116110	+	0.00893399i
$792$	13.3171	−	1.31372i	0.473203	−	0.0466810i
$793$	−38.7738	+	67.1582i	−1.37690	+	2.38486i
$794$	−1.66939	+	0.607607i	−0.0592443	+	0.0215632i
$795$	6.10228	−	0.300264i	0.216426	−	0.0106493i
$796$	2.86301	−	2.40235i	0.101477	−	0.0851491i
$797$	−8.70231	−	49.3532i	−0.308251	−	1.74818i	−0.607791	−	0.794097i	$-0.707944\pi$
$797$	−8.70231	−	49.3532i	−0.308251	−	1.74818i	0.299539	−	0.954084i	$-0.403167\pi$
$798$	1.80522	+	3.33630i	0.0639039	+	0.118104i
$799$	−1.40621	−	1.17995i	−0.0497482	−	0.0417437i
$800$	−2.11080	+	3.65602i	−0.0746282	+	0.129260i
$801$	−14.0674	−	50.2686i	−0.497046	−	1.77616i
$802$	14.8272	+	25.6814i	0.523566	+	0.906843i
$803$	−19.5937	−	16.4411i	−0.691448	−	0.580194i
$804$	7.79528	+	2.41051i	0.274918	+	0.0850122i
$805$	−1.32440	+	0.948182i	−0.0466790	+	0.0334190i
$806$	16.1820	+	5.88977i	0.569987	+	0.207458i
$807$	−13.5582	+	5.70409i	−0.477273	+	0.200793i
$808$	−0.279153	−	0.234237i	−0.00982055	−	0.00824042i
$809$	2.43501	−	4.21755i	0.0856102	−	0.148281i	−0.820041	−	0.572305i	$-0.806049\pi$
$809$	2.43501	−	4.21755i	0.0856102	−	0.148281i	0.905651	+	0.424024i	$0.139383\pi$
$810$	−6.78705	+	4.12138i	−0.238473	+	0.144811i
$811$	15.2009			0.533777			0.266889	−	0.963727i	$-0.414004\pi$
$811$	15.2009			0.533777			0.266889	+	0.963727i	$0.414004\pi$
$812$	−2.95985	+	11.5279i	−0.103870	+	0.404551i
$813$	−0.219117	+	1.73863i	−0.00768476	+	0.0609764i
$814$	−3.49163	−	19.8020i	−0.122382	−	0.694060i
$815$	−2.90384	−	16.4685i	−0.101717	−	0.576866i
$816$	0.350064	−	0.324356i	0.0122547	−	0.0113547i
$817$	−6.85225	−	5.74972i	−0.239730	−	0.201157i
$818$	3.40695	−	5.90102i	0.119121	−	0.206324i
$819$	43.8266	+	14.8907i	1.53142	+	0.520324i
$820$	1.23770	+	2.14377i	0.0432225	+	0.0748636i
$821$	−8.63792	+	48.9881i	−0.301465	+	1.70970i	0.338227	+	0.941065i	$0.390173\pi$
$821$	−8.63792	+	48.9881i	−0.301465	+	1.70970i	−0.639692	+	0.768631i	$0.720938\pi$
$822$	−17.5522	−	27.2180i	−0.612204	−	0.949338i
$823$	−33.6565	−	12.2500i	−1.17319	−	0.427007i	−0.319400	−	0.947620i	$-0.603481\pi$
$823$	−33.6565	−	12.2500i	−1.17319	−	0.427007i	−0.853793	+	0.520613i	$0.825704\pi$
$824$	−6.23962	+	5.23566i	−0.217367	+	0.182393i
$825$	17.6764	+	27.4106i	0.615415	+	0.954316i
$826$	−3.16330	+	12.3203i	−0.110065	+	0.428680i
$827$	1.19083	+	2.06257i	0.0414091	+	0.0717227i	0.885987	−	0.463710i	$-0.153482\pi$
$827$	1.19083	+	2.06257i	0.0414091	+	0.0717227i	−0.844578	+	0.535433i	$0.820149\pi$
$828$	−0.863656	+	1.90692i	−0.0300141	+	0.0662701i
$829$	−10.1895	−	17.6488i	−0.353897	−	0.612968i	0.633031	−	0.774126i	$-0.281810\pi$
$829$	−10.1895	−	17.6488i	−0.353897	−	0.612968i	−0.986929	+	0.161158i	$0.948477\pi$
$830$	−1.43269	+	8.12517i	−0.0497293	+	0.282029i
$831$	−26.7730	+	24.8068i	−0.928745	+	0.860539i
$832$	−4.46729	+	3.74850i	−0.154875	+	0.129956i
$833$	−0.0403983	−	1.92829i	−0.00139972	−	0.0668114i
$834$	−21.9675	−	16.6640i	−0.760671	−	0.577026i
$835$	10.3904	−	3.78180i	0.359575	−	0.130875i
$836$	−1.84620	+	3.19771i	−0.0638520	+	0.110595i
$837$	4.85625	+	14.5552i	0.167857	+	0.503102i
$838$	13.5476	+	23.4652i	0.467996	+	0.810592i
$839$	−4.98838	+	28.2905i	−0.172218	+	0.976696i	0.769088	+	0.639142i	$0.220711\pi$
$839$	−4.98838	+	28.2905i	−0.172218	+	0.976696i	−0.941306	+	0.337554i	$0.890401\pi$
$840$	−3.02419	−	2.68339i	−0.104344	−	0.0925856i
$841$	8.23522	+	2.99738i	0.283973	+	0.103358i
$842$	−26.4296	−	9.61959i	−0.910824	−	0.331513i
$843$	7.09507	+	31.1863i	0.244367	+	1.07411i
$844$	−3.42241	+	19.4094i	−0.117804	+	0.668100i
$845$	−18.5346			−0.637610
$846$	−1.52158	+	19.9290i	−0.0523129	+	0.685174i
$847$	23.4693	+	1.80583i	0.806416	+	0.0620490i
$848$	3.06275	+	2.56995i	0.105175	+	0.0882525i
$849$	−13.4795	−	20.9026i	−0.462617	−	0.717374i
$850$	1.09303	+	0.397832i	0.0374908	+	0.0136455i
$851$	2.95583	+	1.07583i	0.101325	+	0.0368791i
$852$	−8.47334	−	13.1395i	−0.290292	−	0.450152i
$853$	−0.279865	−	0.234835i	−0.00958241	−	0.00804060i	0.637984	−	0.770050i	$-0.279769\pi$
$853$	−0.279865	−	0.234835i	−0.00958241	−	0.00804060i	−0.647566	+	0.762009i	$0.724213\pi$
$854$	−15.2019	−	31.7288i	−0.520200	−	1.08574i
$855$	0.166795	−	2.18462i	0.00570427	−	0.0747123i
$856$	−13.3810			−0.457353
$857$	−7.07269	+	40.1112i	−0.241598	+	1.37017i	0.586663	+	0.809831i	$0.300441\pi$
$857$	−7.07269	+	40.1112i	−0.241598	+	1.37017i	−0.828262	+	0.560341i	$0.810670\pi$
$858$	9.99487	+	43.9323i	0.341219	+	1.49983i
$859$	4.59952	+	1.67409i	0.156934	+	0.0571192i	0.419293	−	0.907851i	$-0.362278\pi$
$859$	4.59952	+	1.67409i	0.156934	+	0.0571192i	−0.262359	+	0.964970i	$0.584500\pi$
$860$	8.95876	+	3.26072i	0.305491	+	0.111190i
$861$	12.1990	−	4.06210i	0.415740	−	0.138436i
$862$	−7.09751	+	40.2520i	−0.241742	+	1.37099i
$863$	−0.198547	−	0.343894i	−0.00675862	−	0.0117063i	0.862626	−	0.505842i	$-0.168818\pi$
$863$	−0.198547	−	0.343894i	−0.00675862	−	0.0117063i	−0.869385	+	0.494135i	$0.835485\pi$
$864$	−5.09095	−	1.04031i	−0.173198	−	0.0353920i
$865$	−3.81602	+	6.60954i	−0.129749	+	0.224731i
$866$	17.8363	−	6.49187i	0.606101	−	0.220603i
$867$	23.3542	+	17.7159i	0.793151	+	0.601664i
$868$	−6.35256	+	4.54801i	−0.215620	+	0.154369i
$869$	−46.3373	+	38.8816i	−1.57189	+	1.31897i
$870$	5.04246	−	4.67214i	0.170955	−	0.158400i
$871$	−4.77048	+	27.0547i	−0.161641	+	0.916714i
$872$	−2.48589	−	4.30569i	−0.0841829	−	0.145809i
$873$	8.86294	−	19.5691i	0.299965	−	0.662312i
$874$	−0.288811	−	0.500235i	−0.00976918	−	0.0169207i
$875$	5.35316	−	20.8493i	0.180970	−	0.704836i
$876$	5.38266	+	8.34683i	0.181863	+	0.282013i
$877$	36.1013	−	30.2926i	1.21905	−	1.02291i	0.220181	−	0.975459i	$-0.429335\pi$
$877$	36.1013	−	30.2926i	1.21905	−	1.02291i	0.998874	−	0.0474488i	$-0.0151091\pi$
$878$	−11.8911	−	4.32800i	−0.401305	−	0.146063i
$879$	−2.56681	−	3.98032i	−0.0865764	−	0.134253i
$880$	0.683379	−	3.87563i	0.0230367	−	0.130648i
$881$	8.78796	+	15.2212i	0.296074	+	0.512815i	0.975234	−	0.221175i	$-0.0709892\pi$
$881$	8.78796	+	15.2212i	0.296074	+	0.512815i	−0.679160	+	0.733990i	$0.737656\pi$
$882$	−16.8079	+	12.5895i	−0.565950	+	0.423911i
$883$	−8.84432	+	15.3188i	−0.297635	+	0.515519i	−0.975594	−	0.219580i	$-0.929531\pi$
$883$	−8.84432	+	15.3188i	−0.297635	+	0.515519i	0.677959	+	0.735099i	$0.262865\pi$
$884$	1.23088	+	1.03283i	0.0413988	+	0.0347378i
$885$	5.38907	−	4.99330i	0.181152	−	0.167848i
$886$	−7.06749	−	40.0817i	−0.237437	−	1.34657i
$887$	0.583826	+	3.31104i	0.0196029	+	0.111174i	0.993039	−	0.117784i	$-0.0375792\pi$
$887$	0.583826	+	3.31104i	0.0196029	+	0.111174i	−0.973436	+	0.228958i	$0.926468\pi$
$888$	−0.976278	+	7.74649i	−0.0327617	+	0.259955i
$889$	13.2976	−	3.71278i	0.445988	−	0.124523i
$890$	−15.3514			−0.514580
$891$	−25.1181	+	31.3165i	−0.841487	+	1.04914i
$892$	7.48888	−	12.9711i	0.250746	−	0.434305i
$893$	−4.22471	−	3.54496i	−0.141375	−	0.118627i
$894$	−2.73450	+	1.15043i	−0.0914553	+	0.0384761i
$895$	−9.24281	−	3.36411i	−0.308953	−	0.112450i
$896$	−0.258184	−	2.63312i	−0.00862534	−	0.0879665i
$897$	−6.73361	−	2.08221i	−0.224829	−	0.0695231i
$898$	−6.45904	−	5.41977i	−0.215541	−	0.180860i
$899$	−6.64188	−	11.5041i	−0.221519	−	0.383683i
$900$	−3.41305	−	12.1963i	−0.113768	−	0.406542i
$901$	0.550804	−	0.954021i	0.0183500	−	0.0317831i
$902$	9.58722	+	8.04464i	0.319220	+	0.267857i
$903$	25.9347	−	42.1844i	0.863053	−	1.40381i
$904$	−0.214962	−	1.21911i	−0.00714952	−	0.0405469i
$905$	9.15777	−	7.68428i	0.304415	−	0.255434i
$906$	0.131980	−	0.00649411i	0.00438475	−	0.000215752i
$907$	−1.00875	+	0.367156i	−0.0334951	+	0.0121912i	−0.358713	−	0.933448i	$-0.616784\pi$
$907$	−1.00875	+	0.367156i	−0.0334951	+	0.0121912i	0.325218	+	0.945639i	$0.394562\pi$
$908$	−7.75143	+	13.4259i	−0.257240	+	0.445553i
$909$	1.08794	−	0.107325i	0.0360848	−	0.00355973i
$910$	7.69061	−	11.2319i	0.254941	−	0.372334i
$911$	−0.225681	+	0.0821413i	−0.00747716	+	0.00272146i	−0.345756	−	0.938324i	$-0.612378\pi$
$911$	−0.225681	+	0.0821413i	−0.00747716	+	0.00272146i	0.338279	+	0.941046i	$0.390155\pi$
$912$	1.05170	−	0.974468i	0.0348254	−	0.0322679i
$913$	7.24341	+	41.0794i	0.239722	+	1.35953i
$914$	4.30174	−	3.60958i	0.142289	−	0.119394i
$915$	−2.54089	+	20.1612i	−0.0839991	+	0.666509i
$916$	2.26839	−	12.8647i	0.0749498	−	0.425061i
$917$	−30.4967	+	44.5394i	−1.00709	+	1.47082i
$918$	−0.0387034	+	1.43118i	−0.00127740	+	0.0472359i
$919$	−14.5162	−	25.1428i	−0.478845	−	0.829384i	0.520861	−	0.853642i	$-0.325611\pi$
$919$	−14.5162	−	25.1428i	−0.478845	−	0.829384i	−0.999706	+	0.0242578i	$0.992278\pi$
$920$	0.471608	+	0.395726i	0.0155484	+	0.0130467i
$921$	−0.235557	+	1.86908i	−0.00776185	+	0.0615881i
$922$	4.56772	+	25.9048i	0.150430	+	0.853130i
$923$	40.3249	−	33.8366i	1.32731	−	1.11374i
$924$	−19.0078	−	7.51916i	−0.625309	−	0.247362i
$925$	−17.8826	+	6.50872i	−0.587975	+	0.214005i
$926$	13.1390			0.431775
$927$	1.86025	−	24.3648i	0.0610986	−	0.800246i
$928$	4.49847			0.147670
$929$	−7.28687	+	41.3259i	−0.239074	+	1.35586i	0.594786	+	0.803884i	$0.297237\pi$
$929$	−7.28687	+	41.3259i	−0.239074	+	1.35586i	−0.833861	+	0.551975i	$0.813874\pi$
$930$	4.50704	−	0.221769i	0.147792	−	0.00727211i
$931$	−0.121370	−	5.79321i	−0.00397773	−	0.189865i
$932$	−5.01592	−	28.4467i	−0.164302	−	0.931802i
$933$	27.0538	+	41.9519i	0.885700	+	1.37344i
$934$	25.2273	−	9.18200i	0.825464	−	0.300444i
$935$	−1.08433			−0.0354614
$936$	1.33186	−	17.4441i	0.0435331	−	0.570179i
$937$	5.18146	−	8.97455i	0.169271	−	0.293186i	−0.768893	−	0.639378i	$-0.779192\pi$
$937$	5.18146	−	8.97455i	0.169271	−	0.293186i	0.938164	+	0.346192i	$0.112525\pi$
$938$	−8.90506	−	8.72045i	−0.290760	−	0.284733i
$939$	27.3812	−	25.3704i	0.893553	−	0.827931i
$940$	5.52347	+	2.01038i	0.180156	+	0.0655714i
$941$	27.1476	−	22.7795i	0.884986	−	0.742591i	−0.0822125	−	0.996615i	$-0.526199\pi$
$941$	27.1476	−	22.7795i	0.884986	−	0.742591i	0.967198	+	0.254024i	$0.0817542\pi$
$942$	5.00334	−	39.7001i	0.163018	−	1.29350i
$943$	−1.83976	+	0.669617i	−0.0599107	+	0.0218057i
$944$	4.80769			0.156477
$945$	12.0988	−	0.856861i	0.393576	−	0.0278737i
$946$	48.2008			1.56714
$947$	−26.4542	+	9.62855i	−0.859647	+	0.312886i	−0.733967	−	0.679185i	$-0.762333\pi$
$947$	−26.4542	+	9.62855i	−0.859647	+	0.312886i	−0.125680	+	0.992071i	$0.540111\pi$
$948$	21.6500	−	9.10838i	0.703160	−	0.295826i
$949$	−25.6163	+	21.4946i	−0.831539	+	0.697744i
$950$	3.28382	+	1.19521i	0.106541	+	0.0387779i
$951$	−0.989351	−	4.34868i	−0.0320819	−	0.141016i
$952$	−0.702132	+	0.196040i	−0.0227562	+	0.00635369i
$953$	−2.74690	+	4.75777i	−0.0889808	+	0.154119i	−0.907081	−	0.420957i	$-0.861694\pi$
$953$	−2.74690	+	4.75777i	−0.0889808	+	0.154119i	0.818100	+	0.575076i	$0.195028\pi$
$954$	−11.9365	+	1.17752i	−0.386457	+	0.0381237i
$955$	20.1261			0.651266
$956$	−20.1559	+	7.33614i	−0.651888	+	0.237268i
$957$	15.8773	−	30.9164i	0.513240	−	0.999384i
$958$	5.22184	+	29.6145i	0.168710	+	0.956802i
$959$	4.82766	+	49.2355i	0.155893	+	1.58990i
$960$	−0.698102	+	1.35935i	−0.0225312	+	0.0438728i
$961$	−3.86890	+	21.9416i	−0.124803	+	0.707793i
$962$	−26.2879			−0.847557
$963$	28.0696	−	28.6977i	0.904529	−	0.924770i
$964$	23.7066			0.763540
$965$	−19.7193	+	7.17723i	−0.634786	+	0.231043i
$966$	2.50542	−	1.98699i	0.0806106	−	0.0639303i
$967$	−2.85297	+	2.39393i	−0.0917455	+	0.0769836i	−0.687507	−	0.726178i	$-0.741295\pi$
$967$	−2.85297	+	2.39393i	−0.0917455	+	0.0769836i	0.595761	+	0.803162i	$0.296850\pi$
$968$	−1.54491	−	8.76163i	−0.0496554	−	0.281610i
$969$	−0.314736	−	0.238751i	−0.0101108	−	0.00766978i
$970$	−4.83969	−	4.06099i	−0.155393	−	0.130390i
$971$	1.86108	+	3.22348i	0.0597248	+	0.103446i	0.894342	−	0.447384i	$-0.147644\pi$
$971$	1.86108	+	3.22348i	0.0597248	+	0.103446i	−0.834617	+	0.550831i	$0.814311\pi$
$972$	12.9105	−	8.73609i	0.414104	−	0.280210i
$973$	18.1987	+	37.9834i	0.583423	+	1.21769i
$974$	2.33305	−	13.2314i	0.0747558	−	0.423961i
$975$	39.3044	−	16.5357i	1.25875	−	0.529568i
$976$	−10.1867	+	8.54764i	−0.326068	+	0.273603i
$977$	−8.26122	−	46.8517i	−0.264300	−	1.49892i	−0.771022	−	0.636809i	$-0.780254\pi$
$977$	−8.26122	−	46.8517i	−0.264300	−	1.49892i	0.506722	−	0.862110i	$-0.330857\pi$
$978$	7.28279	+	32.0114i	0.232878	+	1.02361i
$979$	−72.9333	+	26.5455i	−2.33096	+	0.848399i
$980$	2.23336	+	5.75790i	0.0713421	+	0.183929i
$981$	14.4490	+	3.70074i	0.461320	+	0.118155i
$982$	13.8148	−	23.9279i	0.440847	−	0.763569i
$983$	−20.0207	+	7.28695i	−0.638563	+	0.232418i	−0.640954	−	0.767579i	$-0.721461\pi$
$983$	−20.0207	+	7.28695i	−0.638563	+	0.232418i	0.00239135	+	0.999997i	$0.499239\pi$
$984$	−2.63374	−	4.08411i	−0.0839606	−	0.130197i
$985$	0.0448976	−	0.0376736i	0.00143056	−	0.00120038i
$986$	−0.215231	−	1.22064i	−0.00685436	−	0.0388730i
$987$	15.9899	−	26.0086i	0.508964	−	0.827862i
$988$	3.69795	+	3.10294i	0.117647	+	0.0987178i
$989$	−3.77016	+	6.53011i	−0.119884	+	0.207646i
$990$	6.87838	+	9.59561i	0.218609	+	0.304968i
$991$	26.4657	+	45.8399i	0.840710	+	1.45615i	0.889295	+	0.457334i	$0.151195\pi$
$991$	26.4657	+	45.8399i	0.840710	+	1.45615i	−0.0485851	+	0.998819i	$0.515471\pi$
$992$	2.26209	+	1.89812i	0.0718215	+	0.0602654i
$993$	−8.44594	−	37.1240i	−0.268024	−	1.17810i
$994$	2.33055	+	23.7684i	0.0739206	+	0.753888i
$995$	3.09852	+	1.12777i	0.0982297	+	0.0357527i
$996$	2.02530	−	16.0702i	0.0641740	−	0.509202i
$997$	−37.3043	−	31.3020i	−1.18144	−	0.991344i	−0.999968	−	0.00794769i	$-0.997470\pi$
$997$	−37.3043	−	31.3020i	−1.18144	−	0.991344i	−0.181470	−	0.983397i	$-0.558085\pi$
$998$	4.87952	−	8.45157i	0.154458	−	0.267530i
$999$	−14.5656	−	18.3437i	−0.460836	−	0.580371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.b.25.2	yes	72
7.2	even	3		378.2.v.a.79.11	yes	72
27.13	even	9		378.2.v.a.67.11	✓	72
189.121	even	9	inner	378.2.w.b.121.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.11	✓	72	27.13	even	9
378.2.v.a.79.11	yes	72	7.2	even	3
378.2.w.b.25.2	yes	72	1.1	even	1	trivial
378.2.w.b.121.2	yes	72	189.121	even	9	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-1.37994 - 1.04679i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.829059 + 0.301753i) q^{5} +(-1.65474 - 0.511691i) q^{6} +(1.89032 + 1.85113i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.808471 + 2.88901i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(-1.37994 - 1.04679i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.829059 + 0.301753i) q^{5} +(-1.65474 - 0.511691i) q^{6} +(1.89032 + 1.85113i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.808471 + 2.88901i) q^{9} +0.882266 q^{10} +(4.19158 - 1.52561i) q^{11} +(-1.72996 + 0.0851228i) q^{12} +(-1.01265 - 5.74304i) q^{13} +(2.40944 + 1.09297i) q^{14} +(-0.828181 - 1.28425i) q^{15} +(0.173648 - 0.984808i) q^{16} -0.275531 q^{17} +(1.74781 + 2.43827i) q^{18} -0.827783 q^{19} +(0.829059 - 0.301753i) q^{20} +(-0.670787 - 4.53322i) q^{21} +(3.41700 - 2.86721i) q^{22} +(0.121171 + 0.687193i) q^{23} +(-1.59651 + 0.671670i) q^{24} +(-3.23394 - 2.71360i) q^{25} +(-2.91582 - 5.05034i) q^{26} +(1.90854 - 4.83296i) q^{27} +(2.63795 + 0.202975i) q^{28} +(-0.781152 + 4.43013i) q^{29} +(-1.21747 - 0.923545i) q^{30} +(-2.26209 + 1.89812i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-7.38111 - 2.28244i) q^{33} +(-0.258914 + 0.0942371i) q^{34} +(1.00860 + 2.10511i) q^{35} +(2.47634 + 1.69343i) q^{36} +(2.25391 - 3.90388i) q^{37} +(-0.777861 + 0.283118i) q^{38} +(-4.61434 + 8.98508i) q^{39} +(0.675855 - 0.567110i) q^{40} +(0.487212 + 2.76311i) q^{41} +(-2.18078 - 4.03041i) q^{42} +(8.27783 + 6.94593i) q^{43} +(2.23029 - 3.86298i) q^{44} +(-0.201496 + 2.63912i) q^{45} +(0.348897 + 0.604307i) q^{46} +(5.10365 + 4.28247i) q^{47} +(-1.27051 + 1.17720i) q^{48} +(0.146620 + 6.99846i) q^{49} +(-3.96701 - 1.44387i) q^{50} +(0.380216 + 0.288422i) q^{51} +(-4.46729 - 3.74850i) q^{52} +(-1.99907 + 3.46249i) q^{53} +(0.140468 - 5.19425i) q^{54} +3.93542 q^{55} +(2.54829 - 0.711499i) q^{56} +(1.14229 + 0.866513i) q^{57} +(0.781152 + 4.43013i) q^{58} +(0.834847 + 4.73465i) q^{59} +(-1.45992 - 0.451448i) q^{60} +(-10.1867 - 8.54764i) q^{61} +(-1.47648 + 2.55733i) q^{62} +(-3.81967 + 6.95774i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.893429 - 5.06689i) q^{65} +(-7.71662 + 0.379697i) q^{66} +(-4.42677 - 1.61121i) q^{67} +(-0.211069 + 0.177108i) q^{68} +(0.552137 - 1.07513i) q^{69} +(1.66777 + 1.63319i) q^{70} +(4.51335 + 7.81735i) q^{71} +(2.90619 + 0.744348i) q^{72} +(-2.86709 - 4.96595i) q^{73} +(0.782774 - 4.43933i) q^{74} +(1.62208 + 7.12985i) q^{75} +(-0.634118 + 0.532088i) q^{76} +(10.7475 + 4.87527i) q^{77} +(-1.26298 + 10.0214i) q^{78} +(-12.7430 + 4.63807i) q^{79} +(0.441133 - 0.764065i) q^{80} +(-7.69275 + 4.67136i) q^{81} +(1.40287 + 2.42984i) q^{82} +(-1.62387 + 9.20943i) q^{83} +(-3.42775 - 3.04147i) q^{84} +(-0.228431 - 0.0831422i) q^{85} +(10.1543 + 3.69585i) q^{86} +(5.71535 - 5.29562i) q^{87} +(0.774572 - 4.39282i) q^{88} -17.4000 q^{89} +(0.713287 + 2.54887i) q^{90} +(8.71688 - 12.7307i) q^{91} +(0.534541 + 0.448533i) q^{92} +(5.10848 - 0.251364i) q^{93} +(6.26055 + 2.27866i) q^{94} +(-0.686281 - 0.249786i) q^{95} +(-0.791260 + 1.54075i) q^{96} +(-5.48553 - 4.60290i) q^{97} +(2.53139 + 6.52626i) q^{98} +(7.79627 + 10.8761i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} + 9 q^{35} - 3 q^{36} + 51 q^{39} - 6 q^{41} - 27 q^{42} - 24 q^{43} + 18 q^{45} + 27 q^{47} + 6 q^{48} - 69 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{52} - 15 q^{53} + 45 q^{54} - 72 q^{55} + 6 q^{56} + 57 q^{57} - 3 q^{58} + 15 q^{59} - 33 q^{60} - 18 q^{61} - 24 q^{62} - 12 q^{63} - 36 q^{64} - 90 q^{65} - 36 q^{66} - 66 q^{67} - 18 q^{68} - 39 q^{69} - 12 q^{70} + 12 q^{71} + 30 q^{73} + 9 q^{74} - 21 q^{75} - 87 q^{77} + 6 q^{78} - 45 q^{79} - 6 q^{80} - 24 q^{81} + 33 q^{82} + 18 q^{83} + 6 q^{84} + 51 q^{85} - 12 q^{86} - 18 q^{87} - 12 q^{88} + 72 q^{89} - 69 q^{90} - 30 q^{91} + 12 q^{92} - 48 q^{93} + 21 q^{95} + 48 q^{97} + 6 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

Introduction

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