LMFDB - Embedded newform 756.2.bt.a.103.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(103,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14, 15]))

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

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

chi := DirichletCharacter("756.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bt (of order $18$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.10
Character	$\chi$	$=$	756.103
Dual form			756.2.bt.a.367.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36742 - 0.360769i) q^{2} +(-1.03034 + 1.39226i) q^{3} +(1.73969 + 0.986648i) q^{4} +(1.98405 + 0.349842i) q^{5} +(1.91120 - 1.53209i) q^{6} +(1.38264 - 2.25573i) q^{7} +(-2.02294 - 1.97679i) q^{8} +(-0.876779 - 2.86902i) q^{9} +O(q^{10})$	\(q+(-1.36742 - 0.360769i) q^{2} +(-1.03034 + 1.39226i) q^{3} +(1.73969 + 0.986648i) q^{4} +(1.98405 + 0.349842i) q^{5} +(1.91120 - 1.53209i) q^{6} +(1.38264 - 2.25573i) q^{7} +(-2.02294 - 1.97679i) q^{8} +(-0.876779 - 2.86902i) q^{9} +(-2.58683 - 1.19417i) q^{10} +(-5.05295 + 0.890971i) q^{11} +(-3.16615 + 1.40552i) q^{12} +(-3.16835 + 3.77589i) q^{13} +(-2.70445 + 2.58572i) q^{14} +(-2.53133 + 2.40186i) q^{15} +(2.05305 + 3.43292i) q^{16} -3.82185i q^{17} +(0.163876 + 4.23947i) q^{18} -1.12520 q^{19} +(3.10647 + 2.56618i) q^{20} +(1.71596 + 4.24917i) q^{21} +(7.23095 + 0.604612i) q^{22} +(-3.95084 + 4.70843i) q^{23} +(4.83654 - 0.779686i) q^{24} +(-0.884384 - 0.321890i) q^{25} +(5.69469 - 4.02020i) q^{26} +(4.89780 + 1.73537i) q^{27} +(4.63098 - 2.56008i) q^{28} +(-4.54965 + 3.81761i) q^{29} +(4.32792 - 2.37114i) q^{30} +(1.07665 - 0.391870i) q^{31} +(-1.56890 - 5.43494i) q^{32} +(3.96581 - 7.95303i) q^{33} +(-1.37880 + 5.22608i) q^{34} +(3.53239 - 3.99177i) q^{35} +(1.30538 - 5.85628i) q^{36} +(5.51289 + 9.54861i) q^{37} +(1.53862 + 0.405936i) q^{38} +(-1.99253 - 8.30163i) q^{39} +(-3.32206 - 4.62977i) q^{40} +(-7.61804 + 9.07882i) q^{41} +(-0.813470 - 6.42948i) q^{42} +(0.0383340 - 0.105322i) q^{43} +(-9.66964 - 3.43546i) q^{44} +(-0.735874 - 5.99902i) q^{45} +(7.10113 - 5.01308i) q^{46} +(-4.68179 - 1.70403i) q^{47} +(-6.89488 - 0.678711i) q^{48} +(-3.17659 - 6.23773i) q^{49} +(1.09320 + 0.759218i) q^{50} +(5.32101 + 3.93782i) q^{51} +(-9.23742 + 3.44284i) q^{52} +(0.943162 + 1.63361i) q^{53} +(-6.07130 - 4.13996i) q^{54} -10.3370 q^{55} +(-7.25611 + 1.83001i) q^{56} +(1.15934 - 1.56657i) q^{57} +(7.59857 - 3.57892i) q^{58} +(-4.66457 - 3.91403i) q^{59} +(-6.77353 + 1.68097i) q^{60} +(-1.70936 + 4.69642i) q^{61} +(-1.61361 + 0.147429i) q^{62} +(-7.68399 - 1.98905i) q^{63} +(0.184592 + 7.99787i) q^{64} +(-7.60714 + 6.38315i) q^{65} +(-8.29215 + 9.44441i) q^{66} +(2.37903 + 0.419487i) q^{67} +(3.77082 - 6.64884i) q^{68} +(-2.48463 - 10.3519i) q^{69} +(-6.27037 + 4.18407i) q^{70} +(0.209500 + 0.120955i) q^{71} +(-3.89777 + 7.53707i) q^{72} +(1.87532 + 1.08272i) q^{73} +(-4.09361 - 15.0459i) q^{74} +(1.35937 - 0.899636i) q^{75} +(-1.95750 - 1.11017i) q^{76} +(-4.97664 + 12.6300i) q^{77} +(-0.270338 + 12.0707i) q^{78} +(-1.08725 + 0.191711i) q^{79} +(2.87239 + 7.52935i) q^{80} +(-7.46252 + 5.03099i) q^{81} +(13.6924 - 9.66624i) q^{82} +(0.456505 - 0.383054i) q^{83} +(-1.20720 + 9.08530i) q^{84} +(1.33704 - 7.58275i) q^{85} +(-0.0904155 + 0.130190i) q^{86} +(-0.627399 - 10.2678i) q^{87} +(11.9831 + 8.18624i) q^{88} -0.315840i q^{89} +(-1.15801 + 8.46868i) q^{90} +(4.13668 + 12.3676i) q^{91} +(-11.5188 + 4.29313i) q^{92} +(-0.563739 + 1.90274i) q^{93} +(5.78723 + 4.01918i) q^{94} +(-2.23245 - 0.393641i) q^{95} +(9.18336 + 3.41554i) q^{96} +(1.64335 - 4.51508i) q^{97} +(2.09337 + 9.67563i) q^{98} +(6.98653 + 13.7158i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.36742	−	0.360769i	−0.966914	−	0.255102i
$2$	−1.36742	−	0.360769i	−0.966914	−	0.255102i
$3$	−1.03034	+	1.39226i	−0.594870	+	0.803822i
$3$	−1.03034	+	1.39226i	−0.594870	+	0.803822i
$4$	1.73969	+	0.986648i	0.869846	+	0.493324i
$5$	1.98405	+	0.349842i	0.887296	+	0.156454i	0.598678	−	0.800990i	$-0.295693\pi$
$5$	1.98405	+	0.349842i	0.887296	+	0.156454i	0.288618	+	0.957444i	$0.406804\pi$
$6$	1.91120	−	1.53209i	0.780245	−	0.625474i
$7$	1.38264	−	2.25573i	0.522590	−	0.852584i
$7$	1.38264	−	2.25573i	0.522590	−	0.852584i
$8$	−2.02294	−	1.97679i	−0.715218	−	0.698901i
$9$	−0.876779	−	2.86902i	−0.292260	−	0.956339i
$10$	−2.58683	−	1.19417i	−0.818027	−	0.377629i
$11$	−5.05295	+	0.890971i	−1.52352	+	0.268638i	−0.871815	−	0.489835i	$-0.837057\pi$
$11$	−5.05295	+	0.890971i	−1.52352	+	0.268638i	−0.651705	+	0.758472i	$0.725946\pi$
$12$	−3.16615	+	1.40552i	−0.913990	+	0.405738i
$13$	−3.16835	+	3.77589i	−0.878741	+	1.04724i	0.119775	+	0.992801i	$0.461783\pi$
$13$	−3.16835	+	3.77589i	−0.878741	+	1.04724i	−0.998517	+	0.0544423i	$0.982662\pi$
$14$	−2.70445	+	2.58572i	−0.722796	+	0.691062i
$15$	−2.53133	+	2.40186i	−0.653587	+	0.620158i
$16$	2.05305	+	3.43292i	0.513263	+	0.858231i
$17$		−	3.82185i		−	0.926934i	−0.886114	−	0.463467i	$-0.846605\pi$
$17$		−	3.82185i		−	0.926934i	0.886114	−	0.463467i	$-0.153395\pi$
$18$	0.163876	+	4.23947i	0.0386259	+	0.999254i
$19$	−1.12520			−0.258138			−0.129069	−	0.991636i	$-0.541199\pi$
$19$	−1.12520			−0.258138			−0.129069	+	0.991636i	$0.541199\pi$
$20$	3.10647	+	2.56618i	0.694628	+	0.573815i
$21$	1.71596	+	4.24917i	0.374453	+	0.927246i
$22$	7.23095	+	0.604612i	1.54164	+	0.128904i
$23$	−3.95084	+	4.70843i	−0.823808	+	0.981776i	−0.999997	−	0.00258066i	$-0.999179\pi$
$23$	−3.95084	+	4.70843i	−0.823808	+	0.981776i	0.176189	+	0.984356i	$0.443623\pi$
$24$	4.83654	−	0.779686i	0.987254	−	0.159153i
$25$	−0.884384	−	0.321890i	−0.176877	−	0.0643779i
$26$	5.69469	−	4.02020i	1.11682	−	0.788425i
$27$	4.89780	+	1.73537i	0.942583	+	0.333972i
$28$	4.63098	−	2.56008i	0.875173	−	0.483811i
$29$	−4.54965	+	3.81761i	−0.844849	+	0.708912i	−0.958649	−	0.284591i	$-0.908142\pi$
$29$	−4.54965	+	3.81761i	−0.844849	+	0.708912i	0.113800	+	0.993504i	$0.463698\pi$
$30$	4.32792	−	2.37114i	0.790166	−	0.432908i
$31$	1.07665	−	0.391870i	0.193373	−	0.0703819i	−0.243519	−	0.969896i	$-0.578302\pi$
$31$	1.07665	−	0.391870i	0.193373	−	0.0703819i	0.436891	+	0.899514i	$0.356079\pi$
$32$	−1.56890	−	5.43494i	−0.277345	−	0.960770i
$33$	3.96581	−	7.95303i	0.690360	−	1.38444i
$34$	−1.37880	+	5.22608i	−0.236463	+	0.896266i
$35$	3.53239	−	3.99177i	0.597082	−	0.674733i
$36$	1.30538	−	5.85628i	0.217564	−	0.976046i
$37$	5.51289	+	9.54861i	0.906314	+	1.56978i	0.819144	+	0.573588i	$0.194449\pi$
$37$	5.51289	+	9.54861i	0.906314	+	1.56978i	0.0871693	+	0.996194i	$0.472218\pi$
$38$	1.53862	+	0.405936i	0.249597	+	0.0658516i
$39$	−1.99253	−	8.30163i	−0.319060	−	1.32933i
$40$	−3.32206	−	4.62977i	−0.525264	−	0.732031i
$41$	−7.61804	+	9.07882i	−1.18974	+	1.41787i	−0.304640	+	0.952467i	$0.598536\pi$
$41$	−7.61804	+	9.07882i	−1.18974	+	1.41787i	−0.885097	+	0.465406i	$0.845908\pi$
$42$	−0.813470	−	6.42948i	−0.125521	−	0.992091i
$43$	0.0383340	−	0.105322i	0.00584587	−	0.0160614i	−0.936735	−	0.350038i	$-0.886169\pi$
$43$	0.0383340	−	0.105322i	0.00584587	−	0.0160614i	0.942581	+	0.333977i	$0.108391\pi$
$44$	−9.66964	−	3.43546i	−1.45775	−	0.517916i
$45$	−0.735874	−	5.99902i	−0.109698	−	0.894281i
$46$	7.10113	−	5.01308i	1.04700	−	0.739138i
$47$	−4.68179	−	1.70403i	−0.682909	−	0.248559i	−0.0228131	−	0.999740i	$-0.507262\pi$
$47$	−4.68179	−	1.70403i	−0.682909	−	0.248559i	−0.660096	+	0.751181i	$0.729484\pi$
$48$	−6.89488	−	0.678711i	−0.995190	−	0.0979635i
$49$	−3.17659	−	6.23773i	−0.453799	−	0.891104i
$50$	1.09320	+	0.759218i	0.154602	+	0.107370i
$51$	5.32101	+	3.93782i	0.745090	+	0.551405i
$52$	−9.23742	+	3.44284i	−1.28100	+	0.477436i
$53$	0.943162	+	1.63361i	0.129553	+	0.224393i	0.923504	−	0.383590i	$-0.125312\pi$
$53$	0.943162	+	1.63361i	0.129553	+	0.224393i	−0.793950	+	0.607983i	$0.791979\pi$
$54$	−6.07130	−	4.13996i	−0.826200	−	0.563378i
$55$	−10.3370			−1.39384
$56$	−7.25611	+	1.83001i	−0.969638	+	0.244545i
$57$	1.15934	−	1.56657i	0.153558	−	0.207497i
$58$	7.59857	−	3.57892i	0.997741	−	0.469935i
$59$	−4.66457	−	3.91403i	−0.607275	−	0.509564i	0.286500	−	0.958080i	$-0.407508\pi$
$59$	−4.66457	−	3.91403i	−0.607275	−	0.509564i	−0.893775	+	0.448516i	$0.851953\pi$
$60$	−6.77353	+	1.68097i	−0.874458	+	0.217012i
$61$	−1.70936	+	4.69642i	−0.218861	+	0.601315i	−0.999727	−	0.0233840i	$-0.992556\pi$
$61$	−1.70936	+	4.69642i	−0.218861	+	0.601315i	0.780866	+	0.624699i	$0.214778\pi$
$62$	−1.61361	+	0.147429i	−0.204929	+	0.0187234i
$63$	−7.68399	−	1.98905i	−0.968091	−	0.250597i
$64$	0.184592	+	7.99787i	0.0230740	+	0.999734i
$65$	−7.60714	+	6.38315i	−0.943549	+	0.791732i
$66$	−8.29215	+	9.44441i	−1.02069	+	1.16253i
$67$	2.37903	+	0.419487i	0.290645	+	0.0512485i	0.317070	−	0.948402i	$-0.397301\pi$
$67$	2.37903	+	0.419487i	0.290645	+	0.0512485i	−0.0264248	+	0.999651i	$0.508412\pi$
$68$	3.77082	−	6.64884i	0.457279	−	0.806290i
$69$	−2.48463	−	10.3519i	−0.299115	−	1.24622i
$70$	−6.27037	+	4.18407i	−0.749453	+	0.500092i
$71$	0.209500	+	0.120955i	0.0248630	+	0.0143547i	0.512380	−	0.858759i	$-0.328764\pi$
$71$	0.209500	+	0.120955i	0.0248630	+	0.0143547i	−0.487517	+	0.873114i	$0.662097\pi$
$72$	−3.89777	+	7.53707i	−0.459357	+	0.888252i
$73$	1.87532	+	1.08272i	0.219490	+	0.126723i	0.605714	−	0.795682i	$-0.292888\pi$
$73$	1.87532	+	1.08272i	0.219490	+	0.126723i	−0.386224	+	0.922405i	$0.626221\pi$
$74$	−4.09361	−	15.0459i	−0.475873	−	1.74905i
$75$	1.35937	−	0.899636i	0.156967	−	0.103881i
$76$	−1.95750	−	1.11017i	−0.224540	−	0.127346i
$77$	−4.97664	+	12.6300i	−0.567140	+	1.43932i
$78$	−0.270338	+	12.0707i	−0.0306097	+	1.36674i
$79$	−1.08725	+	0.191711i	−0.122325	+	0.0215692i	−0.234476	−	0.972122i	$-0.575337\pi$
$79$	−1.08725	+	0.191711i	−0.122325	+	0.0215692i	0.112150	+	0.993691i	$0.464226\pi$
$80$	2.87239	+	7.52935i	0.321142	+	0.841807i
$81$	−7.46252	+	5.03099i	−0.829168	+	0.558999i
$82$	13.6924	−	9.66624i	1.51208	−	1.06746i
$83$	0.456505	−	0.383054i	0.0501080	−	0.0420456i	−0.617390	−	0.786657i	$-0.711810\pi$
$83$	0.456505	−	0.383054i	0.0501080	−	0.0420456i	0.667498	+	0.744612i	$0.267365\pi$
$84$	−1.20720	+	9.08530i	−0.131716	+	0.991287i
$85$	1.33704	−	7.58275i	0.145023	−	0.822465i
$86$	−0.0904155	+	0.130190i	−0.00974976	+	0.0140387i
$87$	−0.627399	−	10.2678i	−0.0672643	−	1.10082i
$88$	11.9831	+	8.18624i	1.27740	+	0.872656i
$89$		−	0.315840i		−	0.0334790i	−0.999860	−	0.0167395i	$-0.994671\pi$
$89$		−	0.315840i		−	0.0334790i	0.999860	−	0.0167395i	$-0.00532860\pi$
$90$	−1.15801	+	8.46868i	−0.122065	+	0.892677i
$91$	4.13668	+	12.3676i	0.433641	+	1.29648i
$92$	−11.5188	+	4.29313i	−1.20092	+	0.447590i
$93$	−0.563739	+	1.90274i	−0.0584570	+	0.197305i
$94$	5.78723	+	4.01918i	0.596907	+	0.414547i
$95$	−2.23245	−	0.393641i	−0.229045	−	0.0403868i
$96$	9.18336	+	3.41554i	0.937273	+	0.348597i
$97$	1.64335	−	4.51508i	0.166857	−	0.458437i	−0.827879	−	0.560907i	$-0.810452\pi$
$97$	1.64335	−	4.51508i	0.166857	−	0.458437i	0.994736	+	0.102470i	$0.0326747\pi$
$98$	2.09337	+	9.67563i	0.211462	+	0.977386i
$99$	6.98653	+	13.7158i	0.702173	+	1.37849i
$100$	−1.22096	−	1.43256i	−0.122096	−	0.143256i
$101$	−2.40989	−	2.87199i	−0.239793	−	0.285774i	0.632704	−	0.774394i	$-0.281945\pi$
$101$	−2.40989	−	2.87199i	−0.239793	−	0.285774i	−0.872497	+	0.488620i	$0.837500\pi$
$102$	−5.85543	−	7.30432i	−0.579773	−	0.723236i
$103$	0.374897	−	2.12614i	0.0369397	−	0.209495i	−0.960751	−	0.277411i	$-0.910524\pi$
$103$	0.374897	−	2.12614i	0.0369397	−	0.209495i	0.997691	+	0.0679155i	$0.0216348\pi$
$104$	13.8735	−	1.37525i	1.36041	−	0.134854i
$105$	1.91801	+	9.03090i	0.187179	+	0.881326i
$106$	−0.700348	−	2.57409i	−0.0680238	−	0.250018i
$107$	−0.735766	−	0.424794i	−0.0711291	−	0.0410664i	0.464014	−	0.885828i	$-0.346409\pi$
$107$	−0.735766	−	0.424794i	−0.0711291	−	0.0410664i	−0.535143	+	0.844762i	$0.679742\pi$
$108$	6.80847	+	7.85142i	0.655145	+	0.755503i
$109$	−10.2722	−	17.7920i	−0.983903	−	1.70417i	−0.646715	−	0.762732i	$-0.723858\pi$
$109$	−10.2722	−	17.7920i	−0.983903	−	1.70417i	−0.337188	−	0.941437i	$-0.609476\pi$
$110$	14.1351	+	3.72927i	1.34773	+	0.355572i
$111$	−18.9743	−	2.16298i	−1.80096	−	0.205301i
$112$	10.5824	+	0.115387i	0.999941	+	0.0109030i
$113$	15.3871	−	5.60045i	1.44750	−	0.526846i	0.505606	−	0.862765i	$-0.331269\pi$
$113$	15.3871	−	5.60045i	1.44750	−	0.526846i	0.941891	+	0.335919i	$0.109047\pi$
$114$	−2.15048	+	1.72391i	−0.201411	+	0.161459i
$115$	−9.48589	+	7.95961i	−0.884564	+	0.742237i
$116$	−11.6816	+	2.15256i	−1.08461	+	0.199860i
$117$	13.6110	+	5.77942i	1.25834	+	0.534308i
$118$	4.96637	+	7.03497i	0.457192	+	0.647622i
$119$	−8.62104	−	5.28425i	−0.790289	−	0.484407i
$120$	9.86872	+	0.145085i	0.900886	+	0.0132444i
$121$	14.4018	−	5.24183i	1.30926	−	0.476530i
$122$	4.03174	−	5.80531i	0.365016	−	0.525588i
$123$	−4.79088	−	19.9606i	−0.431979	−	1.79979i
$124$	2.25968	+	0.380545i	0.202925	+	0.0341739i
$125$	−10.3658	−	5.98469i	−0.927145	−	0.535287i
$126$	9.78967	+	5.49202i	0.872133	+	0.489268i
$127$	−1.94424	+	1.12251i	−0.172524	+	0.0996066i	−0.583775	−	0.811915i	$-0.698425\pi$
$127$	−1.94424	+	1.12251i	−0.172524	+	0.0996066i	0.411252	+	0.911522i	$0.365092\pi$
$128$	2.63297	−	11.0031i	0.232724	−	0.972543i
$129$	0.107138	+	0.161888i	0.00943298	+	0.0142535i
$130$	12.7050	−	5.98404i	1.11430	−	0.524835i
$131$	−12.1206	−	10.1704i	−1.05898	−	0.888591i	−0.0649725	−	0.997887i	$-0.520696\pi$
$131$	−12.1206	−	10.1704i	−1.05898	−	0.888591i	−0.994009	+	0.109296i	$0.965140\pi$
$132$	14.7461	−	9.92295i	1.28349	−	0.863682i
$133$	−1.55575	+	2.53814i	−0.134900	+	0.220084i
$134$	−3.10180	−	1.43190i	−0.267955	−	0.123697i
$135$	9.11040	+	5.15653i	0.784098	+	0.443803i
$136$	−7.55500	+	7.73138i	−0.647835	+	0.662960i
$137$	−4.51372	−	1.64286i	−0.385633	−	0.140359i	0.141926	−	0.989877i	$-0.454670\pi$
$137$	−4.51372	−	1.64286i	−0.385633	−	0.140359i	−0.527559	+	0.849518i	$0.676893\pi$
$138$	−0.337104	+	15.0518i	−0.0286962	+	1.28130i
$139$	−0.275555	+	1.56275i	−0.0233722	+	0.132551i	−0.994261	−	0.106979i	$-0.965882\pi$
$139$	−0.275555	+	1.56275i	−0.0233722	+	0.132551i	0.970889	+	0.239530i	$0.0769933\pi$
$140$	10.0837	−	3.45923i	0.852231	−	0.292359i
$141$	7.19632	−	4.76253i	0.606039	−	0.401077i
$142$	−0.242838	−	0.240977i	−0.0203785	−	0.0202224i
$143$	12.6453	−	21.9023i	1.05745	−	1.83156i
$144$	8.04905	−	8.90016i	0.670754	−	0.741680i
$145$	−10.3623	+	5.98268i	−0.860543	+	0.496835i
$146$	−2.17375	−	2.15709i	−0.179901	−	0.178522i
$147$	11.9575	+	2.00436i	0.986240	+	0.165317i
$148$	0.169619	+	22.0509i	0.0139426	+	1.81257i
$149$	7.18228	−	2.61414i	0.588395	−	0.214158i	−0.0306281	−	0.999531i	$-0.509751\pi$
$149$	7.18228	−	2.61414i	0.588395	−	0.214158i	0.619024	+	0.785372i	$0.287529\pi$
$150$	−2.18340	+	0.739763i	−0.178274	+	0.0604014i
$151$	−12.8011	+	2.25718i	−1.04174	+	0.183687i	−0.668242	−	0.743944i	$-0.732953\pi$
$151$	−12.8011	+	2.25718i	−1.04174	+	0.183687i	−0.373498	+	0.927631i	$0.621842\pi$
$152$	2.27621	+	2.22428i	0.184625	+	0.180413i
$153$	−10.9649	+	3.35092i	−0.886463	+	0.270906i
$154$	11.3617	−	15.4751i	0.915549	−	1.24702i
$155$	2.27323	−	0.400832i	0.182590	−	0.0321956i
$156$	4.72440	−	16.4082i	0.378254	−	1.31371i
$157$	−13.1832	+	15.7111i	−1.05213	+	1.25388i	−0.0858741	+	0.996306i	$0.527368\pi$
$157$	−13.1832	+	15.7111i	−1.05213	+	1.25388i	−0.966258	+	0.257576i	$0.917076\pi$
$158$	1.55589	+	0.130095i	0.123780	+	0.0103498i
$159$	−3.24619	−	0.370049i	−0.257439	−	0.0293468i
$160$	−1.21141	−	11.3321i	−0.0957704	−	0.895879i
$161$	5.15832	+	15.4221i	0.406533	+	1.21543i
$162$	12.0194	−	4.18725i	0.944336	−	0.328981i
$163$	14.9432	+	8.62748i	1.17045	+	0.675757i	0.953785	−	0.300490i	$-0.0971503\pi$
$163$	14.9432	+	8.62748i	1.17045	+	0.675757i	0.216660	+	0.976247i	$0.430484\pi$
$164$	−22.2106	+	8.27803i	−1.73436	+	0.646406i
$165$	10.6507	−	14.3918i	0.829155	−	1.12040i
$166$	−0.762430	+	0.359103i	−0.0591760	+	0.0278718i
$167$	15.4282	−	5.61540i	1.19387	−	0.434532i	0.332788	−	0.943002i	$-0.392011\pi$
$167$	15.4282	−	5.61540i	1.19387	−	0.434532i	0.861080	+	0.508469i	$0.169788\pi$
$168$	4.92845	−	11.9879i	0.380238	−	0.924889i
$169$	−1.96149	−	11.1242i	−0.150884	−	0.855704i
$170$	−4.56392	+	9.88646i	−0.350037	+	0.758257i
$171$	0.986550	+	3.22821i	0.0754433	+	0.246867i
$172$	0.170605	−	0.145405i	0.0130085	−	0.0110870i
$173$	13.0899	+	15.6000i	0.995208	+	1.18604i	0.982526	+	0.186123i	$0.0595924\pi$
$173$	13.0899	+	15.6000i	0.995208	+	1.18604i	0.0126817	+	0.999920i	$0.495963\pi$
$174$	−2.84637	+	14.2667i	−0.215782	+	1.08156i
$175$	−1.94888	+	1.54987i	−0.147322	+	0.117159i
$176$	−13.4326	−	15.5172i	−1.01252	−	1.16965i
$177$	10.2555	−	2.46148i	0.770848	−	0.185017i
$178$	−0.113945	+	0.431887i	−0.00854057	+	0.0323713i
$179$			17.3092i			1.29375i	0.762595	+	0.646876i	$0.223925\pi$
$179$			17.3092i			1.29375i	−0.762595	+	0.646876i	$0.776075\pi$
$180$	4.63872	−	11.1625i	0.345750	−	0.832003i
$181$	12.7605	−	7.36726i	0.948478	−	0.547604i	0.0558702	−	0.998438i	$-0.482207\pi$
$181$	12.7605	−	7.36726i	0.948478	−	0.547604i	0.892608	+	0.450834i	$0.148873\pi$
$182$	−1.19473	−	18.4042i	−0.0885591	−	1.36421i
$183$	−4.77741	−	7.21880i	−0.353156	−	0.533629i
$184$	17.2999	−	1.71489i	1.27537	−	0.126424i
$185$	7.59736	+	20.8736i	0.558569	+	1.53466i
$186$	1.45732	−	2.39847i	0.106856	−	0.175865i
$187$	3.40515	+	19.3116i	0.249010	+	1.41220i
$188$	−6.46359	−	7.58377i	−0.471406	−	0.553103i
$189$	10.6864	−	8.64870i	0.777324	−	0.629100i
$190$	2.91069	+	1.34367i	0.211164	+	0.0974803i
$191$	17.4271	−	3.07286i	1.26098	−	0.222345i	0.497094	−	0.867697i	$-0.334401\pi$
$191$	17.4271	−	3.07286i	1.26098	−	0.222345i	0.763885	+	0.645352i	$0.223289\pi$
$192$	−11.3253	−	7.98356i	−0.817334	−	0.576164i
$193$	4.42381	−	1.61014i	0.318433	−	0.115900i	−0.177859	−	0.984056i	$-0.556917\pi$
$193$	4.42381	−	1.61014i	0.318433	−	0.115900i	0.496292	+	0.868156i	$0.334695\pi$
$194$	−3.87606	+	5.58115i	−0.278285	+	0.400703i
$195$	−1.04903	−	17.1680i	−0.0751225	−	1.22942i
$196$	0.628144	−	13.9859i	0.0448675	−	0.998993i
$197$	1.30209	+	2.25528i	0.0927700	+	0.160682i	0.908676	−	0.417503i	$-0.137095\pi$
$197$	1.30209	+	2.25528i	0.0927700	+	0.160682i	−0.815906	+	0.578185i	$0.803761\pi$
$198$	−4.60530	−	21.2758i	−0.327285	−	1.51201i
$199$	−6.63526			−0.470361			−0.235180	−	0.971952i	$-0.575568\pi$
$199$	−6.63526			−0.470361			−0.235180	+	0.971952i	$0.575568\pi$
$200$	1.15275	+	2.39941i	0.0815117	+	0.169664i
$201$	−3.03526	+	2.88001i	−0.214090	+	0.203140i
$202$	2.25921	+	4.79664i	0.158957	+	0.337490i
$203$	2.32094	+	15.5412i	0.162898	+	1.09078i
$204$	5.37167	+	12.1006i	0.376092	+	0.847208i
$205$	−18.2907	+	15.3478i	−1.27748	+	1.07193i
$206$	−1.27969	+	2.77209i	−0.0891601	+	0.193140i
$207$	16.9726	+	7.20678i	1.17968	+	0.500906i
$208$	−19.4671	−	3.12460i	−1.34980	−	0.216652i
$209$	5.68556	−	1.00252i	0.393279	−	0.0693456i
$210$	0.635336	−	13.0410i	0.0438423	−	0.899916i
$211$	−5.07864	−	13.9535i	−0.349628	−	0.960596i	−0.982487	−	0.186329i	$-0.940341\pi$
$211$	−5.07864	−	13.9535i	−0.349628	−	0.960596i	0.632859	−	0.774267i	$-0.281881\pi$
$212$	0.0290190	+	3.77254i	0.00199303	+	0.259099i
$213$	−0.384257	+	0.167053i	−0.0263289	+	0.0114463i
$214$	0.852850	+	0.846315i	0.0582996	+	0.0578529i
$215$	0.112903	−	0.195553i	0.00769989	−	0.0133366i
$216$	−6.47751	−	13.1925i	−0.440739	−	0.897635i
$217$	0.604677	−	2.97045i	0.0410481	−	0.201647i
$218$	7.62768	+	28.0352i	0.516612	+	1.89878i
$219$	−3.43966	+	1.49537i	−0.232430	+	0.101047i
$220$	−17.9832	−	10.1990i	−1.21243	−	0.687616i
$221$	14.4309	+	12.1089i	0.970726	+	0.814535i
$222$	25.1656	+	9.80305i	1.68900	+	0.657938i
$223$	−1.07404	−	6.09119i	−0.0719231	−	0.407896i	−0.999420	−	0.0340645i	$-0.989155\pi$
$223$	−1.07404	−	6.09119i	−0.0719231	−	0.407896i	0.927497	−	0.373832i	$-0.121956\pi$
$224$	−14.4290	−	3.97558i	−0.964075	−	0.265629i
$225$	−0.148097	+	2.81954i	−0.00987312	+	0.187969i
$226$	−23.0611	+	2.10699i	−1.53400	+	0.140155i
$227$	−2.22011	−	12.5909i	−0.147354	−	0.835685i	−0.965447	−	0.260600i	$-0.916080\pi$
$227$	−2.22011	−	12.5909i	−0.147354	−	0.835685i	0.818093	−	0.575086i	$-0.195031\pi$
$228$	3.56255	−	1.58148i	0.235935	−	0.104736i
$229$	−5.09853	−	14.0081i	−0.336920	−	0.925681i	−0.986263	−	0.165185i	$-0.947178\pi$
$229$	−5.09853	−	14.0081i	−0.336920	−	0.925681i	0.649342	−	0.760496i	$-0.275044\pi$
$230$	15.8428	−	7.46194i	1.04464	−	0.492025i
$231$	−12.4565	−	19.9420i	−0.819580	−	1.31209i
$232$	16.7503	+	1.27090i	1.09971	+	0.0834389i
$233$	−13.3328	−	23.0931i	−0.873460	−	1.51288i	−0.858395	−	0.512990i	$-0.828538\pi$
$233$	−13.3328	−	23.0931i	−0.873460	−	1.51288i	−0.0150650	−	0.999887i	$-0.504796\pi$
$234$	−16.5270	−	12.8134i	−1.08040	−	0.837635i
$235$	−8.69278	−	5.01878i	−0.567054	−	0.327389i
$236$	−4.25313	−	11.4115i	−0.276855	−	0.742825i
$237$	0.853330	−	1.71126i	0.0554297	−	0.111159i
$238$	9.88221	+	10.3360i	0.640569	+	0.669984i
$239$	26.1791	+	4.61608i	1.69338	+	0.298589i	0.935375	−	0.353656i	$-0.115062\pi$
$239$	26.1791	+	4.61608i	1.69338	+	0.298589i	0.758008	+	0.652245i	$0.226173\pi$
$240$	−13.4424	−	3.75872i	−0.867701	−	0.242624i
$241$	−3.38366	+	9.29654i	−0.217961	+	0.598843i	−0.999693	−	0.0247716i	$-0.992114\pi$
$241$	−3.38366	+	9.29654i	−0.217961	+	0.598843i	0.781732	+	0.623614i	$0.214336\pi$
$242$	−21.5845	+	1.97207i	−1.38750	+	0.126770i
$243$	0.684517	−	15.5734i	0.0439118	−	0.999035i
$244$	−7.60746	+	6.48379i	−0.487018	+	0.415082i
$245$	−4.12031	−	13.4873i	−0.263237	−	0.861672i
$246$	−0.650005	+	29.0230i	−0.0414428	+	1.85044i
$247$	3.56502	−	4.24862i	0.226837	−	0.270333i
$248$	−2.95265	−	1.33559i	−0.187494	−	0.0848100i
$249$	0.0629524	+	1.03025i	0.00398944	+	0.0652895i
$250$	12.0153	+	11.9233i	0.759916	+	0.754093i
$251$	9.53725	+	16.5190i	0.601986	+	1.04267i	0.992520	+	0.122082i	$0.0389569\pi$
$251$	9.53725	+	16.5190i	0.601986	+	1.04267i	−0.390534	+	0.920588i	$0.627710\pi$
$252$	−11.4053	−	11.0417i	−0.718465	−	0.695563i
$253$	15.7683	−	27.3115i	0.991346	−	1.71706i
$254$	3.06357	−	0.833523i	0.192225	−	0.0522999i
$255$	9.17955	+	9.67436i	0.574846	+	0.605832i
$256$	−7.56995	+	14.0960i	−0.473122	+	0.880997i
$257$	4.39080	+	12.0636i	0.273891	+	0.752509i	0.998023	+	0.0628479i	$0.0200183\pi$
$257$	4.39080	+	12.0636i	0.273891	+	0.752509i	−0.724132	+	0.689661i	$0.757759\pi$
$258$	−0.0880987	−	0.260022i	−0.00548478	−	0.0161883i
$259$	29.1614	+	0.766750i	1.81200	+	0.0476435i
$260$	−19.5320	+	3.59914i	−1.21132	+	0.223209i
$261$	14.9418	+	9.70582i	0.924876	+	0.600775i
$262$	12.9048	+	18.2800i	0.797263	+	1.12934i
$263$	15.9202	+	18.9730i	0.981684	+	1.16993i	0.985456	+	0.169933i	$0.0543551\pi$
$263$	15.9202	+	18.9730i	0.981684	+	1.16993i	−0.00377133	+	0.999993i	$0.501200\pi$
$264$	−23.7441	+	8.24893i	−1.46135	+	0.507686i
$265$	1.29978	+	3.57112i	0.0798449	+	0.219372i
$266$	3.04304	−	2.90944i	0.186581	−	0.178389i
$267$	0.439732	+	0.325424i	0.0269112	+	0.0199157i
$268$	3.72489	+	3.07704i	0.227534	+	0.187960i
$269$	−19.0297	+	10.9868i	−1.16026	+	0.669876i	−0.951366	−	0.308062i	$-0.900319\pi$
$269$	−19.0297	+	10.9868i	−1.16026	+	0.669876i	−0.208893	+	0.977938i	$0.566986\pi$
$270$	−10.5975	−	10.3379i	−0.644941	−	0.629145i
$271$	−11.4301	+	19.7975i	−0.694328	+	1.20261i	0.276079	+	0.961135i	$0.410965\pi$
$271$	−11.4301	+	19.7975i	−0.694328	+	1.20261i	−0.970407	+	0.241476i	$0.922368\pi$
$272$	13.1201	−	7.84646i	0.795524	−	0.475761i
$273$	−21.4812	−	6.98359i	−1.30010	−	0.422666i
$274$	5.57947	+	3.87489i	0.337068	+	0.234091i
$275$	4.75554	+	0.838530i	0.286770	+	0.0505653i
$276$	5.89119	−	20.4606i	0.354608	−	1.23158i
$277$	−11.2315	+	9.42436i	−0.674836	+	0.566255i	−0.914493	−	0.404603i	$-0.867410\pi$
$277$	−11.2315	+	9.42436i	−0.674836	+	0.566255i	0.239656	+	0.970858i	$0.422965\pi$
$278$	0.940590	−	2.03753i	0.0564129	−	0.122203i
$279$	−2.06827	−	2.74535i	−0.123824	−	0.164360i
$280$	−15.0367	+	1.09234i	−0.898616	+	0.0652796i
$281$	−9.15383	−	3.33172i	−0.546072	−	0.198754i	0.0542287	−	0.998529i	$-0.482730\pi$
$281$	−9.15383	−	3.33172i	−0.546072	−	0.198754i	−0.600300	+	0.799775i	$0.704952\pi$
$282$	−11.5586	+	3.91619i	−0.688303	+	0.233206i
$283$	5.15467	−	29.2336i	0.306413	−	1.73776i	−0.310363	−	0.950618i	$-0.600450\pi$
$283$	5.15467	−	29.2336i	0.306413	−	1.73776i	0.616776	−	0.787139i	$-0.288438\pi$
$284$	0.245125	+	0.417126i	0.0145455	+	0.0247519i
$285$	2.84825	−	2.70257i	0.168716	−	0.160086i
$286$	−25.1931	+	25.3876i	−1.48970	+	1.50120i
$287$	9.94630	+	29.7370i	0.587112	+	1.75532i
$288$	−14.2174	+	9.26644i	−0.837765	+	0.546030i
$289$	2.39348			0.140793
$290$	16.3280	−	4.44246i	0.958815	−	0.260870i
$291$	4.59294	+	6.94006i	0.269243	+	0.406834i
$292$	2.19422	+	3.73388i	0.128407	+	0.218509i
$293$	7.53382	+	1.32842i	0.440131	+	0.0776069i	0.389322	−	0.921102i	$-0.372709\pi$
$293$	7.53382	+	1.32842i	0.440131	+	0.0776069i	0.0508082	+	0.998708i	$0.483820\pi$
$294$	−15.6279	−	7.05472i	−0.911437	−	0.411439i
$295$	−7.88545	−	9.39752i	−0.459109	−	0.547145i
$296$	7.72334	−	30.2141i	0.448910	−	1.75616i
$297$	−26.2945	−	4.40494i	−1.52576	−	0.255600i
$298$	−10.7643	+	0.983486i	−0.623560	+	0.0569718i
$299$	−5.26087	−	29.8359i	−0.304244	−	1.72545i
$300$	3.25252	−	0.223866i	0.187784	−	0.0129249i
$301$	−0.184575	−	0.232093i	−0.0106387	−	0.0133776i
$302$	18.3189	+	1.53172i	1.05413	+	0.0881407i
$303$	6.48157	−	0.396049i	0.372357	−	0.0227524i
$304$	−2.31009	−	3.86272i	−0.132493	−	0.221542i
$305$	−5.03446	+	8.71994i	−0.288272	+	0.499302i
$306$	16.2026	−	0.626309i	0.926242	−	0.0358037i
$307$	−9.31882	+	16.1407i	−0.531853	+	0.921197i	0.467455	+	0.884017i	$0.345171\pi$
$307$	−9.31882	+	16.1407i	−0.531853	+	0.921197i	−0.999309	+	0.0371801i	$0.988162\pi$
$308$	−21.1191	+	17.0620i	−1.20337	+	0.972200i
$309$	2.57387	+	2.71261i	0.146423	+	0.154315i
$310$	−3.25307	−	0.272004i	−0.184762	−	0.0154488i
$311$	−3.33985	+	18.9412i	−0.189385	+	1.07406i	0.730805	+	0.682586i	$0.239145\pi$
$311$	−3.33985	+	18.9412i	−0.189385	+	1.07406i	−0.920190	+	0.391471i	$0.871966\pi$
$312$	−12.3798	+	20.7325i	−0.700869	+	1.17375i
$313$	−10.8441	−	12.9235i	−0.612947	−	0.730481i	0.366894	−	0.930263i	$-0.380421\pi$
$313$	−10.8441	−	12.9235i	−0.612947	−	0.730481i	−0.979840	+	0.199781i	$0.935977\pi$
$314$	23.6951	−	16.7276i	1.33719	−	0.943995i
$315$	−14.5496	−	6.63457i	−0.819776	−	0.373816i
$316$	−2.08063	−	0.739213i	−0.117045	−	0.0415840i
$317$	30.3282	+	11.0385i	1.70340	+	0.619986i	0.996205	−	0.0870336i	$-0.0277388\pi$
$317$	30.3282	+	11.0385i	1.70340	+	0.619986i	0.707193	+	0.707020i	$0.249961\pi$
$318$	4.30541	+	1.67714i	0.241435	+	0.0940492i
$319$	19.5878	−	23.3438i	1.09670	−	1.30700i
$320$	−2.43175	+	15.9328i	−0.135939	+	0.890669i
$321$	1.34952	−	0.586693i	0.0753227	−	0.0327460i
$322$	−1.48979	−	22.9495i	−0.0830229	−	1.27893i
$323$			4.30033i			0.239277i
$324$	−17.9463	+	1.38950i	−0.997016	+	0.0771942i
$325$	4.01746	−	2.31948i	0.222848	−	0.128662i
$326$	−17.3212	−	17.1885i	−0.959333	−	0.951982i
$327$	35.3551	+	4.03030i	1.95514	+	0.222876i
$328$	33.3578	−	3.30667i	1.84188	−	0.182580i
$329$	−10.3171	+	8.20476i	−0.568799	+	0.452343i
$330$	−19.7561	+	15.8373i	−1.08754	+	0.871813i
$331$	−9.22133	+	25.3354i	−0.506850	+	1.39256i	0.377619	+	0.925961i	$0.376743\pi$
$331$	−9.22133	+	25.3354i	−0.506850	+	1.39256i	−0.884469	+	0.466599i	$0.845479\pi$
$332$	1.17212	−	0.215985i	0.0643283	−	0.0118537i
$333$	22.5615	−	24.1886i	1.23636	−	1.32553i
$334$	−23.1227	+	2.11262i	−1.26522	+	0.115597i
$335$	4.57337	+	1.66457i	0.249870	+	0.0909452i
$336$	−11.0641	+	14.6145i	−0.603599	+	0.797288i
$337$	15.1471	+	12.7099i	0.825115	+	0.692354i	0.954164	−	0.299285i	$-0.0967480\pi$
$337$	15.1471	+	12.7099i	0.825115	+	0.692354i	−0.129049	+	0.991638i	$0.541192\pi$
$338$	−1.33107	+	15.9191i	−0.0724004	+	0.865883i
$339$	−8.05674	+	27.1932i	−0.437582	+	1.47693i
$340$	9.80755	−	11.8725i	0.531889	−	0.643874i
$341$	−5.09113	+	2.93936i	−0.275700	+	0.159175i
$342$	−0.184393	−	4.77025i	−0.00997082	−	0.257945i
$343$	−18.4627	−	1.45903i	−0.996892	−	0.0787801i
$344$	−0.285746	+	0.137281i	−0.0154064	+	0.00740172i
$345$	−1.30811	−	21.4080i	−0.0704263	−	1.15257i
$346$	−12.2715	−	26.0542i	−0.659719	−	1.40068i
$347$	−7.33039	−	20.1401i	−0.393516	−	1.08118i	−0.965384	−	0.260831i	$-0.916003\pi$
$347$	−7.33039	−	20.1401i	−0.393516	−	1.08118i	0.571868	−	0.820345i	$-0.306219\pi$
$348$	9.03917	−	18.4817i	0.484550	−	0.990726i
$349$	−23.8855	−	28.4656i	−1.27856	−	1.52373i	−0.719200	−	0.694803i	$-0.755492\pi$
$349$	−23.8855	−	28.4656i	−1.27856	−	1.52373i	−0.559359	−	0.828925i	$-0.688953\pi$
$350$	3.22409	−	1.41623i	0.172335	−	0.0757007i
$351$	−22.0705	+	12.9953i	−1.17804	+	0.693638i
$352$	12.7699	+	26.0646i	0.680640	+	1.38925i
$353$	−9.00030	+	24.7281i	−0.479038	+	1.31615i	0.431274	+	0.902221i	$0.358064\pi$
$353$	−9.00030	+	24.7281i	−0.479038	+	1.31615i	−0.910311	+	0.413924i	$0.864158\pi$
$354$	−14.9116	−	0.333963i	−0.792542	−	0.0177499i
$355$	0.373344	+	0.313272i	0.0198150	+	0.0166268i
$356$	0.311623	−	0.549465i	0.0165160	−	0.0291216i
$357$	16.2397	−	6.55813i	0.859496	−	0.347093i
$358$	6.24463	−	23.6690i	0.330039	−	1.25095i
$359$			17.0018i			0.897321i	0.893702	+	0.448660i	$0.148099\pi$
$359$			17.0018i			0.897321i	−0.893702	+	0.448660i	$0.851901\pi$
$360$	−10.3702	+	13.5903i	−0.546556	+	0.716274i
$361$	−17.7339			−0.933365
$362$	−20.1068	+	5.47058i	−1.05679	+	0.287527i
$363$	−7.54084	+	25.4520i	−0.395792	+	1.33588i
$364$	−5.00595	+	25.5973i	−0.262383	+	1.34166i
$365$	3.34196	+	2.80424i	0.174926	+	0.146781i
$366$	3.92842	+	11.5947i	0.205342	+	0.606064i
$367$	0.830009	+	4.70721i	0.0433261	+	0.245715i	0.998777	−	0.0494344i	$-0.0157419\pi$
$367$	0.830009	+	4.70721i	0.0433261	+	0.245715i	−0.955451	+	0.295149i	$0.904631\pi$
$368$	−24.2750	−	3.89629i	−1.26542	−	0.203108i
$369$	32.7266	+	13.8962i	1.70368	+	0.723405i
$370$	−2.85827	−	31.2839i	−0.148594	−	1.62637i
$371$	4.98902	+	0.131178i	0.259017	+	0.00681042i
$372$	−2.85807	+	2.75397i	−0.148184	+	0.142787i
$373$	−0.870824	+	4.93869i	−0.0450896	+	0.255716i	−0.999017	−	0.0443207i	$-0.985888\pi$
$373$	−0.870824	+	4.93869i	−0.0450896	+	0.255716i	0.953928	+	0.300036i	$0.0969988\pi$
$374$	2.31074	−	27.6356i	0.119485	−	1.42900i
$375$	19.0126	−	8.26559i	0.981806	−	0.426833i
$376$	6.10248	+	12.7021i	0.314711	+	0.655060i
$377$		−	29.2745i		−	1.50771i
$378$	−17.7331	+	7.97110i	−0.912090	+	0.409989i
$379$			35.7291i			1.83528i	0.397413	+	0.917640i	$0.369908\pi$
$379$			35.7291i			1.83528i	−0.397413	+	0.917640i	$0.630092\pi$
$380$	−3.49539	−	2.88746i	−0.179310	−	0.148123i
$381$	0.440415	−	3.86347i	0.0225632	−	0.197931i
$382$	−24.9388	−	2.08524i	−1.27598	−	0.106690i
$383$	−2.83874	+	16.0993i	−0.145053	+	0.822636i	0.822272	+	0.569095i	$0.192706\pi$
$383$	−2.83874	+	16.0993i	−0.145053	+	0.822636i	−0.967325	+	0.253541i	$0.918405\pi$
$384$	12.6063	+	15.0027i	0.643311	+	0.765605i
$385$	−14.2924	+	23.3175i	−0.728408	+	1.18837i
$386$	−6.63011	+	0.605763i	−0.337464	+	0.0308325i
$387$	−0.335780	−	0.0176369i	−0.0170687	−	0.000896534i
$388$	7.31372	−	6.23343i	0.371298	−	0.316455i
$389$	−2.64530	−	15.0022i	−0.134122	−	0.760642i	−0.975467	−	0.220145i	$-0.929347\pi$
$389$	−2.64530	−	15.0022i	−0.134122	−	0.760642i	0.841345	−	0.540498i	$-0.181764\pi$
$390$	−4.75920	+	23.8543i	−0.240991	+	1.20791i
$391$	17.9949	+	15.0995i	0.910041	+	0.763615i
$392$	−5.90462	+	18.8980i	−0.298228	+	0.954495i
$393$	26.6482	−	6.39602i	1.34423	−	0.322637i
$394$	−0.966870	−	3.55368i	−0.0487102	−	0.179032i
$395$	−2.22423			−0.111913
$396$	−1.37826	+	30.7545i	−0.0692602	+	1.54547i
$397$		−	4.66445i		−	0.234102i	−0.993126	−	0.117051i	$-0.962656\pi$
$397$		−	4.66445i		−	0.234102i	0.993126	−	0.117051i	$-0.0373441\pi$
$398$	9.07320	+	2.39379i	0.454799	+	0.119990i
$399$	−1.93079	−	4.78116i	−0.0966605	−	0.239357i
$400$	−0.710665	−	3.69688i	−0.0355333	−	0.184844i
$401$	−21.1552	−	17.7514i	−1.05644	−	0.886460i	−0.0626859	−	0.998033i	$-0.519967\pi$
$401$	−21.1552	−	17.7514i	−1.05644	−	0.886460i	−0.993756	+	0.111573i	$0.964411\pi$
$402$	5.18950	−	2.84317i	0.258829	−	0.141804i
$403$	−1.93155	+	5.30690i	−0.0962176	+	0.264356i
$404$	−1.35882	−	7.37408i	−0.0676036	−	0.366874i
$405$	−16.5661	+	7.37105i	−0.823175	+	0.366270i
$406$	2.43307	−	22.0887i	0.120751	−	1.09624i
$407$	−36.3639	−	43.3368i	−1.80249	−	2.14812i
$408$	−2.97984	−	18.4845i	−0.147524	−	0.915119i
$409$	−11.5065	−	31.6140i	−0.568962	−	1.56321i	−0.806128	−	0.591741i	$-0.798441\pi$
$409$	−11.5065	−	31.6140i	−0.568962	−	1.56321i	0.237166	−	0.971469i	$-0.423781\pi$
$410$	30.5482	−	14.3881i	1.50867	−	0.710580i
$411$	6.93797	−	4.59156i	0.342225	−	0.226485i
$412$	2.74996	−	3.32894i	0.135481	−	0.164005i
$413$	−15.2784	+	5.11026i	−0.751802	+	0.251460i
$414$	−20.6087	−	15.9779i	−1.01286	−	0.785271i
$415$	1.03974	−	0.600294i	0.0510388	−	0.0294673i
$416$	25.4925	+	11.2958i	1.24987	+	0.553821i
$417$	−1.89184	−	1.99381i	−0.0926436	−	0.0976374i
$418$	−8.13624	−	0.680308i	−0.397957	−	0.0332750i
$419$	1.63030	+	1.36799i	0.0796456	+	0.0668306i	0.681741	−	0.731593i	$-0.261223\pi$
$419$	1.63030	+	1.36799i	0.0796456	+	0.0668306i	−0.602096	+	0.798424i	$0.705667\pi$
$420$	−5.57357	+	17.6034i	−0.271962	+	0.858958i
$421$	20.2172	+	7.35844i	0.985324	+	0.358629i	0.783908	−	0.620877i	$-0.213223\pi$
$421$	20.2172	+	7.35844i	0.985324	+	0.358629i	0.201416	+	0.979506i	$0.435446\pi$
$422$	1.91068	+	20.9125i	0.0930104	+	1.01800i
$423$	−0.784001	+	14.9262i	−0.0381194	+	0.725736i
$424$	1.32133	−	5.16912i	0.0641696	−	0.251035i
$425$	−1.23021	+	3.37998i	−0.0596741	+	0.163953i
$426$	0.585710	−	0.0898042i	0.0283777	−	0.00435103i
$427$	8.23040	+	10.3493i	0.398297	+	0.500838i
$428$	−0.860883	−	1.46495i	−0.0416123	−	0.0708112i
$429$	17.4647	+	40.1724i	0.843202	+	1.93954i
$430$	−0.224935	+	0.226672i	−0.0108473	+	0.0109311i
$431$	5.69382	−	3.28733i	0.274262	−	0.158345i	−0.356561	−	0.934272i	$-0.616051\pi$
$431$	5.69382	−	3.28733i	0.274262	−	0.158345i	0.630823	+	0.775927i	$0.282717\pi$
$432$	4.09805	+	20.3766i	0.197168	+	0.980370i
$433$		−	1.02882i		−	0.0494420i	−0.999694	−	0.0247210i	$-0.992130\pi$
$433$		−	1.02882i		−	0.0494420i	0.999694	−	0.0247210i	$-0.00786974\pi$
$434$	−1.89849	+	3.84371i	−0.0911307	+	0.184504i
$435$	2.34730	−	20.5913i	0.112544	−	0.987275i
$436$	−0.316054	−	41.0878i	−0.0151363	−	1.96775i
$437$	4.44548	−	5.29791i	0.212656	−	0.253434i
$438$	5.24295	−	0.803876i	0.250518	−	0.0384107i
$439$	−26.8657	−	9.77833i	−1.28223	−	0.466694i	−0.391062	−	0.920364i	$-0.627892\pi$
$439$	−26.8657	−	9.77833i	−1.28223	−	0.466694i	−0.891170	+	0.453670i	$0.850114\pi$
$440$	20.9112	+	20.4341i	0.996902	+	0.974159i
$441$	−15.1110	+	14.5828i	−0.719570	+	0.694420i
$442$	−15.3646	−	21.7643i	−0.730818	−	1.03522i
$443$	−9.50625	−	11.3291i	−0.451655	−	0.538262i	0.491384	−	0.870943i	$-0.336491\pi$
$443$	−9.50625	−	11.3291i	−0.451655	−	0.538262i	−0.943039	+	0.332681i	$0.892047\pi$
$444$	−30.8754	−	22.4839i	−1.46528	−	1.06704i
$445$	0.110494	−	0.626644i	0.00523793	−	0.0297058i
$446$	−0.728844	+	8.71672i	−0.0345118	+	0.412748i
$447$	−3.76067	+	12.6931i	−0.177873	+	0.600362i
$448$	18.2962	+	10.6418i	0.864415	+	0.502778i
$449$	2.76740	−	4.79328i	0.130602	−	0.226209i	−0.793307	−	0.608822i	$-0.791642\pi$
$449$	2.76740	−	4.79328i	0.130602	−	0.226209i	0.923909	+	0.382613i	$0.124976\pi$
$450$	1.21971	−	3.80207i	0.0574978	−	0.179232i
$451$	30.4046	−	52.6623i	1.43170	−	2.47977i
$452$	32.2945	+	5.43860i	1.51900	+	0.255810i
$453$	10.0470	−	20.1482i	0.472048	−	0.946643i
$454$	−1.50657	+	18.0180i	−0.0707066	+	0.845626i
$455$	3.88067	+	25.9852i	0.181928	+	1.21821i
$456$	−5.44206	+	0.877301i	−0.254848	+	0.0410834i
$457$	1.80250	+	10.2225i	0.0843175	+	0.478188i	0.997502	+	0.0706414i	$0.0225046\pi$
$457$	1.80250	+	10.2225i	0.0843175	+	0.478188i	−0.913184	+	0.407547i	$0.866384\pi$
$458$	1.91816	+	20.9944i	0.0896297	+	0.981003i
$459$	6.63232	−	18.7187i	0.309570	−	0.873712i
$460$	−24.3559	+	4.48803i	−1.13560	+	0.209255i
$461$	−10.5614	−	12.5866i	−0.491895	−	0.586218i	0.461803	−	0.886982i	$-0.347203\pi$
$461$	−10.5614	−	12.5866i	−0.491895	−	0.586218i	−0.953698	+	0.300765i	$0.902758\pi$
$462$	9.83891	+	31.7631i	0.457747	+	1.47775i
$463$	−7.31001	−	1.28895i	−0.339725	−	0.0599027i	0.00118316	−	0.999999i	$-0.499623\pi$
$463$	−7.31001	−	1.28895i	−0.339725	−	0.0599027i	−0.340908	+	0.940097i	$0.610735\pi$
$464$	−22.4462	−	7.78085i	−1.04204	−	0.361217i
$465$	−1.78415	+	3.57792i	−0.0827379	+	0.165922i
$466$	9.90030	+	36.3880i	0.458622	+	1.68564i
$467$	0.585850			0.0271099			0.0135550	−	0.999908i	$-0.495685\pi$
$467$	0.585850			0.0271099			0.0135550	+	0.999908i	$0.495685\pi$
$468$	17.9767	+	23.4837i	0.830975	+	1.08553i
$469$	4.23560	−	4.78644i	0.195582	−	0.221017i
$470$	10.0761	+	9.99888i	0.464775	+	0.461214i
$471$	−8.29073	−	34.5423i	−0.382017	−	1.59162i
$472$	1.69892	+	17.1387i	0.0781990	+	0.788874i
$473$	−0.0998609	+	0.566339i	−0.00459161	+	0.0260403i
$474$	−1.78423	+	2.03217i	−0.0819526	+	0.0933405i
$475$	0.995107	+	0.362189i	0.0456586	+	0.0166184i
$476$	−9.78425	−	17.6989i	−0.448461	−	0.811228i
$477$	3.85990	−	4.13826i	0.176732	−	0.189478i
$478$	−34.1325	−	15.7567i	−1.56119	−	0.720696i
$479$	−8.20725	+	6.88670i	−0.374999	+	0.314661i	−0.810735	−	0.585413i	$-0.800932\pi$
$479$	−8.20725	+	6.88670i	−0.374999	+	0.314661i	0.435736	+	0.900074i	$0.356488\pi$
$480$	17.0254	+	9.98935i	0.777098	+	0.455949i
$481$	−53.5212	−	9.43724i	−2.44036	−	0.430301i
$482$	7.98080	−	11.4916i	0.363515	−	0.523427i
$483$	−26.7864	−	8.70835i	−1.21882	−	0.396244i
$484$	30.2266	+	5.09035i	1.37393	+	0.231379i
$485$	4.84007	−	8.38324i	0.219776	−	0.380663i
$486$	−6.55443	+	21.0485i	−0.297315	+	0.954779i
$487$	22.5048	−	12.9932i	1.01979	−	0.588777i	0.105748	−	0.994393i	$-0.466276\pi$
$487$	22.5048	−	12.9932i	1.01979	−	0.588777i	0.914044	+	0.405616i	$0.132943\pi$
$488$	12.7418	−	6.12154i	0.576793	−	0.277109i
$489$	−27.4084	+	11.9156i	−1.23945	+	0.538842i
$490$	0.768415	+	19.9293i	0.0347134	+	0.900315i
$491$	3.45329	+	9.48784i	0.155845	+	0.428180i	0.992902	−	0.118935i	$-0.0379481\pi$
$491$	3.45329	+	9.48784i	0.155845	+	0.428180i	−0.837057	+	0.547115i	$0.815726\pi$
$492$	11.3594	−	39.4522i	0.512123	−	1.77864i
$493$	14.5903	+	17.3881i	0.657115	+	0.783119i
$494$	−6.40765	+	4.52351i	−0.288294	+	0.203523i
$495$	9.06328	+	29.6571i	0.407364	+	1.33299i
$496$	3.55568	+	2.89154i	0.159655	+	0.129834i
$497$	0.562504	−	0.305337i	0.0252318	−	0.0136962i
$498$	0.285600	−	1.43150i	0.0127981	−	0.0641471i
$499$	−2.82088	−	7.75031i	−0.126280	−	0.346952i	0.860401	−	0.509617i	$-0.170213\pi$
$499$	−2.82088	−	7.75031i	−0.126280	−	0.346952i	−0.986681	+	0.162666i	$0.947991\pi$
$500$	−12.1285	−	20.6389i	−0.542403	−	0.923000i
$501$	−8.07824	+	27.2658i	−0.360909	+	1.21815i
$502$	−7.08191	−	26.0292i	−0.316081	−	1.16174i
$503$	−1.95135	+	3.37983i	−0.0870062	+	0.150699i	−0.906244	−	0.422754i	$-0.861063\pi$
$503$	−1.95135	+	3.37983i	−0.0870062	+	0.150699i	0.819238	+	0.573453i	$0.194397\pi$
$504$	11.6123	+	19.2134i	0.517254	+	0.855832i
$505$	−3.77660	−	6.54126i	−0.168056	−	0.291082i
$506$	−31.4151	+	31.6577i	−1.39657	+	1.40736i
$507$	17.5087	+	8.73081i	0.777590	+	0.387749i
$508$	−4.48991	+	0.0345371i	−0.199207	+	0.00153234i
$509$	16.6393	−	19.8299i	0.737524	−	0.878946i	−0.258683	−	0.965962i	$-0.583289\pi$
$509$	16.6393	−	19.8299i	0.737524	−	0.878946i	0.996207	+	0.0870158i	$0.0277331\pi$
$510$	−9.06212	−	16.5406i	−0.401277	−	0.732432i
$511$	5.03522	−	2.73320i	0.222745	−	0.120910i
$512$	15.4367	−	16.5441i	0.682212	−	0.731154i
$513$	−5.51100	−	1.95264i	−0.243316	−	0.0862109i
$514$	−1.65190	−	18.0802i	−0.0728623	−	0.797482i
$515$	1.48763	−	4.08723i	0.0655528	−	0.180105i
$516$	0.0266602	+	0.387343i	0.00117365	+	0.0170518i
$517$	25.1751	+	4.43905i	1.10720	+	0.195229i
$518$	−39.5993	−	11.5690i	−1.73990	−	0.508313i
$519$	−35.2063	+	2.15124i	−1.54539	+	0.0944291i
$520$	28.0069	+	2.12499i	1.22819	+	0.0931868i
$521$	29.8030	+	17.2067i	1.30569	+	0.753841i	0.981374	−	0.192107i	$-0.0615321\pi$
$521$	29.8030	+	17.2067i	1.30569	+	0.753841i	0.324317	+	0.945948i	$0.394865\pi$
$522$	−16.9302	−	18.6625i	−0.741016	−	0.816836i
$523$	20.9450	+	36.2777i	0.915859	+	1.58632i	0.805638	+	0.592408i	$0.201823\pi$
$523$	20.9450	+	36.2777i	0.915859	+	1.58632i	0.110221	+	0.993907i	$0.464844\pi$
$524$	−11.0515	−	29.6521i	−0.482788	−	1.29536i
$525$	−0.149802	−	4.31025i	−0.00653788	−	0.188115i
$526$	−14.9248	−	31.6877i	−0.650754	−	1.38165i
$527$	−1.49767	−	4.11480i	−0.0652394	−	0.179244i
$528$	35.4442	−	2.71364i	1.54251	−	0.118096i
$529$	−2.56626	−	14.5540i	−0.111576	−	0.632781i
$530$	−0.489002	−	5.35215i	−0.0212409	−	0.232483i
$531$	−7.13964	+	16.8145i	−0.309834	+	0.729685i
$532$	−5.21076	+	2.88060i	−0.225915	+	0.124890i
$533$	−10.1440	−	57.5297i	−0.439387	−	2.49189i
$534$	−0.483897	−	0.603635i	−0.0209403	−	0.0261218i
$535$	−1.31119	−	1.10022i	−0.0566876	−	0.0475665i
$536$	−3.98340	−	5.55144i	−0.172057	−	0.239786i
$537$	−24.0989	−	17.8345i	−1.03995	−	0.769614i
$538$	29.9853	−	8.15827i	1.29276	−	0.351728i
$539$	21.6088	+	28.6887i	0.930757	+	1.23571i
$540$	10.7616	+	17.9595i	0.463106	+	0.772855i
$541$	−19.2147	+	33.2808i	−0.826103	+	1.43085i	0.0749709	+	0.997186i	$0.476114\pi$
$541$	−19.2147	+	33.2808i	−0.826103	+	1.43085i	−0.901074	+	0.433666i	$0.857220\pi$
$542$	22.7721	−	22.9479i	0.978144	−	0.985697i
$543$	−2.89054	+	25.3567i	−0.124045	+	1.08816i
$544$	−20.7715	+	5.99609i	−0.890571	+	0.257080i
$545$	−14.1563	−	38.8940i	−0.606388	−	1.66604i
$546$	26.8544	+	17.2993i	1.14926	+	0.740340i
$547$	23.9347	−	4.22033i	1.02337	−	0.180448i	0.363317	−	0.931665i	$-0.381644\pi$
$547$	23.9347	−	4.22033i	1.02337	−	0.180448i	0.660055	+	0.751217i	$0.270533\pi$
$548$	−6.23155	−	7.31152i	−0.266199	−	0.312332i
$549$	14.9728	+	0.786450i	0.639025	+	0.0335649i
$550$	−6.20032	−	2.86228i	−0.264383	−	0.122048i
$551$	5.11925	−	4.29556i	0.218088	−	0.182997i
$552$	−15.4373	+	25.8529i	−0.657055	+	1.10037i
$553$	−1.07083	+	2.71760i	−0.0455363	+	0.115564i
$554$	18.7583	−	8.83511i	0.796962	−	0.375368i
$555$	−36.8894	−	10.9295i	−1.56587	−	0.463931i
$556$	−2.02126	+	2.44682i	−0.0857206	+	0.103768i
$557$	31.7551			1.34551			0.672753	−	0.739867i	$-0.265112\pi$
$557$	31.7551			1.34551			0.672753	+	0.739867i	$0.265112\pi$
$558$	1.83776	+	4.50022i	0.0777985	+	0.190510i
$559$	0.276228	+	0.478440i	0.0116832	+	0.0202359i
$560$	20.9556	+	3.93109i	0.885537	+	0.166119i
$561$	−30.3953	−	15.1567i	−1.28329	−	0.639918i
$562$	11.3152	+	7.85829i	0.477302	+	0.331482i
$563$	−32.2281	+	11.7301i	−1.35825	+	0.494364i	−0.915514	−	0.402286i	$-0.868216\pi$
$563$	−32.2281	+	11.7301i	−1.35825	+	0.494364i	−0.442740	+	0.896650i	$0.645993\pi$
$564$	17.2183	−	1.18511i	0.725022	−	0.0499021i
$565$	32.4881	−	5.72853i	1.36678	−	0.241001i
$566$	−17.5952	+	38.1150i	−0.739581	+	1.60209i
$567$	1.03053	+	23.7895i	0.0432783	+	0.999063i
$568$	−0.184704	−	0.658822i	−0.00774999	−	0.0276435i
$569$	1.74131	+	9.87545i	0.0729995	+	0.414001i	0.999307	+	0.0372314i	$0.0118539\pi$
$569$	1.74131	+	9.87545i	0.0729995	+	0.414001i	−0.926307	+	0.376769i	$0.877035\pi$
$570$	−4.86976	+	2.66799i	−0.203972	+	0.111750i
$571$	−8.90509	−	24.4665i	−0.372667	−	1.02389i	−0.974326	−	0.225141i	$-0.927716\pi$
$571$	−8.90509	−	24.4665i	−0.372667	−	1.02389i	0.601660	−	0.798753i	$-0.294506\pi$
$572$	43.6087	−	25.6268i	1.82337	−	1.07151i
$573$	−13.6777	+	27.4291i	−0.571393	+	1.14587i
$574$	−2.87263	−	44.2513i	−0.119901	−	1.84702i
$575$	5.00966	−	2.89233i	0.208917	−	0.120618i
$576$	22.7842	−	7.54196i	0.949341	−	0.314249i
$577$		−	8.35219i		−	0.347706i	−0.984772	−	0.173853i	$-0.944378\pi$
$577$		−	8.35219i		−	0.347706i	0.984772	−	0.173853i	$-0.0556218\pi$
$578$	−3.27290	−	0.863494i	−0.136135	−	0.0359166i
$579$	−2.31632	+	7.81810i	−0.0962631	+	0.324909i
$580$	−23.9300	+	0.184074i	−0.993640	+	0.00764325i
$581$	−0.232879	−	1.55938i	−0.00966146	−	0.0646939i
$582$	−3.77674	−	11.1470i	−0.156551	−	0.462058i
$583$	−6.22124	−	7.41419i	−0.257658	−	0.307064i
$584$	−1.65336	−	5.89740i	−0.0684166	−	0.244036i
$585$	24.9831	+	16.2284i	1.03293	+	0.670961i
$586$	−9.82267	−	4.53448i	−0.405771	−	0.187318i
$587$	−5.98825	−	33.9611i	−0.247162	−	1.40172i	−0.815419	−	0.578872i	$-0.803493\pi$
$587$	−5.98825	−	33.9611i	−0.247162	−	1.40172i	0.568257	−	0.822851i	$-0.307618\pi$
$588$	18.8248	+	15.2848i	0.776322	+	0.630336i
$589$	−1.21145	+	0.440931i	−0.0499168	+	0.0181682i
$590$	7.39242	+	15.6952i	0.304341	+	0.646161i
$591$	−4.48155	−	0.510873i	−0.184346	−	0.0210145i
$592$	−21.4614	+	38.5291i	−0.882058	+	1.58354i
$593$	−1.47700	−	0.852748i	−0.0606533	−	0.0350182i	0.469367	−	0.883003i	$-0.344482\pi$
$593$	−1.47700	−	0.852748i	−0.0606533	−	0.0350182i	−0.530020	+	0.847985i	$0.677816\pi$
$594$	34.3666	+	15.5097i	1.41008	+	0.636369i
$595$	−15.2559	−	13.5002i	−0.625433	−	0.553456i
$596$	15.0742	+	2.53859i	0.617463	+	0.103985i
$597$	6.83660	−	9.23801i	0.279803	−	0.378086i
$598$	−3.57002	+	42.6962i	−0.145989	+	1.74598i
$599$	−0.131140	+	0.156287i	−0.00535824	+	0.00638571i	−0.768717	−	0.639589i	$-0.779104\pi$
$599$	−0.131140	+	0.156287i	−0.00535824	+	0.00638571i	0.763359	+	0.645975i	$0.223549\pi$
$600$	−4.52833	−	0.867288i	−0.184868	−	0.0354069i
$601$	−42.2648	+	7.45242i	−1.72402	+	0.303990i	−0.945979	−	0.324228i	$-0.894895\pi$
$601$	−42.2648	+	7.45242i	−1.72402	+	0.303990i	−0.778037	+	0.628219i	$0.783784\pi$
$602$	0.168660	+	0.383958i	0.00687405	+	0.0156490i
$603$	−0.882368	−	7.19327i	−0.0359328	−	0.292933i
$604$	−24.4970	−	8.70338i	−0.996770	−	0.354136i
$605$	30.4078	−	5.36172i	1.23625	−	0.217985i
$606$	−9.00593	−	1.79678i	−0.365841	−	0.0729893i
$607$	18.6096	−	6.77334i	0.755341	−	0.274922i	0.0644895	−	0.997918i	$-0.479458\pi$
$607$	18.6096	−	6.77334i	0.755341	−	0.274922i	0.690851	+	0.722997i	$0.257236\pi$
$608$	1.76532	+	6.11538i	0.0715932	+	0.248011i
$609$	−24.0287	−	12.7814i	−0.973692	−	0.517928i
$610$	10.0301	−	10.1076i	0.406108	−	0.409244i
$611$	21.2678	−	12.2790i	0.860402	−	0.496753i
$612$	−22.3818	−	4.98898i	−0.904730	−	0.201667i
$613$	−2.50986	+	4.34721i	−0.101372	+	0.175582i	−0.912250	−	0.409633i	$-0.865657\pi$
$613$	−2.50986	+	4.34721i	−0.101372	+	0.175582i	0.810878	+	0.585215i	$0.198990\pi$
$614$	18.5658	−	18.7092i	0.749256	−	0.755041i
$615$	−2.52230	−	41.2790i	−0.101709	−	1.66453i
$616$	35.0342	−	15.7119i	1.41157	−	0.633050i
$617$	0.345409	−	1.95891i	0.0139056	−	0.0788628i	−0.977065	−	0.212940i	$-0.931696\pi$
$617$	0.345409	−	1.95891i	0.0139056	−	0.0788628i	0.990971	+	0.134078i	$0.0428071\pi$
$618$	−2.54095	−	4.63787i	−0.102212	−	0.186562i
$619$	−6.46845	−	2.35432i	−0.259989	−	0.0946283i	0.208737	−	0.977972i	$-0.433065\pi$
$619$	−6.46845	−	2.35432i	−0.259989	−	0.0946283i	−0.468726	+	0.883343i	$0.655287\pi$
$620$	4.35020	+	1.54555i	0.174708	+	0.0620709i
$621$	−27.5213	+	16.2048i	−1.10439	+	0.650276i
$622$	11.4004	−	24.6957i	0.457114	−	0.990209i
$623$	−0.712449	−	0.436695i	−0.0285437	−	0.0174958i
$624$	24.4081	−	23.8839i	0.977106	−	0.956121i
$625$	−14.8678	−	12.4756i	−0.594712	−	0.499023i
$626$	10.1661	+	21.5842i	0.406319	+	0.862677i
$627$	−4.46232	+	8.94872i	−0.178208	+	0.357378i
$628$	−38.4360	+	14.3253i	−1.53376	+	0.571642i
$629$	36.4933	−	21.0694i	1.45508	−	0.840093i
$630$	17.5019	+	14.3213i	0.697292	+	0.570575i
$631$	9.84521	+	5.68413i	0.391932	+	0.226282i	0.682997	−	0.730421i	$-0.260676\pi$
$631$	9.84521	+	5.68413i	0.391932	+	0.226282i	−0.291065	+	0.956703i	$0.594010\pi$
$632$	2.57842	+	1.76144i	0.102564	+	0.0700665i
$633$	24.6596	+	7.30608i	0.980131	+	0.290391i
$634$	−37.4891	−	26.0358i	−1.48888	−	1.03401i
$635$	−4.25018	+	1.54694i	−0.168663	+	0.0613885i
$636$	−5.28226	−	3.84661i	−0.209455	−	0.152528i
$637$	33.6175	+	7.76882i	1.33197	+	0.307812i
$638$	−35.2065	+	24.8542i	−1.39384	+	0.983986i
$639$	0.163336	−	0.707109i	0.00646148	−	0.0279728i
$640$	9.07329	−	20.9096i	0.358653	−	0.826523i
$641$	8.80831	−	7.39105i	0.347907	−	0.291929i	−0.452042	−	0.891997i	$-0.649304\pi$
$641$	8.80831	−	7.39105i	0.347907	−	0.291929i	0.799949	+	0.600068i	$0.204860\pi$
$642$	−2.05702	+	0.315393i	−0.0811841	+	0.0124476i
$643$	−8.32766	+	3.03102i	−0.328411	+	0.119532i	−0.500963	−	0.865469i	$-0.667021\pi$
$643$	−8.32766	+	3.03102i	−0.328411	+	0.119532i	0.172552	+	0.985000i	$0.444799\pi$
$644$	−6.24229	+	31.9191i	−0.245981	+	1.25779i
$645$	0.155932	+	0.358677i	0.00613982	+	0.0141229i
$646$	1.55143	−	5.88037i	0.0610401	−	0.231360i
$647$	−0.529431	−	0.917002i	−0.0208141	−	0.0360511i	0.855431	−	0.517917i	$-0.173292\pi$
$647$	−0.529431	−	0.917002i	−0.0208141	−	0.0360511i	−0.876245	+	0.481866i	$0.839959\pi$
$648$	25.0415	+	4.57444i	0.983721	+	0.179701i
$649$	27.0571	+	15.6214i	1.06208	+	0.613194i
$650$	−6.33036	+	1.72234i	−0.248297	+	0.0675556i
$651$	3.51261	+	3.90245i	0.137670	+	0.152949i
$652$	17.4843	+	29.7529i	0.684740	+	1.16521i
$653$	−4.88628	+	27.7115i	−0.191215	+	1.08443i	0.726492	+	0.687175i	$0.241150\pi$
$653$	−4.88628	+	27.7115i	−0.191215	+	1.08443i	−0.917707	+	0.397259i	$0.869962\pi$
$654$	−46.8914	−	18.2662i	−1.83360	−	0.714263i
$655$	−20.4899	−	24.4189i	−0.800606	−	0.954125i
$656$	−46.8072	−	7.51284i	−1.82751	−	0.293327i
$657$	1.46209	−	6.32964i	0.0570417	−	0.246943i
$658$	17.0678	−	7.49730i	0.665373	−	0.292275i
$659$	−10.8360	+	29.7718i	−0.422112	+	1.15974i	0.528384	+	0.849006i	$0.322798\pi$
$659$	−10.8360	+	29.7718i	−0.422112	+	1.15974i	−0.950496	+	0.310738i	$0.899424\pi$
$660$	32.7286	−	14.5288i	1.27396	−	0.565535i
$661$	−2.35116	−	0.414572i	−0.0914493	−	0.0161250i	0.127736	−	0.991808i	$-0.459229\pi$
$661$	−2.35116	−	0.414572i	−0.0914493	−	0.0161250i	−0.219186	+	0.975683i	$0.570340\pi$
$662$	21.7497	−	31.3175i	0.845326	−	1.21719i
$663$	−31.7276	+	7.61515i	−1.23220	+	0.295748i
$664$	−1.68070	−	0.127521i	−0.0652238	−	0.00494876i
$665$	−3.97463	+	4.49153i	−0.154130	+	0.174174i
$666$	−39.5776	+	24.9365i	−1.53360	+	0.966271i
$667$		−	36.5045i		−	1.41346i
$668$	32.3807	+	5.45311i	1.25285	+	0.210987i
$669$	9.58716	+	4.78068i	0.370661	+	0.184832i
$670$	−5.65320	−	3.92610i	−0.218402	−	0.151678i
$671$	4.45291	−	25.2537i	0.171903	−	0.974910i
$672$	20.4018	−	15.9927i	0.787018	−	0.616930i
$673$	−17.3339	+	14.5449i	−0.668174	+	0.560665i	−0.912524	−	0.409022i	$-0.865870\pi$
$673$	−17.3339	+	14.5449i	−0.668174	+	0.560665i	0.244350	+	0.969687i	$0.421425\pi$
$674$	−16.1271	−	22.8444i	−0.621194	−	0.879935i
$675$	−3.77294	−	3.11129i	−0.145221	−	0.119753i
$676$	7.56324	−	21.2879i	0.290894	−	0.818765i
$677$	−17.3972	+	3.06760i	−0.668630	+	0.117897i	−0.497651	−	0.867377i	$-0.665804\pi$
$677$	−17.3972	+	3.06760i	−0.668630	+	0.117897i	−0.170979	+	0.985275i	$0.554693\pi$
$678$	20.8274	−	34.2781i	0.799873	−	1.31644i
$679$	−7.91260	−	9.94970i	−0.303658	−	0.381834i
$680$	−17.6943	+	12.6964i	−0.678545	+	0.486885i
$681$	19.8173	+	9.88196i	0.759399	+	0.378678i
$682$	8.02215	−	2.18263i	0.307184	−	0.0835773i
$683$	22.3060	+	12.8784i	0.853517	+	0.492778i	0.861836	−	0.507187i	$-0.169315\pi$
$683$	22.3060	+	12.8784i	0.853517	+	0.492778i	−0.00831912	+	0.999965i	$0.502648\pi$
$684$	−1.46881	+	6.58947i	−0.0561615	+	0.251955i
$685$	−8.38071	−	4.83861i	−0.320211	−	0.184874i
$686$	24.7199	+	8.65588i	0.943812	+	0.330483i
$687$	24.7562	+	7.33468i	0.944506	+	0.279836i
$688$	0.440263	−	0.0846334i	0.0167849	−	0.00322662i
$689$	−9.15658	−	1.61455i	−0.348838	−	0.0615095i
$690$	−5.93459	+	29.7457i	−0.225926	+	1.13240i
$691$	11.2388	−	9.43046i	0.427543	−	0.358751i	−0.403481	−	0.914988i	$-0.632200\pi$
$691$	11.2388	−	9.43046i	0.427543	−	0.358751i	0.831024	+	0.556237i	$0.187755\pi$
$692$	7.38076	+	40.0543i	0.280574	+	1.52263i
$693$	40.5990	+	3.20437i	1.54223	+	0.121724i
$694$	2.75783	+	30.1846i	0.104686	+	1.14579i
$695$	−1.09343	+	3.00417i	−0.0414762	+	0.113955i
$696$	−19.0280	+	22.0113i	−0.721255	+	0.834337i
$697$	34.6979	+	29.1150i	1.31428	+	1.10281i
$698$	22.3920	+	47.5416i	0.847551	+	1.79948i
$699$	45.8889	+	5.23110i	1.73568	+	0.197858i
$700$	−4.91963	+	0.773435i	−0.185945	+	0.0292331i
$701$	4.32120			0.163209			0.0816047	−	0.996665i	$-0.473996\pi$
$701$	4.32120			0.163209			0.0816047	+	0.996665i	$0.473996\pi$
$702$	34.8680	−	9.80773i	1.31601	−	0.370169i
$703$	−6.20309	−	10.7441i	−0.233954	−	0.405220i
$704$	−8.05860	−	40.2483i	−0.303720	−	1.51692i
$705$	15.9440	−	6.93154i	0.600486	−	0.261057i
$706$	21.2284	−	30.5668i	0.798940	−	1.15040i
$707$	−9.81043	+	1.46510i	−0.368959	+	0.0551008i
$708$	20.2700	+	5.83631i	0.761792	+	0.219342i
$709$	48.0651	+	17.4943i	1.80512	+	0.657010i	0.997756	+	0.0669587i	$0.0213296\pi$
$709$	48.0651	+	17.4943i	1.80512	+	0.657010i	0.807365	+	0.590052i	$0.200893\pi$
$710$	−0.397500	−	0.563067i	−0.0149179	−	0.0211315i
$711$	1.50330	+	2.95125i	0.0563782	+	0.110680i
$712$	−0.624350	+	0.638927i	−0.0233985	+	0.0239448i
$713$	−2.40860	+	6.61756i	−0.0902026	+	0.247830i
$714$	−24.5725	+	3.10896i	−0.919603	+	0.116350i
$715$	32.7513	−	39.0314i	1.22483	−	1.45969i
$716$	−17.0781	+	30.1127i	−0.638239	+	1.12536i
$717$	−33.4002	+	31.6919i	−1.24736	+	1.18356i
$718$	6.13372	−	23.2487i	0.228908	−	0.867632i
$719$	−3.44959	−	5.97487i	−0.128648	−	0.222825i	0.794505	−	0.607258i	$-0.207730\pi$
$719$	−3.44959	−	5.97487i	−0.128648	−	0.222825i	−0.923153	+	0.384433i	$0.874397\pi$
$720$	19.0834	−	14.8425i	0.711196	−	0.553147i
$721$	−4.27765	−	3.78536i	−0.159308	−	0.140974i
$722$	24.2498	+	6.39785i	0.902484	+	0.238103i
$723$	−9.45686	−	14.2896i	−0.351705	−	0.531435i
$724$	29.4682	−	0.226674i	1.09518	−	0.00842428i
$725$	5.25249	−	1.91175i	0.195073	−	0.0710006i
$726$	19.4938	−	32.0831i	0.723483	−	1.19072i
$727$	−28.4277	+	23.8536i	−1.05432	+	0.884682i	−0.993542	−	0.113469i	$-0.963804\pi$
$727$	−28.4277	+	23.8536i	−1.05432	+	0.884682i	−0.0607819	+	0.998151i	$0.519359\pi$
$728$	16.0800	−	33.1963i	0.595963	−	1.23034i
$729$	20.9770	+	16.9990i	0.776925	+	0.629593i
$730$	−3.55819	−	5.04026i	−0.131695	−	0.186548i
$731$	−0.402523	−	0.146507i	−0.0148879	−	0.00541874i
$732$	−1.18881	−	17.2721i	−0.0439397	−	0.638395i
$733$	8.60893	−	10.2597i	0.317978	−	0.378951i	−0.583253	−	0.812291i	$-0.698220\pi$
$733$	8.60893	−	10.2597i	0.317978	−	0.378951i	0.901231	+	0.433339i	$0.142665\pi$
$734$	0.563243	−	6.73619i	0.0207897	−	0.248637i
$735$	23.0232	+	8.16001i	0.849222	+	0.300987i
$736$	31.7885	+	14.0855i	1.17174	+	0.519200i
$737$	−12.3949			−0.456571
$738$	−39.7379	−	30.8087i	−1.46277	−	1.13408i
$739$			22.6419i			0.832894i	0.909160	+	0.416447i	$0.136725\pi$
$739$			22.6419i			0.832894i	−0.909160	+	0.416447i	$0.863275\pi$
$740$	−7.37780	+	43.8095i	−0.271213	+	1.61047i
$741$	2.24199	+	9.34097i	0.0823616	+	0.343149i
$742$	−6.77478	−	1.97926i	−0.248710	−	0.0726609i
$743$	11.2597	−	13.4188i	0.413080	−	0.492289i	−0.518882	−	0.854846i	$-0.673652\pi$
$743$	11.2597	−	13.4188i	0.413080	−	0.492289i	0.931962	+	0.362556i	$0.118096\pi$
$744$	4.90174	−	2.73474i	0.179706	−	0.100261i
$745$	15.1646	−	2.67392i	0.555587	−	0.0979649i
$746$	2.97251	−	6.43911i	0.108831	−	0.235753i
$747$	−1.49924	−	0.973868i	−0.0548544	−	0.0356320i
$748$	−13.1298	+	36.9559i	−0.480074	+	1.35124i
$749$	−1.97552	+	1.07235i	−0.0721840	+	0.0391827i
$750$	−28.9802	+	4.44340i	−1.05821	+	0.162250i
$751$	27.2236	+	4.80026i	0.993405	+	0.175164i	0.646646	−	0.762790i	$-0.276171\pi$
$751$	27.2236	+	4.80026i	0.993405	+	0.175164i	0.346759	+	0.937954i	$0.387282\pi$
$752$	−3.76215	−	19.5707i	−0.137191	−	0.713670i
$753$	−32.8254	−	3.74193i	−1.19622	−	0.136363i
$754$	−10.5613	+	40.0306i	−0.384621	+	1.45783i
$755$	−26.1877			−0.953069
$756$	27.1243	−	4.50233i	0.986502	−	0.163748i
$757$	16.3555			0.594452			0.297226	−	0.954807i	$-0.403939\pi$
$757$	16.3555			0.594452			0.297226	+	0.954807i	$0.403939\pi$
$758$	12.8899	−	48.8568i	0.468184	−	1.77456i
$759$	21.7780	+	50.0939i	0.790490	+	1.81829i
$760$	3.73797	+	5.20940i	0.135591	+	0.188965i
$761$	8.06808	+	1.42262i	0.292468	+	0.0515699i	0.317957	−	0.948105i	$-0.397003\pi$
$761$	8.06808	+	1.42262i	0.292468	+	0.0515699i	−0.0254893	+	0.999675i	$0.508114\pi$
$762$	−1.99605	+	5.12410i	−0.0723094	+	0.185627i
$763$	−54.3368	−	1.42870i	−1.96713	−	0.0517223i
$764$	33.3496	+	11.8485i	1.20654	+	0.428665i
$765$	−22.9273	+	2.81240i	−0.828939	+	0.101682i
$766$	9.68989	−	20.9904i	0.350110	−	0.758415i
$767$	29.5579	−	5.21186i	1.06727	−	0.188189i
$768$	−11.8256	−	25.0630i	−0.426719	−	0.904384i
$769$	−9.45493	+	11.2679i	−0.340954	+	0.406333i	−0.909089	−	0.416603i	$-0.863221\pi$
$769$	−9.45493	+	11.2679i	−0.340954	+	0.406333i	0.568135	+	0.822935i	$0.307665\pi$
$770$	27.9560	−	26.7286i	1.00746	−	0.963231i
$771$	−21.3198	−	6.31656i	−0.767813	−	0.227485i
$772$	9.28471	+	1.56360i	0.334164	+	0.0562753i
$773$			6.03098i			0.216919i	0.994101	+	0.108460i	$0.0345918\pi$
$773$			6.03098i			0.216919i	−0.994101	+	0.108460i	$0.965408\pi$
$774$	0.452791	+	0.145256i	0.0162752	+	0.00522112i
$775$	−1.07831			−0.0387342
$776$	−12.2498	+	5.88518i	−0.439741	+	0.211265i
$777$	−31.1138	+	39.8102i	−1.11620	+	1.42818i
$778$	−1.79510	+	21.4687i	−0.0643573	+	0.769691i
$779$	8.57179	−	10.2155i	0.307116	−	0.366007i
$780$	15.1137	−	30.9020i	0.541159	−	1.10647i
$781$	−1.16636	−	0.424520i	−0.0417356	−	0.0151905i
$782$	−19.1592	−	27.1394i	−0.685132	−	0.970504i
$783$	−28.9083	+	10.8026i	−1.03310	+	0.386052i
$784$	14.8919	−	23.7114i	0.531855	−	0.846836i
$785$	−31.6525	+	26.5596i	−1.12973	+	0.947954i
$786$	−38.7469	−	0.867783i	−1.38206	−	0.0309528i
$787$	−13.1453	+	4.78450i	−0.468580	+	0.170549i	−0.565509	−	0.824742i	$-0.691320\pi$
$787$	−13.1453	+	4.78450i	−0.468580	+	0.170549i	0.0969292	+	0.995291i	$0.469098\pi$
$788$	0.0400624	+	5.20820i	0.00142716	+	0.185535i
$789$	−42.8187	+	2.61639i	−1.52439	+	0.0931459i
$790$	3.04146	+	0.802433i	0.108210	+	0.0285493i
$791$	8.64180	−	42.4525i	0.307267	−	1.50944i
$792$	12.9799	−	41.5572i	0.461222	−	1.47667i
$793$	−12.3173	−	21.3342i	−0.437401	−	0.757601i
$794$	−1.68279	+	6.37827i	−0.0597199	+	0.226356i
$795$	−6.31115	−	1.86985i	−0.223833	−	0.0663167i
$796$	−11.5433	−	6.54666i	−0.409141	−	0.232040i
$797$	−20.5335	+	24.4709i	−0.727334	+	0.866802i	−0.995321	−	0.0966200i	$-0.969197\pi$
$797$	−20.5335	+	24.4709i	−0.727334	+	0.866802i	0.267988	+	0.963422i	$0.413641\pi$
$798$	0.915315	+	7.23444i	0.0324018	+	0.256096i
$799$	−6.51255	+	17.8931i	−0.230398	+	0.633012i
$800$	−0.361940	+	5.31159i	−0.0127965	+	0.187793i
$801$	−0.906151	+	0.276922i	−0.0320173	+	0.00978457i
$802$	22.5240	+	31.9058i	0.795351	+	1.12663i
$803$	−10.4406	−	3.80006i	−0.368440	−	0.134101i
$804$	−8.12197	+	2.01561i	−0.286440	+	0.0710849i
$805$	4.83908	+	32.4029i	0.170555	+	1.14205i
$806$	4.55582	−	6.55993i	0.160472	−	0.231064i
$807$	4.31065	−	37.8144i	0.151742	−	1.33113i
$808$	−0.802265	+	10.5737i	−0.0282236	+	0.371982i
$809$	12.2791	+	21.2680i	0.431709	+	0.747742i	0.997021	−	0.0771353i	$-0.0245773\pi$
$809$	12.2791	+	21.2680i	0.431709	+	0.747742i	−0.565311	+	0.824878i	$0.691244\pi$
$810$	25.3121	−	4.10281i	0.889376	−	0.144158i
$811$	45.1575			1.58569			0.792847	−	0.609421i	$-0.208598\pi$
$811$	45.1575			1.58569			0.792847	+	0.609421i	$0.208598\pi$
$812$	−11.2959	+	29.3268i	−0.396409	+	1.02917i
$813$	−15.7863	−	36.3119i	−0.553651	−	1.27351i
$814$	34.0902	+	72.3787i	1.19486	+	2.53687i
$815$	26.6299	+	22.3452i	0.932806	+	0.782717i
$816$	−2.59393	+	26.3512i	−0.0908057	+	0.922476i
$817$	−0.0431333	+	0.118508i	−0.00150904	+	0.00414606i
$818$	4.32897	+	47.3809i	0.151359	+	1.65663i
$819$	31.8560	−	22.7119i	1.11314	−	0.793617i
$820$	−46.9631	+	8.65385i	−1.64002	+	0.302205i
$821$	−6.78392	+	5.69238i	−0.236760	+	0.198666i	−0.753446	−	0.657509i	$-0.771610\pi$
$821$	−6.78392	+	5.69238i	−0.236760	+	0.198666i	0.516686	+	0.856175i	$0.327166\pi$
$822$	−11.1436	+	3.77560i	−0.388679	+	0.131689i
$823$	−31.6633	−	5.58309i	−1.10371	−	0.194614i	−0.408033	−	0.912967i	$-0.633785\pi$
$823$	−31.6633	−	5.58309i	−1.10371	−	0.194614i	−0.695679	+	0.718353i	$0.744896\pi$
$824$	−4.96134	+	3.55997i	−0.172836	+	0.124018i
$825$	−6.06730	+	5.75698i	−0.211236	+	0.200432i
$826$	22.7357	−	1.47591i	0.791076	−	0.0513536i
$827$	−10.4437	−	6.02967i	−0.363163	−	0.209672i	0.307305	−	0.951611i	$-0.400573\pi$
$827$	−10.4437	−	6.02967i	−0.363163	−	0.209672i	−0.670467	+	0.741939i	$0.733906\pi$
$828$	22.4165	+	29.2835i	0.779028	+	1.01767i
$829$	−20.7759	−	11.9949i	−0.721575	−	0.416602i	0.0937568	−	0.995595i	$-0.470112\pi$
$829$	−20.7759	−	11.9949i	−0.721575	−	0.416602i	−0.815332	+	0.578993i	$0.803446\pi$
$830$	−1.63833	+	0.445750i	−0.0568673	+	0.0154722i
$831$	−1.54883	−	25.3475i	−0.0537284	−	0.879296i
$832$	−30.7839	−	24.6430i	−1.06724	−	0.854343i
$833$	−23.8396	+	12.1405i	−0.825995	+	0.420642i
$834$	1.86763	+	3.40890i	0.0646709	+	0.118041i
$835$	32.5748	−	5.74382i	1.12730	−	0.198773i
$836$	10.8803	+	3.86557i	0.376301	+	0.133694i
$837$	5.95327	−	0.0509080i	0.205775	−	0.00175964i
$838$	−1.73579	−	2.45878i	−0.0599618	−	0.0849372i
$839$	5.53757	−	4.64657i	0.191178	−	0.160418i	−0.542175	−	0.840266i	$-0.682399\pi$
$839$	5.53757	−	4.64657i	0.191178	−	0.160418i	0.733353	+	0.679848i	$0.237954\pi$
$840$	13.9722	−	22.0605i	0.482086	−	0.761160i
$841$	1.08938	−	6.17815i	0.0375647	−	0.213040i
$842$	−24.9907	−	17.3558i	−0.861237	−	0.598121i
$843$	14.0702	−	9.31169i	0.484604	−	0.320712i
$844$	4.93187	−	29.2855i	0.169762	−	1.00805i
$845$		−	22.7571i		−	0.782869i
$846$	6.45697	−	20.1276i	0.221995	−	0.692000i
$847$	8.08844	−	39.7341i	0.277922	−	1.36528i
$848$	−3.67168	+	6.59168i	−0.126086	+	0.226359i
$849$	35.3897	+	37.2973i	1.21457	+	1.28004i
$850$	2.90161	−	4.17804i	0.0995245	−	0.143306i
$851$	−66.7395	−	11.7680i	−2.28780	−	0.403401i
$852$	−0.833312	−	0.0885057i	−0.0285488	−	0.00303216i
$853$	2.46646	−	6.77655i	0.0844501	−	0.232025i	−0.890279	−	0.455416i	$-0.849491\pi$
$853$	2.46646	−	6.77655i	0.0844501	−	0.232025i	0.974729	+	0.223391i	$0.0717128\pi$
$854$	−7.52073	−	17.1212i	−0.257354	−	0.585874i
$855$	0.828003	+	6.75008i	0.0283171	+	0.230848i
$856$	0.648681	+	2.31379i	0.0221715	+	0.0790837i
$857$	16.5159	+	19.6829i	0.564172	+	0.672354i	0.970424	−	0.241407i	$-0.0776089\pi$
$857$	16.5159	+	19.6829i	0.564172	+	0.672354i	−0.406252	+	0.913761i	$0.633164\pi$
$858$	−9.38863	−	61.2334i	−0.320523	−	2.09047i
$859$	−5.41887	+	30.7319i	−0.184889	+	1.04856i	0.741208	+	0.671275i	$0.234253\pi$
$859$	−5.41887	+	30.7319i	−0.184889	+	1.04856i	−0.926097	+	0.377285i	$0.876858\pi$
$860$	0.389358	−	0.228807i	0.0132770	−	0.00780225i
$861$	−51.6497	−	16.7915i	−1.76022	−	0.572252i
$862$	−8.97183	+	2.44102i	−0.305582	+	0.0831414i
$863$	−30.0840	−	17.3690i	−1.02407	−	0.591249i	−0.108792	−	0.994065i	$-0.534698\pi$
$863$	−30.0840	−	17.3690i	−1.02407	−	0.591249i	−0.915281	+	0.402816i	$0.868032\pi$
$864$	1.74747	−	29.3419i	0.0594503	−	0.998231i
$865$	20.5136	+	35.5306i	0.697483	+	1.20808i
$866$	−0.371167	+	1.40683i	−0.0126128	+	0.0478062i
$867$	−2.46611	+	3.33235i	−0.0837535	+	0.113173i
$868$	3.98274	−	4.57106i	0.135183	−	0.155152i
$869$	5.32300	−	1.93742i	0.180571	−	0.0657223i
$870$	−10.6384	+	27.3101i	−0.360677	+	0.925900i
$871$	−9.12153	+	7.65387i	−0.309071	+	0.259342i
$872$	−14.3910	+	56.2984i	−0.487341	+	1.90650i
$873$	−14.3947	−	0.756084i	−0.487187	−	0.0255896i
$874$	−7.99017	+	5.64070i	−0.270272	+	0.190799i
$875$	−27.8320	+	15.1077i	−0.940894	+	0.510733i
$876$	−7.45934	−	0.792253i	−0.252028	−	0.0267678i
$877$	14.8706	−	5.41246i	0.502145	−	0.182766i	−0.0785136	−	0.996913i	$-0.525017\pi$
$877$	14.8706	−	5.41246i	0.502145	−	0.182766i	0.580658	+	0.814147i	$0.302795\pi$
$878$	33.2091	+	23.0634i	1.12075	+	0.778353i
$879$	−9.61194	+	9.12032i	−0.324203	+	0.307621i
$880$	−21.2224	−	35.4862i	−0.715408	−	1.19624i
$881$	14.3782	+	8.30124i	0.484413	+	0.279676i	0.722254	−	0.691628i	$-0.243106\pi$
$881$	14.3782	+	8.30124i	0.484413	+	0.279676i	−0.237841	+	0.971304i	$0.576440\pi$
$882$	25.9241	−	14.4893i	0.872911	−	0.487880i
$883$	−26.6463	+	15.3842i	−0.896719	+	0.517721i	−0.876134	−	0.482067i	$-0.839886\pi$
$883$	−26.6463	+	15.3842i	−0.896719	+	0.517721i	−0.0205846	+	0.999788i	$0.506553\pi$
$884$	13.1580	+	35.3040i	0.442552	+	1.18740i
$885$	21.2085	−	1.29592i	0.712917	−	0.0435620i
$886$	8.91187	+	18.9212i	0.299400	+	0.635671i
$887$	−30.3914	−	25.5014i	−1.02044	−	0.856255i	−0.0307613	−	0.999527i	$-0.509793\pi$
$887$	−30.3914	−	25.5014i	−1.02044	−	0.856255i	−0.989683	+	0.143272i	$0.954238\pi$
$888$	34.1082	+	41.8839i	1.14460	+	1.40553i
$889$	−0.156122	+	5.93771i	−0.00523617	+	0.199144i
$890$	−0.377166	+	0.817025i	−0.0126426	+	0.0273867i
$891$	33.2252	−	32.0702i	1.11309	−	1.07439i
$892$	4.14136	−	11.6565i	0.138663	−	0.390288i
$893$	5.26794	+	1.91737i	0.176285	+	0.0641624i
$894$	9.72169	−	16.0001i	0.325142	−	0.535122i
$895$	−6.05550	+	34.3424i	−0.202413	+	1.14794i
$896$	−21.1794	−	21.1526i	−0.707556	−	0.706658i
$897$	46.9598	+	23.4167i	1.56794	+	0.781862i
$898$	−5.51348	+	5.55605i	−0.183987	+	0.185408i
$899$	−3.40239	+	5.89311i	−0.113476	+	0.196546i
$900$	−3.03953	+	4.75901i	−0.101318	+	0.158634i
$901$	6.24339	−	3.60462i	0.207997	−	0.120087i
$902$	−60.5748	+	61.0426i	−2.01692	+	2.03249i
$903$	0.513310	−	0.0178399i	0.0170819	−	0.000593675i
$904$	−42.1981	−	19.0877i	−1.40349	−	0.634848i
$905$	27.8948	−	10.1529i	0.927255	−	0.337493i
$906$	−21.0073	+	23.9264i	−0.697920	+	0.794902i
$907$	−51.4042	+	9.06394i	−1.70685	+	0.300963i	−0.940078	−	0.340960i	$-0.889248\pi$
$907$	−51.4042	+	9.06394i	−1.70685	+	0.300963i	−0.766769	+	0.641923i	$0.778137\pi$
$908$	8.56044	−	24.0947i	0.284088	−	0.799611i
$909$	−6.12685	+	9.43210i	−0.203215	+	0.312843i
$910$	4.06815	−	36.9328i	0.134858	−	1.22431i
$911$	6.09485	−	1.07469i	0.201931	−	0.0356059i	−0.0717675	−	0.997421i	$-0.522864\pi$
$911$	6.09485	−	1.07469i	0.201931	−	0.0356059i	0.273699	+	0.961815i	$0.411753\pi$
$912$	7.75810	+	0.763684i	0.256896	+	0.0252881i
$913$	−1.96541	+	2.34228i	−0.0650455	+	0.0775182i
$914$	1.22318	−	14.6288i	0.0404591	−	0.483877i
$915$	−6.95320	−	15.9938i	−0.229866	−	0.528740i
$916$	4.95118	−	29.4002i	0.163592	−	0.971410i
$917$	−39.7001	+	13.2787i	−1.31101	+	0.438502i
$918$	−15.8223	+	23.2036i	−0.522214	+	0.765833i
$919$	25.2115	+	14.5559i	0.831650	+	0.480153i	0.854417	−	0.519588i	$-0.173914\pi$
$919$	25.2115	+	14.5559i	0.831650	+	0.480153i	−0.0227675	+	0.999741i	$0.507248\pi$
$920$	34.9239	+	2.64980i	1.15141	+	0.0873613i
$921$	−12.8704	−	29.6047i	−0.424095	−	0.975508i
$922$	9.90108	+	21.0215i	0.326075	+	0.692305i
$923$	−1.12048	+	0.407821i	−0.0368810	+	0.0134236i
$924$	−1.99482	−	46.9831i	−0.0656247	−	1.54563i
$925$	−1.80192	−	10.2192i	−0.0592467	−	0.336005i
$926$	9.53086	+	4.39977i	0.313204	+	0.144585i
$927$	−6.42864	+	0.788574i	−0.211144	+	0.0259002i
$928$	27.8864	+	18.7376i	0.915417	+	0.615093i
$929$	−0.642582	−	0.765799i	−0.0210824	−	0.0251251i	0.755400	−	0.655264i	$-0.227442\pi$
$929$	−0.642582	−	0.765799i	−0.0210824	−	0.0251251i	−0.776483	+	0.630139i	$0.782998\pi$
$930$	3.73049	−	4.24887i	0.122328	−	0.139326i
$931$	3.57430	+	7.01867i	0.117143	+	0.230028i
$932$	−0.410220	−	53.3296i	−0.0134372	−	1.74687i
$933$	−22.9299	−	24.1659i	−0.750691	−	0.791156i
$934$	−0.801105	−	0.211357i	−0.0262130	−	0.00691580i
$935$			39.5065i			1.29200i
$936$	−16.1096	−	38.5976i	−0.526560	−	1.26160i
$937$	14.3517	−	8.28598i	0.468851	−	0.270691i	−0.246908	−	0.969039i	$-0.579414\pi$
$937$	14.3517	−	8.28598i	0.468851	−	0.270691i	0.715758	+	0.698348i	$0.246081\pi$
$938$	−7.51865	+	5.01701i	−0.245493	+	0.163811i
$939$	29.1661	−	1.78216i	0.951800	−	0.0581587i
$940$	−10.1710	−	17.3078i	−0.331741	−	0.564519i
$941$	−6.47854	−	17.7996i	−0.211194	−	0.580252i	0.788186	−	0.615437i	$-0.211020\pi$
$941$	−6.47854	−	17.7996i	−0.211194	−	0.580252i	−0.999381	+	0.0351847i	$0.988798\pi$
$942$	−1.12485	+	50.2249i	−0.0366495	+	1.63642i
$943$	−12.6493	−	71.7380i	−0.411919	−	2.33611i
$944$	3.85999	−	24.0488i	0.125632	−	0.782723i
$945$	24.2281	−	13.4209i	0.788142	−	0.436583i
$946$	0.340870	−	0.738399i	0.0110826	−	0.0240074i
$947$	−51.9626	+	9.16241i	−1.68856	+	0.297738i	−0.933675	−	0.358121i	$-0.883418\pi$
$947$	−51.9626	+	9.16241i	−1.68856	+	0.297738i	−0.754883	+	0.655859i	$0.772306\pi$
$948$	3.17294	−	2.13514i	0.103052	−	0.0693460i
$949$	−10.0299	+	3.65058i	−0.325584	+	0.118503i
$950$	−1.23007	−	0.854270i	−0.0399086	−	0.0277162i
$951$	−46.6170	+	30.8512i	−1.51166	+	1.00042i
$952$	6.99400	+	27.7317i	0.226677	+	0.898791i
$953$	−14.9358	−	25.8695i	−0.483818	−	0.837997i	0.516010	−	0.856583i	$-0.327417\pi$
$953$	−14.9358	−	25.8695i	−0.483818	−	0.837997i	−0.999827	+	0.0185859i	$0.994084\pi$
$954$	−6.77107	+	4.26622i	−0.219221	+	0.138124i
$955$	35.6513			1.15365
$956$	40.9891	+	33.8601i	1.32568	+	1.09511i
$957$	12.3185	+	51.3234i	0.398200	+	1.65905i
$958$	13.7073	−	6.45611i	0.442862	−	0.208587i
$959$	−9.94670	+	7.91022i	−0.321196	+	0.255434i
$960$	−19.6770	−	19.8019i	−0.635074	−	0.639103i
$961$	−22.7418	+	19.0826i	−0.733605	+	0.615568i
$962$	69.7815	+	32.2135i	2.24985	+	1.03860i
$963$	−0.573639	+	2.48338i	−0.0184852	+	0.0800256i
$964$	−15.0589	+	12.8346i	−0.485016	+	0.413375i
$965$	9.34037	−	1.64696i	0.300677	−	0.0530175i
$966$	33.4867	+	21.5717i	1.07742	+	0.694058i
$967$	−5.51095	−	15.1412i	−0.177220	−	0.486909i	0.818998	−	0.573797i	$-0.194530\pi$
$967$	−5.51095	−	15.1412i	−0.177220	−	0.486909i	−0.996218	+	0.0868879i	$0.972308\pi$
$968$	−39.4961	−	17.8655i	−1.26945	−	0.574218i
$969$	−5.98718	−	4.43082i	−0.192336	−	0.142339i
$970$	−9.64283	+	9.71729i	−0.309613	+	0.312003i
$971$	1.00282	−	1.73694i	0.0321822	−	0.0557411i	−0.849486	−	0.527612i	$-0.823088\pi$
$971$	1.00282	−	1.73694i	0.0321822	−	0.0557411i	0.881668	+	0.471870i	$0.156421\pi$
$972$	16.5563	−	26.4176i	0.531044	−	0.847344i
$973$	3.14414	+	2.78230i	0.100796	+	0.0891964i
$974$	−35.4612	+	9.64812i	−1.13625	+	0.309146i
$975$	−0.910045	+	7.98321i	−0.0291448	+	0.255667i
$976$	−19.6318	+	3.77390i	−0.628400	+	0.120800i
$977$	10.9807	+	9.21394i	0.351305	+	0.294780i	0.801314	−	0.598244i	$-0.204135\pi$
$977$	10.9807	+	9.21394i	0.351305	+	0.294780i	−0.450009	+	0.893024i	$0.648579\pi$
$978$	41.7777	−	6.40557i	1.33590	−	0.204828i
$979$	0.281405	+	1.59592i	0.00899373	+	0.0510060i
$980$	6.13913	−	27.5290i	0.196107	−	0.879382i
$981$	−42.0392	+	45.0709i	−1.34221	+	1.43900i
$982$	−1.29919	−	14.2197i	−0.0414589	−	0.453770i
$983$	−4.10823	−	23.2989i	−0.131032	−	0.743120i	−0.977541	−	0.210745i	$-0.932411\pi$
$983$	−4.10823	−	23.2989i	−0.131032	−	0.743120i	0.846509	−	0.532375i	$-0.178700\pi$
$984$	−29.7663	+	49.8497i	−0.948914	+	1.58915i
$985$	1.79442	+	4.93013i	0.0571750	+	0.157087i
$986$	−13.6781	−	29.0406i	−0.435598	−	0.924841i
$987$	−0.793026	−	22.8178i	−0.0252423	−	0.726298i
$988$	10.3939	−	3.87387i	0.330675	−	0.123244i
$989$	0.344448	+	0.596602i	0.0109528	+	0.0189708i
$990$	−1.69399	−	43.8235i	−0.0538385	−	1.39280i
$991$	12.5767	+	7.26119i	0.399513	+	0.230659i	0.686274	−	0.727343i	$-0.259245\pi$
$991$	12.5767	+	7.26119i	0.399513	+	0.230659i	−0.286761	+	0.958002i	$0.592578\pi$
$992$	−3.81895	−	5.23674i	−0.121252	−	0.166267i
$993$	−25.7723	−	38.9427i	−0.817860	−	1.23581i
$994$	−0.879337	+	0.214590i	−0.0278909	+	0.00680639i
$995$	−13.1647	−	2.32129i	−0.417349	−	0.0735899i
$996$	−0.906978	+	1.85443i	−0.0287387	+	0.0587599i
$997$	6.53089	−	17.9435i	0.206835	−	0.568276i	−0.792287	−	0.610148i	$-0.791110\pi$
$997$	6.53089	−	17.9435i	0.206835	−	0.568276i	0.999123	+	0.0418721i	$0.0133322\pi$
$998$	1.06127	+	11.6156i	0.0335938	+	0.367687i
$999$	10.4307	+	56.3341i	0.330012	+	1.78233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bt.a.103.10	✓	840
4.3	odd	2	inner	756.2.bt.a.103.117	yes	840
7.3	odd	6		756.2.cd.a.535.103	yes	840
27.16	even	9		756.2.cd.a.691.74	yes	840
28.3	even	6		756.2.cd.a.535.74	yes	840
108.43	odd	18		756.2.cd.a.691.103	yes	840
189.178	odd	18	inner	756.2.bt.a.367.117	yes	840
756.367	even	18	inner	756.2.bt.a.367.10	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bt.a.103.10	✓	840	1.1	even	1	trivial
756.2.bt.a.103.117	yes	840	4.3	odd	2	inner
756.2.bt.a.367.10	yes	840	756.367	even	18	inner
756.2.bt.a.367.117	yes	840	189.178	odd	18	inner
756.2.cd.a.535.74	yes	840	28.3	even	6
756.2.cd.a.535.103	yes	840	7.3	odd	6
756.2.cd.a.691.74	yes	840	27.16	even	9
756.2.cd.a.691.103	yes	840	108.43	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bt (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36742 - 0.360769i) q^{2} +(-1.03034 + 1.39226i) q^{3} +(1.73969 + 0.986648i) q^{4} +(1.98405 + 0.349842i) q^{5} +(1.91120 - 1.53209i) q^{6} +(1.38264 - 2.25573i) q^{7} +(-2.02294 - 1.97679i) q^{8} +(-0.876779 - 2.86902i) q^{9} +O(q^{10})\)	\(q+(-1.36742 - 0.360769i) q^{2} +(-1.03034 + 1.39226i) q^{3} +(1.73969 + 0.986648i) q^{4} +(1.98405 + 0.349842i) q^{5} +(1.91120 - 1.53209i) q^{6} +(1.38264 - 2.25573i) q^{7} +(-2.02294 - 1.97679i) q^{8} +(-0.876779 - 2.86902i) q^{9} +(-2.58683 - 1.19417i) q^{10} +(-5.05295 + 0.890971i) q^{11} +(-3.16615 + 1.40552i) q^{12} +(-3.16835 + 3.77589i) q^{13} +(-2.70445 + 2.58572i) q^{14} +(-2.53133 + 2.40186i) q^{15} +(2.05305 + 3.43292i) q^{16} -3.82185i q^{17} +(0.163876 + 4.23947i) q^{18} -1.12520 q^{19} +(3.10647 + 2.56618i) q^{20} +(1.71596 + 4.24917i) q^{21} +(7.23095 + 0.604612i) q^{22} +(-3.95084 + 4.70843i) q^{23} +(4.83654 - 0.779686i) q^{24} +(-0.884384 - 0.321890i) q^{25} +(5.69469 - 4.02020i) q^{26} +(4.89780 + 1.73537i) q^{27} +(4.63098 - 2.56008i) q^{28} +(-4.54965 + 3.81761i) q^{29} +(4.32792 - 2.37114i) q^{30} +(1.07665 - 0.391870i) q^{31} +(-1.56890 - 5.43494i) q^{32} +(3.96581 - 7.95303i) q^{33} +(-1.37880 + 5.22608i) q^{34} +(3.53239 - 3.99177i) q^{35} +(1.30538 - 5.85628i) q^{36} +(5.51289 + 9.54861i) q^{37} +(1.53862 + 0.405936i) q^{38} +(-1.99253 - 8.30163i) q^{39} +(-3.32206 - 4.62977i) q^{40} +(-7.61804 + 9.07882i) q^{41} +(-0.813470 - 6.42948i) q^{42} +(0.0383340 - 0.105322i) q^{43} +(-9.66964 - 3.43546i) q^{44} +(-0.735874 - 5.99902i) q^{45} +(7.10113 - 5.01308i) q^{46} +(-4.68179 - 1.70403i) q^{47} +(-6.89488 - 0.678711i) q^{48} +(-3.17659 - 6.23773i) q^{49} +(1.09320 + 0.759218i) q^{50} +(5.32101 + 3.93782i) q^{51} +(-9.23742 + 3.44284i) q^{52} +(0.943162 + 1.63361i) q^{53} +(-6.07130 - 4.13996i) q^{54} -10.3370 q^{55} +(-7.25611 + 1.83001i) q^{56} +(1.15934 - 1.56657i) q^{57} +(7.59857 - 3.57892i) q^{58} +(-4.66457 - 3.91403i) q^{59} +(-6.77353 + 1.68097i) q^{60} +(-1.70936 + 4.69642i) q^{61} +(-1.61361 + 0.147429i) q^{62} +(-7.68399 - 1.98905i) q^{63} +(0.184592 + 7.99787i) q^{64} +(-7.60714 + 6.38315i) q^{65} +(-8.29215 + 9.44441i) q^{66} +(2.37903 + 0.419487i) q^{67} +(3.77082 - 6.64884i) q^{68} +(-2.48463 - 10.3519i) q^{69} +(-6.27037 + 4.18407i) q^{70} +(0.209500 + 0.120955i) q^{71} +(-3.89777 + 7.53707i) q^{72} +(1.87532 + 1.08272i) q^{73} +(-4.09361 - 15.0459i) q^{74} +(1.35937 - 0.899636i) q^{75} +(-1.95750 - 1.11017i) q^{76} +(-4.97664 + 12.6300i) q^{77} +(-0.270338 + 12.0707i) q^{78} +(-1.08725 + 0.191711i) q^{79} +(2.87239 + 7.52935i) q^{80} +(-7.46252 + 5.03099i) q^{81} +(13.6924 - 9.66624i) q^{82} +(0.456505 - 0.383054i) q^{83} +(-1.20720 + 9.08530i) q^{84} +(1.33704 - 7.58275i) q^{85} +(-0.0904155 + 0.130190i) q^{86} +(-0.627399 - 10.2678i) q^{87} +(11.9831 + 8.18624i) q^{88} -0.315840i q^{89} +(-1.15801 + 8.46868i) q^{90} +(4.13668 + 12.3676i) q^{91} +(-11.5188 + 4.29313i) q^{92} +(-0.563739 + 1.90274i) q^{93} +(5.78723 + 4.01918i) q^{94} +(-2.23245 - 0.393641i) q^{95} +(9.18336 + 3.41554i) q^{96} +(1.64335 - 4.51508i) q^{97} +(2.09337 + 9.67563i) q^{98} +(6.98653 + 13.7158i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Introduction

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