LMFDB - Embedded newform 756.2.ci.a.95.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(95,756)]

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, 17, 12]))

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

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

chi := DirichletCharacter("756.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ci (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			95.5
Character	$\chi$	$=$	756.95
Dual form			756.2.ci.a.191.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40530 + 0.158515i) q^{2} +(1.04908 + 1.37820i) q^{3} +(1.94975 - 0.445523i) q^{4} +(0.0136217 + 0.00240188i) q^{5} +(-1.69274 - 1.77049i) q^{6} +(-2.34832 - 1.21877i) q^{7} +(-2.66936 + 0.935159i) q^{8} +(-0.798872 + 2.89168i) q^{9} +O(q^{10})$	\(q+(-1.40530 + 0.158515i) q^{2} +(1.04908 + 1.37820i) q^{3} +(1.94975 - 0.445523i) q^{4} +(0.0136217 + 0.00240188i) q^{5} +(-1.69274 - 1.77049i) q^{6} +(-2.34832 - 1.21877i) q^{7} +(-2.66936 + 0.935159i) q^{8} +(-0.798872 + 2.89168i) q^{9} +(-0.0195234 - 0.00121611i) q^{10} +(-0.989827 - 5.61359i) q^{11} +(2.65946 + 2.21975i) q^{12} +(-0.373911 + 2.12055i) q^{13} +(3.49329 + 1.34049i) q^{14} +(0.0109800 + 0.0212932i) q^{15} +(3.60302 - 1.73731i) q^{16} +(-4.46911 + 2.58024i) q^{17} +(0.664281 - 4.19031i) q^{18} +(-1.67374 - 0.966334i) q^{19} +(0.0276290 - 0.00138575i) q^{20} +(-0.783868 - 4.51504i) q^{21} +(2.28084 + 7.73188i) q^{22} +(-5.57999 - 4.68217i) q^{23} +(-4.08920 - 2.69786i) q^{24} +(-4.69828 - 1.71004i) q^{25} +(0.189318 - 3.03929i) q^{26} +(-4.82339 + 1.93259i) q^{27} +(-5.12162 - 1.33005i) q^{28} +(-6.57796 + 1.15987i) q^{29} +(-0.0188055 - 0.0281829i) q^{30} +(7.43341 + 1.31071i) q^{31} +(-4.78794 + 3.01258i) q^{32} +(6.69824 - 7.25327i) q^{33} +(5.87144 - 4.33444i) q^{34} +(-0.0290609 - 0.0222421i) q^{35} +(-0.269287 + 5.99395i) q^{36} -1.62487 q^{37} +(2.50529 + 1.09268i) q^{38} +(-3.31481 + 1.70930i) q^{39} +(-0.0386074 + 0.00632701i) q^{40} +(0.819613 + 0.144520i) q^{41} +(1.81727 + 6.22073i) q^{42} +(3.59069 + 4.27922i) q^{43} +(-4.43089 - 10.5041i) q^{44} +(-0.0178275 + 0.0374709i) q^{45} +(8.58376 + 5.69534i) q^{46} +(-0.133348 - 0.756257i) q^{47} +(6.17421 + 3.14310i) q^{48} +(4.02922 + 5.72410i) q^{49} +(6.87357 + 1.65837i) q^{50} +(-8.24453 - 3.45245i) q^{51} +(0.215725 + 4.30113i) q^{52} +(2.00935 + 1.16010i) q^{53} +(6.47197 - 3.48045i) q^{54} -0.0788442i q^{55} +(7.40825 + 1.05727i) q^{56} +(-0.424081 - 3.32051i) q^{57} +(9.06016 - 2.67268i) q^{58} +(-10.3506 + 3.76730i) q^{59} +(0.0308948 + 0.0366246i) q^{60} +(-1.50186 - 8.51747i) q^{61} +(-10.6540 - 0.663636i) q^{62} +(5.40028 - 5.81695i) q^{63} +(6.25096 - 4.99255i) q^{64} +(-0.0101866 + 0.0279875i) q^{65} +(-8.26330 + 11.2548i) q^{66} +(-0.900117 + 1.07272i) q^{67} +(-7.56407 + 7.02191i) q^{68} +(0.599121 - 12.6023i) q^{69} +(0.0443650 + 0.0266502i) q^{70} +(6.87368 - 11.9056i) q^{71} +(-0.571703 - 8.46600i) q^{72} -0.975165 q^{73} +(2.28344 - 0.257567i) q^{74} +(-2.57209 - 8.26914i) q^{75} +(-3.69389 - 1.13842i) q^{76} +(-4.51721 + 14.3889i) q^{77} +(4.38736 - 2.92753i) q^{78} +(-2.27083 - 2.70627i) q^{79} +(0.0532522 - 0.0150112i) q^{80} +(-7.72361 - 4.62016i) q^{81} +(-1.17471 - 0.0731729i) q^{82} +(0.761271 + 4.31738i) q^{83} +(-3.53990 - 8.45394i) q^{84} +(-0.0670745 + 0.0244131i) q^{85} +(-5.72432 - 5.44441i) q^{86} +(-8.49933 - 7.84895i) q^{87} +(7.89180 + 14.0590i) q^{88} +(12.6403 + 7.29787i) q^{89} +(0.0191133 - 0.0554838i) q^{90} +(3.46252 - 4.52403i) q^{91} +(-12.9656 - 6.64302i) q^{92} +(5.99180 + 11.6198i) q^{93} +(0.307273 + 1.04163i) q^{94} +(-0.0204782 - 0.0171833i) q^{95} +(-9.17486 - 3.43830i) q^{96} +(1.44343 - 1.21118i) q^{97} +(-6.56963 - 7.40540i) q^{98} +(17.0234 + 1.62228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.40530	+	0.158515i	−0.993698	+	0.112087i
$2$	−1.40530	+	0.158515i	−0.993698	+	0.112087i
$3$	1.04908	+	1.37820i	0.605685	+	0.795704i
$3$	1.04908	+	1.37820i	0.605685	+	0.795704i
$4$	1.94975	−	0.445523i	0.974873	−	0.222762i
$5$	0.0136217	+	0.00240188i	0.00609182	+	0.00107415i	0.176693	−	0.984266i	$-0.443460\pi$
$5$	0.0136217	+	0.00240188i	0.00609182	+	0.00107415i	−0.170601	+	0.985340i	$0.554571\pi$
$6$	−1.69274	−	1.77049i	−0.691057	−	0.722801i
$7$	−2.34832	−	1.21877i	−0.887582	−	0.460650i
$7$	−2.34832	−	1.21877i	−0.887582	−	0.460650i
$8$	−2.66936	+	0.935159i	−0.943761	+	0.330629i
$9$	−0.798872	+	2.89168i	−0.266291	+	0.963893i
$10$	−0.0195234	−	0.00121611i	−0.00617383	−	0.000384569i
$11$	−0.989827	−	5.61359i	−0.298444	−	1.69256i	−0.652865	−	0.757474i	$-0.726433\pi$
$11$	−0.989827	−	5.61359i	−0.298444	−	1.69256i	0.354421	−	0.935086i	$-0.384678\pi$
$12$	2.65946	+	2.21975i	0.767719	+	0.640787i
$13$	−0.373911	+	2.12055i	−0.103704	+	0.588136i	0.888026	+	0.459794i	$0.152077\pi$
$13$	−0.373911	+	2.12055i	−0.103704	+	0.588136i	−0.991730	+	0.128342i	$0.959034\pi$
$14$	3.49329	+	1.34049i	0.933622	+	0.358261i
$15$	0.0109800	+	0.0212932i	0.00283502	+	0.00549789i
$16$	3.60302	−	1.73731i	0.900754	−	0.434329i
$17$	−4.46911	+	2.58024i	−1.08392	+	0.625801i	−0.931951	−	0.362585i	$-0.881894\pi$
$17$	−4.46911	+	2.58024i	−1.08392	+	0.625801i	−0.151968	+	0.988385i	$0.548561\pi$
$18$	0.664281	−	4.19031i	0.156573	−	0.987666i
$19$	−1.67374	−	0.966334i	−0.383982	−	0.221692i	0.295567	−	0.955322i	$-0.404491\pi$
$19$	−1.67374	−	0.966334i	−0.383982	−	0.221692i	−0.679549	+	0.733630i	$0.737825\pi$
$20$	0.0276290	−	0.00138575i	0.00617803	−	0.000309862i
$21$	−0.783868	−	4.51504i	−0.171054	−	0.985262i
$22$	2.28084	+	7.73188i	0.486278	+	1.64844i
$23$	−5.57999	−	4.68217i	−1.16351	−	0.976299i	−0.163560	−	0.986533i	$-0.552298\pi$
$23$	−5.57999	−	4.68217i	−1.16351	−	0.976299i	−0.999948	+	0.0102344i	$0.996742\pi$
$24$	−4.08920	−	2.69786i	−0.834705	−	0.550698i
$25$	−4.69828	−	1.71004i	−0.939657	−	0.342007i
$26$	0.189318	−	3.03929i	0.0371282	−	0.596053i
$27$	−4.82339	+	1.93259i	−0.928262	+	0.371927i
$28$	−5.12162	−	1.33005i	−0.967895	−	0.251356i
$29$	−6.57796	+	1.15987i	−1.22150	+	0.215383i	−0.746970	−	0.664858i	$-0.768492\pi$
$29$	−6.57796	+	1.15987i	−1.22150	+	0.215383i	−0.474527	+	0.880241i	$0.657381\pi$
$30$	−0.0188055	−	0.0281829i	−0.00343340	−	0.00514547i
$31$	7.43341	+	1.31071i	1.33508	+	0.235411i	0.795208	−	0.606336i	$-0.207362\pi$
$31$	7.43341	+	1.31071i	1.33508	+	0.235411i	0.539872	+	0.841747i	$0.318473\pi$
$32$	−4.78794	+	3.01258i	−0.846396	+	0.532555i
$33$	6.69824	−	7.25327i	1.16601	−	1.26263i
$34$	5.87144	−	4.33444i	1.00694	−	0.743350i
$35$	−0.0290609	−	0.0222421i	−0.00491218	−	0.00375960i
$36$	−0.269287	+	5.99395i	−0.0448812	+	0.998992i
$37$	−1.62487			−0.267127			−0.133564	−	0.991040i	$-0.542642\pi$
$37$	−1.62487			−0.267127			−0.133564	+	0.991040i	$0.542642\pi$
$38$	2.50529	+	1.09268i	0.406411	+	0.177256i
$39$	−3.31481	+	1.70930i	−0.530794	+	0.273707i
$40$	−0.0386074	+	0.00632701i	−0.00610437	+	0.00100039i
$41$	0.819613	+	0.144520i	0.128002	+	0.0225702i	0.237282	−	0.971441i	$-0.423743\pi$
$41$	0.819613	+	0.144520i	0.128002	+	0.0225702i	−0.109280	+	0.994011i	$0.534855\pi$
$42$	1.81727	+	6.22073i	0.280411	+	0.959880i
$43$	3.59069	+	4.27922i	0.547575	+	0.652574i	0.966868	−	0.255277i	$-0.0821665\pi$
$43$	3.59069	+	4.27922i	0.547575	+	0.652574i	−0.419293	+	0.907851i	$0.637722\pi$
$44$	−4.43089	−	10.5041i	−0.667983	−	1.58355i
$45$	−0.0178275	+	0.0374709i	−0.00265756	+	0.00558583i
$46$	8.58376	+	5.69534i	1.26561	+	0.839732i
$47$	−0.133348	−	0.756257i	−0.0194509	−	0.110311i	0.973537	−	0.228531i	$-0.0733923\pi$
$47$	−0.133348	−	0.756257i	−0.0194509	−	0.110311i	−0.992987	+	0.118220i	$0.962281\pi$
$48$	6.17421	+	3.14310i	0.891171	+	0.453668i
$49$	4.02922	+	5.72410i	0.575603	+	0.817729i
$50$	6.87357	+	1.65837i	0.972070	+	0.234528i
$51$	−8.24453	−	3.45245i	−1.15447	−	0.483440i
$52$	0.215725	+	4.30113i	0.0299157	+	0.596459i
$53$	2.00935	+	1.16010i	0.276005	+	0.159352i	0.631614	−	0.775283i	$-0.282393\pi$
$53$	2.00935	+	1.16010i	0.276005	+	0.159352i	−0.355608	+	0.934635i	$0.615726\pi$
$54$	6.47197	−	3.48045i	0.880724	−	0.473630i
$55$		−	0.0788442i		−	0.0106314i
$56$	7.40825	+	1.05727i	0.989969	+	0.141283i
$57$	−0.424081	−	3.32051i	−0.0561709	−	0.439812i
$58$	9.06016	−	2.67268i	1.18966	−	0.350940i
$59$	−10.3506	+	3.76730i	−1.34753	+	0.490461i	−0.912176	−	0.409799i	$-0.865599\pi$
$59$	−10.3506	+	3.76730i	−1.34753	+	0.490461i	−0.435354	+	0.900260i	$0.643377\pi$
$60$	0.0308948	+	0.0366246i	0.00398850	+	0.00472821i
$61$	−1.50186	−	8.51747i	−0.192293	−	1.09055i	−0.916221	−	0.400674i	$-0.868776\pi$
$61$	−1.50186	−	8.51747i	−0.192293	−	1.09055i	0.723927	−	0.689876i	$-0.242335\pi$
$62$	−10.6540	−	0.663636i	−1.35305	−	0.0842819i
$63$	5.40028	−	5.81695i	0.680372	−	0.732867i
$64$	6.25096	−	4.99255i	0.781369	−	0.624069i
$65$	−0.0101866	+	0.0279875i	−0.00126350	+	0.00347142i
$66$	−8.26330	+	11.2548i	−1.01714	+	1.38537i
$67$	−0.900117	+	1.07272i	−0.109967	+	0.131053i	−0.818220	−	0.574905i	$-0.805039\pi$
$67$	−0.900117	+	1.07272i	−0.109967	+	0.131053i	0.708253	+	0.705958i	$0.249483\pi$
$68$	−7.56407	+	7.02191i	−0.917278	+	0.851532i
$69$	0.599121	−	12.6023i	0.0721257	−	1.51714i
$70$	0.0443650	+	0.0266502i	0.00530263	+	0.00318531i
$71$	6.87368	−	11.9056i	0.815755	−	1.41293i	−0.0930288	−	0.995663i	$-0.529655\pi$
$71$	6.87368	−	11.9056i	0.815755	−	1.41293i	0.908784	−	0.417266i	$-0.137012\pi$
$72$	−0.571703	−	8.46600i	−0.0673758	−	0.997728i
$73$	−0.975165			−0.114134			−0.0570672	−	0.998370i	$-0.518175\pi$
$73$	−0.975165			−0.114134			−0.0570672	+	0.998370i	$0.518175\pi$
$74$	2.28344	−	0.257567i	0.265444	−	0.0299415i
$75$	−2.57209	−	8.26914i	−0.297000	−	0.954837i
$76$	−3.69389	−	1.13842i	−0.423718	−	0.130585i
$77$	−4.51721	+	14.3889i	−0.514784	+	1.63976i
$78$	4.38736	−	2.92753i	0.496770	−	0.331478i
$79$	−2.27083	−	2.70627i	−0.255489	−	0.304479i	0.623020	−	0.782206i	$-0.285905\pi$
$79$	−2.27083	−	2.70627i	−0.255489	−	0.304479i	−0.878509	+	0.477726i	$0.841461\pi$
$80$	0.0532522	−	0.0150112i	0.00595377	−	0.00167831i
$81$	−7.72361	−	4.62016i	−0.858179	−	0.513351i
$82$	−1.17471	−	0.0731729i	−0.129725	−	0.00808060i
$83$	0.761271	+	4.31738i	0.0835604	+	0.473894i	0.997658	+	0.0684002i	$0.0217895\pi$
$83$	0.761271	+	4.31738i	0.0835604	+	0.473894i	−0.914098	+	0.405494i	$0.867099\pi$
$84$	−3.53990	−	8.45394i	−0.386235	−	0.922401i
$85$	−0.0670745	+	0.0244131i	−0.00727525	+	0.00264797i
$86$	−5.72432	−	5.44441i	−0.617269	−	0.587086i
$87$	−8.49933	−	7.84895i	−0.911223	−	0.841496i
$88$	7.89180	+	14.0590i	0.841269	+	1.49870i
$89$	12.6403	+	7.29787i	1.33987	+	0.773573i	0.986788	−	0.162020i	$-0.0518008\pi$
$89$	12.6403	+	7.29787i	1.33987	+	0.773573i	0.353081	+	0.935593i	$0.385134\pi$
$90$	0.0191133	−	0.0554838i	0.00201472	−	0.00584851i
$91$	3.46252	−	4.52403i	0.362971	−	0.474247i
$92$	−12.9656	−	6.64302i	−1.35175	−	0.692582i
$93$	5.99180	+	11.6198i	0.621321	+	1.20491i
$94$	0.307273	+	1.04163i	0.0316928	+	0.107436i
$95$	−0.0204782	−	0.0171833i	−0.00210102	−	0.00176296i
$96$	−9.17486	−	3.43830i	−0.936405	−	0.350920i
$97$	1.44343	−	1.21118i	0.146558	−	0.122977i	−0.566561	−	0.824020i	$-0.691726\pi$
$97$	1.44343	−	1.21118i	0.146558	−	0.122977i	0.713119	+	0.701043i	$0.247282\pi$
$98$	−6.56963	−	7.40540i	−0.663633	−	0.748058i
$99$	17.0234	+	1.62228i	1.71092	+	0.163045i
$100$	−9.92232	−	1.24094i	−0.992232	−	0.124094i
$101$	−7.25909	−	8.65105i	−0.722307	−	0.860812i	0.272546	−	0.962143i	$-0.412134\pi$
$101$	−7.25909	−	8.65105i	−0.722307	−	0.860812i	−0.994853	+	0.101331i	$0.967690\pi$
$102$	12.1333	+	3.54486i	1.20138	+	0.350993i
$103$	−7.42134	−	1.30858i	−0.731247	−	0.128939i	−0.204386	−	0.978890i	$-0.565520\pi$
$103$	−7.42134	−	1.30858i	−0.731247	−	0.128939i	−0.526861	+	0.849952i	$0.676631\pi$
$104$	−0.984952	−	6.01018i	−0.0965825	−	0.589347i
$105$	0.000166923	−	0.0633854i	1.62900e−5	−	0.00618578i
$106$	−3.00764	−	1.31178i	−0.292127	−	0.127411i
$107$	−6.91667	−	11.9800i	−0.668660	−	1.15815i	−0.978279	−	0.207292i	$-0.933535\pi$
$107$	−6.91667	−	11.9800i	−0.668660	−	1.15815i	0.309620	−	0.950861i	$-0.399798\pi$
$108$	−8.54337	+	5.91699i	−0.822086	+	0.569363i
$109$	4.23706	−	7.33880i	0.405837	−	0.702930i	−0.588582	−	0.808438i	$-0.700314\pi$
$109$	4.23706	−	7.33880i	0.405837	−	0.702930i	0.994418	+	0.105508i	$0.0336469\pi$
$110$	0.0124980	+	0.110800i	0.00119164	+	0.0105644i
$111$	−1.70462	−	2.23940i	−0.161795	−	0.212554i
$112$	−10.5784	−	0.311461i	−0.999567	−	0.0294303i
$113$	−2.64126	+	3.14773i	−0.248468	+	0.296113i	−0.875835	−	0.482611i	$-0.839688\pi$
$113$	−2.64126	+	3.14773i	−0.248468	+	0.296113i	0.627366	+	0.778724i	$0.284133\pi$
$114$	1.12231	+	4.59909i	0.105114	+	0.430744i
$115$	−0.0647631	−	0.0771816i	−0.00603919	−	0.00719723i
$116$	−12.3086	+	5.19209i	−1.14282	+	0.482073i
$117$	−5.83325	−	2.77528i	−0.539284	−	0.256575i
$118$	13.9485	−	6.93491i	1.28406	−	0.638411i
$119$	13.6396	−	0.612440i	1.25034	−	0.0561423i
$120$	−0.0492221	−	0.0465712i	−0.00449334	−	0.00425135i
$121$	−20.1960	+	7.35074i	−1.83600	+	0.668249i
$122$	3.46072	+	11.7316i	0.313318	+	1.06212i
$123$	0.660660	+	1.28120i	0.0595697	+	0.115522i
$124$	15.0772	−	0.756205i	1.35397	−	0.0679092i
$125$	−0.119785	−	0.0691580i	−0.0107139	−	0.00618568i
$126$	−6.66695	+	9.03060i	−0.593940	+	0.804510i
$127$	4.35663	−	2.51530i	0.386588	−	0.223197i	−0.294093	−	0.955777i	$-0.595017\pi$
$127$	4.35663	−	2.51530i	0.386588	−	0.223197i	0.680681	+	0.732580i	$0.261684\pi$
$128$	−7.99308	+	8.00691i	−0.706495	+	0.707718i
$129$	−2.13071	+	9.43792i	−0.187598	+	0.830962i
$130$	0.00987883	−	0.0409456i	0.000866431	−	0.00359117i
$131$	12.0272	+	10.0920i	1.05082	+	0.881741i	0.993179	−	0.116596i	$-0.0371984\pi$
$131$	12.0272	+	10.0920i	1.05082	+	0.881741i	0.0576387	+	0.998338i	$0.481643\pi$
$132$	9.82837	−	17.1263i	0.855450	−	1.49065i
$133$	2.75274	+	4.30916i	0.238693	+	0.373651i
$134$	1.09489	−	1.65017i	0.0945845	−	0.142553i
$135$	−0.0703448	+	0.0147400i	−0.00605431	+	0.00126862i
$136$	9.51672	−	11.0669i	0.816052	−	0.948981i
$137$	−4.84376	+	13.3081i	−0.413830	+	1.13699i	0.541307	+	0.840825i	$0.317930\pi$
$137$	−4.84376	+	13.3081i	−0.413830	+	1.13699i	−0.955137	+	0.296164i	$0.904292\pi$
$138$	1.15571	+	17.8050i	0.0983805	+	1.51566i
$139$	1.08536	+	2.98199i	0.0920587	+	0.252929i	0.977173	−	0.212444i	$-0.0681423\pi$
$139$	1.08536	+	2.98199i	0.0920587	+	0.252929i	−0.885115	+	0.465373i	$0.845920\pi$
$140$	−0.0665707	−	0.0304191i	−0.00562625	−	0.00257088i
$141$	0.902380	−	0.977153i	0.0759941	−	0.0822911i
$142$	−7.77238	+	17.8205i	−0.652244	+	1.49546i
$143$	12.2740			1.02640
$144$	2.14540	+	11.8067i	0.178784	+	0.983888i
$145$	−0.0923891			−0.00767249
$146$	1.37040	−	0.154578i	0.113415	−	0.0127930i
$147$	−3.66199	+	11.5581i	−0.302036	+	0.953296i
$148$	−3.16809	+	0.723918i	−0.260415	+	0.0595057i
$149$	3.14028	+	8.62786i	0.257262	+	0.706822i	0.999334	+	0.0365009i	$0.0116212\pi$
$149$	3.14028	+	8.62786i	0.257262	+	0.706822i	−0.742072	+	0.670321i	$0.766157\pi$
$150$	4.92535	+	11.2129i	0.402153	+	0.915531i
$151$	−14.3646	+	2.53287i	−1.16897	+	0.206122i	−0.724245	−	0.689543i	$-0.757811\pi$
$151$	−14.3646	+	2.53287i	−1.16897	+	0.206122i	−0.444730	+	0.895665i	$0.646700\pi$
$152$	5.37149	+	1.01428i	0.435685	+	0.0822689i
$153$	−3.89098	−	14.9845i	−0.314567	−	1.21143i
$154$	4.06719	−	20.9368i	0.327744	−	1.68713i
$155$	0.0981078	+	0.0357083i	0.00788021	+	0.00286816i
$156$	−5.70150	+	4.80953i	−0.456485	+	0.385070i
$157$	9.63440	−	3.50664i	0.768909	−	0.279860i	0.0723691	−	0.997378i	$-0.476944\pi$
$157$	9.63440	−	3.50664i	0.768909	−	0.279860i	0.696540	+	0.717518i	$0.254722\pi$
$158$	3.62019	+	3.44317i	0.288007	+	0.273924i
$159$	0.509116	+	3.98632i	0.0403755	+	0.316136i
$160$	−0.0724558	+	0.0295366i	−0.00572814	+	0.00233507i
$161$	7.39714	+	17.7959i	0.582976	+	1.40252i
$162$	11.5864	+	5.26841i	0.910311	+	0.413926i
$163$	−11.3722	+	6.56577i	−0.890743	+	0.514271i	−0.874186	−	0.485592i	$-0.838604\pi$
$163$	−11.3722	+	6.56577i	−0.890743	+	0.514271i	−0.0165578	+	0.999863i	$0.505271\pi$
$164$	1.66242	−	0.0833796i	0.129813	−	0.00651086i
$165$	0.108663	−	0.0827137i	0.00845941	−	0.00643925i
$166$	−1.75419	−	5.94655i	−0.136151	−	0.461542i
$167$	−8.76693	−	7.35633i	−0.678405	−	0.569250i	0.237135	−	0.971477i	$-0.423792\pi$
$167$	−8.76693	−	7.35633i	−0.678405	−	0.569250i	−0.915540	+	0.402227i	$0.868236\pi$
$168$	6.31470	+	11.3192i	0.487190	+	0.873296i
$169$	7.85907	+	2.86047i	0.604544	+	0.220036i
$170$	0.0903900	−	0.0449401i	0.00693260	−	0.00344675i
$171$	4.13143	−	4.06794i	0.315938	−	0.311083i
$172$	8.90742	+	6.74365i	0.679184	+	0.514198i
$173$	1.72866	−	4.74947i	0.131428	−	0.361095i	−0.856471	−	0.516195i	$-0.827348\pi$
$173$	1.72866	−	4.74947i	0.131428	−	0.361095i	0.987899	+	0.155100i	$0.0495700\pi$
$174$	13.1883	+	9.68287i	0.999802	+	0.734057i
$175$	8.94895	+	9.74182i	0.676477	+	0.736412i
$176$	−13.3189	−	18.5062i	−1.00395	−	1.39496i
$177$	−16.0506	−	10.3130i	−1.20644	−	0.775170i
$178$	−18.9202	−	8.25204i	−1.41813	−	0.618516i
$179$	−1.34848	−	2.33564i	−0.100790	−	0.174574i	0.811220	−	0.584741i	$-0.198804\pi$
$179$	−1.34848	−	2.33564i	−0.100790	−	0.174574i	−0.912010	+	0.410167i	$0.865470\pi$
$180$	−0.0180649	+	0.0810012i	−0.00134648	+	0.00603748i
$181$	4.79202	+	8.30002i	0.356188	+	0.616936i	0.987321	−	0.158739i	$-0.0507429\pi$
$181$	4.79202	+	8.30002i	0.356188	+	0.616936i	−0.631132	+	0.775675i	$0.717410\pi$
$182$	−4.14876	+	6.90649i	−0.307526	+	0.511943i
$183$	10.1632	−	11.0054i	0.751286	−	0.813539i
$184$	19.2736	+	7.28020i	1.42087	+	0.536704i
$185$	−0.0221336	−	0.00390275i	−0.00162729	−	0.000286936i
$186$	−10.2622	−	15.3795i	−0.752461	−	1.12768i
$187$	18.9081	+	22.5337i	1.38269	+	1.64783i
$188$	−0.596926	−	1.41510i	−0.0435353	−	0.103207i
$189$	13.6822	+	1.34024i	0.995237	+	0.0974881i
$190$	0.0315019	+	0.0209015i	0.00228539	+	0.00151636i
$191$	19.7220	−	16.5487i	1.42703	−	1.19742i	0.479592	−	0.877491i	$-0.340785\pi$
$191$	19.7220	−	16.5487i	1.42703	−	1.19742i	0.947441	−	0.319932i	$-0.103660\pi$
$192$	13.4385	+	3.37750i	0.969838	+	0.243750i
$193$	−2.42579	+	13.7573i	−0.174612	+	0.990274i	0.763979	+	0.645241i	$0.223243\pi$
$193$	−2.42579	+	13.7573i	−0.174612	+	0.990274i	−0.938591	+	0.345032i	$0.887868\pi$
$194$	−1.83647	+	1.93088i	−0.131851	+	0.138629i
$195$	−0.0492590	+	0.0153219i	−0.00352751	+	0.00109722i
$196$	10.4062	+	9.36544i	0.743299	+	0.668960i
$197$	18.1556	−	10.4821i	1.29353	−	0.746820i	0.314252	−	0.949340i	$-0.398246\pi$
$197$	18.1556	−	10.4821i	1.29353	−	0.746820i	0.979278	+	0.202520i	$0.0649130\pi$
$198$	−24.1802	+	0.418684i	−1.71841	+	0.0297546i
$199$	−20.8338	+	12.0284i	−1.47687	+	0.852671i	−0.999659	−	0.0261181i	$-0.991685\pi$
$199$	−20.8338	+	12.0284i	−1.47687	+	0.852671i	−0.477211	+	0.878789i	$0.658352\pi$
$200$	14.1406	+	0.171056i	0.999889	+	0.0120955i
$201$	−2.42271	−	0.115177i	−0.170885	−	0.00812399i
$202$	11.5725	+	11.0067i	0.814241	+	0.774426i
$203$	16.8608	+	5.29324i	1.18339	+	0.371512i
$204$	−17.6129	−	3.05828i	−1.23315	−	0.214122i
$205$	0.0108174	+	0.00393722i	0.000755522	+	0.000274987i
$206$	10.6367	+	0.662559i	0.741091	+	0.0461626i
$207$	17.9970	−	12.3951i	1.25088	−	0.861517i
$208$	2.33686	+	8.28999i	0.162032	+	0.574808i
$209$	−3.76789	+	10.3522i	−0.260630	+	0.716075i
$210$	0.00981296	+	0.0891020i	0.000677159	+	0.00614862i
$211$	−11.6247	+	13.8537i	−0.800275	+	0.953731i	−0.999657	−	0.0261913i	$-0.991662\pi$
$211$	−11.6247	+	13.8537i	−0.800275	+	0.953731i	0.199382	+	0.979922i	$0.436107\pi$
$212$	4.43457	+	1.36669i	0.304568	+	0.0938643i
$213$	23.6193	−	3.01655i	1.61837	−	0.206691i
$214$	11.6190	+	15.7391i	0.794260	+	1.07591i
$215$	0.0386332	+	0.0669147i	0.00263476	+	0.00456355i
$216$	11.0681	−	9.66941i	0.753088	−	0.657920i
$217$	−15.8586	−	12.1376i	−1.07655	−	0.823951i
$218$	−4.79103	+	10.9849i	−0.324490	+	0.743989i
$219$	−1.02302	−	1.34397i	−0.0691295	−	0.0908172i
$220$	−0.0351269	−	0.153726i	−0.00236826	−	0.0103642i
$221$	−3.80049	−	10.4418i	−0.255649	−	0.702389i
$222$	2.75048	+	2.87682i	0.184600	+	0.193080i
$223$	3.17794	−	8.73133i	0.212811	−	0.584693i	−0.786654	−	0.617394i	$-0.788189\pi$
$223$	3.17794	−	8.73133i	0.212811	−	0.584693i	0.999465	+	0.0327008i	$0.0104108\pi$
$224$	14.9152	−	1.23914i	0.996567	−	0.0827938i
$225$	8.69820	−	12.2198i	0.579880	−	0.814655i
$226$	3.21280	−	4.84218i	0.213712	−	0.322097i
$227$	0.618441	+	3.50735i	0.0410474	+	0.232791i	0.998429	−	0.0560355i	$-0.0178460\pi$
$227$	0.618441	+	3.50735i	0.0410474	+	0.232791i	−0.957381	+	0.288827i	$0.906735\pi$
$228$	−2.30621	−	6.28521i	−0.152733	−	0.416248i
$229$	15.5815	−	5.67119i	1.02965	−	0.374763i	0.228704	−	0.973496i	$-0.426551\pi$
$229$	15.5815	−	5.67119i	1.02965	−	0.374763i	0.800949	+	0.598733i	$0.204329\pi$
$230$	0.103246	+	0.0981976i	0.00680785	+	0.00647496i
$231$	−24.5697	+	8.86942i	−1.61656	+	0.583565i
$232$	16.4743	−	9.24755i	1.08159	−	0.607132i
$233$		−	5.77554i		−	0.378368i	−0.981942	−	0.189184i	$-0.939416\pi$
$233$		−	5.77554i		−	0.378368i	0.981942	−	0.189184i	$-0.0605843\pi$
$234$	8.63740	+	2.97545i	0.564645	+	0.194511i
$235$		−	0.0106218i		−	0.000692891i
$236$	−18.5026	+	11.9567i	−1.20441	+	0.778315i
$237$	1.34751	−	5.96875i	0.0875299	−	0.387712i
$238$	−19.0707	+	3.02275i	−1.23617	+	0.195936i
$239$	−11.8566	+	4.31546i	−0.766941	+	0.279144i	−0.695716	−	0.718317i	$-0.744913\pi$
$239$	−11.8566	+	4.31546i	−0.766941	+	0.279144i	−0.0712245	+	0.997460i	$0.522691\pi$
$240$	0.0765541	+	0.0576442i	0.00494155	+	0.00372092i
$241$	−21.6170	−	7.86793i	−1.39247	−	0.506818i	−0.466536	−	0.884502i	$-0.654498\pi$
$241$	−21.6170	−	7.86793i	−1.39247	−	0.506818i	−0.925934	+	0.377684i	$0.876720\pi$
$242$	27.2162	−	13.5314i	1.74953	−	0.869830i
$243$	−1.73516	−	15.4916i	−0.111310	−	0.993786i
$244$	−6.72298	−	15.9378i	−0.430395	−	1.02031i
$245$	0.0411364	+	0.0876499i	0.00262811	+	0.00559975i
$246$	−1.13152	−	1.69575i	−0.0721429	−	0.108117i
$247$	2.67499	−	3.18793i	0.170206	−	0.202843i
$248$	−21.0682	+	3.45266i	−1.33783	+	0.219244i
$249$	−5.15159	+	5.57845i	−0.326469	+	0.353520i
$250$	0.179297	+	0.0782001i	0.0113397	+	0.00494581i
$251$	14.4420	+	25.0143i	0.911572	+	1.57889i	0.811844	+	0.583875i	$0.198464\pi$
$251$	14.4420	+	25.0143i	0.911572	+	1.57889i	0.0997284	+	0.995015i	$0.468203\pi$
$252$	7.93760	−	13.7475i	0.500022	−	0.866013i
$253$	−20.7605	+	35.9583i	−1.30520	+	2.26068i
$254$	−5.72366	+	4.22535i	−0.359134	+	0.265122i
$255$	−0.104012	−	0.0668308i	−0.00651351	−	0.00418511i
$256$	9.96348	−	12.5192i	0.622717	−	0.782447i
$257$	5.28642	+	14.5243i	0.329758	+	0.906002i	0.988172	+	0.153346i	$0.0490051\pi$
$257$	5.28642	+	14.5243i	0.329758	+	0.906002i	−0.658415	+	0.752655i	$0.728773\pi$
$258$	1.49823	−	13.6009i	0.0932758	−	0.846753i
$259$	3.81572	+	1.98034i	0.237097	+	0.123052i
$260$	−0.00739224	+	0.0591069i	−0.000458447	+	0.00366566i
$261$	1.90097	−	19.9479i	0.117667	−	1.23475i
$262$	−18.5015	−	12.2758i	−1.14303	−	0.758401i
$263$	−17.4428	+	14.6362i	−1.07557	+	0.902508i	−0.995545	−	0.0942847i	$-0.969944\pi$
$263$	−17.4428	+	14.6362i	−1.07557	+	0.902508i	−0.0800223	+	0.996793i	$0.525499\pi$
$264$	−11.0971	+	25.6255i	−0.682976	+	1.57714i
$265$	0.0245844	+	0.0206288i	0.00151021	+	0.00126721i
$266$	−4.55150	−	5.61931i	−0.279070	−	0.344542i
$267$	3.20271	+	25.0769i	0.196003	+	1.53468i
$268$	−1.27708	+	2.49255i	−0.0780100	+	0.152257i
$269$	−16.1987	−	9.35233i	−0.987653	−	0.570222i	−0.0830813	−	0.996543i	$-0.526476\pi$
$269$	−16.1987	−	9.35233i	−0.987653	−	0.570222i	−0.904572	+	0.426321i	$0.859809\pi$
$270$	0.0965191	−	0.0318649i	0.00587397	−	0.00193924i
$271$	−20.0590	+	11.5811i	−1.21850	+	0.703499i	−0.964596	−	0.263731i	$-0.915047\pi$
$271$	−20.0590	+	11.5811i	−1.21850	+	0.703499i	−0.253900	+	0.967230i	$0.581713\pi$
$272$	−11.6196	+	17.0609i	−0.704541	+	1.03447i
$273$	9.86747	+	0.0259856i	0.597207	+	0.00157272i
$274$	4.69740	−	19.4697i	0.283781	−	1.17621i
$275$	−4.94894	+	28.0669i	−0.298433	+	1.69250i
$276$	−4.44648	−	24.8382i	−0.267647	−	1.49508i
$277$	−12.8292	+	10.7650i	−0.770834	+	0.646807i	−0.940922	−	0.338622i	$-0.890039\pi$
$277$	−12.8292	+	10.7650i	−0.770834	+	0.646807i	0.170088	+	0.985429i	$0.445595\pi$
$278$	−1.99794	−	4.01855i	−0.119829	−	0.241017i
$279$	−9.72850	+	20.4479i	−0.582430	+	1.22419i
$280$	0.0983738	+	0.0321955i	0.00587896	+	0.00192405i
$281$	3.21906	+	3.83632i	0.192033	+	0.228856i	0.853466	−	0.521148i	$-0.174496\pi$
$281$	3.21906	+	3.83632i	0.192033	+	0.228856i	−0.661433	+	0.750004i	$0.730052\pi$
$282$	−1.11322	+	1.51624i	−0.0662915	+	0.0902905i
$283$	18.4885	−	22.0337i	1.09903	−	1.30977i	0.152083	−	0.988368i	$-0.451402\pi$
$283$	18.4885	−	22.0337i	1.09903	−	1.30977i	0.946943	−	0.321400i	$-0.104154\pi$
$284$	8.09772	−	26.2752i	0.480511	−	1.55915i
$285$	0.00219874	−	0.0462496i	0.000130242	−	0.00273959i
$286$	−17.2487	+	1.94562i	−1.01994	+	0.115047i
$287$	−1.74858	−	1.33829i	−0.103215	−	0.0789970i
$288$	−4.88648	−	16.2518i	−0.287938	−	0.957649i
$289$	4.81530	−	8.34034i	0.283253	−	0.490608i
$290$	0.129835	−	0.0146451i	0.00762414	−	0.000859988i
$291$	3.18353	+	0.718713i	0.186622	+	0.0421317i
$292$	−1.90132	+	0.434459i	−0.111267	+	0.0254248i
$293$	4.42501	+	12.1576i	0.258512	+	0.710256i	0.999260	+	0.0384727i	$0.0122492\pi$
$293$	4.42501	+	12.1576i	0.258512	+	0.710256i	−0.740748	+	0.671783i	$0.765529\pi$
$294$	3.31407	−	16.8231i	0.193281	−	0.981144i
$295$	−0.150041	+	0.0264563i	−0.00873574	+	0.00154035i
$296$	4.33737	−	1.51951i	0.252104	−	0.0883199i
$297$	15.6231	+	25.1636i	0.906543	+	1.46014i
$298$	−5.78069	−	11.6270i	−0.334866	−	0.673532i
$299$	12.0152	−	10.0819i	0.694857	−	0.583054i
$300$	−8.69902	−	14.9768i	−0.502238	−	0.864685i
$301$	−3.21673	−	14.4252i	−0.185409	−	0.831453i
$302$	19.7851	−	5.83645i	1.13850	−	0.335850i
$303$	4.30753	−	19.0801i	0.247461	−	1.09612i
$304$	−7.70934	−	0.573906i	−0.442161	−	0.0329158i
$305$		−	0.119630i		−	0.00684999i
$306$	7.84328	+	20.4410i	0.448370	+	1.16853i
$307$	−20.8425	−	12.0334i	−1.18954	−	0.686782i	−0.231339	−	0.972873i	$-0.574311\pi$
$307$	−20.8425	−	12.0334i	−1.18954	−	0.686782i	−0.958202	+	0.286091i	$0.907644\pi$
$308$	−2.39684	+	30.0672i	−0.136573	+	1.71324i
$309$	−5.98208	−	11.6009i	−0.340308	−	0.659952i
$310$	−0.143531	−	0.0346294i	−0.00815203	−	0.00196682i
$311$	−12.0906	−	10.1452i	−0.685597	−	0.575284i	0.232039	−	0.972706i	$-0.425460\pi$
$311$	−12.0906	−	10.1452i	−0.685597	−	0.575284i	−0.917636	+	0.397422i	$0.869905\pi$
$312$	7.24995	−	7.66261i	0.410447	−	0.433810i
$313$	2.06531	+	0.751712i	0.116738	+	0.0424893i	0.399729	−	0.916633i	$-0.369104\pi$
$313$	2.06531	+	0.751712i	0.116738	+	0.0424893i	−0.282991	+	0.959123i	$0.591327\pi$
$314$	−12.9834	+	6.45508i	−0.732695	+	0.364281i
$315$	0.0875328	−	0.0662661i	0.00493192	−	0.00373367i
$316$	−5.63325	−	4.26484i	−0.316895	−	0.239916i
$317$	−4.17377	+	0.735948i	−0.234422	+	0.0413350i	−0.289625	−	0.957140i	$-0.593531\pi$
$317$	−4.17377	+	0.735948i	−0.234422	+	0.0413350i	0.0552028	+	0.998475i	$0.482419\pi$
$318$	−1.34735	−	5.52128i	−0.0755558	−	0.309618i
$319$	13.0221	+	35.7779i	0.729097	+	2.00318i
$320$	0.0971403	−	0.0529931i	0.00543031	−	0.00296241i
$321$	9.25475	−	22.1005i	0.516550	−	1.23353i
$322$	−13.2161	−	23.8361i	−0.736507	−	1.32833i
$323$	9.97350			0.554940
$324$	−17.1175	−	5.56709i	−0.950970	−	0.309283i
$325$	5.38296	−	9.32356i	0.298593	−	0.517178i
$326$	14.9407	−	11.0296i	0.827487	−	0.610871i
$327$	14.5593	−	1.85946i	0.805133	−	0.102828i
$328$	−2.32299	+	0.380693i	−0.128266	+	0.0210203i
$329$	−0.608554	+	1.93845i	−0.0335507	+	0.106870i
$330$	−0.139593	+	0.133462i	−0.00768435	+	0.00734687i
$331$	18.9659	−	3.34420i	1.04246	−	0.183814i	0.373899	−	0.927470i	$-0.378021\pi$
$331$	18.9659	−	3.34420i	1.04246	−	0.183814i	0.668563	+	0.743656i	$0.266910\pi$
$332$	3.40778	+	8.07864i	0.187026	+	0.443373i
$333$	1.29806	−	4.69861i	0.0711335	−	0.257482i
$334$	13.4863	+	8.94817i	0.737936	+	0.489622i
$335$	−0.0148377	+	0.0124503i	−0.000810670	+	0.000680233i
$336$	−10.6683	−	14.9059i	−0.582005	−	0.813185i
$337$	2.39033	−	13.5562i	0.130210	−	0.738455i	−0.847867	−	0.530209i	$-0.822113\pi$
$337$	2.39033	−	13.5562i	0.130210	−	0.738455i	0.978077	−	0.208246i	$-0.0667754\pi$
$338$	−11.4978	−	2.77404i	−0.625397	−	0.150888i
$339$	−7.10908	−	0.337970i	−0.386112	−	0.0183560i
$340$	−0.119902	+	0.0774826i	−0.00650257	+	0.00420208i
$341$		−	43.0255i		−	2.32996i
$342$	−5.16107	+	6.37157i	−0.279079	+	0.344535i
$343$	−2.48557	−	18.3527i	−0.134208	−	0.990953i
$344$	−13.5866	−	8.06490i	−0.732539	−	0.434830i
$345$	0.0384303	−	0.170226i	0.00206902	−	0.00916466i
$346$	−1.67643	+	6.94845i	−0.0901256	+	0.373551i
$347$	−4.98051	+	28.2459i	−0.267368	+	1.51632i	0.494840	+	0.868984i	$0.335227\pi$
$347$	−4.98051	+	28.2459i	−0.267368	+	1.51632i	−0.762208	+	0.647333i	$0.775884\pi$
$348$	−20.0684	−	11.5168i	−1.07578	−	0.617366i
$349$	−3.14734	−	17.8495i	−0.168473	−	0.955460i	−0.945411	−	0.325882i	$-0.894339\pi$
$349$	−3.14734	−	17.8495i	−0.168473	−	0.955460i	0.776937	−	0.629578i	$-0.216772\pi$
$350$	−14.1202	−	12.2716i	−0.754756	−	0.655947i
$351$	−2.29464	−	10.9509i	−0.122479	−	0.584514i
$352$	21.6506	+	23.8956i	1.15398	+	1.27364i
$353$	−6.55109	+	17.9990i	−0.348679	+	0.957988i	0.634108	+	0.773245i	$0.281368\pi$
$353$	−6.55109	+	17.9990i	−0.348679	+	0.957988i	−0.982787	+	0.184743i	$0.940855\pi$
$354$	24.1908	+	11.9486i	1.28572	+	0.635059i
$355$	0.122227	−	0.145665i	0.00648714	−	0.00773107i
$356$	27.8967	+	8.59746i	1.47852	+	0.455664i
$357$	15.1531	+	18.1556i	0.801986	+	0.960898i
$358$	2.26525	+	3.06852i	0.119722	+	0.162176i
$359$	−7.52617	+	13.0357i	−0.397216	+	0.687998i	−0.993381	−	0.114864i	$-0.963357\pi$
$359$	−7.52617	+	13.0357i	−0.397216	+	0.687998i	0.596165	+	0.802862i	$0.296690\pi$
$360$	0.0125467	−	0.116695i	0.000661270	−	0.00615035i
$361$	−7.63240	−	13.2197i	−0.401705	−	0.695774i
$362$	−8.04992	−	10.9044i	−0.423094	−	0.573124i
$363$	−31.3179	−	20.1226i	−1.64377	−	1.05616i
$364$	4.73547	−	10.3633i	0.248206	−	0.543187i
$365$	−0.0132834	−	0.00234223i	−0.000695287	−	0.000122598i
$366$	−12.5379	+	17.0769i	−0.655365	+	0.892622i
$367$	9.62497	−	1.69714i	0.502419	−	0.0885901i	0.0833060	−	0.996524i	$-0.473452\pi$
$367$	9.62497	−	1.69714i	0.502419	−	0.0885901i	0.419113	+	0.907934i	$0.362341\pi$
$368$	−28.2392	−	7.17573i	−1.47207	−	0.374061i
$369$	−1.07267	+	2.25460i	−0.0558410	+	0.117370i
$370$	0.0317230	+	0.00197603i	0.00164920	+	0.000102729i
$371$	−3.30471	−	5.17321i	−0.171572	−	0.268580i
$372$	16.8594	+	19.9861i	0.874118	+	1.03623i
$373$	−3.35172	+	19.0086i	−0.173546	+	0.984226i	0.766263	+	0.642527i	$0.222114\pi$
$373$	−3.35172	+	19.0086i	−0.173546	+	0.984226i	−0.939809	+	0.341700i	$0.888997\pi$
$374$	−30.1435	−	28.6695i	−1.55868	−	1.48246i
$375$	−0.0303504	−	0.237640i	−0.00156729	−	0.0122717i
$376$	1.06318	+	1.89402i	0.0548291	+	0.0976766i
$377$		−	14.3826i		−	0.740742i
$378$	−19.4401	+	0.285401i	−0.999892	+	0.0146794i
$379$		−	30.5848i		−	1.57104i	−0.618838	−	0.785519i	$-0.712396\pi$
$379$		−	30.5848i		−	1.57104i	0.618838	−	0.785519i	$-0.287604\pi$
$380$	−0.0475828	−	0.0243795i	−0.00244095	−	0.00125064i
$381$	8.03702	+	3.36556i	0.411749	+	0.172423i
$382$	−25.0921	+	26.3822i	−1.28382	+	1.34983i
$383$	5.15207	−	29.2188i	0.263258	−	1.49301i	−0.510691	−	0.859764i	$-0.670610\pi$
$383$	5.15207	−	29.2188i	0.263258	−	1.49301i	0.773949	−	0.633248i	$-0.218279\pi$
$384$	−19.4205	−	2.61620i	−0.991048	−	0.133507i
$385$	−0.0960926	+	0.185152i	−0.00489733	+	0.00943620i
$386$	1.22822	−	19.7177i	0.0625147	−	1.00361i
$387$	−15.2426	+	6.96457i	−0.774826	+	0.354029i
$388$	2.27472	−	3.00458i	0.115481	−	0.152535i
$389$	−1.14509	+	0.201910i	−0.0580584	+	0.0102373i	−0.202602	−	0.979261i	$-0.564940\pi$
$389$	−1.14509	+	0.201910i	−0.0580584	+	0.0102373i	0.144544	+	0.989498i	$0.453829\pi$
$390$	0.0667950	−	0.0293402i	0.00338229	−	0.00148570i
$391$	37.0187	+	6.52740i	1.87212	+	0.330105i
$392$	−16.1084	−	11.5117i	−0.813596	−	0.581430i
$393$	−1.29135	+	27.1631i	−0.0651401	+	1.37020i
$394$	−23.8525	+	17.6085i	−1.20167	+	0.887102i
$395$	−0.0244325	−	0.0423184i	−0.00122933	−	0.00212927i
$396$	33.9141	−	4.42131i	1.70425	−	0.222179i
$397$	12.2364	−	21.1941i	0.614127	−	1.06370i	−0.376410	−	0.926453i	$-0.622841\pi$
$397$	12.2364	−	21.1941i	0.614127	−	1.06370i	0.990537	−	0.137246i	$-0.0438252\pi$
$398$	27.3711	−	20.2060i	1.37199	−	1.01284i
$399$	−3.05104	+	8.31447i	−0.152743	+	0.416244i
$400$	−19.8989	+	2.00111i	−0.994943	+	0.100055i
$401$	−0.963922	+	1.14876i	−0.0481360	+	0.0573662i	−0.789575	−	0.613654i	$-0.789699\pi$
$401$	−0.963922	+	1.14876i	−0.0481360	+	0.0573662i	0.741439	+	0.671020i	$0.234144\pi$
$402$	3.42290	−	0.222178i	0.170719	−	0.0110812i
$403$	−5.55887	+	15.2729i	−0.276907	+	0.760795i
$404$	−18.0076	−	13.6333i	−0.895913	−	0.678280i
$405$	−0.0941118	−	0.0814858i	−0.00467645	−	0.00404906i
$406$	−24.5335	−	4.76591i	−1.21758	−	0.236528i
$407$	1.60834	+	9.12136i	0.0797225	+	0.452129i
$408$	25.2362	+	1.50589i	1.24938	+	0.0745527i
$409$	3.33542	−	18.9161i	0.164926	−	0.935340i	−0.784215	−	0.620489i	$-0.786934\pi$
$409$	3.33542	−	18.9161i	0.164926	−	0.935340i	0.949141	−	0.314851i	$-0.101955\pi$
$410$	−0.0158259	−	0.00381826i	−0.000781583	−	0.000188570i
$411$	−23.4227	+	7.28558i	−1.15536	+	0.359371i
$412$	−15.0527	+	0.754977i	−0.741595	+	0.0371951i
$413$	28.8979	+	3.76809i	1.42197	+	0.185415i
$414$	−23.3264	+	20.2716i	−1.14643	+	0.996296i
$415$			0.0606387i			0.00297664i
$416$	−4.59808	−	11.2795i	−0.225440	−	0.553024i
$417$	−2.97116	+	4.62418i	−0.145498	+	0.226447i
$418$	3.65404	−	15.1452i	0.178725	−	0.740776i
$419$	1.32687	−	7.52504i	0.0648217	−	0.367622i	−0.935091	−	0.354408i	$-0.884682\pi$
$419$	1.32687	−	7.52504i	0.0648217	−	0.367622i	0.999913	−	0.0132144i	$-0.00420639\pi$
$420$	−0.0279142	−	0.123660i	−0.00136207	−	0.00603398i
$421$	−4.57960	+	3.84274i	−0.223196	+	0.187284i	−0.747528	−	0.664230i	$-0.768759\pi$
$421$	−4.57960	+	3.84274i	−0.223196	+	0.187284i	0.524332	+	0.851514i	$0.324315\pi$
$422$	14.1401	−	21.3114i	0.688331	−	1.03742i
$423$	2.29338	+	0.218551i	0.111508	+	0.0106263i
$424$	−6.44855	−	1.21766i	−0.313169	−	0.0591347i
$425$	25.4095	−	4.48037i	1.23254	−	0.217330i
$426$	−32.7140	+	7.98318i	−1.58500	+	0.386786i
$427$	−6.85395	+	21.8322i	−0.331686	+	1.05653i
$428$	−18.8231	−	20.2765i	−0.909850	−	0.980100i
$429$	12.8764	+	16.9161i	0.621678	+	0.816715i
$430$	−0.0648983	−	0.0879114i	−0.00312968	−	0.00423947i
$431$	−2.53108	+	4.38396i	−0.121918	+	0.211168i	−0.920524	−	0.390686i	$-0.872238\pi$
$431$	−2.53108	+	4.38396i	−0.121918	+	0.211168i	0.798606	+	0.601854i	$0.205571\pi$
$432$	−14.0212	+	15.3429i	−0.674598	+	0.738186i
$433$	−29.5886			−1.42194			−0.710968	−	0.703225i	$-0.751743\pi$
$433$	−29.5886			−1.42194			−0.710968	+	0.703225i	$0.751743\pi$
$434$	24.2101	+	14.5431i	1.16212	+	0.698091i
$435$	−0.0969233	−	0.127331i	−0.00464712	−	0.00610504i
$436$	4.99158	−	16.1965i	0.239053	−	0.775672i
$437$	4.81491	+	13.2288i	0.230328	+	0.632822i
$438$	1.65070	+	1.72652i	0.0788733	+	0.0824964i
$439$	−40.5976	+	7.15845i	−1.93762	+	0.341654i	−0.999982	−	0.00596909i	$-0.998100\pi$
$439$	−40.5976	+	7.15845i	−1.93762	+	0.341654i	−0.937634	+	0.347623i	$0.886989\pi$
$440$	0.0737319	+	0.210464i	0.00351503	+	0.0100335i
$441$	−19.7711	+	7.07839i	−0.941481	+	0.337066i
$442$	6.99602	+	14.0714i	0.332767	+	0.669308i
$443$	2.65490	+	0.966303i	0.126138	+	0.0459105i	0.404318	−	0.914619i	$-0.367509\pi$
$443$	2.65490	+	0.966303i	0.126138	+	0.0459105i	−0.278180	+	0.960529i	$0.589731\pi$
$444$	−4.32127	−	3.60681i	−0.205079	−	0.171172i
$445$	0.154654	+	0.129770i	0.00733130	+	0.00615169i
$446$	−3.08192	+	12.7739i	−0.145933	+	0.604862i
$447$	−8.59651	+	13.3792i	−0.406601	+	0.632816i
$448$	−20.7640	+	4.10566i	−0.981007	+	0.193974i
$449$	28.5786	+	16.4999i	1.34871	+	0.778677i	0.988067	−	0.154027i	$-0.0492243\pi$
$449$	28.5786	+	16.4999i	1.34871	+	0.778677i	0.360642	+	0.932704i	$0.382558\pi$
$450$	−10.2866	+	18.5513i	−0.484913	+	0.874518i
$451$		−	4.74402i		−	0.223387i
$452$	−3.74739	+	7.31401i	−0.176262	+	0.344022i
$453$	−18.5604	−	17.1401i	−0.872043	−	0.805313i
$454$	−1.42506	−	4.83086i	−0.0668816	−	0.226723i
$455$	0.0580317	−	0.0533086i	0.00272057	−	0.00249914i
$456$	4.23723	+	8.46704i	0.198426	+	0.396505i
$457$	−5.75563	+	4.82954i	−0.269237	+	0.225917i	−0.767403	−	0.641165i	$-0.778451\pi$
$457$	−5.75563	+	4.82954i	−0.269237	+	0.225917i	0.498166	+	0.867082i	$0.334007\pi$
$458$	−20.9977	+	10.4396i	−0.981158	+	0.487812i
$459$	16.5697	−	21.0825i	0.773408	−	0.984046i
$460$	−0.160658	−	0.121631i	−0.00749071	−	0.00567108i
$461$	23.5584	−	4.15398i	1.09722	−	0.193470i	0.404404	−	0.914581i	$-0.367479\pi$
$461$	23.5584	−	4.15398i	1.09722	−	0.193470i	0.692820	+	0.721110i	$0.256368\pi$
$462$	33.1218	−	16.3589i	1.54097	−	0.761084i
$463$	2.52793	+	6.94544i	0.117483	+	0.322782i	0.984471	−	0.175547i	$-0.0561694\pi$
$463$	2.52793	+	6.94544i	0.117483	+	0.322782i	−0.866988	+	0.498329i	$0.833947\pi$
$464$	−21.6854	+	15.6070i	−1.00672	+	0.724538i
$465$	0.0537095	+	0.172673i	0.00249072	+	0.00800752i
$466$	0.915511	+	8.11637i	0.0424102	+	0.375984i
$467$	6.92839	−	12.0003i	0.320608	−	0.555309i	−0.660006	−	0.751260i	$-0.729446\pi$
$467$	6.92839	−	12.0003i	0.320608	−	0.555309i	0.980614	+	0.195952i	$0.0627796\pi$
$468$	−12.6098	−	2.81224i	−0.582889	−	0.129996i
$469$	3.42116	−	1.42205i	0.157974	−	0.0656644i
$470$	0.00168372	+	0.0149269i	7.76642e−5	+	0.000688524i
$471$	14.9401	+	9.59940i	0.688403	+	0.442317i
$472$	24.1064	−	19.7357i	1.10959	−	0.908409i
$473$	20.4676	−	24.3923i	0.941101	−	1.12156i
$474$	−0.947515	+	8.60150i	−0.0435208	+	0.395080i
$475$	6.21123	+	7.40226i	0.284991	+	0.339639i
$476$	26.3209	−	7.27087i	1.20642	−	0.333260i
$477$	−4.95985	+	4.88362i	−0.227096	+	0.223606i
$478$	15.9781	−	7.94397i	0.730819	−	0.363349i
$479$	16.1509	−	13.5522i	0.737952	−	0.619215i	−0.194335	−	0.980935i	$-0.562255\pi$
$479$	16.1509	−	13.5522i	0.737952	−	0.619215i	0.932287	+	0.361720i	$0.117810\pi$
$480$	−0.116719	−	0.0688725i	−0.00532747	−	0.00314359i
$481$	0.607557	−	3.44563i	0.0277022	−	0.157107i
$482$	31.6255	+	7.63020i	1.44050	+	0.347546i
$483$	−16.7662	+	28.8640i	−0.762887	+	1.31336i
$484$	−36.1021	+	23.3299i	−1.64101	+	1.06045i
$485$	0.0225712	−	0.0130315i	0.00102490	−	0.000591728i
$486$	4.89407	+	21.4953i	0.221999	+	0.975047i
$487$	4.59642	+	2.65375i	0.208284	+	0.120253i	0.600514	−	0.799615i	$-0.294963\pi$
$487$	4.59642	+	2.65375i	0.208284	+	0.120253i	−0.392230	+	0.919867i	$0.628296\pi$
$488$	11.9742	+	21.3317i	0.542046	+	0.965641i
$489$	−20.9793	−	8.78523i	−0.948718	−	0.397282i
$490$	−0.0717029	−	0.116654i	−0.00323921	−	0.00526988i
$491$	−30.4604	−	25.5593i	−1.37466	−	1.15348i	−0.971141	−	0.238506i	$-0.923342\pi$
$491$	−30.4604	−	25.5593i	−1.37466	−	1.15348i	−0.403520	−	0.914971i	$-0.632213\pi$
$492$	1.85893	+	2.20368i	0.0838068	+	0.0993496i
$493$	26.4049	−	22.1563i	1.18922	−	0.997871i
$494$	−3.25383	+	4.90403i	−0.146397	+	0.220643i
$495$	0.227992	+	0.0629864i	0.0102475	+	0.00283103i
$496$	29.0598	−	8.19166i	1.30483	−	0.367816i
$497$	−30.6517	+	19.5807i	−1.37492	+	0.878313i
$498$	6.35526	−	8.65602i	0.284786	−	0.387885i
$499$	−3.57679	−	9.82714i	−0.160119	−	0.439923i	0.833526	−	0.552480i	$-0.186318\pi$
$499$	−3.57679	−	9.82714i	−0.160119	−	0.439923i	−0.993645	+	0.112557i	$0.964096\pi$
$500$	−0.264362	−	0.0814735i	−0.0118226	−	0.00364360i
$501$	0.941302	−	19.7999i	0.0420543	−	0.884596i
$502$	−24.2605	−	32.8634i	−1.08280	−	1.46676i
$503$	−7.56216	+	13.0980i	−0.337180	+	0.584013i	−0.983901	−	0.178714i	$-0.942806\pi$
$503$	−7.56216	+	13.0980i	−0.337180	+	0.584013i	0.646721	+	0.762727i	$0.276140\pi$
$504$	−8.97553	+	20.5777i	−0.399802	+	0.916602i
$505$	−0.0781027	−	0.135278i	−0.00347552	−	0.00601978i
$506$	23.4749	−	53.8231i	1.04358	−	2.39273i
$507$	4.30248	+	13.8322i	0.191080	+	0.614310i
$508$	7.37369	−	6.84517i	0.327155	−	0.303705i
$509$	10.3805	−	12.3710i	0.460108	−	0.548335i	−0.485248	−	0.874377i	$-0.661271\pi$
$509$	10.3805	−	12.3710i	0.460108	−	0.548335i	0.945355	+	0.326042i	$0.105715\pi$
$510$	0.156763	+	0.0774299i	0.00694156	+	0.00342865i
$511$	2.29000	+	1.18850i	0.101304	+	0.0525760i
$512$	−12.0172	+	19.1725i	−0.531091	+	0.847315i
$513$	9.94062	+	1.42635i	0.438889	+	0.0629751i
$514$	−9.73134	−	19.5731i	−0.429231	−	0.863331i
$515$	−0.0979485	−	0.0356503i	−0.00431613	−	0.00157094i
$516$	0.0504783	+	19.3508i	0.00222218	+	0.851872i
$517$	−4.11332	+	1.49713i	−0.180904	+	0.0658436i
$518$	−5.67615	−	2.17812i	−0.249396	−	0.0957012i
$519$	8.35922	−	2.60011i	0.366929	−	0.114132i
$520$	0.00101898	−	0.0842349i	4.46851e−5	−	0.00369394i
$521$		−	14.2206i		−	0.623018i	−0.950243	−	0.311509i	$-0.899166\pi$
$521$		−	14.2206i		−	0.623018i	0.950243	−	0.311509i	$-0.100834\pi$
$522$	0.490611	+	28.3342i	0.0214735	+	1.24015i
$523$		−	21.2863i		−	0.930786i	−0.885104	−	0.465393i	$-0.845913\pi$
$523$		−	21.2863i		−	0.930786i	0.885104	−	0.465393i	$-0.154087\pi$
$524$	27.9461	+	14.3184i	1.22083	+	0.625503i
$525$	−4.03803	+	22.5534i	−0.176234	+	0.984309i
$526$	22.1923	−	23.3333i	0.967630	−	1.01738i
$527$	−36.6027	+	13.3223i	−1.59444	+	0.580328i
$528$	11.5327	−	37.7706i	0.501895	−	1.64375i
$529$	5.21968	+	29.6023i	0.226943	+	1.28705i
$530$	−0.0378185	−	0.0250926i	−0.00164273	−	0.00108995i
$531$	−2.62504	−	32.9401i	−0.113917	−	1.42948i
$532$	7.28698	+	7.17535i	0.315931	+	0.311091i
$533$	−0.612924	+	1.68400i	−0.0265487	+	0.0729419i
$534$	−8.47585	−	34.7329i	−0.366786	−	1.50304i
$535$	−0.0654424	−	0.179802i	−0.00282932	−	0.00777350i
$536$	1.39957	−	3.70522i	0.0604524	−	0.160041i
$537$	1.80431	−	4.30874i	0.0778619	−	0.185936i
$538$	24.2466	+	10.5751i	1.04534	+	0.455925i
$539$	28.1445	−	28.2843i	1.21227	−	1.21829i
$540$	−0.130587	+	0.0600795i	−0.00561959	+	0.00258541i
$541$	8.54769	+	14.8050i	0.367494	+	0.636518i	0.989173	−	0.146754i	$-0.0468826\pi$
$541$	8.54769	+	14.8050i	0.367494	+	0.636518i	−0.621679	+	0.783272i	$0.713549\pi$
$542$	26.3531	−	19.4545i	1.13196	−	0.835644i
$543$	−6.41189	+	15.3117i	−0.275161	+	0.657089i
$544$	13.6246	−	25.8176i	0.584151	−	1.10692i
$545$	0.0753430	−	0.0897903i	0.00322734	−	0.00384619i
$546$	−13.8709	+	1.52763i	−0.593619	+	0.0653764i
$547$	15.6179	−	42.9099i	0.667774	−	1.83469i	0.130180	−	0.991490i	$-0.458444\pi$
$547$	15.6179	−	42.9099i	0.667774	−	1.83469i	0.537594	−	0.843204i	$-0.319333\pi$
$548$	−3.51502	+	28.1055i	−0.150154	+	1.20061i
$549$	25.8296	+	2.46147i	1.10238	+	0.105053i
$550$	2.50574	−	40.2269i	0.106845	−	1.71528i
$551$	12.1306	+	4.41518i	0.516781	+	0.188093i
$552$	10.1859	+	34.2003i	0.433540	+	1.45566i
$553$	2.03433	+	9.12281i	0.0865086	+	0.387941i
$554$	16.3225	−	17.1617i	0.693478	−	0.729131i
$555$	−0.0178411	−	0.0345988i	−0.000757311	−	0.00146864i
$556$	3.44472	+	5.33057i	0.146088	+	0.226067i
$557$	0.203736	−	0.117627i	0.00863257	−	0.00498402i	−0.495678	−	0.868507i	$-0.665080\pi$
$557$	0.203736	−	0.117627i	0.00863257	−	0.00498402i	0.504310	+	0.863523i	$0.331747\pi$
$558$	10.4302	−	30.2777i	0.441544	−	1.28176i
$559$	−10.4169	+	6.01420i	−0.440588	+	0.254374i
$560$	−0.143348	−	0.0296507i	−0.00605757	−	0.00125297i
$561$	−11.2200	+	49.6987i	−0.473709	+	2.09828i
$562$	−5.13186	−	4.88092i	−0.216475	−	0.205889i
$563$	2.49355	−	14.1416i	0.105091	−	0.595998i	−0.886094	−	0.463506i	$-0.846591\pi$
$563$	2.49355	−	14.1416i	0.105091	−	0.595998i	0.991184	−	0.132492i	$-0.0422978\pi$
$564$	1.32407	−	2.30723i	0.0557533	−	0.0971520i
$565$	−0.0435389	+	0.0365335i	−0.00183170	+	0.00153698i
$566$	−22.4892	+	33.8947i	−0.945292	+	1.42470i
$567$	12.5066	+	20.2629i	0.525228	+	0.850961i
$568$	−7.21472	+	38.2082i	−0.302723	+	1.60318i
$569$	−6.42183	−	7.65324i	−0.269217	−	0.320841i	0.614450	−	0.788955i	$-0.289378\pi$
$569$	−6.42183	−	7.65324i	−0.269217	−	0.320841i	−0.883668	+	0.468115i	$0.844933\pi$
$570$	0.00424138	+	0.0653432i	0.000177652	+	0.00273693i
$571$	−8.40632	−	1.48226i	−0.351794	−	0.0620307i	−0.00504093	−	0.999987i	$-0.501605\pi$
$571$	−8.40632	−	1.48226i	−0.351794	−	0.0620307i	−0.346753	+	0.937957i	$0.612716\pi$
$572$	23.9312	−	5.46836i	1.00061	−	0.228644i
$573$	43.4973	+	9.81997i	1.81713	+	0.410235i
$574$	2.66942	+	1.60353i	0.111419	+	0.0669301i
$575$	18.2097	+	31.5401i	0.759397	+	1.31531i
$576$	9.44314	+	22.0642i	0.393464	+	0.919340i
$577$	5.95537	+	10.3150i	0.247925	+	0.429419i	0.962950	−	0.269680i	$-0.0869179\pi$
$577$	5.95537	+	10.3150i	0.247925	+	0.429419i	−0.715025	+	0.699099i	$0.753585\pi$
$578$	−5.44488	+	12.4840i	−0.226477	+	0.519266i
$579$	−21.5052	+	11.0893i	−0.893725	+	0.460855i
$580$	−0.180135	+	0.0411615i	−0.00747971	+	0.00170914i
$581$	3.47417	−	11.0664i	0.144133	−	0.459112i
$582$	−4.58774	−	0.505372i	−0.190168	−	0.0209483i
$583$	4.52341	−	12.4280i	0.187340	−	0.514713i
$584$	2.60306	−	0.911934i	0.107716	−	0.0377361i
$585$	−0.0727931	−	0.0518149i	−0.00300962	−	0.00214228i
$586$	−8.14565	−	16.3837i	−0.336494	−	0.676804i
$587$	32.8836	+	11.9686i	1.35725	+	0.493999i	0.915203	−	0.402993i	$-0.132030\pi$
$587$	32.8836	+	11.9686i	1.35725	+	0.493999i	0.442047	+	0.896992i	$0.354252\pi$
$588$	−1.99055	+	24.1669i	−0.0820890	+	0.996625i
$589$	−11.1750	−	9.37694i	−0.460458	−	0.386370i
$590$	0.206660	−	0.0609629i	0.00850804	−	0.00250980i
$591$	33.4931	+	14.0254i	1.37772	+	0.576930i
$592$	−5.85444	+	2.82291i	−0.240616	+	0.116021i
$593$	−31.0652	+	17.9355i	−1.27570	+	0.736523i	−0.976054	−	0.217528i	$-0.930201\pi$
$593$	−31.0652	+	17.9355i	−1.27570	+	0.736523i	−0.299642	+	0.954052i	$0.596867\pi$
$594$	−25.9440	−	32.8859i	−1.06449	−	1.34933i
$595$	0.187266	+	0.0244182i	0.00767717	+	0.00100105i
$596$	9.96666	+	15.4231i	0.408250	+	0.631753i
$597$	−38.4338	−	16.0944i	−1.57299	−	0.658701i
$598$	−15.2868	+	16.0728i	−0.625125	+	0.657264i
$599$	6.79622	−	2.47362i	0.277686	−	0.101070i	−0.199423	−	0.979913i	$-0.563907\pi$
$599$	6.79622	−	2.47362i	0.277686	−	0.101070i	0.477109	+	0.878844i	$0.341685\pi$
$600$	14.5988	+	19.6680i	0.595993	+	0.802942i
$601$	−35.5366	−	12.9343i	−1.44957	−	0.527599i	−0.507097	−	0.861889i	$-0.669281\pi$
$601$	−35.5366	−	12.9343i	−1.44957	−	0.527599i	−0.942470	+	0.334290i	$0.891504\pi$
$602$	6.80708	+	19.7618i	0.277436	+	0.805432i
$603$	−2.38288	−	3.45981i	−0.0970383	−	0.140895i
$604$	−26.8789	+	11.3382i	−1.09369	+	0.461345i
$605$	−0.292760	+	0.0516215i	−0.0119024	+	0.00209871i
$606$	−3.02889	+	27.4961i	−0.123040	+	1.11695i
$607$	−3.27497	−	8.99792i	−0.132927	−	0.365214i	0.855316	−	0.518107i	$-0.173363\pi$
$607$	−3.27497	−	8.99792i	−0.132927	−	0.365214i	−0.988243	+	0.152893i	$0.951141\pi$
$608$	10.9249	−	0.415535i	0.443064	−	0.0168522i
$609$	10.3931	+	28.7905i	0.421150	+	1.16665i
$610$	0.0189632	+	0.168116i	0.000767796	+	0.00680683i
$611$	1.65354			0.0668952
$612$	−14.2624	−	27.4825i	−0.576522	−	1.11091i
$613$	−16.2468			−0.656202			−0.328101	−	0.944643i	$-0.606409\pi$
$613$	−16.2468			−0.656202			−0.328101	+	0.944643i	$0.606409\pi$
$614$	31.1974	+	13.6067i	1.25903	+	0.549122i
$615$	0.00592204	+	0.0190390i	0.000238800	+	0.000767728i
$616$	−1.39782	−	42.6334i	−0.0563196	−	1.71775i
$617$	−6.34195	−	17.4244i	−0.255317	−	0.701479i	−0.999441	−	0.0334366i	$-0.989355\pi$
$617$	−6.34195	−	17.4244i	−0.255317	−	0.701479i	0.744123	−	0.668042i	$-0.232867\pi$
$618$	10.2455	+	15.3545i	0.412136	+	0.617649i
$619$	0.355165	−	0.975807i	0.0142753	−	0.0392210i	−0.932350	−	0.361556i	$-0.882246\pi$
$619$	0.355165	−	0.975807i	0.0142753	−	0.0392210i	0.946626	+	0.322335i	$0.104468\pi$
$620$	0.207194	+	0.0259128i	0.00832112	+	0.00104068i
$621$	35.9632	+	11.8001i	1.44315	+	0.473521i
$622$	18.5992	+	12.3406i	0.745758	+	0.494812i
$623$	−20.7891	−	32.5433i	−0.832896	−	1.30382i
$624$	−8.97372	+	11.9175i	−0.359236	+	0.477082i
$625$	19.1489	+	16.0678i	0.765957	+	0.642714i
$626$	−3.02154	−	0.728999i	−0.120765	−	0.0291367i
$627$	−18.2202	+	5.66734i	−0.727644	+	0.226332i
$628$	17.2224	−	11.1294i	0.687247	−	0.444111i
$629$	7.26173	−	4.19256i	0.289544	−	0.167168i
$630$	−0.112506	+	0.106999i	−0.00448234	+	0.00426295i
$631$	−24.6697	−	14.2431i	−0.982085	−	0.567007i	−0.0791861	−	0.996860i	$-0.525232\pi$
$631$	−24.6697	−	14.2431i	−0.982085	−	0.567007i	−0.902899	+	0.429853i	$0.858565\pi$
$632$	8.59246	+	5.10042i	0.341790	+	0.202884i
$633$	−31.2884	−	1.48747i	−1.24360	−	0.0591217i
$634$	5.74874	−	1.69583i	0.228312	−	0.0673502i
$635$	0.0653862	−	0.0237986i	0.00259477	−	0.000944420i
$636$	2.76864	+	7.54549i	0.109784	+	0.299198i
$637$	−13.6448	+	6.40388i	−0.540628	+	0.253731i
$638$	−23.9713	−	48.2145i	−0.949032	−	1.90883i
$639$	28.9359	+	29.3875i	1.14468	+	1.16255i
$640$	−0.128111	+	0.0898696i	−0.00506404	+	0.00355241i
$641$	−29.6346	−	35.3172i	−1.17050	−	1.39495i	−0.902039	−	0.431654i	$-0.857930\pi$
$641$	−29.6346	−	35.3172i	−1.17050	−	1.39495i	−0.268459	−	0.963291i	$-0.586514\pi$
$642$	−9.50244	+	32.5249i	−0.375031	+	1.28366i
$643$	−0.865546	+	1.03152i	−0.0341338	+	0.0406791i	−0.782841	−	0.622221i	$-0.786230\pi$
$643$	−0.865546	+	1.03152i	−0.0341338	+	0.0406791i	0.748707	+	0.662901i	$0.230675\pi$
$644$	22.3510	+	31.4019i	0.880754	+	1.23741i
$645$	−0.0516926	+	0.123443i	−0.00203540	+	0.00486057i
$646$	−14.0158	+	1.58095i	−0.551443	+	0.0622017i
$647$	15.3895	−	26.6554i	0.605024	−	1.04793i	−0.387023	−	0.922070i	$-0.626497\pi$
$647$	15.3895	−	26.6554i	0.605024	−	1.04793i	0.992048	−	0.125863i	$-0.0401700\pi$
$648$	24.9377	+	5.11007i	0.979644	+	0.200743i
$649$	31.3933	+	54.3748i	1.23230	+	2.13440i
$650$	−6.08676	+	13.9557i	−0.238742	+	0.547387i
$651$	0.0910904	−	34.5896i	0.00357011	−	1.35567i
$652$	−19.2478	+	17.8682i	−0.753802	+	0.699772i
$653$	−2.68956	−	0.474242i	−0.105251	−	0.0185585i	0.120775	−	0.992680i	$-0.461462\pi$
$653$	−2.68956	−	0.474242i	−0.105251	−	0.0185585i	−0.226025	+	0.974121i	$0.572573\pi$
$654$	−20.1655	+	4.92097i	−0.788534	+	0.192425i
$655$	0.139591	+	0.166358i	0.00545427	+	0.00650015i
$656$	3.20416	−	0.903218i	0.125101	−	0.0352647i
$657$	0.779032	−	2.81986i	0.0303929	−	0.110013i
$658$	0.547928	−	2.82058i	0.0213605	−	0.109958i
$659$	12.7083	−	10.6635i	0.495043	−	0.415391i	−0.360786	−	0.932649i	$-0.617492\pi$
$659$	12.7083	−	10.6635i	0.495043	−	0.415391i	0.855830	+	0.517258i	$0.173047\pi$
$660$	0.175015	−	0.209683i	0.00681243	−	0.00816189i
$661$	3.18720	+	2.67438i	0.123968	+	0.104021i	0.702664	−	0.711522i	$-0.251994\pi$
$661$	3.18720	+	2.67438i	0.123968	+	0.104021i	−0.578696	+	0.815543i	$0.696438\pi$
$662$	−26.1227	+	7.70600i	−1.01529	+	0.299502i
$663$	10.4038	−	16.1921i	0.404051	−	0.628848i
$664$	−6.06955	−	10.8127i	−0.235544	−	0.419616i
$665$	0.0271470	+	0.0653099i	0.00105272	+	0.00253261i
$666$	−1.07937	+	6.80872i	−0.0418248	+	0.263833i
$667$	42.1356	+	24.3270i	1.63150	+	0.941946i
$668$	−20.3707	−	10.4371i	−0.788166	−	0.403823i
$669$	15.3674	−	4.78000i	0.594139	−	0.184805i
$670$	0.0188779	−	0.0198484i	0.000729316	−	0.000766812i
$671$	−46.3270	+	16.8616i	−1.78843	+	0.650937i
$672$	17.3550	+	19.2562i	0.669485	+	0.742825i
$673$	−1.93250	−	10.9598i	−0.0744925	−	0.422468i	−0.999133	−	0.0416272i	$-0.986746\pi$
$673$	−1.93250	−	10.9598i	−0.0744925	−	0.422468i	0.924641	−	0.380840i	$-0.124365\pi$
$674$	−1.21027	+	19.4295i	−0.0466177	+	0.748396i
$675$	25.9665	−	0.831685i	0.999449	−	0.0320116i
$676$	16.5976	+	2.07579i	0.638369	+	0.0798379i
$677$	−2.59808	−	3.09627i	−0.0998524	−	0.118999i	0.713804	−	0.700345i	$-0.246971\pi$
$677$	−2.59808	−	3.09627i	−0.0998524	−	0.118999i	−0.813656	+	0.581346i	$0.802526\pi$
$678$	10.0440	−	0.651947i	0.385737	−	0.0250379i
$679$	−4.86579	+	1.08504i	−0.186732	+	0.0416401i
$680$	0.156216	−	0.127893i	0.00599060	−	0.00490446i
$681$	−4.18504	+	4.53182i	−0.160371	+	0.173660i
$682$	6.82019	+	60.4638i	0.261159	+	2.31528i
$683$	−21.7031			−0.830446			−0.415223	−	0.909720i	$-0.636296\pi$
$683$	−21.7031			−0.830446			−0.415223	+	0.909720i	$0.636296\pi$
$684$	6.24288	−	9.77209i	0.238702	−	0.373645i
$685$	−0.0979449	+	0.169646i	−0.00374228	+	0.00648182i
$686$	6.40216	+	25.3971i	0.244435	+	0.969666i
$687$	24.1622	+	15.5249i	0.921846	+	0.592311i
$688$	20.3717	+	9.17994i	0.776662	+	0.349982i
$689$	−3.21137	+	3.82716i	−0.122343	+	0.145803i
$690$	−0.0270227	+	0.245311i	−0.00102874	+	0.00933882i
$691$	5.61793	−	15.4351i	0.213716	−	0.587180i	−0.785794	−	0.618489i	$-0.787745\pi$
$691$	5.61793	−	15.4351i	0.213716	−	0.587180i	0.999510	+	0.0313085i	$0.00996742\pi$
$692$	1.25446	−	10.0304i	0.0476874	−	0.381299i
$693$	−37.9993	−	24.5572i	−1.44347	−	0.932851i
$694$	2.52172	−	40.4834i	0.0957231	−	1.53673i
$695$	0.00762205	+	0.0432268i	0.000289121	+	0.00163969i
$696$	30.0278	+	13.0034i	1.13820	+	0.492894i
$697$	−4.03584	+	1.46892i	−0.152868	+	0.0556395i
$698$	7.25237	+	24.5850i	0.274506	+	0.930555i
$699$	7.95985	−	6.05899i	0.301069	−	0.229172i
$700$	21.7884	+	15.0071i	0.823523	+	0.567215i
$701$			32.0058i			1.20884i	0.796664	+	0.604422i	$0.206596\pi$
$701$			32.0058i			1.20884i	−0.796664	+	0.604422i	$0.793404\pi$
$702$	4.96054	+	15.0255i	0.187224	+	0.567103i
$703$	2.71961	+	1.57017i	0.102572	+	0.0592200i
$704$	−34.2135	−	30.1485i	−1.28947	−	1.13627i
$705$	0.0146390	−	0.0111431i	0.000551336	−	0.000419674i
$706$	6.35315	−	26.3324i	0.239104	−	0.991034i
$707$	6.50308	+	29.1626i	0.244574	+	1.09677i
$708$	−35.8893	−	12.9567i	−1.34880	−	0.486944i
$709$	−5.32213	−	30.1833i	−0.199877	−	1.13356i	−0.905301	−	0.424771i	$-0.860354\pi$
$709$	−5.32213	−	30.1833i	−0.199877	−	1.13356i	0.705424	−	0.708786i	$-0.250757\pi$
$710$	−0.148676	+	0.224078i	−0.00557971	+	0.00840948i
$711$	9.63978	−	4.40455i	0.361520	−	0.165184i
$712$	−40.5661	−	7.65997i	−1.52028	−	0.287069i
$713$	−35.3414	−	42.1182i	−1.32355	−	1.57734i
$714$	−24.1726	−	23.1121i	−0.904637	−	0.864950i
$715$	0.167193	+	0.0294807i	0.00625268	+	0.00110252i
$716$	−3.66977	−	3.95312i	−0.137146	−	0.147735i
$717$	−18.3861	−	11.8135i	−0.686640	−	0.441185i
$718$	8.51018	−	19.5121i	0.317597	−	0.728185i
$719$	18.3973			0.686104			0.343052	−	0.939316i	$-0.388539\pi$
$719$	18.3973			0.686104			0.343052	+	0.939316i	$0.388539\pi$
$720$	0.000865953		0.165980i	3.22722e−5		0.00618572i
$721$	15.8328	+	12.1179i	0.589646	+	0.451292i
$722$	12.8213	+	17.3678i	0.477161	+	0.646363i
$723$	−11.8343	−	38.0466i	−0.440122	−	1.41497i
$724$	13.0411	+	14.0480i	0.484668	+	0.522089i
$725$	32.8885	+	5.79914i	1.22145	+	0.215375i
$726$	47.2009	+	23.3140i	1.75179	+	0.865263i
$727$	46.6327	−	8.22260i	1.72951	−	0.304959i	0.781667	−	0.623695i	$-0.214369\pi$
$727$	46.6327	−	8.22260i	1.72951	−	0.304959i	0.947844	+	0.318736i	$0.103258\pi$
$728$	−5.01202	+	15.3143i	−0.185758	+	0.567585i
$729$	19.5302	−	18.6433i	0.723341	−	0.690491i
$730$	0.0190385	+	0.00118591i	0.000704647	+	4.38925e-5i
$731$	−27.0886	−	9.85944i	−1.00191	−	0.364665i
$732$	14.9125	−	25.9856i	0.551183	−	0.960455i
$733$	3.53949	+	2.96999i	0.130734	+	0.109699i	0.705810	−	0.708401i	$-0.250583\pi$
$733$	3.53949	+	2.96999i	0.130734	+	0.109699i	−0.575076	+	0.818100i	$0.695028\pi$
$734$	−13.2570	+	3.91070i	−0.489323	+	0.144347i
$735$	−0.0776439	+	0.148646i	−0.00286394	+	0.00548288i
$736$	40.8220	+	5.60773i	1.50472	+	0.206704i
$737$	6.91276	+	3.99108i	0.254635	+	0.147013i
$738$	1.15004	−	3.33843i	0.0423335	−	0.122889i
$739$	−11.5549	+	6.67122i	−0.425054	+	0.245405i	−0.697237	−	0.716841i	$-0.745588\pi$
$739$	−11.5549	+	6.67122i	−0.425054	+	0.245405i	0.272184	+	0.962245i	$0.412254\pi$
$740$	−0.0448936	+	0.00225166i	−0.00165032	+	8.27726e-5i
$741$	7.19988	+	0.342287i	0.264494	+	0.0125742i
$742$	5.46415	+	6.74607i	0.200595	+	0.247656i
$743$	−5.07270	+	28.7687i	−0.186099	+	1.05542i	0.738435	+	0.674324i	$0.235565\pi$
$743$	−5.07270	+	28.7687i	−0.186099	+	1.05542i	−0.924535	+	0.381098i	$0.875546\pi$
$744$	−26.8606	−	25.4140i	−0.984758	−	0.931724i
$745$	0.0220530	+	0.125069i	0.000807960	+	0.00458217i
$746$	1.69704	−	27.2441i	0.0621329	−	0.997476i
$747$	−13.0926	−	1.24769i	−0.479035	−	0.0456504i
$748$	46.9052	+	35.5111i	1.71502	+	1.29841i
$749$	1.64172	+	36.5627i	0.0599873	+	1.33597i
$750$	0.0803210	+	0.329145i	0.00293291	+	0.0120187i
$751$	9.48036	+	1.67164i	0.345943	+	0.0609991i	0.343920	−	0.938999i	$-0.388245\pi$
$751$	9.48036	+	1.67164i	0.345943	+	0.0609991i	0.00202294	+	0.999998i	$0.499356\pi$
$752$	−1.79431	−	2.49314i	−0.0654319	−	0.0909154i
$753$	−19.3239	+	46.1460i	−0.704203	+	1.68165i
$754$	2.27986	+	20.2119i	0.0830276	+	0.736074i
$755$	−0.201754			−0.00734259
$756$	27.2740	−	3.48263i	0.991946	−	0.126662i
$757$	18.1573			0.659939			0.329969	−	0.943992i	$-0.392962\pi$
$757$	18.1573			0.659939			0.329969	+	0.943992i	$0.392962\pi$
$758$	4.84816	+	42.9809i	0.176093	+	1.56114i
$759$	−71.3371	+	9.11087i	−2.58937	+	0.330704i
$760$	0.0707328	+	0.0267179i	0.00256575	+	0.000969160i
$761$	1.45089	+	0.255831i	0.0525947	+	0.00927386i	0.199884	−	0.979820i	$-0.435944\pi$
$761$	1.45089	+	0.255831i	0.0525947	+	0.00927386i	−0.147289	+	0.989094i	$0.547055\pi$
$762$	−11.8279	−	3.45563i	−0.428481	−	0.125184i
$763$	−18.8942	+	12.0699i	−0.684018	+	0.436959i
$764$	31.0800	−	41.0524i	1.12444	−	1.48522i
$765$	−0.0170109	−	0.213461i	−0.000615032	−	0.00771769i
$766$	−2.60858	+	41.8779i	−0.0942519	+	1.51311i
$767$	−4.11857	−	23.3576i	−0.148713	−	0.843393i
$768$	27.7064	+	0.598105i	0.999767	+	0.0215823i
$769$	1.27700	−	7.24225i	0.0460499	−	0.261162i	−0.953087	−	0.302696i	$-0.902113\pi$
$769$	1.27700	−	7.24225i	0.0460499	−	0.261162i	0.999137	+	0.0415338i	$0.0132244\pi$
$770$	0.105690	−	0.275426i	0.00380879	−	0.00992566i
$771$	−14.4715	+	22.5229i	−0.521180	+	0.811142i
$772$	1.39954	+	27.9040i	0.0503705	+	1.00429i
$773$	−9.62168	+	5.55508i	−0.346068	+	0.199802i	−0.662952	−	0.748662i	$-0.730697\pi$
$773$	−9.62168	+	5.55508i	−0.346068	+	0.199802i	0.316884	+	0.948464i	$0.397363\pi$
$774$	20.3165	−	12.2035i	0.730261	−	0.438646i
$775$	−32.6829	−	18.8695i	−1.17400	−	0.677812i
$776$	−2.72039	+	4.58292i	−0.0976563	+	0.164517i
$777$	1.27369	+	7.33636i	0.0456932	+	0.263190i
$778$	1.57719	−	0.465259i	0.0565451	−	0.0166803i
$779$	−1.23216	−	1.03391i	−0.0441468	−	0.0370436i
$780$	−0.0892162	+	0.0518198i	−0.00319445	+	0.00185545i
$781$	−73.6366	−	26.8015i	−2.63493	−	0.959035i
$782$	−53.0571	−	3.30493i	−1.89732	−	0.118184i
$783$	29.4865	−	18.3070i	1.05376	−	0.654239i
$784$	24.4619	+	13.6240i	0.873640	+	0.486572i
$785$	0.139660	−	0.0246258i	0.00498467	−	0.000878932i
$786$	−2.49103	−	38.3771i	−0.0888520	−	1.36886i
$787$	28.3277	+	4.99494i	1.00977	+	0.178050i	0.653978	−	0.756513i	$-0.273099\pi$
$787$	28.3277	+	4.99494i	1.00977	+	0.178050i	0.355796	+	0.934564i	$0.384210\pi$
$788$	30.7287	−	28.5262i	1.09466	−	1.01620i
$789$	−38.4705	−	8.68510i	−1.36959	−	0.309198i
$790$	0.0410432	+	0.0555972i	0.00146025	+	0.00197806i
$791$	10.0389	−	4.17280i	0.356941	−	0.148368i
$792$	−46.9587	+	11.5892i	−1.66861	+	0.411803i
$793$	18.6233			0.661333
$794$	−13.8363	+	31.7237i	−0.491030	+	1.12583i
$795$	−0.00263962	+	0.0555234i	−9.36176e−5	+	0.00196921i
$796$	−35.2617	+	32.7343i	−1.24982	+	1.16024i
$797$	−30.5136	−	5.38037i	−1.08085	−	0.190582i	−0.395257	−	0.918571i	$-0.629344\pi$
$797$	−30.5136	−	5.38037i	−1.08085	−	0.190582i	−0.685589	+	0.727988i	$0.740455\pi$
$798$	2.96966	−	12.1680i	0.105125	−	0.430742i
$799$	2.54727	+	3.03572i	0.0901161	+	0.107396i
$800$	27.6467	−	5.96643i	0.977459	−	0.210945i
$801$	−31.2011	+	30.7216i	−1.10244	+	1.08549i
$802$	1.17251	−	1.76715i	0.0414026	−	0.0624001i
$803$	0.965244	+	5.47417i	0.0340627	+	0.193179i
$804$	−4.77499	+	0.854809i	−0.168401	+	0.0301468i
$805$	0.0580182	+	0.260178i	0.00204487	+	0.00917008i
$806$	5.39090	−	22.3441i	0.189887	−	0.787039i
$807$	−4.10432	−	32.1364i	−0.144479	−	1.13125i
$808$	27.4672	+	16.3044i	0.966294	+	0.573585i
$809$	−24.0954	−	13.9115i	−0.847148	−	0.489101i	0.0125398	−	0.999921i	$-0.496008\pi$
$809$	−24.0954	−	13.9115i	−0.847148	−	0.489101i	−0.859687	+	0.510821i	$0.829342\pi$
$810$	0.145172	+	0.0995939i	0.00510083	+	0.00349937i
$811$		−	34.3213i		−	1.20519i	−0.798049	−	0.602593i	$-0.794134\pi$
$811$		−	34.3213i		−	1.20519i	0.798049	−	0.602593i	$-0.205866\pi$
$812$	35.2325	+	2.80860i	1.23642	+	0.0985626i
$813$	−37.0044	−	15.4959i	−1.29780	−	0.543464i
$814$	−3.70608	−	12.5633i	−0.129898	−	0.440344i
$815$	−0.170680	+	0.0621224i	−0.00597866	+	0.00217605i
$816$	−35.7032	+	1.88409i	−1.24986	+	0.0659564i
$817$	−1.87472	−	10.6321i	−0.0655883	−	0.371970i
$818$	−1.68878	+	27.1115i	−0.0590468	+	0.947932i
$819$	10.3159	+	13.6266i	0.360468	+	0.476152i
$820$	0.0228454	+	0.00285717i	0.000797794	+	9.97765e-5i
$821$	9.70850	−	26.6739i	0.338829	−	0.930925i	−0.646898	−	0.762576i	$-0.723934\pi$
$821$	9.70850	−	26.6739i	0.338829	−	0.930925i	0.985727	−	0.168349i	$-0.0538436\pi$
$822$	31.7611	−	13.9513i	1.10780	−	0.486607i
$823$	−11.7048	+	13.9493i	−0.408005	+	0.486242i	−0.930443	−	0.366435i	$-0.880578\pi$
$823$	−11.7048	+	13.9493i	−0.408005	+	0.486242i	0.522438	+	0.852677i	$0.325023\pi$
$824$	21.0340	−	3.44706i	0.732753	−	0.120084i
$825$	−43.8736	+	22.6237i	−1.52748	+	0.787655i
$826$	−41.2076	−	0.714541i	−1.43380	−	0.0248621i
$827$	−20.7902	+	36.0096i	−0.722944	+	1.25218i	0.236870	+	0.971541i	$0.423878\pi$
$827$	−20.7902	+	36.0096i	−0.722944	+	1.25218i	−0.959815	+	0.280635i	$0.909455\pi$
$828$	29.5673	−	32.1853i	1.02753	−	1.11852i
$829$	−24.6751			−0.857002			−0.428501	−	0.903541i	$-0.640958\pi$
$829$	−24.6751			−0.857002			−0.428501	+	0.903541i	$0.640958\pi$
$830$	−0.00961216	−	0.0852157i	−0.000333643	−	0.00295788i
$831$	−28.2952	−	6.38793i	−0.981550	−	0.221595i
$832$	8.24967	+	15.1223i	0.286006	+	0.524270i
$833$	−32.7766	−	15.1853i	−1.13564	−	0.526139i
$834$	3.44237	−	6.96934i	0.119200	−	0.241329i
$835$	−0.101752	−	0.121263i	−0.00352126	−	0.00419648i
$836$	−2.73428	+	21.8628i	−0.0945671	+	0.756141i
$837$	−38.3873	+	8.04366i	−1.32686	+	0.278030i
$838$	−0.671816	+	10.7853i	−0.0232075	+	0.372571i
$839$	1.01814	+	5.77416i	0.0351501	+	0.199346i	0.997326	−	0.0730834i	$-0.0232839\pi$
$839$	1.01814	+	5.77416i	0.0351501	+	0.199346i	−0.962176	+	0.272430i	$0.912173\pi$
$840$	0.0588298	+	0.169354i	0.00202982	+	0.00584328i
$841$	14.6732	−	5.34059i	0.505971	−	0.184158i
$842$	5.82659	−	6.12615i	0.200797	−	0.211121i
$843$	−1.91018	+	8.46111i	−0.0657901	+	0.291416i
$844$	−16.4930	+	32.1903i	−0.567712	+	1.10804i
$845$	0.100184	+	0.0578410i	0.00344642	+	0.00198979i
$846$	−3.25753	+	0.0564047i	−0.111996	+	0.00193923i
$847$	56.3855	+	7.35227i	1.93743	+	0.252627i
$848$	9.25518	+	0.688984i	0.317824	+	0.0236598i
$849$	49.7627	+	2.36575i	1.70785	+	0.0811924i
$850$	−34.9977	+	10.3241i	−1.20041	+	0.354112i
$851$	9.06676	+	7.60792i	0.310805	+	0.260796i
$852$	44.7076	−	16.4044i	1.53166	−	0.562007i
$853$	17.0863	−	14.3371i	0.585022	−	0.490892i	−0.301570	−	0.953444i	$-0.597511\pi$
$853$	17.0863	−	14.3371i	0.585022	−	0.490892i	0.886592	+	0.462552i	$0.153066\pi$
$854$	6.17114	−	31.7672i	0.211172	−	1.08705i
$855$	0.0660479	−	0.0454892i	0.00225879	−	0.00155570i
$856$	29.6663	+	25.5108i	1.01397	+	0.871941i
$857$	16.6234	+	19.8110i	0.567844	+	0.676730i	0.971187	−	0.238319i	$-0.0765963\pi$
$857$	16.6234	+	19.8110i	0.567844	+	0.676730i	−0.403343	+	0.915049i	$0.632152\pi$
$858$	−20.7767	−	21.7311i	−0.709304	−	0.741886i
$859$	−44.1447	−	7.78391i	−1.50620	−	0.265584i	−0.641207	−	0.767368i	$-0.721566\pi$
$859$	−44.1447	−	7.78391i	−1.50620	−	0.265584i	−0.864993	+	0.501785i	$0.832677\pi$
$860$	0.105137	+	0.113255i	0.00358514	+	0.00386195i
$861$	0.0100437	−	3.81387i	0.000342288	−	0.129976i
$862$	2.86201	−	6.56200i	0.0974804	−	0.223503i
$863$	−2.41252	−	4.17861i	−0.0821232	−	0.142242i	0.822039	−	0.569432i	$-0.192837\pi$
$863$	−2.41252	−	4.17861i	−0.0821232	−	0.142242i	−0.904162	+	0.427190i	$0.859503\pi$
$864$	17.2720	−	23.7840i	0.587605	−	0.809148i
$865$	0.0349550	−	0.0605439i	0.00118851	−	0.00205855i
$866$	41.5808	−	4.69024i	1.41297	−	0.159381i
$867$	16.5463	−	2.11322i	0.561941	−	0.0717688i
$868$	−36.3278	−	16.5998i	−1.23305	−	0.563433i
$869$	−12.9442	+	15.4263i	−0.439101	+	0.523300i
$870$	0.156390	+	0.163574i	0.00530213	+	0.00554568i
$871$	−1.93819	−	2.30985i	−0.0656731	−	0.0782662i
$872$	−4.44728	+	23.5522i	−0.150604	+	0.797579i
$873$	2.34924	+	5.14152i	0.0795096	+	0.174014i
$874$	−8.86337	−	17.8273i	−0.299808	−	0.603017i
$875$	0.197007	+	0.308395i	0.00666004	+	0.0104257i
$876$	−2.59341	−	2.16462i	−0.0876231	−	0.0731359i
$877$	23.9288	−	8.70935i	0.808017	−	0.294094i	0.0952123	−	0.995457i	$-0.469647\pi$
$877$	23.9288	−	8.70935i	0.808017	−	0.294094i	0.712804	+	0.701363i	$0.247425\pi$
$878$	55.9171	−	16.4951i	1.88711	−	0.556683i
$879$	−12.1135	+	18.8529i	−0.408577	+	0.635891i
$880$	−0.136977	−	0.284077i	−0.00461750	−	0.00957624i
$881$	−17.4100	−	10.0517i	−0.586558	−	0.338649i	0.177177	−	0.984179i	$-0.443303\pi$
$881$	−17.4100	−	10.0517i	−0.586558	−	0.338649i	−0.763735	+	0.645529i	$0.776637\pi$
$882$	26.6623	−	13.0813i	0.897767	−	0.440470i
$883$	−31.6236	+	18.2579i	−1.06422	+	0.614427i	−0.926596	−	0.376057i	$-0.877280\pi$
$883$	−31.6236	+	18.2579i	−1.06422	+	0.614427i	−0.137623	+	0.990485i	$0.543946\pi$
$884$	−12.0620	−	18.6656i	−0.405691	−	0.627792i
$885$	−0.193867	−	0.179032i	−0.00651677	−	0.00601810i
$886$	−3.88410	−	0.937106i	−0.130489	−	0.0314827i
$887$	−22.3079	−	18.7185i	−0.749024	−	0.628506i	0.186220	−	0.982508i	$-0.440376\pi$
$887$	−22.3079	−	18.7185i	−0.749024	−	0.628506i	−0.935245	+	0.354002i	$0.884821\pi$
$888$	6.64443	+	4.38367i	0.222972	+	0.147106i
$889$	−13.2963	+	0.597025i	−0.445944	+	0.0200236i
$890$	−0.237906	−	0.157851i	−0.00797463	−	0.00529118i
$891$	−18.2906	+	47.9303i	−0.612760	+	1.60573i
$892$	2.30617	−	18.4397i	0.0772163	−	0.617407i
$893$	−0.507606	+	1.39464i	−0.0169864	+	0.0466697i
$894$	9.95988	−	20.1645i	0.333108	−	0.674403i
$895$	−0.0127587	−	0.0350543i	−0.000426477	−	0.00117174i
$896$	28.5289	−	9.06110i	0.953083	−	0.302710i
$897$	26.4998	+	5.98260i	0.884803	+	0.199753i
$898$	−42.7771	−	18.6572i	−1.42749	−	0.622597i
$899$	−50.4169			−1.68150
$900$	11.5151	−	27.7008i	0.383835	−	0.923360i
$901$	−11.9733			−0.398890
$902$	0.751999	+	6.66678i	0.0250388	+	0.221979i
$903$	16.5062	−	19.5664i	0.549291	−	0.651130i
$904$	4.10684	−	10.8724i	0.136591	−	0.361611i
$905$	0.0453400	+	0.124571i	0.00150715	+	0.00414087i
$906$	28.7999	+	21.1449i	0.956813	+	0.702494i
$907$	25.4363	−	4.48511i	0.844599	−	0.148926i	0.265427	−	0.964131i	$-0.414487\pi$
$907$	25.4363	−	4.48511i	0.844599	−	0.148926i	0.579172	+	0.815205i	$0.303376\pi$
$908$	2.76841	+	6.56292i	0.0918729	+	0.217798i
$909$	30.8151	−	14.0799i	1.02207	−	0.467000i
$910$	−0.0731018	+	0.0841135i	−0.00242330	+	0.00278834i
$911$	−32.8796	−	11.9672i	−1.08935	−	0.396491i	−0.265971	−	0.963981i	$-0.585692\pi$
$911$	−32.8796	−	11.9672i	−1.08935	−	0.396491i	−0.823380	+	0.567490i	$0.807915\pi$
$912$	−7.29673	−	11.2271i	−0.241619	−	0.371766i
$913$	23.4825	−	8.54692i	0.777157	−	0.282862i
$914$	7.32284	−	7.69932i	0.242218	−	0.254671i
$915$	0.164874	−	0.125501i	0.00545057	−	0.00414894i
$916$	27.8533	−	17.9993i	0.920298	−	0.594713i
$917$	−15.9439	−	38.3575i	−0.526513	−	1.26668i
$918$	−19.9436	+	32.2538i	−0.658236	+	1.06453i
$919$	14.0968	−	8.13879i	0.465010	−	0.268474i	−0.249138	−	0.968468i	$-0.580147\pi$
$919$	14.0968	−	8.13879i	0.465010	−	0.268474i	0.714149	+	0.699994i	$0.246814\pi$
$920$	0.245053	+	0.145462i	0.00807916	+	0.00479573i
$921$	−5.28092	−	41.3490i	−0.174012	−	1.36250i
$922$	−32.4482	+	9.57196i	−1.06862	+	0.315236i
$923$	22.6762	+	19.0276i	0.746397	+	0.626302i
$924$	−43.9530	+	28.2395i	−1.44595	+	0.929010i
$925$	7.63411	+	2.77859i	0.251008	+	0.0913594i
$926$	−4.65347	−	9.35973i	−0.152922	−	0.307580i
$927$	9.71271	−	20.4148i	0.319007	−	0.670508i
$928$	28.0006	−	25.3700i	0.919166	−	0.832813i
$929$	7.53729	−	20.7085i	0.247290	−	0.679425i	−0.752493	−	0.658601i	$-0.771149\pi$
$929$	7.53729	−	20.7085i	0.247290	−	0.679425i	0.999783	−	0.0208242i	$-0.00662904\pi$
$930$	−0.102849	−	0.234144i	−0.00337256	−	0.00767788i
$931$	−1.21247	−	13.4742i	−0.0397372	−	0.441600i
$932$	−2.57314	−	11.2608i	−0.0842859	−	0.368861i
$933$	1.29817	−	27.3065i	0.0425001	−	0.893973i
$934$	−7.83424	+	17.9623i	−0.256344	+	0.587745i
$935$	0.203437	+	0.352364i	0.00665311	+	0.0115235i
$936$	18.1664	+	1.95320i	0.593786	+	0.0638424i
$937$	25.8784	+	44.8227i	0.845410	+	1.46429i	0.885265	+	0.465087i	$0.153977\pi$
$937$	25.8784	+	44.8227i	0.845410	+	1.46429i	−0.0398551	+	0.999205i	$0.512690\pi$
$938$	−4.58234	+	2.54072i	−0.149619	+	0.0829575i
$939$	1.13066	+	3.63502i	0.0368978	+	0.118624i
$940$	−0.00473227	−	0.0207098i	−0.000154349	−	0.000675480i
$941$	18.4412	+	3.25167i	0.601164	+	0.106002i	0.465944	−	0.884814i	$-0.345715\pi$
$941$	18.4412	+	3.25167i	0.601164	+	0.106002i	0.135220	+	0.990816i	$0.456826\pi$
$942$	−22.5170	−	11.1218i	−0.733643	−	0.362369i
$943$	−3.89676	−	4.64398i	−0.126896	−	0.151229i
$944$	−30.7483	+	31.5558i	−1.00077	+	1.02706i
$945$	0.183157	+	0.0511195i	0.00595809	+	0.00166292i
$946$	−24.8966	+	37.5230i	−0.809458	+	1.21998i
$947$	−20.7704	+	17.4285i	−0.674948	+	0.566349i	−0.914525	−	0.404529i	$-0.867436\pi$
$947$	−20.7704	+	17.4285i	−0.674948	+	0.566349i	0.239577	+	0.970877i	$0.422991\pi$
$948$	−0.0319236	−	12.2379i	−0.00103683	−	0.397468i
$949$	0.364625	−	2.06789i	0.0118362	−	0.0671265i
$950$	−9.90203	−	9.41784i	−0.321264	−	0.305555i
$951$	−5.39289	−	4.98022i	−0.174876	−	0.161495i
$952$	−35.8363	+	14.3900i	−1.16146	+	0.466384i
$953$	−22.6738	+	13.0907i	−0.734476	+	0.424050i	−0.820058	−	0.572281i	$-0.806059\pi$
$953$	−22.6738	+	13.0907i	−0.734476	+	0.424050i	0.0855811	+	0.996331i	$0.472725\pi$
$954$	6.19595	−	7.64917i	0.200601	−	0.247651i
$955$	0.308396	−	0.178052i	0.00997945	−	0.00576164i
$956$	−21.1948	+	13.6964i	−0.685487	+	0.442975i
$957$	−35.6479	+	55.4808i	−1.15233	+	1.79344i
$958$	−20.5486	+	21.6051i	−0.663895	+	0.698028i
$959$	27.5942	−	25.3483i	0.891062	−	0.818540i
$960$	0.174943	+	0.0782849i	0.00564626	+	0.00252663i
$961$	24.4072	+	8.88349i	0.787329	+	0.286564i
$962$	−0.307617	+	4.93845i	−0.00991796	+	0.159222i
$963$	40.1679	−	10.4303i	1.29439	−	0.336111i
$964$	−45.6529	−	5.70960i	−1.47038	−	0.183894i
$965$	−0.0660868	+	0.181572i	−0.00212741	+	0.00584501i
$966$	18.9861	−	43.2204i	0.610869	−	1.39059i
$967$	−10.6499	+	12.6921i	−0.342479	+	0.408151i	−0.909601	−	0.415483i	$-0.863612\pi$
$967$	−10.6499	+	12.6921i	−0.342479	+	0.408151i	0.567122	+	0.823634i	$0.308057\pi$
$968$	47.0362	−	38.5082i	1.51180	−	1.23770i
$969$	10.4630	+	13.7455i	0.336119	+	0.441568i
$970$	−0.0296536	+	0.0218910i	−0.000952120	+	0.000702878i
$971$	14.7715	+	25.5850i	0.474040	+	0.821061i	0.999558	−	0.0297209i	$-0.00946186\pi$
$971$	14.7715	+	25.5850i	0.474040	+	0.821061i	−0.525518	+	0.850782i	$0.676129\pi$
$972$	−10.2850	−	29.4316i	−0.329891	−	0.944019i
$973$	1.08558	−	8.32547i	0.0348022	−	0.266902i
$974$	−6.88002	−	3.00071i	−0.220450	−	0.0961490i
$975$	18.4969	−	2.36234i	0.592374	−	0.0756555i
$976$	−20.2088	−	28.0794i	−0.646867	−	0.898800i
$977$	−3.40729	−	9.36146i	−0.109009	−	0.299500i	0.873179	−	0.487399i	$-0.162054\pi$
$977$	−3.40729	−	9.36146i	−0.109009	−	0.299500i	−0.982188	+	0.187899i	$0.939832\pi$
$978$	30.8749	+	9.02036i	0.987269	+	0.288439i
$979$	28.4556	−	78.1810i	0.909444	−	2.49868i
$980$	0.119256	+	0.152568i	0.00380948	+	0.00487360i
$981$	17.8366	+	18.1150i	0.569478	+	0.578366i
$982$	46.8577	+	31.0902i	1.49529	+	0.992127i
$983$	−3.96847	−	22.5063i	−0.126574	−	0.717839i	−0.980360	−	0.197215i	$-0.936810\pi$
$983$	−3.96847	−	22.5063i	−0.126574	−	0.717839i	0.853786	−	0.520624i	$-0.174301\pi$
$984$	−2.96167	−	2.80217i	−0.0944145	−	0.0893299i
$985$	0.272487	−	0.0991771i	0.00868216	−	0.00316005i
$986$	−33.5947	+	35.3219i	−1.06987	+	1.12488i
$987$	−3.31000	+	1.19488i	−0.105358	+	0.0380334i
$988$	3.79526	−	7.40742i	0.120743	−	0.235662i
$989$		−	40.6902i		−	1.29387i
$990$	−0.330382	−	0.0523747i	−0.0105002	−	0.00166458i
$991$			6.91742i			0.219739i	0.993946	+	0.109870i	$0.0350433\pi$
$991$			6.91742i			0.219739i	−0.993946	+	0.109870i	$0.964957\pi$
$992$	−39.5393	+	16.1182i	−1.25538	+	0.511753i
$993$	24.5057	+	22.6305i	0.777665	+	0.718158i
$994$	39.9710	−	32.3755i	1.26780	−	1.02689i
$995$	−0.312683	+	0.113807i	−0.00991273	+	0.00360794i
$996$	−7.55895	+	13.1717i	−0.239515	+	0.417362i
$997$	7.16060	+	2.60625i	0.226779	+	0.0825407i	0.452910	−	0.891556i	$-0.350386\pi$
$997$	7.16060	+	2.60625i	0.226779	+	0.0825407i	−0.226132	+	0.974097i	$0.572608\pi$
$998$	6.58421	+	13.2431i	0.208420	+	0.419204i
$999$	7.83739	−	3.14021i	0.247964	−	0.0993519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ci.a.95.5	yes	840
4.3	odd	2	inner	756.2.ci.a.95.85	yes	840
7.2	even	3		756.2.bs.a.527.99	yes	840
27.2	odd	18		756.2.bs.a.515.11	✓	840
28.23	odd	6		756.2.bs.a.527.11	yes	840
108.83	even	18		756.2.bs.a.515.99	yes	840
189.2	odd	18	inner	756.2.ci.a.191.85	yes	840
756.191	even	18	inner	756.2.ci.a.191.5	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bs.a.515.11	✓	840	27.2	odd	18
756.2.bs.a.515.99	yes	840	108.83	even	18
756.2.bs.a.527.11	yes	840	28.23	odd	6
756.2.bs.a.527.99	yes	840	7.2	even	3
756.2.ci.a.95.5	yes	840	1.1	even	1	trivial
756.2.ci.a.95.85	yes	840	4.3	odd	2	inner
756.2.ci.a.191.5	yes	840	756.191	even	18	inner
756.2.ci.a.191.85	yes	840	189.2	odd	18	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40530 + 0.158515i) q^{2} +(1.04908 + 1.37820i) q^{3} +(1.94975 - 0.445523i) q^{4} +(0.0136217 + 0.00240188i) q^{5} +(-1.69274 - 1.77049i) q^{6} +(-2.34832 - 1.21877i) q^{7} +(-2.66936 + 0.935159i) q^{8} +(-0.798872 + 2.89168i) q^{9} +O(q^{10})\)	\(q+(-1.40530 + 0.158515i) q^{2} +(1.04908 + 1.37820i) q^{3} +(1.94975 - 0.445523i) q^{4} +(0.0136217 + 0.00240188i) q^{5} +(-1.69274 - 1.77049i) q^{6} +(-2.34832 - 1.21877i) q^{7} +(-2.66936 + 0.935159i) q^{8} +(-0.798872 + 2.89168i) q^{9} +(-0.0195234 - 0.00121611i) q^{10} +(-0.989827 - 5.61359i) q^{11} +(2.65946 + 2.21975i) q^{12} +(-0.373911 + 2.12055i) q^{13} +(3.49329 + 1.34049i) q^{14} +(0.0109800 + 0.0212932i) q^{15} +(3.60302 - 1.73731i) q^{16} +(-4.46911 + 2.58024i) q^{17} +(0.664281 - 4.19031i) q^{18} +(-1.67374 - 0.966334i) q^{19} +(0.0276290 - 0.00138575i) q^{20} +(-0.783868 - 4.51504i) q^{21} +(2.28084 + 7.73188i) q^{22} +(-5.57999 - 4.68217i) q^{23} +(-4.08920 - 2.69786i) q^{24} +(-4.69828 - 1.71004i) q^{25} +(0.189318 - 3.03929i) q^{26} +(-4.82339 + 1.93259i) q^{27} +(-5.12162 - 1.33005i) q^{28} +(-6.57796 + 1.15987i) q^{29} +(-0.0188055 - 0.0281829i) q^{30} +(7.43341 + 1.31071i) q^{31} +(-4.78794 + 3.01258i) q^{32} +(6.69824 - 7.25327i) q^{33} +(5.87144 - 4.33444i) q^{34} +(-0.0290609 - 0.0222421i) q^{35} +(-0.269287 + 5.99395i) q^{36} -1.62487 q^{37} +(2.50529 + 1.09268i) q^{38} +(-3.31481 + 1.70930i) q^{39} +(-0.0386074 + 0.00632701i) q^{40} +(0.819613 + 0.144520i) q^{41} +(1.81727 + 6.22073i) q^{42} +(3.59069 + 4.27922i) q^{43} +(-4.43089 - 10.5041i) q^{44} +(-0.0178275 + 0.0374709i) q^{45} +(8.58376 + 5.69534i) q^{46} +(-0.133348 - 0.756257i) q^{47} +(6.17421 + 3.14310i) q^{48} +(4.02922 + 5.72410i) q^{49} +(6.87357 + 1.65837i) q^{50} +(-8.24453 - 3.45245i) q^{51} +(0.215725 + 4.30113i) q^{52} +(2.00935 + 1.16010i) q^{53} +(6.47197 - 3.48045i) q^{54} -0.0788442i q^{55} +(7.40825 + 1.05727i) q^{56} +(-0.424081 - 3.32051i) q^{57} +(9.06016 - 2.67268i) q^{58} +(-10.3506 + 3.76730i) q^{59} +(0.0308948 + 0.0366246i) q^{60} +(-1.50186 - 8.51747i) q^{61} +(-10.6540 - 0.663636i) q^{62} +(5.40028 - 5.81695i) q^{63} +(6.25096 - 4.99255i) q^{64} +(-0.0101866 + 0.0279875i) q^{65} +(-8.26330 + 11.2548i) q^{66} +(-0.900117 + 1.07272i) q^{67} +(-7.56407 + 7.02191i) q^{68} +(0.599121 - 12.6023i) q^{69} +(0.0443650 + 0.0266502i) q^{70} +(6.87368 - 11.9056i) q^{71} +(-0.571703 - 8.46600i) q^{72} -0.975165 q^{73} +(2.28344 - 0.257567i) q^{74} +(-2.57209 - 8.26914i) q^{75} +(-3.69389 - 1.13842i) q^{76} +(-4.51721 + 14.3889i) q^{77} +(4.38736 - 2.92753i) q^{78} +(-2.27083 - 2.70627i) q^{79} +(0.0532522 - 0.0150112i) q^{80} +(-7.72361 - 4.62016i) q^{81} +(-1.17471 - 0.0731729i) q^{82} +(0.761271 + 4.31738i) q^{83} +(-3.53990 - 8.45394i) q^{84} +(-0.0670745 + 0.0244131i) q^{85} +(-5.72432 - 5.44441i) q^{86} +(-8.49933 - 7.84895i) q^{87} +(7.89180 + 14.0590i) q^{88} +(12.6403 + 7.29787i) q^{89} +(0.0191133 - 0.0554838i) q^{90} +(3.46252 - 4.52403i) q^{91} +(-12.9656 - 6.64302i) q^{92} +(5.99180 + 11.6198i) q^{93} +(0.307273 + 1.04163i) q^{94} +(-0.0204782 - 0.0171833i) q^{95} +(-9.17486 - 3.43830i) q^{96} +(1.44343 - 1.21118i) q^{97} +(-6.56963 - 7.40540i) q^{98} +(17.0234 + 1.62228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Introduction

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