LMFDB - Embedded newform 471.2.q.b.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(19,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 62]))

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

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

chi := DirichletCharacter("471.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.q (of order $39$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			19.4
Character	$\chi$	$=$	471.19
Dual form			471.2.q.b.124.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.84576 - 0.454940i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.42896 + 0.749975i) q^{4} +(1.98261 - 1.48983i) q^{5} +(1.31687 + 1.37101i) q^{6} +(-1.31241 + 0.688808i) q^{7} +(0.549517 + 0.486830i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})$	\(q+(-1.84576 - 0.454940i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.42896 + 0.749975i) q^{4} +(1.98261 - 1.48983i) q^{5} +(1.31687 + 1.37101i) q^{6} +(-1.31241 + 0.688808i) q^{7} +(0.549517 + 0.486830i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-4.33720 + 1.84791i) q^{10} +(2.35497 + 2.45178i) q^{11} +(-0.806905 - 1.39760i) q^{12} +(-2.03045 + 3.51684i) q^{13} +(2.73577 - 0.674307i) q^{14} +(-2.47194 + 0.199556i) q^{15} +(-2.62630 - 3.80485i) q^{16} +(-3.80205 + 2.85706i) q^{17} +(-0.380249 - 1.86258i) q^{18} +(0.748037 - 3.66413i) q^{19} +(3.95040 - 0.642002i) q^{20} +(1.47738 + 0.119267i) q^{21} +(-3.23130 - 5.59677i) q^{22} +(3.71906 + 5.38798i) q^{23} +(-0.204253 - 0.705162i) q^{24} +(0.320041 - 1.10491i) q^{25} +(5.34767 - 5.56752i) q^{26} +(0.120537 - 0.992709i) q^{27} -2.39197 q^{28} +(-1.05481 + 8.68711i) q^{29} +(4.65341 + 0.756252i) q^{30} +(-4.39467 - 5.38249i) q^{31} +(2.59588 + 6.84478i) q^{32} +(-0.680002 - 3.33087i) q^{33} +(8.31747 - 3.54374i) q^{34} +(-1.57579 + 3.32091i) q^{35} +(-0.0649816 + 1.61250i) q^{36} +(9.66439 + 7.26232i) q^{37} +(-3.04766 + 6.42280i) q^{38} +(3.59574 - 1.88719i) q^{39} +(1.81477 + 0.146503i) q^{40} +(6.63453 - 9.61178i) q^{41} +(-2.67264 - 0.892258i) q^{42} +(-4.10373 + 2.59504i) q^{43} +(1.52637 + 5.26966i) q^{44} +(2.19592 + 1.15251i) q^{45} +(-4.41329 - 11.6369i) q^{46} +(8.31571 + 3.54299i) q^{47} +(0.186159 + 4.61949i) q^{48} +(-2.72848 + 3.95289i) q^{49} +(-1.09339 + 1.89380i) q^{50} +(4.74046 - 0.382689i) q^{51} +(-5.53897 + 3.50263i) q^{52} +(7.73116 - 2.58104i) q^{53} +(-0.674105 + 1.77747i) q^{54} +(8.32171 + 1.35241i) q^{55} +(-1.05653 - 0.260410i) q^{56} +(-2.59058 + 2.69708i) q^{57} +(5.89904 - 15.5545i) q^{58} +(5.89208 - 5.21993i) q^{59} +(-3.68197 - 1.56874i) q^{60} +(-1.24722 + 6.10927i) q^{61} +(5.66281 + 11.9341i) q^{62} +(-1.18493 - 0.890414i) q^{63} +(-0.562882 - 4.63575i) q^{64} +(1.21392 + 9.99753i) q^{65} +(-0.260222 + 6.45735i) q^{66} +(-1.62575 - 1.44029i) q^{67} +(-7.57570 + 1.23117i) q^{68} +(-0.263617 - 6.54158i) q^{69} +(4.41935 - 5.41272i) q^{70} +(5.87629 - 1.96179i) q^{71} +(-0.204253 + 0.705162i) q^{72} +(3.05411 + 1.93130i) q^{73} +(-14.5343 - 17.8012i) q^{74} +(-0.861033 + 0.762808i) q^{75} +(3.81692 - 4.67488i) q^{76} +(-4.77949 - 1.59563i) q^{77} +(-7.49545 + 1.84746i) q^{78} +(-3.60087 + 0.887534i) q^{79} +(-10.8755 - 3.63078i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-16.6185 + 14.7228i) q^{82} +(-8.96600 - 10.9814i) q^{83} +(2.02167 + 1.27843i) q^{84} +(-3.28144 + 11.3288i) q^{85} +(8.75511 - 2.92288i) q^{86} +(5.53448 - 6.77850i) q^{87} +(0.100495 + 2.49376i) q^{88} +(-14.9613 + 2.43145i) q^{89} +(-3.52882 - 3.12626i) q^{90} +(0.242361 - 6.01413i) q^{91} +(1.27352 + 10.4884i) q^{92} +(0.837572 + 6.89803i) q^{93} +(-13.7370 - 10.3227i) q^{94} +(-3.97587 - 8.37897i) q^{95} +(1.46429 - 7.17255i) q^{96} +(5.10312 + 2.17423i) q^{97} +(6.83445 - 6.05480i) q^{98} +(-1.20550 + 3.17866i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) $ 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{31}{39}\right)$

Coefficient data

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

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

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

$2$	−1.84576	−	0.454940i	−1.30515	−	0.321691i	−0.475373	−	0.879784i	$-0.657687\pi$
$2$	−1.84576	−	0.454940i	−1.30515	−	0.321691i	−0.829778	+	0.558093i	$0.811533\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	1.42896	+	0.749975i	0.714479	+	0.374988i
$5$	1.98261	−	1.48983i	0.886649	−	0.666273i	−0.0565870	−	0.998398i	$-0.518022\pi$
$5$	1.98261	−	1.48983i	0.886649	−	0.666273i	0.943236	+	0.332125i	$0.107765\pi$
$6$	1.31687	+	1.37101i	0.537610	+	0.559712i
$7$	−1.31241	+	0.688808i	−0.496046	+	0.260345i	−0.694143	−	0.719838i	$-0.744216\pi$
$7$	−1.31241	+	0.688808i	−0.496046	+	0.260345i	0.198097	+	0.980182i	$0.436524\pi$
$8$	0.549517	+	0.486830i	0.194284	+	0.172120i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	−4.33720	+	1.84791i	−1.37154	+	0.584361i
$11$	2.35497	+	2.45178i	0.710049	+	0.739239i	0.974310	−	0.225212i	$-0.0723074\pi$
$11$	2.35497	+	2.45178i	0.710049	+	0.739239i	−0.264261	+	0.964451i	$0.585128\pi$
$12$	−0.806905	−	1.39760i	−0.232933	−	0.403453i
$13$	−2.03045	+	3.51684i	−0.563145	+	0.975395i	0.434075	+	0.900877i	$0.357075\pi$
$13$	−2.03045	+	3.51684i	−0.563145	+	0.975395i	−0.997220	+	0.0745186i	$0.976258\pi$
$14$	2.73577	−	0.674307i	0.731165	−	0.180216i
$15$	−2.47194	+	0.199556i	−0.638253	+	0.0515251i
$16$	−2.62630	−	3.80485i	−0.656574	−	0.951212i
$17$	−3.80205	+	2.85706i	−0.922133	+	0.692938i	−0.951832	−	0.306621i	$-0.900802\pi$
$17$	−3.80205	+	2.85706i	−0.922133	+	0.692938i	0.0296987	+	0.999559i	$0.490545\pi$
$18$	−0.380249	−	1.86258i	−0.0896256	−	0.439015i
$19$	0.748037	−	3.66413i	0.171611	−	0.840608i	−0.799256	−	0.600991i	$-0.794773\pi$
$19$	0.748037	−	3.66413i	0.171611	−	0.840608i	0.970867	−	0.239618i	$-0.0770220\pi$
$20$	3.95040	−	0.642002i	0.883336	−	0.143556i
$21$	1.47738	+	0.119267i	0.322391	+	0.0260261i
$22$	−3.23130	−	5.59677i	−0.688915	−	1.19324i
$23$	3.71906	+	5.38798i	0.775477	+	1.12347i	0.989199	+	0.146578i	$0.0468258\pi$
$23$	3.71906	+	5.38798i	0.775477	+	1.12347i	−0.213722	+	0.976894i	$0.568559\pi$
$24$	−0.204253	−	0.705162i	−0.0416929	−	0.143940i
$25$	0.320041	−	1.10491i	0.0640082	−	0.220982i
$26$	5.34767	−	5.56752i	1.04877	−	1.09188i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	−2.39197			−0.452040
$29$	−1.05481	+	8.68711i	−0.195873	+	1.61316i	0.480771	+	0.876846i	$0.340357\pi$
$29$	−1.05481	+	8.68711i	−0.195873	+	1.61316i	−0.676644	+	0.736311i	$0.736566\pi$
$30$	4.65341	+	0.756252i	0.849592	+	0.138072i
$31$	−4.39467	−	5.38249i	−0.789306	−	0.966724i	0.210636	−	0.977565i	$-0.432447\pi$
$31$	−4.39467	−	5.38249i	−0.789306	−	0.966724i	−0.999941	+	0.0108409i	$0.996549\pi$
$32$	2.59588	+	6.84478i	0.458891	+	1.21000i
$33$	−0.680002	−	3.33087i	−0.118373	−	0.579830i
$34$	8.31747	−	3.54374i	1.42644	−	0.607747i
$35$	−1.57579	+	3.32091i	−0.266357	+	0.561336i
$36$	−0.0649816	+	1.61250i	−0.0108303	+	0.268750i
$37$	9.66439	+	7.26232i	1.58882	+	1.19392i	0.861721	+	0.507382i	$0.169387\pi$
$37$	9.66439	+	7.26232i	1.58882	+	1.19392i	0.727095	+	0.686537i	$0.240870\pi$
$38$	−3.04766	+	6.42280i	−0.494395	+	1.04192i
$39$	3.59574	−	1.88719i	0.575780	−	0.302193i
$40$	1.81477	+	0.146503i	0.286940	+	0.0231642i
$41$	6.63453	−	9.61178i	1.03614	−	1.50111i	0.180473	−	0.983580i	$-0.442237\pi$
$41$	6.63453	−	9.61178i	1.03614	−	1.50111i	0.855667	−	0.517528i	$-0.173147\pi$
$42$	−2.67264	−	0.892258i	−0.412397	−	0.137678i
$43$	−4.10373	+	2.59504i	−0.625814	+	0.395741i	−0.809396	−	0.587264i	$-0.800205\pi$
$43$	−4.10373	+	2.59504i	−0.625814	+	0.395741i	0.183582	+	0.983004i	$0.441231\pi$
$44$	1.52637	+	5.26966i	0.230110	+	0.794431i
$45$	2.19592	+	1.15251i	0.327348	+	0.171806i
$46$	−4.41329	−	11.6369i	−0.650704	−	1.71577i
$47$	8.31571	+	3.54299i	1.21297	+	0.516798i	0.901218	−	0.433365i	$-0.142674\pi$
$47$	8.31571	+	3.54299i	1.21297	+	0.516798i	0.311752	+	0.950164i	$0.399084\pi$
$48$	0.186159	+	4.61949i	0.0268697	+	0.666766i
$49$	−2.72848	+	3.95289i	−0.389783	+	0.564698i
$50$	−1.09339	+	1.89380i	−0.154628	+	0.267824i
$51$	4.74046	−	0.382689i	0.663797	−	0.0535872i
$52$	−5.53897	+	3.50263i	−0.768116	+	0.485727i
$53$	7.73116	−	2.58104i	1.06196	−	0.354533i	0.268576	−	0.963259i	$-0.413447\pi$
$53$	7.73116	−	2.58104i	1.06196	−	0.354533i	0.793381	+	0.608725i	$0.208319\pi$
$54$	−0.674105	+	1.77747i	−0.0917340	+	0.241883i
$55$	8.32171	+	1.35241i	1.12210	+	0.182359i
$56$	−1.05653	−	0.260410i	−0.141184	−	0.0347988i
$57$	−2.59058	+	2.69708i	−0.343131	+	0.357237i
$58$	5.89904	−	15.5545i	0.774581	−	2.04240i
$59$	5.89208	−	5.21993i	0.767084	−	0.679577i	−0.185910	−	0.982567i	$-0.559523\pi$
$59$	5.89208	−	5.21993i	0.767084	−	0.679577i	0.952994	+	0.302990i	$0.0979848\pi$
$60$	−3.68197	−	1.56874i	−0.475340	−	0.202523i
$61$	−1.24722	+	6.10927i	−0.159690	+	0.782212i	0.818501	+	0.574505i	$0.194805\pi$
$61$	−1.24722	+	6.10927i	−0.159690	+	0.782212i	−0.978191	+	0.207707i	$0.933400\pi$
$62$	5.66281	+	11.9341i	0.719177	+	1.51563i
$63$	−1.18493	−	0.890414i	−0.149287	−	0.112182i
$64$	−0.562882	−	4.63575i	−0.0703602	−	0.579469i
$65$	1.21392	+	9.99753i	0.150568	+	1.24004i
$66$	−0.260222	+	6.45735i	−0.0320312	+	0.794845i
$67$	−1.62575	−	1.44029i	−0.198617	−	0.175960i	0.557952	−	0.829873i	$-0.311587\pi$
$67$	−1.62575	−	1.44029i	−0.198617	−	0.175960i	−0.756569	+	0.653914i	$0.773126\pi$
$68$	−7.57570	+	1.23117i	−0.918688	+	0.149301i
$69$	−0.263617	−	6.54158i	−0.0317357	−	0.787514i
$70$	4.41935	−	5.41272i	0.528213	−	0.646944i
$71$	5.87629	−	1.96179i	0.697388	−	0.232822i	0.0541992	−	0.998530i	$-0.482739\pi$
$71$	5.87629	−	1.96179i	0.697388	−	0.232822i	0.643188	+	0.765708i	$0.277611\pi$
$72$	−0.204253	+	0.705162i	−0.0240714	+	0.0831041i
$73$	3.05411	+	1.93130i	0.357457	+	0.226042i	0.701108	−	0.713055i	$-0.252689\pi$
$73$	3.05411	+	1.93130i	0.357457	+	0.226042i	−0.343651	+	0.939098i	$0.611664\pi$
$74$	−14.5343	−	17.8012i	−1.68957	−	2.06935i
$75$	−0.861033	+	0.762808i	−0.0994235	+	0.0880815i
$76$	3.81692	−	4.67488i	0.437830	−	0.536245i
$77$	−4.77949	−	1.59563i	−0.544674	−	0.181839i
$78$	−7.49545	+	1.84746i	−0.848692	+	0.209184i
$79$	−3.60087	+	0.887534i	−0.405129	+	0.0998553i	−0.436614	−	0.899649i	$-0.643822\pi$
$79$	−3.60087	+	0.887534i	−0.405129	+	0.0998553i	0.0314851	+	0.999504i	$0.489976\pi$
$80$	−10.8755	−	3.63078i	−1.21592	−	0.405933i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	−16.6185	+	14.7228i	−1.83521	+	1.62586i
$83$	−8.96600	−	10.9814i	−0.984146	−	1.20536i	−0.978683	−	0.205375i	$-0.934159\pi$
$83$	−8.96600	−	10.9814i	−0.984146	−	1.20536i	−0.00546282	−	0.999985i	$-0.501739\pi$
$84$	2.02167	+	1.27843i	0.220582	+	0.139488i
$85$	−3.28144	+	11.3288i	−0.355922	+	1.22878i
$86$	8.75511	−	2.92288i	0.944088	−	0.315183i
$87$	5.53448	−	6.77850i	0.593358	−	0.726732i
$88$	0.100495	+	2.49376i	0.0107128	+	0.265836i
$89$	−14.9613	+	2.43145i	−1.58590	+	0.257733i	−0.888473	−	0.458928i	$-0.848234\pi$
$89$	−14.9613	+	2.43145i	−1.58590	+	0.257733i	−0.697422	+	0.716661i	$0.745669\pi$
$90$	−3.52882	−	3.12626i	−0.371971	−	0.329537i
$91$	0.242361	−	6.01413i	0.0254064	−	0.630452i
$92$	1.27352	+	10.4884i	0.132774	+	1.09349i
$93$	0.837572	+	6.89803i	0.0868522	+	0.715292i
$94$	−13.7370	−	10.3227i	−1.41686	−	1.06470i
$95$	−3.97587	−	8.37897i	−0.407916	−	0.859664i
$96$	1.46429	−	7.17255i	0.149448	−	0.732045i
$97$	5.10312	+	2.17423i	0.518143	+	0.220760i	0.635175	−	0.772368i	$-0.280928\pi$
$97$	5.10312	+	2.17423i	0.518143	+	0.220760i	−0.117032	+	0.993128i	$0.537338\pi$
$98$	6.83445	−	6.05480i	0.690384	−	0.611627i
$99$	−1.20550	+	3.17866i	−0.121158	+	0.319467i
$100$	1.28598	−	1.33885i	0.128598	−	0.133885i
$101$	−1.83917	−	0.453314i	−0.183004	−	0.0451064i	0.146749	−	0.989174i	$-0.453119\pi$
$101$	−1.83917	−	0.453314i	−0.183004	−	0.0451064i	−0.329753	+	0.944067i	$0.606965\pi$
$102$	−8.92386	−	1.45027i	−0.883594	−	0.143598i
$103$	4.83692	−	12.7539i	0.476596	−	1.25668i	−0.454122	−	0.890940i	$-0.650047\pi$
$103$	4.83692	−	12.7539i	0.476596	−	1.25668i	0.930717	−	0.365739i	$-0.119184\pi$
$104$	−2.82787	+	0.944080i	−0.277295	+	0.0925747i
$105$	3.10676	−	1.96459i	0.303188	−	0.191725i
$106$	−15.4441	+	1.24678i	−1.50006	+	0.121098i
$107$	−7.41041	+	12.8352i	−0.716391	+	1.24083i	0.246029	+	0.969262i	$0.420874\pi$
$107$	−7.41041	+	12.8352i	−0.716391	+	1.24083i	−0.962421	+	0.271564i	$0.912459\pi$
$108$	0.916749	−	1.32814i	0.0882142	−	0.127800i
$109$	0.0290574	+	0.721051i	0.00278319	+	0.0690641i	0.999984	−	0.00570982i	$-0.00181750\pi$
$109$	0.0290574	+	0.721051i	0.00278319	+	0.0690641i	−0.997201	+	0.0747740i	$0.976176\pi$
$110$	−14.7446	−	6.28210i	−1.40585	−	0.598975i
$111$	−4.28679	−	11.3033i	−0.406884	−	1.07286i
$112$	6.06760	+	3.18452i	0.573334	+	0.300909i
$113$	5.14799	+	17.7729i	0.484282	+	1.67193i	0.715167	+	0.698954i	$0.246351\pi$
$113$	5.14799	+	17.7729i	0.484282	+	1.67193i	−0.230885	+	0.972981i	$0.574162\pi$
$114$	6.00861	−	3.79962i	0.562758	−	0.355867i
$115$	15.4006	+	5.14148i	1.43611	+	0.479446i
$116$	−8.02239	+	11.6224i	−0.744861	+	1.07912i
$117$	−4.04773	−	0.326766i	−0.374212	−	0.0302096i
$118$	−13.2501	+	6.95421i	−1.21977	+	0.640187i
$119$	3.02190	−	6.36852i	0.277017	−	0.583801i
$120$	−1.45552	−	1.09376i	−0.132871	−	0.0998458i
$121$	−0.0224318	+	0.556639i	−0.00203925	+	0.0506035i
$122$	5.08142	−	10.7089i	0.460050	−	0.969535i
$123$	−10.7446	+	4.57785i	−0.968809	+	0.412771i
$124$	−2.24306	−	10.9872i	−0.201433	−	0.986684i
$125$	3.38546	+	8.92672i	0.302805	+	0.798430i
$126$	1.78201	+	2.18256i	0.158754	+	0.194438i
$127$	−14.8594	−	2.41489i	−1.31856	−	0.214287i	−0.539899	−	0.841730i	$-0.681537\pi$
$127$	−14.8594	−	2.41489i	−1.31856	−	0.214287i	−0.778663	+	0.627443i	$0.784102\pi$
$128$	0.694735	−	5.72166i	0.0614065	−	0.505728i
$129$	4.85540			0.427494
$130$	2.30767	−	19.0053i	0.202396	−	1.66688i
$131$	6.46177	−	6.72741i	0.564567	−	0.587777i	−0.376323	−	0.926489i	$-0.622812\pi$
$131$	6.46177	−	6.72741i	0.564567	−	0.587777i	0.940890	+	0.338712i	$0.109991\pi$
$132$	1.52637	−	5.26966i	0.132854	−	0.458665i
$133$	1.54215	+	5.32410i	0.133721	+	0.461658i
$134$	2.34551	+	3.39806i	0.202621	+	0.293547i
$135$	−1.23999	−	2.14773i	−0.106722	−	0.184847i
$136$	−3.48019	−	0.280950i	−0.298424	−	0.0240913i
$137$	2.89901	−	0.471135i	0.247679	−	0.0402518i	−0.0353041	−	0.999377i	$-0.511240\pi$
$137$	2.89901	−	0.471135i	0.247679	−	0.0402518i	0.282983	+	0.959125i	$0.408676\pi$
$138$	−2.48945	+	12.1941i	−0.211916	+	1.03803i
$139$	1.47735	+	7.23653i	0.125307	+	0.613794i	0.993139	+	0.116937i	$0.0373076\pi$
$139$	1.47735	+	7.23653i	0.125307	+	0.613794i	−0.867832	+	0.496857i	$0.834487\pi$
$140$	−4.74234	+	3.56364i	−0.400801	+	0.301182i
$141$	−5.13474	−	7.43896i	−0.432424	−	0.626474i
$142$	−11.7387	+	0.947649i	−0.985093	+	0.0795249i
$143$	−13.4041	+	3.30383i	−1.12091	+	0.276280i
$144$	2.31162	−	4.00384i	0.192635	−	0.333653i
$145$	10.8511	+	18.7946i	0.901133	+	1.56081i
$146$	−4.75854	−	4.95417i	−0.393820	−	0.410010i
$147$	4.41877	−	1.88266i	0.364454	−	0.155279i
$148$	8.36346	+	17.6256i	0.687472	+	1.44882i
$149$	−3.85338	−	3.41379i	−0.315681	−	0.279669i	0.490371	−	0.871514i	$-0.336861\pi$
$149$	−3.85338	−	3.41379i	−0.315681	−	0.279669i	−0.806052	+	0.591845i	$0.798400\pi$
$150$	1.93629	−	1.01625i	0.158098	−	0.0829761i
$151$	2.90768	+	3.02722i	0.236624	+	0.246351i	0.828918	−	0.559370i	$-0.188957\pi$
$151$	2.90768	+	3.02722i	0.236624	+	0.246351i	−0.592294	+	0.805722i	$0.701778\pi$
$152$	2.19486	−	1.64933i	0.178027	−	0.133779i
$153$	−4.21112	−	2.21017i	−0.340449	−	0.178681i
$154$	8.09590	+	5.11954i	0.652386	+	0.412544i
$155$	−16.7319	−	4.12404i	−1.34394	−	0.331251i
$156$	6.55352			0.524701
$157$	−3.58359	−	12.0066i	−0.286001	−	0.958229i
$157$	−3.58359	−	12.0066i	−0.286001	−	0.958229i
$158$	7.05012			0.560877
$159$	−7.91378	−	1.95057i	−0.627603	−	0.154690i
$160$	15.3442	+	9.70307i	1.21306	+	0.767095i
$161$	−8.59222	−	4.50955i	−0.677162	−	0.355402i
$162$	1.51974	−	1.14201i	0.119402	−	0.0897250i
$163$	−6.02674	−	6.27451i	−0.472051	−	0.491457i	0.442023	−	0.897003i	$-0.354261\pi$
$163$	−6.02674	−	6.27451i	−0.472051	−	0.491457i	−0.914075	+	0.405546i	$0.867081\pi$
$164$	16.6891	−	8.75910i	1.30320	−	0.683970i
$165$	−6.31061	−	5.59071i	−0.491280	−	0.435236i
$166$	11.5533	+	24.3480i	0.896706	+	1.88977i
$167$	9.10602	−	3.87971i	0.704645	−	0.300221i	−0.00976110	−	0.999952i	$-0.503107\pi$
$167$	9.10602	−	3.87971i	0.704645	−	0.300221i	0.714406	+	0.699731i	$0.246697\pi$
$168$	0.753784	+	0.784773i	0.0581557	+	0.0605465i
$169$	−1.74543	−	3.02318i	−0.134264	−	0.232552i
$170$	11.2107	−	19.4175i	0.859821	−	1.48925i
$171$	3.63103	−	0.894970i	0.277672	−	0.0684400i
$172$	−7.81028	+	0.630511i	−0.595529	+	0.0480760i
$173$	6.48472	+	9.39473i	0.493024	+	0.714268i	0.987968	−	0.154656i	$-0.0494270\pi$
$173$	6.48472	+	9.39473i	0.493024	+	0.714268i	−0.494944	+	0.868925i	$0.664812\pi$
$174$	−13.2991	+	9.99366i	−1.00821	+	0.757617i
$175$	0.341044	+	1.67055i	0.0257805	+	0.126281i
$176$	3.14381	−	15.3994i	0.236974	−	1.16077i
$177$	−7.76981	+	1.26272i	−0.584014	+	0.0949116i
$178$	28.7212	+	2.31861i	2.15274	+	0.173787i
$179$	7.33843	+	12.7105i	0.548500	+	0.950030i	0.998378	+	0.0569398i	$0.0181343\pi$
$179$	7.33843	+	12.7105i	0.548500	+	0.950030i	−0.449877	+	0.893090i	$0.648532\pi$
$180$	2.27352	+	3.29377i	0.169458	+	0.245503i
$181$	2.24526	+	7.75155i	0.166889	+	0.576168i	0.999743	+	0.0226749i	$0.00721825\pi$
$181$	2.24526	+	7.75155i	0.166889	+	0.576168i	−0.832854	+	0.553493i	$0.813295\pi$
$182$	−3.18341	+	10.9904i	−0.235970	+	0.814663i
$183$	4.31933	−	4.49690i	0.319294	−	0.332421i
$184$	−0.579345	+	4.77133i	−0.0427099	+	0.351747i
$185$	29.9803			2.20420
$186$	1.59223	−	13.1132i	0.116748	−	0.961504i
$187$	−15.9586	−	2.59352i	−1.16701	−	0.189657i
$188$	9.22564	+	11.2994i	0.672849	+	0.824091i
$189$	0.525592	+	1.38587i	0.0382312	+	0.100807i
$190$	3.52659	+	17.2744i	0.255846	+	1.25321i
$191$	5.00306	−	2.13160i	0.362008	−	0.154237i	−0.203301	−	0.979116i	$-0.565167\pi$
$191$	5.00306	−	2.13160i	0.362008	−	0.154237i	0.565309	+	0.824879i	$0.308757\pi$
$192$	−2.00191	+	4.21893i	−0.144475	+	0.304475i
$193$	0.246044	−	6.10552i	0.0177106	−	0.439485i	−0.965871	−	0.259022i	$-0.916600\pi$
$193$	0.246044	−	6.10552i	0.0177106	−	0.439485i	0.983582	−	0.180462i	$-0.0577594\pi$
$194$	−8.43000	−	6.33473i	−0.605238	−	0.454807i
$195$	4.31735	−	9.09861i	0.309172	−	0.651565i
$196$	−6.86345	+	3.60222i	−0.490246	+	0.257301i
$197$	−20.2262	−	1.63283i	−1.44106	−	0.116334i	−0.664929	−	0.746906i	$-0.731538\pi$
$197$	−20.2262	−	1.63283i	−1.44106	−	0.116334i	−0.776131	+	0.630572i	$0.782820\pi$
$198$	3.67117	−	5.31861i	0.260899	−	0.377977i
$199$	2.36188	+	0.788513i	0.167430	+	0.0558962i	0.399147	−	0.916887i	$-0.369306\pi$
$199$	2.36188	+	0.788513i	0.167430	+	0.0558962i	−0.231718	+	0.972783i	$0.574434\pi$
$200$	0.713771	−	0.451361i	0.0504712	−	0.0319161i
$201$	0.604284	+	2.08623i	0.0426229	+	0.147151i
$202$	3.18843	+	1.67342i	0.224337	+	0.117741i
$203$	−4.59941	−	12.1276i	−0.322815	−	0.851194i
$204$	7.06092	+	3.00838i	0.494363	+	0.210629i
$205$	−1.16627	−	28.9407i	−0.0814559	−	2.02131i
$206$	−14.7301	+	21.3402i	−1.02629	+	1.48684i
$207$	−3.27344	+	5.66977i	−0.227520	+	0.394076i
$208$	18.7136	−	1.51072i	1.29755	−	0.104749i
$209$	10.7452	−	6.79487i	0.743263	−	0.470011i
$210$	−6.62811	+	2.21279i	−0.457383	+	0.152697i
$211$	−2.98592	+	7.87322i	−0.205559	+	0.542015i	−0.997660	−	0.0683759i	$-0.978218\pi$
$211$	−2.98592	+	7.87322i	−0.205559	+	0.542015i	0.792101	+	0.610391i	$0.208988\pi$
$212$	12.9832	+	2.10998i	0.891691	+	0.144914i
$213$	−6.01510	−	1.48259i	−0.412148	−	0.101585i
$214$	19.5171	−	20.3195i	1.33416	−	1.38901i
$215$	−4.26991	+	11.2588i	−0.291205	+	0.767846i
$216$	0.549517	−	0.486830i	0.0373899	−	0.0331246i
$217$	9.47512	+	4.03697i	0.643213	+	0.274048i
$218$	0.274402	−	1.34411i	0.0185848	−	0.0910345i
$219$	−1.54909	−	3.26464i	−0.104678	−	0.220604i
$220$	10.8771	+	8.17361i	0.733334	+	0.551065i
$221$	−2.32794	−	19.1723i	−0.156594	−	1.28967i
$222$	2.77006	+	22.8135i	0.185914	+	1.53114i
$223$	−0.233598	+	5.79667i	−0.0156429	+	0.388174i	0.972336	+	0.233586i	$0.0750460\pi$
$223$	−0.233598	+	5.79667i	−0.0156429	+	0.388174i	−0.987979	+	0.154588i	$0.950595\pi$
$224$	−8.12161	−	7.19511i	−0.542648	−	0.480744i
$225$	1.13543	−	0.184526i	0.0756954	−	0.0123017i
$226$	−1.41636	−	35.1466i	−0.0942148	−	2.33792i
$227$	−7.97073	+	9.76238i	−0.529036	+	0.647952i	−0.968118	−	0.250496i	$-0.919406\pi$
$227$	−7.97073	+	9.76238i	−0.529036	+	0.647952i	0.439082	+	0.898447i	$0.355304\pi$
$228$	−5.72458	+	1.91115i	−0.379120	+	0.126569i
$229$	3.18691	−	11.0025i	0.210597	−	0.727066i	−0.783768	−	0.621054i	$-0.786705\pi$
$229$	3.18691	−	11.0025i	0.210597	−	0.727066i	0.994365	−	0.106012i	$-0.0338081\pi$
$230$	−26.0868	−	16.4963i	−1.72011	−	1.08773i
$231$	3.18677	+	3.90309i	0.209674	+	0.256804i
$232$	−4.80878	+	4.26021i	−0.315712	+	0.279696i
$233$	0.438171	−	0.536662i	0.0287055	−	0.0351579i	−0.760053	−	0.649861i	$-0.774827\pi$
$233$	0.438171	−	0.536662i	0.0287055	−	0.0351579i	0.788758	+	0.614704i	$0.210724\pi$
$234$	7.32248	+	2.44460i	0.478686	+	0.159809i
$235$	21.7652	−	5.36465i	1.41981	−	0.349951i
$236$	12.3344	−	3.04015i	0.802898	−	0.197897i
$237$	3.51777	+	1.17441i	0.228504	+	0.0762858i
$238$	−8.47501	+	10.3800i	−0.549353	+	0.672835i
$239$	−1.93143	+	1.71110i	−0.124934	+	0.110682i	−0.723276	−	0.690559i	$-0.757365\pi$
$239$	−1.93143	+	1.71110i	−0.124934	+	0.110682i	0.598343	+	0.801240i	$0.295826\pi$
$240$	7.25134	+	8.88128i	0.468072	+	0.573284i
$241$	19.0254	+	12.0309i	1.22553	+	0.774979i	0.980877	−	0.194631i	$-0.0623508\pi$
$241$	19.0254	+	12.0309i	1.22553	+	0.774979i	0.244655	+	0.969610i	$0.421325\pi$
$242$	0.294641	−	1.01722i	0.0189402	−	0.0653892i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	−6.36402	+	7.79451i	−0.407415	+	0.498993i
$245$	0.479634	+	11.9020i	0.0306427	+	0.760391i
$246$	21.9146	−	3.56148i	1.39723	−	0.227071i
$247$	11.3673	+	10.0705i	0.723283	+	0.640773i
$248$	0.205411	−	5.09722i	0.0130436	−	0.323674i
$249$	1.70881	+	14.0734i	0.108292	+	0.891862i
$250$	−2.18763	−	18.0168i	−0.138358	−	1.13948i
$251$	1.29316	+	0.971749i	0.0816237	+	0.0613362i	0.640771	−	0.767732i	$-0.278615\pi$
$251$	1.29316	+	0.971749i	0.0816237	+	0.0613362i	−0.559147	+	0.829068i	$0.688871\pi$
$252$	−1.02542	−	2.16103i	−0.0645954	−	0.136132i
$253$	−4.45190	+	21.8068i	−0.279888	+	1.37098i
$254$	26.3284	+	11.2175i	1.65199	+	0.703846i
$255$	8.82832	−	7.82120i	0.552851	−	0.489783i
$256$	−7.19719	+	18.9774i	−0.449825	+	1.18609i
$257$	−13.4166	+	13.9682i	−0.836906	+	0.871311i	−0.993203	−	0.116399i	$-0.962865\pi$
$257$	−13.4166	+	13.9682i	−0.836906	+	0.871311i	0.156297	+	0.987710i	$0.450044\pi$
$258$	−8.96191	−	2.20891i	−0.557944	−	0.137521i
$259$	−17.6860	−	2.87426i	−1.09896	−	0.178598i
$260$	−5.76326	+	15.1965i	−0.357422	+	0.942445i
$261$	−8.30056	+	2.77114i	−0.513792	+	0.171529i
$262$	−14.9875	+	9.47749i	−0.925928	+	0.585522i
$263$	14.6311	−	1.18115i	0.902194	−	0.0728326i	0.379342	−	0.925256i	$-0.376150\pi$
$263$	14.6311	−	1.18115i	0.902194	−	0.0728326i	0.522851	+	0.852424i	$0.324868\pi$
$264$	1.24789	−	2.16141i	0.0768025	−	0.133026i
$265$	11.4825	−	16.6353i	0.705366	−	1.02190i
$266$	−0.424289	−	10.5286i	−0.0260148	−	0.645551i
$267$	13.9447	+	5.94127i	0.853400	+	0.363600i
$268$	−1.24295	−	3.27739i	−0.0759253	−	0.200199i
$269$	14.0541	+	7.37619i	0.856897	+	0.449734i	0.835145	−	0.550029i	$-0.185383\pi$
$269$	14.0541	+	7.37619i	0.856897	+	0.449734i	0.0217513	+	0.999763i	$0.493076\pi$
$270$	1.31164	+	4.52832i	0.0798242	+	0.275585i
$271$	−10.2571	+	6.48621i	−0.623076	+	0.394009i	−0.808371	−	0.588674i	$-0.799650\pi$
$271$	−10.2571	+	6.48621i	−0.623076	+	0.394009i	0.185295	+	0.982683i	$0.440676\pi$
$272$	20.8560	+	6.96275i	1.26458	+	0.422179i
$273$	−3.41919	+	4.95355i	−0.206939	+	0.299803i
$274$	−5.56523	−	0.449271i	−0.336208	−	0.0271415i
$275$	3.46268	−	1.81736i	0.208808	−	0.109591i
$276$	4.52932	−	9.54535i	0.272633	−	0.574562i
$277$	−7.49011	−	5.62845i	−0.450037	−	0.338181i	0.351436	−	0.936212i	$-0.385694\pi$
$277$	−7.49011	−	5.62845i	−0.450037	−	0.338181i	−0.801473	+	0.598031i	$0.795950\pi$
$278$	0.565350	−	14.0290i	0.0339074	−	0.841405i
$279$	2.97885	−	6.27780i	0.178339	−	0.375842i
$280$	−2.48264	+	1.05775i	−0.148366	+	0.0632129i
$281$	−1.47258	−	7.21319i	−0.0878470	−	0.430303i	−0.999800	−	0.0200079i	$-0.993631\pi$
$281$	−1.47258	−	7.21319i	−0.0878470	−	0.430303i	0.911953	−	0.410295i	$-0.134574\pi$
$282$	6.09324	+	16.0666i	0.362847	+	0.956750i
$283$	−14.8266	−	18.1592i	−0.881348	−	1.07946i	−0.996288	−	0.0860827i	$-0.972565\pi$
$283$	−14.8266	−	18.1592i	−0.881348	−	1.07946i	0.114940	−	0.993372i	$-0.463332\pi$
$284$	9.86827	+	1.60375i	0.585574	+	0.0951651i
$285$	−1.11791	+	9.20679i	−0.0662191	+	0.545363i
$286$	26.2439			1.55184
$287$	−2.08658	+	17.1845i	−0.123167	+	1.01437i
$288$	−5.07108	+	5.27956i	−0.298816	+	0.311101i
$289$	1.56313	−	5.39655i	0.0919488	−	0.317444i
$290$	−11.4781	−	39.6270i	−0.674017	−	2.32698i
$291$	−3.15105	−	4.56508i	−0.184718	−	0.267610i
$292$	2.91577	+	5.05026i	0.170633	+	0.295544i
$293$	2.38230	+	0.192319i	0.139175	+	0.0112354i	0.149858	−	0.988708i	$-0.452118\pi$
$293$	2.38230	+	0.192319i	0.139175	+	0.0112354i	−0.0106825	+	0.999943i	$0.503400\pi$
$294$	−9.01249	+	1.46467i	−0.525619	+	0.0854214i
$295$	3.90486	−	19.1273i	0.227350	−	1.11363i
$296$	1.77524	+	8.69568i	0.103184	+	0.505426i
$297$	2.71776	−	2.04227i	0.157701	−	0.118504i
$298$	5.55935	+	8.05411i	0.322045	+	0.466562i
$299$	−26.5000	+	2.13930i	−1.53254	+	0.123719i
$300$	−1.80247	+	0.444268i	−0.104065	+	0.0256498i
$301$	3.59831	−	6.23246i	0.207403	−	0.359233i
$302$	−3.98969	−	6.91035i	−0.229581	−	0.397646i
$303$	1.31216	+	1.36611i	0.0753819	+	0.0784809i
$304$	−15.9060	+	6.77692i	−0.912273	+	0.388683i
$305$	6.62905	+	13.9704i	0.379578	+	0.799944i
$306$	6.76724	+	5.99525i	0.386857	+	0.342726i
$307$	−13.6836	+	7.18172i	−0.780965	+	0.409882i	−0.807576	−	0.589764i	$-0.799221\pi$
$307$	−13.6836	+	7.18172i	−0.780965	+	0.409882i	0.0266106	+	0.999646i	$0.491529\pi$
$308$	−5.63302	−	5.86459i	−0.320971	−	0.334166i
$309$	−10.9046	+	8.19430i	−0.620343	+	0.466158i
$310$	29.0069	+	15.2240i	1.64748	+	0.864666i
$311$	−25.7454	−	16.2804i	−1.45989	−	0.923177i	−0.999369	−	0.0355275i	$-0.988689\pi$
$311$	−25.7454	−	16.2804i	−1.45989	−	0.923177i	−0.460519	−	0.887650i	$-0.652337\pi$
$312$	2.89466	+	0.713470i	0.163878	+	0.0403923i
$313$	−5.99226			−0.338703			−0.169351	−	0.985556i	$-0.554167\pi$
$313$	−5.99226			−0.338703			−0.169351	+	0.985556i	$0.554167\pi$
$314$	1.15218	+	23.7916i	0.0650214	+	1.34264i
$315$	−3.67581			−0.207108
$316$	−5.81112	−	1.43231i	−0.326901	−	0.0805738i
$317$	−10.9283	−	6.91065i	−0.613795	−	0.388141i	0.191089	−	0.981573i	$-0.438798\pi$
$317$	−10.9283	−	6.91065i	−0.613795	−	0.388141i	−0.804884	+	0.593432i	$0.797773\pi$
$318$	13.7196	+	7.20058i	0.769355	+	0.403789i
$319$	−23.7829	+	17.8717i	−1.33159	+	1.00062i
$320$	−8.02246	−	8.35227i	−0.448469	−	0.466906i
$321$	13.1232	−	6.88758i	0.732465	−	0.384427i
$322$	13.8076	+	12.2325i	0.769469	+	0.681690i
$323$	7.62454	+	16.0684i	0.424241	+	0.894069i
$324$	−1.48467	+	0.632560i	−0.0824818	+	0.0351422i
$325$	3.23596	+	3.36900i	0.179499	+	0.186878i
$326$	8.26942	+	14.3231i	0.458001	+	0.793281i
$327$	0.360818	−	0.624955i	0.0199533	−	0.0345601i
$328$	8.32508	−	2.05195i	0.459676	−	0.113300i
$329$	−13.3541	+	1.07805i	−0.736235	+	0.0594350i
$330$	9.10445	+	13.1901i	0.501184	+	0.726090i
$331$	28.6679	−	21.5426i	1.57573	−	1.18409i	0.686001	−	0.727600i	$-0.259364\pi$
$331$	28.6679	−	21.5426i	1.57573	−	1.18409i	0.889731	−	0.456486i	$-0.150892\pi$
$332$	−4.57629	−	22.4162i	−0.251157	−	1.23025i
$333$	−2.41809	+	11.8446i	−0.132511	+	0.649080i
$334$	−18.5726	+	3.01834i	−1.01625	+	0.165156i
$335$	−5.36902	−	0.433432i	−0.293341	−	0.0236809i
$336$	−3.42626	−	5.93445i	−0.186918	−	0.323751i
$337$	2.51399	+	3.64214i	0.136946	+	0.198400i	0.885456	−	0.464723i	$-0.153846\pi$
$337$	2.51399	+	3.64214i	0.136946	+	0.198400i	−0.748511	+	0.663123i	$0.769231\pi$
$338$	1.84629	+	6.37414i	0.100425	+	0.346707i
$339$	5.14799	−	17.7729i	0.279600	−	0.965292i
$340$	−13.1854	+	13.7274i	−0.715078	+	0.744475i
$341$	2.84739	−	23.4503i	0.154195	−	1.26991i
$342$	−7.10919			−0.384421
$343$	2.10872	−	17.3669i	0.113860	−	0.937724i
$344$	−3.51842	−	0.571798i	−0.189700	−	0.0308293i
$345$	−10.2685	−	12.5766i	−0.552838	−	0.677103i
$346$	−7.69521	−	20.2906i	−0.413697	−	1.09083i
$347$	−2.81329	−	13.7804i	−0.151025	−	0.739770i	−0.982802	−	0.184661i	$-0.940881\pi$
$347$	−2.81329	−	13.7804i	−0.151025	−	0.739770i	0.831777	−	0.555110i	$-0.187324\pi$
$348$	12.9922	−	5.53548i	0.696458	−	0.296733i
$349$	11.2174	−	23.6402i	0.600454	−	1.26543i	−0.344672	−	0.938723i	$-0.612010\pi$
$349$	11.2174	−	23.6402i	0.600454	−	1.26543i	0.945126	−	0.326706i	$-0.105939\pi$
$350$	0.130511	−	3.23859i	0.00697608	−	0.173110i
$351$	3.24645	+	2.43955i	0.173283	+	0.130214i
$352$	−10.6687	+	22.4838i	−0.568642	+	1.19839i
$353$	−2.35128	+	1.23405i	−0.125146	+	0.0656817i	−0.526134	−	0.850401i	$-0.676359\pi$
$353$	−2.35128	+	1.23405i	−0.125146	+	0.0656817i	0.400988	+	0.916083i	$0.368667\pi$
$354$	14.9157	+	1.20412i	0.792759	+	0.0639981i
$355$	8.72763	−	12.6442i	0.463214	−	0.671082i
$356$	−23.2026	−	7.74617i	−1.22974	−	0.410546i
$357$	−5.95784	+	3.76751i	−0.315322	+	0.199398i
$358$	−7.76248	−	26.7992i	−0.410260	−	1.41638i
$359$	−3.74983	−	1.96806i	−0.197909	−	0.103870i	0.362858	−	0.931845i	$-0.381801\pi$
$359$	−3.74983	−	1.96806i	−0.197909	−	0.103870i	−0.560766	+	0.827974i	$0.689493\pi$
$360$	0.645620	+	1.70236i	0.0340272	+	0.0897222i
$361$	4.61334	+	1.96556i	0.242808	+	0.103451i
$362$	−0.617737	−	15.3290i	−0.0324675	−	0.805673i
$363$	0.316463	−	0.458476i	0.0166100	−	0.0240638i
$364$	4.85677	−	8.41218i	0.254564	−	0.440918i
$365$	8.93242	−	0.721100i	0.467544	−	0.0377441i
$366$	−10.0183	+	6.33518i	−0.523664	+	0.331145i
$367$	−18.4996	+	6.17608i	−0.965673	+	0.322389i	−0.755407	−	0.655255i	$-0.772561\pi$
$367$	−18.4996	+	6.17608i	−0.965673	+	0.322389i	−0.210265	+	0.977644i	$0.567433\pi$
$368$	10.7331	−	28.3009i	0.559502	−	1.47529i
$369$	11.5279	+	1.87347i	0.600121	+	0.0975291i
$370$	−55.3366	−	13.6392i	−2.87681	−	0.709070i
$371$	−8.36864	+	8.71268i	−0.434478	+	0.452340i
$372$	−3.97649	+	10.4852i	−0.206172	+	0.543630i
$373$	−10.4781	+	9.28275i	−0.542533	+	0.480642i	−0.889310	−	0.457305i	$-0.848815\pi$
$373$	−10.4781	+	9.28275i	−0.542533	+	0.480642i	0.346777	+	0.937948i	$0.387276\pi$
$374$	28.2759	+	12.0472i	1.46211	+	0.622947i
$375$	1.90967	−	9.35419i	0.0986150	−	0.483048i
$376$	2.84479	+	5.99527i	0.146709	+	0.309182i
$377$	−28.4094	−	21.3483i	−1.46316	−	1.09949i
$378$	−0.339630	−	2.79710i	−0.0174687	−	0.143867i
$379$	1.98578	+	16.3544i	0.102003	+	0.840067i	0.950469	+	0.310818i	$0.100603\pi$
$379$	1.98578	+	16.3544i	0.102003	+	0.840067i	−0.848467	+	0.529249i	$0.822474\pi$
$380$	0.602666	−	14.9550i	0.0309161	−	0.767176i
$381$	11.2684	+	9.98290i	0.577296	+	0.511440i
$382$	−10.2042	+	1.65834i	−0.522093	+	0.0848483i
$383$	−0.911362	−	22.6152i	−0.0465684	−	1.15558i	−0.838475	−	0.544941i	$-0.816552\pi$
$383$	−0.911362	−	22.6152i	−0.0465684	−	1.15558i	0.791906	−	0.610643i	$-0.209089\pi$
$384$	−3.64522	+	4.46458i	−0.186019	+	0.227832i
$385$	−11.8531	+	3.95714i	−0.604089	+	0.201674i
$386$	−3.23178	+	11.1574i	−0.164493	+	0.567897i
$387$	−4.10373	−	2.59504i	−0.208605	−	0.131914i
$388$	5.66152	+	6.93410i	0.287420	+	0.352026i
$389$	21.5670	−	19.1067i	1.09349	−	0.968749i	0.0938512	−	0.995586i	$-0.470082\pi$
$389$	21.5670	−	19.1067i	1.09349	−	0.968749i	0.999640	+	0.0268377i	$0.00854374\pi$
$390$	−12.1081	+	14.8298i	−0.613118	+	0.750934i
$391$	−29.5338	−	9.85984i	−1.49359	−	0.498633i
$392$	−3.42373	+	0.843873i	−0.172924	+	0.0426220i
$393$	−9.05699	+	2.23235i	−0.456865	+	0.112607i
$394$	36.5900	+	12.2155i	1.84338	+	0.615410i
$395$	−5.81682	+	7.12432i	−0.292676	+	0.358463i
$396$	−4.10653	+	3.63807i	−0.206361	+	0.182820i
$397$	−19.6446	−	24.0603i	−0.985935	−	1.20755i	−0.978218	−	0.207581i	$-0.933441\pi$
$397$	−19.6446	−	24.0603i	−0.985935	−	1.20755i	−0.00771685	−	0.999970i	$-0.502456\pi$
$398$	−4.00075	−	2.52992i	−0.200540	−	0.126814i
$399$	1.54215	−	5.32410i	0.0772038	−	0.266539i
$400$	−5.04454	+	1.68412i	−0.252227	+	0.0842058i
$401$	13.3217	−	16.3161i	0.665255	−	0.814790i	−0.326191	−	0.945304i	$-0.605765\pi$
$401$	13.3217	−	16.3161i	0.665255	−	0.814790i	0.991446	+	0.130514i	$0.0416628\pi$
$402$	−0.166256	−	4.12560i	−0.00829209	−	0.205766i
$403$	27.8525	−	4.52647i	1.38743	−	0.225480i
$404$	−2.28812	−	2.02710i	−0.113838	−	0.100852i
$405$	−0.0998589	+	2.47797i	−0.00496203	+	0.123132i
$406$	2.97207	+	24.4772i	0.147501	+	1.21478i
$407$	4.95371	+	40.7975i	0.245546	+	2.02226i
$408$	2.79127	+	2.09750i	0.138188	+	0.103842i
$409$	−3.41522	−	7.19743i	−0.168872	−	0.355890i	0.801317	−	0.598240i	$-0.204133\pi$
$409$	−3.41522	−	7.19743i	−0.168872	−	0.355890i	−0.970189	+	0.242350i	$0.922082\pi$
$410$	−11.0136	+	53.9483i	−0.543924	+	2.66431i
$411$	−2.70202	−	1.15122i	−0.133281	−	0.0567857i
$412$	16.4769	−	14.5972i	0.811757	−	0.719154i
$413$	−4.13732	+	10.9092i	−0.203584	+	0.536808i
$414$	8.62141	−	8.97583i	0.423719	−	0.441138i
$415$	−34.1364	−	8.41387i	−1.67569	−	0.413021i
$416$	−29.3428	−	4.76867i	−1.43865	−	0.233803i
$417$	2.61904	−	6.90583i	0.128255	−	0.338180i
$418$	−22.9244	+	7.65329i	−1.12127	+	0.374335i
$419$	−13.8897	+	8.78328i	−0.678554	+	0.429091i	−0.828791	−	0.559559i	$-0.810971\pi$
$419$	−13.8897	+	8.78328i	−0.678554	+	0.429091i	0.150237	+	0.988650i	$0.451996\pi$
$420$	5.91282	−	0.477332i	0.288516	−	0.0232914i
$421$	8.95474	−	15.5101i	0.436427	−	0.755915i	−0.560983	−	0.827827i	$-0.689577\pi$
$421$	8.95474	−	15.5101i	0.436427	−	0.755915i	0.997411	+	0.0719124i	$0.0229102\pi$
$422$	9.09314	−	13.1737i	0.442647	−	0.641285i
$423$	0.363964	+	9.03168i	0.0176966	+	0.439135i
$424$	5.50493	+	2.34543i	0.267343	+	0.113904i
$425$	1.93998	+	5.11530i	0.0941028	+	0.248129i
$426$	10.4280	+	5.47301i	0.505236	+	0.265168i
$427$	−2.57125	−	8.87698i	−0.124431	−	0.429587i
$428$	−20.2152	+	12.7833i	−0.977141	+	0.617906i
$429$	13.0948	+	4.37170i	0.632225	+	0.211068i
$430$	13.0033	−	18.8386i	0.627076	−	0.908477i
$431$	33.3218	+	2.69002i	1.60506	+	0.129574i	0.850252	−	0.526376i	$-0.176450\pi$
$431$	33.3218	+	2.69002i	1.60506	+	0.129574i	0.754805	+	0.655950i	$0.227732\pi$
$432$	−4.09367	+	2.14853i	−0.196957	+	0.103371i
$433$	0.269122	−	0.567162i	0.0129332	−	0.0272561i	−0.896881	−	0.442272i	$-0.854173\pi$
$433$	0.269122	−	0.567162i	0.0129332	−	0.0272561i	0.909814	+	0.415016i	$0.136224\pi$
$434$	−15.6522	−	11.7619i	−0.751332	−	0.564589i
$435$	0.873857	−	21.6845i	0.0418983	−	1.03969i
$436$	−0.499248	+	1.05214i	−0.0239097	+	0.0503885i
$437$	22.5242	−	9.59668i	1.07748	−	0.459072i
$438$	1.37404	+	6.73049i	0.0656542	+	0.321595i
$439$	3.98012	+	10.4947i	0.189961	+	0.500885i	0.995832	−	0.0912053i	$-0.0290719\pi$
$439$	3.98012	+	10.4947i	0.189961	+	0.500885i	−0.805871	+	0.592091i	$0.798303\pi$
$440$	3.91453	+	4.79443i	0.186618	+	0.228565i
$441$	−4.74092	−	0.770474i	−0.225758	−	0.0366892i
$442$	−4.42542	+	36.4466i	−0.210496	+	1.73359i
$443$	−24.5911			−1.16836			−0.584179	−	0.811625i	$-0.698583\pi$
$443$	−24.5911			−1.16836			−0.584179	+	0.811625i	$0.698583\pi$
$444$	2.35158	−	19.3670i	0.111601	−	0.919116i
$445$	−26.0399	+	27.1104i	−1.23441	+	1.28516i
$446$	3.06830	−	10.5930i	0.145288	−	0.501593i
$447$	1.43228	+	4.94480i	0.0677445	+	0.233881i
$448$	3.93187	+	5.69630i	0.185764	+	0.269125i
$449$	−2.56388	−	4.44077i	−0.120997	−	0.209573i	0.799164	−	0.601113i	$-0.205276\pi$
$449$	−2.56388	−	4.44077i	−0.120997	−	0.209573i	−0.920161	+	0.391540i	$0.871942\pi$
$450$	−2.17968	−	0.175962i	−0.102751	−	0.00829494i
$451$	39.1901	−	6.36900i	1.84539	−	0.299905i
$452$	−5.97298	+	29.2576i	−0.280945	+	1.37616i
$453$	−0.839600	−	4.11263i	−0.0394478	−	0.193228i
$454$	19.1534	−	14.3928i	0.898912	−	0.675489i
$455$	−8.47954	−	12.2847i	−0.397527	−	0.575917i
$456$	−2.73659	+	0.220920i	−0.128153	+	0.0103455i
$457$	−30.4422	+	7.50333i	−1.42403	+	0.350991i	−0.874720	−	0.484629i	$-0.838955\pi$
$457$	−30.4422	+	7.50333i	−1.42403	+	0.350991i	−0.549307	+	0.835620i	$0.685108\pi$
$458$	−10.8878	+	18.8582i	−0.508752	+	0.881184i
$459$	2.37794	+	4.11871i	0.110993	+	0.192245i
$460$	18.1509	+	18.8970i	0.846288	+	0.881079i
$461$	−1.59739	+	0.680586i	−0.0743980	+	0.0316980i	−0.428845	−	0.903378i	$-0.641079\pi$
$461$	−1.59739	+	0.680586i	−0.0743980	+	0.0316980i	0.354447	+	0.935076i	$0.384669\pi$
$462$	−4.10636	−	8.65396i	−0.191045	−	0.402619i
$463$	−18.2617	−	16.1784i	−0.848692	−	0.751876i	0.121916	−	0.992540i	$-0.461096\pi$
$463$	−18.2617	−	16.1784i	−0.848692	−	0.751876i	−0.970608	+	0.240665i	$0.922635\pi$
$464$	35.8234	−	18.8016i	1.66306	−	0.872841i
$465$	11.9375	+	12.4282i	0.553587	+	0.576345i
$466$	−1.05291	+	0.791209i	−0.0487750	+	0.0366521i
$467$	16.4722	+	8.64530i	0.762244	+	0.400057i	0.800594	−	0.599208i	$-0.204518\pi$
$467$	16.4722	+	8.64530i	0.762244	+	0.400057i	−0.0383493	+	0.999264i	$0.512210\pi$
$468$	−5.53897	−	3.50263i	−0.256039	−	0.161909i
$469$	3.12574	+	0.770427i	0.144333	+	0.0355750i
$470$	−42.6141			−1.96564
$471$	−3.38829	+	12.0631i	−0.156124	+	0.555840i
$472$	5.77902			0.266001
$473$	−16.0266	−	3.95021i	−0.736905	−	0.181631i
$474$	−5.95869	−	3.76805i	−0.273692	−	0.173072i
$475$	−3.80913	−	1.99919i	−0.174775	−	0.0917289i
$476$	9.09440	−	6.83400i	0.416841	−	0.313236i
$477$	5.64613	+	5.87825i	0.258519	+	0.269146i
$478$	4.34340	−	2.27959i	0.198663	−	0.104266i
$479$	7.58604	+	6.72065i	0.346615	+	0.307074i	0.818411	−	0.574634i	$-0.194855\pi$
$479$	7.58604	+	6.72065i	0.346615	+	0.307074i	−0.471795	+	0.881708i	$0.656394\pi$
$480$	−7.78279	−	16.4019i	−0.355234	−	0.748640i
$481$	−45.1635	+	19.2423i	−2.05928	+	0.877376i
$482$	−29.6430	−	30.8616i	−1.35020	−	1.40571i
$483$	4.85186	+	8.40367i	0.220767	+	0.382380i
$484$	−0.449519	+	0.778590i	−0.0204327	+	0.0353905i
$485$	13.3567	−	3.29213i	0.606497	−	0.149488i
$486$	−1.89484	+	0.152967i	−0.0859516	+	0.00693873i
$487$	4.46598	+	6.47009i	0.202373	+	0.293188i	0.911009	−	0.412386i	$-0.135305\pi$
$487$	4.46598	+	6.47009i	0.202373	+	0.293188i	−0.708636	+	0.705574i	$0.750689\pi$
$488$	−3.65954	+	2.74997i	−0.165660	+	0.124485i
$489$	1.74024	+	8.52424i	0.0786962	+	0.385479i
$490$	4.52940	−	22.1865i	0.204617	−	1.00228i
$491$	16.3786	−	2.66178i	0.739154	−	0.120124i	0.220835	−	0.975311i	$-0.429122\pi$
$491$	16.3786	−	2.66178i	0.739154	−	0.120124i	0.518320	+	0.855187i	$0.326558\pi$
$492$	−18.7869	−	1.51663i	−0.846977	−	0.0683751i
$493$	−20.8091	−	36.0425i	−0.937197	−	1.62327i
$494$	−16.3998	−	23.7593i	−0.737863	−	1.06898i
$495$	2.34562	+	8.09802i	0.105428	+	0.363979i
$496$	−8.93786	+	30.8571i	−0.401322	+	1.38552i
$497$	−6.36083	+	6.62232i	−0.285322	+	0.297052i
$498$	3.24846	−	26.7535i	0.145567	−	1.19885i
$499$	28.7131			1.28538			0.642688	−	0.766128i	$-0.277819\pi$
$499$	28.7131			1.28538			0.642688	+	0.766128i	$0.277819\pi$
$500$	−1.85714	+	15.2949i	−0.0830538	+	0.684010i
$501$	−9.76990	−	1.58776i	−0.436487	−	0.0709360i
$502$	−1.94478	−	2.38193i	−0.0868000	−	0.106311i
$503$	5.87808	+	15.4992i	0.262090	+	0.691076i	0.999871	+	0.0160356i	$0.00510449\pi$
$503$	5.87808	+	15.4992i	0.262090	+	0.691076i	−0.737781	+	0.675040i	$0.764126\pi$
$504$	−0.217657	−	1.06615i	−0.00969521	−	0.0474903i
$505$	−4.32170	+	1.84131i	−0.192313	+	0.0819371i
$506$	18.1379	−	38.2249i	0.806330	−	1.69930i
$507$	−0.140563	+	3.48804i	−0.00624262	+	0.154909i
$508$	−19.4224	−	14.5950i	−0.861730	−	0.647548i
$509$	−14.4271	+	30.4044i	−0.639469	+	1.34765i	0.282080	+	0.959391i	$0.408976\pi$
$509$	−14.4271	+	30.4044i	−0.639469	+	1.34765i	−0.921549	+	0.388262i	$0.873076\pi$
$510$	−19.8532	+	10.4197i	−0.879112	+	0.461394i
$511$	−5.33856	−	0.430973i	−0.236164	−	0.0190651i
$512$	15.3696	−	22.2667i	0.679247	−	0.984059i
$513$	−3.54725	−	1.18424i	−0.156615	−	0.0522857i
$514$	31.1186	−	19.6782i	1.37258	−	0.867968i
$515$	−9.41147	−	32.4922i	−0.414719	−	1.43178i
$516$	6.93816	+	3.64143i	0.305436	+	0.160305i
$517$	10.8966	+	28.7319i	0.479231	+	1.26363i
$518$	31.3366	+	13.3513i	1.37685	+	0.586621i
$519$	−0.459654	−	11.4062i	−0.0201766	−	0.500676i
$520$	−4.20002	+	6.08479i	−0.184183	+	0.266835i
$521$	−11.8435	+	20.5135i	−0.518873	+	0.898714i	0.480887	+	0.876783i	$0.340315\pi$
$521$	−11.8435	+	20.5135i	−0.518873	+	0.898714i	−0.999759	+	0.0219314i	$0.993018\pi$
$522$	16.5816	−	1.33860i	0.725756	−	0.0585891i
$523$	29.7112	−	18.7882i	1.29918	−	0.821552i	0.307659	−	0.951497i	$-0.400454\pi$
$523$	29.7112	−	18.7882i	1.29918	−	0.821552i	0.991521	+	0.129945i	$0.0414801\pi$
$524$	14.2790	−	4.76703i	0.623781	−	0.208249i
$525$	0.604602	−	1.59421i	0.0263870	−	0.0695768i
$526$	−27.5429	−	4.47616i	−1.20093	−	0.195170i
$527$	32.0868	+	7.90869i	1.39772	+	0.344508i
$528$	−10.8876	+	11.3352i	−0.473821	+	0.493299i
$529$	−7.04307	+	18.5711i	−0.306221	+	0.807437i
$530$	−28.7621	+	25.4810i	−1.24935	+	1.10682i
$531$	7.24184	+	3.08546i	0.314269	+	0.133898i
$532$	−1.78928	+	8.76449i	−0.0775753	+	0.379989i
$533$	20.3320	+	42.8488i	0.880677	+	1.85599i
$534$	−23.0356	−	17.3102i	−0.996850	−	0.749084i
$535$	4.43037	+	36.4874i	0.191542	+	1.57749i
$536$	−0.192202	−	1.58293i	−0.00830188	−	0.0683721i
$537$	0.590978	−	14.6650i	0.0255026	−	0.632840i
$538$	−22.5849	−	20.0085i	−0.973705	−	0.862627i
$539$	−16.1171	+	2.61928i	−0.694212	+	0.112820i
$540$	−0.161153	−	3.99898i	−0.00693494	−	0.172089i
$541$	13.6398	−	16.7057i	0.586420	−	0.718234i	−0.393119	−	0.919487i	$-0.628604\pi$
$541$	13.6398	−	16.7057i	0.586420	−	0.718234i	0.979539	+	0.201253i	$0.0645015\pi$
$542$	21.8831	−	7.30564i	0.939958	−	0.313804i
$543$	2.24526	−	7.75155i	0.0963534	−	0.332651i
$544$	−29.4256	−	18.6076i	−1.26161	−	0.797795i
$545$	1.13185	+	1.38627i	0.0484833	+	0.0593812i
$546$	8.56458	−	7.58756i	0.366530	−	0.324717i
$547$	−0.739508	+	0.905733i	−0.0316191	+	0.0387264i	−0.790172	−	0.612885i	$-0.790009\pi$
$547$	−0.739508	+	0.905733i	−0.0316191	+	0.0387264i	0.758553	+	0.651611i	$0.225906\pi$
$548$	4.49591	+	1.50095i	0.192056	+	0.0641176i
$549$	−6.05410	+	1.49220i	−0.258383	+	0.0636856i
$550$	−7.21808	+	1.77910i	−0.307780	+	0.0758609i
$551$	31.0417	+	10.3632i	1.32242	+	0.441488i
$552$	3.03977	−	3.72304i	0.129381	−	0.158463i
$553$	4.11448	−	3.64512i	0.174966	−	0.155006i
$554$	11.2644	+	13.7963i	0.478577	+	0.586150i
$555$	−25.3391	−	16.0235i	−1.07558	−	0.680158i
$556$	−3.31615	+	11.4487i	−0.140636	+	0.485532i
$557$	43.1744	−	14.4137i	1.82936	−	0.610729i	0.830828	−	0.556530i	$-0.187867\pi$
$557$	43.1744	−	14.4137i	1.82936	−	0.610729i	0.998530	−	0.0541997i	$-0.0172608\pi$
$558$	−8.35427	+	10.2321i	−0.353665	+	0.433160i
$559$	−0.793934	−	19.7013i	−0.0335798	−	0.833275i
$560$	16.7741	−	2.72605i	0.708833	−	0.115197i
$561$	12.1019	+	10.7213i	0.510942	+	0.452655i
$562$	−0.563527	+	13.9838i	−0.0237710	+	0.589870i
$563$	−4.54828	−	37.4584i	−0.191687	−	1.57869i	−0.697848	−	0.716246i	$-0.745859\pi$
$563$	−4.54828	−	37.4584i	−0.191687	−	1.57869i	0.506161	−	0.862439i	$-0.331064\pi$
$564$	−1.75830	−	14.4809i	−0.0740378	−	0.609756i
$565$	36.6851	+	27.5670i	1.54335	+	1.15975i
$566$	19.1050	+	40.2629i	0.803041	+	1.69237i
$567$	0.296476	−	1.45224i	0.0124508	−	0.0609881i
$568$	4.18418	+	1.78271i	0.175564	+	0.0748010i
$569$	17.1138	−	15.1615i	0.717448	−	0.635604i	−0.223284	−	0.974753i	$-0.571678\pi$
$569$	17.1138	−	15.1615i	0.717448	−	0.635604i	0.940732	+	0.339150i	$0.110139\pi$
$570$	6.25192	−	16.4850i	0.261864	−	0.690479i
$571$	24.1079	−	25.0990i	1.00888	−	1.05036i	0.0101555	−	0.999948i	$-0.496767\pi$
$571$	24.1079	−	25.0990i	1.00888	−	1.05036i	0.998729	−	0.0504111i	$-0.0160532\pi$
$572$	−21.6318	−	5.33175i	−0.904469	−	0.222932i
$573$	−5.36780	−	0.872353i	−0.224243	−	0.0364431i
$574$	11.6693	−	30.7693i	0.487066	−	1.28429i
$575$	7.14349	−	2.38485i	0.297904	−	0.0994550i
$576$	3.94687	−	2.49585i	0.164453	−	0.103994i
$577$	10.5995	−	0.855679i	0.441263	−	0.0356224i	0.142161	−	0.989844i	$-0.454595\pi$
$577$	10.5995	−	0.855679i	0.441263	−	0.0356224i	0.299102	+	0.954221i	$0.403313\pi$
$578$	−5.34027	+	9.24962i	−0.222126	+	0.384733i
$579$	−3.47114	+	5.02882i	−0.144256	+	0.208991i
$580$	1.41024	+	34.9948i	0.0585570	+	1.45308i
$581$	19.3311	+	8.23623i	0.801991	+	0.341696i
$582$	3.73925	+	9.85960i	0.154997	+	0.408693i
$583$	24.5348	+	12.8768i	1.01613	+	0.533304i
$584$	0.738071	+	2.54812i	0.0305416	+	0.105442i
$585$	−8.51188	+	5.38258i	−0.351923	+	0.222542i
$586$	−4.30967	−	1.43878i	−0.178031	−	0.0594354i
$587$	−0.369293	+	0.535013i	−0.0152423	+	0.0220823i	−0.830531	−	0.556972i	$-0.811963\pi$
$587$	−0.369293	+	0.535013i	−0.0152423	+	0.0220823i	0.815289	+	0.579055i	$0.196578\pi$
$588$	7.72618	+	0.623722i	0.318622	+	0.0257219i
$589$	−23.0095	+	12.0763i	−0.948090	+	0.497596i
$590$	−15.9092	+	33.5280i	−0.654972	+	1.38032i
$591$	16.2223	+	12.1903i	0.667298	+	0.501442i
$592$	2.25046	−	55.8446i	0.0924933	−	2.29520i
$593$	−3.94472	+	8.31332i	−0.161990	+	0.341387i	−0.968174	−	0.250278i	$-0.919478\pi$
$593$	−3.94472	+	8.31332i	−0.161990	+	0.341387i	0.806184	+	0.591665i	$0.201529\pi$
$594$	−5.94545	+	2.53312i	−0.243945	+	0.103935i
$595$	−3.49679	−	17.1284i	−0.143354	−	0.702196i
$596$	−2.94605	−	7.76811i	−0.120675	−	0.318194i
$597$	−1.57481	−	1.92879i	−0.0644526	−	0.0789401i
$598$	49.8860	+	8.10726i	2.03999	+	0.331531i
$599$	1.28548	−	10.5869i	0.0525232	−	0.432568i	−0.942600	−	0.333925i	$-0.891627\pi$
$599$	1.28548	−	10.5869i	0.0525232	−	0.432568i	0.995123	−	0.0986428i	$-0.0314501\pi$
$600$	−0.844510			−0.0344770
$601$	0.281421	−	2.31771i	0.0114794	−	0.0945415i	−0.985843	−	0.167671i	$-0.946375\pi$
$601$	0.281421	−	2.31771i	0.0114794	−	0.0945415i	0.997322	+	0.0731292i	$0.0232986\pi$
$602$	−9.47702	+	9.86662i	−0.386254	+	0.402133i
$603$	0.604284	−	2.08623i	0.0246083	−	0.0849578i
$604$	1.88462	+	6.50646i	0.0766840	+	0.264744i
$605$	0.784825	+	1.13701i	0.0319077	+	0.0462262i
$606$	−1.80045	−	3.11847i	−0.0731382	−	0.126679i
$607$	13.1836	+	1.06429i	0.535106	+	0.0431982i	0.345067	−	0.938578i	$-0.387856\pi$
$607$	13.1836	+	1.06429i	0.535106	+	0.0431982i	0.190039	+	0.981776i	$0.439138\pi$
$608$	27.0219	−	4.39149i	1.09588	−	0.178099i
$609$	−2.59444	+	12.7084i	−0.105132	+	0.514970i
$610$	−5.87995	−	28.8019i	−0.238072	−	1.16616i
$611$	−29.3447	+	22.0511i	−1.18716	+	0.892093i
$612$	−4.35995	−	6.31647i	−0.176240	−	0.255328i
$613$	−7.36340	+	0.594435i	−0.297405	+	0.0240090i	−0.228269	−	0.973598i	$-0.573306\pi$
$613$	−7.36340	+	0.594435i	−0.297405	+	0.0240090i	−0.0691363	+	0.997607i	$0.522024\pi$
$614$	28.5240	−	7.03052i	1.15113	−	0.283729i
$615$	−14.4821	+	25.0837i	−0.583975	+	1.01147i
$616$	−1.84961	−	3.20362i	−0.0745231	−	0.129078i
$617$	27.0438	+	28.1555i	1.08874	+	1.13350i	0.990384	+	0.138348i	$0.0441792\pi$
$617$	27.0438	+	28.1555i	1.08874	+	1.13350i	0.0983571	+	0.995151i	$0.468641\pi$
$618$	23.8553	−	10.1638i	0.959600	−	0.408848i
$619$	8.79412	+	18.5332i	0.353465	+	0.744913i	0.999836	−	0.0181111i	$-0.00576526\pi$
$619$	8.79412	+	18.5332i	0.353465	+	0.744913i	−0.646371	+	0.763024i	$0.723714\pi$
$620$	−20.8163	−	18.4416i	−0.836001	−	0.740632i
$621$	5.79698	−	3.04249i	0.232625	−	0.122091i
$622$	40.1133	+	41.7624i	1.60840	+	1.67452i
$623$	17.9606	−	13.4965i	0.719577	−	0.540727i
$624$	−16.6240	−	8.72493i	−0.665492	−	0.349277i
$625$	24.8726	+	15.7285i	0.994903	+	0.629139i
$626$	11.0603	+	2.72612i	0.442058	+	0.108958i
$627$	−12.7134			−0.507724
$628$	3.88384	−	19.8445i	0.154982	−	0.791882i
$629$	−57.4934			−2.29241
$630$	6.78467	+	1.67227i	0.270308	+	0.0666249i
$631$	−26.5080	−	16.7626i	−1.05527	−	0.667310i	−0.110107	−	0.993920i	$-0.535119\pi$
$631$	−26.5080	−	16.7626i	−1.05527	−	0.667310i	−0.945159	+	0.326610i	$0.894094\pi$
$632$	−2.41081	−	1.26529i	−0.0958970	−	0.0503307i
$633$	6.73163	−	5.05850i	0.267558	−	0.201057i
$634$	17.0271	+	17.7271i	0.676234	+	0.704035i
$635$	−33.0582	+	17.3503i	−1.31187	+	0.688525i
$636$	−9.84558	−	8.72242i	−0.390403	−	0.345867i
$637$	−8.36162	−	17.6218i	−0.331300	−	0.698199i
$638$	52.0282	−	22.1671i	2.05982	−	0.877605i
$639$	4.29151	+	4.46793i	0.169769	+	0.176749i
$640$	−7.14693	−	12.3788i	−0.282507	−	0.489317i
$641$	2.76650	−	4.79172i	0.109270	−	0.189262i	−0.806205	−	0.591637i	$-0.798482\pi$
$641$	2.76650	−	4.79172i	0.109270	−	0.189262i	0.915475	+	0.402375i	$0.131815\pi$
$642$	−27.3557	+	6.74258i	−1.07964	+	0.266108i
$643$	6.79708	−	0.548717i	0.268051	−	0.0216393i	0.0542894	−	0.998525i	$-0.482711\pi$
$643$	6.79708	−	0.548717i	0.268051	−	0.0216393i	0.213761	+	0.976886i	$0.431429\pi$
$644$	−8.89588	−	12.8879i	−0.350547	−	0.507855i
$645$	9.62634	−	7.23373i	0.379037	−	0.284828i
$646$	−6.76295	−	33.1271i	−0.266085	−	1.30337i
$647$	6.88514	−	33.7256i	0.270683	−	1.32589i	−0.586110	−	0.810231i	$-0.699341\pi$
$647$	6.88514	−	33.7256i	0.270683	−	1.32589i	0.856793	−	0.515661i	$-0.172453\pi$
$648$	−0.724640	+	0.117765i	−0.0284665	+	0.00462626i
$649$	26.6738	+	2.15333i	1.04704	+	0.0845256i
$650$	−4.44013	−	7.69054i	−0.174156	−	0.301648i
$651$	−5.85065	−	8.47614i	−0.229305	−	0.332206i
$652$	−3.90624	−	13.4859i	−0.152980	−	0.528149i
$653$	13.0225	−	44.9589i	0.509610	−	1.75938i	−0.130868	−	0.991400i	$-0.541776\pi$
$653$	13.0225	−	44.9589i	0.509610	−	1.75938i	0.640477	−	0.767977i	$-0.278737\pi$
$654$	−0.950301	+	0.989368i	−0.0371597	+	0.0386874i
$655$	2.78843	−	22.9648i	0.108953	−	0.897307i
$656$	−53.9956			−2.10817
$657$	−0.435562	+	3.58718i	−0.0169929	+	0.139949i
$658$	25.1389	+	4.08547i	0.980017	+	0.159268i
$659$	14.9017	+	18.2512i	0.580487	+	0.710968i	0.978462	−	0.206429i	$-0.0661842\pi$
$659$	14.9017	+	18.2512i	0.580487	+	0.710968i	−0.397975	+	0.917396i	$0.630287\pi$
$660$	−4.82470	−	12.7217i	−0.187801	−	0.495191i
$661$	−4.12665	−	20.2137i	−0.160508	−	0.786220i	−0.977725	−	0.209890i	$-0.932689\pi$
$661$	−4.12665	−	20.2137i	−0.160508	−	0.786220i	0.817217	−	0.576330i	$-0.195516\pi$
$662$	−62.7148	+	26.7203i	−2.43748	+	1.03851i
$663$	−8.27939	+	17.4484i	−0.321545	+	0.677641i
$664$	0.419080	−	10.3994i	0.0162634	−	0.403573i
$665$	10.9895	+	8.25806i	0.426154	+	0.320234i
$666$	9.85181	−	20.7622i	0.381750	−	0.804521i
$667$	−50.7289	+	26.6246i	−1.96423	+	1.03091i
$668$	15.9218	+	1.28534i	0.616034	+	0.0497314i
$669$	3.29556	−	4.77444i	0.127414	−	0.184590i
$670$	9.71276	+	3.24259i	0.375236	+	0.125272i
$671$	−17.9157	+	11.3292i	−0.691630	+	0.437360i
$672$	3.01876	+	10.4220i	0.116451	+	0.402036i
$673$	1.82280	+	0.956677i	0.0702636	+	0.0368772i	0.499489	−	0.866320i	$-0.333521\pi$
$673$	1.82280	+	0.956677i	0.0702636	+	0.0368772i	−0.429225	+	0.903197i	$0.641213\pi$
$674$	−2.98327	−	7.86624i	−0.114911	−	0.302996i
$675$	−1.05828	−	0.450890i	−0.0407331	−	0.0173548i
$676$	−0.226842	−	5.62903i	−0.00872470	−	0.216501i
$677$	−25.2246	+	36.5442i	−0.969462	+	1.40451i	−0.0556137	+	0.998452i	$0.517712\pi$
$677$	−25.2246	+	36.5442i	−0.969462	+	1.40451i	−0.913848	+	0.406056i	$0.866904\pi$
$678$	−17.5876	+	30.4626i	−0.675446	+	1.16991i
$679$	−8.19503	+	0.661571i	−0.314496	+	0.0253888i
$680$	−7.31842	+	4.62789i	−0.280649	+	0.177471i
$681$	11.9544	−	3.99098i	0.458095	−	0.152935i
$682$	−15.9241	+	41.9884i	−0.609765	+	1.60782i
$683$	−19.5144	−	3.17140i	−0.746699	−	0.121350i	−0.224856	−	0.974392i	$-0.572191\pi$
$683$	−19.5144	−	3.17140i	−0.746699	−	0.121350i	−0.521843	+	0.853042i	$0.674755\pi$
$684$	5.85980	+	1.44431i	0.224055	+	0.0552246i
$685$	5.04569	−	5.25312i	0.192786	−	0.200711i
$686$	−11.7931	+	31.0958i	−0.450262	+	1.18724i
$687$	−8.57401	+	7.59591i	−0.327119	+	0.289802i
$688$	20.6514	+	8.79873i	0.787327	+	0.335448i
$689$	−6.62061	+	32.4299i	−0.252225	+	1.23548i
$690$	13.2316	+	27.8850i	0.503719	+	1.06156i
$691$	−20.7118	−	15.5639i	−0.787914	−	0.592079i	0.128778	−	0.991673i	$-0.458895\pi$
$691$	−20.7118	−	15.5639i	−0.787914	−	0.592079i	−0.916692	+	0.399594i	$0.869151\pi$
$692$	2.22057	+	18.2881i	0.0844135	+	0.695208i
$693$	−0.607361	−	5.00207i	−0.0230717	−	0.190013i
$694$	−1.07659	+	26.7152i	−0.0408667	+	1.01410i
$695$	13.7102	+	12.1462i	0.520058	+	0.460731i
$696$	6.34127	−	1.03056i	0.240365	−	0.0390631i
$697$	2.23656	+	55.4997i	0.0847158	+	2.10220i
$698$	−31.4595	+	38.5309i	−1.19076	+	1.45842i
$699$	−0.657165	+	0.219394i	−0.0248563	+	0.00829824i
$700$	−0.765530	+	2.64292i	−0.0289343	+	0.0998928i
$701$	−31.1123	−	19.6742i	−1.17509	−	0.743085i	−0.203347	−	0.979107i	$-0.565182\pi$
$701$	−31.1123	−	19.6742i	−1.17509	−	0.743085i	−0.971748	+	0.236022i	$0.924156\pi$
$702$	−4.88233	−	5.97977i	−0.184272	−	0.225692i
$703$	33.8394	−	29.9791i	1.27628	−	1.13068i
$704$	10.0403	−	12.2971i	0.378407	−	0.463464i
$705$	−21.2630	−	7.09863i	−0.800810	−	0.267350i
$706$	4.90132	−	1.20807i	0.184464	−	0.0454662i
$707$	2.72599	−	0.671897i	0.102522	−	0.0252693i
$708$	−12.0497	−	4.02279i	−0.452857	−	0.151186i
$709$	7.44956	−	9.12405i	0.279774	−	0.342661i	−0.615533	−	0.788111i	$-0.711059\pi$
$709$	7.44956	−	9.12405i	0.279774	−	0.342661i	0.895307	+	0.445450i	$0.146956\pi$
$710$	−21.8615	+	19.3676i	−0.820446	+	0.726852i
$711$	−2.34551	−	2.87272i	−0.0879634	−	0.107736i
$712$	−9.40519	−	5.94748i	−0.352474	−	0.222891i
$713$	12.6568	−	43.6962i	0.473999	−	1.63643i
$714$	12.7107	−	4.24347i	0.475688	−	0.158808i
$715$	−21.6530	+	26.5201i	−0.809776	+	0.991796i
$716$	0.953726	+	23.6665i	0.0356424	+	0.884457i
$717$	2.54695	−	0.413919i	0.0951175	−	0.0154581i
$718$	6.02595	+	5.33853i	0.224886	+	0.199232i
$719$	0.442113	−	10.9709i	0.0164880	−	0.409146i	−0.969779	−	0.243986i	$-0.921545\pi$
$719$	0.442113	−	10.9709i	0.0164880	−	0.409146i	0.986267	−	0.165160i	$-0.0528141\pi$
$720$	−1.38202	−	11.3820i	−0.0515049	−	0.424181i
$721$	2.43695	+	20.0701i	0.0907568	+	0.747449i
$722$	−7.62093	−	5.72675i	−0.283621	−	0.213128i
$723$	−9.64994	−	20.3368i	−0.358885	−	0.756335i
$724$	−2.60508	+	12.7605i	−0.0968170	+	0.474241i
$725$	9.26090	+	3.94570i	0.343941	+	0.146540i
$726$	−0.792696	+	0.702267i	−0.0294197	+	0.0260636i
$727$	−11.2378	+	29.6316i	−0.416786	+	1.09897i	0.548125	+	0.836397i	$0.315342\pi$
$727$	−11.2378	+	29.6316i	−0.416786	+	1.09897i	−0.964911	+	0.262578i	$0.915427\pi$
$728$	3.06104	−	3.18688i	0.113450	−	0.118114i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	−16.8152	−	2.73274i	−0.622358	−	0.101143i
$731$	8.18842	−	21.5911i	0.302860	−	0.798576i
$732$	9.54471	−	3.18649i	0.352783	−	0.117776i
$733$	6.28017	−	3.97134i	0.231963	−	0.146685i	−0.413428	−	0.910537i	$-0.635669\pi$
$733$	6.28017	−	3.97134i	0.231963	−	0.146685i	0.645391	+	0.763852i	$0.276694\pi$
$734$	36.9557	−	2.98337i	1.36406	−	0.110118i
$735$	5.95583	−	10.3158i	0.219684	−	0.380504i
$736$	−27.2253	+	39.4427i	−1.00354	+	1.45388i
$737$	−0.297316	−	7.37783i	−0.0109518	−	0.271766i
$738$	−20.4255	−	8.70250i	−0.751874	−	0.320344i
$739$	−12.1141	−	31.9424i	−0.445626	−	1.17502i	−0.950197	−	0.311649i	$-0.899119\pi$
$739$	−12.1141	−	31.9424i	−0.445626	−	1.17502i	0.504571	−	0.863370i	$-0.331651\pi$
$740$	42.8406	+	22.4845i	1.57485	+	0.826547i
$741$	−4.22516	−	14.5870i	−0.155215	−	0.535865i
$742$	19.4103	−	12.2743i	0.712573	−	0.450604i
$743$	39.6349	+	13.2321i	1.45406	+	0.485438i	0.930419	−	0.366498i	$-0.119443\pi$
$743$	39.6349	+	13.2321i	1.45406	+	0.485438i	0.523646	+	0.851936i	$0.324571\pi$
$744$	−2.89790	+	4.19834i	−0.106242	+	0.153919i
$745$	−12.7257	−	1.02733i	−0.466234	−	0.0376383i
$746$	23.5631	−	12.3669i	0.862706	−	0.452783i
$747$	6.07745	−	12.8080i	0.222362	−	0.468619i
$748$	−20.8591	−	15.6746i	−0.762683	−	0.573119i
$749$	0.884532	−	21.9494i	0.0323201	−	0.802015i
$750$	−7.78039	+	16.3968i	−0.284100	+	0.598728i
$751$	−5.53230	+	2.35709i	−0.201877	+	0.0860115i	−0.490538	−	0.871420i	$-0.663200\pi$
$751$	−5.53230	+	2.35709i	−0.201877	+	0.0860115i	0.288662	+	0.957431i	$0.406790\pi$
$752$	−8.35897	−	40.9450i	−0.304820	−	1.49311i
$753$	−0.573602	−	1.51246i	−0.0209032	−	0.0551172i
$754$	42.7249	+	52.3285i	1.55595	+	1.90569i
$755$	10.2748	+	1.66982i	0.373940	+	0.0607711i
$756$	−0.288320	+	2.37453i	−0.0104861	+	0.0863609i
$757$	−18.1887			−0.661081			−0.330540	−	0.943792i	$-0.607231\pi$
$757$	−18.1887			−0.661081			−0.330540	+	0.943792i	$0.607231\pi$
$758$	3.77497	−	31.0897i	0.137113	−	1.12923i
$759$	15.4177	−	16.0515i	0.559627	−	0.582634i
$760$	1.89432	−	6.53996i	0.0687143	−	0.237229i
$761$	−1.67785	−	5.79259i	−0.0608218	−	0.209981i	0.924352	−	0.381541i	$-0.124607\pi$
$761$	−1.67785	−	5.79259i	−0.0608218	−	0.209981i	−0.985174	+	0.171560i	$0.945119\pi$
$762$	−16.2571	−	23.5525i	−0.588933	−	0.853217i
$763$	−0.534801	−	0.926302i	−0.0193611	−	0.0335344i
$764$	8.74781	+	0.706196i	0.316485	+	0.0255493i
$765$	−11.6418	+	1.89197i	−0.420909	+	0.0684044i
$766$	−8.60640	+	42.1569i	−0.310962	+	1.52319i
$767$	6.39408	+	31.3203i	0.230877	+	1.13091i
$768$	16.2258	−	12.1929i	0.585498	−	0.439973i
$769$	21.6126	+	31.3112i	0.779369	+	1.12911i	0.988500	+	0.151223i	$0.0483212\pi$
$769$	21.6126	+	31.3112i	0.779369	+	1.12911i	−0.209131	+	0.977888i	$0.567063\pi$
$770$	23.6782	−	1.91150i	0.853304	−	0.0688858i
$771$	18.8051	−	4.63504i	0.677249	−	0.166927i
$772$	4.93057	−	8.54000i	0.177455	−	0.307361i
$773$	−11.9710	−	20.7344i	−0.430567	−	0.745764i	0.566355	−	0.824161i	$-0.308353\pi$
$773$	−11.9710	−	20.7344i	−0.430567	−	0.745764i	−0.996922	+	0.0783970i	$0.975020\pi$
$774$	6.39393	+	6.65679i	0.229825	+	0.239273i
$775$	−7.35364	+	3.13309i	−0.264151	+	0.112544i
$776$	1.74577	+	3.67913i	0.0626694	+	0.132073i
$777$	13.4119	+	11.8819i	0.481148	+	0.426260i
$778$	−48.5000	+	25.4548i	−1.73881	+	0.912597i
$779$	−30.2559	−	31.4997i	−1.08403	−	1.12859i
$780$	12.9930	−	9.76364i	0.465225	−	0.349594i
$781$	18.6484	+	9.78741i	0.667291	+	0.350221i
$782$	50.0268	+	31.6350i	1.78895	+	1.13127i
$783$	8.49663	+	2.09423i	0.303645	+	0.0748417i
$784$	22.2059			0.793069
$785$	−24.9926	−	18.4654i	−0.892025	−	0.659058i
$786$	17.7326			0.632503
$787$	38.0454	+	9.37735i	1.35617	+	0.334267i	0.849371	−	0.527796i	$-0.176981\pi$
$787$	38.0454	+	9.37735i	1.35617	+	0.334267i	0.506802	+	0.862063i	$0.330828\pi$
$788$	−27.6779	−	17.5024i	−0.985984	−	0.623498i
$789$	−12.9974	−	6.82154i	−0.462718	−	0.242853i
$790$	13.9776	−	10.5035i	0.497301	−	0.373697i
$791$	−18.9984	−	19.7794i	−0.675505	−	0.703276i
$792$	−2.20991	+	1.15985i	−0.0785257	+	0.0412135i
$793$	−18.9529	−	16.7908i	−0.673038	−	0.596259i
$794$	25.3133	+	53.3467i	0.898336	+	1.89320i
$795$	−18.5959	+	7.92299i	−0.659530	+	0.280999i
$796$	2.78367	+	2.89811i	0.0986645	+	0.102721i
$797$	6.15453	+	10.6600i	0.218005	+	0.377595i	0.954198	−	0.299176i	$-0.0967118\pi$
$797$	6.15453	+	10.6600i	0.218005	+	0.377595i	−0.736193	+	0.676772i	$0.763378\pi$
$798$	−5.26858	+	9.12545i	−0.186506	+	0.323037i
$799$	−41.7393	+	10.2878i	−1.47663	+	0.363956i
$800$	8.39365	−	0.677606i	0.296761	−	0.0239570i
$801$	−8.61049	−	12.4745i	−0.304237	−	0.440763i
$802$	−32.0116	+	24.0552i	−1.13037	+	0.849417i
$803$	2.45720	+	12.0362i	0.0867128	+	0.424747i
$804$	−0.701124	+	3.43433i	−0.0247267	+	0.121120i
$805$	−23.7535	+	3.86031i	−0.837200	+	0.136058i
$806$	−53.4684	−	4.31641i	−1.88334	−	0.152039i
$807$	−7.93611	−	13.7457i	−0.279364	−	0.483873i
$808$	−0.789967	−	1.14446i	−0.0277909	−	0.0402621i
$809$	8.46425	+	29.2220i	0.297587	+	1.02739i	0.960405	+	0.278609i	$0.0898733\pi$
$809$	8.46425	+	29.2220i	0.297587	+	1.02739i	−0.662818	+	0.748781i	$0.730640\pi$
$810$	1.31164	−	4.52832i	0.0460865	−	0.159109i
$811$	24.6008	−	25.6121i	0.863851	−	0.899364i	−0.131918	−	0.991261i	$-0.542114\pi$
$811$	24.6008	−	25.6121i	0.863851	−	0.899364i	0.995769	+	0.0918968i	$0.0292930\pi$
$812$	2.52307	−	20.7793i	0.0885424	−	0.729212i
$813$	12.1359			0.425624
$814$	9.41702	−	77.5561i	0.330066	−	2.71834i
$815$	−21.2966	−	3.46104i	−0.745988	−	0.121235i
$816$	−13.9059	−	17.0317i	−0.486805	−	0.596227i
$817$	6.43883	+	16.9778i	0.225266	+	0.593978i
$818$	3.02929	+	14.8385i	0.105917	+	0.518815i
$819$	5.53737	−	2.35925i	0.193491	−	0.0824390i
$820$	20.0383	−	42.2297i	0.699766	−	1.47473i
$821$	−0.701719	+	17.4130i	−0.0244902	+	0.607717i	0.939621	+	0.342217i	$0.111178\pi$
$821$	−0.701719	+	17.4130i	−0.0244902	+	0.607717i	−0.964111	+	0.265500i	$0.914463\pi$
$822$	4.46355	+	3.35414i	0.155684	+	0.116989i
$823$	12.5582	−	26.4658i	0.437750	−	0.922539i	−0.557947	−	0.829876i	$-0.688411\pi$
$823$	12.5582	−	26.4658i	0.437750	−	0.922539i	0.995698	−	0.0926626i	$-0.0295378\pi$
$824$	8.86694	−	4.65373i	0.308895	−	0.162120i
$825$	−3.89794	−	0.314674i	−0.135709	−	0.0109556i
$826$	12.5996	−	18.2536i	0.438394	−	0.635124i
$827$	15.0436	+	5.02230i	0.523118	+	0.174643i	0.565950	−	0.824440i	$-0.308510\pi$
$827$	15.0436	+	5.02230i	0.523118	+	0.174643i	−0.0428313	+	0.999082i	$0.513638\pi$
$828$	−8.92980	+	5.64687i	−0.310332	+	0.196242i
$829$	−1.72287	−	5.94805i	−0.0598379	−	0.206584i	0.925029	−	0.379896i	$-0.124040\pi$
$829$	−1.72287	−	5.94805i	−0.0598379	−	0.206584i	−0.984867	+	0.173312i	$0.944553\pi$
$830$	59.1799	+	31.0600i	2.05417	+	1.07811i
$831$	3.32235	+	8.76032i	0.115251	+	0.303892i
$832$	17.4461	+	7.43308i	0.604834	+	0.257696i
$833$	−0.919796	−	22.8245i	−0.0318690	−	0.790822i
$834$	−7.97586	+	11.5550i	−0.276181	+	0.400118i
$835$	12.2735	−	21.2584i	0.424743	−	0.735677i
$836$	20.4505	−	1.65093i	0.707295	−	0.0570987i
$837$	−5.87296	+	3.71384i	−0.202999	+	0.128369i
$838$	29.6329	−	9.89290i	1.02365	−	0.341745i
$839$	−14.1340	+	37.2683i	−0.487960	+	1.28664i	0.434542	+	0.900652i	$0.356910\pi$
$839$	−14.1340	+	37.2683i	−0.487960	+	1.28664i	−0.922502	+	0.385993i	$0.873859\pi$
$840$	2.66364	+	0.432883i	0.0919042	+	0.0149359i
$841$	−46.1960	−	11.3863i	−1.59297	−	0.392631i
$842$	−23.5845	+	24.5540i	−0.812775	+	0.846188i
$843$	−2.61059	+	6.88356i	−0.0899135	+	0.237083i
$844$	−10.1715	+	9.01114i	−0.350116	+	0.310176i
$845$	−7.96454	−	3.39337i	−0.273988	−	0.116736i
$846$	3.43708	−	16.8359i	0.118169	−	0.578831i
$847$	−0.353977	−	0.745991i	−0.0121628	−	0.0256326i
$848$	−30.1248	−	22.6373i	−1.03449	−	0.777369i
$849$	2.82577	+	23.2723i	0.0969802	+	0.798703i
$850$	−1.25359	−	10.3242i	−0.0429976	−	0.354117i
$851$	−3.18684	+	79.0806i	−0.109243	+	2.71085i
$852$	−7.48342	−	6.62973i	−0.256378	−	0.227131i
$853$	49.1404	−	7.98610i	1.68254	−	0.273439i	0.757366	−	0.652991i	$-0.226486\pi$
$853$	49.1404	−	7.98610i	1.68254	−	0.273439i	0.925170	+	0.379552i	$0.123922\pi$
$854$	0.707425	+	17.5546i	0.0242076	+	0.600705i
$855$	5.86556	−	7.18400i	0.200598	−	0.245688i
$856$	−10.3207	+	3.44556i	−0.352754	+	0.117767i
$857$	12.7470	−	44.0077i	0.435429	−	1.50327i	−0.380313	−	0.924858i	$-0.624184\pi$
$857$	12.7470	−	44.0077i	0.435429	−	1.50327i	0.815741	−	0.578417i	$-0.196329\pi$
$858$	−22.1811	−	14.0265i	−0.757250	−	0.478856i
$859$	−13.1715	−	16.1322i	−0.449406	−	0.550423i	0.499363	−	0.866393i	$-0.333567\pi$
$859$	−13.1715	−	16.1322i	−0.449406	−	0.550423i	−0.948769	+	0.315970i	$0.897670\pi$
$860$	−14.5454	+	12.8861i	−0.495993	+	0.439411i
$861$	10.9481	−	13.4090i	0.373111	−	0.456977i
$862$	−60.2804	−	20.1246i	−2.05316	−	0.685445i
$863$	−7.89797	+	1.94667i	−0.268850	+	0.0662655i	−0.371436	−	0.928459i	$-0.621134\pi$
$863$	−7.89797	+	1.94667i	−0.268850	+	0.0662655i	0.102586	+	0.994724i	$0.467288\pi$
$864$	7.10777	−	1.75191i	0.241811	−	0.0596011i
$865$	26.8532	+	8.96492i	0.913037	+	0.304816i
$866$	−0.754759	+	0.924412i	−0.0256478	+	0.0314128i
$867$	−4.20541	+	3.72567i	−0.142823	+	0.126530i
$868$	10.5119	+	12.8748i	0.356798	+	0.436998i
$869$	−10.6560	−	6.73842i	−0.361479	−	0.228585i
$870$	−11.4781	+	39.6270i	−0.389144	+	1.34348i
$871$	8.36628	−	2.79307i	0.283481	−	0.0946397i
$872$	−0.335061	+	0.410376i	−0.0113466	+	0.0138971i
$873$	0.223355	+	5.54249i	0.00755941	+	0.187585i
$874$	−45.9403	+	7.46603i	−1.55395	+	0.252542i
$875$	−10.5919	−	9.38362i	−0.358072	−	0.317224i
$876$	0.234813	−	5.82681i	0.00793358	−	0.196870i
$877$	−1.29148	−	10.6363i	−0.0436102	−	0.359163i	−0.998136	−	0.0610333i	$-0.980560\pi$
$877$	−1.29148	−	10.6363i	−0.0436102	−	0.359163i	0.954525	−	0.298129i	$-0.0963627\pi$
$878$	−2.57190	−	21.1815i	−0.0867973	−	0.714840i
$879$	−1.91071	−	1.43580i	−0.0644466	−	0.0484285i
$880$	−16.7096	−	35.2147i	−0.563280	−	1.18709i
$881$	2.89461	−	14.1787i	0.0975220	−	0.477694i	−0.901472	−	0.432838i	$-0.857512\pi$
$881$	2.89461	−	14.1787i	0.0975220	−	0.477694i	0.998993	−	0.0448557i	$-0.0142828\pi$
$882$	8.40009	+	3.57894i	0.282846	+	0.120509i
$883$	−4.15715	+	3.68292i	−0.139899	+	0.123940i	−0.730170	−	0.683265i	$-0.760559\pi$
$883$	−4.15715	+	3.68292i	−0.139899	+	0.123940i	0.590271	+	0.807205i	$0.299021\pi$
$884$	11.0522	−	29.1423i	0.371727	−	0.980162i
$885$	−13.5232	+	14.0792i	−0.454578	+	0.473266i
$886$	45.3893	+	11.1875i	1.52488	+	0.375850i
$887$	14.6480	+	2.38053i	0.491832	+	0.0799305i	0.401269	−	0.915960i	$-0.368569\pi$
$887$	14.6480	+	2.38053i	0.491832	+	0.0799305i	0.0905632	+	0.995891i	$0.471133\pi$
$888$	3.14713	−	8.29831i	0.105611	−	0.278473i
$889$	21.1651	−	7.06595i	0.709855	−	0.236984i
$890$	60.3971	−	38.1928i	2.02452	−	1.28023i
$891$	−3.38855	+	0.273552i	−0.113521	+	0.00916433i
$892$	−4.68116	+	8.10800i	−0.156737	+	0.271476i
$893$	19.2024	−	27.8195i	0.642585	−	0.930945i
$894$	−0.394062	−	9.77854i	−0.0131794	−	0.327043i
$895$	33.4858	+	14.2670i	1.11931	+	0.476892i
$896$	3.02934	+	7.98772i	0.101203	+	0.266851i
$897$	23.5409	+	12.3552i	0.786009	+	0.412529i
$898$	2.71203	+	9.36301i	0.0905016	+	0.312448i
$899$	51.3938	−	32.4995i	1.71408	−	1.08392i
$900$	1.76087	+	0.587866i	0.0586958	+	0.0195955i
$901$	−22.0201	+	31.9016i	−0.733596	+	1.06280i
$902$	−75.2331	−	6.07344i	−2.50499	−	0.202223i
$903$	−6.37229	+	3.34444i	−0.212057	+	0.111296i
$904$	−5.82347	+	12.2727i	−0.193686	+	0.408184i
$905$	16.0000	+	12.0232i	0.531857	+	0.399665i
$906$	−0.321297	+	7.97291i	−0.0106744	+	0.264882i
$907$	16.8804	−	35.5747i	0.560505	−	1.18124i	−0.403407	−	0.915021i	$-0.632174\pi$
$907$	16.8804	−	35.5747i	0.560505	−	1.18124i	0.963912	−	0.266219i	$-0.0857745\pi$
$908$	−18.7114	+	7.97218i	−0.620959	+	0.264566i
$909$	−0.378890	−	1.85593i	−0.0125670	−	0.0615572i
$910$	10.0624	+	26.5324i	0.333566	+	0.879540i
$911$	20.5032	+	25.1118i	0.679301	+	0.831993i	0.993072	−	0.117506i	$-0.0374899\pi$
$911$	20.5032	+	25.1118i	0.679301	+	0.831993i	−0.313771	+	0.949499i	$0.601592\pi$
$912$	17.0656	+	2.77344i	0.565100	+	0.0918377i
$913$	5.80924	−	47.8434i	0.192258	−	1.58338i
$914$	59.6027			1.97148
$915$	1.86391	−	15.3507i	0.0616189	−	0.507477i
$916$	12.8056	−	13.3320i	0.423108	−	0.440502i
$917$	−3.84662	+	13.2801i	−0.127026	+	0.438546i
$918$	−2.51535	−	8.68398i	−0.0830188	−	0.286614i
$919$	−4.24160	−	6.14502i	−0.139918	−	0.202706i	0.746760	−	0.665093i	$-0.231608\pi$
$919$	−4.24160	−	6.14502i	−0.139918	−	0.202706i	−0.886678	+	0.462388i	$0.846993\pi$
$920$	5.95987	+	10.3228i	0.196491	+	0.340333i
$921$	15.4036	+	1.24351i	0.507567	+	0.0409751i
$922$	3.25803	−	0.529482i	0.107298	−	0.0174376i
$923$	−5.03219	+	24.6493i	−0.165636	+	0.811341i
$924$	1.62655	+	7.96735i	0.0535094	+	0.262107i
$925$	11.1172	−	8.35405i	0.365532	−	0.274679i
$926$	26.3465	+	38.1695i	0.865800	+	1.25433i
$927$	13.5961	−	1.09759i	0.446553	−	0.0360495i
$928$	−62.1995	+	15.3308i	−2.04180	+	0.503258i
$929$	−24.6802	+	42.7474i	−0.809733	+	1.40250i	0.103316	+	0.994649i	$0.467055\pi$
$929$	−24.6802	+	42.7474i	−0.809733	+	1.40250i	−0.913049	+	0.407850i	$0.866279\pi$
$930$	−16.3797	−	28.3704i	−0.537110	−	0.930302i
$931$	12.4429	+	12.9544i	0.407799	+	0.424563i
$932$	1.02861	−	0.438250i	0.0336933	−	0.0143554i
$933$	13.0584	+	27.5201i	0.427514	+	0.900967i
$934$	−26.4708	−	23.4510i	−0.866150	−	0.767342i
$935$	−35.5035	+	18.6337i	−1.16109	+	0.609386i
$936$	−2.06521	−	2.15012i	−0.0675037	−	0.0702788i
$937$	−46.7383	+	35.1215i	−1.52687	+	1.14737i	−0.585176	+	0.810907i	$0.698974\pi$
$937$	−46.7383	+	35.1215i	−1.52687	+	1.14737i	−0.941697	+	0.336463i	$0.890769\pi$
$938$	−5.41889	−	2.84405i	−0.176933	−	0.0928615i
$939$	5.06460	+	3.20266i	0.165277	+	0.104515i
$940$	35.1250	+	8.65753i	1.14565	+	0.282377i
$941$	−0.0942981			−0.00307403			−0.00153702	−	0.999999i	$-0.500489\pi$
$941$	−0.0942981			−0.00307403			−0.00153702	+	0.999999i	$0.500489\pi$
$942$	11.7420	−	20.7242i	0.382575	−	0.675232i
$943$	76.4623			2.48995
$944$	−35.3354	−	8.70940i	−1.15007	−	0.283467i
$945$	3.10676	+	1.96459i	0.101063	+	0.0639082i
$946$	27.7843	+	14.5823i	0.903344	+	0.474112i
$947$	−5.66849	+	4.25959i	−0.184201	+	0.138418i	−0.688843	−	0.724911i	$-0.741881\pi$
$947$	−5.66849	+	4.25959i	−0.184201	+	0.138418i	0.504642	+	0.863329i	$0.331625\pi$
$948$	4.14598	+	4.31642i	0.134655	+	0.140191i
$949$	−12.9933	+	6.81941i	−0.421780	+	0.221367i
$950$	6.12124	+	5.42295i	0.198599	+	0.175944i
$951$	5.54300	+	11.6816i	0.179744	+	0.378803i
$952$	4.76097	−	2.02846i	0.154304	−	0.0657428i
$953$	4.52398	+	4.70996i	0.146546	+	0.152571i	0.790430	−	0.612553i	$-0.209857\pi$
$953$	4.52398	+	4.70996i	0.146546	+	0.152571i	−0.643884	+	0.765124i	$0.722678\pi$
$954$	−7.74718	−	13.4185i	−0.250824	−	0.434440i
$955$	6.74336	−	11.6798i	0.218210	−	0.377951i
$956$	−4.04321	+	0.996562i	−0.130767	+	0.0322311i
$957$	29.6529	−	2.39383i	0.958542	−	0.0773815i
$958$	−10.9445	−	15.8559i	−0.353602	−	0.512281i
$959$	−3.48018	+	2.61519i	−0.112381	+	0.0844488i
$960$	2.31650	+	11.3470i	0.0747648	+	0.366222i
$961$	−3.45730	+	16.9350i	−0.111526	+	0.546290i
$962$	92.1151	−	14.9702i	2.96991	−	0.482658i
$963$	−14.7728	−	1.19258i	−0.476045	−	0.0384304i
$964$	18.1636	+	31.4602i	0.585009	+	1.01327i
$965$	−8.60839	−	12.4714i	−0.277114	−	0.401469i
$966$	−5.13222	−	17.7185i	−0.165127	−	0.570083i
$967$	−2.61013	+	9.01122i	−0.0839361	+	0.289781i	−0.991495	−	0.130143i	$-0.958456\pi$
$967$	−2.61013	+	9.01122i	−0.0839361	+	0.289781i	0.907559	+	0.419924i	$0.137943\pi$
$968$	−0.283315	+	0.294962i	−0.00910608	+	0.00948043i
$969$	2.14381	−	17.6559i	0.0688692	−	0.567189i
$970$	−26.1510			−0.839660
$971$	−1.93283	+	15.9183i	−0.0620275	+	0.510842i	0.928273	+	0.371900i	$0.121293\pi$
$971$	−1.93283	+	15.9183i	−0.0620275	+	0.510842i	−0.990300	+	0.138943i	$0.955630\pi$
$972$	1.59291	+	0.258873i	0.0510927	+	0.00830337i
$973$	−6.92347	−	8.47971i	−0.221956	−	0.271847i
$974$	−5.29964	−	13.9740i	−0.169812	−	0.447756i
$975$	−0.934392	−	4.57695i	−0.0299245	−	0.146580i
$976$	26.5204	−	11.2993i	0.848898	−	0.361682i
$977$	18.6267	−	39.2550i	0.595921	−	1.25588i	−0.351590	−	0.936154i	$-0.614359\pi$
$977$	18.6267	−	39.2550i	0.595921	−	1.25588i	0.947511	−	0.319723i	$-0.103590\pi$
$978$	0.665952	−	16.5254i	0.0212948	−	0.528425i
$979$	−41.1947	−	30.9558i	−1.31659	−	0.989353i
$980$	−8.24082	+	17.3672i	−0.263243	+	0.554774i
$981$	−0.638977	+	0.335361i	−0.0204010	+	0.0107073i
$982$	−31.4419	−	2.53825i	−1.00335	−	0.0809989i
$983$	−7.76819	+	11.2542i	−0.247767	+	0.358952i	−0.927059	−	0.374916i	$-0.877672\pi$
$983$	−7.76819	+	11.2542i	−0.247767	+	0.358952i	0.679292	+	0.733868i	$0.262287\pi$
$984$	−8.13298	−	2.71519i	−0.259270	−	0.0865570i
$985$	−42.5333	+	26.8964i	−1.35522	+	0.856992i
$986$	22.0116	+	75.9928i	0.700992	+	2.42010i
$987$	11.8629	+	6.22614i	0.377601	+	0.198180i
$988$	8.69073	+	22.9156i	0.276489	+	0.729041i
$989$	−29.2441	−	12.4597i	−0.929908	−	0.396197i
$990$	−0.645348	−	16.0141i	−0.0205105	−	0.508963i
$991$	−16.3458	+	23.6810i	−0.519243	+	0.752253i	−0.991626	−	0.129140i	$-0.958778\pi$
$991$	−16.3458	+	23.6810i	−0.519243	+	0.752253i	0.472384	+	0.881393i	$0.343394\pi$
$992$	25.4339	−	44.0528i	0.807527	−	1.39868i
$993$	−35.7436	+	2.88552i	−1.13429	+	0.0915693i
$994$	14.7533	−	9.32944i	0.467947	−	0.295912i
$995$	5.85744	−	1.95550i	0.185693	−	0.0619935i
$996$	−8.11284	+	21.3918i	−0.257065	+	0.677825i
$997$	−16.1045	−	2.61724i	−0.510035	−	0.0828888i	−0.100053	−	0.994982i	$-0.531901\pi$
$997$	−16.1045	−	2.61724i	−0.510035	−	0.0828888i	−0.409983	+	0.912093i	$0.634465\pi$
$998$	−52.9976	−	13.0627i	−1.67761	−	0.413494i
$999$	8.37429	−	8.71855i	0.264951	−	0.275843i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.q.b.19.4	✓	336
157.124	even	39	inner	471.2.q.b.124.4	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.q.b.19.4	✓	336	1.1	even	1	trivial
471.2.q.b.124.4	yes	336	157.124	even	39	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.84576 - 0.454940i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.42896 + 0.749975i) q^{4} +(1.98261 - 1.48983i) q^{5} +(1.31687 + 1.37101i) q^{6} +(-1.31241 + 0.688808i) q^{7} +(0.549517 + 0.486830i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\)	\(q+(-1.84576 - 0.454940i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.42896 + 0.749975i) q^{4} +(1.98261 - 1.48983i) q^{5} +(1.31687 + 1.37101i) q^{6} +(-1.31241 + 0.688808i) q^{7} +(0.549517 + 0.486830i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-4.33720 + 1.84791i) q^{10} +(2.35497 + 2.45178i) q^{11} +(-0.806905 - 1.39760i) q^{12} +(-2.03045 + 3.51684i) q^{13} +(2.73577 - 0.674307i) q^{14} +(-2.47194 + 0.199556i) q^{15} +(-2.62630 - 3.80485i) q^{16} +(-3.80205 + 2.85706i) q^{17} +(-0.380249 - 1.86258i) q^{18} +(0.748037 - 3.66413i) q^{19} +(3.95040 - 0.642002i) q^{20} +(1.47738 + 0.119267i) q^{21} +(-3.23130 - 5.59677i) q^{22} +(3.71906 + 5.38798i) q^{23} +(-0.204253 - 0.705162i) q^{24} +(0.320041 - 1.10491i) q^{25} +(5.34767 - 5.56752i) q^{26} +(0.120537 - 0.992709i) q^{27} -2.39197 q^{28} +(-1.05481 + 8.68711i) q^{29} +(4.65341 + 0.756252i) q^{30} +(-4.39467 - 5.38249i) q^{31} +(2.59588 + 6.84478i) q^{32} +(-0.680002 - 3.33087i) q^{33} +(8.31747 - 3.54374i) q^{34} +(-1.57579 + 3.32091i) q^{35} +(-0.0649816 + 1.61250i) q^{36} +(9.66439 + 7.26232i) q^{37} +(-3.04766 + 6.42280i) q^{38} +(3.59574 - 1.88719i) q^{39} +(1.81477 + 0.146503i) q^{40} +(6.63453 - 9.61178i) q^{41} +(-2.67264 - 0.892258i) q^{42} +(-4.10373 + 2.59504i) q^{43} +(1.52637 + 5.26966i) q^{44} +(2.19592 + 1.15251i) q^{45} +(-4.41329 - 11.6369i) q^{46} +(8.31571 + 3.54299i) q^{47} +(0.186159 + 4.61949i) q^{48} +(-2.72848 + 3.95289i) q^{49} +(-1.09339 + 1.89380i) q^{50} +(4.74046 - 0.382689i) q^{51} +(-5.53897 + 3.50263i) q^{52} +(7.73116 - 2.58104i) q^{53} +(-0.674105 + 1.77747i) q^{54} +(8.32171 + 1.35241i) q^{55} +(-1.05653 - 0.260410i) q^{56} +(-2.59058 + 2.69708i) q^{57} +(5.89904 - 15.5545i) q^{58} +(5.89208 - 5.21993i) q^{59} +(-3.68197 - 1.56874i) q^{60} +(-1.24722 + 6.10927i) q^{61} +(5.66281 + 11.9341i) q^{62} +(-1.18493 - 0.890414i) q^{63} +(-0.562882 - 4.63575i) q^{64} +(1.21392 + 9.99753i) q^{65} +(-0.260222 + 6.45735i) q^{66} +(-1.62575 - 1.44029i) q^{67} +(-7.57570 + 1.23117i) q^{68} +(-0.263617 - 6.54158i) q^{69} +(4.41935 - 5.41272i) q^{70} +(5.87629 - 1.96179i) q^{71} +(-0.204253 + 0.705162i) q^{72} +(3.05411 + 1.93130i) q^{73} +(-14.5343 - 17.8012i) q^{74} +(-0.861033 + 0.762808i) q^{75} +(3.81692 - 4.67488i) q^{76} +(-4.77949 - 1.59563i) q^{77} +(-7.49545 + 1.84746i) q^{78} +(-3.60087 + 0.887534i) q^{79} +(-10.8755 - 3.63078i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(-16.6185 + 14.7228i) q^{82} +(-8.96600 - 10.9814i) q^{83} +(2.02167 + 1.27843i) q^{84} +(-3.28144 + 11.3288i) q^{85} +(8.75511 - 2.92288i) q^{86} +(5.53448 - 6.77850i) q^{87} +(0.100495 + 2.49376i) q^{88} +(-14.9613 + 2.43145i) q^{89} +(-3.52882 - 3.12626i) q^{90} +(0.242361 - 6.01413i) q^{91} +(1.27352 + 10.4884i) q^{92} +(0.837572 + 6.89803i) q^{93} +(-13.7370 - 10.3227i) q^{94} +(-3.97587 - 8.37897i) q^{95} +(1.46429 - 7.17255i) q^{96} +(5.10312 + 2.17423i) q^{97} +(6.83445 - 6.05480i) q^{98} +(-1.20550 + 3.17866i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Introduction

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