LMFDB - Embedded newform 429.2.bq.a.29.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(29,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 21, 10]))

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

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

chi := DirichletCharacter("429.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bq (of order $30$, degree $8$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			29.8
Character	$\chi$	$=$	429.29
Dual form			429.2.bq.a.74.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.230857 + 2.19646i) q^{2} +(-1.65359 - 0.515394i) q^{3} +(-2.81485 - 0.598316i) q^{4} +(1.87210 + 2.57672i) q^{5} +(1.51379 - 3.51307i) q^{6} +(-0.269880 + 1.26968i) q^{7} +(0.599043 - 1.84366i) q^{8} +(2.46874 + 1.70450i) q^{9} +O(q^{10})$	\(q+(-0.230857 + 2.19646i) q^{2} +(-1.65359 - 0.515394i) q^{3} +(-2.81485 - 0.598316i) q^{4} +(1.87210 + 2.57672i) q^{5} +(1.51379 - 3.51307i) q^{6} +(-0.269880 + 1.26968i) q^{7} +(0.599043 - 1.84366i) q^{8} +(2.46874 + 1.70450i) q^{9} +(-6.09186 + 3.51714i) q^{10} +(3.00356 + 1.40663i) q^{11} +(4.34625 + 2.44013i) q^{12} +(2.26567 + 2.80477i) q^{13} +(-2.72651 - 0.885896i) q^{14} +(-1.76766 - 5.22572i) q^{15} +(-1.34665 - 0.599567i) q^{16} +(-0.705322 - 6.71069i) q^{17} +(-4.31381 + 5.02899i) q^{18} +(-5.32475 + 4.79443i) q^{19} +(-3.72799 - 8.37321i) q^{20} +(1.10066 - 1.96044i) q^{21} +(-3.78300 + 6.27248i) q^{22} +(0.312865 - 0.180633i) q^{23} +(-1.94079 + 2.73993i) q^{24} +(-1.58966 + 4.89248i) q^{25} +(-6.68361 + 4.32896i) q^{26} +(-3.20379 - 4.09093i) q^{27} +(1.51934 - 3.41250i) q^{28} +(-3.20831 + 3.56319i) q^{29} +(11.8862 - 2.67620i) q^{30} +(-4.43518 - 3.22235i) q^{31} +(3.56635 - 6.17710i) q^{32} +(-4.24170 - 3.87401i) q^{33} +14.9026 q^{34} +(-3.77686 + 1.68157i) q^{35} +(-5.92930 - 6.27502i) q^{36} +(1.14250 - 1.26888i) q^{37} +(-9.30152 - 12.8024i) q^{38} +(-2.30094 - 5.80566i) q^{39} +(5.87208 - 1.90795i) q^{40} +(7.78303 - 1.65433i) q^{41} +(4.05195 + 2.87014i) q^{42} +(-7.40420 - 4.27482i) q^{43} +(-7.61299 - 5.75653i) q^{44} +(0.229683 + 9.55225i) q^{45} +(0.324525 + 0.728896i) q^{46} +(9.17889 + 2.98240i) q^{47} +(1.91780 + 1.68550i) q^{48} +(4.85556 + 2.16183i) q^{49} +(-10.3792 - 4.62110i) q^{50} +(-2.29234 + 11.4603i) q^{51} +(-4.69940 - 9.25060i) q^{52} +(-5.33340 + 7.34080i) q^{53} +(9.72519 - 6.09259i) q^{54} +(1.99848 + 10.3727i) q^{55} +(2.17920 + 1.25816i) q^{56} +(11.2760 - 5.18368i) q^{57} +(-7.08576 - 7.86953i) q^{58} +(-0.624388 + 2.93751i) q^{59} +(1.84908 + 15.7673i) q^{60} +(6.54904 - 0.688332i) q^{61} +(8.10166 - 8.99781i) q^{62} +(-2.83044 + 2.67450i) q^{63} +(10.3593 + 7.52649i) q^{64} +(-2.98555 + 11.0888i) q^{65} +(9.48834 - 8.42240i) q^{66} +(-3.77887 - 6.54520i) q^{67} +(-2.02973 + 19.3116i) q^{68} +(-0.610448 + 0.137444i) q^{69} +(-2.82158 - 8.68394i) q^{70} +(10.2462 - 1.07692i) q^{71} +(4.62141 - 3.53045i) q^{72} +(-6.72677 + 2.18566i) q^{73} +(2.52329 + 2.80239i) q^{74} +(5.15021 - 7.27086i) q^{75} +(17.8570 - 10.3097i) q^{76} +(-2.59657 + 3.43396i) q^{77} +(13.2831 - 3.71364i) q^{78} +(-2.33265 + 3.21061i) q^{79} +(-0.976143 - 4.59239i) q^{80} +(3.18933 + 8.41595i) q^{81} +(1.83691 + 17.4770i) q^{82} +(-8.64090 + 6.27798i) q^{83} +(-4.27116 + 4.85983i) q^{84} +(15.9712 - 14.3805i) q^{85} +(11.0988 - 15.2762i) q^{86} +(7.14170 - 4.23852i) q^{87} +(4.39261 - 4.69493i) q^{88} +(8.52894 - 4.92419i) q^{89} +(-21.0342 - 1.70072i) q^{90} +(-4.17263 + 2.11974i) q^{91} +(-0.988744 + 0.321262i) q^{92} +(5.67321 + 7.61432i) q^{93} +(-8.66975 + 19.4726i) q^{94} +(-22.3224 - 4.74477i) q^{95} +(-9.08094 + 8.37634i) q^{96} +(2.44708 - 1.08951i) q^{97} +(-5.86933 + 10.1660i) q^{98} +(5.01741 + 8.59218i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9}+O(q^{10}) $ 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9	$ 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9} - 52 q^{12} - 20 q^{13} - 3 q^{15} + 30 q^{16} - 20 q^{18} - 10 q^{19} + 4 q^{22} + 5 q^{24} + 60 q^{25} - 24 q^{27} - 10 q^{28} - 65 q^{30} - 8 q^{31} + 49 q^{33} - 24 q^{34} + 3 q^{36} - 6 q^{37} - 35 q^{39} - 120 q^{40} - 13 q^{42} - 32 q^{45} - 30 q^{46} - 33 q^{48} - 26 q^{49} - 100 q^{51} - 60 q^{52} - 42 q^{55} - 20 q^{57} - 34 q^{58} + 32 q^{60} - 30 q^{61} - 45 q^{63} + 40 q^{64} + 42 q^{66} + 32 q^{67} - 33 q^{69} - 268 q^{70} + 55 q^{72} - 40 q^{73} + 9 q^{75} - 32 q^{78} - 37 q^{81} + 28 q^{82} - 180 q^{84} - 10 q^{85} - 142 q^{88} - 30 q^{90} + 8 q^{91} - 26 q^{93} - 90 q^{94} + 330 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) $ 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9 - 52 * q^12 - 20 * q^13 - 3 * q^15 + 30 * q^16 - 20 * q^18 - 10 * q^19 + 4 * q^22 + 5 * q^24 + 60 * q^25 - 24 * q^27 - 10 * q^28 - 65 * q^30 - 8 * q^31 + 49 * q^33 - 24 * q^34 + 3 * q^36 - 6 * q^37 - 35 * q^39 - 120 * q^40 - 13 * q^42 - 32 * q^45 - 30 * q^46 - 33 * q^48 - 26 * q^49 - 100 * q^51 - 60 * q^52 - 42 * q^55 - 20 * q^57 - 34 * q^58 + 32 * q^60 - 30 * q^61 - 45 * q^63 + 40 * q^64 + 42 * q^66 + 32 * q^67 - 33 * q^69 - 268 * q^70 + 55 * q^72 - 40 * q^73 + 9 * q^75 - 32 * q^78 - 37 * q^81 + 28 * q^82 - 180 * q^84 - 10 * q^85 - 142 * q^88 - 30 * q^90 + 8 * q^91 - 26 * q^93 - 90 * q^94 + 330 * q^96 - 14 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−0.230857	+	2.19646i	−0.163241	+	1.55313i	0.539683	+	0.841868i	$0.318544\pi$
$2$	−0.230857	+	2.19646i	−0.163241	+	1.55313i	−0.702924	+	0.711265i	$0.748123\pi$
$3$	−1.65359	−	0.515394i	−0.954702	−	0.297563i
$3$	−1.65359	−	0.515394i	−0.954702	−	0.297563i
$4$	−2.81485	−	0.598316i	−1.40743	−	0.299158i
$5$	1.87210	+	2.57672i	0.837228	+	1.15235i	0.986534	+	0.163555i	$0.0522960\pi$
$5$	1.87210	+	2.57672i	0.837228	+	1.15235i	−0.149306	+	0.988791i	$0.547704\pi$
$6$	1.51379	−	3.51307i	0.618002	−	1.43421i
$7$	−0.269880	+	1.26968i	−0.102005	+	0.479895i	0.897258	+	0.441507i	$0.145556\pi$
$7$	−0.269880	+	1.26968i	−0.102005	+	0.479895i	−0.999263	+	0.0383886i	$0.987778\pi$
$8$	0.599043	−	1.84366i	0.211794	−	0.651834i
$9$	2.46874	+	1.70450i	0.822912	+	0.568168i
$10$	−6.09186	+	3.51714i	−1.92642	+	1.11222i
$11$	3.00356	+	1.40663i	0.905609	+	0.424114i
$11$	3.00356	+	1.40663i	0.905609	+	0.424114i
$12$	4.34625	+	2.44013i	1.25466	+	0.704405i
$13$	2.26567	+	2.80477i	0.628385	+	0.777903i
$13$	2.26567	+	2.80477i	0.628385	+	0.777903i
$14$	−2.72651	−	0.885896i	−0.728690	−	0.236766i
$15$	−1.76766	−	5.22572i	−0.456408	−	1.34927i
$16$	−1.34665	−	0.599567i	−0.336662	−	0.149892i
$17$	−0.705322	−	6.71069i	−0.171066	−	1.62758i	−0.657213	−	0.753705i	$-0.728265\pi$
$17$	−0.705322	−	6.71069i	−0.171066	−	1.62758i	0.486148	−	0.873877i	$-0.338402\pi$
$18$	−4.31381	+	5.02899i	−1.01677	+	1.18534i
$19$	−5.32475	+	4.79443i	−1.22158	+	1.09992i	−0.229632	+	0.973277i	$0.573752\pi$
$19$	−5.32475	+	4.79443i	−1.22158	+	1.09992i	−0.991949	+	0.126639i	$0.959581\pi$
$20$	−3.72799	−	8.37321i	−0.833604	−	1.87231i
$21$	1.10066	−	1.96044i	0.240183	−	0.427804i
$22$	−3.78300	+	6.27248i	−0.806538	+	1.33730i
$23$	0.312865	−	0.180633i	0.0652368	−	0.0376645i	−0.467027	−	0.884243i	$-0.654675\pi$
$23$	0.312865	−	0.180633i	0.0652368	−	0.0376645i	0.532264	+	0.846579i	$0.321342\pi$
$24$	−1.94079	+	2.73993i	−0.396161	+	0.559285i
$25$	−1.58966	+	4.89248i	−0.317932	+	0.978496i
$26$	−6.68361	+	4.32896i	−1.31076	+	0.848980i
$27$	−3.20379	−	4.09093i	−0.616570	−	0.787300i
$28$	1.51934	−	3.41250i	0.287129	−	0.644902i
$29$	−3.20831	+	3.56319i	−0.595769	+	0.661669i	−0.963326	−	0.268332i	$-0.913528\pi$
$29$	−3.20831	+	3.56319i	−0.595769	+	0.661669i	0.367557	+	0.930001i	$0.380194\pi$
$30$	11.8862	−	2.67620i	2.17011	−	0.488605i
$31$	−4.43518	−	3.22235i	−0.796582	−	0.578751i	0.113327	−	0.993558i	$-0.463849\pi$
$31$	−4.43518	−	3.22235i	−0.796582	−	0.578751i	−0.909910	+	0.414807i	$0.863849\pi$
$32$	3.56635	−	6.17710i	0.630448	−	1.09197i
$33$	−4.24170	−	3.87401i	−0.738386	−	0.674378i
$34$	14.9026			2.55578
$35$	−3.77686	+	1.68157i	−0.638406	+	0.284237i
$36$	−5.92930	−	6.27502i	−0.988217	−	1.04584i
$37$	1.14250	−	1.26888i	0.187826	−	0.208602i	−0.641876	−	0.766809i	$-0.721844\pi$
$37$	1.14250	−	1.26888i	0.187826	−	0.208602i	0.829702	+	0.558206i	$0.188510\pi$
$38$	−9.30152	−	12.8024i	−1.50891	−	2.07683i
$39$	−2.30094	−	5.80566i	−0.368445	−	0.929650i
$40$	5.87208	−	1.90795i	0.928457	−	0.301674i
$41$	7.78303	−	1.65433i	1.21551	−	0.258364i	0.444844	−	0.895608i	$-0.353259\pi$
$41$	7.78303	−	1.65433i	1.21551	−	0.258364i	0.770662	+	0.637245i	$0.219926\pi$
$42$	4.05195	+	2.87014i	0.625229	+	0.442872i
$43$	−7.40420	−	4.27482i	−1.12913	−	0.651903i	−0.185414	−	0.982661i	$-0.559363\pi$
$43$	−7.40420	−	4.27482i	−1.12913	−	0.651903i	−0.943716	+	0.330757i	$0.892696\pi$
$44$	−7.61299	−	5.75653i	−1.14770	−	0.867830i
$45$	0.229683	+	9.55225i	0.0342391	+	1.42397i
$46$	0.324525	+	0.728896i	0.0478486	+	0.107470i
$47$	9.17889	+	2.98240i	1.33888	+	0.435028i	0.888937	−	0.458030i	$-0.151445\pi$
$47$	9.17889	+	2.98240i	1.33888	+	0.435028i	0.449942	+	0.893058i	$0.351445\pi$
$48$	1.91780	+	1.68550i	0.276810	+	0.243280i
$49$	4.85556	+	2.16183i	0.693651	+	0.308833i
$50$	−10.3792	−	4.62110i	−1.46783	−	0.653522i
$51$	−2.29234	+	11.4603i	−0.320991	+	1.60476i
$52$	−4.69940	−	9.25060i	−0.651690	−	1.28283i
$53$	−5.33340	+	7.34080i	−0.732599	+	1.00834i	0.266411	+	0.963860i	$0.414162\pi$
$53$	−5.33340	+	7.34080i	−0.732599	+	1.00834i	−0.999010	+	0.0444770i	$0.985838\pi$
$54$	9.72519	−	6.09259i	1.32343	−	0.829096i
$55$	1.99848	+	10.3727i	0.269475	+	1.39865i
$56$	2.17920	+	1.25816i	0.291208	+	0.168129i
$57$	11.2760	−	5.18368i	1.49354	−	0.686595i
$58$	−7.08576	−	7.86953i	−0.930406	−	1.03332i
$59$	−0.624388	+	2.93751i	−0.0812884	+	0.382432i	−0.999920	−	0.0126844i	$-0.995962\pi$
$59$	−0.624388	+	2.93751i	−0.0812884	+	0.382432i	0.918631	+	0.395116i	$0.129296\pi$
$60$	1.84908	+	15.7673i	0.238715	+	2.03554i
$61$	6.54904	−	0.688332i	0.838519	−	0.0881319i	0.324473	−	0.945895i	$-0.394813\pi$
$61$	6.54904	−	0.688332i	0.838519	−	0.0881319i	0.514045	+	0.857763i	$0.328146\pi$
$62$	8.10166	−	8.99781i	1.02891	−	1.14272i
$63$	−2.83044	+	2.67450i	−0.356602	+	0.336956i
$64$	10.3593	+	7.52649i	1.29492	+	0.940811i
$65$	−2.98555	+	11.0888i	−0.370312	+	1.37540i
$66$	9.48834	−	8.42240i	1.16793	−	1.03673i
$67$	−3.77887	−	6.54520i	−0.461663	−	0.799623i	0.537381	−	0.843339i	$-0.319414\pi$
$67$	−3.77887	−	6.54520i	−0.461663	−	0.799623i	−0.999044	+	0.0437162i	$0.986080\pi$
$68$	−2.02973	+	19.3116i	−0.246141	+	2.34188i
$69$	−0.610448	+	0.137444i	−0.0734893	+	0.0165463i
$70$	−2.82158	−	8.68394i	−0.337244	−	1.03793i
$71$	10.2462	−	1.07692i	1.21600	−	0.127807i	0.525282	−	0.850928i	$-0.323960\pi$
$71$	10.2462	−	1.07692i	1.21600	−	0.127807i	0.690722	+	0.723121i	$0.257293\pi$
$72$	4.62141	−	3.53045i	0.544639	−	0.416067i
$73$	−6.72677	+	2.18566i	−0.787308	+	0.255812i	−0.674958	−	0.737857i	$-0.735838\pi$
$73$	−6.72677	+	2.18566i	−0.787308	+	0.255812i	−0.112351	+	0.993669i	$0.535838\pi$
$74$	2.52329	+	2.80239i	0.293326	+	0.325772i
$75$	5.15021	−	7.27086i	0.594695	−	0.839567i
$76$	17.8570	−	10.3097i	2.04834	−	1.18261i
$77$	−2.59657	+	3.43396i	−0.295907	+	0.391336i
$78$	13.2831	−	3.71364i	1.50401	−	0.420487i
$79$	−2.33265	+	3.21061i	−0.262443	+	0.361222i	−0.919820	−	0.392340i	$-0.871666\pi$
$79$	−2.33265	+	3.21061i	−0.262443	+	0.361222i	0.657377	+	0.753562i	$0.271666\pi$
$80$	−0.976143	−	4.59239i	−0.109136	−	0.513445i
$81$	3.18933	+	8.41595i	0.354370	+	0.935105i
$82$	1.83691	+	17.4770i	0.202853	+	1.93002i
$83$	−8.64090	+	6.27798i	−0.948462	+	0.689098i	−0.950443	−	0.310900i	$-0.899370\pi$
$83$	−8.64090	+	6.27798i	−0.948462	+	0.689098i	0.00198049	+	0.999998i	$0.499370\pi$
$84$	−4.27116	+	4.85983i	−0.466022	+	0.530250i
$85$	15.9712	−	14.3805i	1.73231	−	1.55978i
$86$	11.0988	−	15.2762i	1.19681	−	1.64727i
$87$	7.14170	−	4.23852i	0.765670	−	0.454418i
$88$	4.39261	−	4.69493i	0.468254	−	0.500481i
$89$	8.52894	−	4.92419i	0.904066	−	0.521963i	0.0255489	−	0.999674i	$-0.491867\pi$
$89$	8.52894	−	4.92419i	0.904066	−	0.521963i	0.878517	+	0.477711i	$0.158533\pi$
$90$	−21.0342	−	1.70072i	−2.21720	−	0.179272i
$91$	−4.17263	+	2.11974i	−0.437410	+	0.222209i
$92$	−0.988744	+	0.321262i	−0.103084	+	0.0334939i
$93$	5.67321	+	7.61432i	0.588284	+	0.789568i
$94$	−8.66975	+	19.4726i	−0.894216	+	2.00844i
$95$	−22.3224	−	4.74477i	−2.29023	−	0.486803i
$96$	−9.08094	+	8.37634i	−0.926820	+	0.854906i
$97$	2.44708	−	1.08951i	0.248463	−	0.110623i	−0.278727	−	0.960370i	$-0.589912\pi$
$97$	2.44708	−	1.08951i	0.248463	−	0.110623i	0.527190	+	0.849748i	$0.323246\pi$
$98$	−5.86933	+	10.1660i	−0.592892	+	1.02692i
$99$	5.01741	+	8.59218i	0.504268	+	0.863547i
$100$	7.40192	−	12.8205i	0.740192	−	1.28205i
$101$	0.0139318	−	0.132552i	0.00138626	−	0.0131894i	−0.993807	−	0.111121i	$-0.964556\pi$
$101$	0.0139318	−	0.132552i	0.00138626	−	0.0131894i	0.995193	+	0.0979315i	$0.0312226\pi$
$102$	−24.6428	−	7.68072i	−2.44000	−	0.760504i
$103$	−2.64055	−	8.12677i	−0.260181	−	0.800755i	−0.992765	−	0.120078i	$-0.961686\pi$
$103$	−2.64055	−	8.12677i	−0.260181	−	0.800755i	0.732584	−	0.680677i	$-0.238314\pi$
$104$	6.52828	−	2.49696i	0.640151	−	0.244847i
$105$	7.11206	−	0.834054i	0.694066	−	0.0813953i
$106$	−14.8925	−	13.4093i	−1.44649	−	1.30243i
$107$	1.74023	−	0.369896i	0.168234	−	0.0357592i	−0.123024	−	0.992404i	$-0.539259\pi$
$107$	1.74023	−	0.369896i	0.168234	−	0.0357592i	0.291258	+	0.956644i	$0.405926\pi$
$108$	6.57054	+	13.4323i	0.632251	+	1.29252i
$109$			8.00110i			0.766366i	0.923672	+	0.383183i	$0.125172\pi$
$109$			8.00110i			0.766366i	−0.923672	+	0.383183i	$0.874828\pi$
$110$	−23.2446	+	1.99497i	−2.21629	+	0.190213i
$111$	−2.54321	+	1.50937i	−0.241390	+	0.143263i
$112$	1.12469	−	1.54801i	0.106274	−	0.146273i
$113$	6.97418	−	6.27958i	0.656076	−	0.590733i	−0.272374	−	0.962192i	$-0.587809\pi$
$113$	6.97418	−	6.27958i	0.656076	−	0.590733i	0.928450	+	0.371458i	$0.121142\pi$
$114$	8.78261	+	25.9640i	0.822567	+	2.43175i
$115$	1.05115	+	0.468004i	0.0980206	+	0.0436416i
$116$	11.1629	−	8.11029i	1.03645	−	0.753022i
$117$	0.812610	+	10.7861i	0.0751258	+	0.997174i
$118$	−6.30799	−	2.04959i	−0.580698	−	0.188680i
$119$	8.71080	+	0.915542i	0.798518	+	0.0839276i
$120$	−10.6934	+	0.128542i	−0.976167	+	0.0117342i
$121$	7.04280	+	8.44979i	0.640254	+	0.768163i
$122$			14.5436i			1.31672i
$123$	−13.7226	−	1.27574i	−1.23732	−	0.115029i
$124$	10.5564	+	11.7241i	0.947994	+	1.05285i
$125$	−0.436967	+	0.141979i	−0.0390835	+	0.0126990i
$126$	−5.22102	−	6.83439i	−0.465125	−	0.608856i
$127$	−4.26112	+	9.57064i	−0.378113	+	0.849257i	0.619804	+	0.784756i	$0.287212\pi$
$127$	−4.26112	+	9.57064i	−0.378113	+	0.849257i	−0.997918	+	0.0645002i	$0.979455\pi$
$128$	−9.37775	+	10.4151i	−0.828884	+	0.920569i
$129$	10.0403	+	10.8849i	0.884000	+	0.958361i
$130$	−23.6669	−	9.11758i	−2.07573	−	0.799664i
$131$	12.9749			1.13362			0.566811	−	0.823848i	$-0.308177\pi$
$131$	12.9749			1.13362			0.566811	+	0.823848i	$0.308177\pi$
$132$	9.62190	+	13.4427i	0.837479	+	1.17003i
$133$	−4.65036	−	8.05466i	−0.403237	−	0.698428i
$134$	15.2487	−	6.78914i	1.31728	−	0.586492i
$135$	4.54338	−	15.9139i	0.391032	−	1.36965i
$136$	−12.7948	−	2.71961i	−1.09714	−	0.233205i
$137$	0.552292	−	0.0580482i	0.0471855	−	0.00495939i	−0.0809063	−	0.996722i	$-0.525781\pi$
$137$	0.552292	−	0.0580482i	0.0471855	−	0.00495939i	0.128092	+	0.991762i	$0.459115\pi$
$138$	−0.160964	−	1.37256i	−0.0137021	−	0.116840i
$139$	0.257679	−	1.21228i	0.0218560	−	0.102824i	−0.965868	−	0.259037i	$-0.916595\pi$
$139$	0.257679	−	1.21228i	0.0218560	−	0.102824i	0.987724	+	0.156212i	$0.0499283\pi$
$140$	11.6374	−	2.47361i	0.983542	−	0.209058i
$141$	−13.6410	−	9.66243i	−1.14878	−	0.813723i
$142$			22.7541i			1.90948i
$143$	2.85983	+	11.6113i	0.239151	+	0.970982i
$144$	−2.30256	−	3.77554i	−0.191880	−	0.314629i
$145$	−15.1876	−	1.59629i	−1.26127	−	0.132564i
$146$	−3.24779	−	15.2797i	−0.268789	−	1.26455i
$147$	−6.91492	−	6.07732i	−0.570333	−	0.501249i
$148$	−3.97517	+	2.88813i	−0.326757	+	0.237403i
$149$	0.451822	+	4.29880i	0.0370147	+	0.352171i	0.997317	+	0.0732087i	$0.0233239\pi$
$149$	0.451822	+	4.29880i	0.0370147	+	0.352171i	−0.960302	+	0.278963i	$0.910009\pi$
$150$	14.7812	+	12.9908i	1.20688	+	1.06069i
$151$	9.31002	+	3.02501i	0.757638	+	0.246172i	0.662265	−	0.749270i	$-0.269595\pi$
$151$	9.31002	+	3.02501i	0.757638	+	0.246172i	0.0953736	+	0.995442i	$0.469595\pi$
$152$	5.64956	+	12.6891i	0.458240	+	1.02922i
$153$	9.69715	−	17.7692i	0.783968	−	1.43655i
$154$	−6.94311	−	6.49603i	−0.559492	−	0.523465i
$155$		−	17.4608i		−	1.40248i
$156$	3.00319	+	17.7188i	0.240448	+	1.41864i
$157$	5.06570	−	15.5906i	0.404287	−	1.24427i	−0.517203	−	0.855863i	$-0.673027\pi$
$157$	5.06570	−	15.5906i	0.404287	−	1.24427i	0.921490	−	0.388403i	$-0.126973\pi$
$158$	−6.51348	−	5.86476i	−0.518184	−	0.466575i
$159$	12.6027	−	9.38989i	0.999458	−	0.744666i
$160$	22.5933	−	2.37465i	1.78615	−	0.187732i
$161$	0.144910	+	0.445988i	0.0114205	+	0.0351488i
$162$	−19.2216	+	5.06235i	−1.51019	+	0.397736i
$163$	5.45358	−	2.42809i	0.427157	−	0.190183i	−0.181886	−	0.983320i	$-0.558220\pi$
$163$	5.45358	−	2.42809i	0.427157	−	0.190183i	0.609043	+	0.793137i	$0.291554\pi$
$164$	−22.8979			−1.78803
$165$	2.04136	−	18.1822i	0.158920	−	1.41548i
$166$	−11.7945	−	20.4287i	−0.915433	−	1.58558i
$167$	0.469200	−	4.46414i	0.0363078	−	0.345446i	−0.961254	−	0.275663i	$-0.911103\pi$
$167$	0.469200	−	4.46414i	0.0363078	−	0.345446i	0.997562	−	0.0697829i	$-0.0222306\pi$
$168$	−2.95506	−	3.20363i	−0.227988	−	0.247166i
$169$	−2.73345	+	12.7094i	−0.210265	+	0.977644i
$170$	27.8991	+	38.3999i	2.13977	+	2.94514i
$171$	−21.3175	+	2.76012i	−1.63019	+	0.211071i
$172$	18.2841	+	16.4630i	1.39415	+	1.25529i
$173$	1.54988	+	1.72131i	0.117835	+	0.130869i	0.799176	−	0.601097i	$-0.205270\pi$
$173$	1.54988	+	1.72131i	0.117835	+	0.130869i	−0.681341	+	0.731966i	$0.738603\pi$
$174$	7.66104	+	16.6650i	0.580782	+	1.26337i
$175$	−5.78288	−	3.33875i	−0.437145	−	0.252386i
$176$	−3.20138	−	3.69507i	−0.241313	−	0.278527i
$177$	2.54646	−	4.53565i	0.191404	−	0.340920i
$178$	8.84682	+	19.8703i	0.663097	+	1.48934i
$179$	0.703235	+	3.30846i	0.0525623	+	0.247286i	0.996583	−	0.0826010i	$-0.0263227\pi$
$179$	0.703235	+	3.30846i	0.0525623	+	0.247286i	−0.944020	+	0.329887i	$0.892989\pi$
$180$	5.06874	−	27.0256i	0.377802	−	2.01437i
$181$	−5.63035	+	4.09069i	−0.418500	+	0.304058i	−0.777034	−	0.629458i	$-0.783277\pi$
$181$	−5.63035	+	4.09069i	−0.418500	+	0.304058i	0.358534	+	0.933517i	$0.383277\pi$
$182$	−3.69264	−	9.65437i	−0.273717	−	0.715630i
$183$	−11.1842	−	2.23712i	−0.826761	−	0.165373i
$184$	−0.145606	−	0.685024i	−0.0107342	−	0.0505006i
$185$	5.40842	+	0.568448i	0.397635	+	0.0417932i
$186$	−18.0343	+	10.7032i	−1.32234	+	0.784794i
$187$	7.32096	−	21.1481i	0.535362	−	1.54650i
$188$	−24.0528	−	13.8869i	−1.75423	−	1.01281i
$189$	6.05882	−	2.96374i	0.440715	−	0.215581i
$190$	15.5750	−	47.9349i	1.12993	−	3.47756i
$191$	−0.344282	+	1.61972i	−0.0249114	+	0.117199i	−0.988846	−	0.148939i	$-0.952414\pi$
$191$	−0.344282	+	1.61972i	−0.0249114	+	0.117199i	0.963935	+	0.266138i	$0.0857476\pi$
$192$	−13.2510	−	17.7849i	−0.956308	−	1.28351i
$193$	0.293888	−	0.660084i	0.0211545	−	0.0475139i	−0.902659	−	0.430356i	$-0.858388\pi$
$193$	0.293888	−	0.660084i	0.0211545	−	0.0475139i	0.923814	+	0.382842i	$0.125055\pi$
$194$	1.82814	+	5.62643i	0.131253	+	0.403954i
$195$	10.6520	−	16.7976i	0.762805	−	1.20290i
$196$	−12.3742	−	8.99040i	−0.883874	−	0.642172i
$197$	11.5245	+	19.9610i	0.821085	+	1.42216i	0.904875	+	0.425677i	$0.139964\pi$
$197$	11.5245	+	19.9610i	0.821085	+	1.42216i	−0.0837906	+	0.996483i	$0.526703\pi$
$198$	−20.0307	+	9.03697i	−1.42352	+	0.642230i
$199$	7.14875	−	12.3820i	0.506762	−	0.877737i	−0.493208	−	0.869912i	$-0.664176\pi$
$199$	7.14875	−	12.3820i	0.506762	−	0.877737i	0.999969	−	0.00782535i	$-0.00249091\pi$
$200$	8.06781	+	5.86161i	0.570480	+	0.414478i
$201$	2.87536	+	12.7707i	0.202812	+	0.900776i
$202$	0.287929	+	0.0612012i	0.0202586	+	0.00430610i
$203$	−3.65827	−	5.03518i	−0.256760	−	0.353400i
$204$	13.3095	−	30.8874i	0.931848	−	2.16255i
$205$	18.8334	+	16.9576i	1.31538	+	1.18437i
$206$	18.4597	−	3.92374i	1.28615	−	0.273380i
$207$	1.08027	+	0.0873452i	0.0750839	+	0.00607091i
$208$	−1.36942	−	5.13546i	−0.0949523	−	0.356080i
$209$	−22.7372	+	6.91043i	−1.57276	+	0.478004i
$210$	0.190094	+	15.8139i	0.0131178	+	1.09126i
$211$	10.6190	+	1.11610i	0.731043	+	0.0768357i	0.462734	−	0.886497i	$-0.346869\pi$
$211$	10.6190	+	1.11610i	0.731043	+	0.0768357i	0.268309	+	0.963333i	$0.413535\pi$
$212$	19.4049	−	17.4722i	1.33273	−	1.20000i
$213$	−17.4981	−	3.50006i	−1.19895	−	0.239820i
$214$	0.410719	+	3.90773i	0.0280762	+	0.267127i
$215$	−2.84637	−	27.0814i	−0.194121	−	1.84694i
$216$	−9.46151	+	3.45608i	−0.643774	+	0.235156i
$217$	5.28833	−	4.76163i	0.358995	−	0.323241i
$218$	−17.5741	−	1.84711i	−1.19027	−	0.125102i
$219$	12.2498	−	0.147251i	0.827765	−	0.00995032i
$220$	0.580720	−	30.3934i	0.0391521	−	2.04912i
$221$	17.2239	−	17.1825i	1.15860	−	1.15582i
$222$	−2.72815	−	5.93451i	−0.183101	−	0.398298i
$223$	20.2885	−	4.31245i	1.35862	−	0.288783i	0.529715	−	0.848176i	$-0.322299\pi$
$223$	20.2885	−	4.31245i	1.35862	−	0.288783i	0.828903	+	0.559393i	$0.188966\pi$
$224$	6.88048	+	6.19521i	0.459721	+	0.413935i
$225$	−12.2637	+	9.36865i	−0.817581	+	0.624577i
$226$	12.1828	+	16.7682i	0.810389	+	1.11541i
$227$	−19.8446	−	4.21811i	−1.31713	−	0.279966i	−0.504840	−	0.863213i	$-0.668449\pi$
$227$	−19.8446	−	4.21811i	−1.31713	−	0.279966i	−0.812295	+	0.583247i	$0.801782\pi$
$228$	−34.8417	+	7.84471i	−2.30745	+	0.519528i
$229$	3.59316	+	2.61058i	0.237442	+	0.172512i	0.700143	−	0.714003i	$-0.253120\pi$
$229$	3.59316	+	2.61058i	0.237442	+	0.172512i	−0.462701	+	0.886515i	$0.653120\pi$
$230$	−1.27062	+	2.20078i	−0.0837821	+	0.145115i
$231$	6.06351	−	4.34010i	0.398950	−	0.285558i
$232$	4.64741	+	8.04956i	0.305118	+	0.528479i
$233$	11.1269	+	8.08418i	0.728949	+	0.529612i	0.889231	−	0.457459i	$-0.151240\pi$
$233$	11.1269	+	8.08418i	0.728949	+	0.529612i	−0.160282	+	0.987071i	$0.551240\pi$
$234$	−23.8788	−	0.705181i	−1.56101	−	0.0460992i
$235$	9.49896	+	29.2348i	0.619644	+	1.90707i
$236$	3.51512	−	7.89509i	0.228815	−	0.513927i
$237$	5.51198	−	4.10681i	0.358041	−	0.266766i
$238$	−4.02191	+	18.9216i	−0.260702	+	1.22650i
$239$	−0.936609	+	2.88259i	−0.0605842	+	0.186459i	−0.976768	−	0.214299i	$-0.931253\pi$
$239$	−0.936609	+	2.88259i	−0.0605842	+	0.186459i	0.916184	+	0.400758i	$0.131253\pi$
$240$	−0.752750	+	8.09704i	−0.0485898	+	0.522662i
$241$	−22.3748	−	12.9181i	−1.44129	−	0.832127i	−0.443350	−	0.896348i	$-0.646210\pi$
$241$	−22.3748	−	12.9181i	−1.44129	−	0.832127i	−0.997936	+	0.0642215i	$0.979544\pi$
$242$	−20.1855	+	13.5185i	−1.29758	+	0.869005i
$243$	−0.936312	−	15.5603i	−0.0600644	−	0.998195i
$244$	−18.8464	−	1.98084i	−1.20652	−	0.126810i
$245$	3.51964	+	16.5586i	0.224861	+	1.05789i
$246$	5.97007	−	29.8467i	0.380638	−	1.90295i
$247$	−25.5114	−	4.07209i	−1.62325	−	0.259101i
$248$	−8.59779	+	6.24666i	−0.545960	+	0.396663i
$249$	17.5242	−	5.92775i	1.11055	−	0.375656i
$250$	−0.210975	−	0.992559i	−0.0133432	−	0.0627749i
$251$	3.24782	+	7.29471i	0.205000	+	0.460438i	0.986561	−	0.163390i	$-0.0522430\pi$
$251$	3.24782	+	7.29471i	0.205000	+	0.460438i	−0.781561	+	0.623829i	$0.785576\pi$
$252$	9.56748	−	5.83484i	0.602695	−	0.367560i
$253$	1.19379	−	0.102457i	0.0750531	−	0.00644143i
$254$	−20.0378	−	11.5688i	−1.25729	−	0.725894i
$255$	−33.8214	+	15.5480i	−2.11798	+	0.973656i
$256$	−3.57513	−	3.97059i	−0.223446	−	0.248162i
$257$	−15.8293	−	14.2528i	−0.987406	−	0.889065i	0.00642350	−	0.999979i	$-0.497955\pi$
$257$	−15.8293	−	14.2528i	−0.987406	−	0.889065i	−0.993830	+	0.110915i	$0.964622\pi$
$258$	−26.2261	+	19.5403i	−1.63277	+	1.21653i
$259$	1.30273	+	1.79306i	0.0809480	+	0.111415i
$260$	15.0385	−	29.4271i	0.932648	−	1.82499i
$261$	−13.9940	+	3.32800i	−0.866205	+	0.205998i
$262$	−2.99535	+	28.4988i	−0.185053	+	1.76066i
$263$	−6.57993	−	11.3968i	−0.405736	−	0.702755i	0.588671	−	0.808373i	$-0.299651\pi$
$263$	−6.57993	−	11.3968i	−0.405736	−	0.702755i	−0.994407	+	0.105618i	$0.966318\pi$
$264$	−9.68333	+	5.49958i	−0.595968	+	0.338476i
$265$	−28.8999			−1.77530
$266$	18.7653	−	8.35486i	1.15058	−	0.512270i
$267$	−16.6413	+	3.74683i	−1.01843	+	0.229302i
$268$	6.72088	+	20.6847i	0.410543	+	1.26352i
$269$	6.61783	−	0.695562i	0.403496	−	0.0424092i	0.0993931	−	0.995048i	$-0.468310\pi$
$269$	6.61783	−	0.695562i	0.403496	−	0.0424092i	0.304103	+	0.952639i	$0.401643\pi$
$270$	33.9054	+	13.6532i	2.06342	+	0.830907i
$271$	12.5659	+	11.3144i	0.763322	+	0.687298i	0.955805	−	0.294002i	$-0.0949872\pi$
$271$	12.5659	+	11.3144i	0.763322	+	0.687298i	−0.192483	+	0.981300i	$0.561654\pi$
$272$	−3.07369	+	9.45983i	−0.186370	+	0.573587i
$273$	7.99232	−	1.35463i	0.483718	−	0.0819862i
$274$			1.22649i			0.0740949i
$275$	−11.6565	+	12.4588i	−0.702916	+	0.751294i
$276$	1.80056	−	0.0216440i	0.108381	−	0.00130281i
$277$	−10.7764	−	24.2041i	−0.647490	−	1.45429i	−0.876762	−	0.480924i	$-0.840301\pi$
$277$	−10.7764	−	24.2041i	−0.647490	−	1.45429i	0.229273	−	0.973362i	$-0.426365\pi$
$278$	2.60325	+	0.845846i	0.156132	+	0.0507305i
$279$	−5.45679	−	15.5149i	−0.326690	−	0.928854i
$280$	0.837743	+	7.97060i	0.0500647	+	0.476334i
$281$	−19.9874	+	14.5217i	−1.19235	+	0.866293i	−0.993511	−	0.113739i	$-0.963717\pi$
$281$	−19.9874	+	14.5217i	−1.19235	+	0.866293i	−0.198839	+	0.980032i	$0.563717\pi$
$282$	24.3723	−	27.7314i	1.45135	−	1.65138i
$283$	1.51686	+	7.13628i	0.0901682	+	0.424208i	0.999958	+	0.00913927i	$0.00290916\pi$
$283$	1.51686	+	7.13628i	0.0901682	+	0.424208i	−0.909790	+	0.415069i	$0.863758\pi$
$284$	−29.4860	−	3.09910i	−1.74967	−	0.183898i
$285$	34.4667	+	19.3507i	2.04163	+	1.14624i
$286$	−26.1639	+	3.60096i	−1.54710	+	0.212929i
$287$			10.3285i			0.609669i
$288$	19.3333	−	9.17078i	1.13923	−	0.540393i
$289$	−27.9074	+	5.93189i	−1.64161	+	0.348935i
$290$	7.01236	−	32.9906i	0.411780	−	1.93727i
$291$	−4.60800	+	0.540394i	−0.270125	+	0.0316785i
$292$	20.2426	−	2.12758i	1.18461	−	0.124507i
$293$	13.0467	+	2.77317i	0.762198	+	0.162010i	0.572581	−	0.819848i	$-0.305942\pi$
$293$	13.0467	+	2.77317i	0.762198	+	0.162010i	0.189617	+	0.981858i	$0.439275\pi$
$294$	14.9450	−	13.7854i	0.871608	−	0.803978i
$295$	−8.73808	+	3.89044i	−0.508750	+	0.226510i
$296$	−1.65498	−	2.86650i	−0.0961935	−	0.166612i
$297$	−3.86838	−	16.7939i	−0.224466	−	0.974482i
$298$	−9.54645			−0.553011
$299$	1.21548	+	0.468259i	0.0702931	+	0.0270801i
$300$	−18.8474	+	17.3850i	−1.08815	+	1.00372i
$301$	7.42590	−	8.24730i	0.428022	−	0.475367i
$302$	−8.79360	+	19.7507i	−0.506015	+	1.13653i
$303$	−0.0913540	+	0.212007i	−0.00524815	+	0.0121795i
$304$	10.0452	−	3.26387i	0.576129	−	0.187196i
$305$	14.0341	+	15.5864i	0.803590	+	0.892477i
$306$	36.7906	+	25.4016i	2.10318	+	1.45211i
$307$			15.8208i			0.902940i	0.892286	+	0.451470i	$0.149100\pi$
$307$			15.8208i			0.902940i	−0.892286	+	0.451470i	$0.850900\pi$
$308$	9.36356	−	8.11252i	0.533539	−	0.462253i
$309$	0.177898	+	14.7993i	0.0101203	+	0.841902i
$310$	38.3520	+	4.03096i	2.17825	+	0.228943i
$311$	13.9213	+	4.52331i	0.789406	+	0.256494i	0.675851	−	0.737038i	$-0.263776\pi$
$311$	13.9213	+	4.52331i	0.789406	+	0.256494i	0.113555	+	0.993532i	$0.463776\pi$
$312$	−12.0820	+	0.764319i	−0.684011	+	0.0432710i
$313$	3.20414	−	2.32794i	0.181109	−	0.131583i	−0.493537	−	0.869725i	$-0.664296\pi$
$313$	3.20414	−	2.32794i	0.181109	−	0.131583i	0.674646	+	0.738142i	$0.264296\pi$
$314$	33.0747	+	14.7258i	1.86651	+	0.831026i
$315$	−12.1903	−	2.28633i	−0.686847	−	0.128820i
$316$	8.48702	−	7.64175i	0.477432	−	0.429882i
$317$	−0.496354	+	0.683172i	−0.0278780	+	0.0383708i	−0.822728	−	0.568435i	$-0.807549\pi$
$317$	−0.496354	+	0.683172i	−0.0278780	+	0.0383708i	0.794850	+	0.606805i	$0.207549\pi$
$318$	17.7151	+	29.8490i	0.993414	+	1.67385i
$319$	−14.6485	+	6.18938i	−0.820157	+	0.346539i
$320$			40.7834i			2.27986i
$321$	−3.06827	−	0.285245i	−0.171254	−	0.0159208i
$322$	−1.01305	+	0.215330i	−0.0564550	+	0.0119999i
$323$	35.9296	+	32.3511i	1.99917	+	1.80006i
$324$	−3.94209	−	25.5979i	−0.219005	−	1.42211i
$325$	−17.3239	+	6.62612i	−0.960958	+	0.367551i
$326$	4.07421	+	12.5391i	0.225650	+	0.694478i
$327$	4.12372	−	13.2306i	0.228042	−	0.731651i
$328$	1.61233	−	15.3403i	0.0890261	−	0.847027i
$329$	−6.26390	+	10.8494i	−0.345340	+	0.598146i
$330$	39.4653	+	8.68127i	2.17249	+	0.477888i
$331$	−10.3113	+	17.8597i	−0.566762	+	0.981660i	0.430122	+	0.902771i	$0.358471\pi$
$331$	−10.3113	+	17.8597i	−0.566762	+	0.981660i	−0.996883	+	0.0788892i	$0.974863\pi$
$332$	28.0791	−	12.5016i	1.54104	−	0.686116i
$333$	4.98335	−	1.18512i	0.273086	−	0.0649444i
$334$	9.69700	+	2.06116i	0.530596	+	0.112782i
$335$	9.79074	−	21.9904i	0.534925	−	1.20146i
$336$	−2.65762	+	1.98011i	−0.144985	+	0.108024i
$337$	−10.8400	+	3.52212i	−0.590490	+	0.191862i	−0.588995	−	0.808137i	$-0.700476\pi$
$337$	−10.8400	+	3.52212i	−0.590490	+	0.191862i	−0.00149578	+	0.999999i	$0.500476\pi$
$338$	−27.2846	−	8.93797i	−1.48409	−	0.486162i
$339$	−14.7689	+	6.78942i	−0.802138	+	0.368750i
$340$	−53.5606	+	30.9232i	−2.90473	+	1.67705i
$341$	−8.78871	−	15.9172i	−0.475936	−	0.861964i
$342$	−1.14118	−	47.4603i	−0.0617078	−	2.56636i
$343$	−9.39608	+	12.9326i	−0.507340	+	0.698294i
$344$	−12.3168	+	11.0901i	−0.664075	+	0.597936i
$345$	−1.49697	−	1.31565i	−0.0805943	−	0.0708320i
$346$	−4.13859	+	3.00687i	−0.222492	+	0.161650i
$347$	0.410687	+	3.90742i	0.0220468	+	0.209761i	1.00000		0.000935125i	$0.000297660\pi$
$347$	0.410687	+	3.90742i	0.0220468	+	0.209761i	−0.977953	+	0.208826i	$0.933036\pi$
$348$	−22.6388	+	7.65784i	−1.21357	+	0.410503i
$349$	5.60104	+	26.3508i	0.299817	+	1.41053i	0.827681	+	0.561199i	$0.189660\pi$
$349$	5.60104	+	26.3508i	0.299817	+	1.41053i	−0.527864	+	0.849329i	$0.677007\pi$
$350$	8.66845	−	11.9311i	0.463348	−	0.637744i
$351$	4.21536	−	18.2546i	0.224999	−	0.974359i
$352$	19.4007	−	13.5368i	1.03406	−	0.721514i
$353$	5.52250	−	3.18842i	0.293933	−	0.169702i	−0.345781	−	0.938315i	$-0.612386\pi$
$353$	5.52250	−	3.18842i	0.293933	−	0.169702i	0.639714	+	0.768613i	$0.279053\pi$
$354$	9.37450	+	6.64029i	0.498249	+	0.352928i
$355$	21.9569	+	24.3856i	1.16535	+	1.29425i
$356$	−26.9540	+	8.75787i	−1.42856	+	0.464166i
$357$	−13.9323	−	6.00343i	−0.737373	−	0.317735i
$358$	−7.42926	+	0.780846i	−0.392648	+	0.0412690i
$359$	−5.90276	−	18.1668i	−0.311536	−	0.958809i	−0.977157	−	0.212519i	$-0.931833\pi$
$359$	−5.90276	−	18.1668i	−0.311536	−	0.958809i	0.665621	−	0.746290i	$-0.268167\pi$
$360$	17.7487	+	5.29875i	0.935440	+	0.279269i
$361$	3.38040	−	32.1623i	0.177916	−	1.69275i
$362$	−7.68523	−	13.3112i	−0.403927	−	0.699621i
$363$	−7.29094	−	17.6023i	−0.382675	−	0.923883i
$364$	13.0136	−	3.47021i	0.682098	−	0.181888i
$365$	−18.2250	−	13.2412i	−0.953941	−	0.693078i
$366$	7.49571	−	24.0492i	0.391807	−	1.25707i
$367$	5.82923	−	6.47402i	0.304284	−	0.337941i	−0.571539	−	0.820575i	$-0.693653\pi$
$367$	5.82923	−	6.47402i	0.304284	−	0.337941i	0.875822	+	0.482634i	$0.160320\pi$
$368$	−0.529620	+	0.0556653i	−0.0276084	+	0.00290176i
$369$	22.0341	+	9.18210i	1.14705	+	0.478001i
$370$	−2.49715	+	11.7482i	−0.129821	+	0.610758i
$371$	−7.88112	−	8.75287i	−0.409167	−	0.454426i
$372$	−11.4135	−	24.8276i	−0.591761	−	1.28725i
$373$	−6.56651	−	3.79118i	−0.340001	−	0.196300i	0.320271	−	0.947326i	$-0.396226\pi$
$373$	−6.56651	−	3.79118i	−0.340001	−	0.196300i	−0.660273	+	0.751026i	$0.729559\pi$
$374$	44.7609	+	20.9624i	2.31453	+	1.08394i
$375$	0.795741	−	0.00956536i	0.0410919	−	0.000493953i
$376$	10.9971	−	15.1362i	0.567132	−	0.780590i
$377$	−17.2629	−	0.925545i	−0.889086	−	0.0476680i
$378$	5.11103	+	13.9922i	0.262883	+	0.719680i
$379$	−12.7719	−	5.68644i	−0.656051	−	0.292093i	0.0515865	−	0.998669i	$-0.483572\pi$
$379$	−12.7719	−	5.68644i	−0.656051	−	0.292093i	−0.707637	+	0.706576i	$0.750239\pi$
$380$	59.9953	+	26.7116i	3.07770	+	1.37028i
$381$	11.9788	−	13.6298i	0.613693	−	0.698275i
$382$	−3.47817	−	1.13013i	−0.177959	−	0.0578223i
$383$	−10.7294	−	24.0986i	−0.548246	−	1.23138i	−0.949024	−	0.315205i	$-0.897927\pi$
$383$	−10.7294	−	24.0986i	−0.548246	−	1.23138i	0.400778	−	0.916175i	$-0.368740\pi$
$384$	20.8748	−	12.3890i	1.06526	−	0.632224i
$385$	−13.7094	−	0.261943i	−0.698695	−	0.0133498i
$386$	1.38200	+	0.797899i	0.0703421	+	0.0406120i
$387$	−10.9926	−	23.1739i	−0.558784	−	1.17799i
$388$	−7.54004	+	1.60268i	−0.382787	+	0.0813640i
$389$	0.628677	−	0.204270i	0.0318752	−	0.0103569i	−0.293036	−	0.956101i	$-0.594666\pi$
$389$	0.628677	−	0.204270i	0.0318752	−	0.0103569i	0.324911	+	0.945745i	$0.394666\pi$
$390$	34.4363	+	27.2746i	1.74375	+	1.38110i
$391$	−1.43284	−	1.97213i	−0.0724618	−	0.0997351i
$392$	6.89438	−	7.65698i	0.348219	−	0.386736i
$393$	−21.4552	−	6.68719i	−1.08227	−	0.337324i
$394$	−46.5040	+	20.7049i	−2.34284	+	1.04310i
$395$	−12.6398			−0.635977
$396$	−8.98243	−	27.1877i	−0.451384	−	1.36624i
$397$	−4.76679	+	8.25633i	−0.239238	+	0.414373i	−0.960496	−	0.278294i	$-0.910231\pi$
$397$	−4.76679	+	8.25633i	−0.239238	+	0.414373i	0.721258	+	0.692667i	$0.243564\pi$
$398$	25.5463	+	18.5604i	1.28052	+	0.930351i
$399$	3.53848	+	15.7159i	0.177145	+	0.786779i
$400$	5.07409	−	5.63534i	0.253704	−	0.281767i
$401$	1.44446	−	3.24432i	0.0721331	−	0.162014i	−0.873880	−	0.486141i	$-0.838404\pi$
$401$	1.44446	−	3.24432i	0.0721331	−	0.162014i	0.946013	+	0.324128i	$0.105071\pi$
$402$	−28.7142	+	3.36740i	−1.43213	+	0.167951i
$403$	−1.01073	−	19.7405i	−0.0503482	−	0.983342i
$404$	−0.118524	+	0.364779i	−0.00589678	+	0.0181484i
$405$	−15.7148	+	23.9735i	−0.780877	+	1.19125i
$406$	11.9041	−	6.87284i	0.590791	−	0.341093i
$407$	5.21642	−	2.20408i	0.258568	−	0.109252i
$408$	19.7557	+	11.0915i	0.978051	+	0.549110i
$409$	0.225496	+	0.506472i	0.0111501	+	0.0250434i	0.919035	−	0.394177i	$-0.128970\pi$
$409$	0.225496	+	0.506472i	0.0111501	+	0.0250434i	−0.907885	+	0.419220i	$0.862304\pi$
$410$	−41.5946	+	37.4520i	−2.05421	+	1.84962i
$411$	−0.943183	−	0.188660i	−0.0465238	−	0.00930591i
$412$	2.57038	+	24.4556i	0.126634	+	1.20484i
$413$	−3.56120	−	1.58555i	−0.175235	−	0.0780198i
$414$	−0.441239	+	2.35261i	−0.0216857	+	0.115624i
$415$	−32.3532	−	10.5122i	−1.58816	−	0.516024i
$416$	25.4055	−	3.99251i	1.24561	−	0.195749i
$417$	−1.05090	+	1.87182i	−0.0514628	+	0.0916632i
$418$	−9.92944	−	51.5367i	−0.485665	−	2.52074i
$419$	−3.08197	+	1.77938i	−0.150564	+	0.0869283i	−0.573389	−	0.819283i	$-0.694372\pi$
$419$	−3.08197	+	1.77938i	−0.150564	+	0.0869283i	0.422825	+	0.906211i	$0.361038\pi$
$420$	−20.5185	−	1.90752i	−1.00120	−	0.0930775i
$421$	0.131782	−	0.405582i	0.00642265	−	0.0197669i	−0.947794	−	0.318884i	$-0.896692\pi$
$421$	0.131782	−	0.405582i	0.00642265	−	0.0197669i	0.954216	+	0.299117i	$0.0966920\pi$
$422$	−4.90295	+	23.0666i	−0.238672	+	1.12286i
$423$	17.5767	+	23.0082i	0.854611	+	1.11870i
$424$	10.3390	+	14.2305i	0.502108	+	0.691092i
$425$	33.9531	+	7.21696i	1.64697	+	0.350074i
$426$	11.7273	−	37.6260i	0.568191	−	1.82298i
$427$	−0.893489	+	8.50098i	−0.0432389	+	0.411391i
$428$	−5.11980			−0.247475
$429$	1.25538	−	20.6742i	0.0606105	−	0.998161i
$430$	60.1405			2.90023
$431$	−1.25349	+	11.9262i	−0.0603787	+	0.574465i	0.921951	+	0.387306i	$0.126594\pi$
$431$	−1.25349	+	11.9262i	−0.0603787	+	0.574465i	−0.982330	+	0.187158i	$0.940072\pi$
$432$	1.86160	+	7.42994i	0.0895663	+	0.357473i
$433$	−27.3077	−	5.80443i	−1.31232	−	0.278943i	−0.501971	−	0.864885i	$-0.667391\pi$
$433$	−27.3077	−	5.80443i	−1.31232	−	0.278943i	−0.810353	+	0.585942i	$0.800725\pi$
$434$	9.23789	+	12.7149i	0.443433	+	0.610333i
$435$	24.2915	+	10.4672i	1.16469	+	0.501866i
$436$	4.78718	−	22.5219i	0.229265	−	1.07860i
$437$	−0.799897	+	2.46183i	−0.0382643	+	0.117765i
$438$	−2.50453	+	26.9402i	−0.119671	+	1.28725i
$439$	26.7929	−	15.4689i	1.27876	−	0.738290i	0.302136	−	0.953265i	$-0.402300\pi$
$439$	26.7929	−	15.4689i	1.27876	−	0.738290i	0.976620	+	0.214975i	$0.0689669\pi$
$440$	20.3209	+	2.52916i	0.968763	+	0.120573i
$441$	8.30224	+	13.6133i	0.395345	+	0.648253i
$442$	33.7644	+	41.7983i	1.60601	+	1.98814i
$443$	28.0070	+	9.10004i	1.33065	+	0.432356i	0.886141	−	0.463416i	$-0.153376\pi$
$443$	28.0070	+	9.10004i	1.33065	+	0.432356i	0.444514	+	0.895772i	$0.353376\pi$
$444$	8.06184	−	2.72701i	0.382598	−	0.129418i
$445$	28.6553	+	12.7582i	1.35839	+	0.604795i
$446$	4.78839	+	45.5584i	0.226737	+	2.15725i
$447$	1.46845	−	7.34133i	0.0694552	−	0.347233i
$448$	−12.3520	+	11.1218i	−0.583579	+	0.525456i
$449$	−3.75425	−	8.43219i	−0.177174	−	0.397939i	0.803027	−	0.595942i	$-0.203221\pi$
$449$	−3.75425	−	8.43219i	−0.177174	−	0.397939i	−0.980201	+	0.198003i	$0.936555\pi$
$450$	−17.7467	−	29.0996i	−0.836589	−	1.37177i
$451$	25.7039	+	5.97893i	1.21035	+	0.281537i
$452$	−23.3885	+	13.5033i	−1.10010	+	0.635144i
$453$	−13.8359	−	9.80046i	−0.650067	−	0.460466i
$454$	13.8462	−	42.6142i	0.649834	−	1.99998i
$455$	−13.2735	−	6.78334i	−0.622273	−	0.318008i
$456$	−2.80217	−	23.8944i	−0.131223	−	1.11896i
$457$	14.9404	−	33.5568i	0.698884	−	1.56972i	−0.118063	−	0.993006i	$-0.537668\pi$
$457$	14.9404	−	33.5568i	0.698884	−	1.56972i	0.816947	−	0.576713i	$-0.195665\pi$
$458$	−6.56355	+	7.28956i	−0.306694	+	0.340619i
$459$	−25.1933	+	24.3851i	−1.17592	+	1.13820i
$460$	−2.67883	−	1.94628i	−0.124901	−	0.0907460i
$461$	14.3008	−	24.7697i	0.666054	−	1.15364i	−0.312944	−	0.949771i	$-0.601315\pi$
$461$	14.3008	−	24.7697i	0.666054	−	1.15364i	0.978998	−	0.203868i	$-0.0653513\pi$
$462$	8.13307	+	14.3202i	0.378385	+	0.666237i
$463$	14.3852			0.668535			0.334267	−	0.942478i	$-0.391511\pi$
$463$	14.3852			0.668535			0.334267	+	0.942478i	$0.391511\pi$
$464$	6.45685	−	2.87477i	0.299752	−	0.133458i
$465$	−8.99920	+	28.8730i	−0.417328	+	1.33896i
$466$	−20.3253	+	22.5736i	−0.941553	+	1.04570i
$467$	−3.98049	−	5.47868i	−0.184195	−	0.253523i	0.706927	−	0.707287i	$-0.250081\pi$
$467$	−3.98049	−	5.47868i	−0.184195	−	0.253523i	−0.891122	+	0.453764i	$0.850081\pi$
$468$	4.16611	−	30.8475i	0.192578	−	1.42592i
$469$	9.33017	−	3.03156i	0.430827	−	0.139984i
$470$	−66.4060	+	14.1150i	−3.06308	+	0.651078i
$471$	−16.4119	+	23.1697i	−0.756221	+	1.06760i
$472$	5.04175	+	2.91086i	0.232065	+	0.133983i
$473$	−16.2259	−	23.2546i	−0.746068	−	1.06925i
$474$	7.74797	+	13.0549i	0.355876	+	0.599633i
$475$	−14.9921	−	33.6727i	−0.687883	−	1.54501i
$476$	−23.9719	−	7.78893i	−1.09875	−	0.357005i
$477$	−25.6792	+	9.03169i	−1.17577	+	0.413533i
$478$	−6.11527	−	2.72269i	−0.279706	−	0.124533i
$479$	4.02780	+	1.79329i	0.184035	+	0.0819376i	0.496686	−	0.867931i	$-0.334550\pi$
$479$	4.02780	+	1.79329i	0.184035	+	0.0819376i	−0.312651	+	0.949868i	$0.601217\pi$
$480$	−38.5839	−	7.71774i	−1.76111	−	0.352265i
$481$	6.14745	+	0.329593i	0.280299	+	0.0150281i
$482$	33.5395	−	46.1631i	1.52768	−	2.10267i
$483$	−0.00976284	−	0.812169i	−0.000444224	−	0.0369550i
$484$	−14.7688	−	27.9988i	−0.671309	−	1.27267i
$485$	7.38853	+	4.26577i	0.335496	+	0.193699i
$486$	34.3938	+	1.53564i	1.56013	+	0.0696581i
$487$	17.2851	+	19.1970i	0.783261	+	0.869900i	0.994194	−	0.107601i	$-0.0343168\pi$
$487$	17.2851	+	19.1970i	0.783261	+	0.869900i	−0.210933	+	0.977501i	$0.567650\pi$
$488$	2.65410	−	12.4866i	0.120146	−	0.565241i
$489$	−10.2694	+	1.20433i	−0.464400	+	0.0544616i
$490$	−37.1829	+	3.90808i	−1.67975	+	0.176549i
$491$	5.14672	−	5.71602i	0.232268	−	0.257960i	−0.615732	−	0.787956i	$-0.711140\pi$
$491$	5.14672	−	5.71602i	0.232268	−	0.257960i	0.848001	+	0.529995i	$0.177806\pi$
$492$	37.8638	+	11.8015i	1.70703	+	0.532051i
$493$	26.1744	+	19.0168i	1.17884	+	0.856474i
$494$	14.8337	−	55.0947i	0.667399	−	2.47883i
$495$	−12.7466	+	29.0139i	−0.572917	+	1.30408i
$496$	4.04062	+	6.99857i	0.181429	+	0.314245i
$497$	−1.39790	+	13.3001i	−0.0627043	+	0.596591i
$498$	8.97450	+	39.8596i	0.402157	+	1.78615i
$499$	−1.29527	−	3.98644i	−0.0579843	−	0.178457i	0.917869	−	0.396883i	$-0.129908\pi$
$499$	−1.29527	−	3.98644i	−0.0579843	−	0.178457i	−0.975854	+	0.218425i	$0.929908\pi$
$500$	1.31495	−	0.138207i	0.0588062	−	0.00618079i
$501$	−3.07666	+	7.14005i	−0.137455	+	0.318994i
$502$	−16.7723	+	5.44966i	−0.748586	+	0.243230i
$503$	6.76262	+	7.51065i	0.301531	+	0.334884i	0.874801	−	0.484483i	$-0.160992\pi$
$503$	6.76262	+	7.51065i	0.301531	+	0.334884i	−0.573270	+	0.819366i	$0.694326\pi$
$504$	3.23533	+	6.82053i	0.144113	+	0.303810i
$505$	0.367631	−	0.212252i	0.0163594	−	0.00944509i
$506$	−0.0505522	+	2.64577i	−0.00224732	+	0.117619i
$507$	11.0704	−	19.6073i	0.491652	−	0.870792i
$508$	17.7207	−	24.3905i	0.786229	−	1.08215i
$509$	−3.99500	−	18.7950i	−0.177075	−	0.833074i	−0.973563	−	0.228419i	$-0.926644\pi$
$509$	−3.99500	−	18.7950i	−0.177075	−	0.833074i	0.796488	−	0.604655i	$-0.206689\pi$
$510$	−26.3427	−	77.8768i	−1.16648	−	3.44844i
$511$	−0.959678	−	9.13073i	−0.0424537	−	0.403920i
$512$	−13.1299	+	9.53943i	−0.580265	+	0.421587i
$513$	36.6731	+	6.42283i	1.61916	+	0.283575i
$514$	34.9600	−	31.4782i	1.54202	−	1.38844i
$515$	15.9971	−	22.0181i	0.704915	−	0.970233i
$516$	−21.7494	−	36.6466i	−0.957465	−	1.61328i
$517$	23.3743	+	21.8691i	1.02800	+	0.961803i
$518$	−4.23914	+	2.44747i	−0.186257	+	0.107535i
$519$	−1.67571	−	3.64514i	−0.0735554	−	0.160004i
$520$	18.6556	+	12.1470i	0.818101	+	0.532682i
$521$	−10.6872	+	3.47250i	−0.468217	+	0.152133i	−0.533617	−	0.845726i	$-0.679168\pi$
$521$	−10.6872	+	3.47250i	−0.468217	+	0.152133i	0.0654002	+	0.997859i	$0.479168\pi$
$522$	−4.07922	−	31.5055i	−0.178543	−	1.37896i
$523$	16.2022	−	36.3908i	0.708474	−	1.59126i	−0.0946935	−	0.995506i	$-0.530187\pi$
$523$	16.2022	−	36.3908i	0.708474	−	1.59126i	0.803168	−	0.595753i	$-0.203146\pi$
$524$	−36.5224	−	7.76308i	−1.59549	−	0.339132i
$525$	7.84176	+	8.50139i	0.342242	+	0.371031i
$526$	26.5516	−	11.8215i	1.15770	−	0.515443i
$527$	−18.4960	+	32.0359i	−0.805696	+	1.39551i
$528$	3.38936	+	7.76012i	0.147503	+	0.337716i
$529$	−11.4347	+	19.8056i	−0.497163	+	0.861111i
$530$	6.67175	−	63.4775i	0.289802	−	2.75728i
$531$	−6.54846	+	6.18768i	−0.284179	+	0.268522i
$532$	8.27086	+	25.4551i	0.358587	+	1.10362i
$533$	22.2738	+	18.0814i	0.964787	+	0.783193i
$534$	−4.38800	−	37.4170i	−0.189887	−	1.61919i
$535$	4.21099	+	3.79160i	0.182057	+	0.163925i
$536$	−14.3308	+	3.04612i	−0.618998	+	0.131572i
$537$	0.542298	−	5.83329i	0.0234019	−	0.251725i
$538$			14.6964i			0.633607i
$539$	11.5431	+	13.3232i	0.497196	+	0.573869i
$540$	−22.3105	+	42.0770i	−0.960091	+	1.81070i
$541$	−12.8741	+	17.7197i	−0.553502	+	0.761830i	−0.990482	−	0.137641i	$-0.956048\pi$
$541$	−12.8741	+	17.7197i	−0.553502	+	0.761830i	0.436980	+	0.899471i	$0.356048\pi$
$542$	−27.7525	+	24.9884i	−1.19207	+	1.07335i
$543$	11.4186	−	3.86248i	0.490020	−	0.165755i
$544$	−43.9681	−	19.5758i	−1.88511	−	0.839307i
$545$	−20.6166	+	14.9788i	−0.883119	+	0.641623i
$546$	1.13032	+	17.8676i	0.0483730	+	0.764661i
$547$	−10.1394	−	3.29449i	−0.433529	−	0.140862i	0.0841189	−	0.996456i	$-0.473192\pi$
$547$	−10.1394	−	3.29449i	−0.433529	−	0.140862i	−0.517648	+	0.855593i	$0.673192\pi$
$548$	−1.58935	−	0.167048i	−0.0678937	−	0.00713592i
$549$	17.3411	+	9.46356i	0.740101	+	0.403895i
$550$	−24.6743	−	28.4794i	−1.05212	−	1.21436i
$551$		−	34.3551i		−	1.46358i
$552$	−0.112284	+	1.20780i	−0.00477912	+	0.0514072i
$553$	−3.44693	−	3.82820i	−0.146578	−	0.162792i
$554$	55.6513	−	18.0822i	2.36440	−	0.768239i
$555$	−8.65036	−	3.72745i	−0.367187	−	0.158222i
$556$	−1.45066	+	3.25823i	−0.0615215	+	0.138180i
$557$	−12.0732	+	13.4087i	−0.511559	+	0.568144i	−0.942487	−	0.334242i	$-0.891520\pi$
$557$	−12.0732	+	13.4087i	−0.511559	+	0.568144i	0.430928	+	0.902386i	$0.358186\pi$
$558$	35.3377	−	8.40390i	1.49596	−	0.355765i
$559$	−4.78563	−	30.4524i	−0.202410	−	1.28800i
$560$	6.09432			0.257532
$561$	−23.0055	+	31.1972i	−0.971293	+	1.31715i
$562$	−27.2821	−	47.2541i	−1.15083	−	1.99329i
$563$	14.2560	−	6.34716i	0.600817	−	0.267501i	−0.0837079	−	0.996490i	$-0.526676\pi$
$563$	14.2560	−	6.34716i	0.600817	−	0.267501i	0.684525	+	0.728989i	$0.260010\pi$
$564$	32.6163	+	35.3600i	1.37340	+	1.48892i
$565$	29.2371	+	6.21454i	1.23001	+	0.261448i
$566$	−16.0248	+	1.68427i	−0.673571	+	0.0707951i
$567$	−11.5463	+	1.77814i	−0.484900	+	0.0746749i
$568$	4.15245	−	19.5357i	0.174233	−	0.819701i
$569$	−22.4051	+	4.76236i	−0.939272	+	0.199648i	−0.652016	−	0.758206i	$-0.726076\pi$
$569$	−22.4051	+	4.76236i	−0.939272	+	0.199648i	−0.287256	+	0.957854i	$0.592743\pi$
$570$	−50.4600	+	71.2375i	−2.11354	+	2.98381i
$571$		−	29.5260i		−	1.23562i	−0.786326	−	0.617812i	$-0.788019\pi$
$571$		−	29.5260i		−	1.23562i	0.786326	−	0.617812i	$-0.211981\pi$
$572$	−1.10281	−	34.3951i	−0.0461107	−	1.43813i
$573$	1.40410	−	2.50092i	0.0586570	−	0.104477i
$574$	−22.6861	−	2.38440i	−0.946898	−	0.0995230i
$575$	0.386391	+	1.81783i	0.0161136	+	0.0758087i
$576$	12.7455	+	36.2384i	0.531063	+	1.50994i
$577$	29.8787	−	21.7081i	1.24387	−	0.903722i	0.246016	−	0.969266i	$-0.420878\pi$
$577$	29.8787	−	21.7081i	1.24387	−	0.903722i	0.997850	+	0.0655442i	$0.0208783\pi$
$578$	−6.58655	−	62.6669i	−0.273965	−	2.60660i
$579$	−0.826175	+	0.940041i	−0.0343347	+	0.0390668i
$580$	41.7959	+	13.5803i	1.73548	+	0.563892i
$581$	−5.63905	−	12.6655i	−0.233947	−	0.525454i
$582$	−0.123165	−	10.2460i	−0.00510534	−	0.424712i
$583$	−26.3450	+	14.5465i	−1.09110	+	0.602453i
$584$			13.7112i			0.567373i
$585$	−26.2715	+	22.2865i	−1.08619	+	0.921433i
$586$	−9.10310	+	28.0165i	−0.376045	+	1.15735i
$587$	10.4206	+	9.38276i	0.430105	+	0.387268i	0.855553	−	0.517714i	$-0.173217\pi$
$587$	10.4206	+	9.38276i	0.430105	+	0.387268i	−0.425449	+	0.904983i	$0.639884\pi$
$588$	15.8283	+	21.2441i	0.652749	+	0.876091i
$589$	39.0656	−	4.10596i	1.60967	−	0.169183i
$590$	−6.52796	−	20.0910i	−0.268752	−	0.827133i
$591$	−8.76901	−	38.9470i	−0.360709	−	1.60206i
$592$	−2.29933	+	1.02373i	−0.0945018	+	0.0420749i
$593$	−8.61530			−0.353788			−0.176894	−	0.984230i	$-0.556605\pi$
$593$	−8.61530			−0.353788			−0.176894	+	0.984230i	$0.556605\pi$
$594$	37.7802	−	4.61976i	1.55014	−	0.189551i
$595$	13.9484	+	24.1593i	0.571828	+	0.990435i
$596$	1.30023	−	12.3708i	0.0532593	−	0.506729i
$597$	−18.2027	+	16.7904i	−0.744989	+	0.687184i
$598$	−1.30912	+	2.56166i	−0.0535337	+	0.104754i
$599$	4.02997	+	5.54677i	0.164660	+	0.226635i	0.883372	−	0.468673i	$-0.155268\pi$
$599$	4.02997	+	5.54677i	0.164660	+	0.226635i	−0.718712	+	0.695308i	$0.755268\pi$
$600$	−10.3198	−	13.8508i	−0.421305	−	0.565457i
$601$	−13.0818	−	11.7789i	−0.533619	−	0.480472i	0.357708	−	0.933833i	$-0.383558\pi$
$601$	−13.0818	−	11.7789i	−0.533619	−	0.480472i	−0.891327	+	0.453361i	$0.850225\pi$
$602$	16.4006	+	18.2147i	0.668437	+	0.742374i
$603$	1.82728	−	22.5995i	0.0744126	−	0.920322i
$604$	−24.3964	−	14.0853i	−0.992677	−	0.573122i
$605$	−8.58796	+	33.9662i	−0.349150	+	1.38092i
$606$	−0.444575	−	0.249599i	−0.0180596	−	0.0101393i
$607$	5.84688	+	13.1323i	0.237318	+	0.533024i	0.992465	−	0.122531i	$-0.0391012\pi$
$607$	5.84688	+	13.1323i	0.237318	+	0.533024i	−0.755147	+	0.655556i	$0.772435\pi$
$608$	10.6257	+	49.9901i	0.430930	+	2.02737i
$609$	3.45419	+	10.2116i	0.139971	+	0.413794i
$610$	−37.4749	+	27.2271i	−1.51731	+	1.10239i
$611$	12.4314	+	32.5018i	0.502921	+	1.31488i
$612$	−37.9276	+	44.2156i	−1.53313	+	1.78731i
$613$	3.67782	+	17.3028i	0.148546	+	0.698852i	0.987878	+	0.155233i	$0.0496130\pi$
$613$	3.67782	+	17.3028i	0.148546	+	0.698852i	−0.839332	+	0.543619i	$0.817054\pi$
$614$	−34.7498	−	3.65235i	−1.40239	−	0.147397i
$615$	−22.4028	−	37.7476i	−0.903370	−	1.52213i
$616$	4.77560	+	6.84429i	0.192414	+	0.275764i
$617$	9.01374	+	5.20408i	0.362879	+	0.209509i	0.670343	−	0.742051i	$-0.266147\pi$
$617$	9.01374	+	5.20408i	0.362879	+	0.209509i	−0.307464	+	0.951560i	$0.599480\pi$
$618$	−32.5472	−	3.02578i	−1.30924	−	0.121715i
$619$	12.4718	−	38.3842i	0.501284	−	1.54279i	−0.305646	−	0.952145i	$-0.598872\pi$
$619$	12.4718	−	38.3842i	0.501284	−	1.54279i	0.806929	−	0.590648i	$-0.201128\pi$
$620$	−10.4471	+	49.1496i	−0.419564	+	1.97390i
$621$	−1.74131	−	0.701198i	−0.0698763	−	0.0281381i
$622$	−13.1491	+	29.5334i	−0.527232	+	1.18418i
$623$	3.95037	+	12.1580i	0.158268	+	0.487100i
$624$	−0.382324	+	9.19776i	−0.0153052	+	0.368205i
$625$	19.6251	+	14.2584i	0.785003	+	0.570338i
$626$	4.37354	+	7.57519i	0.174802	+	0.302765i
$627$	41.1597	+	0.291595i	1.64376	+	0.0116452i
$628$	−23.5873	+	40.8544i	−0.941236	+	1.63027i
$629$	−9.32088	−	6.77201i	−0.371648	−	0.270018i
$630$	7.83607	−	26.2478i	0.312197	−	1.04574i
$631$	−34.7269	−	7.38144i	−1.38246	−	0.293850i	−0.544123	−	0.839006i	$-0.683137\pi$
$631$	−34.7269	−	7.38144i	−1.38246	−	0.293850i	−0.838335	+	0.545155i	$0.816471\pi$
$632$	4.52193	+	6.22391i	0.179873	+	0.247574i
$633$	−16.9843	−	7.31856i	−0.675064	−	0.290886i
$634$	−1.38598	−	1.24794i	−0.0550441	−	0.0495619i
$635$	−32.6381	+	6.93745i	−1.29520	+	0.275304i
$636$	−41.0928	+	18.8908i	−1.62944	+	0.749068i
$637$	4.93766	+	18.5167i	0.195637	+	0.733659i
$638$	−10.2130	−	33.6037i	−0.404338	−	1.33038i
$639$	27.1309	+	14.8061i	1.07328	+	0.585721i
$640$	−44.3928	−	4.66587i	−1.75478	−	0.184435i
$641$	31.8526	−	28.6803i	1.25810	−	1.13280i	0.272786	−	0.962075i	$-0.412055\pi$
$641$	31.8526	−	28.6803i	1.25810	−	1.13280i	0.985318	−	0.170727i	$-0.0546116\pi$
$642$	1.33486	−	6.67348i	0.0526828	−	0.263381i
$643$	3.28454	+	31.2503i	0.129530	+	1.23239i	0.845390	+	0.534149i	$0.179368\pi$
$643$	3.28454	+	31.2503i	0.129530	+	1.23239i	−0.715861	+	0.698243i	$0.753965\pi$
$644$	−0.141060	−	1.34209i	−0.00555853	−	0.0528859i
$645$	−9.25088	+	46.2487i	−0.364253	+	1.82104i
$646$	−79.3526	+	71.4494i	−3.12209	+	2.81114i
$647$	22.5801	+	2.37326i	0.887715	+	0.0933026i	0.537398	−	0.843329i	$-0.319407\pi$
$647$	22.5801	+	2.37326i	0.887715	+	0.0933026i	0.350317	+	0.936631i	$0.386074\pi$
$648$	17.4267	−	0.838531i	0.684586	−	0.0329406i
$649$	−6.00738	+	7.94473i	−0.235810	+	0.311858i
$650$	−10.5547	−	39.5810i	−0.413988	−	1.55250i
$651$	−11.1989	+	5.14822i	−0.438918	+	0.201775i
$652$	−16.8038	+	3.57176i	−0.658088	+	0.139881i
$653$	−5.25804	−	4.73436i	−0.205763	−	0.185270i	0.559806	−	0.828624i	$-0.310876\pi$
$653$	−5.25804	−	4.73436i	−0.205763	−	0.185270i	−0.765569	+	0.643354i	$0.777542\pi$
$654$	28.1084	+	12.1120i	1.09913	+	0.473616i
$655$	24.2903	+	33.4327i	0.949099	+	1.30632i
$656$	−11.4729	−	2.43864i	−0.447941	−	0.0952129i
$657$	−20.3321	−	6.06999i	−0.793230	−	0.236813i
$658$	−22.3842	−	16.2631i	−0.872627	−	0.634001i
$659$	−21.2746	+	36.8487i	−0.828741	+	1.43542i	0.0702858	+	0.997527i	$0.477609\pi$
$659$	−21.2746	+	36.8487i	−0.828741	+	1.43542i	−0.899027	+	0.437894i	$0.855724\pi$
$660$	−16.6248	+	49.9589i	−0.647121	+	1.94465i
$661$	−22.3084	−	38.6392i	−0.867695	−	1.50289i	−0.864346	−	0.502898i	$-0.832267\pi$
$661$	−22.3084	−	38.6392i	−0.867695	−	1.50289i	−0.00334923	−	0.999994i	$-0.501066\pi$
$662$	−36.8478	−	26.7715i	−1.43213	−	1.04050i
$663$	−37.3371	+	19.5357i	−1.45005	+	0.758705i
$664$	6.39822	+	19.6917i	0.248299	+	0.764186i
$665$	12.0487	−	27.0618i	0.467228	−	1.04941i
$666$	1.45264	+	11.2193i	0.0562886	+	0.434740i
$667$	−0.360140	+	1.69432i	−0.0139447	+	0.0656045i
$668$	−3.99170	+	12.2852i	−0.154443	+	0.475328i
$669$	−35.7715	−	3.32554i	−1.38301	−	0.128573i
$670$	46.0407	+	26.5816i	1.77871	+	1.02694i
$671$	20.6387	+	7.14461i	0.796748	+	0.275815i
$672$	−8.18453	−	13.7905i	−0.315725	−	0.531981i
$673$	−20.8903	−	2.19566i	−0.805263	−	0.0846365i	−0.307052	−	0.951693i	$-0.599343\pi$
$673$	−20.8903	−	2.19566i	−0.805263	−	0.0846365i	−0.498210	+	0.867056i	$0.666009\pi$
$674$	−5.23371	−	24.6227i	−0.201595	−	0.948430i
$675$	25.1077	−	9.17129i	0.966397	−	0.353003i
$676$	15.2985	−	34.1396i	0.588403	−	1.31306i
$677$	27.0703	−	19.6677i	1.04040	−	0.755893i	0.0700340	−	0.997545i	$-0.477689\pi$
$677$	27.0703	−	19.6677i	1.04040	−	0.755893i	0.970363	+	0.241652i	$0.0776892\pi$
$678$	−11.5032	−	34.0068i	−0.441777	−	1.30602i
$679$	0.722915	+	3.40105i	0.0277429	+	0.130520i
$680$	−16.9454	−	38.0600i	−0.649826	−	1.45953i
$681$	30.6410	+	17.2028i	1.17416	+	0.659215i
$682$	36.9904	−	15.6295i	1.41644	−	0.598484i
$683$	−20.7625	−	11.9872i	−0.794454	−	0.458678i	0.0470739	−	0.998891i	$-0.485010\pi$
$683$	−20.7625	−	11.9872i	−0.794454	−	0.458678i	−0.841528	+	0.540213i	$0.818344\pi$
$684$	61.6572	+	4.98529i	2.35752	+	0.190617i
$685$	1.18352	+	1.31443i	0.0452199	+	0.0502218i
$686$	−26.2368	−	23.6237i	−1.00173	−	0.901957i
$687$	−4.59614	−	6.16873i	−0.175354	−	0.235352i
$688$	7.40782	+	10.1960i	0.282421	+	0.388719i
$689$	−32.6730	+	1.67289i	−1.24474	+	0.0637322i
$690$	3.23535	−	2.98432i	0.123168	−	0.113611i
$691$	2.97498	−	28.3051i	0.113174	−	1.07678i	−0.779602	−	0.626275i	$-0.784579\pi$
$691$	2.97498	−	28.3051i	0.113174	−	1.07678i	0.892776	−	0.450501i	$-0.148755\pi$
$692$	−3.33279	−	5.77256i	−0.126694	−	0.219440i
$693$	−12.2634	+	4.05166i	−0.465850	+	0.153910i
$694$	−8.67731			−0.329386
$695$	3.60612	−	1.60555i	0.136788	−	0.0609019i
$696$	−3.53623	−	15.7059i	−0.134041	−	0.595332i
$697$	−16.5913	−	51.0627i	−0.628439	−	1.93414i
$698$	−59.1716	+	6.21919i	−2.23968	+	0.235400i
$699$	−14.2329	−	19.1027i	−0.538336	−	0.722530i
$700$	14.2803	+	12.8581i	0.539746	+	0.485990i
$701$	15.1031	−	46.4826i	0.570436	−	1.75562i	−0.0807825	−	0.996732i	$-0.525742\pi$
$701$	15.1031	−	46.4826i	0.570436	−	1.75562i	0.651219	−	0.758890i	$-0.274258\pi$
$702$	39.1224	+	13.4731i	1.47658	+	0.508509i
$703$			12.2341i			0.461418i
$704$	20.5279	+	37.1780i	0.773676	+	1.40120i
$705$	−0.639960	−	53.2382i	−0.0241023	−	2.00507i
$706$	5.72833	+	12.8660i	0.215588	+	0.484219i
$707$	0.164539	+	0.0534620i	0.00618813	+	0.00201065i
$708$	−9.88167	+	11.2436i	−0.371376	+	0.422560i
$709$	−5.02051	−	47.7669i	−0.188549	−	1.79392i	−0.523847	−	0.851813i	$-0.675504\pi$
$709$	−5.02051	−	47.7669i	−0.188549	−	1.79392i	0.335298	−	0.942112i	$-0.391163\pi$
$710$	−58.6309	+	42.5979i	−2.20038	+	1.59867i
$711$	−11.2312	+	3.95015i	−0.421203	+	0.148142i
$712$	−3.96934	−	18.6743i	−0.148757	−	0.699849i
$713$	−1.96967	−	0.207021i	−0.0737649	−	0.00775300i
$714$	16.4027	−	29.2157i	0.613855	−	1.09337i
$715$	−24.5651	+	29.1064i	−0.918683	+	1.08852i
$716$		−	9.73359i		−	0.363761i
$717$	3.03444	−	4.28390i	0.113323	−	0.159985i
$718$	41.2655	−	8.77125i	1.54001	−	0.327340i
$719$	5.72217	−	26.9207i	0.213401	−	1.00397i	−0.732813	−	0.680430i	$-0.761793\pi$
$719$	5.72217	−	26.9207i	0.213401	−	1.00397i	0.946214	−	0.323542i	$-0.104874\pi$
$720$	5.41791	−	13.0012i	0.201914	−	0.484528i
$721$	11.0311	−	1.15941i	0.410818	−	0.0431787i
$722$	69.8629	+	14.8498i	2.60003	+	0.552653i
$723$	30.3409	+	32.8931i	1.12839	+	1.22331i
$724$	18.2961	−	8.14596i	0.679970	−	0.302742i
$725$	−12.3327	−	21.3609i	−0.458025	−	0.793323i
$726$	40.3460	−	11.9506i	1.49738	−	0.443530i
$727$	6.33446			0.234932			0.117466	−	0.993077i	$-0.462523\pi$
$727$	6.33446			0.234932			0.117466	+	0.993077i	$0.462523\pi$
$728$	1.40850	+	8.96273i	0.0522026	+	0.332181i
$729$	−6.47142	+	26.2130i	−0.239682	+	0.970851i
$730$	33.2913	−	36.9737i	1.23217	−	1.36846i
$731$	−23.4646	+	52.7024i	−0.867870	+	1.94927i
$732$	30.1434	+	12.9889i	1.11413	+	0.480082i
$733$	41.9206	−	13.6208i	1.54837	−	0.503096i	0.594701	−	0.803947i	$-0.297271\pi$
$733$	41.9206	−	13.6208i	1.54837	−	0.503096i	0.953671	+	0.300851i	$0.0972706\pi$
$734$	12.8742	+	14.2983i	0.475196	+	0.527759i
$735$	2.71416	−	29.1952i	0.100113	−	1.07688i
$736$		−	2.57680i		−	0.0949820i
$737$	−2.14343	−	24.9744i	−0.0789542	−	0.919943i
$738$	−25.2549	+	46.2773i	−0.929644	+	1.70349i
$739$	10.6732	+	1.12180i	0.392620	+	0.0412660i	0.298782	−	0.954321i	$-0.403420\pi$
$739$	10.6732	+	1.12180i	0.392620	+	0.0412660i	0.0938380	+	0.995587i	$0.470086\pi$
$740$	−14.8838	−	4.83605i	−0.547140	−	0.177777i
$741$	40.0867	+	19.8820i	1.47262	+	0.730384i
$742$	21.0448	−	15.2899i	0.772577	−	0.561310i
$743$	−45.9486	−	20.4577i	−1.68569	−	0.750518i	−0.999738	−	0.0228733i	$-0.992719\pi$
$743$	−45.9486	−	20.4577i	−1.68569	−	0.750518i	−0.685954	−	0.727645i	$-0.740615\pi$
$744$	17.4367	−	5.89818i	0.639262	−	0.216238i
$745$	−10.2310	+	9.21200i	−0.374833	+	0.337501i
$746$	9.84311	−	13.5479i	0.360382	−	0.496023i
$747$	−32.0330	+	0.770229i	−1.17202	+	0.0281812i
$748$	−33.2607	+	55.1486i	−1.21613	+	2.01643i
$749$			2.30936i			0.0843823i
$750$	−0.162693	+	1.75002i	−0.00594070	+	0.0639018i
$751$	−43.5221	+	9.25090i	−1.58814	+	0.337570i	−0.915475	−	0.402374i	$-0.868185\pi$
$751$	−43.5221	+	9.25090i	−1.58814	+	0.337570i	−0.672668	+	0.739945i	$0.734852\pi$
$752$	−10.5726	−	9.51961i	−0.385543	−	0.347144i
$753$	−1.61091	−	13.7364i	−0.0587048	−	0.500582i
$754$	6.01820	−	37.7037i	0.219170	−	1.37309i
$755$	9.63466	+	29.6524i	0.350641	+	1.07916i
$756$	−18.8280	+	4.71742i	−0.684766	+	0.171571i
$757$	1.16887	−	11.1210i	0.0424832	−	0.404201i	−0.952529	−	0.304448i	$-0.901528\pi$
$757$	1.16887	−	11.1210i	0.0424832	−	0.404201i	0.995012	−	0.0997529i	$-0.0318052\pi$
$758$	15.4385	−	26.7403i	0.560753	−	0.971253i
$759$	−2.02685	−	0.445851i	−0.0735700	−	0.0161834i
$760$	−22.1198	+	38.3126i	−0.802369	+	1.38974i
$761$	10.2910	−	4.58186i	0.373049	−	0.166092i	−0.211644	−	0.977347i	$-0.567882\pi$
$761$	10.2910	−	4.58186i	0.373049	−	0.166092i	0.584693	+	0.811255i	$0.301215\pi$
$762$	27.1719	+	29.4575i	0.984333	+	1.06713i
$763$	−10.1589	−	2.15933i	−0.367775	−	0.0781731i
$764$	1.93821	−	4.35329i	0.0701219	−	0.157496i
$765$	63.9402	−	8.27874i	2.31176	−	0.299319i
$766$	55.4086	−	18.0033i	2.00199	−	0.650487i
$767$	−9.65371	+	4.90418i	−0.348575	+	0.177080i
$768$	3.86539	+	8.40833i	0.139480	+	0.303410i
$769$	32.5858	−	18.8134i	1.17507	−	0.678429i	0.220204	−	0.975454i	$-0.429328\pi$
$769$	32.5858	−	18.8134i	1.17507	−	0.678429i	0.954870	+	0.297025i	$0.0959945\pi$
$770$	3.74026	−	30.0517i	0.134790	−	1.08299i
$771$	18.8295	+	31.7267i	0.678126	+	1.14261i
$772$	−1.22219	+	1.68220i	−0.0439876	+	0.0605438i
$773$	−9.81071	+	8.83360i	−0.352867	+	0.317723i	−0.826432	−	0.563036i	$-0.809633\pi$
$773$	−9.81071	+	8.83360i	−0.352867	+	0.317723i	0.473566	+	0.880758i	$0.342967\pi$
$774$	53.4383	−	18.7949i	1.92080	−	0.675569i
$775$	22.8157	−	16.5766i	0.819565	−	0.595449i
$776$	−0.542785	−	5.16425i	−0.0194848	−	0.185386i
$777$	−1.23006	−	3.63641i	−0.0441281	−	0.130456i
$778$	0.303536	+	1.42802i	0.0108823	+	0.0511971i
$779$	−33.5111	+	46.1241i	−1.20066	+	1.65257i
$780$	−40.0341	+	40.9097i	−1.43345	+	1.46480i
$781$	32.2900	+	11.1780i	1.15543	+	0.399981i
$782$	4.66250	−	2.69189i	0.166731	−	0.0962620i
$783$	24.8556	+	1.70925i	0.888265	+	0.0610838i
$784$	−5.24257	−	5.82246i	−0.187235	−	0.207945i
$785$	49.6562	−	16.1343i	1.77230	−	0.575857i
$786$	19.6412	−	45.5817i	0.700580	−	1.62585i
$787$	−47.5073	+	4.99322i	−1.69345	+	0.177989i	−0.901555	−	0.432665i	$-0.857573\pi$
$787$	−47.5073	+	4.99322i	−1.69345	+	0.177989i	−0.791898	+	0.610654i	$0.790907\pi$
$788$	−20.4967	−	63.0825i	−0.730166	−	2.24722i
$789$	5.00669	+	22.2369i	0.178243	+	0.791654i
$790$	2.91799	−	27.7628i	0.103817	−	0.987757i
$791$	6.09089	+	10.5497i	0.216567	+	0.375105i
$792$	18.8467	−	4.10333i	0.669690	−	0.145805i
$793$	16.7686	+	16.8090i	0.595470	+	0.596905i
$794$	−17.0343	−	12.3761i	−0.604523	−	0.439212i
$795$	47.7886	+	14.8948i	1.69489	+	0.528265i
$796$	−27.5310	+	30.5763i	−0.975812	+	1.08375i
$797$	−43.2175	+	4.54235i	−1.53084	+	0.160898i	−0.832161	−	0.554534i	$-0.812897\pi$
$797$	−43.2175	+	4.54235i	−1.53084	+	0.160898i	−0.698683	+	0.715432i	$0.746230\pi$
$798$	−35.3363	+	4.14399i	−1.25089	+	0.146696i
$799$	13.5399	−	63.7002i	0.479007	−	2.25355i
$800$	24.5520	+	27.2678i	0.868046	+	0.964063i
$801$	29.4490	+	2.38110i	1.04053	+	0.0841321i
$802$	6.79256	+	3.92169i	0.239854	+	0.138480i
$803$	−23.2787	−	2.89729i	−0.821487	−	0.102243i
$804$	−0.452796	−	37.6680i	−0.0159689	−	1.32845i
$805$	−0.877901	+	1.20833i	−0.0309420	+	0.0425879i
$806$	43.5925	+	2.33719i	1.53548	+	0.0823242i
$807$	−11.3017	−	2.26062i	−0.397838	−	0.0795775i
$808$	−0.236036	−	0.105090i	−0.00830370	−	0.00369705i
$809$	−5.09496	−	2.26842i	−0.179129	−	0.0797536i	0.315212	−	0.949021i	$-0.397924\pi$
$809$	−5.09496	−	2.26842i	−0.179129	−	0.0797536i	−0.494342	+	0.869268i	$0.664591\pi$
$810$	−49.0290	−	40.0515i	−1.72270	−	1.40727i
$811$	2.19477	+	0.713123i	0.0770687	+	0.0250411i	0.347298	−	0.937755i	$-0.387099\pi$
$811$	2.19477	+	0.713123i	0.0770687	+	0.0250411i	−0.270229	+	0.962796i	$0.587099\pi$
$812$	7.28487	+	16.3621i	0.255649	+	0.574197i
$813$	−14.9475	−	25.1857i	−0.524231	−	0.883302i
$814$	3.63693	+	11.9665i	0.127474	+	0.419425i
$815$	16.4662	+	9.50674i	0.576785	+	0.333007i
$816$	9.95817	−	14.0586i	0.348606	−	0.492148i
$817$	59.9208	−	12.7366i	2.09636	−	0.445596i
$818$	−1.16450	+	0.378370i	−0.0407159	+	0.0132294i
$819$	−13.9142	−	1.87919i	−0.486202	−	0.0656641i
$820$	−42.8672	−	59.0016i	−1.49699	−	2.06042i
$821$	−2.53677	+	2.81737i	−0.0885339	+	0.0983269i	−0.785784	−	0.618501i	$-0.787740\pi$
$821$	−2.53677	+	2.81737i	−0.0885339	+	0.0983269i	0.697250	+	0.716828i	$0.254407\pi$
$822$	0.632125	−	2.02811i	0.0220479	−	0.0707385i
$823$	−3.07309	+	1.36823i	−0.107121	+	0.0476934i	−0.459598	−	0.888127i	$-0.652006\pi$
$823$	−3.07309	+	1.36823i	−0.107121	+	0.0476934i	0.352476	+	0.935821i	$0.385340\pi$
$824$	−16.5648			−0.577063
$825$	25.6964	−	14.5941i	0.894633	−	0.508100i
$826$	4.30473	−	7.45601i	0.149781	−	0.259428i
$827$	−16.1435	−	11.7290i	−0.561366	−	0.407856i	0.270593	−	0.962694i	$-0.412780\pi$
$827$	−16.1435	−	11.7290i	−0.561366	−	0.407856i	−0.831959	+	0.554838i	$0.812780\pi$
$828$	−2.98854	−	0.892207i	−0.103859	−	0.0310063i
$829$	−22.4166	+	24.8962i	−0.778561	+	0.864680i	−0.993720	−	0.111900i	$-0.964306\pi$
$829$	−22.4166	+	24.8962i	−0.778561	+	0.864680i	0.215159	+	0.976579i	$0.430973\pi$
$830$	30.5586	−	68.6358i	1.06071	−	2.38239i
$831$	5.34506	+	45.5779i	0.185418	+	1.58108i
$832$	2.36078	+	46.1081i	0.0818455	+	1.59851i
$833$	11.0827	−	34.1089i	0.383991	−	1.18180i
$834$	−3.86876	−	2.74038i	−0.133964	−	0.0948917i
$835$	12.3812	−	7.14831i	0.428471	−	0.247378i
$836$	68.1365	−	5.84782i	2.35655	−	0.202251i
$837$	1.02700	+	28.4678i	0.0354984	+	0.983990i
$838$	−3.19684	−	7.18022i	−0.110433	−	0.248037i
$839$	20.5832	−	18.5332i	0.710610	−	0.639836i	−0.232392	−	0.972622i	$-0.574655\pi$
$839$	20.5832	−	18.5332i	0.710610	−	0.639836i	0.943002	+	0.332786i	$0.107989\pi$
$840$	2.72271	−	13.6119i	0.0939426	−	0.469655i
$841$	0.628254	+	5.97743i	0.0216639	+	0.206118i
$842$	0.860424	+	0.383085i	0.0296522	+	0.0132020i
$843$	40.5355	−	13.7116i	1.39612	−	0.472252i
$844$	−29.2232	−	9.49519i	−1.00590	−	0.326838i
$845$	−37.8658	+	16.7499i	−1.30262	+	0.576213i
$846$	−54.5944	+	33.2950i	−1.87699	+	1.14471i
$847$	−12.6293	+	6.66170i	−0.433947	+	0.228899i
$848$	11.5835	−	6.68775i	0.397780	−	0.229658i
$849$	1.16973	−	12.5823i	0.0401449	−	0.431823i
$850$	−23.6901	+	72.9106i	−0.812564	+	2.50081i
$851$	0.128248	−	0.603360i	0.00439629	−	0.0206829i
$852$	47.1606	+	20.3216i	1.61569	+	0.696206i
$853$	−18.6882	−	25.7220i	−0.639870	−	0.880706i	0.358738	−	0.933438i	$-0.383207\pi$
$853$	−18.6882	−	25.7220i	−0.639870	−	0.880706i	−0.998609	+	0.0527321i	$0.983207\pi$
$854$	−18.4658	−	3.92503i	−0.631887	−	0.134312i
$855$	−47.0206	−	49.7622i	−1.60807	−	1.70183i
$856$	0.360505	−	3.42997i	0.0123218	−	0.117234i
$857$	9.49568			0.324366			0.162183	−	0.986761i	$-0.448146\pi$
$857$	9.49568			0.324366			0.162183	+	0.986761i	$0.448146\pi$
$858$	45.1204	+	7.53020i	1.54038	+	0.257077i
$859$	−49.1845			−1.67815			−0.839077	−	0.544012i	$-0.816905\pi$
$859$	−49.1845			−1.67815			−0.839077	+	0.544012i	$0.816905\pi$
$860$	−8.19113	+	77.9334i	−0.279315	+	2.65751i
$861$	5.32323	−	17.0791i	0.181415	−	0.582053i
$862$	−25.9061	−	5.50650i	−0.882364	−	0.187552i
$863$	−0.195996	−	0.269765i	−0.00667178	−	0.00918291i	0.805668	−	0.592367i	$-0.201807\pi$
$863$	−0.195996	−	0.269765i	−0.00667178	−	0.00918291i	−0.812340	+	0.583184i	$0.801807\pi$
$864$	−36.6960	+	5.20046i	−1.24842	+	0.176923i
$865$	−1.53382	+	7.21606i	−0.0521515	+	0.245354i
$866$	19.0534	−	58.6403i	0.647461	−	1.99268i
$867$	49.2047	+	4.57437i	1.67108	+	0.155354i
$868$	−17.7348	+	10.2392i	−0.601960	+	0.347542i
$869$	−11.5224	+	6.36211i	−0.390870	+	0.215820i
$870$	−28.5988	+	50.9388i	−0.969589	+	1.72699i
$871$	9.79607	−	25.4281i	0.331927	−	0.861600i
$872$	14.7513	+	4.79300i	0.499543	+	0.162311i
$873$	7.89826	+	1.48134i	0.267316	+	0.0501359i
$874$	−5.22265	−	2.32527i	−0.176659	−	0.0786536i
$875$	−0.0623402	−	0.593127i	−0.00210748	−	0.0200514i
$876$	−34.5695	−	6.91476i	−1.16800	−	0.233628i
$877$	−9.57571	+	8.62201i	−0.323349	+	0.291145i	−0.814778	−	0.579773i	$-0.803141\pi$
$877$	−9.57571	+	8.62201i	−0.323349	+	0.291145i	0.491429	+	0.870917i	$0.336475\pi$
$878$	27.7915	+	62.4207i	0.937917	+	2.10660i
$879$	−20.1447	−	11.3099i	−0.679464	−	0.381474i
$880$	3.52788	−	15.1666i	0.118925	−	0.511266i
$881$	17.7858	−	10.2687i	0.599220	−	0.345960i	−0.169515	−	0.985528i	$-0.554220\pi$
$881$	17.7858	−	10.2687i	0.599220	−	0.345960i	0.768735	+	0.639568i	$0.220887\pi$
$882$	−31.8178	+	15.0928i	−1.07136	+	0.508202i
$883$	3.14011	−	9.66427i	0.105673	−	0.325229i	−0.884215	−	0.467081i	$-0.845306\pi$
$883$	3.14011	−	9.66427i	0.105673	−	0.325229i	0.989888	+	0.141852i	$0.0453057\pi$
$884$	−58.7633	+	38.0609i	−1.97642	+	1.28013i
$885$	16.4543	−	1.92965i	0.553106	−	0.0648645i
$886$	−26.4535	+	59.4156i	−0.888724	+	1.99611i
$887$	17.8647	−	19.8408i	0.599839	−	0.666189i	−0.364394	−	0.931245i	$-0.618724\pi$
$887$	17.8647	−	19.8408i	0.599839	−	0.666189i	0.964233	+	0.265056i	$0.0853904\pi$
$888$	1.25928	+	5.59299i	0.0422586	+	0.187689i
$889$	−11.0017	−	7.99319i	−0.368985	−	0.268083i
$890$	−34.6381	+	59.9949i	−1.16107	+	2.01103i
$891$	−2.25876	+	29.7640i	−0.0756713	+	0.997133i
$892$	−59.6893			−1.99855
$893$	−63.1742	+	28.1270i	−2.11404	+	0.941233i
$894$	15.7859	+	4.92019i	0.527961	+	0.164556i
$895$	−7.20846	+	8.00581i	−0.240952	+	0.267605i
$896$	−10.6930	−	14.7176i	−0.357226	−	0.491680i
$897$	−1.76857	−	1.40076i	−0.0590509	−	0.0467701i
$898$	19.3877	−	6.29944i	0.646975	−	0.210215i
$899$	25.7113	−	5.46511i	0.857521	−	0.182272i
$900$	40.1260	−	19.0338i	1.33753	−	0.634461i
$901$	53.0236	+	30.6132i	1.76647	+	1.01987i
$902$	−19.0664	+	55.0773i	−0.634842	+	1.83387i
$903$	−16.5300	+	9.81041i	−0.550085	+	0.326470i
$904$	−7.39961	−	16.6198i	−0.246107	−	0.552766i
$905$	−21.0811	−	6.84967i	−0.700760	−	0.227691i
$906$	24.7205	−	28.1275i	0.821282	−	0.934474i
$907$	30.9217	+	13.7672i	1.02674	+	0.457134i	0.849809	−	0.527090i	$-0.176717\pi$
$907$	30.9217	+	13.7672i	1.02674	+	0.457134i	0.176929	+	0.984224i	$0.443384\pi$
$908$	53.3360	+	23.7467i	1.77002	+	0.788063i
$909$	0.260329	−	0.303489i	0.00863458	−	0.0100661i
$910$	17.9637	−	27.5889i	0.595489	−	0.914562i
$911$	−15.9497	+	21.9528i	−0.528436	+	0.727329i	−0.986891	−	0.161388i	$-0.948403\pi$
$911$	−15.9497	+	21.9528i	−0.528436	+	0.727329i	0.458455	+	0.888718i	$0.348403\pi$
$912$	−18.2928	+	0.219892i	−0.605734	+	0.00728135i
$913$	−34.7843	+	6.70179i	−1.15119	+	0.221797i
$914$	70.2570	+	40.5629i	2.32390	+	1.34170i
$915$	−15.1735	−	33.0067i	−0.501621	−	1.09117i
$916$	−8.55226	−	9.49825i	−0.282575	−	0.313831i
$917$	−3.50166	+	16.4740i	−0.115635	+	0.544019i
$918$	−47.7449	−	60.9655i	−1.57581	−	2.01216i
$919$	6.46461	−	0.679458i	0.213248	−	0.0224132i	0.00269787	−	0.999996i	$-0.499141\pi$
$919$	6.46461	−	0.679458i	0.213248	−	0.0224132i	0.210550	+	0.977583i	$0.432475\pi$
$920$	1.49253	−	1.65762i	0.0492072	−	0.0546501i
$921$	8.15395	−	26.1611i	0.268682	−	0.862039i
$922$	51.1042	+	37.1294i	1.68303	+	1.22279i
$923$	26.2351	+	26.2984i	0.863540	+	0.865621i
$924$	−19.6647	+	8.58887i	−0.646920	+	0.282553i
$925$	4.39176	+	7.60676i	0.144400	+	0.250109i
$926$	−3.32092	+	31.5964i	−0.109132	+	1.03832i
$927$	7.33330	−	24.5637i	0.240857	−	0.806777i
$928$	10.5682	+	32.5257i	0.346920	+	1.06771i
$929$	14.1715	−	1.48949i	0.464953	−	0.0488685i	0.130844	−	0.991403i	$-0.458231\pi$
$929$	14.1715	−	1.48949i	0.464953	−	0.0488685i	0.334109	+	0.942534i	$0.391565\pi$
$930$	−61.3410	−	26.4320i	−2.01145	−	0.866738i
$931$	−36.2194	+	11.7684i	−1.18704	+	0.385693i
$932$	−26.4838	−	29.4132i	−0.867505	−	0.963462i
$933$	−20.6889	−	14.6547i	−0.677325	−	0.479773i
$934$	12.9526	−	7.47821i	0.423823	−	0.244694i
$935$	68.1984	−	20.7273i	2.23033	−	0.677854i
$936$	20.3727	+	4.96315i	0.665903	+	0.162226i
$937$	1.80036	−	2.47799i	0.0588153	−	0.0809522i	−0.778596	−	0.627525i	$-0.784068\pi$
$937$	1.80036	−	2.47799i	0.0588153	−	0.0809522i	0.837411	+	0.546573i	$0.184068\pi$
$938$	4.50476	+	21.1932i	0.147086	+	0.691983i
$939$	−6.49814	+	2.19807i	−0.212059	+	0.0717314i
$940$	−9.24656	−	87.9751i	−0.301589	−	2.86943i
$941$	26.5510	−	19.2904i	0.865537	−	0.628849i	−0.0638487	−	0.997960i	$-0.520338\pi$
$941$	26.5510	−	19.2904i	0.865537	−	0.628849i	0.929386	+	0.369110i	$0.120338\pi$
$942$	−47.1025	−	41.3970i	−1.53468	−	1.34879i
$943$	2.13621	−	1.92345i	0.0695645	−	0.0626362i
$944$	2.60207	−	3.58144i	0.0846901	−	0.116566i
$945$	18.9795	+	10.0635i	0.617402	+	0.327365i
$946$	54.8238	−	30.2711i	1.78248	−	0.984198i
$947$	−21.6347	+	12.4908i	−0.703033	+	0.405896i	−0.808476	−	0.588529i	$-0.799707\pi$
$947$	−21.6347	+	12.4908i	−0.703033	+	0.405896i	0.105443	+	0.994425i	$0.466374\pi$
$948$	−17.9726	+	8.26217i	−0.583722	+	0.268343i
$949$	−21.3709	−	13.9150i	−0.693729	−	0.451701i
$950$	77.4219	−	25.1559i	2.51190	−	0.816165i
$951$	1.17287	−	0.873871i	0.0380329	−	0.0283372i
$952$	6.90609	−	15.5113i	0.223828	−	0.502725i
$953$	−39.4787	−	8.39147i	−1.27884	−	0.271826i	−0.482084	−	0.876125i	$-0.660120\pi$
$953$	−39.4787	−	8.39147i	−1.27884	−	0.271826i	−0.796758	+	0.604299i	$0.793453\pi$
$954$	−13.9095	−	58.4884i	−0.450338	−	1.89363i
$955$	−4.81810	+	2.14516i	−0.155910	+	0.0694156i
$956$	4.36112	−	7.55367i	0.141049	−	0.244303i
$957$	27.4126	−	2.68497i	0.886123	−	0.0867929i
$958$	−4.86875	+	8.43291i	−0.157302	+	0.272455i
$959$	−0.0753494	+	0.716901i	−0.00243316	+	0.0231500i
$960$	21.0196	−	67.4392i	0.678403	−	2.17659i
$961$	−0.292209	−	0.899328i	−0.00942611	−	0.0290106i
$962$	−2.14312	+	13.4265i	−0.0690970	+	0.432889i
$963$	4.92665	+	2.05305i	0.158759	+	0.0661585i
$964$	55.2526	+	49.7497i	1.77957	+	1.60233i
$965$	2.25104	−	0.478473i	0.0724636	−	0.0154026i
$966$	1.78615	+	0.166051i	0.0574685	+	0.00534262i
$967$			18.8597i			0.606487i	0.952913	+	0.303243i	$0.0980695\pi$
$967$			18.8597i			0.606487i	−0.952913	+	0.303243i	$0.901930\pi$
$968$	19.7975	−	7.92276i	0.636316	−	0.254647i
$969$	−42.7393	−	72.0135i	−1.37298	−	2.31341i
$970$	−11.0753	+	15.2438i	−0.355607	+	0.489450i
$971$	36.0939	−	32.4991i	1.15831	−	1.04295i	0.159868	−	0.987138i	$-0.448893\pi$
$971$	36.0939	−	32.4991i	1.15831	−	1.04295i	0.998441	−	0.0558087i	$-0.0177737\pi$
$972$	−6.67440	+	44.3602i	−0.214081	+	1.42286i
$973$	1.46967	+	0.654341i	0.0471156	+	0.0209772i
$974$	−46.1559	+	33.5342i	−1.47893	+	1.07451i
$975$	32.0618	−	2.02825i	1.02680	−	0.0649560i
$976$	−9.23197	−	2.99965i	−0.295508	−	0.0960164i
$977$	41.9428	+	4.40837i	1.34187	+	0.141036i	0.748094	−	0.663593i	$-0.230969\pi$
$977$	41.9428	+	4.40837i	1.34187	+	0.141036i	0.593777	+	0.804630i	$0.297636\pi$
$978$	−0.274486	−	22.8344i	−0.00877709	−	0.730165i
$979$	32.5437	−	2.79307i	1.04010	−	0.0892668i
$980$		−	48.7159i		−	1.55617i
$981$	−13.6379	+	19.7526i	−0.435425	+	0.630652i
$982$	11.3669	+	12.6242i	0.362731	+	0.402853i
$983$	3.04989	−	0.990969i	0.0972764	−	0.0316070i	−0.259974	−	0.965615i	$-0.583714\pi$
$983$	3.04989	−	0.990969i	0.0972764	−	0.0316070i	0.357251	+	0.934008i	$0.383714\pi$
$984$	−10.5724	+	24.5356i	−0.337037	+	0.782167i
$985$	−29.8589	+	67.0643i	−0.951385	+	2.13685i
$986$	−47.8122	+	53.1009i	−1.52265	+	1.69108i
$987$	15.9497	−	14.7121i	0.507683	−	0.468291i
$988$	69.3745	+	26.7262i	2.20710	+	0.850274i
$989$	−3.08868			−0.0982144
$990$	−60.7852	−	34.6955i	−1.93188	−	1.10269i
$991$	24.2294	+	41.9665i	0.769671	+	1.33311i	0.937741	+	0.347335i	$0.112913\pi$
$991$	24.2294	+	41.9665i	0.769671	+	1.33311i	−0.168070	+	0.985775i	$0.553753\pi$
$992$	−35.7222	+	15.9046i	−1.13418	+	0.504970i
$993$	26.2555	−	24.2183i	0.833194	−	0.768546i
$994$	−28.8905	−	6.14086i	−0.916350	−	0.194776i
$995$	45.2882	−	4.75998i	1.43573	−	0.150901i
$996$	−52.8747	+	6.20077i	−1.67540	+	0.196479i
$997$	−3.90927	+	18.3917i	−0.123808	+	0.582470i	0.871881	+	0.489717i	$0.162900\pi$
$997$	−3.90927	+	18.3917i	−0.123808	+	0.582470i	−0.995689	+	0.0927526i	$0.970433\pi$
$998$	9.05508	−	1.92472i	0.286633	−	0.0609258i
$999$	−8.85123	−	0.608677i	−0.280041	−	0.0192577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bq.a.29.8	✓	416
3.2	odd	2	inner	429.2.bq.a.29.45	yes	416
11.8	odd	10	inner	429.2.bq.a.107.8	yes	416
13.9	even	3	inner	429.2.bq.a.425.45	yes	416
33.8	even	10	inner	429.2.bq.a.107.45	yes	416
39.35	odd	6	inner	429.2.bq.a.425.8	yes	416
143.74	odd	30	inner	429.2.bq.a.74.45	yes	416
429.74	even	30	inner	429.2.bq.a.74.8	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bq.a.29.8	✓	416	1.1	even	1	trivial
429.2.bq.a.29.45	yes	416	3.2	odd	2	inner
429.2.bq.a.74.8	yes	416	429.74	even	30	inner
429.2.bq.a.74.45	yes	416	143.74	odd	30	inner
429.2.bq.a.107.8	yes	416	11.8	odd	10	inner
429.2.bq.a.107.45	yes	416	33.8	even	10	inner
429.2.bq.a.425.8	yes	416	39.35	odd	6	inner
429.2.bq.a.425.45	yes	416	13.9	even	3	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bq (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.230857 + 2.19646i) q^{2} +(-1.65359 - 0.515394i) q^{3} +(-2.81485 - 0.598316i) q^{4} +(1.87210 + 2.57672i) q^{5} +(1.51379 - 3.51307i) q^{6} +(-0.269880 + 1.26968i) q^{7} +(0.599043 - 1.84366i) q^{8} +(2.46874 + 1.70450i) q^{9} +O(q^{10})\)	\(q+(-0.230857 + 2.19646i) q^{2} +(-1.65359 - 0.515394i) q^{3} +(-2.81485 - 0.598316i) q^{4} +(1.87210 + 2.57672i) q^{5} +(1.51379 - 3.51307i) q^{6} +(-0.269880 + 1.26968i) q^{7} +(0.599043 - 1.84366i) q^{8} +(2.46874 + 1.70450i) q^{9} +(-6.09186 + 3.51714i) q^{10} +(3.00356 + 1.40663i) q^{11} +(4.34625 + 2.44013i) q^{12} +(2.26567 + 2.80477i) q^{13} +(-2.72651 - 0.885896i) q^{14} +(-1.76766 - 5.22572i) q^{15} +(-1.34665 - 0.599567i) q^{16} +(-0.705322 - 6.71069i) q^{17} +(-4.31381 + 5.02899i) q^{18} +(-5.32475 + 4.79443i) q^{19} +(-3.72799 - 8.37321i) q^{20} +(1.10066 - 1.96044i) q^{21} +(-3.78300 + 6.27248i) q^{22} +(0.312865 - 0.180633i) q^{23} +(-1.94079 + 2.73993i) q^{24} +(-1.58966 + 4.89248i) q^{25} +(-6.68361 + 4.32896i) q^{26} +(-3.20379 - 4.09093i) q^{27} +(1.51934 - 3.41250i) q^{28} +(-3.20831 + 3.56319i) q^{29} +(11.8862 - 2.67620i) q^{30} +(-4.43518 - 3.22235i) q^{31} +(3.56635 - 6.17710i) q^{32} +(-4.24170 - 3.87401i) q^{33} +14.9026 q^{34} +(-3.77686 + 1.68157i) q^{35} +(-5.92930 - 6.27502i) q^{36} +(1.14250 - 1.26888i) q^{37} +(-9.30152 - 12.8024i) q^{38} +(-2.30094 - 5.80566i) q^{39} +(5.87208 - 1.90795i) q^{40} +(7.78303 - 1.65433i) q^{41} +(4.05195 + 2.87014i) q^{42} +(-7.40420 - 4.27482i) q^{43} +(-7.61299 - 5.75653i) q^{44} +(0.229683 + 9.55225i) q^{45} +(0.324525 + 0.728896i) q^{46} +(9.17889 + 2.98240i) q^{47} +(1.91780 + 1.68550i) q^{48} +(4.85556 + 2.16183i) q^{49} +(-10.3792 - 4.62110i) q^{50} +(-2.29234 + 11.4603i) q^{51} +(-4.69940 - 9.25060i) q^{52} +(-5.33340 + 7.34080i) q^{53} +(9.72519 - 6.09259i) q^{54} +(1.99848 + 10.3727i) q^{55} +(2.17920 + 1.25816i) q^{56} +(11.2760 - 5.18368i) q^{57} +(-7.08576 - 7.86953i) q^{58} +(-0.624388 + 2.93751i) q^{59} +(1.84908 + 15.7673i) q^{60} +(6.54904 - 0.688332i) q^{61} +(8.10166 - 8.99781i) q^{62} +(-2.83044 + 2.67450i) q^{63} +(10.3593 + 7.52649i) q^{64} +(-2.98555 + 11.0888i) q^{65} +(9.48834 - 8.42240i) q^{66} +(-3.77887 - 6.54520i) q^{67} +(-2.02973 + 19.3116i) q^{68} +(-0.610448 + 0.137444i) q^{69} +(-2.82158 - 8.68394i) q^{70} +(10.2462 - 1.07692i) q^{71} +(4.62141 - 3.53045i) q^{72} +(-6.72677 + 2.18566i) q^{73} +(2.52329 + 2.80239i) q^{74} +(5.15021 - 7.27086i) q^{75} +(17.8570 - 10.3097i) q^{76} +(-2.59657 + 3.43396i) q^{77} +(13.2831 - 3.71364i) q^{78} +(-2.33265 + 3.21061i) q^{79} +(-0.976143 - 4.59239i) q^{80} +(3.18933 + 8.41595i) q^{81} +(1.83691 + 17.4770i) q^{82} +(-8.64090 + 6.27798i) q^{83} +(-4.27116 + 4.85983i) q^{84} +(15.9712 - 14.3805i) q^{85} +(11.0988 - 15.2762i) q^{86} +(7.14170 - 4.23852i) q^{87} +(4.39261 - 4.69493i) q^{88} +(8.52894 - 4.92419i) q^{89} +(-21.0342 - 1.70072i) q^{90} +(-4.17263 + 2.11974i) q^{91} +(-0.988744 + 0.321262i) q^{92} +(5.67321 + 7.61432i) q^{93} +(-8.66975 + 19.4726i) q^{94} +(-22.3224 - 4.74477i) q^{95} +(-9.08094 + 8.37634i) q^{96} +(2.44708 - 1.08951i) q^{97} +(-5.86933 + 10.1660i) q^{98} +(5.01741 + 8.59218i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9}+O(q^{10}) \) 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9	\( 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9} - 52 q^{12} - 20 q^{13} - 3 q^{15} + 30 q^{16} - 20 q^{18} - 10 q^{19} + 4 q^{22} + 5 q^{24} + 60 q^{25} - 24 q^{27} - 10 q^{28} - 65 q^{30} - 8 q^{31} + 49 q^{33} - 24 q^{34} + 3 q^{36} - 6 q^{37} - 35 q^{39} - 120 q^{40} - 13 q^{42} - 32 q^{45} - 30 q^{46} - 33 q^{48} - 26 q^{49} - 100 q^{51} - 60 q^{52} - 42 q^{55} - 20 q^{57} - 34 q^{58} + 32 q^{60} - 30 q^{61} - 45 q^{63} + 40 q^{64} + 42 q^{66} + 32 q^{67} - 33 q^{69} - 268 q^{70} + 55 q^{72} - 40 q^{73} + 9 q^{75} - 32 q^{78} - 37 q^{81} + 28 q^{82} - 180 q^{84} - 10 q^{85} - 142 q^{88} - 30 q^{90} + 8 q^{91} - 26 q^{93} - 90 q^{94} + 330 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) \) 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9 - 52 * q^12 - 20 * q^13 - 3 * q^15 + 30 * q^16 - 20 * q^18 - 10 * q^19 + 4 * q^22 + 5 * q^24 + 60 * q^25 - 24 * q^27 - 10 * q^28 - 65 * q^30 - 8 * q^31 + 49 * q^33 - 24 * q^34 + 3 * q^36 - 6 * q^37 - 35 * q^39 - 120 * q^40 - 13 * q^42 - 32 * q^45 - 30 * q^46 - 33 * q^48 - 26 * q^49 - 100 * q^51 - 60 * q^52 - 42 * q^55 - 20 * q^57 - 34 * q^58 + 32 * q^60 - 30 * q^61 - 45 * q^63 + 40 * q^64 + 42 * q^66 + 32 * q^67 - 33 * q^69 - 268 * q^70 + 55 * q^72 - 40 * q^73 + 9 * q^75 - 32 * q^78 - 37 * q^81 + 28 * q^82 - 180 * q^84 - 10 * q^85 - 142 * q^88 - 30 * q^90 + 8 * q^91 - 26 * q^93 - 90 * q^94 + 330 * q^96 - 14 * q^97 - 4 * q^99

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