LMFDB - Embedded newform 230.2.g.b.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(31,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("230.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.g (of order $11$, degree $10$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} + 12 x^{18} + 16 x^{17} - 49 x^{16} + 59 x^{15} - 197 x^{14} + 42 x^{13} + 1625 x^{12} + \cdots + 529 $ x^20 - 5x^19 + 12x^18 + 16x^17 - 49x^16 + 59x^15 - 197x^14 + 42x^13 + 1625x^12 - 5910x^11 + 14651x^10 - 22501x^9 + 26003x^8 - 19607x^7 + 13040x^6 + 348x^5 + 7193x^4 + 10771x^3 + 8781x^2 + 3105*x + 529
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			101.1
Root			$2.57205 - 2.96831i$ of defining polynomial
Character	$\chi$	$=$	230.101
Dual form			230.2.g.b.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 - 0.281733i) q^{2} +(-0.880272 - 1.01589i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-1.13082 - 0.726736i) q^{6} +(0.394126 - 0.863015i) q^{7} +(0.654861 - 0.755750i) q^{8} +(0.169795 - 1.18095i) q^{9} +O(q^{10})$	\(q+(0.959493 - 0.281733i) q^{2} +(-0.880272 - 1.01589i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-1.13082 - 0.726736i) q^{6} +(0.394126 - 0.863015i) q^{7} +(0.654861 - 0.755750i) q^{8} +(0.169795 - 1.18095i) q^{9} +(-0.415415 - 0.909632i) q^{10} +(-2.60241 - 0.764136i) q^{11} +(-1.28976 - 0.378708i) q^{12} +(0.976226 + 2.13764i) q^{13} +(0.135021 - 0.939095i) q^{14} +(-0.880272 + 1.01589i) q^{15} +(0.415415 - 0.909632i) q^{16} +(0.813173 + 0.522595i) q^{17} +(-0.169795 - 1.18095i) q^{18} +(6.69874 - 4.30502i) q^{19} +(-0.654861 - 0.755750i) q^{20} +(-1.22366 + 0.359300i) q^{21} -2.71227 q^{22} +(-3.77640 + 2.95615i) q^{23} -1.34421 q^{24} +(-0.959493 + 0.281733i) q^{25} +(1.53892 + 1.77601i) q^{26} +(-4.74165 + 3.04727i) q^{27} +(-0.135021 - 0.939095i) q^{28} +(8.70219 + 5.59256i) q^{29} +(-0.558406 + 1.22274i) q^{30} +(-1.71788 + 1.98253i) q^{31} +(0.142315 - 0.989821i) q^{32} +(1.51455 + 3.31640i) q^{33} +(0.927466 + 0.272329i) q^{34} +(-0.910321 - 0.267294i) q^{35} +(-0.495629 - 1.08528i) q^{36} +(-0.528289 + 3.67433i) q^{37} +(5.21453 - 6.01789i) q^{38} +(1.31225 - 2.87344i) q^{39} +(-0.841254 - 0.540641i) q^{40} +(0.263236 + 1.83085i) q^{41} +(-1.07287 + 0.689492i) q^{42} +(3.32782 + 3.84050i) q^{43} +(-2.60241 + 0.764136i) q^{44} -1.19309 q^{45} +(-2.79058 + 3.90034i) q^{46} -1.77280 q^{47} +(-1.28976 + 0.378708i) q^{48} +(3.99457 + 4.60997i) q^{49} +(-0.841254 + 0.540641i) q^{50} +(-0.184916 - 1.28612i) q^{51} +(1.97695 + 1.27051i) q^{52} +(-0.247099 + 0.541071i) q^{53} +(-3.69106 + 4.25971i) q^{54} +(-0.385997 + 2.68467i) q^{55} +(-0.394126 - 0.863015i) q^{56} +(-10.2701 - 3.01558i) q^{57} +(9.92530 + 2.91433i) q^{58} +(-0.515591 - 1.12899i) q^{59} +(-0.191301 + 1.33053i) q^{60} +(7.96212 - 9.18877i) q^{61} +(-1.08975 + 2.38621i) q^{62} +(-0.952257 - 0.611979i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(1.97695 - 1.27051i) q^{65} +(2.38754 + 2.75536i) q^{66} +(-1.83771 + 0.539600i) q^{67} +0.966621 q^{68} +(6.32737 + 1.23418i) q^{69} -0.948752 q^{70} +(-13.6915 + 4.02020i) q^{71} +(-0.781311 - 0.901681i) q^{72} +(-2.73824 + 1.75976i) q^{73} +(0.528289 + 3.67433i) q^{74} +(1.13082 + 0.726736i) q^{75} +(3.30787 - 7.24322i) q^{76} +(-1.68514 + 1.94475i) q^{77} +(0.449558 - 3.12675i) q^{78} +(-4.75243 - 10.4064i) q^{79} +(-0.959493 - 0.281733i) q^{80} +(3.83532 + 1.12615i) q^{81} +(0.768383 + 1.68252i) q^{82} +(2.15288 - 14.9736i) q^{83} +(-0.835159 + 0.963825i) q^{84} +(0.401549 - 0.879269i) q^{85} +(4.27501 + 2.74738i) q^{86} +(-1.97888 - 13.7634i) q^{87} +(-2.28171 + 1.46637i) q^{88} +(0.720233 + 0.831193i) q^{89} +(-1.14477 + 0.336134i) q^{90} +2.22957 q^{91} +(-1.57869 + 4.52855i) q^{92} +3.52623 q^{93} +(-1.70099 + 0.499455i) q^{94} +(-5.21453 - 6.01789i) q^{95} +(-1.13082 + 0.726736i) q^{96} +(0.109251 + 0.759860i) q^{97} +(5.13154 + 3.29784i) q^{98} +(-1.34428 + 2.94357i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 + 8 * q^13 + 3 * q^14 - 3 * q^15 - 2 * q^16 + 8 * q^17 + 27 * q^18 - q^19 - 2 * q^20 - 31 * q^21 - 18 * q^22 - 9 * q^23 - 8 * q^24 - 2 * q^25 - 8 * q^26 - 18 * q^27 - 3 * q^28 + 20 * q^29 + 3 * q^30 - 17 * q^31 + 2 * q^32 + 17 * q^33 + 3 * q^34 - 3 * q^35 + 17 * q^36 + 6 * q^37 - 21 * q^38 - 75 * q^39 + 2 * q^40 - 2 * q^41 + 42 * q^42 - 18 * q^43 + 7 * q^44 + 28 * q^45 - 2 * q^46 + 42 * q^47 + 8 * q^48 - 19 * q^49 + 2 * q^50 + 26 * q^51 + 19 * q^52 + 19 * q^53 - 26 * q^54 - 15 * q^55 - 19 * q^56 + 7 * q^57 - 9 * q^58 + 25 * q^59 - 3 * q^60 - 49 * q^61 - 38 * q^62 - 87 * q^63 - 2 * q^64 + 19 * q^65 - 6 * q^66 + 19 * q^67 - 36 * q^68 + 36 * q^69 + 14 * q^70 + 7 * q^71 - 17 * q^72 - 10 * q^73 - 6 * q^74 - 3 * q^75 - q^76 - 29 * q^77 - 2 * q^78 - 33 * q^79 - 2 * q^80 + 72 * q^81 + 2 * q^82 - 41 * q^83 + 13 * q^84 - 14 * q^85 - 48 * q^86 - 16 * q^87 - 7 * q^88 + 55 * q^89 + 5 * q^90 + 13 * q^92 + 10 * q^93 + 13 * q^94 + 21 * q^95 + 3 * q^96 - 9 * q^97 + 41 * q^98 + 59 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{5}{11}\right)$

Coefficient data

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

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

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

$2$	0.959493	−	0.281733i	0.678464	−	0.199215i
$2$	0.959493	−	0.281733i	0.678464	−	0.199215i
$3$	−0.880272	−	1.01589i	−0.508225	−	0.586523i	0.442418	−	0.896809i	$-0.354121\pi$
$3$	−0.880272	−	1.01589i	−0.508225	−	0.586523i	−0.950643	+	0.310286i	$0.899575\pi$
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	−0.142315	−	0.989821i	−0.0636451	−	0.442662i
$5$	−0.142315	−	0.989821i	−0.0636451	−	0.442662i
$6$	−1.13082	−	0.726736i	−0.461657	−	0.296689i
$7$	0.394126	−	0.863015i	0.148966	−	0.326189i	−0.820409	−	0.571778i	$-0.806254\pi$
$7$	0.394126	−	0.863015i	0.148966	−	0.326189i	0.969374	+	0.245589i	$0.0789813\pi$
$8$	0.654861	−	0.755750i	0.231528	−	0.267198i
$9$	0.169795	−	1.18095i	0.0565984	−	0.393650i
$10$	−0.415415	−	0.909632i	−0.131366	−	0.287651i
$11$	−2.60241	−	0.764136i	−0.784655	−	0.230396i	−0.135223	−	0.990815i	$-0.543175\pi$
$11$	−2.60241	−	0.764136i	−0.784655	−	0.230396i	−0.649432	+	0.760420i	$0.724993\pi$
$12$	−1.28976	−	0.378708i	−0.372322	−	0.109324i
$13$	0.976226	+	2.13764i	0.270756	+	0.592874i	0.995352	−	0.0963001i	$-0.0307009\pi$
$13$	0.976226	+	2.13764i	0.270756	+	0.592874i	−0.724596	+	0.689174i	$0.757974\pi$
$14$	0.135021	−	0.939095i	0.0360860	−	0.250984i
$15$	−0.880272	+	1.01589i	−0.227285	+	0.262301i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	0.813173	+	0.522595i	0.197223	+	0.126748i	0.635525	−	0.772080i	$-0.280784\pi$
$17$	0.813173	+	0.522595i	0.197223	+	0.126748i	−0.438302	+	0.898828i	$0.644420\pi$
$18$	−0.169795	−	1.18095i	−0.0400211	−	0.278353i
$19$	6.69874	−	4.30502i	1.53680	−	0.987639i	0.548319	−	0.836269i	$-0.315268\pi$
$19$	6.69874	−	4.30502i	1.53680	−	0.987639i	0.988477	−	0.151370i	$-0.0483685\pi$
$20$	−0.654861	−	0.755750i	−0.146431	−	0.168991i
$21$	−1.22366	+	0.359300i	−0.267025	+	0.0784057i
$22$	−2.71227			−0.578259
$23$	−3.77640	+	2.95615i	−0.787433	+	0.616400i
$23$	−3.77640	+	2.95615i	−0.787433	+	0.616400i
$24$	−1.34421			−0.274386
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$	1.53892	+	1.77601i	0.301808	+	0.348305i
$27$	−4.74165	+	3.04727i	−0.912530	+	0.586448i
$28$	−0.135021	−	0.939095i	−0.0255167	−	0.177472i
$29$	8.70219	+	5.59256i	1.61596	+	1.03851i	0.958529	+	0.284995i	$0.0919919\pi$
$29$	8.70219	+	5.59256i	1.61596	+	1.03851i	0.657428	+	0.753518i	$0.271644\pi$
$30$	−0.558406	+	1.22274i	−0.101950	+	0.223240i
$31$	−1.71788	+	1.98253i	−0.308540	+	0.356074i	−0.888749	−	0.458393i	$-0.848425\pi$
$31$	−1.71788	+	1.98253i	−0.308540	+	0.356074i	0.580210	+	0.814467i	$0.302971\pi$
$32$	0.142315	−	0.989821i	0.0251579	−	0.174977i
$33$	1.51455	+	3.31640i	0.263649	+	0.577311i
$34$	0.927466	+	0.272329i	0.159059	+	0.0467040i
$35$	−0.910321	−	0.267294i	−0.153872	−	0.0451810i
$36$	−0.495629	−	1.08528i	−0.0826049	−	0.180880i
$37$	−0.528289	+	3.67433i	−0.0868502	+	0.604056i	0.899191	+	0.437556i	$0.144156\pi$
$37$	−0.528289	+	3.67433i	−0.0868502	+	0.604056i	−0.986041	+	0.166500i	$0.946753\pi$
$38$	5.21453	−	6.01789i	0.845908	−	0.976230i
$39$	1.31225	−	2.87344i	0.210129	−	0.460118i
$40$	−0.841254	−	0.540641i	−0.133014	−	0.0854828i
$41$	0.263236	+	1.83085i	0.0411106	+	0.285930i	0.999998	+	0.00214267i	$0.000682034\pi$
$41$	0.263236	+	1.83085i	0.0411106	+	0.285930i	−0.958887	+	0.283788i	$0.908409\pi$
$42$	−1.07287	+	0.689492i	−0.165547	+	0.106391i
$43$	3.32782	+	3.84050i	0.507487	+	0.585671i	0.950453	−	0.310867i	$-0.100619\pi$
$43$	3.32782	+	3.84050i	0.507487	+	0.585671i	−0.442966	+	0.896538i	$0.646074\pi$
$44$	−2.60241	+	0.764136i	−0.392328	+	0.115198i
$45$	−1.19309			−0.177856
$46$	−2.79058	+	3.90034i	−0.411449	+	0.575074i
$47$	−1.77280			−0.258589			−0.129295	−	0.991606i	$-0.541271\pi$
$47$	−1.77280			−0.258589			−0.129295	+	0.991606i	$0.541271\pi$
$48$	−1.28976	+	0.378708i	−0.186161	+	0.0546618i
$49$	3.99457	+	4.60997i	0.570652	+	0.658568i
$50$	−0.841254	+	0.540641i	−0.118971	+	0.0764582i
$51$	−0.184916	−	1.28612i	−0.0258934	−	0.180092i
$52$	1.97695	+	1.27051i	0.274153	+	0.176188i
$53$	−0.247099	+	0.541071i	−0.0339417	+	0.0743219i	−0.925843	−	0.377907i	$-0.876644\pi$
$53$	−0.247099	+	0.541071i	−0.0339417	+	0.0743219i	0.891902	+	0.452229i	$0.149371\pi$
$54$	−3.69106	+	4.25971i	−0.502290	+	0.579673i
$55$	−0.385997	+	2.68467i	−0.0520478	+	0.362000i
$56$	−0.394126	−	0.863015i	−0.0526673	−	0.115325i
$57$	−10.2701	−	3.01558i	−1.36031	−	0.399423i
$58$	9.92530	+	2.91433i	1.30326	+	0.382670i
$59$	−0.515591	−	1.12899i	−0.0671243	−	0.146982i	0.873096	−	0.487548i	$-0.162109\pi$
$59$	−0.515591	−	1.12899i	−0.0671243	−	0.146982i	−0.940221	+	0.340566i	$0.889381\pi$
$60$	−0.191301	+	1.33053i	−0.0246969	+	0.171771i
$61$	7.96212	−	9.18877i	1.01944	−	1.17650i	0.0352559	−	0.999378i	$-0.488775\pi$
$61$	7.96212	−	9.18877i	1.01944	−	1.17650i	0.984189	−	0.177123i	$-0.0566792\pi$
$62$	−1.08975	+	2.38621i	−0.138398	+	0.303049i
$63$	−0.952257	−	0.611979i	−0.119973	−	0.0771021i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	1.97695	−	1.27051i	0.245210	−	0.157587i
$66$	2.38754	+	2.75536i	0.293885	+	0.339162i
$67$	−1.83771	+	0.539600i	−0.224512	+	0.0659227i	−0.392054	−	0.919942i	$-0.628235\pi$
$67$	−1.83771	+	0.539600i	−0.224512	+	0.0659227i	0.167542	+	0.985865i	$0.446417\pi$
$68$	0.966621			0.117220
$69$	6.32737	+	1.23418i	0.761726	+	0.148577i
$70$	−0.948752			−0.113398
$71$	−13.6915	+	4.02020i	−1.62489	+	0.477110i	−0.962326	−	0.271898i	$-0.912349\pi$
$71$	−13.6915	+	4.02020i	−1.62489	+	0.477110i	−0.662561	+	0.749008i	$0.730531\pi$
$72$	−0.781311	−	0.901681i	−0.0920784	−	0.106264i
$73$	−2.73824	+	1.75976i	−0.320487	+	0.205964i	−0.690985	−	0.722869i	$-0.742823\pi$
$73$	−2.73824	+	1.75976i	−0.320487	+	0.205964i	0.370499	+	0.928833i	$0.379187\pi$
$74$	0.528289	+	3.67433i	0.0614123	+	0.427132i
$75$	1.13082	+	0.726736i	0.130576	+	0.0839162i
$76$	3.30787	−	7.24322i	0.379439	−	0.830855i
$77$	−1.68514	+	1.94475i	−0.192039	+	0.221625i
$78$	0.449558	−	3.12675i	0.0509025	−	0.354034i
$79$	−4.75243	−	10.4064i	−0.534691	−	1.17081i	−0.963572	−	0.267448i	$-0.913820\pi$
$79$	−4.75243	−	10.4064i	−0.534691	−	1.17081i	0.428882	−	0.903361i	$-0.358908\pi$
$80$	−0.959493	−	0.281733i	−0.107275	−	0.0314987i
$81$	3.83532	+	1.12615i	0.426147	+	0.125128i
$82$	0.768383	+	1.68252i	0.0848537	+	0.185804i
$83$	2.15288	−	14.9736i	0.236309	−	1.64356i	−0.433589	−	0.901111i	$-0.642753\pi$
$83$	2.15288	−	14.9736i	0.236309	−	1.64356i	0.669898	−	0.742453i	$-0.266338\pi$
$84$	−0.835159	+	0.963825i	−0.0911233	+	0.105162i
$85$	0.401549	−	0.879269i	0.0435541	−	0.0953701i
$86$	4.27501	+	2.74738i	0.460986	+	0.296258i
$87$	−1.97888	−	13.7634i	−0.212158	−	1.47559i
$88$	−2.28171	+	1.46637i	−0.243231	+	0.156315i
$89$	0.720233	+	0.831193i	0.0763445	+	0.0881063i	0.792637	−	0.609694i	$-0.208708\pi$
$89$	0.720233	+	0.831193i	0.0763445	+	0.0881063i	−0.716292	+	0.697800i	$0.754162\pi$
$90$	−1.14477	+	0.336134i	−0.120669	+	0.0354316i
$91$	2.22957			0.233722
$92$	−1.57869	+	4.52855i	−0.164590	+	0.472134i
$93$	3.52623			0.365653
$94$	−1.70099	+	0.499455i	−0.175443	+	0.0515148i
$95$	−5.21453	−	6.01789i	−0.534999	−	0.617422i
$96$	−1.13082	+	0.726736i	−0.115414	+	0.0741722i
$97$	0.109251	+	0.759860i	0.0110928	+	0.0771521i	0.994616	−	0.103631i	$-0.0330460\pi$
$97$	0.109251	+	0.759860i	0.0110928	+	0.0771521i	−0.983523	+	0.180783i	$0.942137\pi$
$98$	5.13154	+	3.29784i	0.518364	+	0.333132i
$99$	−1.34428	+	2.94357i	−0.135105	+	0.295840i
$100$	−0.654861	+	0.755750i	−0.0654861	+	0.0755750i
$101$	−0.0775147	+	0.539127i	−0.00771300	+	0.0536451i	−0.993314	−	0.115440i	$-0.963172\pi$
$101$	−0.0775147	+	0.539127i	−0.00771300	+	0.0536451i	0.985601	+	0.169085i	$0.0540813\pi$
$102$	−0.539767	−	1.18192i	−0.0534449	−	0.117028i
$103$	0.459764	+	0.134999i	0.0453019	+	0.0133018i	0.304305	−	0.952575i	$-0.401576\pi$
$103$	0.459764	+	0.134999i	0.0453019	+	0.0133018i	−0.259003	+	0.965876i	$0.583394\pi$
$104$	2.25481	+	0.662072i	0.221102	+	0.0649215i
$105$	0.529788	+	1.16007i	0.0517021	+	0.113212i
$106$	−0.0846524	+	0.588770i	−0.00822216	+	0.0571864i
$107$	−3.18526	+	3.67599i	−0.307931	+	0.355371i	−0.888530	−	0.458818i	$-0.848273\pi$
$107$	−3.18526	+	3.67599i	−0.307931	+	0.355371i	0.580599	+	0.814190i	$0.302818\pi$
$108$	−2.34145	+	5.12706i	−0.225306	+	0.493351i
$109$	5.98554	+	3.84667i	0.573311	+	0.368444i	0.794941	−	0.606686i	$-0.207502\pi$
$109$	5.98554	+	3.84667i	0.573311	+	0.368444i	−0.221631	+	0.975131i	$0.571138\pi$
$110$	0.385997	+	2.68467i	0.0368033	+	0.255973i
$111$	4.19774	−	2.69773i	0.398432	−	0.256057i
$112$	−0.621300	−	0.717019i	−0.0587074	−	0.0677519i
$113$	−9.49209	+	2.78713i	−0.892941	+	0.262191i	−0.695844	−	0.718193i	$-0.744969\pi$
$113$	−9.49209	+	2.78713i	−0.892941	+	0.262191i	−0.197097	+	0.980384i	$0.563151\pi$
$114$	−10.7037			−1.00249
$115$	3.46350	+	3.31725i	0.322973	+	0.309335i
$116$	10.3443			0.960446
$117$	2.69020	−	0.789915i	0.248709	−	0.0730276i
$118$	−0.812779	−	0.937997i	−0.0748224	−	0.0863496i
$119$	0.771499	−	0.495813i	0.0707232	−	0.0454511i
$120$	0.191301	+	1.33053i	0.0174633	+	0.121460i
$121$	−3.06517	−	1.96987i	−0.278652	−	0.179079i
$122$	5.05082	−	11.0597i	0.457280	−	1.00130i
$123$	1.62822	−	1.87906i	0.146811	−	0.169429i
$124$	−0.373330	+	2.59657i	−0.0335260	+	0.233179i
$125$	0.415415	+	0.909632i	0.0371558	+	0.0813600i
$126$	−1.08610	−	0.318907i	−0.0967574	−	0.0284105i
$127$	2.40610	+	0.706495i	0.213507	+	0.0626913i	0.386737	−	0.922190i	$-0.373602\pi$
$127$	2.40610	+	0.706495i	0.213507	+	0.0626913i	−0.173230	+	0.984881i	$0.555420\pi$
$128$	−0.415415	−	0.909632i	−0.0367178	−	0.0804009i
$129$	0.972139	−	6.76137i	0.0855920	−	0.595306i
$130$	1.53892	−	1.77601i	0.134973	−	0.155767i
$131$	4.20646	−	9.21086i	0.367520	−	0.804756i	−0.632035	−	0.774939i	$-0.717780\pi$
$131$	4.20646	−	9.21086i	0.367520	−	0.804756i	0.999555	−	0.0298169i	$-0.00949242\pi$
$132$	3.06710	+	1.97111i	0.266957	+	0.171563i
$133$	−1.07515	−	7.47783i	−0.0932273	−	0.648410i
$134$	−1.61125	+	1.03549i	−0.139190	+	0.0894523i
$135$	3.69106	+	4.25971i	0.317676	+	0.366618i
$136$	0.927466	−	0.272329i	0.0795295	−	0.0233520i
$137$	−18.0249			−1.53997			−0.769985	−	0.638062i	$-0.779736\pi$
$137$	−18.0249			−1.53997			−0.769985	+	0.638062i	$0.779736\pi$
$138$	6.41878	−	0.598442i	0.546403	−	0.0509428i
$139$	3.29781			0.279716			0.139858	−	0.990172i	$-0.455335\pi$
$139$	3.29781			0.279716			0.139858	+	0.990172i	$0.455335\pi$
$140$	−0.910321	+	0.267294i	−0.0769361	+	0.0225905i
$141$	1.56054	+	1.80096i	0.131421	+	0.151668i
$142$	−12.0043	+	7.71471i	−1.00738	+	0.647404i
$143$	−0.907093	−	6.30897i	−0.0758549	−	0.527583i
$144$	−1.00370	−	0.645036i	−0.0836413	−	0.0537530i
$145$	4.29718	−	9.40952i	0.356862	−	0.781418i
$146$	−2.13154	+	2.45993i	−0.176407	+	0.203585i
$147$	1.16691	−	8.11606i	0.0962454	−	0.669401i
$148$	1.54207	+	3.37666i	0.126757	+	0.277560i
$149$	−14.4081	−	4.23061i	−1.18036	−	0.346585i	−0.368047	−	0.929807i	$-0.619973\pi$
$149$	−14.4081	−	4.23061i	−1.18036	−	0.346585i	−0.812312	+	0.583223i	$0.801792\pi$
$150$	1.28976	+	0.378708i	0.105309	+	0.0309214i
$151$	7.19480	+	15.7544i	0.585505	+	1.28208i	0.938121	+	0.346309i	$0.112565\pi$
$151$	7.19480	+	15.7544i	0.585505	+	1.28208i	−0.352616	+	0.935768i	$0.614708\pi$
$152$	1.13323	−	7.88176i	0.0919167	−	0.639295i
$153$	0.755231	−	0.871583i	0.0610568	−	0.0704633i
$154$	−1.06898	+	2.34073i	−0.0861406	+	0.188622i
$155$	2.20683	+	1.41825i	0.177257	+	0.113916i
$156$	−0.449558	−	3.12675i	−0.0359935	−	0.250340i
$157$	12.1908	−	7.83457i	0.972934	−	0.625266i	0.0453853	−	0.998970i	$-0.485548\pi$
$157$	12.1908	−	7.83457i	0.972934	−	0.625266i	0.927548	+	0.373703i	$0.121912\pi$
$158$	−7.49174	−	8.64593i	−0.596011	−	0.687833i
$159$	0.767182	−	0.225265i	0.0608415	−	0.0178647i
$160$	−1.00000			−0.0790569
$161$	1.06283	+	4.42418i	0.0837626	+	0.348674i
$162$	3.99724			0.314053
$163$	−8.94660	+	2.62696i	−0.700752	+	0.205759i	−0.612653	−	0.790352i	$-0.709897\pi$
$163$	−8.94660	+	2.62696i	−0.700752	+	0.205759i	−0.0880994	+	0.996112i	$0.528079\pi$
$164$	1.21128	+	1.39789i	0.0945851	+	0.109157i
$165$	3.06710	−	1.97111i	0.238773	−	0.153450i
$166$	−2.15288	−	14.9736i	−0.167096	−	1.16218i
$167$	15.9339	+	10.2401i	1.23301	+	0.792405i	0.984356	−	0.176189i	$-0.0563770\pi$
$167$	15.9339	+	10.2401i	1.23301	+	0.792405i	0.248649	+	0.968594i	$0.420013\pi$
$168$	−0.529788	+	1.16007i	−0.0408741	+	0.0895017i
$169$	4.89672	−	5.65111i	0.376670	−	0.434701i
$170$	0.137564	−	0.956782i	0.0105507	−	0.0733818i
$171$	−3.94660	−	8.64185i	−0.301804	−	0.660859i
$172$	4.87587	+	1.43168i	0.371782	+	0.109165i
$173$	−13.1452	−	3.85978i	−0.999412	−	0.293454i	−0.259197	−	0.965824i	$-0.583458\pi$
$173$	−13.1452	−	3.85978i	−0.999412	−	0.293454i	−0.740215	+	0.672371i	$0.765276\pi$
$174$	−5.77633	−	12.6484i	−0.437902	−	0.958872i
$175$	−0.135021	+	0.939095i	−0.0102067	+	0.0709889i
$176$	−1.77616	+	2.04980i	−0.133883	+	0.154509i
$177$	−0.693064	+	1.51760i	−0.0520939	+	0.114070i
$178$	0.925233	+	0.594611i	0.0693491	+	0.0445680i
$179$	−1.11854	−	7.77965i	−0.0836039	−	0.581478i	−0.987961	−	0.154702i	$-0.950558\pi$
$179$	−1.11854	−	7.77965i	−0.0836039	−	0.581478i	0.904357	−	0.426776i	$-0.140351\pi$
$180$	−1.00370	+	0.645036i	−0.0748110	+	0.0480781i
$181$	8.20420	+	9.46815i	0.609814	+	0.703762i	0.973739	−	0.227666i	$-0.0731093\pi$
$181$	8.20420	+	9.46815i	0.609814	+	0.703762i	−0.363926	+	0.931428i	$0.618564\pi$
$182$	2.13926	−	0.628142i	0.158572	−	0.0465610i
$183$	−16.3436			−1.20815
$184$	−0.238903	+	4.78988i	−0.0176122	+	0.353114i
$185$	3.71211			0.272920
$186$	3.38339	−	0.993454i	0.248082	−	0.0728436i
$187$	−1.71687	−	1.98138i	−0.125550	−	0.144893i
$188$	−1.49137	+	0.958446i	−0.108769	+	0.0699019i
$189$	0.761036	+	5.29312i	0.0553572	+	0.385018i
$190$	−6.69874	−	4.30502i	−0.485978	−	0.312319i
$191$	−6.92285	+	15.1589i	−0.500920	+	1.09686i	0.475250	+	0.879851i	$0.342358\pi$
$191$	−6.92285	+	15.1589i	−0.500920	+	1.09686i	−0.976169	+	0.217010i	$0.930370\pi$
$192$	−0.880272	+	1.01589i	−0.0635281	+	0.0733154i
$193$	−3.28832	+	22.8708i	−0.236699	+	1.64628i	0.431370	+	0.902175i	$0.358030\pi$
$193$	−3.28832	+	22.8708i	−0.236699	+	1.64628i	−0.668068	+	0.744100i	$0.732879\pi$
$194$	0.318903	+	0.698301i	0.0228959	+	0.0501351i
$195$	−3.03094	−	0.889965i	−0.217050	−	0.0637317i
$196$	5.85278	+	1.71853i	0.418056	+	0.122752i
$197$	5.55677	+	12.1676i	0.395904	+	0.866908i	0.997669	+	0.0682354i	$0.0217369\pi$
$197$	5.55677	+	12.1676i	0.395904	+	0.866908i	−0.601766	+	0.798673i	$0.705536\pi$
$198$	−0.460531	+	3.20306i	−0.0327285	+	0.227632i
$199$	11.3419	−	13.0892i	0.804004	−	0.927871i	−0.194589	−	0.980885i	$-0.562337\pi$
$199$	11.3419	−	13.0892i	0.804004	−	0.927871i	0.998594	+	0.0530142i	$0.0168828\pi$
$200$	−0.415415	+	0.909632i	−0.0293743	+	0.0643207i
$201$	2.16586	+	1.39191i	0.152768	+	0.0981779i
$202$	0.0775147	+	0.539127i	0.00545391	+	0.0379328i
$203$	8.25622	−	5.30595i	0.579473	−	0.372405i
$204$	−0.850889	−	0.981978i	−0.0595741	−	0.0687522i
$205$	1.77475	−	0.521114i	0.123954	−	0.0363962i
$206$	0.479174			0.0333856
$207$	2.84986	+	4.96168i	0.198079	+	0.344860i
$208$	2.35000			0.162943
$209$	−20.7225	+	6.08466i	−1.43340	+	0.420885i
$210$	0.835159	+	0.963825i	0.0576315	+	0.0665102i
$211$	−12.3076	+	7.90963i	−0.847292	+	0.544521i	−0.890729	−	0.454535i	$-0.849806\pi$
$211$	−12.3076	+	7.90963i	−0.847292	+	0.544521i	0.0434372	+	0.999056i	$0.486169\pi$
$212$	0.0846524	+	0.588770i	0.00581395	+	0.0404369i
$213$	16.1363	+	10.3702i	1.10564	+	0.710555i
$214$	−2.02059	+	4.42448i	−0.138125	+	0.302451i
$215$	3.32782	−	3.84050i	0.226955	−	0.261920i
$216$	−0.802144	+	5.57904i	−0.0545790	+	0.379605i
$217$	1.03390	+	2.26392i	0.0701856	+	0.153685i
$218$	6.82681	+	2.00453i	0.462370	+	0.135764i
$219$	4.19811	+	1.23268i	0.283682	+	0.0832966i
$220$	1.12672	+	2.46717i	0.0759634	+	0.166337i
$221$	−0.323277	+	2.24844i	−0.0217459	+	0.151246i
$222$	3.26767	−	3.77109i	0.219312	−	0.253099i
$223$	−6.48513	+	14.2004i	−0.434276	+	0.950932i	0.558337	+	0.829614i	$0.311439\pi$
$223$	−6.48513	+	14.2004i	−0.434276	+	0.950932i	−0.992614	+	0.121318i	$0.961288\pi$
$224$	−0.798141	−	0.512934i	−0.0533280	−	0.0342718i
$225$	0.169795	+	1.18095i	0.0113197	+	0.0787300i
$226$	−8.32237	+	5.34846i	−0.553596	+	0.355774i
$227$	4.08468	+	4.71397i	0.271109	+	0.312877i	0.874936	−	0.484239i	$-0.160903\pi$
$227$	4.08468	+	4.71397i	0.271109	+	0.312877i	−0.603826	+	0.797116i	$0.706358\pi$
$228$	−10.2701	+	3.01558i	−0.680156	+	0.199712i
$229$	9.80799			0.648130			0.324065	−	0.946035i	$-0.394950\pi$
$229$	9.80799			0.648130			0.324065	+	0.946035i	$0.394950\pi$
$230$	4.25778	+	2.20710i	0.280750	+	0.145532i
$231$	3.45902			0.227587
$232$	9.92530	−	2.91433i	0.651628	−	0.191335i
$233$	0.882901	+	1.01892i	0.0578408	+	0.0667518i	0.783933	−	0.620846i	$-0.213211\pi$
$233$	0.882901	+	1.01892i	0.0578408	+	0.0667518i	−0.726092	+	0.687598i	$0.758665\pi$
$234$	2.35869	−	1.51583i	0.154192	−	0.0990932i
$235$	0.252295	+	1.75475i	0.0164579	+	0.114467i
$236$	−1.04412	−	0.671015i	−0.0679664	−	0.0436794i
$237$	−6.38828	+	13.9884i	−0.414963	+	0.908643i
$238$	0.600562	−	0.693085i	0.0389286	−	0.0449260i
$239$	−2.78404	+	19.3634i	−0.180085	+	1.25252i	0.676473	+	0.736467i	$0.263507\pi$
$239$	−2.78404	+	19.3634i	−0.180085	+	1.25252i	−0.856558	+	0.516050i	$0.827402\pi$
$240$	0.558406	+	1.22274i	0.0360449	+	0.0789274i
$241$	−27.9027	−	8.19296i	−1.79737	−	0.527755i	−0.799983	−	0.600022i	$-0.795158\pi$
$241$	−27.9027	−	8.19296i	−1.79737	−	0.527755i	−0.997385	+	0.0722672i	$0.976977\pi$
$242$	−3.49599	−	1.02651i	−0.224730	−	0.0659868i
$243$	4.79226	+	10.4936i	0.307424	+	0.673164i
$244$	1.73033	−	12.0347i	0.110773	−	0.770445i
$245$	3.99457	−	4.60997i	0.255203	−	0.294520i
$246$	1.03287	−	2.26167i	0.0658533	−	0.144199i
$247$	15.7421	+	10.1168i	1.00164	+	0.643717i
$248$	0.373330	+	2.59657i	0.0237065	+	0.164882i
$249$	−17.1066	+	10.9937i	−1.08409	+	0.696700i
$250$	0.654861	+	0.755750i	0.0414170	+	0.0477978i
$251$	−18.6384	+	5.47273i	−1.17645	+	0.345436i	−0.810803	−	0.585319i	$-0.800969\pi$
$251$	−18.6384	+	5.47273i	−1.17645	+	0.345436i	−0.365643	+	0.930755i	$0.619151\pi$
$252$	−1.13195			−0.0713062
$253$	12.0866	−	4.80743i	0.759879	−	0.302241i
$254$	2.50768			0.157346
$255$	−1.24671	+	0.366067i	−0.0780720	+	0.0229240i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	6.47270	−	4.15975i	0.403756	−	0.259478i	−0.322965	−	0.946411i	$-0.604680\pi$
$257$	6.47270	−	4.15975i	0.403756	−	0.259478i	0.726721	+	0.686933i	$0.241043\pi$
$258$	−0.972139	−	6.76137i	−0.0605227	−	0.420945i
$259$	2.96279	+	1.90407i	0.184099	+	0.118313i
$260$	0.976226	−	2.13764i	0.0605430	−	0.132571i
$261$	8.08213	−	9.32727i	0.500271	−	0.577344i
$262$	1.44107	−	10.0228i	0.0890295	−	0.619214i
$263$	−6.62042	−	14.4967i	−0.408233	−	0.893905i	−0.996369	−	0.0851427i	$-0.972865\pi$
$263$	−6.62042	−	14.4967i	−0.408233	−	0.893905i	0.588136	−	0.808762i	$-0.299862\pi$
$264$	3.49819	+	1.02716i	0.215298	+	0.0632173i
$265$	0.570730	+	0.167581i	0.0350597	+	0.0102944i
$266$	−3.13835	−	6.87202i	−0.192424	−	0.421351i
$267$	0.210398	−	1.46335i	0.0128762	−	0.0895557i
$268$	−1.25425	+	1.44748i	−0.0766155	+	0.0884190i
$269$	−10.3574	+	22.6795i	−0.631501	+	1.38280i	0.275350	+	0.961344i	$0.411206\pi$
$269$	−10.3574	+	22.6795i	−0.631501	+	1.38280i	−0.906851	+	0.421451i	$0.861521\pi$
$270$	4.74165	+	3.04727i	0.288567	+	0.185451i
$271$	0.582094	+	4.04855i	0.0353597	+	0.245932i	0.999834	−	0.0182464i	$-0.00580832\pi$
$271$	0.582094	+	4.04855i	0.0353597	+	0.245932i	−0.964474	+	0.264178i	$0.914899\pi$
$272$	0.813173	−	0.522595i	0.0493059	−	0.0316870i
$273$	−1.96263	−	2.26499i	−0.118783	−	0.137083i
$274$	−17.2948	+	5.07820i	−1.04481	+	0.306785i
$275$	2.71227			0.163556
$276$	5.99017	−	2.38258i	0.360566	−	0.143414i
$277$	25.8748			1.55467			0.777334	−	0.629088i	$-0.216572\pi$
$277$	25.8748			1.55467			0.777334	+	0.629088i	$0.216572\pi$
$278$	3.16422	−	0.929099i	0.189777	−	0.0557237i
$279$	2.04959	+	2.36535i	0.122706	+	0.141610i
$280$	−0.798141	+	0.512934i	−0.0476980	+	0.0306537i
$281$	−2.80749	−	19.5265i	−0.167481	−	1.16485i	−0.884068	−	0.467358i	$-0.845206\pi$
$281$	−2.80749	−	19.5265i	−0.167481	−	1.16485i	0.716588	−	0.697497i	$-0.245703\pi$
$282$	2.00472	+	1.28836i	0.119379	+	0.0767204i
$283$	−7.95030	+	17.4087i	−0.472596	+	1.03484i	0.511837	+	0.859083i	$0.328965\pi$
$283$	−7.95030	+	17.4087i	−0.472596	+	1.03484i	−0.984433	+	0.175759i	$0.943762\pi$
$284$	−9.34458	+	10.7842i	−0.554499	+	0.639926i
$285$	−1.52330	+	10.5948i	−0.0902322	+	0.627579i
$286$	−2.64779	−	5.79785i	−0.156567	−	0.342834i
$287$	1.68380	+	0.494408i	0.0993914	+	0.0291840i
$288$	−1.14477	−	0.336134i	−0.0674560	−	0.0198069i
$289$	−6.67391	−	14.6138i	−0.392583	−	0.859637i
$290$	1.47215	−	10.2390i	0.0864476	−	0.601256i
$291$	0.675762	−	0.779871i	0.0396139	−	0.0457168i
$292$	−1.35216	+	2.96081i	−0.0791289	+	0.173268i
$293$	−15.0301	−	9.65923i	−0.878065	−	0.564298i	0.0221445	−	0.999755i	$-0.492951\pi$
$293$	−15.0301	−	9.65923i	−0.878065	−	0.564298i	−0.900210	+	0.435456i	$0.856587\pi$
$294$	−1.16691	−	8.11606i	−0.0680557	−	0.473338i
$295$	−1.04412	+	0.671015i	−0.0607910	+	0.0390680i
$296$	2.43092	+	2.80543i	0.141294	+	0.163062i
$297$	14.6682	−	4.30698i	0.851137	−	0.249916i
$298$	−15.0164			−0.869876
$299$	−10.0058	−	5.18669i	−0.578650	−	0.299954i
$300$	1.34421			0.0776081
$301$	4.62599	−	1.35831i	0.266638	−	0.0782919i
$302$	11.3419	+	13.0892i	0.652653	+	0.753202i
$303$	0.615926	−	0.395832i	0.0353840	−	0.0227399i
$304$	−1.13323	−	7.88176i	−0.0649950	−	0.452050i
$305$	−10.2284	−	6.57337i	−0.585675	−	0.376390i
$306$	0.479086	−	1.04905i	0.0273875	−	0.0599703i
$307$	17.3367	−	20.0076i	0.989458	−	1.14190i	−0.000423703	−	1.00000i	$-0.500135\pi$
$307$	17.3367	−	20.0076i	0.989458	−	1.14190i	0.989882	−	0.141895i	$-0.0453197\pi$
$308$	−0.366215	+	2.54708i	−0.0208670	+	0.145133i
$309$	−0.267573	−	0.585904i	−0.0152217	−	0.0333309i
$310$	2.51701	+	0.739060i	0.142956	+	0.0419758i
$311$	0.822783	+	0.241591i	0.0466558	+	0.0136994i	0.304977	−	0.952360i	$-0.401351\pi$
$311$	0.822783	+	0.241591i	0.0466558	+	0.0136994i	−0.258321	+	0.966059i	$0.583169\pi$
$312$	−1.31225	−	2.87344i	−0.0742918	−	0.162676i
$313$	1.84294	−	12.8179i	0.104169	−	0.724512i	−0.869065	−	0.494697i	$-0.835279\pi$
$313$	1.84294	−	12.8179i	0.104169	−	0.724512i	0.973234	−	0.229814i	$-0.0738119\pi$
$314$	9.48976	−	10.9518i	0.535538	−	0.618044i
$315$	−0.470229	+	1.02966i	−0.0264944	+	0.0580147i
$316$	−9.62411	−	6.18504i	−0.541399	−	0.347936i
$317$	−4.50006	−	31.2986i	−0.252749	−	1.75791i	−0.581554	−	0.813508i	$-0.697555\pi$
$317$	−4.50006	−	31.2986i	−0.252749	−	1.75791i	0.328805	−	0.944398i	$-0.393354\pi$
$318$	0.672641	−	0.432280i	0.0377199	−	0.0242411i
$319$	−18.3732	−	21.2038i	−1.02870	−	1.18718i
$320$	−0.959493	+	0.281733i	−0.0536373	+	0.0157493i
$321$	6.53829			0.364932
$322$	2.26621	+	3.94554i	0.126291	+	0.219876i
$323$	7.69701			0.428273
$324$	3.83532	−	1.12615i	0.213074	−	0.0625641i
$325$	−1.53892	−	1.77601i	−0.0853641	−	0.0985155i
$326$	−7.84410	+	5.04110i	−0.434445	+	0.279201i
$327$	−1.36111	−	9.46675i	−0.0752697	−	0.523512i
$328$	1.55605	+	1.00001i	0.0859183	+	0.0552163i
$329$	−0.698705	+	1.52995i	−0.0385209	+	0.0843489i
$330$	2.38754	−	2.75536i	0.131430	−	0.151678i
$331$	−1.76125	+	12.2498i	−0.0968072	+	0.673309i	0.882408	+	0.470485i	$0.155921\pi$
$331$	−1.76125	+	12.2498i	−0.0968072	+	0.673309i	−0.979215	+	0.202824i	$0.934988\pi$
$332$	−6.28421	−	13.7605i	−0.344891	−	0.755206i
$333$	4.24950	+	1.24777i	0.232871	+	0.0683772i
$334$	18.1735	+	5.33622i	0.994409	+	0.291985i
$335$	0.795641	+	1.74221i	0.0434705	+	0.0951872i
$336$	−0.181497	+	1.26234i	−0.00990150	+	0.0688664i
$337$	−15.4974	+	17.8849i	−0.844196	+	0.974254i	−0.999908	−	0.0135485i	$-0.995687\pi$
$337$	−15.4974	+	17.8849i	−0.844196	+	0.974254i	0.155712	+	0.987802i	$0.450233\pi$
$338$	3.10626	−	6.80177i	0.168958	−	0.369967i
$339$	11.1870	+	7.18946i	0.607596	+	0.390478i
$340$	−0.137564	−	0.956782i	−0.00746048	−	0.0518888i
$341$	5.98554	−	3.84667i	0.324135	−	0.208309i
$342$	−6.22143	−	7.17991i	−0.336416	−	0.388245i
$343$	11.9251	−	3.50152i	0.643894	−	0.189064i
$344$	5.08172			0.273988
$345$	0.321136	−	6.43861i	0.0172894	−	0.346643i
$346$	−13.7002			−0.736525
$347$	34.5578	−	10.1471i	1.85516	−	0.544724i	0.855525	−	0.517762i	$-0.173235\pi$
$347$	34.5578	−	10.1471i	1.85516	−	0.544724i	0.999636	−	0.0269624i	$-0.00858343\pi$
$348$	−9.10581	−	10.5087i	−0.488123	−	0.563323i
$349$	−23.1192	+	14.8578i	−1.23754	+	0.795321i	−0.985049	−	0.172277i	$-0.944888\pi$
$349$	−23.1192	+	14.8578i	−1.23754	+	0.795321i	−0.252495	+	0.967598i	$0.581251\pi$
$350$	0.135021	+	0.939095i	0.00721720	+	0.0501967i
$351$	−11.1429	−	7.16109i	−0.594763	−	0.382231i
$352$	−1.12672	+	2.46717i	−0.0600543	+	0.131501i
$353$	21.1770	−	24.4396i	1.12714	−	1.30079i	0.178675	−	0.983908i	$-0.442819\pi$
$353$	21.1770	−	24.4396i	1.12714	−	1.30079i	0.948465	−	0.316881i	$-0.102636\pi$
$354$	−0.237433	+	1.65138i	−0.0126194	+	0.0877701i
$355$	5.92779	+	12.9801i	0.314614	+	0.688910i
$356$	1.05528	+	0.309857i	0.0559295	+	0.0164224i
$357$	−1.18282	−	0.347307i	−0.0626014	−	0.0183814i
$358$	−3.26502	−	7.14939i	−0.172561	−	0.377857i
$359$	−1.16361	+	8.09311i	−0.0614132	+	0.427138i	0.935800	+	0.352532i	$0.114679\pi$
$359$	−1.16361	+	8.09311i	−0.0614132	+	0.427138i	−0.997213	+	0.0746063i	$0.976230\pi$
$360$	−0.781311	+	0.901681i	−0.0411787	+	0.0475227i
$361$	18.4470	−	40.3934i	0.970897	−	2.12597i
$362$	10.5394	+	6.77324i	0.553937	+	0.355993i
$363$	0.697021	+	4.84789i	0.0365841	+	0.254448i
$364$	1.87563	−	1.20540i	0.0983098	−	0.0631799i
$365$	2.13154	+	2.45993i	0.111570	+	0.128758i
$366$	−15.6816	+	4.60452i	−0.819688	+	0.240682i
$367$	−15.4442			−0.806182			−0.403091	−	0.915160i	$-0.632064\pi$
$367$	−15.4442			−0.806182			−0.403091	+	0.915160i	$0.632064\pi$
$368$	1.12024	+	4.66316i	0.0583965	+	0.243084i
$369$	2.20684			0.114883
$370$	3.56175	−	1.04582i	0.185166	−	0.0543698i
$371$	0.369565	+	0.426500i	0.0191868	+	0.0221428i
$372$	2.96645	−	1.90642i	0.153803	−	0.0988435i
$373$	1.65672	+	11.5227i	0.0857816	+	0.596624i	0.986690	+	0.162614i	$0.0519926\pi$
$373$	1.65672	+	11.5227i	0.0857816	+	0.596624i	−0.900908	+	0.434010i	$0.857098\pi$
$374$	−2.20555	−	1.41742i	−0.114046	−	0.0732930i
$375$	0.558406	−	1.22274i	0.0288359	−	0.0631419i
$376$	−1.16094	+	1.33979i	−0.0598707	+	0.0690944i
$377$	−3.45955	+	24.0617i	−0.178176	+	1.23924i
$378$	2.22145	+	4.86430i	0.114259	+	0.250193i
$379$	−9.87315	−	2.89902i	−0.507150	−	0.148913i	0.0181411	−	0.999835i	$-0.494225\pi$
$379$	−9.87315	−	2.89902i	−0.507150	−	0.148913i	−0.525291	+	0.850923i	$0.676043\pi$
$380$	−7.64026	−	2.24338i	−0.391937	−	0.115083i
$381$	−1.40030	−	3.06623i	−0.0717397	−	0.157088i
$382$	−2.37166	+	16.4953i	−0.121345	+	0.843972i
$383$	18.7966	−	21.6924i	0.960460	−	1.10843i	−0.0335824	−	0.999436i	$-0.510692\pi$
$383$	18.7966	−	21.6924i	0.960460	−	1.10843i	0.994042	−	0.108994i	$-0.0347629\pi$
$384$	−0.558406	+	1.22274i	−0.0284960	+	0.0623976i
$385$	2.16478	+	1.39122i	0.110327	+	0.0709030i
$386$	3.28832	+	22.8708i	0.167371	+	1.16409i
$387$	5.10049	−	3.27789i	0.259273	−	0.166624i
$388$	0.502720	+	0.580169i	0.0255217	+	0.0294536i
$389$	32.5670	−	9.56253i	1.65121	−	0.484840i	0.682059	−	0.731297i	$-0.261085\pi$
$389$	32.5670	−	9.56253i	1.65121	−	0.484840i	0.969154	+	0.246457i	$0.0792666\pi$
$390$	−3.15890			−0.159957
$391$	−4.61573	+	0.430339i	−0.233428	+	0.0217632i
$392$	6.09987			0.308090
$393$	−13.0600	+	3.83477i	−0.658791	+	0.193438i
$394$	8.75970	+	10.1092i	0.441308	+	0.509296i
$395$	−9.62411	+	6.18504i	−0.484242	+	0.311203i
$396$	0.460531	+	3.20306i	0.0231425	+	0.160960i
$397$	−31.4515	−	20.2126i	−1.57851	−	1.01444i	−0.976385	−	0.216039i	$-0.930686\pi$
$397$	−31.4515	−	20.2126i	−1.57851	−	1.01444i	−0.602121	−	0.798405i	$-0.705677\pi$
$398$	7.19479	−	15.7544i	0.360642	−	0.789697i
$399$	−6.65021	+	7.67475i	−0.332927	+	0.384218i
$400$	−0.142315	+	0.989821i	−0.00711574	+	0.0494911i
$401$	−0.148996	−	0.326255i	−0.00744049	−	0.0162924i	0.905875	−	0.423545i	$-0.139214\pi$
$401$	−0.148996	−	0.326255i	−0.00744049	−	0.0162924i	−0.913316	+	0.407252i	$0.866487\pi$
$402$	2.47027	+	0.725337i	0.123206	+	0.0361765i
$403$	−5.91497	−	1.73679i	−0.294646	−	0.0865158i
$404$	0.226264	+	0.495450i	0.0112571	+	0.0246495i
$405$	0.568867	−	3.95656i	0.0282672	−	0.196603i
$406$	6.42693	−	7.41707i	0.318963	−	0.368103i
$407$	4.18251	−	9.15842i	0.207319	−	0.453966i
$408$	−1.09308	−	0.702478i	−0.0541154	−	0.0347778i
$409$	−3.44922	−	23.9899i	−0.170553	−	1.18622i	−0.877719	−	0.479175i	$-0.840936\pi$
$409$	−3.44922	−	23.9899i	−0.170553	−	1.18622i	0.707166	−	0.707047i	$-0.249973\pi$
$410$	1.55605	−	1.00001i	0.0768476	−	0.0493870i
$411$	15.8668	+	18.3113i	0.782651	+	0.903228i
$412$	0.459764	−	0.134999i	0.0226509	−	0.00665092i
$413$	−1.17754			−0.0579430
$414$	4.13228	+	3.95780i	0.203091	+	0.194515i
$415$	−15.1276			−0.742583
$416$	2.25481	−	0.662072i	0.110551	−	0.0324608i
$417$	−2.90296	−	3.35020i	−0.142159	−	0.164060i
$418$	−18.1688	+	11.6764i	−0.888666	+	0.571111i
$419$	0.474938	+	3.30327i	0.0232023	+	0.161375i	0.998128	−	0.0611536i	$-0.0194779\pi$
$419$	0.474938	+	3.30327i	0.0232023	+	0.161375i	−0.974926	+	0.222529i	$0.928569\pi$
$420$	1.07287	+	0.689492i	0.0523507	+	0.0336438i
$421$	6.24796	−	13.6811i	0.304507	−	0.666778i	−0.694081	−	0.719897i	$-0.744189\pi$
$421$	6.24796	−	13.6811i	0.304507	−	0.666778i	0.998588	+	0.0531193i	$0.0169164\pi$
$422$	−9.58068	+	11.0567i	−0.466380	+	0.538231i
$423$	−0.301012	+	2.09359i	−0.0146357	+	0.101794i
$424$	0.247099	+	0.541071i	0.0120002	+	0.0262768i
$425$	−0.927466	−	0.272329i	−0.0449887	−	0.0132099i
$426$	18.4043	+	5.40400i	0.891693	+	0.261825i
$427$	−4.79197	−	10.4930i	−0.231900	−	0.507790i
$428$	−0.692224	+	4.81452i	−0.0334599	+	0.232719i
$429$	−5.61072	+	6.47511i	−0.270888	+	0.312621i
$430$	2.11102	−	4.62249i	0.101802	−	0.222916i
$431$	20.9325	+	13.4525i	1.00828	+	0.647983i	0.936948	−	0.349469i	$-0.113638\pi$
$431$	20.9325	+	13.4525i	1.00828	+	0.647983i	0.0713339	+	0.997452i	$0.477274\pi$
$432$	0.802144	+	5.57904i	0.0385932	+	0.268422i
$433$	−22.5841	+	14.5139i	−1.08532	+	0.697494i	−0.955781	−	0.294080i	$-0.904987\pi$
$433$	−22.5841	+	14.5139i	−1.08532	+	0.697494i	−0.129541	+	0.991574i	$0.541350\pi$
$434$	1.62984	+	1.88093i	0.0782347	+	0.0902877i
$435$	−13.3417	+	3.91748i	−0.639686	+	0.187829i
$436$	7.11502			0.340748
$437$	−12.5708	+	36.0599i	−0.601343	+	1.72498i
$438$	4.37534			0.209062
$439$	−5.23613	+	1.53747i	−0.249907	+	0.0733793i	−0.404287	−	0.914632i	$-0.632480\pi$
$439$	−5.23613	+	1.53747i	−0.249907	+	0.0733793i	0.154380	+	0.988012i	$0.450662\pi$
$440$	1.77616	+	2.04980i	0.0846752	+	0.0977203i
$441$	6.12241	−	3.93463i	0.291543	−	0.187364i
$442$	0.323277	+	2.24844i	0.0153767	+	0.106947i
$443$	8.19390	+	5.26590i	0.389304	+	0.250191i	0.720621	−	0.693329i	$-0.243857\pi$
$443$	8.19390	+	5.26590i	0.389304	+	0.250191i	−0.331317	+	0.943519i	$0.607493\pi$
$444$	2.07287	−	4.53894i	0.0983739	−	0.215409i
$445$	0.720233	−	0.831193i	0.0341423	−	0.0394023i
$446$	−2.22171	+	15.4523i	−0.105201	+	0.731688i
$447$	8.38524	+	18.3611i	0.396608	+	0.868451i
$448$	−0.910321	−	0.267294i	−0.0430086	−	0.0126285i
$449$	−19.3195	−	5.67273i	−0.911746	−	0.267713i	−0.207970	−	0.978135i	$-0.566686\pi$
$449$	−19.3195	−	5.67273i	−0.911746	−	0.267713i	−0.703775	+	0.710423i	$0.748504\pi$
$450$	0.495629	+	1.08528i	0.0233642	+	0.0511605i
$451$	0.713969	−	4.96576i	0.0336195	−	0.233829i
$452$	−6.47842	+	7.47649i	−0.304719	+	0.351665i
$453$	9.67134	−	21.1773i	0.454399	−	0.994996i
$454$	5.24730	+	3.37223i	0.246268	+	0.158267i
$455$	−0.317301	−	2.20687i	−0.0148753	−	0.103460i
$456$	−9.00453	+	5.78686i	−0.421676	+	0.270994i
$457$	−24.1113	−	27.8260i	−1.12788	−	1.30164i	−0.948112	−	0.317936i	$-0.897010\pi$
$457$	−24.1113	−	27.8260i	−1.12788	−	1.30164i	−0.179769	−	0.983709i	$-0.557535\pi$
$458$	9.41070	−	2.76323i	0.439733	−	0.129117i
$459$	−5.44827			−0.254303
$460$	4.70712	+	0.918142i	0.219471	+	0.0428086i
$461$	16.5267			0.769725			0.384863	−	0.922974i	$-0.374249\pi$
$461$	16.5267			0.769725			0.384863	+	0.922974i	$0.374249\pi$
$462$	3.31891	−	0.974520i	0.154410	−	0.0453388i
$463$	0.730726	+	0.843303i	0.0339597	+	0.0391916i	0.772475	−	0.635045i	$-0.219018\pi$
$463$	0.730726	+	0.843303i	0.0339597	+	0.0391916i	−0.738516	+	0.674236i	$0.764473\pi$
$464$	8.70219	−	5.59256i	0.403989	−	0.259628i
$465$	−0.501835	−	3.49034i	−0.0232720	−	0.161861i
$466$	1.13420	+	0.728907i	0.0525409	+	0.0337660i
$467$	−4.90824	+	10.7475i	−0.227126	+	0.497337i	−0.988546	−	0.150923i	$-0.951776\pi$
$467$	−4.90824	+	10.7475i	−0.227126	+	0.497337i	0.761419	+	0.648260i	$0.224503\pi$
$468$	1.83608	−	2.11895i	0.0848729	−	0.0979486i
$469$	−0.258606	+	1.79864i	−0.0119413	+	0.0830535i
$470$	0.736447	+	1.61259i	0.0339697	+	0.0743834i
$471$	−18.6903	−	5.48796i	−0.861202	−	0.252872i
$472$	−1.19087	−	0.349672i	−0.0548144	−	0.0160949i
$473$	−5.72566	−	12.5375i	−0.263266	−	0.576473i
$474$	−2.18853	+	15.2215i	−0.100522	+	0.699148i
$475$	−5.21453	+	6.01789i	−0.239259	+	0.276120i
$476$	0.380970	−	0.834208i	0.0174617	−	0.0382359i
$477$	0.597023	+	0.383683i	0.0273358	+	0.0175676i
$478$	2.78404	+	19.3634i	0.127339	+	0.885664i
$479$	21.7441	−	13.9741i	0.993515	−	0.638494i	0.0604390	−	0.998172i	$-0.480750\pi$
$479$	21.7441	−	13.9741i	0.993515	−	0.638494i	0.933076	+	0.359678i	$0.117114\pi$
$480$	0.880272	+	1.01589i	0.0401787	+	0.0463687i
$481$	−8.37011	+	2.45769i	−0.381644	+	0.112061i
$482$	−29.0806			−1.32459
$483$	3.55889	−	4.97420i	0.161935	−	0.226334i
$484$	−3.64358			−0.165617
$485$	0.736578	−	0.216279i	0.0334463	−	0.00982072i
$486$	7.55453	+	8.71839i	0.342680	+	0.395474i
$487$	5.63832	−	3.62353i	0.255497	−	0.164198i	−0.406623	−	0.913596i	$-0.633294\pi$
$487$	5.63832	−	3.62353i	0.255497	−	0.164198i	0.662119	+	0.749398i	$0.269657\pi$
$488$	−1.73033	−	12.0347i	−0.0783285	−	0.544787i
$489$	10.5441	+	6.77630i	0.476822	+	0.306435i
$490$	2.53398	−	5.54864i	0.114473	−	0.250662i
$491$	−21.6358	+	24.9691i	−0.976411	+	1.12684i	0.0154976	+	0.999880i	$0.495067\pi$
$491$	−21.6358	+	24.9691i	−0.976411	+	1.12684i	−0.991908	+	0.126958i	$0.959479\pi$
$492$	0.353845	−	2.46105i	0.0159526	−	0.110953i
$493$	4.15375	+	9.09544i	0.187075	+	0.409638i
$494$	17.9546	+	5.27195i	0.807817	+	0.237196i
$495$	3.10492	+	0.911686i	0.139556	+	0.0409772i
$496$	1.08975	+	2.38621i	0.0489310	+	0.107144i
$497$	−1.92670	+	13.4005i	−0.0864242	+	0.601093i
$498$	−13.3164	+	15.3679i	−0.596720	+	0.688652i
$499$	−12.0213	+	26.3230i	−0.538147	+	1.17838i	0.423954	+	0.905684i	$0.360642\pi$
$499$	−12.0213	+	26.3230i	−0.538147	+	1.17838i	−0.962101	+	0.272694i	$0.912085\pi$
$500$	0.841254	+	0.540641i	0.0376220	+	0.0241782i
$501$	−3.62338	−	25.2012i	−0.161881	−	1.12591i
$502$	−16.3416	+	10.5021i	−0.729361	+	0.468732i
$503$	5.48080	+	6.32518i	0.244377	+	0.282026i	0.864666	−	0.502347i	$-0.167530\pi$
$503$	5.48080	+	6.32518i	0.244377	+	0.282026i	−0.620289	+	0.784373i	$0.712985\pi$
$504$	−1.08610	+	0.318907i	−0.0483787	+	0.0142053i
$505$	0.544671			0.0242375
$506$	10.2426	−	8.01789i	0.455340	−	0.356439i
$507$	−10.0513			−0.446395
$508$	2.40610	−	0.706495i	0.106753	−	0.0313456i
$509$	9.93170	+	11.4618i	0.440215	+	0.508035i	0.931889	−	0.362744i	$-0.118160\pi$
$509$	9.93170	+	11.4618i	0.440215	+	0.508035i	−0.491674	+	0.870779i	$0.663615\pi$
$510$	−1.09308	+	0.702478i	−0.0484023	+	0.0311062i
$511$	0.439488	+	3.05671i	0.0194418	+	0.135221i
$512$	−0.841254	−	0.540641i	−0.0371785	−	0.0238932i
$513$	−18.6445	+	40.8258i	−0.823175	+	1.80250i
$514$	5.03857	−	5.81482i	0.222242	−	0.256481i
$515$	0.0681935	−	0.474296i	0.00300497	−	0.0209000i
$516$	−2.83766	−	6.21361i	−0.124921	−	0.273539i
$517$	4.61354	+	1.35466i	0.202903	+	0.0595778i
$518$	3.37921	+	0.992227i	0.148474	+	0.0435959i
$519$	7.65025	+	16.7517i	0.335809	+	0.735318i
$520$	0.334440	−	2.32608i	0.0146662	−	0.102005i
$521$	−15.8093	+	18.2449i	−0.692618	+	0.799323i	−0.987735	−	0.156138i	$-0.950096\pi$
$521$	−15.8093	+	18.2449i	−0.692618	+	0.799323i	0.295118	+	0.955461i	$0.404641\pi$
$522$	5.12695	−	11.2265i	0.224400	−	0.491368i
$523$	11.4773	+	7.37601i	0.501867	+	0.322530i	0.766963	−	0.641692i	$-0.221767\pi$
$523$	11.4773	+	7.37601i	0.501867	+	0.322530i	−0.265096	+	0.964222i	$0.585403\pi$
$524$	−1.44107	−	10.0228i	−0.0629534	−	0.437850i
$525$	1.07287	−	0.689492i	0.0468239	−	0.0300919i
$526$	−10.4364	−	12.0443i	−0.455050	−	0.525156i
$527$	−2.43299	+	0.714391i	−0.105983	+	0.0311194i
$528$	3.64587			0.158666
$529$	5.52233	−	22.3272i	0.240101	−	0.970748i
$530$	0.594825			0.0258375
$531$	−1.42082	+	0.417191i	−0.0616585	+	0.0181046i
$532$	−4.94729	−	5.70948i	−0.214492	−	0.247537i
$533$	−3.65671	+	2.35003i	−0.158390	+	0.101791i
$534$	−0.210398	−	1.46335i	−0.00910482	−	0.0633254i
$535$	4.09188	+	2.62969i	0.176908	+	0.113692i
$536$	−0.795641	+	1.74221i	−0.0343665	+	0.0752521i
$537$	−6.91862	+	7.98452i	−0.298561	+	0.344557i
$538$	−3.54828	+	24.6789i	−0.152977	+	1.06398i
$539$	−6.87284	−	15.0494i	−0.296034	−	0.648224i
$540$	5.40809	+	1.58796i	0.232727	+	0.0683349i
$541$	6.09926	+	1.79090i	0.262227	+	0.0769969i	0.410204	−	0.911994i	$-0.365458\pi$
$541$	6.09926	+	1.79090i	0.262227	+	0.0769969i	−0.147976	+	0.988991i	$0.547276\pi$
$542$	1.69912	+	3.72056i	0.0729836	+	0.159812i
$543$	2.39665	−	16.6691i	0.102850	−	0.715339i
$544$	0.633002	−	0.730523i	0.0271397	−	0.0313209i
$545$	2.95569	−	6.47205i	0.126608	−	0.277232i
$546$	−2.52125	−	1.62031i	−0.107899	−	0.0693427i
$547$	−4.71756	−	32.8114i	−0.201708	−	1.40291i	−0.799214	−	0.601047i	$-0.794750\pi$
$547$	−4.71756	−	32.8114i	−0.201708	−	1.40291i	0.597505	−	0.801865i	$-0.296159\pi$
$548$	−15.1635	+	9.74499i	−0.647753	+	0.416285i
$549$	−9.49956	−	10.9631i	−0.405431	−	0.467893i
$550$	2.60241	−	0.764136i	0.110967	−	0.0325828i
$551$	82.3698			3.50907
$552$	5.07628	−	3.97369i	0.216061	−	0.169132i
$553$	−10.8539			−0.461555
$554$	24.8267	−	7.28978i	1.05479	−	0.309713i
$555$	−3.26767	−	3.77109i	−0.138705	−	0.160074i
$556$	2.77429	−	1.78293i	0.117656	−	0.0756130i
$557$	5.10770	+	35.5248i	0.216420	+	1.50524i	0.751104	+	0.660184i	$0.229522\pi$
$557$	5.10770	+	35.5248i	0.216420	+	1.50524i	−0.534684	+	0.845052i	$0.679569\pi$
$558$	2.63296	+	1.69210i	0.111462	+	0.0716324i
$559$	−4.96090	+	10.8629i	−0.209824	+	0.459450i
$560$	−0.621300	+	0.717019i	−0.0262547	+	0.0302996i
$561$	−0.501542	+	3.48830i	−0.0211751	+	0.147276i
$562$	−8.19502	−	17.9446i	−0.345686	−	0.756947i
$563$	35.7649	+	10.5015i	1.50731	+	0.442586i	0.928018	−	0.372535i	$-0.121511\pi$
$563$	35.7649	+	10.5015i	1.50731	+	0.442586i	0.579291	+	0.815121i	$0.303330\pi$
$564$	2.28649	+	0.671373i	0.0962784	+	0.0282699i
$565$	4.10962	+	8.99882i	0.172893	+	0.378583i
$566$	−2.72365	+	18.9434i	−0.114484	+	0.796251i
$567$	2.48349	−	2.86610i	0.104297	−	0.120365i
$568$	−5.92779	+	12.9801i	−0.248725	+	0.544631i
$569$	−12.7490	−	8.19330i	−0.534467	−	0.343481i	0.245405	−	0.969421i	$-0.421079\pi$
$569$	−12.7490	−	8.19330i	−0.534467	−	0.343481i	−0.779871	+	0.625940i	$0.784716\pi$
$570$	1.52330	+	10.5948i	0.0638038	+	0.443765i
$571$	−12.0702	+	7.75707i	−0.505123	+	0.324623i	−0.768263	−	0.640135i	$-0.778879\pi$
$571$	−12.0702	+	7.75707i	−0.505123	+	0.324623i	0.263139	+	0.964758i	$0.415242\pi$
$572$	−4.17398	−	4.81703i	−0.174523	−	0.201410i
$573$	21.4937	−	6.31113i	0.897914	−	0.263651i
$574$	1.75488			0.0732474
$575$	2.79058	−	3.90034i	0.116375	−	0.162655i
$576$	−1.19309			−0.0497123
$577$	−20.6351	+	6.05900i	−0.859048	+	0.252239i	−0.681451	−	0.731864i	$-0.738651\pi$
$577$	−20.6351	+	6.05900i	−0.859048	+	0.252239i	−0.177598	+	0.984103i	$0.556833\pi$
$578$	−10.5208	−	12.1416i	−0.437606	−	0.505024i
$579$	26.1288	−	16.7919i	1.08587	−	0.697849i
$580$	−1.47215	−	10.2390i	−0.0611277	−	0.425152i
$581$	−12.0739	−	7.75944i	−0.500911	−	0.321916i
$582$	0.428674	−	0.938664i	0.0177691	−	0.0389089i
$583$	1.05650	−	1.21927i	0.0437559	−	0.0504970i
$584$	−0.463228	+	3.22182i	−0.0191685	+	0.133320i
$585$	−1.16473	−	2.55040i	−0.0481557	−	0.105446i
$586$	−17.1426	−	5.03351i	−0.708152	−	0.207932i
$587$	−40.8487	−	11.9943i	−1.68601	−	0.495056i	−0.708456	−	0.705755i	$-0.750608\pi$
$587$	−40.8487	−	11.9943i	−1.68601	−	0.495056i	−0.977551	+	0.210699i	$0.932426\pi$
$588$	−3.40620	−	7.45854i	−0.140469	−	0.307585i
$589$	−2.97276	+	20.6760i	−0.122490	+	0.851939i
$590$	−0.812779	+	0.937997i	−0.0334616	+	0.0386167i
$591$	7.46948	−	16.3559i	0.307253	−	0.672791i
$592$	3.12283	+	2.00692i	0.128347	+	0.0824839i
$593$	−0.0154349	−	0.107352i	−0.000633834	−	0.00440841i	0.989502	−	0.144519i	$-0.0461634\pi$
$593$	−0.0154349	−	0.107352i	−0.000633834	−	0.00440841i	−0.990136	+	0.140110i	$0.955254\pi$
$594$	12.8606	−	8.26503i	0.527679	−	0.339118i
$595$	−0.600562	−	0.693085i	−0.0246206	−	0.0284137i
$596$	−14.4081	+	4.23061i	−0.590180	+	0.173292i
$597$	−23.2811			−0.952833
$598$	−11.0617	−	2.15764i	−0.452349	−	0.0882323i
$599$	20.9206			0.854794			0.427397	−	0.904064i	$-0.359431\pi$
$599$	20.9206			0.854794			0.427397	+	0.904064i	$0.359431\pi$
$600$	1.28976	−	0.378708i	0.0526543	−	0.0154607i
$601$	20.8989	+	24.1186i	0.852482	+	0.983817i	0.999986	−	0.00524473i	$-0.00166946\pi$
$601$	20.8989	+	24.1186i	0.852482	+	0.983817i	−0.147504	+	0.989061i	$0.547124\pi$
$602$	4.05592	−	2.60658i	0.165307	−	0.106236i
$603$	0.325207	+	2.26187i	0.0132435	+	0.0921103i
$604$	14.5701	+	9.36366i	0.592851	+	0.381002i
$605$	−1.51360	+	3.31431i	−0.0615364	+	0.134746i
$606$	0.479458	−	0.553324i	0.0194766	−	0.0224772i
$607$	4.12285	−	28.6751i	0.167341	−	1.16388i	−0.717010	−	0.697063i	$-0.754490\pi$
$607$	4.12285	−	28.6751i	0.167341	−	1.16388i	0.884351	−	0.466822i	$-0.154601\pi$
$608$	−3.30787	−	7.24322i	−0.134152	−	0.293752i
$609$	−12.6580	−	3.71671i	−0.512927	−	0.150609i
$610$	−11.6660	−	3.42544i	−0.472342	−	0.138692i
$611$	−1.73065	−	3.78960i	−0.0700146	−	0.153311i
$612$	0.164127	−	1.14153i	0.00663446	−	0.0461437i
$613$	30.1772	−	34.8264i	1.21885	−	1.40662i	0.332821	−	0.942990i	$-0.392000\pi$
$613$	30.1772	−	34.8264i	1.21885	−	1.40662i	0.886026	−	0.463635i	$-0.153455\pi$
$614$	10.9976	−	24.0815i	0.443829	−	0.971850i
$615$	−2.09166	−	1.34423i	−0.0843437	−	0.0542044i
$616$	0.366215	+	2.54708i	0.0147552	+	0.102625i
$617$	−4.30175	+	2.76457i	−0.173182	+	0.111297i	−0.624360	−	0.781137i	$-0.714640\pi$
$617$	−4.30175	+	2.76457i	−0.173182	+	0.111297i	0.451178	+	0.892434i	$0.351004\pi$
$618$	−0.421803	−	0.486787i	−0.0169674	−	0.0195814i
$619$	19.0453	−	5.59220i	0.765495	−	0.224770i	0.124401	−	0.992232i	$-0.460299\pi$
$619$	19.0453	−	5.59220i	0.765495	−	0.224770i	0.641094	+	0.767462i	$0.278481\pi$
$620$	2.62327			0.105353
$621$	8.89814	−	25.5247i	0.357070	−	1.02427i
$622$	0.857519			0.0343834
$623$	1.00119	−	0.293977i	0.0401120	−	0.0117779i
$624$	−2.06864	−	2.38734i	−0.0828119	−	0.0955700i
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$	−1.84294	−	12.8179i	−0.0736586	−	0.512307i
$627$	24.4227	+	15.6955i	0.975350	+	0.626819i
$628$	6.01989	−	13.1817i	0.240220	−	0.526008i
$629$	−2.34978	+	2.71179i	−0.0936917	+	0.108126i
$630$	−0.161093	+	1.12043i	−0.00641811	+	0.0446390i
$631$	7.15925	+	15.6766i	0.285005	+	0.624074i	0.996940	−	0.0781713i	$-0.0249081\pi$
$631$	7.15925	+	15.6766i	0.285005	+	0.624074i	−0.711935	+	0.702246i	$0.752181\pi$
$632$	−10.9768	−	3.22308i	−0.436634	−	0.128207i
$633$	18.8693	+	5.54054i	0.749989	+	0.220217i
$634$	−13.1356	−	28.7630i	−0.521682	−	1.14232i
$635$	0.356880	−	2.48215i	0.0141623	−	0.0985013i
$636$	0.523607	−	0.604275i	0.0207624	−	0.0239611i
$637$	−5.95485	+	13.0393i	−0.235940	+	0.516636i
$638$	−23.6027	−	15.1685i	−0.934441	−	0.600529i
$639$	2.42290	+	16.8517i	0.0958485	+	0.666641i
$640$	−0.841254	+	0.540641i	−0.0332535	+	0.0213707i
$641$	19.8264	+	22.8809i	0.783096	+	0.903741i	0.997329	−	0.0730419i	$-0.0232707\pi$
$641$	19.8264	+	22.8809i	0.783096	+	0.903741i	−0.214233	+	0.976783i	$0.568725\pi$
$642$	6.27344	−	1.84205i	0.247593	−	0.0726999i
$643$	−2.96160			−0.116794			−0.0583971	−	0.998293i	$-0.518599\pi$
$643$	−2.96160			−0.116794			−0.0583971	+	0.998293i	$0.518599\pi$
$644$	3.28600	+	3.14725i	0.129487	+	0.124019i
$645$	−6.83090			−0.268966
$646$	7.38523	−	2.16850i	0.290568	−	0.0853185i
$647$	−12.6003	−	14.5415i	−0.495370	−	0.571687i	0.451923	−	0.892057i	$-0.350738\pi$
$647$	−12.6003	−	14.5415i	−0.495370	−	0.571687i	−0.947293	+	0.320370i	$0.896193\pi$
$648$	3.36269	−	2.16107i	0.132099	−	0.0848949i
$649$	0.479079	+	3.33207i	0.0188055	+	0.130795i
$650$	−1.97695	−	1.27051i	−0.0775423	−	0.0498334i
$651$	1.38978	−	3.04319i	0.0544697	−	0.119272i
$652$	−6.10612	+	7.04684i	−0.239134	+	0.275975i
$653$	1.12153	−	7.80045i	0.0438890	−	0.305255i	−0.956039	−	0.293240i	$-0.905266\pi$
$653$	1.12153	−	7.80045i	0.0438890	−	0.305255i	0.999928	−	0.0120148i	$-0.00382451\pi$
$654$	−3.97307	−	8.69981i	−0.155359	−	0.340189i
$655$	−9.71575	−	2.85280i	−0.379626	−	0.111468i
$656$	1.77475	+	0.521114i	0.0692924	+	0.0203461i
$657$	1.61325	+	3.53252i	0.0629389	+	0.137817i
$658$	−0.239366	+	1.66482i	−0.00933144	+	0.0649016i
$659$	8.73231	−	10.0776i	0.340163	−	0.392569i	−0.559734	−	0.828673i	$-0.689097\pi$
$659$	8.73231	−	10.0776i	0.340163	−	0.392569i	0.899896	+	0.436104i	$0.143642\pi$
$660$	1.51455	−	3.31640i	0.0589537	−	0.129091i
$661$	−14.5309	−	9.33841i	−0.565185	−	0.363222i	0.226632	−	0.973980i	$-0.427228\pi$
$661$	−14.5309	−	9.33841i	−0.565185	−	0.363222i	−0.791817	+	0.610758i	$0.790865\pi$
$662$	1.76125	+	12.2498i	0.0684530	+	0.476101i
$663$	2.56873	−	1.65082i	0.0997613	−	0.0641127i
$664$	−9.90644	−	11.4326i	−0.384445	−	0.443673i
$665$	−7.24871	+	2.12841i	−0.281093	+	0.0825363i
$666$	4.42890			0.171617
$667$	−49.3954	+	4.60528i	−1.91260	+	0.178317i
$668$	18.9407			0.732838
$669$	20.1347	−	5.91209i	0.778454	−	0.228575i
$670$	1.25425	+	1.44748i	0.0484559	+	0.0559211i
$671$	−27.7421	+	17.8288i	−1.07097	+	0.688273i
$672$	0.181497	+	1.26234i	0.00700142	+	0.0486959i
$673$	−28.0410	−	18.0208i	−1.08090	−	0.694652i	−0.126135	−	0.992013i	$-0.540257\pi$
$673$	−28.0410	−	18.0208i	−1.08090	−	0.694652i	−0.954765	+	0.297361i	$0.903894\pi$
$674$	−9.83086	+	21.5266i	−0.378670	+	0.829173i
$675$	3.69106	−	4.25971i	0.142069	−	0.163956i
$676$	1.06416	−	7.40138i	0.0409292	−	0.284669i
$677$	2.87675	+	6.29920i	0.110562	+	0.242098i	0.956823	−	0.290671i	$-0.0938786\pi$
$677$	2.87675	+	6.29920i	0.110562	+	0.242098i	−0.846261	+	0.532769i	$0.821151\pi$
$678$	12.7594	+	3.74649i	0.490021	+	0.143883i
$679$	0.698830	+	0.205195i	0.0268186	+	0.00787466i
$680$	−0.401549	−	0.879269i	−0.0153987	−	0.0337184i
$681$	1.19324	−	8.29914i	0.0457249	−	0.318024i
$682$	4.65935	−	5.37717i	0.178416	−	0.205903i
$683$	−4.12430	+	9.03096i	−0.157812	+	0.345560i	−0.971978	−	0.235072i	$-0.924467\pi$
$683$	−4.12430	+	9.03096i	−0.157812	+	0.345560i	0.814166	+	0.580632i	$0.197195\pi$
$684$	−7.99223	−	5.13629i	−0.305591	−	0.196391i
$685$	2.56521	+	17.8414i	0.0980116	+	0.681686i
$686$	10.4555	−	6.71937i	0.399194	−	0.256547i
$687$	−8.63369	−	9.96381i	−0.329396	−	0.380143i
$688$	4.87587	−	1.43168i	0.185891	−	0.0545825i
$689$	−1.39784			−0.0532534
$690$	−1.50584	−	6.26828i	−0.0573263	−	0.238629i
$691$	−27.7379			−1.05520			−0.527599	−	0.849494i	$-0.676908\pi$
$691$	−27.7379			−1.05520			−0.527599	+	0.849494i	$0.676908\pi$
$692$	−13.1452	+	3.85978i	−0.499706	+	0.146727i
$693$	2.01053	+	2.32027i	0.0763736	+	0.0881398i
$694$	30.2992	−	19.4721i	1.15014	−	0.739152i
$695$	−0.469327	−	3.26424i	−0.0178026	−	0.123820i
$696$	−11.6976	−	7.51759i	−0.443396	−	0.284953i
$697$	−0.742735	+	1.62636i	−0.0281331	+	0.0616029i
$698$	−17.9968	+	20.7694i	−0.681189	+	0.786134i
$699$	0.257918	−	1.79386i	0.00975534	−	0.0678499i
$700$	0.394126	+	0.863015i	0.0148966	+	0.0326189i
$701$	0.904891	+	0.265700i	0.0341773	+	0.0100354i	0.298777	−	0.954323i	$-0.403421\pi$
$701$	0.904891	+	0.265700i	0.0341773	+	0.0100354i	−0.264599	+	0.964358i	$0.585240\pi$
$702$	−12.7090	−	3.73171i	−0.479671	−	0.140844i
$703$	12.2792	+	26.8877i	0.463118	+	1.01409i
$704$	−0.385997	+	2.68467i	−0.0145478	+	0.101182i
$705$	1.56054	−	1.80096i	0.0587734	−	0.0678282i
$706$	13.4338	−	29.4159i	0.505587	−	1.10708i
$707$	0.434724	+	0.279380i	0.0163495	+	0.0105072i
$708$	0.237433	+	1.65138i	0.00892328	+	0.0620628i
$709$	−34.6129	+	22.2444i	−1.29992	+	0.835406i	−0.993203	−	0.116396i	$-0.962866\pi$
$709$	−34.6129	+	22.2444i	−1.29992	+	0.835406i	−0.306714	+	0.951802i	$0.599229\pi$
$710$	9.34458	+	10.7842i	0.350696	+	0.404724i
$711$	−13.0964	+	3.84544i	−0.491152	+	0.144215i
$712$	1.09983			0.0412177
$713$	0.626707	−	12.5651i	0.0234704	−	0.470568i
$714$	−1.23275			−0.0461347
$715$	−6.11566	+	1.79572i	−0.228713	+	0.0671561i
$716$	−5.14698	−	5.93993i	−0.192351	−	0.221985i
$717$	22.1218	−	14.2168i	0.826154	−	0.530937i
$718$	1.16361	+	8.09311i	0.0434257	+	0.302032i
$719$	19.5253	+	12.5481i	0.728171	+	0.467967i	0.851470	−	0.524403i	$-0.175711\pi$
$719$	19.5253	+	12.5481i	0.728171	+	0.467967i	−0.123300	+	0.992369i	$0.539348\pi$
$720$	−0.495629	+	1.08528i	−0.0184710	+	0.0404459i
$721$	0.297711	−	0.343577i	0.0110873	−	0.0127955i
$722$	6.31968	−	43.9543i	0.235194	−	1.63581i
$723$	16.2388	+	35.5580i	0.603927	+	1.32242i
$724$	12.0207	+	3.52959i	0.446745	+	0.131176i
$725$	−9.92530	−	2.91433i	−0.368616	−	0.108236i
$726$	2.03459	+	4.45514i	0.0755109	+	0.165346i
$727$	−1.00575	+	6.99513i	−0.0373011	+	0.259435i	−0.999935	−	0.0113699i	$-0.996381\pi$
$727$	−1.00575	+	6.99513i	−0.0373011	+	0.259435i	0.962634	+	0.270805i	$0.0872899\pi$
$728$	1.46006	−	1.68500i	0.0541133	−	0.0624501i
$729$	11.4234	−	25.0137i	0.423087	−	0.926432i
$730$	2.73824	+	1.75976i	0.101347	+	0.0651316i
$731$	0.699063	+	4.86209i	0.0258558	+	0.179831i
$732$	−13.7491	+	8.83601i	−0.508181	+	0.326588i
$733$	−15.9594	−	18.4181i	−0.589472	−	0.680287i	0.380141	−	0.924928i	$-0.375875\pi$
$733$	−15.9594	−	18.4181i	−0.589472	−	0.680287i	−0.969614	+	0.244641i	$0.921330\pi$
$734$	−14.8186	+	4.35114i	−0.546965	+	0.160603i
$735$	−8.19952			−0.302444
$736$	2.38863	+	4.15866i	0.0880459	+	0.153290i
$737$	5.19480			0.191353
$738$	2.11745	−	0.621738i	0.0779442	−	0.0228865i
$739$	−14.8364	−	17.1222i	−0.545767	−	0.629849i	0.414124	−	0.910220i	$-0.364088\pi$
$739$	−14.8364	−	17.1222i	−0.545767	−	0.629849i	−0.959892	+	0.280371i	$0.909542\pi$
$740$	3.12283	−	2.00692i	0.114797	−	0.0737759i
$741$	−3.57975	−	24.8977i	−0.131505	−	0.914639i
$742$	0.474754	+	0.305106i	0.0174288	+	0.0112008i
$743$	17.5984	−	38.5351i	0.645623	−	1.41372i	−0.249711	−	0.968320i	$-0.580336\pi$
$743$	17.5984	−	38.5351i	0.645623	−	1.41372i	0.895334	−	0.445396i	$-0.146937\pi$
$744$	2.30919	−	2.66495i	0.0846590	−	0.0977017i
$745$	−2.13705	+	14.8635i	−0.0782956	+	0.544558i
$746$	4.83593	+	10.5892i	0.177056	+	0.387699i
$747$	−17.3175	−	5.08488i	−0.633615	−	0.186046i
$748$	−2.51554	−	0.738629i	−0.0919773	−	0.0270070i
$749$	1.91704	+	4.19773i	0.0700471	+	0.153382i
$750$	0.191301	−	1.33053i	0.00698534	−	0.0485841i
$751$	−4.39128	+	5.06781i	−0.160240	+	0.184927i	−0.830192	−	0.557477i	$-0.811769\pi$
$751$	−4.39128	+	5.06781i	−0.160240	+	0.184927i	0.669952	+	0.742405i	$0.266315\pi$
$752$	−0.736447	+	1.61259i	−0.0268554	+	0.0588052i
$753$	21.9665	+	14.1170i	0.800506	+	0.514454i
$754$	3.45955	+	24.0617i	0.125990	+	0.876277i
$755$	14.5701	−	9.36366i	0.530262	−	0.340778i
$756$	3.50190	+	4.04141i	0.127363	+	0.146985i
$757$	20.9972	−	6.16533i	0.763156	−	0.224083i	0.123082	−	0.992396i	$-0.460722\pi$
$757$	20.9972	−	6.16533i	0.763156	−	0.224083i	0.640073	+	0.768314i	$0.278904\pi$
$758$	−10.2900			−0.373748
$759$	−15.5233	−	8.04680i	−0.563461	−	0.292080i
$760$	−7.96281			−0.288841
$761$	−3.79905	+	1.11550i	−0.137715	+	0.0404369i	−0.349864	−	0.936801i	$-0.613772\pi$
$761$	−3.79905	+	1.11550i	−0.137715	+	0.0404369i	0.212148	+	0.977237i	$0.431954\pi$
$762$	−2.20744	−	2.54752i	−0.0799671	−	0.0922869i
$763$	5.67879	−	3.64954i	0.205586	−	0.132122i
$764$	2.37166	+	16.4953i	0.0858037	+	0.596778i
$765$	−0.970192	−	0.623505i	−0.0350774	−	0.0225429i
$766$	11.9237	−	26.1093i	0.430822	−	0.943368i
$767$	1.91003	−	2.20429i	0.0689673	−	0.0795925i
$768$	−0.191301	+	1.33053i	−0.00690299	+	0.0480114i
$769$	2.40214	+	5.25996i	0.0866235	+	0.189679i	0.947986	−	0.318312i	$-0.103116\pi$
$769$	2.40214	+	5.25996i	0.0866235	+	0.189679i	−0.861363	+	0.507990i	$0.830389\pi$
$770$	2.46904	+	0.724975i	0.0889779	+	0.0261263i
$771$	−9.92358	−	2.91382i	−0.357389	−	0.104939i
$772$	9.59857	+	21.0179i	0.345460	+	0.756452i
$773$	0.756702	−	5.26298i	0.0272167	−	0.189296i	−0.971678	−	0.236311i	$-0.924062\pi$
$773$	0.756702	−	5.26298i	0.0272167	−	0.189296i	0.998894	+	0.0470146i	$0.0149707\pi$
$774$	3.97040	−	4.58209i	0.142713	−	0.164700i
$775$	1.08975	−	2.38621i	0.0391448	−	0.0857152i
$776$	0.645809	+	0.415036i	0.0231832	+	0.0148989i
$777$	−0.673739	−	4.68596i	−0.0241703	−	0.168108i
$778$	28.5537	−	18.3504i	1.02370	−	0.657893i
$779$	9.64519	+	11.1311i	0.345575	+	0.398814i
$780$	−3.03094	+	0.889965i	−0.108525	+	0.0318659i
$781$	38.7029			1.38490
$782$	−4.30752	+	1.71331i	−0.154037	+	0.0612678i
$783$	−58.3048			−2.08364
$784$	5.85278	−	1.71853i	0.209028	−	0.0613761i
$785$	−9.48976	−	10.9518i	−0.338704	−	0.390885i
$786$	−11.4506	+	7.35887i	−0.408430	+	0.262482i
$787$	5.45323	+	37.9281i	0.194387	+	1.35199i	0.820227	+	0.572038i	$0.193847\pi$
$787$	5.45323	+	37.9281i	0.194387	+	1.35199i	−0.625840	+	0.779951i	$0.715244\pi$
$788$	11.2530	+	7.23185i	0.400871	+	0.257624i
$789$	−8.89925	+	19.4866i	−0.316822	+	0.693742i
$790$	−7.49174	+	8.64593i	−0.266544	+	0.307608i
$791$	−1.33574	+	9.29029i	−0.0474935	+	0.330325i
$792$	1.34428	+	2.94357i	0.0477670	+	0.104595i
$793$	27.4151	+	8.04979i	0.973538	+	0.285857i
$794$	−35.8721	−	10.5330i	−1.27305	−	0.373802i
$795$	−0.332153	−	0.727315i	−0.0117803	−	0.0257952i
$796$	2.46483	−	17.1432i	0.0873634	−	0.607626i
$797$	−22.3134	+	25.7511i	−0.790382	+	0.912149i	−0.997813	−	0.0661004i	$-0.978944\pi$
$797$	−22.3134	+	25.7511i	−0.790382	+	0.912149i	0.207431	+	0.978250i	$0.433490\pi$
$798$	−4.21860	+	9.23745i	−0.149337	+	0.327002i
$799$	−1.44159	−	0.926454i	−0.0509998	−	0.0327756i
$800$	0.142315	+	0.989821i	0.00503159	+	0.0349955i
$801$	1.10389	−	0.709427i	0.0390040	−	0.0250664i
$802$	−0.234877	−	0.271063i	−0.00829380	−	0.00957156i
$803$	8.47071	−	2.48722i	0.298925	−	0.0877722i
$804$	2.57456			0.0907977
$805$	4.22789	−	1.68164i	0.149014	−	0.0592699i
$806$	−6.16469			−0.217142
$807$	32.1572	−	9.44220i	1.13199	−	0.332381i
$808$	0.356683	+	0.411635i	0.0125481	+	0.0144813i
$809$	3.93833	−	2.53101i	0.138464	−	0.0889857i	−0.469575	−	0.882893i	$-0.655593\pi$
$809$	3.93833	−	2.53101i	0.138464	−	0.0889857i	0.608039	+	0.793907i	$0.291956\pi$
$810$	−0.568867	−	3.95656i	−0.0199879	−	0.139019i
$811$	−18.2153	−	11.7063i	−0.639625	−	0.411062i	0.180237	−	0.983623i	$-0.442314\pi$
$811$	−18.2153	−	11.7063i	−0.639625	−	0.411062i	−0.819862	+	0.572561i	$0.805950\pi$
$812$	4.07696	−	8.92730i	0.143073	−	0.313287i
$813$	3.60047	−	4.15517i	0.126274	−	0.145728i
$814$	1.43286	−	9.96578i	0.0502218	−	0.349301i
$815$	3.87345	+	8.48168i	0.135681	+	0.297100i
$816$	−1.24671	−	0.366067i	−0.0436436	−	0.0128149i
$817$	38.8256	+	11.4002i	1.35834	+	0.398844i
$818$	−10.0682	−	22.0463i	−0.352027	−	0.770832i
$819$	0.378570	−	2.63301i	0.0132283	−	0.0920048i
$820$	1.21128	−	1.39789i	0.0422997	−	0.0488165i
$821$	−7.01500	+	15.3607i	−0.244825	+	0.536092i	−0.991655	−	0.128923i	$-0.958848\pi$
$821$	−7.01500	+	15.3607i	−0.244825	+	0.536092i	0.746829	+	0.665016i	$0.231575\pi$
$822$	20.3830	+	13.0993i	0.710937	+	0.456892i
$823$	−3.47898	−	24.1968i	−0.121270	−	0.843448i	−0.956121	−	0.292973i	$-0.905356\pi$
$823$	−3.47898	−	24.1968i	−0.121270	−	0.843448i	0.834851	−	0.550476i	$-0.185554\pi$
$824$	0.403107	−	0.259061i	0.0140429	−	0.00902481i
$825$	−2.38754	−	2.75536i	−0.0831234	−	0.0959295i
$826$	−1.12984	+	0.331752i	−0.0393122	+	0.0115431i
$827$	33.2499			1.15621			0.578106	−	0.815961i	$-0.303792\pi$
$827$	33.2499			1.15621			0.578106	+	0.815961i	$0.303792\pi$
$828$	5.07994	+	2.63328i	0.176540	+	0.0915128i
$829$	31.6911			1.10068			0.550338	−	0.834942i	$-0.314499\pi$
$829$	31.6911			1.10068			0.550338	+	0.834942i	$0.314499\pi$
$830$	−14.5148	+	4.26193i	−0.503816	+	0.147934i
$831$	−22.7769	−	26.2859i	−0.790121	−	0.911848i
$832$	1.97695	−	1.27051i	0.0685383	−	0.0440469i
$833$	0.839125	+	5.83625i	0.0290740	+	0.202214i
$834$	−3.72923	−	2.39663i	−0.129133	−	0.0829886i
$835$	7.86826	−	17.2291i	0.272292	−	0.596237i
$836$	−14.1432	+	16.3222i	−0.489154	+	0.564514i
$837$	2.10424	−	14.6353i	0.0727332	−	0.505871i
$838$	1.38634	+	3.03566i	0.0478903	+	0.104865i
$839$	−9.23454	−	2.71151i	−0.318812	−	0.0936116i	0.118411	−	0.992965i	$-0.462220\pi$
$839$	−9.23454	−	2.71151i	−0.318812	−	0.0936116i	−0.437223	+	0.899353i	$0.644038\pi$
$840$	1.22366	+	0.359300i	0.0422204	+	0.0123970i
$841$	32.4044	+	70.9558i	1.11739	+	2.44675i
$842$	2.14046	−	14.8872i	0.0737650	−	0.513047i
$843$	−17.3654	+	20.0407i	−0.598096	+	0.690240i
$844$	−6.07756	+	13.3080i	−0.209198	+	0.458081i
$845$	−6.29047	−	4.04264i	−0.216399	−	0.139071i
$846$	0.301012	+	2.09359i	0.0103490	+	0.0719790i
$847$	−2.90809	+	1.86891i	−0.0999230	+	0.0642166i
$848$	0.389527	+	0.449538i	0.0133764	+	0.0154372i
$849$	24.6837	−	7.24780i	0.847143	−	0.248744i
$850$	−0.966621			−0.0331548
$851$	−8.86685	−	15.4374i	−0.303952	−	0.529188i
$852$	19.1813			0.657141
$853$	11.4990	−	3.37640i	0.393717	−	0.115606i	−0.0788804	−	0.996884i	$-0.525135\pi$
$853$	11.4990	−	3.37640i	0.393717	−	0.115606i	0.472598	+	0.881278i	$0.343316\pi$
$854$	−7.55407	−	8.71786i	−0.258495	−	0.298319i
$855$	−7.99223	+	5.13629i	−0.273329	+	0.175658i
$856$	0.692224	+	4.81452i	0.0236597	+	0.164557i
$857$	10.6910	+	6.87068i	0.365197	+	0.234698i	0.710350	−	0.703849i	$-0.248537\pi$
$857$	10.6910	+	6.87068i	0.365197	+	0.234698i	−0.345153	+	0.938546i	$0.612173\pi$
$858$	−3.55919	+	7.79354i	−0.121509	+	0.266067i
$859$	−13.0520	+	15.0628i	−0.445328	+	0.513935i	−0.933385	−	0.358876i	$-0.883160\pi$
$859$	−13.0520	+	15.0628i	−0.445328	+	0.513935i	0.488058	+	0.872811i	$0.337706\pi$
$860$	0.723204	−	5.02999i	0.0246610	−	0.171521i
$861$	−0.979937	−	2.14576i	−0.0333961	−	0.0731274i
$862$	23.8746	+	7.01020i	0.813171	+	0.238769i
$863$	−32.1818	−	9.44944i	−1.09548	−	0.321663i	−0.316426	−	0.948617i	$-0.602483\pi$
$863$	−32.1818	−	9.44944i	−1.09548	−	0.321663i	−0.779056	+	0.626954i	$0.784301\pi$
$864$	2.34145	+	5.12706i	0.0796577	+	0.174426i
$865$	−1.94974	+	13.5607i	−0.0662930	+	0.461078i
$866$	−17.5802	+	20.2887i	−0.597401	+	0.689437i
$867$	−8.97115	+	19.6441i	−0.304676	+	0.667148i
$868$	2.09374	+	1.34556i	0.0710661	+	0.0456714i
$869$	4.41588	+	30.7131i	0.149799	+	1.04187i
$870$	−11.6976	+	7.51759i	−0.396585	+	0.254870i
$871$	−2.94749	−	3.40158i	−0.0998719	−	0.115258i
$872$	6.82681	−	2.00453i	0.231185	−	0.0678821i
$873$	0.915908			0.0309988
$874$	−1.90234	+	38.1409i	−0.0643476	+	1.29013i
$875$	0.948752			0.0320737
$876$	4.19811	−	1.23268i	0.141841	−	0.0416483i
$877$	8.67982	+	10.0170i	0.293097	+	0.338252i	0.883131	−	0.469127i	$-0.155431\pi$
$877$	8.67982	+	10.0170i	0.293097	+	0.338252i	−0.590034	+	0.807378i	$0.700886\pi$
$878$	−4.59088	+	2.95038i	−0.154935	+	0.0995704i
$879$	3.41784	+	23.7716i	0.115281	+	0.801796i
$880$	2.28171	+	1.46637i	0.0769164	+	0.0494312i
$881$	15.4456	−	33.8211i	0.520375	−	1.13946i	−0.448923	−	0.893571i	$-0.648192\pi$
$881$	15.4456	−	33.8211i	0.520375	−	1.13946i	0.969297	−	0.245891i	$-0.0790805\pi$
$882$	4.76589	−	5.50014i	0.160476	−	0.185199i
$883$	5.19401	−	36.1252i	0.174792	−	1.21571i	−0.693795	−	0.720172i	$-0.744063\pi$
$883$	5.19401	−	36.1252i	0.174792	−	1.21571i	0.868588	−	0.495536i	$-0.165028\pi$
$884$	0.943640	+	2.06628i	0.0317381	+	0.0694967i
$885$	1.60078	+	0.470033i	0.0538098	+	0.0158000i
$886$	9.34557	+	2.74411i	0.313971	+	0.0921901i
$887$	−13.3372	−	29.2043i	−0.447818	−	0.980584i	−0.990097	−	0.140386i	$-0.955166\pi$
$887$	−13.3372	−	29.2043i	−0.447818	−	0.980584i	0.542279	−	0.840198i	$-0.317562\pi$
$888$	0.710132	−	4.93908i	0.0238305	−	0.165745i
$889$	1.55802	−	1.79805i	0.0522544	−	0.0603048i
$890$	0.456884	−	1.00044i	0.0153148	−	0.0335347i
$891$	−9.12054	−	5.86142i	−0.305550	−	0.196365i
$892$	2.22171	+	15.4523i	0.0743882	+	0.517381i
$893$	−11.8755	+	7.63193i	−0.397399	+	0.255393i
$894$	13.2185	+	15.2550i	0.442093	+	0.510202i
$895$	−7.54128	+	2.21432i	−0.252077	+	0.0740165i
$896$	−0.948752			−0.0316956
$897$	3.53872	+	14.7305i	0.118154	+	0.491836i
$898$	−20.1352			−0.671919
$899$	−26.0367	+	7.64508i	−0.868374	+	0.254978i
$900$	0.781311	+	0.901681i	0.0260437	+	0.0300560i
$901$	−0.483695	+	0.310852i	−0.0161142	+	0.0103560i
$902$	−0.713969	−	4.96576i	−0.0237726	−	0.165342i
$903$	−5.45202	−	3.50380i	−0.181432	−	0.116599i
$904$	−4.10962	+	8.99882i	−0.136684	+	0.299296i
$905$	8.20420	−	9.46815i	0.272717	−	0.314732i
$906$	3.31325	−	23.0442i	0.110075	−	0.765592i
$907$	−6.70798	−	14.6884i	−0.222735	−	0.487721i	0.764967	−	0.644069i	$-0.222755\pi$
$907$	−6.70798	−	14.6884i	−0.222735	−	0.487721i	−0.987702	+	0.156348i	$0.950028\pi$
$908$	5.98481	+	1.75730i	0.198613	+	0.0583180i
$909$	0.623520	+	0.183082i	0.0206809	+	0.00607245i
$910$	−0.926196	−	2.02809i	−0.0307031	−	0.0672304i
$911$	2.58194	−	17.9578i	0.0855435	−	0.594968i	−0.901288	−	0.433219i	$-0.857378\pi$
$911$	2.58194	−	17.9578i	0.0855435	−	0.594968i	0.986832	−	0.161749i	$-0.0517134\pi$
$912$	−7.00943	+	8.08932i	−0.232106	+	0.267864i
$913$	−17.0445	+	37.3223i	−0.564091	+	1.23519i
$914$	−30.9742	−	19.9059i	−1.02453	−	0.658428i
$915$	2.32593	+	16.1772i	0.0768930	+	0.534803i
$916$	8.25101	−	5.30260i	0.272621	−	0.175203i
$917$	−6.29123	−	7.26047i	−0.207755	−	0.239762i
$918$	−5.22757	+	1.53495i	−0.172536	+	0.0506610i
$919$	−3.38889			−0.111789			−0.0558945	−	0.998437i	$-0.517801\pi$
$919$	−3.38889			−0.111789			−0.0558945	+	0.998437i	$0.517801\pi$
$920$	4.77512	−	0.445199i	0.157431	−	0.0146778i
$921$	−35.5865			−1.17262
$922$	15.8573	−	4.65611i	0.522231	−	0.153341i
$923$	−21.9598	−	25.3429i	−0.722815	−	0.834173i
$924$	2.90992	−	1.87009i	0.0957292	−	0.0615214i
$925$	−0.528289	−	3.67433i	−0.0173700	−	0.120811i
$926$	0.938712	+	0.603274i	0.0308480	+	0.0198248i
$927$	0.237493	−	0.520036i	0.00780028	−	0.0170802i
$928$	6.77409	−	7.81771i	0.222370	−	0.256629i
$929$	4.64983	−	32.3403i	0.152556	−	1.06105i	−0.759360	−	0.650671i	$-0.774488\pi$
$929$	4.64983	−	32.3403i	0.152556	−	1.06105i	0.911915	−	0.410378i	$-0.134603\pi$
$930$	−1.46485	−	3.20757i	−0.0480343	−	0.105180i
$931$	46.6046	+	13.6843i	1.52740	+	0.448486i
$932$	1.29362	+	0.379840i	0.0423738	+	0.0124421i
$933$	−0.478843	−	1.04852i	−0.0156766	−	0.0343270i
$934$	−1.68149	+	11.6950i	−0.0550200	+	0.382672i
$935$	−1.71687	+	1.98138i	−0.0561478	+	0.0647980i
$936$	1.16473	−	2.55040i	0.0380704	−	0.0833625i
$937$	−22.6138	−	14.5330i	−0.738759	−	0.474772i	0.116358	−	0.993207i	$-0.462878\pi$
$937$	−22.6138	−	14.5330i	−0.738759	−	0.474772i	−0.855117	+	0.518436i	$0.826515\pi$
$938$	0.258606	+	1.79864i	0.00844377	+	0.0587277i
$939$	−14.6438	+	9.41103i	−0.477884	+	0.307117i
$940$	1.16094	+	1.33979i	0.0378655	+	0.0436992i
$941$	−47.5240	+	13.9543i	−1.54924	+	0.454898i	−0.940873	−	0.338759i	$-0.889993\pi$
$941$	−47.5240	+	13.9543i	−1.54924	+	0.454898i	−0.608366	+	0.793657i	$0.708175\pi$
$942$	−19.4793			−0.634671
$943$	−6.40635	−	6.13584i	−0.208619	−	0.199811i
$944$	−1.24115			−0.0403959
$945$	5.13094	−	1.50658i	0.166909	−	0.0490090i
$946$	−9.02594	−	10.4165i	−0.293459	−	0.338669i
$947$	25.1217	−	16.1447i	0.816346	−	0.524634i	−0.0645661	−	0.997913i	$-0.520566\pi$
$947$	25.1217	−	16.1447i	0.816346	−	0.524634i	0.880912	+	0.473280i	$0.156930\pi$
$948$	2.18853	+	15.2215i	0.0710800	+	0.494372i
$949$	−6.43487	−	4.13544i	−0.208885	−	0.134242i
$950$	−3.30787	+	7.24322i	−0.107321	+	0.235001i
$951$	−27.8346	+	32.1228i	−0.902599	+	1.04165i
$952$	0.130515	−	0.907748i	0.00423000	−	0.0294203i
$953$	8.31715	+	18.2120i	0.269419	+	0.589945i	0.995187	−	0.0979942i	$-0.0312427\pi$
$953$	8.31715	+	18.2120i	0.269419	+	0.589945i	−0.725768	+	0.687940i	$0.758515\pi$
$954$	0.680935	+	0.199941i	0.0220461	+	0.00647331i
$955$	15.9899	+	4.69504i	0.517419	+	0.151928i
$956$	8.12658	+	17.7947i	0.262833	+	0.575523i
$957$	−5.36727	+	37.3302i	−0.173499	+	1.20671i
$958$	16.9264	−	19.5341i	0.546867	−	0.631118i
$959$	−7.10407	+	15.5557i	−0.229402	+	0.502321i
$960$	1.13082	+	0.726736i	0.0364972	+	0.0234553i
$961$	3.43241	+	23.8730i	0.110723	+	0.770096i
$962$	−7.33865	+	4.71627i	−0.236608	+	0.152059i
$963$	3.80032	+	4.38580i	0.122464	+	0.141331i
$964$	−27.9027	+	8.19296i	−0.898684	+	0.263878i
$965$	23.1060			0.743808
$966$	2.01334	−	5.77536i	0.0647782	−	0.185819i
$967$	11.9160			0.383194			0.191597	−	0.981474i	$-0.438633\pi$
$967$	11.9160			0.383194			0.191597	+	0.981474i	$0.438633\pi$
$968$	−3.49599	+	1.02651i	−0.112365	+	0.0329934i
$969$	−6.77546	−	7.81930i	−0.217659	−	0.251192i
$970$	0.645809	−	0.415036i	0.0207357	−	0.0133260i
$971$	−1.73092	−	12.0388i	−0.0555478	−	0.386344i	−0.998563	−	0.0535935i	$-0.982932\pi$
$971$	−1.73092	−	12.0388i	−0.0555478	−	0.386344i	0.943015	−	0.332750i	$-0.107977\pi$
$972$	9.70477	+	6.23688i	0.311281	+	0.200048i
$973$	1.29975	−	2.84605i	0.0416681	−	0.0912403i
$974$	4.38906	−	5.06525i	0.140635	−	0.162301i
$975$	−0.449558	+	3.12675i	−0.0143974	+	0.100136i
$976$	−5.05082	−	11.0597i	−0.161673	−	0.354014i
$977$	36.8633	+	10.8241i	1.17936	+	0.346292i	0.811928	−	0.583757i	$-0.198418\pi$
$977$	36.8633	+	10.8241i	1.17936	+	0.346292i	0.367434	+	0.930049i	$0.380236\pi$
$978$	12.0261	+	3.53119i	0.384553	+	0.112915i
$979$	−1.23919	−	2.71346i	−0.0396048	−	0.0867225i
$980$	0.868102	−	6.03778i	0.0277305	−	0.192870i
$981$	5.55904	−	6.41548i	0.177487	−	0.204830i
$982$	−13.7248	+	30.0531i	−0.437976	+	0.959035i
$983$	7.96442	+	5.11842i	0.254025	+	0.163252i	0.661456	−	0.749984i	$-0.269939\pi$
$983$	7.96442	+	5.11842i	0.254025	+	0.163252i	−0.407431	+	0.913236i	$0.633575\pi$
$984$	−0.353845	−	2.46105i	−0.0112802	−	0.0784553i
$985$	11.2530	−	7.23185i	0.358550	−	0.230426i
$986$	6.54797	+	7.55676i	0.208530	+	0.240656i
$987$	2.16931	−	0.636966i	0.0690498	−	0.0202749i
$988$	18.7126			0.595328
$989$	−23.9203	−	4.66574i	−0.760620	−	0.148362i
$990$	3.23600			0.102847
$991$	−39.2366	+	11.5209i	−1.24639	+	0.365974i	−0.837413	−	0.546570i	$-0.815933\pi$
$991$	−39.2366	+	11.5209i	−1.24639	+	0.365974i	−0.408979	+	0.912544i	$0.634115\pi$
$992$	1.71788	+	1.98253i	0.0545426	+	0.0629455i
$993$	13.9948	−	8.99390i	0.444111	−	0.285413i
$994$	1.92670	+	13.4005i	0.0611111	+	0.425037i
$995$	−14.5701	−	9.36364i	−0.461904	−	0.296847i
$996$	−8.44732	+	18.4970i	−0.267663	+	0.586101i
$997$	35.4903	−	40.9580i	1.12399	−	1.29715i	0.174044	−	0.984738i	$-0.444316\pi$
$997$	35.4903	−	40.9580i	1.12399	−	1.29715i	0.949946	−	0.312416i	$-0.101138\pi$
$998$	−4.11831	+	28.6435i	−0.130363	+	0.906694i
$999$	−8.69172	−	19.0322i	−0.274994	−	0.602153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.g.b.101.1	yes	20
23.8	even	11		5290.2.a.bj.1.6		10
23.15	odd	22		5290.2.a.bi.1.6		10
23.18	even	11	inner	230.2.g.b.41.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.b.41.1	✓	20	23.18	even	11	inner
230.2.g.b.101.1	yes	20	1.1	even	1	trivial
5290.2.a.bi.1.6		10	23.15	odd	22
5290.2.a.bj.1.6		10	23.8	even	11

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 - 0.281733i) q^{2} +(-0.880272 - 1.01589i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-1.13082 - 0.726736i) q^{6} +(0.394126 - 0.863015i) q^{7} +(0.654861 - 0.755750i) q^{8} +(0.169795 - 1.18095i) q^{9} +O(q^{10})\)	\(q+(0.959493 - 0.281733i) q^{2} +(-0.880272 - 1.01589i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-1.13082 - 0.726736i) q^{6} +(0.394126 - 0.863015i) q^{7} +(0.654861 - 0.755750i) q^{8} +(0.169795 - 1.18095i) q^{9} +(-0.415415 - 0.909632i) q^{10} +(-2.60241 - 0.764136i) q^{11} +(-1.28976 - 0.378708i) q^{12} +(0.976226 + 2.13764i) q^{13} +(0.135021 - 0.939095i) q^{14} +(-0.880272 + 1.01589i) q^{15} +(0.415415 - 0.909632i) q^{16} +(0.813173 + 0.522595i) q^{17} +(-0.169795 - 1.18095i) q^{18} +(6.69874 - 4.30502i) q^{19} +(-0.654861 - 0.755750i) q^{20} +(-1.22366 + 0.359300i) q^{21} -2.71227 q^{22} +(-3.77640 + 2.95615i) q^{23} -1.34421 q^{24} +(-0.959493 + 0.281733i) q^{25} +(1.53892 + 1.77601i) q^{26} +(-4.74165 + 3.04727i) q^{27} +(-0.135021 - 0.939095i) q^{28} +(8.70219 + 5.59256i) q^{29} +(-0.558406 + 1.22274i) q^{30} +(-1.71788 + 1.98253i) q^{31} +(0.142315 - 0.989821i) q^{32} +(1.51455 + 3.31640i) q^{33} +(0.927466 + 0.272329i) q^{34} +(-0.910321 - 0.267294i) q^{35} +(-0.495629 - 1.08528i) q^{36} +(-0.528289 + 3.67433i) q^{37} +(5.21453 - 6.01789i) q^{38} +(1.31225 - 2.87344i) q^{39} +(-0.841254 - 0.540641i) q^{40} +(0.263236 + 1.83085i) q^{41} +(-1.07287 + 0.689492i) q^{42} +(3.32782 + 3.84050i) q^{43} +(-2.60241 + 0.764136i) q^{44} -1.19309 q^{45} +(-2.79058 + 3.90034i) q^{46} -1.77280 q^{47} +(-1.28976 + 0.378708i) q^{48} +(3.99457 + 4.60997i) q^{49} +(-0.841254 + 0.540641i) q^{50} +(-0.184916 - 1.28612i) q^{51} +(1.97695 + 1.27051i) q^{52} +(-0.247099 + 0.541071i) q^{53} +(-3.69106 + 4.25971i) q^{54} +(-0.385997 + 2.68467i) q^{55} +(-0.394126 - 0.863015i) q^{56} +(-10.2701 - 3.01558i) q^{57} +(9.92530 + 2.91433i) q^{58} +(-0.515591 - 1.12899i) q^{59} +(-0.191301 + 1.33053i) q^{60} +(7.96212 - 9.18877i) q^{61} +(-1.08975 + 2.38621i) q^{62} +(-0.952257 - 0.611979i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(1.97695 - 1.27051i) q^{65} +(2.38754 + 2.75536i) q^{66} +(-1.83771 + 0.539600i) q^{67} +0.966621 q^{68} +(6.32737 + 1.23418i) q^{69} -0.948752 q^{70} +(-13.6915 + 4.02020i) q^{71} +(-0.781311 - 0.901681i) q^{72} +(-2.73824 + 1.75976i) q^{73} +(0.528289 + 3.67433i) q^{74} +(1.13082 + 0.726736i) q^{75} +(3.30787 - 7.24322i) q^{76} +(-1.68514 + 1.94475i) q^{77} +(0.449558 - 3.12675i) q^{78} +(-4.75243 - 10.4064i) q^{79} +(-0.959493 - 0.281733i) q^{80} +(3.83532 + 1.12615i) q^{81} +(0.768383 + 1.68252i) q^{82} +(2.15288 - 14.9736i) q^{83} +(-0.835159 + 0.963825i) q^{84} +(0.401549 - 0.879269i) q^{85} +(4.27501 + 2.74738i) q^{86} +(-1.97888 - 13.7634i) q^{87} +(-2.28171 + 1.46637i) q^{88} +(0.720233 + 0.831193i) q^{89} +(-1.14477 + 0.336134i) q^{90} +2.22957 q^{91} +(-1.57869 + 4.52855i) q^{92} +3.52623 q^{93} +(-1.70099 + 0.499455i) q^{94} +(-5.21453 - 6.01789i) q^{95} +(-1.13082 + 0.726736i) q^{96} +(0.109251 + 0.759860i) q^{97} +(5.13154 + 3.29784i) q^{98} +(-1.34428 + 2.94357i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 + 8 * q^13 + 3 * q^14 - 3 * q^15 - 2 * q^16 + 8 * q^17 + 27 * q^18 - q^19 - 2 * q^20 - 31 * q^21 - 18 * q^22 - 9 * q^23 - 8 * q^24 - 2 * q^25 - 8 * q^26 - 18 * q^27 - 3 * q^28 + 20 * q^29 + 3 * q^30 - 17 * q^31 + 2 * q^32 + 17 * q^33 + 3 * q^34 - 3 * q^35 + 17 * q^36 + 6 * q^37 - 21 * q^38 - 75 * q^39 + 2 * q^40 - 2 * q^41 + 42 * q^42 - 18 * q^43 + 7 * q^44 + 28 * q^45 - 2 * q^46 + 42 * q^47 + 8 * q^48 - 19 * q^49 + 2 * q^50 + 26 * q^51 + 19 * q^52 + 19 * q^53 - 26 * q^54 - 15 * q^55 - 19 * q^56 + 7 * q^57 - 9 * q^58 + 25 * q^59 - 3 * q^60 - 49 * q^61 - 38 * q^62 - 87 * q^63 - 2 * q^64 + 19 * q^65 - 6 * q^66 + 19 * q^67 - 36 * q^68 + 36 * q^69 + 14 * q^70 + 7 * q^71 - 17 * q^72 - 10 * q^73 - 6 * q^74 - 3 * q^75 - q^76 - 29 * q^77 - 2 * q^78 - 33 * q^79 - 2 * q^80 + 72 * q^81 + 2 * q^82 - 41 * q^83 + 13 * q^84 - 14 * q^85 - 48 * q^86 - 16 * q^87 - 7 * q^88 + 55 * q^89 + 5 * q^90 + 13 * q^92 + 10 * q^93 + 13 * q^94 + 21 * q^95 + 3 * q^96 - 9 * q^97 + 41 * q^98 + 59 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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