LMFDB - Embedded newform 345.2.m.a.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [345,2,Mod(16,345)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(345, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("345.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.m (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:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.3
Character	$\chi$	$=$	345.31
Dual form			345.2.m.a.256.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.101148 - 0.703501i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(1.43430 + 0.421149i) q^{4} +(0.654861 + 0.755750i) q^{5} +(-0.681946 + 0.200237i) q^{6} +(-3.66580 - 2.35586i) q^{7} +(1.03186 - 2.25945i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.101148 - 0.703501i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(1.43430 + 0.421149i) q^{4} +(0.654861 + 0.755750i) q^{5} +(-0.681946 + 0.200237i) q^{6} +(-3.66580 - 2.35586i) q^{7} +(1.03186 - 2.25945i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(0.597909 - 0.384253i) q^{10} +(-0.657690 - 4.57433i) q^{11} +(-0.212740 - 1.47964i) q^{12} +(1.03496 - 0.665127i) q^{13} +(-2.02814 + 2.34060i) q^{14} +(0.415415 - 0.909632i) q^{15} +(1.02995 + 0.661907i) q^{16} +(4.83727 - 1.42035i) q^{17} +(0.465433 + 0.537138i) q^{18} +(2.46370 + 0.723408i) q^{19} +(0.620985 + 1.35977i) q^{20} +(-0.620143 + 4.31319i) q^{21} -3.28457 q^{22} +(1.09255 - 4.66973i) q^{23} -2.48392 q^{24} +(-0.142315 + 0.989821i) q^{25} +(-0.363234 - 0.795371i) q^{26} +(0.959493 + 0.281733i) q^{27} +(-4.26569 - 4.92287i) q^{28} +(-1.56489 + 0.459493i) q^{29} +(-0.597909 - 0.384253i) q^{30} +(-3.89122 + 8.52058i) q^{31} +(3.82307 - 4.41206i) q^{32} +(-3.88775 + 2.49850i) q^{33} +(-0.509938 - 3.54669i) q^{34} +(-0.620143 - 4.31319i) q^{35} +(-1.25755 + 0.808179i) q^{36} +(-5.06618 + 5.84668i) q^{37} +(0.758118 - 1.66005i) q^{38} +(-1.03496 - 0.665127i) q^{39} +(2.38330 - 0.699801i) q^{40} +(3.94217 + 4.54951i) q^{41} +(2.97161 + 0.872542i) q^{42} +(-0.578970 - 1.26777i) q^{43} +(0.983151 - 6.83796i) q^{44} -1.00000 q^{45} +(-3.17465 - 1.24095i) q^{46} -7.40920 q^{47} +(0.174236 - 1.21184i) q^{48} +(4.98006 + 10.9048i) q^{49} +(0.681946 + 0.200237i) q^{50} +(-3.30147 - 3.81010i) q^{51} +(1.76456 - 0.518122i) q^{52} +(3.96873 + 2.55055i) q^{53} +(0.295250 - 0.646508i) q^{54} +(3.02635 - 3.49260i) q^{55} +(-9.10554 + 5.85177i) q^{56} +(-0.365424 - 2.54158i) q^{57} +(0.164968 + 1.14738i) q^{58} +(7.21664 - 4.63785i) q^{59} +(0.978922 - 1.12974i) q^{60} +(-0.252306 + 0.552472i) q^{61} +(5.60065 + 3.59932i) q^{62} +(4.18103 - 1.22766i) q^{63} +(-1.11370 - 1.28528i) q^{64} +(1.18042 + 0.346604i) q^{65} +(1.36446 + 2.98775i) q^{66} +(-1.71325 + 11.9159i) q^{67} +7.53629 q^{68} +(-4.70159 + 0.946055i) q^{69} -3.09706 q^{70} +(-1.09362 + 7.60626i) q^{71} +(1.03186 + 2.25945i) q^{72} +(11.7467 + 3.44914i) q^{73} +(3.60071 + 4.15545i) q^{74} +(0.959493 - 0.281733i) q^{75} +(3.22903 + 2.07517i) q^{76} +(-8.36555 + 18.3180i) q^{77} +(-0.572602 + 0.660818i) q^{78} +(11.7822 - 7.57197i) q^{79} +(0.174236 + 1.21184i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(3.59933 - 2.31315i) q^{82} +(-1.66688 + 1.92368i) q^{83} +(-2.70597 + 5.92524i) q^{84} +(4.24117 + 2.72563i) q^{85} +(-0.950437 + 0.279074i) q^{86} +(1.06805 + 1.23259i) q^{87} +(-11.0141 - 3.23404i) q^{88} +(0.0938560 + 0.205516i) q^{89} +(-0.101148 + 0.703501i) q^{90} -5.36090 q^{91} +(3.53370 - 6.23767i) q^{92} +9.36706 q^{93} +(-0.749428 + 5.21239i) q^{94} +(1.06667 + 2.33567i) q^{95} +(-5.60151 - 1.64475i) q^{96} +(-11.0717 - 12.7774i) q^{97} +(8.17527 - 2.40048i) q^{98} +(3.88775 + 2.49850i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9} - 7 q^{11} - 2 q^{12} + 7 q^{13} - 47 q^{14} - 3 q^{15} + 26 q^{16} + 15 q^{17} - 7 q^{19} - 2 q^{20} - 12 q^{21} - 18 q^{22} + 12 q^{23} - 3 q^{25} - 18 q^{26} + 3 q^{27} + 2 q^{28} - 6 q^{29} + 22 q^{31} + 33 q^{32} - 4 q^{33} - 53 q^{34} - 12 q^{35} - 9 q^{36} - 23 q^{37} + 21 q^{38} - 7 q^{39} + 11 q^{40} + 26 q^{41} + 3 q^{42} - 19 q^{43} - 47 q^{44} - 30 q^{45} - 44 q^{46} + 14 q^{47} + 7 q^{48} + 2 q^{49} - 11 q^{50} - 15 q^{51} + 55 q^{52} - 14 q^{53} - 11 q^{54} - 4 q^{55} + 6 q^{56} - 26 q^{57} - 18 q^{58} + 40 q^{59} - 9 q^{60} + 37 q^{61} + 19 q^{62} - 10 q^{63} + 14 q^{64} + 4 q^{65} - 4 q^{66} - 108 q^{67} + 54 q^{68} + 21 q^{69} - 30 q^{70} + 39 q^{71} + 22 q^{72} + 57 q^{73} - 11 q^{74} + 3 q^{75} + 22 q^{76} + 2 q^{77} + 7 q^{78} + 55 q^{79} + 7 q^{80} - 3 q^{81} - 26 q^{82} - 79 q^{83} - 2 q^{84} + 18 q^{85} - 44 q^{86} - 5 q^{87} - 8 q^{88} - 30 q^{89} + 40 q^{91} + 35 q^{92} + 44 q^{93} - 29 q^{94} + 7 q^{95} + 22 q^{96} - 52 q^{97} + 28 q^{98} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9 - 7 * q^11 - 2 * q^12 + 7 * q^13 - 47 * q^14 - 3 * q^15 + 26 * q^16 + 15 * q^17 - 7 * q^19 - 2 * q^20 - 12 * q^21 - 18 * q^22 + 12 * q^23 - 3 * q^25 - 18 * q^26 + 3 * q^27 + 2 * q^28 - 6 * q^29 + 22 * q^31 + 33 * q^32 - 4 * q^33 - 53 * q^34 - 12 * q^35 - 9 * q^36 - 23 * q^37 + 21 * q^38 - 7 * q^39 + 11 * q^40 + 26 * q^41 + 3 * q^42 - 19 * q^43 - 47 * q^44 - 30 * q^45 - 44 * q^46 + 14 * q^47 + 7 * q^48 + 2 * q^49 - 11 * q^50 - 15 * q^51 + 55 * q^52 - 14 * q^53 - 11 * q^54 - 4 * q^55 + 6 * q^56 - 26 * q^57 - 18 * q^58 + 40 * q^59 - 9 * q^60 + 37 * q^61 + 19 * q^62 - 10 * q^63 + 14 * q^64 + 4 * q^65 - 4 * q^66 - 108 * q^67 + 54 * q^68 + 21 * q^69 - 30 * q^70 + 39 * q^71 + 22 * q^72 + 57 * q^73 - 11 * q^74 + 3 * q^75 + 22 * q^76 + 2 * q^77 + 7 * q^78 + 55 * q^79 + 7 * q^80 - 3 * q^81 - 26 * q^82 - 79 * q^83 - 2 * q^84 + 18 * q^85 - 44 * q^86 - 5 * q^87 - 8 * q^88 - 30 * q^89 + 40 * q^91 + 35 * q^92 + 44 * q^93 - 29 * q^94 + 7 * q^95 + 22 * q^96 - 52 * q^97 + 28 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$	$1$

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 $

$2$	0.101148	−	0.703501i	0.0715226	−	0.497451i	−0.922300	−	0.386474i	$-0.873693\pi$
$2$	0.101148	−	0.703501i	0.0715226	−	0.497451i	0.993823	−	0.110977i	$-0.0353979\pi$
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$	1.43430	+	0.421149i	0.717151	+	0.210575i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$6$	−0.681946	+	0.200237i	−0.278403	+	0.0817466i
$7$	−3.66580	−	2.35586i	−1.38554	−	0.890433i	−0.386054	−	0.922476i	$-0.626162\pi$
$7$	−3.66580	−	2.35586i	−1.38554	−	0.890433i	−0.999486	+	0.0320432i	$0.989799\pi$
$8$	1.03186	−	2.25945i	0.364816	−	0.798837i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	0.597909	−	0.384253i	0.189075	−	0.121511i
$11$	−0.657690	−	4.57433i	−0.198301	−	1.37921i	−0.809213	−	0.587515i	$-0.800106\pi$
$11$	−0.657690	−	4.57433i	−0.198301	−	1.37921i	0.610912	−	0.791698i	$-0.290803\pi$
$12$	−0.212740	−	1.47964i	−0.0614128	−	0.427135i
$13$	1.03496	−	0.665127i	0.287046	−	0.184473i	−0.389192	−	0.921157i	$-0.627246\pi$
$13$	1.03496	−	0.665127i	0.287046	−	0.184473i	0.676238	+	0.736684i	$0.263609\pi$
$14$	−2.02814	+	2.34060i	−0.542044	+	0.625552i
$15$	0.415415	−	0.909632i	0.107260	−	0.234866i
$16$	1.02995	+	0.661907i	0.257487	+	0.165477i
$17$	4.83727	−	1.42035i	1.17321	−	0.344486i	0.363658	−	0.931533i	$-0.381528\pi$
$17$	4.83727	−	1.42035i	1.17321	−	0.344486i	0.809553	+	0.587047i	$0.199710\pi$
$18$	0.465433	+	0.537138i	0.109704	+	0.126605i
$19$	2.46370	+	0.723408i	0.565212	+	0.165961i	0.551841	−	0.833949i	$-0.313926\pi$
$19$	2.46370	+	0.723408i	0.565212	+	0.165961i	0.0133711	+	0.999911i	$0.495744\pi$
$20$	0.620985	+	1.35977i	0.138856	+	0.304053i
$21$	−0.620143	+	4.31319i	−0.135326	+	0.941215i
$22$	−3.28457			−0.700273
$23$	1.09255	−	4.66973i	0.227813	−	0.973705i
$23$	1.09255	−	4.66973i	0.227813	−	0.973705i
$24$	−2.48392			−0.507028
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$	−0.363234	−	0.795371i	−0.0712360	−	0.155985i
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$	−4.26569	−	4.92287i	−0.806140	−	0.930335i
$29$	−1.56489	+	0.459493i	−0.290593	+	0.0853257i	−0.423780	−	0.905765i	$-0.639297\pi$
$29$	−1.56489	+	0.459493i	−0.290593	+	0.0853257i	0.133187	+	0.991091i	$0.457479\pi$
$30$	−0.597909	−	0.384253i	−0.109163	−	0.0701546i
$31$	−3.89122	+	8.52058i	−0.698883	+	1.53034i	0.142437	+	0.989804i	$0.454506\pi$
$31$	−3.89122	+	8.52058i	−0.698883	+	1.53034i	−0.841320	+	0.540537i	$0.818221\pi$
$32$	3.82307	−	4.41206i	0.675830	−	0.779949i
$33$	−3.88775	+	2.49850i	−0.676770	+	0.434933i
$34$	−0.509938	−	3.54669i	−0.0874536	−	0.608253i
$35$	−0.620143	−	4.31319i	−0.104823	−	0.729062i
$36$	−1.25755	+	0.808179i	−0.209592	+	0.134697i
$37$	−5.06618	+	5.84668i	−0.832875	+	0.961189i	−0.999692	−	0.0247990i	$-0.992105\pi$
$37$	−5.06618	+	5.84668i	−0.832875	+	0.961189i	0.166818	+	0.985988i	$0.446651\pi$
$38$	0.758118	−	1.66005i	0.122983	−	0.269295i
$39$	−1.03496	−	0.665127i	−0.165726	−	0.106506i
$40$	2.38330	−	0.699801i	0.376833	−	0.110648i
$41$	3.94217	+	4.54951i	0.615664	+	0.710514i	0.974878	−	0.222741i	$-0.0715005\pi$
$41$	3.94217	+	4.54951i	0.615664	+	0.710514i	−0.359214	+	0.933255i	$0.616955\pi$
$42$	2.97161	+	0.872542i	0.458529	+	0.134636i
$43$	−0.578970	−	1.26777i	−0.0882920	−	0.193333i	0.860335	−	0.509729i	$-0.170254\pi$
$43$	−0.578970	−	1.26777i	−0.0882920	−	0.193333i	−0.948627	+	0.316396i	$0.897527\pi$
$44$	0.983151	−	6.83796i	0.148216	−	1.03086i
$45$	−1.00000			−0.149071
$46$	−3.17465	−	1.24095i	−0.468076	−	0.182967i
$47$	−7.40920			−1.08074			−0.540372	−	0.841426i	$-0.681716\pi$
$47$	−7.40920			−1.08074			−0.540372	+	0.841426i	$0.681716\pi$
$48$	0.174236	−	1.21184i	0.0251488	−	0.174914i
$49$	4.98006	+	10.9048i	0.711437	+	1.55783i
$50$	0.681946	+	0.200237i	0.0964417	+	0.0283178i
$51$	−3.30147	−	3.81010i	−0.462299	−	0.533521i
$52$	1.76456	−	0.518122i	0.244701	−	0.0718506i
$53$	3.96873	+	2.55055i	0.545148	+	0.350345i	0.784049	−	0.620699i	$-0.213151\pi$
$53$	3.96873	+	2.55055i	0.545148	+	0.350345i	−0.238902	+	0.971044i	$0.576787\pi$
$54$	0.295250	−	0.646508i	0.0401785	−	0.0879786i
$55$	3.02635	−	3.49260i	0.408074	−	0.470942i
$56$	−9.10554	+	5.85177i	−1.21678	+	0.781976i
$57$	−0.365424	−	2.54158i	−0.0484015	−	0.336640i
$58$	0.164968	+	1.14738i	0.0216614	+	0.150658i
$59$	7.21664	−	4.63785i	0.939526	−	0.603797i	0.0212658	−	0.999774i	$-0.493230\pi$
$59$	7.21664	−	4.63785i	0.939526	−	0.603797i	0.918260	+	0.395977i	$0.129594\pi$
$60$	0.978922	−	1.12974i	0.126378	−	0.145848i
$61$	−0.252306	+	0.552472i	−0.0323044	+	0.0707369i	−0.925096	−	0.379732i	$-0.876016\pi$
$61$	−0.252306	+	0.552472i	−0.0323044	+	0.0707369i	0.892792	+	0.450469i	$0.148743\pi$
$62$	5.60065	+	3.59932i	0.711283	+	0.457114i
$63$	4.18103	−	1.22766i	0.526760	−	0.154671i
$64$	−1.11370	−	1.28528i	−0.139213	−	0.160660i
$65$	1.18042	+	0.346604i	0.146413	+	0.0429909i
$66$	1.36446	+	2.98775i	0.167954	+	0.367767i
$67$	−1.71325	+	11.9159i	−0.209306	+	1.45576i	0.566121	+	0.824322i	$0.308443\pi$
$67$	−1.71325	+	11.9159i	−0.209306	+	1.45576i	−0.775428	+	0.631436i	$0.782466\pi$
$68$	7.53629			0.913910
$69$	−4.70159	+	0.946055i	−0.566005	+	0.113892i
$70$	−3.09706			−0.370169
$71$	−1.09362	+	7.60626i	−0.129788	+	0.902697i	0.816032	+	0.578007i	$0.196169\pi$
$71$	−1.09362	+	7.60626i	−0.129788	+	0.902697i	−0.945820	+	0.324690i	$0.894740\pi$
$72$	1.03186	+	2.25945i	0.121605	+	0.266279i
$73$	11.7467	+	3.44914i	1.37485	+	0.403691i	0.883972	−	0.467540i	$-0.154860\pi$
$73$	11.7467	+	3.44914i	1.37485	+	0.403691i	0.490874	+	0.871231i	$0.336678\pi$
$74$	3.60071	+	4.15545i	0.418575	+	0.483061i
$75$	0.959493	−	0.281733i	0.110793	−	0.0325317i
$76$	3.22903	+	2.07517i	0.370395	+	0.238039i
$77$	−8.36555	+	18.3180i	−0.953343	+	2.08753i
$78$	−0.572602	+	0.660818i	−0.0648344	+	0.0748229i
$79$	11.7822	−	7.57197i	1.32560	−	0.851914i	0.329855	−	0.944032i	$-0.393000\pi$
$79$	11.7822	−	7.57197i	1.32560	−	0.851914i	0.995748	+	0.0921180i	$0.0293637\pi$
$80$	0.174236	+	1.21184i	0.0194802	+	0.135488i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	3.59933	−	2.31315i	0.397480	−	0.255445i
$83$	−1.66688	+	1.92368i	−0.182964	+	0.211152i	−0.839821	−	0.542864i	$-0.817340\pi$
$83$	−1.66688	+	1.92368i	−0.182964	+	0.211152i	0.656857	+	0.754015i	$0.271886\pi$
$84$	−2.70597	+	5.92524i	−0.295245	+	0.646497i
$85$	4.24117	+	2.72563i	0.460019	+	0.295637i
$86$	−0.950437	+	0.279074i	−0.102488	+	0.0300933i
$87$	1.06805	+	1.23259i	0.114507	+	0.132148i
$88$	−11.0141	−	3.23404i	−1.17411	−	0.344750i
$89$	0.0938560	+	0.205516i	0.00994872	+	0.0217846i	0.914541	−	0.404493i	$-0.132552\pi$
$89$	0.0938560	+	0.205516i	0.00994872	+	0.0217846i	−0.904592	+	0.426278i	$0.859825\pi$
$90$	−0.101148	+	0.703501i	−0.0106620	+	0.0741556i
$91$	−5.36090			−0.561975
$92$	3.53370	−	6.23767i	0.368414	−	0.650322i
$93$	9.36706			0.971319
$94$	−0.749428	+	5.21239i	−0.0772976	+	0.537617i
$95$	1.06667	+	2.33567i	0.109438	+	0.239635i
$96$	−5.60151	−	1.64475i	−0.571702	−	0.167867i
$97$	−11.0717	−	12.7774i	−1.12416	−	1.29735i	−0.949867	−	0.312654i	$-0.898782\pi$
$97$	−11.0717	−	12.7774i	−1.12416	−	1.29735i	−0.174292	−	0.984694i	$-0.555764\pi$
$98$	8.17527	−	2.40048i	0.825827	−	0.242485i
$99$	3.88775	+	2.49850i	0.390733	+	0.251109i
$100$	−0.620985	+	1.35977i	−0.0620985	+	0.135977i
$101$	5.86185	−	6.76494i	0.583276	−	0.673137i	−0.385030	−	0.922904i	$-0.625809\pi$
$101$	5.86185	−	6.76494i	0.583276	−	0.673137i	0.968306	+	0.249768i	$0.0803542\pi$
$102$	−3.01435	+	1.93721i	−0.298465	+	0.191812i
$103$	−1.29837	−	9.03038i	−0.127932	−	0.889789i	−0.948169	−	0.317766i	$-0.897068\pi$
$103$	−1.29837	−	9.03038i	−0.127932	−	0.889789i	0.820237	−	0.572024i	$-0.193842\pi$
$104$	−0.434894	−	3.02475i	−0.0426449	−	0.296602i
$105$	−3.66580	+	2.35586i	−0.357745	+	0.229909i
$106$	2.19575	−	2.53403i	0.213270	−	0.246126i
$107$	−5.13617	+	11.2466i	−0.496532	+	1.08725i	0.481049	+	0.876694i	$0.340256\pi$
$107$	−5.13617	+	11.2466i	−0.496532	+	1.08725i	−0.977581	+	0.210560i	$0.932471\pi$
$108$	1.25755	+	0.808179i	0.121008	+	0.0777671i
$109$	−11.4567	+	3.36399i	−1.09735	+	0.322211i	−0.779799	−	0.626029i	$-0.784679\pi$
$109$	−11.4567	+	3.36399i	−1.09735	+	0.322211i	−0.317552	+	0.948241i	$0.602861\pi$
$110$	−2.15094	−	2.48232i	−0.205084	−	0.236679i
$111$	7.42290	+	2.17956i	0.704550	+	0.206875i
$112$	−2.21621	−	4.85283i	−0.209412	−	0.458549i
$113$	1.09213	−	7.59592i	0.102739	−	0.714564i	−0.871721	−	0.490002i	$-0.836996\pi$
$113$	1.09213	−	7.59592i	0.102739	−	0.714564i	0.974460	−	0.224562i	$-0.0720950\pi$
$114$	−1.82497			−0.170924
$115$	4.24461	−	2.23232i	0.395812	−	0.208165i
$116$	−2.43804			−0.226366
$117$	−0.175084	+	1.21773i	−0.0161865	+	0.112580i
$118$	−2.53279	−	5.54603i	−0.233162	−	0.510553i
$119$	−21.0786	−	6.18924i	−1.93227	−	0.567367i
$120$	−1.62662	−	1.87722i	−0.148489	−	0.171366i
$121$	−9.93754	+	2.91793i	−0.903413	+	0.265266i
$122$	0.363145	+	0.233379i	0.0328776	+	0.0211291i
$123$	2.50074	−	5.47586i	0.225484	−	0.493742i
$124$	−9.16962	+	10.5823i	−0.823456	+	0.950319i
$125$	−0.841254	+	0.540641i	−0.0752440	+	0.0483564i
$126$	−0.440758	−	3.06554i	−0.0392658	−	0.273100i
$127$	1.49221	+	10.3785i	0.132412	+	0.920946i	0.942397	+	0.334496i	$0.108566\pi$
$127$	1.49221	+	10.3785i	0.132412	+	0.920946i	−0.809985	+	0.586450i	$0.800525\pi$
$128$	8.80562	−	5.65903i	0.778314	−	0.500192i
$129$	−0.912688	+	1.05330i	−0.0803577	+	0.0927378i
$130$	0.363234	−	0.795371i	0.0318577	−	0.0697587i
$131$	8.48589	+	5.45355i	0.741416	+	0.476479i	0.856027	−	0.516932i	$-0.172926\pi$
$131$	8.48589	+	5.45355i	0.741416	+	0.476479i	−0.114611	+	0.993410i	$0.536562\pi$
$132$	−6.62845	+	1.94629i	−0.576932	+	0.169403i
$133$	−7.32718	−	8.45602i	−0.635347	−	0.733230i
$134$	8.20956	+	2.41054i	0.709198	+	0.208239i
$135$	0.415415	+	0.909632i	0.0357532	+	0.0782887i
$136$	1.78216	−	12.3952i	0.152819	−	1.06288i
$137$	10.2521			0.875897			0.437948	−	0.899000i	$-0.355705\pi$
$137$	10.2521			0.875897			0.437948	+	0.899000i	$0.355705\pi$
$138$	0.189993	+	3.40327i	0.0161733	+	0.289706i
$139$	13.5229			1.14699			0.573497	−	0.819208i	$-0.305586\pi$
$139$	13.5229			1.14699			0.573497	+	0.819208i	$0.305586\pi$
$140$	0.927023	−	6.44759i	0.0783478	−	0.544921i
$141$	3.07789	+	6.73965i	0.259205	+	0.567581i
$142$	5.24040	+	1.53872i	0.439764	+	0.129126i
$143$	−3.72319	−	4.29680i	−0.311349	−	0.359316i
$144$	−1.17471	+	0.344925i	−0.0978923	+	0.0287438i
$145$	−1.37205	−	0.881761i	−0.113942	−	0.0732263i
$146$	3.61463	−	7.91494i	0.299149	−	0.655045i
$147$	7.85057	−	9.06004i	0.647504	−	0.747260i
$148$	−9.72876	+	6.25229i	−0.799699	+	0.513935i
$149$	−2.66302	−	18.5217i	−0.218163	−	1.51736i	−0.744813	−	0.667273i	$-0.767461\pi$
$149$	−2.66302	−	18.5217i	−0.218163	−	1.51736i	0.526650	−	0.850082i	$-0.323448\pi$
$150$	−0.101148	−	0.703501i	−0.00825872	−	0.0574407i
$151$	0.438023	−	0.281500i	0.0356458	−	0.0229081i	−0.522697	−	0.852519i	$-0.675074\pi$
$151$	0.438023	−	0.281500i	0.0356458	−	0.0229081i	0.558342	+	0.829611i	$0.311438\pi$
$152$	4.17669	−	4.82016i	0.338775	−	0.390967i
$153$	−2.09431	+	4.58590i	−0.169315	+	0.370748i
$154$	12.0406	+	7.73801i	0.970257	+	0.623547i
$155$	−8.98763	+	2.63901i	−0.721904	+	0.211970i
$156$	−1.20433	−	1.38987i	−0.0964232	−	0.111278i
$157$	17.9345	+	5.26603i	1.43133	+	0.420275i	0.903320	−	0.428966i	$-0.141122\pi$
$157$	17.9345	+	5.26603i	1.43133	+	0.420275i	0.528005	+	0.849241i	$0.322940\pi$
$158$	−4.13514	−	9.05470i	−0.328974	−	0.720353i
$159$	0.671391	−	4.66963i	0.0532448	−	0.370325i
$160$	5.83799			0.461534
$161$	−15.0063	+	14.5444i	−1.18266	+	1.14626i
$162$	−0.710736			−0.0558407
$163$	0.161972	−	1.12654i	0.0126866	−	0.0882375i	−0.982494	−	0.186292i	$-0.940353\pi$
$163$	0.161972	−	1.12654i	0.0126866	−	0.0882375i	0.995181	+	0.0980547i	$0.0312620\pi$
$164$	3.73825	+	8.18562i	0.291908	+	0.639189i
$165$	−4.43417	−	1.30199i	−0.345200	−	0.101360i
$166$	1.18471	+	1.36723i	0.0919515	+	0.106118i
$167$	−10.2472	+	3.00884i	−0.792949	+	0.232831i	−0.653030	−	0.757332i	$-0.726502\pi$
$167$	−10.2472	+	3.00884i	−0.792949	+	0.232831i	−0.139919	+	0.990163i	$0.544684\pi$
$168$	9.10554	+	5.85177i	0.702507	+	0.451474i
$169$	−4.77165	+	10.4485i	−0.367050	+	0.803728i
$170$	2.34647	−	2.70798i	0.179966	−	0.207692i
$171$	−2.16010	+	1.38821i	−0.165187	+	0.106159i
$172$	−0.296499	−	2.06219i	−0.0226078	−	0.157241i
$173$	1.86990	+	13.0054i	0.142165	+	0.988783i	0.928593	+	0.371100i	$0.121019\pi$
$173$	1.86990	+	13.0054i	0.142165	+	0.988783i	−0.786427	+	0.617683i	$0.788072\pi$
$174$	0.975163	−	0.626699i	0.0739269	−	0.0475099i
$175$	2.85358	−	3.29321i	0.215711	−	0.248943i
$176$	2.35040	−	5.14665i	0.177168	−	0.387943i
$177$	−7.21664	−	4.63785i	−0.542436	−	0.348602i
$178$	0.154074	−	0.0452402i	0.0115483	−	0.00339090i
$179$	−1.03998	−	1.20020i	−0.0777317	−	0.0897071i	0.715552	−	0.698560i	$-0.246175\pi$
$179$	−1.03998	−	1.20020i	−0.0777317	−	0.0897071i	−0.793283	+	0.608853i	$0.791630\pi$
$180$	−1.43430	−	0.421149i	−0.106907	−	0.0313906i
$181$	−6.10344	−	13.3647i	−0.453665	−	0.993388i	−0.988886	−	0.148676i	$-0.952499\pi$
$181$	−6.10344	−	13.3647i	−0.453665	−	0.993388i	0.535221	−	0.844712i	$-0.320228\pi$
$182$	−0.542245	+	3.77140i	−0.0401939	+	0.279555i
$183$	0.607358			0.0448972
$184$	−9.42366	−	7.28705i	−0.694721	−	0.537209i
$185$	−7.73627			−0.568782
$186$	0.947462	−	6.58974i	0.0694713	−	0.483183i
$187$	−9.67858	−	21.1931i	−0.707768	−	1.54980i
$188$	−10.6270	−	3.12038i	−0.775057	−	0.227577i
$189$	−2.85358	−	3.29321i	−0.207568	−	0.239546i
$190$	1.75104	−	0.514152i	0.127034	−	0.0373005i
$191$	−1.38889	−	0.892585i	−0.100496	−	0.0645852i	0.489427	−	0.872044i	$-0.337206\pi$
$191$	−1.38889	−	0.892585i	−0.100496	−	0.0645852i	−0.589924	+	0.807459i	$0.700842\pi$
$192$	−0.706483	+	1.54698i	−0.0509860	+	0.111644i
$193$	−2.50747	+	2.89377i	−0.180491	+	0.208298i	−0.838785	−	0.544464i	$-0.816733\pi$
$193$	−2.50747	+	2.89377i	−0.180491	+	0.208298i	0.658293	+	0.752762i	$0.271279\pi$
$194$	−10.1088	+	6.49653i	−0.725769	+	0.466424i
$195$	−0.175084	−	1.21773i	−0.0125380	−	0.0872038i
$196$	2.55036	+	17.7381i	0.182169	+	1.26701i
$197$	−14.3411	+	9.21649i	−1.02176	+	0.656648i	−0.940412	−	0.340038i	$-0.889560\pi$
$197$	−14.3411	+	9.21649i	−1.02176	+	0.656648i	−0.0813521	+	0.996685i	$0.525924\pi$
$198$	2.15094	−	2.48232i	0.152861	−	0.176410i
$199$	11.1501	−	24.4152i	0.790407	−	1.73075i	0.114924	−	0.993374i	$-0.463338\pi$
$199$	11.1501	−	24.4152i	0.790407	−	1.73075i	0.675483	−	0.737375i	$-0.263935\pi$
$200$	2.08960	+	1.34291i	0.147757	+	0.0949579i
$201$	11.5508	−	3.39162i	0.814730	−	0.239226i
$202$	−4.16623	−	4.80808i	−0.293135	−	0.338296i
$203$	6.81907	+	2.00226i	0.478605	+	0.140531i
$204$	−3.13069	−	6.85525i	−0.219192	−	0.479964i
$205$	−0.856716	+	5.95859i	−0.0598356	+	0.416166i
$206$	−6.48421			−0.451776
$207$	2.81367	+	3.88371i	0.195564	+	0.269937i
$208$	1.50620			0.104436
$209$	1.68876	−	11.7456i	0.116814	−	0.812458i
$210$	1.28657	+	2.81718i	0.0887814	+	0.194404i
$211$	−15.9803	−	4.69223i	−1.10013	−	0.323027i	−0.319225	−	0.947679i	$-0.603423\pi$
$211$	−15.9803	−	4.69223i	−1.10013	−	0.323027i	−0.780903	+	0.624652i	$0.785241\pi$
$212$	4.61820	+	5.32969i	0.317180	+	0.366045i
$213$	7.37320	−	2.16497i	0.505203	−	0.148341i
$214$	7.39251	+	4.75088i	0.505342	+	0.324763i
$215$	0.578970	−	1.26777i	0.0394854	−	0.0864610i
$216$	1.62662	−	1.87722i	0.110678	−	0.127729i
$217$	34.3377	−	22.0675i	2.33100	−	1.49804i
$218$	1.20775	+	8.40006i	0.0817989	+	0.568924i
$219$	−1.74230	−	12.1180i	−0.117734	−	0.818858i
$220$	5.81161	−	3.73490i	0.391819	−	0.251807i
$221$	4.06166	−	4.68741i	0.273217	−	0.315309i
$222$	2.28414	−	5.00156i	0.153301	−	0.335683i
$223$	21.1644	+	13.6015i	1.41727	+	0.910825i	0.999998	+	0.00204439i	$0.000650750\pi$
$223$	21.1644	+	13.6015i	1.41727	+	0.910825i	0.417274	+	0.908781i	$0.362986\pi$
$224$	−24.4088	+	7.16707i	−1.63088	+	0.478870i
$225$	−0.654861	−	0.755750i	−0.0436574	−	0.0503833i
$226$	−5.23327	−	1.53663i	−0.348112	−	0.102215i
$227$	−2.55955	−	5.60464i	−0.169883	−	0.371993i	0.805472	−	0.592634i	$-0.201912\pi$
$227$	−2.55955	−	5.60464i	−0.169883	−	0.371993i	−0.975355	+	0.220642i	$0.929185\pi$
$228$	0.546255	−	3.79929i	0.0361766	−	0.251614i
$229$	−2.39666			−0.158376			−0.0791879	−	0.996860i	$-0.525233\pi$
$229$	−2.39666			−0.158376			−0.0791879	+	0.996860i	$0.525233\pi$
$230$	−1.14111	−	3.21189i	−0.0752425	−	0.211785i
$231$	20.1378			1.32497
$232$	−0.576540	+	4.00992i	−0.0378517	+	0.263264i
$233$	−2.36137	−	5.17067i	−0.154698	−	0.338742i	0.816376	−	0.577521i	$-0.195980\pi$
$233$	−2.36137	−	5.17067i	−0.154698	−	0.338742i	−0.971074	+	0.238779i	$0.923253\pi$
$234$	0.838969	+	0.246343i	0.0548451	+	0.0161040i
$235$	−4.85200	−	5.59950i	−0.316509	−	0.365271i
$236$	12.3041	−	3.61280i	0.800927	−	0.235173i
$237$	−11.7822	−	7.57197i	−0.765337	−	0.491853i
$238$	−6.48620	+	14.2028i	−0.420438	+	0.920631i
$239$	−17.8238	+	20.5697i	−1.15292	+	1.33055i	−0.217897	+	0.975972i	$0.569920\pi$
$239$	−17.8238	+	20.5697i	−1.15292	+	1.33055i	−0.935028	+	0.354575i	$0.884626\pi$
$240$	1.02995	−	0.661907i	0.0664828	−	0.0427259i
$241$	−0.0357629	−	0.248736i	−0.00230369	−	0.0160225i	0.988637	−	0.150321i	$-0.0480309\pi$
$241$	−0.0357629	−	0.248736i	−0.00230369	−	0.0160225i	−0.990941	+	0.134299i	$0.957122\pi$
$242$	1.04760	+	7.28622i	0.0673423	+	0.468376i
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$	−0.594556	+	0.686154i	−0.0380626	+	0.0439265i
$245$	−4.98006	+	10.9048i	−0.318164	+	0.696683i
$246$	−3.59933	−	2.31315i	−0.229485	−	0.147481i
$247$	3.03099	−	0.889978i	0.192857	−	0.0566280i
$248$	15.2367	+	17.5840i	0.967529	+	1.11659i
$249$	2.44229	+	0.717121i	0.154774	+	0.0454457i
$250$	0.295250	+	0.646508i	0.0186733	+	0.0408888i
$251$	0.486591	−	3.38432i	0.0307134	−	0.213616i	−0.968685	−	0.248292i	$-0.920131\pi$
$251$	0.486591	−	3.38432i	0.0307134	−	0.213616i	0.999399	+	0.0346757i	$0.0110398\pi$
$252$	6.51389			0.410336
$253$	−22.0794	−	1.92646i	−1.38812	−	0.121116i
$254$	7.45225			0.467596
$255$	0.717479	−	4.99017i	0.0449302	−	0.312497i
$256$	−4.50343	−	9.86113i	−0.281464	−	0.616320i
$257$	−9.04702	−	2.65645i	−0.564338	−	0.165704i	−0.0128944	−	0.999917i	$-0.504105\pi$
$257$	−9.04702	−	2.65645i	−0.564338	−	0.165704i	−0.551443	+	0.834212i	$0.685923\pi$
$258$	0.648680	+	0.748617i	0.0403851	+	0.0466069i
$259$	32.3456	−	9.49752i	2.00986	−	0.590147i
$260$	1.54711	+	0.994269i	0.0959478	+	0.0616619i
$261$	0.677523	−	1.48357i	0.0419376	−	0.0918306i
$262$	4.69491	−	5.41822i	0.290053	−	0.334739i
$263$	−17.8768	+	11.4887i	−1.10233	+	0.708423i	−0.959608	−	0.281340i	$-0.909221\pi$
$263$	−17.8768	+	11.4887i	−1.10233	+	0.708423i	−0.142720	+	0.989763i	$0.545585\pi$
$264$	1.63365	+	11.3623i	0.100544	+	0.699299i
$265$	0.671391	+	4.66963i	0.0412432	+	0.286853i
$266$	−6.68995	+	4.29937i	−0.410187	+	0.263611i
$267$	0.147955	−	0.170749i	0.00905468	−	0.0104497i
$268$	−7.47568	+	16.3695i	−0.456650	+	0.999924i
$269$	−9.56230	−	6.14532i	−0.583024	−	0.374687i	0.215632	−	0.976475i	$-0.430819\pi$
$269$	−9.56230	−	6.14532i	−0.583024	−	0.374687i	−0.798656	+	0.601788i	$0.794455\pi$
$270$	0.681946	−	0.200237i	0.0415019	−	0.0121861i
$271$	13.1096	+	15.1292i	0.796349	+	0.919036i	0.998175	−	0.0603853i	$-0.0192329\pi$
$271$	13.1096	+	15.1292i	0.796349	+	0.919036i	−0.201826	+	0.979421i	$0.564687\pi$
$272$	5.92227	+	1.73894i	0.359091	+	0.105439i
$273$	2.22700	+	4.87644i	0.134784	+	0.295136i
$274$	1.03698	−	7.21237i	0.0626464	−	0.435715i
$275$	4.62137			0.278679
$276$	−7.14194	−	0.623144i	−0.429894	−	0.0375089i
$277$	−6.26539			−0.376451			−0.188225	−	0.982126i	$-0.560274\pi$
$277$	−6.26539			−0.376451			−0.188225	+	0.982126i	$0.560274\pi$
$278$	1.36781	−	9.51335i	0.0820360	−	0.570573i
$279$	−3.89122	−	8.52058i	−0.232961	−	0.510114i
$280$	−10.3853	−	3.04941i	−0.620642	−	0.182237i
$281$	3.47224	+	4.00718i	0.207137	+	0.239048i	0.849806	−	0.527095i	$-0.176719\pi$
$281$	3.47224	+	4.00718i	0.207137	+	0.239048i	−0.642670	+	0.766143i	$0.722173\pi$
$282$	5.05268	−	1.48360i	0.300883	−	0.0883471i
$283$	−7.92183	−	5.09105i	−0.470904	−	0.302632i	0.283582	−	0.958948i	$-0.408477\pi$
$283$	−7.92183	−	5.09105i	−0.470904	−	0.302632i	−0.754486	+	0.656316i	$0.772114\pi$
$284$	−4.77195	+	10.4491i	−0.283163	+	0.620040i
$285$	1.68149	−	1.94055i	0.0996031	−	0.114948i
$286$	−3.39940	+	2.18466i	−0.201011	+	0.129182i
$287$	−3.73317	−	25.9648i	−0.220362	−	1.53265i
$288$	0.830833	+	5.77857i	0.0489573	+	0.340505i
$289$	7.08049	−	4.55036i	0.416500	−	0.267668i
$290$	−0.759100	+	0.876048i	−0.0445759	+	0.0514433i
$291$	−7.02339	+	15.3791i	−0.411718	+	0.901537i
$292$	15.3957	+	9.89422i	0.900965	+	0.579015i
$293$	11.6498	−	3.42070i	0.680591	−	0.199840i	0.0768770	−	0.997041i	$-0.475505\pi$
$293$	11.6498	−	3.42070i	0.680591	−	0.199840i	0.603714	+	0.797201i	$0.293687\pi$
$294$	−5.57968	−	6.43930i	−0.325414	−	0.375547i
$295$	8.23095	+	2.41682i	0.479224	+	0.140713i
$296$	7.98272	+	17.4797i	0.463986	+	1.01599i
$297$	0.657690	−	4.57433i	0.0381630	−	0.265430i
$298$	−13.2994			−0.770413
$299$	−1.97522	−	5.55966i	−0.114230	−	0.321523i
$300$	1.49485			0.0863055
$301$	−0.864301	+	6.01135i	−0.0498175	+	0.346488i
$302$	−0.153730	−	0.336623i	−0.00884619	−	0.0193705i
$303$	−8.58871	−	2.52187i	−0.493408	−	0.144878i
$304$	2.05865	+	2.37581i	0.118072	+	0.136262i
$305$	−0.582756	+	0.171113i	−0.0333685	+	0.00979788i
$306$	3.01435	+	1.93721i	0.172319	+	0.110743i
$307$	−5.36629	+	11.7505i	−0.306270	+	0.670638i	−0.998707	−	0.0508407i	$-0.983810\pi$
$307$	−5.36629	+	11.7505i	−0.306270	+	0.670638i	0.692437	+	0.721479i	$0.256537\pi$
$308$	−19.7133	+	22.7504i	−1.12327	+	1.29632i
$309$	−7.67496	+	4.93240i	−0.436613	+	0.280594i
$310$	0.947462	+	6.58974i	0.0538122	+	0.374272i
$311$	−2.93159	−	20.3897i	−0.166235	−	1.15619i	−0.886580	−	0.462576i	$-0.846925\pi$
$311$	−2.93159	−	20.3897i	−0.166235	−	1.15619i	0.720344	−	0.693617i	$-0.243984\pi$
$312$	−2.57075	+	1.65212i	−0.145540	+	0.0935330i
$313$	−2.61466	+	3.01748i	−0.147789	+	0.170558i	−0.824817	−	0.565399i	$-0.808722\pi$
$313$	−2.61466	+	3.01748i	−0.147789	+	0.170558i	0.677028	+	0.735957i	$0.263268\pi$
$314$	5.51870	−	12.0843i	0.311438	−	0.681955i
$315$	3.66580	+	2.35586i	0.206544	+	0.132738i
$316$	20.0882	−	5.89843i	1.13005	−	0.331812i
$317$	−11.1549	−	12.8734i	−0.626520	−	0.723042i	0.350412	−	0.936596i	$-0.386042\pi$
$317$	−11.1549	−	12.8734i	−0.626520	−	0.723042i	−0.976931	+	0.213553i	$0.931496\pi$
$318$	−3.21718	−	0.944649i	−0.180410	−	0.0529733i
$319$	3.13109	+	6.85612i	0.175307	+	0.383869i
$320$	0.242030	−	1.68336i	0.0135299	−	0.0941025i
$321$	12.3639			0.690088
$322$	8.71412	+	12.0281i	0.485619	+	0.670300i
$323$	12.9451			0.720284
$324$	0.212740	−	1.47964i	0.0118189	−	0.0822022i
$325$	0.511067	+	1.11908i	0.0283489	+	0.0620755i
$326$	−0.776140	−	0.227895i	−0.0429864	−	0.0126219i
$327$	7.81927	+	9.02392i	0.432406	+	0.499024i
$328$	14.3472	−	4.21270i	0.792189	−	0.232608i
$329$	27.1606	+	17.4551i	1.49741	+	0.962330i
$330$	−1.36446	+	2.98775i	−0.0751111	+	0.164470i
$331$	4.25838	−	4.91444i	0.234062	−	0.270122i	−0.626552	−	0.779379i	$-0.715534\pi$
$331$	4.25838	−	4.91444i	0.234062	−	0.270122i	0.860614	+	0.509258i	$0.170080\pi$
$332$	−3.20097	+	2.05714i	−0.175676	+	0.112900i
$333$	−1.10099	−	7.65753i	−0.0603337	−	0.419630i
$334$	1.08024	+	7.51323i	0.0591081	+	0.411106i
$335$	−10.1274	+	6.50847i	−0.553317	+	0.355595i
$336$	−3.49364	+	4.03188i	−0.190594	+	0.219957i
$337$	−14.5211	+	31.7968i	−0.791015	+	1.73208i	−0.117293	+	0.993097i	$0.537422\pi$
$337$	−14.5211	+	31.7968i	−0.791015	+	1.73208i	−0.673722	+	0.738985i	$0.735305\pi$
$338$	6.86786	+	4.41371i	0.373562	+	0.240074i
$339$	−7.36318	+	2.16202i	−0.399913	+	0.117425i
$340$	4.93522	+	5.69555i	0.267650	+	0.308885i
$341$	41.5352	+	12.1958i	2.24926	+	0.660441i
$342$	0.758118	+	1.66005i	0.0409943	+	0.0897650i
$343$	3.09337	−	21.5149i	0.167026	−	1.16169i
$344$	−3.46187			−0.186652
$345$	−3.79387	−	2.93369i	−0.204255	−	0.157945i
$346$	9.33846			0.502039
$347$	4.19888	−	29.2038i	0.225408	−	1.56774i	−0.491689	−	0.870771i	$-0.663620\pi$
$347$	4.19888	−	29.2038i	0.225408	−	1.56774i	0.717097	−	0.696974i	$-0.245471\pi$
$348$	1.01280	+	2.21772i	0.0542917	+	0.118882i
$349$	23.4831	+	6.89525i	1.25702	+	0.369094i	0.841384	−	0.540437i	$-0.181741\pi$
$349$	23.4831	+	6.89525i	1.25702	+	0.369094i	0.415635	+	0.909532i	$0.363559\pi$
$350$	−2.02814	−	2.34060i	−0.108409	−	0.125110i
$351$	1.18042	−	0.346604i	0.0630063	−	0.0185003i
$352$	−22.6966	−	14.5862i	−1.20973	−	0.777449i
$353$	−11.4799	+	25.1374i	−0.611011	+	1.33793i	0.310869	+	0.950453i	$0.399380\pi$
$353$	−11.4799	+	25.1374i	−0.611011	+	1.33793i	−0.921880	+	0.387475i	$0.873347\pi$
$354$	−3.99269	+	4.60780i	−0.212209	+	0.244902i
$355$	−6.46459	+	4.15454i	−0.343105	+	0.220500i
$356$	0.0480650	+	0.334299i	0.00254744	+	0.0177178i
$357$	3.12644	+	21.7449i	0.165469	+	1.15086i
$358$	−0.949534	+	0.610229i	−0.0501844	+	0.0322516i
$359$	−2.35158	+	2.71387i	−0.124112	+	0.143233i	−0.814405	−	0.580297i	$-0.802936\pi$
$359$	−2.35158	+	2.71387i	−0.124112	+	0.143233i	0.690293	+	0.723530i	$0.257482\pi$
$360$	−1.03186	+	2.25945i	−0.0543836	+	0.119084i
$361$	−10.4373	−	6.70765i	−0.549332	−	0.353034i
$362$	−10.0194	+	2.94197i	−0.526609	+	0.154626i
$363$	6.78244	+	7.82735i	0.355986	+	0.410830i
$364$	−7.68915	−	2.25774i	−0.403021	−	0.118338i
$365$	5.08576	+	11.1363i	0.266201	+	0.582898i
$366$	0.0614332	−	0.427277i	0.00321117	−	0.0223341i
$367$	−23.9262			−1.24894			−0.624468	−	0.781051i	$-0.714684\pi$
$367$	−23.9262			−1.24894			−0.624468	+	0.781051i	$0.714684\pi$
$368$	4.21619	−	4.08640i	0.219784	−	0.213018i
$369$	−6.01986			−0.313382
$370$	−0.782510	+	5.44248i	−0.0406808	+	0.282941i
$371$	−8.53982	−	18.6996i	−0.443365	−	0.970835i
$372$	13.4352	+	3.94493i	0.696583	+	0.204535i
$373$	−7.86705	−	9.07906i	−0.407340	−	0.470096i	0.514599	−	0.857431i	$-0.327941\pi$
$373$	−7.86705	−	9.07906i	−0.407340	−	0.470096i	−0.921939	+	0.387335i	$0.873396\pi$
$374$	−15.8884	+	4.66525i	−0.821568	+	0.241234i
$375$	0.841254	+	0.540641i	0.0434421	+	0.0279186i
$376$	−7.64524	+	16.7407i	−0.394273	+	0.863338i
$377$	−1.31397	+	1.51641i	−0.0676731	+	0.0780989i
$378$	−2.60541	+	1.67440i	−0.134008	+	0.0861217i
$379$	3.63306	+	25.2685i	0.186618	+	1.29795i	0.840687	+	0.541521i	$0.182151\pi$
$379$	3.63306	+	25.2685i	0.186618	+	1.29795i	−0.654070	+	0.756434i	$0.726940\pi$
$380$	0.546255	+	3.79929i	0.0280223	+	0.194899i
$381$	8.82076	−	5.66876i	0.451901	−	0.290419i
$382$	−0.768418	+	0.886802i	−0.0393157	+	0.0453727i
$383$	−3.34538	+	7.32537i	−0.170941	+	0.374309i	−0.975641	−	0.219373i	$-0.929599\pi$
$383$	−3.34538	+	7.32537i	−0.170941	+	0.374309i	0.804700	+	0.593682i	$0.202326\pi$
$384$	−8.80562	−	5.65903i	−0.449360	−	0.288786i
$385$	−19.3221	+	5.67348i	−0.984745	+	0.289147i
$386$	1.78215	+	2.05671i	0.0907088	+	0.104684i
$387$	1.33726	+	0.392655i	0.0679767	+	0.0199598i
$388$	−10.4989	−	22.9895i	−0.533003	−	1.16711i
$389$	−0.0762867	+	0.530585i	−0.00386789	+	0.0269017i	−0.991664	−	0.128851i	$-0.958871\pi$
$389$	−0.0762867	+	0.530585i	−0.00386789	+	0.0269017i	0.987796	+	0.155753i	$0.0497803\pi$
$390$	−0.874388			−0.0442763
$391$	−1.34768	−	24.1405i	−0.0681553	−	1.22084i
$392$	29.7776			1.50400
$393$	1.43556	−	9.98452i	0.0724143	−	0.503653i
$394$	5.03323	+	11.0212i	0.253571	+	0.555242i
$395$	13.4382	+	3.94582i	0.676151	+	0.198536i
$396$	4.52396	+	5.22093i	0.227338	+	0.262362i
$397$	−3.66484	+	1.07609i	−0.183933	+	0.0540076i	−0.372402	−	0.928072i	$-0.621466\pi$
$397$	−3.66484	+	1.07609i	−0.183933	+	0.0540076i	0.188469	+	0.982079i	$0.439647\pi$
$398$	−16.0483	−	10.3136i	−0.804431	−	0.516976i
$399$	−4.64804	+	10.1778i	−0.232693	+	0.509527i
$400$	−0.801746	+	0.925264i	−0.0400873	+	0.0462632i
$401$	22.0646	−	14.1800i	1.10185	−	0.708117i	0.142349	−	0.989817i	$-0.454534\pi$
$401$	22.0646	−	14.1800i	1.10185	−	0.708117i	0.959503	+	0.281699i	$0.0908981\pi$
$402$	−1.21767	−	8.46905i	−0.0607317	−	0.422398i
$403$	1.64002	+	11.4066i	0.0816953	+	0.568203i
$404$	11.2567	−	7.23426i	0.560043	−	0.359918i
$405$	0.654861	−	0.755750i	0.0325403	−	0.0375535i
$406$	2.09833	−	4.59470i	0.104138	−	0.228031i
$407$	30.0766	+	19.3291i	1.49084	+	0.958107i
$408$	−12.0154	+	3.52804i	−0.594850	+	0.174664i
$409$	18.6251	+	21.4945i	0.920951	+	1.06283i	0.997833	+	0.0657944i	$0.0209581\pi$
$409$	18.6251	+	21.4945i	0.920951	+	1.06283i	−0.0768818	+	0.997040i	$0.524496\pi$
$410$	4.10522	+	1.20540i	0.202742	+	0.0595306i
$411$	−4.25888	−	9.32565i	−0.210075	−	0.460000i
$412$	1.94088	−	13.4991i	0.0956202	−	0.665053i
$413$	−37.3809			−1.83939
$414$	3.01680	−	1.58659i	0.148267	−	0.0779768i
$415$	−2.54540			−0.124949
$416$	1.02214	−	7.10912i	0.0501144	−	0.348554i
$417$	−5.61760	−	12.3008i	−0.275095	−	0.602374i
$418$	−8.09221	−	2.37609i	−0.395803	−	0.116218i
$419$	−5.43501	−	6.27233i	−0.265517	−	0.306423i	0.607298	−	0.794474i	$-0.292254\pi$
$419$	−5.43501	−	6.27233i	−0.265517	−	0.306423i	−0.872815	+	0.488051i	$0.837708\pi$
$420$	−6.25003	+	1.83517i	−0.304970	+	0.0895474i
$421$	1.66726	+	1.07148i	0.0812572	+	0.0522208i	0.580639	−	0.814161i	$-0.302803\pi$
$421$	1.66726	+	1.07148i	0.0812572	+	0.0522208i	−0.499381	+	0.866382i	$0.666439\pi$
$422$	−4.91737	+	10.7675i	−0.239374	+	0.524156i
$423$	4.85200	−	5.59950i	0.235912	−	0.272257i
$424$	9.85801	−	6.33536i	0.478747	−	0.307672i
$425$	0.717479	+	4.99017i	0.0348028	+	0.242059i
$426$	−0.777271	−	5.40604i	−0.0376589	−	0.261924i
$427$	2.22645	−	1.43085i	0.107746	−	0.0692439i
$428$	−12.1033	+	13.9680i	−0.585037	+	0.675168i
$429$	−2.36183	+	5.17169i	−0.114030	+	0.249692i
$430$	−0.833314	−	0.535538i	−0.0401860	−	0.0258260i
$431$	−20.5663	+	6.03882i	−0.990645	+	0.290879i	−0.736612	−	0.676316i	$-0.763575\pi$
$431$	−20.5663	+	6.03882i	−0.990645	+	0.290879i	−0.254033	+	0.967196i	$0.581757\pi$
$432$	0.801746	+	0.925264i	0.0385740	+	0.0445168i
$433$	−23.1899	−	6.80916i	−1.11443	−	0.327228i	−0.327862	−	0.944726i	$-0.606328\pi$
$433$	−23.1899	−	6.80916i	−1.11443	−	0.327228i	−0.786572	+	0.617498i	$0.788146\pi$
$434$	−12.0513	−	26.3887i	−0.578483	−	1.26670i
$435$	−0.232109	+	1.61435i	−0.0111288	+	0.0774024i
$436$	−17.8491			−0.854816
$437$	6.06984	−	10.7145i	0.290360	−	0.512542i
$438$	−8.70125			−0.415762
$439$	2.66606	−	18.5429i	0.127244	−	0.885003i	−0.821781	−	0.569803i	$-0.807019\pi$
$439$	2.66606	−	18.5429i	0.127244	−	0.885003i	0.949025	−	0.315200i	$-0.102072\pi$
$440$	−4.76859	−	10.4418i	−0.227334	−	0.497792i
$441$	−11.5026	−	3.37745i	−0.547741	−	0.160831i
$442$	−2.88677	−	3.33151i	−0.137310	−	0.158464i
$443$	37.0301	−	10.8730i	1.75935	−	0.516592i	0.767176	−	0.641437i	$-0.221661\pi$
$443$	37.0301	−	10.8730i	1.75935	−	0.516592i	0.992176	+	0.124844i	$0.0398431\pi$
$444$	9.72876	+	6.25229i	0.461707	+	0.296721i
$445$	−0.0938560	+	0.205516i	−0.00444920	+	0.00974239i
$446$	11.7094	−	13.5134i	0.554458	−	0.639878i
$447$	−15.7417	+	10.1166i	−0.744555	+	0.478496i
$448$	1.05466	+	7.33530i	0.0498278	+	0.346560i
$449$	−1.14408	−	7.95722i	−0.0539923	−	0.375524i	−0.998846	−	0.0480313i	$-0.984705\pi$
$449$	−1.14408	−	7.95722i	−0.0539923	−	0.375524i	0.944854	−	0.327493i	$-0.106204\pi$
$450$	−0.597909	+	0.384253i	−0.0281857	+	0.0181138i
$451$	18.2182	−	21.0250i	0.857864	−	0.990027i
$452$	4.76546	−	10.4349i	0.224148	−	0.490816i
$453$	−0.438023	−	0.281500i	−0.0205801	−	0.0132260i
$454$	−4.20176	+	1.23375i	−0.197199	+	0.0579027i
$455$	−3.51064	−	4.05149i	−0.164581	−	0.189937i
$456$	−6.11963	−	1.79689i	−0.286578	−	0.0841469i
$457$	6.17157	+	13.5138i	0.288694	+	0.632151i	0.997299	−	0.0734544i	$-0.0234023\pi$
$457$	6.17157	+	13.5138i	0.288694	+	0.632151i	−0.708605	+	0.705606i	$0.750675\pi$
$458$	−0.242418	+	1.68605i	−0.0113274	+	0.0787841i
$459$	5.04149			0.235317
$460$	7.02820	−	1.41421i	0.327691	−	0.0659381i
$461$	−19.0154			−0.885633			−0.442817	−	0.896612i	$-0.646021\pi$
$461$	−19.0154			−0.885633			−0.442817	+	0.896612i	$0.646021\pi$
$462$	2.03690	−	14.1670i	0.0947654	−	0.659108i
$463$	7.50408	+	16.4316i	0.348744	+	0.763643i	0.999989	+	0.00477501i	$0.00151994\pi$
$463$	7.50408	+	16.4316i	0.348744	+	0.763643i	−0.651245	+	0.758868i	$0.725753\pi$
$464$	−1.91589	−	0.562558i	−0.0889432	−	0.0261161i
$465$	6.13412	+	7.07915i	0.284463	+	0.328288i
$466$	−3.87642	+	1.13822i	−0.179572	+	0.0527270i
$467$	−0.662084	−	0.425495i	−0.0306376	−	0.0196896i	0.525232	−	0.850959i	$-0.323978\pi$
$467$	−0.662084	−	0.425495i	−0.0306376	−	0.0196896i	−0.555870	+	0.831269i	$0.687615\pi$
$468$	−0.763971	+	1.67286i	−0.0353146	+	0.0773282i
$469$	34.3526	−	39.6451i	1.58626	−	1.83064i
$470$	−4.43003	+	2.84701i	−0.204342	+	0.131323i
$471$	−2.66009	−	18.5013i	−0.122571	−	0.852497i
$472$	−3.03246	−	21.0912i	−0.139580	−	0.970803i
$473$	−5.41840	+	3.48220i	−0.249138	+	0.160112i
$474$	−6.51864	+	7.52292i	−0.299411	+	0.345539i
$475$	−1.06667	+	2.33567i	−0.0489420	+	0.107168i
$476$	−27.6265	−	17.7545i	−1.26626	−	0.813775i
$477$	−4.52655	+	1.32911i	−0.207256	+	0.0608559i
$478$	12.6680	+	14.6197i	0.579421	+	0.668687i
$479$	4.60419	+	1.35191i	0.210371	+	0.0617704i	0.385220	−	0.922825i	$-0.374126\pi$
$479$	4.60419	+	1.35191i	0.210371	+	0.0617704i	−0.174849	+	0.984595i	$0.555944\pi$
$480$	−2.42519	−	5.31042i	−0.110694	−	0.242387i
$481$	−1.35450	+	9.42073i	−0.0617597	+	0.429548i
$482$	−0.178604			−0.00813517
$483$	19.4639	+	7.60827i	0.885636	+	0.346188i
$484$	−15.4823			−0.703742
$485$	2.40611	−	16.7348i	0.109256	−	0.759890i
$486$	0.295250	+	0.646508i	0.0133928	+	0.0293262i
$487$	−13.1678	−	3.86642i	−0.596690	−	0.175204i	−0.0305782	−	0.999532i	$-0.509735\pi$
$487$	−13.1678	−	3.86642i	−0.596690	−	0.175204i	−0.566112	+	0.824328i	$0.691553\pi$
$488$	0.987941	+	1.14015i	0.0447220	+	0.0516119i
$489$	−1.09202	+	0.320647i	−0.0493830	+	0.0145002i
$490$	7.16783	+	4.60648i	0.323809	+	0.208100i
$491$	12.2098	−	26.7358i	0.551022	−	1.20657i	−0.405281	−	0.914192i	$-0.632826\pi$
$491$	12.2098	−	26.7358i	0.551022	−	1.20657i	0.956303	−	0.292377i	$-0.0944463\pi$
$492$	5.89298	−	6.80086i	0.265676	−	0.306606i
$493$	−6.91716	+	4.44539i	−0.311533	+	0.200210i
$494$	−0.319522	−	2.22232i	−0.0143760	−	0.0999871i
$495$	0.657690	+	4.57433i	0.0295610	+	0.205601i
$496$	−9.64758	+	6.20012i	−0.433189	+	0.278394i
$497$	21.9283	−	25.3066i	0.983618	−	1.13516i
$498$	0.751529	−	1.64562i	0.0336768	−	0.0737420i
$499$	−24.2339	−	15.5742i	−1.08486	−	0.697196i	−0.129183	−	0.991621i	$-0.541236\pi$
$499$	−24.2339	−	15.5742i	−1.08486	−	0.697196i	−0.955675	+	0.294425i	$0.904872\pi$
$500$	−1.43430	+	0.421149i	−0.0641440	+	0.0188344i
$501$	6.99376	+	8.07123i	0.312458	+	0.360596i
$502$	−2.33165	−	0.684636i	−0.104067	−	0.0305568i
$503$	14.8509	+	32.5190i	0.662171	+	1.44995i	0.880485	+	0.474073i	$0.157217\pi$
$503$	14.8509	+	32.5190i	0.662171	+	1.44995i	−0.218315	+	0.975878i	$0.570056\pi$
$504$	1.54038	−	10.7136i	0.0686141	−	0.477222i
$505$	8.95130			0.398328
$506$	−3.58856	+	15.3381i	−0.159531	+	0.681860i
$507$	11.4865			0.510132
$508$	−2.23063	+	15.5144i	−0.0989684	+	0.688340i
$509$	11.6110	+	25.4246i	0.514650	+	1.12693i	0.971426	+	0.237344i	$0.0762768\pi$
$509$	11.6110	+	25.4246i	0.514650	+	1.12693i	−0.456776	+	0.889582i	$0.650996\pi$
$510$	−3.43802	−	1.00949i	−0.152238	−	0.0447012i
$511$	−34.9353	−	40.3174i	−1.54544	−	1.78354i
$512$	12.6937	−	3.72720i	0.560987	−	0.164721i
$513$	2.16010	+	1.38821i	0.0953706	+	0.0612910i
$514$	−2.78390	+	6.09590i	−0.122793	+	0.268879i
$515$	5.97445	−	6.89488i	0.263266	−	0.303825i
$516$	−1.75267	+	1.12637i	−0.0771569	+	0.0495857i
$517$	4.87296	+	33.8922i	0.214312	+	1.49058i
$518$	−3.40982	−	23.7158i	−0.149819	−	1.04201i
$519$	11.0534	−	7.10356i	0.485188	−	0.311812i
$520$	2.00116	−	2.30946i	0.0877567	−	0.101277i
$521$	−4.79919	+	10.5088i	−0.210256	+	0.460397i	−0.985150	−	0.171694i	$-0.945076\pi$
$521$	−4.79919	+	10.5088i	−0.210256	+	0.460397i	0.774894	+	0.632091i	$0.217803\pi$
$522$	−0.975163	−	0.626699i	−0.0426817	−	0.0274299i
$523$	4.62081	−	1.35679i	0.202054	−	0.0593283i	−0.179140	−	0.983824i	$-0.557331\pi$
$523$	4.62081	−	1.35679i	0.202054	−	0.0593283i	0.381193	+	0.924495i	$0.375513\pi$
$524$	9.87458	+	11.3959i	0.431373	+	0.497831i
$525$	−4.18103	−	1.22766i	−0.182475	−	0.0535795i
$526$	6.27411	+	13.7384i	0.273564	+	0.599022i
$527$	−6.72067	+	46.7433i	−0.292757	+	2.03617i
$528$	−5.65795			−0.246230
$529$	−20.6127	−	10.2038i	−0.896203	−	0.443645i
$530$	3.35300			0.145645
$531$	−1.22084	+	8.49112i	−0.0529799	+	0.368483i
$532$	−6.94815	−	15.2143i	−0.301240	−	0.659624i
$533$	7.10599	+	2.08651i	0.307794	+	0.0903766i
$534$	−0.105157	−	0.121357i	−0.00455057	−	0.00525164i
$535$	−11.8631	+	3.48333i	−0.512887	+	0.150597i
$536$	25.1556	+	16.1665i	1.08655	+	0.698286i
$537$	−0.659717	+	1.44458i	−0.0284689	+	0.0623382i
$538$	−5.29045	+	6.10551i	−0.228088	+	0.263227i
$539$	46.6069	−	29.9524i	2.00750	−	1.29014i
$540$	0.212740	+	1.47964i	0.00915487	+	0.0636735i
$541$	−4.67920	−	32.5446i	−0.201175	−	1.39920i	−0.800806	−	0.598924i	$-0.795595\pi$
$541$	−4.67920	−	32.5446i	−0.201175	−	1.39920i	0.599631	−	0.800276i	$-0.295314\pi$
$542$	11.9695	−	7.69230i	0.514132	−	0.330413i
$543$	−9.62147	+	11.1038i	−0.412897	+	0.476509i
$544$	12.2266	−	26.7724i	0.524209	−	1.14786i
$545$	−10.0449	−	6.45544i	−0.430275	−	0.276521i
$546$	3.65584	−	1.07345i	0.156456	−	0.0459395i
$547$	12.7241	+	14.6843i	0.544041	+	0.627857i	0.959484	−	0.281762i	$-0.0909189\pi$
$547$	12.7241	+	14.6843i	0.544041	+	0.627857i	−0.415443	+	0.909619i	$0.636373\pi$
$548$	14.7046	+	4.31767i	0.628151	+	0.184442i
$549$	−0.252306	−	0.552472i	−0.0107681	−	0.0235790i
$550$	0.467444	−	3.25114i	0.0199319	−	0.138629i
$551$	−4.18782			−0.178407
$552$	−2.71381	+	11.5992i	−0.115507	+	0.493695i
$553$	−61.0298			−2.59525
$554$	−0.633733	+	4.40771i	−0.0269247	+	0.187266i
$555$	3.21376	+	7.03716i	0.136417	+	0.298711i
$556$	19.3959	+	5.69514i	0.822568	+	0.241528i
$557$	−6.53233	−	7.53871i	−0.276784	−	0.319425i	0.600289	−	0.799783i	$-0.295052\pi$
$557$	−6.53233	−	7.53871i	−0.276784	−	0.319425i	−0.877073	+	0.480358i	$0.840507\pi$
$558$	−6.38783	+	1.87564i	−0.270418	+	0.0794020i
$559$	−1.44244	−	0.926997i	−0.0610085	−	0.0392078i
$560$	2.21621	−	4.85283i	0.0936521	−	0.205069i
$561$	−15.2573	+	17.6079i	−0.644165	+	0.743406i
$562$	3.17027	−	2.03741i	0.133730	−	0.0859428i
$563$	−6.20689	−	43.1698i	−0.261589	−	1.81939i	−0.520923	−	0.853604i	$-0.674412\pi$
$563$	−6.20689	−	43.1698i	−0.261589	−	1.81939i	0.259334	−	0.965788i	$-0.416497\pi$
$564$	1.57623	+	10.9629i	0.0663714	+	0.461623i
$565$	6.45580	−	4.14889i	0.271598	−	0.174545i
$566$	−4.38284	+	5.05807i	−0.184225	+	0.212606i
$567$	−1.81019	+	3.96376i	−0.0760207	+	0.166462i
$568$	16.0575	+	10.3195i	0.673759	+	0.432998i
$569$	16.7520	−	4.91884i	0.702282	−	0.206209i	0.0889527	−	0.996036i	$-0.471648\pi$
$569$	16.7520	−	4.91884i	0.702282	−	0.206209i	0.613329	+	0.789827i	$0.289830\pi$
$570$	−1.19510	−	1.37922i	−0.0500571	−	0.0577690i
$571$	26.0400	+	7.64605i	1.08974	+	0.319977i	0.776769	−	0.629785i	$-0.216857\pi$
$571$	26.0400	+	7.64605i	1.08974	+	0.319977i	0.312973	+	0.949762i	$0.398675\pi$
$572$	−3.53060	−	7.73093i	−0.147622	−	0.323246i
$573$	−0.234958	+	1.63417i	−0.00981552	+	0.0682685i
$574$	−18.6439			−0.778180
$575$	4.46671	+	1.74600i	0.186275	+	0.0728133i
$576$	1.70067			0.0708612
$577$	1.63008	−	11.3374i	0.0678610	−	0.471984i	−0.927347	−	0.374203i	$-0.877916\pi$
$577$	1.63008	−	11.3374i	0.0678610	−	0.471984i	0.995208	−	0.0977811i	$-0.0311745\pi$
$578$	−2.48500	−	5.44140i	−0.103363	−	0.226332i
$579$	3.67391	+	1.07876i	0.152682	+	0.0448316i
$580$	−1.59658	−	1.84255i	−0.0662943	−	0.0765077i
$581$	10.6424	−	3.12489i	0.441520	−	0.129642i
$582$	10.1088	+	6.49653i	0.419023	+	0.269290i
$583$	9.05687	−	19.8318i	0.375097	−	0.821349i
$584$	19.9141	−	22.9820i	0.824050	−	0.951004i
$585$	−1.03496	+	0.665127i	−0.0427903	+	0.0274996i
$586$	−1.22811	−	8.54168i	−0.0507327	−	0.352853i
$587$	0.0579765	+	0.403236i	0.00239295	+	0.0166433i	0.990983	−	0.133988i	$-0.0427784\pi$
$587$	0.0579765	+	0.403236i	0.00239295	+	0.0166433i	−0.988590	+	0.150631i	$0.951869\pi$
$588$	15.0757	−	9.68858i	0.621713	−	0.399550i
$589$	−15.7507	+	18.1772i	−0.648995	+	0.748980i
$590$	2.53279	−	5.54603i	0.104273	−	0.228326i
$591$	14.3411	+	9.21649i	0.589916	+	0.379116i
$592$	−9.08785	+	2.66843i	−0.373508	+	0.109672i
$593$	−9.01730	−	10.4065i	−0.370296	−	0.427344i	0.539767	−	0.841814i	$-0.318512\pi$
$593$	−9.01730	−	10.4065i	−0.370296	−	0.427344i	−0.910063	+	0.414470i	$0.863967\pi$
$594$	−3.15153	−	0.925371i	−0.129309	−	0.0379684i
$595$	−9.12604	−	19.9832i	−0.374131	−	0.819233i
$596$	3.98082	−	27.6872i	0.163061	−	1.13411i
$597$	−26.8408			−1.09852
$598$	−4.11102	+	0.827219i	−0.168112	+	0.0338275i
$599$	−18.4867			−0.755348			−0.377674	−	0.925939i	$-0.623276\pi$
$599$	−18.4867			−0.755348			−0.377674	+	0.925939i	$0.623276\pi$
$600$	0.353498	−	2.45864i	0.0144315	−	0.100373i
$601$	−1.12386	−	2.46090i	−0.0458431	−	0.100382i	0.885325	−	0.464973i	$-0.153936\pi$
$601$	−1.12386	−	2.46090i	−0.0458431	−	0.100382i	−0.931168	+	0.364591i	$0.881209\pi$
$602$	4.14157	+	1.21607i	0.168798	+	0.0495635i
$603$	−7.88349	−	9.09804i	−0.321041	−	0.370501i
$604$	0.746810	−	0.219283i	0.0303873	−	0.00892251i
$605$	−8.71293	−	5.59946i	−0.354231	−	0.227650i
$606$	−2.64287	+	5.78709i	−0.107359	+	0.235084i
$607$	16.7700	−	19.3536i	0.680672	−	0.785538i	−0.305334	−	0.952245i	$-0.598768\pi$
$607$	16.7700	−	19.3536i	0.680672	−	0.785538i	0.986006	+	0.166707i	$0.0533135\pi$
$608$	12.6106	−	8.10436i	0.511428	−	0.328675i
$609$	−1.01142	−	7.03461i	−0.0409850	−	0.285057i
$610$	0.0614332	+	0.427277i	0.00248736	+	0.0173000i
$611$	−7.66822	+	4.92806i	−0.310223	+	0.199368i
$612$	−4.93522	+	5.69555i	−0.199495	+	0.230229i
$613$	8.49645	−	18.6046i	0.343168	−	0.751434i	−0.656828	−	0.754040i	$-0.728102\pi$
$613$	8.49645	−	18.6046i	0.343168	−	0.751434i	0.999997	+	0.00260653i	$0.000829685\pi$
$614$	7.72372	+	4.96374i	0.311704	+	0.200320i
$615$	5.77602	−	1.69599i	0.232912	−	0.0683890i
$616$	32.7566	+	37.8031i	1.31980	+	1.52313i
$617$	−27.9970	−	8.22067i	−1.12712	−	0.330952i	−0.335544	−	0.942025i	$-0.608920\pi$
$617$	−27.9970	−	8.22067i	−1.12712	−	0.330952i	−0.791574	+	0.611073i	$0.790738\pi$
$618$	2.69364	+	5.89825i	0.108354	+	0.237262i
$619$	−4.29205	+	29.8519i	−0.172512	+	1.19985i	0.701041	+	0.713121i	$0.252719\pi$
$619$	−4.29205	+	29.8519i	−0.172512	+	1.19985i	−0.873554	+	0.486728i	$0.838190\pi$
$620$	−14.0024			−0.562350
$621$	2.36391	−	4.17276i	0.0948604	−	0.167447i
$622$	−14.6407			−0.587038
$623$	0.140111	−	0.974492i	0.00561342	−	0.0390422i
$624$	−0.625700	−	1.37009i	−0.0250480	−	0.0548476i
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$	1.85833	+	2.14463i	0.0742739	+	0.0857167i
$627$	−11.3857	+	3.34314i	−0.454700	+	0.133512i
$628$	23.5057	+	15.1062i	0.937978	+	0.602802i
$629$	−16.2021	+	35.4778i	−0.646022	+	1.41459i
$630$	2.02814	−	2.34060i	0.0808031	−	0.0932518i
$631$	−12.4261	+	7.98579i	−0.494676	+	0.317909i	−0.764084	−	0.645117i	$-0.776809\pi$
$631$	−12.4261	+	7.98579i	−0.494676	+	0.317909i	0.269407	+	0.963026i	$0.413172\pi$
$632$	−4.95094	−	34.4345i	−0.196938	−	1.36973i
$633$	2.37024	+	16.4854i	0.0942087	+	0.655236i
$634$	−10.1848	+	6.54534i	−0.404488	+	0.259949i
$635$	−6.86638	+	7.92423i	−0.272484	+	0.314463i
$636$	2.92959	−	6.41490i	0.116166	−	0.254367i
$637$	12.4072	+	7.97365i	0.491593	+	0.315928i
$638$	5.14000	−	1.50924i	0.203494	−	0.0597513i
$639$	−5.03226	−	5.80754i	−0.199073	−	0.229743i
$640$	10.0433	+	2.94897i	0.396995	+	0.116568i
$641$	18.5845	+	40.6943i	0.734043	+	1.60733i	0.793112	+	0.609076i	$0.208460\pi$
$641$	18.5845	+	40.6943i	0.734043	+	1.60733i	−0.0590688	+	0.998254i	$0.518813\pi$
$642$	1.25059	−	8.69805i	0.0493569	−	0.343285i
$643$	−3.20427			−0.126364			−0.0631821	−	0.998002i	$-0.520125\pi$
$643$	−3.20427			−0.126364			−0.0631821	+	0.998002i	$0.520125\pi$
$644$	−27.6489	+	14.5411i	−1.08952	+	0.573000i
$645$	−1.39371			−0.0548774
$646$	1.30937	−	9.10689i	0.0515166	−	0.358306i
$647$	−5.23244	−	11.4574i	−0.205708	−	0.450439i	0.778455	−	0.627700i	$-0.216003\pi$
$647$	−5.23244	−	11.4574i	−0.205708	−	0.450439i	−0.984164	+	0.177261i	$0.943276\pi$
$648$	−2.38330	−	0.699801i	−0.0936249	−	0.0274908i
$649$	−25.9614	−	29.9610i	−1.01907	−	1.17607i
$650$	0.838969	−	0.246343i	0.0329071	−	0.00966239i
$651$	−34.3377	−	22.0675i	−1.34580	−	0.864895i
$652$	0.706759	−	1.54759i	0.0276788	−	0.0606081i
$653$	−6.18321	+	7.13581i	−0.241968	+	0.279246i	−0.863724	−	0.503965i	$-0.831874\pi$
$653$	−6.18321	+	7.13581i	−0.241968	+	0.279246i	0.621756	+	0.783211i	$0.286419\pi$
$654$	7.13924	−	4.58811i	0.279167	−	0.179409i
$655$	1.43556	+	9.98452i	0.0560919	+	0.390128i
$656$	1.04888	+	7.29510i	0.0409518	+	0.284826i
$657$	−10.2991	+	6.61885i	−0.401807	+	0.258226i
$658$	15.0269	−	17.3420i	0.585810	−	0.676061i
$659$	−16.3484	+	35.7980i	−0.636844	+	1.39449i	0.265767	+	0.964037i	$0.414375\pi$
$659$	−16.3484	+	35.7980i	−0.636844	+	1.39449i	−0.902611	+	0.430457i	$0.858353\pi$
$660$	−5.81161	−	3.73490i	−0.226217	−	0.145381i
$661$	21.0402	−	6.17796i	0.818369	−	0.240295i	0.154356	−	0.988015i	$-0.450670\pi$
$661$	21.0402	−	6.17796i	0.818369	−	0.240295i	0.664014	+	0.747720i	$0.268852\pi$
$662$	−3.02659	−	3.49287i	−0.117632	−	0.135754i
$663$	−5.95109	−	1.74740i	−0.231121	−	0.0678633i
$664$	2.62649	+	5.75120i	0.101927	+	0.223190i
$665$	1.59235	−	11.0750i	0.0617486	−	0.429471i
$666$	−5.49844			−0.213060
$667$	0.435985	+	7.80963i	0.0168814	+	0.302390i
$668$	−15.9647			−0.617693
$669$	3.58038	−	24.9021i	0.138425	−	0.962770i
$670$	3.55435	+	7.78294i	0.137317	+	0.300681i
$671$	2.69313	+	0.790775i	0.103967	+	0.0305275i
$672$	16.6592	+	19.2257i	0.642642	+	0.741648i
$673$	14.6466	−	4.30064i	0.564587	−	0.165778i	0.0130301	−	0.999915i	$-0.495852\pi$
$673$	14.6466	−	4.30064i	0.564587	−	0.165778i	0.551557	+	0.834137i	$0.314034\pi$
$674$	20.9003	+	13.4318i	0.805050	+	0.517374i
$675$	−0.415415	+	0.909632i	−0.0159893	+	0.0350118i
$676$	−11.2444	+	12.9767i	−0.432475	+	0.499103i
$677$	3.42321	−	2.19997i	0.131565	−	0.0845516i	−0.473203	−	0.880953i	$-0.656902\pi$
$677$	3.42321	−	2.19997i	0.131565	−	0.0845516i	0.604768	+	0.796402i	$0.293266\pi$
$678$	0.776214	+	5.39869i	0.0298103	+	0.207335i
$679$	10.4847	+	72.9227i	0.402366	+	2.79852i
$680$	10.5347	−	6.77025i	0.403988	−	0.259627i
$681$	−4.03488	+	4.65650i	−0.154617	+	0.178437i
$682$	12.7810	−	27.9865i	0.489410	−	1.07166i
$683$	11.9135	+	7.65632i	0.455856	+	0.292961i	0.748347	−	0.663307i	$-0.230848\pi$
$683$	11.9135	+	7.65632i	0.455856	+	0.292961i	−0.292491	+	0.956268i	$0.594484\pi$
$684$	−3.68288	+	1.08139i	−0.140818	+	0.0413480i
$685$	6.71370	+	7.74803i	0.256517	+	0.296037i
$686$	−14.8228	−	4.35238i	−0.565939	−	0.166175i
$687$	0.995609	+	2.18008i	0.0379848	+	0.0831752i
$688$	0.242835	−	1.68896i	0.00925801	−	0.0643909i
$689$	5.80392			0.221112
$690$	−2.44760	+	2.37225i	−0.0931786	+	0.0903102i
$691$	−34.9938			−1.33123			−0.665614	−	0.746297i	$-0.731830\pi$
$691$	−34.9938			−1.33123			−0.665614	+	0.746297i	$0.731830\pi$
$692$	−2.79522	+	19.4412i	−0.106258	+	0.739043i
$693$	−8.36555	−	18.3180i	−0.317781	−	0.695843i
$694$	−20.1202	−	5.90783i	−0.763754	−	0.224258i
$695$	8.85559	+	10.2199i	0.335912	+	0.387663i
$696$	3.88706	−	1.14134i	0.147339	−	0.0432625i
$697$	25.5313	+	16.4079i	0.967066	+	0.621495i
$698$	7.22609	−	15.8229i	0.273511	−	0.598906i
$699$	−3.72246	+	4.29595i	−0.140796	+	0.162488i
$700$	5.47983	−	3.52167i	0.207118	−	0.133107i
$701$	−3.83585	−	26.6789i	−0.144878	−	1.00765i	−0.924441	−	0.381324i	$-0.875468\pi$
$701$	−3.83585	−	26.6789i	−0.144878	−	1.00765i	0.779563	−	0.626323i	$-0.215441\pi$
$702$	−0.124438	−	0.865488i	−0.00469662	−	0.0326657i
$703$	−16.7111	+	10.7396i	−0.630271	+	0.405051i
$704$	−5.14682	+	5.93975i	−0.193978	+	0.223863i
$705$	−3.07789	+	6.73965i	−0.115920	+	0.253830i
$706$	16.5230	+	10.6187i	0.621852	+	0.399640i
$707$	−37.4256	+	10.9892i	−1.40754	+	0.413290i
$708$	−8.39762	−	9.69136i	−0.315602	−	0.364224i
$709$	−13.9982	−	4.11024i	−0.525713	−	0.154363i	0.00809776	−	0.999967i	$-0.497422\pi$
$709$	−13.9982	−	4.11024i	−0.525713	−	0.154363i	−0.533811	+	0.845604i	$0.679241\pi$
$710$	2.26884	+	4.96808i	0.0851482	+	0.186449i
$711$	−1.99320	+	13.8630i	−0.0747508	+	0.519903i
$712$	0.561199			0.0210318
$713$	35.5374	+	27.4801i	1.33089	+	1.02914i
$714$	15.6138			0.584331
$715$	0.809128	−	5.62761i	0.0302597	−	0.210461i
$716$	−0.986181	−	2.15944i	−0.0368553	−	0.0807019i
$717$	26.1152	+	7.66811i	0.975289	+	0.286371i
$718$	1.67135	+	1.92885i	0.0623744	+	0.0719839i
$719$	−27.2208	+	7.99275i	−1.01517	+	0.298079i	−0.746665	−	0.665200i	$-0.768346\pi$
$719$	−27.2208	+	7.99275i	−1.01517	+	0.298079i	−0.268500	+	0.963280i	$0.586528\pi$
$720$	−1.02995	−	0.661907i	−0.0383839	−	0.0246678i
$721$	−16.5148	+	36.1623i	−0.615042	+	1.34675i
$722$	−5.77456	+	6.66419i	−0.214907	+	0.248016i
$723$	−0.211402	+	0.135860i	−0.00786212	+	0.00505268i
$724$	−3.12566	−	21.7394i	−0.116164	−	0.807940i
$725$	−0.232109	−	1.61435i	−0.00862032	−	0.0599556i
$726$	6.19259	−	3.97973i	0.229828	−	0.147702i
$727$	−29.2188	+	33.7203i	−1.08367	+	1.25062i	−0.117396	+	0.993085i	$0.537455\pi$
$727$	−29.2188	+	33.7203i	−1.08367	+	1.25062i	−0.966270	+	0.257532i	$0.917091\pi$
$728$	−5.53168	+	12.1127i	−0.205018	+	0.448926i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	8.34879	−	2.45143i	0.309003	−	0.0907313i
$731$	−4.60131	−	5.31019i	−0.170186	−	0.196405i
$732$	0.871135	+	0.255788i	0.0321981	+	0.00945421i
$733$	15.4999	+	33.9400i	0.572501	+	1.25360i	0.945455	+	0.325753i	$0.105618\pi$
$733$	15.4999	+	33.9400i	0.572501	+	1.25360i	−0.372954	+	0.927850i	$0.621655\pi$
$734$	−2.42009	+	16.8321i	−0.0893271	+	0.621284i
$735$	11.9882			0.442190
$736$	−16.4262	−	22.6731i	−0.605478	−	0.835741i
$737$	55.6341			2.04931
$738$	−0.608899	+	4.23498i	−0.0224139	+	0.155892i
$739$	−2.07163	−	4.53623i	−0.0762061	−	0.166868i	0.867694	−	0.497098i	$-0.165601\pi$
$739$	−2.07163	−	4.53623i	−0.0762061	−	0.166868i	−0.943901	+	0.330230i	$0.892874\pi$
$740$	−11.0962	−	3.25812i	−0.407903	−	0.119771i
$741$	−2.06867	−	2.38737i	−0.0759945	−	0.0877023i
$742$	−14.0190	+	4.11635i	−0.514653	+	0.151116i
$743$	−42.4440	−	27.2771i	−1.55712	−	1.00070i	−0.983359	−	0.181675i	$-0.941848\pi$
$743$	−42.4440	−	27.2771i	−1.55712	−	1.00070i	−0.573759	−	0.819024i	$-0.694516\pi$
$744$	9.66547	−	21.1644i	0.354353	−	0.775925i
$745$	12.2539	−	14.1417i	0.448946	−	0.518112i
$746$	−7.18287	+	4.61615i	−0.262983	+	0.169009i
$747$	−0.362248	−	2.51949i	−0.0132540	−	0.0921833i
$748$	−4.95654	−	34.4735i	−0.181229	−	1.26048i
$749$	45.3237	−	29.1278i	1.65609	−	1.06431i
$750$	0.465433	−	0.537138i	0.0169952	−	0.0196135i
$751$	−17.1645	+	37.5850i	−0.626341	+	1.37150i	0.284475	+	0.958683i	$0.408181\pi$
$751$	−17.1645	+	37.5850i	−0.626341	+	1.37150i	−0.910816	+	0.412812i	$0.864547\pi$
$752$	−7.63109	−	4.90420i	−0.278277	−	0.178838i
$753$	−3.28062	+	0.963277i	−0.119552	+	0.0351038i
$754$	0.933888	+	1.07776i	0.0340102	+	0.0392499i
$755$	0.499587	+	0.146692i	0.0181818	+	0.00533867i
$756$	−2.70597	−	5.92524i	−0.0984151	−	0.215499i
$757$	2.75675	−	19.1736i	0.100196	−	0.696876i	−0.876367	−	0.481644i	$-0.840040\pi$
$757$	2.75675	−	19.1736i	0.100196	−	0.696876i	0.976563	−	0.215233i	$-0.0690510\pi$
$758$	18.1439			0.659016
$759$	7.41976	+	20.8844i	0.269320	+	0.758057i
$760$	6.37799			0.231354
$761$	−1.26103	+	8.77063i	−0.0457122	+	0.317935i	0.954117	+	0.299435i	$0.0967982\pi$
$761$	−1.26103	+	8.77063i	−0.0457122	+	0.317935i	−0.999829	+	0.0185000i	$0.994111\pi$
$762$	−3.09578	−	6.77880i	−0.112148	−	0.245570i
$763$	49.9230	+	14.6587i	1.80733	+	0.530681i
$764$	−1.61618	−	1.86517i	−0.0584712	−	0.0674793i
$765$	−4.83727	+	1.42035i	−0.174892	+	0.0513529i
$766$	4.81503	+	3.09443i	0.173974	+	0.111806i
$767$	4.38416	−	9.59997i	0.158303	−	0.346635i
$768$	−7.09921	+	8.19292i	−0.256171	+	0.295637i
$769$	−28.3494	+	18.2190i	−1.02230	+	0.656995i	−0.940549	−	0.339658i	$-0.889689\pi$
$769$	−28.3494	+	18.2190i	−1.02230	+	0.656995i	−0.0817546	+	0.996652i	$0.526052\pi$
$770$	2.03690	+	14.1670i	0.0734049	+	0.510543i
$771$	1.34188	+	9.33299i	0.0483267	+	0.336119i
$772$	−4.81518	+	3.09453i	−0.173302	+	0.111374i
$773$	23.8039	−	27.4712i	0.856167	−	0.988070i	−0.143832	−	0.989602i	$-0.545942\pi$
$773$	23.8039	−	27.4712i	0.856167	−	0.988070i	0.999999	+	0.00153248i	$0.000487803\pi$
$774$	0.411494	−	0.901047i	0.0147909	−	0.0323875i
$775$	−7.88007	−	5.06422i	−0.283061	−	0.181912i
$776$	−40.2943	+	11.8315i	−1.44648	+	0.424725i
$777$	−22.0761	−	25.4772i	−0.791975	−	0.913988i
$778$	0.365551	+	0.107336i	0.0131056	+	0.00384817i
$779$	6.42119	+	14.0604i	0.230063	+	0.503768i
$780$	0.261725	−	1.82034i	0.00937126	−	0.0651785i
$781$	35.5128			1.27075
$782$	−17.1192	−	1.49368i	−0.612182	−	0.0534137i
$783$	−1.63095			−0.0582856
$784$	−2.08877	+	14.5277i	−0.0745989	+	0.518847i
$785$	7.76477	+	17.0025i	0.277137	+	0.606844i
$786$	−6.87892	−	2.01983i	−0.245363	−	0.0720451i
$787$	15.5721	+	17.9712i	0.555087	+	0.640604i	0.962061	−	0.272836i	$-0.0879615\pi$
$787$	15.5721	+	17.9712i	0.555087	+	0.640604i	−0.406974	+	0.913440i	$0.633416\pi$
$788$	−24.4511	+	7.17948i	−0.871033	+	0.255758i
$789$	17.8768	+	11.4887i	0.636429	+	0.409008i
$790$	4.13514	−	9.05470i	0.147122	−	0.322152i
$791$	−21.8985	+	25.2722i	−0.778620	+	0.898575i
$792$	9.65684	−	6.20607i	0.343141	−	0.220523i
$793$	0.106339	+	0.739601i	0.00377620	+	0.0262640i
$794$	0.386341	+	2.68706i	0.0137107	+	0.0953603i
$795$	3.96873	−	2.55055i	0.140757	−	0.0904587i
$796$	26.2750	−	30.3230i	0.931293	−	1.07477i
$797$	−14.8876	+	32.5992i	−0.527345	+	1.15472i	0.439239	+	0.898370i	$0.355248\pi$
$797$	−14.8876	+	32.5992i	−0.527345	+	1.15472i	−0.966583	+	0.256353i	$0.917479\pi$
$798$	6.68995	+	4.29937i	0.236822	+	0.152196i
$799$	−35.8403	+	10.5237i	−1.26794	+	0.372301i
$800$	3.82307	+	4.41206i	0.135166	+	0.155990i
$801$	−0.216781	−	0.0636527i	−0.00765959	−	0.00224906i
$802$	−7.74388	−	16.9567i	−0.273446	−	0.598763i
$803$	8.05183	−	56.0017i	0.284143	−	1.97626i
$804$	17.9957			0.634659
$805$	−20.8189	−	1.81648i	−0.733771	−	0.0640225i
$806$	8.19044			0.288496
$807$	−1.61765	+	11.2510i	−0.0569441	+	0.396055i
$808$	−9.23646	−	20.2250i	−0.324937	−	0.711514i
$809$	17.7782	+	5.22014i	0.625047	+	0.183530i	0.578892	−	0.815404i	$-0.303485\pi$
$809$	17.7782	+	5.22014i	0.625047	+	0.183530i	0.0461545	+	0.998934i	$0.485303\pi$
$810$	−0.465433	−	0.537138i	−0.0163536	−	0.0188731i
$811$	29.3364	−	8.61394i	1.03014	−	0.302476i	0.277372	−	0.960763i	$-0.410536\pi$
$811$	29.3364	−	8.61394i	1.03014	−	0.302476i	0.752768	+	0.658286i	$0.228718\pi$
$812$	8.93736	+	5.74369i	0.313640	+	0.201564i
$813$	8.31614	−	18.2098i	0.291660	−	0.638645i
$814$	16.6402	−	19.2039i	0.583240	−	0.673095i
$815$	0.957452	−	0.615317i	0.0335381	−	0.0215536i
$816$	−0.878409	−	6.10947i	−0.0307505	−	0.213874i
$817$	−0.509296	−	3.54223i	−0.0178180	−	0.123927i
$818$	17.0053	−	10.9286i	0.594577	−	0.382111i
$819$	3.51064	−	4.05149i	0.122672	−	0.141571i
$820$	−3.73825	+	8.18562i	−0.130545	+	0.285854i
$821$	23.9087	+	15.3652i	0.834420	+	0.536249i	0.886679	−	0.462385i	$-0.153006\pi$
$821$	23.9087	+	15.3652i	0.834420	+	0.536249i	−0.0522598	+	0.998634i	$0.516642\pi$
$822$	−6.99138	+	2.05286i	−0.243853	+	0.0716016i
$823$	20.3101	+	23.4391i	0.707967	+	0.817037i	0.989806	−	0.142424i	$-0.0454898\pi$
$823$	20.3101	+	23.4391i	0.707967	+	0.817037i	−0.281839	+	0.959462i	$0.590944\pi$
$824$	−21.7434	−	6.38445i	−0.757468	−	0.222413i
$825$	−1.91979	−	4.20375i	−0.0668384	−	0.146356i
$826$	−3.78101	+	26.2975i	−0.131558	+	0.915007i
$827$	0.982592			0.0341681			0.0170840	−	0.999854i	$-0.494562\pi$
$827$	0.982592			0.0341681			0.0170840	+	0.999854i	$0.494562\pi$
$828$	2.40004	+	6.75540i	0.0834070	+	0.234766i
$829$	−31.9397			−1.10931			−0.554656	−	0.832080i	$-0.687150\pi$
$829$	−31.9397			−1.10931			−0.554656	+	0.832080i	$0.687150\pi$
$830$	−0.257463	+	1.79069i	−0.00893665	+	0.0621558i
$831$	2.60274	+	5.69920i	0.0902879	+	0.197703i
$832$	−2.00751	−	0.589457i	−0.0695978	−	0.0204358i
$833$	39.5786	+	45.6761i	1.37132	+	1.58258i
$834$	−9.22186	+	2.70778i	−0.319327	+	0.0937628i
$835$	−8.98439	−	5.77392i	−0.310918	−	0.199815i
$836$	7.36883	−	16.1355i	0.254856	−	0.558057i
$837$	−6.13412	+	7.07915i	−0.212026	+	0.244691i
$838$	−4.96234	+	3.18910i	−0.171421	+	0.110166i
$839$	4.59819	+	31.9811i	0.158747	+	1.10411i	0.900946	+	0.433931i	$0.142874\pi$
$839$	4.59819	+	31.9811i	0.158747	+	1.10411i	−0.742199	+	0.670180i	$0.766217\pi$
$840$	1.54038	+	10.7136i	0.0531483	+	0.369654i
$841$	−22.1586	+	14.2405i	−0.764090	+	0.491051i
$842$	0.922429	−	1.06454i	0.0317890	−	0.0366865i
$843$	2.20264	−	4.82310i	0.0758629	−	0.166117i
$844$	−20.9444	−	13.4602i	−0.720937	−	0.463318i
$845$	−11.0212	+	3.23611i	−0.379140	+	0.111326i
$846$	−3.44849	−	3.97977i	−0.118561	−	0.136827i
$847$	43.3032	+	12.7150i	1.48792	+	0.436892i
$848$	2.39936	+	5.25386i	0.0823943	+	0.180418i
$849$	−1.34014	+	9.32085i	−0.0459933	+	0.319891i
$850$	3.58317			0.122902
$851$	21.7673	+	30.0455i	0.746175	+	1.02995i
$852$	11.4872			0.393544
$853$	−2.87282	+	19.9809i	−0.0983634	+	0.684133i	0.879655	+	0.475613i	$0.157774\pi$
$853$	−2.87282	+	19.9809i	−0.0983634	+	0.684133i	−0.978018	+	0.208520i	$0.933135\pi$
$854$	−0.781406	−	1.71104i	−0.0267392	−	0.0585506i
$855$	−2.46370	−	0.723408i	−0.0842568	−	0.0247400i
$856$	20.1114	+	23.2098i	0.687395	+	0.793296i
$857$	26.5094	−	7.78386i	0.905544	−	0.265892i	0.204380	−	0.978892i	$-0.434482\pi$
$857$	26.5094	−	7.78386i	0.905544	−	0.265892i	0.701164	+	0.713000i	$0.252664\pi$
$858$	3.39940	+	2.18466i	0.116053	+	0.0745830i
$859$	11.9049	−	26.0681i	0.406189	−	0.889431i	−0.590416	−	0.807099i	$-0.701036\pi$
$859$	11.9049	−	26.0681i	0.406189	−	0.889431i	0.996605	−	0.0823313i	$-0.0262366\pi$
$860$	1.36434	−	1.57453i	0.0465235	−	0.0536910i
$861$	−22.0676	+	14.1820i	−0.752062	+	0.483321i
$862$	2.16807	+	15.0792i	0.0738447	+	0.513601i
$863$	−1.46544	−	10.1924i	−0.0498842	−	0.346952i	−0.999443	−	0.0333641i	$-0.989378\pi$
$863$	−1.46544	−	10.1924i	−0.0498842	−	0.346952i	0.949559	−	0.313588i	$-0.101531\pi$
$864$	4.91123	−	3.15626i	0.167083	−	0.107378i
$865$	−8.60431	+	9.92990i	−0.292555	+	0.337627i
$866$	−7.13587	+	15.6254i	−0.242487	+	0.530972i
$867$	−7.08049	−	4.55036i	−0.240466	−	0.154538i
$868$	58.5444	−	17.1902i	1.98713	−	0.583473i
$869$	−42.3858	−	48.9158i	−1.43784	−	1.65935i
$870$	1.11222	+	0.326578i	0.0377079	+	0.0110720i
$871$	6.15245	+	13.4720i	0.208468	+	0.456481i
$872$	−4.22090	+	29.3570i	−0.142938	+	0.994153i
$873$	16.9069			0.572213
$874$	−6.92368	−	5.35389i	−0.234197	−	0.181098i
$875$	4.35754			0.147312
$876$	2.60449	−	18.1146i	0.0879976	−	0.612037i
$877$	−10.0839	−	22.0806i	−0.340509	−	0.745610i	0.659473	−	0.751729i	$-0.270780\pi$
$877$	−10.0839	−	22.0806i	−0.340509	−	0.745610i	−0.999981	+	0.00611859i	$0.998052\pi$
$878$	−12.7753	−	3.75116i	−0.431145	−	0.126596i
$879$	−7.95110	−	9.17606i	−0.268184	−	0.309501i
$880$	5.42876	−	1.59403i	0.183003	−	0.0537347i
$881$	−0.493082	−	0.316885i	−0.0166124	−	0.0106761i	0.532308	−	0.846551i	$-0.321325\pi$
$881$	−0.493082	−	0.316885i	−0.0166124	−	0.0106761i	−0.548921	+	0.835874i	$0.684961\pi$
$882$	−3.53951	+	7.75044i	−0.119181	+	0.260971i
$883$	22.9173	−	26.4479i	0.771227	−	0.890044i	−0.225216	−	0.974309i	$-0.572309\pi$
$883$	22.9173	−	26.4479i	0.771227	−	0.890044i	0.996443	+	0.0842652i	$0.0268543\pi$
$884$	7.79975	−	5.01259i	0.262334	−	0.168592i
$885$	−1.22084	−	8.49112i	−0.0410380	−	0.285426i
$886$	−3.90365	−	27.1505i	−0.131146	−	0.912139i
$887$	−6.13466	+	3.94251i	−0.205982	+	0.132376i	−0.639565	−	0.768737i	$-0.720885\pi$
$887$	−6.13466	+	3.94251i	−0.205982	+	0.132376i	0.433583	+	0.901114i	$0.357249\pi$
$888$	12.5840	−	14.5227i	0.422291	−	0.487349i
$889$	18.9803	−	41.5610i	0.636578	−	1.39391i
$890$	0.135087	+	0.0868154i	0.00452814	+	0.00291006i
$891$	−4.43417	+	1.30199i	−0.148550	+	0.0436183i
$892$	24.6279	+	28.4221i	0.824602	+	0.951641i
$893$	−18.2541	−	5.35988i	−0.610849	−	0.179362i
$894$	5.52477	+	12.0976i	0.184776	+	0.404603i
$895$	0.226009	−	1.57193i	0.00755465	−	0.0525437i
$896$	−45.6115			−1.52377
$897$	−4.23671	+	4.10629i	−0.141459	+	0.137105i
$898$	−5.71364			−0.190667
$899$	2.17418	−	15.1218i	0.0725130	−	0.504339i
$900$	−0.620985	−	1.35977i	−0.0206995	−	0.0453256i
$901$	22.8205	+	6.70071i	0.760262	+	0.223233i
$902$	−12.9484	−	14.9432i	−0.431133	−	0.497554i
$903$	5.82716	−	1.71101i	0.193916	−	0.0569388i
$904$	−16.0357	−	10.3055i	−0.533339	−	0.342756i
$905$	6.10344	−	13.3647i	0.202885	−	0.444257i
$906$	−0.242341	+	0.279676i	−0.00805124	+	0.00929162i
$907$	4.40313	−	2.82972i	0.146204	−	0.0939593i	−0.465494	−	0.885051i	$-0.654123\pi$
$907$	4.40313	−	2.82972i	0.146204	−	0.0939593i	0.611698	+	0.791092i	$0.290487\pi$
$908$	−1.31078	−	9.11670i	−0.0434999	−	0.302548i
$909$	1.27390	+	8.86019i	0.0422527	+	0.293874i
$910$	−3.20533	+	2.05994i	−0.106256	+	0.0682863i
$911$	−32.2500	+	37.2185i	−1.06849	+	1.23310i	−0.0971849	+	0.995266i	$0.530984\pi$
$911$	−32.2500	+	37.2185i	−1.06849	+	1.23310i	−0.971305	+	0.237837i	$0.923562\pi$
$912$	1.30592	−	2.85957i	0.0432433	−	0.0946897i
$913$	9.89586	+	6.35968i	0.327505	+	0.210475i
$914$	10.1313	−	2.97480i	0.335112	−	0.0983978i
$915$	0.397735	+	0.459011i	0.0131487	+	0.0151744i
$916$	−3.43754	−	1.00935i	−0.113579	−	0.0333499i
$917$	−18.2597	−	39.9832i	−0.602989	−	1.32036i
$918$	0.509938	−	3.54669i	0.0168304	−	0.117058i
$919$	31.8816			1.05168			0.525838	−	0.850585i	$-0.323752\pi$
$919$	31.8816			1.05168			0.525838	+	0.850585i	$0.323752\pi$
$920$	−0.663998	−	11.8939i	−0.0218914	−	0.392131i
$921$	12.9179			0.425659
$922$	−1.92337	+	13.3773i	−0.0633428	+	0.440559i
$923$	3.92729	+	8.59956i	0.129268	+	0.283058i
$924$	28.8837	+	8.48102i	0.950205	+	0.279005i
$925$	−5.06618	−	5.84668i	−0.166575	−	0.192238i
$926$	12.3187	−	3.61710i	0.404818	−	0.118865i
$927$	7.67496	+	4.93240i	0.252079	+	0.162001i
$928$	−3.95537	+	8.66106i	−0.129841	+	0.284313i
$929$	34.8309	−	40.1970i	1.14276	−	1.31882i	0.202146	−	0.979355i	$-0.435208\pi$
$929$	34.8309	−	40.1970i	1.14276	−	1.31882i	0.940618	−	0.339466i	$-0.110246\pi$
$930$	5.60065	−	3.59932i	0.183653	−	0.118026i
$931$	4.38076	+	30.4688i	0.143573	+	0.998575i
$932$	−1.20929	−	8.41079i	−0.0396116	−	0.275505i
$933$	−17.3293	+	11.1368i	−0.567335	+	0.364604i
$934$	−0.366305	+	0.422739i	−0.0119859	+	0.0138324i
$935$	9.67858	−	21.1931i	0.316524	−	0.693090i
$936$	2.57075	+	1.65212i	0.0840276	+	0.0540013i
$937$	9.43218	−	2.76954i	0.308136	−	0.0904769i	−0.124009	−	0.992281i	$-0.539575\pi$
$937$	9.43218	−	2.76954i	0.308136	−	0.0904769i	0.432145	+	0.901804i	$0.357757\pi$
$938$	−24.4157	−	28.1772i	−0.797199	−	0.920017i
$939$	3.83097	+	1.12487i	0.125019	+	0.0367088i
$940$	−4.60101	−	10.0748i	−0.150068	−	0.328604i
$941$	7.14689	−	49.7077i	0.232982	−	1.62042i	−0.452106	−	0.891964i	$-0.649327\pi$
$941$	7.14689	−	49.7077i	0.232982	−	1.62042i	0.685088	−	0.728461i	$-0.259764\pi$
$942$	−13.2848			−0.432842
$943$	25.5520	−	13.4383i	0.832087	−	0.437611i
$944$	10.5026			0.341830
$945$	0.620143	−	4.31319i	0.0201732	−	0.140308i
$946$	1.90167	+	4.16407i	0.0618286	+	0.135386i
$947$	−36.7106	−	10.7792i	−1.19293	−	0.350277i	−0.375787	−	0.926706i	$-0.622628\pi$
$947$	−36.7106	−	10.7792i	−1.19293	−	0.350277i	−0.817147	+	0.576429i	$0.804446\pi$
$948$	−13.7103	−	15.8226i	−0.445291	−	0.513893i
$949$	14.4514	−	4.24333i	0.469114	−	0.137744i
$950$	1.53526	+	0.986651i	0.0498104	+	0.0320112i
$951$	−7.07616	+	15.4946i	−0.229460	+	0.502448i
$952$	−35.7344	+	41.2397i	−1.15816	+	1.33659i
$953$	−30.0809	+	19.3318i	−0.974417	+	0.626220i	−0.927952	−	0.372700i	$-0.878432\pi$
$953$	−30.0809	+	19.3318i	−0.974417	+	0.626220i	−0.0464650	+	0.998920i	$0.514796\pi$
$954$	0.477181	+	3.31887i	0.0154493	+	0.107452i
$955$	−0.234958	−	1.63417i	−0.00760307	−	0.0528805i
$956$	−34.2276	+	21.9968i	−1.10700	+	0.711426i
$957$	4.93585	−	5.69627i	0.159553	−	0.184134i
$958$	1.41678	−	3.10231i	0.0457740	−	0.100231i
$959$	−37.5821	−	24.1526i	−1.21359	−	0.779927i
$960$	−1.63178	+	0.479133i	−0.0526654	+	0.0154640i
$961$	−37.1580	−	42.8826i	−1.19865	−	1.38331i
$962$	6.49049	+	1.90578i	0.209262	+	0.0614448i
$963$	−5.13617	−	11.2466i	−0.165511	−	0.362418i
$964$	0.0534603	−	0.371824i	0.00172184	−	0.0119757i
$965$	−3.82901			−0.123260
$966$	7.32117	−	12.9233i	0.235555	−	0.415800i
$967$	−49.2572			−1.58400			−0.792002	−	0.610518i	$-0.790961\pi$
$967$	−49.2572			−1.58400			−0.792002	+	0.610518i	$0.790961\pi$
$968$	−3.66121	+	25.4643i	−0.117676	+	0.818453i
$969$	−5.37759	−	11.7753i	−0.172753	−	0.378276i
$970$	−11.5296	−	3.38540i	−0.370193	−	0.108699i
$971$	−10.9840	−	12.6763i	−0.352495	−	0.406801i	0.551616	−	0.834098i	$-0.314011\pi$
$971$	−10.9840	−	12.6763i	−0.352495	−	0.406801i	−0.904111	+	0.427297i	$0.859466\pi$
$972$	−1.43430	+	0.421149i	−0.0460053	+	0.0135084i
$973$	−49.5720	−	31.8580i	−1.58921	−	1.02132i
$974$	−4.05193	+	8.87249i	−0.129832	+	0.284293i
$975$	0.805647	−	0.929766i	0.0258014	−	0.0297764i
$976$	−0.625547	+	0.402014i	−0.0200233	+	0.0128682i
$977$	2.01904	+	14.0427i	0.0645949	+	0.449267i	0.996292	+	0.0860321i	$0.0274188\pi$
$977$	2.01904	+	14.0427i	0.0645949	+	0.449267i	−0.931697	+	0.363235i	$0.881672\pi$
$978$	0.115119	+	0.800672i	0.00368111	+	0.0256027i
$979$	0.878370	−	0.564494i	0.0280728	−	0.0180413i
$980$	−11.7355	+	13.5435i	−0.374876	+	0.432630i
$981$	4.96020	−	10.8613i	0.158367	−	0.346775i
$982$	−17.5737	−	11.2939i	−0.560798	−	0.360403i
$983$	9.42584	−	2.76767i	0.300637	−	0.0882751i	−0.127935	−	0.991783i	$-0.540835\pi$
$983$	9.42584	−	2.76767i	0.300637	−	0.0882751i	0.428572	+	0.903507i	$0.359017\pi$
$984$	−9.79203	−	11.3006i	−0.312159	−	0.360250i
$985$	−16.3568	−	4.80279i	−0.521171	−	0.153030i
$986$	2.42768	+	5.31587i	0.0773130	+	0.169292i
$987$	4.59476	−	31.9573i	0.146253	−	1.01721i
$988$	4.72217			0.150232
$989$	−6.55268	+	1.31853i	−0.208363	+	0.0419268i
$990$	3.28457			0.104391
$991$	−6.40282	+	44.5326i	−0.203392	+	1.41463i	0.590731	+	0.806869i	$0.298839\pi$
$991$	−6.40282	+	44.5326i	−0.203392	+	1.41463i	−0.794123	+	0.607757i	$0.792070\pi$
$992$	22.7169	+	49.7431i	0.721262	+	1.57934i
$993$	−6.23933	−	1.83203i	−0.197999	−	0.0581378i
$994$	−15.5852	−	17.9863i	−0.494333	−	0.570491i
$995$	25.7535	−	7.56192i	0.816442	−	0.239729i
$996$	3.20097	+	2.05714i	0.101427	+	0.0651829i
$997$	19.6672	−	43.0651i	0.622866	−	1.36389i	−0.290551	−	0.956860i	$-0.593839\pi$
$997$	19.6672	−	43.0651i	0.622866	−	1.36389i	0.913417	−	0.407026i	$-0.133434\pi$
$998$	−13.4077	+	15.4733i	−0.424412	+	0.489798i
$999$	−6.50816	+	4.18254i	−0.205909	+	0.132330i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.m.a.31.3	✓	30
23.3	even	11	inner	345.2.m.a.256.3	yes	30
23.7	odd	22		7935.2.a.bq.1.7		15
23.16	even	11		7935.2.a.bp.1.7		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.a.31.3	✓	30	1.1	even	1	trivial
345.2.m.a.256.3	yes	30	23.3	even	11	inner
7935.2.a.bp.1.7		15	23.16	even	11
7935.2.a.bq.1.7		15	23.7	odd	22

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:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.101148 - 0.703501i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(1.43430 + 0.421149i) q^{4} +(0.654861 + 0.755750i) q^{5} +(-0.681946 + 0.200237i) q^{6} +(-3.66580 - 2.35586i) q^{7} +(1.03186 - 2.25945i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.101148 - 0.703501i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(1.43430 + 0.421149i) q^{4} +(0.654861 + 0.755750i) q^{5} +(-0.681946 + 0.200237i) q^{6} +(-3.66580 - 2.35586i) q^{7} +(1.03186 - 2.25945i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(0.597909 - 0.384253i) q^{10} +(-0.657690 - 4.57433i) q^{11} +(-0.212740 - 1.47964i) q^{12} +(1.03496 - 0.665127i) q^{13} +(-2.02814 + 2.34060i) q^{14} +(0.415415 - 0.909632i) q^{15} +(1.02995 + 0.661907i) q^{16} +(4.83727 - 1.42035i) q^{17} +(0.465433 + 0.537138i) q^{18} +(2.46370 + 0.723408i) q^{19} +(0.620985 + 1.35977i) q^{20} +(-0.620143 + 4.31319i) q^{21} -3.28457 q^{22} +(1.09255 - 4.66973i) q^{23} -2.48392 q^{24} +(-0.142315 + 0.989821i) q^{25} +(-0.363234 - 0.795371i) q^{26} +(0.959493 + 0.281733i) q^{27} +(-4.26569 - 4.92287i) q^{28} +(-1.56489 + 0.459493i) q^{29} +(-0.597909 - 0.384253i) q^{30} +(-3.89122 + 8.52058i) q^{31} +(3.82307 - 4.41206i) q^{32} +(-3.88775 + 2.49850i) q^{33} +(-0.509938 - 3.54669i) q^{34} +(-0.620143 - 4.31319i) q^{35} +(-1.25755 + 0.808179i) q^{36} +(-5.06618 + 5.84668i) q^{37} +(0.758118 - 1.66005i) q^{38} +(-1.03496 - 0.665127i) q^{39} +(2.38330 - 0.699801i) q^{40} +(3.94217 + 4.54951i) q^{41} +(2.97161 + 0.872542i) q^{42} +(-0.578970 - 1.26777i) q^{43} +(0.983151 - 6.83796i) q^{44} -1.00000 q^{45} +(-3.17465 - 1.24095i) q^{46} -7.40920 q^{47} +(0.174236 - 1.21184i) q^{48} +(4.98006 + 10.9048i) q^{49} +(0.681946 + 0.200237i) q^{50} +(-3.30147 - 3.81010i) q^{51} +(1.76456 - 0.518122i) q^{52} +(3.96873 + 2.55055i) q^{53} +(0.295250 - 0.646508i) q^{54} +(3.02635 - 3.49260i) q^{55} +(-9.10554 + 5.85177i) q^{56} +(-0.365424 - 2.54158i) q^{57} +(0.164968 + 1.14738i) q^{58} +(7.21664 - 4.63785i) q^{59} +(0.978922 - 1.12974i) q^{60} +(-0.252306 + 0.552472i) q^{61} +(5.60065 + 3.59932i) q^{62} +(4.18103 - 1.22766i) q^{63} +(-1.11370 - 1.28528i) q^{64} +(1.18042 + 0.346604i) q^{65} +(1.36446 + 2.98775i) q^{66} +(-1.71325 + 11.9159i) q^{67} +7.53629 q^{68} +(-4.70159 + 0.946055i) q^{69} -3.09706 q^{70} +(-1.09362 + 7.60626i) q^{71} +(1.03186 + 2.25945i) q^{72} +(11.7467 + 3.44914i) q^{73} +(3.60071 + 4.15545i) q^{74} +(0.959493 - 0.281733i) q^{75} +(3.22903 + 2.07517i) q^{76} +(-8.36555 + 18.3180i) q^{77} +(-0.572602 + 0.660818i) q^{78} +(11.7822 - 7.57197i) q^{79} +(0.174236 + 1.21184i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(3.59933 - 2.31315i) q^{82} +(-1.66688 + 1.92368i) q^{83} +(-2.70597 + 5.92524i) q^{84} +(4.24117 + 2.72563i) q^{85} +(-0.950437 + 0.279074i) q^{86} +(1.06805 + 1.23259i) q^{87} +(-11.0141 - 3.23404i) q^{88} +(0.0938560 + 0.205516i) q^{89} +(-0.101148 + 0.703501i) q^{90} -5.36090 q^{91} +(3.53370 - 6.23767i) q^{92} +9.36706 q^{93} +(-0.749428 + 5.21239i) q^{94} +(1.06667 + 2.33567i) q^{95} +(-5.60151 - 1.64475i) q^{96} +(-11.0717 - 12.7774i) q^{97} +(8.17527 - 2.40048i) q^{98} +(3.88775 + 2.49850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{4} + 3 q^{5} + 11 q^{6} + q^{7} + 22 q^{8} - 3 q^{9} - 7 q^{11} - 2 q^{12} + 7 q^{13} - 47 q^{14} - 3 q^{15} + 26 q^{16} + 15 q^{17} - 7 q^{19} - 2 q^{20} - 12 q^{21} - 18 q^{22} + 12 q^{23} - 3 q^{25} - 18 q^{26} + 3 q^{27} + 2 q^{28} - 6 q^{29} + 22 q^{31} + 33 q^{32} - 4 q^{33} - 53 q^{34} - 12 q^{35} - 9 q^{36} - 23 q^{37} + 21 q^{38} - 7 q^{39} + 11 q^{40} + 26 q^{41} + 3 q^{42} - 19 q^{43} - 47 q^{44} - 30 q^{45} - 44 q^{46} + 14 q^{47} + 7 q^{48} + 2 q^{49} - 11 q^{50} - 15 q^{51} + 55 q^{52} - 14 q^{53} - 11 q^{54} - 4 q^{55} + 6 q^{56} - 26 q^{57} - 18 q^{58} + 40 q^{59} - 9 q^{60} + 37 q^{61} + 19 q^{62} - 10 q^{63} + 14 q^{64} + 4 q^{65} - 4 q^{66} - 108 q^{67} + 54 q^{68} + 21 q^{69} - 30 q^{70} + 39 q^{71} + 22 q^{72} + 57 q^{73} - 11 q^{74} + 3 q^{75} + 22 q^{76} + 2 q^{77} + 7 q^{78} + 55 q^{79} + 7 q^{80} - 3 q^{81} - 26 q^{82} - 79 q^{83} - 2 q^{84} + 18 q^{85} - 44 q^{86} - 5 q^{87} - 8 q^{88} - 30 q^{89} + 40 q^{91} + 35 q^{92} + 44 q^{93} - 29 q^{94} + 7 q^{95} + 22 q^{96} - 52 q^{97} + 28 q^{98} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^4 + 3 * q^5 + 11 * q^6 + q^7 + 22 * q^8 - 3 * q^9 - 7 * q^11 - 2 * q^12 + 7 * q^13 - 47 * q^14 - 3 * q^15 + 26 * q^16 + 15 * q^17 - 7 * q^19 - 2 * q^20 - 12 * q^21 - 18 * q^22 + 12 * q^23 - 3 * q^25 - 18 * q^26 + 3 * q^27 + 2 * q^28 - 6 * q^29 + 22 * q^31 + 33 * q^32 - 4 * q^33 - 53 * q^34 - 12 * q^35 - 9 * q^36 - 23 * q^37 + 21 * q^38 - 7 * q^39 + 11 * q^40 + 26 * q^41 + 3 * q^42 - 19 * q^43 - 47 * q^44 - 30 * q^45 - 44 * q^46 + 14 * q^47 + 7 * q^48 + 2 * q^49 - 11 * q^50 - 15 * q^51 + 55 * q^52 - 14 * q^53 - 11 * q^54 - 4 * q^55 + 6 * q^56 - 26 * q^57 - 18 * q^58 + 40 * q^59 - 9 * q^60 + 37 * q^61 + 19 * q^62 - 10 * q^63 + 14 * q^64 + 4 * q^65 - 4 * q^66 - 108 * q^67 + 54 * q^68 + 21 * q^69 - 30 * q^70 + 39 * q^71 + 22 * q^72 + 57 * q^73 - 11 * q^74 + 3 * q^75 + 22 * q^76 + 2 * q^77 + 7 * q^78 + 55 * q^79 + 7 * q^80 - 3 * q^81 - 26 * q^82 - 79 * q^83 - 2 * q^84 + 18 * q^85 - 44 * q^86 - 5 * q^87 - 8 * q^88 - 30 * q^89 + 40 * q^91 + 35 * q^92 + 44 * q^93 - 29 * q^94 + 7 * q^95 + 22 * q^96 - 52 * q^97 + 28 * q^98 + 4 * q^99

Introduction

L-functions

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