LMFDB - Embedded newform 322.2.i.e.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.1
Character	$\chi$	$=$	322.85
Dual form			322.2.i.e.197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{2} +(-1.71143 + 1.09987i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.475695 + 1.04163i) q^{5} +(-0.289523 + 2.01368i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.473040 - 1.03581i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{2} +(-1.71143 + 1.09987i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.475695 + 1.04163i) q^{5} +(-0.289523 + 2.01368i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.473040 - 1.03581i) q^{9} +(1.09872 + 0.322614i) q^{10} +(3.36896 + 3.88799i) q^{11} +(1.33224 + 1.53748i) q^{12} +(-0.870228 - 0.255522i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(-1.95977 - 1.25947i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.937384 + 6.51965i) q^{17} +(-0.473040 - 1.03581i) q^{18} +(0.887536 + 6.17295i) q^{19} +(0.963326 - 0.619092i) q^{20} +(1.33224 - 1.53748i) q^{21} +5.14455 q^{22} +(-3.59512 + 3.17414i) q^{23} +2.03438 q^{24} +(2.41560 - 2.78775i) q^{25} +(-0.762989 + 0.490343i) q^{26} +(-0.538884 - 3.74802i) q^{27} +(0.415415 + 0.909632i) q^{28} +(1.28958 - 8.96921i) q^{29} +(-2.23522 + 0.656321i) q^{30} +(2.48641 + 1.59792i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-10.0420 - 2.94861i) q^{33} +(4.31337 + 4.97789i) q^{34} +(-0.749886 - 0.865415i) q^{35} +(-1.09259 - 0.320814i) q^{36} +(3.54907 - 7.77138i) q^{37} +(5.24641 + 3.37166i) q^{38} +(1.77038 - 0.519830i) q^{39} +(0.162966 - 1.13345i) q^{40} +(1.59609 + 3.49495i) q^{41} +(-0.289523 - 2.01368i) q^{42} +(-10.5306 + 6.76758i) q^{43} +(3.36896 - 3.88799i) q^{44} +1.30395 q^{45} +(0.0445515 + 4.79562i) q^{46} +2.75888 q^{47} +(1.33224 - 1.53748i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.524961 - 3.65118i) q^{50} +(-5.56650 - 12.1889i) q^{51} +(-0.129075 + 0.897735i) q^{52} +(7.77095 - 2.28176i) q^{53} +(-3.18546 - 2.04717i) q^{54} +(-2.44724 + 5.35870i) q^{55} +(0.959493 + 0.281733i) q^{56} +(-8.30840 - 9.58841i) q^{57} +(-5.93398 - 6.84818i) q^{58} +(-3.19778 - 0.938954i) q^{59} +(-0.967746 + 2.11907i) q^{60} +(-9.21601 - 5.92277i) q^{61} +(2.83588 - 0.832691i) q^{62} +(-0.162056 + 1.12713i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.147804 - 1.02800i) q^{65} +(-8.80455 + 5.65834i) q^{66} +(-0.772457 + 0.891463i) q^{67} +6.58669 q^{68} +(2.66166 - 9.38648i) q^{69} -1.14511 q^{70} +(2.58202 - 2.97982i) q^{71} +(-0.957950 + 0.615637i) q^{72} +(-0.646002 - 4.49304i) q^{73} +(-3.54907 - 7.77138i) q^{74} +(-1.06797 + 7.42791i) q^{75} +(5.98380 - 1.75700i) q^{76} +(-4.32787 - 2.78135i) q^{77} +(0.766490 - 1.67838i) q^{78} +(8.52438 + 2.50298i) q^{79} +(-0.749886 - 0.865415i) q^{80} +(7.28171 + 8.40354i) q^{81} +(3.68653 + 1.08246i) q^{82} +(2.03696 - 4.46033i) q^{83} +(-1.71143 - 1.09987i) q^{84} +(-7.23695 + 2.12496i) q^{85} +(-1.78145 + 12.3903i) q^{86} +(7.65795 + 16.7686i) q^{87} +(-0.732146 - 5.09219i) q^{88} +(9.53097 - 6.12518i) q^{89} +(0.853909 - 0.985463i) q^{90} +0.906966 q^{91} +(3.65347 + 3.10680i) q^{92} -6.01284 q^{93} +(1.80668 - 2.08502i) q^{94} +(-6.00771 + 3.86092i) q^{95} +(-0.289523 - 2.01368i) q^{96} +(5.84308 + 12.7945i) q^{97} +(0.142315 - 0.989821i) q^{98} +(5.62089 - 1.65044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8	$ 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} + 2 q^{12} + 4 q^{13} + 4 q^{14} - 11 q^{15} - 4 q^{16} - 21 q^{17} + 4 q^{19} + 2 q^{20} + 2 q^{21} - 11 q^{23} - 2 q^{24} + 5 q^{25} - 15 q^{26} + 95 q^{27} - 4 q^{28} + 22 q^{30} - 12 q^{31} + 4 q^{32} - 8 q^{33} + 10 q^{34} - 9 q^{35} + 41 q^{37} + 7 q^{38} - 38 q^{39} - 13 q^{40} + 25 q^{41} - 2 q^{42} - 59 q^{43} - 6 q^{45} + 11 q^{46} - 60 q^{47} + 2 q^{48} - 4 q^{49} + 61 q^{50} - 87 q^{51} + 4 q^{52} + 47 q^{53} - 29 q^{54} - 30 q^{55} + 4 q^{56} + 20 q^{57} - 96 q^{59} - 11 q^{60} + 84 q^{61} - 65 q^{62} - 4 q^{64} + 52 q^{65} - 3 q^{66} + 11 q^{67} - 10 q^{68} - 42 q^{69} - 2 q^{70} - 13 q^{71} + 11 q^{72} - 48 q^{73} - 41 q^{74} + 23 q^{75} + 26 q^{76} - 83 q^{78} + 80 q^{79} - 9 q^{80} + 2 q^{81} + 30 q^{82} - 20 q^{83} + 2 q^{84} - 71 q^{85} - 40 q^{86} + 99 q^{87} - 30 q^{89} + 116 q^{90} + 26 q^{91} - 22 q^{92} + 20 q^{93} - 17 q^{94} - 4 q^{95} - 2 q^{96} - 56 q^{97} + 4 q^{98} + 138 q^{99}+O(q^{100}) $ 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^10 + 2 * q^12 + 4 * q^13 + 4 * q^14 - 11 * q^15 - 4 * q^16 - 21 * q^17 + 4 * q^19 + 2 * q^20 + 2 * q^21 - 11 * q^23 - 2 * q^24 + 5 * q^25 - 15 * q^26 + 95 * q^27 - 4 * q^28 + 22 * q^30 - 12 * q^31 + 4 * q^32 - 8 * q^33 + 10 * q^34 - 9 * q^35 + 41 * q^37 + 7 * q^38 - 38 * q^39 - 13 * q^40 + 25 * q^41 - 2 * q^42 - 59 * q^43 - 6 * q^45 + 11 * q^46 - 60 * q^47 + 2 * q^48 - 4 * q^49 + 61 * q^50 - 87 * q^51 + 4 * q^52 + 47 * q^53 - 29 * q^54 - 30 * q^55 + 4 * q^56 + 20 * q^57 - 96 * q^59 - 11 * q^60 + 84 * q^61 - 65 * q^62 - 4 * q^64 + 52 * q^65 - 3 * q^66 + 11 * q^67 - 10 * q^68 - 42 * q^69 - 2 * q^70 - 13 * q^71 + 11 * q^72 - 48 * q^73 - 41 * q^74 + 23 * q^75 + 26 * q^76 - 83 * q^78 + 80 * q^79 - 9 * q^80 + 2 * q^81 + 30 * q^82 - 20 * q^83 + 2 * q^84 - 71 * q^85 - 40 * q^86 + 99 * q^87 - 30 * q^89 + 116 * q^90 + 26 * q^91 - 22 * q^92 + 20 * q^93 - 17 * q^94 - 4 * q^95 - 2 * q^96 - 56 * q^97 + 4 * q^98 + 138 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$3$	−1.71143	+	1.09987i	−0.988096	+	0.635011i	−0.931636	−	0.363394i	$-0.881618\pi$
$3$	−1.71143	+	1.09987i	−0.988096	+	0.635011i	−0.0564606	+	0.998405i	$0.517982\pi$
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	0.475695	+	1.04163i	0.212737	+	0.465830i	0.985676	−	0.168651i	$-0.0539412\pi$
$5$	0.475695	+	1.04163i	0.212737	+	0.465830i	−0.772939	+	0.634481i	$0.781214\pi$
$6$	−0.289523	+	2.01368i	−0.118197	+	0.822080i
$7$	−0.959493	+	0.281733i	−0.362654	+	0.106485i
$7$	−0.959493	+	0.281733i	−0.362654	+	0.106485i
$8$	−0.841254	−	0.540641i	−0.297428	−	0.191145i
$9$	0.473040	−	1.03581i	0.157680	−	0.345271i
$10$	1.09872	+	0.322614i	0.347447	+	0.102020i
$11$	3.36896	+	3.88799i	1.01578	+	1.17227i	0.984966	+	0.172749i	$0.0552648\pi$
$11$	3.36896	+	3.88799i	1.01578	+	1.17227i	0.0308149	+	0.999525i	$0.490190\pi$
$12$	1.33224	+	1.53748i	0.384584	+	0.443834i
$13$	−0.870228	−	0.255522i	−0.241358	−	0.0708690i	0.158816	−	0.987308i	$-0.449232\pi$
$13$	−0.870228	−	0.255522i	−0.241358	−	0.0708690i	−0.400174	+	0.916439i	$0.631050\pi$
$14$	−0.415415	+	0.909632i	−0.111024	+	0.243109i
$15$	−1.95977	−	1.25947i	−0.506012	−	0.325194i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	−0.937384	+	6.51965i	−0.227349	+	1.58125i	0.481859	+	0.876249i	$0.339962\pi$
$17$	−0.937384	+	6.51965i	−0.227349	+	1.58125i	−0.709208	+	0.704999i	$0.750947\pi$
$18$	−0.473040	−	1.03581i	−0.111497	−	0.244144i
$19$	0.887536	+	6.17295i	0.203615	+	1.41617i	0.793444	+	0.608643i	$0.208286\pi$
$19$	0.887536	+	6.17295i	0.203615	+	1.41617i	−0.589830	+	0.807528i	$0.700805\pi$
$20$	0.963326	−	0.619092i	0.215406	−	0.138433i
$21$	1.33224	−	1.53748i	0.290718	−	0.335507i
$22$	5.14455			1.09682
$23$	−3.59512	+	3.17414i	−0.749634	+	0.661853i
$23$	−3.59512	+	3.17414i	−0.749634	+	0.661853i
$24$	2.03438			0.415267
$25$	2.41560	−	2.78775i	0.483121	−	0.557551i
$26$	−0.762989	+	0.490343i	−0.149634	+	0.0961642i
$27$	−0.538884	−	3.74802i	−0.103708	−	0.721307i
$28$	0.415415	+	0.909632i	0.0785061	+	0.171904i
$29$	1.28958	−	8.96921i	0.239469	−	1.66554i	−0.415280	−	0.909694i	$-0.636316\pi$
$29$	1.28958	−	8.96921i	0.239469	−	1.66554i	0.654749	−	0.755847i	$-0.272775\pi$
$30$	−2.23522	+	0.656321i	−0.408094	+	0.119827i
$31$	2.48641	+	1.59792i	0.446573	+	0.286995i	0.744536	−	0.667582i	$-0.232671\pi$
$31$	2.48641	+	1.59792i	0.446573	+	0.286995i	−0.297963	+	0.954577i	$0.596307\pi$
$32$	−0.415415	+	0.909632i	−0.0734357	+	0.160802i
$33$	−10.0420	−	2.94861i	−1.74810	−	0.513287i
$34$	4.31337	+	4.97789i	0.739736	+	0.853701i
$35$	−0.749886	−	0.865415i	−0.126754	−	0.146282i
$36$	−1.09259	−	0.320814i	−0.182099	−	0.0534690i
$37$	3.54907	−	7.77138i	0.583464	−	1.27761i	−0.355848	−	0.934544i	$-0.615808\pi$
$37$	3.54907	−	7.77138i	0.583464	−	1.27761i	0.939312	−	0.343064i	$-0.111465\pi$
$38$	5.24641	+	3.37166i	0.851081	+	0.546956i
$39$	1.77038	−	0.519830i	0.283487	−	0.0832394i
$40$	0.162966	−	1.13345i	0.0257672	−	0.179215i
$41$	1.59609	+	3.49495i	0.249268	+	0.545820i	0.992361	−	0.123368i	$-0.0393695\pi$
$41$	1.59609	+	3.49495i	0.249268	+	0.545820i	−0.743093	+	0.669188i	$0.766642\pi$
$42$	−0.289523	−	2.01368i	−0.0446744	−	0.310717i
$43$	−10.5306	+	6.76758i	−1.60590	+	1.03205i	−0.641664	+	0.766986i	$0.721756\pi$
$43$	−10.5306	+	6.76758i	−1.60590	+	1.03205i	−0.964232	+	0.265061i	$0.914608\pi$
$44$	3.36896	−	3.88799i	0.507890	−	0.586137i
$45$	1.30395			0.194382
$46$	0.0445515	+	4.79562i	0.00656877	+	0.707076i
$47$	2.75888			0.402424			0.201212	−	0.979548i	$-0.435512\pi$
$47$	2.75888			0.402424			0.201212	+	0.979548i	$0.435512\pi$
$48$	1.33224	−	1.53748i	0.192292	−	0.221917i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	−0.524961	−	3.65118i	−0.0742407	−	0.516355i
$51$	−5.56650	−	12.1889i	−0.779467	−	1.70679i
$52$	−0.129075	+	0.897735i	−0.0178994	+	0.124493i
$53$	7.77095	−	2.28176i	1.06742	−	0.313423i	0.299586	−	0.954069i	$-0.403152\pi$
$53$	7.77095	−	2.28176i	1.06742	−	0.313423i	0.767836	+	0.640646i	$0.221333\pi$
$54$	−3.18546	−	2.04717i	−0.433486	−	0.278585i
$55$	−2.44724	+	5.35870i	−0.329985	+	0.722567i
$56$	0.959493	+	0.281733i	0.128218	+	0.0376481i
$57$	−8.30840	−	9.58841i	−1.10047	−	1.27002i
$58$	−5.93398	−	6.84818i	−0.779170	−	0.899210i
$59$	−3.19778	−	0.938954i	−0.416316	−	0.122241i	0.0668648	−	0.997762i	$-0.478700\pi$
$59$	−3.19778	−	0.938954i	−0.416316	−	0.122241i	−0.483181	+	0.875521i	$0.660519\pi$
$60$	−0.967746	+	2.11907i	−0.124935	+	0.273571i
$61$	−9.21601	−	5.92277i	−1.17999	−	0.758333i	−0.204605	−	0.978845i	$-0.565591\pi$
$61$	−9.21601	−	5.92277i	−1.17999	−	0.758333i	−0.975384	+	0.220512i	$0.929227\pi$
$62$	2.83588	−	0.832691i	0.360158	−	0.105752i
$63$	−0.162056	+	1.12713i	−0.0204172	+	0.142005i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	−0.147804	−	1.02800i	−0.0183329	−	0.127508i
$66$	−8.80455	+	5.65834i	−1.08377	+	0.696494i
$67$	−0.772457	+	0.891463i	−0.0943706	+	0.108910i	−0.800970	−	0.598704i	$-0.795683\pi$
$67$	−0.772457	+	0.891463i	−0.0943706	+	0.108910i	0.706600	+	0.707613i	$0.250228\pi$
$68$	6.58669			0.798754
$69$	2.66166	−	9.38648i	0.320426	−	1.13000i
$70$	−1.14511			−0.136867
$71$	2.58202	−	2.97982i	0.306430	−	0.353639i	−0.581559	−	0.813504i	$-0.697557\pi$
$71$	2.58202	−	2.97982i	0.306430	−	0.353639i	0.887989	+	0.459865i	$0.152102\pi$
$72$	−0.957950	+	0.615637i	−0.112896	+	0.0725536i
$73$	−0.646002	−	4.49304i	−0.0756088	−	0.525871i	−0.992064	−	0.125734i	$-0.959872\pi$
$73$	−0.646002	−	4.49304i	−0.0756088	−	0.525871i	0.916455	−	0.400137i	$-0.131038\pi$
$74$	−3.54907	−	7.77138i	−0.412571	−	0.903405i
$75$	−1.06797	+	7.42791i	−0.123319	+	0.857701i
$76$	5.98380	−	1.75700i	0.686389	−	0.201542i
$77$	−4.32787	−	2.78135i	−0.493207	−	0.316965i
$78$	0.766490	−	1.67838i	0.0867879	−	0.190039i
$79$	8.52438	+	2.50298i	0.959068	+	0.281608i	0.723557	−	0.690264i	$-0.242506\pi$
$79$	8.52438	+	2.50298i	0.959068	+	0.281608i	0.235510	+	0.971872i	$0.424324\pi$
$80$	−0.749886	−	0.865415i	−0.0838398	−	0.0967563i
$81$	7.28171	+	8.40354i	0.809079	+	0.933727i
$82$	3.68653	+	1.08246i	0.407109	+	0.119538i
$83$	2.03696	−	4.46033i	0.223586	−	0.489585i	−0.764282	−	0.644882i	$-0.776906\pi$
$83$	2.03696	−	4.46033i	0.223586	−	0.489585i	0.987868	+	0.155298i	$0.0496336\pi$
$84$	−1.71143	−	1.09987i	−0.186733	−	0.120006i
$85$	−7.23695	+	2.12496i	−0.784957	+	0.230484i
$86$	−1.78145	+	12.3903i	−0.192099	+	1.33608i
$87$	7.65795	+	16.7686i	0.821018	+	1.79778i
$88$	−0.732146	−	5.09219i	−0.0780470	−	0.542829i
$89$	9.53097	−	6.12518i	1.01028	−	0.649268i	0.0728151	−	0.997345i	$-0.476802\pi$
$89$	9.53097	−	6.12518i	1.01028	−	0.649268i	0.937466	+	0.348077i	$0.113165\pi$
$90$	0.853909	−	0.985463i	0.0900099	−	0.103877i
$91$	0.906966			0.0950759
$92$	3.65347	+	3.10680i	0.380900	+	0.323906i
$93$	−6.01284			−0.623502
$94$	1.80668	−	2.08502i	0.186345	−	0.215054i
$95$	−6.00771	+	3.86092i	−0.616378	+	0.396122i
$96$	−0.289523	−	2.01368i	−0.0295493	−	0.205520i
$97$	5.84308	+	12.7945i	0.593274	+	1.29909i	0.933443	+	0.358725i	$0.116789\pi$
$97$	5.84308	+	12.7945i	0.593274	+	1.29909i	−0.340169	+	0.940364i	$0.610484\pi$
$98$	0.142315	−	0.989821i	0.0143760	−	0.0999871i
$99$	5.62089	−	1.65044i	0.564921	−	0.165876i
$100$	−3.10316	−	1.99428i	−0.310316	−	0.199428i
$101$	−1.16867	+	2.55903i	−0.116287	+	0.254633i	−0.958821	−	0.284009i	$-0.908335\pi$
$101$	−1.16867	+	2.55903i	−0.116287	+	0.254633i	0.842535	+	0.538642i	$0.181063\pi$
$102$	−12.8571	−	3.77518i	−1.27304	−	0.373798i
$103$	−9.42476	−	10.8768i	−0.928649	−	1.07172i	−0.997253	−	0.0740743i	$-0.976400\pi$
$103$	−9.42476	−	10.8768i	−0.928649	−	1.07172i	0.0686035	−	0.997644i	$-0.478146\pi$
$104$	0.593937	+	0.685439i	0.0582403	+	0.0672129i
$105$	2.23522	+	0.656321i	0.218136	+	0.0640504i
$106$	3.36445	−	7.36712i	0.326785	−	0.715558i
$107$	−2.33352	−	1.49966i	−0.225589	−	0.144978i	0.422964	−	0.906146i	$-0.360990\pi$
$107$	−2.33352	−	1.49966i	−0.225589	−	0.144978i	−0.648554	+	0.761169i	$0.724626\pi$
$108$	−3.63318	+	1.06680i	−0.349603	+	0.102653i
$109$	−2.27672	+	15.8349i	−0.218070	+	1.51671i	0.527080	+	0.849816i	$0.323287\pi$
$109$	−2.27672	+	15.8349i	−0.218070	+	1.51671i	−0.745150	+	0.666897i	$0.767622\pi$
$110$	2.44724	+	5.35870i	0.233335	+	0.510932i
$111$	2.47352	+	17.2037i	0.234776	+	1.63290i
$112$	0.841254	−	0.540641i	0.0794910	−	0.0510858i
$113$	−1.17201	+	1.35257i	−0.110253	+	0.127239i	−0.808194	−	0.588917i	$-0.799555\pi$
$113$	−1.17201	+	1.35257i	−0.110253	+	0.127239i	0.697940	+	0.716156i	$0.254100\pi$
$114$	−12.6873			−1.18827
$115$	−5.01644	−	2.23485i	−0.467786	−	0.208401i
$116$	−9.06144			−0.841334
$117$	−0.676326	+	0.780522i	−0.0625264	+	0.0721593i
$118$	−2.80372	+	1.80184i	−0.258103	+	0.165873i
$119$	−0.937384	−	6.51965i	−0.0859299	−	0.597655i
$120$	0.967746	+	2.11907i	0.0883427	+	0.193444i
$121$	−2.20110	+	15.3090i	−0.200100	+	1.39172i
$122$	−10.5113	+	3.08641i	−0.951652	+	0.279430i
$123$	−6.57560	−	4.22588i	−0.592902	−	0.381035i
$124$	1.22780	−	2.68851i	0.110260	−	0.241436i
$125$	9.54650	+	2.80311i	0.853865	+	0.250717i
$126$	0.745702	+	0.860586i	0.0664324	+	0.0766671i
$127$	0.354138	+	0.408697i	0.0314247	+	0.0362660i	0.771244	−	0.636539i	$-0.219635\pi$
$127$	0.354138	+	0.408697i	0.0314247	+	0.0362660i	−0.739820	+	0.672805i	$0.765089\pi$
$128$	0.959493	+	0.281733i	0.0848080	+	0.0249019i
$129$	10.5789	−	23.1645i	0.931419	−	2.03952i
$130$	−0.873704	−	0.561496i	−0.0766289	−	0.0492464i
$131$	15.3033	−	4.49345i	1.33705	−	0.392595i	0.466437	−	0.884554i	$-0.345537\pi$
$131$	15.3033	−	4.49345i	1.33705	−	0.392595i	0.870618	+	0.491960i	$0.163719\pi$
$132$	−1.48947	+	10.3595i	−0.129641	+	0.901675i
$133$	−2.59070	−	5.67285i	−0.224643	−	0.491898i
$134$	0.167871	+	1.16757i	0.0145018	+	0.100863i
$135$	3.64769	−	2.34423i	0.313943	−	0.201759i
$136$	4.31337	−	4.97789i	0.369868	−	0.426851i
$137$	19.1337			1.63470			0.817352	−	0.576138i	$-0.195441\pi$
$137$	19.1337			1.63470			0.817352	+	0.576138i	$0.195441\pi$
$138$	−5.35082	−	8.15839i	−0.455492	−	0.694488i
$139$	7.78005			0.659895			0.329948	−	0.943999i	$-0.392969\pi$
$139$	7.78005			0.659895			0.329948	+	0.943999i	$0.392969\pi$
$140$	−0.749886	+	0.865415i	−0.0633769	+	0.0731409i
$141$	−4.72164	+	3.03441i	−0.397634	+	0.255544i
$142$	−0.561128	−	3.90273i	−0.0470888	−	0.327510i
$143$	−1.93830	−	4.24428i	−0.162089	−	0.354925i
$144$	−0.162056	+	1.12713i	−0.0135047	+	0.0939273i
$145$	9.95601	−	2.92335i	0.826802	−	0.242771i
$146$	−3.81866	−	2.45410i	−0.316034	−	0.203103i
$147$	−0.845114	+	1.85054i	−0.0697038	+	0.152630i
$148$	−8.19737	−	2.40696i	−0.673819	−	0.197851i
$149$	6.47659	+	7.47439i	0.530583	+	0.612326i	0.956249	−	0.292555i	$-0.0945054\pi$
$149$	6.47659	+	7.47439i	0.530583	+	0.612326i	−0.425665	+	0.904881i	$0.639960\pi$
$150$	4.91426	+	5.67136i	0.401248	+	0.463065i
$151$	13.7947	+	4.05050i	1.12260	+	0.329625i	0.789795	−	0.613371i	$-0.210187\pi$
$151$	13.7947	+	4.05050i	1.12260	+	0.329625i	0.332804	+	0.942996i	$0.392005\pi$
$152$	2.59070	−	5.67285i	0.210134	−	0.460129i
$153$	6.30973	+	4.05501i	0.510111	+	0.327829i
$154$	−4.93616	+	1.44939i	−0.397767	+	0.116795i
$155$	−0.481663	+	3.35004i	−0.0386881	+	0.269082i
$156$	−0.766490	−	1.67838i	−0.0613683	−	0.134378i
$157$	0.376981	+	2.62196i	0.0300864	+	0.209255i	0.999319	−	0.0368899i	$-0.0117451\pi$
$157$	0.376981	+	2.62196i	0.0300864	+	0.209255i	−0.969233	+	0.246145i	$0.920836\pi$
$158$	7.47391	−	4.80319i	0.594592	−	0.382121i
$159$	−10.7898	+	12.4521i	−0.855688	+	0.987517i
$160$	−1.14511			−0.0905287
$161$	2.55523	−	4.05842i	0.201380	−	0.319849i
$162$	11.1195			0.873628
$163$	−5.75366	+	6.64008i	−0.450662	+	0.520091i	−0.934932	−	0.354827i	$-0.884540\pi$
$163$	−5.75366	+	6.64008i	−0.450662	+	0.520091i	0.484270	+	0.874918i	$0.339085\pi$
$164$	3.23223	−	2.07723i	0.252395	−	0.162204i
$165$	−1.70560	−	11.8627i	−0.132781	−	0.923510i
$166$	−2.03696	−	4.46033i	−0.158099	−	0.346189i
$167$	1.08538	−	7.54899i	0.0839893	−	0.584158i	−0.903752	−	0.428057i	$-0.859198\pi$
$167$	1.08538	−	7.54899i	0.0839893	−	0.584158i	0.987741	−	0.156101i	$-0.0498926\pi$
$168$	−1.95198	+	0.573152i	−0.150598	+	0.0442197i
$169$	−10.2443	−	6.58361i	−0.788022	−	0.506431i
$170$	−3.13326	+	6.86088i	−0.240310	+	0.526205i
$171$	6.81386	+	2.00073i	0.521069	+	0.153000i
$172$	8.19735	+	9.46025i	0.625042	+	0.721337i
$173$	−13.7140	−	15.8268i	−1.04266	−	1.20329i	−0.978691	−	0.205338i	$-0.934171\pi$
$173$	−13.7140	−	15.8268i	−1.04266	−	1.20329i	−0.0639655	−	0.997952i	$-0.520375\pi$
$174$	17.6877	+	5.19359i	1.34090	+	0.393725i
$175$	−1.53235	+	3.35539i	−0.115835	+	0.253643i
$176$	−4.32787	−	2.78135i	−0.326226	−	0.209652i
$177$	6.50552	−	1.91019i	0.488985	−	0.143579i
$178$	1.61235	−	11.2142i	0.120851	−	0.840538i
$179$	0.0278506	+	0.0609843i	0.00208165	+	0.00455818i	0.910670	−	0.413135i	$-0.135566\pi$
$179$	0.0278506	+	0.0609843i	0.00208165	+	0.00455818i	−0.908588	+	0.417693i	$0.862839\pi$
$180$	−0.185572	−	1.29068i	−0.0138317	−	0.0962018i
$181$	−16.4992	+	10.6034i	−1.22637	+	0.788143i	−0.983322	−	0.181871i	$-0.941785\pi$
$181$	−16.4992	+	10.6034i	−1.22637	+	0.788143i	−0.243052	+	0.970013i	$0.578148\pi$
$182$	0.593937	−	0.685439i	0.0440255	−	0.0508081i
$183$	22.2869			1.64749
$184$	4.74047	−	0.726587i	0.349472	−	0.0535647i
$185$	9.78315			0.719272
$186$	−3.93757	+	4.54420i	−0.288717	+	0.333197i
$187$	−28.5064	+	18.3199i	−2.08459	+	1.33969i
$188$	−0.392630	−	2.73080i	−0.0286355	−	0.199164i
$189$	1.57299	+	3.44438i	0.114419	+	0.250542i
$190$	−1.01632	+	7.06869i	−0.0737319	+	0.512816i
$191$	14.4622	−	4.24649i	1.04645	−	0.307265i	0.287067	−	0.957910i	$-0.407320\pi$
$191$	14.4622	−	4.24649i	1.04645	−	0.307265i	0.759382	+	0.650645i	$0.225501\pi$
$192$	−1.71143	−	1.09987i	−0.123512	−	0.0793764i
$193$	3.48486	−	7.63078i	0.250846	−	0.549275i	−0.741759	−	0.670666i	$-0.766008\pi$
$193$	3.48486	−	7.63078i	0.250846	−	0.549275i	0.992605	+	0.121391i	$0.0387355\pi$
$194$	13.4959	+	3.96275i	0.968947	+	0.284509i
$195$	1.38363	+	1.59679i	0.0990837	+	0.114349i
$196$	−0.654861	−	0.755750i	−0.0467758	−	0.0539821i
$197$	13.5093	+	3.96669i	0.962498	+	0.282615i	0.724981	−	0.688769i	$-0.241848\pi$
$197$	13.5093	+	3.96669i	0.962498	+	0.282615i	0.237517	+	0.971383i	$0.423667\pi$
$198$	2.43358	−	5.32880i	0.172947	−	0.378701i
$199$	−0.239720	−	0.154059i	−0.0169933	−	0.0109209i	0.532117	−	0.846671i	$-0.321397\pi$
$199$	−0.239720	−	0.154059i	−0.0169933	−	0.0109209i	−0.549110	+	0.835750i	$0.685033\pi$
$200$	−3.53931	+	1.03923i	−0.250267	+	0.0734850i
$201$	0.341514	−	2.37528i	0.0240885	−	0.167539i
$202$	1.16867	+	2.55903i	0.0822273	+	0.180053i
$203$	1.28958	+	8.96921i	0.0905106	+	0.629515i
$204$	−11.2727	+	7.24451i	−0.789246	+	0.507217i
$205$	−2.88118	+	3.32506i	−0.201231	+	0.232233i
$206$	−14.3920			−1.00274
$207$	1.58718	+	5.22537i	0.110317	+	0.363188i
$208$	0.906966			0.0628868
$209$	−21.0103	+	24.2472i	−1.45331	+	1.67721i
$210$	1.95977	−	1.25947i	0.135237	−	0.0869117i
$211$	−2.60121	−	18.0918i	−0.179074	−	1.24549i	−0.858911	−	0.512125i	$-0.828858\pi$
$211$	−2.60121	−	18.0918i	−0.179074	−	1.24549i	0.679836	−	0.733364i	$-0.262051\pi$
$212$	−3.36445	−	7.36712i	−0.231072	−	0.505976i
$213$	−1.14155	+	7.93965i	−0.0782176	+	0.544016i
$214$	−2.66149	+	0.781485i	−0.181936	+	0.0534212i
$215$	−12.0586	−	7.74961i	−0.822392	−	0.528519i
$216$	−1.57299	+	3.44438i	−0.107029	+	0.234360i
$217$	−2.83588	−	0.832691i	−0.192512	−	0.0565267i
$218$	10.4763	+	12.0903i	0.709546	+	0.818860i
$219$	6.04736	+	6.97902i	0.408643	+	0.471599i
$220$	5.65243	+	1.65970i	0.381087	+	0.111897i
$221$	2.48165	−	5.43406i	0.166934	−	0.365534i
$222$	14.6215	+	9.39668i	0.981332	+	0.630664i
$223$	6.83251	−	2.00621i	0.457539	−	0.134345i	−0.0448381	−	0.998994i	$-0.514277\pi$
$223$	6.83251	−	2.00621i	0.457539	−	0.134345i	0.502377	+	0.864649i	$0.332459\pi$
$224$	0.142315	−	0.989821i	0.00950881	−	0.0661352i
$225$	−1.74492	−	3.82084i	−0.116328	−	0.254722i
$226$	0.254702	+	1.77149i	0.0169425	+	0.117838i
$227$	3.79600	−	2.43954i	0.251950	−	0.161918i	−0.408570	−	0.912727i	$-0.633972\pi$
$227$	3.79600	−	2.43954i	0.251950	−	0.161918i	0.660520	+	0.750809i	$0.270336\pi$
$228$	−8.30840	+	9.58841i	−0.550237	+	0.635008i
$229$	−2.12039			−0.140119			−0.0700597	−	0.997543i	$-0.522319\pi$
$229$	−2.12039			−0.140119			−0.0700597	+	0.997543i	$0.522319\pi$
$230$	−4.97406	+	2.32766i	−0.327980	+	0.153481i
$231$	10.4660			0.688612
$232$	−5.93398	+	6.84818i	−0.389585	+	0.449605i
$233$	−6.67494	+	4.28973i	−0.437290	+	0.281029i	−0.740706	−	0.671829i	$-0.765509\pi$
$233$	−6.67494	+	4.28973i	−0.437290	+	0.281029i	0.303416	+	0.952858i	$0.401873\pi$
$234$	0.146980	+	1.02227i	0.00960837	+	0.0668277i
$235$	1.31239	+	2.87372i	0.0856106	+	0.187461i
$236$	−0.474305	+	3.29886i	−0.0308746	+	0.214738i
$237$	−17.3419	+	5.09203i	−1.12648	+	0.330763i
$238$	−5.54108	−	3.56104i	−0.359175	−	0.230828i
$239$	−5.33758	+	11.6877i	−0.345259	+	0.756012i	0.654741	+	0.755853i	$0.272778\pi$
$239$	−5.33758	+	11.6877i	−0.345259	+	0.756012i	−1.00000		0.000158583i	$0.999950\pi$
$240$	2.23522	+	0.656321i	0.144283	+	0.0423653i
$241$	−13.8373	−	15.9691i	−0.891336	−	1.02866i	−0.999404	−	0.0345135i	$-0.989012\pi$
$241$	−13.8373	−	15.9691i	−0.891336	−	1.02866i	0.108068	−	0.994144i	$-0.465534\pi$
$242$	10.1283	+	11.6887i	0.651074	+	0.751380i
$243$	−10.8054	−	3.17276i	−0.693168	−	0.203532i
$244$	−4.55091	+	9.96510i	−0.291342	+	0.637950i
$245$	0.963326	+	0.619092i	0.0615446	+	0.0395523i
$246$	−7.49981	+	2.20214i	−0.478171	+	0.140404i
$247$	0.804965	−	5.59865i	0.0512187	−	0.356234i
$248$	−1.22780	−	2.68851i	−0.0779656	−	0.170721i
$249$	1.41966	+	9.87395i	0.0899673	+	0.625736i
$250$	8.37008	−	5.37912i	0.529370	−	0.340206i
$251$	15.5569	−	17.9536i	0.981944	−	1.13322i	−0.00913607	−	0.999958i	$-0.502908\pi$
$251$	15.5569	−	17.9536i	0.981944	−	1.13322i	0.991080	−	0.133266i	$-0.0425464\pi$
$252$	1.13872			0.0717325
$253$	−24.4528	−	3.28423i	−1.53734	−	0.206478i
$254$	0.540784			0.0339318
$255$	10.0484	−	11.5964i	0.629253	−	0.726197i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−0.0515727	−	0.358696i	−0.00321702	−	0.0223749i	0.988150	−	0.153493i	$-0.0490523\pi$
$257$	−0.0515727	−	0.358696i	−0.00321702	−	0.0223749i	−0.991367	+	0.131118i	$0.958143\pi$
$258$	−10.5789	−	23.1645i	−0.658612	−	1.44216i
$259$	−1.21586	+	8.45647i	−0.0755497	+	0.525460i
$260$	−0.996505	+	0.292600i	−0.0618006	+	0.0181463i
$261$	−8.68041	−	5.57856i	−0.537304	−	0.345304i
$262$	6.62560	−	14.5080i	0.409331	−	0.896310i
$263$	−10.3563	−	3.04087i	−0.638594	−	0.187508i	−0.0536215	−	0.998561i	$-0.517076\pi$
$263$	−10.3563	−	3.04087i	−0.638594	−	0.187508i	−0.584972	+	0.811053i	$0.698895\pi$
$264$	6.85377	+	7.90967i	0.421820	+	0.486806i
$265$	6.07334	+	7.00901i	0.373082	+	0.430560i
$266$	−5.98380	−	1.75700i	−0.366891	−	0.107729i
$267$	−9.57470	+	20.9657i	−0.585962	+	1.28308i
$268$	0.992321	+	0.637726i	0.0606157	+	0.0389553i
$269$	−5.70794	+	1.67600i	−0.348019	+	0.102188i	−0.451070	−	0.892488i	$-0.648958\pi$
$269$	−5.70794	+	1.67600i	−0.348019	+	0.102188i	0.103051	+	0.994676i	$0.467140\pi$
$270$	0.617080	−	4.29189i	0.0375543	−	0.261196i
$271$	8.78026	+	19.2261i	0.533363	+	1.16790i	0.964128	+	0.265438i	$0.0855164\pi$
$271$	8.78026	+	19.2261i	0.533363	+	1.16790i	−0.430765	+	0.902464i	$0.641756\pi$
$272$	−0.937384	−	6.51965i	−0.0568373	−	0.395312i
$273$	−1.55221	+	0.997546i	−0.0939441	+	0.0603742i
$274$	12.5299	−	14.4603i	0.756961	−	0.873579i
$275$	18.9768			1.14435
$276$	−9.66974	−	1.29873i	−0.582050	−	0.0781744i
$277$	3.12398			0.187702			0.0938508	−	0.995586i	$-0.470082\pi$
$277$	3.12398			0.187702			0.0938508	+	0.995586i	$0.470082\pi$
$278$	5.09485	−	5.87977i	0.305569	−	0.352645i
$279$	2.83132	−	1.81958i	0.169507	−	0.108936i
$280$	0.162966	+	1.13345i	0.00973907	+	0.0677367i
$281$	1.87893	+	4.11429i	0.112088	+	0.245438i	0.957360	−	0.288898i	$-0.0932889\pi$
$281$	1.87893	+	4.11429i	0.112088	+	0.245438i	−0.845272	+	0.534336i	$0.820562\pi$
$282$	−0.798760	+	5.55550i	−0.0475655	+	0.330825i
$283$	−8.47256	+	2.48777i	−0.503641	+	0.147882i	−0.523677	−	0.851917i	$-0.675440\pi$
$283$	−8.47256	+	2.48777i	−0.503641	+	0.147882i	0.0200357	+	0.999799i	$0.493622\pi$
$284$	−3.31695	−	2.13167i	−0.196825	−	0.126491i
$285$	6.03527	−	13.2154i	0.357499	−	0.782813i
$286$	−4.47693	−	1.31455i	−0.264726	−	0.0777307i
$287$	−2.51608	−	2.90371i	−0.148520	−	0.171401i
$288$	0.745702	+	0.860586i	0.0439409	+	0.0507105i
$289$	−25.3158	−	7.43338i	−1.48916	−	0.437258i
$290$	4.31048	−	9.43864i	0.253120	−	0.554256i
$291$	−24.0724	−	15.4704i	−1.41115	−	0.906890i
$292$	−4.35538	+	1.27885i	−0.254879	+	0.0748392i
$293$	−0.125141	+	0.870376i	−0.00731083	+	0.0508479i	−0.993150	−	0.116844i	$-0.962722\pi$
$293$	−0.125141	+	0.870376i	−0.00731083	+	0.0508479i	0.985839	+	0.167692i	$0.0536314\pi$
$294$	0.845114	+	1.85054i	0.0492880	+	0.107926i
$295$	−0.543130	−	3.77755i	−0.0316222	−	0.219937i
$296$	−7.18719	+	4.61893i	−0.417747	+	0.268470i
$297$	12.7568	−	14.7221i	0.740224	−	0.854264i
$298$	9.89003			0.572914
$299$	3.93963	−	1.84359i	0.227835	−	0.106618i
$300$	7.50429			0.433260
$301$	8.19735	−	9.46025i	0.472488	−	0.545280i
$302$	12.0948	−	7.77285i	0.695977	−	0.447277i
$303$	−0.814503	−	5.66499i	−0.0467920	−	0.325445i
$304$	−2.59070	−	5.67285i	−0.148587	−	0.325360i
$305$	1.78531	−	12.4171i	0.102226	−	0.711000i
$306$	7.19657	−	2.11310i	0.411400	−	0.120798i
$307$	−4.69960	−	3.02025i	−0.268220	−	0.172375i	0.399617	−	0.916682i	$-0.369143\pi$
$307$	−4.69960	−	3.02025i	−0.268220	−	0.172375i	−0.667837	+	0.744308i	$0.732780\pi$
$308$	−2.13712	+	4.67965i	−0.121774	+	0.266648i
$309$	28.0929	+	8.24881i	1.59815	+	0.469258i
$310$	2.21637	+	2.55783i	0.125881	+	0.145275i
$311$	3.29162	+	3.79873i	0.186650	+	0.215406i	0.841361	−	0.540474i	$-0.181755\pi$
$311$	3.29162	+	3.79873i	0.186650	+	0.215406i	−0.654711	+	0.755880i	$0.727209\pi$
$312$	−1.77038	−	0.519830i	−0.100228	−	0.0294296i
$313$	−1.68783	+	3.69583i	−0.0954018	+	0.208901i	−0.951316	−	0.308217i	$-0.900268\pi$
$313$	−1.68783	+	3.69583i	−0.0954018	+	0.208901i	0.855914	+	0.517118i	$0.172995\pi$
$314$	2.22842	+	1.43212i	0.125757	+	0.0808190i
$315$	−1.25114	+	0.367366i	−0.0704935	+	0.0206988i
$316$	1.26436	−	8.79383i	0.0711259	−	0.494691i
$317$	−9.78151	−	21.4185i	−0.549384	−	1.20298i	−0.957069	−	0.289861i	$-0.906391\pi$
$317$	−9.78151	−	21.4185i	−0.549384	−	1.20298i	0.407685	−	0.913123i	$-0.366336\pi$
$318$	2.34485	+	16.3088i	0.131493	+	0.914552i
$319$	39.2168	−	25.2031i	2.19572	−	1.41110i
$320$	−0.749886	+	0.865415i	−0.0419199	+	0.0483781i
$321$	5.64309			0.314966
$322$	−1.39383	−	4.58882i	−0.0776751	−	0.255725i
$323$	−41.0774			−2.28561
$324$	7.28171	−	8.40354i	0.404539	−	0.466863i
$325$	−2.81446	+	1.80874i	−0.156118	+	0.100331i
$326$	1.25039	+	8.69666i	0.0692527	+	0.481663i
$327$	−13.5199	−	29.6045i	−0.747655	−	1.63714i
$328$	0.546797	−	3.80305i	0.0301918	−	0.209989i
$329$	−2.64713	+	0.777267i	−0.145941	+	0.0428521i
$330$	−10.0822	−	6.47941i	−0.555005	−	0.356680i
$331$	9.52995	−	20.8677i	0.523813	−	1.14699i	−0.444162	−	0.895946i	$-0.646499\pi$
$331$	9.52995	−	20.8677i	0.523813	−	1.14699i	0.967976	−	0.251045i	$-0.0807741\pi$
$332$	−4.70482	−	1.38146i	−0.258211	−	0.0758175i
$333$	−6.37085	−	7.35236i	−0.349121	−	0.402907i
$334$	−4.99437	−	5.76381i	−0.273280	−	0.315382i
$335$	−1.29603	−	0.380547i	−0.0708094	−	0.0207915i
$336$	−0.845114	+	1.85054i	−0.0461047	+	0.100955i
$337$	12.8690	+	8.27038i	0.701017	+	0.450516i	0.841987	−	0.539498i	$-0.181386\pi$
$337$	12.8690	+	8.27038i	0.701017	+	0.450516i	−0.140970	+	0.990014i	$0.545022\pi$
$338$	−11.6841	+	3.43077i	−0.635534	+	0.186609i
$339$	0.518162	−	3.60389i	0.0281427	−	0.195737i
$340$	3.13326	+	6.86088i	0.169925	+	0.372083i
$341$	2.16394	+	15.0505i	0.117184	+	0.815030i
$342$	5.97418	−	3.83937i	0.323047	−	0.207610i
$343$	−0.654861	+	0.755750i	−0.0353592	+	0.0408066i
$344$	12.5177			0.674909
$345$	11.0433	−	1.69265i	0.594554	−	0.0911291i
$346$	−20.9419			−1.12584
$347$	−22.8624	+	26.3846i	−1.22732	+	1.41640i	−0.349820	+	0.936817i	$0.613757\pi$
$347$	−22.8624	+	26.3846i	−1.22732	+	1.41640i	−0.877497	+	0.479582i	$0.840788\pi$
$348$	15.5080	−	9.96642i	0.831319	−	0.534256i
$349$	−4.01721	−	27.9403i	−0.215036	−	1.49561i	−0.756005	−	0.654566i	$-0.772851\pi$
$349$	−4.01721	−	27.9403i	−0.215036	−	1.49561i	0.540968	−	0.841043i	$-0.318058\pi$
$350$	1.53235	+	3.35539i	0.0819077	+	0.179353i
$351$	−0.488750	+	3.39933i	−0.0260875	+	0.181443i
$352$	−4.93616	+	1.44939i	−0.263098	+	0.0772526i
$353$	13.2831	+	8.53653i	0.706988	+	0.454354i	0.844089	−	0.536203i	$-0.180142\pi$
$353$	13.2831	+	8.53653i	0.706988	+	0.454354i	−0.137101	+	0.990557i	$0.543778\pi$
$354$	2.81658	−	6.16745i	0.149700	−	0.327796i
$355$	4.33211	+	1.27202i	0.229925	+	0.0675119i
$356$	−7.41924	−	8.56226i	−0.393219	−	0.453799i
$357$	8.77504	+	10.1269i	0.464425	+	0.535975i
$358$	0.0643271	+	0.0188881i	0.00339979	+	0.000998269i
$359$	4.34427	−	9.51262i	0.229282	−	0.502057i	−0.759668	−	0.650312i	$-0.774638\pi$
$359$	4.34427	−	9.51262i	0.229282	−	0.502057i	0.988949	+	0.148255i	$0.0473656\pi$
$360$	−1.09696	−	0.704971i	−0.0578147	−	0.0371552i
$361$	−19.0872	+	5.60450i	−1.00459	+	0.294974i
$362$	−2.79117	+	19.4130i	−0.146700	+	1.02032i
$363$	−13.0709	−	28.6212i	−0.686042	−	1.50222i
$364$	−0.129075	−	0.897735i	−0.00676536	−	0.0470541i
$365$	4.37277	−	2.81021i	0.228881	−	0.147093i
$366$	14.5948	−	16.8433i	0.762882	−	0.880413i
$367$	−11.8106			−0.616510			−0.308255	−	0.951304i	$-0.599745\pi$
$367$	−11.8106			−0.616510			−0.308255	+	0.951304i	$0.599745\pi$
$368$	2.55523	−	4.05842i	0.133201	−	0.211560i
$369$	4.37514			0.227761
$370$	6.40660	−	7.39361i	0.333063	−	0.384376i
$371$	−6.81333	+	4.37866i	−0.353730	+	0.227329i
$372$	0.855716	+	5.95164i	0.0443668	+	0.308578i
$373$	−0.595147	−	1.30319i	−0.0308155	−	0.0674766i	0.893598	−	0.448867i	$-0.148172\pi$
$373$	−0.595147	−	1.30319i	−0.0308155	−	0.0674766i	−0.924414	+	0.381391i	$0.875445\pi$
$374$	−4.82242	+	33.5407i	−0.249361	+	1.73435i
$375$	−19.4213	+	5.70259i	−1.00291	+	0.294481i
$376$	−2.32092	−	1.49156i	−0.119692	−	0.0769215i
$377$	−3.41406	+	7.47574i	−0.175833	+	0.385020i
$378$	3.63318	+	1.06680i	0.186871	+	0.0548702i
$379$	1.42911	+	1.64928i	0.0734084	+	0.0847178i	0.791266	−	0.611472i	$-0.209422\pi$
$379$	1.42911	+	1.64928i	0.0734084	+	0.0847178i	−0.717857	+	0.696190i	$0.754877\pi$
$380$	4.67661	+	5.39709i	0.239905	+	0.276865i
$381$	−1.05560	−	0.309951i	−0.0540799	−	0.0158793i
$382$	6.26146	−	13.7107i	0.320364	−	0.701499i
$383$	5.08709	+	3.26927i	0.259938	+	0.167052i	0.664119	−	0.747627i	$-0.268807\pi$
$383$	5.08709	+	3.26927i	0.259938	+	0.167052i	−0.404181	+	0.914679i	$0.632443\pi$
$384$	−1.95198	+	0.573152i	−0.0996114	+	0.0292485i
$385$	0.838386	−	5.83110i	0.0427281	−	0.297180i
$386$	−3.48486	−	7.63078i	−0.177375	−	0.388396i
$387$	2.02857	+	14.1090i	0.103118	+	0.717203i
$388$	11.8328	−	7.60446i	0.600718	−	0.386058i
$389$	−3.14995	+	3.63524i	−0.159709	+	0.184314i	−0.829964	−	0.557817i	$-0.811639\pi$
$389$	−3.14995	+	3.63524i	−0.159709	+	0.184314i	0.670255	+	0.742131i	$0.266185\pi$
$390$	2.11286			0.106989
$391$	−17.3243	−	26.4143i	−0.876125	−	1.33583i
$392$	−1.00000			−0.0505076
$393$	−21.2483	+	24.5219i	−1.07184	+	1.23697i
$394$	11.8445	−	7.61202i	0.596719	−	0.383488i
$395$	1.44783	+	10.0699i	0.0728482	+	0.506671i
$396$	−2.43358	−	5.32880i	−0.122292	−	0.267782i
$397$	0.641754	−	4.46350i	0.0322087	−	0.224017i	−0.967359	−	0.253409i	$-0.918448\pi$
$397$	0.641754	−	4.46350i	0.0322087	−	0.224017i	0.999568	+	0.0293924i	$0.00935723\pi$
$398$	−0.273413	+	0.0802814i	−0.0137050	+	0.00402414i
$399$	10.6732	+	6.85926i	0.534329	+	0.343393i
$400$	−1.53235	+	3.35539i	−0.0766177	+	0.167769i
$401$	25.5730	+	7.50891i	1.27705	+	0.374977i	0.848816	−	0.528689i	$-0.177316\pi$
$401$	25.5730	+	7.50891i	1.27705	+	0.374977i	0.428239	+	0.903666i	$0.359134\pi$
$402$	−1.57147	−	1.81358i	−0.0783780	−	0.0904530i
$403$	−1.75544	−	2.02589i	−0.0874449	−	0.100917i
$404$	2.69930	+	0.792586i	0.134295	+	0.0394326i
$405$	−5.28948	+	11.5823i	−0.262836	+	0.575531i
$406$	7.62297	+	4.89899i	0.378322	+	0.243133i
$407$	42.1718	−	12.3827i	2.09038	−	0.613790i
$408$	−1.90700	+	13.2635i	−0.0944105	+	0.656640i
$409$	14.4205	+	31.5766i	0.713050	+	1.56136i	0.823396	+	0.567468i	$0.192077\pi$
$409$	14.4205	+	31.5766i	0.713050	+	1.56136i	−0.110346	+	0.993893i	$0.535196\pi$
$410$	0.626141	+	4.35491i	0.0309229	+	0.215074i
$411$	−32.7461	+	21.0446i	−1.61525	+	1.03806i
$412$	−9.42476	+	10.8768i	−0.464325	+	0.535859i
$413$	3.33278			0.163996
$414$	4.98845	+	2.22238i	0.245169	+	0.109224i
$415$	5.61497			0.275628
$416$	0.593937	−	0.685439i	0.0291201	−	0.0336064i
$417$	−13.3150	+	8.55705i	−0.652040	+	0.419041i
$418$	4.56597	+	31.7570i	0.223329	+	1.55329i
$419$	−15.6508	−	34.2705i	−0.764592	−	1.67422i	−0.738209	−	0.674572i	$-0.764328\pi$
$419$	−15.6508	−	34.2705i	−0.764592	−	1.67422i	−0.0263832	−	0.999652i	$-0.508399\pi$
$420$	0.331535	−	2.30588i	0.0161773	−	0.112515i
$421$	3.46629	−	1.01779i	0.168937	−	0.0496042i	−0.196170	−	0.980570i	$-0.562851\pi$
$421$	3.46629	−	1.01779i	0.168937	−	0.0496042i	0.365107	+	0.930966i	$0.381032\pi$
$422$	−15.3763	−	9.88174i	−0.748506	−	0.481035i
$423$	1.30506	−	2.85769i	0.0634543	−	0.138946i
$424$	−7.77095	−	2.28176i	−0.377391	−	0.110812i
$425$	15.9108	+	18.3621i	0.771789	+	0.890692i
$426$	5.25283	+	6.06209i	0.254500	+	0.293709i
$427$	10.5113	+	3.08641i	0.508679	+	0.149362i
$428$	−1.15230	+	2.52319i	−0.0556986	+	0.121963i
$429$	7.98543	+	5.13193i	0.385540	+	0.247772i
$430$	−13.7535	+	4.03839i	−0.663252	+	0.194748i
$431$	−0.977032	+	6.79540i	−0.0470620	+	0.327323i	0.952666	+	0.304018i	$0.0983281\pi$
$431$	−0.977032	+	6.79540i	−0.0470620	+	0.327323i	−0.999728	+	0.0233055i	$0.992581\pi$
$432$	1.57299	+	3.44438i	0.0756808	+	0.165718i
$433$	0.00687744	+	0.0478336i	0.000330509	+	0.00229874i	0.989986	−	0.141165i	$-0.0450849\pi$
$433$	0.00687744	+	0.0478336i	0.000330509	+	0.00229874i	−0.989656	+	0.143464i	$0.954176\pi$
$434$	−2.48641	+	1.59792i	−0.119352	+	0.0767027i
$435$	−13.8237	+	15.9534i	−0.662797	+	0.764909i
$436$	15.9978			0.766155
$437$	−22.7846	−	19.3753i	−1.08993	−	0.926846i
$438$	9.23457			0.441245
$439$	−13.7428	+	15.8601i	−0.655910	+	0.756961i	−0.982103	−	0.188342i	$-0.939689\pi$
$439$	−13.7428	+	15.8601i	−0.655910	+	0.756961i	0.326193	+	0.945303i	$0.394234\pi$
$440$	4.95588	−	3.18495i	0.236262	−	0.151837i
$441$	−0.162056	−	1.12713i	−0.00771697	−	0.0536727i
$442$	−2.48165	−	5.43406i	−0.118040	−	0.258472i
$443$	−1.66294	+	11.5660i	−0.0790088	+	0.549518i	0.911418	+	0.411481i	$0.134988\pi$
$443$	−1.66294	+	11.5660i	−0.0790088	+	0.549518i	−0.990427	+	0.138037i	$0.955921\pi$
$444$	16.6766	−	4.89669i	0.791436	−	0.232387i
$445$	10.9140	+	7.01399i	0.517373	+	0.332495i
$446$	2.95815	−	6.47745i	0.140073	−	0.306716i
$447$	−19.3051	−	5.66849i	−0.913101	−	0.268111i
$448$	−0.654861	−	0.755750i	−0.0309393	−	0.0357058i
$449$	4.19602	+	4.84247i	0.198023	+	0.228530i	0.846073	−	0.533067i	$-0.178961\pi$
$449$	4.19602	+	4.84247i	0.198023	+	0.228530i	−0.648050	+	0.761598i	$0.724415\pi$
$450$	−4.03027	−	1.18340i	−0.189989	−	0.0557858i
$451$	−8.21118	+	17.9800i	−0.386649	+	0.846644i
$452$	1.50560	+	0.967589i	0.0708174	+	0.0455116i
$453$	−28.0638	+	8.24027i	−1.31855	+	0.387162i
$454$	0.642170	−	4.46639i	0.0301385	−	0.209618i
$455$	0.431439	+	0.944720i	0.0202262	+	0.0442892i
$456$	1.80559	+	12.5581i	0.0845544	+	0.588089i
$457$	1.64350	−	1.05622i	0.0768798	−	0.0494077i	−0.501636	−	0.865079i	$-0.667268\pi$
$457$	1.64350	−	1.05622i	0.0768798	−	0.0494077i	0.578516	+	0.815671i	$0.303632\pi$
$458$	−1.38856	+	1.60248i	−0.0648832	+	0.0748792i
$459$	24.9409			1.16414
$460$	−1.49819	+	5.28343i	−0.0698533	+	0.246341i
$461$	25.0428			1.16636			0.583180	−	0.812343i	$-0.301808\pi$
$461$	25.0428			1.16636			0.583180	+	0.812343i	$0.301808\pi$
$462$	6.85377	−	7.90967i	0.318866	−	0.367991i
$463$	8.54122	−	5.48911i	0.396944	−	0.255101i	−0.326907	−	0.945056i	$-0.606006\pi$
$463$	8.54122	−	5.48911i	0.396944	−	0.255101i	0.723851	+	0.689956i	$0.242370\pi$
$464$	1.28958	+	8.96921i	0.0598671	+	0.416385i
$465$	−2.86028	−	6.26313i	−0.132642	−	0.290446i
$466$	−1.12920	+	7.85376i	−0.0523092	+	0.363818i
$467$	29.2796	−	8.59726i	1.35490	−	0.397834i	0.477936	−	0.878395i	$-0.341385\pi$
$467$	29.2796	−	8.59726i	1.35490	−	0.397834i	0.876961	+	0.480561i	$0.159567\pi$
$468$	0.868829	+	0.558362i	0.0401616	+	0.0258103i
$469$	0.490013	−	1.07298i	0.0226267	−	0.0495455i
$470$	3.03125	+	0.890054i	0.139821	+	0.0410551i
$471$	−3.52900	−	4.07268i	−0.162608	−	0.187659i
$472$	2.18251	+	2.51875i	0.100458	+	0.115935i
$473$	−61.7894	−	18.1430i	−2.84108	−	0.834216i
$474$	−7.50821	+	16.4407i	−0.344863	+	0.755145i
$475$	19.3526	+	12.4372i	0.887958	+	0.570656i
$476$	−6.31989	+	1.85569i	−0.289672	+	0.0850552i
$477$	1.31250	−	9.12862i	0.0600951	−	0.417971i
$478$	5.33758	+	11.6877i	0.244135	+	0.534581i
$479$	1.53196	+	10.6550i	0.0699970	+	0.486840i	0.994422	+	0.105476i	$0.0336365\pi$
$479$	1.53196	+	10.6550i	0.0699970	+	0.486840i	−0.924425	+	0.381364i	$0.875454\pi$
$480$	1.95977	−	1.25947i	0.0894511	−	0.0574867i
$481$	−5.07426	+	5.85601i	−0.231366	+	0.267011i
$482$	−21.1301			−0.962449
$483$	0.0906349	+	9.75614i	0.00412403	+	0.443920i
$484$	15.4664			0.703018
$485$	−10.5476	+	12.1726i	−0.478943	+	0.552729i
$486$	−9.47386	+	6.08848i	−0.429743	+	0.276179i
$487$	3.39612	+	23.6206i	0.153893	+	1.07035i	0.909614	+	0.415455i	$0.136378\pi$
$487$	3.39612	+	23.6206i	0.153893	+	1.07035i	−0.755721	+	0.654894i	$0.772713\pi$
$488$	4.55091	+	9.96510i	0.206010	+	0.451099i
$489$	2.54377	−	17.6923i	0.115033	−	0.800075i
$490$	1.09872	−	0.322614i	0.0496352	−	0.0145742i
$491$	−13.5427	−	8.70334i	−0.611172	−	0.392776i	0.198124	−	0.980177i	$-0.436515\pi$
$491$	−13.5427	−	8.70334i	−0.611172	−	0.392776i	−0.809296	+	0.587401i	$0.800151\pi$
$492$	−3.24706	+	7.11008i	−0.146389	+	0.320547i
$493$	57.2673	+	16.8152i	2.57919	+	0.757318i
$494$	−3.70404	−	4.27469i	−0.166653	−	0.192327i
$495$	4.39298	+	5.06976i	0.197450	+	0.227869i
$496$	−2.83588	−	0.832691i	−0.127335	−	0.0373889i
$497$	−1.63792	+	3.58655i	−0.0734709	+	0.160879i
$498$	8.39191	+	5.39316i	0.376051	+	0.241673i
$499$	−25.0452	+	7.35394i	−1.12118	+	0.329207i	−0.789234	−	0.614092i	$-0.789522\pi$
$499$	−25.0452	+	7.35394i	−1.12118	+	0.329207i	−0.331943	+	0.943299i	$0.607704\pi$
$500$	1.41597	−	9.84826i	0.0633239	−	0.440427i
$501$	6.44536	+	14.1134i	0.287957	+	0.630539i
$502$	−3.38084	−	23.5143i	−0.150894	−	1.04949i
$503$	−10.6759	+	6.86099i	−0.476015	+	0.305916i	−0.756560	−	0.653925i	$-0.773121\pi$
$503$	−10.6759	+	6.86099i	−0.476015	+	0.305916i	0.280544	+	0.959841i	$0.409485\pi$
$504$	0.745702	−	0.860586i	0.0332162	−	0.0383335i
$505$	−3.22148			−0.143354
$506$	−18.4953	+	16.3295i	−0.822214	+	0.725935i
$507$	24.7735			1.10023
$508$	0.354138	−	0.408697i	0.0157123	−	0.0181330i
$509$	32.2157	−	20.7037i	1.42793	−	0.917678i	0.428031	−	0.903764i	$-0.359207\pi$
$509$	32.2157	−	20.7037i	1.42793	−	0.917678i	0.999903	−	0.0139135i	$-0.00442893\pi$
$510$	−2.18372	−	15.1881i	−0.0966967	−	0.672541i
$511$	1.88567	+	4.12904i	0.0834172	+	0.182658i
$512$	0.142315	−	0.989821i	0.00628949	−	0.0437443i
$513$	22.6580	−	6.65300i	1.00038	−	0.293737i
$514$	−0.304858	−	0.195920i	−0.0134467	−	0.00864166i
$515$	6.84620	−	14.9911i	0.301680	−	0.660587i
$516$	−24.4343	−	7.17455i	−1.07566	−	0.315842i
$517$	9.29457	+	10.7265i	0.408775	+	0.471751i
$518$	5.59476	+	6.45670i	0.245820	+	0.283691i
$519$	40.8780	+	12.0029i	1.79435	+	0.526868i
$520$	−0.431439	+	0.944720i	−0.0189199	+	0.0414287i
$521$	−22.5868	−	14.5157i	−0.989547	−	0.635943i	−0.0575249	−	0.998344i	$-0.518321\pi$
$521$	−22.5868	−	14.5157i	−0.989547	−	0.635943i	−0.932022	+	0.362401i	$0.881957\pi$
$522$	−9.90046	+	2.90704i	−0.433331	+	0.127238i
$523$	1.26724	−	8.81388i	0.0554127	−	0.385404i	−0.943176	−	0.332294i	$-0.892177\pi$
$523$	1.26724	−	8.81388i	0.0554127	−	0.385404i	0.998589	−	0.0531102i	$-0.0169135\pi$
$524$	−6.62560	−	14.5080i	−0.289441	−	0.633787i
$525$	−1.06797	−	7.42791i	−0.0466101	−	0.324180i
$526$	−9.08004	+	5.83539i	−0.395908	+	0.254435i
$527$	−12.7486	+	14.7127i	−0.555338	+	0.640895i
$528$	10.4660			0.455474
$529$	2.84972	−	22.8228i	0.123901	−	0.992295i
$530$	9.27425			0.402847
$531$	−2.48526	+	2.86814i	−0.107851	+	0.124467i
$532$	−5.24641	+	3.37166i	−0.227461	+	0.146180i
$533$	−0.495926	−	3.44924i	−0.0214809	−	0.149403i
$534$	9.57470	+	20.9657i	0.414338	+	0.907274i
$535$	0.452044	−	3.14403i	0.0195435	−	0.135928i
$536$	1.13179	−	0.332324i	0.0488860	−	0.0143542i
$537$	−0.114739	−	0.0737384i	−0.00495136	−	0.00318205i
$538$	−2.47127	+	5.41132i	−0.106544	+	0.233299i
$539$	4.93616	+	1.44939i	0.212615	+	0.0624295i
$540$	−2.83949	−	3.27695i	−0.122192	−	0.141017i
$541$	2.65338	+	3.06217i	0.114078	+	0.131653i	0.809916	−	0.586546i	$-0.199512\pi$
$541$	2.65338	+	3.06217i	0.114078	+	0.131653i	−0.695838	+	0.718198i	$0.744967\pi$
$542$	20.2800	+	5.95473i	0.871099	+	0.255778i
$543$	16.5749	−	36.2939i	0.711296	−	1.55752i
$544$	−5.54108	−	3.56104i	−0.237572	−	0.152678i
$545$	−17.5771	+	5.16111i	−0.752921	+	0.221078i
$546$	−0.262588	+	1.82634i	−0.0112377	+	0.0781600i
$547$	−1.09667	−	2.40137i	−0.0468902	−	0.102675i	0.884737	−	0.466090i	$-0.154338\pi$
$547$	−1.09667	−	2.40137i	−0.0468902	−	0.102675i	−0.931627	+	0.363415i	$0.881611\pi$
$548$	−2.72301	−	18.9390i	−0.116321	−	0.809033i
$549$	−10.4944	+	6.74436i	−0.447892	+	0.287842i
$550$	12.4272	−	14.3417i	0.529897	−	0.611534i
$551$	56.5110			2.40745
$552$	−7.31385	+	6.45741i	−0.311298	+	0.274846i
$553$	−8.88426			−0.377797
$554$	2.04577	−	2.36095i	0.0869165	−	0.100307i
$555$	−16.7432	+	10.7602i	−0.710710	+	0.456745i
$556$	−1.10722	−	7.70086i	−0.0469565	−	0.326589i
$557$	12.2829	+	26.8957i	0.520442	+	1.13961i	0.969272	+	0.245992i	$0.0791136\pi$
$557$	12.2829	+	26.8957i	0.520442	+	1.13961i	−0.448830	+	0.893617i	$0.648159\pi$
$558$	0.478975	−	3.33135i	0.0202766	−	0.141027i
$559$	10.8933	−	3.19855i	0.460736	−	0.135284i
$560$	0.963326	+	0.619092i	0.0407079	+	0.0261614i
$561$	28.6372	−	62.7066i	1.20906	−	2.64748i
$562$	4.33981	+	1.27428i	0.183064	+	0.0537524i
$563$	−30.8816	−	35.6393i	−1.30151	−	1.50202i	−0.735269	−	0.677776i	$-0.762944\pi$
$563$	−30.8816	−	35.6393i	−1.30151	−	1.50202i	−0.566237	−	0.824242i	$-0.691601\pi$
$564$	3.67549	+	4.24174i	0.154766	+	0.178609i
$565$	−1.96639	−	0.577385i	−0.0827268	−	0.0242908i
$566$	−3.66822	+	8.03227i	−0.154187	+	0.337622i
$567$	−9.35430	−	6.01164i	−0.392844	−	0.252465i
$568$	−3.78315	+	1.11083i	−0.158737	+	0.0466095i
$569$	−1.93942	+	13.4889i	−0.0813046	+	0.565486i	0.907927	+	0.419128i	$0.137664\pi$
$569$	−1.93942	+	13.4889i	−0.0813046	+	0.565486i	−0.989232	+	0.146358i	$0.953245\pi$
$570$	−6.03527	−	13.2154i	−0.252790	−	0.553532i
$571$	−5.04281	−	35.0735i	−0.211035	−	1.46778i	−0.769710	−	0.638394i	$-0.779599\pi$
$571$	−5.04281	−	35.0735i	−0.211035	−	1.46778i	0.558675	−	0.829386i	$-0.311310\pi$
$572$	−3.92523	+	2.52259i	−0.164122	+	0.105475i
$573$	−20.0805	+	23.1742i	−0.838876	+	0.968114i
$574$	−3.84216			−0.160369
$575$	0.164339	+	17.6898i	0.00685339	+	0.737714i
$576$	1.13872			0.0474466
$577$	−21.1152	+	24.3683i	−0.879038	+	1.01446i	0.120724	+	0.992686i	$0.461478\pi$
$577$	−21.1152	+	24.3683i	−0.879038	+	1.01446i	−0.999763	+	0.0217783i	$0.993067\pi$
$578$	−22.1961	+	14.2646i	−0.923235	+	0.593327i
$579$	2.42877	+	16.8925i	0.100936	+	0.702027i
$580$	−4.31048	−	9.43864i	−0.178983	−	0.391918i
$581$	−0.697833	+	4.85353i	−0.0289510	+	0.201359i
$582$	−27.4558	+	8.06175i	−1.13808	+	0.334170i
$583$	35.0515	+	22.5262i	1.45168	+	0.932941i
$584$	−1.88567	+	4.12904i	−0.0780296	+	0.170861i
$585$	−1.13474	−	0.333189i	−0.0469156	−	0.0137757i
$586$	0.575836	+	0.664551i	0.0237876	+	0.0274523i
$587$	−29.9790	−	34.5976i	−1.23737	−	1.42800i	−0.866400	−	0.499351i	$-0.833572\pi$
$587$	−29.9790	−	34.5976i	−1.23737	−	1.42800i	−0.370967	−	0.928646i	$-0.620974\pi$
$588$	1.95198	+	0.573152i	0.0804982	+	0.0236364i
$589$	−7.65710	+	16.7667i	−0.315505	+	0.690860i
$590$	−3.21056	−	2.06330i	−0.132177	−	0.0849447i
$591$	−27.4831	+	8.06977i	−1.13050	+	0.331946i
$592$	−1.21586	+	8.45647i	−0.0499714	+	0.347559i
$593$	8.01362	+	17.5474i	0.329080	+	0.720584i	0.999776	−	0.0211474i	$-0.00673194\pi$
$593$	8.01362	+	17.5474i	0.329080	+	0.720584i	−0.670696	+	0.741732i	$0.734005\pi$
$594$	−2.77232	−	19.2819i	−0.113750	−	0.791145i
$595$	6.34513	−	4.07777i	0.260125	−	0.167172i
$596$	6.47659	−	7.47439i	0.265292	−	0.306163i
$597$	0.579710			0.0237259
$598$	1.18662	−	4.18467i	0.0485244	−	0.171124i
$599$	−20.2433			−0.827117			−0.413559	−	0.910478i	$-0.635714\pi$
$599$	−20.2433			−0.827117			−0.413559	+	0.910478i	$0.635714\pi$
$600$	4.91426	−	5.67136i	0.200624	−	0.231532i
$601$	13.7643	−	8.84578i	0.561458	−	0.360827i	−0.228922	−	0.973445i	$-0.573520\pi$
$601$	13.7643	−	8.84578i	0.561458	−	0.360827i	0.790379	+	0.612618i	$0.209884\pi$
$602$	−1.78145	−	12.3903i	−0.0726067	−	0.504991i
$603$	0.557986	+	1.22182i	0.0227230	+	0.0497563i
$604$	2.04608	−	14.2308i	0.0832536	−	0.579042i
$605$	−16.9933	+	4.98968i	−0.690875	+	0.202859i
$606$	−4.81470	−	3.09422i	−0.195584	−	0.125694i
$607$	8.53523	−	18.6895i	0.346434	−	0.758585i	−0.653564	−	0.756871i	$-0.726727\pi$
$607$	8.53523	−	18.6895i	0.346434	−	0.758585i	0.999999	−	0.00171426i	$-0.000545666\pi$
$608$	−5.98380	−	1.75700i	−0.242675	−	0.0712559i
$609$	−12.0720	−	13.9318i	−0.489182	−	0.564546i
$610$	−8.21507	−	9.48070i	−0.332619	−	0.383862i
$611$	−2.40086	−	0.704955i	−0.0971282	−	0.0285194i
$612$	3.11577	−	6.82259i	0.125948	−	0.275787i
$613$	30.9478	+	19.8889i	1.24997	+	0.803307i	0.986879	−	0.161464i	$-0.0516216\pi$
$613$	30.9478	+	19.8889i	1.24997	+	0.803307i	0.263091	+	0.964771i	$0.415258\pi$
$614$	−5.36013	+	1.57388i	−0.216317	+	0.0635165i
$615$	1.27381	−	8.85955i	0.0513650	−	0.357252i
$616$	2.13712	+	4.67965i	0.0861072	+	0.188548i
$617$	1.23847	+	8.61372i	0.0498588	+	0.346775i	0.999446	+	0.0332733i	$0.0105932\pi$
$617$	1.23847	+	8.61372i	0.0498588	+	0.346775i	−0.949588	+	0.313502i	$0.898498\pi$
$618$	24.6310	−	15.8294i	0.990802	−	0.636750i
$619$	−23.8212	+	27.4912i	−0.957456	+	1.10496i	0.0369481	+	0.999317i	$0.488236\pi$
$619$	−23.8212	+	27.4912i	−0.957456	+	1.10496i	−0.994404	+	0.105646i	$0.966309\pi$
$620$	3.38449			0.135924
$621$	13.8341	+	11.7641i	0.555142	+	0.472076i
$622$	5.02644			0.201542
$623$	−7.41924	+	8.56226i	−0.297245	+	0.343040i
$624$	−1.55221	+	0.997546i	−0.0621382	+	0.0399338i
$625$	−1.00337	−	6.97860i	−0.0401348	−	0.279144i
$626$	1.68783	+	3.69583i	0.0674593	+	0.147715i
$627$	9.28894	−	64.6060i	0.370964	−	2.58011i
$628$	2.54162	−	0.746288i	0.101422	−	0.0297801i
$629$	47.3399	+	30.4235i	1.88756	+	1.21306i
$630$	−0.541682	+	1.18612i	−0.0215811	+	0.0472561i
$631$	−5.13348	−	1.50733i	−0.204361	−	0.0600057i	0.177950	−	0.984040i	$-0.443053\pi$
$631$	−5.13348	−	1.50733i	−0.204361	−	0.0600057i	−0.382311	+	0.924034i	$0.624872\pi$
$632$	−5.81795	−	6.71427i	−0.231426	−	0.267079i
$633$	24.3504	+	28.1019i	0.967842	+	1.11695i
$634$	−22.5926	−	6.63377i	−0.897265	−	0.263461i
$635$	−0.257248	+	0.563294i	−0.0102086	+	0.0223537i
$636$	13.8609	+	8.90787i	0.549621	+	0.353220i
$637$	−0.870228	+	0.255522i	−0.0344797	+	0.0101241i
$638$	6.63430	−	46.1426i	0.262654	−	1.82680i
$639$	−1.86513	−	4.08407i	−0.0737835	−	0.161563i
$640$	0.162966	+	1.13345i	0.00644179	+	0.0448036i
$641$	25.7211	−	16.5299i	1.01592	−	0.652894i	0.0770029	−	0.997031i	$-0.475465\pi$
$641$	25.7211	−	16.5299i	1.01592	−	0.652894i	0.938919	+	0.344137i	$0.111829\pi$
$642$	3.69544	−	4.26476i	0.145847	−	0.168317i
$643$	−24.3109			−0.958728			−0.479364	−	0.877616i	$-0.659133\pi$
$643$	−24.3109			−0.958728			−0.479364	+	0.877616i	$0.659133\pi$
$644$	−4.38076	−	1.95165i	−0.172626	−	0.0769057i
$645$	29.1611			1.14822
$646$	−26.9000	+	31.0442i	−1.05837	+	1.22142i
$647$	6.34360	−	4.07678i	0.249393	−	0.160275i	−0.409972	−	0.912098i	$-0.634462\pi$
$647$	6.34360	−	4.07678i	0.249393	−	0.160275i	0.659365	+	0.751823i	$0.270825\pi$
$648$	−1.58247	−	11.0063i	−0.0621651	−	0.432368i
$649$	−7.12257	−	15.5963i	−0.279585	−	0.612206i
$650$	−0.476122	+	3.31150i	−0.0186750	+	0.129888i
$651$	5.76928	−	1.69401i	0.226116	−	0.0663936i
$652$	7.39133	+	4.75012i	0.289467	+	0.186029i
$653$	−13.7764	+	30.1661i	−0.539112	+	1.18049i	0.422572	+	0.906330i	$0.361128\pi$
$653$	−13.7764	+	30.1661i	−0.539112	+	1.18049i	−0.961684	+	0.274161i	$0.911600\pi$
$654$	−31.2273	−	9.16916i	−1.22108	−	0.358543i
$655$	11.9602	+	13.8028i	0.467324	+	0.539320i
$656$	−2.51608	−	2.90371i	−0.0982365	−	0.113371i
$657$	−4.95954	−	1.45625i	−0.193490	−	0.0568139i
$658$	−1.14608	+	2.50957i	−0.0446789	+	0.0978331i
$659$	14.9368	+	9.59931i	0.581856	+	0.373936i	0.798210	−	0.602379i	$-0.205780\pi$
$659$	14.9368	+	9.59931i	0.581856	+	0.373936i	−0.216354	+	0.976315i	$0.569417\pi$
$660$	−11.4992	+	3.37648i	−0.447607	+	0.131429i
$661$	3.29130	−	22.8915i	0.128017	−	0.890375i	−0.820047	−	0.572296i	$-0.806053\pi$
$661$	3.29130	−	22.8915i	0.128017	−	0.890375i	0.948064	−	0.318080i	$-0.103038\pi$
$662$	−9.52995	−	20.8677i	−0.370392	−	0.811045i
$663$	1.72958	+	12.0295i	0.0671715	+	0.467188i
$664$	−4.12504	+	2.65100i	−0.160083	+	0.102879i
$665$	4.67661	−	5.39709i	0.181351	−	0.209290i
$666$	−9.72856			−0.376974
$667$	23.8333	+	36.3386i	0.922829	+	1.40704i
$668$	−7.62662			−0.295083
$669$	−9.48681	+	10.9484i	−0.366781	+	0.423288i
$670$	−1.13631	+	0.730265i	−0.0438997	+	0.0282126i
$671$	−8.02073	−	55.7854i	−0.309637	−	2.15357i
$672$	0.845114	+	1.85054i	0.0326010	+	0.0713862i
$673$	−3.98906	+	27.7445i	−0.153767	+	1.06947i	0.756066	+	0.654496i	$0.227119\pi$
$673$	−3.98906	+	27.7445i	−0.153767	+	1.06947i	−0.909832	+	0.414976i	$0.863790\pi$
$674$	14.6777	−	4.30976i	0.565364	−	0.166006i
$675$	−11.7503	−	7.55146i	−0.452269	−	0.290656i
$676$	−5.05868	+	11.0770i	−0.194565	+	0.426037i
$677$	−34.7249	−	10.1961i	−1.33459	−	0.391870i	−0.464851	−	0.885389i	$-0.653892\pi$
$677$	−34.7249	−	10.1961i	−1.33459	−	0.391870i	−0.869735	+	0.493519i	$0.835710\pi$
$678$	−2.38432	−	2.75165i	−0.0915691	−	0.105676i
$679$	−9.21103	−	10.6301i	−0.353487	−	0.407946i
$680$	7.23695	+	2.12496i	0.277524	+	0.0814885i
$681$	−3.81342	+	8.35023i	−0.146131	+	0.319981i
$682$	12.7915	+	8.22059i	0.489811	+	0.314783i
$683$	−19.4808	+	5.72007i	−0.745411	+	0.218872i	−0.632315	−	0.774712i	$-0.717895\pi$
$683$	−19.4808	+	5.72007i	−0.745411	+	0.218872i	−0.113096	+	0.993584i	$0.536077\pi$
$684$	1.01065	−	7.02924i	0.0386433	−	0.268770i
$685$	9.10182	+	19.9302i	0.347763	+	0.761494i
$686$	0.142315	+	0.989821i	0.00543361	+	0.0377916i
$687$	3.62891	−	2.33216i	0.138451	−	0.0889773i
$688$	8.19735	−	9.46025i	0.312521	−	0.360669i
$689$	−7.34553			−0.279843
$690$	5.95264	−	9.45445i	0.226613	−	0.359925i
$691$	13.2065			0.502397			0.251199	−	0.967936i	$-0.419175\pi$
$691$	13.2065			0.502397			0.251199	+	0.967936i	$0.419175\pi$
$692$	−13.7140	+	15.8268i	−0.521328	+	0.601645i
$693$	−4.92822	+	3.16718i	−0.187208	+	0.120311i
$694$	4.96847	+	34.5565i	0.188601	+	1.31175i
$695$	3.70093	+	8.10391i	0.140384	+	0.307399i
$696$	2.62350	−	18.2468i	0.0994434	−	0.691644i
$697$	−24.2820	+	7.12985i	−0.919747	+	0.270062i
$698$	−23.7466	−	15.2610i	−0.898821	−	0.577637i
$699$	6.70557	−	14.6832i	0.253628	−	0.555368i
$700$	3.53931	+	1.03923i	0.133773	+	0.0392794i
$701$	−20.1289	−	23.2299i	−0.760257	−	0.877383i	0.235264	−	0.971932i	$-0.424405\pi$
$701$	−20.1289	−	23.2299i	−0.760257	−	0.877383i	−0.995520	+	0.0945486i	$0.969859\pi$
$702$	2.24898	+	2.59546i	0.0848822	+	0.0979593i
$703$	51.1222	+	15.0108i	1.92811	+	0.566145i
$704$	−2.13712	+	4.67965i	−0.0805459	+	0.176371i
$705$	−5.40679	−	3.47473i	−0.203631	−	0.130866i
$706$	15.1501	−	4.44846i	0.570180	−	0.167420i
$707$	0.400368	−	2.78462i	0.0150574	−	0.104727i
$708$	−2.81658	−	6.16745i	−0.105854	−	0.231787i
$709$	−3.26661	−	22.7198i	−0.122680	−	0.853259i	−0.954499	−	0.298213i	$-0.903610\pi$
$709$	−3.26661	−	22.7198i	−0.122680	−	0.853259i	0.831819	−	0.555046i	$-0.187300\pi$
$710$	3.79826	−	2.44099i	0.142546	−	0.0916088i
$711$	6.62500	−	7.64566i	0.248457	−	0.286735i
$712$	−11.3295			−0.424591
$713$	−14.0110	+	2.14750i	−0.524715	+	0.0804247i
$714$	13.3999			0.501477
$715$	3.49892	−	4.03797i	0.130852	−	0.151011i
$716$	0.0564000	−	0.0362461i	0.00210777	−	0.00135458i
$717$	−3.72002	−	25.8733i	−0.138927	−	0.966256i
$718$	−4.34427	−	9.51262i	−0.162127	−	0.355008i
$719$	−3.31125	+	23.0303i	−0.123489	+	0.858883i	0.830066	+	0.557665i	$0.188303\pi$
$719$	−3.31125	+	23.0303i	−0.123489	+	0.858883i	−0.953555	+	0.301219i	$0.902607\pi$
$720$	−1.25114	+	0.367366i	−0.0466271	+	0.0136909i
$721$	12.1073	+	7.78091i	0.450900	+	0.289776i
$722$	−8.26384	+	18.0953i	−0.307548	+	0.673437i
$723$	41.2454	+	12.1108i	1.53393	+	0.450404i
$724$	12.8435	+	14.8222i	0.477326	+	0.550863i
$725$	−21.8889	−	25.2611i	−0.812931	−	0.938173i
$726$	−30.1901	−	8.86460i	−1.12046	−	0.328996i
$727$	18.9577	−	41.5117i	0.703104	−	1.53958i	−0.133064	−	0.991107i	$-0.542482\pi$
$727$	18.9577	−	41.5117i	0.703104	−	1.53958i	0.836167	−	0.548474i	$-0.184791\pi$
$728$	−0.762989	−	0.490343i	−0.0282782	−	0.0181733i
$729$	−10.0248	+	2.94355i	−0.371289	+	0.109020i
$730$	0.739742	−	5.14502i	0.0273791	−	0.190426i
$731$	−34.2511	−	74.9994i	−1.26682	−	2.77395i
$732$	−3.17175	−	22.0600i	−0.117231	−	0.815362i
$733$	15.8954	−	10.2154i	0.587111	−	0.377313i	−0.213102	−	0.977030i	$-0.568357\pi$
$733$	15.8954	−	10.2154i	0.587111	−	0.377313i	0.800212	+	0.599717i	$0.204720\pi$
$734$	−7.73432	+	8.92588i	−0.285479	+	0.329460i
$735$	−2.32959			−0.0859282
$736$	−1.39383	−	4.58882i	−0.0513773	−	0.169146i
$737$	−6.06838			−0.223532
$738$	2.86511	−	3.30651i	0.105466	−	0.121714i
$739$	13.2871	−	8.53911i	0.488774	−	0.314116i	−0.272938	−	0.962032i	$-0.587995\pi$
$739$	13.2871	−	8.53911i	0.488774	−	0.314116i	0.761712	+	0.647915i	$0.224359\pi$
$740$	−1.39229	−	9.68357i	−0.0511815	−	0.355975i
$741$	4.78015	+	10.4671i	0.175603	+	0.384518i
$742$	−1.15261	+	8.01658i	−0.0423137	+	0.294298i
$743$	19.9832	−	5.86761i	0.733114	−	0.215262i	0.106194	−	0.994345i	$-0.466134\pi$
$743$	19.9832	−	5.86761i	0.733114	−	0.215262i	0.626920	+	0.779084i	$0.284315\pi$
$744$	5.05832	+	3.25079i	0.185447	+	0.119180i
$745$	−4.70464	+	10.3017i	−0.172365	+	0.377426i
$746$	−1.37462	−	0.403626i	−0.0503285	−	0.0147778i
$747$	−3.65651	−	4.21983i	−0.133785	−	0.154396i
$748$	22.1903	+	25.6090i	0.811359	+	0.936358i
$749$	2.66149	+	0.781485i	0.0972489	+	0.0285549i
$750$	−8.40848	+	18.4120i	−0.307034	+	0.672312i
$751$	−30.3258	−	19.4892i	−1.10660	−	0.711172i	−0.146054	−	0.989277i	$-0.546657\pi$
$751$	−30.3258	−	19.4892i	−1.10660	−	0.711172i	−0.960551	+	0.278105i	$0.910294\pi$
$752$	−2.64713	+	0.777267i	−0.0965308	+	0.0283440i
$753$	−6.87793	+	47.8371i	−0.250646	+	1.74328i
$754$	3.41406	+	7.47574i	0.124333	+	0.272250i
$755$	2.34298	+	16.2958i	0.0852697	+	0.593063i
$756$	3.18546	−	2.04717i	0.115854	−	0.0744549i
$757$	15.3281	−	17.6895i	0.557108	−	0.642937i	−0.405417	−	0.914132i	$-0.632874\pi$
$757$	15.3281	−	17.6895i	0.557108	−	0.642937i	0.962524	+	0.271195i	$0.0874190\pi$
$758$	2.18231			0.0792651
$759$	45.4616	−	21.2742i	1.65015	−	0.772205i
$760$	7.14138			0.259045
$761$	2.54775	−	2.94026i	0.0923557	−	0.106584i	−0.707690	−	0.706523i	$-0.750263\pi$
$761$	2.54775	−	2.94026i	0.0923557	−	0.106584i	0.800046	+	0.599938i	$0.204808\pi$
$762$	−0.925515	+	0.594792i	−0.0335279	+	0.0215470i
$763$	−2.27672	−	15.8349i	−0.0824229	−	0.573264i
$764$	−6.26146	−	13.7107i	−0.226532	−	0.496035i
$765$	−1.22231	+	8.50133i	−0.0441926	+	0.307366i
$766$	5.80208	−	1.70365i	0.209638	−	0.0615552i
$767$	2.54288	+	1.63421i	0.0918179	+	0.0590078i
$768$	−0.845114	+	1.85054i	−0.0304954	+	0.0667756i
$769$	−12.9703	−	3.80842i	−0.467721	−	0.137335i	0.0393757	−	0.999224i	$-0.487463\pi$
$769$	−12.9703	−	3.80842i	−0.467721	−	0.137335i	−0.507097	+	0.861889i	$0.669281\pi$
$770$	−3.85783	−	4.45217i	−0.139026	−	0.160445i
$771$	0.482783	+	0.557161i	0.0173870	+	0.0200657i
$772$	−8.04906	−	2.36342i	−0.289692	−	0.0850612i
$773$	−20.9651	+	45.9071i	−0.754061	+	1.65116i	0.00486750	+	0.999988i	$0.498451\pi$
$773$	−20.9651	+	45.9071i	−0.754061	+	1.65116i	−0.758928	+	0.651174i	$0.774277\pi$
$774$	11.9913	+	7.70637i	0.431020	+	0.277000i
$775$	10.4608	−	3.07157i	0.375763	−	0.110334i
$776$	2.00175	−	13.9225i	0.0718586	−	0.499787i
$777$	−7.22017	−	15.8100i	−0.259022	−	0.567180i
$778$	0.684550	+	4.76115i	0.0245423	+	0.170695i
$779$	−20.1576	+	12.9545i	−0.722220	+	0.464143i
$780$	1.38363	−	1.59679i	0.0495418	−	0.0571743i
$781$	20.2842			0.725827
$782$	−31.3076	−	4.20488i	−1.11956	−	0.150366i
$783$	−34.3117			−1.22620
$784$	−0.654861	+	0.755750i	−0.0233879	+	0.0269911i
$785$	−2.55178	+	1.63993i	−0.0910768	+	0.0585315i
$786$	4.61771	+	32.1168i	0.164708	+	1.14557i
$787$	−7.51262	−	16.4503i	−0.267796	−	0.586392i	0.727186	−	0.686440i	$-0.240828\pi$
$787$	−7.51262	−	16.4503i	−0.267796	−	0.586392i	−0.994983	+	0.100048i	$0.968100\pi$
$788$	2.00374	−	13.9363i	0.0713803	−	0.496461i
$789$	21.0686	−	6.18630i	0.750062	−	0.220238i
$790$	8.55843	+	5.50017i	0.304495	+	0.195687i
$791$	0.743471	−	1.62798i	0.0264348	−	0.0578841i
$792$	−5.62089	−	1.65044i	−0.199730	−	0.0586459i
$793$	6.50663	+	7.50905i	0.231057	+	0.266654i
$794$	−2.95303	−	3.40798i	−0.104799	−	0.120945i
$795$	−18.1031	−	5.31555i	−0.642051	−	0.188523i
$796$	−0.118375	+	0.259205i	−0.00419569	+	0.00918728i
$797$	4.62580	+	2.97282i	0.163854	+	0.105303i	0.619998	−	0.784603i	$-0.287133\pi$
$797$	4.62580	+	2.97282i	0.163854	+	0.105303i	−0.456144	+	0.889906i	$0.650770\pi$
$798$	12.1734	−	3.57442i	0.430932	−	0.126533i
$799$	−2.58613	+	17.9869i	−0.0914908	+	0.636332i
$800$	1.53235	+	3.35539i	0.0541769	+	0.118631i
$801$	−1.83602	−	12.7698i	−0.0648725	−	0.451198i
$802$	22.4216	−	14.4095i	0.791735	−	0.508817i
$803$	15.2926	−	17.6486i	0.539663	−	0.622804i
$804$	−2.39971			−0.0846311
$805$	5.44287	+	0.731026i	0.191836	+	0.0257653i
$806$	−2.68064			−0.0944214
$807$	7.92537	−	9.14637i	0.278986	−	0.321967i
$808$	2.36666	−	1.52096i	0.0832589	−	0.0535073i
$809$	4.25551	+	29.5977i	0.149616	+	1.04060i	0.916850	+	0.399233i	$0.130724\pi$
$809$	4.25551	+	29.5977i	0.149616	+	1.04060i	−0.767234	+	0.641368i	$0.778367\pi$
$810$	5.28948	+	11.5823i	0.185853	+	0.406962i
$811$	−7.80790	+	54.3051i	−0.274172	+	1.90691i	0.128752	+	0.991677i	$0.458903\pi$
$811$	−7.80790	+	54.3051i	−0.274172	+	1.90691i	−0.402924	+	0.915233i	$0.632006\pi$
$812$	8.69439	−	2.55290i	0.305113	−	0.0895893i
$813$	−36.1730	−	23.2470i	−1.26864	−	0.815308i
$814$	18.2584	−	39.9803i	0.639956	−	1.40131i
$815$	−9.65347	−	2.83452i	−0.338146	−	0.0992888i
$816$	8.77504	+	10.1269i	0.307188	+	0.354514i
$817$	−51.1222	−	58.9981i	−1.78854	−	2.06408i
$818$	33.3074	+	9.77994i	1.16457	+	0.341948i
$819$	0.429032	−	0.939449i	0.0149916	−	0.0328270i
$820$	3.70125	+	2.37865i	0.129253	+	0.0830661i
$821$	−17.5020	+	5.13904i	−0.610823	+	0.179354i	−0.572491	−	0.819911i	$-0.694023\pi$
$821$	−17.5020	+	5.13904i	−0.610823	+	0.179354i	−0.0383321	+	0.999265i	$0.512204\pi$
$822$	−5.53965	+	38.5291i	−0.193218	+	1.34386i
$823$	1.58617	+	3.47323i	0.0552904	+	0.121069i	0.935261	−	0.353960i	$-0.115165\pi$
$823$	1.58617	+	3.47323i	0.0552904	+	0.121069i	−0.879970	+	0.475029i	$0.842438\pi$
$824$	2.04820	+	14.2455i	0.0713523	+	0.496266i
$825$	−32.4776	+	20.8721i	−1.13072	+	0.726673i
$826$	2.18251	−	2.51875i	0.0759392	−	0.0876385i
$827$	−41.8302			−1.45458			−0.727289	−	0.686332i	$-0.759220\pi$
$827$	−41.8302			−1.45458			−0.727289	+	0.686332i	$0.759220\pi$
$828$	4.94630	−	2.31467i	0.171896	−	0.0804404i
$829$	−48.1199			−1.67127			−0.835636	−	0.549283i	$-0.814901\pi$
$829$	−48.1199			−1.67127			−0.835636	+	0.549283i	$0.814901\pi$
$830$	3.67702	−	4.24351i	0.127631	−	0.147294i
$831$	−5.34648	+	3.43597i	−0.185467	+	0.119193i
$832$	−0.129075	−	0.897735i	−0.00447486	−	0.0311234i
$833$	2.73621	+	5.99147i	0.0948041	+	0.207592i
$834$	−2.25250	+	15.6665i	−0.0779978	+	0.542487i
$835$	8.37954	−	2.46045i	0.289986	−	0.0851475i
$836$	26.9904	+	17.3457i	0.933484	+	0.599914i
$837$	4.64915	−	10.1802i	0.160698	−	0.351880i
$838$	−36.1490	−	10.6143i	−1.24875	−	0.366665i
$839$	−21.5671	−	24.8898i	−0.744580	−	0.859291i	0.249451	−	0.968387i	$-0.419750\pi$
$839$	−21.5671	−	24.8898i	−0.744580	−	0.859291i	−0.994031	+	0.109096i	$0.965204\pi$
$840$	−1.52556	−	1.76059i	−0.0526367	−	0.0607460i
$841$	−50.9584	−	14.9627i	−1.75719	−	0.515957i
$842$	1.50074	−	3.28616i	0.0517189	−	0.113249i
$843$	−7.74086	−	4.97475i	−0.266609	−	0.171339i
$844$	−17.5374	+	5.14946i	−0.603664	+	0.177252i
$845$	1.98450	−	13.8025i	0.0682689	−	0.474821i
$846$	−1.30506	−	2.85769i	−0.0448690	−	0.0982494i
$847$	−2.20110	−	15.3090i	−0.0756306	−	0.526023i
$848$	−6.81333	+	4.37866i	−0.233971	+	0.150364i
$849$	11.7640	−	13.5764i	0.403739	−	0.465940i
$850$	24.2965			0.833364
$851$	11.9081	+	39.2043i	0.408204	+	1.34390i
$852$	8.02129			0.274805
$853$	2.08561	−	2.40693i	0.0714101	−	0.0824116i	−0.718920	−	0.695092i	$-0.755363\pi$
$853$	2.08561	−	2.40693i	0.0714101	−	0.0824116i	0.790330	+	0.612681i	$0.209909\pi$
$854$	9.21601	−	5.92277i	0.315365	−	0.202673i
$855$	1.15731	+	8.04924i	0.0395790	+	0.275278i
$856$	1.15230	+	2.52319i	0.0393848	+	0.0862408i
$857$	−0.781122	+	5.43282i	−0.0266826	+	0.185582i	−0.998804	−	0.0488973i	$-0.984429\pi$
$857$	−0.781122	+	5.43282i	−0.0266826	+	0.185582i	0.972121	+	0.234479i	$0.0753384\pi$
$858$	9.10780	−	2.67429i	0.310935	−	0.0912988i
$859$	35.2916	+	22.6805i	1.20413	+	0.773850i	0.979667	−	0.200632i	$-0.0642996\pi$
$859$	35.2916	+	22.6805i	1.20413	+	0.773850i	0.224467	+	0.974482i	$0.427936\pi$
$860$	−5.95461	+	13.0388i	−0.203050	+	0.444618i
$861$	7.49981	+	2.20214i	0.255593	+	0.0750489i
$862$	4.49580	+	5.18843i	0.153128	+	0.176719i
$863$	−4.55379	−	5.25535i	−0.155013	−	0.178894i	0.672931	−	0.739705i	$-0.265035\pi$
$863$	−4.55379	−	5.25535i	−0.155013	−	0.178894i	−0.827944	+	0.560811i	$0.810489\pi$
$864$	3.63318	+	1.06680i	0.123603	+	0.0362932i
$865$	9.96194	−	21.8136i	0.338716	−	0.741685i
$866$	0.0406540	+	0.0261268i	0.00138148	+	0.000887823i
$867$	51.5020	−	15.1224i	1.74910	−	0.513582i
$868$	−0.420627	+	2.92552i	−0.0142770	+	0.0992987i
$869$	18.9868	+	41.5752i	0.644081	+	1.41034i
$870$	3.00419	+	20.8946i	0.101851	+	0.708392i
$871$	0.900002	−	0.578396i	0.0304954	−	0.0195982i
$872$	10.4763	−	12.0903i	0.354773	−	0.409430i
$873$	16.0168			0.542086
$874$	−29.5636	+	4.53130i	−1.00000	+	0.153274i
$875$	−9.94953			−0.336355
$876$	6.04736	−	6.97902i	0.204321	−	0.235799i
$877$	36.7520	−	23.6190i	1.24103	−	0.797558i	0.255454	−	0.966821i	$-0.417775\pi$
$877$	36.7520	−	23.6190i	1.24103	−	0.797558i	0.985571	+	0.169263i	$0.0541386\pi$
$878$	2.98661	+	20.7723i	0.100793	+	0.701031i
$879$	−0.743131	−	1.62723i	−0.0250652	−	0.0548851i
$880$	0.838386	−	5.83110i	0.0282620	−	0.196566i
$881$	−16.1939	+	4.75497i	−0.545588	+	0.160199i	−0.542900	−	0.839797i	$-0.682674\pi$
$881$	−16.1939	+	4.75497i	−0.545588	+	0.160199i	−0.00268774	+	0.999996i	$0.500856\pi$
$882$	−0.957950	−	0.615637i	−0.0322559	−	0.0207296i
$883$	1.66112	−	3.63733i	0.0559010	−	0.122406i	−0.879620	−	0.475677i	$-0.842203\pi$
$883$	1.66112	−	3.63733i	0.0559010	−	0.122406i	0.935521	+	0.353271i	$0.114931\pi$
$884$	−5.73192	−	1.68304i	−0.192785	−	0.0566069i
$885$	5.08435	+	5.86765i	0.170908	+	0.197239i
$886$	7.65202	+	8.83090i	0.257075	+	0.296680i
$887$	24.8096	+	7.28476i	0.833025	+	0.244598i	0.670316	−	0.742076i	$-0.266159\pi$
$887$	24.8096	+	7.28476i	0.833025	+	0.244598i	0.162709	+	0.986674i	$0.447977\pi$
$888$	7.22017	−	15.8100i	0.242293	−	0.530548i
$889$	−0.454936	−	0.292370i	−0.0152581	−	0.00980576i
$890$	12.4480	−	3.65505i	0.417257	−	0.122518i
$891$	−8.14108	+	56.6224i	−0.272736	+	1.89692i
$892$	−2.95815	−	6.47745i	−0.0990463	−	0.216881i
$893$	2.44861	+	17.0304i	0.0819395	+	0.569901i
$894$	−16.9261	+	10.8778i	−0.566094	+	0.363807i
$895$	−0.0502744	+	0.0580198i	−0.00168049	+	0.00193939i
$896$	−1.00000			−0.0334077
$897$	−4.71470	+	7.48827i	−0.157419	+	0.250026i
$898$	6.40751			0.213821
$899$	17.5385	−	20.2405i	0.584942	−	0.675059i
$900$	−3.53362	+	2.27092i	−0.117787	+	0.0756973i
$901$	7.59189	+	52.8028i	0.252923	+	1.75911i
$902$	8.21118	+	17.9800i	0.273402	+	0.598667i
$903$	−3.62416	+	25.2066i	−0.120605	+	0.838823i
$904$	1.71721	−	0.504219i	0.0571136	−	0.0167701i
$905$	−18.8933	−	12.1420i	−0.628036	−	0.403614i
$906$	−12.1503	+	26.6054i	−0.403666	+	0.883906i
$907$	13.8640	+	4.07083i	0.460346	+	0.135170i	0.503679	−	0.863891i	$-0.331979\pi$
$907$	13.8640	+	4.07083i	0.460346	+	0.135170i	−0.0433329	+	0.999061i	$0.513798\pi$
$908$	−2.95494	−	3.41018i	−0.0980631	−	0.113171i
$909$	2.09785	+	2.42105i	0.0695813	+	0.0803011i
$910$	0.996505	+	0.292600i	0.0330338	+	0.00969960i
$911$	−15.2224	+	33.3324i	−0.504341	+	1.10435i	0.470693	+	0.882297i	$0.344004\pi$
$911$	−15.2224	+	33.3324i	−0.504341	+	1.10435i	−0.975034	+	0.222056i	$0.928723\pi$
$912$	10.6732	+	6.85926i	0.353426	+	0.227133i
$913$	24.2042	−	7.10699i	0.801042	−	0.235207i
$914$	0.278031	−	1.93375i	0.00919646	−	0.0639628i
$915$	10.6017	+	23.2146i	0.350483	+	0.767451i
$916$	0.301763	+	2.09881i	0.00997053	+	0.0693466i
$917$	−13.4175	+	8.62287i	−0.443083	+	0.284752i
$918$	16.3328	−	18.8491i	0.539064	−	0.622113i
$919$	−48.5697			−1.60217			−0.801084	−	0.598552i	$-0.795743\pi$
$919$	−48.5697			−1.60217			−0.801084	+	0.598552i	$0.795743\pi$
$920$	3.01185	+	4.59217i	0.0992978	+	0.151399i
$921$	11.3649			0.374487
$922$	16.3996	−	18.9261i	0.540091	−	0.623298i
$923$	−3.00836	+	1.93335i	−0.0990213	+	0.0636371i
$924$	−1.48947	−	10.3595i	−0.0489998	−	0.340801i
$925$	−13.0916	−	28.6665i	−0.430448	−	0.942549i
$926$	1.44492	−	10.0496i	0.0474830	−	0.330251i
$927$	−15.7246	+	4.61716i	−0.516463	+	0.151647i
$928$	7.62297	+	4.89899i	0.250236	+	0.160817i
$929$	12.2956	−	26.9236i	0.403406	−	0.883336i	−0.593507	−	0.804829i	$-0.702257\pi$
$929$	12.2956	−	26.9236i	0.403406	−	0.883336i	0.996914	−	0.0785077i	$-0.0250155\pi$
$930$	−6.60644	−	1.93983i	−0.216634	−	0.0636094i
$931$	4.08399	+	4.71317i	0.133847	+	0.154468i
$932$	5.19601	+	5.99651i	0.170201	+	0.196422i
$933$	−9.81149	−	2.88091i	−0.321214	−	0.0943168i
$934$	12.6767	−	27.7580i	0.414793	−	0.908270i
$935$	−32.6429	−	20.9783i	−1.06754	−	0.686063i
$936$	0.990944	−	0.290967i	0.0323900	−	0.00951057i
$937$	3.14250	−	21.8565i	0.102661	−	0.714022i	−0.871865	−	0.489746i	$-0.837089\pi$
$937$	3.14250	−	21.8565i	0.102661	−	0.714022i	0.974526	−	0.224275i	$-0.0720015\pi$
$938$	−0.490013	−	1.07298i	−0.0159995	−	0.0350340i
$939$	−1.17633	−	8.18156i	−0.0383881	−	0.266995i
$940$	2.65770	−	1.70800i	0.0866847	−	0.0557089i
$941$	−12.6430	+	14.5909i	−0.412152	+	0.475648i	−0.923430	−	0.383767i	$-0.874627\pi$
$941$	−12.6430	+	14.5909i	−0.412152	+	0.475648i	0.511278	+	0.859415i	$0.329172\pi$
$942$	−5.38893			−0.175581
$943$	−16.8316	−	7.49855i	−0.548112	−	0.244186i
$944$	3.33278			0.108473
$945$	−2.83949	+	3.27695i	−0.0923686	+	0.106599i
$946$	−54.1750	+	34.8162i	−1.76138	+	1.13197i
$947$	−5.68469	−	39.5379i	−0.184728	−	1.28481i	−0.845400	−	0.534134i	$-0.820638\pi$
$947$	−5.68469	−	39.5379i	−0.184728	−	1.28481i	0.660672	−	0.750674i	$-0.270271\pi$
$948$	7.50821	+	16.4407i	0.243855	+	0.533968i
$949$	−0.585902	+	4.07504i	−0.0190192	+	0.132281i
$950$	22.0726	−	6.48111i	0.716131	−	0.210275i
$951$	40.2980	+	25.8979i	1.30675	+	0.839798i
$952$	−2.73621	+	5.99147i	−0.0886811	+	0.194185i
$953$	33.5036	+	9.83755i	1.08529	+	0.318670i	0.774993	−	0.631970i	$-0.217754\pi$
$953$	33.5036	+	9.83755i	1.08529	+	0.318670i	0.310296	+	0.950640i	$0.399572\pi$
$954$	−6.03945	−	6.96990i	−0.195534	−	0.225659i
$955$	11.3029	+	13.0442i	0.365752	+	0.422100i
$956$	12.3283	+	3.61992i	0.398726	+	0.117077i
$957$	−39.3967	+	86.2667i	−1.27351	+	2.78861i
$958$	9.05574	+	5.81977i	0.292578	+	0.188028i
$959$	−18.3587	+	5.39059i	−0.592833	+	0.174071i
$960$	0.331535	−	2.30588i	0.0107002	−	0.0744219i
$961$	−9.24896	−	20.2524i	−0.298354	−	0.653303i
$962$	1.10274	+	7.66974i	0.0355538	+	0.247282i
$963$	−2.65722	+	1.70769i	−0.0856276	+	0.0550295i
$964$	−13.8373	+	15.9691i	−0.445668	+	0.514329i
$965$	9.60615			0.309233
$966$	7.43255	+	6.32042i	0.239138	+	0.203356i
$967$	43.0426			1.38416			0.692079	−	0.721822i	$-0.256695\pi$
$967$	43.0426			1.38416			0.692079	+	0.721822i	$0.256695\pi$
$968$	10.1283	−	11.6887i	0.325537	−	0.375690i
$969$	70.3012	−	45.1798i	2.25840	−	1.45139i
$970$	2.29222	+	15.9427i	0.0735987	+	0.511890i
$971$	−2.91007	−	6.37216i	−0.0933886	−	0.204492i	0.857173	−	0.515029i	$-0.172219\pi$
$971$	−2.91007	−	6.37216i	−0.0933886	−	0.204492i	−0.950562	+	0.310536i	$0.899491\pi$
$972$	−1.60269	+	11.1470i	−0.0514064	+	0.357539i
$973$	−7.46490	+	2.19189i	−0.239314	+	0.0702689i
$974$	20.0752	+	12.9016i	0.643251	+	0.413392i
$975$	2.82737	−	6.19108i	0.0905484	−	0.198273i
$976$	10.5113	+	3.08641i	0.336460	+	0.0987935i
$977$	6.51424	+	7.51784i	0.208409	+	0.240517i	0.850325	−	0.526258i	$-0.176406\pi$
$977$	6.51424	+	7.51784i	0.208409	+	0.240517i	−0.641916	+	0.766775i	$0.721860\pi$
$978$	−11.7052	−	13.5085i	−0.374290	−	0.431953i
$979$	55.9242	+	16.4208i	1.78734	+	0.524812i
$980$	0.475695	−	1.04163i	0.0151955	−	0.0332735i
$981$	15.3251	+	9.84883i	0.489292	+	0.314449i
$982$	−15.4461	+	4.53539i	−0.492905	+	0.144730i
$983$	−0.183810	+	1.27842i	−0.00586262	+	0.0407754i	−0.992543	−	0.121897i	$-0.961102\pi$
$983$	−0.183810	+	1.27842i	−0.00586262	+	0.0407754i	0.986680	+	0.162672i	$0.0520113\pi$
$984$	3.24706	+	7.11008i	0.103513	+	0.226661i
$985$	2.29450	+	15.9586i	0.0731088	+	0.508483i
$986$	50.2102	−	32.2681i	1.59902	−	1.02763i
$987$	3.67549	−	4.24174i	0.116992	−	0.135016i
$988$	−5.65623			−0.179949
$989$	16.3774	−	57.7557i	0.520770	−	1.83652i
$990$	6.70826			0.213202
$991$	−12.8752	+	14.8587i	−0.408993	+	0.472003i	−0.922452	−	0.386111i	$-0.873818\pi$
$991$	−12.8752	+	14.8587i	−0.408993	+	0.472003i	0.513459	+	0.858114i	$0.328364\pi$
$992$	−2.48641	+	1.59792i	−0.0789437	+	0.0507341i
$993$	6.64189	+	46.1953i	0.210774	+	1.46596i
$994$	1.63792	+	3.58655i	0.0519518	+	0.113759i
$995$	0.0464381	−	0.322984i	0.00147219	−	0.0102393i
$996$	9.57141	−	2.81042i	0.303282	−	0.0890516i
$997$	3.34282	+	2.14830i	0.105868	+	0.0680374i	0.592504	−	0.805568i	$-0.298140\pi$
$997$	3.34282	+	2.14830i	0.105868	+	0.0680374i	−0.486635	+	0.873605i	$0.661776\pi$
$998$	−10.8434	+	23.7437i	−0.343241	+	0.751594i
$999$	−31.0398	−	9.11412i	−0.982057	−	0.288358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.e.85.1	✓	40
23.6	even	11		7406.2.a.bt.1.4		20
23.13	even	11	inner	322.2.i.e.197.1	yes	40
23.17	odd	22		7406.2.a.bs.1.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.e.85.1	✓	40	1.1	even	1	trivial
322.2.i.e.197.1	yes	40	23.13	even	11	inner
7406.2.a.bs.1.4		20	23.17	odd	22
7406.2.a.bt.1.4		20	23.6	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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{2} +(-1.71143 + 1.09987i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.475695 + 1.04163i) q^{5} +(-0.289523 + 2.01368i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.473040 - 1.03581i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{2} +(-1.71143 + 1.09987i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.475695 + 1.04163i) q^{5} +(-0.289523 + 2.01368i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.473040 - 1.03581i) q^{9} +(1.09872 + 0.322614i) q^{10} +(3.36896 + 3.88799i) q^{11} +(1.33224 + 1.53748i) q^{12} +(-0.870228 - 0.255522i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(-1.95977 - 1.25947i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.937384 + 6.51965i) q^{17} +(-0.473040 - 1.03581i) q^{18} +(0.887536 + 6.17295i) q^{19} +(0.963326 - 0.619092i) q^{20} +(1.33224 - 1.53748i) q^{21} +5.14455 q^{22} +(-3.59512 + 3.17414i) q^{23} +2.03438 q^{24} +(2.41560 - 2.78775i) q^{25} +(-0.762989 + 0.490343i) q^{26} +(-0.538884 - 3.74802i) q^{27} +(0.415415 + 0.909632i) q^{28} +(1.28958 - 8.96921i) q^{29} +(-2.23522 + 0.656321i) q^{30} +(2.48641 + 1.59792i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-10.0420 - 2.94861i) q^{33} +(4.31337 + 4.97789i) q^{34} +(-0.749886 - 0.865415i) q^{35} +(-1.09259 - 0.320814i) q^{36} +(3.54907 - 7.77138i) q^{37} +(5.24641 + 3.37166i) q^{38} +(1.77038 - 0.519830i) q^{39} +(0.162966 - 1.13345i) q^{40} +(1.59609 + 3.49495i) q^{41} +(-0.289523 - 2.01368i) q^{42} +(-10.5306 + 6.76758i) q^{43} +(3.36896 - 3.88799i) q^{44} +1.30395 q^{45} +(0.0445515 + 4.79562i) q^{46} +2.75888 q^{47} +(1.33224 - 1.53748i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.524961 - 3.65118i) q^{50} +(-5.56650 - 12.1889i) q^{51} +(-0.129075 + 0.897735i) q^{52} +(7.77095 - 2.28176i) q^{53} +(-3.18546 - 2.04717i) q^{54} +(-2.44724 + 5.35870i) q^{55} +(0.959493 + 0.281733i) q^{56} +(-8.30840 - 9.58841i) q^{57} +(-5.93398 - 6.84818i) q^{58} +(-3.19778 - 0.938954i) q^{59} +(-0.967746 + 2.11907i) q^{60} +(-9.21601 - 5.92277i) q^{61} +(2.83588 - 0.832691i) q^{62} +(-0.162056 + 1.12713i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.147804 - 1.02800i) q^{65} +(-8.80455 + 5.65834i) q^{66} +(-0.772457 + 0.891463i) q^{67} +6.58669 q^{68} +(2.66166 - 9.38648i) q^{69} -1.14511 q^{70} +(2.58202 - 2.97982i) q^{71} +(-0.957950 + 0.615637i) q^{72} +(-0.646002 - 4.49304i) q^{73} +(-3.54907 - 7.77138i) q^{74} +(-1.06797 + 7.42791i) q^{75} +(5.98380 - 1.75700i) q^{76} +(-4.32787 - 2.78135i) q^{77} +(0.766490 - 1.67838i) q^{78} +(8.52438 + 2.50298i) q^{79} +(-0.749886 - 0.865415i) q^{80} +(7.28171 + 8.40354i) q^{81} +(3.68653 + 1.08246i) q^{82} +(2.03696 - 4.46033i) q^{83} +(-1.71143 - 1.09987i) q^{84} +(-7.23695 + 2.12496i) q^{85} +(-1.78145 + 12.3903i) q^{86} +(7.65795 + 16.7686i) q^{87} +(-0.732146 - 5.09219i) q^{88} +(9.53097 - 6.12518i) q^{89} +(0.853909 - 0.985463i) q^{90} +0.906966 q^{91} +(3.65347 + 3.10680i) q^{92} -6.01284 q^{93} +(1.80668 - 2.08502i) q^{94} +(-6.00771 + 3.86092i) q^{95} +(-0.289523 - 2.01368i) q^{96} +(5.84308 + 12.7945i) q^{97} +(0.142315 - 0.989821i) q^{98} +(5.62089 - 1.65044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8	\( 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} + 2 q^{12} + 4 q^{13} + 4 q^{14} - 11 q^{15} - 4 q^{16} - 21 q^{17} + 4 q^{19} + 2 q^{20} + 2 q^{21} - 11 q^{23} - 2 q^{24} + 5 q^{25} - 15 q^{26} + 95 q^{27} - 4 q^{28} + 22 q^{30} - 12 q^{31} + 4 q^{32} - 8 q^{33} + 10 q^{34} - 9 q^{35} + 41 q^{37} + 7 q^{38} - 38 q^{39} - 13 q^{40} + 25 q^{41} - 2 q^{42} - 59 q^{43} - 6 q^{45} + 11 q^{46} - 60 q^{47} + 2 q^{48} - 4 q^{49} + 61 q^{50} - 87 q^{51} + 4 q^{52} + 47 q^{53} - 29 q^{54} - 30 q^{55} + 4 q^{56} + 20 q^{57} - 96 q^{59} - 11 q^{60} + 84 q^{61} - 65 q^{62} - 4 q^{64} + 52 q^{65} - 3 q^{66} + 11 q^{67} - 10 q^{68} - 42 q^{69} - 2 q^{70} - 13 q^{71} + 11 q^{72} - 48 q^{73} - 41 q^{74} + 23 q^{75} + 26 q^{76} - 83 q^{78} + 80 q^{79} - 9 q^{80} + 2 q^{81} + 30 q^{82} - 20 q^{83} + 2 q^{84} - 71 q^{85} - 40 q^{86} + 99 q^{87} - 30 q^{89} + 116 q^{90} + 26 q^{91} - 22 q^{92} + 20 q^{93} - 17 q^{94} - 4 q^{95} - 2 q^{96} - 56 q^{97} + 4 q^{98} + 138 q^{99}+O(q^{100}) \) 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^10 + 2 * q^12 + 4 * q^13 + 4 * q^14 - 11 * q^15 - 4 * q^16 - 21 * q^17 + 4 * q^19 + 2 * q^20 + 2 * q^21 - 11 * q^23 - 2 * q^24 + 5 * q^25 - 15 * q^26 + 95 * q^27 - 4 * q^28 + 22 * q^30 - 12 * q^31 + 4 * q^32 - 8 * q^33 + 10 * q^34 - 9 * q^35 + 41 * q^37 + 7 * q^38 - 38 * q^39 - 13 * q^40 + 25 * q^41 - 2 * q^42 - 59 * q^43 - 6 * q^45 + 11 * q^46 - 60 * q^47 + 2 * q^48 - 4 * q^49 + 61 * q^50 - 87 * q^51 + 4 * q^52 + 47 * q^53 - 29 * q^54 - 30 * q^55 + 4 * q^56 + 20 * q^57 - 96 * q^59 - 11 * q^60 + 84 * q^61 - 65 * q^62 - 4 * q^64 + 52 * q^65 - 3 * q^66 + 11 * q^67 - 10 * q^68 - 42 * q^69 - 2 * q^70 - 13 * q^71 + 11 * q^72 - 48 * q^73 - 41 * q^74 + 23 * q^75 + 26 * q^76 - 83 * q^78 + 80 * q^79 - 9 * q^80 + 2 * q^81 + 30 * q^82 - 20 * q^83 + 2 * q^84 - 71 * q^85 - 40 * q^86 + 99 * q^87 - 30 * q^89 + 116 * q^90 + 26 * q^91 - 22 * q^92 + 20 * q^93 - 17 * q^94 - 4 * q^95 - 2 * q^96 - 56 * q^97 + 4 * q^98 + 138 * q^99

Introduction

L-functions

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