LMFDB - Embedded newform 418.2.j.a.177.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(23,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("418.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.j (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			177.4
Character	$\chi$	$=$	418.177
Dual form			418.2.j.a.111.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(2.23098 + 0.812012i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.126679 - 0.718430i) q^{5} +(-2.23098 + 0.812012i) q^{6} +(1.60753 - 2.78432i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.01980 + 1.69481i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(2.23098 + 0.812012i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.126679 - 0.718430i) q^{5} +(-2.23098 + 0.812012i) q^{6} +(1.60753 - 2.78432i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.01980 + 1.69481i) q^{9} +(0.558839 + 0.468922i) q^{10} +(0.500000 + 0.866025i) q^{11} +(1.18708 - 2.05609i) q^{12} +(0.351408 - 0.127902i) q^{13} +(0.558288 + 3.16621i) q^{14} +(0.300756 - 1.70567i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.28318 - 1.07671i) q^{17} -2.63666 q^{18} +(3.36181 - 2.77457i) q^{19} -0.729513 q^{20} +(5.84727 - 4.90644i) q^{21} +(-0.939693 - 0.342020i) q^{22} +(-1.22345 + 6.93853i) q^{23} +(0.412269 + 2.33810i) q^{24} +(4.19837 - 1.52808i) q^{25} +(-0.186980 + 0.323860i) q^{26} +(-0.431319 - 0.747067i) q^{27} +(-2.46287 - 2.06660i) q^{28} +(-1.27510 - 1.06993i) q^{29} +(0.865992 + 1.49994i) q^{30} +(-3.91341 + 6.77823i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.412269 + 2.33810i) q^{33} +(-0.290872 + 1.64962i) q^{34} +(-2.20398 - 0.802182i) q^{35} +(2.01980 - 1.69481i) q^{36} -5.41057 q^{37} +(-0.791831 + 4.28637i) q^{38} +0.887845 q^{39} +(0.558839 - 0.468922i) q^{40} +(-6.54570 - 2.38244i) q^{41} +(-1.32547 + 7.51710i) q^{42} +(-0.186967 - 1.06034i) q^{43} +(0.939693 - 0.342020i) q^{44} +(0.961737 - 1.66578i) q^{45} +(-3.52278 - 6.10164i) q^{46} +(5.29285 + 4.44123i) q^{47} +(-1.81872 - 1.52608i) q^{48} +(-1.66828 - 2.88955i) q^{49} +(-2.23391 + 3.86924i) q^{50} +(3.73705 - 1.36017i) q^{51} +(-0.0649376 - 0.368280i) q^{52} +(-1.97094 + 11.1778i) q^{53} +(0.810615 + 0.295040i) q^{54} +(0.558839 - 0.468922i) q^{55} +3.21505 q^{56} +(9.75312 - 3.46021i) q^{57} +1.66452 q^{58} +(3.30138 - 2.77019i) q^{59} +(-1.62753 - 0.592373i) q^{60} +(-0.664334 + 3.76763i) q^{61} +(-1.35911 - 7.70792i) q^{62} +(7.96576 - 2.89930i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.136405 - 0.236260i) q^{65} +(-1.81872 - 1.52608i) q^{66} +(-2.82523 - 2.37065i) q^{67} +(-0.837534 - 1.45065i) q^{68} +(-8.36367 + 14.4863i) q^{69} +(2.20398 - 0.802182i) q^{70} +(0.989315 + 5.61069i) q^{71} +(-0.457851 + 2.59660i) q^{72} +(0.528836 + 0.192481i) q^{73} +(4.14474 - 3.47785i) q^{74} +10.6073 q^{75} +(-2.14865 - 3.79253i) q^{76} +3.21505 q^{77} +(-0.680129 + 0.570696i) q^{78} +(-13.9085 - 5.06227i) q^{79} +(-0.126679 + 0.718430i) q^{80} +(-1.72919 - 9.80673i) q^{81} +(6.54570 - 2.38244i) q^{82} +(3.78718 - 6.55959i) q^{83} +(-3.81653 - 6.61043i) q^{84} +(-0.936094 - 0.785476i) q^{85} +(0.824799 + 0.692088i) q^{86} +(-1.97592 - 3.42240i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-8.37006 + 3.04645i) q^{89} +(0.334008 + 1.89425i) q^{90} +(0.208778 - 1.18404i) q^{91} +(6.62067 + 2.40973i) q^{92} +(-14.2348 + 11.9444i) q^{93} -6.90933 q^{94} +(-2.41921 - 2.06374i) q^{95} +2.37416 q^{96} +(9.64968 - 8.09704i) q^{97} +(3.13534 + 1.14117i) q^{98} +(-0.457851 + 2.59660i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{8}+O(q^{10}) $ 24 * q + 12 * q^8	$ 24 q + 12 q^{8} + 12 q^{11} - 3 q^{12} - 3 q^{13} + 3 q^{14} + 27 q^{15} - 6 q^{18} - 21 q^{19} - 18 q^{20} + 15 q^{21} + 9 q^{23} + 36 q^{25} - 21 q^{27} - 3 q^{28} - 9 q^{30} - 27 q^{31} - 9 q^{34} - 45 q^{35} + 18 q^{37} + 9 q^{38} + 36 q^{39} - 18 q^{41} + 39 q^{42} - 48 q^{43} + 36 q^{45} - 18 q^{46} - 9 q^{47} + 6 q^{49} + 3 q^{50} - 18 q^{51} - 3 q^{52} - 36 q^{53} - 45 q^{54} + 18 q^{58} + 9 q^{59} - 9 q^{60} + 15 q^{61} - 33 q^{62} + 87 q^{63} - 12 q^{64} - 36 q^{65} + 33 q^{67} + 9 q^{68} - 18 q^{69} + 45 q^{70} - 9 q^{71} - 3 q^{73} + 3 q^{74} + 42 q^{75} + 9 q^{76} + 12 q^{78} + 15 q^{79} - 108 q^{81} + 18 q^{82} + 36 q^{83} - 9 q^{84} - 99 q^{85} - 33 q^{86} + 63 q^{87} - 12 q^{88} - 27 q^{89} - 36 q^{90} - 21 q^{91} - 9 q^{92} - 21 q^{93} + 54 q^{94} + 18 q^{95} - 6 q^{96} + 45 q^{97} + 39 q^{98}+O(q^{100}) $ 24 * q + 12 * q^8 + 12 * q^11 - 3 * q^12 - 3 * q^13 + 3 * q^14 + 27 * q^15 - 6 * q^18 - 21 * q^19 - 18 * q^20 + 15 * q^21 + 9 * q^23 + 36 * q^25 - 21 * q^27 - 3 * q^28 - 9 * q^30 - 27 * q^31 - 9 * q^34 - 45 * q^35 + 18 * q^37 + 9 * q^38 + 36 * q^39 - 18 * q^41 + 39 * q^42 - 48 * q^43 + 36 * q^45 - 18 * q^46 - 9 * q^47 + 6 * q^49 + 3 * q^50 - 18 * q^51 - 3 * q^52 - 36 * q^53 - 45 * q^54 + 18 * q^58 + 9 * q^59 - 9 * q^60 + 15 * q^61 - 33 * q^62 + 87 * q^63 - 12 * q^64 - 36 * q^65 + 33 * q^67 + 9 * q^68 - 18 * q^69 + 45 * q^70 - 9 * q^71 - 3 * q^73 + 3 * q^74 + 42 * q^75 + 9 * q^76 + 12 * q^78 + 15 * q^79 - 108 * q^81 + 18 * q^82 + 36 * q^83 - 9 * q^84 - 99 * q^85 - 33 * q^86 + 63 * q^87 - 12 * q^88 - 27 * q^89 - 36 * q^90 - 21 * q^91 - 9 * q^92 - 21 * q^93 + 54 * q^94 + 18 * q^95 - 6 * q^96 + 45 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	2.23098	+	0.812012i	1.28806	+	0.468815i	0.893090	−	0.449879i	$-0.148533\pi$
$3$	2.23098	+	0.812012i	1.28806	+	0.468815i	0.394970	+	0.918694i	$0.370755\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.126679	−	0.718430i	−0.0566524	−	0.321292i	0.943291	−	0.331968i	$-0.107713\pi$
$5$	−0.126679	−	0.718430i	−0.0566524	−	0.321292i	−0.999943	+	0.0106764i	$0.996602\pi$
$6$	−2.23098	+	0.812012i	−0.910796	+	0.331503i
$7$	1.60753	−	2.78432i	0.607588	−	1.05237i	−0.384049	−	0.923313i	$-0.625471\pi$
$7$	1.60753	−	2.78432i	0.607588	−	1.05237i	0.991637	−	0.129060i	$-0.0411961\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.01980	+	1.69481i	0.673265	+	0.564937i
$10$	0.558839	+	0.468922i	0.176721	+	0.148286i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	1.18708	−	2.05609i	0.342681	−	0.593541i
$13$	0.351408	−	0.127902i	0.0974631	−	0.0354737i	−0.292828	−	0.956165i	$-0.594596\pi$
$13$	0.351408	−	0.127902i	0.0974631	−	0.0354737i	0.390291	+	0.920691i	$0.372374\pi$
$14$	0.558288	+	3.16621i	0.149209	+	0.846205i
$15$	0.300756	−	1.70567i	0.0776548	−	0.440402i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	1.28318	−	1.07671i	0.311216	−	0.261141i	−0.473778	−	0.880644i	$-0.657110\pi$
$17$	1.28318	−	1.07671i	0.311216	−	0.261141i	0.784994	+	0.619503i	$0.212666\pi$
$18$	−2.63666			−0.621466
$19$	3.36181	−	2.77457i	0.771251	−	0.636531i
$19$	3.36181	−	2.77457i	0.771251	−	0.636531i
$20$	−0.729513			−0.163124
$21$	5.84727	−	4.90644i	1.27598	−	1.07067i
$22$	−0.939693	−	0.342020i	−0.200343	−	0.0729189i
$23$	−1.22345	+	6.93853i	−0.255107	+	1.44678i	0.540691	+	0.841221i	$0.318163\pi$
$23$	−1.22345	+	6.93853i	−0.255107	+	1.44678i	−0.795798	+	0.605562i	$0.792948\pi$
$24$	0.412269	+	2.33810i	0.0841541	+	0.477262i
$25$	4.19837	−	1.52808i	0.839674	−	0.305616i
$26$	−0.186980	+	0.323860i	−0.0366699	+	0.0635141i
$27$	−0.431319	−	0.747067i	−0.0830074	−	0.143773i
$28$	−2.46287	−	2.06660i	−0.465439	−	0.390550i
$29$	−1.27510	−	1.06993i	−0.236780	−	0.198682i	0.516675	−	0.856182i	$-0.327170\pi$
$29$	−1.27510	−	1.06993i	−0.236780	−	0.198682i	−0.753455	+	0.657500i	$0.771614\pi$
$30$	0.865992	+	1.49994i	0.158108	+	0.273851i
$31$	−3.91341	+	6.77823i	−0.702869	+	1.21741i	0.264586	+	0.964362i	$0.414765\pi$
$31$	−3.91341	+	6.77823i	−0.702869	+	1.21741i	−0.967455	+	0.253043i	$0.918568\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	0.412269	+	2.33810i	0.0717669	+	0.407010i
$34$	−0.290872	+	1.64962i	−0.0498842	+	0.282907i
$35$	−2.20398	−	0.802182i	−0.372540	−	0.135593i
$36$	2.01980	−	1.69481i	0.336633	−	0.282468i
$37$	−5.41057			−0.889492			−0.444746	−	0.895657i	$-0.646706\pi$
$37$	−5.41057			−0.889492			−0.444746	+	0.895657i	$0.646706\pi$
$38$	−0.791831	+	4.28637i	−0.128452	+	0.695342i
$39$	0.887845			0.142169
$40$	0.558839	−	0.468922i	0.0883603	−	0.0741431i
$41$	−6.54570	−	2.38244i	−1.02227	−	0.372074i	−0.224135	−	0.974558i	$-0.571956\pi$
$41$	−6.54570	−	2.38244i	−1.02227	−	0.372074i	−0.798131	+	0.602484i	$0.794178\pi$
$42$	−1.32547	+	7.51710i	−0.204524	+	1.15991i
$43$	−0.186967	−	1.06034i	−0.0285122	−	0.161700i	0.967227	−	0.253912i	$-0.0817174\pi$
$43$	−0.186967	−	1.06034i	−0.0285122	−	0.161700i	−0.995739	+	0.0922117i	$0.970606\pi$
$44$	0.939693	−	0.342020i	0.141664	−	0.0515615i
$45$	0.961737	−	1.66578i	0.143367	−	0.248320i
$46$	−3.52278	−	6.10164i	−0.519406	−	0.899638i
$47$	5.29285	+	4.44123i	0.772042	+	0.647820i	0.941231	−	0.337764i	$-0.109670\pi$
$47$	5.29285	+	4.44123i	0.772042	+	0.647820i	−0.169189	+	0.985584i	$0.554115\pi$
$48$	−1.81872	−	1.52608i	−0.262509	−	0.220271i
$49$	−1.66828	−	2.88955i	−0.238326	−	0.412793i
$50$	−2.23391	+	3.86924i	−0.315922	+	0.547193i
$51$	3.73705	−	1.36017i	0.523292	−	0.190463i
$52$	−0.0649376	−	0.368280i	−0.00900523	−	0.0510712i
$53$	−1.97094	+	11.1778i	−0.270729	+	1.53538i	0.481479	+	0.876457i	$0.340100\pi$
$53$	−1.97094	+	11.1778i	−0.270729	+	1.53538i	−0.752209	+	0.658925i	$0.771011\pi$
$54$	0.810615	+	0.295040i	0.110311	+	0.0401498i
$55$	0.558839	−	0.468922i	0.0753539	−	0.0632294i
$56$	3.21505			0.429629
$57$	9.75312	−	3.46021i	1.29183	−	0.458315i
$58$	1.66452			0.218562
$59$	3.30138	−	2.77019i	0.429803	−	0.360648i	−0.402074	−	0.915607i	$-0.631711\pi$
$59$	3.30138	−	2.77019i	0.429803	−	0.360648i	0.831877	+	0.554959i	$0.187266\pi$
$60$	−1.62753	−	0.592373i	−0.210114	−	0.0764751i
$61$	−0.664334	+	3.76763i	−0.0850593	+	0.482395i	0.912284	+	0.409557i	$0.134317\pi$
$61$	−0.664334	+	3.76763i	−0.0850593	+	0.482395i	−0.997344	+	0.0728381i	$0.976794\pi$
$62$	−1.35911	−	7.70792i	−0.172608	−	0.978906i
$63$	7.96576	−	2.89930i	1.00359	−	0.365278i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.136405	−	0.236260i	−0.0169189	−	0.0293044i
$66$	−1.81872	−	1.52608i	−0.223868	−	0.187848i
$67$	−2.82523	−	2.37065i	−0.345157	−	0.289621i	0.453685	−	0.891162i	$-0.350109\pi$
$67$	−2.82523	−	2.37065i	−0.345157	−	0.289621i	−0.798842	+	0.601541i	$0.794554\pi$
$68$	−0.837534	−	1.45065i	−0.101566	−	0.175917i
$69$	−8.36367	+	14.4863i	−1.00687	+	1.74394i
$70$	2.20398	−	0.802182i	0.263426	−	0.0958791i
$71$	0.989315	+	5.61069i	0.117410	+	0.665866i	0.985529	+	0.169509i	$0.0542182\pi$
$71$	0.989315	+	5.61069i	0.117410	+	0.665866i	−0.868119	+	0.496357i	$0.834671\pi$
$72$	−0.457851	+	2.59660i	−0.0539582	+	0.306012i
$73$	0.528836	+	0.192481i	0.0618956	+	0.0225281i	0.372782	−	0.927919i	$-0.378404\pi$
$73$	0.528836	+	0.192481i	0.0618956	+	0.0225281i	−0.310887	+	0.950447i	$0.600626\pi$
$74$	4.14474	−	3.47785i	0.481816	−	0.404291i
$75$	10.6073			1.22483
$76$	−2.14865	−	3.79253i	−0.246467	−	0.435033i
$77$	3.21505			0.366389
$78$	−0.680129	+	0.570696i	−0.0770094	+	0.0646186i
$79$	−13.9085	−	5.06227i	−1.56483	−	0.569550i	−0.592990	−	0.805209i	$-0.702053\pi$
$79$	−13.9085	−	5.06227i	−1.56483	−	0.569550i	−0.971836	+	0.235659i	$0.924275\pi$
$80$	−0.126679	+	0.718430i	−0.0141631	+	0.0803229i
$81$	−1.72919	−	9.80673i	−0.192132	−	1.08964i
$82$	6.54570	−	2.38244i	0.722851	−	0.263096i
$83$	3.78718	−	6.55959i	0.415697	−	0.720009i	−0.579804	−	0.814756i	$-0.696871\pi$
$83$	3.78718	−	6.55959i	0.415697	−	0.720009i	0.995501	+	0.0947470i	$0.0302042\pi$
$84$	−3.81653	−	6.61043i	−0.416418	−	0.721257i
$85$	−0.936094	−	0.785476i	−0.101534	−	0.0851968i
$86$	0.824799	+	0.692088i	0.0889404	+	0.0746298i
$87$	−1.97592	−	3.42240i	−0.211841	−	0.366920i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−8.37006	+	3.04645i	−0.887224	+	0.322923i	−0.745122	−	0.666929i	$-0.767609\pi$
$89$	−8.37006	+	3.04645i	−0.887224	+	0.322923i	−0.142103	+	0.989852i	$0.545386\pi$
$90$	0.334008	+	1.89425i	0.0352075	+	0.199672i
$91$	0.208778	−	1.18404i	0.0218859	−	0.124121i
$92$	6.62067	+	2.40973i	0.690252	+	0.251231i
$93$	−14.2348	+	11.9444i	−1.47608	+	1.23857i
$94$	−6.90933			−0.712643
$95$	−2.41921	−	2.06374i	−0.248205	−	0.211736i
$96$	2.37416			0.242312
$97$	9.64968	−	8.09704i	0.979776	−	0.822130i	−0.00427945	−	0.999991i	$-0.501362\pi$
$97$	9.64968	−	8.09704i	0.979776	−	0.822130i	0.984056	+	0.177861i	$0.0569178\pi$
$98$	3.13534	+	1.14117i	0.316718	+	0.115276i
$99$	−0.457851	+	2.59660i	−0.0460157	+	0.260968i
$100$	−0.775827	−	4.39993i	−0.0775827	−	0.439993i
$101$	−2.43370	+	0.885796i	−0.242163	+	0.0881400i	−0.460250	−	0.887789i	$-0.652240\pi$
$101$	−2.43370	+	0.885796i	−0.242163	+	0.0881400i	0.218088	+	0.975929i	$0.430018\pi$
$102$	−1.98844	+	3.44408i	−0.196885	+	0.341015i
$103$	−7.96372	−	13.7936i	−0.784689	−	1.35912i	−0.929185	−	0.369615i	$-0.879490\pi$
$103$	−7.96372	−	13.7936i	−0.784689	−	1.35912i	0.144496	−	0.989505i	$-0.453844\pi$
$104$	0.286471	+	0.240377i	0.0280908	+	0.0235710i
$105$	−4.26566	−	3.57931i	−0.416285	−	0.349305i
$106$	−5.67509	−	9.82955i	−0.551214	−	0.954730i
$107$	−7.27568	+	12.6018i	−0.703366	+	1.21827i	0.263912	+	0.964547i	$0.414987\pi$
$107$	−7.27568	+	12.6018i	−0.703366	+	1.21827i	−0.967278	+	0.253719i	$0.918346\pi$
$108$	−0.810615	+	0.295040i	−0.0780015	+	0.0283902i
$109$	−0.436766	−	2.47702i	−0.0418346	−	0.237256i	0.956720	−	0.291012i	$-0.0939918\pi$
$109$	−0.436766	−	2.47702i	−0.0418346	−	0.237256i	−0.998554	+	0.0537559i	$0.982881\pi$
$110$	−0.126679	+	0.718430i	−0.0120783	+	0.0684996i
$111$	−12.0709	−	4.39345i	−1.14572	−	0.417007i
$112$	−2.46287	+	2.06660i	−0.232720	+	0.195275i
$113$	−13.7654			−1.29494			−0.647472	−	0.762089i	$-0.724174\pi$
$113$	−13.7654			−1.29494			−0.647472	+	0.762089i	$0.724174\pi$
$114$	−5.24715	+	8.91986i	−0.491441	+	0.835421i
$115$	5.13983			0.479292
$116$	−1.27510	+	1.06993i	−0.118390	+	0.0993408i
$117$	0.926543	+	0.337234i	0.0856589	+	0.0311773i
$118$	−0.748362	+	4.24417i	−0.0688923	+	0.390708i
$119$	−0.935170	−	5.30361i	−0.0857269	−	0.486181i
$120$	1.62753	−	0.592373i	0.148573	−	0.0540760i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−1.91287	−	3.31320i	−0.173184	−	0.299963i
$123$	−12.6688	−	10.6304i	−1.14231	−	0.958508i
$124$	5.99569	+	5.03098i	0.538429	+	0.451796i
$125$	−3.45345	−	5.98154i	−0.308886	−	0.535006i
$126$	−4.23849	+	7.34129i	−0.377595	+	0.654014i
$127$	5.51333	−	2.00669i	0.489229	−	0.178065i	−0.0856142	−	0.996328i	$-0.527285\pi$
$127$	5.51333	−	2.00669i	0.489229	−	0.178065i	0.574843	+	0.818264i	$0.305063\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	0.443890	−	2.51742i	0.0390823	−	0.221647i
$130$	0.256357	+	0.0933063i	0.0224840	+	0.00818351i
$131$	4.49757	−	3.77391i	0.392954	−	0.329728i	−0.424809	−	0.905283i	$-0.639659\pi$
$131$	4.49757	−	3.77391i	0.392954	−	0.329728i	0.817763	+	0.575556i	$0.195214\pi$
$132$	2.37416			0.206644
$133$	−2.32110	−	13.8205i	−0.201265	−	1.19839i
$134$	3.68808			0.318601
$135$	−0.482076	+	0.404510i	−0.0414905	+	0.0348147i
$136$	1.57405	+	0.572907i	0.134974	+	0.0491263i
$137$	0.563095	−	3.19347i	0.0481084	−	0.272836i	−0.951259	−	0.308392i	$-0.900209\pi$
$137$	0.563095	−	3.19347i	0.0481084	−	0.272836i	0.999368	+	0.0355559i	$0.0113202\pi$
$138$	−2.90467	−	16.4732i	−0.247262	−	1.40229i
$139$	−1.91849	+	0.698274i	−0.162724	+	0.0592268i	−0.422098	−	0.906550i	$-0.638706\pi$
$139$	−1.91849	+	0.698274i	−0.162724	+	0.0592268i	0.259374	+	0.965777i	$0.416484\pi$
$140$	−1.17271	+	2.03120i	−0.0991122	+	0.171667i
$141$	8.20194	+	14.2062i	0.690728	+	1.19638i
$142$	−4.36434	−	3.66212i	−0.366247	−	0.307318i
$143$	0.286471	+	0.240377i	0.0239559	+	0.0201014i
$144$	−1.31833	−	2.28341i	−0.109861	−	0.190284i
$145$	−0.607145	+	1.05161i	−0.0504206	+	0.0873311i
$146$	−0.528836	+	0.192481i	−0.0437668	+	0.0159298i
$147$	−1.37556	−	7.80120i	−0.113455	−	0.643433i
$148$	−0.939535	+	5.32837i	−0.0772293	+	0.437989i
$149$	12.8940	+	4.69305i	1.05632	+	0.384470i	0.811045	−	0.584984i	$-0.198899\pi$
$149$	12.8940	+	4.69305i	1.05632	+	0.384470i	0.245276	+	0.969453i	$0.421121\pi$
$150$	−8.12568	+	6.81825i	−0.663459	+	0.556708i
$151$	−9.52205			−0.774894			−0.387447	−	0.921892i	$-0.626643\pi$
$151$	−9.52205			−0.774894			−0.387447	+	0.921892i	$0.626643\pi$
$152$	4.08375	+	1.52412i	0.331236	+	0.123623i
$153$	4.41658			0.357059
$154$	−2.46287	+	2.06660i	−0.198464	+	0.166531i
$155$	5.36543	+	1.95286i	0.430962	+	0.156857i
$156$	0.154173	−	0.874356i	0.0123437	−	0.0700045i
$157$	3.31134	+	18.7795i	0.264274	+	1.49877i	0.771095	+	0.636720i	$0.219709\pi$
$157$	3.31134	+	18.7795i	0.264274	+	1.49877i	−0.506821	+	0.862051i	$0.669180\pi$
$158$	13.9085	−	5.06227i	1.10650	−	0.402733i
$159$	−13.4736	+	23.3370i	−1.06853	+	1.85074i
$160$	−0.364757	−	0.631777i	−0.0288365	−	0.0499463i
$161$	17.3523	+	14.5603i	1.36756	+	1.14752i
$162$	7.62828	+	6.40089i	0.599334	+	0.502901i
$163$	−2.22494	−	3.85370i	−0.174271	−	0.301845i	0.765638	−	0.643272i	$-0.222423\pi$
$163$	−2.22494	−	3.85370i	−0.174271	−	0.301845i	−0.939909	+	0.341426i	$0.889090\pi$
$164$	−3.48289	+	6.03255i	−0.271968	+	0.471063i
$165$	1.62753	−	0.592373i	0.126703	−	0.0461162i
$166$	1.31527	+	7.45930i	0.102085	+	0.578954i
$167$	2.51606	−	14.2693i	0.194699	−	1.10419i	−0.718148	−	0.695890i	$-0.755010\pi$
$167$	2.51606	−	14.2693i	0.194699	−	1.10419i	0.912847	−	0.408302i	$-0.133879\pi$
$168$	7.17273	+	2.61066i	0.553388	+	0.201417i
$169$	−9.85145	+	8.26635i	−0.757804	+	0.635873i
$170$	1.22198			0.0937218
$171$	11.4925	+	0.0935487i	0.878856	+	0.00715385i
$172$	−1.07670			−0.0820975
$173$	−13.6082	+	11.4186i	−1.03461	+	0.868141i	−0.991392	−	0.130925i	$-0.958205\pi$
$173$	−13.6082	+	11.4186i	−1.03461	+	0.868141i	−0.0432175	+	0.999066i	$0.513761\pi$
$174$	3.71352	+	1.35161i	0.281521	+	0.102465i
$175$	2.49433	−	14.1460i	0.188553	−	1.06934i
$176$	−0.173648	−	0.984808i	−0.0130892	−	0.0742327i
$177$	9.61475	−	3.49948i	0.722689	−	0.263037i
$178$	4.45361	−	7.71389i	0.333813	−	0.578180i
$179$	−3.87332	−	6.70879i	−0.289506	−	0.501439i	0.684186	−	0.729307i	$-0.260158\pi$
$179$	−3.87332	−	6.70879i	−0.289506	−	0.501439i	−0.973692	+	0.227869i	$0.926824\pi$
$180$	−1.47347	−	1.23639i	−0.109826	−	0.0921548i
$181$	19.0899	+	16.0183i	1.41894	+	1.19063i	0.951904	+	0.306398i	$0.0991238\pi$
$181$	19.0899	+	16.0183i	1.41894	+	1.19063i	0.467039	+	0.884237i	$0.345321\pi$
$182$	0.601152	+	1.04123i	0.0445604	+	0.0771808i
$183$	−4.54148	+	7.86607i	−0.335716	+	0.581477i
$184$	−6.62067	+	2.40973i	−0.488082	+	0.177647i
$185$	0.685403	+	3.88712i	0.0503919	+	0.285786i
$186$	3.22676	−	18.2999i	0.236597	−	1.34181i
$187$	1.57405	+	0.572907i	0.115106	+	0.0418951i
$188$	5.29285	−	4.44123i	0.386021	−	0.323910i
$189$	−2.77343			−0.201737
$190$	3.17977	+	0.0258832i	0.230685	+	0.00187776i
$191$	19.4031			1.40396			0.701979	−	0.712198i	$-0.252300\pi$
$191$	19.4031			1.40396			0.701979	+	0.712198i	$0.252300\pi$
$192$	−1.81872	+	1.52608i	−0.131254	+	0.110136i
$193$	10.3317	+	3.76044i	0.743693	+	0.270682i	0.685949	−	0.727649i	$-0.259387\pi$
$193$	10.3317	+	3.76044i	0.743693	+	0.270682i	0.0577439	+	0.998331i	$0.481609\pi$
$194$	−2.18740	+	12.4054i	−0.157046	+	0.890655i
$195$	−0.112471	−	0.637854i	−0.00805421	−	0.0456777i
$196$	−3.13534	+	1.14117i	−0.223953	+	0.0815123i
$197$	3.24428	−	5.61926i	0.231146	−	0.400356i	−0.727000	−	0.686638i	$-0.759086\pi$
$197$	3.24428	−	5.61926i	0.231146	−	0.400356i	0.958146	+	0.286282i	$0.0924193\pi$
$198$	−1.31833	−	2.28341i	−0.0936895	−	0.162275i
$199$	0.251021	+	0.210632i	0.0177944	+	0.0149313i	0.651641	−	0.758527i	$-0.274081\pi$
$199$	0.251021	+	0.210632i	0.0177944	+	0.0149313i	−0.633847	+	0.773458i	$0.718525\pi$
$200$	3.42254	+	2.87185i	0.242010	+	0.203071i
$201$	−4.37805	−	7.58301i	−0.308804	−	0.534864i
$202$	1.29495	−	2.24291i	0.0911121	−	0.157811i
$203$	−5.02879	+	1.83033i	−0.352952	+	0.128464i
$204$	−0.690579	−	3.91647i	−0.0483502	−	0.274208i
$205$	−0.882416	+	5.00443i	−0.0616306	+	0.349524i
$206$	14.9669	+	5.44750i	1.04279	+	0.379546i
$207$	−14.2306	+	11.9409i	−0.989095	+	0.829950i
$208$	−0.373961			−0.0259295
$209$	4.08375	+	1.52412i	0.282479	+	0.105426i
$210$	5.56842			0.384257
$211$	15.3654	−	12.8931i	1.05780	−	0.887599i	0.0639075	−	0.997956i	$-0.479644\pi$
$211$	15.3654	−	12.8931i	1.05780	−	0.887599i	0.993892	+	0.110357i	$0.0351993\pi$
$212$	10.6657	+	3.88199i	0.732522	+	0.266616i
$213$	−2.34880	+	13.3207i	−0.160937	+	0.912719i
$214$	−2.52682	−	14.3303i	−0.172730	−	0.979598i
$215$	−0.738096	+	0.268645i	−0.0503377	+	0.0183214i
$216$	0.431319	−	0.747067i	0.0293476	−	0.0508315i
$217$	12.5818	+	21.7924i	0.854110	+	1.47936i
$218$	1.92678	+	1.61676i	0.130498	+	0.109501i
$219$	1.02353	+	0.858842i	0.0691636	+	0.0580352i
$220$	−0.364757	−	0.631777i	−0.0245919	−	0.0425944i
$221$	0.313205	−	0.542487i	0.0210684	−	0.0364916i
$222$	12.0709	−	4.39345i	0.810145	−	0.294869i
$223$	−4.27553	−	24.2477i	−0.286311	−	1.62375i	−0.700565	−	0.713588i	$-0.747069\pi$
$223$	−4.27553	−	24.2477i	−0.286311	−	1.62375i	0.414255	−	0.910161i	$-0.364042\pi$
$224$	0.558288	−	3.16621i	0.0373022	−	0.211551i
$225$	11.0697	+	4.02902i	0.737977	+	0.268602i
$226$	10.5449	−	8.84826i	0.701439	−	0.588577i
$227$	6.02151			0.399662			0.199831	−	0.979830i	$-0.435961\pi$
$227$	6.02151			0.399662			0.199831	+	0.979830i	$0.435961\pi$
$228$	−1.71402	−	10.2058i	−0.113514	−	0.675896i
$229$	3.84343			0.253981			0.126991	−	0.991904i	$-0.459468\pi$
$229$	3.84343			0.253981			0.126991	+	0.991904i	$0.459468\pi$
$230$	−3.93734	+	3.30382i	−0.259621	+	0.217848i
$231$	7.17273	+	2.61066i	0.471931	+	0.171769i
$232$	0.289041	−	1.63923i	0.0189765	−	0.107621i
$233$	2.31607	+	13.1351i	0.151731	+	0.860508i	0.961714	+	0.274055i	$0.0883651\pi$
$233$	2.31607	+	13.1351i	0.151731	+	0.860508i	−0.809983	+	0.586453i	$0.800524\pi$
$234$	−0.926543	+	0.337234i	−0.0605700	+	0.0220457i
$235$	2.52022	−	4.36515i	0.164401	−	0.284751i
$236$	−2.15482	−	3.73226i	−0.140267	−	0.242950i
$237$	−26.9190	−	22.5877i	−1.74858	−	1.46723i
$238$	4.12548	+	3.46169i	0.267415	+	0.224388i
$239$	3.76797	+	6.52632i	0.243730	+	0.422152i	0.961774	−	0.273845i	$-0.0882957\pi$
$239$	3.76797	+	6.52632i	0.243730	+	0.422152i	−0.718044	+	0.695998i	$0.754962\pi$
$240$	−0.865992	+	1.49994i	−0.0558995	+	0.0968208i
$241$	4.26485	−	1.55228i	0.274723	−	0.0999911i	−0.200985	−	0.979594i	$-0.564414\pi$
$241$	4.26485	−	1.55228i	0.274723	−	0.0999911i	0.475708	+	0.879603i	$0.342192\pi$
$242$	−0.173648	−	0.984808i	−0.0111625	−	0.0633058i
$243$	3.65600	−	20.7342i	0.234532	−	1.33010i
$244$	3.59503	+	1.30848i	0.230148	+	0.0837671i
$245$	−1.86460	+	1.56459i	−0.119125	+	0.0999579i
$246$	16.5379			1.05442
$247$	0.826493	−	1.40499i	0.0525885	−	0.0893974i
$248$	−7.82682			−0.497004
$249$	13.7756	−	11.5591i	0.872994	−	0.732529i
$250$	6.49036	+	2.36230i	0.410486	+	0.149405i
$251$	−3.87628	+	21.9835i	−0.244669	+	1.38758i	0.576592	+	0.817032i	$0.304382\pi$
$251$	−3.87628	+	21.9835i	−0.244669	+	1.38758i	−0.821261	+	0.570553i	$0.806729\pi$
$252$	−1.47201	−	8.34820i	−0.0927281	−	0.525887i
$253$	−6.62067	+	2.40973i	−0.416238	+	0.151498i
$254$	−2.93358	+	5.08111i	−0.184069	+	0.318817i
$255$	−1.45059	−	2.51250i	−0.0908398	−	0.157339i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	8.66660	+	7.27214i	0.540608	+	0.453624i	0.871746	−	0.489958i	$-0.162988\pi$
$257$	8.66660	+	7.27214i	0.540608	+	0.453624i	−0.331138	+	0.943582i	$0.607433\pi$
$258$	1.27813	+	2.21379i	0.0795729	+	0.137824i
$259$	−8.69763	+	15.0647i	−0.540445	+	0.936077i
$260$	−0.256357	+	0.0933063i	−0.0158986	+	0.00578661i
$261$	−0.762102	−	4.32209i	−0.0471729	−	0.267531i
$262$	−1.01952	+	5.78196i	−0.0629859	+	0.357211i
$263$	−28.0546	−	10.2110i	−1.72992	−	0.629640i	−0.731297	−	0.682060i	$-0.761084\pi$
$263$	−28.0546	−	10.2110i	−1.72992	−	0.629640i	−0.998625	+	0.0524195i	$0.983307\pi$
$264$	−1.81872	+	1.52608i	−0.111934	+	0.0939239i
$265$	8.28011			0.508643
$266$	10.6617	+	9.09517i	0.653713	+	0.557661i
$267$	−21.1472			−1.29419
$268$	−2.82523	+	2.37065i	−0.172578	+	0.144811i
$269$	−1.38890	−	0.505518i	−0.0846827	−	0.0308220i	0.299331	−	0.954149i	$-0.403236\pi$
$269$	−1.38890	−	0.505518i	−0.0846827	−	0.0308220i	−0.384014	+	0.923327i	$0.625459\pi$
$270$	0.109278	−	0.619745i	0.00665044	−	0.0377165i
$271$	1.38592	+	7.85992i	0.0841883	+	0.477456i	0.997529	+	0.0702590i	$0.0223826\pi$
$271$	1.38592	+	7.85992i	0.0841883	+	0.477456i	−0.913340	+	0.407197i	$0.866506\pi$
$272$	−1.57405	+	0.572907i	−0.0954407	+	0.0347376i
$273$	1.42723	−	2.47204i	0.0863801	−	0.149615i
$274$	1.62137	+	2.80829i	0.0979503	+	0.169655i
$275$	3.42254	+	2.87185i	0.206387	+	0.173179i
$276$	12.8139	+	10.7521i	0.771305	+	0.647202i
$277$	−7.44338	−	12.8923i	−0.447230	−	0.774624i	0.550975	−	0.834522i	$-0.314256\pi$
$277$	−7.44338	−	12.8923i	−0.447230	−	0.774624i	−0.998205	+	0.0598974i	$0.980923\pi$
$278$	1.02081	−	1.76809i	0.0612240	−	0.106043i
$279$	−19.3921	+	7.05815i	−1.16097	+	0.422560i
$280$	−0.407278	−	2.30979i	−0.0243395	−	0.138036i
$281$	−4.25227	+	24.1158i	−0.253669	+	1.43863i	0.545796	+	0.837918i	$0.316227\pi$
$281$	−4.25227	+	24.1158i	−0.253669	+	1.43863i	−0.799465	+	0.600712i	$0.794884\pi$
$282$	−15.4146	−	5.61046i	−0.917926	−	0.334098i
$283$	−0.954351	+	0.800796i	−0.0567303	+	0.0476024i	−0.670712	−	0.741718i	$-0.734011\pi$
$283$	−0.954351	+	0.800796i	−0.0567303	+	0.0476024i	0.613982	+	0.789320i	$0.289567\pi$
$284$	5.69724			0.338069
$285$	−3.72143	−	6.56860i	−0.220438	−	0.389091i
$286$	−0.373961			−0.0221128
$287$	−17.1558	+	14.3955i	−1.01268	+	0.849737i
$288$	2.47765	+	0.901789i	0.145997	+	0.0531385i
$289$	−2.46479	+	13.9785i	−0.144988	+	0.822265i
$290$	−0.210859	−	1.19584i	−0.0123821	−	0.0702223i
$291$	28.1032	−	10.2287i	1.64744	−	0.599618i
$292$	0.281388	−	0.487378i	0.0164670	−	0.0285216i
$293$	14.5860	+	25.2636i	0.852121	+	1.47592i	0.879291	+	0.476286i	$0.158017\pi$
$293$	14.5860	+	25.2636i	0.852121	+	1.47592i	−0.0271696	+	0.999631i	$0.508649\pi$
$294$	6.06826	+	5.09187i	0.353908	+	0.296964i
$295$	−2.40840	−	2.02089i	−0.140222	−	0.117661i
$296$	−2.70528	−	4.68569i	−0.157241	−	0.272350i
$297$	0.431319	−	0.747067i	0.0250277	−	0.0433492i
$298$	−12.8940	+	4.69305i	−0.746932	+	0.271861i
$299$	0.457522	+	2.59474i	0.0264592	+	0.150058i
$300$	1.84194	−	10.4462i	0.106345	−	0.603110i
$301$	−3.25288	−	1.18395i	−0.187493	−	0.0682418i
$302$	7.29431	−	6.12066i	0.419741	−	0.352204i
$303$	−6.14883			−0.353241
$304$	−4.10802	+	1.45744i	−0.235611	+	0.0835900i
$305$	2.79093			0.159808
$306$	−3.38329	+	2.83892i	−0.193410	+	0.162290i
$307$	−25.0978	−	9.13484i	−1.43240	−	0.521353i	−0.494785	−	0.869015i	$-0.664753\pi$
$307$	−25.0978	−	9.13484i	−1.43240	−	0.521353i	−0.937620	+	0.347663i	$0.886975\pi$
$308$	0.558288	−	3.16621i	0.0318114	−	0.180411i
$309$	−6.56639	−	37.2399i	−0.373549	−	2.11850i
$310$	−5.36543	+	1.95286i	−0.304736	+	0.110915i
$311$	10.5997	−	18.3593i	0.601056	−	1.04106i	−0.391606	−	0.920133i	$-0.628080\pi$
$311$	10.5997	−	18.3593i	0.601056	−	1.04106i	0.992661	−	0.120926i	$-0.0385865\pi$
$312$	0.443922	+	0.768896i	0.0251322	+	0.0435302i
$313$	−4.26238	−	3.57656i	−0.240924	−	0.202159i	0.514329	−	0.857593i	$-0.328041\pi$
$313$	−4.26238	−	3.57656i	−0.240924	−	0.202159i	−0.755252	+	0.655434i	$0.772486\pi$
$314$	−14.6079	−	12.2575i	−0.824371	−	0.691730i
$315$	−3.09204	−	5.35556i	−0.174217	−	0.301752i
$316$	−7.40055	+	12.8181i	−0.416313	+	0.721076i
$317$	5.11460	−	1.86156i	0.287264	−	0.104556i	−0.194369	−	0.980928i	$-0.562266\pi$
$317$	5.11460	−	1.86156i	0.287264	−	0.104556i	0.481633	+	0.876373i	$0.340044\pi$
$318$	−4.67933	−	26.5378i	−0.262404	−	1.48817i
$319$	0.289041	−	1.63923i	0.0161832	−	0.0917794i
$320$	0.685518	+	0.249508i	0.0383216	+	0.0139479i
$321$	−26.4648	+	22.2066i	−1.47712	+	1.23945i
$322$	−22.6519			−1.26234
$323$	1.32637	−	7.17996i	0.0738012	−	0.399504i
$324$	−9.95801			−0.553223
$325$	1.27990	−	1.07396i	0.0709959	−	0.0595726i
$326$	4.18151	+	1.52195i	0.231593	+	0.0842928i
$327$	1.03695	−	5.88086i	0.0573437	−	0.325212i
$328$	−1.20960	−	6.85996i	−0.0667887	−	0.378778i
$329$	20.8742	−	7.59758i	1.15083	−	0.418868i
$330$	−0.865992	+	1.49994i	−0.0476713	+	0.0825691i
$331$	14.6130	+	25.3104i	0.803201	+	1.39118i	0.917499	+	0.397738i	$0.130205\pi$
$331$	14.6130	+	25.3104i	0.803201	+	1.39118i	−0.114298	+	0.993447i	$0.536462\pi$
$332$	−5.80230	−	4.86871i	−0.318443	−	0.267205i
$333$	−10.9282	−	9.16988i	−0.598864	−	0.502507i
$334$	7.24471	+	12.5482i	0.396413	+	0.686608i
$335$	−1.34525	+	2.33004i	−0.0734989	+	0.127304i
$336$	−7.17273	+	2.61066i	−0.391305	+	0.142423i
$337$	0.491064	+	2.78497i	0.0267500	+	0.151707i	0.995257	−	0.0972790i	$-0.0310139\pi$
$337$	0.491064	+	2.78497i	0.0267500	+	0.151707i	−0.968507	+	0.248986i	$0.919903\pi$
$338$	2.23314	−	12.6648i	0.121467	−	0.688873i
$339$	−30.7105	−	11.1777i	−1.66797	−	0.607090i
$340$	−0.936094	+	0.785476i	−0.0507668	+	0.0425984i
$341$	−7.82682			−0.423846
$342$	−8.86393	+	7.31560i	−0.479306	+	0.395582i
$343$	11.7781			0.635960
$344$	0.824799	−	0.692088i	0.0444702	−	0.0373149i
$345$	11.4669	+	4.17361i	0.617357	+	0.224699i
$346$	3.08472	−	17.4943i	0.165836	−	0.940501i
$347$	−2.46923	−	14.0037i	−0.132555	−	0.751759i	−0.976531	−	0.215377i	$-0.930902\pi$
$347$	−2.46923	−	14.0037i	−0.132555	−	0.751759i	0.843975	−	0.536382i	$-0.180209\pi$
$348$	−3.71352	+	1.35161i	−0.199066	+	0.0724540i
$349$	−9.80875	+	16.9893i	−0.525051	+	0.909414i	0.474524	+	0.880243i	$0.342620\pi$
$349$	−9.80875	+	16.9893i	−0.525051	+	0.909414i	−0.999574	+	0.0291716i	$0.990713\pi$
$350$	7.18212	+	12.4398i	0.383901	+	0.664935i
$351$	−0.247121	−	0.207359i	−0.0131903	−	0.0110680i
$352$	0.766044	+	0.642788i	0.0408303	+	0.0342607i
$353$	−15.6030	−	27.0253i	−0.830466	−	1.43841i	−0.897669	−	0.440671i	$-0.854741\pi$
$353$	−15.6030	−	27.0253i	−0.830466	−	1.43841i	0.0672025	−	0.997739i	$-0.478593\pi$
$354$	−5.11590	+	8.86101i	−0.271907	+	0.470957i
$355$	3.90556	−	1.42151i	0.207286	−	0.0754458i
$356$	1.54672	+	8.77191i	0.0819762	+	0.464910i
$357$	2.22025	−	12.5916i	0.117508	−	0.666421i
$358$	7.27946	+	2.64951i	0.384732	+	0.140031i
$359$	−6.68686	+	5.61094i	−0.352919	+	0.296134i	−0.801961	−	0.597376i	$-0.796210\pi$
$359$	−6.68686	+	5.61094i	−0.352919	+	0.296134i	0.449042	+	0.893511i	$0.351765\pi$
$360$	1.92347			0.101376
$361$	3.60348	−	18.6552i	0.189657	−	0.981850i
$362$	−24.9201			−1.30977
$363$	−1.81872	+	1.52608i	−0.0954578	+	0.0800986i
$364$	−1.12980	−	0.411212i	−0.0592174	−	0.0215534i
$365$	0.0712916	−	0.404315i	0.00373157	−	0.0211628i
$366$	−1.57724	−	8.94497i	−0.0824436	−	0.467561i
$367$	11.9764	−	4.35904i	0.625161	−	0.227540i	−0.00996269	−	0.999950i	$-0.503171\pi$
$367$	11.9764	−	4.35904i	0.625161	−	0.227540i	0.635124	+	0.772410i	$0.280949\pi$
$368$	3.52278	−	6.10164i	0.183638	−	0.318070i
$369$	−9.18319	−	15.9057i	−0.478058	−	0.828020i
$370$	−3.02364	−	2.53713i	−0.157192	−	0.131899i
$371$	27.9541	+	23.4563i	1.45130	+	1.21779i
$372$	9.29108	+	16.0926i	0.481720	+	0.834364i
$373$	−7.79198	+	13.4961i	−0.403454	+	0.698802i	−0.994140	−	0.108099i	$-0.965524\pi$
$373$	−7.79198	+	13.4961i	−0.403454	+	0.698802i	0.590687	+	0.806901i	$0.298857\pi$
$374$	−1.57405	+	0.572907i	−0.0813921	+	0.0296243i
$375$	−2.84750	−	16.1490i	−0.147044	−	0.833929i
$376$	−1.19979	+	6.80436i	−0.0618745	+	0.350908i
$377$	−0.584927	−	0.212896i	−0.0301253	−	0.0109647i
$378$	2.12457	−	1.78273i	0.109276	−	0.0916935i
$379$	31.8392			1.63547			0.817734	−	0.575596i	$-0.195230\pi$
$379$	31.8392			1.63547			0.817734	+	0.575596i	$0.195230\pi$
$380$	−2.45248	+	2.02409i	−0.125810	+	0.103834i
$381$	13.9296			0.713636
$382$	−14.8636	+	12.4721i	−0.760489	+	0.638126i
$383$	−17.3378	−	6.31045i	−0.885921	−	0.322449i	−0.141324	−	0.989963i	$-0.545136\pi$
$383$	−17.3378	−	6.31045i	−0.885921	−	0.322449i	−0.744597	+	0.667515i	$0.767358\pi$
$384$	0.412269	−	2.33810i	0.0210385	−	0.119315i
$385$	−0.407278	−	2.30979i	−0.0207568	−	0.117718i
$386$	−10.3317	+	3.76044i	−0.525871	+	0.191401i
$387$	1.41944	−	2.45855i	0.0721543	−	0.124975i
$388$	−6.29838	−	10.9091i	−0.319752	−	0.553826i
$389$	−18.8343	−	15.8038i	−0.954935	−	0.801285i	0.0251869	−	0.999683i	$-0.491982\pi$
$389$	−18.8343	−	15.8038i	−0.954935	−	0.801285i	−0.980122	+	0.198397i	$0.936426\pi$
$390$	0.496163	+	0.416330i	0.0251242	+	0.0210817i
$391$	5.90090	+	10.2207i	0.298421	+	0.516881i
$392$	1.66828	−	2.88955i	0.0842610	−	0.145944i
$393$	13.0985	−	4.76745i	0.660730	−	0.240486i
$394$	1.12673	+	6.38999i	0.0567637	+	0.321923i
$395$	−1.87498	+	10.6336i	−0.0943406	+	0.535032i
$396$	2.47765	+	0.901789i	0.124506	+	0.0453166i
$397$	4.19095	−	3.51662i	0.210338	−	0.176494i	−0.531532	−	0.847038i	$-0.678384\pi$
$397$	4.19095	−	3.51662i	0.210338	−	0.176494i	0.741870	+	0.670544i	$0.233939\pi$
$398$	−0.327685			−0.0164253
$399$	6.04409	−	32.7182i	0.302583	−	1.63796i
$400$	−4.46781			−0.223391
$401$	−0.0438950	+	0.0368323i	−0.00219201	+	0.00183932i	−0.643883	−	0.765124i	$-0.722678\pi$
$401$	−0.0438950	+	0.0368323i	−0.00219201	+	0.00183932i	0.641691	+	0.766963i	$0.278233\pi$
$402$	8.22804	+	2.99476i	0.410378	+	0.149365i
$403$	−0.508255	+	2.88246i	−0.0253180	+	0.143586i
$404$	0.449730	+	2.55055i	0.0223749	+	0.126894i
$405$	−6.82640	+	2.48461i	−0.339206	+	0.123461i
$406$	2.67576	−	4.63455i	0.132796	−	0.230009i
$407$	−2.70528	−	4.68569i	−0.134096	−	0.232261i
$408$	3.04647	+	2.55629i	0.150823	+	0.126555i
$409$	6.16526	+	5.17326i	0.304852	+	0.255801i	0.782361	−	0.622826i	$-0.214015\pi$
$409$	6.16526	+	5.17326i	0.304852	+	0.255801i	−0.477508	+	0.878627i	$0.658460\pi$
$410$	−2.54082	−	4.40082i	−0.125482	−	0.217341i
$411$	3.84939	−	6.66734i	0.189876	−	0.328876i
$412$	−14.9669	+	5.44750i	−0.737366	+	0.268379i
$413$	−2.40602	−	13.6452i	−0.118393	−	0.671438i
$414$	3.22582	−	18.2945i	0.158540	−	0.899126i
$415$	−5.19237	−	1.88987i	−0.254883	−	0.0927699i
$416$	0.286471	−	0.240377i	0.0140454	−	0.0117855i
$417$	−4.84713			−0.237365
$418$	−4.10802	+	1.45744i	−0.200930	+	0.0712858i
$419$	18.5908			0.908222			0.454111	−	0.890945i	$-0.349957\pi$
$419$	18.5908			0.908222			0.454111	+	0.890945i	$0.349957\pi$
$420$	−4.26566	+	3.57931i	−0.208143	+	0.174652i
$421$	12.5918	+	4.58305i	0.613688	+	0.223364i	0.630116	−	0.776501i	$-0.283007\pi$
$421$	12.5918	+	4.58305i	0.613688	+	0.223364i	−0.0164281	+	0.999865i	$0.505229\pi$
$422$	−3.48306	+	19.7534i	−0.169553	+	0.961581i
$423$	3.16344	+	17.9408i	0.153812	+	0.872309i
$424$	−10.6657	+	3.88199i	−0.517972	+	0.188526i
$425$	3.74194	−	6.48123i	0.181511	−	0.314386i
$426$	−6.76309	−	11.7140i	−0.327673	−	0.567546i
$427$	9.42234	+	7.90628i	0.455979	+	0.382612i
$428$	11.1470	+	9.35343i	0.538810	+	0.452115i
$429$	0.443922	+	0.768896i	0.0214328	+	0.0371227i
$430$	0.392733	−	0.680233i	0.0189393	−	0.0328038i
$431$	29.8216	−	10.8542i	1.43646	−	0.522828i	0.497683	−	0.867359i	$-0.334184\pi$
$431$	29.8216	−	10.8542i	1.43646	−	0.522828i	0.938775	+	0.344531i	$0.111962\pi$
$432$	0.149796	+	0.849533i	0.00720704	+	0.0408732i
$433$	−6.30465	+	35.7554i	−0.302982	+	1.71830i	0.329872	+	0.944026i	$0.392994\pi$
$433$	−6.30465	+	35.7554i	−0.302982	+	1.71830i	−0.632854	+	0.774271i	$0.718117\pi$
$434$	−23.6461	−	8.60647i	−1.13505	−	0.413124i
$435$	−2.20845	+	1.85311i	−0.105887	+	0.0888497i
$436$	−2.51524			−0.120458
$437$	15.1385	+	26.7205i	0.724171	+	1.27822i
$438$	−1.33612			−0.0638424
$439$	10.8308	−	9.08809i	0.516924	−	0.433751i	−0.346634	−	0.938001i	$-0.612675\pi$
$439$	10.8308	−	9.08809i	0.516924	−	0.433751i	0.863558	+	0.504250i	$0.168231\pi$
$440$	0.685518	+	0.249508i	0.0326808	+	0.0118948i
$441$	1.52765	−	8.66372i	0.0727451	−	0.412558i
$442$	0.108775	+	0.616893i	0.00517389	+	0.0293426i
$443$	14.1114	−	5.13612i	0.670451	−	0.244024i	0.0157092	−	0.999877i	$-0.494999\pi$
$443$	14.1114	−	5.13612i	0.670451	−	0.244024i	0.654742	+	0.755852i	$0.272777\pi$
$444$	−6.42279	+	11.1246i	−0.304812	+	0.527950i
$445$	3.24897	+	5.62738i	0.154016	+	0.266763i
$446$	18.8614	+	15.8266i	0.893113	+	0.749411i
$447$	24.9556	+	20.9402i	1.18036	+	0.990440i
$448$	1.60753	+	2.78432i	0.0759485	+	0.131547i
$449$	3.95305	−	6.84689i	0.186556	−	0.323125i	−0.757544	−	0.652784i	$-0.773601\pi$
$449$	3.95305	−	6.84689i	0.186556	−	0.323125i	0.944100	+	0.329660i	$0.106934\pi$
$450$	−11.0697	+	4.02902i	−0.521828	+	0.189930i
$451$	−1.20960	−	6.85996i	−0.0569576	−	0.323023i
$452$	−2.39035	+	13.5563i	−0.112432	+	0.637636i
$453$	−21.2435	−	7.73202i	−0.998109	−	0.363282i
$454$	−4.61275	+	3.87056i	−0.216487	+	0.181654i
$455$	−0.877097			−0.0411189
$456$	7.87319	+	6.71635i	0.368696	+	0.314522i
$457$	−0.101475			−0.00474680			−0.00237340	−	0.999997i	$-0.500755\pi$
$457$	−0.101475			−0.00474680			−0.00237340	+	0.999997i	$0.500755\pi$
$458$	−2.94424	+	2.47051i	−0.137575	+	0.115439i
$459$	−1.35783	−	0.494211i	−0.0633783	−	0.0230678i
$460$	0.892523	−	5.06175i	0.0416141	−	0.236005i
$461$	−4.88826	−	27.7227i	−0.227669	−	1.29118i	−0.857516	−	0.514457i	$-0.827994\pi$
$461$	−4.88826	−	27.7227i	−0.227669	−	1.29118i	0.629847	−	0.776719i	$-0.283118\pi$
$462$	−7.17273	+	2.61066i	−0.333706	+	0.121459i
$463$	−7.69898	+	13.3350i	−0.357802	+	0.619731i	−0.987593	−	0.157033i	$-0.949807\pi$
$463$	−7.69898	+	13.3350i	−0.357802	+	0.619731i	0.629791	+	0.776764i	$0.283140\pi$
$464$	0.832261	+	1.44152i	0.0386367	+	0.0669208i
$465$	10.3844	+	8.71358i	0.481567	+	0.404083i
$466$	−10.2173	−	8.57332i	−0.473307	−	0.397151i
$467$	−3.66129	−	6.34155i	−0.169424	−	0.293452i	0.768793	−	0.639497i	$-0.220858\pi$
$467$	−3.66129	−	6.34155i	−0.169424	−	0.293452i	−0.938218	+	0.346046i	$0.887524\pi$
$468$	0.493003	−	0.853907i	0.0227891	−	0.0394718i
$469$	−11.1423	+	4.05546i	−0.514503	+	0.187264i
$470$	0.875264	+	4.96387i	0.0403729	+	0.228966i
$471$	−7.86167	+	44.5857i	−0.362247	+	2.05440i
$472$	4.04974	+	1.47399i	0.186405	+	0.0678457i
$473$	0.824799	−	0.692088i	0.0379243	−	0.0318223i
$474$	35.1402			1.61404
$475$	9.87433	−	16.7858i	0.453065	−	0.770185i
$476$	−5.38543			−0.246841
$477$	−22.9251	+	19.2364i	−1.04967	+	0.880775i
$478$	−7.08147	−	2.57744i	−0.323899	−	0.117890i
$479$	2.69206	−	15.2674i	0.123003	−	0.697588i	−0.859470	−	0.511186i	$-0.829206\pi$
$479$	2.69206	−	15.2674i	0.123003	−	0.697588i	0.982474	−	0.186402i	$-0.0596825\pi$
$480$	−0.300756	−	1.70567i	−0.0137276	−	0.0778529i
$481$	−1.90132	+	0.692024i	−0.0866927	+	0.0315536i
$482$	−2.26928	+	3.93051i	−0.103363	+	0.179030i
$483$	26.8896	+	46.5742i	1.22352	+	2.11920i
$484$	0.766044	+	0.642788i	0.0348202	+	0.0292176i
$485$	−7.03956	−	5.90690i	−0.319650	−	0.268218i
$486$	10.5270	+	18.2333i	0.477515	+	0.827081i
$487$	20.0321	−	34.6966i	0.907740	−	1.57225i	0.0905443	−	0.995892i	$-0.471139\pi$
$487$	20.0321	−	34.6966i	0.907740	−	1.57225i	0.817196	−	0.576360i	$-0.195527\pi$
$488$	−3.59503	+	1.30848i	−0.162739	+	0.0592323i
$489$	−1.83455	−	10.4042i	−0.0829611	−	0.470496i
$490$	0.422671	−	2.39709i	0.0190943	−	0.108289i
$491$	−27.9363	−	10.1680i	−1.26075	−	0.458874i	−0.376727	−	0.926324i	$-0.622951\pi$
$491$	−27.9363	−	10.1680i	−1.26075	−	0.458874i	−0.884020	+	0.467450i	$0.845173\pi$
$492$	−12.6688	+	10.6304i	−0.571153	+	0.479254i
$493$	−2.78818			−0.125574
$494$	0.269981	+	1.60754i	0.0121470	+	0.0723269i
$495$	1.92347			0.0864538
$496$	5.99569	−	5.03098i	0.269215	−	0.225898i
$497$	17.2123	+	6.26476i	0.772076	+	0.281013i
$498$	−3.12268	+	17.7096i	−0.139931	+	0.793586i
$499$	−2.22337	−	12.6094i	−0.0995319	−	0.564473i	−0.993264	−	0.115873i	$-0.963034\pi$
$499$	−2.22337	−	12.6094i	−0.0995319	−	0.564473i	0.893732	−	0.448601i	$-0.148078\pi$
$500$	−6.49036	+	2.36230i	−0.290258	+	0.105645i
$501$	17.2001	−	29.7915i	0.768446	−	1.33099i
$502$	−11.1613	−	19.3319i	−0.498153	−	0.862827i
$503$	−30.6108	−	25.6855i	−1.36487	−	1.14526i	−0.974446	−	0.224622i	$-0.927885\pi$
$503$	−30.6108	−	25.6855i	−1.36487	−	1.14526i	−0.390420	−	0.920637i	$-0.627670\pi$
$504$	6.49375	+	5.44890i	0.289255	+	0.242713i
$505$	0.944681	+	1.63623i	0.0420377	+	0.0728115i
$506$	3.52278	−	6.10164i	0.156607	−	0.271251i
$507$	−28.6908	+	10.4426i	−1.27420	+	0.463772i
$508$	−1.01882	−	5.77803i	−0.0452029	−	0.256359i
$509$	2.20305	−	12.4941i	0.0976485	−	0.553792i	−0.896255	−	0.443539i	$-0.853723\pi$
$509$	2.20305	−	12.4941i	0.0976485	−	0.553792i	0.993904	−	0.110253i	$-0.0351661\pi$
$510$	2.72623	+	0.992265i	0.120719	+	0.0439382i
$511$	1.38604	−	1.16303i	0.0613150	−	0.0514494i
$512$	−1.00000			−0.0441942
$513$	−3.52280	−	1.31477i	−0.155536	−	0.0580484i
$514$	−11.3134			−0.499015
$515$	−8.90088	+	7.46873i	−0.392220	+	0.329111i
$516$	−2.40210	−	0.874292i	−0.105746	−	0.0384886i
$517$	−1.19979	+	6.80436i	−0.0527668	+	0.299255i
$518$	−3.02066	−	17.1310i	−0.132720	−	0.752692i
$519$	−39.6317	+	14.4247i	−1.73964	+	0.633176i
$520$	0.136405	−	0.236260i	0.00598174	−	0.0103607i
$521$	−20.6770	−	35.8135i	−0.905874	−	1.56902i	−0.819740	−	0.572736i	$-0.805882\pi$
$521$	−20.6770	−	35.8135i	−0.905874	−	1.56902i	−0.0861344	−	0.996284i	$-0.527451\pi$
$522$	3.36199	+	2.82105i	0.147150	+	0.123474i
$523$	23.7745	+	19.9492i	1.03959	+	0.872318i	0.991961	−	0.126548i	$-0.0403896\pi$
$523$	23.7745	+	19.9492i	1.03959	+	0.872318i	0.0476271	+	0.998865i	$0.484834\pi$
$524$	−2.93558	−	5.08457i	−0.128241	−	0.222120i
$525$	17.0515	−	29.5341i	0.744190	−	1.28898i
$526$	28.0546	−	10.2110i	1.22324	−	0.445223i
$527$	2.27661	+	12.9113i	0.0991705	+	0.562424i
$528$	0.412269	−	2.33810i	0.0179417	−	0.101753i
$529$	−25.0334	−	9.11142i	−1.08841	−	0.396149i
$530$	−6.34293	+	5.32235i	−0.275519	+	0.231188i
$531$	11.3631			0.493115
$532$	−14.0136	−	0.114070i	−0.607568	−	0.00494557i
$533$	−2.60493			−0.112832
$534$	16.1997	−	13.5932i	0.701030	−	0.588234i
$535$	9.97521	+	3.63068i	0.431266	+	0.156968i
$536$	0.640428	−	3.63205i	0.0276623	−	0.156881i
$537$	−3.19370	−	18.1124i	−0.137818	−	0.781607i
$538$	1.38890	−	0.505518i	0.0598797	−	0.0217944i
$539$	1.66828	−	2.88955i	0.0718580	−	0.124462i
$540$	0.314653	+	0.544995i	0.0135405	+	0.0234528i
$541$	3.52702	+	2.95952i	0.151638	+	0.127240i	0.715451	−	0.698663i	$-0.246221\pi$
$541$	3.52702	+	2.95952i	0.151638	+	0.127240i	−0.563812	+	0.825903i	$0.690666\pi$
$542$	−6.11393	−	5.13020i	−0.262616	−	0.220361i
$543$	29.5822	+	51.2379i	1.26950	+	2.19883i
$544$	0.837534	−	1.45065i	0.0359090	−	0.0621961i
$545$	−1.72424	+	0.627572i	−0.0738583	+	0.0268822i
$546$	0.495673	+	2.81110i	0.0212129	+	0.120304i
$547$	−2.79111	+	15.8292i	−0.119339	+	0.676808i	0.865170	+	0.501478i	$0.167210\pi$
$547$	−2.79111	+	15.8292i	−0.119339	+	0.676808i	−0.984510	+	0.175330i	$0.943901\pi$
$548$	−3.04717	−	1.10908i	−0.130169	−	0.0473775i
$549$	−7.72723	+	6.48392i	−0.329790	+	0.276727i
$550$	−4.46781			−0.190508
$551$	−7.25524	−	0.0590573i	−0.309084	−	0.00251593i
$552$	−16.7273			−0.711963
$553$	−36.4532	+	30.5879i	−1.55015	+	1.30073i
$554$	13.9890	+	5.09157i	0.594335	+	0.216320i
$555$	−1.62726	+	9.22865i	−0.0690733	+	0.391734i
$556$	0.354523	+	2.01060i	0.0150351	+	0.0852684i
$557$	0.0372355	−	0.0135526i	0.00157772	−	0.000574242i	−0.341231	−	0.939979i	$-0.610844\pi$
$557$	0.0372355	−	0.0135526i	0.00157772	−	0.000574242i	0.342809	+	0.939405i	$0.388622\pi$
$558$	10.3183	−	17.8719i	0.436809	−	0.756576i
$559$	−0.201322	−	0.348699i	−0.00851500	−	0.0147484i
$560$	1.79670	+	1.50761i	0.0759244	+	0.0637081i
$561$	3.04647	+	2.55629i	0.128622	+	0.107927i
$562$	−12.2439	−	21.2071i	−0.516479	−	0.894568i
$563$	21.7221	−	37.6238i	0.915479	−	1.58566i	0.109280	−	0.994011i	$-0.465145\pi$
$563$	21.7221	−	37.6238i	0.915479	−	1.58566i	0.806199	−	0.591645i	$-0.201521\pi$
$564$	15.4146	−	5.61046i	0.649072	−	0.236243i
$565$	1.74379	+	9.88951i	0.0733617	+	0.416055i
$566$	0.216334	−	1.22689i	0.00909319	−	0.0515700i
$567$	−30.0848	−	10.9500i	−1.26344	−	0.459855i
$568$	−4.36434	+	3.66212i	−0.183124	+	0.153659i
$569$	−0.117265			−0.00491599			−0.00245799	−	0.999997i	$-0.500782\pi$
$569$	−0.117265			−0.00491599			−0.00245799	+	0.999997i	$0.500782\pi$
$570$	7.07300	+	2.63976i	0.296255	+	0.110567i
$571$	12.4104			0.519360			0.259680	−	0.965695i	$-0.416383\pi$
$571$	12.4104			0.519360			0.259680	+	0.965695i	$0.416383\pi$
$572$	0.286471	−	0.240377i	0.0119779	−	0.0100507i
$573$	43.2880	+	15.7555i	1.80838	+	0.658197i
$574$	3.88891	−	22.0551i	0.162320	−	0.920563i
$575$	5.46614	+	31.0000i	0.227954	+	1.29279i
$576$	−2.47765	+	0.901789i	−0.103235	+	0.0375746i
$577$	8.60550	−	14.9052i	0.358252	−	0.620510i	−0.629417	−	0.777067i	$-0.716706\pi$
$577$	8.60550	−	14.9052i	0.358252	−	0.620510i	0.987669	+	0.156558i	$0.0500397\pi$
$578$	−7.09707	−	12.2925i	−0.295199	−	0.511300i
$579$	19.9964	+	16.7790i	0.831021	+	0.697310i
$580$	0.930200	+	0.780530i	0.0386245	+	0.0324098i
$581$	−12.1760	−	21.0894i	−0.505145	−	0.874937i
$582$	−14.9534	+	25.9000i	−0.619838	+	1.07359i
$583$	−10.6657	+	3.88199i	−0.441728	+	0.160776i
$584$	0.0977249	+	0.554226i	0.00404389	+	0.0229340i
$585$	0.124906	−	0.708377i	0.00516422	−	0.0292878i
$586$	−27.4126	−	9.97738i	−1.13241	−	0.412162i
$587$	−6.80918	+	5.71358i	−0.281045	+	0.235825i	−0.772403	−	0.635133i	$-0.780945\pi$
$587$	−6.80918	+	5.71358i	−0.281045	+	0.235825i	0.491358	+	0.870958i	$0.336501\pi$
$588$	−7.92155			−0.326679
$589$	5.65056	+	33.6451i	0.232827	+	1.38632i
$590$	3.14394			0.129434
$591$	11.8009	−	9.90210i	0.485422	−	0.407318i
$592$	5.08427	+	1.85052i	0.208962	+	0.0760560i
$593$	−2.14327	+	12.1551i	−0.0880134	+	0.499149i	0.908652	+	0.417554i	$0.137112\pi$
$593$	−2.14327	+	12.1551i	−0.0880134	+	0.499149i	−0.996666	+	0.0815949i	$0.973999\pi$
$594$	0.149796	+	0.849533i	0.00614619	+	0.0348568i
$595$	−3.69181	+	1.34371i	−0.151349	+	0.0550867i
$596$	6.86078	−	11.8832i	0.281028	−	0.486756i
$597$	0.388988	+	0.673748i	0.0159202	+	0.0275747i
$598$	−2.01835	−	1.69360i	−0.0825364	−	0.0692563i
$599$	−17.4409	−	14.6347i	−0.712618	−	0.597957i	0.212715	−	0.977114i	$-0.431770\pi$
$599$	−17.4409	−	14.6347i	−0.712618	−	0.597957i	−0.925332	+	0.379157i	$0.876214\pi$
$600$	5.30366	+	9.18621i	0.216521	+	0.375025i
$601$	20.9755	−	36.3307i	0.855609	−	1.48196i	−0.0204691	−	0.999790i	$-0.506516\pi$
$601$	20.9755	−	36.3307i	0.855609	−	1.48196i	0.876079	−	0.482168i	$-0.160151\pi$
$602$	3.25288	−	1.18395i	0.132577	−	0.0482543i
$603$	−1.68859	−	9.57646i	−0.0687646	−	0.389984i
$604$	−1.65349	+	9.37739i	−0.0672794	+	0.381561i
$605$	0.685518	+	0.249508i	0.0278703	+	0.0101439i
$606$	4.71028	−	3.95239i	0.191342	−	0.160555i
$607$	−37.8741			−1.53726			−0.768631	−	0.639693i	$-0.779062\pi$
$607$	−37.8741			−1.53726			−0.768631	+	0.639693i	$0.779062\pi$
$608$	2.21010	−	3.75705i	0.0896315	−	0.152369i
$609$	−12.7054			−0.514849
$610$	−2.13798	+	1.79398i	−0.0865643	+	0.0726360i
$611$	2.42800	+	0.883718i	0.0982262	+	0.0357514i
$612$	0.766930	−	4.34948i	0.0310013	−	0.175817i
$613$	1.87132	+	10.6128i	0.0755818	+	0.428646i	0.998994	+	0.0448368i	$0.0142768\pi$
$613$	1.87132	+	10.6128i	0.0755818	+	0.428646i	−0.923413	+	0.383809i	$0.874612\pi$
$614$	25.0978	−	9.13484i	1.01286	−	0.368652i
$615$	−6.03231	+	10.4483i	−0.243246	+	0.421315i
$616$	1.60753	+	2.78432i	0.0647691	+	0.112183i
$617$	−11.5342	−	9.67836i	−0.464350	−	0.389636i	0.380379	−	0.924831i	$-0.375794\pi$
$617$	−11.5342	−	9.67836i	−0.464350	−	0.389636i	−0.844729	+	0.535195i	$0.820238\pi$
$618$	28.9675	+	24.3066i	1.16524	+	0.977755i
$619$	23.0923	+	39.9971i	0.928160	+	1.60762i	0.786399	+	0.617719i	$0.211943\pi$
$619$	23.0923	+	39.9971i	0.928160	+	1.60762i	0.141761	+	0.989901i	$0.454724\pi$
$620$	2.85488	−	4.94481i	0.114655	−	0.198588i
$621$	5.71124	−	2.07872i	0.229184	−	0.0834162i
$622$	3.68125	+	20.8774i	0.147605	+	0.837108i
$623$	−4.97280	+	28.2021i	−0.199231	+	1.12990i
$624$	−0.834301	−	0.303661i	−0.0333988	−	0.0121562i
$625$	13.2529	−	11.1205i	0.530115	−	0.444819i
$626$	5.56414			0.222388
$627$	7.87319	+	6.71635i	0.314425	+	0.268225i
$628$	19.0693			0.760946
$629$	−6.94271	+	5.82563i	−0.276824	+	0.232283i
$630$	5.81113	+	2.11508i	0.231521	+	0.0842667i
$631$	−4.29360	+	24.3502i	−0.170925	+	0.969366i	0.771817	+	0.635845i	$0.219348\pi$
$631$	−4.29360	+	24.3502i	−0.170925	+	0.969366i	−0.942743	+	0.333521i	$0.891763\pi$
$632$	−2.57018	−	14.5762i	−0.102236	−	0.579811i
$633$	44.7494	−	16.2874i	1.77863	−	0.647368i
$634$	−2.72142	+	4.71364i	−0.108081	+	0.187202i
$635$	−2.14009	−	3.70674i	−0.0849267	−	0.147097i
$636$	20.6428	+	17.3213i	0.818539	+	0.686836i
$637$	−0.955828	−	0.802035i	−0.0378713	−	0.0317778i
$638$	0.832261	+	1.44152i	0.0329495	+	0.0570702i
$639$	−7.51083	+	13.0091i	−0.297124	+	0.514634i
$640$	−0.685518	+	0.249508i	−0.0270975	+	0.00986268i
$641$	3.32246	+	18.8426i	0.131229	+	0.744239i	0.977412	+	0.211345i	$0.0677844\pi$
$641$	3.32246	+	18.8426i	0.131229	+	0.744239i	−0.846182	+	0.532894i	$0.821104\pi$
$642$	5.99908	−	34.0224i	0.236765	−	1.34276i
$643$	9.88274	+	3.59702i	0.389737	+	0.141853i	0.529454	−	0.848339i	$-0.322397\pi$
$643$	9.88274	+	3.59702i	0.389737	+	0.141853i	−0.139717	+	0.990192i	$0.544619\pi$
$644$	17.3523	−	14.5603i	0.683778	−	0.573758i
$645$	−1.86482			−0.0734274
$646$	3.59913	+	6.35275i	0.141606	+	0.249945i
$647$	−7.46531			−0.293492			−0.146746	−	0.989174i	$-0.546880\pi$
$647$	−7.46531			−0.293492			−0.146746	+	0.989174i	$0.546880\pi$
$648$	7.62828	−	6.40089i	0.299667	−	0.251451i
$649$	4.04974	+	1.47399i	0.158966	+	0.0578590i
$650$	−0.290129	+	1.64540i	−0.0113798	+	0.0645380i
$651$	10.3742	+	58.8350i	0.406597	+	2.30593i
$652$	−4.18151	+	1.52195i	−0.163761	+	0.0596040i
$653$	23.0255	−	39.8813i	0.901057	−	1.56068i	0.0749335	−	0.997189i	$-0.476126\pi$
$653$	23.0255	−	39.8813i	0.901057	−	1.56068i	0.826124	−	0.563489i	$-0.190541\pi$
$654$	2.98579	+	5.17154i	0.116754	+	0.202223i
$655$	−3.28103	−	2.75311i	−0.128201	−	0.107573i
$656$	5.33610	+	4.47752i	0.208340	+	0.174818i
$657$	0.741923	+	1.28505i	0.0289452	+	0.0501345i
$658$	−11.1069	+	19.2378i	−0.432993	+	0.749966i
$659$	5.50979	−	2.00540i	0.214631	−	0.0781193i	−0.232467	−	0.972604i	$-0.574680\pi$
$659$	5.50979	−	2.00540i	0.214631	−	0.0781193i	0.447098	+	0.894485i	$0.352458\pi$
$660$	−0.300756	−	1.70567i	−0.0117069	−	0.0663932i
$661$	−1.68170	+	9.53740i	−0.0654106	+	0.370962i	0.934478	+	0.356021i	$0.115867\pi$
$661$	−1.68170	+	9.53740i	−0.0654106	+	0.370962i	−0.999888	+	0.0149405i	$0.995244\pi$
$662$	−27.4634	−	9.99585i	−1.06739	−	0.388500i
$663$	1.13926	−	0.955953i	0.0442452	−	0.0371262i
$664$	7.57437			0.293942
$665$	−9.63505	+	3.41832i	−0.373631	+	0.132557i
$666$	14.2658			0.552789
$667$	8.98378	−	7.53829i	0.347853	−	0.291884i
$668$	−13.6156	−	4.95568i	−0.526804	−	0.191741i
$669$	10.1508	−	57.5681i	0.392453	−	2.22571i
$670$	−0.467201	−	2.64963i	−0.0180495	−	0.102364i
$671$	−3.59503	+	1.30848i	−0.138785	+	0.0505134i
$672$	3.81653	−	6.61043i	0.147226	−	0.255003i
$673$	−12.8204	−	22.2056i	−0.494190	−	0.855962i	0.505788	−	0.862658i	$-0.331202\pi$
$673$	−12.8204	−	22.2056i	−0.494190	−	0.855962i	−0.999978	+	0.00669613i	$0.997869\pi$
$674$	−2.16632	−	1.81776i	−0.0834435	−	0.0700174i
$675$	−2.95242	−	2.47737i	−0.113639	−	0.0953541i
$676$	6.43008	+	11.1372i	0.247311	+	0.428355i
$677$	18.3843	−	31.8425i	0.706564	−	1.22381i	−0.259560	−	0.965727i	$-0.583577\pi$
$677$	18.3843	−	31.8425i	0.706564	−	1.22381i	0.966124	−	0.258078i	$-0.0830892\pi$
$678$	30.7105	−	11.1777i	1.17943	−	0.429277i
$679$	−7.03262	−	39.8840i	−0.269887	−	1.53061i
$680$	0.212195	−	1.20342i	0.00813731	−	0.0461490i
$681$	13.4339	+	4.88954i	0.514788	+	0.187368i
$682$	5.99569	−	5.03098i	0.229587	−	0.192646i
$683$	24.8271			0.949981			0.474991	−	0.879991i	$-0.342451\pi$
$683$	24.8271			0.949981			0.474991	+	0.879991i	$0.342451\pi$
$684$	2.08779	−	11.3017i	0.0798285	−	0.432131i
$685$	−2.36562			−0.0903855
$686$	−9.02258	+	7.57084i	−0.344484	+	0.289056i
$687$	8.57464	+	3.12091i	0.327143	+	0.119070i
$688$	−0.186967	+	1.06034i	−0.00712804	+	0.0404251i
$689$	0.737054	+	4.18004i	0.0280795	+	0.159247i
$690$	−11.4669	+	4.17361i	−0.436537	+	0.158886i
$691$	17.3332	−	30.0219i	0.659384	−	1.14209i	−0.321391	−	0.946947i	$-0.604150\pi$
$691$	17.3332	−	30.0219i	0.659384	−	1.14209i	0.980775	−	0.195141i	$-0.0625164\pi$
$692$	8.88210	+	15.3842i	0.337647	+	0.584821i
$693$	6.49375	+	5.44890i	0.246677	+	0.206987i
$694$	10.8930	+	9.14028i	0.413491	+	0.346960i
$695$	0.744693	+	1.28985i	0.0282478	+	0.0489266i
$696$	1.97592	−	3.42240i	0.0748972	−	0.129726i
$697$	−10.9645	+	3.99074i	−0.415309	+	0.151160i
$698$	−3.40654	−	19.3195i	−0.128940	−	0.731253i
$699$	−5.49873	+	31.1849i	−0.207981	+	1.17952i
$700$	−13.4980	−	4.91286i	−0.510176	−	0.185689i
$701$	−18.3580	+	15.4042i	−0.693372	+	0.581808i	−0.919879	−	0.392201i	$-0.871714\pi$
$701$	−18.3580	+	15.4042i	−0.693372	+	0.581808i	0.226508	+	0.974009i	$0.427269\pi$
$702$	0.322593			0.0121755
$703$	−18.1893	+	15.0120i	−0.686022	+	0.566189i
$704$	−1.00000			−0.0376889
$705$	9.16713	−	7.69214i	0.345254	−	0.289703i
$706$	29.3241	+	10.6731i	1.10363	+	0.401688i
$707$	−1.44591	+	8.20014i	−0.0543789	+	0.308398i
$708$	−1.77673	−	10.0764i	−0.0667738	−	0.378693i
$709$	40.0208	−	14.5664i	1.50301	−	0.547052i	0.546175	−	0.837671i	$-0.316084\pi$
$709$	40.0208	−	14.5664i	1.50301	−	0.547052i	0.956839	+	0.290619i	$0.0938613\pi$
$710$	−2.07811	+	3.59938i	−0.0779899	+	0.135082i
$711$	−19.5127	−	33.7970i	−0.731783	−	1.26749i
$712$	−6.82333	−	5.72546i	−0.255715	−	0.214571i
$713$	−42.2431	−	35.4461i	−1.58202	−	1.32747i
$714$	6.39295	+	11.0729i	0.239250	+	0.414393i
$715$	0.136405	−	0.236260i	0.00510125	−	0.00883562i
$716$	−7.27946	+	2.64951i	−0.272046	+	0.0990168i
$717$	3.10684	+	17.6198i	0.116027	+	0.658022i
$718$	1.51579	−	8.59646i	0.0565687	−	0.320817i
$719$	−4.21084	−	1.53262i	−0.157038	−	0.0571570i	0.262305	−	0.964985i	$-0.415517\pi$
$719$	−4.21084	−	1.53262i	−0.157038	−	0.0571570i	−0.419343	+	0.907828i	$0.637739\pi$
$720$	−1.47347	+	1.23639i	−0.0549129	+	0.0460774i
$721$	−51.2076			−1.90707
$722$	9.23088	+	16.6070i	0.343538	+	0.618047i
$723$	10.7753			0.400738
$724$	19.0899	−	16.0183i	0.709471	−	0.595317i
$725$	−6.98827	−	2.54352i	−0.259538	−	0.0944641i
$726$	0.412269	−	2.33810i	0.0153007	−	0.0867749i
$727$	−4.09307	−	23.2129i	−0.151803	−	0.860920i	−0.961650	−	0.274279i	$-0.911561\pi$
$727$	−4.09307	−	23.2129i	−0.151803	−	0.860920i	0.809847	−	0.586641i	$-0.199550\pi$
$728$	1.12980	−	0.411212i	0.0418730	−	0.0152405i
$729$	10.0559	−	17.4173i	0.372439	−	0.645084i
$730$	0.205276	+	0.355549i	0.00759761	+	0.0131594i
$731$	−1.38159	−	1.15929i	−0.0511001	−	0.0428781i
$732$	6.95795	+	5.83841i	0.257173	+	0.215794i
$733$	−8.16694	−	14.1456i	−0.301653	−	0.522478i	0.674858	−	0.737948i	$-0.264205\pi$
$733$	−8.16694	−	14.1456i	−0.301653	−	0.522478i	−0.976511	+	0.215470i	$0.930872\pi$
$734$	−6.37249	+	11.0375i	−0.235213	+	0.407401i
$735$	−5.43037	+	1.97649i	−0.200302	+	0.0729040i
$736$	1.22345	+	6.93853i	0.0450970	+	0.255758i
$737$	0.640428	−	3.63205i	0.0235905	−	0.133788i
$738$	17.2587	+	6.28167i	0.635303	+	0.231231i
$739$	25.3086	−	21.2365i	0.930993	−	0.781196i	−0.0450023	−	0.998987i	$-0.514330\pi$
$739$	25.3086	−	21.2365i	0.930993	−	0.781196i	0.975995	+	0.217791i	$0.0698851\pi$
$740$	3.94708			0.145098
$741$	2.98476	−	2.46339i	0.109648	−	0.0904949i
$742$	−36.4915			−1.33964
$743$	−16.5704	+	13.9042i	−0.607909	+	0.510096i	−0.893977	−	0.448113i	$-0.852096\pi$
$743$	−16.5704	+	13.9042i	−0.607909	+	0.510096i	0.286068	+	0.958209i	$0.407652\pi$
$744$	−17.4615	−	6.35547i	−0.640170	−	0.233003i
$745$	1.73823	−	9.85798i	0.0636838	−	0.361168i
$746$	−2.70613	−	15.3472i	−0.0990783	−	0.561901i
$747$	18.7666	−	6.83048i	0.686634	−	0.249914i
$748$	0.837534	−	1.45065i	0.0306233	−	0.0530410i
$749$	23.3917	+	40.5156i	0.854713	+	1.48041i
$750$	12.5617	+	10.5405i	0.458687	+	0.384884i
$751$	34.5969	+	29.0303i	1.26246	+	1.05933i	0.995415	+	0.0956454i	$0.0304915\pi$
$751$	34.5969	+	29.0303i	1.26246	+	1.05933i	0.267044	+	0.963684i	$0.413953\pi$
$752$	−3.45466	−	5.98365i	−0.125979	−	0.218201i
$753$	−26.4988	+	45.8972i	−0.965669	+	1.67259i
$754$	0.584927	−	0.212896i	0.0213018	−	0.00775321i
$755$	1.20624	+	6.84093i	0.0438996	+	0.248967i
$756$	−0.481601	+	2.73129i	−0.0175156	+	0.0993362i
$757$	16.5047	+	6.00723i	0.599874	+	0.218336i	0.624067	−	0.781371i	$-0.285479\pi$
$757$	16.5047	+	6.00723i	0.599874	+	0.218336i	−0.0241926	+	0.999707i	$0.507702\pi$
$758$	−24.3902	+	20.4658i	−0.885893	+	0.743352i
$759$	−16.7273			−0.607164
$760$	0.577651	−	3.12697i	0.0209536	−	0.113427i
$761$	−22.9518			−0.832003			−0.416001	−	0.909364i	$-0.636569\pi$
$761$	−22.9518			−0.832003			−0.416001	+	0.909364i	$0.636569\pi$
$762$	−10.6707	+	8.95378i	−0.386559	+	0.324361i
$763$	−7.59893	−	2.76578i	−0.275100	−	0.100128i
$764$	3.36931	−	19.1083i	0.121897	−	0.691314i
$765$	−0.559486	−	3.17300i	−0.0202282	−	0.114720i
$766$	17.3378	−	6.31045i	0.626440	−	0.228006i
$767$	0.805820	−	1.39572i	0.0290965	−	0.0503966i
$768$	1.18708	+	2.05609i	0.0428351	+	0.0741926i
$769$	34.1848	+	28.6845i	1.23274	+	1.03439i	0.998057	+	0.0623155i	$0.0198485\pi$
$769$	34.1848	+	28.6845i	1.23274	+	1.03439i	0.234679	+	0.972073i	$0.424596\pi$
$770$	1.79670	+	1.50761i	0.0647485	+	0.0543305i
$771$	13.4300	+	23.2614i	0.483669	+	0.837740i
$772$	5.49739	−	9.52176i	0.197855	−	0.342696i
$773$	−4.10369	+	1.49362i	−0.147600	+	0.0537219i	−0.414764	−	0.909929i	$-0.636136\pi$
$773$	−4.10369	+	1.49362i	−0.147600	+	0.0537219i	0.267164	+	0.963651i	$0.413913\pi$
$774$	0.492967	+	2.79575i	0.0177193	+	0.100491i
$775$	−6.07226	+	34.4375i	−0.218122	+	1.23703i
$776$	11.8371	+	4.30834i	0.424926	+	0.154661i
$777$	−31.6370	+	26.5466i	−1.13497	+	0.952355i
$778$	24.5864			0.881464
$779$	−28.6156	+	10.1522i	−1.02526	+	0.363741i
$780$	−0.647694			−0.0231912
$781$	−4.36434	+	3.66212i	−0.156168	+	0.131041i
$782$	−11.0901	−	4.03645i	−0.396580	−	0.144343i
$783$	−0.249338	+	1.41407i	−0.00891061	+	0.0505346i
$784$	0.579388	+	3.28587i	0.0206924	+	0.117353i
$785$	13.0723	−	4.75793i	0.466571	−	0.169818i
$786$	−6.96954	+	12.0716i	−0.248595	+	0.430580i
$787$	−16.6589	−	28.8540i	−0.593824	−	1.02853i	−0.993712	−	0.111970i	$-0.964284\pi$
$787$	−16.6589	−	28.8540i	−0.593824	−	1.02853i	0.399887	−	0.916564i	$-0.369049\pi$
$788$	−4.97053	−	4.17077i	−0.177068	−	0.148578i
$789$	−54.2979	−	45.5614i	−1.93306	−	1.62203i
$790$	−5.39880	−	9.35099i	−0.192081	−	0.332693i
$791$	−22.1283	+	38.3274i	−0.786793	+	1.36276i
$792$	−2.47765	+	0.901789i	−0.0880393	+	0.0320437i
$793$	0.248435	+	1.40895i	0.00882219	+	0.0500331i
$794$	−0.950010	+	5.38778i	−0.0337146	+	0.191205i
$795$	18.4728	+	6.72355i	0.655163	+	0.238460i
$796$	0.251021	−	0.210632i	0.00889720	−	0.00746564i
$797$	−14.4360			−0.511348			−0.255674	−	0.966763i	$-0.582297\pi$
$797$	−14.4360			−0.511348			−0.255674	+	0.966763i	$0.582297\pi$
$798$	16.4008	+	28.9486i	0.580582	+	1.02477i
$799$	11.5736			0.409444
$800$	3.42254	−	2.87185i	0.121005	−	0.101535i
$801$	−22.0690	−	8.03245i	−0.779768	−	0.283813i
$802$	0.00995020	−	0.0564304i	0.000351354	−	0.00199263i
$803$	0.0977249	+	0.554226i	0.00344864	+	0.0195582i
$804$	−8.22804	+	2.99476i	−0.290181	+	0.105617i
$805$	8.26242	−	14.3109i	0.291212	−	0.504394i
$806$	−1.46346	−	2.53479i	−0.0515483	−	0.0892842i
$807$	−2.68813	−	2.25561i	−0.0946266	−	0.0794011i
$808$	−1.98397	−	1.66475i	−0.0697960	−	0.0585658i
$809$	6.65016	+	11.5184i	0.233807	+	0.404966i	0.958925	−	0.283659i	$-0.0915483\pi$
$809$	6.65016	+	11.5184i	0.233807	+	0.404966i	−0.725118	+	0.688624i	$0.758215\pi$
$810$	3.63225	−	6.29124i	0.127624	−	0.221052i
$811$	34.1108	−	12.4153i	1.19779	−	0.435960i	0.335338	−	0.942098i	$-0.391149\pi$
$811$	34.1108	−	12.4153i	1.19779	−	0.435960i	0.862453	+	0.506137i	$0.168927\pi$
$812$	0.929282	+	5.27022i	0.0326114	+	0.184949i
$813$	−3.29039	+	18.6607i	−0.115399	+	0.654460i
$814$	5.08427	+	1.85052i	0.178204	+	0.0648608i
$815$	−2.48677	+	2.08664i	−0.0871076	+	0.0730920i
$816$	−3.97688			−0.139219
$817$	−3.57054	−	3.04591i	−0.124917	−	0.106563i
$818$	−8.04817			−0.281398
$819$	2.42841	−	2.03768i	0.0848555	−	0.0712022i
$820$	4.77517	+	1.73802i	0.166756	+	0.0606943i
$821$	7.14433	−	40.5175i	0.249339	−	1.41407i	−0.560858	−	0.827912i	$-0.689529\pi$
$821$	7.14433	−	40.5175i	0.249339	−	1.41407i	0.810197	−	0.586158i	$-0.199360\pi$
$822$	1.33688	+	7.58182i	0.0466290	+	0.264446i
$823$	2.42309	−	0.881931i	0.0844634	−	0.0307422i	−0.299443	−	0.954114i	$-0.596801\pi$
$823$	2.42309	−	0.881931i	0.0844634	−	0.0307422i	0.383906	+	0.923372i	$0.374579\pi$
$824$	7.96372	−	13.7936i	0.277429	−	0.480522i
$825$	5.30366	+	9.18621i	0.184650	+	0.319823i
$826$	10.6141	+	8.90630i	0.369312	+	0.309890i
$827$	−28.1468	−	23.6180i	−0.978761	−	0.821278i	0.00514069	−	0.999987i	$-0.498364\pi$
$827$	−28.1468	−	23.6180i	−0.978761	−	0.821278i	−0.983902	+	0.178708i	$0.942808\pi$
$828$	9.28837	+	16.0879i	0.322793	+	0.559094i
$829$	−3.51739	+	6.09230i	−0.122164	+	0.211594i	−0.920621	−	0.390458i	$-0.872317\pi$
$829$	−3.51739	+	6.09230i	−0.122164	+	0.211594i	0.798457	+	0.602052i	$0.205650\pi$
$830$	5.19237	−	1.88987i	0.180230	−	0.0655982i
$831$	−6.13736	−	34.8067i	−0.212903	−	1.20743i
$832$	−0.0649376	+	0.368280i	−0.00225131	+	0.0127678i
$833$	−5.25191	−	1.91154i	−0.181968	−	0.0662309i
$834$	3.71312	−	3.11568i	0.128575	−	0.107887i
$835$	−10.5702			−0.365798
$836$	2.21010	−	3.75705i	0.0764380	−	0.129940i
$837$	6.75172			0.233373
$838$	−14.2414	+	11.9500i	−0.491961	+	0.412805i
$839$	48.9197	+	17.8053i	1.68890	+	0.614708i	0.994486	−	0.104870i	$-0.0334427\pi$
$839$	48.9197	+	17.8053i	1.68890	+	0.614708i	0.694411	+	0.719578i	$0.255665\pi$
$840$	0.966946	−	5.48382i	0.0333628	−	0.189210i
$841$	−4.55468	−	25.8309i	−0.157058	−	0.890720i
$842$	−12.5918	+	4.58305i	−0.433943	+	0.157942i
$843$	−29.0691	+	50.3492i	−1.00119	+	1.73412i
$844$	−10.0291	−	17.3709i	−0.345215	−	0.597930i
$845$	7.18676	+	6.03041i	0.247232	+	0.207452i
$846$	−13.9554	−	11.7100i	−0.479797	−	0.402598i
$847$	1.60753	+	2.78432i	0.0552353	+	0.0956703i
$848$	5.67509	−	9.82955i	0.194884	−	0.337548i
$849$	−2.77940	+	1.01162i	−0.0953887	+	0.0347186i
$850$	1.29956	+	7.37019i	0.0445746	+	0.252795i
$851$	6.61956	−	37.5414i	0.226916	−	1.28690i
$852$	12.7105	+	4.62623i	0.435453	+	0.158492i
$853$	1.99211	−	1.67157i	0.0682084	−	0.0572336i	−0.608046	−	0.793902i	$-0.708046\pi$
$853$	1.99211	−	1.67157i	0.0682084	−	0.0572336i	0.676254	+	0.736668i	$0.263602\pi$
$854$	−12.3000			−0.420897
$855$	−1.38865	−	8.26843i	−0.0474908	−	0.282775i
$856$	−14.5514			−0.497355
$857$	−17.1302	+	14.3739i	−0.585155	+	0.491004i	−0.886636	−	0.462469i	$-0.846964\pi$
$857$	−17.1302	+	14.3739i	−0.585155	+	0.491004i	0.301480	+	0.953472i	$0.402519\pi$
$858$	−0.834301	−	0.303661i	−0.0284826	−	0.0103668i
$859$	−9.43869	+	53.5295i	−0.322044	+	1.82640i	0.207638	+	0.978206i	$0.433422\pi$
$859$	−9.43869	+	53.5295i	−0.322044	+	1.82640i	−0.529682	+	0.848196i	$0.677689\pi$
$860$	0.136395	+	0.773533i	0.00465102	+	0.0263772i
$861$	−49.9637	+	18.1853i	−1.70276	+	0.619753i
$862$	−15.8678	+	27.4838i	−0.540458	+	0.936101i
$863$	1.44407	+	2.50120i	0.0491566	+	0.0851418i	0.889557	−	0.456825i	$-0.151013\pi$
$863$	1.44407	+	2.50120i	0.0491566	+	0.0851418i	−0.840400	+	0.541966i	$0.817680\pi$
$864$	−0.660819	−	0.554493i	−0.0224815	−	0.0188642i
$865$	9.92734	+	8.33002i	0.337540	+	0.283229i
$866$	−18.1535	−	31.4428i	−0.616881	−	1.06847i
$867$	−16.8496	+	29.1844i	−0.572243	+	0.991154i
$868$	23.6461	−	8.60647i	0.802601	−	0.292123i
$869$	−2.57018	−	14.5762i	−0.0871875	−	0.494465i
$870$	0.500614	−	2.83913i	0.0169724	−	0.0962554i
$871$	−1.29602	−	0.471713i	−0.0439140	−	0.0159834i
$872$	1.92678	−	1.61676i	0.0652491	−	0.0547505i
$873$	33.2133			1.12410
$874$	−28.7724	−	10.7383i	−0.973240	−	0.363229i
$875$	−22.2060			−0.750701
$876$	1.02353	−	0.858842i	0.0345818	−	0.0290176i
$877$	2.80856	+	1.02223i	0.0948385	+	0.0345184i	0.389004	−	0.921236i	$-0.372819\pi$
$877$	2.80856	+	1.02223i	0.0948385	+	0.0345184i	−0.294165	+	0.955755i	$0.595042\pi$
$878$	−2.45514	+	13.9238i	−0.0828568	+	0.469904i
$879$	12.0267	+	68.2067i	0.405650	+	2.30056i
$880$	−0.685518	+	0.249508i	−0.0231088	+	0.00841092i
$881$	−11.3471	+	19.6537i	−0.382292	+	0.662150i	−0.991390	−	0.130946i	$-0.958199\pi$
$881$	−11.3471	+	19.6537i	−0.382292	+	0.662150i	0.609097	+	0.793096i	$0.291532\pi$
$882$	4.39869	+	7.61875i	0.148111	+	0.256537i
$883$	−17.7068	−	14.8578i	−0.595883	−	0.500005i	0.294236	−	0.955733i	$-0.404935\pi$
$883$	−17.7068	−	14.8578i	−0.595883	−	0.500005i	−0.890119	+	0.455728i	$0.849379\pi$
$884$	−0.479858	−	0.402648i	−0.0161394	−	0.0135425i
$885$	−3.73212	−	6.46422i	−0.125454	−	0.217292i
$886$	−7.50850	+	13.0051i	−0.252253	+	0.436915i
$887$	−36.4434	+	13.2643i	−1.22365	+	0.445372i	−0.871418	−	0.490541i	$-0.836799\pi$
$887$	−36.4434	+	13.2643i	−1.22365	+	0.445372i	−0.352231	+	0.935913i	$0.614577\pi$
$888$	−2.23061	−	12.6504i	−0.0748544	−	0.424520i
$889$	3.27557	−	18.5767i	0.109859	−	0.623041i
$890$	−6.10607	−	2.22243i	−0.204676	−	0.0744959i
$891$	7.62828	−	6.40089i	0.255557	−	0.214438i
$892$	−24.6218			−0.824399
$893$	30.1161	+	0.245143i	1.00780	+	0.00820341i
$894$	−32.5772			−1.08955
$895$	−4.32913	+	3.63257i	−0.144707	+	0.121423i
$896$	−3.02116	−	1.09961i	−0.100930	−	0.0367355i
$897$	−1.08623	+	6.16034i	−0.0362683	+	0.205688i
$898$	1.37288	+	7.78599i	0.0458136	+	0.259822i
$899$	12.2422	−	4.45581i	0.408301	−	0.148610i
$900$	5.89004	−	10.2018i	0.196335	−	0.340062i
$901$	9.50616	+	16.4652i	0.316696	+	0.548534i
$902$	5.33610	+	4.47752i	0.177673	+	0.149085i
$903$	−6.29574	−	5.28276i	−0.209509	−	0.175799i
$904$	−6.88272	−	11.9212i	−0.228916	−	0.396494i
$905$	9.08978	−	15.7440i	0.302154	−	0.523347i
$906$	21.2435	−	7.73202i	0.705770	−	0.256879i
$907$	−9.32347	−	52.8760i	−0.309581	−	1.75572i	−0.601119	−	0.799160i	$-0.705278\pi$
$907$	−9.32347	−	52.8760i	−0.309581	−	1.75572i	0.291538	−	0.956559i	$-0.405833\pi$
$908$	1.04563	−	5.93003i	0.0347003	−	0.196795i
$909$	−6.41684	−	2.33554i	−0.212833	−	0.0774649i
$910$	0.671895	−	0.563787i	0.0222731	−	0.0186894i
$911$	−37.6996			−1.24905			−0.624523	−	0.781007i	$-0.714706\pi$
$911$	−37.6996			−1.24905			−0.624523	+	0.781007i	$0.714706\pi$
$912$	−10.3484	−	0.0842355i	−0.342670	−	0.00278932i
$913$	7.57437			0.250675
$914$	0.0777344	−	0.0652269i	0.00257123	−	0.00215751i
$915$	6.22653	+	2.26627i	0.205843	+	0.0749206i
$916$	0.667405	−	3.78504i	0.0220517	−	0.125061i
$917$	−3.27780	−	18.5893i	−0.108242	−	0.613873i
$918$	1.35783	−	0.494211i	0.0448152	−	0.0163114i
$919$	−20.7219	+	35.8914i	−0.683552	+	1.18395i	0.290337	+	0.956924i	$0.406232\pi$
$919$	−20.7219	+	35.8914i	−0.683552	+	1.18395i	−0.973890	+	0.227023i	$0.927101\pi$
$920$	2.56992	+	4.45123i	0.0847276	+	0.146753i
$921$	−48.5751	−	40.7594i	−1.60060	−	1.34307i
$922$	21.5644	+	18.0947i	0.710187	+	0.595918i
$923$	1.06527	+	1.84511i	0.0350639	+	0.0607324i
$924$	3.81653	−	6.61043i	0.125555	−	0.217467i
$925$	−22.7156	+	8.26779i	−0.746883	+	0.271843i
$926$	−2.67383	−	15.1640i	−0.0878675	−	0.498321i
$927$	7.29239	−	41.3572i	0.239513	−	1.35835i
$928$	−1.56414	−	0.569300i	−0.0513453	−	0.0186882i
$929$	13.9350	−	11.6928i	0.457191	−	0.383629i	−0.384905	−	0.922956i	$-0.625766\pi$
$929$	13.9350	−	11.6928i	0.457191	−	0.383629i	0.842096	+	0.539327i	$0.181321\pi$
$930$	−13.5559			−0.444516
$931$	−13.6257	−	5.08533i	−0.446565	−	0.166665i
$932$	13.3377			0.436892
$933$	38.5558	−	32.3522i	1.26226	−	1.05916i
$934$	6.88098	+	2.50447i	0.225153	+	0.0819488i
$935$	0.212195	−	1.20342i	0.00693952	−	0.0393560i
$936$	0.171218	+	0.971027i	0.00559644	+	0.0317390i
$937$	−51.9390	+	18.9042i	−1.69677	+	0.617575i	−0.995451	−	0.0952713i	$-0.969628\pi$
$937$	−51.9390	+	18.9042i	−1.69677	+	0.617575i	−0.701321	+	0.712846i	$0.747406\pi$
$938$	5.92868	−	10.2688i	0.193578	−	0.335287i
$939$	−6.60509	−	11.4403i	−0.215549	−	0.373342i
$940$	−3.86120	−	3.23993i	−0.125939	−	0.105675i
$941$	22.7097	+	19.0557i	0.740315	+	0.621198i	0.932922	−	0.360078i	$-0.117250\pi$
$941$	22.7097	+	19.0557i	0.740315	+	0.621198i	−0.192608	+	0.981276i	$0.561694\pi$
$942$	−22.6368	−	39.2080i	−0.737546	−	1.27747i
$943$	24.5389	−	42.5027i	0.799098	−	1.38408i
$944$	−4.04974	+	1.47399i	−0.131808	+	0.0479741i
$945$	0.351334	+	1.99251i	0.0114289	+	0.0648165i
$946$	−0.186967	+	1.06034i	−0.00607881	+	0.0344747i
$947$	−0.188932	−	0.0687658i	−0.00613948	−	0.00223459i	0.338949	−	0.940805i	$-0.389929\pi$
$947$	−0.188932	−	0.0687658i	−0.00613948	−	0.00223459i	−0.345088	+	0.938570i	$0.612151\pi$
$948$	−26.9190	+	22.5877i	−0.874288	+	0.733615i
$949$	0.210456			0.00683169
$950$	3.22553	+	19.2058i	0.104650	+	0.623117i
$951$	12.9222			0.419031
$952$	4.12548	−	3.46169i	0.133708	−	0.112194i
$953$	−35.2763	−	12.8395i	−1.14271	−	0.415913i	−0.299819	−	0.953996i	$-0.596926\pi$
$953$	−35.2763	−	12.8395i	−1.14271	−	0.415913i	−0.842891	+	0.538084i	$0.819148\pi$
$954$	5.19669	−	29.4719i	0.168249	−	0.954188i
$955$	−2.45796	−	13.9398i	−0.0795376	−	0.451080i
$956$	7.08147	−	2.57744i	0.229031	−	0.0833605i
$957$	1.97592	−	3.42240i	0.0638725	−	0.110630i
$958$	7.75149	+	13.4260i	0.250439	+	0.433773i
$959$	−7.98644	−	6.70142i	−0.257896	−	0.216400i
$960$	1.32678	+	1.11330i	0.0428215	+	0.0359315i
$961$	−15.1296	−	26.2052i	−0.488051	−	0.845329i
$962$	1.01167	−	1.75227i	0.0326176	−	0.0564953i
$963$	−36.0531	+	13.1223i	−1.16179	+	0.422859i
$964$	−0.788113	−	4.46961i	−0.0253834	−	0.143957i
$965$	1.39280	−	7.89898i	0.0448359	−	0.254277i
$966$	−50.5360	−	18.3936i	−1.62597	−	0.591804i
$967$	41.6782	−	34.9722i	1.34028	−	1.12463i	0.358729	−	0.933442i	$-0.383210\pi$
$967$	41.6782	−	34.9722i	1.34028	−	1.12463i	0.981553	−	0.191188i	$-0.0612341\pi$
$968$	−1.00000			−0.0321412
$969$	8.78933	−	14.9414i	0.282354	−	0.479986i
$970$	9.18950			0.295057
$971$	−6.55982	+	5.50435i	−0.210515	+	0.176643i	−0.741948	−	0.670457i	$-0.766098\pi$
$971$	−6.55982	+	5.50435i	−0.210515	+	0.176643i	0.531433	+	0.847100i	$0.321654\pi$
$972$	−19.7843	−	7.20091i	−0.634583	−	0.230969i
$973$	−1.13981	+	6.46418i	−0.0365406	+	0.207232i
$974$	6.95707	+	39.4555i	0.222919	+	1.26424i
$975$	3.72750	−	1.35670i	0.119376	−	0.0434491i
$976$	1.91287	−	3.31320i	0.0612296	−	0.106053i
$977$	0.603352	+	1.04504i	0.0193029	+	0.0334337i	0.875516	−	0.483190i	$-0.160522\pi$
$977$	0.603352	+	1.04504i	0.0193029	+	0.0334337i	−0.856213	+	0.516624i	$0.827189\pi$
$978$	8.09306	+	6.79088i	0.258787	+	0.217148i
$979$	−6.82333	−	5.72546i	−0.218075	−	0.182986i
$980$	1.21703	+	2.10796i	0.0388767	+	0.0673364i
$981$	3.31590	−	5.74332i	0.105869	−	0.183370i
$982$	27.9363	−	10.1680i	0.891483	−	0.324473i
$983$	−7.03801	−	39.9145i	−0.224478	−	1.27308i	−0.863681	−	0.504038i	$-0.831847\pi$
$983$	−7.03801	−	39.9145i	−0.224478	−	1.27308i	0.639204	−	0.769037i	$-0.279264\pi$
$984$	2.87178	−	16.2867i	0.0915490	−	0.519200i
$985$	−4.44803	−	1.61895i	−0.141726	−	0.0515841i
$986$	2.13587	−	1.79221i	0.0680201	−	0.0570756i
$987$	52.7393			1.67871
$988$	−1.24013	−	1.05791i	−0.0394537	−	0.0336566i
$989$	7.58595			0.241219
$990$	−1.47347	+	1.23639i	−0.0468299	+	0.0392949i
$991$	−34.7729	−	12.6563i	−1.10460	−	0.402041i	−0.275589	−	0.961276i	$-0.588873\pi$
$991$	−34.7729	−	12.6563i	−1.10460	−	0.402041i	−0.829009	+	0.559235i	$0.811095\pi$
$992$	−1.35911	+	7.70792i	−0.0431519	+	0.244727i
$993$	12.0489	+	68.3330i	0.382362	+	2.16848i
$994$	−17.2123	+	6.26476i	−0.545940	+	0.198706i
$995$	0.119525	−	0.207023i	0.00378920	−	0.00656309i
$996$	−8.99140	−	15.5736i	−0.284903	−	0.493467i
$997$	−1.28399	−	1.07740i	−0.0406645	−	0.0341215i	0.622229	−	0.782835i	$-0.286227\pi$
$997$	−1.28399	−	1.07740i	−0.0406645	−	0.0341215i	−0.662893	+	0.748714i	$0.730672\pi$
$998$	9.80836	+	8.23019i	0.310478	+	0.260522i
$999$	2.33368	+	4.04206i	0.0738344	+	0.127885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.j.a.177.4	yes	24
19.4	even	9		7942.2.a.bt.1.1		12
19.15	odd	18		7942.2.a.bx.1.12		12
19.16	even	9	inner	418.2.j.a.111.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.a.111.4	✓	24	19.16	even	9	inner
418.2.j.a.177.4	yes	24	1.1	even	1	trivial
7942.2.a.bt.1.1		12	19.4	even	9
7942.2.a.bx.1.12		12	19.15	odd	18

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.j (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(2.23098 + 0.812012i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.126679 - 0.718430i) q^{5} +(-2.23098 + 0.812012i) q^{6} +(1.60753 - 2.78432i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.01980 + 1.69481i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(2.23098 + 0.812012i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.126679 - 0.718430i) q^{5} +(-2.23098 + 0.812012i) q^{6} +(1.60753 - 2.78432i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.01980 + 1.69481i) q^{9} +(0.558839 + 0.468922i) q^{10} +(0.500000 + 0.866025i) q^{11} +(1.18708 - 2.05609i) q^{12} +(0.351408 - 0.127902i) q^{13} +(0.558288 + 3.16621i) q^{14} +(0.300756 - 1.70567i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.28318 - 1.07671i) q^{17} -2.63666 q^{18} +(3.36181 - 2.77457i) q^{19} -0.729513 q^{20} +(5.84727 - 4.90644i) q^{21} +(-0.939693 - 0.342020i) q^{22} +(-1.22345 + 6.93853i) q^{23} +(0.412269 + 2.33810i) q^{24} +(4.19837 - 1.52808i) q^{25} +(-0.186980 + 0.323860i) q^{26} +(-0.431319 - 0.747067i) q^{27} +(-2.46287 - 2.06660i) q^{28} +(-1.27510 - 1.06993i) q^{29} +(0.865992 + 1.49994i) q^{30} +(-3.91341 + 6.77823i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.412269 + 2.33810i) q^{33} +(-0.290872 + 1.64962i) q^{34} +(-2.20398 - 0.802182i) q^{35} +(2.01980 - 1.69481i) q^{36} -5.41057 q^{37} +(-0.791831 + 4.28637i) q^{38} +0.887845 q^{39} +(0.558839 - 0.468922i) q^{40} +(-6.54570 - 2.38244i) q^{41} +(-1.32547 + 7.51710i) q^{42} +(-0.186967 - 1.06034i) q^{43} +(0.939693 - 0.342020i) q^{44} +(0.961737 - 1.66578i) q^{45} +(-3.52278 - 6.10164i) q^{46} +(5.29285 + 4.44123i) q^{47} +(-1.81872 - 1.52608i) q^{48} +(-1.66828 - 2.88955i) q^{49} +(-2.23391 + 3.86924i) q^{50} +(3.73705 - 1.36017i) q^{51} +(-0.0649376 - 0.368280i) q^{52} +(-1.97094 + 11.1778i) q^{53} +(0.810615 + 0.295040i) q^{54} +(0.558839 - 0.468922i) q^{55} +3.21505 q^{56} +(9.75312 - 3.46021i) q^{57} +1.66452 q^{58} +(3.30138 - 2.77019i) q^{59} +(-1.62753 - 0.592373i) q^{60} +(-0.664334 + 3.76763i) q^{61} +(-1.35911 - 7.70792i) q^{62} +(7.96576 - 2.89930i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.136405 - 0.236260i) q^{65} +(-1.81872 - 1.52608i) q^{66} +(-2.82523 - 2.37065i) q^{67} +(-0.837534 - 1.45065i) q^{68} +(-8.36367 + 14.4863i) q^{69} +(2.20398 - 0.802182i) q^{70} +(0.989315 + 5.61069i) q^{71} +(-0.457851 + 2.59660i) q^{72} +(0.528836 + 0.192481i) q^{73} +(4.14474 - 3.47785i) q^{74} +10.6073 q^{75} +(-2.14865 - 3.79253i) q^{76} +3.21505 q^{77} +(-0.680129 + 0.570696i) q^{78} +(-13.9085 - 5.06227i) q^{79} +(-0.126679 + 0.718430i) q^{80} +(-1.72919 - 9.80673i) q^{81} +(6.54570 - 2.38244i) q^{82} +(3.78718 - 6.55959i) q^{83} +(-3.81653 - 6.61043i) q^{84} +(-0.936094 - 0.785476i) q^{85} +(0.824799 + 0.692088i) q^{86} +(-1.97592 - 3.42240i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-8.37006 + 3.04645i) q^{89} +(0.334008 + 1.89425i) q^{90} +(0.208778 - 1.18404i) q^{91} +(6.62067 + 2.40973i) q^{92} +(-14.2348 + 11.9444i) q^{93} -6.90933 q^{94} +(-2.41921 - 2.06374i) q^{95} +2.37416 q^{96} +(9.64968 - 8.09704i) q^{97} +(3.13534 + 1.14117i) q^{98} +(-0.457851 + 2.59660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{8}+O(q^{10}) \) 24 * q + 12 * q^8	\( 24 q + 12 q^{8} + 12 q^{11} - 3 q^{12} - 3 q^{13} + 3 q^{14} + 27 q^{15} - 6 q^{18} - 21 q^{19} - 18 q^{20} + 15 q^{21} + 9 q^{23} + 36 q^{25} - 21 q^{27} - 3 q^{28} - 9 q^{30} - 27 q^{31} - 9 q^{34} - 45 q^{35} + 18 q^{37} + 9 q^{38} + 36 q^{39} - 18 q^{41} + 39 q^{42} - 48 q^{43} + 36 q^{45} - 18 q^{46} - 9 q^{47} + 6 q^{49} + 3 q^{50} - 18 q^{51} - 3 q^{52} - 36 q^{53} - 45 q^{54} + 18 q^{58} + 9 q^{59} - 9 q^{60} + 15 q^{61} - 33 q^{62} + 87 q^{63} - 12 q^{64} - 36 q^{65} + 33 q^{67} + 9 q^{68} - 18 q^{69} + 45 q^{70} - 9 q^{71} - 3 q^{73} + 3 q^{74} + 42 q^{75} + 9 q^{76} + 12 q^{78} + 15 q^{79} - 108 q^{81} + 18 q^{82} + 36 q^{83} - 9 q^{84} - 99 q^{85} - 33 q^{86} + 63 q^{87} - 12 q^{88} - 27 q^{89} - 36 q^{90} - 21 q^{91} - 9 q^{92} - 21 q^{93} + 54 q^{94} + 18 q^{95} - 6 q^{96} + 45 q^{97} + 39 q^{98}+O(q^{100}) \) 24 * q + 12 * q^8 + 12 * q^11 - 3 * q^12 - 3 * q^13 + 3 * q^14 + 27 * q^15 - 6 * q^18 - 21 * q^19 - 18 * q^20 + 15 * q^21 + 9 * q^23 + 36 * q^25 - 21 * q^27 - 3 * q^28 - 9 * q^30 - 27 * q^31 - 9 * q^34 - 45 * q^35 + 18 * q^37 + 9 * q^38 + 36 * q^39 - 18 * q^41 + 39 * q^42 - 48 * q^43 + 36 * q^45 - 18 * q^46 - 9 * q^47 + 6 * q^49 + 3 * q^50 - 18 * q^51 - 3 * q^52 - 36 * q^53 - 45 * q^54 + 18 * q^58 + 9 * q^59 - 9 * q^60 + 15 * q^61 - 33 * q^62 + 87 * q^63 - 12 * q^64 - 36 * q^65 + 33 * q^67 + 9 * q^68 - 18 * q^69 + 45 * q^70 - 9 * q^71 - 3 * q^73 + 3 * q^74 + 42 * q^75 + 9 * q^76 + 12 * q^78 + 15 * q^79 - 108 * q^81 + 18 * q^82 + 36 * q^83 - 9 * q^84 - 99 * q^85 - 33 * q^86 + 63 * q^87 - 12 * q^88 - 27 * q^89 - 36 * q^90 - 21 * q^91 - 9 * q^92 - 21 * q^93 + 54 * q^94 + 18 * q^95 - 6 * q^96 + 45 * q^97 + 39 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more