LMFDB - Embedded newform 294.2.p.a.131.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(5,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 29]))

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

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

chi := DirichletCharacter("294.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.p (of order $42$, degree $12$, 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:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			131.12
Character	$\chi$	$=$	294.131
Dual form			294.2.p.a.101.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.930874 - 0.365341i) q^{2} +(-1.29829 - 1.14649i) q^{3} +(0.733052 - 0.680173i) q^{4} +(1.59223 - 1.08556i) q^{5} +(-1.62740 - 0.592921i) q^{6} +(1.91180 + 1.82894i) q^{7} +(0.433884 - 0.900969i) q^{8} +(0.371113 + 2.97696i) q^{9} +O(q^{10})$	\(q+(0.930874 - 0.365341i) q^{2} +(-1.29829 - 1.14649i) q^{3} +(0.733052 - 0.680173i) q^{4} +(1.59223 - 1.08556i) q^{5} +(-1.62740 - 0.592921i) q^{6} +(1.91180 + 1.82894i) q^{7} +(0.433884 - 0.900969i) q^{8} +(0.371113 + 2.97696i) q^{9} +(1.08556 - 1.59223i) q^{10} +(0.652132 - 4.32662i) q^{11} +(-1.73153 + 0.0426233i) q^{12} +(-2.72177 - 2.17054i) q^{13} +(2.44783 + 1.00405i) q^{14} +(-3.31176 - 0.416101i) q^{15} +(0.0747301 - 0.997204i) q^{16} +(2.73850 - 0.844714i) q^{17} +(1.43306 + 2.63559i) q^{18} +(-4.83029 - 2.78877i) q^{19} +(0.428815 - 1.87876i) q^{20} +(-0.385212 - 4.56636i) q^{21} +(-0.973637 - 4.26578i) q^{22} +(-1.92503 + 6.24079i) q^{23} +(-1.59626 + 0.672274i) q^{24} +(-0.469963 + 1.19745i) q^{25} +(-3.32661 - 1.02612i) q^{26} +(2.93125 - 4.29043i) q^{27} +(2.64544 + 0.0403496i) q^{28} +(6.29435 + 1.43664i) q^{29} +(-3.23485 + 0.822584i) q^{30} +(-2.87900 + 1.66219i) q^{31} +(-0.294755 - 0.955573i) q^{32} +(-5.80709 + 4.86954i) q^{33} +(2.24059 - 1.78681i) q^{34} +(5.02945 + 0.836703i) q^{35} +(2.29689 + 1.92984i) q^{36} +(7.08497 + 6.57390i) q^{37} +(-5.51524 - 0.831289i) q^{38} +(1.04514 + 5.93847i) q^{39} +(-0.287216 - 1.90555i) q^{40} +(5.79984 + 2.79305i) q^{41} +(-2.02686 - 4.10997i) q^{42} +(-0.565103 + 0.272139i) q^{43} +(-2.46480 - 3.61520i) q^{44} +(3.82257 + 4.33713i) q^{45} +(0.488057 + 6.51267i) q^{46} +(-0.490473 - 1.24971i) q^{47} +(-1.24031 + 1.20898i) q^{48} +(0.309979 + 6.99313i) q^{49} +1.28637i q^{50} +(-4.52382 - 2.04298i) q^{51} +(-3.47154 + 0.260156i) q^{52} +(-3.51633 - 3.78970i) q^{53} +(1.16115 - 5.06475i) q^{54} +(-3.65847 - 7.59688i) q^{55} +(2.47732 - 0.928929i) q^{56} +(3.07381 + 9.15852i) q^{57} +(6.38411 - 0.962250i) q^{58} +(-1.59180 - 1.08527i) q^{59} +(-2.71071 + 1.94754i) q^{60} +(-9.97775 + 10.7535i) q^{61} +(-2.07272 + 2.59910i) q^{62} +(-4.73517 + 6.37010i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-6.68992 - 0.501340i) q^{65} +(-3.62662 + 6.65449i) q^{66} +(2.49630 + 4.32372i) q^{67} +(1.43291 - 2.48187i) q^{68} +(9.65425 - 5.89532i) q^{69} +(4.98746 - 1.05860i) q^{70} +(-8.32433 + 1.89997i) q^{71} +(2.84317 + 0.957292i) q^{72} +(10.7216 + 4.20791i) q^{73} +(8.99693 + 3.53103i) q^{74} +(1.98301 - 1.01582i) q^{75} +(-5.43770 + 1.24112i) q^{76} +(9.15985 - 7.07893i) q^{77} +(3.14246 + 5.14613i) q^{78} +(0.441270 - 0.764303i) q^{79} +(-0.963539 - 1.66890i) q^{80} +(-8.72455 + 2.20957i) q^{81} +(6.41933 + 0.481063i) q^{82} +(-6.56486 - 8.23208i) q^{83} +(-3.38829 - 3.08537i) q^{84} +(3.44332 - 4.31778i) q^{85} +(-0.426616 + 0.459783i) q^{86} +(-6.52479 - 9.08160i) q^{87} +(-3.61520 - 2.46480i) q^{88} +(-1.87383 + 0.282434i) q^{89} +(5.14286 + 2.64078i) q^{90} +(-1.23371 - 9.12758i) q^{91} +(2.83367 + 5.88417i) q^{92} +(5.64346 + 1.14274i) q^{93} +(-0.913137 - 0.984128i) q^{94} +(-10.7183 + 0.803225i) q^{95} +(-0.712879 + 1.57854i) q^{96} -13.3614i q^{97} +(2.84343 + 6.39648i) q^{98} +(13.1222 + 0.335709i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9}+O(q^{10}) $ 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9	$ 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9} + 6 q^{10} - 12 q^{15} + 18 q^{16} - 4 q^{18} - 12 q^{19} + 10 q^{22} - 6 q^{24} + 16 q^{25} - 42 q^{27} + 2 q^{28} + 4 q^{30} + 6 q^{31} + 18 q^{33} - 10 q^{36} - 36 q^{37} + 4 q^{39} - 22 q^{40} + 20 q^{42} + 40 q^{43} - 14 q^{45} - 156 q^{46} - 134 q^{49} - 12 q^{51} + 16 q^{52} - 18 q^{54} - 322 q^{55} - 34 q^{57} - 164 q^{58} - 6 q^{60} + 56 q^{61} - 24 q^{63} + 36 q^{64} - 28 q^{69} - 4 q^{70} + 4 q^{72} - 24 q^{73} + 84 q^{75} + 16 q^{78} + 22 q^{79} - 52 q^{81} + 24 q^{82} + 42 q^{84} + 32 q^{85} - 94 q^{87} - 2 q^{88} + 42 q^{90} - 100 q^{91} - 266 q^{93} - 88 q^{94} - 6 q^{96} + 224 q^{99}+O(q^{100}) $ 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9 + 6 * q^10 - 12 * q^15 + 18 * q^16 - 4 * q^18 - 12 * q^19 + 10 * q^22 - 6 * q^24 + 16 * q^25 - 42 * q^27 + 2 * q^28 + 4 * q^30 + 6 * q^31 + 18 * q^33 - 10 * q^36 - 36 * q^37 + 4 * q^39 - 22 * q^40 + 20 * q^42 + 40 * q^43 - 14 * q^45 - 156 * q^46 - 134 * q^49 - 12 * q^51 + 16 * q^52 - 18 * q^54 - 322 * q^55 - 34 * q^57 - 164 * q^58 - 6 * q^60 + 56 * q^61 - 24 * q^63 + 36 * q^64 - 28 * q^69 - 4 * q^70 + 4 * q^72 - 24 * q^73 + 84 * q^75 + 16 * q^78 + 22 * q^79 - 52 * q^81 + 24 * q^82 + 42 * q^84 + 32 * q^85 - 94 * q^87 - 2 * q^88 + 42 * q^90 - 100 * q^91 - 266 * q^93 - 88 * q^94 - 6 * q^96 + 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{41}{42}\right)$

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 $

$2$	0.930874	−	0.365341i	0.658227	−	0.258335i
$2$	0.930874	−	0.365341i	0.658227	−	0.258335i
$3$	−1.29829	−	1.14649i	−0.749568	−	0.661927i
$3$	−1.29829	−	1.14649i	−0.749568	−	0.661927i
$4$	0.733052	−	0.680173i	0.366526	−	0.340086i
$5$	1.59223	−	1.08556i	0.712066	−	0.485478i	−0.152305	−	0.988334i	$-0.548670\pi$
$5$	1.59223	−	1.08556i	0.712066	−	0.485478i	0.864371	+	0.502855i	$0.167717\pi$
$6$	−1.62740	−	0.592921i	−0.664385	−	0.242059i
$7$	1.91180	+	1.82894i	0.722593	+	0.691273i
$7$	1.91180	+	1.82894i	0.722593	+	0.691273i
$8$	0.433884	−	0.900969i	0.153401	−	0.318541i
$9$	0.371113	+	2.97696i	0.123704	+	0.992319i
$10$	1.08556	−	1.59223i	0.343285	−	0.503506i
$11$	0.652132	−	4.32662i	0.196625	−	1.30452i	−0.644884	−	0.764281i	$-0.723094\pi$
$11$	0.652132	−	4.32662i	0.196625	−	1.30452i	0.841509	−	0.540243i	$-0.181668\pi$
$12$	−1.73153	+	0.0426233i	−0.499849	+	0.0123043i
$13$	−2.72177	−	2.17054i	−0.754882	−	0.601999i	0.168580	−	0.985688i	$-0.446082\pi$
$13$	−2.72177	−	2.17054i	−0.754882	−	0.601999i	−0.923462	+	0.383689i	$0.874653\pi$
$14$	2.44783	+	1.00405i	0.654211	+	0.268344i
$15$	−3.31176	−	0.416101i	−0.855093	−	0.107437i
$16$	0.0747301	−	0.997204i	0.0186825	−	0.249301i
$17$	2.73850	−	0.844714i	0.664183	−	0.204873i	0.0557089	−	0.998447i	$-0.482258\pi$
$17$	2.73850	−	0.844714i	0.664183	−	0.204873i	0.608474	+	0.793574i	$0.291782\pi$
$18$	1.43306	+	2.63559i	0.337776	+	0.621214i
$19$	−4.83029	−	2.78877i	−1.10814	−	0.639787i	−0.169796	−	0.985479i	$-0.554311\pi$
$19$	−4.83029	−	2.78877i	−1.10814	−	0.639787i	−0.938348	+	0.345692i	$0.887644\pi$
$20$	0.428815	−	1.87876i	0.0958860	−	0.420104i
$21$	−0.385212	−	4.56636i	−0.0840602	−	0.996461i
$22$	−0.973637	−	4.26578i	−0.207580	−	0.909468i
$23$	−1.92503	+	6.24079i	−0.401396	+	1.30129i	0.499144	+	0.866519i	$0.333648\pi$
$23$	−1.92503	+	6.24079i	−0.401396	+	1.30129i	−0.900539	+	0.434774i	$0.856828\pi$
$24$	−1.59626	+	0.672274i	−0.325835	+	0.137227i
$25$	−0.469963	+	1.19745i	−0.0939926	+	0.239489i
$26$	−3.32661	−	1.02612i	−0.652401	−	0.201239i
$27$	2.93125	−	4.29043i	0.564119	−	0.825694i
$28$	2.64544	+	0.0403496i	0.499942	+	0.00762536i
$29$	6.29435	+	1.43664i	1.16883	+	0.266778i	0.762525	−	0.646959i	$-0.223959\pi$
$29$	6.29435	+	1.43664i	1.16883	+	0.266778i	0.406306	+	0.913737i	$0.366817\pi$
$30$	−3.23485	+	0.822584i	−0.590600	+	0.150183i
$31$	−2.87900	+	1.66219i	−0.517083	+	0.298538i	−0.735740	−	0.677264i	$-0.763166\pi$
$31$	−2.87900	+	1.66219i	−0.517083	+	0.298538i	0.218657	+	0.975802i	$0.429832\pi$
$32$	−0.294755	−	0.955573i	−0.0521058	−	0.168923i
$33$	−5.80709	+	4.86954i	−1.01088	+	0.847677i
$34$	2.24059	−	1.78681i	0.384257	−	0.306435i
$35$	5.02945	+	0.836703i	0.850132	+	0.141429i
$36$	2.29689	+	1.92984i	0.382815	+	0.321641i
$37$	7.08497	+	6.57390i	1.16476	+	1.08074i	0.995460	+	0.0951775i	$0.0303419\pi$
$37$	7.08497	+	6.57390i	1.16476	+	1.08074i	0.169302	+	0.985564i	$0.445849\pi$
$38$	−5.51524	−	0.831289i	−0.894690	−	0.134853i
$39$	1.04514	+	5.93847i	0.167356	+	0.950916i
$40$	−0.287216	−	1.90555i	−0.0454129	−	0.301295i
$41$	5.79984	+	2.79305i	0.905782	+	0.436202i	0.827974	−	0.560766i	$-0.189493\pi$
$41$	5.79984	+	2.79305i	0.905782	+	0.436202i	0.0778085	+	0.996968i	$0.475208\pi$
$42$	−2.02686	−	4.10997i	−0.312752	−	0.634182i
$43$	−0.565103	+	0.272139i	−0.0861775	+	0.0415009i	−0.476476	−	0.879187i	$-0.658086\pi$
$43$	−0.565103	+	0.272139i	−0.0861775	+	0.0415009i	0.390299	+	0.920688i	$0.372372\pi$
$44$	−2.46480	−	3.61520i	−0.371582	−	0.545011i
$45$	3.82257	+	4.33713i	0.569835	+	0.646541i
$46$	0.488057	+	6.51267i	0.0719602	+	0.960241i
$47$	−0.490473	−	1.24971i	−0.0715429	−	0.182288i	0.890629	−	0.454730i	$-0.150264\pi$
$47$	−0.490473	−	1.24971i	−0.0715429	−	0.182288i	−0.962172	+	0.272441i	$0.912169\pi$
$48$	−1.24031	+	1.20898i	−0.179023	+	0.174502i
$49$	0.309979	+	6.99313i	0.0442827	+	0.999019i
$50$			1.28637i			0.181920i
$51$	−4.52382	−	2.04298i	−0.633462	−	0.286074i
$52$	−3.47154	+	0.260156i	−0.481416	+	0.0360771i
$53$	−3.51633	−	3.78970i	−0.483005	−	0.520555i	0.443786	−	0.896133i	$-0.353635\pi$
$53$	−3.51633	−	3.78970i	−0.483005	−	0.520555i	−0.926791	+	0.375577i	$0.877444\pi$
$54$	1.16115	−	5.06475i	0.158012	−	0.689226i
$55$	−3.65847	−	7.59688i	−0.493307	−	1.02436i
$56$	2.47732	−	0.928929i	0.331045	−	0.124133i
$57$	3.07381	+	9.15852i	0.407137	+	1.21308i
$58$	6.38411	−	0.962250i	0.838275	−	0.126350i
$59$	−1.59180	−	1.08527i	−0.207235	−	0.141290i	0.455255	−	0.890361i	$-0.349548\pi$
$59$	−1.59180	−	1.08527i	−0.207235	−	0.141290i	−0.662490	+	0.749071i	$0.730500\pi$
$60$	−2.71071	+	1.94754i	−0.349951	+	0.251427i
$61$	−9.97775	+	10.7535i	−1.27752	+	1.37684i	−0.386880	+	0.922130i	$0.626447\pi$
$61$	−9.97775	+	10.7535i	−1.27752	+	1.37684i	−0.890640	+	0.454709i	$0.849743\pi$
$62$	−2.07272	+	2.59910i	−0.263235	+	0.330087i
$63$	−4.73517	+	6.37010i	−0.596576	+	0.802557i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	−6.68992	−	0.501340i	−0.829783	−	0.0621836i
$66$	−3.62662	+	6.65449i	−0.446406	+	0.819111i
$67$	2.49630	+	4.32372i	0.304972	+	0.528227i	0.977255	−	0.212067i	$-0.0680196\pi$
$67$	2.49630	+	4.32372i	0.304972	+	0.528227i	−0.672283	+	0.740294i	$0.734686\pi$
$68$	1.43291	−	2.48187i	0.173766	−	0.300971i
$69$	9.65425	−	5.89532i	1.16224	−	0.709713i
$70$	4.98746	−	1.05860i	0.596116	−	0.126527i
$71$	−8.32433	+	1.89997i	−0.987916	+	0.225485i	−0.685804	−	0.727787i	$-0.740549\pi$
$71$	−8.32433	+	1.89997i	−0.987916	+	0.225485i	−0.302113	+	0.953272i	$0.597692\pi$
$72$	2.84317	+	0.957292i	0.335070	+	0.112818i
$73$	10.7216	+	4.20791i	1.25486	+	0.492498i	0.897313	−	0.441395i	$-0.145516\pi$
$73$	10.7216	+	4.20791i	1.25486	+	0.492498i	0.357552	+	0.933893i	$0.383612\pi$
$74$	8.99693	+	3.53103i	1.04587	+	0.410474i
$75$	1.98301	−	1.01582i	0.228978	−	0.117297i
$76$	−5.43770	+	1.24112i	−0.623747	+	0.142366i
$77$	9.15985	−	7.07893i	1.04386	−	0.806718i
$78$	3.14246	+	5.14613i	0.355813	+	0.582685i
$79$	0.441270	−	0.764303i	0.0496468	−	0.0859908i	−0.840134	−	0.542379i	$-0.817524\pi$
$79$	0.441270	−	0.764303i	0.0496468	−	0.0859908i	0.889781	+	0.456388i	$0.150857\pi$
$80$	−0.963539	−	1.66890i	−0.107727	−	0.186589i
$81$	−8.72455	+	2.20957i	−0.969395	+	0.245508i
$82$	6.41933	+	0.481063i	0.708897	+	0.0531245i
$83$	−6.56486	−	8.23208i	−0.720587	−	0.903588i	0.277784	−	0.960644i	$-0.410400\pi$
$83$	−6.56486	−	8.23208i	−0.720587	−	0.903588i	−0.998371	+	0.0570559i	$0.981829\pi$
$84$	−3.38829	−	3.08537i	−0.369693	−	0.336641i
$85$	3.44332	−	4.31778i	0.373480	−	0.468329i
$86$	−0.426616	+	0.459783i	−0.0460032	+	0.0495797i
$87$	−6.52479	−	9.08160i	−0.699531	−	0.973650i
$88$	−3.61520	−	2.46480i	−0.385381	−	0.262748i
$89$	−1.87383	+	0.282434i	−0.198625	+	0.0299379i	−0.247601	−	0.968862i	$-0.579642\pi$
$89$	−1.87383	+	0.282434i	−0.198625	+	0.0299379i	0.0489761	+	0.998800i	$0.484404\pi$
$90$	5.14286	+	2.64078i	0.542105	+	0.278362i
$91$	−1.23371	−	9.12758i	−0.129328	−	0.956830i
$92$	2.83367	+	5.88417i	0.295430	+	0.613467i
$93$	5.64346	+	1.14274i	0.585200	+	0.118497i
$94$	−0.913137	−	0.984128i	−0.0941829	−	0.101505i
$95$	−10.7183	+	0.803225i	−1.09967	+	0.0824092i
$96$	−0.712879	+	1.57854i	−0.0727579	+	0.161110i
$97$		−	13.3614i		−	1.35664i	−0.734765	−	0.678322i	$-0.762707\pi$
$97$		−	13.3614i		−	1.35664i	0.734765	−	0.678322i	$-0.237293\pi$
$98$	2.84343	+	6.39648i	0.287230	+	0.646142i
$99$	13.1222	+	0.335709i	1.31883	+	0.0337400i
$100$	0.469963	+	1.19745i	0.0469963	+	0.119745i
$101$	−0.135976	−	1.81447i	−0.0135301	−	0.180546i	−0.999874	−	0.0158499i	$-0.994955\pi$
$101$	−0.135976	−	1.81447i	−0.0135301	−	0.180546i	0.986344	−	0.164696i	$-0.0526644\pi$
$102$	−4.95749	−	0.249020i	−0.490865	−	0.0246566i
$103$	4.50901	+	6.61350i	0.444286	+	0.651648i	0.981425	−	0.191846i	$-0.0614474\pi$
$103$	4.50901	+	6.61350i	0.444286	+	0.651648i	−0.537139	+	0.843494i	$0.680495\pi$
$104$	−3.13652	+	1.51047i	−0.307561	+	0.148113i
$105$	−5.57041	−	6.85250i	−0.543616	−	0.668736i
$106$	−4.65779	−	2.24307i	−0.452405	−	0.217867i
$107$	1.64012	+	10.8815i	0.158556	+	1.05195i	0.916617	+	0.399767i	$0.130909\pi$
$107$	1.64012	+	10.8815i	0.158556	+	1.05195i	−0.758060	+	0.652184i	$0.773853\pi$
$108$	−0.769479	−	5.13886i	−0.0740431	−	0.494487i
$109$	−15.7605	−	2.37552i	−1.50959	−	0.227533i	−0.658508	−	0.752573i	$-0.728812\pi$
$109$	−15.7605	−	2.37552i	−1.50959	−	0.227533i	−0.851078	+	0.525040i	$0.824050\pi$
$110$	−6.18102	−	5.73515i	−0.589337	−	0.546825i
$111$	−1.66143	−	16.6577i	−0.157696	−	1.58108i
$112$	1.96669	−	1.76978i	0.185835	−	0.167229i
$113$	15.2416	−	12.1547i	1.43381	−	1.14342i	0.468133	−	0.883658i	$-0.344927\pi$
$113$	15.2416	−	12.1547i	1.43381	−	1.14342i	0.965672	−	0.259764i	$-0.0836448\pi$
$114$	6.20731	+	7.40243i	0.581368	+	0.693301i
$115$	3.70968	+	12.0265i	0.345929	+	1.12148i
$116$	5.59125	−	3.22811i	0.519135	−	0.299722i
$117$	5.45151	−	8.90810i	0.503993	−	0.823554i
$118$	−1.87826	−	0.428700i	−0.172908	−	0.0394650i
$119$	6.78039	+	3.39361i	0.621558	+	0.311092i
$120$	−1.81181	+	2.80325i	−0.165395	+	0.255901i
$121$	−7.78302	−	2.40074i	−0.707547	−	0.218249i
$122$	−5.35935	+	13.6554i	−0.485212	+	1.23630i
$123$	−4.32766	−	10.2757i	−0.390212	−	0.926525i
$124$	−0.979878	+	3.17669i	−0.0879957	+	0.285275i
$125$	2.69569	+	11.8106i	0.241110	+	1.05637i
$126$	−2.08059	+	7.65971i	−0.185354	+	0.682381i
$127$	−2.43999	+	10.6903i	−0.216515	+	0.948612i	0.743516	+	0.668718i	$0.233157\pi$
$127$	−2.43999	+	10.6903i	−0.216515	+	0.948612i	−0.960031	+	0.279894i	$0.909701\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	1.04567	+	0.294571i	0.0920664	+	0.0259355i
$130$	−6.41063	+	1.97742i	−0.562250	+	0.173431i
$131$	0.338698	−	4.51961i	0.0295922	−	0.394880i	−0.962666	−	0.270691i	$-0.912748\pi$
$131$	0.338698	−	4.51961i	0.0295922	−	0.394880i	0.992259	−	0.124190i	$-0.0396331\pi$
$132$	−0.944770	+	7.51944i	−0.0822317	+	0.654484i
$133$	−4.13408	−	14.1659i	−0.358470	−	1.22834i
$134$	3.90337	+	3.11284i	0.337200	+	0.268908i
$135$	0.00968006	−	10.0134i	0.000833127	−	0.861815i
$136$	0.427128	−	2.83381i	0.0366259	−	0.242997i
$137$	3.81896	−	5.60138i	0.326276	−	0.478559i	−0.627695	−	0.778460i	$-0.716001\pi$
$137$	3.81896	−	5.60138i	0.326276	−	0.478559i	0.953970	+	0.299901i	$0.0969537\pi$
$138$	6.83309	−	9.01489i	0.581671	−	0.767399i
$139$	−5.52085	+	11.4642i	−0.468272	+	0.972377i	0.524392	+	0.851477i	$0.324293\pi$
$139$	−5.52085	+	11.4642i	−0.468272	+	0.972377i	−0.992665	+	0.120901i	$0.961422\pi$
$140$	4.25595	−	2.80755i	0.359693	−	0.237281i
$141$	−0.796001	+	2.18480i	−0.0670354	+	0.183994i
$142$	−7.05476	+	4.80986i	−0.592023	+	0.403634i
$143$	−11.1660	+	10.3606i	−0.933750	+	0.866394i
$144$	2.99637	−	0.147607i	0.249697	−	0.0123006i
$145$	11.5816	−	4.54544i	0.961799	−	0.377478i
$146$	11.5177			0.953216
$147$	7.61513	−	9.43450i	0.628085	−	0.778145i
$148$	9.66504			0.794461
$149$	−5.61292	+	2.20291i	−0.459829	+	0.180469i	−0.583937	−	0.811799i	$-0.698488\pi$
$149$	−5.61292	+	2.20291i	−0.459829	+	0.180469i	0.124108	+	0.992269i	$0.460393\pi$
$150$	1.47481	−	1.67008i	0.120418	−	0.136361i
$151$	8.00589	−	7.42838i	0.651510	−	0.604513i	−0.283569	−	0.958952i	$-0.591519\pi$
$151$	8.00589	−	7.42838i	0.651510	−	0.604513i	0.935079	+	0.354439i	$0.115328\pi$
$152$	−4.60838	+	3.14194i	−0.373789	+	0.254845i
$153$	3.53097	+	7.83890i	0.285462	+	0.633738i
$154$	5.94045	−	9.93606i	0.478695	−	0.800670i
$155$	−2.77961	+	5.77191i	−0.223263	+	0.463611i
$156$	4.80533	+	3.64233i	0.384734	+	0.291620i
$157$	−13.0248	+	19.1038i	−1.03949	+	1.52465i	−0.201105	+	0.979570i	$0.564453\pi$
$157$	−13.0248	+	19.1038i	−1.03949	+	1.52465i	−0.838384	+	0.545081i	$0.816499\pi$
$158$	0.131536	−	0.872684i	0.0104644	−	0.0694270i
$159$	0.220352	+	8.95157i	0.0174750	+	0.709906i
$160$	−1.50665	−	1.20151i	−0.119111	−	0.0949880i
$161$	−15.0943	+	8.41040i	−1.18960	+	0.662832i
$162$	−7.31421	+	5.24427i	−0.574658	+	0.412029i
$163$	0.985326	−	13.1483i	0.0771767	−	1.02985i	−0.815383	−	0.578922i	$-0.803474\pi$
$163$	0.985326	−	13.1483i	0.0771767	−	1.02985i	0.892560	−	0.450929i	$-0.148907\pi$
$164$	6.15134	−	1.89744i	0.480339	−	0.148165i
$165$	−3.96002	+	14.0574i	−0.308287	+	1.09436i
$166$	−9.11857	−	5.26461i	−0.707738	−	0.408613i
$167$	2.18483	−	9.57234i	0.169067	−	0.740730i	−0.817306	−	0.576204i	$-0.804533\pi$
$167$	2.18483	−	9.57234i	0.169067	−	0.740730i	0.986373	−	0.164526i	$-0.0526095\pi$
$168$	−4.28128	−	1.63420i	−0.330308	−	0.126082i
$169$	−0.195986	−	0.858670i	−0.0150758	−	0.0660515i
$170$	1.62783	−	5.27730i	0.124849	−	0.404750i
$171$	6.50946	−	15.4145i	0.497791	−	1.17878i
$172$	−0.229148	+	0.583860i	−0.0174724	+	0.0445189i
$173$	−9.42829	−	2.90824i	−0.716820	−	0.221110i	−0.0851732	−	0.996366i	$-0.527144\pi$
$173$	−9.42829	−	2.90824i	−0.716820	−	0.221110i	−0.631646	+	0.775257i	$0.717621\pi$
$174$	−9.39163	−	6.07005i	−0.711978	−	0.460169i
$175$	−3.08853	+	1.42975i	−0.233471	+	0.108079i
$176$	−4.26578	−	0.973637i	−0.321546	−	0.0733907i
$177$	0.822363	+	3.23398i	0.0618126	+	0.243081i
$178$	−1.64111	+	0.947495i	−0.123006	+	0.0710178i
$179$	−3.25575	−	10.5549i	−0.243346	−	0.788909i	−0.992032	−	0.125984i	$-0.959791\pi$
$179$	−3.25575	−	10.5549i	−0.243346	−	0.788909i	0.748686	−	0.662925i	$-0.230685\pi$
$180$	5.75213	+	0.579332i	0.428739	+	0.0431809i
$181$	1.06069	−	0.845872i	0.0788405	−	0.0628732i	−0.583277	−	0.812274i	$-0.698230\pi$
$181$	1.06069	−	0.845872i	0.0788405	−	0.0628732i	0.662117	+	0.749400i	$0.269658\pi$
$182$	−4.48310	−	8.04590i	−0.332310	−	0.596402i
$183$	25.2828	−	2.52169i	1.86896	−	0.186409i
$184$	4.78752	+	4.44216i	0.352940	+	0.327481i
$185$	18.4173	+	2.77595i	1.35406	+	0.204092i
$186$	5.67084	−	0.998038i	0.415806	−	0.0731797i
$187$	−1.86889	−	12.3993i	−0.136667	−	0.906726i
$188$	−1.20956	−	0.582492i	−0.0882161	−	0.0424826i
$189$	13.4509	−	2.84139i	0.978408	−	0.206681i
$190$	−9.68393	+	4.66353i	−0.702546	+	0.338328i
$191$	−4.20572	−	6.16866i	−0.304315	−	0.446349i	0.643370	−	0.765556i	$-0.277536\pi$
$191$	−4.20572	−	6.16866i	−0.304315	−	0.446349i	−0.947685	+	0.319207i	$0.896583\pi$
$192$	−0.0868930	+	1.72987i	−0.00627096	+	0.124843i
$193$	−1.05602	−	14.0916i	−0.0760141	−	1.01434i	−0.896608	−	0.442826i	$-0.853976\pi$
$193$	−1.05602	−	14.0916i	−0.0760141	−	1.01434i	0.820594	−	0.571512i	$-0.193643\pi$
$194$	−4.88147	−	12.4378i	−0.350469	−	0.892980i
$195$	8.11068	+	8.32083i	0.580818	+	0.595867i
$196$	4.98377	+	4.91549i	0.355984	+	0.351106i
$197$		−	15.5486i		−	1.10779i	−0.832586	−	0.553896i	$-0.813141\pi$
$197$		−	15.5486i		−	1.10779i	0.832586	−	0.553896i	$-0.186859\pi$
$198$	12.3377	−	4.48156i	0.876804	−	0.318491i
$199$	10.7443	−	0.805177i	0.761646	−	0.0570775i	0.311757	−	0.950162i	$-0.399083\pi$
$199$	10.7443	−	0.805177i	0.761646	−	0.0570775i	0.449889	+	0.893084i	$0.351464\pi$
$200$	0.874953	+	0.942975i	0.0618685	+	0.0666784i
$201$	1.71619	−	8.47543i	0.121051	−	0.597811i
$202$	−0.789475	−	1.63936i	−0.0555473	−	0.115345i
$203$	9.40602	+	14.2585i	0.660173	+	1.00075i
$204$	−4.70577	+	1.57937i	−0.329470	+	0.110578i
$205$	12.2667	−	1.84891i	0.856743	−	0.129133i
$206$	6.61350	+	4.50901i	0.460784	+	0.314157i
$207$	−19.2930	−	3.41469i	−1.34095	−	0.237337i
$208$	−2.36787	+	2.55195i	−0.164182	+	0.176946i
$209$	−15.2159	+	19.0802i	−1.05251	+	1.31980i
$210$	−7.68885	−	4.34372i	−0.530581	−	0.299745i
$211$	−6.01190	−	7.53869i	−0.413876	−	0.518985i	0.530574	−	0.847639i	$-0.321976\pi$
$211$	−6.01190	−	7.53869i	−0.413876	−	0.518985i	−0.944450	+	0.328654i	$0.893405\pi$
$212$	−5.15530	−	0.386336i	−0.354068	−	0.0265337i
$213$	12.9857	+	7.07706i	0.889765	+	0.484912i
$214$	5.50219	+	9.53007i	0.376122	+	0.651462i
$215$	−0.604349	+	1.04676i	−0.0412162	+	0.0713886i
$216$	−2.59372	−	4.50251i	−0.176481	−	0.306357i
$217$	−8.54411	−	2.08773i	−0.580012	−	0.141724i
$218$	−15.5389	+	3.54666i	−1.05243	+	0.240210i
$219$	−9.09537	−	17.7553i	−0.614608	−	1.19979i
$220$	−7.84904	−	3.08052i	−0.529182	−	0.207689i
$221$	−9.28703	−	3.64489i	−0.624714	−	0.245182i
$222$	−7.63232	−	14.8992i	−0.512248	−	0.999970i
$223$	13.9753	−	3.18977i	0.935855	−	0.213603i	0.272712	−	0.962096i	$-0.412079\pi$
$223$	13.9753	−	3.18977i	0.935855	−	0.213603i	0.663143	+	0.748493i	$0.269222\pi$
$224$	1.18417	−	2.36596i	0.0791206	−	0.158082i
$225$	−3.73916	−	0.954673i	−0.249277	−	0.0636449i
$226$	9.74735	−	16.8829i	0.648384	−	1.12303i
$227$	5.18143	+	8.97450i	0.343903	+	0.595658i	0.985154	−	0.171673i	$-0.0549174\pi$
$227$	5.18143	+	8.97450i	0.343903	+	0.595658i	−0.641251	+	0.767332i	$0.721584\pi$
$228$	8.48264	+	4.62294i	0.561776	+	0.306162i
$229$	4.50798	+	0.337827i	0.297896	+	0.0223242i	0.222840	−	0.974855i	$-0.428467\pi$
$229$	4.50798	+	0.337827i	0.297896	+	0.0223242i	0.0750562	+	0.997179i	$0.476086\pi$
$230$	7.84701	+	9.83984i	0.517417	+	0.648820i
$231$	−20.0081	−	1.31120i	−1.31643	−	0.0862708i
$232$	4.02539	−	5.04768i	0.264280	−	0.331396i
$233$	−17.0290	+	18.3529i	−1.11561	+	1.20234i	−0.138325	+	0.990387i	$0.544172\pi$
$233$	−17.0290	+	18.3529i	−1.11561	+	1.20234i	−0.977281	+	0.211950i	$0.932019\pi$
$234$	1.82018	−	10.2840i	0.118989	−	0.672285i
$235$	−2.13758	−	1.45738i	−0.139440	−	0.0950687i
$236$	−1.90504	+	0.287139i	−0.124008	+	0.0186912i
$237$	−1.44916	+	0.486374i	−0.0941333	+	0.0315934i
$238$	7.55152	+	0.681867i	0.489492	+	0.0441989i
$239$	−8.31301	−	17.2621i	−0.537724	−	1.11660i	−0.976003	−	0.217756i	$-0.930126\pi$
$239$	−8.31301	−	17.2621i	−0.537724	−	1.11660i	0.438279	−	0.898839i	$-0.355588\pi$
$240$	−0.662426	+	3.27140i	−0.0427594	+	0.211168i
$241$	−8.23876	−	8.87928i	−0.530705	−	0.571964i	0.409613	−	0.912259i	$-0.365664\pi$
$241$	−8.23876	−	8.87928i	−0.530705	−	0.571964i	−0.940319	+	0.340295i	$0.889473\pi$
$242$	−8.12210	+	0.608667i	−0.522108	+	0.0391266i
$243$	13.8603	+	7.13396i	0.889136	+	0.457644i
$244$			14.6694i			0.939114i
$245$	8.08504	+	10.7982i	0.516534	+	0.689869i
$246$	−7.78262	−	7.98427i	−0.496202	−	0.509059i
$247$	7.09380	+	18.0747i	0.451367	+	1.15007i
$248$	0.248431	+	3.31508i	0.0157754	+	0.210508i
$249$	−0.914916	+	18.2142i	−0.0579804	+	1.15428i
$250$	6.82424	+	10.0093i	0.431603	+	0.633045i
$251$	−7.02560	+	3.38335i	−0.443452	+	0.213555i	−0.642266	−	0.766482i	$-0.722005\pi$
$251$	−7.02560	+	3.38335i	−0.443452	+	0.213555i	0.198814	+	0.980037i	$0.436291\pi$
$252$	0.861638	+	7.89035i	0.0542781	+	0.497045i
$253$	25.7461	+	12.3987i	1.61864	+	0.779498i
$254$	1.63428	+	10.8428i	0.102544	+	0.680335i
$255$	−9.42073	+	1.65800i	−0.589949	+	0.103828i
$256$	−0.988831	−	0.149042i	−0.0618019	−	0.00931514i
$257$	−8.29617	−	7.69772i	−0.517501	−	0.480171i	0.377641	−	0.925952i	$-0.376735\pi$
$257$	−8.29617	−	7.69772i	−0.517501	−	0.480171i	−0.895142	+	0.445781i	$0.852926\pi$
$258$	1.08101	−	0.107819i	0.0673007	−	0.00671254i
$259$	1.52183	+	25.5260i	0.0945621	+	1.58611i
$260$	−5.24506	+	4.18280i	−0.325285	+	0.259406i
$261$	−1.94092	+	19.2712i	−0.120140	+	1.19286i
$262$	−1.33591	−	4.33093i	−0.0825331	−	0.267566i
$263$	21.3092	−	12.3029i	1.31398	−	0.758627i	0.331228	−	0.943551i	$-0.392537\pi$
$263$	21.3092	−	12.3029i	1.31398	−	0.758627i	0.982753	+	0.184924i	$0.0592038\pi$
$264$	1.86770	+	7.34482i	0.114949	+	0.452042i
$265$	−9.71275	−	2.21687i	−0.596649	−	0.136181i
$266$	−9.02368	−	11.6763i	−0.553277	−	0.715919i
$267$	2.75658	+	1.78164i	0.168700	+	0.109035i
$268$	4.77080	+	1.47160i	0.291423	+	0.0898920i
$269$	−3.51543	+	8.95717i	−0.214340	+	0.546128i	−0.997092	−	0.0762047i	$-0.975720\pi$
$269$	−3.51543	+	8.95717i	−0.214340	+	0.546128i	0.782753	+	0.622333i	$0.213815\pi$
$270$	−3.64929	−	9.32474i	−0.222089	−	0.567485i
$271$	−6.15735	+	19.9616i	−0.374032	+	1.21258i	0.551584	+	0.834119i	$0.314024\pi$
$271$	−6.15735	+	19.9616i	−0.374032	+	1.21258i	−0.925616	+	0.378463i	$0.876453\pi$
$272$	−0.637704	−	2.79396i	−0.0386665	−	0.169409i
$273$	−8.86299	+	13.2647i	−0.536412	+	0.802815i
$274$	1.50855	−	6.60940i	0.0911350	−	0.399289i
$275$	4.87441	+	2.81424i	0.293938	+	0.169705i
$276$	3.06723	−	10.8881i	0.184626	−	0.655389i
$277$	30.8897	−	9.52820i	1.85598	−	0.572494i	0.857682	−	0.514180i	$-0.171904\pi$
$277$	30.8897	−	9.52820i	1.85598	−	0.572494i	0.998298	−	0.0583143i	$-0.0185725\pi$
$278$	−0.950885	+	12.6887i	−0.0570303	+	0.761016i
$279$	−6.01670	−	7.95379i	−0.360210	−	0.476181i
$280$	2.93604	−	4.16834i	0.175462	−	0.249106i
$281$	−14.9147	−	11.8941i	−0.889738	−	0.709542i	0.0678463	−	0.997696i	$-0.478387\pi$
$281$	−14.9147	−	11.8941i	−0.889738	−	0.709542i	−0.957584	+	0.288153i	$0.906959\pi$
$282$	0.0572221	+	2.32459i	0.00340753	+	0.138427i
$283$	−0.0602975	+	0.400048i	−0.00358432	+	0.0237804i	−0.990551	−	0.137141i	$-0.956209\pi$
$283$	−0.0602975	+	0.400048i	−0.00358432	+	0.0237804i	0.986967	+	0.160922i	$0.0514467\pi$
$284$	−4.80986	+	7.05476i	−0.285412	+	0.418623i
$285$	14.8363	+	11.2456i	0.878829	+	0.666133i
$286$	−6.60903	+	13.7238i	−0.390800	+	0.811504i
$287$	5.97982	+	15.9473i	0.352978	+	0.941340i
$288$	2.73531	−	1.23210i	0.161180	−	0.0726021i
$289$	−7.26024	+	4.94995i	−0.427073	+	0.291173i
$290$	9.12037	−	8.46247i	0.535566	−	0.496933i
$291$	−15.3187	+	17.3470i	−0.898000	+	1.01690i
$292$	10.7216	−	4.20791i	0.627432	−	0.246249i
$293$	−1.58808			−0.0927765			−0.0463882	−	0.998923i	$-0.514771\pi$
$293$	−1.58808			−0.0927765			−0.0463882	+	0.998923i	$0.514771\pi$
$294$	3.64191	−	11.5644i	0.212401	−	0.674452i
$295$	−3.71263			−0.216158
$296$	8.99693	−	3.53103i	0.522936	−	0.205237i
$297$	−16.6515	−	15.4803i	−0.966217	−	0.898258i
$298$	−4.42011	+	4.10126i	−0.256050	+	0.237580i
$299$	18.7853	−	12.8076i	1.08638	−	0.740684i
$300$	0.762715	−	2.09344i	0.0440353	−	0.120865i
$301$	−1.57809	−	0.513262i	−0.0909597	−	0.0295839i
$302$	4.73858	−	9.83976i	0.272675	−	0.566215i
$303$	−1.90374	+	2.51160i	−0.109367	+	0.144288i
$304$	−3.14194	+	4.60838i	−0.180203	+	0.264309i
$305$	−4.21330	+	27.9534i	−0.241253	+	1.60061i
$306$	6.15076	+	6.00702i	0.351616	+	0.343399i
$307$	6.07033	+	4.84092i	0.346452	+	0.276286i	0.781219	−	0.624257i	$-0.214598\pi$
$307$	6.07033	+	4.84092i	0.346452	+	0.276286i	−0.434767	+	0.900543i	$0.643169\pi$
$308$	1.89976	−	11.4195i	0.108249	−	0.650687i
$309$	1.72833	−	13.7558i	0.0983210	−	0.782539i
$310$	−0.478746	+	6.38843i	−0.0271910	+	0.362838i
$311$	−19.0510	+	5.87646i	−1.08028	+	0.333223i	−0.783290	−	0.621656i	$-0.786460\pi$
$311$	−19.0510	+	5.87646i	−1.08028	+	0.333223i	−0.296993	+	0.954880i	$0.595984\pi$
$312$	5.80385	+	1.63497i	0.328578	+	0.0925618i
$313$	−11.2879	−	6.51706i	−0.638029	−	0.368366i	0.145826	−	0.989310i	$-0.453416\pi$
$313$	−11.2879	−	6.51706i	−0.638029	−	0.368366i	−0.783855	+	0.620944i	$0.786749\pi$
$314$	−5.14500	+	22.5417i	−0.290349	+	1.27210i
$315$	−0.624336	+	15.2830i	−0.0351774	+	0.861097i
$316$	−0.196384	−	0.860414i	−0.0110475	−	0.0484021i
$317$	4.56335	−	14.7940i	0.256303	−	0.830915i	−0.732380	−	0.680896i	$-0.761590\pi$
$317$	4.56335	−	14.7940i	0.256303	−	0.830915i	0.988683	−	0.150019i	$-0.0479334\pi$
$318$	3.47550	+	8.25228i	0.194896	+	0.462765i
$319$	10.3206	−	26.2963i	0.577840	−	1.47231i
$320$	−1.84146	−	0.568016i	−0.102941	−	0.0317531i
$321$	10.3462	−	16.0077i	0.577467	−	0.893462i
$322$	−10.9782	+	13.3436i	−0.611791	+	0.743608i
$323$	−15.5834	−	3.55682i	−0.867086	−	0.197907i
$324$	−4.89266	+	7.55393i	−0.271814	+	0.419663i
$325$	3.87823	−	2.23910i	0.215126	−	0.124203i
$326$	−3.88639	−	12.5994i	−0.215247	−	0.697814i
$327$	17.7382	+	21.1534i	0.980927	+	1.16979i
$328$	5.03291	−	4.01361i	0.277896	−	0.221615i
$329$	1.34794	−	3.28624i	0.0743146	−	0.181176i
$330$	1.44945	+	14.5324i	0.0797898	+	0.799981i
$331$	−4.20048	−	3.89747i	−0.230879	−	0.214224i	0.556246	−	0.831017i	$-0.312241\pi$
$331$	−4.20048	−	3.89747i	−0.230879	−	0.214224i	−0.787125	+	0.616793i	$0.788432\pi$
$332$	−10.4116	−	1.56930i	−0.571412	−	0.0861265i
$333$	−16.9409	+	23.5313i	−0.928355	+	1.28951i
$334$	−1.46337	−	9.70885i	−0.0800722	−	0.531245i
$335$	8.66835	+	4.17446i	0.473602	+	0.228075i
$336$	−4.58237	+	0.0428910i	−0.249989	+	0.00233990i
$337$	−22.0235	+	10.6060i	−1.19970	+	0.577743i	−0.923589	−	0.383383i	$-0.874759\pi$
$337$	−22.0235	+	10.6060i	−1.19970	+	0.577743i	−0.276107	+	0.961127i	$0.589044\pi$
$338$	−0.496145	−	0.727712i	−0.0269868	−	0.0395823i
$339$	−33.7233	−	1.69395i	−1.83160	−	0.0920029i
$340$	−0.412708	−	5.50721i	−0.0223823	−	0.298670i
$341$	5.31417	+	13.5403i	0.287778	+	0.733247i
$342$	0.427936	−	16.7271i	0.0231401	−	0.904500i
$343$	−12.1974	+	13.9364i	−0.658597	+	0.752496i
$344$			0.627217i			0.0338173i
$345$	8.97203	−	19.8670i	0.483038	−	1.06960i
$346$	−9.83905	+	0.737335i	−0.528951	+	0.0396394i
$347$	14.0500	+	15.1423i	0.754246	+	0.812883i	0.987180	−	0.159609i	$-0.0510233\pi$
$347$	14.0500	+	15.1423i	0.754246	+	0.812883i	−0.232935	+	0.972492i	$0.574833\pi$
$348$	−10.9601	−	2.21930i	−0.587521	−	0.118967i
$349$	−3.45435	−	7.17303i	−0.184907	−	0.383964i	0.787824	−	0.615901i	$-0.211208\pi$
$349$	−3.45435	−	7.17303i	−0.184907	−	0.383964i	−0.972731	+	0.231937i	$0.925494\pi$
$350$	−2.35269	+	2.45928i	−0.125756	+	0.131454i
$351$	−17.2907	+	5.31518i	−0.922910	+	0.283703i
$352$	−4.32662	+	0.652132i	−0.230609	+	0.0347588i
$353$	28.1100	+	19.1651i	1.49615	+	1.02006i	0.987241	+	0.159233i	$0.0509023\pi$
$353$	28.1100	+	19.1651i	1.49615	+	1.02006i	0.508906	+	0.860822i	$0.330050\pi$
$354$	1.94702	+	2.70998i	0.103483	+	0.144034i
$355$	−11.1917	+	12.0618i	−0.593993	+	0.640172i
$356$	−1.18151	+	1.48156i	−0.0626198	+	0.0785227i
$357$	−4.91217	−	12.1796i	−0.259980	−	0.644611i
$358$	−6.88682	−	8.63580i	−0.363980	−	0.456416i
$359$	−10.1473	−	0.760433i	−0.535552	−	0.0401341i	−0.195791	−	0.980646i	$-0.562727\pi$
$359$	−10.1473	−	0.760433i	−0.535552	−	0.0401341i	−0.339762	+	0.940512i	$0.610346\pi$
$360$	5.56617	−	1.56221i	0.293363	−	0.0823355i
$361$	6.05446	+	10.4866i	0.318656	+	0.551928i
$362$	0.678337	−	1.17491i	0.0356526	−	0.0617521i
$363$	7.35218	+	12.0400i	0.385890	+	0.631938i
$364$	−7.11270	−	5.85186i	−0.372807	−	0.306721i
$365$	21.6391	−	4.93899i	1.13264	−	0.258518i
$366$	22.6138	−	11.5842i	1.18204	−	0.605516i
$367$	1.79502	+	0.704495i	0.0936994	+	0.0367743i	0.411728	−	0.911307i	$-0.364925\pi$
$367$	1.79502	+	0.704495i	0.0936994	+	0.0367743i	−0.318028	+	0.948081i	$0.603021\pi$
$368$	6.07948	+	2.38602i	0.316915	+	0.124380i
$369$	−6.16241	+	18.3024i	−0.320802	+	0.952785i
$370$	18.1583	−	4.14452i	0.944006	−	0.215463i
$371$	0.208598	−	13.6763i	0.0108299	−	0.710038i
$372$	4.91421	−	3.00084i	0.254790	−	0.155586i
$373$	3.13256	−	5.42575i	0.162198	−	0.280935i	−0.773459	−	0.633847i	$-0.781475\pi$
$373$	3.13256	−	5.42575i	0.162198	−	0.280935i	0.935657	+	0.352912i	$0.114808\pi$
$374$	−6.26967	−	10.8594i	−0.324197	−	0.561526i
$375$	10.0410	−	18.4242i	0.518513	−	0.951420i
$376$	−1.33875	−	0.100326i	−0.0690410	−	0.00517391i
$377$	−14.0135	−	17.5723i	−0.721730	−	0.905021i
$378$	11.4830	−	7.55914i	0.590622	−	0.388800i
$379$	−3.65672	+	4.58538i	−0.187833	+	0.235535i	−0.866827	−	0.498608i	$-0.833845\pi$
$379$	−3.65672	+	4.58538i	−0.187833	+	0.235535i	0.678994	+	0.734143i	$0.262416\pi$
$380$	−7.31074	+	7.87910i	−0.375033	+	0.404189i
$381$	15.4242	−	11.0817i	0.790205	−	0.567732i
$382$	−6.16866	−	4.20572i	−0.315616	−	0.215183i
$383$	5.61543	−	0.846390i	0.286935	−	0.0432485i	−0.00399759	−	0.999992i	$-0.501272\pi$
$383$	5.61543	−	0.846390i	0.286935	−	0.0432485i	0.290933	+	0.956743i	$0.406034\pi$
$384$	0.551106	+	1.64204i	0.0281235	+	0.0837948i
$385$	6.89996	−	21.2148i	0.351654	−	1.08121i
$386$	−6.13128	−	12.7317i	−0.312074	−	0.648028i
$387$	−1.01986	−	1.58129i	−0.0518426	−	0.0803817i
$388$	−9.08806	−	9.79460i	−0.461376	−	0.497245i
$389$	32.8598	−	2.46250i	1.66606	−	0.124854i	0.791949	−	0.610587i	$-0.209067\pi$
$389$	32.8598	−	2.46250i	1.66606	−	0.124854i	0.874107	+	0.485734i	$0.161447\pi$
$390$	10.5900	+	4.78248i	0.536243	+	0.242170i
$391$			18.7165i			0.946532i
$392$	6.43509	+	2.75493i	0.325021	+	0.139145i
$393$	−5.62143	+	5.47945i	−0.283564	+	0.276402i
$394$	−5.68054	−	14.4738i	−0.286181	−	0.729178i
$395$	−0.127095	−	1.69597i	−0.00639486	−	0.0853335i
$396$	9.84757	−	8.67925i	0.494859	−	0.436149i
$397$	−7.80113	−	11.4422i	−0.391527	−	0.574265i	0.578978	−	0.815343i	$-0.303452\pi$
$397$	−7.80113	−	11.4422i	−0.391527	−	0.574265i	−0.970506	+	0.241078i	$0.922499\pi$
$398$	9.70746	−	4.67486i	0.486591	−	0.234330i
$399$	−10.8738	+	23.1311i	−0.544372	+	1.15800i
$400$	1.15898	+	0.558134i	0.0579489	+	0.0279067i
$401$	−3.78241	−	25.0947i	−0.188885	−	1.25317i	−0.859412	−	0.511283i	$-0.829170\pi$
$401$	−3.78241	−	25.0947i	−0.188885	−	1.25317i	0.670528	−	0.741884i	$-0.266068\pi$
$402$	−1.49887	−	8.51655i	−0.0747568	−	0.424767i
$403$	11.4438	+	1.72488i	0.570057	+	0.0859222i
$404$	−1.33383	−	1.23761i	−0.0663604	−	0.0615735i
$405$	−11.4928	+	12.9892i	−0.571084	+	0.645438i
$406$	13.9651	+	9.83650i	0.693074	+	0.488177i
$407$	33.0631	−	26.3669i	1.63887	−	1.30696i
$408$	−3.80347	+	3.18941i	−0.188300	+	0.157899i
$409$	−10.5676	−	34.2594i	−0.522536	−	1.69402i	−0.703641	−	0.710556i	$-0.748444\pi$
$409$	−10.5676	−	34.2594i	−0.522536	−	1.69402i	0.181105	−	0.983464i	$-0.442033\pi$
$410$	10.7433	−	6.20262i	0.530572	−	0.306326i
$411$	−11.3801	+	2.89381i	−0.561337	+	0.142741i
$412$	7.80366	+	1.78113i	0.384459	+	0.0877502i
$413$	−1.05831	−	4.98612i	−0.0520763	−	0.245351i
$414$	−19.2068	+	3.86986i	−0.943964	+	0.190193i
$415$	−19.3892	−	5.98077i	−0.951777	−	0.293584i
$416$	−1.27185	+	3.24062i	−0.0623576	+	0.158885i
$417$	20.3112	−	8.55419i	0.994645	−	0.418901i
$418$	−7.19333	+	23.3202i	−0.351837	+	1.14063i
$419$	1.10027	+	4.82058i	0.0537515	+	0.235501i	0.994667	−	0.103142i	$-0.0328895\pi$
$419$	1.10027	+	4.82058i	0.0537515	+	0.235501i	−0.940915	+	0.338642i	$0.890032\pi$
$420$	−8.74428	−	1.23440i	−0.426677	−	0.0602326i
$421$	−0.589336	+	2.58205i	−0.0287225	+	0.125841i	−0.987257	−	0.159136i	$-0.949129\pi$
$421$	−0.589336	+	2.58205i	−0.0287225	+	0.125841i	0.958534	+	0.284978i	$0.0919862\pi$
$422$	−8.35051	−	4.82117i	−0.406497	−	0.234691i
$423$	3.53830	−	1.92390i	0.172038	−	0.0935432i
$424$	−4.94008	+	1.52381i	−0.239911	+	0.0740029i
$425$	−0.275492	+	3.67619i	−0.0133633	+	0.178321i
$426$	14.6736	+	1.84364i	0.710938	+	0.0893247i
$427$	−38.7429	+	2.30981i	−1.87490	+	0.111780i
$428$	8.60357	+	6.86112i	0.415869	+	0.331645i
$429$	26.3750	−	0.649248i	1.27340	−	0.0313460i
$430$	−0.180147	+	1.19520i	−0.00868746	+	0.0576375i
$431$	11.3493	−	16.6463i	0.546676	−	0.801826i	−0.449116	−	0.893474i	$-0.648261\pi$
$431$	11.3493	−	16.6463i	0.546676	−	0.801826i	0.995792	+	0.0916474i	$0.0292133\pi$
$432$	−4.05938	−	3.24367i	−0.195307	−	0.156061i
$433$	10.6630	−	22.1419i	0.512430	−	1.06407i	−0.470890	−	0.882192i	$-0.656067\pi$
$433$	10.6630	−	22.1419i	0.512430	−	1.06407i	0.983321	−	0.181881i	$-0.0582184\pi$
$434$	−8.71622	+	1.17811i	−0.418392	+	0.0565509i
$435$	−20.2476	−	7.37691i	−0.970797	−	0.353696i
$436$	−13.1691	+	8.97851i	−0.630683	+	0.429993i
$437$	26.7025	−	24.7763i	1.27736	−	1.18521i
$438$	−14.9534	−	13.2050i	−0.714500	−	0.630959i
$439$	29.0552	−	11.4033i	1.38673	−	0.544251i	0.449598	−	0.893231i	$-0.351567\pi$
$439$	29.0552	−	11.4033i	1.38673	−	0.544251i	0.937130	+	0.348980i	$0.113472\pi$
$440$	−8.43190			−0.401975
$441$	−20.7032	+	3.51803i	−0.985868	+	0.167525i
$442$	−9.97668			−0.474543
$443$	−1.95411	+	0.766931i	−0.0928425	+	0.0364380i	−0.411308	−	0.911497i	$-0.634928\pi$
$443$	−1.95411	+	0.766931i	−0.0928425	+	0.0364380i	0.318465	+	0.947935i	$0.396833\pi$
$444$	−12.5480	−	11.0809i	−0.595503	−	0.525876i
$445$	−2.67696	+	2.48385i	−0.126900	+	0.117746i
$446$	11.8439	−	8.07502i	0.560824	−	0.382363i
$447$	9.81282	+	3.57516i	0.464130	+	0.169099i
$448$	0.237931	−	2.63503i	0.0112412	−	0.124494i
$449$	−11.1540	+	23.1615i	−0.526389	+	1.09306i	0.453081	+	0.891470i	$0.350325\pi$
$449$	−11.1540	+	23.1615i	−0.526389	+	1.09306i	−0.979470	+	0.201589i	$0.935389\pi$
$450$	−3.82946	+	0.477388i	−0.180523	+	0.0225043i
$451$	15.8667	−	23.2722i	0.747135	−	1.09585i
$452$	2.90553	−	19.2770i	0.136665	−	0.906711i
$453$	−18.9105	+	0.465502i	−0.888494	+	0.0218712i
$454$	8.10201	+	6.46113i	0.380246	+	0.303236i
$455$	−11.8729	−	13.1939i	−0.556610	−	0.618540i
$456$	9.58522	+	1.20432i	0.448869	+	0.0563975i
$457$	−0.594664	+	7.93524i	−0.0278172	+	0.371195i	0.965871	+	0.259022i	$0.0834001\pi$
$457$	−0.594664	+	7.93524i	−0.0278172	+	0.371195i	−0.993689	+	0.112173i	$0.964219\pi$
$458$	4.31978	−	1.33248i	0.201850	−	0.0622626i
$459$	4.40302	−	14.2254i	0.205515	−	0.663985i
$460$	10.8995	+	6.29281i	0.508191	+	0.293404i
$461$	2.60314	−	11.4051i	0.121240	−	0.531188i	−0.877433	−	0.479699i	$-0.840746\pi$
$461$	2.60314	−	11.4051i	0.121240	−	0.531188i	0.998674	−	0.0514895i	$-0.0163969\pi$
$462$	−19.1040	+	6.08921i	−0.888800	+	0.283296i
$463$	2.35165	+	10.3032i	0.109290	+	0.478832i	0.999719	+	0.0237091i	$0.00754753\pi$
$463$	2.35165	+	10.3032i	0.109290	+	0.478832i	−0.890429	+	0.455123i	$0.849595\pi$
$464$	1.90300	−	6.16939i	0.0883447	−	0.286407i
$465$	10.2262	−	4.30682i	0.474228	−	0.199724i
$466$	−9.14677	+	23.3056i	−0.423716	+	1.07961i
$467$	−13.0995	−	4.04066i	−0.606173	−	0.186980i	−0.0235506	−	0.999723i	$-0.507497\pi$
$467$	−13.0995	−	4.04066i	−0.606173	−	0.186980i	−0.582622	+	0.812743i	$0.697973\pi$
$468$	−2.06280	−	10.2381i	−0.0953531	−	0.473255i
$469$	−3.13538	+	12.8317i	−0.144778	+	0.592512i
$470$	−2.52225	−	0.575688i	−0.116343	−	0.0265545i
$471$	38.8123	−	9.86950i	1.78838	−	0.454763i
$472$	−1.66845	+	0.963280i	−0.0767967	+	0.0443386i
$473$	0.808921	+	2.62246i	0.0371942	+	0.120581i
$474$	−1.17130	+	0.982191i	−0.0537994	+	0.0451135i
$475$	5.60946	−	4.47339i	0.257380	−	0.205253i
$476$	7.27862	−	2.12415i	0.333615	−	0.0973601i
$477$	9.97682	−	11.8744i	0.456807	−	0.543690i
$478$	−14.0449	−	13.0318i	−0.642400	−	0.596060i
$479$	15.9780	+	2.40829i	0.730053	+	0.110038i	0.503542	−	0.863971i	$-0.332030\pi$
$479$	15.9780	+	2.40829i	0.730053	+	0.110038i	0.226511	+	0.974009i	$0.427268\pi$
$480$	0.578543	+	3.28728i	0.0264068	+	0.150043i
$481$	−5.01477	−	33.2708i	−0.228654	−	1.51702i
$482$	−10.9132	−	5.25553i	−0.497083	−	0.239383i
$483$	29.2392	+	6.38633i	1.33043	+	0.290588i
$484$	−7.33828	+	3.53393i	−0.333558	+	0.160633i
$485$	−14.5046	−	21.2744i	−0.658621	−	0.966020i
$486$	15.5085	+	1.57710i	0.703479	+	0.0715386i
$487$	0.158707	+	2.11779i	0.00719168	+	0.0959663i	0.999645	−	0.0266604i	$-0.00848727\pi$
$487$	0.158707	+	2.11779i	0.00719168	+	0.0959663i	−0.992453	+	0.122627i	$0.960868\pi$
$488$	5.35935	+	13.6554i	0.242606	+	0.618151i
$489$	−16.3536	+	15.9406i	−0.739536	+	0.720858i
$490$	11.4712	+	7.09792i	0.518214	+	0.320651i
$491$			37.8718i			1.70913i	0.519344	+	0.854565i	$0.326176\pi$
$491$			37.8718i			1.70913i	−0.519344	+	0.854565i	$0.673824\pi$
$492$	−10.1616	−	4.58904i	−0.458121	−	0.206890i
$493$	18.4506	−	1.38268i	0.830973	−	0.0622729i
$494$	13.2069	+	14.2336i	0.594205	+	0.640400i
$495$	21.2579	−	13.7104i	0.955471	−	0.616237i
$496$	1.44239	+	2.99516i	0.0647654	+	0.134487i
$497$	−19.3894	−	11.5923i	−0.869734	−	0.519986i
$498$	5.80272	+	17.2894i	0.260026	+	0.774755i
$499$	8.70183	−	1.31159i	0.389548	−	0.0587148i	0.0486514	−	0.998816i	$-0.484508\pi$
$499$	8.70183	−	1.31159i	0.389548	−	0.0587148i	0.340896	+	0.940101i	$0.389270\pi$
$500$	10.0093	+	6.82424i	0.447631	+	0.305189i
$501$	−13.8112	+	9.92279i	−0.617037	+	0.443318i
$502$	−5.30387	+	5.71621i	−0.236723	+	0.255127i
$503$	−5.29402	+	6.63849i	−0.236048	+	0.295995i	−0.885720	−	0.464219i	$-0.846335\pi$
$503$	−5.29402	+	6.63849i	−0.236048	+	0.295995i	0.649672	+	0.760215i	$0.274906\pi$
$504$	3.68474	+	7.03013i	0.164132	+	0.313147i
$505$	−2.18622	−	2.74143i	−0.0972855	−	0.121992i
$506$	28.4961	+	2.13549i	1.26681	+	0.0949340i
$507$	−0.730012	+	1.33950i	−0.0324210	+	0.0594892i
$508$	5.48262	+	9.49617i	0.243252	+	0.421325i
$509$	−20.7355	+	35.9149i	−0.919085	+	1.59190i	−0.118277	+	0.992981i	$0.537737\pi$
$509$	−20.7355	+	35.9149i	−0.919085	+	1.59190i	−0.800808	+	0.598921i	$0.795596\pi$
$510$	−8.16378	+	4.98517i	−0.361498	+	0.220747i
$511$	12.8015	+	27.6538i	0.566306	+	1.22333i
$512$	−0.974928	+	0.222521i	−0.0430861	+	0.00983413i
$513$	−26.1238	+	12.5495i	−1.15339	+	0.554072i
$514$	−10.5350	−	4.13467i	−0.464678	−	0.182373i
$515$	14.3587	+	5.63539i	0.632721	+	0.248325i
$516$	0.966892	−	0.495303i	0.0425650	−	0.0218045i
$517$	−5.72685	+	1.30712i	−0.251867	+	0.0574869i
$518$	10.7423	+	23.2055i	0.471990	+	1.01959i
$519$	8.90638	+	14.5852i	0.390947	+	0.640219i
$520$	−3.35434	+	5.80989i	−0.147098	+	0.254781i
$521$	1.87234	+	3.24299i	0.0820287	+	0.142078i	0.904121	−	0.427276i	$-0.140527\pi$
$521$	1.87234	+	3.24299i	0.0820287	+	0.142078i	−0.822092	+	0.569354i	$0.807193\pi$
$522$	5.23380	+	18.6481i	0.229077	+	0.816206i
$523$	19.5290	+	1.46349i	0.853942	+	0.0639941i	0.494505	−	0.869175i	$-0.335349\pi$
$523$	19.5290	+	1.46349i	0.853942	+	0.0639941i	0.359438	+	0.933169i	$0.382969\pi$
$524$	−2.82583	−	3.54348i	−0.123447	−	0.154798i
$525$	5.64900	+	1.68475i	0.246543	+	0.0735284i
$526$	15.3414	−	19.2375i	0.668918	−	0.838796i
$527$	−6.48005	+	6.98383i	−0.282275	+	0.304220i
$528$	4.42196	+	6.15475i	0.192441	+	0.267851i
$529$	−16.2382	−	11.0710i	−0.706008	−	0.481348i
$530$	−9.85126	+	1.48484i	−0.427911	+	0.0644972i
$531$	2.64007	−	5.14148i	0.114569	−	0.223121i
$532$	−12.6657	−	7.57243i	−0.549129	−	0.328306i
$533$	−9.72338	−	20.1908i	−0.421166	−	0.874561i
$534$	3.21693	+	0.651396i	0.139210	+	0.0281887i
$535$	14.4240	+	15.5453i	0.623602	+	0.672083i
$536$	4.97864	−	0.373098i	0.215045	−	0.0161154i
$537$	−7.87418	+	17.4360i	−0.339796	+	0.752418i
$538$			9.62232i			0.414848i
$539$	30.4587	+	3.21929i	1.31195	+	0.138665i
$540$	−6.80374	−	7.34692i	−0.292786	−	0.316161i
$541$	−8.99479	−	22.9183i	−0.386716	−	0.985336i	−0.983171	−	0.182690i	$-0.941520\pi$
$541$	−8.99479	−	22.9183i	−0.386716	−	0.985336i	0.596455	−	0.802647i	$-0.296576\pi$
$542$	1.56109	+	20.8313i	0.0670545	+	0.894781i
$543$	−2.34687	−	0.117886i	−0.100714	−	0.00505895i
$544$	−1.61437	−	2.36785i	−0.0692156	−	0.101521i
$545$	−27.6731	+	13.3267i	−1.18539	+	0.570852i
$546$	−3.40419	+	15.5858i	−0.145686	+	0.667009i
$547$	−24.9951	−	12.0370i	−1.06871	−	0.514665i	−0.185021	−	0.982735i	$-0.559235\pi$
$547$	−24.9951	−	12.0370i	−1.06871	−	0.514665i	−0.883692	+	0.468070i	$0.844950\pi$
$548$	−1.01041	−	6.70366i	−0.0431627	−	0.286366i
$549$	−35.7155	−	25.7126i	−1.52430	−	1.09739i
$550$	5.56562	+	0.838883i	0.237319	+	0.0357701i
$551$	−26.3971	−	24.4929i	−1.12455	−	1.04343i
$552$	−1.12268	−	11.2561i	−0.0477843	−	0.479090i
$553$	2.24148	−	0.654140i	0.0953176	−	0.0278169i
$554$	25.2733	−	20.1548i	1.07376	−	0.856296i
$555$	−20.7283	−	24.7192i	−0.879868	−	1.04927i
$556$	3.75054	+	12.1590i	0.159058	+	0.515655i
$557$	−8.48153	+	4.89681i	−0.359374	+	0.207485i	−0.668806	−	0.743437i	$-0.733194\pi$
$557$	−8.48153	+	4.89681i	−0.359374	+	0.207485i	0.309432	+	0.950922i	$0.399861\pi$
$558$	−8.50664	−	5.20583i	−0.360115	−	0.220380i
$559$	2.12877	+	0.485878i	0.0900373	+	0.0205504i
$560$	1.21021	−	4.95286i	0.0511409	−	0.209296i
$561$	−11.7893	+	18.2405i	−0.497745	+	0.770116i
$562$	−18.2291	−	5.62294i	−0.768949	−	0.237189i
$563$	15.1276	−	38.5446i	0.637554	−	1.62446i	−0.135984	−	0.990711i	$-0.543420\pi$
$563$	15.1276	−	38.5446i	0.637554	−	1.62446i	0.773538	−	0.633750i	$-0.218485\pi$
$564$	0.902534	+	2.14299i	0.0380035	+	0.0902363i
$565$	11.0733	−	35.8988i	0.465857	−	1.51027i
$566$	0.0900246	+	0.394423i	0.00378401	+	0.0165789i
$567$	−20.7208	−	11.7324i	−0.870191	−	0.492714i
$568$	−1.89997	+	8.32433i	−0.0797211	+	0.349281i
$569$	30.5614	+	17.6446i	1.28120	+	0.739701i	0.977068	−	0.212929i	$-0.0683003\pi$
$569$	30.5614	+	17.6446i	1.28120	+	0.739701i	0.304132	+	0.952630i	$0.401634\pi$
$570$	17.9193	+	5.04793i	0.750555	+	0.211434i
$571$	3.70952	−	1.14423i	0.155238	−	0.0478847i	−0.216162	−	0.976358i	$-0.569354\pi$
$571$	3.70952	−	1.14423i	0.155238	−	0.0478847i	0.371400	+	0.928473i	$0.378878\pi$
$572$	−1.13831	+	15.1897i	−0.0475950	+	0.635112i
$573$	−1.61207	+	12.8305i	−0.0673454	+	0.536003i
$574$	11.3927	+	12.6603i	0.475521	+	0.528429i
$575$	−6.56832	−	5.23806i	−0.273918	−	0.218442i
$576$	2.09609	−	2.14625i	0.0873373	−	0.0894271i
$577$	−4.90365	+	32.5336i	−0.204142	+	1.35439i	0.618480	+	0.785801i	$0.287749\pi$
$577$	−4.90365	+	32.5336i	−0.204142	+	1.35439i	−0.822621	+	0.568590i	$0.807489\pi$
$578$	−4.94995	+	7.26024i	−0.205891	+	0.301986i
$579$	−14.7849	+	19.5057i	−0.614440	+	0.810631i
$580$	5.39823	−	11.2095i	0.224149	−	0.465450i
$581$	2.50523	−	27.7448i	0.103934	−	1.15105i
$582$	−7.92225	+	21.7444i	−0.328388	+	0.901334i
$583$	−18.6897	+	12.7424i	−0.774048	+	0.527737i
$584$	8.44311	−	7.83406i	0.349378	−	0.324176i
$585$	−0.990246	−	20.1017i	−0.0409416	−	0.831102i
$586$	−1.47830	+	0.580190i	−0.0610680	+	0.0239674i
$587$	−23.7054			−0.978427			−0.489214	−	0.872164i	$-0.662716\pi$
$587$	−23.7054			−0.978427			−0.489214	+	0.872164i	$0.662716\pi$
$588$	−0.834807	−	12.0956i	−0.0344269	−	0.498813i
$589$	18.5418			0.764004
$590$	−3.45599	+	1.35638i	−0.142281	+	0.0558412i
$591$	−17.8263	+	20.1866i	−0.733277	+	0.830365i
$592$	7.08497	−	6.57390i	0.291191	−	0.270185i
$593$	−1.49423	+	1.01875i	−0.0613605	+	0.0418349i	−0.593612	−	0.804752i	$-0.702299\pi$
$593$	−1.49423	+	1.01875i	−0.0613605	+	0.0418349i	0.532251	+	0.846586i	$0.321346\pi$
$594$	−21.1560	−	8.32674i	−0.868042	−	0.341650i
$595$	14.4799	−	1.95714i	0.593618	−	0.0802349i
$596$	−2.61620	+	5.43260i	−0.107164	+	0.222528i
$597$	−14.8724	−	11.2729i	−0.608686	−	0.461371i
$598$	12.8076	−	18.7853i	0.523743	−	0.768189i
$599$	1.74111	−	11.5515i	0.0711397	−	0.471981i	−0.924688	−	0.380726i	$-0.875674\pi$
$599$	1.74111	−	11.5515i	0.0711397	−	0.471981i	0.995828	−	0.0912549i	$-0.0290878\pi$
$600$	−0.0548292	−	2.22738i	−0.00223839	−	0.0909324i
$601$	−14.0068	−	11.1700i	−0.571349	−	0.455636i	0.294703	−	0.955589i	$-0.404779\pi$
$601$	−14.0068	−	11.1700i	−0.571349	−	0.455636i	−0.866052	+	0.499953i	$0.833351\pi$
$602$	−1.65652	+	0.0987601i	−0.0675147	+	0.00402516i
$603$	−11.9451	+	9.03597i	−0.486443	+	0.367973i
$604$	0.816150	−	10.8908i	0.0332087	−	0.443139i
$605$	−14.9985	+	4.62642i	−0.609775	+	0.188091i
$606$	−0.854548	+	3.03349i	−0.0347136	+	0.123227i
$607$	35.9405	+	20.7502i	1.45878	+	0.842226i	0.998951	−	0.0457817i	$-0.0145779\pi$
$607$	35.9405	+	20.7502i	1.45878	+	0.842226i	0.459828	+	0.888008i	$0.347911\pi$
$608$	−1.24112	+	5.43770i	−0.0503340	+	0.220528i
$609$	4.13557	−	29.2957i	0.167582	−	1.18712i
$610$	6.29048	+	27.5604i	0.254694	+	1.11589i
$611$	−1.37758	+	4.46600i	−0.0557308	+	0.180675i
$612$	7.92019	+	3.34465i	0.320155	+	0.135200i
$613$	−13.7356	+	34.9977i	−0.554775	+	1.41354i	0.328417	+	0.944533i	$0.393485\pi$
$613$	−13.7356	+	34.9977i	−0.554775	+	1.41354i	−0.883192	+	0.469011i	$0.844610\pi$
$614$	7.41930	+	2.28855i	0.299418	+	0.0923584i
$615$	−18.0455	−	11.6632i	−0.727664	−	0.470307i
$616$	−2.40358	−	11.3242i	−0.0968430	−	0.456264i
$617$	−21.6825	−	4.94889i	−0.872905	−	0.199235i	−0.237475	−	0.971394i	$-0.576320\pi$
$617$	−21.6825	−	4.94889i	−0.872905	−	0.199235i	−0.635430	+	0.772159i	$0.719177\pi$
$618$	−3.41670	−	13.4363i	−0.137440	−	0.540488i
$619$	18.5553	−	10.7129i	0.745799	−	0.430587i	−0.0783752	−	0.996924i	$-0.524973\pi$
$619$	18.5553	−	10.7129i	0.745799	−	0.430587i	0.824174	+	0.566337i	$0.191640\pi$
$620$	1.88830	+	6.12172i	0.0758360	+	0.245854i
$621$	21.1329	+	26.5525i	0.848035	+	1.06551i
$622$	−15.5872	+	12.4304i	−0.624988	+	0.498412i
$623$	−4.09894	−	2.88715i	−0.164220	−	0.115671i
$624$	5.99997	−	0.598435i	0.240191	−	0.0239566i
$625$	12.3984	+	11.5040i	0.495936	+	0.460162i
$626$	−12.8885	−	1.94263i	−0.515130	−	0.0776433i
$627$	41.6299	−	7.32664i	1.66254	−	0.292598i
$628$	3.44607	+	22.8632i	0.137513	+	0.912340i
$629$	24.9552	+	12.0178i	0.995031	+	0.479181i
$630$	5.00232	+	14.4546i	0.199297	+	0.575885i
$631$	−28.0413	+	13.5040i	−1.11631	+	0.537585i	−0.898750	−	0.438462i	$-0.855523\pi$
$631$	−28.0413	+	13.5040i	−1.11631	+	0.537585i	−0.217558	+	0.976047i	$0.569809\pi$
$632$	−0.497153	−	0.729190i	−0.0197757	−	0.0290056i
$633$	−0.837853	+	16.6800i	−0.0333017	+	0.662970i
$634$	−1.15696	−	15.4385i	−0.0459487	−	0.613143i
$635$	7.71997	+	19.6702i	0.306358	+	0.780587i
$636$	6.25014	+	6.41209i	0.247834	+	0.254256i
$637$	14.3352	−	19.7065i	0.567980	−	0.780800i
$638$		−	28.2491i		−	1.11839i
$639$	−8.74541	−	24.0761i	−0.345963	−	0.952435i
$640$	−1.92169	+	0.144011i	−0.0759615	+	0.00569252i
$641$	−3.52614	−	3.80027i	−0.139274	−	0.150102i	0.659563	−	0.751649i	$-0.270741\pi$
$641$	−3.52614	−	3.80027i	−0.139274	−	0.150102i	−0.798837	+	0.601548i	$0.794551\pi$
$642$	3.78271	−	18.6810i	0.149292	−	0.737281i
$643$	11.4570	+	23.7908i	0.451822	+	0.938217i	0.995119	+	0.0986773i	$0.0314612\pi$
$643$	11.4570	+	23.7908i	0.451822	+	0.938217i	−0.543298	+	0.839540i	$0.682825\pi$
$644$	−5.34436	+	16.4320i	−0.210597	+	0.647510i
$645$	1.98472	−	0.666120i	0.0781484	−	0.0262285i
$646$	−15.8057	+	2.38232i	−0.621866	+	0.0937312i
$647$	−3.35424	−	2.28689i	−0.131869	−	0.0899067i	0.495589	−	0.868557i	$-0.334952\pi$
$647$	−3.35424	−	2.28689i	−0.131869	−	0.0899067i	−0.627458	+	0.778650i	$0.715905\pi$
$648$	−1.79468	+	8.81925i	−0.0705019	+	0.346453i
$649$	−5.73361	+	6.17936i	−0.225064	+	0.242561i
$650$	2.79211	−	3.50120i	0.109516	−	0.137328i
$651$	8.69918	+	12.5062i	0.340948	+	0.490158i
$652$	−8.22080	−	10.3086i	−0.321951	−	0.403714i
$653$	−7.91203	−	0.592925i	−0.309622	−	0.0232029i	−0.0809867	−	0.996715i	$-0.525807\pi$
$653$	−7.91203	−	0.592925i	−0.309622	−	0.0232029i	−0.228635	+	0.973512i	$0.573426\pi$
$654$	24.2403	+	13.2107i	0.947870	+	0.516579i
$655$	−4.36704	−	7.56393i	−0.170634	−	0.295547i
$656$	3.21867	−	5.57489i	0.125668	−	0.217663i
$657$	−8.54785	+	33.4793i	−0.333483	+	1.30615i
$658$	0.0541697	−	3.55153i	0.00211175	−	0.138453i
$659$	−29.0612	+	6.63302i	−1.13206	+	0.258386i	−0.747207	−	0.664591i	$-0.768606\pi$
$659$	−29.0612	+	6.63302i	−1.13206	+	0.258386i	−0.384855	+	0.922977i	$0.625749\pi$
$660$	6.65853	+	12.9983i	0.259183	+	0.505957i
$661$	17.2684	+	6.77733i	0.671661	+	0.263608i	0.676568	−	0.736380i	$-0.263467\pi$
$661$	17.2684	+	6.77733i	0.671661	+	0.263608i	−0.00490650	+	0.999988i	$0.501562\pi$
$662$	−5.33402	−	2.09345i	−0.207313	−	0.0813642i
$663$	7.87842	+	15.3796i	0.305973	+	0.597296i
$664$	−10.2652	+	2.34297i	−0.398368	+	0.0909249i
$665$	−21.9603	−	18.0675i	−0.851585	−	0.700627i
$666$	−7.17287	+	28.0939i	−0.277943	+	1.08862i
$667$	−21.0826	+	36.5161i	−0.816321	+	1.41391i
$668$	−4.90926	−	8.50308i	−0.189945	−	0.328994i
$669$	−21.8010	−	11.8813i	−0.842877	−	0.459358i
$670$	9.59424	+	0.718989i	0.370658	+	0.0277770i
$671$	40.0193	+	50.1826i	1.54493	+	1.93728i
$672$	−4.24994	+	1.71406i	−0.163945	+	0.0661211i
$673$	24.6297	−	30.8847i	0.949406	−	1.19052i	−0.0321773	−	0.999482i	$-0.510244\pi$
$673$	24.6297	−	30.8847i	0.949406	−	1.19052i	0.981583	−	0.191035i	$-0.0611845\pi$
$674$	−16.6263	+	17.9189i	−0.640421	+	0.690210i
$675$	3.75998	+	5.52636i	0.144722	+	0.212710i
$676$	−0.727712	−	0.496145i	−0.0279889	−	0.0190825i
$677$	11.7201	−	1.76652i	0.450441	−	0.0678931i	0.0800957	−	0.996787i	$-0.474477\pi$
$677$	11.7201	−	1.76652i	0.450441	−	0.0678931i	0.370345	+	0.928894i	$0.379239\pi$
$678$	−32.0110	+	10.7436i	−1.22937	+	0.412607i
$679$	24.4372	−	25.5444i	0.937812	−	0.980302i
$680$	−2.39619	−	4.97574i	−0.0918897	−	0.190811i
$681$	3.56219	−	17.5920i	0.136503	−	0.674125i
$682$	9.89364	+	10.6628i	0.378847	+	0.408300i
$683$	−20.1215	+	1.50790i	−0.769928	+	0.0576981i	−0.453901	−	0.891052i	$-0.649968\pi$
$683$	−20.1215	+	1.50790i	−0.769928	+	0.0576981i	−0.316027	+	0.948750i	$0.602349\pi$
$684$	−5.71276	−	15.7272i	−0.218433	−	0.601344i
$685$		−	13.0644i		−	0.499165i
$686$	−6.26268	+	17.4293i	−0.239110	+	0.665452i
$687$	−5.46535	−	5.60696i	−0.208516	−	0.213919i
$688$	0.229148	+	0.583860i	0.00873620	+	0.0222595i
$689$	1.34494	+	17.9470i	0.0512382	+	0.683726i
$690$	1.09360	−	21.7715i	0.0416328	−	0.828827i
$691$	−26.6365	−	39.0685i	−1.01330	−	1.48624i	−0.867822	−	0.496876i	$-0.834480\pi$
$691$	−26.6365	−	39.0685i	−1.01330	−	1.48624i	−0.145478	−	0.989362i	$-0.546472\pi$
$692$	−8.88953	+	4.28097i	−0.337929	+	0.162738i
$693$	24.4730	+	24.6414i	0.929652	+	0.936050i
$694$	18.6109	+	8.96255i	0.706461	+	0.340214i
$695$	3.65461	+	24.2468i	0.138627	+	0.919732i
$696$	−11.0132	+	1.93827i	−0.417456	+	0.0734700i
$697$	18.2422	+	2.74956i	0.690971	+	0.104147i
$698$	−5.83617	−	5.41517i	−0.220902	−	0.204967i
$699$	43.1500	−	4.30376i	1.63208	−	0.162783i
$700$	−1.29158	+	3.14881i	−0.0488170	+	0.119014i
$701$	28.1255	−	22.4294i	1.06229	−	0.847146i	0.0736226	−	0.997286i	$-0.476544\pi$
$701$	28.1255	−	22.4294i	1.06229	−	0.847146i	0.988665	+	0.150140i	$0.0479726\pi$
$702$	−14.1536	+	11.2648i	−0.534194	+	0.425161i
$703$	−15.8894	−	51.5122i	−0.599280	−	1.94282i
$704$	−3.78928	+	2.18774i	−0.142814	+	0.0824537i
$705$	1.10433	+	4.34281i	0.0415913	+	0.163560i
$706$	33.1687	+	7.57054i	1.24832	+	0.284921i
$707$	3.05859	−	3.71759i	0.115030	−	0.139815i
$708$	2.80250	+	1.81133i	0.105324	+	0.0680738i
$709$	−6.23401	−	1.92294i	−0.234123	−	0.0722175i	0.175473	−	0.984484i	$-0.443854\pi$
$709$	−6.23401	−	1.92294i	−0.234123	−	0.0722175i	−0.409597	+	0.912267i	$0.634331\pi$
$710$	−6.01139	+	15.3168i	−0.225603	+	0.574828i
$711$	2.43906	+	1.03000i	0.0914718	+	0.0386281i
$712$	−0.558558	+	1.81080i	−0.0209329	+	0.0678627i
$713$	−4.83122	−	21.1670i	−0.180931	−	0.792709i
$714$	−9.02230	−	9.54301i	−0.337651	−	0.357138i
$715$	−6.53182	+	28.6178i	−0.244276	+	1.07024i
$716$	−9.56577	−	5.52280i	−0.357490	−	0.206397i
$717$	−8.99821	+	31.9421i	−0.336044	+	1.19290i
$718$	−9.72364	+	2.99935i	−0.362883	+	0.111935i
$719$	−2.03516	+	27.1573i	−0.0758987	+	1.01280i	0.821106	+	0.570776i	$0.193358\pi$
$719$	−2.03516	+	27.1573i	−0.0758987	+	1.01280i	−0.897004	+	0.442021i	$0.854261\pi$
$720$	4.61066	−	3.48776i	0.171829	−	0.129981i
$721$	−3.47534	+	20.8904i	−0.129428	+	0.777999i
$722$	9.46713	+	7.54978i	0.352330	+	0.280974i
$723$	0.516285	+	20.9735i	0.0192008	+	0.780015i
$724$	0.202202	−	1.34152i	0.00751477	−	0.0498572i
$725$	−4.67842	+	6.86198i	−0.173752	+	0.254847i
$726$	11.2427	+	8.52170i	0.417255	+	0.316270i
$727$	−22.2518	+	46.2062i	−0.825272	+	1.71369i	−0.134144	+	0.990962i	$0.542829\pi$
$727$	−22.2518	+	46.2062i	−0.825272	+	1.71369i	−0.691127	+	0.722733i	$0.742886\pi$
$728$	−8.75895	−	2.84878i	−0.324628	−	0.105583i
$729$	−9.81560	−	25.1526i	−0.363541	−	0.931578i
$730$	18.3389	−	12.5032i	0.678752	−	0.462765i
$731$	−1.31765	+	1.22260i	−0.0487352	+	0.0452196i
$732$	16.8184	−	19.0452i	0.621626	−	0.703930i
$733$	12.9345	−	5.07640i	0.477745	−	0.187501i	−0.114235	−	0.993454i	$-0.536442\pi$
$733$	12.9345	−	5.07640i	0.477745	−	0.187501i	0.591980	+	0.805953i	$0.298346\pi$
$734$	1.92832			0.0711756
$735$	1.88328	−	23.2886i	0.0694657	−	0.859012i
$736$	6.53094			0.240734
$737$	20.3350	−	7.98090i	0.749049	−	0.293980i
$738$	0.950193	+	19.2886i	0.0349771	+	0.710024i
$739$	−6.24702	+	5.79639i	−0.229801	+	0.213224i	−0.786666	−	0.617379i	$-0.788194\pi$
$739$	−6.24702	+	5.79639i	−0.229801	+	0.213224i	0.556865	+	0.830603i	$0.312004\pi$
$740$	15.3889	−	10.4920i	0.565708	−	0.385693i
$741$	11.5127	−	31.5992i	0.422929	−	1.16082i
$742$	−4.80234	−	12.8071i	−0.176299	−	0.470164i
$743$	−1.71093	+	3.55278i	−0.0627679	+	0.130339i	−0.929993	−	0.367578i	$-0.880187\pi$
$743$	−1.71093	+	3.55278i	−0.0627679	+	0.130339i	0.867225	+	0.497917i	$0.165901\pi$
$744$	3.47818	−	4.58876i	0.127516	−	0.168232i
$745$	−6.54565	+	9.60071i	−0.239814	+	0.351743i
$746$	0.933768	−	6.19514i	0.0341877	−	0.226820i
$747$	22.0702	−	22.5983i	0.807508	−	0.826830i
$748$	−9.80365	−	7.81815i	−0.358457	−	0.285860i
$749$	−16.7659	+	23.8029i	−0.612614	+	0.869739i
$750$	2.61577	−	20.8189i	0.0955143	−	0.760200i
$751$	−1.63326	+	21.7944i	−0.0595986	+	0.795288i	0.884692	+	0.466176i	$0.154369\pi$
$751$	−1.63326	+	21.7944i	−0.0595986	+	0.795288i	−0.944291	+	0.329113i	$0.893250\pi$
$752$	−1.28286	+	0.395711i	−0.0467812	+	0.0144301i
$753$	13.0002	+	3.66222i	0.473755	+	0.133459i
$754$	−19.4647	−	11.2379i	−0.708861	−	0.409261i
$755$	4.68322	−	20.5185i	0.170440	−	0.746746i
$756$	7.92756	−	11.2318i	0.288323	−	0.408497i
$757$	6.43709	+	28.2027i	0.233960	+	1.02505i	0.946320	+	0.323231i	$0.104769\pi$
$757$	6.43709	+	28.2027i	0.233960	+	1.02505i	−0.712360	+	0.701814i	$0.752374\pi$
$758$	−1.72872	+	5.60436i	−0.0627898	+	0.203560i
$759$	−19.2109	−	45.6148i	−0.697313	−	1.65571i
$760$	−3.92681	+	10.0054i	−0.142440	+	0.362932i
$761$	−30.8662	−	9.52096i	−1.11890	−	0.345134i	−0.320491	−	0.947252i	$-0.603848\pi$
$761$	−30.8662	−	9.52096i	−1.11890	−	0.345134i	−0.798408	+	0.602117i	$0.794324\pi$
$762$	10.3094	−	15.9507i	0.373469	−	0.577834i
$763$	−25.7864	−	33.3666i	−0.933529	−	1.20795i
$764$	−7.27877	−	1.66133i	−0.263337	−	0.0601048i
$765$	14.1317	+	8.64823i	0.510933	+	0.312677i
$766$	4.91804	−	2.83943i	0.177696	−	0.102593i
$767$	1.97689	+	6.40891i	0.0713813	+	0.231412i
$768$	1.11291	+	1.32719i	0.0401588	+	0.0478907i
$769$	−25.5985	+	20.4141i	−0.923106	+	0.736153i	−0.964802	−	0.262978i	$-0.915295\pi$
$769$	−25.5985	+	20.4141i	−0.923106	+	0.736153i	0.0416958	+	0.999130i	$0.486724\pi$
$770$	−1.32767	−	22.2692i	−0.0478458	−	0.802526i
$771$	1.94546	+	19.5054i	0.0700640	+	0.702469i
$772$	−10.3589	−	9.61162i	−0.372824	−	0.345930i
$773$	−35.0834	−	5.28798i	−1.26186	−	0.190195i	−0.516171	−	0.856486i	$-0.672643\pi$
$773$	−35.0834	−	5.28798i	−1.26186	−	0.190195i	−0.745692	+	0.666290i	$0.767881\pi$
$774$	−1.52708	−	1.09939i	−0.0548896	−	0.0395167i
$775$	−0.637361	−	4.22861i	−0.0228947	−	0.151896i
$776$	−12.0382	−	5.79729i	−0.432146	−	0.208111i
$777$	27.2895	−	34.8849i	0.979006	−	1.25149i
$778$	29.6886	−	14.2973i	1.06439	−	0.512583i
$779$	−20.2257	−	29.6657i	−0.724661	−	1.06288i
$780$	11.6051	+	0.582938i	0.415531	+	0.0208725i
$781$	2.79189	+	37.2552i	0.0999018	+	1.33310i
$782$	6.83789	+	17.4227i	0.244523	+	0.623033i
$783$	24.6141	−	22.7943i	0.879636	−	0.814602i
$784$	6.99674	+	0.213485i	0.249884	+	0.00762447i
$785$			44.5568i			1.59030i
$786$	−3.23097	+	7.15442i	−0.115245	+	0.255190i
$787$	37.5911	−	2.81706i	1.33998	−	0.100417i	0.614638	−	0.788810i	$-0.289302\pi$
$787$	37.5911	−	2.81706i	1.33998	−	0.100417i	0.725339	+	0.688392i	$0.241683\pi$
$788$	−10.5757	−	11.3979i	−0.376745	−	0.406034i
$789$	−41.7706	−	8.45813i	−1.48707	−	0.301117i
$790$	−0.737917	−	1.53230i	−0.0262539	−	0.0545168i
$791$	51.3691	+	4.63839i	1.82648	+	0.164922i
$792$	5.99596	−	11.6770i	0.213057	−	0.414924i
$793$	50.4979	−	7.61133i	1.79323	−	0.270286i
$794$	−11.4422	−	7.80113i	−0.406067	−	0.276852i
$795$	10.0683	+	14.0137i	0.357087	+	0.497016i
$796$	7.32850	−	7.89824i	0.259752	−	0.279946i
$797$	−12.0240	+	15.0777i	−0.425913	+	0.534078i	−0.947770	−	0.318955i	$-0.896668\pi$
$797$	−12.0240	+	15.0777i	−0.425913	+	0.534078i	0.521857	+	0.853033i	$0.325240\pi$
$798$	−1.67142	+	25.5048i	−0.0591677	+	0.902859i
$799$	−2.39880	−	3.00800i	−0.0848636	−	0.106416i
$800$	1.28277	+	0.0961304i	0.0453528	+	0.00339872i
$801$	−1.53619	−	5.47348i	−0.0542787	−	0.193396i
$802$	−12.6891	−	21.9781i	−0.448066	−	0.776073i
$803$	25.1979	−	43.6440i	0.889214	−	1.54016i
$804$	−4.50670	−	7.38024i	−0.158939	−	0.260281i
$805$	−14.9035	+	29.7770i	−0.525280	+	1.04950i
$806$	11.2829	−	2.57525i	0.397423	−	0.0907093i
$807$	14.8334	−	7.59859i	0.522159	−	0.267483i
$808$	−1.69378	−	0.664758i	−0.0595868	−	0.0233861i
$809$	−12.3665	−	4.85349i	−0.434783	−	0.170640i	0.137847	−	0.990453i	$-0.455982\pi$
$809$	−12.3665	−	4.85349i	−0.434783	−	0.170640i	−0.572630	+	0.819814i	$0.694077\pi$
$810$	−5.95290	+	16.2901i	−0.209164	+	0.572376i
$811$	7.11354	−	1.62362i	0.249790	−	0.0570130i	−0.0957923	−	0.995401i	$-0.530538\pi$
$811$	7.11354	−	1.62362i	0.249790	−	0.0570130i	0.345583	+	0.938388i	$0.387681\pi$
$812$	16.5934	+	4.05454i	0.582313	+	0.142286i
$813$	30.8799	−	18.8566i	1.08300	−	0.661331i
$814$	21.1446	−	36.6236i	0.741118	−	1.28365i
$815$	−12.7044	−	22.0047i	−0.445015	−	0.770789i
$816$	−2.37533	+	4.35850i	−0.0831533	+	0.152578i
$817$	3.48855	+	0.261430i	0.122049	+	0.00914629i
$818$	−22.3535	−	28.0304i	−0.781572	−	0.980060i
$819$	26.7146	−	7.06005i	0.933483	−	0.246698i
$820$	7.73455	−	9.69881i	0.270102	−	0.338697i
$821$	24.8438	−	26.7753i	0.867056	−	0.934464i	−0.131325	−	0.991339i	$-0.541923\pi$
$821$	24.8438	−	26.7753i	0.867056	−	0.934464i	0.998381	+	0.0568749i	$0.0181136\pi$
$822$	−9.53617	+	6.85138i	−0.332612	+	0.238969i
$823$	−12.0266	−	8.19959i	−0.419221	−	0.285820i	0.335281	−	0.942118i	$-0.391169\pi$
$823$	−12.0266	−	8.19959i	−0.419221	−	0.285820i	−0.754501	+	0.656298i	$0.772121\pi$
$824$	7.91494	−	1.19299i	0.275730	−	0.0415596i
$825$	−3.10189	−	9.24218i	−0.107994	−	0.321771i
$826$	−2.80679	−	4.25481i	−0.0976608	−	0.148044i
$827$	24.2131	+	50.2790i	0.841972	+	1.74837i	0.639029	+	0.769182i	$0.279336\pi$
$827$	24.2131	+	50.2790i	0.841972	+	1.74837i	0.202943	+	0.979191i	$0.434950\pi$
$828$	−16.4653	+	10.6194i	−0.572209	+	0.369050i
$829$	−13.4501	−	14.4958i	−0.467142	−	0.503460i	0.454903	−	0.890541i	$-0.349674\pi$
$829$	−13.4501	−	14.4958i	−0.467142	−	0.503460i	−0.922046	+	0.387081i	$0.873483\pi$
$830$	−20.2339	+	1.51632i	−0.702329	+	0.0526323i
$831$	−51.0278	−	23.0444i	−1.77013	−	0.799401i
$832$			3.48127i			0.120691i
$833$	6.75608	+	18.8888i	0.234084	+	0.654459i
$834$	15.7820	−	15.3834i	0.546486	−	0.532684i
$835$	−6.91264	−	17.6131i	−0.239222	−	0.609527i
$836$	1.82375	+	24.3362i	0.0630756	+	0.841685i
$837$	−1.30754	+	17.2244i	−0.0451951	+	0.595363i
$838$	2.78536	+	4.08538i	0.0962188	+	0.141127i
$839$	20.9854	−	10.1060i	0.724496	−	0.348899i	−0.0350208	−	0.999387i	$-0.511150\pi$
$839$	20.9854	−	10.1060i	0.724496	−	0.348899i	0.759517	+	0.650488i	$0.225435\pi$
$840$	−8.59080	+	2.04557i	−0.296411	+	0.0705790i
$841$	11.4268	+	5.50285i	0.394027	+	0.189753i
$842$	0.394731	+	2.61887i	0.0136033	+	0.0902522i
$843$	5.72715	+	32.5416i	0.197254	+	1.12079i
$844$	−9.53465	−	1.43712i	−0.328196	−	0.0494676i
$845$	−1.24419	−	1.15444i	−0.0428015	−	0.0397140i
$846$	2.59083	−	3.08359i	0.0890746	−	0.106016i
$847$	−10.4888	−	18.8244i	−0.360399	−	0.646814i
$848$	−4.04188	+	3.22329i	−0.138799	+	0.110688i
$849$	0.536935	−	0.450248i	0.0184276	−	0.0154525i
$850$	1.08661	+	3.52272i	0.0372706	+	0.120828i
$851$	−54.6650	+	31.5609i	−1.87389	+	1.08189i
$852$	14.3328	−	3.64467i	0.491034	−	0.124864i
$853$	−7.59657	−	1.73387i	−0.260102	−	0.0593665i	0.0904815	−	0.995898i	$-0.471159\pi$
$853$	−7.59657	−	1.73387i	−0.260102	−	0.0593665i	−0.350583	+	0.936532i	$0.614017\pi$
$854$	−35.2209	+	16.3045i	−1.20523	+	0.557929i
$855$	−6.36886	−	31.6098i	−0.217810	−	1.08103i
$856$	10.5155	+	3.24360i	0.359412	+	0.110864i
$857$	−5.72719	+	14.5926i	−0.195637	+	0.498475i	−0.994706	−	0.102765i	$-0.967231\pi$
$857$	−5.72719	+	14.5926i	−0.195637	+	0.498475i	0.799069	+	0.601240i	$0.205326\pi$
$858$	24.3146	−	10.2403i	0.830088	−	0.349597i
$859$	−4.67335	+	15.1506i	−0.159453	+	0.516933i	−0.999680	−	0.0253017i	$-0.991945\pi$
$859$	−4.67335	+	15.1506i	−0.159453	+	0.516933i	0.840227	+	0.542234i	$0.182422\pi$
$860$	0.268960	+	1.17839i	0.00917148	+	0.0401829i
$861$	10.5199	−	27.5600i	0.358518	−	0.939244i
$862$	4.48316	−	19.6420i	0.152697	−	0.669009i
$863$	30.8196	+	17.7937i	1.04911	+	0.605704i	0.922400	−	0.386236i	$-0.126225\pi$
$863$	30.8196	+	17.7937i	1.04911	+	0.605704i	0.126710	+	0.991940i	$0.459558\pi$
$864$	−4.96382	−	1.53639i	−0.168873	−	0.0522691i
$865$	−18.1691	+	5.60441i	−0.617766	+	0.190556i
$866$	1.83654	−	24.5069i	0.0624082	−	0.832780i
$867$	15.1010	+	1.89734i	0.512856	+	0.0644370i
$868$	−7.68329	+	4.28106i	−0.260788	+	0.145309i
$869$	−3.01908	−	2.40763i	−0.102415	−	0.0816734i
$870$	−21.5430	+	0.530303i	−0.730377	+	0.0179790i
$871$	2.59044	−	17.1865i	0.0877739	−	0.582342i
$872$	−8.97851	+	13.1691i	−0.304051	+	0.445961i
$873$	39.7763	−	4.95858i	1.34622	−	0.167823i
$874$	15.8049	−	32.8192i	0.534608	−	1.11013i
$875$	−16.4472	+	27.5098i	−0.556017	+	0.930000i
$876$	−18.7440	−	6.82911i	−0.633302	−	0.230734i
$877$	3.08771	−	2.10516i	0.104265	−	0.0710864i	−0.510065	−	0.860136i	$-0.670379\pi$
$877$	3.08771	−	2.10516i	0.104265	−	0.0710864i	0.614330	+	0.789049i	$0.289426\pi$
$878$	22.8806	−	21.2301i	0.772183	−	0.716481i
$879$	2.06178	+	1.82072i	0.0695423	+	0.0614113i
$880$	−7.84904	+	3.08052i	−0.264591	+	0.103844i
$881$	21.4542			0.722809			0.361405	−	0.932409i	$-0.382297\pi$
$881$	21.4542			0.722809			0.361405	+	0.932409i	$0.382297\pi$
$882$	−17.9868	+	10.8386i	−0.605647	+	0.364954i
$883$	−37.6383			−1.26663			−0.633314	−	0.773895i	$-0.718306\pi$
$883$	−37.6383			−1.26663			−0.633314	+	0.773895i	$0.718306\pi$
$884$	−9.28703	+	3.64489i	−0.312357	+	0.122591i
$885$	4.82007	+	4.25650i	0.162025	+	0.143081i
$886$	−1.53884	+	1.42783i	−0.0516982	+	0.0479689i
$887$	23.1343	−	15.7727i	0.776775	−	0.529596i	−0.108816	−	0.994062i	$-0.534706\pi$
$887$	23.1343	−	15.7727i	0.776775	−	0.529596i	0.885591	+	0.464466i	$0.153754\pi$
$888$	−15.7289	−	5.73060i	−0.527828	−	0.192306i
$889$	−24.2167	+	15.9752i	−0.812202	+	0.535790i
$890$	−1.58445	+	3.29015i	−0.0531110	+	0.110286i
$891$	3.87041	+	39.1887i	0.129664	+	1.31287i
$892$	8.07502	−	11.8439i	0.270372	−	0.396563i
$893$	−1.11601	+	7.40426i	−0.0373459	+	0.247774i
$894$	10.4406	−	0.257007i	0.349187	−	0.00859560i
$895$	−16.6419	−	13.2714i	−0.556276	−	0.443616i
$896$	−0.741201	−	2.53981i	−0.0247618	−	0.0848490i
$897$	−39.0726	−	4.90923i	−1.30460	−	0.163914i
$898$	−1.92111	+	25.6354i	−0.0641083	+	0.855466i
$899$	−20.5094	+	6.32631i	−0.684026	+	0.210994i
$900$	−3.39034	+	1.84345i	−0.113011	+	0.0614483i
$901$	−12.8307	−	7.40779i	−0.427452	−	0.246789i
$902$	6.26763	−	27.4603i	0.208689	−	0.914327i
$903$	1.46037	+	2.47563i	0.0485981	+	0.0823839i
$904$	−4.33798	−	19.0059i	−0.144279	−	0.632127i
$905$	0.770613	−	2.49827i	0.0256160	−	0.0830452i
$906$	−17.4333	+	7.34212i	−0.579181	+	0.243926i
$907$	−10.0690	+	25.6553i	−0.334334	+	0.851870i	0.660544	+	0.750787i	$0.270326\pi$
$907$	−10.0690	+	25.6553i	−0.334334	+	0.851870i	−0.994878	+	0.101082i	$0.967769\pi$
$908$	9.90246	+	3.05450i	0.328625	+	0.101367i
$909$	5.35113	−	1.07817i	0.177486	−	0.0357605i
$910$	−15.8724	−	7.94421i	−0.526166	−	0.263348i
$911$	−32.5895	−	7.43834i	−1.07974	−	0.246443i	−0.354580	−	0.935026i	$-0.615376\pi$
$911$	−32.5895	−	7.43834i	−1.07974	−	0.246443i	−0.725158	+	0.688582i	$0.758233\pi$
$912$	9.36261	−	2.38080i	0.310027	−	0.0788362i
$913$	−39.8982	+	23.0352i	−1.32044	+	0.762355i
$914$	2.34551	+	7.60396i	0.0775826	+	0.251517i
$915$	37.5184	−	31.4611i	1.24032	−	1.04007i
$916$	3.53437	−	2.81856i	0.116779	−	0.0931279i
$917$	8.91361	−	8.02115i	0.294353	−	0.264882i
$918$	−1.09847	−	14.8507i	−0.0362548	−	0.490145i
$919$	42.7041	+	39.6236i	1.40868	+	1.30706i	0.892837	+	0.450379i	$0.148711\pi$
$919$	42.7041	+	39.6236i	1.40868	+	1.30706i	0.515842	+	0.856684i	$0.327479\pi$
$920$	12.4451	+	1.87579i	0.410301	+	0.0618430i
$921$	−2.33096	−	13.2445i	−0.0768078	−	0.436421i
$922$	−1.74356	−	11.5677i	−0.0574209	−	0.380963i
$923$	26.7809	+	12.8970i	0.881503	+	0.424509i
$924$	−15.5588	+	12.6478i	−0.511847	+	0.416081i
$925$	−11.2016	+	5.39439i	−0.368305	+	0.177366i
$926$	5.95328	+	8.73186i	0.195637	+	0.286947i
$927$	−18.0148	+	15.8775i	−0.591682	+	0.521485i
$928$	−0.482474	−	6.43817i	−0.0158380	−	0.211343i
$929$	2.36490	+	6.02567i	0.0775899	+	0.197696i	0.964406	−	0.264427i	$-0.0851830\pi$
$929$	2.36490	+	6.02567i	0.0775899	+	0.197696i	−0.886816	+	0.462123i	$0.847088\pi$
$930$	7.94583	−	7.74515i	0.260554	−	0.253973i
$931$	18.0049	−	34.6433i	0.590088	−	1.13539i
$932$			25.0363i			0.820090i
$933$	31.4710	+	14.2125i	1.03032	+	0.465296i
$934$	−13.6702	+	1.02444i	−0.447303	+	0.0335207i
$935$	−16.4359	−	17.7137i	−0.537511	−	0.579299i
$936$	−5.66060	−	8.77672i	−0.185022	−	0.286876i
$937$	−15.8479	−	32.9086i	−0.517730	−	1.07508i	−0.981912	−	0.189338i	$-0.939366\pi$
$937$	−15.8479	−	32.9086i	−0.517730	−	1.07508i	0.464182	−	0.885740i	$-0.346348\pi$
$938$	1.76930	+	13.0902i	0.0577696	+	0.427409i
$939$	7.18318	+	21.4025i	0.234414	+	0.698444i
$940$	−2.55822	+	0.385590i	−0.0834400	+	0.0125766i
$941$	3.01734	+	2.05719i	0.0983625	+	0.0670624i	0.611502	−	0.791243i	$-0.290565\pi$
$941$	3.01734	+	2.05719i	0.0983625	+	0.0670624i	−0.513140	+	0.858305i	$0.671518\pi$
$942$	32.5236	−	23.3670i	1.05968	−	0.761337i
$943$	−28.5957	+	30.8188i	−0.931204	+	1.00360i
$944$	−1.20119	+	1.50625i	−0.0390954	+	0.0490241i
$945$	18.3324	−	19.1259i	0.596352	−	0.622166i
$946$	1.71109	+	2.14564i	0.0556325	+	0.0697609i
$947$	−38.2528	−	2.86665i	−1.24305	−	0.0931535i	−0.563084	−	0.826400i	$-0.690385\pi$
$947$	−38.2528	−	2.86665i	−1.24305	−	0.0931535i	−0.679963	+	0.733246i	$0.738004\pi$
$948$	−0.731494	+	1.34222i	−0.0237578	+	0.0435932i
$949$	−20.0482	−	34.7245i	−0.650792	−	1.12720i
$950$	3.58738	−	6.21353i	0.116390	−	0.201594i
$951$	−22.8858	+	13.9751i	−0.742122	+	0.453173i
$952$	5.99944	−	4.63649i	0.194443	−	0.150270i
$953$	29.4182	−	6.71452i	0.952950	−	0.217505i	0.282340	−	0.959314i	$-0.408889\pi$
$953$	29.4182	−	6.71452i	0.952950	−	0.217505i	0.670610	+	0.741810i	$0.266032\pi$
$954$	4.94897	−	14.6985i	0.160229	−	0.475881i
$955$	−13.3929	−	5.25634i	−0.433385	−	0.170091i
$956$	−17.8351	−	6.99976i	−0.576829	−	0.226389i
$957$	−43.5476	+	22.3078i	−1.40769	+	0.721110i
$958$	15.7533	−	3.59560i	0.508967	−	0.116168i
$959$	17.5457	−	3.72411i	0.566579	−	0.120258i
$960$	1.73953	+	2.84867i	0.0561430	+	0.0919405i
$961$	−9.97425	+	17.2759i	−0.321750	+	0.557287i
$962$	−16.8233	−	29.1388i	−0.542405	−	0.939473i
$963$	−31.7850	+	8.92081i	−1.02426	+	0.287469i
$964$	−12.0789	−	0.905187i	−0.389035	−	0.0291541i
$965$	−16.9788	−	21.2907i	−0.546566	−	0.685372i
$966$	29.5512	−	4.73741i	0.950794	−	0.152424i
$967$	27.4319	−	34.3985i	0.882149	−	1.10618i	−0.111512	−	0.993763i	$-0.535569\pi$
$967$	27.4319	−	34.3985i	0.882149	−	1.10618i	0.993661	−	0.112417i	$-0.0358592\pi$
$968$	−5.53992	+	5.97062i	−0.178060	+	0.191903i
$969$	16.1540	+	22.4841i	0.518940	+	0.722292i
$970$	−21.2744	−	14.5046i	−0.683079	−	0.465715i
$971$	−31.5644	+	4.75756i	−1.01295	+	0.152677i	−0.634482	−	0.772938i	$-0.718787\pi$
$971$	−31.5644	+	4.75756i	−1.01295	+	0.152677i	−0.378466	+	0.925615i	$0.623548\pi$
$972$	15.0126	−	4.19780i	0.481530	−	0.134645i
$973$	−31.5220	+	11.8199i	−1.01055	+	0.378930i
$974$	0.921452	+	1.91341i	0.0295252	+	0.0613098i
$975$	−7.60218	−	1.53936i	−0.243465	−	0.0492991i
$976$	9.97775	+	10.7535i	0.319380	+	0.344210i
$977$	54.4560	−	4.08092i	1.74220	−	0.130560i	0.834727	−	0.550664i	$-0.185625\pi$
$977$	54.4560	−	4.08092i	1.74220	−	0.130560i	0.907476	+	0.420104i	$0.138006\pi$
$978$	−9.39940	+	20.8133i	−0.300560	+	0.665537i
$979$			8.29151i			0.264998i
$980$	13.2714	+	2.41639i	0.423938	+	0.0771886i
$981$	1.22288	−	47.8000i	0.0390437	−	1.52614i
$982$	13.8361	+	35.2539i	0.441528	+	1.12500i
$983$	−1.57046	−	20.9563i	−0.0500897	−	0.668401i	−0.964580	−	0.263792i	$-0.915027\pi$
$983$	−1.57046	−	20.9563i	−0.0500897	−	0.668401i	0.914490	−	0.404609i	$-0.132592\pi$
$984$	−11.1358	−	0.559360i	−0.354995	−	0.0178317i
$985$	−16.8790	−	24.7569i	−0.537808	−	0.788820i
$986$	16.6700	−	8.02787i	0.530882	−	0.255659i
$987$	−5.51767	+	2.72108i	−0.175629	+	0.0866129i
$988$	17.4940	+	8.42468i	0.556559	+	0.268025i
$989$	−0.610524	−	4.05056i	−0.0194135	−	0.128800i
$990$	14.7794	−	20.5290i	0.469722	−	0.652455i
$991$	34.6953	+	5.22948i	1.10213	+	0.166120i	0.674819	−	0.737984i	$-0.264222\pi$
$991$	34.6953	+	5.22948i	1.10213	+	0.166120i	0.427314	+	0.904103i	$0.359460\pi$
$992$	2.43694	+	2.26115i	0.0773730	+	0.0717917i
$993$	0.985015	+	9.87586i	0.0312585	+	0.313401i
$994$	−22.2842	−	3.70722i	−0.706813	−	0.117586i
$995$	16.2334	−	12.9457i	0.514632	−	0.410405i
$996$	11.7181	+	13.9742i	0.371302	+	0.442791i
$997$	4.64949	+	15.0733i	0.147251	+	0.477375i	0.998908	−	0.0467244i	$-0.0148782\pi$
$997$	4.64949	+	15.0733i	0.147251	+	0.477375i	−0.851657	+	0.524099i	$0.824402\pi$
$998$	7.62113	−	4.40006i	0.241243	−	0.139282i
$999$	48.9726	−	11.1279i	1.54943	−	0.352071i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.p.a.131.12	yes	216
3.2	odd	2	inner	294.2.p.a.131.3	yes	216
49.3	odd	42	inner	294.2.p.a.101.3	✓	216
147.101	even	42	inner	294.2.p.a.101.12	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.p.a.101.3	✓	216	49.3	odd	42	inner
294.2.p.a.101.12	yes	216	147.101	even	42	inner
294.2.p.a.131.3	yes	216	3.2	odd	2	inner
294.2.p.a.131.12	yes	216	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.p (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.930874 - 0.365341i) q^{2} +(-1.29829 - 1.14649i) q^{3} +(0.733052 - 0.680173i) q^{4} +(1.59223 - 1.08556i) q^{5} +(-1.62740 - 0.592921i) q^{6} +(1.91180 + 1.82894i) q^{7} +(0.433884 - 0.900969i) q^{8} +(0.371113 + 2.97696i) q^{9} +O(q^{10})\)	\(q+(0.930874 - 0.365341i) q^{2} +(-1.29829 - 1.14649i) q^{3} +(0.733052 - 0.680173i) q^{4} +(1.59223 - 1.08556i) q^{5} +(-1.62740 - 0.592921i) q^{6} +(1.91180 + 1.82894i) q^{7} +(0.433884 - 0.900969i) q^{8} +(0.371113 + 2.97696i) q^{9} +(1.08556 - 1.59223i) q^{10} +(0.652132 - 4.32662i) q^{11} +(-1.73153 + 0.0426233i) q^{12} +(-2.72177 - 2.17054i) q^{13} +(2.44783 + 1.00405i) q^{14} +(-3.31176 - 0.416101i) q^{15} +(0.0747301 - 0.997204i) q^{16} +(2.73850 - 0.844714i) q^{17} +(1.43306 + 2.63559i) q^{18} +(-4.83029 - 2.78877i) q^{19} +(0.428815 - 1.87876i) q^{20} +(-0.385212 - 4.56636i) q^{21} +(-0.973637 - 4.26578i) q^{22} +(-1.92503 + 6.24079i) q^{23} +(-1.59626 + 0.672274i) q^{24} +(-0.469963 + 1.19745i) q^{25} +(-3.32661 - 1.02612i) q^{26} +(2.93125 - 4.29043i) q^{27} +(2.64544 + 0.0403496i) q^{28} +(6.29435 + 1.43664i) q^{29} +(-3.23485 + 0.822584i) q^{30} +(-2.87900 + 1.66219i) q^{31} +(-0.294755 - 0.955573i) q^{32} +(-5.80709 + 4.86954i) q^{33} +(2.24059 - 1.78681i) q^{34} +(5.02945 + 0.836703i) q^{35} +(2.29689 + 1.92984i) q^{36} +(7.08497 + 6.57390i) q^{37} +(-5.51524 - 0.831289i) q^{38} +(1.04514 + 5.93847i) q^{39} +(-0.287216 - 1.90555i) q^{40} +(5.79984 + 2.79305i) q^{41} +(-2.02686 - 4.10997i) q^{42} +(-0.565103 + 0.272139i) q^{43} +(-2.46480 - 3.61520i) q^{44} +(3.82257 + 4.33713i) q^{45} +(0.488057 + 6.51267i) q^{46} +(-0.490473 - 1.24971i) q^{47} +(-1.24031 + 1.20898i) q^{48} +(0.309979 + 6.99313i) q^{49} +1.28637i q^{50} +(-4.52382 - 2.04298i) q^{51} +(-3.47154 + 0.260156i) q^{52} +(-3.51633 - 3.78970i) q^{53} +(1.16115 - 5.06475i) q^{54} +(-3.65847 - 7.59688i) q^{55} +(2.47732 - 0.928929i) q^{56} +(3.07381 + 9.15852i) q^{57} +(6.38411 - 0.962250i) q^{58} +(-1.59180 - 1.08527i) q^{59} +(-2.71071 + 1.94754i) q^{60} +(-9.97775 + 10.7535i) q^{61} +(-2.07272 + 2.59910i) q^{62} +(-4.73517 + 6.37010i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-6.68992 - 0.501340i) q^{65} +(-3.62662 + 6.65449i) q^{66} +(2.49630 + 4.32372i) q^{67} +(1.43291 - 2.48187i) q^{68} +(9.65425 - 5.89532i) q^{69} +(4.98746 - 1.05860i) q^{70} +(-8.32433 + 1.89997i) q^{71} +(2.84317 + 0.957292i) q^{72} +(10.7216 + 4.20791i) q^{73} +(8.99693 + 3.53103i) q^{74} +(1.98301 - 1.01582i) q^{75} +(-5.43770 + 1.24112i) q^{76} +(9.15985 - 7.07893i) q^{77} +(3.14246 + 5.14613i) q^{78} +(0.441270 - 0.764303i) q^{79} +(-0.963539 - 1.66890i) q^{80} +(-8.72455 + 2.20957i) q^{81} +(6.41933 + 0.481063i) q^{82} +(-6.56486 - 8.23208i) q^{83} +(-3.38829 - 3.08537i) q^{84} +(3.44332 - 4.31778i) q^{85} +(-0.426616 + 0.459783i) q^{86} +(-6.52479 - 9.08160i) q^{87} +(-3.61520 - 2.46480i) q^{88} +(-1.87383 + 0.282434i) q^{89} +(5.14286 + 2.64078i) q^{90} +(-1.23371 - 9.12758i) q^{91} +(2.83367 + 5.88417i) q^{92} +(5.64346 + 1.14274i) q^{93} +(-0.913137 - 0.984128i) q^{94} +(-10.7183 + 0.803225i) q^{95} +(-0.712879 + 1.57854i) q^{96} -13.3614i q^{97} +(2.84343 + 6.39648i) q^{98} +(13.1222 + 0.335709i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9}+O(q^{10}) \) 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9	\( 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9} + 6 q^{10} - 12 q^{15} + 18 q^{16} - 4 q^{18} - 12 q^{19} + 10 q^{22} - 6 q^{24} + 16 q^{25} - 42 q^{27} + 2 q^{28} + 4 q^{30} + 6 q^{31} + 18 q^{33} - 10 q^{36} - 36 q^{37} + 4 q^{39} - 22 q^{40} + 20 q^{42} + 40 q^{43} - 14 q^{45} - 156 q^{46} - 134 q^{49} - 12 q^{51} + 16 q^{52} - 18 q^{54} - 322 q^{55} - 34 q^{57} - 164 q^{58} - 6 q^{60} + 56 q^{61} - 24 q^{63} + 36 q^{64} - 28 q^{69} - 4 q^{70} + 4 q^{72} - 24 q^{73} + 84 q^{75} + 16 q^{78} + 22 q^{79} - 52 q^{81} + 24 q^{82} + 42 q^{84} + 32 q^{85} - 94 q^{87} - 2 q^{88} + 42 q^{90} - 100 q^{91} - 266 q^{93} - 88 q^{94} - 6 q^{96} + 224 q^{99}+O(q^{100}) \) 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9 + 6 * q^10 - 12 * q^15 + 18 * q^16 - 4 * q^18 - 12 * q^19 + 10 * q^22 - 6 * q^24 + 16 * q^25 - 42 * q^27 + 2 * q^28 + 4 * q^30 + 6 * q^31 + 18 * q^33 - 10 * q^36 - 36 * q^37 + 4 * q^39 - 22 * q^40 + 20 * q^42 + 40 * q^43 - 14 * q^45 - 156 * q^46 - 134 * q^49 - 12 * q^51 + 16 * q^52 - 18 * q^54 - 322 * q^55 - 34 * q^57 - 164 * q^58 - 6 * q^60 + 56 * q^61 - 24 * q^63 + 36 * q^64 - 28 * q^69 - 4 * q^70 + 4 * q^72 - 24 * q^73 + 84 * q^75 + 16 * q^78 + 22 * q^79 - 52 * q^81 + 24 * q^82 + 42 * q^84 + 32 * q^85 - 94 * q^87 - 2 * q^88 + 42 * q^90 - 100 * q^91 - 266 * q^93 - 88 * q^94 - 6 * q^96 + 224 * q^99

Introduction

L-functions

Modular forms

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