LMFDB - Embedded newform 280.2.br.a.107.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(67,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 3, 8]))

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

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

chi := DirichletCharacter("280.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.br (of order $12$, degree $4$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.11
Character	$\chi$	$=$	280.107
Dual form			280.2.br.a.123.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16591 + 0.800411i) q^{2} +(-0.0613082 - 0.0164275i) q^{3} +(0.718686 - 1.86641i) q^{4} +(2.08260 - 0.814111i) q^{5} +(0.0846285 - 0.0299188i) q^{6} +(-0.779437 - 2.52833i) q^{7} +(0.655974 + 2.75131i) q^{8} +(-2.59459 - 1.49799i) q^{9} +O(q^{10})$	\(q+(-1.16591 + 0.800411i) q^{2} +(-0.0613082 - 0.0164275i) q^{3} +(0.718686 - 1.86641i) q^{4} +(2.08260 - 0.814111i) q^{5} +(0.0846285 - 0.0299188i) q^{6} +(-0.779437 - 2.52833i) q^{7} +(0.655974 + 2.75131i) q^{8} +(-2.59459 - 1.49799i) q^{9} +(-1.77650 + 2.61611i) q^{10} +(-2.16564 - 3.75099i) q^{11} +(-0.0747218 + 0.102620i) q^{12} +(0.0784147 + 0.0784147i) q^{13} +(2.93246 + 2.32394i) q^{14} +(-0.141054 + 0.0156998i) q^{15} +(-2.96698 - 2.68273i) q^{16} +(-0.843938 + 3.14962i) q^{17} +(4.22406 - 0.330221i) q^{18} +(-4.88981 - 2.82314i) q^{19} +(-0.0227305 - 4.47208i) q^{20} +(0.00625171 + 0.167812i) q^{21} +(5.52727 + 2.63992i) q^{22} +(5.28899 - 1.41718i) q^{23} +(0.00498050 - 0.179454i) q^{24} +(3.67445 - 3.39093i) q^{25} +(-0.154188 - 0.0286604i) q^{26} +(0.269104 + 0.269104i) q^{27} +(-5.27908 - 0.362328i) q^{28} +3.04792 q^{29} +(0.151890 - 0.131206i) q^{30} +(6.50896 - 3.75795i) q^{31} +(5.60651 + 0.753009i) q^{32} +(0.0711520 + 0.265543i) q^{33} +(-1.53703 - 4.34766i) q^{34} +(-3.68160 - 4.63096i) q^{35} +(-4.66055 + 3.76599i) q^{36} +(0.958303 + 3.57643i) q^{37} +(7.96074 - 0.622341i) q^{38} +(-0.00351931 - 0.00609562i) q^{39} +(3.60600 + 5.19584i) q^{40} +10.9345 q^{41} +(-0.141607 - 0.190649i) q^{42} +(-6.94288 + 6.94288i) q^{43} +(-8.55731 + 1.34618i) q^{44} +(-6.62301 - 1.00742i) q^{45} +(-5.03215 + 5.88567i) q^{46} +(0.578402 + 2.15863i) q^{47} +(0.137830 + 0.213213i) q^{48} +(-5.78496 + 3.94136i) q^{49} +(-1.56993 + 6.89459i) q^{50} +(0.103481 - 0.179234i) q^{51} +(0.202710 - 0.0899986i) q^{52} +(0.598900 - 2.23513i) q^{53} +(-0.529143 - 0.0983568i) q^{54} +(-7.56388 - 6.04875i) q^{55} +(6.44494 - 3.80299i) q^{56} +(0.253409 + 0.253409i) q^{57} +(-3.55360 + 2.43959i) q^{58} +(1.74237 - 1.00596i) q^{59} +(-0.0720714 + 0.274548i) q^{60} +(-8.64141 - 4.98912i) q^{61} +(-4.58095 + 9.59126i) q^{62} +(-1.76509 + 7.72757i) q^{63} +(-7.13940 + 3.60957i) q^{64} +(0.227145 + 0.0994682i) q^{65} +(-0.295500 - 0.252648i) q^{66} +(1.34960 - 5.03678i) q^{67} +(5.27196 + 3.83872i) q^{68} -0.347539 q^{69} +(7.99908 + 2.45249i) q^{70} +0.0667621i q^{71} +(2.41944 - 8.12115i) q^{72} +(8.15766 + 2.18584i) q^{73} +(-3.97991 - 3.40276i) q^{74} +(-0.280978 + 0.147530i) q^{75} +(-8.78337 + 7.09746i) q^{76} +(-7.79579 + 8.39912i) q^{77} +(0.00898219 + 0.00429004i) q^{78} +(-5.28206 + 9.14880i) q^{79} +(-8.36307 - 3.17159i) q^{80} +(4.48188 + 7.76284i) q^{81} +(-12.7486 + 8.75206i) q^{82} +(2.51622 - 2.51622i) q^{83} +(0.317699 + 0.108936i) q^{84} +(0.806553 + 7.24646i) q^{85} +(2.53761 - 13.6519i) q^{86} +(-0.186863 - 0.0500697i) q^{87} +(8.89954 - 8.41889i) q^{88} +(7.53726 + 4.35164i) q^{89} +(8.52818 - 4.12657i) q^{90} +(0.137139 - 0.259378i) q^{91} +(1.15608 - 10.8899i) q^{92} +(-0.460786 + 0.123467i) q^{93} +(-2.40215 - 2.05380i) q^{94} +(-12.4819 - 1.89861i) q^{95} +(-0.331355 - 0.138267i) q^{96} +(-6.25104 - 6.25104i) q^{97} +(3.59003 - 9.22560i) q^{98} +12.9764i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) $ 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8	$ 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) $ 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8 - 2 * q^10 - 8 * q^11 - 14 * q^12 + 4 * q^16 - 4 * q^17 - 16 * q^18 + 8 * q^20 - 4 * q^25 - 20 * q^26 - 40 * q^27 - 34 * q^28 - 12 * q^30 + 18 * q^32 + 20 * q^33 - 32 * q^35 - 48 * q^36 - 16 * q^38 - 22 * q^40 - 32 * q^41 + 30 * q^42 - 16 * q^43 + 20 * q^46 + 36 * q^48 + 68 * q^50 - 8 * q^51 - 32 * q^52 - 52 * q^56 - 40 * q^57 - 14 * q^58 - 50 * q^60 + 56 * q^62 - 4 * q^65 - 60 * q^66 - 28 * q^67 - 40 * q^68 + 64 * q^70 - 48 * q^72 - 4 * q^73 - 4 * q^75 - 144 * q^76 + 184 * q^78 - 40 * q^80 + 32 * q^81 + 74 * q^82 - 16 * q^83 - 56 * q^86 - 64 * q^88 - 56 * q^90 + 16 * q^91 + 44 * q^92 - 104 * q^96 - 48 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.16591	+	0.800411i	−0.824422	+	0.565976i
$2$	−1.16591	+	0.800411i	−0.824422	+	0.565976i
$3$	−0.0613082	−	0.0164275i	−0.0353963	−	0.00948441i	0.241077	−	0.970506i	$-0.422499\pi$
$3$	−0.0613082	−	0.0164275i	−0.0353963	−	0.00948441i	−0.276474	+	0.961021i	$0.589166\pi$
$4$	0.718686	−	1.86641i	0.359343	−	0.933206i
$5$	2.08260	−	0.814111i	0.931367	−	0.364081i
$5$	2.08260	−	0.814111i	0.931367	−	0.364081i
$6$	0.0846285	−	0.0299188i	0.0345494	−	0.0122143i
$7$	−0.779437	−	2.52833i	−0.294600	−	0.955621i
$7$	−0.779437	−	2.52833i	−0.294600	−	0.955621i
$8$	0.655974	+	2.75131i	0.231922	+	0.972734i
$9$	−2.59459	−	1.49799i	−0.864862	−	0.499329i
$10$	−1.77650	+	2.61611i	−0.561778	+	0.827288i
$11$	−2.16564	−	3.75099i	−0.652964	−	1.13097i	−0.982400	−	0.186789i	$-0.940192\pi$
$11$	−2.16564	−	3.75099i	−0.652964	−	1.13097i	0.329436	−	0.944178i	$-0.393142\pi$
$12$	−0.0747218	+	0.102620i	−0.0215703	+	0.0296239i
$13$	0.0784147	+	0.0784147i	0.0217483	+	0.0217483i	0.717897	−	0.696149i	$-0.245105\pi$
$13$	0.0784147	+	0.0784147i	0.0217483	+	0.0217483i	−0.696149	+	0.717897i	$0.745105\pi$
$14$	2.93246	+	2.32394i	0.783733	+	0.621098i
$15$	−0.141054	+	0.0156998i	−0.0364201	+	0.00405367i
$16$	−2.96698	−	2.68273i	−0.741746	−	0.670681i
$17$	−0.843938	+	3.14962i	−0.204685	+	0.763895i	0.784860	+	0.619673i	$0.212735\pi$
$17$	−0.843938	+	3.14962i	−0.204685	+	0.763895i	−0.989545	+	0.144222i	$0.953932\pi$
$18$	4.22406	−	0.330221i	0.995619	−	0.0778338i
$19$	−4.88981	−	2.82314i	−1.12180	−	0.647672i	−0.179940	−	0.983678i	$-0.557590\pi$
$19$	−4.88981	−	2.82314i	−1.12180	−	0.647672i	−0.941860	+	0.336006i	$0.890924\pi$
$20$	−0.0227305	−	4.47208i	−0.00508270	−	0.999987i
$21$	0.00625171	+	0.167812i	0.00136424	+	0.0366196i
$22$	5.52727	+	2.63992i	1.17842	+	0.562832i
$23$	5.28899	−	1.41718i	1.10283	−	0.295503i	0.338914	−	0.940817i	$-0.389940\pi$
$23$	5.28899	−	1.41718i	1.10283	−	0.295503i	0.763917	+	0.645315i	$0.223274\pi$
$24$	0.00498050	−	0.179454i	0.00101664	−	0.0366309i
$25$	3.67445	−	3.39093i	0.734890	−	0.678187i
$26$	−0.154188	−	0.0286604i	−0.0302388	−	0.00562077i
$27$	0.269104	+	0.269104i	0.0517890	+	0.0517890i
$28$	−5.27908	−	0.362328i	−0.997653	−	0.0684735i
$29$	3.04792			0.565985			0.282992	−	0.959122i	$-0.408673\pi$
$29$	3.04792			0.565985			0.282992	+	0.959122i	$0.408673\pi$
$30$	0.151890	−	0.131206i	0.0277312	−	0.0239548i
$31$	6.50896	−	3.75795i	1.16904	−	0.674947i	0.215589	−	0.976484i	$-0.430833\pi$
$31$	6.50896	−	3.75795i	1.16904	−	0.674947i	0.953455	+	0.301537i	$0.0974996\pi$
$32$	5.60651	+	0.753009i	0.991101	+	0.133114i
$33$	0.0711520	+	0.265543i	0.0123860	+	0.0462251i
$34$	−1.53703	−	4.34766i	−0.263599	−	0.745618i
$35$	−3.68160	−	4.63096i	−0.622304	−	0.782776i
$36$	−4.66055	+	3.76599i	−0.776758	+	0.627664i
$37$	0.958303	+	3.57643i	0.157544	+	0.587962i	0.998874	+	0.0474405i	$0.0151064\pi$
$37$	0.958303	+	3.57643i	0.157544	+	0.587962i	−0.841330	+	0.540522i	$0.818227\pi$
$38$	7.96074	−	0.622341i	1.29140	−	0.100957i
$39$	−0.00351931	−	0.00609562i	−0.000563540	−	0.000976080i
$40$	3.60600	+	5.19584i	0.570159	+	0.821535i
$41$	10.9345			1.70768			0.853838	−	0.520539i	$-0.174269\pi$
$41$	10.9345			1.70768			0.853838	+	0.520539i	$0.174269\pi$
$42$	−0.141607	−	0.190649i	−0.0218505	−	0.0294178i
$43$	−6.94288	+	6.94288i	−1.05878	+	1.05878i	−0.0606187	+	0.998161i	$0.519307\pi$
$43$	−6.94288	+	6.94288i	−1.05878	+	1.05878i	−0.998161	+	0.0606187i	$0.980693\pi$
$44$	−8.55731	+	1.34618i	−1.29006	+	0.202945i
$45$	−6.62301	−	1.00742i	−0.987301	−	0.150178i
$46$	−5.03215	+	5.88567i	−0.741950	+	0.867794i
$47$	0.578402	+	2.15863i	0.0843686	+	0.314868i	0.995194	−	0.0979242i	$-0.0312203\pi$
$47$	0.578402	+	2.15863i	0.0843686	+	0.314868i	−0.910825	+	0.412792i	$0.864554\pi$
$48$	0.137830	+	0.213213i	0.0198940	+	0.0307747i
$49$	−5.78496	+	3.94136i	−0.826422	+	0.563051i
$50$	−1.56993	+	6.89459i	−0.222022	+	0.975042i
$51$	0.103481	−	0.179234i	0.0144902	−	0.0250977i
$52$	0.202710	−	0.0899986i	0.0281108	−	0.0124806i
$53$	0.598900	−	2.23513i	0.0822653	−	0.307018i	−0.912517	−	0.409039i	$-0.865864\pi$
$53$	0.598900	−	2.23513i	0.0822653	−	0.307018i	0.994782	+	0.102021i	$0.0325307\pi$
$54$	−0.529143	−	0.0983568i	−0.0720073	−	0.0133847i
$55$	−7.56388	−	6.04875i	−1.01991	−	0.815614i
$56$	6.44494	−	3.80299i	0.861241	−	0.508196i
$57$	0.253409	+	0.253409i	0.0335648	+	0.0335648i
$58$	−3.55360	+	2.43959i	−0.466610	+	0.320334i
$59$	1.74237	−	1.00596i	0.226837	−	0.130964i	−0.382275	−	0.924049i	$-0.624859\pi$
$59$	1.74237	−	1.00596i	0.226837	−	0.130964i	0.609112	+	0.793084i	$0.291526\pi$
$60$	−0.0720714	+	0.274548i	−0.00930438	+	0.0354441i
$61$	−8.64141	−	4.98912i	−1.10642	−	0.638792i	−0.168520	−	0.985698i	$-0.553899\pi$
$61$	−8.64141	−	4.98912i	−1.10642	−	0.638792i	−0.937900	+	0.346907i	$0.887232\pi$
$62$	−4.58095	+	9.59126i	−0.581781	+	1.21809i
$63$	−1.76509	+	7.72757i	−0.222381	+	0.973583i
$64$	−7.13940	+	3.60957i	−0.892425	+	0.451197i
$65$	0.227145	+	0.0994682i	0.0281738	+	0.0123375i
$66$	−0.295500	−	0.252648i	−0.0363735	−	0.0310988i
$67$	1.34960	−	5.03678i	0.164880	−	0.615340i	−0.833176	−	0.553008i	$-0.813480\pi$
$67$	1.34960	−	5.03678i	0.164880	−	0.615340i	0.998055	−	0.0623316i	$-0.0198536\pi$
$68$	5.27196	+	3.83872i	0.639319	+	0.465513i
$69$	−0.347539			−0.0418388
$70$	7.99908	+	2.45249i	0.956073	+	0.293128i
$71$			0.0667621i			0.00792320i	0.999992	+	0.00396160i	$0.00126102\pi$
$71$			0.0667621i			0.00792320i	−0.999992	+	0.00396160i	$0.998739\pi$
$72$	2.41944	−	8.12115i	0.285134	−	0.957087i
$73$	8.15766	+	2.18584i	0.954781	+	0.255833i	0.702390	−	0.711792i	$-0.252116\pi$
$73$	8.15766	+	2.18584i	0.954781	+	0.255833i	0.252391	+	0.967625i	$0.418783\pi$
$74$	−3.97991	−	3.40276i	−0.462655	−	0.395563i
$75$	−0.280978	+	0.147530i	−0.0324446	+	0.0170353i
$76$	−8.78337	+	7.09746i	−1.00752	+	0.814134i
$77$	−7.79579	+	8.39912i	−0.888413	+	0.957169i
$78$	0.00898219	+	0.00429004i	0.00101703	+	0.000485752i
$79$	−5.28206	+	9.14880i	−0.594278	+	1.02932i	0.399370	+	0.916790i	$0.369229\pi$
$79$	−5.28206	+	9.14880i	−0.594278	+	1.02932i	−0.993648	+	0.112530i	$0.964104\pi$
$80$	−8.36307	−	3.17159i	−0.935020	−	0.354595i
$81$	4.48188	+	7.76284i	0.497987	+	0.862538i
$82$	−12.7486	+	8.75206i	−1.40785	+	0.966503i
$83$	2.51622	−	2.51622i	0.276192	−	0.276192i	−0.555395	−	0.831587i	$-0.687433\pi$
$83$	2.51622	−	2.51622i	0.276192	−	0.276192i	0.831587	+	0.555395i	$0.187433\pi$
$84$	0.317699	+	0.108936i	0.0346638	+	0.0118859i
$85$	0.806553	+	7.24646i	0.0874830	+	0.785988i
$86$	2.53761	−	13.6519i	0.273637	−	1.47212i
$87$	−0.186863	−	0.0500697i	−0.0200338	−	0.00536803i
$88$	8.89954	−	8.41889i	0.948694	−	0.897457i
$89$	7.53726	+	4.35164i	0.798948	+	0.461273i	0.843103	−	0.537752i	$-0.180726\pi$
$89$	7.53726	+	4.35164i	0.798948	+	0.461273i	−0.0441551	+	0.999025i	$0.514060\pi$
$90$	8.52818	−	4.12657i	0.898949	−	0.434978i
$91$	0.137139	−	0.259378i	0.0143761	−	0.0271902i
$92$	1.15608	−	10.8899i	0.120530	−	1.13535i
$93$	−0.460786	+	0.123467i	−0.0477813	+	0.0128030i
$94$	−2.40215	−	2.05380i	−0.247763	−	0.211833i
$95$	−12.4819	−	1.89861i	−1.28061	−	0.194794i
$96$	−0.331355	−	0.138267i	−0.0338188	−	0.0141118i
$97$	−6.25104	−	6.25104i	−0.634697	−	0.634697i	0.314546	−	0.949242i	$-0.398148\pi$
$97$	−6.25104	−	6.25104i	−0.634697	−	0.634697i	−0.949242	+	0.314546i	$0.898148\pi$
$98$	3.59003	−	9.22560i	0.362647	−	0.931926i
$99$			12.9764i			1.30417i
$100$	−3.68811	−	9.29505i	−0.368811	−	0.929505i
$101$	12.3989	−	7.15853i	1.23374	−	0.712300i	0.265932	−	0.963992i	$-0.414320\pi$
$101$	12.3989	−	7.15853i	1.23374	−	0.712300i	0.967807	+	0.251692i	$0.0809869\pi$
$102$	0.0228116	+	0.291797i	0.00225869	+	0.0288922i
$103$	4.30313	−	1.15302i	0.424000	−	0.113610i	−0.0405086	−	0.999179i	$-0.512898\pi$
$103$	4.30313	−	1.15302i	0.424000	−	0.113610i	0.464508	+	0.885569i	$0.346231\pi$
$104$	−0.164305	+	0.267181i	−0.0161114	+	0.0261993i
$105$	0.149637	+	0.344395i	0.0146031	+	0.0336096i
$106$	1.09076	+	3.08532i	0.105944	+	0.299673i
$107$	−5.61056	+	1.50334i	−0.542393	+	0.145334i	−0.519605	−	0.854407i	$-0.673921\pi$
$107$	−5.61056	+	1.50334i	−0.542393	+	0.145334i	−0.0227880	+	0.999740i	$0.507254\pi$
$108$	0.695659	−	0.308857i	0.0669398	−	0.0297198i
$109$	6.91643	+	11.9796i	0.662474	+	1.14744i	0.979964	+	0.199177i	$0.0638269\pi$
$109$	6.91643	+	11.9796i	0.662474	+	1.14744i	−0.317489	+	0.948262i	$0.602840\pi$
$110$	13.6603	+	0.998081i	1.30246	+	0.0951633i
$111$		−	0.235007i		−	0.0223059i
$112$	−4.47025	+	9.59254i	−0.422399	+	0.906410i
$113$	−4.78662	+	4.78662i	−0.450287	+	0.450287i	−0.895450	−	0.445163i	$-0.853146\pi$
$113$	−4.78662	+	4.78662i	−0.450287	+	0.450287i	0.445163	+	0.895450i	$0.353146\pi$
$114$	−0.498282	−	0.0926203i	−0.0466684	−	0.00867469i
$115$	9.86111	−	7.25724i	0.919553	−	0.676741i
$116$	2.19050	−	5.68867i	0.203383	−	0.528180i
$117$	−0.0859897	−	0.320918i	−0.00794975	−	0.0296689i
$118$	−1.22626	+	2.56746i	−0.112887	+	0.236354i
$119$	8.62109	−	0.321173i	0.790294	−	0.0294418i
$120$	−0.135723	−	0.377785i	−0.0123897	−	0.0344869i
$121$	−3.87997	+	6.72031i	−0.352725	+	0.610937i
$122$	14.0684	−	1.09982i	1.27370	−	0.0995729i
$123$	−0.670372	−	0.179626i	−0.0604454	−	0.0161963i
$124$	−2.33598	−	14.8492i	−0.209777	−	1.33350i
$125$	4.89181	−	10.0534i	0.437537	−	0.899201i
$126$	−4.12730	−	10.4224i	−0.367689	−	0.928505i
$127$	13.2205	−	13.2205i	1.17313	−	1.17313i	0.191667	−	0.981460i	$-0.438611\pi$
$127$	13.2205	−	13.2205i	1.17313	−	1.17313i	0.981460	−	0.191667i	$-0.0613893\pi$
$128$	5.43474	−	9.92288i	0.480368	−	0.877067i
$129$	0.539710	−	0.311602i	0.0475188	−	0.0274350i
$130$	−0.344445	+	0.0658382i	−0.0302099	+	0.00577439i
$131$	−4.32591	+	7.49269i	−0.377956	+	0.654639i	−0.990765	−	0.135592i	$-0.956706\pi$
$131$	−4.32591	+	7.49269i	−0.377956	+	0.654639i	0.612809	+	0.790231i	$0.290040\pi$
$132$	0.546748	+	0.0580429i	0.0475883	+	0.00505199i
$133$	−3.32653	+	14.5635i	−0.288447	+	1.26282i
$134$	2.45798	+	6.95265i	0.212337	+	0.600618i
$135$	0.779515	+	0.341355i	0.0670900	+	0.0293792i
$136$	−9.21917	−	0.255866i	−0.790538	−	0.0219403i
$137$	−0.260016	+	0.970394i	−0.0222147	+	0.0829064i	−0.976143	−	0.217127i	$-0.930331\pi$
$137$	−0.260016	+	0.970394i	−0.0222147	+	0.0829064i	0.953929	+	0.300034i	$0.0969980\pi$
$138$	0.405199	−	0.278174i	0.0344928	−	0.0236797i
$139$		−	4.43604i		−	0.376260i	−0.982144	−	0.188130i	$-0.939757\pi$
$139$		−	4.43604i		−	0.376260i	0.982144	−	0.188130i	$-0.0602426\pi$
$140$	−11.2892	+	3.54317i	−0.954111	+	0.299453i
$141$		−	0.141843i		−	0.0119454i
$142$	−0.0534371	−	0.0778385i	−0.00448434	−	0.00653206i
$143$	0.124315	−	0.463951i	0.0103958	−	0.0387975i
$144$	3.67941	+	11.4051i	0.306617	+	0.950422i
$145$	6.34760	−	2.48135i	0.527140	−	0.206064i
$146$	−11.2606	+	3.98099i	−0.931938	+	0.329469i
$147$	0.419412	−	0.146605i	0.0345925	−	0.0120918i
$148$	7.36381	+	0.781745i	0.605302	+	0.0642590i
$149$	1.41586	−	2.45235i	0.115992	−	0.200904i	−0.802184	−	0.597077i	$-0.796329\pi$
$149$	1.41586	−	2.45235i	0.115992	−	0.200904i	0.918176	+	0.396173i	$0.129662\pi$
$150$	0.209510	−	0.396905i	0.0171064	−	0.0324071i
$151$	−11.8521	+	6.84282i	−0.964512	+	0.556861i	−0.897559	−	0.440895i	$-0.854661\pi$
$151$	−11.8521	+	6.84282i	−0.964512	+	0.556861i	−0.0669530	+	0.997756i	$0.521328\pi$
$152$	4.55973	−	15.3053i	0.369843	−	1.24142i
$153$	6.90775	−	6.90775i	0.558459	−	0.558459i
$154$	2.36643	−	16.0324i	0.190693	−	1.29193i
$155$	10.4962	−	13.1253i	0.843073	−	1.05425i
$156$	−0.0139062	+	0.00218764i	−0.00111339	+	0.000175152i
$157$	−6.74129	−	1.80632i	−0.538013	−	0.144160i	−0.0204272	−	0.999791i	$-0.506503\pi$
$157$	−6.74129	−	1.80632i	−0.538013	−	0.144160i	−0.517586	+	0.855631i	$0.673169\pi$
$158$	−1.16440	−	14.8945i	−0.0926343	−	1.18494i
$159$	−0.0734350	+	0.127193i	−0.00582378	+	0.0100871i
$160$	12.2892	−	2.99610i	0.971543	−	0.236863i
$161$	−7.70554	−	12.2677i	−0.607282	−	0.966833i
$162$	−11.4389	−	5.46342i	−0.898727	−	0.429247i
$163$	3.22957	+	12.0529i	0.252959	+	0.944057i	0.969214	+	0.246219i	$0.0791881\pi$
$163$	3.22957	+	12.0529i	0.252959	+	0.944057i	−0.716255	+	0.697839i	$0.754145\pi$
$164$	7.85844	−	20.4082i	0.613641	−	1.59361i
$165$	0.364362	+	0.495094i	0.0283656	+	0.0385430i
$166$	−0.919675	+	4.94770i	−0.0713806	+	0.384016i
$167$	2.22706	−	2.22706i	0.172335	−	0.172335i	−0.615669	−	0.788005i	$-0.711114\pi$
$167$	2.22706	−	2.22706i	0.172335	−	0.172335i	0.788005	+	0.615669i	$0.211114\pi$
$168$	−0.457601	+	0.127281i	−0.0353047	+	0.00981991i
$169$		−	12.9877i		−	0.999054i
$170$	−6.74051	−	7.80313i	−0.516973	−	0.598473i
$171$	8.45803	+	14.6497i	0.646802	+	1.12029i
$172$	7.96852	+	17.9480i	0.607594	+	1.36852i
$173$	−7.95339	+	2.13110i	−0.604685	+	0.162025i	−0.548156	−	0.836376i	$-0.684670\pi$
$173$	−7.95339	+	2.13110i	−0.604685	+	0.162025i	−0.0565289	+	0.998401i	$0.518003\pi$
$174$	0.257941	−	0.0911901i	0.0195545	−	0.00691311i
$175$	−11.4374	−	6.64721i	−0.864588	−	0.502482i
$176$	−3.63748	+	16.9389i	−0.274185	+	1.27682i
$177$	−0.123347	+	0.0330507i	−0.00927131	+	0.00248424i
$178$	−12.2709	+	0.959290i	−0.919740	+	0.0719018i
$179$	−6.58626	+	3.80258i	−0.492280	+	0.284218i	−0.725520	−	0.688201i	$-0.758401\pi$
$179$	−6.58626	+	3.80258i	−0.492280	+	0.284218i	0.233240	+	0.972419i	$0.425067\pi$
$180$	−6.64013	+	11.6372i	−0.494926	+	0.867389i
$181$		−	25.2582i		−	1.87743i	−0.344700	−	0.938713i	$-0.612019\pi$
$181$		−	25.2582i		−	1.87743i	0.344700	−	0.938713i	$-0.387981\pi$
$182$	0.0477170	+	0.412179i	0.00353702	+	0.0305527i
$183$	0.447831	+	0.447831i	0.0331046	+	0.0331046i
$184$	7.36854	+	13.6220i	0.543216	+	1.00423i
$185$	4.90737	+	6.66812i	0.360797	+	0.490250i
$186$	0.438410	−	0.512770i	0.0321458	−	0.0375981i
$187$	13.6419	−	3.65533i	0.997592	−	0.267304i
$188$	4.44457	+	0.471837i	0.324154	+	0.0344123i
$189$	0.470635	−	0.890133i	0.0342336	−	0.0647477i
$190$	16.0724	−	7.77701i	1.16601	−	0.564204i
$191$	17.4537	+	10.0769i	1.26290	+	0.729137i	0.973635	−	0.228111i	$-0.0732548\pi$
$191$	17.4537	+	10.0769i	1.26290	+	0.729137i	0.289268	+	0.957248i	$0.406588\pi$
$192$	0.497000	−	0.104014i	0.0358679	−	0.00750657i
$193$	−23.7708	−	6.36936i	−1.71106	−	0.458476i	−0.735374	−	0.677662i	$-0.762993\pi$
$193$	−23.7708	−	6.36936i	−1.71106	−	0.458476i	−0.975683	+	0.219186i	$0.929660\pi$
$194$	12.2915	+	2.28474i	0.882481	+	0.164035i
$195$	−0.0122918	−	0.00982963i	−0.000880236	−	0.000703915i
$196$	3.19863	+	13.6297i	0.228473	+	0.973550i
$197$	−17.0328	+	17.0328i	−1.21354	+	1.21354i	−0.243685	+	0.969854i	$0.578356\pi$
$197$	−17.0328	+	17.0328i	−1.21354	+	1.21354i	−0.969854	+	0.243685i	$0.921644\pi$
$198$	−10.3864	−	15.1293i	−0.738131	−	1.07519i
$199$	2.23548	+	3.87197i	0.158469	+	0.274477i	0.934317	−	0.356444i	$-0.116011\pi$
$199$	2.23548	+	3.87197i	0.158469	+	0.274477i	−0.775848	+	0.630920i	$0.782677\pi$
$200$	11.7398	+	7.88518i	0.830133	+	0.557566i
$201$	−0.165483	+	0.286625i	−0.0116723	+	0.0202170i
$202$	−8.72626	+	18.2704i	−0.613978	+	1.28550i
$203$	−2.37566	−	7.70617i	−0.166739	−	0.540867i
$204$	−0.260154	−	0.321950i	−0.0182144	−	0.0225410i
$205$	22.7721	−	8.90186i	1.59047	−	0.621733i
$206$	−4.09416	+	4.78858i	−0.285254	+	0.333636i
$207$	−15.8457	−	4.24583i	−1.10135	−	0.295106i
$208$	−0.0222899	−	0.443020i	−0.00154552	−	0.0307179i
$209$			24.4555i			1.69163i
$210$	−0.450121	−	0.281762i	−0.0310613	−	0.0194435i
$211$	8.99792			0.619443			0.309721	−	0.950827i	$-0.399764\pi$
$211$	8.99792			0.619443			0.309721	+	0.950827i	$0.399764\pi$
$212$	−3.74124	−	2.72415i	−0.256950	−	0.187095i
$213$	0.00109673	−	0.00409306i	7.51469e−5	−	0.000280452i
$214$	5.33811	−	6.24351i	0.364905	−	0.426798i
$215$	−8.80697	+	20.1115i	−0.600631	+	1.37159i
$216$	−0.563862	+	0.916912i	−0.0383659	+	0.0623879i
$217$	−14.5747	−	13.5277i	−0.989394	−	0.918323i
$218$	−17.6525	−	8.43115i	−1.19558	−	0.571029i
$219$	−0.464223	−	0.268020i	−0.0313693	−	0.0181111i
$220$	−16.7255	+	9.77016i	−1.12763	+	0.658704i
$221$	−0.313153	+	0.180799i	−0.0210650	+	0.0121619i
$222$	0.188102	+	0.273997i	0.0126246	+	0.0183895i
$223$	13.4784	+	13.4784i	0.902579	+	0.902579i	0.995659	−	0.0930799i	$-0.0296712\pi$
$223$	13.4784	+	13.4784i	0.902579	+	0.902579i	−0.0930799	+	0.995659i	$0.529671\pi$
$224$	−2.46607	−	14.7621i	−0.164771	−	0.986332i
$225$	−14.6132	+	3.29380i	−0.974216	+	0.219587i
$226$	1.74950	−	9.41202i	0.116375	−	0.626078i
$227$	−4.54526	+	16.9631i	−0.301679	+	1.12588i	0.634087	+	0.773262i	$0.281376\pi$
$227$	−4.54526	+	16.9631i	−0.301679	+	1.12588i	−0.935766	+	0.352621i	$0.885291\pi$
$228$	0.655086	−	0.290844i	0.0433841	−	0.0192616i
$229$	12.5666	−	21.7660i	0.830424	−	1.43834i	−0.0672793	−	0.997734i	$-0.521432\pi$
$229$	12.5666	−	21.7660i	0.830424	−	1.43834i	0.897703	−	0.440602i	$-0.145235\pi$
$230$	−5.68838	+	16.3542i	−0.375080	+	1.07837i
$231$	0.615922	−	0.386870i	0.0405247	−	0.0254542i
$232$	1.99936	+	8.38577i	0.131264	+	0.550553i
$233$	1.59009	+	5.93431i	0.104171	+	0.388770i	0.998250	−	0.0591391i	$-0.0188355\pi$
$233$	1.59009	+	5.93431i	0.104171	+	0.388770i	−0.894079	+	0.447909i	$0.852169\pi$
$234$	0.357122	+	0.305334i	0.0233458	+	0.0199603i
$235$	2.96194	+	4.02467i	0.193216	+	0.262541i
$236$	−0.625314	−	3.97494i	−0.0407045	−	0.258747i
$237$	0.474125	−	0.474125i	0.0307978	−	0.0307978i
$238$	−9.79433	+	7.27487i	−0.634872	+	0.471560i
$239$	−1.72326			−0.111469			−0.0557343	−	0.998446i	$-0.517750\pi$
$239$	−1.72326			−0.111469			−0.0557343	+	0.998446i	$0.517750\pi$
$240$	0.460624	+	0.331829i	0.0297331	+	0.0214195i
$241$	−10.5167	−	18.2154i	−0.677439	−	1.17336i	−0.975749	−	0.218890i	$-0.929756\pi$
$241$	−10.5167	−	18.2154i	−0.677439	−	1.17336i	0.298310	−	0.954469i	$-0.403577\pi$
$242$	−0.855314	−	10.9408i	−0.0549817	−	0.703304i
$243$	−0.442748	−	1.65236i	−0.0284023	−	0.105999i
$244$	−15.5222	+	12.5428i	−0.993708	+	0.802972i
$245$	−8.83905	+	12.9179i	−0.564706	+	0.825292i
$246$	0.925367	−	0.327146i	0.0589992	−	0.0208581i
$247$	−0.162058	−	0.604808i	−0.0103115	−	0.0384830i
$248$	14.6090	+	15.4430i	0.927671	+	0.980634i
$249$	−0.195600	+	0.112930i	−0.0123957	+	0.00715665i
$250$	2.34342	+	15.6368i	0.148211	+	0.988956i
$251$	11.1344			0.702800			0.351400	−	0.936225i	$-0.385706\pi$
$251$	11.1344			0.702800			0.351400	+	0.936225i	$0.385706\pi$
$252$	13.1543	+	8.84808i	0.828642	+	0.557377i
$253$	−16.7699	−	16.7699i	−1.05431	−	1.05431i
$254$	−4.83205	+	25.9957i	−0.303190	+	1.63111i
$255$	0.0695927	−	0.457517i	0.00435806	−	0.0286508i
$256$	1.60596	+	15.9192i	0.100373	+	0.994950i
$257$	9.83331	−	2.63483i	0.613385	−	0.164356i	0.0612661	−	0.998121i	$-0.480486\pi$
$257$	9.83331	−	2.63483i	0.613385	−	0.164356i	0.552119	+	0.833765i	$0.313819\pi$
$258$	−0.379843	+	0.795288i	−0.0236480	+	0.0495125i
$259$	8.29549	−	5.21052i	0.515456	−	0.323766i
$260$	0.348894	−	0.352459i	0.0216375	−	0.0218586i
$261$	−7.90810	−	4.56574i	−0.489499	−	0.282612i
$262$	−0.953617	−	12.1983i	−0.0589147	−	0.753613i
$263$	−1.37630	+	5.13642i	−0.0848662	+	0.316725i	−0.995289	−	0.0969544i	$-0.969090\pi$
$263$	−1.37630	+	5.13642i	−0.0848662	+	0.316725i	0.910423	+	0.413679i	$0.135757\pi$
$264$	−0.683916	+	0.369950i	−0.0420921	+	0.0227688i
$265$	−0.572370	−	5.14245i	−0.0351604	−	0.315898i
$266$	−7.77839	−	19.6423i	−0.476923	−	1.20435i
$267$	−0.390609	−	0.390609i	−0.0239049	−	0.0239049i
$268$	−8.43076	−	6.13877i	−0.514990	−	0.374985i
$269$	0.844120	+	1.46206i	0.0514669	+	0.0891433i	0.890611	−	0.454766i	$-0.150277\pi$
$269$	0.844120	+	1.46206i	0.0514669	+	0.0891433i	−0.839144	+	0.543909i	$0.816944\pi$
$270$	−1.18207	+	0.225943i	−0.0719383	+	0.0137505i
$271$	11.9114	+	6.87705i	0.723566	+	0.417751i	0.816064	−	0.577962i	$-0.196152\pi$
$271$	11.9114	+	6.87705i	0.723566	+	0.417751i	−0.0924980	+	0.995713i	$0.529485\pi$
$272$	10.9535	−	7.08081i	0.664154	−	0.429337i
$273$	−0.0126687	+	0.0136491i	−0.000766744	+	0.000826084i
$274$	−0.473558	−	1.33951i	−0.0286087	−	0.0809228i
$275$	−20.6769	−	6.43930i	−1.24686	−	0.388304i
$276$	−0.249771	+	0.648651i	−0.0150345	+	0.0390442i
$277$	26.5298	+	7.10864i	1.59402	+	0.427117i	0.943230	−	0.332140i	$-0.107771\pi$
$277$	26.5298	+	7.10864i	1.59402	+	0.427117i	0.650791	+	0.759257i	$0.274437\pi$
$278$	3.55065	+	5.17202i	0.212954	+	0.310197i
$279$	−22.5174			−1.34808
$280$	10.3262	−	13.1670i	0.617107	−	0.786879i
$281$	8.63212			0.514949			0.257475	−	0.966285i	$-0.417110\pi$
$281$	8.63212			0.514949			0.257475	+	0.966285i	$0.417110\pi$
$282$	0.113533	+	0.165376i	0.00676078	+	0.00984801i
$283$	−15.9555	−	4.27527i	−0.948457	−	0.254138i	−0.248750	−	0.968568i	$-0.580020\pi$
$283$	−15.9555	−	4.27527i	−0.948457	−	0.254138i	−0.699707	+	0.714430i	$0.746686\pi$
$284$	0.124605	+	0.0479809i	0.00739397	+	0.00284714i
$285$	0.734052	+	0.321446i	0.0434815	+	0.0190408i
$286$	0.226411	+	0.640428i	0.0133880	+	0.0378693i
$287$	−8.52272	−	27.6460i	−0.503080	−	1.63189i
$288$	−13.4186	−	10.3522i	−0.790698	−	0.610011i
$289$	5.51456	+	3.18384i	0.324386	+	0.187284i
$290$	−5.41463	+	7.97371i	−0.317958	+	0.468232i
$291$	0.280551	+	0.485929i	0.0164462	+	0.0284856i
$292$	9.94246	−	13.6546i	0.581838	−	0.799076i
$293$	−2.65520	−	2.65520i	−0.155118	−	0.155118i	0.625281	−	0.780400i	$-0.284984\pi$
$293$	−2.65520	−	2.65520i	−0.155118	−	0.155118i	−0.780400	+	0.625281i	$0.784984\pi$
$294$	−0.371651	+	0.506630i	−0.0216752	+	0.0295473i
$295$	2.80970	−	3.51349i	0.163587	−	0.204563i
$296$	−9.21125	+	4.98263i	−0.535393	+	0.289610i
$297$	0.426625	−	1.59219i	0.0247553	−	0.0923880i
$298$	0.312117	+	3.99248i	0.0180805	+	0.231278i
$299$	0.525862	+	0.303607i	0.0304114	+	0.0175580i
$300$	0.0734169	+	0.630449i	0.00423873	+	0.0363990i
$301$	22.9655	+	12.1424i	1.32371	+	0.699876i
$302$	8.34142	−	17.4647i	0.479995	−	1.00498i
$303$	−0.877753	+	0.235193i	−0.0504256	+	0.0135115i
$304$	6.93429	+	21.4942i	0.397709	+	1.23278i
$305$	−22.0583	−	3.35528i	−1.26305	−	0.192123i
$306$	−2.52477	+	13.5828i	−0.144331	+	0.776480i
$307$	10.6866	+	10.6866i	0.609915	+	0.609915i	0.942924	−	0.333009i	$-0.108064\pi$
$307$	10.6866	+	10.6866i	0.609915	+	0.609915i	−0.333009	+	0.942924i	$0.608064\pi$
$308$	10.0735	+	20.5865i	0.573990	+	1.17302i
$309$	−0.282758			−0.0160855
$310$	−1.73193	+	23.7042i	−0.0983672	+	1.34631i
$311$	11.8745	−	6.85572i	0.673339	−	0.388752i	−0.124002	−	0.992282i	$-0.539573\pi$
$311$	11.8745	−	6.85572i	0.673339	−	0.388752i	0.797341	+	0.603530i	$0.206239\pi$
$312$	0.0144624	−	0.0136813i	0.000818770	−	0.000774549i
$313$	−6.30585	−	23.5338i	−0.356428	−	1.33021i	−0.878678	−	0.477415i	$-0.841574\pi$
$313$	−6.30585	−	23.5338i	−0.356428	−	1.33021i	0.522250	−	0.852792i	$-0.325093\pi$
$314$	9.30553	−	3.28979i	0.525141	−	0.185654i
$315$	2.61512	+	17.5304i	0.147345	+	0.987727i
$316$	13.2793	+	16.4336i	0.747018	+	0.924463i
$317$	5.49549	+	20.5094i	0.308657	+	1.15193i	0.929751	+	0.368189i	$0.120022\pi$
$317$	5.49549	+	20.5094i	0.308657	+	1.15193i	−0.621094	+	0.783736i	$0.713311\pi$
$318$	−0.0161883	−	0.207074i	−0.000907792	−	0.0116121i
$319$	−6.60069	−	11.4327i	−0.369568	−	0.640110i
$320$	−11.9299	+	13.3296i	−0.666903	+	0.745145i
$321$	0.368669			0.0205771
$322$	18.8032	+	8.13546i	1.04786	+	0.453371i
$323$	13.0185	−	13.0185i	0.724369	−	0.724369i
$324$	17.7097	−	2.78599i	0.983873	−	0.154777i
$325$	0.554030	+	0.0222316i	0.0307320	+	0.00123319i
$326$	−13.4127	−	11.4676i	−0.742859	−	0.635133i
$327$	−0.227239	−	0.848068i	−0.0125664	−	0.0468983i
$328$	7.17272	+	30.0841i	0.396047	+	1.66111i
$329$	5.00690	−	3.14491i	0.276039	−	0.173384i
$330$	−0.821091	−	0.285595i	−0.0451996	−	0.0157215i
$331$	−7.09183	+	12.2834i	−0.389802	+	0.675157i	−0.992423	−	0.122871i	$-0.960790\pi$
$331$	−7.09183	+	12.2834i	−0.389802	+	0.675157i	0.602621	+	0.798028i	$0.294123\pi$
$332$	−2.88794	−	6.50468i	−0.158496	−	0.356991i
$333$	2.87105	−	10.7149i	0.157332	−	0.587173i
$334$	−0.813987	+	4.37912i	−0.0445394	+	0.239615i
$335$	−1.28982	−	11.5883i	−0.0704701	−	0.633137i
$336$	0.431645	−	0.514666i	0.0235481	−	0.0280774i
$337$	−0.288884	−	0.288884i	−0.0157365	−	0.0157365i	0.699195	−	0.714931i	$-0.253542\pi$
$337$	−0.288884	−	0.288884i	−0.0157365	−	0.0157365i	−0.714931	+	0.699195i	$0.753542\pi$
$338$	10.3955	+	15.1425i	0.565440	+	0.823642i
$339$	0.372091	−	0.214827i	0.0202092	−	0.0116678i
$340$	14.1045	+	3.70256i	0.764925	+	0.200800i
$341$	−28.1921	−	16.2767i	−1.52669	−	0.881433i
$342$	−21.5871	−	10.3104i	−1.16730	−	0.557520i
$343$	14.4741	+	11.5543i	0.781527	+	0.623872i
$344$	−23.6564	−	14.5477i	−1.27547	−	0.784357i
$345$	−0.723785	+	0.282935i	−0.0389673	+	0.0152327i
$346$	7.56717	−	8.85065i	0.406813	−	0.475814i
$347$	8.22946	−	30.7128i	0.441781	−	1.64875i	−0.282518	−	0.959262i	$-0.591170\pi$
$347$	8.22946	−	30.7128i	0.441781	−	1.64875i	0.724299	−	0.689486i	$-0.242164\pi$
$348$	−0.227746	+	0.312778i	−0.0122085	+	0.0167667i
$349$	0.351671			0.0188245			0.00941226	−	0.999956i	$-0.497004\pi$
$349$	0.351671			0.0188245			0.00941226	+	0.999956i	$0.497004\pi$
$350$	18.6555	−	1.40459i	0.997178	−	0.0750784i
$351$			0.0422033i			0.00225265i
$352$	−9.31714	−	22.6607i	−0.496605	−	1.20782i
$353$	−19.1176	−	5.12253i	−1.01753	−	0.272645i	−0.288755	−	0.957403i	$-0.593241\pi$
$353$	−19.1176	−	5.12253i	−1.01753	−	0.272645i	−0.728770	+	0.684758i	$0.759908\pi$
$354$	0.117357	−	0.137262i	0.00623745	−	0.00729540i
$355$	0.0543517	+	0.139039i	0.00288469	+	0.00737941i
$356$	13.5389	−	10.9402i	0.717559	−	0.579828i
$357$	−0.533819	−	0.121932i	−0.0282527	−	0.00645334i
$358$	4.63535	−	9.70518i	0.244986	−	0.512934i
$359$	7.04245	−	12.1979i	0.371686	−	0.643780i	−0.618139	−	0.786069i	$-0.712113\pi$
$359$	7.04245	−	12.1979i	0.371686	−	0.643780i	0.989825	+	0.142289i	$0.0454464\pi$
$360$	−1.57279	−	18.8828i	−0.0828933	−	0.995211i
$361$	6.44018	+	11.1547i	0.338957	+	0.587091i
$362$	20.2169	+	29.4487i	1.06258	+	1.54779i
$363$	0.348272	−	0.348272i	0.0182795	−	0.0182795i
$364$	−0.385546	−	0.442369i	−0.0202081	−	0.0231865i
$365$	18.7686	−	2.08901i	0.982396	−	0.109344i
$366$	−0.880578	−	0.163681i	−0.0460286	−	0.00855575i
$367$	6.94892	+	1.86196i	0.362731	+	0.0971934i	0.435581	−	0.900149i	$-0.356543\pi$
$367$	6.94892	+	1.86196i	0.362731	+	0.0971934i	−0.0728505	+	0.997343i	$0.523210\pi$
$368$	−19.4942	−	9.98416i	−1.01621	−	0.520460i
$369$	−28.3704	−	16.3797i	−1.47690	−	0.852691i
$370$	−11.0588	−	3.84650i	−0.574919	−	0.199970i
$371$	−6.11795	+	0.227920i	−0.317628	+	0.0118330i
$372$	−0.100720	+	0.948751i	−0.00522207	+	0.0491904i
$373$	0.838599	−	0.224702i	0.0434210	−	0.0116346i	−0.237043	−	0.971499i	$-0.576178\pi$
$373$	0.838599	−	0.224702i	0.0434210	−	0.0116346i	0.280464	+	0.959864i	$0.409512\pi$
$374$	−12.9794	+	15.1809i	−0.671149	+	0.784984i
$375$	−0.465060	+	0.535994i	−0.0240156	+	0.0276786i
$376$	−5.55963	+	3.00736i	−0.286716	+	0.155093i
$377$	0.239002	+	0.239002i	0.0123092	+	0.0123092i
$378$	0.163755	+	1.41451i	0.00842266	+	0.0727548i
$379$		−	16.4371i		−	0.844316i	−0.906522	−	0.422158i	$-0.861273\pi$
$379$		−	16.4371i		−	0.844316i	0.906522	−	0.422158i	$-0.138727\pi$
$380$	−12.5141	+	21.9318i	−0.641961	+	1.12508i
$381$	−1.02770	+	0.593344i	−0.0526508	+	0.0303979i
$382$	−28.4150	+	2.22138i	−1.45384	+	0.113656i
$383$	3.23942	−	0.868001i	0.165527	−	0.0443528i	−0.175104	−	0.984550i	$-0.556026\pi$
$383$	3.23942	−	0.868001i	0.165527	−	0.0443528i	0.340631	+	0.940197i	$0.389359\pi$
$384$	−0.496202	+	0.519075i	−0.0253217	+	0.0264889i
$385$	−9.39770	+	23.8386i	−0.478951	+	1.21493i
$386$	32.8126	−	11.6003i	1.67012	−	0.590439i
$387$	28.4143	−	7.61358i	1.44438	−	0.387020i
$388$	−16.1595	+	7.17448i	−0.820376	+	0.364229i
$389$	−0.136918	−	0.237149i	−0.00694201	−	0.0120239i	0.862534	−	0.506000i	$-0.168876\pi$
$389$	−0.136918	−	0.237149i	−0.00694201	−	0.0120239i	−0.869476	+	0.493976i	$0.835543\pi$
$390$	0.0221989	+	0.00162195i	0.00112408	+	8.21306e-5i
$391$			17.8543i			0.902931i
$392$	−14.6387	−	13.3308i	−0.739364	−	0.673306i
$393$	0.388300	−	0.388300i	0.0195871	−	0.0195871i
$394$	6.22547	−	33.4920i	0.313634	−	1.68730i
$395$	−3.55229	+	23.3535i	−0.178735	+	1.17504i
$396$	24.2193	+	9.32593i	1.21706	+	0.468646i
$397$	−3.98239	−	14.8625i	−0.199870	−	0.745927i	−0.990952	−	0.134216i	$-0.957148\pi$
$397$	−3.98239	−	14.8625i	−0.199870	−	0.745927i	0.791082	−	0.611711i	$-0.209518\pi$
$398$	−5.70554	−	2.72506i	−0.285993	−	0.136595i
$399$	0.443186	−	0.838218i	0.0221870	−	0.0419634i
$400$	−19.9990	+	0.203305i	−0.999948	+	0.0101653i
$401$	−5.27304	+	9.13318i	−0.263323	+	0.456089i	−0.967123	−	0.254309i	$-0.918152\pi$
$401$	−5.27304	+	9.13318i	−0.263323	+	0.456089i	0.703800	+	0.710398i	$0.251485\pi$
$402$	−0.0364796	−	0.466633i	−0.00181944	−	0.0232735i
$403$	0.805076	+	0.215720i	0.0401037	+	0.0107458i
$404$	−4.44982	−	28.2862i	−0.221387	−	1.40729i
$405$	15.6538	+	12.5182i	0.777842	+	0.622032i
$406$	8.93790	+	7.08318i	0.443581	+	0.351532i
$407$	11.3398	−	11.3398i	0.562095	−	0.562095i
$408$	0.561008	+	0.167135i	0.0277740	+	0.00827439i
$409$	23.4708	−	13.5509i	1.16056	−	0.670048i	0.209119	−	0.977890i	$-0.432940\pi$
$409$	23.4708	−	13.5509i	1.16056	−	0.670048i	0.951437	+	0.307843i	$0.0996070\pi$
$410$	−19.4251	+	28.6058i	−0.959335	+	1.41274i
$411$	0.0318823	−	0.0552217i	0.00157264	−	0.00272389i
$412$	0.940587	−	8.86006i	0.0463394	−	0.436504i
$413$	−3.90146	−	3.62121i	−0.191978	−	0.178188i
$414$	21.8730	−	7.73278i	1.07500	−	0.380046i
$415$	3.19180	−	7.28878i	0.156680	−	0.357792i
$416$	0.380586	+	0.498680i	0.0186598	+	0.0244498i
$417$	−0.0728730	+	0.271966i	−0.00356860	+	0.0133182i
$418$	−19.5745	−	28.5129i	−0.957419	−	1.39461i
$419$		−	16.6818i		−	0.814959i	−0.913214	−	0.407479i	$-0.866408\pi$
$419$		−	16.6818i		−	0.814959i	0.913214	−	0.407479i	$-0.133592\pi$
$420$	0.750326	−	0.0317726i	0.0366121	−	0.00155034i
$421$			10.6070i			0.516953i	0.966018	+	0.258476i	$0.0832204\pi$
$421$			10.6070i			0.516953i	−0.966018	+	0.258476i	$0.916780\pi$
$422$	−10.4908	+	7.20203i	−0.510682	+	0.350590i
$423$	1.73288	−	6.46718i	0.0842553	−	0.314445i
$424$	6.54239	+	0.181575i	0.317726	+	0.00881807i
$425$	7.57914	+	14.4348i	0.367643	+	0.700193i
$426$	0.00199744	+	0.00564997i	9.67763e−5	+	0.000273742i
$427$	−5.87873	+	25.7371i	−0.284492	+	1.24551i
$428$	−1.22637	+	11.5520i	−0.0592787	+	0.558389i
$429$	−0.0152431	+	0.0264018i	−0.000735943	+	0.00127469i
$430$	−5.82935	−	30.4974i	−0.281116	−	1.47071i
$431$	−31.2821	+	18.0607i	−1.50680	+	0.869953i	−0.506835	+	0.862043i	$0.669185\pi$
$431$	−31.2821	+	18.0607i	−1.50680	+	0.869953i	−0.999969	+	0.00791023i	$0.997482\pi$
$432$	−0.0764944	−	1.52036i	−0.00368034	−	0.0731482i
$433$	−2.55043	+	2.55043i	−0.122566	+	0.122566i	−0.765729	−	0.643163i	$-0.777622\pi$
$433$	−2.55043	+	2.55043i	−0.122566	+	0.122566i	0.643163	+	0.765729i	$0.277622\pi$
$434$	27.8205	+	4.10638i	1.33543	+	0.197113i
$435$	−0.429922	+	0.0478517i	−0.0206132	+	0.00229431i
$436$	27.3296	−	4.29933i	1.30885	−	0.205901i
$437$	−29.8631	−	8.00178i	−1.42854	−	0.382777i
$438$	0.755768	−	0.0590831i	0.0361120	−	0.00282310i
$439$	−7.28333	+	12.6151i	−0.347614	+	0.602085i	−0.985825	−	0.167776i	$-0.946341\pi$
$439$	−7.28333	+	12.6151i	−0.347614	+	0.602085i	0.638211	+	0.769862i	$0.279675\pi$
$440$	11.6803	−	24.7784i	0.556835	−	1.18126i
$441$	20.9137	−	1.56041i	0.995889	−	0.0743054i
$442$	0.220395	−	0.461447i	0.0104831	−	0.0219488i
$443$	2.79617	+	10.4354i	0.132850	+	0.495802i	0.999997	−	0.00224887i	$-0.000715839\pi$
$443$	2.79617	+	10.4354i	0.132850	+	0.495802i	−0.867148	+	0.498051i	$0.834049\pi$
$444$	−0.438620	−	0.168896i	−0.0208160	−	0.00801546i
$445$	19.2398	+	2.92656i	0.912055	+	0.138732i
$446$	−26.5028	−	4.92632i	−1.25494	−	0.233268i
$447$	−0.127090	+	0.127090i	−0.00601115	+	0.00601115i
$448$	14.6909	+	15.2374i	0.694081	+	0.719897i
$449$			18.2050i			0.859149i	0.903031	+	0.429574i	$0.141336\pi$
$449$			18.2050i			0.859149i	−0.903031	+	0.429574i	$0.858664\pi$
$450$	14.4013	−	15.5369i	0.678884	−	0.732415i
$451$	−23.6801	−	41.0151i	−1.11505	−	1.93133i
$452$	5.49372	+	12.3739i	0.258403	+	0.582018i
$453$	0.839042	−	0.224821i	0.0394217	−	0.0105630i
$454$	−8.27811	−	23.4155i	−0.388511	−	1.09894i
$455$	0.0744440	−	0.651827i	0.00348999	−	0.0305581i
$456$	−0.530976	+	0.863435i	−0.0248652	+	0.0404340i
$457$	13.7782	−	3.69187i	0.644519	−	0.172698i	0.0782693	−	0.996932i	$-0.475061\pi$
$457$	13.7782	−	3.69187i	0.644519	−	0.172698i	0.566249	+	0.824234i	$0.308394\pi$
$458$	2.77022	+	35.4356i	0.129444	+	1.65580i
$459$	−1.07468	+	0.620467i	−0.0501618	+	0.0289609i
$460$	−6.45796	−	23.6206i	−0.301104	−	1.10131i
$461$			17.8896i			0.833202i	0.909089	+	0.416601i	$0.136779\pi$
$461$			17.8896i			0.833202i	−0.909089	+	0.416601i	$0.863221\pi$
$462$	−0.408455	+	0.944046i	−0.0190030	+	0.0439210i
$463$	−15.5156	−	15.5156i	−0.721073	−	0.721073i	0.247751	−	0.968824i	$-0.420309\pi$
$463$	−15.5156	−	15.5156i	−0.721073	−	0.721073i	−0.968824	+	0.247751i	$0.920309\pi$
$464$	−9.04313	−	8.17674i	−0.419817	−	0.379595i
$465$	−0.859117	+	0.632264i	−0.0398406	+	0.0293205i
$466$	−6.60379	−	5.64614i	−0.305915	−	0.261552i
$467$	−33.7488	+	9.04295i	−1.56171	+	0.418458i	−0.933203	−	0.359349i	$-0.882999\pi$
$467$	−33.7488	+	9.04295i	−1.56171	+	0.418458i	−0.628503	+	0.777807i	$0.716332\pi$
$468$	−0.660764	−	0.0701469i	−0.0305438	−	0.00324254i
$469$	−13.7866	+	0.513609i	−0.636605	+	0.0237163i
$470$	−6.67474	−	2.32163i	−0.307883	−	0.107089i
$471$	0.383623	+	0.221485i	0.0176764	+	0.0102055i
$472$	3.91065	+	4.13391i	0.180002	+	0.190279i
$473$	41.0785	+	11.0069i	1.88879	+	0.506100i
$474$	−0.173292	+	0.932282i	−0.00795956	+	0.0428211i
$475$	−27.5404	+	6.20757i	−1.26364	+	0.284823i
$476$	5.59641	−	16.3213i	0.256511	−	0.748086i
$477$	−4.90209	+	4.90209i	−0.224451	+	0.224451i
$478$	2.00917	−	1.37932i	0.0918971	−	0.0630885i
$479$	14.1930	+	24.5830i	0.648496	+	1.12323i	0.983482	+	0.181005i	$0.0579349\pi$
$479$	14.1930	+	24.5830i	0.648496	+	1.12323i	−0.334986	+	0.942223i	$0.608732\pi$
$480$	−0.802645	−	0.0181941i	−0.0366355	−	0.000830444i
$481$	−0.205300	+	0.355590i	−0.00936087	+	0.0162135i
$482$	26.8413	+	12.8199i	1.22259	+	0.583929i
$483$	0.270885	+	0.878695i	0.0123257	+	0.0399820i
$484$	9.75438	+	12.0714i	0.443381	+	0.548701i
$485$	−18.1074	−	7.92938i	−0.822217	−	0.360054i
$486$	1.83877	+	1.57212i	0.0834083	+	0.0713128i
$487$	18.4315	+	4.93870i	0.835209	+	0.223794i	0.650985	−	0.759091i	$-0.274356\pi$
$487$	18.4315	+	4.93870i	0.835209	+	0.223794i	0.184224	+	0.982884i	$0.441023\pi$
$488$	8.05807	−	27.0479i	0.364772	−	1.22440i
$489$		−	0.791996i		−	0.0358153i
$490$	−0.0340729	−	22.1359i	−0.00153925	−	0.999999i
$491$	−16.3415			−0.737483			−0.368742	−	0.929532i	$-0.620211\pi$
$491$	−16.3415			−0.737483			−0.368742	+	0.929532i	$0.620211\pi$
$492$	−0.817042	+	1.12210i	−0.0368351	+	0.0505880i
$493$	−2.57226	+	9.59979i	−0.115849	+	0.432353i
$494$	0.673040	+	0.575438i	0.0302815	+	0.0258902i
$495$	10.5642	+	27.0246i	0.474826	+	1.21467i
$496$	−29.3935	−	6.31198i	−1.31981	−	0.283416i
$497$	0.168797	−	0.0520368i	0.00757157	−	0.00233417i
$498$	0.137662	−	0.288227i	0.00616878	−	0.0129157i
$499$	1.25495	+	0.724547i	0.0561794	+	0.0324352i	0.527827	−	0.849352i	$-0.323007\pi$
$499$	1.25495	+	0.724547i	0.0561794	+	0.0324352i	−0.471647	+	0.881787i	$0.656340\pi$
$500$	−15.2480	−	16.3553i	−0.681913	−	0.731433i
$501$	−0.173122	+	0.0999522i	−0.00773453	+	0.00446553i
$502$	−12.9818	+	8.91213i	−0.579404	+	0.397768i
$503$	−7.99645	−	7.99645i	−0.356544	−	0.356544i	0.505993	−	0.862537i	$-0.331126\pi$
$503$	−7.99645	−	7.99645i	−0.356544	−	0.356544i	−0.862537	+	0.505993i	$0.831126\pi$
$504$	−22.4188	+	0.212772i	−0.998612	+	0.00947763i
$505$	19.9942	−	25.0025i	0.889730	−	1.11259i
$506$	32.9749	+	6.12935i	1.46591	+	0.272483i
$507$	−0.213355	+	0.796253i	−0.00947544	+	0.0353628i
$508$	−15.1735	−	34.1762i	−0.673214	−	1.51632i
$509$	10.0666	−	17.4358i	0.446193	−	0.772829i	−0.551942	−	0.833883i	$-0.686113\pi$
$509$	10.0666	−	17.4358i	0.446193	−	0.772829i	0.998134	+	0.0610542i	$0.0194462\pi$
$510$	0.285063	+	0.589126i	0.0126228	+	0.0260869i
$511$	−0.831851	−	22.3290i	−0.0367989	−	0.987777i
$512$	−14.6143	−	17.2749i	−0.645867	−	0.763450i
$513$	−0.556150	−	2.07558i	−0.0245546	−	0.0916392i
$514$	−9.35579	+	10.9427i	−0.412666	+	0.482660i
$515$	8.02300	−	5.90450i	0.353536	−	0.260183i
$516$	−0.193695	−	1.23126i	−0.00852695	−	0.0542034i
$517$	6.84438	−	6.84438i	0.301016	−	0.301016i
$518$	−5.50123	+	12.7148i	−0.241710	+	0.558655i
$519$	0.522617			0.0229403
$520$	−0.124667	+	0.690194i	−0.00546700	+	0.0302670i
$521$	1.94229	+	3.36415i	0.0850933	+	0.147386i	0.905431	−	0.424493i	$-0.139548\pi$
$521$	1.94229	+	3.36415i	0.0850933	+	0.147386i	−0.820338	+	0.571879i	$0.806214\pi$
$522$	12.8746	−	1.00649i	0.563505	−	0.0440528i
$523$	1.51422	+	5.65116i	0.0662124	+	0.247108i	0.991097	−	0.133139i	$-0.0425057\pi$
$523$	1.51422	+	5.65116i	0.0662124	+	0.247108i	−0.924885	+	0.380247i	$0.875839\pi$
$524$	10.8755	+	13.4588i	0.475097	+	0.587951i
$525$	0.592011	+	0.595417i	0.0258375	+	0.0259861i
$526$	−2.50660	−	7.09020i	−0.109293	−	0.309147i
$527$	6.34295	+	23.6722i	0.276303	+	1.03118i
$528$	0.501272	−	0.978742i	0.0218151	−	0.0425943i
$529$	6.04643	−	3.49091i	0.262888	−	0.151779i
$530$	4.78340	+	5.53749i	0.207778	+	0.240533i
$531$	−6.02764			−0.261577
$532$	24.7908	+	16.6753i	1.07482	+	0.722965i
$533$	0.857422	+	0.857422i	0.0371391	+	0.0371391i
$534$	0.768063	+	0.142767i	0.0332373	+	0.00617813i
$535$	−10.4607	+	7.69848i	−0.452254	+	0.332834i
$536$	14.7430	+	0.409173i	0.636802	+	0.0176736i
$537$	0.466259	−	0.124934i	0.0201206	−	0.00539129i
$538$	−2.15441	−	1.02898i	−0.0928834	−	0.0443627i
$539$	27.3121	+	13.1638i	1.17642	+	0.567004i
$540$	1.19734	−	1.20957i	0.0515251	−	0.0520516i
$541$	−8.59386	−	4.96167i	−0.369479	−	0.213319i	0.303752	−	0.952751i	$-0.401761\pi$
$541$	−8.59386	−	4.96167i	−0.369479	−	0.213319i	−0.673231	+	0.739432i	$0.735094\pi$
$542$	−19.3921	+	1.51600i	−0.832960	+	0.0651177i
$543$	−0.414928	+	1.54853i	−0.0178063	+	0.0664539i
$544$	−7.10324	+	17.0229i	−0.304549	+	0.729850i
$545$	24.1569	+	19.3180i	1.03477	+	0.827492i
$546$	0.00384562	−	0.0260538i	0.000164577	−	0.00111500i
$547$	13.2213	+	13.2213i	0.565302	+	0.565302i	0.930809	−	0.365506i	$-0.119104\pi$
$547$	13.2213	+	13.2213i	0.565302	+	0.565302i	−0.365506	+	0.930809i	$0.619104\pi$
$548$	1.62428	+	1.18271i	0.0693860	+	0.0505227i
$549$	14.9473	+	25.8894i	0.637934	+	1.10493i
$550$	29.2615	−	9.04238i	1.24771	−	0.385568i
$551$	−14.9038	−	8.60469i	−0.634922	−	0.366572i
$552$	−0.227977	−	0.956187i	−0.00970333	−	0.0406980i
$553$	27.2483	+	6.22391i	1.15871	+	0.264667i
$554$	−36.6212	+	12.9467i	−1.55588	+	0.550053i
$555$	−0.191322	−	0.489426i	−0.00812116	−	0.0207750i
$556$	−8.27947	−	3.18812i	−0.351128	−	0.135206i
$557$	10.7659	+	2.88472i	0.456167	+	0.122230i	0.479584	−	0.877496i	$-0.340788\pi$
$557$	10.7659	+	2.88472i	0.456167	+	0.122230i	−0.0234166	+	0.999726i	$0.507454\pi$
$558$	26.2532	−	18.0232i	1.11139	−	0.762982i
$559$	−1.08885			−0.0460534
$560$	−1.50036	+	23.6167i	−0.0634018	+	0.997988i
$561$	−0.896406			−0.0378463
$562$	−10.0643	+	6.90924i	−0.424535	+	0.291449i
$563$	14.2140	+	3.80862i	0.599047	+	0.160514i	0.545585	−	0.838056i	$-0.316308\pi$
$563$	14.2140	+	3.80862i	0.599047	+	0.160514i	0.0534623	+	0.998570i	$0.482974\pi$
$564$	−0.264738	−	0.101941i	−0.0111475	−	0.00429248i
$565$	−6.07177	+	13.8654i	−0.255441	+	0.583324i
$566$	22.0246	−	7.78639i	0.925765	−	0.327287i
$567$	16.1337	−	17.3823i	0.677553	−	0.729990i
$568$	−0.183683	+	0.0437942i	−0.00770717	+	0.00183756i
$569$	10.9495	+	6.32172i	0.459029	+	0.265020i	0.711636	−	0.702549i	$-0.247955\pi$
$569$	10.9495	+	6.32172i	0.459029	+	0.265020i	−0.252607	+	0.967569i	$0.581288\pi$
$570$	−1.11313	+	0.212766i	−0.0466237	+	0.00891178i
$571$	−10.1205	−	17.5292i	−0.423529	−	0.733574i	0.572752	−	0.819728i	$-0.305876\pi$
$571$	−10.1205	−	17.5292i	−0.423529	−	0.733574i	−0.996282	+	0.0861540i	$0.972542\pi$
$572$	−0.776579	−	0.565458i	−0.0324704	−	0.0236430i
$573$	−0.904515	−	0.904515i	−0.0377867	−	0.0377867i
$574$	32.0648	+	25.4110i	1.33836	+	1.06063i
$575$	14.6285	−	23.1420i	0.610053	−	0.965087i
$576$	23.9309	+	1.32936i	0.997120	+	0.0553902i
$577$	−11.8140	+	44.0906i	−0.491825	+	1.83552i	0.0553062	+	0.998469i	$0.482387\pi$
$577$	−11.8140	+	44.0906i	−0.491825	+	1.83552i	−0.547131	+	0.837047i	$0.684280\pi$
$578$	−8.97785	+	0.701855i	−0.373429	+	0.0291933i
$579$	1.35271	+	0.780988i	0.0562167	+	0.0324567i
$580$	−0.0692808	−	13.6305i	−0.00287673	−	0.565977i
$581$	−8.32310	−	4.40062i	−0.345300	−	0.182568i
$582$	−0.716039	−	0.341992i	−0.0296808	−	0.0141760i
$583$	−9.68095	+	2.59400i	−0.400944	+	0.107433i
$584$	−0.662704	+	23.8781i	−0.0274229	+	0.988082i
$585$	−0.440345	−	0.598338i	−0.0182060	−	0.0247383i
$586$	5.22097	+	0.970470i	0.215676	+	0.0400898i
$587$	−18.2111	−	18.2111i	−0.751651	−	0.751651i	0.223136	−	0.974787i	$-0.428370\pi$
$587$	−18.2111	−	18.2111i	−0.751651	−	0.751651i	−0.974787	+	0.223136i	$0.928370\pi$
$588$	0.0277996	−	0.888158i	0.00114643	−	0.0366270i
$589$	−42.4368			−1.74858
$590$	−0.463617	+	6.34532i	−0.0190868	+	0.261232i
$591$	1.32406	−	0.764446i	0.0544645	−	0.0314451i
$592$	6.75132	−	13.1821i	0.277478	−	0.541780i
$593$	8.65642	+	32.3062i	0.355476	+	1.32666i	0.879884	+	0.475189i	$0.157620\pi$
$593$	8.65642	+	32.3062i	0.355476	+	1.32666i	−0.524408	+	0.851467i	$0.675713\pi$
$594$	0.776997	+	2.19782i	0.0318806	+	0.0901776i
$595$	17.6928	−	7.68739i	0.725334	−	0.315152i
$596$	−3.55953	−	4.40505i	−0.145804	−	0.180438i
$597$	−0.0734468	−	0.274107i	−0.00300598	−	0.0112185i
$598$	−0.856117	+	0.0669281i	−0.0350092	+	0.00273689i
$599$	−22.0291	−	38.1554i	−0.900083	−	1.55899i	−0.827385	−	0.561635i	$-0.810172\pi$
$599$	−22.0291	−	38.1554i	−0.900083	−	1.55899i	−0.0726981	−	0.997354i	$-0.523161\pi$
$600$	−0.590215	−	0.676282i	−0.0240954	−	0.0276091i
$601$	−20.6846			−0.843744			−0.421872	−	0.906655i	$-0.638627\pi$
$601$	−20.6846			−0.843744			−0.421872	+	0.906655i	$0.638627\pi$
$602$	−36.4945	+	4.22489i	−1.48741	+	0.172194i
$603$	−11.0467	+	11.0467i	−0.449855	+	0.449855i
$604$	4.25358	+	27.0388i	0.173076	+	1.10019i
$605$	−2.60936	+	17.1544i	−0.106085	+	0.697427i
$606$	0.835128	−	0.976776i	0.0339248	−	0.0396788i
$607$	5.23271	+	19.5287i	0.212389	+	0.792647i	0.987069	+	0.160294i	$0.0512442\pi$
$607$	5.23271	+	19.5287i	0.212389	+	0.792647i	−0.774680	+	0.632353i	$0.782089\pi$
$608$	−25.2890	−	19.5100i	−1.02560	−	0.791236i
$609$	0.0190547	+	0.511477i	0.000772137	+	0.0207261i
$610$	28.4036	−	13.7438i	1.15003	−	0.556468i
$611$	−0.123913	+	0.214623i	−0.00501297	+	0.00868273i
$612$	−7.92821	−	17.8572i	−0.320479	−	0.721835i
$613$	−1.97479	+	7.37000i	−0.0797609	+	0.297672i	−0.994271	−	0.106892i	$-0.965910\pi$
$613$	−1.97479	+	7.37000i	−0.0797609	+	0.297672i	0.914510	+	0.404564i	$0.132577\pi$
$614$	−21.0132	−	3.90592i	−0.848025	−	0.157630i
$615$	−1.54235	+	0.171669i	−0.0621936	+	0.00692235i
$616$	−28.2224	−	15.9390i	−1.13711	−	0.642202i
$617$	5.12158	+	5.12158i	0.206187	+	0.206187i	0.802645	−	0.596457i	$-0.203426\pi$
$617$	5.12158	+	5.12158i	0.206187	+	0.206187i	−0.596457	+	0.802645i	$0.703426\pi$
$618$	0.329670	−	0.226323i	0.0132613	−	0.00910403i
$619$	−4.67244	+	2.69763i	−0.187801	+	0.108427i	−0.590953	−	0.806706i	$-0.701248\pi$
$619$	−4.67244	+	2.69763i	−0.187801	+	0.108427i	0.403152	+	0.915133i	$0.367915\pi$
$620$	−16.9538	−	29.0231i	−0.680881	−	1.16560i
$621$	1.80465	+	1.04192i	0.0724183	+	0.0418107i
$622$	−8.35714	+	17.4976i	−0.335091	+	0.701590i
$623$	5.12758	−	22.4485i	0.205432	−	0.899382i
$624$	−0.00591115	+	0.0275269i	−0.000236636	+	0.00110196i
$625$	2.00313	−	24.9196i	0.0801252	−	0.996785i
$626$	26.1887	+	22.3909i	1.04671	+	0.894922i
$627$	0.401743	−	1.49933i	0.0160441	−	0.0598773i
$628$	−8.21621	+	11.2838i	−0.327862	+	0.450274i
$629$	−12.0732			−0.481388
$630$	−17.0805	−	18.3457i	−0.680504	−	0.730910i
$631$			16.5518i			0.658916i	0.944170	+	0.329458i	$0.106866\pi$
$631$			16.5518i			0.658916i	−0.944170	+	0.329458i	$0.893134\pi$
$632$	−28.6361	−	8.53121i	−1.13908	−	0.339353i
$633$	−0.551647	−	0.147813i	−0.0219260	−	0.00587505i
$634$	−22.8232	−	19.5135i	−0.906426	−	0.774980i
$635$	16.7700	−	38.2959i	0.665498	−	1.51973i
$636$	0.184618	+	0.228472i	0.00732058	+	0.00905950i
$637$	−0.762686	−	0.144565i	−0.0302187	−	0.00572788i
$638$	16.8467	+	8.04626i	0.666967	+	0.318554i
$639$	0.100009	−	0.173220i	0.00395628	−	0.00685248i
$640$	3.24008	−	25.0899i	0.128075	−	0.991764i
$641$	4.31596	+	7.47546i	0.170470	+	0.295263i	0.938584	−	0.345050i	$-0.112138\pi$
$641$	4.31596	+	7.47546i	0.170470	+	0.295263i	−0.768114	+	0.640313i	$0.778805\pi$
$642$	−0.429835	+	0.295087i	−0.0169642	+	0.0116462i
$643$	−16.3559	+	16.3559i	−0.645015	+	0.645015i	−0.951784	−	0.306769i	$-0.900752\pi$
$643$	−16.3559	+	16.3559i	−0.645015	+	0.645015i	0.306769	+	0.951784i	$0.400752\pi$
$644$	−28.4345	+	5.56507i	−1.12048	+	0.219294i
$645$	0.870322	−	1.08833i	0.0342689	−	0.0428528i
$646$	−4.75823	+	25.5985i	−0.187210	+	1.00716i
$647$	−31.0040	−	8.30749i	−1.21889	−	0.326601i	−0.408647	−	0.912692i	$-0.633999\pi$
$647$	−31.0040	−	8.30749i	−1.21889	−	0.326601i	−0.810245	+	0.586091i	$0.800666\pi$
$648$	−18.4180	+	17.4233i	−0.723527	+	0.684450i
$649$	−7.54668	−	4.35708i	−0.296233	−	0.171030i
$650$	−0.663742	+	0.417531i	−0.0260341	+	0.0163769i
$651$	0.671321	+	1.06879i	0.0263111	+	0.0418891i
$652$	24.8167	+	2.63455i	0.971899	+	0.103177i
$653$	−28.0249	+	7.50926i	−1.09670	+	0.293860i	−0.761420	−	0.648258i	$-0.775498\pi$
$653$	−28.0249	+	7.50926i	−1.09670	+	0.293860i	−0.335280	+	0.942118i	$0.608831\pi$
$654$	0.943743	+	0.806885i	0.0369033	+	0.0315517i
$655$	−2.90925	+	19.1260i	−0.113674	+	0.747316i
$656$	−32.4423	−	29.3342i	−1.26666	−	1.14531i
$657$	−17.8914	−	17.8914i	−0.698010	−	0.698010i
$658$	−3.32037	+	7.67425i	−0.129442	+	0.299174i
$659$			17.3903i			0.677431i	0.940889	+	0.338716i	$0.109992\pi$
$659$			17.3903i			0.677431i	−0.940889	+	0.338716i	$0.890008\pi$
$660$	1.18591	−	0.324233i	0.0461615	−	0.0126208i
$661$	−15.1986	+	8.77491i	−0.591157	+	0.341305i	−0.765555	−	0.643371i	$-0.777535\pi$
$661$	−15.1986	+	8.77491i	−0.591157	+	0.341305i	0.174398	+	0.984675i	$0.444202\pi$
$662$	−1.56335	−	19.9977i	−0.0607612	−	0.777233i
$663$	0.0221690	−	0.00594015i	0.000860971	−	0.000230696i
$664$	8.57349	+	5.27233i	0.332716	+	0.204606i
$665$	4.92851	+	33.0382i	0.191119	+	1.28117i
$666$	5.22894	+	14.7906i	0.202617	+	0.573124i
$667$	16.1204	−	4.31945i	0.624185	−	0.167250i
$668$	−2.55606	−	5.75717i	−0.0988968	−	0.222752i
$669$	−0.604919	−	1.04775i	−0.0233875	−	0.0405084i
$670$	10.7792	+	12.4785i	0.416437	+	0.482088i
$671$			43.2185i			1.66843i
$672$	−0.0913135	+	0.945547i	−0.00352250	+	0.0364753i
$673$	7.44324	−	7.44324i	0.286916	−	0.286916i	−0.548944	−	0.835859i	$-0.684970\pi$
$673$	7.44324	−	7.44324i	0.286916	−	0.286916i	0.835859	+	0.548944i	$0.184970\pi$
$674$	0.568038	+	0.105587i	0.0218800	+	0.00406704i
$675$	1.90132	+	0.0762945i	0.0731818	+	0.00293658i
$676$	−24.2404	−	9.33407i	−0.932323	−	0.359003i
$677$	10.5614	+	39.4156i	0.405907	+	1.51486i	0.802377	+	0.596817i	$0.203568\pi$
$677$	10.5614	+	39.4156i	0.405907	+	1.51486i	−0.396470	+	0.918047i	$0.629765\pi$
$678$	−0.261874	+	0.548294i	−0.0100572	+	0.0210571i
$679$	−10.9324	+	20.6770i	−0.419548	+	0.793511i
$680$	−19.4082	+	6.97256i	−0.744269	+	0.267386i
$681$	0.557323	−	0.965312i	0.0213567	−	0.0369908i
$682$	45.8974	−	3.58809i	1.75750	−	0.137395i
$683$	15.7008	+	4.20701i	0.600773	+	0.160977i	0.546372	−	0.837542i	$-0.316008\pi$
$683$	15.7008	+	4.20701i	0.600773	+	0.160977i	0.0544011	+	0.998519i	$0.482675\pi$
$684$	33.4211	−	5.25761i	1.27789	−	0.201030i
$685$	0.248498	+	2.23262i	0.00949462	+	0.0853042i
$686$	−26.1236	−	1.88601i	−0.997404	−	0.0720082i
$687$	−1.12800	+	1.12800i	−0.0430357	+	0.0430357i
$688$	39.2253	−	1.97356i	1.49545	−	0.0752412i
$689$	0.222229	−	0.128304i	0.00846626	−	0.00488800i
$690$	0.617403	−	0.909202i	0.0235041	−	0.0346127i
$691$	−15.4680	+	26.7914i	−0.588431	+	1.01919i	0.406007	+	0.913870i	$0.366921\pi$
$691$	−15.4680	+	26.7914i	−0.588431	+	1.01919i	−0.994438	+	0.105323i	$0.966412\pi$
$692$	−1.73847	+	16.3759i	−0.0660867	+	0.622518i
$693$	32.8086	−	10.1143i	1.24630	−	0.384209i
$694$	14.9880	+	42.3952i	0.568938	+	1.60930i
$695$	−3.61143	−	9.23850i	−0.136989	−	0.350436i
$696$	0.0151802	−	0.546961i	0.000575403	−	0.0207325i
$697$	−9.22800	+	34.4394i	−0.349536	+	1.30448i
$698$	−0.410016	+	0.281481i	−0.0155194	+	0.0106542i
$699$		−	0.389943i		−	0.0147490i
$700$	−20.6263	+	16.5697i	−0.779603	+	0.626275i
$701$			44.8729i			1.69483i	0.530933	+	0.847414i	$0.321842\pi$
$701$			44.8729i			1.69483i	−0.530933	+	0.847414i	$0.678158\pi$
$702$	−0.0337800	−	0.0492052i	−0.00127494	−	0.00185713i
$703$	5.41084	−	20.1935i	0.204074	−	0.761613i
$704$	29.0008	+	18.9628i	1.09301	+	0.714688i
$705$	−0.115476	−	0.295403i	−0.00434908	−	0.0111255i
$706$	26.3895	−	9.32949i	0.993180	−	0.351120i
$707$	−27.7633	−	25.7690i	−1.04415	−	0.969144i
$708$	−0.0269614	+	0.253969i	−0.00101327	+	0.00954474i
$709$	12.6190	−	21.8567i	0.473915	−	0.820844i	−0.525639	−	0.850708i	$-0.676174\pi$
$709$	12.6190	−	21.8567i	0.473915	−	0.820844i	0.999554	+	0.0298631i	$0.00950714\pi$
$710$	−0.174657	−	0.118603i	−0.00655477	−	0.00445108i
$711$	27.4095	−	15.8249i	1.02794	−	0.593480i
$712$	−7.02846	+	23.5919i	−0.263403	+	0.884144i
$713$	29.1001	−	29.1001i	1.08981	−	1.08981i
$714$	0.719981	−	0.285113i	0.0269446	−	0.0106701i
$715$	−0.118808	−	1.06743i	−0.00444318	−	0.0399196i
$716$	2.36373	+	15.0255i	0.0883366	+	0.561531i
$717$	0.105650	+	0.0283089i	0.00394557	+	0.00105721i
$718$	1.55246	+	19.8585i	0.0579373	+	0.741111i
$719$	6.52310	−	11.2983i	0.243271	−	0.421357i	−0.718373	−	0.695658i	$-0.755113\pi$
$719$	6.52310	−	11.2983i	0.243271	−	0.421357i	0.961644	+	0.274301i	$0.0884463\pi$
$720$	16.9477	+	20.7567i	0.631604	+	0.773558i
$721$	−6.26923	−	9.98104i	−0.233478	−	0.371713i
$722$	−16.4370	−	7.85060i	−0.611723	−	0.292169i
$723$	0.345525	+	1.28952i	0.0128502	+	0.0479577i
$724$	−47.1421	−	18.1527i	−1.75202	−	0.674639i
$725$	11.1994	−	10.3353i	0.415936	−	0.383843i
$726$	−0.127293	+	0.684814i	−0.00472427	+	0.0254158i
$727$	3.91750	−	3.91750i	0.145292	−	0.145292i	−0.630719	−	0.776011i	$-0.717240\pi$
$727$	3.91750	−	3.91750i	0.145292	−	0.145292i	0.776011	+	0.630719i	$0.217240\pi$
$728$	0.803588	+	0.207167i	0.0297830	+	0.00767813i
$729$		−	26.7827i		−	0.991952i
$730$	−20.2105	+	17.4582i	−0.748023	+	0.646158i
$731$	−16.0081	−	27.7268i	−0.592080	−	1.02551i
$732$	1.15769	−	0.513987i	0.0427893	−	0.0189975i
$733$	5.63626	−	1.51023i	0.208180	−	0.0557817i	−0.153222	−	0.988192i	$-0.548965\pi$
$733$	5.63626	−	1.51023i	0.208180	−	0.0557817i	0.361402	+	0.932410i	$0.382298\pi$
$734$	−9.59214	+	3.39112i	−0.354052	+	0.125168i
$735$	0.754114	−	0.646768i	0.0278159	−	0.0238564i
$736$	30.7199	−	3.96278i	1.13235	−	0.146070i
$737$	−21.8157	+	5.84549i	−0.803590	+	0.215321i
$738$	46.1878	−	3.61079i	1.70019	−	0.132915i
$739$	−28.1532	+	16.2543i	−1.03563	+	0.597924i	−0.918594	−	0.395204i	$-0.870674\pi$
$739$	−28.1532	+	16.2543i	−1.03563	+	0.597924i	−0.117040	+	0.993127i	$0.537341\pi$
$740$	15.9723	−	4.36690i	0.587154	−	0.160530i
$741$			0.0397419i			0.00145996i
$742$	6.95054	−	5.16261i	0.255163	−	0.189525i
$743$	0.677329	+	0.677329i	0.0248488	+	0.0248488i	0.719422	−	0.694573i	$-0.244407\pi$
$743$	0.677329	+	0.677329i	0.0248488	+	0.0248488i	−0.694573	+	0.719422i	$0.744407\pi$
$744$	−0.641960	−	1.18677i	−0.0235354	−	0.0435092i
$745$	0.952195	−	6.25993i	0.0348857	−	0.229346i
$746$	−0.797876	+	0.933206i	−0.0292123	+	0.0341671i
$747$	−10.2978	+	2.75930i	−0.376778	+	0.100957i
$748$	2.98187	−	28.0884i	0.109028	−	1.02701i
$749$	8.17404	+	13.0136i	0.298673	+	0.475507i
$750$	0.113202	−	0.997158i	0.00413355	−	0.0364111i
$751$	−37.0877	−	21.4126i	−1.35335	−	0.781357i	−0.364633	−	0.931151i	$-0.618806\pi$
$751$	−37.0877	−	21.4126i	−1.35335	−	0.781357i	−0.988717	+	0.149794i	$0.952139\pi$
$752$	4.07489	−	7.95630i	0.148596	−	0.290136i
$753$	−0.682633	−	0.182911i	−0.0248765	−	0.00666565i
$754$	−0.469954	−	0.0873547i	−0.0171147	−	0.00318127i
$755$	−19.1124	+	23.8998i	−0.695572	+	0.869803i
$756$	−1.32312	−	1.51812i	−0.0481213	−	0.0552136i
$757$	1.64720	−	1.64720i	0.0598686	−	0.0598686i	−0.676539	−	0.736407i	$-0.736521\pi$
$757$	1.64720	−	1.64720i	0.0598686	−	0.0598686i	0.736407	+	0.676539i	$0.236521\pi$
$758$	13.1564	+	19.1641i	0.477863	+	0.696073i
$759$	0.752644	+	1.30362i	0.0273192	+	0.0473183i
$760$	−2.96411	−	35.5869i	−0.107520	−	1.29087i
$761$	9.17622	−	15.8937i	0.332638	−	0.576146i	−0.650390	−	0.759600i	$-0.725395\pi$
$761$	9.17622	−	15.8937i	0.332638	−	0.576146i	0.983028	+	0.183455i	$0.0587280\pi$
$762$	0.723288	−	1.51437i	0.0262020	−	0.0548598i
$763$	24.8976	−	26.8244i	0.901352	−	0.971109i
$764$	31.3513	−	25.3336i	1.13425	−	0.916538i
$765$	8.76241	−	20.0098i	0.316806	−	0.723455i
$766$	−3.08211	+	3.60488i	−0.111361	+	0.130250i
$767$	0.215509	+	0.0577455i	0.00778158	+	0.00208507i
$768$	0.163054	−	1.00236i	0.00588369	−	0.0361695i
$769$			20.3737i			0.734693i	0.930084	+	0.367346i	$0.119734\pi$
$769$			20.3737i			0.734693i	−0.930084	+	0.367346i	$0.880266\pi$
$770$	−8.12385	−	35.3157i	−0.292763	−	1.27269i
$771$	−0.646146			−0.0232704
$772$	−28.9715	+	39.7885i	−1.04271	+	1.43202i
$773$	12.6011	−	47.0279i	0.453230	−	1.69148i	−0.240010	−	0.970770i	$-0.577151\pi$
$773$	12.6011	−	47.0279i	0.453230	−	1.69148i	0.693240	−	0.720707i	$-0.256183\pi$
$774$	−27.0344	+	31.6198i	−0.971733	+	1.13655i
$775$	11.1739	−	35.8798i	0.401377	−	1.28884i
$776$	13.0980	−	21.2990i	0.470191	−	0.764591i
$777$	−0.594177	+	0.183173i	−0.0213160	+	0.00657131i
$778$	0.349450	+	0.166903i	0.0125284	+	0.00598377i
$779$	−53.4675	−	30.8695i	−1.91567	−	1.10601i
$780$	−0.0271801	+	0.0158772i	−0.000973203	+	0.000568494i
$781$	0.250424	−	0.144582i	0.00896088	−	0.00517357i
$782$	−14.2908	−	20.8165i	−0.511037	−	0.744396i
$783$	0.820206	+	0.820206i	0.0293118	+	0.0293118i
$784$	27.7374	+	3.82551i	0.990623	+	0.136626i
$785$	−15.5100	+	1.72631i	−0.553574	+	0.0616145i
$786$	−0.141923	+	0.763521i	−0.00506221	+	0.0272339i
$787$	−0.0980324	+	0.365862i	−0.00349448	+	0.0130416i	−0.967651	−	0.252292i	$-0.918816\pi$
$787$	−0.0980324	+	0.365862i	−0.00349448	+	0.0130416i	0.964157	+	0.265334i	$0.0854822\pi$
$788$	19.5490	+	44.0315i	0.696405	+	1.56856i
$789$	0.168757	−	0.292295i	0.00600790	−	0.0104060i
$790$	−14.5507	−	30.0713i	−0.517692	−	1.06989i
$791$	15.8330	+	8.37130i	0.562958	+	0.297649i
$792$	−35.7020	+	8.51216i	−1.26862	+	0.302467i
$793$	−0.286393	−	1.06883i	−0.0101701	−	0.0379554i
$794$	16.5392	+	14.1407i	0.586954	+	0.501836i
$795$	−0.0493865	+	0.324677i	−0.00175156	+	0.0115151i
$796$	8.83330	−	1.38960i	0.313088	−	0.0492532i
$797$	35.6244	−	35.6244i	1.26188	−	1.26188i	0.311702	−	0.950180i	$-0.399101\pi$
$797$	35.6244	−	35.6244i	1.26188	−	1.26188i	0.950180	−	0.311702i	$-0.100899\pi$
$798$	0.154205	+	1.33202i	0.00545878	+	0.0471529i
$799$	−7.28698			−0.257795
$800$	23.1542	−	16.2444i	0.818626	−	0.574327i
$801$	−13.0374	−	22.5814i	−0.460653	−	0.797875i
$802$	−1.16241	−	14.8691i	−0.0410460	−	0.525045i
$803$	−9.46746	−	35.3330i	−0.334099	−	1.24688i
$804$	0.416030	+	0.514853i	0.0146722	+	0.0181575i
$805$	−26.0349	−	19.2756i	−0.917608	−	0.679376i
$806$	−1.11131	+	0.392882i	−0.0391442	+	0.0138387i
$807$	−0.0277335	−	0.103503i	−0.000976267	−	0.00364348i
$808$	27.8287	+	29.4175i	0.979010	+	1.03490i
$809$	12.0731	−	6.97043i	0.424469	−	0.245067i	−0.272518	−	0.962151i	$-0.587857\pi$
$809$	12.0731	−	6.97043i	0.424469	−	0.245067i	0.696988	+	0.717083i	$0.254523\pi$
$810$	−28.2705	−	2.06557i	−0.993325	−	0.0725768i
$811$	35.6360			1.25135			0.625674	−	0.780084i	$-0.284824\pi$
$811$	35.6360			1.25135			0.625674	+	0.780084i	$0.284824\pi$
$812$	−16.0902	−	1.10435i	−0.564656	−	0.0387549i
$813$	−0.617294	−	0.617294i	−0.0216494	−	0.0216494i
$814$	−4.14469	+	22.2978i	−0.145271	+	0.781536i
$815$	16.5383	+	22.4722i	0.579312	+	0.787166i
$816$	−0.787860	+	0.254173i	−0.0275806	+	0.00889784i
$817$	53.5501	−	14.3487i	1.87348	−	0.501998i
$818$	−16.5185	+	34.5854i	−0.577557	+	1.20925i
$819$	−0.744364	+	0.467546i	−0.0260102	+	0.0163374i
$820$	−0.248546	−	48.8998i	−0.00867960	−	1.70765i
$821$	−0.252521	−	0.145793i	−0.00881305	−	0.00508822i	0.495587	−	0.868558i	$-0.334953\pi$
$821$	−0.252521	−	0.145793i	−0.00881305	−	0.00508822i	−0.504400	+	0.863470i	$0.668286\pi$
$822$	0.00702823	+	0.0899024i	0.000245138	+	0.00313570i
$823$	9.53713	−	35.5931i	0.332444	−	1.24070i	−0.574171	−	0.818736i	$-0.694675\pi$
$823$	9.53713	−	35.5931i	0.332444	−	1.24070i	0.906614	−	0.421961i	$-0.138658\pi$
$824$	5.99505	+	11.0829i	0.208847	+	0.386090i
$825$	1.16188	+	0.734451i	0.0404515	+	0.0255703i
$826$	7.44720	+	1.09923i	0.259121	+	0.0382470i
$827$	−1.33262	−	1.33262i	−0.0463397	−	0.0463397i	0.683557	−	0.729897i	$-0.260432\pi$
$827$	−1.33262	−	1.33262i	−0.0463397	−	0.0463397i	−0.729897	+	0.683557i	$0.760432\pi$
$828$	−19.3125	+	26.5231i	−0.671156	+	0.921742i
$829$	−11.4707	−	19.8679i	−0.398395	−	0.690041i	0.595133	−	0.803627i	$-0.297099\pi$
$829$	−11.4707	−	19.8679i	−0.398395	−	0.690041i	−0.993528	+	0.113587i	$0.963766\pi$
$830$	2.11266	+	11.0528i	0.0733315	+	0.383648i
$831$	−1.50972	−	0.871636i	−0.0523715	−	0.0302367i
$832$	−0.842877	−	0.276790i	−0.0292215	−	0.00959597i
$833$	−7.53163	−	21.5467i	−0.260955	−	0.746548i
$834$	−0.132721	−	0.375415i	−0.00459575	−	0.0129996i
$835$	2.82501	−	6.45116i	0.0977634	−	0.223251i
$836$	45.6441	+	17.5759i	1.57863	+	0.607874i
$837$	2.76286	+	0.740306i	0.0954984	+	0.0255887i
$838$	13.3523	+	19.4494i	0.461247	+	0.671870i
$839$	41.0795			1.41822			0.709111	−	0.705097i	$-0.249096\pi$
$839$	41.0795			1.41822			0.709111	+	0.705097i	$0.249096\pi$
$840$	−0.849380	+	0.637613i	−0.0293064	+	0.0219997i
$841$	−19.7102			−0.679661
$842$	−8.48994	−	12.3668i	−0.292583	−	0.426187i
$843$	−0.529220	−	0.141804i	−0.0182273	−	0.00488399i
$844$	6.46668	−	16.7938i	0.222592	−	0.578067i
$845$	−10.5734	−	27.0482i	−0.363737	−	0.930486i
$846$	3.15603	+	8.92716i	0.108506	+	0.306922i
$847$	20.0154	+	4.57181i	0.687737	+	0.157089i
$848$	−7.77316	+	5.02489i	−0.266931	+	0.172556i
$849$	0.907972	+	0.524218i	0.0311615	+	0.0179911i
$850$	−20.3904	−	10.7633i	−0.699385	−	0.369178i
$851$	10.1369	+	17.5576i	0.347489	+	0.601868i
$852$	−0.00685113	−	0.00498858i	−0.000234716	−	0.000170906i
$853$	33.5497	+	33.5497i	1.14872	+	1.14872i	0.986805	+	0.161916i	$0.0517674\pi$
$853$	33.5497	+	33.5497i	1.14872	+	1.14872i	0.161916	+	0.986805i	$0.448233\pi$
$854$	−13.7462	−	34.7125i	−0.470384	−	1.18784i
$855$	29.5412	+	23.6238i	1.01029	+	0.807916i
$856$	−7.81654	−	14.4502i	−0.267164	−	0.493898i
$857$	−1.01448	+	3.78609i	−0.0346539	+	0.129330i	−0.981086	−	0.193573i	$-0.937992\pi$
$857$	−1.01448	+	3.78609i	−0.0346539	+	0.129330i	0.946432	+	0.322904i	$0.104659\pi$
$858$	−0.00336024	−	0.0429828i	−0.000114717	−	0.00146741i
$859$	33.5816	+	19.3883i	1.14579	+	0.661522i	0.947858	−	0.318694i	$-0.103244\pi$
$859$	33.5816	+	19.3883i	1.14579	+	0.661522i	0.197931	+	0.980216i	$0.436578\pi$
$860$	31.2069	+	30.8913i	1.06415	+	1.05338i
$861$	0.0683591	+	1.83493i	0.00232967	+	0.0625343i
$862$	22.0160	−	46.0956i	0.749869	−	1.57002i
$863$	−26.6465	+	7.13990i	−0.907057	+	0.243045i	−0.682044	−	0.731311i	$-0.738909\pi$
$863$	−26.6465	+	7.13990i	−0.907057	+	0.243045i	−0.225012	+	0.974356i	$0.572242\pi$
$864$	1.30609	+	1.71137i	0.0444342	+	0.0582220i
$865$	−14.8288	+	10.9132i	−0.504193	+	0.371059i
$866$	0.932178	−	5.01497i	0.0316767	−	0.170415i
$867$	−0.285786	−	0.285786i	−0.00970579	−	0.00970579i
$868$	−35.7229	+	17.4801i	−1.21252	+	0.593315i
$869$	45.7561			1.55217
$870$	0.462949	−	0.399905i	0.0156954	−	0.0135581i
$871$	0.500786	−	0.289129i	0.0169685	−	0.00979675i
$872$	−28.4226	+	26.8876i	−0.962511	+	0.910527i
$873$	6.85490	+	25.5828i	0.232003	+	0.865848i
$874$	41.2223	−	14.5734i	1.39437	−	0.492951i
$875$	−29.2311	−	4.53217i	−0.988193	−	0.153215i
$876$	−0.833865	+	0.673810i	−0.0281737	+	0.0227659i
$877$	−12.8461	−	47.9425i	−0.433784	−	1.61890i	−0.743961	−	0.668223i	$-0.767055\pi$
$877$	−12.8461	−	47.9425i	−0.433784	−	1.61890i	0.310177	−	0.950679i	$-0.399612\pi$
$878$	−1.60556	−	20.5377i	−0.0541850	−	0.693114i
$879$	0.119167	+	0.206404i	0.00401941	+	0.00696183i
$880$	6.21476	+	38.2384i	0.209499	+	1.28901i
$881$	−31.8450			−1.07289			−0.536443	−	0.843937i	$-0.680232\pi$
$881$	−31.8450			−1.07289			−0.536443	+	0.843937i	$0.680232\pi$
$882$	−23.1345	+	18.5588i	−0.778978	+	0.624908i
$883$	−14.9298	+	14.9298i	−0.502426	+	0.502426i	−0.912191	−	0.409765i	$-0.865611\pi$
$883$	−14.9298	+	14.9298i	−0.502426	+	0.502426i	0.409765	+	0.912191i	$0.365611\pi$
$884$	0.112387	+	0.714411i	0.00377998	+	0.0240282i
$885$	−0.229975	+	0.169249i	−0.00773053	+	0.00568925i
$886$	−11.6127	−	9.92868i	−0.390136	−	0.333560i
$887$	6.36600	+	23.7582i	0.213749	+	0.797724i	0.986603	+	0.163139i	$0.0521620\pi$
$887$	6.36600	+	23.7582i	0.213749	+	0.797724i	−0.772854	+	0.634584i	$0.781171\pi$
$888$	0.646577	−	0.154159i	0.0216977	−	0.00517322i
$889$	−43.7303	−	23.1212i	−1.46667	−	0.775462i
$890$	−24.7743	+	11.9877i	−0.830437	+	0.401827i
$891$	19.4123	−	33.6230i	0.650335	−	1.12641i
$892$	34.8429	−	15.4695i	1.16663	−	0.517956i
$893$	3.26581	−	12.1882i	0.109286	−	0.407862i
$894$	0.0464511	−	0.249899i	0.00155356	−	0.00835788i
$895$	−10.6208	+	13.2812i	−0.355015	+	0.443942i
$896$	−29.3244	−	6.00659i	−0.979660	−	0.200666i
$897$	−0.0272522	−	0.0272522i	−0.000909924	−	0.000909924i
$898$	−14.5715	−	21.2254i	−0.486257	−	0.708301i
$899$	19.8388	−	11.4539i	0.661661	−	0.382010i
$900$	−4.35474	+	29.6415i	−0.145158	+	0.988051i
$901$	6.53436	+	3.77262i	0.217691	+	0.125684i
$902$	60.4377	+	28.8661i	2.01236	+	0.961135i
$903$	−1.20850	−	1.12169i	−0.0402165	−	0.0373276i
$904$	−16.3094	−	10.0296i	−0.542441	−	0.333578i
$905$	−20.5630	−	52.6027i	−0.683536	−	1.74857i
$906$	−0.798298	+	0.933699i	−0.0265217	+	0.0310201i
$907$	−10.5359	+	39.3206i	−0.349840	+	1.30562i	0.537015	+	0.843573i	$0.319552\pi$
$907$	−10.5359	+	39.3206i	−0.349840	+	1.30562i	−0.886855	+	0.462048i	$0.847115\pi$
$908$	28.3936	+	20.6745i	0.942273	+	0.686106i
$909$	−42.8935			−1.42269
$910$	0.434934	+	0.819557i	0.0144179	+	0.0271680i
$911$		−	23.8129i		−	0.788957i	−0.918905	−	0.394478i	$-0.870925\pi$
$911$		−	23.8129i		−	0.788957i	0.918905	−	0.394478i	$-0.129075\pi$
$912$	−0.0720330	−	1.43169i	−0.00238525	−	0.0474078i
$913$	−14.8876	−	3.98911i	−0.492707	−	0.132020i
$914$	−13.1092	+	15.3326i	−0.433612	+	0.507158i
$915$	1.29724	+	0.568069i	0.0428853	+	0.0187798i
$916$	−31.5928	−	39.0973i	−1.04386	−	1.29181i
$917$	22.3158	+	5.09726i	0.736933	+	0.168326i
$918$	0.756351	−	1.58359i	0.0249633	−	0.0522664i
$919$	−3.50221	+	6.06601i	−0.115527	+	0.200099i	−0.917990	−	0.396603i	$-0.870189\pi$
$919$	−3.50221	+	6.06601i	−0.115527	+	0.200099i	0.802463	+	0.596702i	$0.203522\pi$
$920$	26.4355	+	22.3704i	0.871554	+	0.737530i
$921$	−0.479621	−	0.830728i	−0.0158041	−	0.0273734i
$922$	−14.3190	−	20.8577i	−0.471572	−	0.686910i
$923$	−0.00523513	+	0.00523513i	−0.000172316	+	0.000172316i
$924$	−0.279404	−	1.42760i	−0.00919170	−	0.0469647i
$925$	15.6487	+	9.89188i	0.514526	+	0.325243i
$926$	30.5087	+	5.67093i	1.00258	+	0.186358i
$927$	−12.8920	−	3.45441i	−0.423430	−	0.113458i
$928$	17.0882	+	2.29511i	0.560948	+	0.0753407i
$929$	−15.6193	−	9.01781i	−0.512453	−	0.295865i	0.221389	−	0.975186i	$-0.428941\pi$
$929$	−15.6193	−	9.01781i	−0.512453	−	0.295865i	−0.733841	+	0.679321i	$0.762274\pi$
$930$	0.495582	−	1.42481i	0.0162508	−	0.0467213i
$931$	39.4143	−	2.94079i	1.29175	−	0.0963804i
$932$	12.2186	+	1.29714i	0.400235	+	0.0424891i
$933$	−0.840624	+	0.225245i	−0.0275208	+	0.00737418i
$934$	32.1099	−	37.5561i	1.05067	−	1.22887i
$935$	25.4347	−	18.7186i	0.831804	−	0.612163i
$936$	0.826537	−	0.447098i	0.0270162	−	0.0146138i
$937$	−25.9344	−	25.9344i	−0.847239	−	0.847239i	0.142548	−	0.989788i	$-0.454470\pi$
$937$	−25.9344	−	25.9344i	−0.847239	−	0.847239i	−0.989788	+	0.142548i	$0.954470\pi$
$938$	15.6628	−	11.6337i	0.511408	−	0.379855i
$939$			1.54640i			0.0504649i
$940$	9.64040	−	2.63573i	0.314435	−	0.0859679i
$941$	17.8863	−	10.3267i	0.583077	−	0.336640i	−0.179278	−	0.983798i	$-0.557376\pi$
$941$	17.8863	−	10.3267i	0.583077	−	0.336640i	0.762355	+	0.647159i	$0.224043\pi$
$942$	−0.624548	+	0.0488249i	−0.0203489	+	0.00159080i
$943$	57.8322	−	15.4961i	1.88328	−	0.504623i
$944$	−7.86828	−	1.68964i	−0.256091	−	0.0549931i
$945$	0.255477	−	2.23694i	0.00831066	−	0.0727677i
$946$	−56.7038	+	20.0466i	−1.84360	+	0.651770i
$947$	23.0440	−	6.17463i	0.748831	−	0.200649i	0.135831	−	0.990732i	$-0.456629\pi$
$947$	23.0440	−	6.17463i	0.748831	−	0.200649i	0.612999	+	0.790083i	$0.289963\pi$
$948$	−0.544166	−	1.22566i	−0.0176737	−	0.0398076i
$949$	0.468278	+	0.811082i	0.0152010	+	0.0263288i
$950$	27.1410	−	29.2811i	0.880571	−	0.950005i
$951$		−	1.34767i		−	0.0437013i
$952$	6.53885	+	23.5086i	0.211925	+	0.761918i
$953$	−37.2424	+	37.2424i	−1.20640	+	1.20640i	−0.234216	+	0.972185i	$0.575252\pi$
$953$	−37.2424	+	37.2424i	−1.20640	+	1.20640i	−0.972185	+	0.234216i	$0.924748\pi$
$954$	1.79170	−	9.63907i	0.0580085	−	0.312076i
$955$	44.5527	+	6.77690i	1.44169	+	0.219295i
$956$	−1.23848	+	3.21631i	−0.0400554	+	0.104023i
$957$	0.216866	+	0.809353i	0.00701027	+	0.0261627i
$958$	−36.2243	−	17.3013i	−1.17035	−	0.558980i
$959$	2.65615	−	0.0989529i	0.0857715	−	0.00319536i
$960$	0.950373	−	0.621233i	0.0306732	−	0.0200502i
$961$	12.7444	−	22.0739i	0.411108	−	0.712060i
$962$	−0.0452570	−	0.578910i	−0.00145914	−	0.0186648i
$963$	16.8091	+	4.50398i	0.541665	+	0.145139i
$964$	−41.5557	+	6.53729i	−1.33842	+	0.210552i
$965$	−54.6904	+	6.08721i	−1.76054	+	0.195954i
$966$	−1.01914	−	0.807659i	−0.0327904	−	0.0259860i
$967$	−42.0389	+	42.0389i	−1.35188	+	1.35188i	−0.468320	+	0.883559i	$0.655141\pi$
$967$	−42.0389	+	42.0389i	−1.35188	+	1.35188i	−0.883559	+	0.468320i	$0.844859\pi$
$968$	−21.0348	−	6.26665i	−0.676084	−	0.201418i
$969$	−1.01200	+	0.584280i	−0.0325102	+	0.0187698i
$970$	27.4584	−	5.24847i	0.881636	−	0.168518i
$971$	−21.4885	+	37.2192i	−0.689600	+	1.19442i	0.282367	+	0.959306i	$0.408880\pi$
$971$	−21.4885	+	37.2192i	−0.689600	+	1.19442i	−0.971967	+	0.235116i	$0.924453\pi$
$972$	−3.40218	−	0.361176i	−0.109125	−	0.0115847i
$973$	−11.2158	+	3.45761i	−0.359562	+	0.110846i
$974$	−25.4424	+	8.99467i	−0.815227	+	0.288208i
$975$	−0.0336014	−	0.0104643i	−0.00107610	−	0.000335126i
$976$	12.2545	+	37.9852i	0.392256	+	1.21588i
$977$	4.42361	−	16.5091i	0.141524	−	0.528174i	−0.858362	−	0.513045i	$-0.828517\pi$
$977$	4.42361	−	16.5091i	0.141524	−	0.528174i	0.999886	−	0.0151290i	$-0.00481588\pi$
$978$	0.633922	+	0.923395i	0.0202706	+	0.0295269i
$979$		−	37.6963i		−	1.20478i
$980$	17.7575	+	25.7812i	0.567244	+	0.823550i
$981$		−	41.4429i		−	1.32317i
$982$	19.0527	−	13.0799i	0.607997	−	0.417398i
$983$	−12.8082	+	47.8010i	−0.408519	+	1.52461i	0.388953	+	0.921258i	$0.372837\pi$
$983$	−12.8082	+	47.8010i	−0.408519	+	1.52461i	−0.797472	+	0.603356i	$0.793830\pi$
$984$	0.0544591	−	1.96223i	0.00173609	−	0.0625536i
$985$	−21.6060	+	49.3392i	−0.688424	+	1.57208i
$986$	−4.68476	−	13.2513i	−0.149193	−	0.422009i
$987$	−0.358627	+	0.110558i	−0.0114152	+	0.00351910i
$988$	−1.24529	−	0.132200i	−0.0396180	−	0.00420585i
$989$	−26.8815	+	46.5602i	−0.854782	+	1.48053i
$990$	−33.9477	−	23.0525i	−1.07893	−	0.732657i
$991$	−10.4546	+	6.03598i	−0.332102	+	0.191739i	−0.656774	−	0.754087i	$-0.728079\pi$
$991$	−10.4546	+	6.03598i	−0.332102	+	0.191739i	0.324672	+	0.945827i	$0.394746\pi$
$992$	39.3223	−	16.1677i	1.24848	−	0.513324i
$993$	0.636573	−	0.636573i	0.0202010	−	0.0202010i
$994$	−0.155151	+	0.195777i	−0.00492109	+	0.00620967i
$995$	7.80783	+	6.24384i	0.247525	+	0.197943i
$996$	0.0701986	+	0.446232i	0.00222433	+	0.0141394i
$997$	−26.4899	−	7.09794i	−0.838943	−	0.224794i	−0.186332	−	0.982487i	$-0.559660\pi$
$997$	−26.4899	−	7.09794i	−0.838943	−	0.224794i	−0.652611	+	0.757693i	$0.726327\pi$
$998$	−2.04309	+	0.159722i	−0.0646730	+	0.00505590i
$999$	−0.704548	+	1.22031i	−0.0222909	+	0.0386090i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.br.a.107.11	yes	176
5.3	odd	4	inner	280.2.br.a.163.32	yes	176
7.4	even	3	inner	280.2.br.a.67.20	✓	176
8.3	odd	2	inner	280.2.br.a.107.3	yes	176
35.18	odd	12	inner	280.2.br.a.123.3	yes	176
40.3	even	4	inner	280.2.br.a.163.20	yes	176
56.11	odd	6	inner	280.2.br.a.67.32	yes	176
280.123	even	12	inner	280.2.br.a.123.11	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.br.a.67.20	✓	176	7.4	even	3	inner
280.2.br.a.67.32	yes	176	56.11	odd	6	inner
280.2.br.a.107.3	yes	176	8.3	odd	2	inner
280.2.br.a.107.11	yes	176	1.1	even	1	trivial
280.2.br.a.123.3	yes	176	35.18	odd	12	inner
280.2.br.a.123.11	yes	176	280.123	even	12	inner
280.2.br.a.163.20	yes	176	40.3	even	4	inner
280.2.br.a.163.32	yes	176	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16591 + 0.800411i) q^{2} +(-0.0613082 - 0.0164275i) q^{3} +(0.718686 - 1.86641i) q^{4} +(2.08260 - 0.814111i) q^{5} +(0.0846285 - 0.0299188i) q^{6} +(-0.779437 - 2.52833i) q^{7} +(0.655974 + 2.75131i) q^{8} +(-2.59459 - 1.49799i) q^{9} +O(q^{10})\)	\(q+(-1.16591 + 0.800411i) q^{2} +(-0.0613082 - 0.0164275i) q^{3} +(0.718686 - 1.86641i) q^{4} +(2.08260 - 0.814111i) q^{5} +(0.0846285 - 0.0299188i) q^{6} +(-0.779437 - 2.52833i) q^{7} +(0.655974 + 2.75131i) q^{8} +(-2.59459 - 1.49799i) q^{9} +(-1.77650 + 2.61611i) q^{10} +(-2.16564 - 3.75099i) q^{11} +(-0.0747218 + 0.102620i) q^{12} +(0.0784147 + 0.0784147i) q^{13} +(2.93246 + 2.32394i) q^{14} +(-0.141054 + 0.0156998i) q^{15} +(-2.96698 - 2.68273i) q^{16} +(-0.843938 + 3.14962i) q^{17} +(4.22406 - 0.330221i) q^{18} +(-4.88981 - 2.82314i) q^{19} +(-0.0227305 - 4.47208i) q^{20} +(0.00625171 + 0.167812i) q^{21} +(5.52727 + 2.63992i) q^{22} +(5.28899 - 1.41718i) q^{23} +(0.00498050 - 0.179454i) q^{24} +(3.67445 - 3.39093i) q^{25} +(-0.154188 - 0.0286604i) q^{26} +(0.269104 + 0.269104i) q^{27} +(-5.27908 - 0.362328i) q^{28} +3.04792 q^{29} +(0.151890 - 0.131206i) q^{30} +(6.50896 - 3.75795i) q^{31} +(5.60651 + 0.753009i) q^{32} +(0.0711520 + 0.265543i) q^{33} +(-1.53703 - 4.34766i) q^{34} +(-3.68160 - 4.63096i) q^{35} +(-4.66055 + 3.76599i) q^{36} +(0.958303 + 3.57643i) q^{37} +(7.96074 - 0.622341i) q^{38} +(-0.00351931 - 0.00609562i) q^{39} +(3.60600 + 5.19584i) q^{40} +10.9345 q^{41} +(-0.141607 - 0.190649i) q^{42} +(-6.94288 + 6.94288i) q^{43} +(-8.55731 + 1.34618i) q^{44} +(-6.62301 - 1.00742i) q^{45} +(-5.03215 + 5.88567i) q^{46} +(0.578402 + 2.15863i) q^{47} +(0.137830 + 0.213213i) q^{48} +(-5.78496 + 3.94136i) q^{49} +(-1.56993 + 6.89459i) q^{50} +(0.103481 - 0.179234i) q^{51} +(0.202710 - 0.0899986i) q^{52} +(0.598900 - 2.23513i) q^{53} +(-0.529143 - 0.0983568i) q^{54} +(-7.56388 - 6.04875i) q^{55} +(6.44494 - 3.80299i) q^{56} +(0.253409 + 0.253409i) q^{57} +(-3.55360 + 2.43959i) q^{58} +(1.74237 - 1.00596i) q^{59} +(-0.0720714 + 0.274548i) q^{60} +(-8.64141 - 4.98912i) q^{61} +(-4.58095 + 9.59126i) q^{62} +(-1.76509 + 7.72757i) q^{63} +(-7.13940 + 3.60957i) q^{64} +(0.227145 + 0.0994682i) q^{65} +(-0.295500 - 0.252648i) q^{66} +(1.34960 - 5.03678i) q^{67} +(5.27196 + 3.83872i) q^{68} -0.347539 q^{69} +(7.99908 + 2.45249i) q^{70} +0.0667621i q^{71} +(2.41944 - 8.12115i) q^{72} +(8.15766 + 2.18584i) q^{73} +(-3.97991 - 3.40276i) q^{74} +(-0.280978 + 0.147530i) q^{75} +(-8.78337 + 7.09746i) q^{76} +(-7.79579 + 8.39912i) q^{77} +(0.00898219 + 0.00429004i) q^{78} +(-5.28206 + 9.14880i) q^{79} +(-8.36307 - 3.17159i) q^{80} +(4.48188 + 7.76284i) q^{81} +(-12.7486 + 8.75206i) q^{82} +(2.51622 - 2.51622i) q^{83} +(0.317699 + 0.108936i) q^{84} +(0.806553 + 7.24646i) q^{85} +(2.53761 - 13.6519i) q^{86} +(-0.186863 - 0.0500697i) q^{87} +(8.89954 - 8.41889i) q^{88} +(7.53726 + 4.35164i) q^{89} +(8.52818 - 4.12657i) q^{90} +(0.137139 - 0.259378i) q^{91} +(1.15608 - 10.8899i) q^{92} +(-0.460786 + 0.123467i) q^{93} +(-2.40215 - 2.05380i) q^{94} +(-12.4819 - 1.89861i) q^{95} +(-0.331355 - 0.138267i) q^{96} +(-6.25104 - 6.25104i) q^{97} +(3.59003 - 9.22560i) q^{98} +12.9764i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) \) 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) \) 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8 - 2 * q^10 - 8 * q^11 - 14 * q^12 + 4 * q^16 - 4 * q^17 - 16 * q^18 + 8 * q^20 - 4 * q^25 - 20 * q^26 - 40 * q^27 - 34 * q^28 - 12 * q^30 + 18 * q^32 + 20 * q^33 - 32 * q^35 - 48 * q^36 - 16 * q^38 - 22 * q^40 - 32 * q^41 + 30 * q^42 - 16 * q^43 + 20 * q^46 + 36 * q^48 + 68 * q^50 - 8 * q^51 - 32 * q^52 - 52 * q^56 - 40 * q^57 - 14 * q^58 - 50 * q^60 + 56 * q^62 - 4 * q^65 - 60 * q^66 - 28 * q^67 - 40 * q^68 + 64 * q^70 - 48 * q^72 - 4 * q^73 - 4 * q^75 - 144 * q^76 + 184 * q^78 - 40 * q^80 + 32 * q^81 + 74 * q^82 - 16 * q^83 - 56 * q^86 - 64 * q^88 - 56 * q^90 + 16 * q^91 + 44 * q^92 - 104 * q^96 - 48 * q^97 + 70 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more